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LIMDEP TUTORIAL BY MIN AHN
INSTRUCTION FOR ACCESSING AN INSTRUCTOR VOLUME
1. At the ASU PC Network logon you will get a message: “Click OK for the next two
requests.”
Click on the OK button here.
Click OK and wait 1-2 minutes while the logon scripts execute.
Click OK to get to the sign on screen with the ASU logo displayed over an ASU
photograph back ground.
2. At the sign on screen enter your ASURITE ID and password. Enter both items in lower
case.
Click on OK.
Wait during the message “Mounting AFS volumes.” Soon the Window 95 desktop will
be displayed.
3. Double click on the Applications folder icon on the desktop.
4. Double click on the Instructor Volumes folder icon on the desktop.
5. Find the icon named ECN527 , and double click on it.
6. The U: drive instructor volume is now mounted but you can not see it until the current
window is closed. Close the instructor volume window by clicking on X in the upper
right corner of the window.
7. Double click on the U: drive icon on the desktop.
8. Go to the directory Limdep/Program. Click on the LIMDEP icon.
9. Now you entered the LIMDEP program (Version 7.0 for windows).
When you have finished using the instructors volume, be sure to LOG OUT so that the next
computer user does not have access to your files.
10. Double click on the Log Out icon on the desktop. Click on Log Me Out. DO NOT turn
the computer off.
HOW TO READ DATA
Basic Format:
READ ; NOBS = ...
; NVAR = ...
; NAMES = ... (THE NAMES OF VARIABLES)
; FILE = ... (THE FILE CONTAINING RAW DATA)
; FORMAT = ... (SEE LIMDEP MANUAL) $
Example: Using MWPSID82.DB (MW_READ.LIM)
READ ; NOBS=1962; NVAR=
; FILE=MWPSID82.DB
; NAMES= NLF, EMP, WRATE, LRATE, ED,
URB, MINOR, AGE, TENURE, EXP,
REGS, OCCW, OCCB, INDUMG, INDUMN,
UNION, UNEMPR, OFINC, LOFINC, KIDS,
WUNE80, HWORK, USPELL, SEARCH, KIDS5 $
CREATE; LF = 1 - NLF $
(1) This problem is available in MW_READ.LIM. Run the program
to read the data,MWPSID82.DB
(2) To save the data, click File/Project save as.
PROBIT ESTIMATION
Example: (MW_PROB.LIM)
/* Basic Program */
title ; Employment Probability $
probit ; lhs = emp
; rhs = one,ed,urb,minor,lofinc
; maxit = 1000
; start = 0,0,0,0,
; tlf = 0.00001 ; tlb = 0.00001 ; tlg = 0.
; alg = newton? Can choose bhhh, bfgs, dfp, stedes
; margin $? estimate p = Pr(y=1) at sample mean
? Saving estimates and covariance matrix
? [Wald Test]
title; Wald test for b1 = 0 and b2 = b3 $
wald ; labels = b1,b2,b3,b4,b
; start = uprb; var = uprc ;
; fn1 = b
; fn2 = b2 - b3 $
? [LR test]
