Method: Finite Mixture Regression Model

PRELIMINARY

Do All Countries Follow the Same Growth Process?

Lewis Davis

Union College

Ann Owen

Hamilton College

Julio Videras

Hamilton College

July 2007

Abstract

We estimate a finite mixture model in which countries are sorted into groups based on the similarity of the conditional distributions of their growth rates. We strongly reject the hypothesis that all countries follow a common growth process in favor of a model in which there are four classes of countries, each with its own distinct growth process. Group membership does not conform to the usual categories used to control for parameter heterogeneity such as region or income. However, the growth processes we do identify correspond to a significant degree with established theories of economic growth. The behavior of one group is broadly consistent with the neoclassical model, the behavior of two of the groups are consistent with two different endogenous growth models, and results for the fourth group are consistent with a poverty trap model. Overall, these results suggest that the findings of a typical cross-country growth regression may be misleading because they do not accurately reflect the experience of any particular group of countries.

1 Introduction

Are the policy recommendations inferred from cross-country growth regressions equally valid for Brazil, France and Zaire? Does the experience of OECD countries give us valuable insights into growth in less developed countries? Is it possible to draw lessons from East Asian development that are relevant for the countries of Africa and Latin America? Put differently, is there a universal growth model, a single set of equations that govern the evolution of per capita income in every country or, at least, every developing country? And if not, is it possible to group countries in such a way that within each group it makes sense to talk about their common growth experience, or must we go to the extreme of assuming that each country’s growth experience is fundamentally idiosyncratic? As these questions are meant to suggest, the issue of heterogeneity in the process of economic growth is of fundamental importance to the study of growth economics.

A casual reading of growth empirics suggests that this literature infrequently and inconsistently deals with the issue of heterogeneity in the economic growth process. Pioneered by Barro (1991) and Mankiw, Romer and Weil (1992), the bread and butter of the empirical growth literature is the broad sample cross-country growth regression. For Solow (1994: 51) the advent of cross-country growth empirics raises “the recurrent suspicion that the experiences of very different national economies are not to be explained as if they represented different ‘points’ on some well-defined surface.”[1] Temple (1999: 126) points out that cross-country growth regressions will still provide useful information about parameter averages, but this is very different from providing insight into the parameter values for a particular country, especially if Solow’s suspicions are well founded. The common practice of including regional dummy variables, for example, is insufficient to account for heterogeneity in the growth process because it allows for differences in intercepts but not in slopes.

Alternatively, many studies begin by identifying a group of countries for which the growth process is assumed to be similar, generally associated by income level or region, and restricting the sample to developed countries, or developing countries, or Latin American countries, or African countries. Attempts to separate countries by their level of development typically rely on a somewhat arbitrary income threshold and may still result in groups with countries that follow very different growth processes. A similar skepticism applies to geographic groupings. Does it make sense to talk about an “East Asian model” and a “Latin American model” and an “African model”? If so, where do Chile and the Philippines belong? It is hard to claim that these groups reflect coherent analytical categories, rather than the accidents of geography.

In contrast to these standard approaches, we estimate a finite mixture model in which countries are sorted into groups based on the similarity of the conditional distributions of their growth rates. We model the distribution of growth rates as a function of a number of variables identified as fundamental determinants of growth: initial income, proxies for the rates of investment of human and physical capital, and the population growth rate. We also extend our analysis to use variables that describe natural resource endowments and institutional and policy factors to sort countries into the different growth regimes.

Our results are as follows. First, we strongly reject the hypothesis that the countries in our sample follow a common growth process in favor of a model in which there are four classes of countries with distinct growth processes. Moreover, many of the parameter estimates differ across groups and from those found in a standard growth regression that assumes only one class. Thus, inference based on population averages will be faulty when applied to any of the groups of countries. Second, we find that class membership does not conform to the usual categories used to control for parameter heterogeneity such as income or geography. For example, we find two groups of mostly developed countries and two classes of less developed countries. Therefore, our method improves upon the standard treatment of dividing countries by income level because we also allow parameter heterogeneity among countries with similar incomes. We also find that while institutional factors and natural resource endowments play a clear role in defining class membership, the roles of macroeconomic policy and openness are more complex and need to be interpreted in the context of other country-specific factors. Our third and final main result is that the growth processes that we find correspond to a significant degree with established theories of economic growth. Three of the groups may be interpreted as following Mankiw, Romer and Weil’s (1992) neoclassical growth model, Lucas’s (1988) model of education-driven growth and Rebelo’s (1991) model of growth due to physical capital accumulation. The final group exhibits behavior consistent with a poverty trap and features greater inconsistency in growth rates, perhaps because of greater susceptibility to random shocks as in Easterly, Kremer, Pritchett and Summers (1993).

These results have important implications for the practice of growth economics. Cross-country growth empirics have been used to discriminate among the many competing models of growth that were developed as part of the new growth theory. An example of this is Mankiw, Romer and Weil (1992) who argue that the observed pattern of growth was consistent with a three-factor neoclassical model. Our results suggest a more pluralistic interpretation of the evidence. No one model explains the experiences of all four classes of countries identified in our analysis. Moreover, the fact that countries are sorted into groups with different levels of development suggests that models that propose different growth processes are relevant at different stages of development. To a certain extent, our results are related to a growing theoretical literature that attempts to model regime switching as part of a unified growth theory. (See, for example, Galor, 2005; Hanson and Prescott, 2002; or Galor and Weil, 2000.)

For growth policy, our results suggest a middle ground to the two extremes mentioned at the start of the paper. All countries do not follow the same growth process, but neither is each country’s growth process entirely unique, an assumption that leads to what Hausmann, Rodrik and Velasco (2005: 1) refer to as an “attitude of nihilism” regarding our ability to formulate policy recommendations. Our analysis shows that countries can be grouped in a meaningful way, such that valid inferences regarding policy variables may be drawn.

