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Unformatted text preview: Econ 103 UCLA, Fall 2010 Problem Set 4 Solutions Part 1: True or False and explain briefly why. 1. The difference between an unbalanced and a balanced panel is that an unbalanced panel contains missing observations for at least one time period or one entity. TRUE By definition, a balanced panel is when we observe all our variables of interest for all entities and all time periods, and an unbalanced panel is when we dont. 2. In the Fixed Effects regression model the slope coefficients are allowed to differ across entities, but the intercept is fixed (remains unchanged). FALSE It is the intercept that is entity-specific, while the slope is common to all enti- ties. 3. In the Fixed Effects regression model, using ( n- 1) binary variables for the entities, the coefficient of the binary variable indicates the difference in fixed effects between the i th and the excluded entity. TRUE The intercept can be thought of as the fixed effect of the excluded entity, and the effect of the i th entity is the constant plus the coefficient on Di . The coefficient itself tells us the difference between being entity i and the excluded entity. 4. Corr ( u it ,u is | X it ,X is , i ) = 0 for t 6 = s , means that conditional on the regressors, the errors are uncorrelated over time. TRUE This means that we assume away autocorrelation. 5. If you included both time and entity fixed effects in the regression model which includes a constant, then you must exclude one of the entity binary variables and one of the time binary variables for the OLS estimator to exist. TRUE Else we would have perfect multicollinearity. 6. Consider estimating the effect of the beer tax on the fatality rate, using time and state fixed effect for the Northeast Region of the United States (Maine, Vermont, New Hampshire, Massachusetts, Connecticut and Rhode Island) for the period 1991-2001. If Beer Tax is the only explanatory variable, the number of coefficients you need to estimate, excluding the constant, is 18. FALSE 1 constant + 5 state effects + 10 time effects + 1 Beer Tax = 17 coefficients to be estimated 7. Consider the regression example from your textbook, which estimates the effect of beer taxes on fatality rates across the 48 contiguous U.S. states. If beer taxes were set nationally by the federal government rather than by the states, then it would not make sense to use state fixed effect. FALSE We could not put time fixed effects, because those would absorb the effect of the beer tax. 1 Econ 103 UCLA, Fall 2010 8. When you add state fixed effects to a simple regression model for U.S. states over a certain time period, and the regression R 2 increases significantly, then it is safe to assume that state fixed effects account for a large amount of the variation in the data....
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