title; LR test for b1 = 0 and b2 = b3 $
calc ; list
; lrt = 2*(ulogl - rlogl)
; pval = 1 - chi(lrt,2) $
? [LM test]
probit ; lhs = emp; rhs = x
; start = rprb ; maxit = 0 $
title ; LM test for b1 = 0 and b2 = b3 $
calc ; list
; lmt = lmstat
; pval = 1 - chi(lmt,2) $
/* Wald for hypo 3 */
title; Wald test for b1 = 0, b2 = b3 and b4^2 = b5 $
wald ; labels = b1,b2,b3,b4,b
; start = uprb
; var = uprc
; fn1 = b1 ;fn2 = b2 - b3; fn3 = b4^2-b5 $
/* Estimating Pr(y=1) and dPr(y=1)/dx_j */
? Estimating Pr(y=1) at mean of x
? Based on unrestricted probit
matrix ; mx = mean(x) $? It is a column vector
calc ; xb1 = mx(1,1) ; xb2 = mx(2,1); xb3 = mx(3,1)
; xb4 = mx(4,1) ; xb5 = mx(5,1) $
title ; Pr(emp=1) at means of regressors $
wald ; labels = b1,b2,b3,b4,b5; start = uprb; var = uprc;
; fn1 = phi(xb1b1+xb2b2+xb3b3+xb4b4+xb5*b5) $
? Estimating dPr(y=1)/dx
title ; Marginal effects $
wald ; labels = b1,b2,b3,b4,b
; start = uprb
; var = uprc
; fn1 = xb1b1+xb2b2+xb3b3+xb4b4+xb5*b
; fn2 = n01(fn1)*b
; fn3 = n01(fn1)*b
; fn4 = n01(fn1)*b3 $
Output:
--> RESET
--> LOAD;file="C:\Aaschool\ECON727\DATA\MW.lpj"$ LOAD has reconstructed your previous session. --> title ; Employment Probability probit ; lhs = emp ; rhs = one,ed,urb,minor,lofinc ; maxit = 1000 ; start = 0,0,0,0, ; tlf = 0.00001 ; tlb = 0.00001 ; tbg = 0. ; alg = newton? Can choose bhhh, bfgs, dfp, stedes ; margin $? estimate p = Pr(y=1) at sample mean --> matrix ; prb = b ; prc = varb $ --> calc ; plogl = logl $ --> namelist ; x = one,ed,urb,minor,lofinc $ --> probit ; lhs = emp ; rhs = x ; maxit = 1000 $ +-----------------------------------------------------------------------+ | Dependent variable is binary, y=0 or y not equal 0 | | Ordinary least squares regression Weighting variable = none | | Dep. var. = EMP Mean= .4704383282 , S.D.= .4992525893 | | Model size: Observations = 1962, Parameters = 5, Deg.Fr.= 1957 | | Residuals: Sum of squares= 474.9962035 , Std.Dev.= .49266 | | Fit: R-squared= .028211, Adjusted R-squared = .02622 | | Model test: F[ 4, 1957] = 14.20, Prob value = .00000 | | Diagnostic: Log-L = -1392.4945, Restricted(b=0) Log-L = -1420.5675 | | LogAmemiyaPrCrt.= -1.413, Akaike Info. Crt.= 1.425 | +-----------------------------------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Constant .9170578290 .17362375 5.282. ED .2915849316E-01 .51513883E-02 5.660 .0000 12. URB .6459244774E-01 .24441441E-01 2.643 .0082. MINOR .2566128748E-01 .26742220E-01 .960 .3373. LOFINC -.8619967756E-01 .17367289E-01 -4.963 .0000 9. Normal exit from iterations. Exit status=0.
