``` help frcount
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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

options               Description
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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 robust. vcetype may be robust

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approximating integrals with Adaptive Gauss Hermite method. The
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
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)         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.
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