## Tuesday, February 12, 2013

### Forecast Errors and Fiscal Multipliers: What am I Missing Here?

Today Mark Thoma's blog has a link to a paper by Olivier Blanchard and Daniel Leigh called "Growth Forecast Errors and Fiscal Multipliers." They find that "fiscal multipliers were substantially
higher than implicitly assumed by forecasters." I hope someone else who has read the paper can help me understand one part of it that is confusing me. This is their primary claim:

Under rational expectations, and assuming that forecasters used the correct model for forecasting, the coefficient on the fiscal consolidation forecast should be zero. If, on the other hand, forecasters underestimated fiscal multipliers, there should be a negative relation between fiscal consolidation forecasts and subsequent growth forecast errors (pg. 1).

I wanted to model it to convince myself. Here is my model:

They run the regression with one year of data at a time, not many years of data. Forecasted consolidation can certainly differ from actual consolidation. From (2) then, I am confused about why "the coefficient on the fiscal consolidation forecast should be zero." I think I'm missing something simple. Can someone chime in?

1. Hi Carola, thanks for this post. I didn't read the whole paper, just the section that matched your notation on page 4. I think that the "beta" in the regression is not a structural parameter (as it is in the model you wrote down, Y = b F + e). All Blanchard and Leigh are saying is that if forecasts of GDP are efficient, the forecast of F should be uncorrelated with the forecast error of GDP -- since F is then just uncorrelated noise, its coefficient in their regression should be zero.

2. Under rational expectation, forecast error of consolidation will be orthogonal to predicted consolidation. Thus you can estimate coefficient before the first term in last line of your equation (1) just by running the regression as Blanchard & Leigh do (the second term can be subsumed as error). Or at least I think you can do it if betas (actual and perceived) were constant across countries, maybe you'd need some further assumptions if they're random themselves.

3. Little elaboration: If forecasts of GDP are efficient, then no information available at t should help predict t+1. Since forecasts of F are available at t, they can't possibly help predict GDP at t+1, which is why the forecasting errors must be uncorrelated with forecasts of F.

4. OK, thanks. It does seem intuitively like when you only consider one time period of forecasts, the people who make the highest forecasts will have the highest forecast errors. But with rational expectations, not so.

A number of papers have shown empirical departures from rational expectations in forecast data. I wonder how much the departure matters for Blanchard and Leigh's result.

I think they do assume that actual and perceived betas are constant across countries (which is odd given the suggestion that the multiplier may be different at the ZLB). I think you would have to interpret the coefficient differently without this assumption. Especially if forecasters have heterogeneous perceived betas, which are correlated with forecast errors. For example, forecasters who are really wrong about the size of the multiplier may also be really wrong about other aspects of how the economy works. Forecasters who understand the multiplier well may be better forecasters.

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