Detrending and the money-output link: international evidence.

Kutan, Ali M.

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 includes a linear, deterministic time trend. This model is referred to as the TS specification. This version assumes that the data are stationary around a deterministic trend term. Both specifications use the log level of the data (except for the interest rate) and allow us to test whether the impact of money on output, if there is any, is transitory. Furthermore, the TS version allows us to interpret the results in terms of "detrended" variables (Krol and Ohanian 1990). The third specification uses log first-differences of the data, except the interest rate, which is measured as a simple first difference. In this DS model any impact of money on output is viewed as long lasting, since the series are assumed to have stochastic trends with fluctuations that are not mean reverting over time. VARs include a constant term and quarterly seasonal dummies. (6)

Before turning to the results, a brief discussion of lag length selection is in order. Swanson (1998) notes that many studies select the structure of the VAR by simply assigning ad hoc lag lengths. It is well known that inferences drawn from VARs are sensitive to the lag length used. (7) In this paper the lag structure for each VAR is chosen using the Akaike AIC and the Schwarz SC criterion. To keep the analysis manageable, three alternative lag lengths are tested (eight, six, and four) for each monetary aggregate and for each stationarity assumption. In all but two cases, both lag-length selection criteria select four lags. The exceptions are the TS model using M1 for Portugal, where eight lags are chosen, and the TS and DS models with Turkish M2, where six lags are selected. (8)

Variance decompositions derived from the VARs provide information on the quantitative importance of money and interest rates in explaining output. (9) We focus on the relative proportion of the total variation in output explained by money and interest rates. Consequently, the full set of variance decompositions (VDC) results are not reported. (10) Six sets of variance decompositions are presented for each country. These combinations reflect (i) the three VAR specifications and (ii) the fact that two alternative orderings of the variables are used for each VAR. One version, referred to as "Order 1" in subsequent discussion, uses the ordering interest rate, money, prices, and real output. As suggested by Sims (1980) and discussed in Todd (1990), an ordering that places the short-term interest rate first assumes little contemporaneous feedback from output to money. Because there are different priors about the presence of contemporaneous feedback from output to money or interest rates, an alternative ordering of output, prices, interest rate, and money is estimated as a robustness test. This is referred to as "Order 2." All reported variance decompositions assume a 4-year horizon. (11)

The variance decompositions using M1 are found in Table 2. (12) There are two aspects to interpreting the array of results in Table 2. First, beneath each column heading is listed a ratio, the numerator of which is the VDC for M1, the denominator being the VDC for the interest rate. Second, this ratio is reported for the two orderings discussed above. Last, because of the large number of combinations estimated, it is useful to establish some criterion for evaluating the results. The following setup is used: When the VDC of money exceeds 10% and exceeds the VDC for the interest rate by 5% (not percentage points), the result appears in bold. Although one may quibble over our benchmark, we believe that this approach is reasonable and one that sets an acceptable minimum for money to be thought of as providing useful information about the behavior of real output.

The results in Table 2 provide an interesting comparison to previous work which focused on the United States. First, the results indicate that when the stationary specification without trend is used, M1's VDC exceeds that of the interest rate for Germany, the Netherlands, New Zealand, Portugal, Singapore, and Switzerland, although this finding is sensitive to the ordering in New Zealand and Singapore. This suggests that M1 plays only a minor role relative to interest rates in explaining output in most other countries in our sample.

Turning to the results from the TS and DS specifications, the evidence for the United States corroborates our earlier finding that the VDC of M1 increases in absolute size and is larger than the interest rate when the TS specification is used relative to the DS model. As seen in Table 1, the TS specification delivers a VDC for M1 indicating that about 25% of the variance in real output is explained by money, compared with around 13-17% for the interest rate. When the DS specification is used, however, the results are dramatically altered. Now the interest rate dominates M1, the latter accounting for less than 3% of the variance in output. (13) Finding that money's importance is affected by the specification occurs not only for the United States, but also for Australia, Israel, Portugal, Spain, and Sweden. In other words, in these six countries one would have rejected the usefulness of money on the basis of the TS or DS specification alone when this conclusion is reversed using the alternative model. (14) Thus country-specific analyses must recognize that model specification can significantly affect the conclusions reached.