| Binomial Probit Model | | Maximum Likelihood Estimates | | Dependent variable EMP | | Weighting variable ONE | | Number of observations 1962 | | Iterations completed 4 | | Log likelihood function -1331.862 | | Restricted log likelihood -1356.524 | | Chi-squared 49.32278 | | Degrees of freedom 2 | | Significance level .0000000 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Index function for probability Constant .0000000000 ........(Fixed Parameter)........ ED .8579347233E-01 .12778130E-01 6.714 .0000 12. URB .8579347233E-01 .12778130E-01 6.714 .0000. MINOR .1336072788 .63756953E-01 2.096 .0361. LOFINC -.1233762049 .17163930E-01 -7.188 .0000 9. Frequencies of actual & predicted outcomes Predicted outcome has maximum probability. Predicted ------ ---------- + ----- Actual 0 1 | Total ------ ---------- + ----- 0 756 283 | 1039 1 571 352 | 923 ------ ---------- + ----- Total 1327 635 | 1962 --> matrix ; rprb = b $ --> calc ; rlogl = logl $ --> title; Wald test for b1 = 0 and b2 = b3 $ --> wald ; labels = b1,b2,b3,b4,b ; start = uprb ; var = uprc ; fn1 = b ; fn2 = b2 - b3 $ +-----------------------------------------------+ | WALD procedure. Estimates and standard errors | | for nonlinear functions and joint test of | | nonlinear restrictions. | | Wald Statistic = 8.06527 | | Prob. from Chi-squared[ 2] = .01773 | +-----------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Fncn( 1) 1.228085188 .47320614 2.595. Fncn( 2) -.9457399616E-01 .65465798E-01 -1.445. --> title; LR test for b1 = 0 and b2 = b3 $ --> calc ; list ; lrt = 2(ulogl - rlogl) ; pval = 1 - chi(lrt,2) $* LRT = .81630295544032380D+ PVAL = .16881874007718900D-
--> probit ; lhs = emp ; rhs = x ; start = rprb ; maxit = 0 $ +-----------------------------------------------------------------------+ | Dependent variable is binary, y=0 or y not equal 0 | | Ordinary least squares regression Weighting variable = none | | Dep. var. = EMP Mean= .4704383282 , S.D.= .4992525893 | | Model size: Observations = 1962, Parameters = 5, Deg.Fr.= 1957 | | Residuals: Sum of squares= 474.9962035 , Std.Dev.= .49266 | | Fit: R-squared= .028211, Adjusted R-squared = .02622 | | Model test: F[ 4, 1957] = 14.20, Prob value = .00000 | | Diagnostic: Log-L = -1392.4945, Restricted(b=0) Log-L = -1420.5675 | | LogAmemiyaPrCrt.= -1.413, Akaike Info. Crt.= 1.425 | +-----------------------------------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Constant .9170578290 .17362375 5.282. ED .2915849316E-01 .51513883E-02 5.660 .0000 12. URB .6459244774E-01 .24441441E-01 2.643 .0082. MINOR .2566128748E-01 .26742220E-01 .960 .3373. LOFINC -.8619967756E-01 .17367289E-01 -4.963 .0000 9. Maximum iterations reached. Exit iterations with status=1. Maxit = 0. Computing LM statistic at starting values. No iterations computed and no parameter update done. +---------------------------------------------+ | Binomial Probit Model | | Maximum Likelihood Estimates | | Dependent variable EMP | | Weighting variable ONE | | Number of observations 1962 | | Iterations completed 1 | | LM Stat. at start values 8.027283 | | LM statistic kept as scalar LMSTAT | | Log likelihood function -1331.862 | | Restricted log likelihood -1356.524 | | Chi-squared 49.32278 | | Degrees of freedom 4 | | Significance level .0000000 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Index function for probability Constant .0000000000 .46145275 .000 1. ED .8579347233E-01 .13444274E-01 6.381 .0000 12. URB .8579347233E-01 .62895744E-01 1.364 .1725. MINOR .1336072788 .68714027E-01 1.944 .0518. LOFINC -.1233762049 .46617697E-01 -2.647 .0081 9. Frequencies of actual & predicted outcomes Predicted outcome has maximum probability. Predicted ------ ---------- + ----- Actual 0 1 | Total ------ ---------- + ----- 0 756 283 | 1039 1 571 352 | 923 ------ ---------- + ----- Total 1327 635 | 1962
| WALD procedure. Estimates and standard errors | | for nonlinear functions and joint test of | | nonlinear restrictions. | | Wald Statistic = 60.67600 | | Prob. from Chi-squared[ 4] = .00000 | +-----------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Fncn( 1) -.7523894869E-01 .28569505E-01 -2.634. Fncn( 2) .4885503289 .18831825 2.594. Fncn( 3) .3035246511E-01 .53493381E-02 5.674. Fncn( 4) .6797539012E-01 .25106007E-01 2.708.
