Best Validation Tests for PPMLHDFE Analysis?

[Alexis Laub]

I am conducting a PPMLHDFE analysis with fixed effects for country and year to examine the impact of renewable energy policies on non-hydro renewable electricity generation. My dataset consists of 120 countries from 2011 to 2020and, my dependent variable is the share of non-hydro renewable electricity generation (percentage of total electricity production).

So far, I have applied the following validation checks:

• RESET test (to check functional form misspecification)
• Correlation matrix (all values are below 0.75, no obvious multicollinearity issues)
• Placebo test (successful, indicating that policy variables are relevant)
• Multiway clustering – Standard errors clustered at both country and year levels.

Are there any additional robustness checks or diagnostic tests that would be useful for validating my results? I have considered tests for heteroskedasticity, endogeneity, and multicollinearity, but I am unsure which are best suited for PPMLHDFE models.

Would a White test or VIF test be applicable in this context, or are there better alternatives? Also, are there specific tests for detecting endogeneity in a PPML setting?

Any recommendations or insights would be greatly appreciated!

[Joao Santos Silva]

Dear Alexis Laub,

There is no need to test of heteroskedasticity because models for that kind of that are inherently heteroskedastic; that is why ppml and ppmlhdfe by default report robust standard errors. Likewise, there are no tests for collinearity because any economics dataset will have collinearity. Endogeneity can be tested if you have an instruments, but the value of the test will depend on the validity of the instruments, which is something that cannot be tested. Therefore, I suggest that you do not worry about those, at least in this context.

Best wishes,

Joao

[Alexis Laub]

Joao Santos Silva Thank you for your insights! That makes sense, and I appreciate the clarification. So, just to confirm—are you saying that further tests are unnecessary and that the model, as it stands, is already robust enough?

[Nick Cox]

The idea of testing every possible complication is partly cultural. The more you test, the more likely you are to find something not ideal and what do you do then?

How well does your model work? Is there a better model lurking nearby that would work better for your purpose and your data? are easy to ask and much harder to answer.

I can't see that #1 gives anyone scope to comment by way of declaring your model good enough or not.

[Joao Santos Silva]

Dear

Like Nick said, the idea of testing against any possible alternative is partly cultural and it has a lot to do with how econometrics/statistics is taught. But I think there is also a psychological aspect to it: people test against every possible alternative because they get comfort from the fact that the model "passes" the tests and are left with the misleading impression that they have found the "true model". In your case, you are using a rather robust approach and the validity of the results depends on the correct functional form and on valid standard errors. If the model passes the RESET, the exponential functional form is probably adequate. So the main threat to the validity of your results is that you may not be using valid standard errors. So, focus on thinking about that and, in any case, be cautious when you make inference.

Best wishes,

Joao

[Alexis Laub]

That makes sense.

However, I have a relatively low number of year clusters (10 years) in my panel. Given this, would clustering by both country and year still be appropriate, or could this lead to unreliable standard errors? Would it be better to cluster only by country in this case, or should I consider alternative approaches?

I’d appreciate any insights on this!

[Joao Santos Silva]

Dear Alexis Laub,

Clustering is a bit of an art, so you will have to be careful about that. Anyway, 10 clusters is really too few to be comfortable.

Best wishes,

Joao