One of the most interesting outcomes in Table 2 is the robustness of results for Germany, New Zealand, and Switzerland. For those countries the VDC evidence indicates that money exceeds the variance in real output accounted for by the interest rate regardless of specification and ordering. Is there a common factor explaining this outcome? One obvious possibility is that Germany and Switzerland are recognized as countries in which the central bank follows a credible low-inflation policy. Such policy actions also have occurred, though more recently, in New Zealand. (15) In such a policy environment, movements of money may be more exogenous to output than in policy regimes where money growth is secondary to controlling interest rates as a means to stabilize economic activity. Below we investigate other potential explanations for this outcome, ones that focus on the development and structure of the countries' financial markets.

Table 3 presents the battery of results with M2 replacing M1. The U.S. results are qualitatively identical to Table 2: The VDC for M2 exceeds that for the interest rate only when the TS specification is used. The switch to a broader measure of money affects the results for several other countries. For instance, for the Netherlands and for Singapore the VDC for M2 does not exceed that of the interest rate, even though it did for M1. The results for Portugal indicate that M2 has a greater explanatory power than the interest rate when the DS specification is used. Using M1, we found exactly the opposite: M1 dominated the interest rate when the TS model is used. There also are minor changes in the M1 versus M2 results for Canada, Japan, and Norway. These results indicate that changes in the monetary aggregate can affect outcome, but not always in a predictable fashion (e.g., moving to a broader measure leads to increased importance of the interest rate).

The most noticeable change between Tables 2 and 3 is that the results for Turkey indicate that M2 but not M1 plays a prominent role in explaining the variance of output. This switch may be explained by the significant trend of "dollarization" in Turkey. (16) Since Turkey's M2 includes foreign currency deposits, the behavior of M2 and its potential impact on real output in Turkey may reflect nonpolicy actions taken by the public in how they manage their portfolio of financial assets. For the broader M2 measure the specification (TS vs. DS) and ordering have no effect on the significance of money in explaining output variance. The most striking result in Table 2 is that M2 dominates the interest rate in Germany, New Zealand, and Switzerland. This finding not only appears to be robust across specifications, but also across definitions of money.

Overall, the results in Tables 2 and 3 suggest that the behavior of money may be more important in explaining real output fluctuations than some have concluded. (17) Although interpreting results such as these can be likened to a beauty contest, a money-friendly view is that the results do not reject the notion that in many countries money can serve as a useful indicator of future real output behavior. Such a conclusion is supported by the data in half of the countries tested. Viewing the results slightly differently, the fact that interest rates dominate money in only half of the countries is not overwhelming support for the predominant view among economists and policy makers that interest rates are the only variable worth considering in policy analysis and deliberations.

Perhaps the most interesting finding is that money dominates the interest rate in Germany, New Zealand, and Switzerland. (18) This statement also is true for M2 in Turkey. What separates these countries from the others? Is there something unique about them that generates this outcome? In the next section, we investigate this question by comparing the financial development and structure of these countries with the others used.

4. The Role of Financial Size and Structure (19)

Are Germany, New Zealand, and Switzerland characterized by some financial market development or structure that helps explain our findings? To answer this we utilize the data set constructed by Beck, Demirguc-Kunt, and Levine (1999). This data set is a comprehensive collection of economic and social measures used primarily in research on economic growth. We selected several measures to capture the relative size of the central bank and the banking system, measured relative to total financial assets and to GDP. We also gauge the "depth" of the country's financial markets using statistics such as the ratio of liquid liabilities to GDP and private credit extended by the banking system relative to GDP. Measures of the structure and efficiency of the countries' financial system also are used, including the three-bank concentration ratio, overhead costs, and net interest margins of commercial banks. Finally, we include measures of the relative size of the stock and bond markets. A complete listing of the measures use d and their mnemonics is provided in Table 4. Table 5 presents summary statistics associated with each financial measure listed in Table 4 available, for each country. For the sake of comparison, Germany, New Zealand, and Switzerland are separated from other countries.