[EXERCISE] Use MWPSID82.DB. Do probit for:
LHS=EMP,
RHS=ONE, ED, URB, MINOR, AGE, REGS, UNEMPR, LOFINC, KIDS5,
EXP.
Construct Wald, LR and LM statistics for Ho: no effect of other family income, and the effect of
AGE = the effect of EXP.
[EXERCISE] Use MWPSID82.DB. Do PROBIT as you did above. Estimate the same model by
BHHH. Compare your new result with the result from the above program.
INFORMATION ON MWPSID82.DB
This is the data set of married women in 1981 sampled from PSID. Total number of
observations are 1962, and 25 variables are observed.
VARIABLES DEFINITION
NLF NLF=1 IF NON-LABOR-FORCE (HOUSEWIFE)
EMP EMP=1 IF EMPLOYED
WRATE HOURLY WAGE RATE ($)
LRATE Log of WRATE = LOG(WRATE+1)
ED YEARS OF EDUCATION
URB URB=1 IF RESIDENT IN SMSA
MINOR MINOR=1 IF BLACK AND HISPANIC
AGE YEARS OF AGE
TENURE MONTHS UNDER THE CURRENT EMPLOYER
EXP NUMBER OF YEARS WORKED SINCE AGE 18
REGS REGS=1 IF LIVES IN THE SOUTH OF U.S.
OCCW OCCW=1 IF WHITE COLOR
OCCB OCCB=1 IF BLUE COLOR
INDUMG INDUMG=1 IF IN THE MANUFACTURING INDUSTRY
INDUMN INDUMN=1 IF NOT IN MANUFACTURING SECTOR
UNION UNION=1 IF UNION MEMBER
UNEMPR % UNEMPLOYMENT RATE IN THE RESIDENT'S COUNTY, 1980
OFINC OTHER FAMILY MEMBER'S INCOME IN 1980 ($)
LOFINC LOG OF (OFINC+1)
KIDS NUMBER OF CHILDREN 17 YEARS OF AGE
HWORK HOURS OF HOMEWORK PER WEEK
USPELL UNEMPLOYED WEEKS FOR EMPLOYED WIFE
SEARCH WEEKS LOOKING FOR JOB IN 1980
WUNE80 ACTUAL UNEMPLOYED HOURS
KIDS5 NUMBER OF CHILDREN 5 YEARS OF AGE
Frequencies of actual & predicted outcomes Predicted outcome is the sign of x(i)*theta. Predicted ------ ---------- + ----- Actual 0 1 | Total ------ ---------- + ----- 0 558 481 | 1039 1 328 595 | 923 ------ ---------- + ----- Total 886 1076 | 1962
Example 2: (MSE2.LIM)
This program is for Monte Carlo Simulation:
Model: ys = b1 + b2*x2 + e, b1 = b2 = 1/SQR(2)
Compare the finite-sample biases
in estimates b2 by MSE(MSCORE) and Probit.
? Define Sample Size
CALC ; SS = 100 $
SAMPLE ; 1 - SS $
? Define # of simulations
CALC ; SN = 10 $
? VALUE FOR B
CALC ; TB2 = 1/SQR(2) $
? INITIAL VALUE FOR BIAS BY MSE, PROBIT AND LOGIT
CALC ; BIASMB2 = 0; BIASPB2 = 0 $
? BEGIN THE PROCEDURE
PROCEDURE
CREATE ; X2 = RNN(1,1) ; E = RNN(0,1) $
CREATE ; YS = (1/SQR(2)) + (1/SQR(2))*X2 + E $
CREATE ; Y = YS>0 $
NAMELIST ; X = ONE,X2 $
? MSE
MSCORE ; LHS=Y ; RHS=X $
CALC ; BIASMB2 = BIASMB2 + (B(2,1)-TB2) $
? PROBIT
PROBIT ; LHS=Y ; RHS=X $
CALC ; BIASPB2 = BIASPB2 + (B(2,1)-TB2) $
ENDPROCEDURE
EXECUTE ; SILENT ; I = 1, SN $
CALC ; LIST
; BIASM = BIASMB2/SN
; BIASP = BIASPB2/SN $
[EXERCISE] Run the program with SN = 100. Which estimator has smaller bias? Changing
SS = 50, 100 and 1000, see how the biases of MSE and Probit estimates change.
