Money growth, output growth, and inflation: estimation of a modern quantity theory.

• Author: Moroney, John R.

1. Introduction

   During the years 1980-1993, annual inflation averaged 81.5% in Latin America, 12.3% in Africa, but only 6.4% among 16 countries in the OECD. Within Latin America, inflation ranged from 8.2% in Honduras to 374.3% in Argentina and in Africa from -0.6% in the Republic of the Congo to 61.6% in Sierra Leone. What are the reasons for these large differences? If cross-country differences in inflation can be linked closely to corresponding differences in money growth, the reason is clear. But if the link is weak, then other reasons must be sought.

   Several authors have recently rejected money growth as an explanation of inflation. There are three lines of criticism. The first, typified by Baba, Hendry, and Starr (1992); Estrella and Mishkin (1997); and Cochrane (1998), argues that the income velocity of (and thus the demand for) monetary aggregates is so unstable that money growth is an unreliable explanation.

   A second criticism, closely related to the first, is a time-series issue: If money, the price level, and output are not cointegrated, then there is no stable long-run relationship among them. Some researchers find evidence of cointegration (Hoffman and Rasche 1991; Baba, Hendry, and Starr 1992; Stock and Watson 1993; Hoffman, Rasche, and Tieslau 1995; Swanson 1998; Carlson et al. 2000; Dutkowsky and Atesoglu 2001), but others do not (Stock and Watson 1989; Hafer and Jansen 1991; Friedman and Kuttner 1993; Thoma 1994). The cointegration question remains unsettled.

   A third criticism is quite distinct from the first two. It argues that in dynamic general equilibrium models with infinitely lived households, money in the household utility function, and rational expectations, there is a class of policy rules with a unique solution that shows that the price level is independent of monetary policy but dependent strictly on fiscal policy. This "fiscal theory of price level determination" breaks any link between money growth and inflation. The key fiscalist models were developed by Leeper (1991), Sims (1994, 1996), and Woodford (1994, 1995, 1998). A simple version is summarized succinctly by McCallum (2001), who demonstrates an alternative mathematical solution to a "fiscalist model" that yields a monetary explanation of the price level. But the monetarist foundations are under vigorous attack. (1)

   This paper specifies and estimates a modern version of the quantity theory of money growth, real GDP growth, and inflation. Its traditional feature is that a country's long-run inflation rate increases with its money growth rate. The modern wrinkle is that inflation is mitigated by real GDP growth. I assume that real GDP growth is governed by exogenous forces such as growth in human capital, physical capital formation, and technological progress. The model makes no attempt to explain GDP growth rates; long-run neutrality is presupposed.

   I show that the quantity theory can be written as a regression model whose theoretical implications can easily be tested (section 3). This paper then makes three empirical contributions. The first is to estimate a long-run version of the quantity theory and test its implications statistically (sections 5 and 6). The estimates are long run in the important sense that inflation, money growth, and real GDP growth rates are annual averages computed for 81 countries over the 14 years from 1980 to 1993. Short-run changes in the series are excluded by design. The second is to partition statistically the roles of money and real GDP growth as determinants of inflation (section 7). The third is to conduct out-of-sample forecasts (section 8). Here we discover how well the model, estimated for one group of countries, predicts inflation in others.

   This paper differs from previous work in three important ways. First, earlier research has not been based on theoretically grounded regression models (Friedman 1956, 1968; Klein 1956; Friedman and Friedman 1980; Friedman and Schwartz 1982; McCandless and Weber 1995; Rolnick and Weber 1997). I advance this work by specifying the quantity theory as a regression model whose theoretical implications are tested explicitly.

   Second, this paper develops a simple method to distinguish between money growth and real GDP growth as determinants of inflation. Both are statistically significant, but money growth is far more important.

   Third, I estimate the model using subsamples of countries, then predict inflation outside the sample. The quantity theory predicts inflation with stunning accuracy for all countries experiencing actual inflation greater than 60% but less accurately for a group of 16 OECD countries characterized by low money growth. These results strongly suggest that high long-run inflation is driven by equally high long-term money growth. The relation is essentially one for one. But to forecast inflation within an important group of countries marked by low long-run money growth, the one-for-one relation breaks down.

2. Background

   The quantity theory can be traced to Richard Cantillon and David Hume. As Lucas (1996, p. 662) puts it, "These are two of Hume's statements of what we now call the Quantity Theory of Money: the doctrine that changes in the number of units of money in circulation will have proportional effects on all prices that are stated in money terms, and no effect at all on anything real, on how much people work or on the goods they produce or consume."

