Fluctuations in Convex Models of Endogenous Growth I: Growth Effects∗

Is there a trade-off between fluctuations and growth? The empirical evidence is mixed, with some studies finding a positive relationship, while others find a negative one. Our objectives in this paper are to understand how fundamental uncertainty can affect the long run growth rate, and to identify those factors that are important in determining the nature of this relationship. Qualitatively, we show that the relationship between volatility in fundamentals (or policies) and mean growth can be either positive or negative. We identify the curvature of the utility function as a key parameter that determines the sign of the relationship. Quantitatively, for reasonably calibrated models, an increase in uncertainty always increases the growth rate. We find that moving from a deterministic world to one with uncertainty that resembles the average uncertainty in a large sample of countries, growth rates increase by 0.2% to 0.80%, with 0.25% being a “reasonable” estimate. Though these are nontrivial changes, they are not large enough by themselves to account for the large differences in growth rates observed in the data. We also find that differences in the curvature of preferences have very substantial effects on the estimated variability of stationary objects like the consumption-output ratio and hours worked. For this reason, we expect that the models considered in this paper will provide the basis of sharp estimates of the curvature parameter. ∗We thank Fernando Alvarez, Craig Burnside, Larry Christiano, Martin Eichenbaum, and Ellen McGrattan for their help, and the National Science Foundation for financial support.