Macroeconomic Theory
Spring 2017
Jeffrey Parker, Reed College

February 3 paper of the week

Assigned paper

Barro, Robert J., and Xavier Sala-i-Martin. 1992. Convergence. Journal of Political Economy 100 (2):223-51.

Reading suggestions

• The neoclassical growth model presented by Barro and Sala-i-Martin in equations (1) through (10) is a version of the Ramsey model that we are studying in Chapter 2 of Romer's text. The Ramsey model's convergence dynamics differ in minor ways from those of the Solow model, but these differences are not important. You may ignore the details of the derivation of equation (10).
• An important theoretical concept in this paper is the idea of "variance." The variance of a random variable (sometimes expressed as its square root, the standard deviation) measures how widely it tends to be dispersed around its mean (average). A variable with a small variance rarely takes on values that are distant from the average (either above or below); one with a large variance often does. If the cross-area variance of income is large, then there are wide dispersions across areas in income.
• The discussion at the bottom of page 227 and top of 228 examines the difference between "beta-convergence" and "sigma-convergence." The former is the tendency, on average and other things held equal, of poorer economies to grow faster than richer ones. The latter is the tendency for the variance (dispersion) of per-capita income across areas to fall over time. They are clearly related, but not the same. The connections are explored in the first question for analysis below.
• The sections on "Results with Gross State Product" and "Income versus Product" can be thought of as providing additional supporting evidence and justification for the "robustness" of the basic analysis. Skim them, but don't worry about the details.

Questions for analysis

1. In equation (13), explain why the first term can be interpreted as the long-run steady-state value of the cross-area income variance and the second as the "convergence term" that brings the variance back toward the steady-state value. Based on equation (13), how is the steady-state variance of per-capita income in the long run affected by the magnitude of beta? What would happen to cross-area variance in the steady state if beta were infinitely large? If beta were zero? What condition would be necessary for steady-state variance to be zero?
2. What is the rationale for including the "sectoral composition" variable in some of the convergence regressions? What about the "south" dummy variable? Do you think that the presence of these variables makes the results more reliable? Are there meaningful differences between the results with and without the variables?
3. How do you explain the differences across the rows of Table 3? Why are the "additional variables" so important to the 98 country sample but not for the 48 U.S. states?
4. What conclusions do you draw from the paper about the empirical validity of the Solow model's convergence implications? How convincing do you think the results are: weak, suggestive, strong, or conclusive?