Package 'momentfit'

Title: Methods of Moments
Description: Several classes for moment-based models are defined. The classes are defined for moment conditions derived from a single equation or a system of equations. The conditions can also be expressed as functions or formulas. Several methods are also offered to facilitate the development of different estimation techniques. The methods that are currently provided are the Generalized method of moments (Hansen 1982; <doi:10.2307/1912775>), for single equations and systems of equation, and the Generalized Empirical Likelihood (Smith 1997; <doi:10.1111/j.0013-0133.1997.174.x>, Kitamura 1997; <doi:10.1214/aos/1069362388>, Newey and Smith 2004; <doi:10.1111/j.1468-0262.2004.00482.x>, and Anatolyev 2005 <doi:10.1111/j.1468-0262.2005.00601.x>).
Authors: Pierre Chausse <[email protected]>
Maintainer: Pierre Chausse <[email protected]>
License: GPL (>= 2)
Version: 0.5
Built: 2024-10-29 03:15:58 UTC
Source: https://github.com/pchausse/momentfit

Help Index

Subsetting methods

Description

Different subsetting methods for S4 class objects of the package. The subset method returns an new object with observations selected by the second argument. See example.

Methods

signature(x = "momentWeights", i = "integer", j = "missing")

It creates a partition from the weighting matrix.

signature(x = "momentWeights", i = "missing", j = "missing")

It generates the whole weighting matrix.

signature(x = "sysMomentWeights", i = "missing", j = "list")

It creates a partition from the weighting matrix. j has no effect here. It creates a partition from the weighting matrix in a systemof equations. i selects the equation and the list j the moments in each equation. Missing i means all equations.

signature(x = "sysMomentWeights", i = "numeric", j = "missing")

It creates a partition from the weighting matrix. j has no effect here. It creates a partition from the weighting matrix in a systemof equations. i selects the equation and the list j the moments in each equation. Missing j means all moments.

signature(x = "sysMomentWeights", i = "missing", j = "missing")

No effect. It returns x.

signature(x = "snonlinearModel", i = "numeric", j="missing")

It generates a system of equations with a subset of equations selected by i. If the number of remaining equations is one, it returns an object of class "nonlinearGmm".

signature(x = "slinearModel", i = "numeric", j="missing")

It generates a system of equations with a subset of equations selected by i. If the number of remaining equations is one, it returns an object of class "linearModel".

signature(x = "rslinearModel", i = "numeric", j="missing")

It is only use to select one equation when no cross-equation restrictions are imposed. Only one equation can be selected.

signature(x = "rsnonlinearModel", i = "numeric", j="missing")

It is only use to select one equation when no cross-equation restrictions are imposed. Only one equation can be selected.

signature(x = "sysMomentModel", i = "numeric", j="list")

It generates a system of equations with a subset of equations selected by i and a subset of moment conditions selected by j. If the number of remaining equations is one, it returns an object of class "linearGmm".

signature(x = "sysMomentModel", i = "missing", j="missing")

No effect. It returns x.

signature(x = "momentModel", i = "missing", j = "missing")

Returns the model without any change.

signature(x = "functionModel", i = "numeric", j = "missing")

It generates the same model with a subset of the moment conditions.

signature(x = "formulaModel", i = "numeric", j = "missing")

It generates the same model with a subset of the moment conditions.

signature(x = "rfuncionModel", i = "numeric", j = "missing")

It generates the same model with a subset of the moment conditions. j has no effect here.

Examples

data(simData)
model1 <- momentModel(y~x1+x2, ~x2+x3+z1+z2+z3, data=simData, vcov="MDS")
w <- evalWeights(model1, theta=1:3)
w[]
w[1:3]

## A model with a subset of the instruments
model1[1:4]

## Selecting the observations:

subset(model1, simData[["x1"]]<3)
subset(model1, 1:25)

Class "allNLModel"

Description

A union class for all nonlinear models. It includes "nonlinearModel", "formulaModel", and "functionModel".

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

solveGmm

signature(object = "allNLModel", wObj = "momentWeights"): ...

Examples

showClass("allNLModel")

~~ Methods for Function bread in Package sandwich ~~

Description

It computes the bread in the sandwich representation of the covariance matrix of the GMM estimator.

Usage

## S4 method for signature 'gmmfit'
bread(x, ...)

## S4 method for signature 'sgmmfit'
bread(x, ...)

## S4 method for signature 'tsls'
bread(x, ...)

Arguments

x

GMM fit object
...

Arguments to pass to other methods

Methods

signature(x = "gmmfit")
signature(x = "sgmmfit")
signature(x = "tsls")

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

res <- gmmFit(model1)
m <- meatGmm(res)
b <- bread(res)

## Sandwich vcov
b

## TSLS
model2 <- momentModel(y~x1, ~z1+z2, data=simData, vcov="iid")
res <- tsls(model2)
bread(res)

Cigarette Consumption Panel Data

Description

Panel data on cigarette consumption for the 48 continental US States from 1985–1995.

Usage

data("CigarettesSW")

Format

A data frame containing 48 observations on 7 variables for 2 periods.

state

Factor indicating state.

year

Factor indicating year.

cpi

Consumer price index.

population

State population.

packs

Number of packs per capita.

income

State personal income (total, nominal).

tax

Average state, federal and average local excise taxes for fiscal year.

price

Average price during fiscal year, including sales tax.

taxs

Average excise taxes for fiscal year, including sales tax.

Source

Online complements to Stock and Watson (2007). The dataset and this help file comes from the AER package.

References

Stock, J.H. and Watson, M.W. (2007). Introduction to Econometrics, 2nd ed. Boston: Addison Wesley.

Christian Kleiber and Achim Zeileis (2008). Applied Econometrics with R. New York: Springer-Verlag. ISBN 978-0-387-77316-2. URL https://CRAN.R-project.org/package=AER

Examples

## Stock and Watson (2007)
## data and transformations
data(CigarettesSW)
CigarettesSW$rprice <- with(CigarettesSW, price/cpi)
CigarettesSW$rincome <- with(CigarettesSW, income/population/cpi)
CigarettesSW$tdiff <- with(CigarettesSW, (taxs - tax)/cpi)
c1985 <- subset(CigarettesSW, year == "1985")
c1995 <- subset(CigarettesSW, year == "1995")

## Equation 12.15
model1 <- momentModel(log(packs)~log(rprice)+log(rincome),
                   ~log(rincome)+tdiff, data = c1995, vcov="MDS")
res1 <- gmmFit(model1)

## HC0 robust se (different from the textbook)
summary(res1, sandwich=TRUE)

## HC1 robust se (like in the textbook)
## A little harder to get, but is it really worth it
## in the case of GMM?

summary(res1, sandwich=TRUE, df.adj=TRUE)@coef

## Equation 12.16
model2<- momentModel(log(packs)~log(rprice)+log(rincome),
                  ~log(rincome)+tdiff+I(tax/cpi), data = c1995,
                  centeredVcov=FALSE, vcov="MDS")
res2<- tsls(model2)
summary(res2, sandwich=TRUE, df.adj=TRUE)

## Table 12.1
data <- data.frame(dQ=log(c1995$pack/c1985$pack),
                   dP=log(c1995$rprice/c1985$rprice),
                   dTs=c1995$tdiff-c1985$tdiff,
                   dT=c1995$tax/c1995$cpi-c1985$tax/c1985$cpi,
                   dInc=log(c1995$rincome/c1985$rincome))
model1 <- momentModel(dQ~dP+dInc, ~dInc+dTs, vcov="MDS", data=data)
model2 <- momentModel(dQ~dP+dInc, ~dInc+dT, vcov="MDS", data=data)
model3 <- momentModel(dQ~dP+dInc, ~dInc+dTs+dT, vcov="MDS", data=data)

res1 <- tsls(model1)
summary(res1, TRUE, TRUE)
res2 <- tsls(model2)
summary(res2, TRUE, TRUE)
res3 <- tsls(model3)
summary(res3, TRUE, TRUE)

~~ Methods for Function coef in Package stats ~~

Description

It extract the coefficient estimates of some moment-based models.

Methods

signature(object = "gmmfit")
signature(object = "gelfit")
signature(object = "sgmmfit")
signature(object = "momentModel")
signature(object = "rlinearModel")

It gives the unrestricted representation of a restricted model. See examples.

signature(object = "rslinearModel")

It gives the unrestricted representation of a restricted model.

signature(object = "rsnonlinearModel")

It gives the unrestricted representation of a restricted model.

signature(object = "rfunctionModel")

It gives the unrestricted representation of a restricted model. See examples.

signature(object = "rformulaModel")

It gives the unrestricted representation of a restricted model. See examples.

signature(object = "rnonlinearModel")

It gives the unrestricted representation of a restricted nonlinear model.

Examples

data(simData)
model1 <- momentModel(y~x1+x2+x3+z1, ~x1+x2+z1+z2+z3+z4, data=simData)
res1 <- gmmFit(model1)
coef(res1)

### Restricted models
rmodel1 <- restModel(model1, R=c("x1=1", "x2=2*x3"))
res2 <- gmmFit(rmodel1)
res2
coef(rmodel1, coef(res2))

Class "confint"

Description

A class to store a confidence interval result.

Objects from the Class

Objects can be created by calls of the form new("confint", ...). It is generated by the "confint" method (see confint-methods).

Slots

interval:

Object of class "matrix" ~~

type:

Object of class "character" ~~

level:

Object of class "numeric" ~~

theta:

Object of class "numeric" ~~

Methods

print

signature(x = "confint"): ...

show

signature(object = "confint"): ...

Examples

showClass("confint")

~~ Methods for Function confint in Package stats ~~

Description

Method to contruct confidence intervals for objects of class "gmmfit" and "gelfit".

Usage

## S4 method for signature 'gmmfit'
confint(object, parm, level = 0.95, vcov=NULL,
                    area=FALSE, npoints=50, ...)

## S4 method for signature 'gelfit'
confint(object, parm, level = 0.95, lambda = FALSE,
                    type = c("Wald", "invLR", "invLM", "invJ"),
                    fact = 3, corr = NULL, vcov=NULL,
                    area = FALSE, npoints = 20, cores=4, ...)

## S4 method for signature 'numeric'
confint(object, parm, level = 0.95, gelType="EL", 
                    type = c("Wald", "invLR", "invLM", "invJ"),
                    fact = 3, vcov="iid") 

## S4 method for signature 'data.frame'
confint(object, parm, level = 0.95, gelType="EL", 
                    type = c("Wald", "invLR", "invLM", "invJ"),
                    fact = 3, vcov="iid", npoints=10, 
                    cores=4) 

## S4 method for signature 'matrix'
confint(object, parm, level = 0.95, gelType="EL", 
                    type = c("Wald", "invLR", "invLM", "invJ"),
                    fact = 3, vcov="iid", npoints=10, 
                    cores=4) 

## S4 method for signature 'ANY'
confint(object, parm, level = 0.95, ...)

Arguments

object

Object of class "gmmfit", "gelfit", "numeric" or "data.frame".
parm

Vector of integers or characters for selecting the elements for which the intervals should be computed.
level

The confidence level.
lambda

Should be compute intervals for the Lagrange multipliers?
type

The type of confidence intervals. The default is the Wald interval, and the others are computed by inverting the LR, LM or J specification test.
fact

For the inversion of the specification tests, uniroot searches within fact standard error of the coefficient estimates
corr

Correction to apply to the specification tests
vcov

For Wald intervals, an optional covariance matrix can be provided. For "numeric" or "data.frame", it specifies the type of observations.
cores

The number of cores for mclapply. It is set to 1 for Windows OS.
gelType

Type of GEL confidence interval.
npoints

Number of equally spaced points for the confidence region
area

If TRUE, a cnnfidence region is computed. The length of "parm" must be 2 in that case.
...

Other arguments to pass to gmmFit or gelFit.

Methods

signature(object = "ANY")

The method from the stats in used in that case.

signature(object = "gelfit")

Method for any GEL fit class.

signature(object = "gmmfit")

Method for any GMM fit class.

signature(object = "numeric")

It computes the GEL confidence interval for the mean.

signature(object = "data.frame")

It computes the 2D GEL confidence region for the means of two variables.

signature(object = "matrix")

It converts the object into a data.frame and call its method.

Consumption data from Greene (2012) applications.

Description

Quarterly macroeconomic US data from 1950 to 2000.

Usage

data("ConsumptionG")

Format

A data frame with 204 observations on the following 14 variables.

YEAR

Year

QTR

Quarter

REALGDP

Read GDP

REALCONS

Real Consumption

REALINVS

Real Investment

REALGOVT

Real public expenditure

REALDPI

ector

CPI_U

CPI

M1

Money stock

TBILRATE

Interest rate

UNEMP

Unemployment rate

POP

Population

INFL

Inflation

REALINT

Real interest rate.

Source

Greene (2012) online resources: (http://pages.stern.nyu.edu/~wgreene/Text/Edition7/tablelist8new.htm)

References

Green, W.H.. (2012). Econometric Analysis, 7th edition, Prentice Hall.

Examples

data(ConsumptionG)
## Get the data ready for Table 8.2 of Greene (2012)
Y <- ConsumptionG$REALDPI
C <- ConsumptionG$REALCONS
n <- nrow(ConsumptionG)
Y1 <- Y[-c(1,n)]; Y2 <- Y[-c(n-1,n)]; Y <- Y[-c(1:2)]
C1 <- C[-c(1,n)]; C <- C[-(1:2)]
dat <- data.frame(Y=Y,Y1=Y1,Y2=Y2,C=C,C1=C1)

## Starting at the NLS estimates (from the table)
theta0=c(alpha=468, beta=0.0971, gamma=1.24)

## Greene (2012) seems to assume iid errors (probably wrong assumption here)
model <- momentModel(C~alpha+beta*Y^gamma, ~C1+Y1+Y2, data=dat, theta0=theta0, vcov="iid")

### Scaling the parameters increase the speed of convergence
res <- gmmFit(model, control=list(parscale=c(1000,.1,1)))

### It also seems that there is a degree of freedom adjustment for the
### estimate of the variance of the error term.
summary(res, df.adj=TRUE)@coef

~~ Methods for Function Dresiduals in Package Gmm ~~

Description

It returns the matrix of derivatives of the residuals with respect to the coefficients.

Methods

signature(object = "linearModel")
signature(object = "nonlinearModel")
signature(object = "rsnonlinearModel")
signature(object = "sysMomentModel")

Examples

data(simData)

theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

Dresiduals(model1, theta)[1:3,]

~~ Methods for Function DWH in Package momentfit ~~

Description

It performs the Durbin-Wu-Hausman test on GMM fit models.

Usage

## S4 method for signature 'gmmfit,missing'
DWH(object1, object2)

## S4 method for signature 'gmmfit,lm'
DWH(object1, object2,
tol=sqrt(.Machine$double.eps), v1=NULL, v2=NULL, ...)

## S4 method for signature 'gmmfit,gmmfit'
DWH(object1, object2,
tol=sqrt(.Machine$double.eps), v1=NULL, v2=NULL, ...)

Arguments

object1

Object of class "gmmfit".
object2

Object of class "gmmfit" or "lm". If missing, the DWH test is a two step test in which the fitted endogenous variables from the first step are added to the regression. In that case, the test a a test of significance of the coefficients of the fitted endogenous variables.
v1

Alternatively, we can provide a different covariance matrix for object1
v2

Alternatively, we can provide a different covariance matrix for object2
tol

Tolerance for the Moore-Penrose generalized inverse
...

Argument to pass to vcov

Methods

signature(object1 = "gmmfit", object2 = "lm")
signature(object1 = "gmmfit", object2 = "gmmfit")
signature(object1 = "gmmfit", object2 = "missing")

References

Green, W.H.. (2012). Econometric Analysis, 7th edition, Prentice Hall.

Examples

### Exampe 8.7 of Greene (2012)
data(ConsumptionG)
Y <- ConsumptionG$REALDPI
C <- ConsumptionG$REALCONS
n <- nrow(ConsumptionG)
Y1 <- Y[-n]; Y <- Y[-1]
C1 <- C[-n]; C <- C[-1]
dat <- data.frame(Y=Y,Y1=Y1,C=C,C1=C1)



model1 <- momentModel(C~Y, ~Y, data=dat, vcov="iid")
model2 <- momentModel(C~Y, ~Y1+C1, data=dat, vcov="iid")
res1 <- tsls(model1)
res2 <- tsls(model2)
res <- lm(C~Y)

## Exampke 8.7-2. The difference is explained by the rounding
## error in Greene. Only the first the 3 digits of the t-test are used.
DWH(res2)

## Example 8.7-1. Not quite the same.
DWH(res2, res1)

## using lm object to compare OLS and 2SLS:
## The same adjustment on the vcov must be done (it is by default in lm)
## otherwise the different in the covariance matrices is mostly caused by the
## different ways to compute them.
DWH(res2, res, df.adj=TRUE)

## To reproduce the same results as Exampke 8.7-1,
## we need to specify the variance.
## But it is not necessary as the above way is
## asymptotically equivalent
X <- model.matrix(model1)
Xhat <- qr.fitted(res2@wObj@w, X)
s2 <- sum(residuals(res)^2)/(res$df.residual)
v1 <-  solve(crossprod(Xhat))*s2
v2 <- solve(crossprod(X))*s2
DWH(res2, res, v1=v1, v2=v2)

~~ Methods for Function estfun in Package sandwich ~~

Description

Estimating equations for moment models.

Methods

signature(x = "momentModel")

~~ Methods for Function evalDMoment in Package momentfit ~~

Description

It computes the matrix of derivatives of the sample moments with respect to the coefficients.

Usage

## S4 method for signature 'functionModel'
evalDMoment(object, theta, impProb=NULL,
lambda=NULL)

## S4 method for signature 'rfunctionModel'
evalDMoment(object, theta, impProb=NULL,
lambda=NULL)

## S4 method for signature 'rnonlinearModel'
evalDMoment(object, theta, impProb=NULL,
lambda=NULL)

## S4 method for signature 'formulaModel'
evalDMoment(object, theta, impProb=NULL,
lambda=NULL)

## S4 method for signature 'rformulaModel'
evalDMoment(object, theta, impProb=NULL,
lambda=NULL)

## S4 method for signature 'regModel'
evalDMoment(object, theta, impProb=NULL,
lambda=NULL)

## S4 method for signature 'sysModel'
evalDMoment(object, theta)

## S4 method for signature 'rslinearModel'
evalDMoment(object, theta)

## S4 method for signature 'rsnonlinearModel'
evalDMoment(object, theta, impProb=NULL)

Arguments

object

An model object
theta

A numerical vector of coefficients
impProb

If a vector of implied probablities is provided, the sample means are computed using them. If not provided, the means are computed using the uniform weight
lambda

A vector of Lagrange multipliers associated with the moment conditions. Its length must therefore match the number of conditions. See details below.

Details

Without the argument lambda, the method returns a q×kq \times k matrix, where kk is the number of coefficients, and qq is the number of moment conditions. That matrix is the derivative of the sample mean of the moments with respect to the coefficient.

If lambda is provided, the method returns an n×kn \times k matrix, where nn is the sample size. The ith row is Gi′λG_i'\lambda, where $G_i$ is the derivative of the moment function evaluated at the ith observation. For now, this option is used to compute robust-to-misspecified standard errors of GEL estimators.