Do the financial data reveal any discernible pattern that explains our empirical results? In brief, the answer is no. For one thing, there is a great deal of variation in each measure across countries. In Germany and Switzerland, for example, central banks assets are less than one percent of total assets (CBA/TA). In New Zealand, however, the figure is over 6%. (For purpose of comparison, the figure for the United States is less than 3%.) Glancing down this column reveals that Germany and Switzerland have among the lowest measures in this category. Even so, similarly low measures are reported for France and the Netherlands, two countries for which money was not found to exert much influence on output relative to interest rates. The measure "deposit bank assets relative to total" (DBA/TA) indicates less dispersal among countries, but no clear pattern emerges that would distinguish one country from another. Size of the central bank and of the commercial banking system relative to the whole financial system thus do not appear as a likely explanations for our empirical results.

When measures of the financial system relative to GDP are considered, the size of the financial markets relative to GDP in Switzerland is larger than the average. Although "central bank assets to GDP" seem extraordinary, the other three measures all register the largest values of any country in the sample. Still, the fact that such is not found for Germany and New Zealand suggests that this characteristic isn't unique and is not an explanation for finding that money explains the behavior of real output better than interest rates.

Is there any evidence in measures of financial market structure and efficiency that solve the puzzle? The statistics under this umbrella heading presented in Table 5 suggest that the answer is no. Regardless of the specific measure used, whether it is the three-bank concentration ratio, measures of efficiency, or size of the stock and bond markets, there is no apparent pattern that accounts for the findings in Tables 2 and 3.

5. Conclusions

This study examines the empirical relation between money, interest rates, and output across a sample of diverse economies. Previous analyses often rely on U.S. data or other financially developed countries from a specific region, such as the EU. In contrast, the evidence presented in this paper is based on a diverse sample of 20 countries, including industrial countries from different regions as well as economically and financially less-developed countries.

Our results indicate that rejecting money as an informative tool in setting monetary policy is unwarranted. First, the results suggest that money often plays a significant role in explaining the fluctuations of real output. Across the different specifications used and countries examined, money accounts for more of the variance in real output than nominal interest rates in about half of the countries. Second, the results indicate that concern over the stationarity assumption, found to be important for the United States, can alter conclusions about the relative importance of money and interest rates in other countries. In summary, the results do not support an out-and-out rejection of money as an informative economic variable when it comes to setting or evaluating monetary policy.

The most intriguing result is that in Germany, New Zealand, and Switzerland money, Ml or M2, always explains a greater percentage of the variation in real output than do interest rates. Other than the well-known bias toward low-inflation policies by these central banks, a review of data measuring the size, structure, and efficiency of their financial systems provides no obvious pattern to explain the results.

Appendix

All quarterly data are taken from IMF's International Financial Statistics CD-ROM tape. The following further describes the data and indicates the sample periods for each country:

Prices: CPI, 1990 = 100, line 64

Money: Narrow money (Ml) line 34 and M2 = Ml + quasi money (line 5)

Output: Real GDP (1990 prices), line 90

Interest rate: Money market rate (line 60B) for all countries, except Mexico and Israel (T-bill rate, line 60C), and Finland (central bank rate, line 60)

Table 1

Summary Statistics

 Mean and Standard Deviation (in Parentheses)
Country [DELTA]RGDP [DELTA]M1 [DELTA]M2 [DELTA]CPI

United States 288 (0.92) 5.48 (1.77) 7.24 (1.17) 4.28 (0.80)
Australia 3.21 (1.25) 10.72 (2.65) 11.44 (1.99) 7.16 (1.61)
Canada 2.80 (0.86) 8.72 (2.66) 9.24 (1.81) 5.04 (1.15)
Finland 2.52 (6.02) 15.72 (10.16) 10.96 (2.21) 6.96 (1.56)
France 2.48 (0.71) 7.96 (5.13) 13.08 (6.53) 6.04 (1.38)
Germany 3.12 (1.53) 7.88 (1.80) 8.28 (1.96) 3.20 (0.91)
Israel 4.56 (2.26) 21.68 (5.02) 19.44 (2.11) 12.96 (1.50)
Italy 2.40 (0.86) 11.28 (14.34) 10.76 (9.37) 9.28 (2.09)
Japan 5.04 (1.61) 10.80 (2.51) 11.20 (2.83) 4.32 (1.61)
Korea 5.48 (21.37) 13.84 (6.88) 18.48 (2.32) 7.92 (1.90)
Mexico 2.64 (5.34) 35.84 (8.98) 34.48 (15.56) 28.64 (7.32)
Netherlands 2.24 (0.92) 6.40 (1.80) 6.04 (1.27) 2.88 (0.78)
New Zealand 2.24 (2.90) 13.80 (10.81) 15.60 (10.13) 5.28 (1.59)
Norway 3.44 (4.00) 11.96 (3.67) 9.04 (2.20) 6.04 (1.28)
Portugal 2.68 (1.75) 14.48 (11.47) 14.96 (4.11) 11.20 (2.20)
Singapore 6.84 (3.44) 8.44 (2.81) 11.84 (1.78) 1.68 (0.63)
Spain 2.32 (0.48) 11.68 (2.04) 11.28 (2.63) 9.44 (1.94)
Sweden 2.64 (11.96) 3.72 (53.64) 11.96 (8.06) 7.92 (1.60)
Switzerland 1.68 (1.25) 4.24 (3.95) 6.48 (2.19) 2.88 (0.84)
Turkey 5.56 (27.47) 52.28 (12.31) 60.56 (5.20) 56.28 (5.04)

