2008 exam summary

# 2008 exam summary - What are the distinctive features of...

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What are the distinctive features of panel data compared to cross sectional data Panel data observational units or people are followed over time. They allow the study of individual units rather than the aggregative approach used by cross sectional data. Panel data allows us to control for unobserved individual effect (omitted variables) that are constant. Also, in panel data, you can’t treat the set of observations in each time period as being an independent random sample which you can after pooling independent cross sections. Partial effect of bdrms on price Change in price/ change in bedrooms β0 +β1 area+β2bdrms+β3 area×bdrms+u therefore partial effect is B2bdrms +B3area What is a P value? If the P value was 0.022, should you reject the null at 1%? The p-value is the minimum significance level for which the null hypothesis would be rejected. It is obtained by assuming the test stat corresponds to the critical value (so it is on the boundary of the rejection region) and then finding the significance level which implies that critical value. If the p-value=0.022 the null would NOT be rejected at the 1% level of significance. In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true Desirable properties of a proxy variable and suggest a proxy for family income Properties of a good proxy variable: (i) the error term in the model is uncorrelated with all the included explanatory variables and the proxy - and (ii) the expected value of faminc conditional on the proxy is not related to the other explanatory variables (eg. E[faminc|cigs, proxy] = E[faminc|proxy]). Potential proxies would include family wealth, house value, parent’s occupation or education, (or measures for low income e.g. unemployment status, poverty indicators; or measures of high income).Requires discussion of a variable correlated with family income. What is meant by the sampling distribution of an estimator? What is known about the sampling distribution of the OLS estimator under the first 4 Gauss Markov assumptions? The estimator (e.g. ˆβ ) used with one random sample of data (say of size n) drawn from the population will provide an estimate (e.g. 0.078) of the underlying population parameter (e.g. β). A new random sample (of size n) will lead to a similar, though likely different, estimated value due to the new draw of errors in the sample. Over many independent samples the estimator will generate a distribution over the range of possible values for the estimate. This is the ‘sampling distribution’ of the estimator. The statistical properties of the estimator relate to the characteristics (.e.g the mean, variance, shape) of the sampling distribution. Under the first 4 GM assumptions, the expected value of the OLS estimator is equal to the population parameter (i.e. OLS is unbiased). That is, the mean of the sampling distribution is equal to the true value of the population parameter.

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2008 exam summary - What are the distinctive features of...

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