Interesting paper Jeff! Monte Carlo simulations to explore the robustness of empirical assumptions is a cool technique. After reading Ioannidis, Stanley, and Doucouliagos (2017) on low statistical power in empirical economics, I developed a similar technique to map out power curves for econometric hypothesis tests over a range of sample sizes and error distributions. Within languages like R, it’s quite straight forward to set up a simulated data generating process and see how getting your assumptions wrong can affect your findings.
Would be interested in following up with ordinal explanatory variables as well. Do reasonable transformations of ordinal variables of interest matter? How about controls? How about when ordinal variables are fed into data reduction routines such as PCA or other factor analysis techniques?

Ioannidis, John P. A., T. D. Stanley, and Hristos Doucouliagos. “The Power of Bias in Economics Research.” The Economic Journal 127 (2017): 236-265.

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