Tutorial 10 Over the last few years, researchers have puzzled over why so many people default on their mortgage payments. One explanation for this is that people took on too much mortgage debt prior to the financial crisis and are now struggling to meet the interest payments because of deterioration in the economic climate. Investigate whether mortgage default rates are related to mortgage debt using the data contained in the file mortgages.dta. The file contains the average rate of mortgage default (mdefault), and mortgage debt (mdebt) in all U.S. counties. There is also a dummy variable, judicial, that is equal to 1 if the state uses judicial foreclosure laws, 0 if not. Estimate an OLS model with heteroskedasticity-robust standard errors. What do the results tell you? reg mdefault mdebt, robust A 1 unit increase (equal to $10,000) increases mortgage defaults by 0.5 percentage points. People struggle to pay the higher interest rate and choose to default on the mortgage instead. One explanation for higher default rates in some states is that they use judicial foreclosure laws. In such states lenders must go to court to evict defaulters. Often this process takes 8 months during which the borrower effectively lives rent free. Are default rates higher in judicial foreclosure states? reg mdefault mdebt judicial, robust Default rates are 0.34 percentage points higher in judicial foreclosure states. Effect is statistically significant. There seems to be moral hazard among borrowers in these states. Estimate a fixed effects regression using the variables included in question 2. You must first tell STATA the cross-sectional and time variables. xtset countyfipscode year xtreg mdefault mdebt judicial, fe Coefficient magnitude is much bigger than before (2.42 versus 0.51). The fixed effects appear to be capturing some time-invariant omitted variables. These were biasing the OLS estimates downwards. Why is the judicial dummy variable dropped from the estimating equation? It is time invariant and hence captured by the individual fixed effects. Estimate the relationship using a random effects estimator. Comment on the differences with the results obtained from the FE specification. xtreg mdefault mdebt judicial, re Again the coefficient magnitude is much bigger than in the OLS case (1.30 versus 0.51). But the result is quite different from that estimates using the fixed effects estimator. The standard errors are much smaller (because there are fewer variables in the estimating equation) and we are able to include the time-invariant judicial dummy. Which of the estimates are prepared? The FE or RE model? Use a hausman test to investigate. xtreg mdefault mdebt, fe eststo fe_results xtreg mdefault mdebt, re eststo re_results hausman fe_results re_results Have to store the results, hence why we use the eststo command. The p-value is equal to zero (and the chi-2 statistic is huge, much bigger than the critical value) meaning that we reject the null-hypothesis of equality between the FE and RE coefficient estimates. We therefore prefer to use the unbiased FE estimator rather than the more efficient RE model. FE model would also be preferred because the sample was constructed non-randomly.
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