Econometrics

Econometrics **Tables 7 and 8 is attached.** Let yct be the labor force participation rate of married, non-Hispanic females in city c in year t . Let commute ct be the average commute time in year t and city c and let unemp ct be the male unemployment rate in year t and city c . Table 7 from Black, Kolesnikova, and Taylor (2014) in the attached screenshot shows the results of running Ordinary Least Square using a cross-section (with t =1990) for the regression model y ct = β 0 + β commute *  commute ct + β unemp  * unemp ct + (Delta) u ct Table 8 shows the results a regression model that uses differences in the 1980 and 1990 observations for each city, ∆y ct = β 0 + β commute *   ∆commute ct + β unemp  *  ∆ unemp ct + ∆ u ct

(a)  Let ξ c t be a random, idiosyncratic effect that is uncorrelated with everything. Let   ξ c  be a city-specific effect that is correlated with commute times and unemployment but that is constant over time. (One could think of ξ c  being an omitted variable that measures local traditions of good governance, for example.) Suppose the error term u c  is a combination of both effects, u ct = ξ c + ξ ct . Are the results of cross section OLS regression reported in table7 in unbiased? Why or why not?

(b) Continue assuming the error term  u ct is a combination of both effects, u ct = ξ c + ξ ct  as described previously. Are the results of difference-in-differences regression reported in table8 unbiased? Why or why not?

(c) Continue assuming the error term uct is a combination of both effects, u ct = ξ c + ξ ct described previously. How large must the magnitude of any bias in tables 7 and 8 be?

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