# Correct Equation for Pooled OLS Regression (with Time Dummies and Interaction Terms)

I have a question regarding a pooled OLS regression. Basically, I’m not sure I’m writing out the equation properly.

The data is on feature films released between 2006 and 2016 (11 years); box office revenue is the dependent variable. What I’m interested in is the coefficient of the variable CritSentiment and if it increases over time (CritSentiment is a binary variable that takes the value 1 if critical reception for a film is positive and 0 otherwise).

So aside from a bunch of film-specific controls (such as production budget), I’m including yearly time dummies to control for any trend-effects, as well as interaction terms between these time dummies and CritSentiment. The coefficients of these interaction terms should measure the estimated difference between the coefficient of CritSentiment in year t and the coefficient in the (omitted) base year.

$$\textit{Revenue}_{it} = \alpha + \beta_1 \textit{Budget}_{it} + \ ... \ + \beta_{15} CritSentiment_{it} \ + \sum_{t=1}^{11-1} \gamma_t Year_t \ + \sum_{t=1}^{11-1} \delta_{t} Year_{it} CritSentiment_{it} \ + \epsilon_{it}$$

What I’m unsure about is basically just whether the above equation correctly assigns the i and t subscripts, which I find a bit confusing (especially when it comes to the intercept and interaction terms).

You should not have both i and t subscripts for any film-specific variables if you only have one set of values per film. The i subscript is used on all film-related variables, including year of release. I included t superscripts to make it clear that there are multiple Year variables. And if you are not doing a fixed effects model (film fixed effects), there should not be any subscript on the intercept term.