The Great Moderation and the relationship between output growth and its volatility.

1. Introduction

Macroeconomic volatility has declined substantially over the past 20 years. Kim and Nelson (1999), McConnell and Perez-Quiros (2000), Blanchard and Simon (2001), Stock and Watson (2003), and Ahmed, Levin, and Wilson (2004), among others, have documented this Great Moderation in the volatility of U.S. gross domestic product (GDP) growth. Moreover, the current Federal Reserve Board Chairman Bernanke (2004) also addressed this issue. Most research focuses on the causes of the Great Moderation, such as good policies, structural change, good luck, or output composition shifts. (1) This paper empirically investigates the effect of the Great Moderation on the relationship between the output growth rate and its volatility. (2)

Macroeconomists have long focused on business cycles and economic growth. Recently, increasing attention has been paid to the relationship between business cycle volatility and the long-run trend in growth. Alternative models give rise to negative, positive, or independent relationships between the output growth rate and its volatility. For example, the misperceptions theory, proposed originally by Friedman (1968), Phelps (1968), and Lucas (1972), argues that output fluctuations around its natural rate reflect price misperceptions due to monetary shocks, whilst the long-run growth rate of potential output reflects technology and other real factors. The standard dichotomy in macroeconomics implies no relationship between the output growth rate and its volatility.

Bernanke (1983) and Pindyck (1991) demonstrated that irreversibility makes investment especially sensitive to various forms of risk. Output volatility generates risk about future demand that impedes investment, leading to a negative relationship between output volatility and growth. Martin and Rogers (1997) argued that learning-by-doing generates growth whereby production complements productivity-improving activities and stabilization policy can positively affect human capital accumulation and growth. One natural conclusion, therefore, implies that short-term economic instability can prove detrimental to human capital accumulation and growth (Martin and Rogers 2000).

In contrast, Black (1987) argued that technology comes with varying levels of risk and expected returns that are associated with the degree of specialization. More specialization means more output volatility. Investment occurs in specialized technologies only if expected returns sufficiently compensate for associated risk. Thus, when high expected return technologies emerge, high output volatility and high growth coexist. Mirman (1971) argued that higher output volatility leads to higher precautionary saving, implying a positive relationship between output volatility and growth. Bean (1990) and Saint-Paul (1993) showed that the opportunity cost of productivity-improving activities falls in recessions, implying that higher output volatility may positively affect growth. According to Blackburn (1999), a relative increase in the volatility of shocks increases the pace of knowledge accumulation and, hence, growth, implying a positive relation between output variability and long-term growth.

In a simple stochastic growth model, Blackburn and Galindev (2003) illustrated that different mechanisms of endogenous technological change can lead to different implications for the relationship between output variability and growth. Generally, the relationship is more likely to exhibit a positive correlation if internal learning drives technological change through deliberate actions that substitute for production activities. The relationship exhibits a negative correlation if external learning drives technological change through nondeliberate actions that complement production activity. Blackburn and Pelloni (2004) predicted that real shocks generate a positive correlation between output variability and growth, and nominal shocks produce a negative relationship.

The statistical evidence also exhibits ambiguity. The empirical literature presents two approaches. Using cross-country data, Kormendi and Meguire (1985) and Grier and Tullock (1989) found a positive relationship between growth and its standard deviation, but Ramey and Ramey (1995), Miller (1996), Martin and Rogers (2000), and Kneller and Young (2001) reported a negative relationship. More recently, Rafferty (2005) discovered that unexpected volatility reduced growth and expected volatility increased it, while the combined effect of expected and unexpected volatility reduced growth.

Applying generalized autoregressive conditional heteroscedasticity in mean (GARCH-M) models, Caporale and McKiernan (1996, 1998) found a positive relationship between output volatility and growth for the United Kingdom and the United States, whereas Fountas and Karanasos (2006) found a positive relationship for Germany and Japan. Speight (1999), Grier and Perry (2000), and Fountas and Karanasos (2006), however, concluded that no relationship exists in the United Kingdom and the United States. In contrast, Macri and Sinha (2000) and Henry and Olekalns (2002) discovered a negative link between volatility and growth for Australia and the United States.

The lack of robust evidence concerning the relationship between the output growth rate and its volatility motivates our analysis. While many empirical studies employ postwar data, no one explicitly considers the effect of the Great Moderation on this relationship. (3) The volatility of U.S. GDP growth has fallen by more than half since the early to mid-1980s. Although no agreement exists on the causes of the Great Moderation, the reduced volatility implies that empirical models for output growth over periods that span the break may experience model misspecification.

In addition to considering the relationship between the output growth rate and its volatility, we first consider the possibility that structural change affects the process(es) generating the volatility of output growth. Deibold (1986) first raised the concern that structural changes may confound persistence estimation in GARCH models. He noted that Engle and Bollerslev's (1986) integrated GARCH (IGARCH) values may result from instability in the constant term of the conditional variance, that is, nonstationarity of the unconditional variance. Neglecting such changes can lead to spuriously measured persistence; the sum of the estimated autoregressive parameters of the conditional variance is heavily biased towards one. Lamoureux and Lastrapes (1990) explored Diebold's conjecture and provided confirmation that the failure to account for discrete shifts in unconditional variance, the misspecification of the GARCH model, can produce an upward bias in GARCH estimates of persistence in variance, and this vitiates the usefulness of GARCH when the degree of persistence proves important. The longer the sample period, the higher is the probability that such changes will occur. Inclusion of dummy variables to account for such shifts diminishes the degree of GARCH persistence. More recently, Mikosch and Starica (2004) argued theoretically that the IGARCH model makes sense when nonstationarity data reflect changes in the unconditional variance. Hillebrand (2005) showed that in the presence of neglected parameter change points, even a single deterministic change point, GARCH inappropriately measures volatility persistence. Before carrying out GARCH estimations, we performed a thorough change-point study of the data to avoid the spurious effect of almost-integration.

The identification of change points will occur endogenously in the data-generating process. We employed Inclan and Tiao's (1994) iterated cumulative sums of squares (ICSS) algorithm to detect sudden changes in the variance of output growth, as well as the time point and magnitude of each detected change in the variance. (4) The algorithm finds one change point at 1982:I, two years earlier than that of 1984:I in McConnell and Perez-Quiros (2000). Most analysts argue that the break date occurred some time in the early to mid-1980s, but the exact timing of the decline remains controversial. For example, Blanchard and Simon (2001) analyzed the large decline in U.S. output volatility starting in 1982:I.

This paper employs GARCH-M and ARCH-M models to examine the effect of the Great Moderation on the volatility-growth relationship over the period 1947:I to 2006:IV with the break date of 1982:I. Our empirical results show strong evidence of IGARCH effects and no evidence of significant links between volatility and growth for the United States. Moreover, the time-varying variance falls sharply or even disappears once we allow for the structural break in the unconditional variance of output growth. That is, the IGARCH effect proves spurious due to the Great Moderation. These results prove robust to the alternative break 1984:I. Section 2 discusses the data and the Great Moderation in output volatility. Section 3 presents the methodology and empirical results. Section 4 considers additional evidence, and section 5 concludes.

2. Data and the Great Moderation