   The quantity theory thus contains two testable propositions. The first is that long-run inflation rates are equal to money growth rates. The second is the long-run superneutrality of money: A country's long-run rate of real economic growth is independent of its money growth rate. (2)

   Long-run superneutrality is of course not short-run superneutrality. Bruno and Easterly (1998) showed that countries experiencing short periods of high inflation also experienced decreases in growth of real GDP per capita. But following the episodes of high inflation, their per capita growth rates increased to rates above the world average (1998, tables 2 and 3). Money growth is far from neutral in the short run. (3)

   Time-Series Evidence on Money Growth and Inflation

   Cagan (1956) established the high correlation between monthly inflation and money growth during hyperinflations in Germany, Greece, Hungary, Poland, and Russia. Klein (1956), Friedman and Friedman (1980), and Lucas (1980) showed that annual inflation is closely correlated with annual money growth in Germany (Klein), in the United States (Lucas), and in United States, Germany, Japan, the United Kingdom, and Brazil (Friedman and Friedman). Hallman, Porter, and Small (1991) studied the dynamics of quarterly adjustment in inflation rates, adjustment of M2 velocity to its long-run equilibrium level (what they call the velocity gap), and adjustment of GNP to its long-run equilibrium level (what they call the output gap) in the United States for the years 1955-1988. Using inflation and monetary growth rates over periods averaging four years in the United States and 5.6 years in the United Kingdom, Friedman and Schwartz (1982) found inflation to depend almost entirely on money growth.

   Cross-Section Evidence

   Others have explained differences in inflation rates across countries by differences in their money growth rates. The research setup has two steps. First, compute long-run average annual inflation and money growth rates for several countries. Second, estimate a cross-section regression of the countries' long-run inflation on their long-run money growth rates.

   Lothian (1985) applied this method using 14-year average inflation and money (M1) growth rates for 20 OECD countries. He obtained a regression coefficient of .891 with standard error .149. Duck (1993) regressed 13-year average annual inflation on money (M2) growth rates using a 33-country sample. Like Lothian, he obtained regression coefficients close to one.

   Using a 62-country sample, Dwyer and Hafer (1988) found a money growth coefficient of 1.031 with standard error .025. McCandless and Weber (1995) and Rolnick and Weber (1997) also found close cross-country correlation between long-term inflation and money growth.

   These cross-section studies support a monetary explanation of long-run inflation. But they share a common statistical shortcoming: None tests for homoscedasticity or normality of regression disturbances. If the residuals were to display heteroscedasticity, the models should be reestimated with corrections for heteroscedastic errors. And standard t-tests applied to estimated regression coefficients also require normally distributed disturbances. It is thus worthwhile to report tests for homoscedasticity and normality in the regressions that follow.

3. The Quantity Theory as a Regression Model

   Begin with the simplest quantity theory:

   [M.sup.s.sub.i] [V.sub.i] = [P.sub.i][Q.sup.D.sub.i] is a monetary measure of aggregate demand (1)

   where [M.sup.s.sub.i] is the money supply (M2) in country i, [V.sub.i] is the velocity of circulation in country i, [P.sub.i] is the aggregate price level (GDP deflator) in country i, and [Q.sup.D.sub.i] is real GDP demanded in country i.

   Taking logarithms of Equation 1 and differentiating with respect to time, we have

   d log [P.sub.i]/dt = d log [M.sup.s.sub.i]/dt + d log [V.sub.i]/dt - d log [Q.sup.D.sub.i]/dt. (2)

   As it stands, Equation 2 provides no basis for statistical estimation. To express it as a regression equation, I make five simplifying assumptions:

   (i) d log [V.sub.i]/dt is random variable within each country that is uncorrelated with money growth and GDP growth.

   (ii) [M.sup.s.sub.i] = [M.sup.D.sub.i] (money supply = money demand).

   (iii) [M.sup.s.sub.i] is exogenous. (4)

   (iv) [Q.sup.s.sub.i] = [Q.sup.D.sub.i] (aggregate real supply equals aggregate real demand).

   (v) d log [Q.sup.s.sub.i]/dt is exogenous (long-run superneutrality).

   Using these five assumptions in Equation 2, one obtains

   d log [P.sub.i]/dt = d log [M.sup.s.sub.i]/dt...