frmhet: Fitting Fractional Regression Models under Unobserved...

In frmhet: Regression Analysis of Fractional Responses Under Unobserved Heterogeneity

Description

frmhet is used to fit fractional regression models under unobserved heterogeneity, i.e. regression models for proportions, percentages or fractions that suffer from neglected heterogeneity and/or endogeneity issues.

Usage

frmhet(y, x, z = x, var.endog, start, type = "GMMx", link = "logit", intercept = T,
	table = T, variance = T, var.type = "robust", var.cluster, adjust = 0, ...)

Arguments

y	a numeric vector containing the values of the response variable.
x	a numeric matrix, with column names, containing the values of all covariates (exogenous and endogenous).
z	a numeric matrix, with column names, containing the values of all exogenous variables (covariates and instrumental variables). Defaults to x.
var.endog	a numeric vector containing the values of the endogenous covariate (or of some transformation of it), which will be used as dependent variable in the linear reduced form assumed for application of xv-type estimators.
start	a numeric vector containing the initial values for the parameters to be optimized. Optional.
type	a description of the estimator to compute: GMMx (the default), GMMxv, GMMz, LINx, LINxv, LINz or QMLxv.
link	a description of the link function to use. Available options for all estimators: logit and cloglog. Additional available options for QML and LIN estimators: probit, cauchit and loglog.
intercept	a logical value indicating whether the model should include a constant term or not.
table	a logical value indicating whether a summary table with the regression results should be printed.
variance	a logical value indicating whether the variance of the estimated parameters should be calculated. Defaults to TRUE whenever table = TRUE.
var.type	a description of the type of variance of the estimated parameters to be calculated. Options are robust, the default, and cluster.
var.cluster	a numeric vector containing the values of the variable that specifies to which cluster each observation belongs.
adjust	the numeric value to be added to the response variable in case of boundary observations when the LIN estimators are applied or the string drop, which implies that the boundary observations are dropped.
...	Arguments to pass to nlminb.

Details

frmhet computes the GMM estimators proposed in Ramalho and Ramalho (2016) for fractional regression models with unobserved heterogeneity: GMMx, which allows for neglected heterogeneity but not for endogeneity; GMMxv, which allows both issues and assumes a linear reduced form for the endogeneous covariate (or for a transformation of it); and GMMz, which also allows for both issues but does not require the assumption of a reduced form for the endogenous covariate. In addition, frmhet also computes three linearized estimators (LINx, LINxv and LINz) that have similar features to their GMM counterparts as well as a QML estimator that allows for endogeneity but not for neglected heterogeneity (QMLxv); see Ramalho and Ramalho (2016) for details on each estimator. For overidentified models, frmhet calculates Hansen's J statistic. For GMMx and LINx, frmhet stores the information needed to implement the RESET test (frmhet.reset). For all estimators, frmhet stores the information needed to calculate partial effects (frmhet.pe).

Value

frmhet returns a list with the following elements:

class	"frmhet".
formula	the model formula.
type	the name of the estimator computed.
link	the name of the specified link.
adjust	The value or the type of the adjustment applied to LIN estimators.
p	a named vector of coefficients.
Hy	the transformed values of the response variable when GMM or LIN estimators are computed or the values of the response variable in the QML case.
xbhat	the fitted mean values of the linear predictor (for xv-type estimators, includes the term relative to the first-stage residual).
converged	logical. Was the algorithm judged to have converged?
x.names	a vector containing the names of the covariates.

In case of an overidentifying model, the following element is also returned:

J	the result of Hansen's J test of overidentifying moment conditions.

If variance = TRUE or table = TRUE and the algorithm converged successfully, the previous list also contains the following elements:

p.var	a named covariance matrix.
var.type	covariance matrix type.

If var.type = "cluster", the list also contains the following element:

var.cluster

the variable that specifies to which cluster each observation belongs.

Author(s)

Joaquim J.S. Ramalho <[e-mail]>

References

Ramalho, E.A. and J.J.S. Ramalho (2016), "Moment-based estimation of nonlinear regression models with boundary outcomes and endogeneity, with applications to nonnegative and fractional responses", Econometric Reviews, forthcoming (DOI: 10.1080/07474938.2014.976531).

See Also

frmhet.reset, for the RESET test.
frmhet.pe, for computing partial effects.
frm, for fitting standard cross-sectional fractional regression models.
frmpd, for fitting panel data fractional regression models.

Examples

N <- 250
u <- rnorm(N)

X <- cbind(rnorm(N),rnorm(N))
dimnames(X)[[2]] <- c("X1","X2")

Z <- cbind(rnorm(N),rnorm(N),rnorm(N))
dimnames(Z)[[2]] <- c("Z1","Z2","Z3")

y <- exp(X[,1]+X[,2]+u)/(1+exp(X[,1]+X[,2]+u))

#Exogeneity, GMMx estimator
frmhet(y,X,type="GMMx")

#Endogeneity, GMMz estimator
frmhet(y,X,Z,type="GMMz")

#Endogeneity, GMMxv estimator
frmhet(y,X,Z,X[,1],type="GMMxv")

## See the website http://evunix.uevora.pt/~jsr/FRM.htm for more examples.

Example output

*** Fractional logit regression model ***
*** Estimator: GMMx

          Estimate Std. Error t value Pr(>|t|)    
INTERCEPT 0.554438   0.079733   6.954    0.000 ***
X1        1.117545   0.075542  14.794    0.000 ***
X2        0.911219   0.085960  10.601    0.000 ***

Note: robust standard errors

Number of observations: 250 



*** Fractional logit regression model ***
*** Estimator: GMMz

          Estimate Std. Error t value Pr(>|t|)  
INTERCEPT 1.657879   2.103106   0.788    0.431  
X1        2.724974   1.492216   1.826    0.068 *
X2        0.850187   0.537686   1.581    0.114  

Note: robust standard errors

Number of observations: 250 

J test of overidentifying moment conditions: 0.005818133 (p-value: 0.939199 )

*** Fractional logit regression model ***
*** Estimator: GMMxv

           Estimate Std. Error t value Pr(>|t|)    
INTERCEPT  0.608909   0.187904   3.241    0.001 ***
X1        -0.704951   3.761500  -0.187    0.851    
X2         0.911348   0.083615  10.899    0.000 ***
vhat       1.819200   3.771578   0.482    0.630    

Reduced form:
             Estimate Std. Error t value Pr(>|t|)    
Z_INTERCEPT  0.033065   0.057744   0.573    0.567    
Z_Z1         0.029255   0.058260   0.502    0.616    
Z_Z2        -0.011648   0.059955  -0.194    0.846    
Z_Z3        -0.020201   0.056958  -0.355    0.723    

Note: robust standard errors

Number of observations: 250 

frmhet documentation built on May 2, 2019, 2:46 a.m.