Methods

signature(object = "functionModel")
signature(object = "rfunctionModel")

The theta vector must match the number of coefficients in the restricted model.

signature(object = "formulaModel")
signature(object = "rformulaModel")

The theta vector must match the number of coefficients in the restricted model.

signature(object = "regModel")
signature(object = "sysModel")
signature(object = "rslinearModel")

Examples

data(simData)
theta <- c(1,1)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
G <- evalDMoment(model1, theta)

## A nonlinearModel
g <- y~beta0+x1^beta1
h <- ~z1+z2
model2 <- momentModel(g, h, c(beta0=1, beta1=2), data=simData)
G <- evalDMoment(model2, c(beta0=1, beta1=2))

## A functionModel
fct <- function(tet, x)
    {
        m1 <- (tet[1] - x)
        m2 <- (tet[2]^2 - (x - tet[1])^2)
        m3 <- x^3 - tet[1]*(tet[1]^2 + 3*tet[2]^2)
        f <- cbind(m1, m2, m3)
        return(f)
    }
dfct <- function(tet, x)
        {
        jacobian <- matrix(c( 1, 2*(-tet[1]+mean(x)), -3*tet[1]^2-3*tet[2]^2,0, 2*tet[2],
			   -6*tet[1]*tet[2]), nrow=3,ncol=2)
        return(jacobian)
        }
X <- rnorm(200)
model3 <- momentModel(fct, X, theta0=c(beta0=1, beta1=2), grad=dfct)
G <- evalDMoment(model3, c(beta0=1, beta1=2))

~~ Methods for Function evalGel in Package modelfit ~~

Description

Method to simply evaluate a GEL model at a fixed coefficient vector. It creates a "gelfit" object using that fixed vector.

Usage

## S4 method for signature 'momentModel'
evalGel(model, theta, lambda=NULL,
                                gelType="EL", rhoFct=NULL,
                                lamSlv=NULL, lControl=list(), ...)

Arguments

model

An object of class "momentModel".
theta

A vector of coefficients at which the model is estimated
lambda

The Lagrange multiplier vector. If not provided, the optimal vector is obtained for the given theta
gelType

The type of GEL. It is either "EL", "ET", "EEL", "HD", "ETEL" or "ETHD".
rhoFct

An alternative objective function for GEL. This argument is only used if we want to fit the model with a different GEL method. see rhoFct.
lamSlv

An alternative solver for the Lagrange multiplier. By default, either Wu_lam, EEL_lam, REEL_lam or getLambda is used.
lControl

A list of controls for the Lagrange multiplier algorithm.
...

Other arguments to pass. Not used for the moment.

Methods

signature(model = "momentModel")

Examples

data(simData)
theta <- c(beta0=1,beta1=2)

## A linear model with optimal lambda
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
evalGel(model1, c(1,1))

## A nonlinear model with fixed lambda
g <- y~beta0+x1^beta1
h <- ~z1+z2
model2 <- momentModel(g, h, c(beta0=1, beta1=2), data=simData)
evalGel(model2, theta=c(beta1=2, beta0=0.5), lambda=c(.1,.2,.3), gelType="ET")

~~ Methods for Function evalGelObj in Package Gmm ~~

Description

~~ Methods to compute the GEL objective function. ~~

Usage

## S4 method for signature 'momentModel,numeric,numeric'
evalGelObj(object, theta,
                                                   lambda, gelType,
                                                   rhoFct=NULL, ...)

Arguments

object

An object of class "momentModel"
theta

The vector for coefficients.
lambda

Vector of Lagrange multiplier.
gelType

The type of GEL. It is either "EL", "ET", "EEL", "HD", "ETEL" or "ETHD".
rhoFct

An alternative objective function for GEL. This argument is only used if we want to fit the model with a different GEL method. see rhoFct.
...

Arguments to pass to other methods

Methods

signature(object = "momentModel", theta = "numeric", lambda = "numeric")

Examples

data(simData)

theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
evalGelObj(model1, theta, c(.2,.3,.4), gelType="EL")

~~ Methods for Function evalGmm in Package modelfit ~~

Description

Method to simply evaluate a GMM model at a fixed coefficient vector. It creates a "gmmfit" object using that fixed vector.

Usage

## S4 method for signature 'momentModel'
evalGmm(model, theta, wObj=NULL, ...)
## S4 method for signature 'sysModel'
evalGmm(model, theta, wObj=NULL, ...)

Arguments

model

An object of class "momentModel".
theta

A vector of coefficients at which the model is estimated
wObj

An object of class "momentWeights". If not provided, the optimal weights based on the specification of the model evaluated at theta will be computed.

...

Other arguments to pass. Not used for the moment.

Methods

signature(model = "momentModel")
signature(model = "sysModel")

Examples

data(simData)
theta <- c(beta0=1,beta1=2)

## A linear model
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
evalGmm(model1, c(1,1))

## A nonlinear model
g <- y~beta0+x1^beta1
h <- ~z1+z2
model2 <- momentModel(g, h, c(beta0=1, beta1=2), data=simData)
evalGmm(model2, theta=c(beta1=2, beta0=0.5))

## A function model
fct <- function(tet, x)
    {
        m1 <- (tet[1] - x)
        m2 <- (tet[2]^2 - (x - tet[1])^2)
        m3 <- x^3 - tet[1]*(tet[1]^2 + 3*tet[2]^2)
        f <- cbind(m1, m2, m3)
        return(f)
    }
dfct <- function(tet, x)
        {
        jacobian <- matrix(c( 1, 2*(-tet[1]+mean(x)), -3*tet[1]^2-3*tet[2]^2,0, 2*tet[2],
			   -6*tet[1]*tet[2]), nrow=3,ncol=2)
        return(jacobian)
        }
model3 <- momentModel(fct, simData$x3, theta0=c(beta0=1, beta1=2), grad=dfct)
evalGmm(model3, theta=c(beta1=.1, beta0=0.3))

~~ Methods for Function evalGmmObj in Package momentfit ~~

Description

~~ Methods to compute the GMM objective function. ~~

Usage

## S4 method for signature 'momentModel,numeric,momentWeights'
evalGmmObj(object, theta,
wObj, ...)

## S4 method for signature 'sysModel,list,sysMomentWeights'
evalGmmObj(object, theta,
wObj, ...)

Arguments

object

An object of class "momentModel", or "sysMomentModels".
theta

The vector for coefficients for single equation, or a list of vector for system of equations.
wObj

An object of class "momentWeights" or "sysMomentWeights".
...

Arguments to pass to other methods

Methods

signature(object = "momentModel", theta = "numeric", wObj = "momentWeights")
signature(object = "sysModel", theta = "list", wObj = "sysMomentWeights")

Examples

data(simData)

theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
w <- evalWeights(model1, theta)
evalGmmObj(model1, theta, w)

~~ Methods for Function evalMoment in Package momentfit ~~

Description

Method to evaluate the moment matrix at a given coefficient vector.

Methods

signature(object = "functionModel")
signature(object = "formulaModel")
signature(object = "regModel")
signature(object = "sysModel")
signature(object = "rsysModel")

Examples

data(simData)
theta <- c(1,1)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
gt <- evalMoment(model1, theta)

## A nonlinearGmm
g <- y~beta0+x1^beta1
h <- ~z1+z2
model2 <- momentModel(g, h, c(beta0=1, beta1=2), data=simData)
gt <- evalMoment(model2, c(beta0=1, beta1=2))

## A functionGmm
fct <- function(tet, x)
    {
        m1 <- (tet[1] - x)
        m2 <- (tet[2]^2 - (x - tet[1])^2)
        m3 <- x^3 - tet[1]*(tet[1]^2 + 3*tet[2]^2)
        f <- cbind(m1, m2, m3)
        return(f)
    }
dfct <- function(tet, x)
        {
        jacobian <- matrix(c( 1, 2*(-tet[1]+mean(x)), -3*tet[1]^2-3*tet[2]^2,0, 2*tet[2],
			   -6*tet[1]*tet[2]), nrow=3,ncol=2)
        return(jacobian)
        }
X <- rnorm(200)
model3 <- momentModel(fct, X, theta0=c(beta0=1, beta1=2), grad=dfct)
gt <- evalMoment(model3, c(beta0=1, beta1=2))

Methods for Function evalWeights in Package Gmm

Description

This is a constructor for objects of class momentWeights

Usage

## S4 method for signature 'momentModel'
evalWeights(object, theta=NULL, w="optimal",
...)

## S4 method for signature 'sysModel'
evalWeights(object, theta = NULL, w="optimal",
wObj=NULL)

## S4 method for signature 'rslinearModel'
evalWeights(object, theta = NULL, w="optimal",
wObj=NULL)

Arguments

object

Object of class momentModel
theta

The vector of coefficients to compute the optimal weights. If NULL, theta0 for the object is used.
w

A matrix for fixed weights, one of "optimal" or "ident"
wObj

An object of class "sysMomentWeights". Providing it avoid having to recompute Z'Z.
...

Arguments to pass to other methods

Methods

signature(object = "momentModel")
signature(object = "sysModel")
signature(object = "rslinearModel")

System of equations with restrictions on the coefficients. It only affects the computation of the weights when there are cross-equation restrictions.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

## Identity weights object
wObj1 <- evalWeights(model1, w="ident")

## Identity weights object (an alternative way less efficient)
wObj1 <- evalWeights(model1, w=diag(3))

## Optimal weights 
wObj1 <- evalWeights(model1, theta, w="optimal")

Class "formulaModel"

Description

Class for moment-based models for which moments are expressed using formulas.

Objects from the Class

Objects can be created by calls of the form new("formulaModel", ...). It is generated my momentModel.

Slots

modelF:

Object of class "data.frame" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "numeric" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "character" ~~

momNames:

Object of class "character" ~~

fRHS:

Object of class "list" ~~

fLHS:

Object of class "list" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

varNames:

Object of class "character" ~~

isEndo:

Object of class "logical" ~~

isMDE:

Object of class "logical" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "allNLModel", directly. Class "momentModel", directly.

Methods

[

signature(x = "formulaModel", i = "numeric", j = "missing"): ...

evalDMoment

signature(object = "formulaModel"): ...

evalMoment

signature(object = "formulaModel"): ...

gmmFit

signature(model = "formulaModel"): ...

modelDims

signature(object = "formulaModel"): ...

momentStrength

signature(object = "formulaModel"): ...

restModel

signature(object = "formulaModel"): ...

subset

signature(x = "formulaModel"): ...

Examples

showClass("formulaModel")

Class "functionModel"

Description

Class for moment-based models for which moment conditions are defined using a function.

Objects from the Class

Objects can be created by calls of the form new("functionModel", ...). It is generated my momentModel.

Slots

X:

Object of class "ANY" ~~

fct:

Object of class "function" ~~

dfct:

Object of class "functionORNULL" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "numeric" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "character" ~~

momNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

varNames:

Object of class "character" ~~

isEndo:

Object of class "logical" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "allNLModel", directly. Class "momentModel", directly.

Methods

[

signature(x = "functionModel", i = "numeric", j = "missing"): ...

evalDMoment

signature(object = "functionModel"): ...

evalMoment

signature(object = "functionModel"): ...

modelDims

signature(object = "functionModel"): ...

momentStrength

signature(object = "functionModel"): ...

restModel

signature(object = "functionModel"): ...

subset

signature(x = "functionModel"): ...

Examples

showClass("functionModel")

GEL estimation

Description

The main functions and methods to fit any model with GEL. As opposed to gelFit, models don't need to be created. It is all done by the functions. It is meant to be more user friendly.

Usage

gel4(g, x=NULL, theta0=NULL,lambda0=NULL, getVcov=FALSE, 
     gelType = c("EL","ET","EEL","HD", "REEL","ETEL","ETHD"),
     vcov = c("MDS","iid","HAC"), grad=NULL,
     vcovOptions=list(), centeredVcov = TRUE,
     cstLHS=NULL, cstRHS=NULL, lamSlv=NULL,
     rhoFct=NULL, initTheta=c("gmm", "theta0"),
     data = parent.frame(),
     coefSlv=c("optim","nlminb","constrOptim"),
     smooth=FALSE, 
     lControl=list(), tControl=list())

Arguments

g

A function of the form g(θ,x)g(\theta,x) and which returns a n×qn \times q matrix with typical element gi(θ,xt)g_i(\theta,x_t) for i=1,...qi=1,...q and t=1,...,nt=1,...,n. This matrix is then used to build the q sample moment conditions. It can also be a formula if the model is linear (see detailsbelow).
x

The matrix or vector of data from which the function g(θ,x)g(\theta,x) is computed. If "g" is a formula, it is an n×Nhn \times Nh matrix of instruments or a formula (see details below).
theta0

A k×1k \times 1 vector of starting values. It is required only when "g" is a function, a formula or a list of formulas. For these cases, they are needed to create the "momentModel" object.
lambda0

The q×1q \times 1 vector of starting values for the Lagrange multipliers. By default a zero vector is used.
getVcov

Should the method computes the covariance matrices of the coefficients and Lagrange multipliers.
gelType

A character string specifying the type of GEL.
vcov

Assumption on the properties of the moment conditions.
grad

A function of the form G(θ,x)G(\theta,x) which returns a q×kq\times k matrix of derivatives of gˉ(θ)\bar{g}(\theta) with respect to θ\theta.
vcovOptions

A list of options for the covariance matrix of the moment conditions. See vcovHAC for the default values.
centeredVcov

Should the moment function be centered when computing its covariance matrix. Doing so may improve inference.
cstLHS

The left hand side of the constraints to impose on the coefficients. See restModel for more details.
cstRHS

The right hand side of the constraints to impose on the coefficients. See restModel for more details.
lamSlv

An alternative solver for the Lagrange multiplier. By default, either Wu_lam, EEL_lam, REEL_lam or getLambda is used. See the vignette for the required format.
rhoFct

An optional function that return ρ(v)\rho(v). This is for users who want a GEL model that is not built in the package. The four arguments of the function must be "gmat", the matrix of moments, "lambda", the vector of Lagrange multipliers, "derive", which specify the order of derivative to return, and k a numeric scale factor required for time series and kernel smoothed moments.
initTheta

Method to obtain the starting values for the coefficient vector. By default the GMM estimate with identity matrix is used. The second argument means that "theta0" is used instead.

data

A required data.frame, in which all variables in g and x can be found.
smooth

If TRUE, "vcov" is set to "MDS" and the moment conditions are smoothed using a kernel. See the vignette for more details.
coefSlv

Minimization solver for the coefficient vector.
lControl

A list of controls for the Lagrange multiplier algorithm.
tControl

A list of controls for the coefficient algorithm.

Value

It returns an object of class "gelfit"

References

Anatolyev, S. (2005), GMM, GEL, Serial Correlation, and Asymptotic Bias. Econometrica, 73, 983-1002.

Andrews DWK (1991), Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica, 59, 817–858.

Kitamura, Yuichi (1997), Empirical Likelihood Methods With Weakly Dependent Processes. The Annals of Statistics, 25, 2084-2102.

Kitamura, Y. and Otsu, T. and Evdokimov, K. (2013), Robustness, Infinitesimal Neighborhoods and Moment Restrictions. Econometrica, 81, 1185-1201.

Newey, W.K. and Smith, R.J. (2004), Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators. Econometrica, 72, 219-255.

Smith, R.J. (2004), GEL Criteria for Moment Condition Models. Working paper, CEMMAP.

See Also

gelFit, momentModel

Examples

data(simData)
res <- gel4(y~x1, ~z1+z2, vcov="MDS", gelType="ET", data=simData)
res

Class "gelfit"

Description

A class to store fitted models obtained using a GEL method.

Objects from the Class

Objects can be created by calls of the form new("gelfit", ...). It is created by gelFit.

Slots

theta:

Object of class "numeric" ~~

convergence:

Object of class "numeric" ~~

lambda:

Object of class "numeric" ~~

lconvergence:

Object of class "numeric" ~~

call:

Object of class "callORNULL" ~~

gelType:

Object of class "list" ~~

vcov:

Object of class "list" ~~

model:

Object of class "momentModel" ~~

restrictedLam:

Object of class "integer" ~~

Methods

coef

signature(object = "gelfit"): ...

confint

signature(object = "gelfit"): ...

getImpProb

signature(object = "gelfit"): ...

momFct

signature(eta = "numeric", object = "gelfit"): ...

print

signature(x = "gelfit"): ...

residuals

signature(object = "gelfit"): ...

show

signature(object = "gelfit"): ...

specTest

signature(object = "gelfit", which = "missing"): ...

summary

signature(object = "gelfit"): ...

update

signature(object = "gelfit"): ...

vcov

signature(object = "gelfit"): ...

Examples

showClass("gelfit")

~~ Methods for Function gelFit in Package momentfit ~~

Description

Method to fit a model using GEL, from an object of class "momentModel" or its restricted counterpart.

Usage

## S4 method for signature 'momentModel'
gelFit(model, gelType="EL", rhoFct=NULL,
              initTheta=c("gmm", "modelTheta0"), theta0=NULL,
              lambda0=NULL, vcov=FALSE, ...)

## S4 method for signature 'rmomentModel'
gelFit(model, gelType="EL", rhoFct=NULL,
              initTheta=c("gmm", "modelTheta0"), theta0=NULL,
              lambda0=NULL, vcov=FALSE, ...)

Arguments

model

A model class object
gelType

The type of GEL. It is either "EL", "ET", "EEL", "HD", "ETEL" or "ETHD".
rhoFct

An alternative objective function for GEL. This argument is only used if we want to fit the model with a different GEL method. see rhoFct.
initTheta

Method to obtain the starting values for the coefficient vector. By default the GMM estimate with identity matrix is used. The second argument means that the theta0 of the object, if any, should be used.
theta0

An optional initial vector for optim when the model is nonlinear. If provided, the argument "initTheta" is ignored.
lambda0

Manual starting values for the Lagrange multiplier. By default, it is a vector of zeros.
vcov

Should the method computes the covariance matrices of the coefficients and Lagrange multipliers.
...

Arguments to pass to other methods (mostly the optimization algorithm)

Methods

signature(model = "momentModel")

The main method for all moment-based models.

signature(model = "rmomentModel")

The main method for all restricted moment-based models.

Examples

data(simData)

theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

## EL estimate
res1 <- gelFit(model1)
res1

## ET estimate
res2 <- gelFit(model1, gelType="ET")
res2

## Restricted models by EL
## using the Brent method
R <- matrix(c(0,1), ncol=2)
q <- 2
rmodel1 <- restModel(model1, R, q)
gelFit(rmodel1, tControl=list(method="Brent", lower=-10, upper=10))

~~ Methods for Function getImpProb in Package momenfit ~~

Description

Method to evaluate the implied probabilities of GEL.

Methods

signature(object = "gelfit")

~~ Methods for Function getRestrict in Package momentfit ~~

Description

It computes the matrices related to linear and nonlinear contraints. Those matrices are used to perform hypothesis tests.

