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  • DID model with multiple categories

    Dear STATA experts,

    I am writing my thesis using firm-level panel data ranging from 2007 to 2016.
    Here is the simple representation of my dataset.
    The firms fall into 24 industry categories.

    Code:
    year    id  industry   growth     X1       X2    recession
    2007    1      10      0.22      0.42      112      0
    2008    1      10      0.25      0.22      132      0
    2009    1      10      0.21      0.65      128      0
    2010    1      10      0.28      0.56      122      0
    2011    1      10      0.19      0.47      128      1
    2012    1      10      0.18      0.32      129      1
    2013    1      10      0.18      0.65      132      1
    2014    1      10      0.16      0.55      127      1
    2015    1      10      0.19      0.45      122      1
    2016    1      10      0.18      0.42      128      1
    2007    2      11      0.22      0.21      501      0
    2008    2      11      0.24      0.22      499      0
    2009    2      11      0.29      0.24      489      0
    2010    2      11      0.22      0.26      468      0
    2011    2      11      0.24      0.20      496      1
    2012    2      11      0.02      0.27      497      1
    2013    2      11      0.02      0.18      501      1
    2014    2      11      0.10      0.19      458      1
    2015    2      11      0.13      0.21      456      1
    2016    2      11      0.21      0.22      432      1
    I would like to examine the effect of explanatory variables X1 and X2 on the growth of firms.
    I can identify with my data that the year 2011 to 2016 is a recession period so I formulated a recession dummy.
    The purpose of my study is to figure out if the explanatory variable X2 has a significant positive or negative effect, especially during the recession period.
    Therefore, I performed DID(difference-in-difference) estimation by using an interaction variable between X2 and the recession dummy under the framework of the panel fixed effect model.

    I formulated the interaction term 'X2_recession' by manually multiplying X2 to the recession dummy variable and I also generated industry and year dummy variables.
    I estimated two models, one with a recession dummy, and the other with individual year dummies.
    I understand that industry dummies are time-invariant for most cases and therefore not estimated under the fixed effect model, but I still included them since I found some researches with firm-level fixed effects model considered industry dummies.
    The following is the code I used and I got coefficients for industry dummies even though all of them were not significant.

    Code:
    xtreg growth X1 X2 X2_recession recession industry_* fe
    xtreg growth X1 X2 X2_recession year_* industry_*, fe
    I presented the result to my dissertation committee and got a comment to analyze the interaction term for each industry separately.
    Therefore, what I am trying to do is to adopt interaction terms 'X2_recession_industry*' between three variables: X2, the recession dummy, and the industry dummies.
    I manually multiplied X2 to 24 industry dummies, creating 'X2_industry*', and again, multiplied recession dummy variable to this, creating 'X2_recession_industry*'.
    (Therefore, I have X2_industry1, X2_industry2, X2_industry3, X2_industry4, X2_industry5, X2_industry6, ... , X2_industry24
    and X2_recession_industry1, X2_recession_industry2, X2_recession_industry3, X2_recession_industry4, X2_recession_industry5, X2_recession_industry6, ... , X2_recession_industry24.)


    The following is the code I am trying to estimate.
    Code:
    xtreg growth X1 X2_industry* X2_recession_industry* recession industry_*, fe
    xtreg growth X1 X2_industry* X2_recession_industry* year_* industry_*, fe
    For X2_industry* and X2_recession_industry*, all industry categories -24- are considered.

    Most examples I found on DID estimation deal with binary variables only, and I think this may be different from my case.
    Here are some questions about my models.

    1) (main curiosity) In my revised model, is it okay to include all -24- interaction terms for X2_industry* and X2_recession_industry*? (no reference level?)
    When I tried to estimate with all - 24 - interaction variables, STATA gave me coefficients for all the interaction terms.
    However, it seems like one needs to include n-1 interaction terms when the interaction terms are the multiplication of binary variables.
    If I can include all -24- interaction terms, how do I interpret the result without a base level?

    2) Is it wise to include industry dummies just because preceding studies included them? (and also because they are not excluded for collinearity anyway?)
    I am still doubting what I have done.

    3) Should I include interaction term for all explanatory variables including X1 because a recession is a macroeconomic shock that might affect all economic variables?
    The additional effect of X1 during the recession is not my interest and I don't want my model to become too complicated.
    I found some literature that considers interaction term between a macro shock and all explanatory variables, but I want to know if it is a necessity for the model's integrity.

    Any comment will be greatly appreciated.

    Thank you in advance.
    Hyeseon
    Last edited by Hyeseon Shin; 17 May 2019, 10:05.
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