Hello! I have a rather general question about my statistical approach - if helpful, I can also post some Stata code I used for this, but I'd like to first make sure whether my approach makes sense.

I'm working on a project replicating the results of Dell, Jones and Olken (2012). The model of interest uses a panel regression (> 100 countries and about 50 years) with country- and year- fixed effects, analyzing the effect of temperature (measured as yearly average) on economic growth. The model includes lags of the explanatory variable temperature, but no lags of the dependent variable growth. The estimator used in Stata is the user-written command "cgmreg" by Cameron, Gelbach and Miller (2011), which applies two-way clustering on the error term.
Temperature is measures in levels, growth is obtained by taking the difference in ln(GDP) from year to year.

I want to analyze the nature of effects found by this empirical specification and evaluate the interpretative claims the authors make in the paper. I'm interested in the following scenarios:

(1) effects of temporary changes in temperature
(2) effects of persistent changes in temperature
-> for both scenarios: are potential effects on growth temporary or persistent?
-> What is the effect when looking at the level (not growth rate) of economic output - is there for example a persistent effect on the level of GDP, even though the effect on the growth rate is only temporary?


I tried to code a little simulation for different temperature scenarios in Stata, using a simplified model of growth and illustrating the effects. But I'd like to simulate different temperature scenarios with the exact empirical model in Dell, Jones and Olken (2012).

I tried this now by (1) estimating the model with the original data, then (2) obtaining fitted values for growth with the "predict" command, and then (3) manipulating the temperature variable (for example adding 1°C for every year starting from year X) and using "predict" again to obtain fitted values for this counterfactual scenario. Asking very bluntly, is this approach valid for comparing different temperature scenarios or am I doing something stupid here?

Apart from that, I'd also like to compare different coefficient (of temperature and its lags) scenarios. I'd like to simulate and illustrate how it looks when for example temperature has an immediate effect on growth, but the cumulated effect (contemporaneous coefficient + all lags) is zero. I tried this once by manipulating the estimates obtained from the original model and data and predicting fitted values with the original data, but the results don't really make sense. As the actually obtained estimates show a persistent negative temperature effect on growth, when manipulating this effect to be zero while keeping all fixed effects, growth basically shoots through the roof exponentially. So I guess this approach doesn't make a lot of sense.

Is there a valid way to simulate the effects of different "coefficient configurations" in this fixed effects panel context?

Thank you for any help!



Sources:

- Dell, Melissa, Benjamin F. Jones, and Benjamin A. Olken. 2012. "Temperature Shocks and Economic Growth: Evidence from the Last Half Century." American Economic Journal: Macroeconomics, 4 (3): 66-95.

- Cameron, A. Colin, Jonah B. Gelbach, and Douglas L. Miller. 2011. “Robust Inference with Multiway Clustering.” Journal of Business and Economic Statistics 29 (2): 238–49.