 Mean and
 Standard
 Deviation (in
 Parentheses)
Country R Sample Period

United States 6.41 (3.32) 1957:4-1998:3
Australia 9.37 (3.76) 1970:1-1996:3
Canada 8.91 (3.67) 1975:2-1998:2
Finland 8.12 (1.38) 1970:2-1996:2
France 8.82 (3.14) 1970:2-1998:2
Germany 5.52 (2.50) 1960:2-1998:3
Israel 14.60 (3.60) 1986:2-1998:2
Italy 12.37 (4.24) 1970:2-1997:2
Japan 6.41 (3.12) 1957:4-1998:2
Korea 14.25 (3.94) 1977:1-1998:2
Mexico 39.75 (31.11) 1987:1-1997:3
Netherlands 6.52 (2.46) 1997:2-1997:4
New Zealand 12.71 (5.70) 1983:2-1998:2
Norway 9.87 (3.50) 1973:2-1998:2
Portugal 13.33 (4.49) 1981:2-1997:4
Singapore 4.27 (1.51) 1984:4-1998:1
Spain 12.39 (4.95) 1974:2-1998:2
Sweden 9.42 (3.17) 1969:2-1989:4
Switzerland 3.36 (2.33) 1976:1-1998:2
Turkey 68.35 (32.30) 1987:2-1998:1

RGDP is real GDP (1990$), M1 is the narrow definition of money, M2 is
the broad definition of money, CPI is the consumer price index, and R is
a short-term interest rate. [DELTA] is the difference operator. All
variables except the interest rate are expressed in logarithms. A more
complete description of the data and the sample periods is found in the
data Appendix.
Table 2

Variance Decompositions

 Money/Rate
 Trend Difference
Money: M1 Stationary Stationary Stationary
Country Order Without Trend (TS) (DS)

