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The file PENSION contains information on participant-directed pension plans for U.S. workers. Someof the observations are for couples within the same family, so this data set constitutes a small clustersample (with cluster sizes of two).(i) Ignoring the clustering by family, use OLS to estimate the model$p c t s t c k=\beta_{0}+\beta_{1}$ choice $+\beta_{2}$ prfshr $+\beta_{3}$ female $+\beta_{4} a g e$$+\beta_{5} e d u c+\beta_{6} f i n c 25+\beta_{7} f i n c 35+\beta_{8} f i n c 50+\beta_{9} f i n c 75$$+\beta_{10} f i n c 100+\beta_{11} f i n c l 0 l+\beta_{12}$ wealth $89+\beta_{13} s t c k i n 89$$+\beta_{14} i r a i n 89+u$where the variables are defined in the data set. The variable of most interest is choice, which is adummy variable equal to one if the worker has a choice in how to allocate pension funds amongdifferent investments. What is the estimated effect of choice? Is it statistically significant?(ii) Are the income, wealth, stock holding, and IRA holding control variables important? Explain.(iii) Determine how many different families there are in the data set.(iv) Now, obtain the standard errors for OLS that are robust to cluster correlation within a family.Do they differ much from the usual OLS standard errors? Are you surprised?(v) Estimate the equation by differencing across only the spouses within a family. Why do theexplanatory variables asked about in part (ii) drop out in the first-differenced estimation?(vi) Are any of the remaining explanatory variables in part (v) significant? Are you surprised?

(i) see video (ii) no (iii) 171 families (iv) cluster robust se of choice is the same as usual ols se (v) see video (vi) none

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Chapter 14

Advanced Panel Data Methods

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part one. These are the old ls Estimates we have 194 observations and our square is 0.1. Investment choice is associated with about 11.7% points. More instructs. The T statistic is only 0.1 point eight. So this variable is marginal. Marginally significant. Part two. The variables income, wealth, stockholding and I are a are not very important. The F test for joint significance is one point Oh three. There are nine n 179 degrees of freedom, and the P value of this test is 1790.42 So we cannot reject the null hypothesis that these variables are jointly insignificant. Also, when we drop, yeah, is variable. From the estimation, we find that the estimate on investment choice change little. It only falls to yeah, 11.15 In the sample, there are 171 different families. Our store, the cluster robust standard barrel for variable choice is 6.2, which is very close to the usual L s standard error. This is not very surprising because at least 171 of the 190 for observations can be assumed independent of one another. Probably the explanatory variables adequately capture the within family correlation. Part five. We will use the data from 23 families with spouse, and we were in difference within these families. We get these results. Okay, We don't have estimates on the income and wealth variables and the stock and I are a because these variables are defined at the family level. So they are the same for the husband and wife, and they are dropped out from there. Regression Part six. As you can see here, none of the explanatory variables is significant. And this is not surprising because we have a very small observation. Small, simple. And we are removing much of the variation in the explanatory variables by using within family differences.

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