Introduction
The empirical study of economic growth occupies a position that is notably uneasy. Understanding the wealth of nations is one of the oldest and most important research agendas in the entire discipline.
At the same time, it is also one of the areas in which genuine progress seems hardest to achieve. The contributions of individual papers can often appear slender. Even when the study of growth is viewed in terms of a collective endeavor, the various papers cannot easily be distilled into a consensus that would meet standards of evidence routinely applied in other fields of economics.A traditional defense of empirical growth research would be in terms of expected payoffs. Each time an empirical growth paper is written, the probability of gaining genuine understanding may be low, but the payoff to that understanding is potentially vast. But even this argument relies on being able to discriminate between the status of different pieces of evidence - the good, the bad and the ugly - and this process of discrimination carries many difficulties of its own.
Rodriguez and Rodrik (2001) begin their skeptical critique of evidence on trade policy and growth with an apt quote from Mark Twain: “It isn’t what we don’t know that kills us. It’s what we know that ain’t so”. This point applies with especial force in the identification of empirically salient growth determinants. As illustrated in Appendix B of this chapter, approximately as many growth determinants have been proposed as there are countries for which data are available. It is hard to believe that all these determinants are central, yet the embarrassment of riches also makes it hard to identify the subset that truly matters.
There are other respects in which it is difficult to reconcile alternative empirical studies, including the functional form posited for the growth process. An important distinction between the neoclassical growth model of Solow (1956) and Swan (1956) and many of the models that have been produced in the endogenous growth theory literature launched by Romer (1986) and Lucas (1988) is that the latter can require the specification of a nonlinear data generating process.
But researchers have not yet agreed on the empirical specification of growth nonlinearities, or the methods that should be used to distinguish neoclassical and endogenous growth models empirically.These and other difficulties inherent in the empirical study of growth have prompted the field to evolve continuously, and to adopt a wide range of methods. We argue that a sufficiently rich set of statistical tools for the study of growth have been developed and applied that they collectively define an area of growth econometrics. This chapter is designed to provide an overview of the current state of this field. The chapter will both survey the body of econometric and statistical methods that have been brought to bear on growth questions and provide some assessments of the value of these tools.
Much of growth econometrics reflects the specialized questions that naturally arise in growth contexts. For example, statistical tools are often used to draw inferences about long-run outcomes from contemporary behaviors. This is most clearly seen in the context of debates over economic convergence; as discussed below, many of the differences between neoclassical and endogenous growth perspectives may be reduced to questions concerning the long-run effects of initial conditions. The available growth data typically span at most 140 years (and many fewer if one wants to work with a data set that non- trivially spans countries outside Western Europe and the United States) and the use of these data to examine hypotheses about long-run behavior can be a difficult undertaking. Such exercises lead to complicated questions concerning how one can identify the steady-state behavior of a stochastic process from observations along its transition path.
As we have already mentioned, another major and difficult set of growth questions involves the identification of empirically salient determinants of growth when the range of potential factors is large relative to the number of observations.
Model uncertainty is in fact a fundamental problem facing growth researchers. Individual researchers, seeking to communicate the extent of support for particular growth determinants, typically emphasize a single model (or small set of models) and then carry out inference as if that model had generated the data. Standard inference procedures based on a single model, and which are conditional on the truth of that model, can grossly overstate the precision of inferences about a given phenomenon. Such procedures ignore the uncertainty that surrounds the validity of the model. Given that there are usually other models that have strong claims on our attention, the standard errors can understate the true degree of uncertainty about the parameters, and the choice of which models to report can appear arbitrary. The need to properly account for model uncertainty naturally leads to Bayesian or pseudo-Bayesian approaches to data analysis.[312]Yet another set of questions involves the characterization of interesting patterns in a data set comprised of objects as complex and heterogeneous as countries. Assumptions about parameter constancy across units of observation seem particularly unappealing for cross-country data. On the other hand, much of the interest in growth economics stems precisely from the objective of understanding the distribution of outcomes across countries. The search for data patterns has led to a far greater use of classification and pattern recognition methods, for example, than appears in other areas of economics. Here and elsewhere, growth econometrics has imported a range of methods from statistics, rather than simply relying on the tools of mainstream econometrics.