United States 1 28.17/26.82 25.45/12.78 2.81/21.94
 2 25.40/30.37 24.51/16.58 2.25/13.02
 Standard 0.03565 0.2488 0.00860
 Error (SE)
Australia 1 13.10/20.56 12.98/7.19 7.88/8.47
 2 10.52/22.05 13.20/5.17 7.51/8.58
 SE 0.03117 0.01936 0.01215
Canada 1 16.08/51.44 21.00/44.12 1.97/10.5
 2 16.10/47.95 21.12/43.85 13.56/11.94
 SE 0.02655 0.02446 0.00848
Finland 1 2.50/45.13 3.18/7.85 1.70/21.54
 2 0.68/46.24 0.48/9.18 1.76/23.98
 SE 0.03901 0.02284 0.2577
France 1 8.66/42.45 4.23/36.15 11.45/17.15
 2 9.09/53.40 5.06/48.46 10.37/16.23
 SE 0.02393 0.02026 0.00692
Germany 1 52.32/9.74 27.53/4.30 16.01/2.92
 2 43.43/8.54 22.94/4.90 25.58/2.26
 SE 0.04511 0.03134 0.01514
Israel 1 10.59/8.36 10.25/9.14 29.6/8.53
 2 4.78/1.83 5.51/2.40 12.36/5.88
 SE 0.03028 0.02393 0.01980
Italy 1 12.34/44.17 13.61/45.58 11.46/15.59
 2 7.31/43.00 7.38/46.35 2.44/16.67
 SE 0.02314 0.02190 0.00857
Japan 1 0.67/0.28 0.93/0.21 6.94/4.77
 2 2.53/0.15 3.07/0.16 2.68/4.59
 SE 0.06386 0.06473 0.01617
Korea 1 8.60/35.70 6.73/35.47 3.76/6.13
 2 5.42/7.98 4.39/9.29 2.94/3.23
 SE 0.06953 0.06101 0.04988
Mexico 1 6.29/35.44 13.35/18.02 17.36/18.00
 2 4.07/9.52 8.86/16.54 14.46/15.70
 SE 0.03081 0.02407 0.01986
Netherlands 1 31.00/23.68 14.81/21.85 10.69/9.01
 2 34.17/22.90 16.74/12.62 7.90/3.58
 SE 0.01726 0.01482 0.00926
New Zealand 1 20.56/24.26 21.78/13.53 25.48/4.34
 2 34.10/6.45 11.04/6.54 16.27/2.84
 SE 0.05654 0.02457 0.02799
Norway 1 7.32/30.51 14.06/30.33 8.32/19.34
 2 6.67/13.34 14.22/21.49 8.06/16.82
 SE 0.04337 0.03087 0.02393
Portugal 1 37.23/24.02 52.50/17.41 11.65/16.46
 2 17.63/7.10 49.74/24.19 7.71/11.98
 SE 0.01640 0.01326 0.01424
Singapore 1 57.23/33.65 36.20/28.88 19.44/6.85
 2 29.09/30.73 23.15/29.54 21.31/5.84
 SE 0.08495 0.02432 0.01567
Spain 1 5.41/14.03 6.85/1.76 22.35/7.69
 2 6.91/14.11 4.33/3.16 20.16/11.45
 SE 0.03454 0.02458 0.00440
Sweden 1 16.79/19.45 10.95/11.12 13.72/4.53
 2 8.71/16.91 6.37/8.07 15.64/1.94
 SE 0.02496 0.02328 0.02423
Switzerland 1 59.61/16.27 42.95/17.54 26.16/11.01
 2 53.33/13.94 39.19/12.42 21.61/8.46
 SE 0.03620 0.03060 0.01094
Turkey 1 12.09/35.02 17.96/32.06 20.08/18.59
 2 14.59/34.75 23.78/30.95 19.19/21.38
 SE 0.04056 0.04044 0.04805

Order 1: R, M, CPI, RGDP. Order 2: RDGP, CPI, R, M. Variable definitions
and sources are documented in Table 1 and the data Appendix. Results in
bold indicate that the VDC of money exceeds 10% and exceeds the VDC for
the interest rate by 5% (not percentage points).
Table 3

Variance Decompositions

 Money/Rate
 Trend Difference
Money: M2 Stationary Stationery Stationary
Country Order Without Trend (TS) (DS)

