Econometrics II, first problem set. Note: “Matlab” can be read as “Stata”, or any other software package you like, as long as it allows you to minimize functions of parameters and data, with and without constraints.

1. Obtain the Nerlove data in .xls format from http://fhayashi.fc2web. com/datasets.htm and (a) import it into Matlab (b) import it into Gretl

2. Obtain the Nerlove data in plain text format from my github page at https://github.com/mcreel/Econometrics/blob/master/Examples/Data/ nerlove.data, and import it into Matlab. The Matlab command to read the data is data = importdata(’nerlove.data’); 3. Numerically compute the OLS estimator of the Nerlove model

ln C = β + βQ ln Q + βL ln PL + βF ln PF + βK ln PK + 

(a) using Gretl’s Model->OLS command. Note that the data are given in levels, you need to compute the logarithms. (b) using Matlab’s fminunc to minimize the sum of squared residuals. The important part of this problem is to learn how to minimize a function that depends on both parameters and data. Try to write your function so that it is re-usable, with a different data set. Verify that you get the same results using Gretl and Matlab. 4. For the Nerlove model,

(a) test the joint restrictions of constant returns to scale (βQ = 1) and homogeneity of degree one (βL + βF + βK = 1) using the F test. Use GRETL (Tests->Linear Restrictions in the model window), or any other software you like. Report the p value of the test statistic, and whether or not you reject the restrictions. (b) compute the restricted OLS estimator using Matlab’s fmincon, min- imizing the sum of squared errors subject to the restrictions.

5. Get the Card data set from https://github.com/mcreel/Econometrics/ blob/master/Examples/Data/card.gdt or https://github.com/mcreel/ Econometrics/blob/master/Examples/Data/card.csv, and

1 (a) Use it to replicate Table 2, column 1 of Card’s 1993 working pa- per “Using geographic variation in college proximity to estimate the return to schooling” , National Bureau of Economic Research work- ing paper No. w4483, 1993. (available at http://www.nber.org/ papers/w4483.pdf). Note: the regressors in this specification are ed- ucation, experience, experience squared (divided by 100), and dummy variables for black, smsa, and south. (b) estimate the same model, but treating education, experience, and ex- perience squared as endogenous. Estimate by 2SLS. As instruments for the endogenous variables, use nearc4, age, and age squared. Com- pare the estimated coefficient of education with the results of Card, Table 4, row 1, column 3 (the IV results). Why are the results not exactly the same? (c) compare the OLS and 2SLS results, and give an economic interpre- tation of the results.

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