Usage

## S4 method for signature 'rlinearModel'
getRestrict(object, theta)

## S4 method for signature 'rslinearModel'
getRestrict(object, theta)

## S4 method for signature 'rsnonlinearModel'
getRestrict(object, theta)

## S4 method for signature 'rnonlinearModel'
getRestrict(object, theta)

## S4 method for signature 'rformulaModel'
getRestrict(object, theta)

## S4 method for signature 'momentModel'
getRestrict(object, theta, R, rhs=NULL)

## S4 method for signature 'sysModel'
getRestrict(object, theta, R, rhs=NULL)

## S4 method for signature 'rfunctionModel'
getRestrict(object, theta)

Arguments

object

Object of class included in momentModel, rmomentModel, and rsysModel.
theta

A vector of coefficients for the unrestricted model (see examples).
R

A matrix, character or list of formulas that specifies the contraints to impose on the coefficients. See restModel for more details.
rhs

The right hand side for the restriction on the coefficients. See restModel for more details. It is ignored for objects of class "nonlinearModel".

Methods

signature(object = "momentModel")

A restricted model is created from the constraints, and the restriction matrices are returned. The methods is applied to linear and nonlinear models in a regression form.

signature(object = "sysModel")

A restricted model is created from the constraints, and the restriction matrices are returned. The methods is applied to systems of linear and nonlinear models.

signature(object = "rlinearModel")

The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.

signature(object = "rslinearModel")

The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.

signature(object = "rsnonlinearModel")

The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.

signature(object = "rnonlinearModel")

The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.

signature(object = "rfunctionModel")

The restriction matrices are evaluated at the coefficient vector theta of the unrestricted representation.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)

## Unrestricted model
model1 <- momentModel(y~x1+x2+x3+z1, ~x1+x2+z1+z2+z3+z4, data=simData)

## The restricted model
R1 <- c("x1","2*x2+z1=2", "4+x3*5=3")
res <- gmmFit(model1)
rest <- getRestrict(model1, coef(res), R1)

## it allows to test the restriction
g <- rest$R-rest$q
v <- rest$dR%*%vcov(res)%*%t(rest$dR)
(test <- crossprod(g, solve(v, g)))
(pv <- 1-pchisq(test, length(rest$R)))


## Delta Method:
## To impose nonlinear restrictions, we need to convert
## the linear model into a nonlinear one
NLmodel <- as(model1, "nonlinearModel")
R1 <- c("theta2=2", "theta3=theta4^2")
res <- gmmFit(NLmodel)
rest <- getRestrict(NLmodel, coef(res), R1)

g <- rest$R-rest$q
v <- rest$dR%*%vcov(res)%*%t(rest$dR)
(test <- crossprod(g, solve(v, g)))
(pv <- 1-pchisq(test, length(rest$R)))

## See hypothesisTest method for an easier approach.

GMM estimation

Description

The main functions and methods to fit any model with GMM. As opposed to gmmFit, models don't need to be created. It is all done by the functions. It is meant to be more user friendly. This document needs to changed. It is just a copy and paste from the gmm package

Usage

gmm4(g, x, theta0 = NULL, grad = NULL, 
     type = c("twostep", "iter", "cue", "onestep"),
     vcov = c("iid", "HAC", "MDS", "TrueFixed", "CL"),
     initW = c("ident", "tsls", "EbyE"), weights = "optimal", 
     itermaxit = 50, cstLHS=NULL, cstRHS=NULL,
     vcovOptions=list(), survOptions=list(),
     itertol = 1e-07, centeredVcov = TRUE,
     data = parent.frame(), ...)

## S4 method for signature 'formula'
tsls(model, x, vcov = c("iid", "HAC", "MDS", "CL"),
         vcovOptions=list(), survOptions=list(), centeredVcov = TRUE,
         data = parent.frame())

## S4 method for signature 'list'
tsls(model, x=NULL, vcov = c("iid", "HAC", "MDS",
          "CL"), vcovOptions=list(), survOptions=list(),
          centeredVcov = TRUE, data = parent.frame())

## S4 method for signature 'list'
ThreeSLS(model, x=NULL, vcov = c("iid", "HAC", "MDS",
          "CL"), vcovOptions=list(), survOptions=list(),
          centeredVcov = TRUE, data = parent.frame())

Arguments

model

A formula or a list of formulas.
g

A function of the form g(θ,x)g(\theta,x) and which returns a n×qn \times q matrix with typical element gi(θ,xt)g_i(\theta,x_t) for i=1,...qi=1,...q and t=1,...,nt=1,...,n. This matrix is then used to build the q sample moment conditions. It can also be a formula if the model is linear or nonlinear, or a list of formulas for systems of equations.
x

The matrix or vector of data from which the function g(θ,x)g(\theta,x) is computed. If "g" is a formula, it is an n×Nhn \times Nh matrix of instruments or a formula (see details below).
theta0

A k×1k \times 1 vector of starting values. It is required only when "g" is a function or a nonlinear equation defined by a formula, in which case, it must be a named vector
grad

A function of the form G(θ,x)G(\theta,x) which returns a q×kq\times k matrix of derivatives of gˉ(θ)\bar{g}(\theta) with respect to θ\theta. By default, the numerical algorithm numericDeriv is used. It is of course strongly suggested to provide this function when it is possible. This gradient is used to compute the asymptotic covariance matrix of θ^\hat{\theta} and to obtain the analytical gradient of the objective function if the method is set to "CG" or "BFGS" in optim and if "type" is not set to "cue". If "g" is a formula, the gradiant is not required (see the details below).
type

What GMM methods should we use? for type=="onestep", if "weights" is not a matrix, the model will be estimated with the weights equals to the identity matrix
vcov

Assumption on the properties of the random vector x. By default, x is a weakly dependant process. The "iid" option will avoid using the HAC matrix which will accelerate the estimation if one is ready to make that assumption. The option "TrueFixed" is used only when the matrix of weights is provided and it is the optimal one. For type CL, clustered covariance matrix is computed. The options are then included in vcovOptions (see meatCL).
initW

How should be compute the initial coefficient vector in the first. It only makes a difference for linear models for which the choice is GMM with identity matrix or two-stage least quares.
weights

What weighting matrix to use? The choices are "optimal", in which case it is the inverse of the moment vovariance matrix, "ident" for the identity matrix, or a fixed matrix.
itermaxit

Maximum iterations for iterative GMM
itertol

Tolance for the stopping rule in iterative GMM
centeredVcov

Should the moment function be centered when computing its covariance matrix. Doing so may improve inference.
data

A data.frame or a matrix with column names (Optional).

cstLHS

The left hand side of the constraints to impose on the coefficients. See restModel for more details.
cstRHS

The right hand side of the constraints to impose on the coefficients. See restModel for more details.
vcovOptions

A list of options for the covariance matrix of the moment conditions. See vcovHAC for the default values.
survOptions

If needed, a list with the type of survey weights and the weights as a numeric vector, data.frame or formula. The type is either "sampling" or "fequency".
...

Arguments to pass to optim when the model is nonlinear.

Value

It returns an object of class "gmmfit"

References

Zeileis A (2006), Object-oriented Computation of Sandwich Estimators. Journal of Statistical Software, 16(9), 1–16. URL doi:10.18637/jss.v016.i09.

Andrews DWK (1991), Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica, 59, 817–858.

Newey WK & West KD (1987), A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica, 55, 703–708.

Newey WK & West KD (1994), Automatic Lag Selection in Covariance Matrix Estimation. Review of Economic Studies, 61, 631-653.

Hansen, L.P. (1982), Large Sample Properties of Generalized Method of Moments Estimators. Econometrica, 50, 1029-1054,

Hansen, L.P. and Heaton, J. and Yaron, A.(1996), Finite-Sample Properties of Some Alternative GMM Estimators. Journal of Business and Economic Statistics, 14 262-280.

See Also

gmmFit, momentModel

Examples

data(simData)

res <- gmm4(y~x1, ~z1+z2, vcov="MDS", type="iter", data=simData)
res

Class "gmmfit"

Description

A class to store a fitted model obtained using GMM.

Objects from the Class

Objects can be created by calls of the form new("gmmfit", ...). Generated by gmmFit.

Slots

theta:

Object of class "numeric" ~~

convergence:

Object of class "numericORNULL" ~~

convIter:

Object of class "numericORNULL" ~~

call:

Object of class "callORNULL" ~~

type:

Object of class "character" ~~

wObj:

Object of class "momentWeights" ~~

niter:

Object of class "integer" ~~

efficientGmm:

Object of class "logical" ~~

model:

Object of class "momentModel" ~~

Methods

bread

signature(x = "gmmfit"): ...

coef

signature(object = "gmmfit"): ...

confint

signature(object = "gmmfit"): ...

DWH

signature(object1 = "gmmfit", object2 = "gmmfit"): ...

DWH

signature(object1 = "gmmfit", object2 = "lm"): ...

DWH

signature(object1 = "gmmfit", object2 = "missing"): ...

hypothesisTest

signature(object.u = "gmmfit", object.r = "gmmfit"): ...

hypothesisTest

signature(object.u = "gmmfit", object.r = "missing"): ...

hypothesisTest

signature(object.u = "missing", object.r = "gmmfit"): ...

meatGmm

signature(object = "gmmfit"): ...

print

signature(x = "gmmfit"): ...

residuals

signature(object = "gmmfit"): ...

show

signature(object = "gmmfit"): ...

specTest

signature(object = "gmmfit", which = "missing"): ...

specTest

signature(object = "gmmfit", which = "numeric"): ...

summary

signature(object = "gmmfit"): ...

update

signature(object = "gmmfit"): ...

vcov

signature(object = "gmmfit"): ...

Examples

showClass("gmmfit")

~~ Methods for Function gmmFit in Package momentfit ~~

Description

Method to fit a model using GMM, from an object of class "momentModel" or "sysModel".

Usage

## S4 method for signature 'momentModel'
gmmFit(model, type=c("twostep", "iter","cue",
              "onestep"), itertol=1e-7, initW=c("ident", "tsls"),
              weights="optimal", itermaxit=100,
              efficientWeights=FALSE, theta0=NULL, ...)

## S4 method for signature 'formulaModel'
gmmFit(model, type=c("twostep", "iter","cue",
              "onestep"), itertol=1e-7, initW=c("ident", "tsls"),
              weights="optimal", itermaxit=100,
              efficientWeights=FALSE, theta0=NULL, ...)

## S4 method for signature 'sysModel'
gmmFit(model, type=c("twostep", "iter","cue",
              "onestep"), itertol=1e-7, initW=c("ident", "tsls", "EbyE"),
              weights="optimal", itermaxit=100,
              efficientWeights=FALSE, theta0=NULL, EbyE=FALSE, ...)

## S4 method for signature 'rnonlinearModel'
gmmFit(model, type=c("twostep", "iter","cue",
              "onestep"), itertol=1e-7, initW=c("ident", "tsls"),
              weights="optimal", itermaxit=100,
              efficientWeights=FALSE, theta0=NULL, ...)

## S4 method for signature 'rlinearModel'
gmmFit(model, type=c("twostep", "iter","cue",
              "onestep"), itertol=1e-7, initW=c("ident", "tsls"),
              weights="optimal", itermaxit=100,
              efficientWeights=FALSE, ...)

## S4 method for signature 'rformulaModel'
gmmFit(model, type=c("twostep", "iter","cue",
              "onestep"), itertol=1e-7, initW=c("ident", "tsls"),
              weights="optimal", itermaxit=100,
              efficientWeights=FALSE, theta0=NULL, ...)

## S4 method for signature 'rslinearModel'
gmmFit(model, type=c("twostep", "iter","cue",
              "onestep"), itertol=1e-7, initW=c("ident", "tsls", "EbyE"),
              weights="optimal", itermaxit=100,
              efficientWeights=FALSE, theta0=NULL, EbyE=FALSE, ...)

Arguments

model

A model class object.
type

What GMM methods should we use? for type=="onestep", if "weights" is not a matrix, the model will be estimated with the weights equals to the identity matrix. For restricted

itertol

Tolance for the stopping rule in iterative GMM
initW

How should be compute the initial coefficient vector in the first. For single equation GMM, it only makes a difference for linear models for which the choice is GMM with identity matrix or two-stage least quares. For system of equations, "tsls", refers to equation by equation two-stage least squares. It is also possible to start at the equation by equation estimate using the same GMM type as specified by "type".
weights

What weighting matrix to use? The choices are "optimal", in which case it is the inverse of the moment vovariance matrix, "ident" for the identity matrix, or a fixed matrix. It is also possible for weights to be an object of class gmmWeights.
itermaxit

Maximum iterations for iterative GMM
EbyE

Should the system be estimated equation by equation?
efficientWeights

If weights is a matrix or a gmmWeights class object, setting efficientWeights to TRUE implies that the resulting one-step GMM is efficient. As a result, the default covariance matrix for the coefficient estimates will not be a sandwich type.
theta0

An optional initial vector for optim when the model is nonlinear. By default, the theta0 argument of the model is used
...

Arguments to pass to other methods (mostly the optimization algorithm)

Methods

signature(model = "momentModel")

The main method for all moment-based models.

signature(model = "rnonlinearModel")

It makes a difference only if the number of contraints is equal to the number of coefficients, in which case, the method evalGmm is called at the contrained vector. If not, the next method is called.

signature(model = "rformulaModel")

It makes a difference only if the number of contraints is equal to the number of coefficients, in which case, the method evalGmm is called at the contrained vector. If not, the next method is called.

signature(model = "rlinearModel")

It makes a difference only if the number of contraints is equal to the number of coefficients, in which case, the method evalGmm is called at the contrained vector. If not, the next method is called.

signature(model = "sysModel")

Method to estimate system of equations using GMM methods.

Examples

data(simData)

theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

## Efficient GMM with HAC vcov and tsls as first step.
res1 <- gmmFit(model1, init="tsls")

## GMM with identity. Two ways.
res2 <- gmmFit(model1, type="onestep")
res3 <- gmmFit(model1, weights=diag(3))

## nonlinear regression with iterative GMM.
g <- y~beta0+x1^beta1
h <- ~z1+z2
model2 <- momentModel(g, h, c(beta0=1, beta1=2), data=simData)
res4 <- gmmFit(model2, type="iter")

## GMM for with no endogenous vaiables is
## OLS with Robust standard error

library(lmtest)
model3 <- momentModel(y~x1, ~x1, data=simData, vcov="MDS")
resGmm <- gmmFit(model3)
resLm <- lm(y~x1, simData)
summary(resGmm)
coeftest(resLm, vcov=vcovHC(resLm, "HC0"))
summary(resGmm, df.adj=TRUE)
coeftest(resLm, vcov=vcovHC(resLm, "HC1"))

### All constrained
R <- diag(2)
q <- c(1,2)
rmodel1 <- restModel(model1, R, q)
gmmFit(rmodel1)

## Only one constraint
R <- matrix(c(0,1), ncol=2)
q <- 2
rmodel1 <- restModel(model1, R, q)
gmmFit(rmodel1)

Return to Education Data

Description

Labour data on 758 young workers between 16 and 30 years hold. Each observation provides information on one individual at two points in time: in 1980 (variable with 80) and in the year given be the YEAR (variable without 80).

Usage

data("Griliches")

Format

A data.frame with 758 observations and 20 variables.

RNS, RNS80

Dummy for residency in the southern states

MRT, MRT80

Dummy for marital status (1 if married)

SMSA, SMSA80

Dummy for residency in metropolitan areas

MED

Mother's education in years

IQ

IQ score

KWW

"Knowledge of the World of Work" test score

Year

The year of the first observation

AGE, AGE80

Age in years

S, S80

Completed years of schooling

EXPR, EXPR80

Experience in years

TENURE, TENURE80

Tenure im years

LW, LW80

log wage

Source

Online complements of Fumio Hayashi (2000)

References

Griliches, Z. (1976). Wages of Very Young Men. Journal of Political Economy, 84, S69–S85.

Blackburn, M. and Neumark, D. (1992). Unobserved Ability, Efficiency Wages, and Interindustry Wage Differentials. Quarterly Journal of Economics, 107, 1421–1436.

Hayashi, F. (2000). Econometrics, New Jersey: Princeton University Press.

Health data from Greene (2012) applications.

Description

The dataset is used in Greene (2012) and is taken from Riphahn, Wambach, Million (2003).

Usage

data("HealthRWM")

Format

A data frame with 27326 observations on the following 25 variables.

ID

Person-identification number

female

Female=1; male=0

year

Calendar year of the observation

age

Age in years

hsat

Health satisfaction, coded 0 (low) to 10 (high)

handdum

Handicapped=1; otherwise=0

handper

Degree of handicap in percent (0 to 100)

hhninc

Household nominal monthly net income in German marks/10,000

hhkids

Children under age 16 in the household=1; otherwise=0

educ

Years of schooling

married

Married=1; otherwise=0

haupts

Highest schooling degree is Hauptschul degree=1; otherwise=0

reals

Highest schooling degree is Realschul degree=1; otherwise=0

fachhs

Highest schooling degree is Polytechnical degree=1; otherwise=0

abitur

Highest schooling degree is Abitur=1; otherwise=0

univ

Highest schooling degree is university degree=1; otherwise=0

working

Employed=1; otherwise=0

bluec

Blue-collar employee=1; otherwise=0

whitec

White-collar employee=1; otherwise=0

self

Self-employed=1; otherwise=0

beamt

Civil servant=1; otherwise=0

docvis

Number of doctor visits in last three months,

hospvis

Number of hospital visits in last calendar year,

public

Insured in public health insurance=1; otherwise=0

addon

Insured by add-on insurance=1; otherwise=0

Source

On Greene (2012) online resources, and on the Journal of Applied Econometrics website (http://qed.econ.queensu.ca/jae/2003-v18.4/riphahn-wambach-million/).

References

Riphahn, R.T. and Wambach, A. and Million, A. (2003), Incentive Effects in the Demand for Health Care: A Bivariate Panel Count Data Estimation, Journal of Applied Econometrics, Vol. 18, No. 4, 387–405.

Green, W.H.. (2012). Econometric Analysis, 7th edition, Prentice Hall.

Examples

###### Example 13.7 of Greene (2012)
####################################

## Selecting the same data point and scaling income
##########
data(HealthRWM)
dat88 <- subset(HealthRWM, year==1988 & hhninc>0)
dat88$hhninc <- dat88$hhninc/10000

### A guess start
thet0 <- c(b0=log(mean(dat88$hhninc)),b1=0,b2=0,b3=0)

## Table 13.2 First column
g <- hhninc~exp(b0+b1*age+b2*educ+b3*female)
res0 <- nls(g, dat88, start=thet0, control=list(maxiter=100))
summary(res0)$coef

## Table 13.2 Second column
## Trying very hard to reproduce the results, 
## Who is right?
h1 <- ~age+educ+female
model1 <- momentModel(g, h1, thet0, vcov="MDS", data=dat88)
res1 <- gmmFit(model1, control=list(reltol=1e-10, abstol=1e-10))
summary(res1)@coef

## Table 13.2 third column (close enough)
## Here a sandwich vcov is required because it is not
## efficient GMM
h2 <- ~age+educ+female+hsat+married
model2 <- momentModel(g, h2, thet0, vcov="MDS", data=dat88)
res2 <- gmmFit(model2, type="onestep")
summary(res2, sandwich=TRUE)@coef

## Table 13.2 fourth column (Can't get closer than that)
res3 <- gmmFit(model2)
summary(res3)@coef

# Lets see what happens if we start on Greene solution
             
update(res3, theta0=c(b0=-1.61192, b1=.00092, b2=.04647, b3=-.01517))

## No...

Class "hypothesisTest"

Description

A class to store results form an hypothesis test.

