*! version 1.0.5 15Jun2010
help frcount

Title

frcount -- Estimating fractional response model under the presence of count endogeneity and unobservable heterogeneity

Syntax

frcount depvar indepvars [if] [in], endog(endogenous variable) iv(iv varlist)
quad(numeric) [options]

Model
noconstant suppress constant term

qmle estimates the model with Quasi-Maximum Likelihood Estimator (QMLE) method, this is default method

nls estimates the model with Non-linear least square estimator (NSL) method

Average Partial Effects
apevce(vcetype) reports Average Partial Effects (APE) for the countinous and count variables. The default option
is { opt robust}. vcetype may be robust

quad(numeric) defines the number of quadrature points using in approximating integrals with Adaptive Gauss Hermite method. The quadrature number depends on sample sizes, it could be 35 quadrature points or more. endog(endogenous variable) allows only for one count endogenous variable.

Description

frcount fits a fractional response model under the presence of count endogeneity and unobservable heterogeneity. The dependent variable
y1 is a fractional response variable where 0<=y1<=1. The endogenous variable y2 is a count variable where it can be any numeric number.
The approach for this command is based on the chapter by Hoa Nguyen (2010) in Advances in Econometrics, Volume 26, Maximum Simulated Likelihood Methods and Applications,
edited by Carter Hill and Greene.

Consider the model using cross section data set:

y1 = x1*b1 + x2*b2 + y2*b3 + eta1*a1 + e1

where

y1 is the fractional response variable such as the passing rates, fractions of women employed in firms, etc.;

x1 and x2 are exogenous variables;

y2 is the count endogenous variable and we use a set of k instrument variables z1...zk for the endogenous variable;

a1 is unobservable heterogeneity variable which we do not observe;

e1 is the disturbance term;

Estimation for -frcount- command was based on Quasi-Maximum Likelihood Estimator (QMLE) by default or by Non-linear Least Squares (NLS). Estimation procedure involves solving equations with no closed form solution, so we approximate some integrals in those equations
by using the Adaptive Gauss Hermite method. For details on the Adaptive Gauss Hermite method, please see mannual on -xtprobit-. The detailed procedure of this method was discussed in Hoa Nguyen (2010). The command provides regular outputs for an estimation command. In addition, the command provides output for Average Partial Effects of the all continuous and count variables,
with changes in the count variable with values from 0 to 1, 1 to 2, and 2 to 3.

For more details of the estimation procedures and simulations for this command, -frcount-, please refer to Minh Nguyen and Hoa Nguyen (2010b).

Return values

Scalars
e(n_quad) number of quadrature points
e(N) number of observations
e(cilevel) confidence interval level
e(converge) convergence or not
e(errcode) error code
e(llog) log-likelihood value
e(tol) convergence tolerance

Macros
e(cmd) name of the command
e(cmdline) the full command typed
e(depvar) dependent variable
e(endog) endogenous variable
e(exog) exogenous variables (excluded)
e(iv) exogenous variables (included iv)
e(ivar) ID variable
e(method) display estimation method
e(properties) b V ape Vape
e(title) title of regression
e(version) version of the command

Matrices
e(b) estimated parameters
e(V) variance-covariance of estimated parameters
e(ape) estimated average partial effects
e(Vape) variance–covariance matrix of average partial effects

Examples

Fractional response model with one instrument variable

. use frcount_example.dta, clear

. frcount y1 x1 x2, endog(y2) iv(iv) quad(35)

. frcount y1 x1 x2, endog(y2) iv(iv) quad(35) nls

. frcount y1 x1 x2, endog(y2) iv(iv) quad(35) qmle apevce(robust)

References

Hoa Bao Nguyen. 2010.
Estimating fractional response model under the presence of count endogenous variable and unobservable heterogeneity. Forthcoming in Advances in Econometrics, Volume 26, Maximum Simulated Likelihood Methods and Applications, edited by Carter Hill and Greene.

Minh Cong Nguyen and Hoa Bao Nguyen. 2010b. Stata module: Estimation of fractional response model under the presence of count endogeneity. Working Paper.

Acknowledgements

We would like to thank Jeffrey Wooldridge, David Drukker, Jeffrey Pitblado, Isabel Canette, Carter Hill, and participants at the 2009 Stata DC Conference, Mid West Econometrics conference,
and the 8th Annual Advances in Econometrics Conference at Louisiana State University for various comments and suggestion in developing the paper and the command.

Authors

Hoa Bao Nguyen

Ph.D. Candidate

Economics Department

Michigan State University

East Lansing, MI

nguye147@msu.edu

Minh Cong Nguyen

Enterprise Analysis Unit

The World Bank, 2010

mnguyen3@worldbank.org

Version

This is version 1.0.5 released June 15, 2010.