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We want to estimate the effect of crises on a country's unemployment rate and distinguish the strength of this effect according to the debt level in a country (i.e. via the interaction effect crisis x debt level). We also control for country fixed effects and time fixed effects and a bunch of control variables.

However, we have the problem that the crises a) probably have a delayed effect on the unemployment and b) that the crises themselves may last for a longer period of time. We are planning a dynamic panel model. How do we need to specify this in order to address the two problems mentioned above? Is it sufficient to include the lags of the crises in the model?

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An autoregressive distributed lag (ADL) model, with 1+ lags of both unemployment rate and crisis should be able to estimate both short and long run effects of crisis on unemployment. Beck and Katz (2011) is a good primer on this: https://doi.org/10.1146/annurev-polisci-071510-103222. That's issue (a).

Issue (b) seems like a measurement issue: if crises last for several years, then that should be reflected in how they are measured across time.

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