Whichever techniques are applied, the weakness of the available data represents a major constraint on the potential of empirical growth research. Perhaps the main obstacle to understanding growth is the small number of countries in the world. This is a problem for the obvious reason (a fundamental lack of variation or information) but also because it limits the extent to which researchers can address problems such as measurement error and parameter heterogeneity.
Sometimes the problem is stark: imagine trying to infer the consequences of democracy for growth in poorer countries. Because the twentieth century provided relatively few examples of stable, multi-party democracies among the poorer nations of the world, statistical evidence can make only a limited contribution to this debate, unless one is willing to make exchangeability assumptions about nations that would seem not to be credible.[313]With a larger group of countries to work with, many of the difficulties that face growth researchers could be addressed in ways that are now standard in the microeconometrics literature. For example, the well known concerns expressed by Harberger (1987), Solow (1994) and many others about assuming a common linear model for a set of very different countries could, in principle, be addressed by estimating more general models that allow for heterogeneity. This can be done using interaction terms, nonlinearities or semiparametric methods, so that the marginal effect of a given explanatory variable can differ across countries or over time. The problem is that these solutions will require large samples if the conclusions are to be robust. Similarly, some methods for addressing other problems, such as measurement error, are only useful in samples larger than those available to growth researchers. This helps to explain the need for new statistical methods for growth contexts, and why growth econometrics has evolved in such a pragmatic and eclectic fashion.
One common response to the lack of cross-country variation has been to draw on variation in growth and other variables over time, primarily using panel data methods. Many empirical growth papers are now based on the estimation of dynamic panel data models with fixed effects. Our survey will discuss not only the relevant technical issues, but also some issues of interpretation that are raised by these studies, and especially their treatment of fixed effects as nuisance parameters.
We also discuss the merits of alternatives. These include the before-and-after studies of specific events, such as stock market liberalizations or democratizations, which form an increasingly popular method for examining certain hypotheses. The correspondence between these studies and the microeconometric literature on treatment effects helps to clarify the strengths and limitations of the event-study approach, and of cross-country evidence more generally.Despite the many difficulties that arise in empirical growth research, we believe some progress has been made. Researchers have uncovered stylized facts that growth theories should endeavor to explain, and developed methods to investigate the links between these stylized facts and substantive economic arguments. We would also argue that an important contribution of growth econometrics has been the clarification of the limits that exist in employing statistical methods to address growth questions. One implication of these limits is that narrative and historical approaches [Landes (1998) and Mokyr (1992) are standard and valuable examples] have a lasting role to play in empirical growth analysis. This is unsurprising given the importance that many authors ascribe to political, social and cultural factors in growth, factors that often do not readily lend themselves to statistical analysis.[314] For these reasons, Willard Quine’s classic statement of the underdetermination of theories by data, cited at the beginning of this chapter, seems especially relevant to the study of growth.
The chapter is organized as follows. Section 2 describes a set of stylized facts concerning economic growth. These facts constitute the objects that formal statistical analysis has attempted to explain. Section 3 describes the relationship between theoretical growth models and econometric frameworks for growth, with a primary focus on cross-country growth regressions. Section 4 discusses the convergence hypothesis. Section 5 describes methods for identifying growth determinants, and a range of questions concerning model specification and evaluation are addressed. Section 6 discusses econometric issues that arise according to whether one is using cross-section, time series or panel data, and also examines the issue of endogeneity in some depth. Section 7 evaluates the implications of different data and error properties for growth analysis. Section 8 concludes with some thoughts on the progress made thus far, and possible directions for future research.
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