Consider the time and entity fixed effect model with a single explanatory variable $$Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } X _ { i t } + \gamma _ { 2 } D 2 _ { i } + \ldots + \gamma _ { n } D n _ { i } + \delta _ { 2 } B 2 _ { t } + \ldots + \delta _ { T } B T _ { t } + u _ { i t } ,$$ Assume that you had estimated the above equation by OLS. Typically the coefficients for the entity and time binary variables are not reported. Can you think of situations where the pattern of these coefficients might be of interest? What could you do, for example, if you had a strong theoretical justification for believing that a few macroeconomic variables had an effect on $Y _ { i t }$ ?

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The Answer of Consider the time and entity fixed effect model with a single explanatory variable $$Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } X _ { i t } + \gamma _ { 2 } D 2 _ { i } + \ldots + \gamma _ { n } D n _ { i } + \delta _ { 2 } B 2 _ { t } + \ldots + \delta _ { T } B T _ { t } + u _ { i t } ,$$ Assume that you had estimated the above equation by OLS. Typically the coefficients for the entity and time binary variables are not reported. Can you think of situations where the pattern of these coefficients might be of interest? What could you do, for example, if you had a strong theoretical justification for believing that a few macroeconomic variables had an effect on $Y _ { i t }$ ?

Consider the Time and Entity Fixed Effect Model with a Single