Objects from the Class

Objects can be created by calls of the form new("hypothesisTest", ...). It is created by hypothesisTest.

Slots

test:

Object of class "numeric" ~~

hypothesis:

Object of class "character" ~~

dist:

Object of class "character" ~~

df:

Object of class "integer" ~~

pvalue:

Object of class "numeric" ~~

type:

Object of class "character" ~~

Methods

print

signature(x = "hypothesisTest"): ...

show

signature(object = "hypothesisTest"): ...

Examples

showClass("hypothesisTest")

~~ Methods for Function hypothesisTest in Package momentfit ~~

Description

Performs hypothesis tests on the coefficients estimated by any GMM fit method.

Usage

## S4 method for signature 'gmmfit,missing'
hypothesisTest(object.u, object.r, R,
rhs=NULL, vcov=NULL, ...)

## S4 method for signature 'sgmmfit,missing'
hypothesisTest(object.u, object.r, R,
rhs=NULL, vcov=NULL, ...)

## S4 method for signature 'gmmfit,gmmfit'
hypothesisTest(object.u, object.r,
type=c("Wald", "LR", "LM"), sameVcov=TRUE, vcov=NULL,
firstStepWeight=FALSE, wObj=NULL, ...)

## S4 method for signature 'sgmmfit,sgmmfit'
hypothesisTest(object.u, object.r,
type=c("Wald", "LR", "LM"), sameVcov=TRUE, vcov=NULL,
firstStepWeight=FALSE, wObj=NULL, ...)

## S4 method for signature 'missing,gmmfit'
hypothesisTest(object.u, object.r, wObj=NULL)

## S4 method for signature 'missing,sgmmfit'
hypothesisTest(object.u, object.r, wObj=NULL)

Arguments

object.u

An object of class gmmfit or sgmmfit obtained using an unrestricted "momentModel" or "sysModel".
object.r

An object of class gmmfit obtained using a restricted "momentModel" or "sysModel".
R

If it is an object of class gmmfit, one of the model fit must be the restricted version of the other. The restrictions are then tested. If R is a character type, it expresses the restrictions using the coefficient names. If it numeric, it must be a matrix and the restrictions are Rθ=0R\theta=0 for NULL rhs, or Rθ=rhsR\theta=rhs otherwise. If missing, the gmmfit must be a fitted restricted model, in which case, a LM test is performed.
rhs

A vector of right hand sides if R is numeric
type

Should we perform a Wald, LR or LM test?
sameVcov

For the LR test, should we use the same estimate of the covariance matrix of the moment conditions? See details below.
vcov

For the Wald test, it is possible to provide the method with the covariance matrix of the coefficients.
wObj

For the LR test, it is possible to provide the gmmWeights object. In that case, the provided gmm weights object if used for the restricted and unrestricted models.
...

Other argument to pass to specTest.
firstStepWeight

Should we use the first step weighting matrix to compute the test (By default, the optimal weighting matrix is recomputed using the final vector of coefficient estimates). See details below.

Details

The LR test is the difference between the J-tests of the restricted and unrestricted models. It is therefore ngˉr′Wrgˉr−ngˉu′Wugˉun\bar{g}_r'W_r\bar{g}_r - n\bar{g}_u'W_u\bar{g}_u, where gˉr\bar{g}_r and gˉu\bar{g}_u are respectively the restricted and unrestricted sample mean of the moment conditions, and WrW_r and WuW_u their respective optimal weigthing matrix. The test is therefore invalid if either of the weighting matrices does not converge to the inverse of the covariance matrix of the moment conditions. The restricted and unrestricted models must therefore be estimated by efficient GMM. This is not required for the Wald test.

Asymptotically, it makes no difference which consistent estimate of WuW_u or WrW_r is used. However, it will make a difference in finite samples.

If sameVcov=TRUE, both WrW_r and WuW_u are equal to the the optimal weighting matrix from the unrestricted model if firstStepWeight=FALSE, and they are equal to the first step weighting matrix (or the last step for iteratice GMM) of the unrestricted model if it is TRUE. For CUE, the value of firstStepWeight makes no difference since the weighting matrix and coefficients are computed simultaneously. Having Wr=WuW_r=W_u prevents the test to be negative in small samples.

If wObj is provided, both WrW_r and WuW_u are equal to it. Of cource, wObj must be a consistent estimate of the optimal weighting matrix for the test to be valid.

Methods

signature(object.u = "gmmfit", object.r = "gmmfit")

Used to test a restricted model against an unrestricted one.

signature(object.u = "sgmmfit", object.r = "sgmmfit")

Used to test a restricted model against an unrestricted one (for systems of equations).

signature(object.u = "missing", object.r= "gmmfit")

Used to test a restricted model using the LM test.

signature(object.u = "missing", object.r= "sgmmfit")

Used to test a restricted model using the LM test (for systems of equations).

signature(object.u = "gmmfit", object.r = "missing")

Perform a Wald test using an unrestricted model and a restriction matrix or vector.

signature(object.u = "sgmmfit", object.r = "missing")

Perform a Wald test using an unrestricted model and a restriction matrix or vector in systems of linear equations.

Examples

data(simData)

## Unrestricted model
model1 <- momentModel(y~x1+x2+x3, ~x2+x3+z1+z2+z3, data=simData, vcov="MDS")
res1 <- gmmFit(model1)

## Wald test 
R <- c("x1=0.5","x2=x3")
hypothesisTest(object.u=res1, R=R)

## LR tests

rmodel1 <- restModel(model1, R)
res2 <- gmmFit(rmodel1)
hypothesisTest(object.u=res1, object.r=res2, type="LR")

### LR and Wald should be the same as long as the same weighting
### matrix if used for both GMM fits, for the LR and Wald as well

# Unrestricted model and save the weights
res1 <- gmmFit(model1)
w <- res1@wObj
# estimate models with the same weights
res2 <- gmmFit(rmodel1, weights=w)

# LR test with the same weights
hypothesisTest(res1, res2, type="LR", wObj=w)

# Wald test with vcov based on the same weights (or the bread)
hypothesisTest(object.u=res1, R=R, breadOnly=TRUE)

### Another example with real data
data(Mroz)
model <- momentModel(log(wage)~educ+exper+I(exper^2),
                  ~exper+I(exper^2)+fatheduc+motheduc, vcov="MDS",
                  data=Mroz, centeredVcov=FALSE)
R <- c("educ=0","I(exper^2)=0")
rmodel <- restModel(model, R)

res1 <- gmmFit(model)
res2 <- gmmFit(rmodel, weights=res1@wObj)

hypothesisTest(object.u=res1, object.r=res2, type="LR", wObj=res1@wObj)
hypothesisTest(object.u=res1, object.r=res2, type="Wald",
vcov=vcov(res1, breadOnly=TRUE))

## LM test (identical to the other two tests as well)

hypothesisTest(object.r=res2)
# or 
hypothesisTest(object.u=res1, object.r=res2, type="LM")

## Wald with the Delta Method:
## To impose nonlinear restrictions, we need to convert
## the linear model into a nonlinear one
NLmodel <- as(model1, "nonlinearModel")
R1 <- c("theta2=2", "theta3=theta4^2")
rNLmodel <- restModel(NLmodel, R1)
res.u <- gmmFit(NLmodel)
res.r <- gmmFit(rNLmodel)
hypothesisTest(object.u=res.u, R=R1)

## LM

hypothesisTest(object.r=res.r)

## LR

hypothesisTest(object.r=res.r, object.u=res.u, type="LR")

A kernel smoothing utility for "momentModel" classes

Description

It either generates the optimal bandwidth and kernel weights or the smoothed moments of moment based models.

Usage

## S4 method for signature 'momentModel'
kernapply(x, theta=NULL, smooth=TRUE, ...)

Arguments

x

An object of class "momentModel".
theta

An optional vector of coefficients. For smooth=FALSE, it is used to obtain the optimal bandwidth. If NULL, the bandwidth is obtained using one step GMM with the identity matrix as weights. For smooth=TRUE, the coefficient is required since the function returns the smoothed moments at a given vector of coefficients.
smooth

By default, it returns the smoothed moment matrix. If FALSE, it computes the optimal bandwidth and kernel weights.
...

Other arguments to pass. Currently not used

Value

It return an object of class "sSpec".

References

Anatolyev, S. (2005), GMM, GEL, Serial Correlation, and Asymptotic Bias. Econometrica, 73, 983-1002.

Kitamura, Yuichi (1997), Empirical Likelihood Methods With Weakly Dependent Processes. The Annals of Statistics, 25, 2084-2102.

Smith, R.J. (2011), GEL Criteria for Moment Condition Models. Econometric Theory, 27(6), 1192–1235.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)

## A linearModel
model1 <- momentModel(y~x1, ~z1+z2, data=simData,vcov="HAC",vcovOptions=list(kernel="Bartlett"))

### get the bandwidth
### Notice that the kernel name is the not the same
### That's because a Truncated kernel for smoothing
### lead to a Bartlett kernel for the HAC of the moments
### See Smith (2011)
kernapply(model1, smooth=FALSE)


### Adding the kernel option to the model

model2 <- momentModel(y~x1, ~z1+z2,
data=simData,vcov="HAC",vcovOptions=list(kernel="Bartlett"), smooth=TRUE)

kernapply(model2, theta)$smoothx[1:5,]

Klein (1950) macro data.

Description

The data is used to reproduce examples of Greene (2012)

Usage

data("Klein")

Format

A data frame with 22 observations on the following 10 variables.

YEAR

a numeric vector

C

a numeric vector

P

a numeric vector

WP

a numeric vector

I

a numeric vector

K1

a numeric vector

X

a numeric vector

WG

a numeric vector

G

a numeric vector

T

a numeric vector

Source

On Greene (2012) online resources.

References

Klein, L. (1950), Economic Fluctuations in the United-States 1921-1941, New York: John Wiley and Sons.

Green, W.H.. (2012). Econometric Analysis, 7th edition, Prentice Hall.

Examples

data(Klein)

Labour data from Greene (2012) applications,

Description

A panel data set of 565 individuals from 1976 to 1982 used by Cornwell and Rupert (1988)

Usage

data("LabourCR")

Format

A data frame with 4165 observations on the following 12 variables.

EXP

Year of full time experience.

WKS

Weeks worked.

OCC

1 if blue-collar occupation, 0 otherwise.

IND

1 if works in a manufacture industry, 0 otherwise.

SOUTH

1 if resides in the south, 0 otherwise.

SMSA

1 if resides in an SMSA, 0 otherwise.

MS

1 if married, 0 otherwise.

FEM

1 if the individual is a female and 0 otherwise.

UNION

1 if wage is set by a union contract and 0 otherwise.

ED

Years of education.

BLK

1 if the individual is black and 0 otherwise.

LWAGE

Log wage.

Source

Greene (2012) online resources: (http://pages.stern.nyu.edu/~wgreene/Text/Edition7/tablelist8new.htm)

References

Green, W.H.. (2012). Econometric Analysis, 7th edition, Prentice Hall.

Cornwell, C. and Rupert, P. (1988), Efficient Estimation with Panel Data: An Empirical Comparision of Instrumental Variable Estimators, Journal of Applied Econometrics, No.3, 149–155.

Examples

data(LabourCR)
## Table 8.1 of Greene (2012)
## Model with Z2 (iid is assumed in Table 8.1 given the s.e.)
model2 <- momentModel(WKS~LWAGE+ED+UNION+FEM, ~IND+ED+UNION+FEM+SMSA, vcov="iid",
                   data=LabourCR)
## Model with Z1 using the subsetting method '['
model1 <- model2[-6L]

# Second column
res1 <- tsls(model1)
summary(res1)@coef

# Third column
res2 <- tsls(model2)
summary(res2)@coef

Algorithms to solve for the Lagrange multiplier

Description

The algorithms finds the vector or Lagrange multipliers that maximizes the GEL objective function for a given vector of coefficient θ\theta.

Usage

Wu_lam(gmat, tol=1e-8, maxiter=50, k=1)

EEL_lam(gmat, k=1) 

REEL_lam(gmat, tol=NULL, maxiter=50, k=1)

ETXX_lam(gmat, lambda0, k, gelType, algo, method, control)

getLambda(gmat, lambda0=NULL, gelType=NULL, rhoFct=NULL, 
          tol = 1e-07, maxiter = 100, k = 1, method="BFGS", 
          algo = c("nlminb", "optim", "Wu"), control = list(),
          restrictedLam=integer())

Arguments

gmat

The n×qn \times q matrix of moments
lambda0

The q×1q \times 1 vector of starting values for the Lagrange multipliers.
tol

A tolerance level for the stopping rule in the Wu algorithm
maxiter

The maximum number of iteration in the Wu algorithm
gelType

A character string specifying the type of GEL. The available types are "EL", "ET", "EEL", "HD" and "REEL". For the latter, the algorithm restricts the implied probabilities to be non negative.
rhoFct

An optional function that return ρ(v)\rho(v). This is for users who want a GEL model that is not built in the package. The four arguments of the function must be "gmat", the matrix of moments, "lambda", the vector of Lagrange multipliers, "derive", which specify the order of derivative to return, and k a numeric scale factor required for time series and kernel smoothed moments.
k

A numeric scaling factor that is required when "gmat" is a matrix of time series which require smoothing. The value depends on the kernel and is automatically set when the "gelModels" is created.
method

This is the method for optim.
algo

Which algorithm should be used to maximize the GEL objective function. If set to "Wu", which is only for "EL", the Wu (2005) algorithm is used.
control

A list of control to pass to either optim or nlminb.
restrictedLam

A vector of integers indicating which "lambda" are restricted to be equal to 0.

Details

The ETXX_lam is used for ETEL and ETHD. In general, it computes lambda using ET, and returns the value of the objective function determined by the gelType.

Value

It returns the vector ρ(gmatλ)\rho(gmat \lambda) when derive=0, ρ′(gmatλ)\rho'(gmat \lambda) when derive=1 and ρ′′(gmatλ)\rho''(gmat \lambda) when derive=2.

References

Anatolyev, S. (2005), GMM, GEL, Serial Correlation, and Asymptotic Bias. Econometrica, 73, 983-1002.

Kitamura, Yuichi (1997), Empirical Likelihood Methods With Weakly Dependent Processes. The Annals of Statistics, 25, 2084-2102.

Kitamura, Y. and Otsu, T. and Evdokimov, K. (2013), Robustness, Infinitesimal Neighborhoods and Moment Restrictions. Econometrica, 81, 1185-1201.

Newey, W.K. and Smith, R.J. (2004), Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators. Econometrica, 72, 219-255.

Smith, R.J. (2011), GEL Criteria for Moment Condition Models. Econometric Theory, 27(6), 1192–1235.

Wu, C. (2005), Algorithms and R codes for the pseudo empirical likelihood method in survey sampling. Survey Methodology, 31(2), page 239.

Class "linearModel"

Description

Class for moment-based models for which moment conditions are linear and expressed by a formula.

Objects from the Class

Objects can be created by calls of the form new("linearModel", ...). It is generated my momentModel.

Slots

modelF:

Object of class "data.frame" ~~

instF:

Object of class "data.frame" ~~

vcov:

Object of class "character" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "character" ~~

momNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

varNames:

Object of class "character" ~~

isEndo:

Object of class "logical" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "regModel", directly. Class "momentModel", directly.

Methods

Dresiduals

signature(object = "linearModel"): ...

merge

signature(x = "linearModel", y = "linearModel"): ...

merge

signature(x = "slinearModel", y = "linearModel"): ...

model.matrix

signature(object = "linearModel"): ...

modelDims

signature(object = "linearModel"): ...

modelResponse

signature(object = "linearModel"): ...

momentStrength

signature(object = "linearModel"): ...

residuals

signature(object = "linearModel"): ...

restModel

signature(object = "linearModel"): ...

solveGmm

signature(object = "linearModel", wObj = "momentWeights"): ...

tsls

signature(model = "linearModel"): ...

Examples

showClass("linearModel")

Manufacturing Costs data from Bernt and Wood (1975)

Description

The data is used to reproduce examples of Greene (2012)

Usage

data("ManufactCost")

Format

A data frame with 25 observations on the following 10 variables.

Year

a numeric vector

Cost

a numeric vector

K

a numeric vector

L

a numeric vector

E

a numeric vector

M

a numeric vector

Pk

a numeric vector

Pl

a numeric vector

Pe

a numeric vector

Pm

a numeric vector

Source

On Greene (2012) online resources.

References

Berndt, E. and Wood, D. (1975), Technology, Prices, and the Derived Demand for Energy, Review of Economics and Statistics, Vol. 57, 376–384.

Green, W.H.. (2012). Econometric Analysis, 7th edition, Prentice Hall.

Examples

data(ManufactCost)

Class "mconfint"

Description

A class to store confidence region.

Objects from the Class

Objects can be created by calls of the form new("mconfint", ...). It is created by the "confint" method with the option area=TRUE (see confint-methods).

Slots

areaPoints:

Object of class "matrix" ~~

type:

Object of class "character" ~~

level:

Object of class "numeric" ~~

theta:

Object of class "numeric" ~~

Methods

plot

signature(x = "mconfint"): ...

print

signature(x = "mconfint"): ...

show

signature(object = "mconfint"): ...

Examples

showClass("mconfint")

~~ Methods for Function meatGmm in Package momentfit ~~

Description

It computes the meat in the sandwich representation of the covariance matrix of the GMM estimator.

Usage

## S4 method for signature 'gmmfit'
meatGmm(object, robust=FALSE)

## S4 method for signature 'sgmmfit'
meatGmm(object, robust=FALSE)

## S4 method for signature 'tsls'
meatGmm(object, robust=FALSE)

Arguments

object

GMM fit object
robust

If TRUE, the meat is robust to the failure of the assumption that the weighting matrix is the inverse of the covariance matrix of the moment conditions. (see details)

Details

If robust=FALSE, then the meat is G′V−1GG'V^{-1}G, where GG and VV are respectively the sample mean of the derivatives and the covariance matrix of the moment conditions. If it is TRUE, the meat is G′WVWGG'WVWG, where WW is the weighting matrix.

For tsls objects, the function makes use of the QR representation of the weighting matrix. It is simply possible to get the meat in a more stable way. In that case, W=(σ2Z′Z/n)−1W=(\sigma^2Z'Z/n)^{-1}. If robust is FALSE, V is assumed to be σ2Z′Z/n\sigma^2Z'Z/n which is the inverse of the bread. Therefore, a sandwich covariance matrix with robust=FALSE will result in a non-sandwich matrix.

For sgmmfit, the covariance is for the vectorized coefficient vector of all equations.

Methods

signature(object = "gmmfit")

General GMM fit.

signature(object = "tsls")

For model estimated by two-stage least squares.

signature(object = "sgmmfit")

For system of equations.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

res <- gmmFit(model1)
meatGmm(res)

## It is a slightly different because the weighting matrix
## is computed using the first step estimate and the covariance
## matrix of the moment conditions is based on the final estimate.
## They should, however, be asymptotically equivalent.

meatGmm(res, robust=TRUE)

## TSLS
res2 <- tsls(model1)

## Robust meat
meatGmm(res2, TRUE)

## It makes no difference is the model is assumed iid
model2 <- momentModel(y~x1, ~z1+z2, data=simData, vcov="iid")
res2 <- tsls(model2)
meatGmm(res2, FALSE)
meatGmm(res2, TRUE)

~~ Methods for Function merge in Package base ~~

Description

It allows to merge momentModel classes into system objects.

