Examining the robustness of the inflation and growth relationship.

1. Introduction

Whether or not inflation affects long-run growth has been one of the most widely studied questions since the resurgence of interest in economic growth. If higher inflation does reduce long-run growth, it can be addressed by known policies that may be easier to implement than promoting investment in human capital or the development of new technologies. Despite this research, the reliability of estimates is questionable since Levine and Renelt (1992) have shown the results are sensitive to changes in model specification. (1) However, Levine and ReneWs study was limited to a linear relationship in cross-sectional data averaged over 30 years, and subsequent work has shown that inflation's effects are more pronounced in higher frequency data and also non-linear.

This paper uses Bayesian Model Averaging (BMA) to examine whether inflation's effect on long-run economic growth is robust to alternative model specifications. Fernandez, Ley, and Steel (2001) and Sala-i-Martin, Doppelhofer, and Miller (2004) use Bayesian Model Averaging to overcome some shortcomings of extreme bounds tests to re-examine the robustness of determinants of growth, but inflation is not considered. Unlike these previous studies, this paper applies these methods to panel data and also allows for non-linear effects. (2) While inflation is not robust in the cross-sectional data, it is one of the more robust variables when using panel data. Even allowing for high inflation to drive the results, we find that inflation is not robust when using cross-sectional data, suggesting that the original results of Levine and Renelt were not due to the simple linear relationship assumed. Although non-linear effects are important in the panel data, it Is the higher frequency of the data that makes the difference with regard to robustness. One of the main criticisms of growth regressions is that they are reduced form regressions revealing correlation, yet many variables, inflation in particular, are endogenous variables. Using Bayesian Model Averaging but instrumenting for inflation, inflation is not robust even allowing for panel data and non-linearities.

The paper proceeds as follows: Section 2 provides a brief literature review, section 3 provides an overview of the Bayesian Model Averaging methodology, and section 4 proceeds to the application on inflation and growth. Section 5 concludes.

2. Literature Review

Over the last 20 years, many economists have examined the relationship between inflation and economic growth. The typical approach has been to run linear regressions with the growth rate of per capita GDP as the dependent variable and numerous factors, including inflation, as independent variables. Kormendi and McGuire (1985), Fischer (1993), and Barro (1996, 1997), using similar methods, report statistically significant negative coefficients on inflation, at least when inflation is above some moderate level, such as 10%. This apparent non-linearity has been addressed in detail by some authors. Fischer (1993) uses a spline regression and finds a negative relationship at all levels of inflation. Barro (1996) found inflation to be harmful to growth, but showed the results were driven by the observations where inflation exceeded 20%. For inflation below 20%, the point estimate was negative but statistically insignificant. Sarel (1996) tests for a structural break and finds that inflation is negatively related to growth after 8%. The point estimate for inflation at rates less than 8% is positive but statistically insignificant. Khan and Senhadji (2001) use recently developed methods on determining threshold effects and find a threshold at 11% for a large sample of countries. Looking separately at Organization for Economic Co-operation and Development (OECD) and non-OECD countries, they find the thresholds to be 1% and 11%, respectively.

Many of the early growth papers focused on cross-sectional data covering a large number of countries and looked at averages over long periods of time, for example, 30 to 35 years. Some researchers, including Fischer (1993) and Barro (1996), also utilize panel data to increase the sample size and take into consideration the time dimension of inflation and growth. To avoid the influence of business cycles, the usual approach is to take five- or 10-year averages. Using higher frequency data usually strengthens the findings. Rather than using linear regressions over long period averages, Bruno and Easterly (1998) take a time series approach. They find that inflation "crises," which are episodes of over 40% inflation, have a negative effect on output, but that economies are able to rebound rather quickly, suggesting that the inflation-growth relationship "is only present with high frequency data and with extreme inflation observation."

Most of the results cited here find a negative relationship between inflation and long-run growth rates using growth regression. There are a few papers that take alternative approaches. Bullard and Keating (1995) and Rapach (2003) use a structural vector auto-regression (VAR) to identify inflation shocks and find no evidence of permanent negative effects on output, but find some positive permanent effects, at least for some low-inflation countries. (3)

Despite these alternative findings, the key issue for the credibility of these empirical results is their fragility. The seminal work of Levine and Renelt (1992) finds that only investment's share in GDP and possibly initial GDP and trade are "robust" using Leamer's extreme bounds analysis. In fact, inflation is a notoriously fragile variable. The extreme bounds method examines robustness by regressing many possible combinations of independent variables on a particular dependent variable--in our case, growth. If an independent variable is statistically insignificant in even one specification, the variable is labeled "fragile." More recently, Sala-iMartin (1997); Fernandez, Ley, and Steel (2001); and Sala-i-Martin, Doppelhofer, and Miller (2004) examined the robustness of variables using alternative methods that they believe have higher power than the extreme bounds test. They find several variables are likely to be important in determining economic growth. Sala-i-Martin (1997) runs a large number of regressions and measures what percentage of the distribution lies to the relevant side of zero. Sala-i-Martin, Doppelhofer, and Miller (2004), henceforth SDM, and Fernandez, Ley, and Steel (2001), henceforth FLS, use methods similar to Sala-i-Martin (1997), but rely on the theoretical results of Bayesian Model Averaging. Bayesian Model Averaging also utilizes a large number of regressions, but the models are weighted by a Bayesian posterior probability. In contrast to Levine and Renelt's (1992) findings, several variables are found to be robust. Surprisingly, despite the large literature on inflation and growth and the inclusion of inflation in Levine and Renelt's original work, these papers do not consider inflation when re-evaluating robust determinants of growth. This paper fills this void by applying these methods to simple growth regressions that include inflation, and then extends these results to allow for higher frequency data and non-linearities that have proved to be important in previous work.

3. Accounting for Model Uncertainty

Model uncertainty addresses the question of what variables to include in a regression. Usually one relies on past research and theory as a guide to selecting such variables. A typical approach is to run a reasonable regression and then check for robustness by adding and omitting a few variables on the right-hand side. If the coefficients of interest remain statistically significant, the results are labeled robust. However, a difficulty for growth economists is that past research has included an enormous number of possible variables and theory does not offer enough guidance to eliminate many. For example, Brock and Durlauf (2001) note that there have been more variables proposed than there are country observations, and theories can be developed that can support any of them. Bayesian Model Averaging provides a formal way to measure the importance of variables under model uncertainty. It allows the right-hand-side variables to vary over all possible combinations and then considers the posterior probability of which variables are in the true model. This approach has been used to study the possible determinants of economic growth by SDM, FLS, and Brock and Durlauf (2001), and each of these papers devotes a few pages to explain the methodology. There are also good references to the procedure in general terms, rather than specifically economic growth, such as Raftery (1995) and Hoeting et al. (1999). Therefore, the next subsection lays out the basics of the approach (the reader can consult the references for more technical details).

Bayesian Model Averaging

This section draws from Raftery (1995) to lay out the essential ideas. Let M = {[M.sub.1], [M.sub.2], ..., [M.sub.K]} represent the set of all K possible models, and [[beta].sub.0] represent a coefficient of interest. For example, here the focus is on the effect of inflation on growth, so [[beta].sub.0] will be the coefficient on inflation in a growth regression. The Bayesian approach is concerned with the probability distribution of the coefficient of interest conditional on the data, p([[beta].sub.0]|[D). From probability theory, the posterior distribution of [[beta].sub.0] is

p([[beta].sub.0]|D) = [K.summation over (i=1)] p([[beta].sub.0]|D, [M.sub.i])p([M.sub.i]|D), (1)