How competitive is stepwise regression when it comes to pure prediction? When we want to do inference on parameters or nested models, stepwise variable selection causes a number of problems, discussed by Frank Harrell and others.
However, if we validate the stepwise model-building on some kind of holdout data, we would be getting an honest assessment of how our modeling performs, which we do not get from an adjusted $R^2$ that only considers selected variables.
How competitive is stepwise regression in this setting of pure prediction compared to alternatives that deal with large numbers of candidate variables (e.g., ridge or LASSO regression)? Simulations and published results (simulated, empirical, or theoretical/theorems) would be appreciated!
While I can believe that a stepwise procedure would underperform competitors, it is not as obvious why that is the case as it is that the usual adjusted $R^2$ is an inappropriate measure of performance.

Stepwise regression is not generally bad at prediction, in the sense that it is not generally worse than, say, LASSO or best subset selection. Which is to say it may be quite good! Recent evidence on that can be found in Hastie et al. (2020). (I regard the authors as pretty much the ultimate experts in the field.) Noting that LASSO does not universally dominate ridge nor the other way around (see e.g. Tibshirani (1996)), I conjecture that stepwise regression may do better or worse than ridge, too.
References:

*

*Hastie, T., Tibshirani, R., & Tibshirani, R. (2020). Best subset, forward stepwise or lasso? Analysis and recommendations based on extensive comparisons. Statistical Science, 35(4), 579-592.

*Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267-288.

