Detrending and the money-output link: international evidence.

• Author: Hafer, R.W.

1. Introduction and Background

   The question of whether there exists an empirical link between nominal money and real output has been subjected to a variety of modern econometric techniques, producing conflicting results. For example, Stock and Watson (1989) use a vector autoregressive (VAR) model that accounts for several important economic variables and find that money exerts a statistically significant effect on real economic activity. Friedman and Kuttner (1992, 1993), on the other hand, show that using the same specification as Stock and Watson but extending their sample through the 1980s obviates the money-income link. Friedman and Kuttner's results indicate that interest rates are relatively more useful in explaining movements in output. (1) Thoma (1994) also reports that changes in money do not have a statistically significant impact on output in the United States.

   More recent studies, both theoretical and empirical, also have shown money to have little or no direct effect on economic cycles. Rudebusch and Svensson (1999, 2002), for example, conclude that the behavior of money (real or nominal) has no marginally significant impact on deviations of real output from potential (the output gap) once past movements in the gap and real rates of interest are accounted for. Such findings, on the basis of what Meyer (2001) refers to as the "consensus macro model," have achieved an influential position among macroeconomists and policymakers. (2)

   Other studies challenge the argument that money does not affect real output. An early study by Christiano and Ljungqvist (1988) using a bivariate VAR model reports the existence of a statistically significant money-to-output relation in U.S. data. Davis and Tanner (1997), using monthly U.S. data extending back to the mid-1800s, find that even after interest rate effects are allowed for, money remains statistically significant in explaining short-run movements in real output. Using a rolling regression approach, Swanson (1998) reports a statistically significant relation between money--measured as simple sum aggregates and as Divisia measures--and output, even after an interest rate spread variable is added to the model. Hafer and Kutan (1997) considered whether different stationarity properties of the data have influenced reported outcomes. Since most prior studies assume difference stationarity, Hafer and Kutan demonstrate that estimating VAR models that include money and interest rate variables under the ex istence of trend stationarity can dramatically affect the conclusion. Indeed, they find that using a trend-stationarity assumption yields the finding that money significantly affects real output movements in the United States.

   A common characteristic of this literature is its focus on the United States. There are a few exceptions. For example, Krol and Ohanian (1990) apply the Stock-Watson specification to data for Canada, Germany, Japan, and the UK. Although money (actual and detrended) significantly affects output in the UK, Krol and Ohanian find no such affect in Japan, Canada, and Germany. They conclude that although detrending the growth rate of U.S. money affects conclusions about the role of money, little is gained from this approach when applied to the other countries. Another exception to the U.S. focus is a recent study by Hayo (1999). Using data from 14 European Union (EU) countries plus Canada, Japan, and the United States, Hayo shows that money-output test results are not sensitive to the use of data in levels versus data in differences.

   An obvious question to ask, then, is whether nominal money is relatively more useful than interest rates in explaining movements in real output across a wider variety of countries that includes industrial and developing economies. Although the studies of Krol and Ohanian and Hayo represent a broader analysis, they too focus on the money-output relation in relatively industrialized, financially developed countries. To address this question, we estimate an unconstrained, four-variable (output, money, prices, and interest rates) VAR model for a sample of 20 industrialized and developing countries. (3) In addition to analyzing a broader set of countries, we also determine whether the statistical importance (or lack thereof) of money is a function of the definition of money used. Thus our investigation compares the usefulness of both a narrow (M1) and broad (M2) measure of money in addition to a short-term interest rate. (4) As in Hafer and Kutan (1997), we explore the sensitivity of our results to the use of diff erent stationarity assumptions. Unlike previous work in this area, we evaluate the empirical results by considering the financial development of the countries used. To this end the recent data set constructed by Beck, Demirguc-Kunt, and Levine (1999) is used to explore a potential link between financial development and our empirical results.

   The format of the paper is to briefly discuss the econometric issues involved with the use of trend and difference stationary data in section 2. In section 3 the data are described along with the specification of the estimated VARs. This section also presents the estimation results. Measures of financial market development and structure are then examined in section 4 to see if there is a discernible pattern between the importance of money in explaining real output and a country's financial development. Conclusions and policy implications close the paper in section 5.

2. Econometric Issues

   This study uses both stationary (with and without trend) and difference stationary (DS) specifications of a VAR model given evidence indicating that unit root tests may falsely indicate difference stationarity. Several studies have questioned the use of difference stationarity because of the low power of unit root tests. For example, Dejong et al. (1992) show that the power of augmented Dickey-Fuller and Phillips-Perron tests against the alternative null hypothesis of trend stationarity is quite low. Dejong and Whiteman (1991) use Bayesian analysis to test for the presence of a unity root in the data and report mixed results: When a zero-trend prior is assigned to trend-stationary alternatives, the data do not reject the presence of a unit root in the data. Relaxing this prior, however, often leads to rejection of the unit-root hypothesis. Rudebusch (1993) also reports that unit-root tests cannot distinguish between data simulated by a trend-stationary model or a difference-stationary model. In a more recent paper, Canova (1998) studies the business cycle properties of a small set of real macroeconomic time series for the period 1955-1986. He finds that using different detrending techniques, including a linear time trend and first-order differences, produces different--both quantitatively and qualitatively--"stylized facts" of U.S. business cycles.

   Concern about the stationarity properties of the data is important because of the economic implications. If money and real output are characterized by a difference-stationary model, then effects of monetary shocks on real output diminish very slowly. In other words, a monetary shock has a permanent impact on the level of output because the shock affects the stochastic component of real output. If the money and output series are represented by a stationary model, however, then money shocks have only a transitory impact on output since they are mean reverting. Our own work (1997) suggests that testing the money-output link for the United States is sensitive to which model is used.

3. Data and Estimation Results

   Data

   The data used are quarterly observations of money, measured as a narrow (M1) and a broad (M2) aggregate; real output, measured as real GDP ($1990); the price level, measured as the consumer price index (CPI) (1990 = 100); and a short-term interest rate. Complete descriptions of the data and sample periods used are provided in the data Appendix. We use the CPI to increase the sample of countries: Using the GDP deflator results in a reduction in country coverage. All data are taken from the IMF's International Financial Statistics CD-ROM release as of December 1998. Country-specific sample periods are dictated by the availability of data. In determining the country sample, we used the ad hoc rule that countries with fewer than ten years of data are omitted. This criterion and data availability results in a sample of 20 countries, a sample that extends the usual range of economic settings in which the relative impacts of money and interest rates on real output is tested.

   To provide some background information on the diversity of the sample, Table 1 reports summary statistics on real output growth, inflation, and money growth for the countries included. As one can quickly see, the sample covers a broad set of economic experiences. For example, real output growth ranges from an average of 1.7% in Switzerland to an average of 6.8% in Singapore. This range is dwarfed by that for inflation. In our sample, average inflation runs from less than 2% to more than 50%. Interestingly, money growth, measured as M1 or M2, exhibits a range similar to that of inflation. Indeed, if one believes that long-run money growth and inflation move one-for-one, then such an outcome is expected. Finding such a close relation between money growth and inflation across countries over time would suggest that there is little relation between money growth and the growth of real output in the long run. And that is what the data in Table 1 suggest. (5) Even though the data do not suggest a reliable long-run re lation between average money growth and real output growth, that does not preclude the existence of a short-run relation. To a large extent that is the question addressed in the remainder of this paper.

   Estimation Results

   Three VAR models are estimated for each country. One is a levels specification without a deterministic trend. Another VAR specification...