United States 1 9.74/36.72 26.76/16.54 4.70/25.10
 2 5.25/36.66 19.58/15.62 3.46/11.76
 Standard 0.03714 0.02721 0.00861
 Error (SE)
Australia 1 13.10/20.56 12.98/7.19 9.47/5.97
 2 10.53/22.05 13.20/5.17 7.18/6.19
 SE 0.03121 0.01879 0.01216
Canada 1 5.46/69.95 14.71/48.23 4.84/7.84
 2 4.23/64.84 13.68/51.65 3.75/10.02
 SE 0.02959 0.02404 0.00845
Finland 1 22.51/40.14 18.31/9.78 4.07/21.48
 2 10.82/40.39 3.98/11.05 1.54/24.13
 SE 0.03521 0.02447 0.02579
France 1 5.96/47.33 7.93/34.29 10.75/15.50
 2 3.68/59.15 3.79/45.82 7.06/14.68
 SE 0.02285 0.01975 0.00694
Germany 1 36.27/13.11 37.66/4.58 14.92/2.78
 2 27.68/10.57 33.37/2.41 15.24/2.08
 SE 0.04369 0.02923 0.01509
Israel 1 10.08/13.59 8.94/14.00 12.17/9.41
 2 4.31/3.90 5.60/4.22 11.21/6.70
 SE 0.02524 0.02382 0.01976
Italy 1 13.13/33.49 10.36/50.40 8.67/15.68
 2 6.70/26.66 6.54/40.32 3.87/15.60
 SE 0.02011 0.02129 0.00858
Japan 1 7.99/1.07 7.46/3.87 12.88/4.32
 2 4.45/0.12 4.68/1.15 9.90/3.91
 SE 0.05681 0.05723 0.01585
Korea 1 4.31/42.80 4.92/41.90 2.07/5.68
 2 4.03/15.41 4.57/19.44 1.79/5.71
 SE 0.07344 0.06480 0.05050
Mexico 1 7.66/36.15 14.56/44.40 19.79/21.81
 2 5.64/6.45 3.98/12.33 9.28/20.07
 SE 0.02943 0.02592 0.01965
Netherlands 1 17.22/43.95 20.23/21.99 4.94/7.94
 2 10.11/40.90 11.19/14.05 2.90/2.51
 SE 0.01758 0.01485 0.00923
New Zealand 1 12.37/22.13 34.84/12.72 26.43/9.74
 2 22.67/3.48 13.06/3.54 13.35/2.39
 SE 0.04008 0.02751 0.02729
Norway 1 1.01/46.67 7.54/8.71 6.12/15.02
 2 2.57/31.38 10.77/4.84 4.17/13.32
 SE 0.04776 0.03200 0.02390
Portugal 1 3.71/70.88 4.68/69.07 20.54/12.83
 2 1.86/62.92 2.11/64.98 20.18/9.27
 SE 0.02156 0.02144 0.01528
Singapore 1 26.38/29.15 14.81/25.17 7.39/10.08
 2 32.80/31.87 14.36/25.78 6.41/9.46
 SE 0.03932 0.02610 0.00439
Spain 1 1.00/31.89 5.34/2.19 7.39/8.01
 2 0.34/29.36 2.89/2.69 10.44/10.87
 SE 0.03598 0.02610 0.00439
Sweden 1 3.06/30.44 3.60/19.13 1.18/5.34
 2 3.15/22.12 3.97/11.86 1.36/2.84
 SE 0.02451 0.02258 0.02285
Switzerland 1 47.00/17.45 45.73/17.23 15.35/7.53
 2 46.00/16.60 46.39/15.78 15.02/5.62
 SE 0.02717 0.02697 0.01080
Turkey 1 25.65/19.21 35.99/27.47 41.72/18.27
 2 10.89/5.55 35.37/7.45 40.39/13.49
 SE 0.04690 0.03845 0.05139

Notes: See Table 2.
Table 4

Description of Financial Development Variables

Variable Definition


CBA/TA Central bank assets to total
 financial assets






DBA/TA Deposit money bank assets to
 total financial assets





CBA/GDP Central bank assets to GDP


DBA/GDP Deposit money banks assets
 to GDP

LL/GDP Liquid liabilities to GDP





PC/GDP Private credit by deposit
 money banks to GDP


CONC Three-bank concentration
 ratio


OVER/TA Overhead costs to total
 assets


NIM/TA Net interest margin to
 total assets



CAP/GDP Stock market capitalization
 to GDP


DEBT/GDP Long-term private debt issues
 to GDP


Variable Description/Page Reference to Beck,
 Demirgue-Kunt, and Levine (1999)

CBA/TA Central bank defined as
 institutions that perform duties
 of central banks. Total financial
 assets equal sum of central bank,
 deposit money bank, and other
 financial institutions assets.
 End-of-period. pages 5-6

DBA/TA Deposit money banks are all
 financial institutions whose
 liabilities are in the form of
 deposits transferable by check
 or otherwise used in making
 payments. End-of-period. Page 6

CBA/GDP Central bank assets defined above,
 GDP as measured in IMF. Page 6

DBA/GDP Deposit money banks and GDP as
 defined above. Page 6

LL/GDP Sum of currency, demand deposits
 and interest-bearing liabilities
 of banks and other financial
 intermediaries relative to GDP.
 Pages 6-7

PC/GDP Claims on private sector by
 deposit money banks relative to
 GDP. Page 7

CONC Ratio of three largest banks'
 assets to total banking sector
 assets. Page 11

OVER/TA Accounting value of bank's overhead
 costs relative to its total
 assets. End-of-period. Page 10

NIM/TA Accounting value of value of bank's
 net interst revenue relative to
 total assets. End-of-period. Page
 10

