* BIVARIATE PROBIT MODELS - Testing for zero error correlation by * computing a Lagrange multiplier test statistic using the results * from the estimation of 2 independent probits. * * Reference: Greene, Econometric Analysis, 2nd Edition, 1993, * Examples 21.11 and 21.12, pp. 660-3. * * The data set on voting behaviour is from Pindyck and Rubinfeld, * Econometric Models and Economic Forecasts, * 1991, Third Edition, Table 10.8, p. 282; * 1998, Fourth Edition, Table 11.8, p. 332. * * The variables are: * YESVM = dummy variable equal to 1 if individual voted yes in the * election; 0 if individual voted no. * PUB12 = 1 if 1 or 2 children in public school; = 0 otherwise * PUB34 = 1 if 3 or 4 children in public school; = 0 otherwise * PUB5 = 1 if 5 or more children in public school; = 0 otherwise * PRIV = 1 if 1 or more children in private school; = 0 otherwise * YEARS = number of years living in the community * SCHOOL= 1 if individual is employed as a teacher; = 0 otherwise * LOGINC= logarithm of annual household income (in dollars) * PTCON = logarithm of property taxes (in dollars) paid per year * SAMPLE 1 95 READ (school.txt) PUB12 PUB34 PUB5 PRIV YEARS SCHOOL LOGINC PTCON YESVM IF ((PUB12+PUB34+PUB5).GE.1) PUBLIC=1 PROBIT PUBLIC LOGINC PTCON / INDEX=XB1 PROBIT YESVM LOGINC PTCON YEARS / INDEX=XB2 RENAME PUBLIC Y1 RENAME YESVM Y2 * Lagrange multiplier test - Greene (1993, Section 21.6, pp. 660-663) GENR Q1=2*Y1-1 GENR Q2=2*Y2-1 GENR W1=Q1*XB1 GENR W2=Q2*XB2 GENR NORM1=EXP(-(W1**2)/2)/(2*\$PI) GENR NORM2=EXP(-(W2**2)/2)/(2*\$PI) GENR CDF1=NCDF(W1) GENR CDF2=NCDF(W2) GENR CDFN1=NCDF(-W1) GENR CDFN2=NCDF(-W2) GENR GV=Q1*Q2*NORM1*NORM2/(CDF1*CDF2) GENR HV=NORM1*NORM1*NORM2*NORM2/(CDF1*CDFN1*CDF2*CDFN2) ?STAT GV HV / SUMS=TOT GEN1 TOP=(TOT:1)**2 GEN1 LM=TOP/TOT:2 * The test statistic can be compared with a chi-square distribution * with 1 degree of freedom. The 5% critical value is 3.84. * If the test statistic exceeds the critical value then there is * evidence to reject the null hypothesis of zero error correlation. PRINT LM STOP