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  • Interrupted time series regression with panel data and fixed effects

    Hi all,

    I am doing a study where I measure the effect of a policy change on a dependent variable.
    I am using an interrupted time series model with panel data and fixed effects. Is it correct to use this general regression: Yt = β0 + β1Tt + β2Xt + β3XtTt + εt and add a year fixed effect to recover the true post-effect? Or should I run this regression without the year fixed effect and only consider β3 for the post-effect?

    Thanks in advance.

  • #2
    Please describe your data.

    1) Why are they panel? What is the other (panel) dimension besides time?
    2) How many panel units are you studying? Home many years are recorded in your data set?
    3) Are there many missing values?
    4) Are you adjusting for effects of other covariates, which may influence the dependent variable as well?

    Thank you.


    • #3
      My data consist of around 5000 European companies. I have obtained data for my variables three years before and 3 years after the policy change. Dimensions are: companyID, year, sector and country.
      I have about 18,000 company-year observations left after eliminating observations for missing data for key independent variables. I have 8 independent variables.


      • #4
        And what is the dependent variable?


        • #5
          Dependent variable is capital expenditures (CAPEX), the independent variables are sales growth, tobin's q, ...


          • #6
            Thank you. Yes, you have enough data to consider a relatively rich model. This model can contain year effects, generally speaking... In my opinion, you would benefit from considering at least two frameworks:

            1] g(Capital Expenditure) = [dummy variables for each year, except for the reference one] + [independent variables, including sector and country dummies] + [selected interactions]

            2] g(Capital Expenditure) = [company random effect] + [dummy variables for each year, except for the reference one] + [independent variables, including sector and country dummies] + [selected interactions],

            where g() is the optimal linear or non-linear transformation... The two frameworks can be compared using AIC or BIC. Once the optimal framework has been identified, the model should be polished via backward stepwise selection... A random intercept for each company (framework 2) is an important feature because heterogeneity over the companies can be explained by geography and sector only partially.


            • #7
              Let me offer a slightly different suggestion to Sergey's. I have a bit of experience with capital expenditure models and a lot of experience with corporate data.

              If what you're really attempting to do is look at how the policy change changed how specific firms invest, then a fixed effects estimator with fixed effects for firm may be the best thing to do. As has been discussed extensively on this listserv, fixed effects have estimation advantages, but perhaps of more importance they are best for understanding within panel changes over time. Sector and country dummies are fine, but they're not nearly as close to what's going on as firm dummies. Firms within sectors obviously vary enormously.

              I assume that the policy intervention applies equally to all firms. You also need to ask if there is something that moderates the influence of the policy change on capital expenditures. If we did not have moderators and we assume the policy intervention applies equally to all firms, then year dummies would probably be good enough. On the other hand, as your equation originally posted seems to suggest the effect of the policy change may depend on firm level variables that vary over time, then you may want to interact your time variable with those firm level variables. In many cases, folks prefer to use year dummies in place of year as a continuous variable – it removes the assumption that the influence of time is linear.

              Some of the issues with your specification will also depend on the norms in your particular discipline. Some disciplines are more accepting of random effects while others are more demanding of fixed effects. Some find firm level fixed effects de rigueur while others are happy with sector or country effects.


              • #8
                Thank you Phil, this is what I was looking for!