Usage

## S4 method for signature 'linearModel,linearModel'
merge(x, y, ...)

## S4 method for signature 'nonlinearModel,nonlinearModel'
merge(x, y, ...)

## S4 method for signature 'slinearModel,linearModel'
merge(x, y, ...)

## S4 method for signature 'snonlinearModel,nonlinearModel'
merge(x, y, ...)

Arguments

x

An object on which the other objects are merged to.
y

An object to be merged to x.
...

Other objects of the same class as y to be merged to x.

Methods

signature(x = "linearModel", y = "linearModel")

Merging linear models into a system of equations.

signature(x = "nonlinearModel", y = "nonlinearModel")

Merging nonlinear models into a system of equations.

signature(x = "slinearModel", y = "linearModel")

Adding linear equations to a system of linear equations.

signature(x = "snonlinearModel", y = "nonlinearModel")

Adding nonlinear equations to a system of nonlinear equations.

Examples

data(simData)
g1 <- y1~x1+x4; h1 <- ~z1+z2+z3+z4+x4
g2 <- y2~x1+x2+x3; h2 <- ~z1+z2+z3+z4+x3
g3 <- y3~x2+x3+x4; h3 <- ~z2+z3+z4+x3+x4
## Linear models
m1 <- momentModel(g1, h1, data=simData)
m2 <- momentModel(g2, h2, data=simData)
m3 <- momentModel(g3, h3, data=simData)

##
(sys1 <- merge(m1, m2))

## add an equation to the model

(sys2 <- merge(sys1, m3))

## want to get back the first?

sys2[1:2]

## Nonlinear (not really, just written as nonlinear)

nlg <- list(y1~theta0+theta1*x1+theta2*x4,
            y2~alpha0+alpha1*x1+alpha2*x2+alpha3*x3,
            y3~beta0+beta1*x2+beta2*x3+beta3*x4)
theta0 <- list(c(theta0=1,theta1=2,theta2=3),
              c(alpha0=1,alpha1=2,alpha2=3, alpha3=4),
              c(beta0=1,beta1=2,beta2=3,beta3=4))

nm1 <- momentModel(nlg[[1]], h1, theta0[[1]], data=simData)
nm2 <- momentModel(nlg[[2]], h2, theta0[[2]], data=simData)
nm3 <- momentModel(nlg[[3]], h3, theta0[[3]], data=simData)

merge(nm1, nm2, nm3)

~~ Methods for Function model.matrix in Package stats ~~

Description

Model matrix form momentModel. It returns the matrix of regressors or the instruments. In restricted models, it returns the reduced matrix of regressors.

Usage

## S4 method for signature 'linearModel'
model.matrix(object,
type=c("regressors","instruments"))
## S4 method for signature 'rlinearModel'
model.matrix(object,
type=c("regressors","instruments"))
## S4 method for signature 'nonlinearModel'
model.matrix(object,
type=c("regressors","instruments"))
## S4 method for signature 'slinearModel'
model.matrix(object,
type=c("regressors","instruments"))
## S4 method for signature 'rslinearModel'
model.matrix(object,
type=c("regressors","instruments"))
## S4 method for signature 'rsnonlinearModel'
model.matrix(object,
type=c("regressors","instruments"))
## S4 method for signature 'snonlinearModel'
model.matrix(object,
type=c("regressors","instruments"))

Arguments

object

Object of class linearModel, rlinearModel or any system of equations class.
type

Should the function returns the matrix of instruments or the matrix of regressors. For nonlinearModel classes, type='regressors' will produce an error message, because there is no such model matrix in this case, at least not for now.

Methods

signature(object = "linearModel")

Linear models with not restrictions.

signature(object = "nonlinearModel")

Nonlinear models with not restrictions.

signature(object = "rlinearModel")

linear models with restrictions.

signature(object = "slinearModel")

System of linear equations with no restrictions.

signature(object = "rslinearModel")

System of linear equations with restrictions.

signature(object = "rsnonlinearModel")

System of nonlinear equations with restrictions.

signature(object = "snonlinearModel")

System of nonlinear equations with no restrictions.

Examples

data(simData)

## Unrestricted model
model1 <- momentModel(y~x1+x2+x3, ~x2+x3+z1+z2, data=simData)
model.matrix(model1)[1:3,]

## Restrictions change the response
R <- c("x2=2","x3+x1=3")
rmodel1 <- restModel(model1, R)
rmodel1
model.matrix(rmodel1)[1:3,]

Methods for Function modelDims

Description

It extracts important information from the model. It is mostly used by other methods when a modelModel has been modifed. An example is when restrictions have been imposed on coefficients.

Methods

signature(object = "rlinearModel")
signature(object = "rnonlinearModel")
signature(object = "rfunctionModel")
signature(object = "linearModel")
signature(object = "nonlinearModel")
signature(object = "functionModel")
signature(object = "formulaModel")
signature(object = "rformulaModel")
signature(object = "slinearModel")
signature(object = "rslinearModel")
signature(object = "rsnonlinearModel")
signature(object = "snonlinearModel")
signature(object = "sfunctionModel")

Examples

data(simData)

model1 <- momentModel(y~x1+x2, ~x2+z1+z2, data=simData)
modelDims(model1)

## Unrestricted model

rmodel1 <- restModel(model1, R=c("x1+x2=4"))
modelDims(rmodel1)

~~ Methods for Function modelResponse in Package momentfit ~~

Description

Return the response vector in models with and without restrictions

Methods

signature(object = "linearModel")

For linear models without restrictions on the coefficients.

signature(object = "slinearModel")

For system of linear models without restrictions on the coefficients.

signature(object = "rslinearModel")

For system of linear models with restrictions on the coefficients.

signature(object = "rlinearModel")

For linear models with restrictions on the coefficients.

Examples

data(simData)

## Unrestricted model
model1 <- momentModel(y~x1+x2+x3, ~x2+x3+z1+z2, data=simData)
y <- modelResponse(model1)

## Restrictions change the response
R <- c("x2=2","x3=3")
rmodel1 <- restModel(model1, R)
rmodel1
restY <- modelResponse(rmodel1)

Constructor for "momentModel" classes

Description

It builds an object class "momentModel", which is a union class for "linearModel", "nonlinearModel", "formulaModel" and "functionModel" classes. These are classes for moment based models. This is the first step before running any estimation algorithm.

Usage

momentModel(g, x=NULL, theta0=NULL,grad=NULL,
            vcov = c("iid", "HAC", "MDS", "CL"),
            vcovOptions=list(), centeredVcov = TRUE, data=parent.frame(),
            na.action="na.omit", survOptions=list(), smooth=FALSE)

Arguments

g

A function of the form g(θ,x)g(\theta,x) and which returns a n×qn \times q matrix with typical element gi(θ,xt)g_i(\theta,x_t) for i=1,...qi=1,...q and t=1,...,nt=1,...,n. This matrix is then used to build the q sample moment conditions. It can also be a formula if the model is linear (see detailsbelow).
x

The matrix or vector of data from which the function g(θ,x)g(\theta,x) is computed. If "g" is a formula, it is an n×Nhn \times Nh matrix of instruments or a formula (see details below).
theta0

A k×1k \times 1 vector of starting values. It is required only when "g" is a function because only then a numerical algorithm is used to minimize the objective function. If the dimension of θ\theta is one, see the argument "optfct".
grad

A function of the form G(θ,x)G(\theta,x) which returns a q×kq\times k matrix of derivatives of gˉ(θ)\bar{g}(\theta) with respect to θ\theta. By default, the numerical algorithm numericDeriv is used. It is of course strongly suggested to provide this function when it is possible. This gradient is used to compute the asymptotic covariance matrix of θ^\hat{\theta} and to obtain the analytical gradient of the objective function if the method is set to "CG" or "BFGS" in optim and if "type" is not set to "cue". If "g" is a formula, the gradiant is not required (see the details below).
vcov

Assumption on the properties of the moment conditions. By default, they are weakly dependant processes. For MDS, we assume that the conditions are martingale difference sequences, which implies they are serially uncorrelated, but may be heteroscedastic. There is a difference between iid and MDS only when g is a formula. In that case, residuals are assumed homoscedastic as well as serially uncorrelated. For type CL, clustered covariance matrix is computed. The options are then included in vcovOptions (see meatCL).

vcovOptions

A list of options for the covariance matrix of the moment conditions. See vcovHAC for the default values.
centeredVcov

Should the moment function be centered when computing its covariance matrix. Doing so may improve inference.
data

A data.frame or a matrix with column names (Optional).

na.action

Action to take for missing values. If missing values are present and the option is set to "na.pass", the model won't be estimable.
survOptions

If needed, a list with the type of survey weights and the weights as a numeric vector, data.frame or formula. The type is either "sampling" or "fequency".
smooth

If TRUE, the moment function is smoothed using a kernel method.

Value

'momentModel' returns an object of one of the subclasses of "momentModel".

References

Andrews DWK (1991), Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica, 59, 817–858.

Newey WK & West KD (1987), A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica, 55, 703–708.

Newey WK & West KD (1994), Automatic Lag Selection in Covariance Matrix Estimation. Review of Economic Studies, 61, 631-653.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)

## A linearModel
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

## A nonlinearModel
g <- y~beta0+x1^beta1
h <- ~z1+z2
model2 <- momentModel(g, h, c(beta0=1, beta1=2), data=simData)

## A functionModel
fct <- function(tet, x)
    {
        m1 <- (tet[1] - x)
        m2 <- (tet[2]^2 - (x - tet[1])^2)
        m3 <- x^3 - tet[1]*(tet[1]^2 + 3*tet[2]^2)
        f <- cbind(m1, m2, m3)
        return(f)
    }
dfct <- function(tet, x)
        {
        jacobian <- matrix(c( 1, 2*(-tet[1]+mean(x)), -3*tet[1]^2-3*tet[2]^2,0, 2*tet[2],
			   -6*tet[1]*tet[2]), nrow=3,ncol=2)
        return(jacobian)
        }
model3 <- momentModel(fct, simData$x3, theta0=c(beta0=1, beta1=2), grad=dfct)

Class "momentModel"

Description

A union class for all moment based models. It is created by momentModel.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

[

signature(x = "momentModel", i = "missing", j = "missing"): ...

coef

signature(object = "momentModel"): ...

evalGel

signature(model = "momentModel"): ...

evalGelObj

signature(object = "momentModel", theta = "numeric", lambda = "numeric"): ...

evalGmm

signature(model = "momentModel"): ...

evalGmmObj

signature(object = "momentModel", theta = "numeric", wObj = "momentWeights"): ...

evalWeights

signature(object = "momentModel"): ...

gelFit

signature(model = "momentModel"): ...

getRestrict

signature(object = "momentModel"): ...

gmmFit

signature(model = "momentModel"): ...

kernapply

signature(x = "momentModel"): ...

print

signature(x = "momentModel"): ...

show

signature(object = "momentModel"): ...

solveGel

signature(object = "momentModel"): ...

update

signature(object = "momentModel"): ...

vcov

signature(object = "momentModel"): ...

vcovHAC

signature(x = "momentModel"): ...

Examples

showClass("momentModel")

~~ Methods for Function momentStrength in Package momentfit ~~

Description

It produces measures of the strength of the moment conditons.

Usage

## S4 method for signature 'linearModel'
momentStrength(object, theta,
vcovType=c("OLS","HC","HAC","CL"))

Arguments

object

An object of class "linearModel"
theta

Coefficient vector at which the strength must be measured. It does not impact the measure for objects of class linearModel.
vcovType

Type of covariance matrix used to compute the F-test of the first-stage regression. For HC, the function vcovHC is used with "HC1", and vcovHAC is used with the default setup is "HAC" is chosen. In summary for gmmfit objects, it is adjusted to the type of covariance that is set in the object. For type CL, clustered covariance matrix is computed. The options are the one included in the vcovOptions slot of the object (see meatCL). The object must have be defined with clusters for that to work. See momentModel.

Methods

signature(object = "functionModel")

Not implemented yet. In that case, we want some measure of the rank of the matrix of derivatives.

signature(object = "formulaModel")

Not implemented yet. In that case, we want some measure of the rank of the matrix of derivatives.

signature(object = "linearModel")

It returns the F-test of the first stage regression. It is a measure of the strength of the instruments.

signature(object = "rlinearModel")

Returns nothing for now.

signature(object = "nonlinearModel")

Not implemented yet.

Examples

data(simData)

theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
momentStrength(model1)

Class "momentWeights"

Description

A class to store the weighting matrix of a set of moment conditions.

Objects from the Class

Objects can be created by calls of the form new("momentWeights", ...). It is created my evalWeights.

Slots

w:

Object of class "ANY" ~~

type:

Object of class "character" ~~

wSpec:

Object of class "list" ~~

Methods

[

signature(x = "momentWeights", i = "missing", j = "missing"): ...

[

signature(x = "momentWeights", i = "numeric", j = "missing"): ...

evalGmmObj

signature(object = "momentModel", theta = "numeric", wObj = "momentWeights"): ...

print

signature(x = "momentWeights"): ...

quadra

signature(w = "momentWeights", x = "matrixORnumeric", y = "matrixORnumeric"): ...

quadra

signature(w = "momentWeights", x = "matrixORnumeric", y = "missing"): ...

quadra

signature(w = "momentWeights", x = "missing", y = "missing"): ...

show

signature(object = "momentWeights"): ...

solveGmm

signature(object = "allNLModel", wObj = "momentWeights"): ...

solveGmm

signature(object = "linearModel", wObj = "momentWeights"): ...

Examples

showClass("momentWeights")

Methods for Function momFct in Package momentfit

Description

The methods computes the moment matrix. It is use to create special moment functions

Usage

## S4 method for signature 'numeric,gelfit'
momFct(eta, object)

Arguments

eta

A vector that includes the coefficient and the Lagrange multipliers
object

An object of class "gmmfit"

Methods

signature(eta = "numeric", object = "gelfit")

Labour data on married women

Description

The dataset was used by Mroz (1987) and in examples in Wooldridge (2016)

Usage

data("Mroz")

Format

A data frame with 753 observations on the following 22 variables.

inlf

=1 if in lab frce, 1975

hours

hours worked, 1975

kidslt6

number of kids < 6 years

kidsge6

number of kids 6-18

age

woman's age in years

educ

years of schooling

wage

Estimated wage from earnings and hours

repwage

reported wage at interview in 1976

hushrs

hours worked by husband, 1975

husage

husband's age

huseduc

husband's years of schooling

huswage

husband's hourly wage, 1975

faminc

family income, 1975

mtr

federal marginal tax rate facing woman

motheduc

mother's years of schooling

fatheduc

father's years of schooling

unem

unemployment rate in county of residence

city

=1 if live in SMSA

exper

actual labor market experience

nwifeinc

(faminc−wage∗hours)/1000faminc - wage*hours)/1000

Source

From Wooldridge (2016) online resources.

References

Mroz, T.A. (1987), The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions, Econometrica, 55, 657–678. 387–405.

Wooldridge, J.M. (2016). Introductory Econometrics, A Modern Approach, 6th edition, Cengage Learning.

Examples

## Example 15.1 of Wooldridge (2016)

data(Mroz)
Mroz <- subset(Mroz, hours>0)
## I guess IID is assumed (That's how we get the same s.e.)
## By default a sandwich vcov is computed because it is 
## a just-identified model.
res4 <- gmm4(log(wage)~educ, ~fatheduc, vcov="iid", data=Mroz)
summary(res4)

## If we adjust the variance of the residuals, however,
## we are a little off (very little)

summary(res4, df.adj=TRUE)


## Example 15.5 of Wooldridge (2016)
## Need to adjust for degrees of freedom in order
## to get the same s.e.
## The first stage F-test is very different though
## Cannot get the same even if do it manually
## with the linearHypothesis from the car package
model <- momentModel(log(wage)~educ+exper+I(exper^2),
~exper+I(exper^2)+fatheduc+motheduc, vcov="iid", data=Mroz)
res <- tsls(model)
summary(res, df.adj=TRUE)

Class "nonlinearModel"

Description

Class for moment-based models for which moment conditions are orthogonality conditions between instruments and the residuals from a nonlinear regression.

Objects from the Class

Objects can be created by calls of the form new("nonlinearModel", ...). It is generated my momentModel.

Slots

modelF:

Object of class "data.frame" ~~

instF:

Object of class "data.frame" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "numeric" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "character" ~~

momNames:

Object of class "character" ~~

fRHS:

Object of class "expression" ~~

fLHS:

Object of class "expressionORNULL" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

varNames:

Object of class "character" ~~

isEndo:

Object of class "logical" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "regModel", directly. Class "allNLModel", directly. Class "momentModel", directly.

Methods

Dresiduals

signature(object = "nonlinearModel"): ...

merge

signature(x = "nonlinearModel", y = "nonlinearModel"): ...

merge

signature(x = "snonlinearModel", y = "nonlinearModel"): ...

model.matrix

signature(object = "nonlinearModel"): ...

modelDims

signature(object = "nonlinearModel"): ...

momentStrength

signature(object = "nonlinearModel"): ...

residuals

signature(object = "nonlinearModel"): ...

restModel

signature(object = "nonlinearModel"): ...

Examples

showClass("nonlinearModel")

~~ Methods for Function plot from package graphics ~~

Description

It plots the confidence region.

Usage

## S4 method for signature 'ANY'
plot(x, y, ...) 

## S4 method for signature 'mconfint'
plot(x, y, main=NULL, xlab=NULL, ylab=NULL, 
                          pch=21, bg=1, Pcol=1, ylim=NULL, xlim=NULL,
                          add=FALSE, addEstimates=TRUE, ...)

Arguments

x

An object to plot
y

On used for "ANY".
main

Optional title
xlab

Optional label for the x-axis.
ylab

Optional label for the y-axis.
pch

Type of points (see points).
bg

Background color for points.
Pcol

The color for the points. If col is used, it is passed to polygon
xlim

Optional range for the x-axis.
ylim

Optional range for the y-axis.
add

If TRUE, the region is added to an existing plot.
addEstimates

Should we add the point estimate to the confidence region? This option is only used when add is FALSE.
...

Arguments to pass to polygon

Methods

signature(object = "ANY")

It uses the plot from package graphics

signature(object = "mconfint")

Plot the 2D confidence region.

Methods for Function print in Package base

Description

Print method for all "momentModel", "gmmfit", "summaryGmm" "hypothesisTest" and "specTest" objects.