Predicted ------ -------------------- + ----- Actual 0 1 2 3 | Total ------ -------------------- + ----- 0 194 3 0 0 | 197 1 4 25 6 0 | 35 2 0 5 8 6 | 19 3 0 0 4 245 | 249 ------ -------------------- + ----- Total 198 33 18 251 | 500
Program for Ordered Probit with HET: (ORD_PROB.LIM)
NAMELIST ; X = ONE,X1,X2 $
ORDERED ; LHS=Y ; RHS=X ; HET ; RH2 = X1,x2 ; MARGIN ; PAR $
Output:
| Ordered Probit Model | | Maximum Likelihood Estimates | | Dependent variable Y | | Weighting variable ONE | | Number of observations 500 | | Iterations completed 21 | | Log likelihood function -61.69838 | | Restricted log likelihood -512.2856 | | Chi-squared 901.1745 | | Degrees of freedom 4 | | Significance level .0000000 | | Cell frequencies for outcomes | | Y Count Freq Y Count Freq Y Count Freq | | 0 197 .394 1 35 .070 2 19 .038 | | 3 249 .498 | | Terms 4 to 5 are for variance. | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Index function for probability Constant 1.952765793 .50647697 3.856. X1 2.202009071 .42735794 5.153 .0000. X2 .5724646749 .13028472 4.394 .0000. Variance function X1 -.3920695036E-01 .15416593 -.254 .7993. X2 .2509306915E-01 .47567677E-01 .528 .5978. Threshold parameters for index Mu( 1) 3.507495686 .81328128 4.313. Mu( 2) 5.161587990 1.1134873 4.636. +------------------------------------------------------+ | Marginal Effects for OrdProbt | +----------+----------+----------+----------+----------+ | Variable | Y=0 | Y=1 | Y=2 | Y=3 | +----------+----------+----------+----------+----------+ | ONE | .0000 | -.5186 | -.0741 | .5928 | | X1 | .0000 | -.5848 | -.0836 | .6684 | | X2 | .0000 | -.1520 | -.0217 | .1738 | | X1 | .0001 | .4693 | -.9134 | .4439 | | X2 | .0002 | .5292 | -1.0300 | .5006 | +----------+----------+----------+----------+----------+
Frequencies of actual & predicted outcomes Predicted outcome has maximum probability. Predicted ------ -------------------- + ----- Actual 0 __1 2 3 | Total ------ -------------------- + ----- 0 194 3 0 0 | 197 1 4 25 6 0 | 35 2 0 5 8 6 | 19 3 0 0 4 245 | 249 ------ -------------------- + ----- Total 198 33 18 251 | 500
[EXERCISE]
1) Use ORD_DATA.DB. Test for the existence of HET by Wald, LR and LM.
2) Make a program which computes the marginal effects of X1 on Pr(y=1) at the sample
means of X1 and X2.
MULTINOMIAL LOGIT
Example: (MW_MLM.LIM)
? Creating variable for occupation
? OCC = 0, if service; = 1, if white; = 2, if blue.
CREATE ; OCC = OCCW + 2*OCCB $
? Choose employed only
REJECT; EMP = 0 $
? Do MLM
? Coefficients for OCC = 0 are set to zeros.
