# How Big Is the Random Walk in GNP?

*John H. Cochrane*
Link

Abstract

This paper presents a measure of the persistence of fluctuations in GNP based on the variance of its long differences. That measure finds little long-term persistence in GNP. Previous research on this question found a great deal of persistence in GNP, suggesting models such as a random walk. A reconciliation of this paper’s results with previous research shows that conventional criteria for time series model building can produce misleading estimates of persistence.

It’s very difficult to distinguish between permanent shocks and merely transitory shocks with high persistence.

This paper reexamines the long-run properties of GNP and argues that GNP does, in fact, revert toward a “trend” following a shock. However, that reversion occurs over a time horizon characteristic of business cycles-several years at least. Therefore, the short-run properties of GNP are consistent with a model with very persistent shocks,

For stationary time series, long-term forecasts do not change in response to shocks. In other words, the impulse response function should fade to zero over a long enough horizon. This seems to be roughly the case for my analysis in Don’t Discount Interest Rates.

If the variance of the shocks to the random walk component is zero, the series is trend-stationary, and long-term forecasts do not change in response to shocks. If the variance of the shocks to the random walk component is equal to the variance of first differences, the series is a pure random walk.

For a time series with permanent fluctuations, like a random walk, lower values today imply lower forecasts out into the indefinite future. This seems to be what I found in Beats and Misses Are Forever – lower revenue today forecasts lower revenue one, two, and three years out.

Fluctuations in a random walk are permanent in the following sense: suppose that $ϵ_{t}=−1$, so that $y_{t}$ falls one unit below last period’s expected value. Then, since $y_{t+j}=y_{t}+jμ+ϵ_{t+1}+...+ϵ_{t+p}$ forecasts $E_{t}(y_{t+j})$ fall by one unit for the indefinite future. Also, a low or negative growth rate today implies nothing about growth rates in the future, and there is no tendency for future levels of GNP to revert to a trend line.

How much does a one-unit shock to GNP affect forecasts in the far future? If by one unit, it finds a random walk; if by zero, it finds a trend-stationary process like (1). It can also find numbers between zero and one, characterizing a series that returns toward a “trend” in the far future,

The size of the random walk component seems to have implications for the plausibility of various economic models. In particular, if the economy has a large random walk component, that is favorable of RBC style models of the economy, where fluctuations originate from real productivity shocks. If the random walk component is small or non-existant, that militates in favor of Keynesian or monetary theories of the business cycle, where the economy fluctuates around an exogenous trend due to monetary or fiscal policy.

The size of a random walk in GNP has been cast as a direct test between competing models of the economy. For example, Nelson and Plosser (1982) interpreted their result that GNP has a large random walk component as evidence for stochastic equilibrium models over traditional monetary or Keynesian business cycle models. They argued that traditional models produce only temporary deviations from trend, while models that find the ultimate source of GNP variability in technology shocks can produce permanent fluctuations.

- This suggests that software companies are better modeled with an RBC-like approach, which is what I would have guessed (refer to Beats and Misses Are Forever)
- Venture capital seems to be better modeled by a Keynesian or monetarist approach, which is also quite intuitive given the whole premise of Don’t Discount Interest Rates is exactly that monetary policy has a large effect on venture activity

## References

Permanent and Transitory Components of GNP and Stock Prices

An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data