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 
                varlist) quad(numeric) [options]

    options               Description
    -------------------------------------------------------------------------
    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

    -------------------------------------------------------------------------
    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.