Convergence

An issue that has attracted considerable attention in empirical work on growth is whether poor countries tend to grow faster than rich countries. There are at least three reasons that one might expect such convergence. First, the Solow model predicts countries converge to their balanced growth paths. Thus to the extent that differences in output per worker arise from countries being at different points relative to their balanced growth paths, one would expect the poorer countries to catch up to the richer. Second, the Solow model implies that the rate of return on capital is lower in countries with more capital per worker. Thus there are incentives for capital to flow from rich to poor countries; this will also tend to cause convergence. And third, if there are lags in the diffusion of knowledge, income differences can arise because some countries are not yet employing the best available technologies. These differences might tend to shrink as poorer countries gain access to state-of-the-art methods.

Baumol (1986) examines convergence from 1870 to 1979 among the 16 industrialized countries for which Maddison (1982) provides data. Baumol regresses output growth over this period on a constant and initial income; that is, he estimates

1 [( / ), 979] - 1 [( / ), 870] = + [( / ), 87 ] + f, (1-31)

"Other authors examining the same issue, however, argue for a larger role for the residual. See, for example. Page (1994).

inputs. But more complicated adjustments are also possible. For example, if there is evidence of imperfect competition, one can try to adjust the data on income shares to obtain a better estimate of the elasticity of output with respect to the different inputs.

Growth accounting has been appUed to many issues. For example. Young (1994) uses detailed growth accounting to argue that the unusually rapid growth of Hong Kong, Singapore, South Korea, and Taiwan over the past three decades is almost entirely due to rising investment, increasing labor-force participation, and improving labor quality (in terms of education), and not to rapid technological progress and other forces affecting the Solow residual. 1

To give another example, growth accounting has been used extensively to study the productivity slowdown-the reduced growth rate of output per worker-hour in the United States and other industrialized countries that began in the early 1970s (see, for example, Denison, 1985; Baily and Gordon, 1988; Griliches, 1988; and Jorgenson, 1988). Some candidate explanations that have been proposed on the basis of this research include slower growth in workers skills, the disruptions caused by the oil-price increases of the 1970s, a slowdown in the rate of inventive activity, and the effects of govemment regulations.

Germany

Canada

+ United States

Denmark

Switzerland

6.0 6.2 6.4 6.6 6.8 7.0 Log per capita income in 1870

FIGURE 1.7 Initial income and subsequent growth in Baumols sample (from De Long, 1988; used with permission)

Baumol considers output per worker rather than output per person. This choice has little effect on the results.

Here ln(y/N) is log income per person, a is an error term, and z indexes countries. If there is convergence, b will be negative: countries with higher initial incomes have lower growth. A value for b of -1 corresponds to perfect convergence: higher initial income on average lowers subsequent growth one-for-one, and so output per person in 1979 is uncorrelated with its value in 1870. A value for b of 0, on the other hand, implies that growth is uncorrelated with initial income and thus that there is no convergence. The results are

In[(y/N)a979] - ln[(y/N)u87o] = 8.457 - 0.9951 [( / ),187 ],

(0.094) (132)

= 0.87, s.e.e. = 0.15, l

where the number in parentheses, 0.094, is the standard error of the regression coefficient. Figure 1.7 shows the scatterplot corresponding to this regression.

The regression suggests almost perfect convergence. The estimate of b is almost exactly equal to -1, and it is estimated fairly precisely; the two-standard-error confidence interval is (0.81,1.18). In this sample, per capita income today is essentially unrelated to per capita income a hundred years ago.

2.6 p 2.4 -2.2 -

I 2.0 -

S 1.8f-

« P

1.4 1.2

East Germany -i-

Spam ++ Ireland +

Chile "Portugal +

Argentina

+New Zealand +

.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 Log per capita income m 1870

FIGURE 1.8 Initial income and subsequent growth in the expanded sample (from De Long, 1988; used with permission)

Smce a large fracUon of the world was richer than Japan in 1870, it is not possible to consider all countries at least as nch as Japan. In addition, one has to deal with the fact that countries borders are not fixed. De Long chooses to use 1979 borders. Thus his 1870 income estimates are estimates of average incomes m 1870 in the geographic regions defined by 1979 borders.

De Long (1988) demonstrates, however, that Baumols finding is largely spurious. There are two problems. The first is sample selection. Since historical data are constructed retrospectively, the countries that have long data series are generally those that are the most industrialized today. Thus countries that were not rich a hundred years ago are typically m the sample only if they grew rapidly over the next hundred years. Countries that were nch a hundred years ago, in contrast, are generally included even if their subsequent growth was only moderate. Because of this, we are likely to see poorer countries growing faster than richer ones in the sample of countries \ consider even if there is no tendency for this to occur on average.

The natural way to eliminate this bias is to use a rule for choosing the sample that is not based on the variable we are trying to explain, which is growth over the penod 1870-1979. Lack of data makes it impossible to include the entire world. De Long therefore considers the richest countries as of 1870; specifically, his sample consists of all countries at least as rich as the second poorest country in Baumols sample in 1870, Finland. This causes him to add seven countries to Baumols list (Argentina, Chile, East Germany, Ireland, New Zealand, Portugal, and Spain), and to drop one ijapan).20

Figure 1.8 shows the scatterplot for the unbiased sample. The inclusion of the new countries weakens the case for convergence considerably. The