PS2 - Solutions problem set 2 Econometrics Master EAP PDF

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Solutions problem set 2 Econometrics Master EAP...

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Problem Set #2 Empirical Applications and Policies (EAP) Econometrics ´ Oscar Mart´ınez P´erez

Exercise 1 Use PHILLIPS.RAW data set (Wooldridge, 2006; static Phillips curve example) to analyze the following model: inf lationt = β1 + β2 unemploymentt + ut 1. Estimate the equation by OLS. clear all use PHILLIPS.DTA, clear gen periodm = _n + 47 tsset periodm, yearly reg inf unem

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The resulting ecuation is: inf\ lationt = 1.42 + 0.46unemploymentt 2. To determine whether there is a tradeoff, on average, between unemployment and inflation, we can test H0 : β2 ≥ 0 against Ha : β2 < 0. Carry out this test. The critical value for a t student distribution with 48 degrees of freedom is 1.67 and our statistic t is 1.62. As we are not in the rejection area, we can say that our β2 is grater or equal to 0. 3. Test autocorrelation process in ut . bgodfrey, lags(1 2 3)

dwstat

To determine if there is autocorrelation I have run two tests. The first one is the Breush-Godfrey test, wich tests in the autoregressive model of order q (I have tested for three lags) the following null: H0 : ρ1 = 0, ρ2 = 0, ρ3 = 0 The second one is the Durbin-Watson test. What it test is if in a AR1 proces of ut, the coeficient is equal to 0 or not. The results of the two tests are the same, we can conclude at 90%, 95% and 99% of confidence that we have autocorrelation in ut1 1 The critical values dL for a positive autocorrelation of the Durbin-Watson test for a sample of aproximately 50 observarions are for 90%, 95% and 99% of confidence 1.32, 1.42 and 1.50 respectively.

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4. Estimate the first equation by Prais-Winsten estimation procedure. Afterwards, test H0 : β2 ≥ 0 against Ha : β2 < 0 and compare your results to outcome obtained in 2. Why do you get this results? prais inf unem

In this case our statistic is negative, so we can conclude wothout calculating anything else that our β2 is statisticalli less than 0 because we reject H0 . In the OLS estimation we have a β2 positive. The economic intuituin says us that the unemployment and the inflation are negatively correlated so it did not make sense. Then we show we have an autocorrelation problem, so solving it with the Prais-Winsten estimation we now have a negative beta. It is basically because with the presence of autocorrelation the estimations of the variances with OLS are biased, we can not do inference and the model will be inefficient.

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Exercise 2 The data in FERTIL2.RAW includes, for women in Botswana during 1988, information on number of children, years of education, age, and religious and economic status variables. 1. Estimate the model childreni = β1 + β2 educi + β3 agei + β4 agei2 + ui . by OLS, and interpret the estimates. In particular, holding age fixed, what is the estimated effect of another year of education on fertility? If 100 women receive another year of education, how many fewer children are they expected to have? clear all use FERTIL2.DTA, clear reg children educ age agesq

As we can see all the variables included in the model are relevant, they are significant at any level. And as expected, the education has a negative impact, it means the more years of education, the less number of children. In particular, if we increase one year the education, it decrease in mean 0.095 the expected number of childrens. It means that if 100 women receive another year of education, 9 fewer children they are expected to have. And for the age we can see that there is a pointin wich having more age does not mean to have more children but less.

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2. Add the binary variables electric, tv, and bicycle to the model and assume these are exogenous. Let as assume educ endogenous. The variable frsthalf is a dummy variable equal to one if the woman was born during the first six months of the year. The variable urban is another dummy variable equal to one if the woman lives in urban area. Test whether frsthalf and urban are reasonable IV candidates for educ.

reg educ age agesq frsthalf urban

test (frsthalf=0) (urban=0)

First we start doing a regression with our variable educ as endogenous, the two instruments to test and all the others exogenous variables. After that we test jointly if the coefficients of our instruments are 0 or not. As we can see we han reject the null hipotesis in wich rhey are 0, so we have two good instruments.

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3. Add the binary variables electric, tv, and bicycle to the model and assume these are exogenous. Estimate the equation by OLS and 2SLS (assuming that educ is endogenous) and compare the estimated coefficients on educ.

reg children age agesq electric tv bicycle educ frsthalf urban

As the variable educ is endogenous and can be explained with our instruments frsthalf and urban the estimation by OLS is not valid. In the case estimated by OLS we have a βeduc = −0.073 and even it is significant, when we stimate the model by 2SLS we can se the difference. In this second case (table at the end of the documet) the βeduc = − 0.23 and also significant but it has a bigger impact on the expected number of childrens.

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ivreg children age agesq electric tv bicycle (educ = frsthalf urban), first

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