NAMELIST; X = ONE,ED,URB,MINOR,LOFINC $
LOGIT ; LHS = OCC ; RHS = X ; MARGIN $
? MLM with restriction b_1 = b_
CALC ; K = COL(X) $
LOGIT ; LHS = OCC ; RHS = X
; RST = K_B,K_B $
SAMPLE ; ALL $
Predicted ------ --------------- + ----- Actual 0 1 2 | Total ------ --------------- + ----- 0 33 131 24 | 188 1 14 557 12 | 583 2 27 85 40 | 152 ------ --------------- + ----- Total 74 773 76 | 923 Normal exit from iterations. Exit status=0. +---------------------------------------------+ | Multinomial Logit Model | | Maximum Likelihood Estimates | | Dependent variable OCC | | Weighting variable ONE | | Number of observations 923 | | Iterations completed 5 | | Log likelihood function -930.7384 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Characteristics in numerator of Prob[Y = 1] Constant -2.246577102 1.4168164 -1.586. ED .2945460414 .44213261E-01 6.662 .0000 12. URB -.6619168682E-01 .19853983 -.333 .7388. MINOR -.7559059112 .18812078 -4.018 .0001. LOFINC -.3209143823E-01 .14166104 -.227 .8208 9. Characteristics in numerator of Prob[Y = 2] Constant -2.246577102 1.4168164 -1.586. ED .2945460414 .44213261E-01 6.662 .0000 12. URB -.6619168682E-01 .19853983 -.333 .7388. MINOR -.7559059112 .18812078 -4.018 .0001. LOFINC -.3209143823E-01 .14166104 -.227 .8208 9. Frequencies of actual & predicted outcomes Predicted outcome has maximum probability. Predicted ------ --------------- + ----- Actual 0 1 2 | Total ------ --------------- + ----- 0 50 138 0 | 188 1 16 567 0 | 583 2 48 104 0 | 152 ------ --------------- + ----- Total 114 809 0 | 923
[Exercise] Use MWPSID82.DB. Do MLM for:
LHS = OCC
RHS = ONE, ED,URB,MINOR,LOFINC,AGE,EXP,KIDS5.
1) Test Ho: Each women is equally likely to be a white- or blue-collar worker. Use LM, LR
and Wald.
2) Estimate the probability of being a white collar at sample means of regressors.
BIVARIATE PROBIT MODEL
Consider the following model: (same as in the class)
Y1*^ = 11 + 12 X12 + 13 X
Y
= 21 + 22 X22 + 23 X
Y1 = 1 IF Y1*^ >= 0; Y1 = 0, OTHERWISE
Y2 = 1 IF Y2*^ >= 0; Y2 = 0, OTHERWISE
Full Observability:
NAMELIST ; X1 = ONE,X12,X
; X2 = ONE,X22,X23 $
? CREATE INITIAL VALUES FOR BIVARIATE PROBIT
PROBIT ; LHS = Y1 ; RHS = X1 $
MATRIX ; BT = B $
PROBIT ; LHS = Y2 ; RHS = X2 $
MATRIX ; BP = B $
? MLE FOR FULL OBSERVABILITY MODEL
BIVA ; LHS = Y1,Y2 ; RH1 = X1 ; RH2 = X
; START = BT,BP,
; TLF = 0.00001 ; TLB = 0.00001 ; TLG = 0.
; MAXIT = 1000
; PAR $
COMMENT: The first part of the program creates initial values for the bivariate Probit. In
BIVA command, you have to specify the initial values using Subcommand, "START = ...". If
you omit "PAR", LIMDEP store the estimates of 's and Separately. is stored as a scaler in the
name of "RHO". This is not good when you want to test some hypotheses using all estimates. If
you use "PAR", all estimates of are are stored in the matrix, B, and covariance matrix of all the
estimated parameters in VARB. It is better idea to use "PAR". Whether you use "PAR" or not,
is stored as a scaler.
Censored Probit
Y2 is observed only if Y1 = 1.
NAMELIST ; X1 = ONE,X12,X
; X2 = ONE,X22,X23 $
