Instrumental Variables Probit

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The following example may help you - adapted from Adkins(2009) as described below.

The example script can be downloaded here: IVProbit_Example.sha

The accompanying data is here: bank.shd

The SHAZAM Procedure can be downloaded here:IVProbit.prc

EXAMPLE FILE

* Example calling Instrumental Variables Probit Procedure
*
* Sample data is from Adkins(2009) to determine whether managerial incentives 
* affect the use of foreign exchange derivatives by bank holding companies.
* Example replicates the results found in that paper.
*
* N.B. To reuse, set variables X,Y, X1 and Y1 to your own problem
*

* Read the data and create a constant by hand
read(bank.shd) / names
genr const = 1

* Set up matrices with all the variables of interest
*  y  = r.h.s. endogenous variables
*  x  = the complete set of instruments
*  x1 = r.h.s. exogenous variables
*  y1 = dichotomous l.h.s. variable
matrix y  = eqrat|bonus|optval
matrix x  = const|ltass|linsown|linstown|roe|mktbk|perfor|dealdum|div|dum97|dum98|dum99|dum00|no_emp|no_subs|no_off|ceo_age|gap|cfa 
matrix x1 = const|ltass|linsown|linstown|roe|mktbk|perfor|dealdum|div|dum97|dum98|dum99|dum00
matrix y1 = d2

* Disable irrelevant output
set nooutput
set noecho
set nodoecho

* Call the Proc
exec IVProbit

* Print results
set output
print delt se

SHAZAM PROCEDURE

The procedure IVProbit is below:

* SHAZAM Procedure - Instrumental Variables Probit Estimator by AGLS
* 
* Produces Amemiya's Generalised Least Squares Estimator (AGLS) 
*
* This procedure produces a consistent estimator of the standard errors and can therefore 
* easily be used for subsequent hypothesis testing of the parameters.
*
* References:
*
* Amemiya, T., 1978, The estimation of a simultaneous equation generalized probit model, Econometrica 46, 1193-1205. 
* Amemiya, T., 1981, Qualitative response models: a survey, Journal of Economic Literature 19, 1483-1536. 
* Newey, W.K., 1987, Efficient estimation oflimited dependent variable models with endogenous explanatory variables, Journal of Econometrics 36, 231-250
*
*  Based on a program created and described by Lee C. Adkins in the paper
*  Adkins, L., 2009, An Instrumental Variables Probit Estimator using gretl
*  Steps defined below are described in that paper; Newey 1987 also a good reference
*
* Definitions of required input variables to be declared in calling routine.
*  y  = r.h.s. endogenous variables
*  x  = the complete set of instruments
*  x1 = r.h.s. exogenous variables
*  y1 = dichotomous l.h.s. variable
*
proc IVProbit

* Define equation matrices and useful parameters
matrix Z = X1|Y
gen1 nx=$rows
matrix b = INV(X'X)*X'Y
gen1 kx=$rows
gen1 ky=$cols
matrix d = INV(X'X)*X'Z
gen1   s = ky
gen1 kx1 = kx+1
gen1 kxy = kx+ky

* Step 1: Regress each y variable and store resid / pred
dim myres nx ky mypred nx ky
do #=1,ky
  * Select the regressand vector from the matrix using its index
  matrix ycol = y(0,#)
  * Regress each y variable on x and store resid / pred
  ols ycol x / resid=resid# pred=pred# noconstant
  copy resid# myres / frow=1;nx trow=1;nx fcol=1;1 tcol=#;#
  copy pred# mypred / frow=1;nx trow=1;nx fcol=1;1 tcol=#;#
endo

* Step 2 ...