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  • Interpreting fixed effects (LSDV and within-estimator)

    Dear all,

    I would like to pose a theoretical question. I am studying the impact of firm dynamics (let's take net entry of firms as an example) on productivity growth at regional level using panel data. I have taken account of fixed effects through LSDV and within-estimator. The first through country dummies, the second accounting for individual effects.

    From a textbook point of view, with these estimators I canceled the fixed effects through de-meaning the X and the Y, on the basis of the country mean in first case or the regional mean in the second.

    My question is when interpreting the coefficients, does this mean that an increase of X from the country/region mean, produce a beta effect on Y. Or, is it to be interpreted as OLS regression: an increase of X produces a beta effect on Y?

    To be precise, I need to confront the peak of a curvilinear relationship of the explanatory variable, and I need to understand if the peak is an absolute value, or rather should be seen as with respect to the country/region mean?


    Thanks to whom will help me.

  • #2
    You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

    Why do you talk about LSDV instead of a simple panel estimator like xtreg? It is problematic to have country and individual effects normally - since individuals don't change country much, they fully account for country fixed effects.

    The within estimate is to be interpreted within - a change in x for panel A has a beta effect on y for panel A. The cross-panel interpretation (firms with higher x will have higher y) is not available in a within estimator since you're not using cross-panel variation in estimating the parameters. The within and between theories and parameters often differ dramatically and for good reason. For example, the between model of housing costs has to do with mortgages and taxes, but the within has to do with variation in heating and repair dependent on the weather. Interpreting within as between is a mistake that was often made in the past (and may still be seen).

    A peak is just a curvilinear relation within if estimated within. There are estimation problems with such models since apparently fixed effects estimators of interactions in panel estimators are not true fixed effects (see Myles , Strategy Science, 2018 or 2019).

    Comment


    • #3
      Thanks for your useful answer, Phil.

      I believe you have misunderstood the estimations conducted. I am looking at regions i that belong to countries j.
      These are the two codes: OLS with fe at country level and within estimator, so having the region as id.

      Code:
      reg gr1y_gva_pw_manual capital_deepening L.ln_gva_pw_manual  ///
      L.ln_patent_stock_ L.edu_tert_share_ ///
      L.hhi_emp_ L.secondary_emp_share L.tertiary_emp_share ///
      L.c.net_growth_biz_non_emp_tot4_#L.c.net_growth_biz_non_emp_tot4_ ///
      L.ln_avg_active_non_emp_ ///
      L.ln_avg_born_non_emp_ ///
       d_country_* d_year_21 d_year_22 d_year_23 d_year_24 d_year_25 ///
      if sample == 1, cluster(id)
      
      *FE churn
      xtreg gr1y_gva_pw_manual capital_deepening L.ln_gva_pw_manual ///
      L.ln_patent_stock_ L.edu_tert_share_ ///
      L.hhi_emp_ L.secondary_emp_share L.tertiary_emp_share ///
      L.c.net_growth_biz_non_emp_tot4_#L.c.net_growth_biz_non_emp_tot4_ ///
      L.ln_avg_born_non_emp_ ///
      L.ln_avg_active_non_emp_ ///
      d_year_21 d_year_22 d_year_23 d_year_24 d_year_25 ///
      if sample == 1, cluster(id) fe
      The first a -reg- with country dummies and the second is, as you suggested, -xtreg- looking at only within variation . May you correct me if I am wrong, but in the first I am looking at variations from country mean, thus accounting for example for governmental policies, interregional infrastructure allowing for a higher variation of data. I am then better able to grasp the underlying variability, while accounting for some fixed effects. The second, as you say, allows only for regional variation from its mean.

      Is there something wrong in my reasoning?

      Comment

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