Methods

signature(x = "ANY")
signature(x = "momentModel")
signature(x = "sSpec")
signature(x = "confint")
signature(x = "mconfint")
signature(x = "sysModel")
signature(x = "sysMomentWeights")
signature(x = "gmmfit")
signature(x = "gelfit")
signature(x = "sgmmfit")
signature(x = "summaryGmm")
signature(x = "summaryGel")
signature(x = "summarySysGmm")
signature(x = "specTest")
signature(x = "rlinearModel")
signature(x = "rformulaModel")
signature(x = "rslinearModel")
signature(x = "rsnonlinearModel")
signature(x = "rnonlinearModel")
signature(x = "rfunctionModel")
signature(x = "hypothesisTest")
signature(x = "momentWeights")

~~ Methods for Function printRestrict in Package momentfit ~~

Description

It prints the detailed restrictions imposed on "momentModel" classes.

Methods

signature(object = "rgelModels")
signature(object = "rlinearModel")
signature(object = "rnonlinearModel")
signature(object = "rfunctionModel")
signature(object = "rformulaModel")
signature(object = "rslinearModel")
signature(object = "rsnonlinearModel")

Examples

data(simData)
theta <- c(beta0=1,beta1=2)

## Unrestricted model
model1 <- momentModel(y~x1+x2+x3+z1, ~x1+x2+z1+z2+z3+z4, data=simData)

## restricted model
R <- matrix(c(1,1,0,0,0,0,0,2,0,0,0,0,0,1,-1),3,5, byrow=TRUE)
q <- c(0,1,3)
rmodel1 <- restModel(model1, R, q)
printRestrict(rmodel1)

~~ Methods for Function quadra in Package momentfit ~~

Description

~~ Computes the quadratic form, where the center matrix is a class momentWeights object ~~

Usage

## S4 method for signature 'momentWeights,missing,missing'
quadra(w, x, y)

## S4 method for signature 'momentWeights,matrixORnumeric,missing'
quadra(w, x, y)

## S4 method for signature 'momentWeights,matrixORnumeric,matrixORnumeric'
quadra(w, x,
y)

## S4 method for signature 'sysMomentWeights,matrixORnumeric,matrixORnumeric'
quadra(w, x,
y)

## S4 method for signature 'sysMomentWeights,matrixORnumeric,missing'
quadra(w, x, y)

## S4 method for signature 'sysMomentWeights,missing,missing'
quadra(w, x, y)

Arguments

w

An object of class "momentWeights"
x

A matrix or numeric vector
y

A matrix or numeric vector

Methods

signature(w = "momentWeights", x = "matrixORnumeric", y = "matrixORnumeric")

It computes x′Wyx'Wy, where WW is the weighting matrix.

signature(w = "momentWeights", x = "matrixORnumeric", y = "missing")

It computes x′Wxx'Wx, where WW is the weighting matrix.

signature(w = "momentWeights", x = "missing", y = "missing")

It computes WW, where WW is the weighting matrix. When WW is the inverse of the covariance matrix of the moment conditions, it is saved as either a QR decompisition, a Cholesky decomposition or a covariance matrix into the momentWeights object. The quadra method with no y and x is therefore a way to invert it. The same applies to system of equations

Examples

data(simData)

theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

gbar <- evalMoment(model1, theta)
gbar <- colMeans(gbar)

### Onjective function of GMM with identity matrix
wObj <- evalWeights(model1, w="ident")
quadra(wObj, gbar)

### Onjective function of GMM with efficient weights
wObj <- evalWeights(model1, theta)
quadra(wObj, gbar)

Class "regModel"

Description

A union class for "linearModel" and "nonlinearModel" classes.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

[

signature(x = "regModel", i = "numeric", j = "missing"): ...

evalDMoment

signature(object = "regModel"): ...

evalMoment

signature(object = "regModel"): ...

subset

signature(x = "regModel"): ...

Examples

showClass("regModel")

~~ Methods for Function residuals in Package stats ~~

Description

It computes the residual for a given coefficient vector, when the model is a linear of nonlinear regression with instruments. The method can be called on a momentModel class for a given coefficient theta or on a gmmfit object.

Methods

signature(object = "rsysModel")
signature(object = "linearModel")
signature(object = "nonlinearModel")
signature(object = "gmmfit")
signature(object = "gelfit")
signature(object = "sgmmfit")
signature(object = "sysModel")

Examples

x <- rchisq(200,5)
z1 <- rnorm(200)
z2 <- .2*x+rnorm(200)
y <- x+rnorm(200)
dat <- data.frame(y=y,z1=z1,x=x,z2=z2)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x, ~z1+z2, data=dat)

## residuals for a given theta
e <- residuals(model1, theta)

## residuals of the fit
res <- gmmFit(model1)
e <- residuals(res)

~~ Methods for Function restModel in Package momentfit ~~

Description

It converts momentModel objects into its restricted counterpart.

Usage

## S4 method for signature 'linearModel'
restModel(object, R, rhs=NULL)

## S4 method for signature 'slinearModel'
restModel(object, R, rhs=NULL)

## S4 method for signature 'snonlinearModel'
restModel(object, R, rhs=NULL)

## S4 method for signature 'nonlinearModel'
restModel(object, R, rhs=NULL)

## S4 method for signature 'formulaModel'
restModel(object, R, rhs=NULL)

## S4 method for signature 'functionModel'
restModel(object, R, rhs=NULL)

Arguments

object

An object of class "momentModel" or "sysModel".
R

Either a matrix or a vector of characters for linear models and a list of formulas for nonlinear models
rhs

The right hand side of the linear restrictions. It is ignored for nonlinear models.

Methods

signature(object = "linearModel")

Method for object of class linearModel.

signature(object = "linearGel")

Method for all classes related to linearGel.

signature(object = "slinearModel")

Method for object of class slinearModel.

signature(object = "snonlinearModel")

Method for object of class snonlinearModel.

signature(object = "nonlinearModel")

Method for object of class nonlinearModel.

signature(object = "nonlinearGel")

Method for object of class nonlinearGel.

signature(object = "functionModel")

Method for object of class functionModel.

signature(object = "functionGel")

Method for object of class functionGel.

signature(object = "formulaModel")

Method for object of class formulaModel.

signature(object = "formulaGel")

Method for object of class formulaGel.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)

## Unrestricted model
model1 <- momentModel(y~x1+x2+x3+z1, ~x1+x2+z1+z2+z3+z4, data=simData)

## Using matrix R
R <- matrix(c(1,1,0,0,0,0,0,2,0,0,0,0,0,1,-1),3,5, byrow=TRUE)
q <- c(0,1,3)

rmodel1 <- restModel(model1, R, q)
rmodel1

## Using character
## Many ways to write the constraints

R1 <- c("x1","2*x2+z1=2", "4+x3*5=3")
rmodel1 <- restModel(model1, R1)
rmodel1

## Works with interaction and identity function I()

model1 <- momentModel(y~x1*x2+exp(x3)+I(z1^2), ~x1+x2+z1+z2+z3+z4, data=simData)
R1 <- c("x1","exp(x3)+2*x1:x2", "I(z1^2)=3")
rmodel1 <- restModel(model1, R1)
rmodel1

## nonlinear constraints on a linear model
## we need to convert the linear model into a nonlinear one

model <- momentModel(y~x1+x2+x3+z1, ~x1+x2+z1+z2+z3+z4, data=simData)
NLmodel <- as(model, "nonlinearModel")

## To avoid having unconventional parameter names, which happens
## when I() is used or with interaction, the X's and coefficients are
## renamed

NLmodel@parNames

## Restriction can be a list of formula or vector of characters
## For the latter, it will be converted into a list of formulas

R1 <- c("theta2=2", "theta3=theta4^2")
rmod1 <- restModel(NLmodel, R1)
res1 <- gmmFit(rmod1)
res1
## recover the orignial form
coef(rmod1, coef(res1))

## with formulas

R2 <- list(theta2~2, theta3~1/theta4)
rmod2 <- restModel(NLmodel, R2)
res2 <- gmmFit(rmod2)
res2
coef(rmod2, coef(res2))

## The same can be done with function based models

Class "rformulaModel"

Description

A class for restricted moment-based models for which moment conditions are expressed using a list of formulas.

Objects from the Class

Objects can be created by calls of the form new("rformulaModel", ...). It is created by restModel-methods.

Slots

R:

Object of class "list" ~~

cstSpec:

Object of class "list" ~~

modelF:

Object of class "data.frame" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "numeric" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "character" ~~

momNames:

Object of class "character" ~~

fRHS:

Object of class "list" ~~

fLHS:

Object of class "list" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

varNames:

Object of class "character" ~~

isEndo:

Object of class "logical" ~~

isMDE:

Object of class "logical" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "formulaModel", directly. Class "rmomentModel", directly. Class "allNLModel", by class "formulaModel", distance 2. Class "momentModel", by class "formulaModel", distance 2.

Methods

coef

signature(object = "rformulaModel"): ...

evalDMoment

signature(object = "rformulaModel"): ...

getRestrict

signature(object = "rformulaModel"): ...

gmmFit

signature(model = "rformulaModel"): ...

modelDims

signature(object = "rformulaModel"): ...

print

signature(x = "rformulaModel"): ...

printRestrict

signature(object = "rformulaModel"): ...

Examples

showClass("rformulaModel")

Class "rfunctionModel"

Description

A restricted moment-based model for which moment conditions are defined by a function.

Objects from the Class

Objects can be created by calls of the form new("rfunctionModel", ...). It is created by restModel-methods.

Slots

R:

Object of class "list" ~~

cstSpec:

Object of class "list" ~~

X:

Object of class "ANY" ~~

fct:

Object of class "function" ~~

dfct:

Object of class "functionORNULL" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "numeric" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "character" ~~

momNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

varNames:

Object of class "character" ~~

isEndo:

Object of class "logical" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "functionModel", directly. Class "rmomentModel", directly. Class "allNLModel", by class "functionModel", distance 2. Class "momentModel", by class "functionModel", distance 2.

Methods

[

signature(x = "rfunctionModel", i = "numeric", j = "missing"): ...

coef

signature(object = "rfunctionModel"): ...

evalDMoment

signature(object = "rfunctionModel"): ...

getRestrict

signature(object = "rfunctionModel"): ...

modelDims

signature(object = "rfunctionModel"): ...

print

signature(x = "rfunctionModel"): ...

printRestrict

signature(object = "rfunctionModel"): ...

Examples

showClass("rfunctionModel")

GEL objective functions

Description

Functions that returns the GEL function ρ(g(θ,x)′λ)\rho(g(\theta,x)'\lambda) and its derivatives.

Usage

rhoET(gmat, lambda, derive = 0, k = 1)

rhoETEL(gmat, lambda, derive = 0, k = 1)

rhoEL(gmat, lambda, derive = 0, k = 1)

rhoEEL(gmat, lambda, derive = 0, k = 1)

rhoREEL(gmat, lambda, derive = 0, k = 1)

rhoHD(gmat, lambda, derive = 0, k = 1)

rhoETHD(gmat, lambda, derive = 0, k = 1)

Arguments

gmat

The n×qn \times q matrix of moments
lambda

The q×1q \times 1 vector of Lagrange multipliers.
derive

An integer which indicates which derivative to return
k

A numeric scaling factor that is required when "gmat" is a matrix of time series which require smoothing. The value depends on the kernel and is automatically set when the "gelModels" is created.

Value

It returns the vector ρ(gmatλ)\rho(gmat \lambda) when derive=0, ρ′(gmatλ)\rho'(gmat \lambda) when derive=1 and ρ′′(gmatλ)\rho''(gmat \lambda) when derive=2.

References

Anatolyev, S. (2005), GMM, GEL, Serial Correlation, and Asymptotic Bias. Econometrica, 73, 983-1002.

Kitamura, Yuichi (1997), Empirical Likelihood Methods With Weakly Dependent Processes. The Annals of Statistics, 25, 2084-2102.

Kitamura, Y. and Otsu, T. and Evdokimov, K. (2013), Robustness, Infinitesimal Neighborhoods and Moment Restrictions. Econometrica, 81, 1185-1201.

Newey, W.K. and Smith, R.J. (2004), Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators. Econometrica, 72, 219-255.

Smith, R.J. (2011), GEL Criteria for Moment Condition Models. Econometric Theory, 27(6), 1192–1235.

Class "rlinearModel"

Description

A class for restricted moment-based models for which moment conditions are orthogonality conditions between instruments and the residuals from a linear regression.

Objects from the Class

Objects can be created by calls of the form new("rlinearModel", ...). It is created by restModel-methods.

Slots

cstLHS:

Object of class "matrix" ~~

cstRHS:

Object of class "numeric" ~~

cstSpec:

Object of class "list" ~~

modelF:

Object of class "data.frame" ~~

instF:

Object of class "data.frame" ~~

vcov:

Object of class "character" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "character" ~~

momNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

varNames:

Object of class "character" ~~

isEndo:

Object of class "logical" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "linearModel", directly. Class "rmomentModel", directly. Class "regModel", by class "linearModel", distance 2. Class "momentModel", by class "linearModel", distance 2.

Methods

coef

signature(object = "rlinearModel"): ...

getRestrict

signature(object = "rlinearModel"): ...

gmmFit

signature(model = "rlinearModel"): ...

model.matrix

signature(object = "rlinearModel"): ...

modelDims

signature(object = "rlinearModel"): ...

modelResponse

signature(object = "rlinearModel"): ...

momentStrength

signature(object = "rlinearModel"): ...

print

signature(x = "rlinearModel"): ...

printRestrict

signature(object = "rlinearModel"): ...

Examples

showClass("rlinearModel")

Class "rmomentModel"

Description

A union class for all restricted moment-based models.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

gelFit

signature(model = "rmomentModel"): ...

Examples

showClass("rmomentModel")

Class "rnonlinearModel"

Description

A class for restricted moment-based models for which moment conditions are orthogonality conditions between instruments and the residuals from a nonlinear regression.

Objects from the Class

Objects can be created by calls of the form new("rnonlinearModel", ...). It is created by restModel-methods.

Slots

R:

Object of class "list" ~~

cstSpec:

Object of class "list" ~~

modelF:

Object of class "data.frame" ~~

instF:

Object of class "data.frame" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "numeric" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "character" ~~

momNames:

Object of class "character" ~~

fRHS:

Object of class "expression" ~~

fLHS:

Object of class "expressionORNULL" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

varNames:

Object of class "character" ~~

isEndo:

Object of class "logical" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "nonlinearModel", directly. Class "rmomentModel", directly. Class "regModel", by class "nonlinearModel", distance 2. Class "allNLModel", by class "nonlinearModel", distance 2. Class "momentModel", by class "nonlinearModel", distance 2.

Methods

coef

signature(object = "rnonlinearModel"): ...

evalDMoment

signature(object = "rnonlinearModel"): ...

getRestrict

signature(object = "rnonlinearModel"): ...

gmmFit

signature(model = "rnonlinearModel"): ...

modelDims

signature(object = "rnonlinearModel"): ...

print

signature(x = "rnonlinearModel"): ...

printRestrict

signature(object = "rnonlinearModel"): ...

Examples

showClass("rnonlinearModel")

Class "rslinearModel"

Description

A class for restricted system of linear equations.

Objects from the Class

Objects can be created by calls of the form new("rslinearModel", ...). It is created by restModel-methods.

Slots

cstLHS:

Object of class "matrix" ~~

cstRHS:

Object of class "numeric" ~~

cstSpec:

Object of class "list" ~~

modelT:

Object of class "list" ~~

instT:

Object of class "list" ~~

data:

Object of class "data.frame" ~~

vcov:

Object of class "character" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "list" ~~

momNames:

Object of class "list" ~~

eqnNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

sameMom:

Object of class "logical" ~~

SUR:

Object of class "logical" ~~

varNames:

Object of class "list" ~~

isEndo:

Object of class "list" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "slinearModel", directly. Class "rsysModel", directly. Class "sysModel", by class "slinearModel", distance 2.

Methods

[

signature(x = "rslinearModel", i = "numeric", j = "missing"): ...

coef

signature(object = "rslinearModel"): ...

evalDMoment

signature(object = "rslinearModel"): ...

evalMoment

signature(object = "rslinearModel"): ...

evalWeights

signature(object = "rslinearModel"): ...

getRestrict

signature(object = "rslinearModel"): ...

gmmFit

signature(model = "rslinearModel"): ...

model.matrix

signature(object = "rslinearModel"): ...

modelDims

signature(object = "rslinearModel"): ...

modelResponse

signature(object = "rslinearModel"): ...

print

signature(x = "rslinearModel"): ...

printRestrict

signature(object = "rslinearModel"): ...

residuals

signature(object = "rslinearModel"): ...

solveGmm

signature(object = "rslinearModel", wObj = "sysMomentWeights"): ...

ThreeSLS

signature(model = "rslinearModel"): ...

Examples

showClass("rslinearModel")

Class "rsnonlinearModel"

Description

A class for restricted systems of nonlinear equations.

Objects from the Class

Objects can be created by calls of the form new("rsnonlinearModel", ...). It is created by restModel-methods.

Slots

R:

Object of class "list" ~~

cstSpec:

Object of class "list" ~~

data:

Object of class "data.frame" ~~

instT:

Object of class "list" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "list" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "list" ~~

momNames:

Object of class "list" ~~

fRHS:

Object of class "list" ~~

fLHS:

Object of class "list" ~~

eqnNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

sameMom:

Object of class "logical" ~~

SUR:

Object of class "logical" ~~

varNames:

Object of class "list" ~~

isEndo:

Object of class "list" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "snonlinearModel", directly. Class "rsysModel", directly. Class "sysModel", by class "snonlinearModel", distance 2.

Methods

No methods defined with class "rsnonlinearModel" in the signature.

Examples

showClass("rsnonlinearModel")

Class "rsysModel"

Description

A union class for all systems of equations. (see link{systemGmm})

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "rsysModel" in the signature.

Examples

showClass("rsysModel")

Methods for Function setCoef in Package momentfit ~~

Description

The method validates the coefficient theta and returns a coefficient object in a format that satisfies the moment model.

Usage

## S4 method for signature 'momentModel'
setCoef(model, theta)
## S4 method for signature 'sysModel'
setCoef(model, theta)

Arguments

model

A moment model object.
theta

A coefficient object. The type depends on the model object. See the examples below.

Methods

signature(object = "momentModel")

Methods for all single equation models including the restricted ones.

signature(object = "sysModel")

Methods for all system of equations models including the restricted ones.

Examples

### A few system of equation models:
data(simData)
h <- list(~z1+z2+z3, ~x3+z1+z2+z3+z4, ~x3+x4+z1+z2+z3)
nlg <- list(Supply=y1~theta0+theta1*x1+theta2*z2,
            Demand1=y2~alpha0+alpha1*x1+alpha2*x2+alpha3*x3,
            Demand2=y3~beta0+beta1*x3+beta2*x4+beta3*z1)
g <- list(Supply=y1~x1+z2, Demand1=y2~x1+x2+x3, Demand2=y3~x3+x4+z1)
theta0 <- list(c(theta0=1,theta1=2,theta2=3),
               c(alpha0=1,alpha1=2,alpha2=3, alpha3=4),
               c(beta0=1,beta1=2,beta2=3,beta3=4))
nlin <- sysMomentModel(nlg, h, theta0, data=simData)
lin <- sysMomentModel(g, h, data=simData)

### from numeric vector to the proper format with names:
setCoef(nlin, 1:11)

### reorder the equation and name the coefficients
setCoef(nlin, list(Demand1=1:4, Supply=1:3, Demand2=1:4))

### reorder the coefficint to match the order in the model
tet <- do.call("c", theta0)
set.seed(112233)
setCoef(nlin, tet[sample(11)])

### It validates length and names and provide source of errors
## Not run: 
setCoef(nlin, list(Demand1=1:4, Supply=1:2, Demand2=1:4))
names(tet)[4] <- "gamma3"
setCoef(nlin, tet)
setCoef(nlin, list(Demand1=1:4, Supply=1:3, Demand4=1:4))

## End(Not run)

### a single equation model
single <- momentModel(nlg[[1]], h[[1]], theta0[[1]], data=simData)
setCoef(single, c(theta1=4, theta0=6, theta2=8))
setCoef(single, 1:3)

Class "sfunctionModel"

Description

A class for systems of nonlinear equations.

