PROBLEM 23: INSTRUMENTAL VARIABLES

OBJECT OF THE PROBLEM

To run a model using instrumental variables.

INTRODUCTION

Here is an example of the use of instrumental

variables. He uses information from one industry to create an

instrument to be used in analyzing a second industry. In this

case he takes the ratio of money wages to product price for the

knitting-mill product industry and uses it to analyze the

furniture manufacturing industry. We are satisfied that wages

in the knitting industry are unrelated to measurement errors in

the furniture industry, but are related to wages in the furniture

industry.

PROBLEM PROGRAM

The following program can be used for the problem:

//PROB23 JOB (AF,A699),yourname,REGION=4096K,TIME=1

/*OPENBIN

//S1 EXEC SAS,WORK=100

//SYSIN DD *

DATA LORENZ; INPUT FW FP LVRATIO KP KW;

X=FW/FP; X=LOG(X);

Y=(1/LVRATIO)*(1/FP);

Y=LOG(Y);

ZSTAR=KW/KP;

ZSTAR=LOG(ZSTAR);

CARDS;

3515 1.0000 .1706 1.0000 2698

2668 1.5470 .2385 1.4891 2260

1834 .9482 .3678 1.0346 1548

1713 .8195 .3857 .7358 1487

1288 .8941 .5040 .7713 1169

1342 .9437 .5228 .8990 1021

1078 .6646 .6291 .6030 802

738 1.8260 .7200 2.2570 845

448 1.4590 .9415 .9720 364

471 1.7580 .9017 1.2458 546

464 2.2300 1.0863 1.3901 523

PROC MEANS;VAR X ZSTAR;

OUTPUT OUT=WORKERS MEAN=MX MZSTAR;

PROC PRINT DATA=LORENZ;

DATA CRAYPO; SET WORKERS;

DO I=1 TO 11; OUTPUT; END;

DATA CALC; MERGE LORENZ CRAYPO;

Z=ZSTAR*MX/MZSTAR;

YSTAR=Z*Y; XSTAR=X*Z;

PROC PRINT DATA=CALC;

PROC REG DATA=CALC; MODEL Y=X;

PROC REG DATA=CALC; MODEL YSTAR=Z XSTAR/NOINT;

//

DISCUSSION OF THE PROGRAM

Between the first DATA statement and the CARDS statement we create the variables X, Y, AND Z* used by Kmenta. Using PROC MEANS we then calculate the mean of X and Z* and output them to a data set called WORKERS. We need the means in order to construct our instrumental variable later in the program. Beginning with data step CRAYPO we calculate our instrumental variable Z. First we use a DO, OUTPUT, and END statement to create a column of mean observations for X and ZSTAR. This is needed to transform the data. We transform X and Y by multiplying them by Z. Z is derived using ZSTAR and the means of X and ZSTAR.

We then run two models in REG. The first model represents

the original equation. The second is the instrumental variables

model. Note that Z takes the place of the intercept in the second

model.

INSTRUCTIONS FOR WRITE-UP

Give an intuitive and econometrics notation explanation of each step of the program, and an intuitive explanation of what the problem is trying to accomplish. Write down the estimated models (original model and instrumental variable model). Analyze them in terms of t and F-statistic, R-square, etc. Give an intuitive explanation of each model. Label all output. read page 356 in kmenta and compare your results to his. Label the data by nation on the two PROC PRINT output pages. Under what circumstances is Kmenta's technique valid? In general, what properties does the OLS estimators have and what properties does the OLS instrumental variable estimators have?