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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).

Thanks a lot in advance.

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  • $\begingroup$ You are pooling multiple years of films but you only have one revenue value per film, one budget value per film, and one critical sentiment value per film, right? How can critical sentiment change across multiple years for the same film? Are there any variables (independent or dependent) that have multiple values per film (one per year)? $\endgroup$ – AlexK Apr 1 at 8:16
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I am not sure if I understand your research question correctly, but you may be trying to determine if the effect of critical reception on a film's revenue changes over time. That means you only have one observation per film with its revenue and film-specific control variable values (including year of release and single critical reception value) saved in multiple variables. In that case, this is the model equation you should have:

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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.

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    $\begingroup$ Yes, I’m trying to determine if the effect of critical sentiment in 2016 (for example) was larger than in the previous years. Your answer makes perfect sense, thanks a lot! $\endgroup$ – Gerdium Apr 2 at 17:40

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