Convergence and Modernization Revisited*

In an 80-country panel since the 1960s, the convergence rate for per capita GDP is around 1.7% per year. This “beta convergence” is conditional on an array of explanatory variables that hold constant countries’ long-run characteristics. The introduction of country fixed effects generates a much higher—and, I argue, misleading—convergence rate. In a much longer time frame—28 countries since 1870—estimation with country fixed effects is more appropriate, and the estimated convergence rate is around 2.4% per year. Combining the point estimates from the post-1960s and post-1870 panels suggests that the conditional convergence rate is between 1.7% and 2.4% per year, an interval that contains the “iron-law” rate of 2%. In the post-1960s panel, estimation without country fixed effects supports the modernization hypothesis, in the form of positive effects of per capita GDP and schooling on democracy and maintenance of law and order. The long-term panel with country fixed effects also supports modernization, in the sense of a positive effect of per capita GDP on the Polity indicator for democracy. A measure of dispersion—the standard deviation of the log of per capita GDP across 25 countries—is reasonably stable since 1870. This lack of “sigma convergence” is consistent with the presence of beta convergence. For 34 countries—including China and India—observed since 1896, the dispersion of per capita GDP declines since the late 1970s, especially when the country data are weighted by population. This sigma convergence reflects particularly the incorporation of China and India into the world market economy. For 29 countries since 1919, the levels and trends in cross-country dispersion are similar for consumption and GDP. *This paper was prepared for presentation at the Nobel Symposium on Growth and Development, Stockholm, September 3-5, 2012. I appreciate excellent research assistance from David Hsu and comments from Philippe Aghion, Xavier Gabaix, Elhanan Helpman, Andrei Shleifer, and Ugo Troiano. According to the “iron law of convergence,” countries eliminate gaps in levels of real per capita GDP at a rate around 2% per year. Convergence at a 2% rate implies that it takes 35 years for half of an initial gap to vanish and 115 years for 90% to disappear. Convergence-rate parameters are important to pin down because they provide guidance on how fast countries like China and India are likely to catch up to richer countries. The convergence rate may also reveal how fast a poor African country could develop or how rapidly North Korea could catch up to the South, and so on. Empirically, the iron law takes the form of unconditional or absolute convergence in some samples of economies; those that are reasonably homogeneous in terms of long-run or steady-state characteristics. For example, a roughly 2% convergence rate emerged for per capita personal income in a long-term panel of U.S. states in Barro and Sala-i-Martin (1992). This convergence was absolute in the sense of not having to be conditioned on a set of variables that capture differences in long-run positions. The results implied—in accordance with the data— that the U.S. South would not get close in per capita income to the rest of the country for about a century. Applying these results to East versus West Germany suggested that a short time frame for convergence was not a realistic expectation. And, looking forward to the potential reunification of North and South Korea, the iron law presents a pessimistic outlook on how rapidly the large gap in per capita product could be eliminated. I first heard this term applied to my empirical findings on economic growth by Rudi Dornbusch. However, Larry Summers said that Rudi got the term from him. Baumol (1986, Figure 2) reported unconditional convergence from 1870 to 1979 for 16 countries (all subsequently OECD members), using data from Maddison (1982). However, De Long (1988) showed that Baumol’s results depended on a sample-selection issue, whereby only countries that were rich toward the end of the sample (1979) were considered. Unconditional convergence did not hold for an expanded sample of 22 countries that were selected based on per capita income in 1870 (De Long [1988, Figure 2]). The general idea of this sample-selection criticism of Baumol’s (1986) findings were presented previously by Romer (1986, pp. 1012-1013). Rodrik (2012) finds unconditional convergence in labor productivity across manufacturing industries for recent decades in 118 countries. Barro (2002) found that the predicted slow convergence between East and West Germany accorded with regional data on GDP per worker through the late 1990s. However, wage rates converged faster because of the German government’s transfer and subsidy policies. 2 The 2% convergence rate holds in contexts of conditional convergence for heterogeneous collections of economies that differ substantially in terms of long-run properties. This convergence is conditional in the sense of holding only with an allowance for differences in constant or slowly varying cross-economy characteristics, such as saving rates or fertility rates or quantity of human capital or institutional quality or colonial history or geographical features. For example, a convergence rate around 2% appeared in a cross section of 98 countries in Barro and Sala-i-Martin (1992, Table 3), after conditioning on an array of variables that differed by country. Because of the conditioning variables, these results were more pessimistic than the iron-law convergence rate would suggest. Poor places—for example, many sub-Saharan African countries or North Korea or Burma or Bolivia or Venezuela—might not converge at all if key underlying variables, such as the quality of human capital and institutions, were not improved. The present study uses updated cross-country panels to reexamine the iron law of convergence. One data set comprises a large number of countries with observations for many variables since the 1960s. Another data set exploits recent advances in long-term nationalaccounts information. These data cover over a century but apply to fewer countries and variables. In both contexts, the distinction between absolute and conditional convergence is important. And, within the context of conditional convergence, a key technical issue is whether the cross-country regressions include country fixed effects. Many analyses of economic growth stress effects from the quality of institutions, gauged particularly by maintenance of the rule of law and democracy. A prominent feature of this 4 In earlier work, Barro (1991) reported conditional convergence for the cross section of 98 countries but did not express the results in terms of a convergence rate. 5 Knack and Keefer (1995) and Mauro (1995) studied growth effects from rule of law and corruption. Przeworski and Limongi (1993) and Barro (1997, Ch. 2) assessed growth effects from democracy. King and Levine (1993) examined effects of financial institutions on economic growth. Glaeser, La Porta, Lopez-de-Silanes, and Shleifer (2004) argued that institutions should be measured by basic legal constraints on the government, rather than political outcomes, which include official corruption and risk of expropriation. 