A study attempts to investigate the role of the various determinants of regional Canadian unemployment rates in order to get a better picture of Canadian aggregate unemployment rate behavior

The annual data (1967-1991) is for five regions (Atlantic region, Quebec, Ontario, Prairies, and British Columbia), and four age-gender groups (female and male, adult and young). Focusing on young females, the authors find significant effects for the following variables: the regional relative minimum wage rate (minimum wages divided by average hourly earnings), the regional share of youth in the labor force, the regional share of adult females in the labor force, United States activity shocks (deviations of United States GDP from trend), an indicator of the degree of monetary tightness in Canada, regional union density, and a regional index of unemployment insurance generosity. Explain why the authors only used region fixed effects. How would their specification have to change if they also employed time fixed effects?
What will be an ideal response?

Answer: Since the study used Canada-wide effects (United States activity shocks, and monetary tightness), these are identical for all regions at a point in time. Using time fixed effects in addition to these two variables would have generated perfect multicollinearity among the regressors, and hence the OLS estimator would not exist. An alternative specification would include time fixed effects, but eliminate the two variables which are constant across all regions at a given point in time.