Objects from the Class

Objects can be created by calls of the form new("sfunctionModel", ...). It is created by momentModel.

Slots

X:

Object of class "ANY" ~~

fct:

Object of class "list" ~~

dfct:

Object of class "list" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "list" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "list" ~~

momNames:

Object of class "list" ~~

eqnNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

sameMom:

Object of class "logical" ~~

SUR:

Object of class "logical" ~~

varNames:

Object of class "list" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "sysModel", directly.

Examples

showClass("sfunctionModel")

Class "sgmmfit"

Description

Class to store fitted system of equations obtained using the GMM method.

Objects from the Class

Objects can be created by calls of the form new("sgmmfit", ...). It is created by gmmFit.

Slots

theta:

Object of class "list" ~~

convergence:

Object of class "numericORNULL" ~~

convIter:

Object of class "numericORNULL" ~~

call:

Object of class "callORNULL" ~~

type:

Object of class "character" ~~

wObj:

Object of class "sysMomentWeights" ~~

niter:

Object of class "integer" ~~

efficientGmm:

Object of class "logical" ~~

model:

Object of class "sysModel" ~~

Methods

bread

signature(x = "sgmmfit"): ...

coef

signature(object = "sgmmfit"): ...

hypothesisTest

signature(object.u = "missing", object.r = "sgmmfit"): ...

hypothesisTest

signature(object.u = "sgmmfit", object.r = "missing"): ...

hypothesisTest

signature(object.u = "sgmmfit", object.r = "sgmmfit"): ...

meatGmm

signature(object = "sgmmfit"): ...

print

signature(x = "sgmmfit"): ...

residuals

signature(object = "sgmmfit"): ...

show

signature(object = "sgmmfit"): ...

specTest

signature(object = "sgmmfit", which = "missing"): ...

summary

signature(object = "sgmmfit"): ...

vcov

signature(object = "sgmmfit"): ...

Examples

showClass("sgmmfit")

~~ Methods for Function show in Package methods ~~

Description

Display method for all objects.

Methods

signature(object = "ANY")
signature(object = "confint")
signature(object = "mconfint")
signature(object = "sSpec")
signature(object = "momentModel")
signature(object = "sysModel")
signature(object = "gmmfit")
signature(object = "gelfit")
signature(object = "sgmmfit")
signature(object = "specTest")
signature(object = "summarySysGmm")
signature(object = "summaryGmm")
signature(object = "summaryGel")
signature(object = "hypothesisTest")
signature(object = "momentWeights")
signature(object = "sysMomentWeights")

Simulated data.

Description

This dataset is used in several documentation files to illustrate the different functionality of the package.

Usage

data("simData")

Format

A data frame with 50 observations on the following 12 variables. See the examples for the method used to generate them.

y

a numeric vector

y1

a numeric vector

y3

a numeric vector

y2

a numeric vector

z1

a numeric vector

x1

a numeric vector

z2

a numeric vector

x2

a numeric vector

z3

a numeric vector

x3

a numeric vector

x4

a numeric vector

z4

a numeric vector

z5

a numeric vector

Examples

# Here is how the data was simulated
set.seed(1122)
n <- 50
x1 <- rchisq(n,5)
x2 <- rchisq(n,5)
x3 <- rnorm(n)
x4 <- rnorm(n)
z1 <- .2*x1+rnorm(n)
z2 <- .2*x2+rnorm(n)
z3 <- rnorm(n)
z4 <- rnorm(n)
z5 <- rnorm(n)
y <- y1 <- x1+rnorm(n)
y2 <- 2*x1+rnorm(n)
y3 <- 0.5*x2+rnorm(n)
simData <- data.frame(y=y, y1=y1,y3=y3,y2=y2, z1=z1,x1=x1,z2=z2,x2=x2,z3=z3,x3=x3,
                  x4=x4,z4=z4,z5=z5)

Class "slinearModel"

Description

A class for systems of linear equations.

Objects from the Class

Objects can be created by calls of the form new("slinearModel", ...). It is created by momentModel.

Slots

modelT:

Object of class "list" ~~

instT:

Object of class "list" ~~

data:

Object of class "data.frame" ~~

vcov:

Object of class "character" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "list" ~~

momNames:

Object of class "list" ~~

eqnNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

sameMom:

Object of class "logical" ~~

SUR:

Object of class "logical" ~~

varNames:

Object of class "list" ~~

isEndo:

Object of class "list" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "sysModel", directly.

Methods

[

signature(x = "slinearModel", i = "numeric", j = "missing"): ...

merge

signature(x = "slinearModel", y = "linearModel"): ...

model.matrix

signature(object = "slinearModel"): ...

modelDims

signature(object = "slinearModel"): ...

modelResponse

signature(object = "slinearModel"): ...

restModel

signature(object = "slinearModel"): ...

solveGmm

signature(object = "slinearModel", wObj = "sysMomentWeights"): ...

ThreeSLS

signature(model = "slinearModel"): ...

tsls

signature(model = "slinearModel"): ...

Examples

showClass("slinearModel")

Class "snonlinearModel"

Description

A class for systems of nonlinear equations.

Objects from the Class

Objects can be created by calls of the form new("snonlinearModel", ...). It is created by momentModel.

Slots

data:

Object of class "data.frame" ~~

instT:

Object of class "list" ~~

vcov:

Object of class "character" ~~

theta0:

Object of class "list" ~~

n:

Object of class "integer" ~~

q:

Object of class "integer" ~~

k:

Object of class "integer" ~~

parNames:

Object of class "list" ~~

momNames:

Object of class "list" ~~

fRHS:

Object of class "list" ~~

fLHS:

Object of class "list" ~~

eqnNames:

Object of class "character" ~~

vcovOptions:

Object of class "list" ~~

centeredVcov:

Object of class "logical" ~~

sameMom:

Object of class "logical" ~~

SUR:

Object of class "logical" ~~

varNames:

Object of class "list" ~~

isEndo:

Object of class "list" ~~

omit:

Object of class "integer" ~~

survOptions:

Object of class "list" ~~

sSpec:

Object of class "sSpec" ~~

smooth:

Object of class "logical" ~~

Extends

Class "sysModel", directly.

Methods

[

signature(x = "snonlinearModel", i = "numeric", j = "missing"): ...

merge

signature(x = "snonlinearModel", y = "nonlinearModel"): ...

model.matrix

signature(object = "snonlinearModel"): ...

modelDims

signature(object = "snonlinearModel"): ...

solveGmm

signature(object = "snonlinearModel", wObj = "sysMomentWeights"): ...

Examples

showClass("snonlinearModel")

~~ Methods for Function solveGel in Package momentfit ~~

Description

It fits a moment-based model using GEL methods.

Usage

## S4 method for signature 'momentModel'
solveGel(object, gelType="EL", theta0=NULL,
                                  lambda0=NULL, lamSlv=NULL,
                                  coefSlv=c("optim","nlminb","constrOptim"),
                                  rhoFct=NULL, 
                                  lControl=list(), tControl=list())

Arguments

object

An object of class "gelModels"
gelType

The type of GEL. It is either "EL", "ET", "EEL", "HD", "ETEL" or "ETHD".
theta0

The vector of coefficients for the starting values used in minimization algorithm. If NULL, the starting values in the object is used. For linear models, it must be provided because "linearGel" objects do not have a theta0 slot.
lambda0

The q×1q \times 1 vector of starting values for the Lagrange multipliers. By default a zero vector is used.
lamSlv

An alternative solver for the Lagrange multiplier. By default, either Wu_lam, EEL_lam, REEL_lam or getLambda is used.
coefSlv

Minimization solver for the coefficient vector.
rhoFct

An alternative objective function for GEL. This argument is only used if we want to fit the model with a different GEL method. see rhoFct.
lControl

A list of controls for the Lagrange multiplier algorithm.
tControl

A list of controls for the coefficient algorithm.

Value

A list with the following:

theta

The vector of solution
lambda

The vector of Lagrange multiplier
lconvergence

convergence code for the Lagrange multiplier. 0 means normal convergence.
convergence

convergence code for the coefficients. 0 means normal convergence. For higher numbers, see optim, constrOptim or nlminb

Methods

signature(object = "momentModel")

The method applies to all GEL classes.

Examples

data(simData)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

## Get a good starting value
theta0 <- gmmFit(model1)@theta

## EL by default, with Wu algorithm
res2 <- solveGel(model1, theta0=theta0)

## Change solver parameters
res3 <- solveGel(model1, theta0=theta0,
                 tControl=list(method="Nelder", control=list(maxit=2000)))

~~ Methods for Function solveGmm in Package momentfit ~~

Description

The main function to get the GMM solution for a given weighting matrix.

Usage

## S4 method for signature 'linearModel,momentWeights'
solveGmm(object, wObj, theta0=NULL,
...)

## S4 method for signature 'allNLModel,momentWeights'
solveGmm(object, wObj, theta0=NULL,
algo=c("optim","nlminb"), ...)

## S4 method for signature 'rnonlinearModel,momentWeights'
solveGmm(object, wObj, theta0=NULL,
...)

## S4 method for signature 'slinearModel,sysMomentWeights'
solveGmm(object, wObj, theta0=NULL)

## S4 method for signature 'rslinearModel,sysMomentWeights'
solveGmm(object, wObj, theta0=NULL)

## S4 method for signature 'snonlinearModel,sysMomentWeights'
solveGmm(object, wObj,
theta0=NULL, ...)

## S4 method for signature 'sfunctionModel,sysMomentWeights'
solveGmm(object, wObj,
theta0=NULL, ...)

Arguments

object

A moment-based model
theta0

The vector of coefficients for the starting values used in optim. If NULL, the starting values in the object if used. For system of equations, it is a list of vectors.
wObj

An object of class "momentWeights" or "sysMomentWeights".
algo

The numerical algorithm to minimize the objective function.
...

Arguments to pass to optim.

Value

A list with the following:

theta

The vector of solution
convergence

convergence code. 0 means normal convergence. For higher numbers, see optim

Methods

signature(object = "allNLMoment", wObj = "momentWeights")

Method to solve either nonlinear regressions or models in which moments are computed with a function. The objective is minimized using optim.

signature(object = "rnonlinearModel", wObj = "momentWeights")

Method to solve restricted nonlinear models. It computes the analytical solution.

signature(object = "linearModel", wObj = "momentWeights")

Method to solve linear models. It computes the analytical solution.

signature(object = "slinearModel", wObj = "sysMomentWeights")

Method to solve system of linear models. It computes the analytical solution.

signature(object = "rslinearModel", wObj = "sysMomentWeights")

Method to solve system of linear models in which restrictions have been imposed on the coefficients. It computes the analytical solution.

signature(object = "slinearModel", wObj = "sysMomentWeights")

Method to solve system of nonlinear models. The solution is obtained with optim using the analytical derivatives.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

## A manual two-step GMM
w0 <- evalWeights(model1, w="ident")
theta0 <- solveGmm(model1, w0)$theta
w <- evalWeights(model1, theta0)
theta1 <- solveGmm(model1, w)$theta

Class "specTest"

Description

A class to store results from a specification test.

Objects from the Class

Objects can be created by calls of the form new("specTest", ...). It is created my specTest-methods.

Slots

test:

Object of class "matrix" ~~

testname:

Object of class "character" ~~

Methods

print

signature(x = "specTest"): ...

show

signature(object = "specTest"): ...

Examples

showClass("specTest")

~~ Methods for Function specTest in Package momentfit ~~

Description

It computes tests of specification for GMM fit.

Usage

## S4 method for signature 'gmmfit,missing'
specTest(object, which, df.adj=FALSE, wObj=NULL)

## S4 method for signature 'sgmmfit,missing'
specTest(object, which, df.adj=FALSE, wObj=NULL)

## S4 method for signature 'gmmfit,numeric'
specTest(object, which)

## S4 method for signature 'gelfit,missing'
specTest(object, which,
                    type = c("All", "LR", "LM", "J"))

Arguments

object

GMM or GEL fit object
which

Which sub-moment conditions to test.
df.adj

Should we adjust the covariance matrix of the moment conditions for degrees of freedom. If TRUE the covariance matrix is multiplied by n/(n-k), where n is the sample size and k is the number of coefficients. For heteroscedastic robust covariance matrix, adjusting is equivalent to computing HC1 while not adjusting is HC0.
wObj

An object of class gmmWeights. If NULL (the recommended value), the optimal weights is computed at the fitted coefficient estimates. It is used by hypothesisTest if one wants the LR statistics to be computed using the same weights for the restricted and unrestricted model.
type

For GEL, three specification tests are available

Methods

signature(object = "gmmfit", which="missing")
signature(object = "sgmmfit", which="missing")
signature(object = "gmmfit", which="numeric")

References

Eichenbaum, M. and Hansen L. and Singleton, K. (1985). A time Series Analysis of Representative Agent Models of Consumption and Leisure Choise under Uncertainty. Quarterly Journal of Economics, 103, 51–78.

Hayashi, F. (2000). Econometrics, New Jersey: Princeton University Press.

Examples

data(simData)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

res <- gmmFit(model1)
specTest(res)

## Hayashi Example 3.3 (there is not result in the book but
## that's how we would do it for YEAR=1967
data(Griliches)
dat <- subset(Griliches, YEAR==67)
model <- momentModel(LW~S+EXPR+IQ, ~S+EXPR+AGE+MED, data=dat, vcov="MDS")
res <- gmmFit(model)
## testing the orthogonality conditions of S
specTest(res, 2)

Class "sSpec"

Description

A class to store the specifications of the kernel used to smooth moment conditions.

Objects from the Class

Objects can be created by calls of the form new("sSpec", ...). It is created by kernapply-methods.

Slots

k:

Object of class "numeric" ~~

kernel:

Object of class "character" ~~

bw:

Object of class "numeric" ~~

w:

Object of class "tskernel" ~~

bwMet:

Object of class "character" ~~

Methods

print

signature(x = "sSpec"): ...

show

signature(object = "sSpec"): ...

Examples

showClass("sSpec")

Class "stsls"

Description

A class to store a fitted system of equations obtained using the two-stage least squares method.

Objects from the Class

Objects can be created by calls of the form new("stsls", ...). It is created my tsls-methods.

Slots

theta:

Object of class "list" ~~

convergence:

Object of class "numericORNULL" ~~

convIter:

Object of class "numericORNULL" ~~

call:

Object of class "callORNULL" ~~

type:

Object of class "character" ~~

wObj:

Object of class "sysMomentWeights" ~~

niter:

Object of class "integer" ~~

efficientGmm:

Object of class "logical" ~~

model:

Object of class "sysModel" ~~

Extends

Class "sgmmfit", directly.

Methods

No methods defined with class "stsls" in the signature.

Examples

showClass("stsls")

~~ Methods for Function summary in Package base ~~

Description

Compute several results from a moment based model fit.

Usage

## S4 method for signature 'gmmfit'
summary(object, testStrength=TRUE, ...)

## S4 method for signature 'gelfit'
summary(object, ...)

## S4 method for signature 'sgmmfit'
summary(object, testStrength=TRUE, ...)

Arguments

object

A fit object from the package (GMM and GEL are the only methods for now)
testStrength

Should the first stage F-statistics be computed?
...

Other arguments to pass to vcov-methods

Methods

signature(object = "gmmfit")
signature(object = "gmmfit")
signature(object = "sgmmfit")

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

res <- gmmFit(model1)
summary(res)

## Fixed and True Weights matrix
## Consider the moment of a normal distribution:
## Using the first three non centered moments

g <- function(theta, x)
{
mu <- theta[1]
sig2 <- theta[2]
m1 <- x-mu
m2 <- x^2-mu^2-sig2
m3 <- x^3-mu^3-3*mu*sig2
cbind(m1,m2,m3)
}

dg <- function(theta, x)
{
mu <- theta[1]
sig2 <- theta[2]
G <- matrix(c(-1,-2*mu,-3*mu^2-3*sig2, 0, -1, -3*mu),3,2)
}

x <- simData$x3
model <- momentModel(g, x, c(mu=.1, sig2=1.5), vcov="iid")
res1 <- gmmFit(model)
summary(res1)
## Same results (that's because the moment vcov is centered by default)
W <- solve(var(cbind(x,x^2,x^3)))
res2 <- gmmFit(model, weights=W)
res2
## If is therefore more efficient in this case to do the following:
summary(res2, breadOnly=TRUE)

Class "summaryGel"

Description

Class to store the summary of a model fitted by GEL.

Objects from the Class

Objects can be created by calls of the form new("summaryGel", ...). It is created by link{summary-methods}.

Slots

coef:

Object of class "matrix" ~~

specTest:

Object of class "specTest" ~~

model:

Object of class "momentModel" ~~

lambda:

Object of class "matrix" ~~

convergence:

Object of class "numeric" ~~

lconvergence:

Object of class "numeric" ~~

impProb:

Object of class "list" ~~

gelType:

Object of class "list" ~~

restrictedLam:

Object of class "integer" ~~

Methods

print

signature(x = "summaryGel"): ...

show

signature(object = "summaryGel"): ...

Examples

showClass("summaryGel")

Class "summaryGmm"

Description

A class to store the summary of a model fitted by GMM.

Objects from the Class

Objects can be created by calls of the form new("summaryGmm", ...). It is created by link{summary-methods}.

Slots

coef:

Object of class "matrix" ~~

specTest:

Object of class "specTest" ~~

strength:

Object of class "list" ~~

model:

Object of class "momentModel" ~~

sandwich:

Object of class "logical" ~~

type:

Object of class "character" ~~

convergence:

Object of class "numericORNULL" ~~

convIter:

Object of class "numericORNULL" ~~

wSpec:

Object of class "list" ~~

niter:

Object of class "integer" ~~

df.adj:

Object of class "logical" ~~

breadOnly:

Object of class "logical" ~~

Methods

print

signature(x = "summaryGmm"): ...

show

signature(object = "summaryGmm"): ...

Examples

showClass("summaryGmm")

Class "summarySysGmm"

Description

A class to store the summary of a system of equations fitted by GMM.

Objects from the Class

Objects can be created by calls of the form new("summarySysGmm", ...). It is created by summary-methods.

Slots

coef:

Object of class "list" ~~

specTest:

Object of class "specTest" ~~

strength:

Object of class "list" ~~

model:

Object of class "sysModel" ~~

sandwich:

Object of class "logical" ~~

type:

Object of class "character" ~~

convergence:

Object of class "numericORNULL" ~~

convIter:

Object of class "numericORNULL" ~~

wSpec:

Object of class "list" ~~

niter:

Object of class "integer" ~~

df.adj:

Object of class "logical" ~~

breadOnly:

Object of class "logical" ~~

Methods

print

signature(x = "summarySysGmm"): ...

show

signature(object = "summarySysGmm"): ...

