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I am doing a difference-in-difference analysis of an event that affected several states in the US. I am interested to understand the effects of this event on state-level unemployment rates. I have state level data on demographics for several years before and after this event. My question is what covariates should I include if I am estimating equation of the following form:

$$ \mbox{unempRate}_{jt} = \gamma_j + \alpha_t + \beta D_{jt} + \delta X_{jt} + \epsilon_{jt} $$

where $\gamma_j$ are state-fixed effects; $\alpha_t$ are time fixed effects; $D_{jt}$ are dummies - 1 if state $j$ is affected at time $t$, and 0 otherwise; and $X_{jt}$ are time-varying state level covariates. Coefficient of interest is $\beta$.

So far, I have included population and average household income at the state level.

What more covariates can I include? How does one decide which covariates to include in a setting like this? What is the guiding philosophy?

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  • $\begingroup$ Covariates should be pre-determined $\endgroup$
    – Papayapap
    Commented Feb 2, 2023 at 23:00
  • $\begingroup$ @Papayapap, could you clarify with some details? How does one 'pre-determine'? $\endgroup$
    – funcard
    Commented Feb 3, 2023 at 2:00
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    $\begingroup$ They should not be affected by the treatment, either measured before or invariant. $\endgroup$
    – Papayapap
    Commented Feb 3, 2023 at 9:05
  • $\begingroup$ Average household income could easily be argued to be affected by the treatment under the assumption that the treatment has a non-zero effect on the unemployment rate. However, variables describing the quality of the labour force could be a suggestion. Perhaps, something like average educational level, shares of education groups, degree of urbanization/labour market access variables (area of land per citizens with a road density higher than x ... or something like that). Immigrants can have a hard time achieving full labour market integration so share of certain type of immigrants. $\endgroup$
    – Jesper Hybel
    Commented Feb 3, 2023 at 23:48
  • $\begingroup$ @JesperHybel, thanks. What's the general philosophy that guides the choice of a particular covariate? Trying to find a reference on this question, but no luck so far. $\endgroup$
    – funcard
    Commented Feb 3, 2023 at 23:55

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Understanding back-door criterion via Directed Acyclic Graphs (http://causality.cs.ucla.edu/blog/index.php/category/back-door-criterion/) helped me understand how to add covariates on my econometric model. While studying the material, I also found a wonderful website that tells which variables to condition on and how to test whether the DAG you draw is correct: http://www.dagitty.net/dags.html

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