CAP/GDP Value of listed shares on country's
 stock market relative to GDP.
 Values are end-of-year. Page 17

DEBT/GDP Enquity issues, both long-term and
 debt issues, relative to GDP.
 Nominal measure. Page 18

Source: Beck, Demirguc- Kunt, and Levine (1999).
Table 5

Measures of Financial Size, Structure and Efficiency

 Size
Country CBA/T DBA/T CBA/GDP DMBA/GP LL/GDP

Germany 0.95 93.43 1.14 110.12 64.10
New Zealand 6.12 66.62 3.91 48.84 55.43
Switzerland 0.77 81.27 1.45 154.31 138.18
Australia 2.86 55.05 2.88 56.11 56.42
Canada 4.68 60.87 4.20 53.68 68.53
Finland na na 1.55 68.14 51.09
France 0.74 72.24 1.06 93.87 68.02
Israel na na 11.17 97.01 62.94
Italy na na 11.98 69.39 69.70
Japan 1.80 50.12 4.19 119.16 168.31
Korea, Rep. of 3.11 57.03 2.49 48.35 46.15
Mexico 17.60 48.78 7.69 19.18 23.37
Netherlands 0.46 51.42 0.84 93.66 81.76
Norway 2.38 54.76 2.88 93.13 53.83
Portugal na na 14.07 79.80 73.19
Singapore na na na 89.63 102.71
Spain 7.14 85.99 7.30 87.45 72.85
Sweden 5.50 41.23 7.25 54.12 49.82
Turkey 34.38 59.61 9.26 18.64 21.82
United States 2.91 47.15 4.66 75.13 62.61

 Size Structure and Efficiency
Country PC/GDP CONC OVER/A NIM/TA CAP/GDP

Germany 92.26 44.16 2.77 2.46 18.64
New Zealand 54.17 76.94 2.75 2.51 40.47
Switzerland 177.64 73.92 4.94 1.55 70.59
Australia 81.23 67.44 2.61 1.92 43.10
Canada 76.63 58.01 2.44 1.75 45.54
Finland 66.99 86.46 1.65 1.60 18.44
France 90.89 40.66 4.41 3.51 19.77
Israel 50.54 86.39 3.82 3.30 28.89
Italy 50.50 35.81 3.56 3.60 11.87
Japan 169.26 20.99 1.39 1.75 73.01
Korea, Rep. of 80.90 33.40 2.48 2.29 24.55
Mexico 17.61 59.06 5.03 5.35 14.55
Netherlands 127.97 73.34 1.00 1.46 40.92
Norway 88.51 84.54 2.48 3.13 15.19
Portugal 63.21 45.27 2.56 3.46 7.75
Singapore 94.80 72.91 1.43 2.09 123.06
Spain 72.02 46.44 3.49 3.76 18.08
Sweden 108.94 88.57 3.07 2.66 38.09
Turkey 13.82 44.77 6.36 9.37 6.14
United States 130.74 18.21 3.65 3.88 58.18

 Structure
 and
 Efficiency
Country DEBT/GDP

Germany 37.43
New Zealand 0.00
Switzerland 62.09
Australia 13.76
Canada 8.62
Finland 39.09
France 41.24
Israel 0.00
Italy 28.10
Japan 29.99
Korea, Rep. of 32.19
Mexico 0.97
Netherlands 16.56
Norway 19.17
Portugal 10.59
Singapore 3.65
Spain 9.28
Sweden 57.56
Turkey 0.69
United States 52.58

Notes: All measures are in percentages.

Source: Beck, Demirgue-Kunt, and Levine (1999).

Definitions of the measures used are provided in the data appendix to
this paper.

Received May 2000; accepted December 2001.

(1.) The importance of interest races has been questioned in several studies. Bernanke (1990) reports that the empirical significance of the interest rate variable declines throughout the 1980s. Hafer and Kutan (1997) demonstrate that the impact of interest rates on output and the apparent decline in money's importance through the 1980s is largely a function of the stationarity assumption used.

(2.) This consensus model can be written as a three-equation dynamic system, including an aggregate demand equation, a Phillips curve, and a monetary policy rule. In this model, aggregate demand movements are driven by past deviations of output from potential and changes in the real rate of interest. As such, monetary policy works only indirectly through the interest rate channel. For another discussion of this model, see MeCallum (2001). Nelson (2000) provides empirical estimates that refute the findings of Rudebusch and Svensson, at least for the United Kingdom and the United States. Where Rudebusch and Svensson find that M2 has no predictive power over output in the United States, Nelson finds that movements in the St. Louis adjusted monetary base do. See also Hafer (2001).