3 analysis is two-way causation between economic development and institutional quality. Specifically, according to the “modernization hypothesis,” economic development spurs the introduction and maintenance of higher quality institutions, including well-functioning representative democracy. The validity of the modernization thesis is important for its own sake—particularly for understanding how democracy evolves—as well as for assessing institutional determinants of economic growth. I use the two updated panel data sets to reassess the empirical status of the modernization hypothesis. From an econometric standpoint, the analysis of modernization turns out to have significant parallels with the study of convergence. Both types of results are sensitive to the treatment of country fixed effects. I. Thoughts on Country Fixed Effects Cross-country empirical findings concerning convergence and modernization are sensitive to the seemingly mundane issue of whether the panel regressions include country fixed effects. The incorporation of these fixed effects into cross-country panel regressions has become almost routine. However, the merits of including these fixed effects are not straightforward, as they involve a tradeoff between two forces, highlighted by Nerlove (2000). To fix ideas, consider cross-country panel regressions for the growth rate of per capita GDP. Country fixed effects are attractive as a way to allow for unobserved, persistent country characteristics that influence long-run per capita GDP and are also correlated with observed per capita GDP. That is, rich countries tend to have prospered because they possess persistently favorable characteristics that lead to high steady-state per capita GDP. From this omittedContributions to the modernization literature include Aristotle (1932), Lipset (1959), Dahl (1991), and Huntington (1991). Marx (1913) extended the modernization idea to a predicted collapse of organized religion under capitalism. This approach applied to economic growth seems to have begun with Knight, Loayza, and Vllanueva (1993); Islam (1995); and Caselli, Esquivel, and Lefort (1996). Acemoglu, Johnson, Robinson, and Yared (2005, 2008) advocate the use of country fixed effects in studies of the modernization hypothesis. 4 variables perspective, the exclusion of country fixed effects tends to bias upward the estimated effect of lagged GDP on current GDP and, thereby, bias downward the estimated convergence rate. One example of this effect is the tendency to estimate an absolute convergence rate near zero in a panel of heterogeneous countries. However, this bias may be small if the framework without country fixed effects includes a sufficiently rich set of explanatory variables so that little remains of omitted variables that are conditionally correlated with per capita GDP. The second force involves the Hurwicz (1950)-type bias in the estimated coefficient of a lagged dependent variable. In samples that are small in the time dimension, Nickell (1981), Arellano and Bond (1991), Kiviet (1995), and Nerlove (2000), among others, show that this force biases downward the fixed-effects estimator (based on least squares with dummy variables) for the coefficient of the lagged dependent variable. Although this bias vanishes as the sample becomes large in the time dimension, in the usual panel context with moderate time frames, the Hurwicz bias tends to be substantial. (As I discuss later, the effective time dimension cannot be expanded by observing the data more frequently; for example, annually, rather than every five or ten years.) On this ground, the estimated convergence rate tends to be overestimated (because the persistence in the level of the dependent variable is underestimated), thereby offsetting the omitted-variables bias. When country fixed effects are included and the time dimension of the sample is moderate—say 20 or even 40 years—the panel effectively comprises multiple cases of short time series. Since the regression for each country features a similar Hurwicz bias, this bias tends to apply also to the overall sample. In contrast, if country fixed effects are excluded, the observations are effectively stacked in the time and country dimensions. That is, with 80 The Hurwicz bias arises because the realized error terms appear in the sample mean of the lagged dependent variable. Moreover, this effect co-varies negatively with the terms involving departures of the dependent variable from its sample mean. 5 countries and 10 time periods (as in the subsequent analysis of data since the 1960s), the 800 observations amount to a large sample in the relevant time dimension, and one would anticipate that the Hurwicz bias would be small. In other words, the bias may arise mostly because of the inclusion of country fixed effects. Inclusion of country fixed effects also affects the estimated coefficients of explanatory variables—X variables—other than lagged dependent variables. Coefficients on country variables that are constant (such as geographical features and colonial history) cannot be estimated at all, and variables that have little within-country time variation cannot be estimated with precision. In effect, the inclusion of country fixed effects throws out much of the information in isolating the effects of X variables on growth rates. There is also small-sample bias in the estimated coefficients of time-varying X variables, as illustrated by Arellano and Bond (1991, Table 1) and Kiviet (1995, Table 2). Problems in estimating coefficients of X variables in a fixed-effects context apply to the recent debate about the modernization hypothesis in Glaeser, la Porta, Lopez-de-Silanes, and Shleifer (2004); Glaeser, Ponzetto, and Shleifer (2007); and Acemoglu, Johnson, Robinson, and Yared (2005, 2008). The failure in the Acemoglu, et al. studies to find statistically significant effects on democracy from per capita GDP and education depends, in their main analysis, on the inclusion of country fixed effects. This result is not surprising because, with country fixed effects, it is challenging to estimate statistically significant coefficients on X variables that do not have a lot of independent variation over time within countries. In contrast, without country fixed However, these analyses assume strict exogeneity of the X variables. This setup, therefore, does not allow for the relevant case in which some of the X variables are jointly determined with per capita GDP. More generally, the nature of the bias in estimated coefficients of the X variables depends on the way that these variables co-vary with per capita GDP and each other. 6 effects, as in the Glaeser, et al. studies and Barro (1999), the typically substantial cross-sectional variation in the X variables makes it easier to isolate statistically significant effects. The perspective changes in the context of panel data observed for over a century. In this setting, the econometric problems posed by the inclusion of country fixed effects should be much less serious. In particular, the Hurwicz bias may be minor in this context. II. The Framework of Conditional Convergence This section summarizes well-known implications of the neoclassical growth model and its extensions for empirical analyses of conditional convergence. The model features a production function,