Predictions made in early 2009 about whether the stimulus package would work varied widely because the models used to make the predictions varied widely. Models used by Christy Romer and Jared Bernstein predicted large effects of the 2009 stimulus (ARRA), while models used by John Cogan, Tobias Cwik, Volker Wieland and me predicted small effects.
Now that ARRA is winding down people are asking which prediction was right. Did ARRA stimulate the economy significantly or not? To answer this question the same models are again being used, but now to evaluate the policy. CBO, for example, takes this approach in their congressionally mandated impact studies of ARRA.
But you learn virtually nothing about whether a stimulus package worked using this approach because the models simply repeat the same prediction story over again.
Unfortunately, the complexity of models with a hundred or more equations makes it difficult to see this point, so I created an illustration with stylized one-equation models which people seem to like. A little algebra is needed.
Consider two models relating the size of the stimulus package (symbolized by S) to GDP (symbolized by Y). Model A is Y= αS + Z and Model B is Y = Z, where Z is an unobservable shock and α is a coefficient which we set to 1.5.
Suppose that a stimulus is enacted with S = 2, but Y falls to -1. Then the shock implied by Model A is Z = – 4 while the shock implied by model B is Z= -1.
Now consider policy evaluation of the stimulus based on a counterfactual where there is no stimulus so S=0.
Economists using Model A would say: Just as we predicted, the stimulus package worked. Without it, Y would have fallen to -4 rather than -1. The decline in output would have been 4 times as deep, a Great Depression 2.0.
Economists using Model B would simply say: Just as we predicted the stimulus package didn’t work.
The best way to way to deal with this problem is to look empirically at the direct effect of the stimulus using actual data, but without imposing a specific model structure like Model A or Model B. In a paper forthcoming in the Journal of Economic Literature I use this direct approach and find that the ARRA did not stimulate the economy.