Our work is related to that of other researchers who have examined with increasing methodological sophistication the idea that countries cannot be treated as a homogeneous group in terms of economic growth. In a seminal paper in this literature, Durlauf and Johnson (1995) apply regression tree analysis to identify country groupings. These authors use output per capita and adult literacy rates to identify countries with common growth processes. More recently, Bloom, Canning, and Sevilla (2003), Paap, Franses, and van Dijk (2005), and Sirimaneetham and Temple (2006) have explored the existence of multiple growth regimes. Sirimaneetham and Temple (2006) use principal components analysis to generate an index of policy quality, sort economies into groups based on the value of the index, and then explore whether average growth rates vary across groups. Bloom, Canning, and Sevilla (2003) find evidence that a model with two income regimes is statistically superior to a model with one regime. These authors also argue that geographical variables determine the likelihood that a country is assigned to any of the two regimes. Rather than assuming a priori the number of growth regimes, Paap, Franses, and van Dijk (2005) apply latent class models to a panel of countries allowing the growth rates data to determine the number of groupings. They find that a model assuming three groupings of countries is statistically superior to a model that assumes economies are homogenous.

Our research shares the same motivation of these papers but our methodology complements and advances the existing literature. Contrary to Durlauf and Johnson (1995) and Sirimaneetham and Temple (2006), we assign countries into growth regimes based on the distribution of the growth rate itself rather than predetermined factors. In this aspect, our methodology is similar to the work by Paap, Franses, and van Dijk (2005).[2] However, this paper makes two additional original contributions. First, we estimate the marginal effects of growth fundamentals within regimes. For example, somewhat anticipating our results, we identify a group of countries for which investment in human capital appears to be more important in driving growth than investment in physical capital. Second, we account for sources of systematic heterogeneity that explain the assignment of countries to specific latent regimes.

The remainder of the paper is organized as follows. The following section provides an interpretative framework for our results and discusses our choice of regressors and covariates. Section 3 provides more detail on our econometric approach and related empirical literature. Section 4 presents and discusses our empirical findings, and the final section concludes.

2 Interpretative Framework

The empirical model we estimate includes regressors that capture the proximate determinants of economic growth. Investment, schooling, and population growth are direct measures of the growth of productive factors. Initial income controls for transitional dynamics that occur when earlier gains are easier than later ones, either due to technical transfer or diminishing marginal returns to capital. The equation we estimate is:

where gi is the 30-year average growth rate of real per capital income,is initial income,is the average investment rate,is the average secondary school enrollment rate, ni is the average population growth rate over the period for country i, and the constant term captures increases in labor productivity that are orthogonal to factor accumulation and initial conditions. The use of natural logs is suggested by the neoclassical growth model.

This model deliberately lacks novelty. The regressors are those suggested by the augmented neoclassical model employed by Mankiw, Romer and Weil (1992). They are also among the handful of variables identified by Levine and Renelt (1992) as being robust determinants of economic growth. While neither of these papers has gone unchallenged, they both exerted a large impact on later growth empirics, allowing comparison of our results with other empirical work on growth. In addition, the prosaic nature of our growth regression focuses attention on our primary contribution, the identification of different growth regimes. Second, the focus on proximate determinants of growth is appealing for its theoretical minimalism. Other variables that affect growth must, of necessity, operate through the variables we use. If openness to international trade or high inflation rates and good institutions affect economic growth, presumably they must do so through their impact on accumulation, convergence or innovation; and these effects will be captured in the coefficients we estimate.

As we explain in more detail below, we also employ covariates that are not direct determinants of growth but sort countries into different growth regimes. In choosing our covariates, we focus on variables that play a central role in determining a country’s growth process, and more particularly how it responds to capital accumulation, population growth and the dynamics of convergence. As there is an immense literature related to each of our covariates, we discuss only briefly some of the previous work that motivated our choice to use measures of institutional quality, natural resource endowments, openness, and macro policy to sort countries into growth regimes.

Institutions are widely held to play a significant role in economic growth, e.g. Mauro (1995), Acemoglu, Johnson and Robinson (2001), Dollar and Kraay (2003) and Rodrik, Subramanian and Trebbi (2004). Keefer and Knack (1995) find that institutional quality directly affects the dynamics of convergence as indicated by the coefficient on initial income. Glaeser, Scheinkman and Shleifer (2003) and Zak and Knack (2001) argue that institutions and trust play a fundamental role in investment decisions. Murphy, Shleifer and Vishny (1993) suggest the absence of property rights distorts the allocation of resources as agents seek to avoid predation. Davis (2003a, 2003b) shows that low institutional quality may generate a poverty trap and separate countries into different growth regimes associated with stagnation and industrialization, and Davis (forthcoming) argues that, by influencing the cost of impersonal exchange, institutions may play a role in the realization of scale effects.

Democratic political institutions may also affect the economics of accumulation. A central thesis in the theoretical literature on democracy and growth is that populist policies may blunt incentives to invest in physical capital as in Alesina and Rodrik (1994) and Persson and Tabellini (1994), while also potentially subsidizing the accumulation of human capital as suggested by Bourguignon and Verdier (2000) and Benabou (2000). Openness potentially affects all the variables that influence economic growth. Ventura (1998) notes that factor price equalization implies that in an open economy capital accumulation will shift the composition of output rather than driving down the return to capital. Openness may also prove favorable to taking advantage of international technology flows, e.g. Fagerberg (1994). In Schumpeterian growth models, openness may also influence the incentives for innovation and imitation. (See Dinopoulos and Sener (2003) for a review of this literature.)