Long run neutrality of money in Mexico.
| Autor | Wallace, Frederick H. |
Introduction
Intuitively, it would seem that permanently changing the quantity of money in an economy should have no long run effect on real variables; absolute prices should change, but nothing more. (1) In such an economy money is long run neutral (LRN). Macroeconomic models with optimizing agents are usually characterized by LRN, although many do allow for short run non-neutrality from a wide variety of sources. Exactly how money affects output and other real variables in the short run is an unresolved issue, but the absence of long run neutrality in a modern macro model would be surprising. (2) Despite its theoretical appeal in mainstream economics, the empirical evidence regarding long run neutrality (LRN) of money is not conclusive. Fisher and Seater (1993, henceforth FS) show that long-run propositions like monetary neutrality, superneutrality, or purchasing power parity may, under certain circumstances, be tested using ordinary least squares regressions (OLS). (3) We use the FS methodology with bootstrapped errors to examine long run neutrality of money with respect to real GDP and real output in ten industrial sectors of the Mexican economy.
Coe and Nason (2004, henceforth CN) have applied the OLS test of Fisher and Seater to data for Australia, Canada, the United Kingdom, and the United States. Using money and real output data for these four countries, they find that large size distortions characterize the FS test and that the power of the test is low. Indeed, in most of their OLS regressions, power declines as the horizon lengthens and is approximately equal to test size at the longest horizons (see Table 3 in CN). Shelley (2006) shows that despite errors in programming the bootstrap procedure, the CN conclusions regarding the size and power of OLS estimates remain valid. These problems with the FS test cast doubt on the long run neutrality results reported in such published papers as Fisher and Seater (1993), Boschen and Otrok (1994), Olekalns (1996), Haug and Lucas (1997),Wallace (1999), and Noriega (2004). Rejections of LRN in these papers may be due to size distortions. In contrast, our tests results are based on bootstrapped confidence intervals. Our hypothesis tests are of correct size; therefore rejections of LRN are strong evidence against this hypothesis.
There are two major objectives in this study. First, we wish to determine whether money is long run neutral with respect to real GDP and real output in ten different industries in Mexico. Second, we ask whether the long run effect of money on real output differs across sectors. For example, is money LRN with respect to some industries and not LRN for others? Or, are the effects of changes in money relatively consistent regardless of the industry? Briefly previewing the findings, for five industries and real GDP there is evidence that money is not long run neutral at the 90% confidence level or better in Mexico. Our rejections of LRN are strong evidence against this theory, as they are based on empirical confidence bands with correct size. Furthermore, the effects of a permanent change in money differ across the sectors we study.
This study makes three contributions to the long run monetary neutrality literature. First, this is the only application of the FS test to money neutrality (other than those of Coe and Nason) that addresses the size distortion problem. Second, only a few studies have examined long run neutrality in developing countries, which are often characterized by highly constrained financial markets. Wallace (1999) and Noriega (2004) apply the FS test to data for Mexico, Bai and Ratti (2000) use the FS test to study superneutrality in Argentina and Brazil, and Wallace, Shelley, and Cabrera (2004) examine superneutrality in Nicaragua. During the period under study, federal government intervention in Mexican financial markets included the imposition of capital controls, controls on interest rates, fixed exchange rates, and the nationalization of almost all banks. Thus, we ask whether money is long run neutral with respect to output in each of a wide variety of Mexican industrial sectors, regardless of financial constraints.
Third, in our view it is important to verify results from testing macroeconomic hypotheses or propositions using aggregate data, with tests at more disaggregated levels. Garrett (2003) demonstrates that regression results with aggregate data can differ from those using the disaggregated components. Conceivably, one could reject LRN at the aggregate level, as we find in Mexico for 1932-2001, yet miss significant industry-specific effects. Application of the test to disaggregated data could help to identify the sources of non-neutrality and suggest how monetary policy might be transmitted to the real economy.
The following section contains a brief overview of the FS test and a discussion of the bootstrapping procedure. A description of the data series and an examination of their time series properties are provided in section two. The third section presents our interpretations of the FS test results for long run money neutrality in the ten industrial sectors and the aggregate economy. Conclusions are provided in the final section.
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The Fisher-Seater Methodology and the Bootstrapping Experiment
We begin with a very concise description of the FS test derivation. The stationary and invertible, two variable, log-linear ARIMA model given by equations (1) and (2) is the starting point.
a(L)[[DELTA].sup.
] [m.sub.t] = b(L)[[DELTA].sup. ] [y.sub.t] + [u.sub.t] (1) d(L)[[DELTA].sup.
] [y.sub.t] = c(L)[[DELTA].sup. ] [m.sub.t] + [w.sub.t] (2) The terms [m.sub.t] and [y.sub.t] are log money and log real output respectively, while [u.sub.t] and [w.sub.t] are mean zero, i.i.d. error vectors. L is the lag operator and [a.sub.0] = [d.sub.0] = 1, so that a(L) = 1-[a.sub.1]-[a.sub.2]-..., b(L) = [b.sub.1] + [b.sub.2] +..., c(L) = [c.sub.1] + [c.sub.2] +..., and d(L) = 1 - [d.sub.1] - [d.sub.2] -.... The order of integration of variable q = m, y is given by x
. (4) The long run response of output to a permanent change in money is given by the long run derivative ([LRD.sub.ym]), displayed in equation (3)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If the limit of the denominator in equation (3) is zero, then there are no permanent changes in the monetary variable, hence
= 0 and LRN cannot be tested. Provided that permanent changes in money have occurred, ...[greater than or equal to] 1 and
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