Examples

showClass("summarySysGmm")

Class "sysModel"

Description

A union class for all systems of equations.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

[

signature(x = "sysModel", i = "missing", j = "list"): ...

[

signature(x = "sysModel", i = "missing", j = "missing"): ...

[

signature(x = "sysModel", i = "numeric", j = "list"): ...

Dresiduals

signature(object = "sysModel"): ...

evalDMoment

signature(object = "sysModel"): ...

evalGmmObj

signature(object = "sysModel", theta = "list", wObj = "sysMomentWeights"): ...

evalMoment

signature(object = "sysModel"): ...

evalWeights

signature(object = "sysModel"): ...

getRestrict

signature(object = "sysModel"): ...

gmmFit

signature(model = "sysModel"): ...

print

signature(x = "sysModel"): ...

residuals

signature(object = "sysModel"): ...

show

signature(object = "sysModel"): ...

subset

signature(x = "sysModel"): ...

vcov

signature(object = "sysModel"): ...

Examples

showClass("sysModel")

Constructor for "sysMomentModel" classes

Description

It builds the object of either class "slinearModel" or "snonlinearModel", which are system of equations based on moment conditions.

Usage

sysMomentModel(g, h=NULL, theta0=NULL, grad=NULL, 
            vcov = c("iid", "HAC", "MDS", "CL"),
            vcovOptions=list(), centeredVcov = TRUE,
            data=parent.frame(),na.action="na.omit",
            survOptions=list())

Arguments

g

A list of linear or nonlinear regression formulas for each equation in the system.
h

A list of linear formulas for the instruments in each equation in the system.
theta0

A list of vectors of starting values. It is required only when the equations are nonlinear, in which case, it must be a list of named vector, with the names corresponding to the coefficient names in the regression formulas.
grad

A list of functions that returns the derivative of the moment functions. Only used if g is a list of functions.
vcov

Assumption on the properties of the moment conditions. By default, they are weakly dependant processes. For MDS, we assume that the conditions are martingale difference sequences, which implies they are serially uncorrelated, but may be heteroscedastic. There is a difference between iid and MDS only when g is a formula. In that case, residuals are assumed homoscedastic as well as serially uncorrelated. For type CL, clustered covariance matrix is computed. The options are then included in vcovOptions (see meatCL).
vcovOptions

A list of options for the covariance matrix of the moment conditions. See vcovHAC for the default values.
centeredVcov

Should the moment function be centered when computing its covariance matrix. Doing so may improve inference.
data

A data.frame or a matrix with column names (Optional).

na.action

Action to take for missing values. If missing values are present and the option is set to "na.pass", the model won't be estimable.
survOptions

If needed, a list with the type of survey weights and the weights as a numeric vector, data.frame or formula. The type is either "sampling" or "fequency".

Value

'sysMomentModel' returns an object of one of the subclasses of "sysMomentModel".

References

Hayashi, F. (2000). Econometrics, New Jersey: Princeton University Press.

Andrews DWK (1991), Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica, 59, 817–858.

Newey WK & West KD (1987), A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica, 55, 703–708.

Newey WK & West KD (1994), Automatic Lag Selection in Covariance Matrix Estimation. Review of Economic Studies, 61, 631-653.

Examples

set.seed(1122)
x1 <- rchisq(50,5)
x2 <- rchisq(50,5)
x3 <- rnorm(50)
x4 <- rnorm(50)
z1 <- .2*x1+rnorm(50)
z2 <- .2*x2+rnorm(50)
z3 <- rnorm(50)
z4 <- rnorm(50)
z5 <- rnorm(50)
y1 <- x1+rnorm(50)
y2 <- 2*x1+rnorm(50)
y3 <- 0.5*x2+rnorm(50)
dat <- data.frame(y1=y1,y3=y3,y2=y2, z1=z1,x1=x1,z2=z2,x2=x2,z3=z3,x3=x3,
                  x4=x4,z4=z4,z5=z5)

g1 <- y1~x1+x4; h1 <- ~z1+z2+z3+z4+x4
g2 <- y2~x1+x2+x3; h2 <- ~z1+z2+z3+z4+x3
g3 <- y3~x2+x3+x4; h3 <- ~z2+z3+z4+x3+x4
g <- list(g1,g2,g3)
h <- list(h1,h2,h3)

smodel <- sysMomentModel(g, h, data=dat)

## not really nonlinear
nlg <- list(y1~theta0+theta1*x1+theta2*x4,
            y2~alpha0+alpha1*x1+alpha2*x2+alpha3*x3,
            y3~beta0+beta1*x2+beta2*x3+beta3*x4)
theta0 <- list(c(theta0=1,theta1=2,theta2=3),
              c(alpha0=1,alpha1=2,alpha2=3, alpha3=4),
              c(beta0=1,beta1=2,beta2=3,beta3=4))
snmodel <- sysMomentModel(nlg, h, theta0, data=dat)

Class "sysMomentWeights"

Description

A class to store the weighting matrix of the moment conditions from a system of equations.

Objects from the Class

Objects can be created by calls of the form new("sysMomentWeights", ...). It is created by the evalWeights method.

Slots

w:

Object of class "ANY" ~~

type:

Object of class "character" ~~

wSpec:

Object of class "list" ~~

Sigma:

Object of class "ANY" ~~

momNames:

Object of class "list" ~~

eqnNames:

Object of class "character" ~~

sameMom:

Object of class "logical" ~~

Methods

[

signature(x = "sysMomentWeights", i = "missing", j = "list"): ...

[

signature(x = "sysMomentWeights", i = "numeric", j = "list"): ...

[

signature(x = "sysMomentWeights", i = "numeric", j = "missing"): ...

evalGmmObj

signature(object = "sysModel", theta = "list", wObj = "sysMomentWeights"): ...

print

signature(x = "sysMomentWeights"): ...

quadra

signature(w = "sysMomentWeights", x = "matrixORnumeric", y = "matrixORnumeric"): ...

quadra

signature(w = "sysMomentWeights", x = "matrixORnumeric", y = "missing"): ...

quadra

signature(w = "sysMomentWeights", x = "missing", y = "missing"): ...

show

signature(object = "sysMomentWeights"): ...

solveGmm

signature(object = "rslinearModel", wObj = "sysMomentWeights"): ...

solveGmm

signature(object = "slinearModel", wObj = "sysMomentWeights"): ...

solveGmm

signature(object = "snonlinearModel", wObj = "sysMomentWeights"): ...

Examples

showClass("sysMomentWeights")

A guide to estimating systems of equations

Description

This document is meant to describe how to create system of equations objects, estimating them and peforming hypothesis tests.

Details

Instread of repeating the same example for each method, we are going through all methods and classes for systems of equations.

Examples

data(simData)

## first, we create an sysGmm object
g1 <- y1~x1+x4; h1 <- ~x4+z1+z2+z3+z4
g2 <- y2~x1+x2+x3; h2 <- ~x3+z1+z2+z3+z4
g3 <- y3~x2+x3+x4; h3 <- ~x3+x4+z1+z2+z3+z4
g <- list(g1,g2,g3)
h <- list(h1,h2,h3)
smodel <- sysMomentModel(g, h, data=simData, vcov="MDS")

## The show or print method
smodel

## The ']' method
smodel[1:2]
smodel[1] ## becomes a one equation model

## equation by equation 2SLS
tsls(smodel)

## or manually
lapply(1:3, function(i) coef(tsls(smodel[i])))

## Fitting the model by two-step GMM
res <- gmmFit(smodel)

## testing Overidentifying restrictions
specTest(res)

## All info using the summary method
## which includes equation by equation measures of
## the instrument stengths
summary(res)

### When the error id iid (homoscedastic), we have a
### FIVE estimator with 2SLS  as the first step
smodel <- sysMomentModel(g, h, data=simData, vcov="iid")
gmmFit(smodel)

### When the error is iid (homoscedastic), 
### all instruments are the same, and the first step is 2SLS,
### we have 3SLS
smodel <- sysMomentModel(g, ~x4+z1+z2+z3+z4, data=simData, vcov="iid")
gmmFit(smodel, initW='tsls')

### When the error is iid (homoscedastic), 
### the instruments are the same and are the union of all regressors,
### we have SUR
smodel <- sysMomentModel(g, NULL, data=simData, vcov="iid")
gmmFit(smodel, initW='tsls')

############ Restricted models ##################

## unrestricted
smodel <- sysMomentModel(g, h, data=simData, vcov="MDS")
res <- gmmFit(smodel)

## no cross-equation restrictions
R1 <- list(c("x1=-12*x4"), character(), c("x2=0.8", "x4=0.3"))
rm1 <- restModel(smodel, R1)
(res1 <- gmmFit(rm1))

## Cross equation restrictions
R2<- c("Eqn1.x1=1", "Eqn2.x1=Eqn3.x2")
rm2 <- restModel(smodel, R2)
(es2 <- gmmFit(rm2))## no longer expressed as a system

## testing the restriction

hypothesisTest(res, res1, type="LR")
hypothesisTest(res, res1, type="LM")
hypothesisTest(res, res1, type="Wald")

~~ Methods for Function ThreeSLS in Package momentfit ~~

Description

Method to estimate system of equations by Three-Stage least squares (3SLS) or, as a special case, by Seemingly Unrelatd Regressions (SUR).

Usage

## S4 method for signature 'slinearModel'
ThreeSLS(model, coefOnly=FALSE, qrZ=NULL,
Sigma=NULL)
## S4 method for signature 'rslinearModel'
ThreeSLS(model, coefOnly=FALSE, qrZ=NULL,
Sigma=NULL)

Arguments

model

An object of class "slinearModel" in which instruments are the same in each equation and the error terms are homoscedastic.
coefOnly

Should the method return the only the coefficients or create an object of class "sgmmfit".
qrZ

The qr decomposition of the common instruments. It is mostly used by gmmFit to avoid recomputing it in iterative GMM or CUE. It should not be used directly unless the user knows what he is doing.
Sigma

The covariance matrix of the residuals. If not provided, it is computed using the residuals of the equation by equation two-stage least squares. It should not be used directly unless the user knows what he is doing.

Methods

signature(model = "slinearModel")

The method is specifically for system of linear models with the same instruments and homoscedastic errors. It becomes SUR as a special case when the instruments are the union of all regressors.

signature(model = "rslinearModel")

This method is for restricted models that does not impose cross-equation restrictions. With such restrictions 3SLS is not possible as we can no longer write the model as a system of equations.

Class "tsls"

Description

Class that contains a fitted model using two-stage least squares

Objects from the Class

Objects can be created by calls of the form new("tsls", ...). It is created my the

Slots

theta:

Object of class "numeric" ~~

convergence:

Object of class "numericORNULL" ~~

convIter:

Object of class "numericORNULL" ~~

call:

Object of class "callORNULL" ~~

type:

Object of class "character" ~~

wObj:

Object of class "momentWeights" ~~

niter:

Object of class "integer" ~~

efficientGmm:

Object of class "logical" ~~

model:

Object of class "momentModel" ~~

Extends

Class "gmmfit", directly.

Examples

showClass("tsls")

~~ Methods for Function tsls in Package momentfit ~~

Description

It estimates a linear model using two-stage least squares.

Usage

## S4 method for signature 'linearModel'
tsls(model)

## S4 method for signature 'slinearModel'
tsls(model)

Arguments

model

An object of class linearModel or slinearModel.

Methods

signature(model = "linearModel")
signature(model = "slinearModel")

2SLS for equation by equation estimation of a system of equations.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
res <- tsls(model1)
summary(res)

## Econometrics, Fumio Hayashi (2000)
## Empirical exercises (b) and (c)
data(Griliches)
Griliches$YEAR <- as.factor(Griliches$YEAR)
model1  <- momentModel(LW~S+IQ+EXPR+TENURE+RNS+SMSA+YEAR-1,
                   ~S+EXPR+TENURE+RNS+SMSA+YEAR+MED+KWW+MRT+AGE-1,
                   data=Griliches, vcov="MDS")
res <- tsls(model1)
summary(res)

~~ Methods for Function update in Package stats ~~

Description

The method is used to refit a model with either a different method or with modifications to the momentModel.

Usage

## S4 method for signature 'gmmfit'
update(object, ..., evaluate=TRUE)

## S4 method for signature 'momentModel'
update(object, ...)

## S4 method for signature 'gelfit'
update(object, newModel=NULL, ...,
evaluate=TRUE)

## S4 method for signature 'list'
update(object, ...)

Arguments

object

An object produced by "gelFit", "gmmFit" or a model. It can also be a list, in which case, it is used to change elements of a list.

...

Arguments to modify the model or the GMM method
newModel

When provided, the new model is estimated using the same specification. For example, it is particularly useful to estimate the restricted model using the same optim specification as the unrestricted model.
evaluate

The modified call argument is only evaluated when evaluate is TRUE

Methods

signature(object = "ANY")

That just calls "update" from the "stats" package.

signature(object = "gmmfit")
signature(object = "momentModel")
signature(object = "list")

Examples

x <- rchisq(200,5)
z1 <- rnorm(200)
z2 <- .2*x+rnorm(200)
y <- x+rnorm(200)
dat <- data.frame(y=y,z1=z1,x=x,z2=z2)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x, ~z1+z2, data=dat)

(res <- gmmFit(model1))

## lets change to iterative
update(res, type="iter")

## Let change the HAC specification in the model1 object
## to MDS
update(res, vcov="MDS")

~~ Methods for Function vcov in Package stats ~~

Description

Computes the covariance matrix of the coefficient estimated by GMM or GEL.

Usage

## S4 method for signature 'gmmfit'
vcov(object, sandwich=NULL, df.adj=FALSE,
breadOnly=FALSE, modelVcov=NULL)

## S4 method for signature 'sgmmfit'
vcov(object, sandwich=NULL, df.adj=FALSE,
breadOnly=FALSE, modelVcov=NULL)

## S4 method for signature 'tsls'
vcov(object, sandwich=TRUE, df.adj=FALSE)

## S4 method for signature 'gelfit'
vcov(object, withImpProb=FALSE, tol=1e-10,
                        robToMiss=FALSE)

## S4 method for signature 'momentModel'
vcov(object, theta)

## S4 method for signature 'sysModel'
vcov(object, theta)

Arguments

object

A fitted model or a model, For fitted models, it computes the covariance matrix of the estimators. For models, it computes the covariance matrix of the moment conditions, in which case, the coefficient vector must be provided.

theta

Coefficient vector to compute the covariance matrix of the moment conditions.
sandwich

Should we compute the sandwich covariance matrix. This is only necessary if the weighting matrix is not the optimal one, or if we think it is a bad estimate of it. If NULL, it will be set to "TRUE" for One-Step GMM, which includes just-identified GMM like IV, and "FALSE" otherwise.

df.adj

Should we adjust for degrees of freedom. If TRUE the covariance matrix is multiplied by n/(n-k), where n is the sample size and k is the number of coefficients. For heteroscedastic robust covariance matrix, adjusting is equivalent to computing HC1 while not adjusting is HC0.
breadOnly

If TRUE, the covariance matrix is set to the bread (see details below).
modelVcov

Should be one of "iid", "MDS" or "HAC". It is meant to change the way the variance of the moments is computed. If it is set to a different specification included in the model, sandwich is set to TRUE.

withImpProb

Should we compute the moments with the implied probabilities
tol

Any diagonal less than "tol" is set to tol
robToMiss

Should we compute a covariance matrix that is robust to misspecification?

Details

If sandwich=FALSE, then it returns (G′V−1G)−1/n(G'V^{-1}G)^{-1}/n, where GG and VV are respectively the matrix of average derivatives and the covariance matrix of the moment conditions. If it is TRUE, it returns (G′WG)−1G′WVWG(G′WG)−1/n(G'WG)^{-1}G'WVWG(G'WG)^{-1}/n, where WW is the weighting matrix used to obtain the vector of estimates.

If breadOnly=TRUE, it returns (G′WG)−1/n(G'WG)^{-1}/n, where the value of WW depends on the type of GMM. For two-step GMM, it is the first step weighting matrix, for one-step GMM, it is either the identity matrix or the fixed weighting matrix that was provided when gmmFit was called, for iterative GMM, it is the weighting matrix used in the last step. For CUE, the result is identical to sandwich=FALSE and beadOnly=FALSE, because the weighting and coefficient estimates are obtained simultaneously, which makes WW identical to VV.

breadOnly=TRUE should therefore be used with caution because it will produce valid standard errors only if the weighting matrix converges to the the inverse of the covariance matrix of the moment conditions.

For "tsls" objects, sandwich is TRUE by default. If we assume that the error term is iid, then setting it to FALSE to result in the usual σ2(X^′X^)−1\sigma^2(\hat{X}'\hat{X})^{-1} covariance matrix. If FALSE, it returns a robust covariance matrix determined by the value of vcov in the momentModel.

Methods

signature(object = "gmmfit")

For any model estimated by any GMM methods.

signature(object = "gelfit")

For any model estimated by any GMM methods.

signature(object = "sgmmfit")

For any system of equations estimated by any GMM methods.

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

## optimal matrix
res <- gmmFit(model1)
vcov(res)

## not the optimal matrix
res <- gmmFit(model1, weights=diag(3))
vcov(res, TRUE)

## Model with heteroscedasticity
## MDS is for models with no autocorrelation.
## No restrictions are imposed on the structure of the
## variance of the moment conditions
model2 <- momentModel(y~x1, ~z1+z2, data=simData, vcov="MDS")
res <- tsls(model2)

## HC0 type of robust variance
vcov(res, sandwich=TRUE)
## HC1 type of robust variance
vcov(res, sandwich=TRUE, df.adj=TRUE)

## Fixed and True Weights matrix
## Consider the moment of a normal distribution:
## Using the first three non centered moments

g <- function(theta, x)
{
mu <- theta[1]
sig2 <- theta[2]
m1 <- x-mu
m2 <- x^2-mu^2-sig2
m3 <- x^3-mu^3-3*mu*sig2
cbind(m1,m2,m3)
}

dg <- function(theta, x)
{
mu <- theta[1]
sig2 <- theta[2]
G <- matrix(c(-1,-2*mu,-3*mu^2-3*sig2, 0, -1, -3*mu),3,2)
}

x <- simData$x3

model <- momentModel(g, x, c(mu=.1, sig2=1.5), vcov="iid")
res1 <- gmmFit(model)
summary(res1)
## Same results (that's because the moment vcov is centered by default)
W <- solve(var(cbind(x,x^2,x^3)))
res2 <- gmmFit(model, weights=W)
res2
## If is therefore more efficient in this case to do the following:
## the option breadOnly of summary() is passed to vcov()
summary(res2, breadOnly=TRUE)

~~ Methods for Function vcovHAC in Package sandwich ~~

Description

Methods to compute the HAC covariance matrix of the moment matrix ~~

Methods

signature(x = "momentModel")

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)

# a warning is given if the model is not set as being HAC
vcovHAC(model1, theta)

model1 <- momentModel(y~x1, ~z1+z2, data=simData, vcov="HAC",vcovOptions=list(kernel="B"))
vcovHAC(model1, theta)