Money growth, output growth, and inflation: a reexamination of the modern quantity theory's linchpin prediction.

• Author: Brumm, Harold J.

JEL Classification: E31, E51

1. Introduction

   Over the years, the quantity theory of money has been extended and refined. All versions, however, begin with the well-known equation of exchange, MV = PQ, where Q is the level of national output (real gross domestic product, GDP), P is the general price level, V is the velocity of money circulation, and M is the quantity of money. To convert this equation--actually an identity--into a theory, one of the four variables contained therein must be specified as functionally dependent on the other three. Monetarists argue that P is the dependent variable (Sprinkel 1971). Specifically, they argue that M is determined by the national monetary authority; that V is determined by a variety of both secular and cyclical factors; (1) that changes in V do not consistently offset changes in M; and that Q is determined by capital, labor, and technological advances (Sprinkel 1971).

   The monetarist theory of inflation is a long-run theory; it does not purport to explain short-run increases in the general price level (Hafer and Wheelock 2001). Monetarists argue that short-run inflation stabilization is not feasible and, therefore, that monetary policy should be confined to inflation concerns over a relatively long horizon. (2)

   John Moroney (2002, p. 399) asserts that in the traditional version of the quantity theory, "... a country's long-ran inflation rate increases [one-to-one] with its money growth rate. The modern wrinkle is that inflation is mitigated by real GDP growth" (emphasis added). This assertion is consistent with the famous dictum of Milton Friedman (1968, p. 18) that "... inflation is always and everywhere a monetary phenomenon, produced in the first instance by an unduly rapid growth in the quantity of money" (emphasis added). Friedman's assertion is not that an increased money growth rate is the sole cause of inflation in the long run--just the most important cause (Friedman and Friedman 1980). An increase in inflation can also be caused by a decrease in the growth rate of Q (or, theoretically, even an increase in the growth rate of V), as is easily seen by solving the equation of exchange for P and then taking logs and first differences.

   After taking logs and first differences. (3) Moroney (2002) obtains an estimating equation in which inflation is functionally dependent on the growth rates of the money stock and real GDP:

   (1) Y= [[beta].sub.0] + [[beta].sub.1]X + [[beta].sub.2]Z + u ([[beta].sub.0] = 0, [[beta].sub.1] = 1, [[beta].sub.2] = -1]),

   where Y is [DELTA] ln P, X is [DELTA] ln M, Z is [DELTA] ln Q, and u is a random disturbance term that includes velocity changes. ([DELTA] is the first difference operator.) The modern quantity theory's model-implied restrictions--which are testable predictions--are that the intercept is zero, the coefficient of the money stock growth rate is plus one, and the coefficient of the growth rate of real GDP is minus one. Arguably, this joint hypothesis is the linchpin prediction of the modern quantity theory: If the hypothesis is rejected by the data, the theory falls.

   Using long-run (1980-1993) cross-section data on 81 countries, which he takes from the World Bank's World Development Report 1995, Moroney (2002) tests the joint hypothesis ([[beta].sub.0] = 0, [[beta].sub.1] = 1, [[beta].sub.2] = -1) and incorrectly claims that the hypothesis cannot be rejected at even the 0.0l level of significance. (4) As will be shown in the next section, the joint hypothesis is rejected decisively. Fortunately, however, it will also be shown that a modification to Moroney's model specification helps to salvage the most substantive part of the modern quantity theory's implied restrictions.

2. Modification to the Quantity Theory Setup

   In contrast to the conventional quantity theory setup, in which the economy's real activity is determined entirely outside its monetary sector (Fama 1982; Moroney 2002)--that is, in which no provision is made for the possibility that the monetary authority's actions could have an adverse effect on output (5)--the present article entertains the possibility that Y and Z are jointly determined. The motivation for exploring this possible joint determination is that some researchers, most notably Robert Barro (1997), have demonstrated that a negative correlation emerges when the long-run average rate of growth of GDP per capita is regressed on the long-run average inflation rate (and a set of control variables). While some argue that this evidence is far from conclusive (Bruno and Easterly 1998), (6) it is suggestive. Formally, Barro's regression equation is (2) [DELTA] In (GDP/POP) = [[gamma].sub.0] + [[gamma].sub.1] Y + [[gamma].sub.2][W.sub.2] + ... + [[gamma].sub.k][W.sub.k] + [[epsilon].sub.1],

   where [DELTA] In (GDP/POP) is the average annual growth rate of real GDP per capita over a long-run period, Y is (as in the quantity theory inflation equation) the average inflation rate over the period, the Ws are controls, and [[epsilon].sub.1] is the usual disturbance term.

   In their oft-cited critique of the cross-country economic growth regression literature, Ross Levine and David Renelt (1992) employ the following base regression equation: (7)

   (3) [DELTA] In (GDP/POP) = [[delta].sub.0] + [[delta].sub.1] INITIAL +...