(3.) Hayo (1999) uses a similar VAR model.

(4.) Nelson's (2000) work demonstrates that conclusions about money are subject to this concern.

(5.) Running a regression of real output growth on money growth across countries results in an estimated coefficient on money growth of 0.04 for M1 and M2, statistically insignificant at the 5% level. Conversely, a regression of inflation on money growth yields estimated coefficients of 1.02 for M1 and 0.97 for M2, both significant at the 1% level of significance. These results support the belief that increasing money growth does not permanently increase real output growth, but is more likely to lead to higher inflation. For a similar analysis and a review of the relevant literature, see Dwyer and Hater (1999) and Hater (2001).

(6.) We searched for apparent structural breaks in data. Time-series plots of the data indicated a significant break for M1 for Finland during the second quarter of 1991. Therefore, for Finland, the estimated VAR models with M1 include a dummy variable that takes a value of 1 starting from 1991:II to the end and zero otherwise.

(7.) See, among others, Hafer and Sheehan (1991) and the articles cited therein.

(8.) A complete listing of the lag-length test results is available on request.

(9.) In an earlier version of this paper we also reported Wald tests. Such tests can be viewed as "within-sample" tests, because they do not provide an indication of the dynamic characteristics of variables in the system and their usefulness is limited to the sample period used. As a result, we rely on variance decompositions, which are considered as out-of-sample tests, to gauge the relative strength of money and interest rates on output. For further discussion of these issues, see Masih and Masih (2001).

(10.) The complete set of results is available upon request.

(11.) Increasing the horizon does not affect the qualitative outcomes reported.

(12.) For ease of presentation, only the VDC results for money and interest rates are presented. A full set of results is available upon request. One could also consider the impact of exchange rates on output within the VAR model. We believe that the domestic interest rate captures this impact through interest parity relation, which states that [i.sub.d] - [i.sub.f] = e, where [i.sub.d] and [i.sub.f] are domestic and foreign interest rates, respectively, and e is the expected change in the exchange rate. Assuming that this parity relation holds, which is a reasonable assumption because of the increasing level of world capital mobility, domestic interest rates may capture foreign influences, such as changes in foreign interest rates and exchange rates, In case of a fixed exchange rate regime, using exchange rates is not relevant. Therefore, our VAR models do not include exchange rates.

(13.) It is unresolved in the literature whether the interest rate should be included in its level of first-differenced form. Bernanke and Blinder (1992) argue that including a first-differenced interest rate in a VAR model is questionable. Because there is no agreed-upon procedure, the DS specification was estimated with the interest rate in its level form. These results led to the same conclusions as the DS specification, except for Mexico, where the results are markedly different from those reported in Table 2. In that case the DS specification with the levels of the interest rate produced an M1 VDC that was larger than that for the interest rate, and exceeded 10%. Complete results using this specification are available upon request.

(14.) One could draw a similar conclusion for Canada and the Netherlands. However, in those cases a change in the VAR ordering changes the outcome, suggesting that the sensitivity of money's role is explained by more than the use of the TS or DS specifications alone.

(15.) For a discussion of central bank policies in Germany, see von Hagen (1999); for Switzerland, see Bernanke et al. (1999, chapter 4); and for New Zealand, see Evans et al. (1996) and Bernanke et al. (1999, chapter 5). For a general discussion of the role of central banks, see Bernanke et al. (1999) and Mishkin (1999).

(16.) The dollarization ratio based on the IMF data, as measured by the ratio of foreign currency deposits to GDP, was about 5% in 1990. This ratio jumped to around 15% in 1995 and then to 20% in 2000.

(17.) The results of Nelson (2000) and Hafer (2001) agree with this assessment.

(18.) This outcome is robust to changing the sample period. At the suggestion of the referee, the VAR models were reestimated using a common sample. Attempting to maximize the sample length and the number of countries produced a limited subset of the original countries sample. Even so, over a common sample period of 1977/I-1996/II, M1 and M2 still generate VDCs that are large relative to the interest rate for Germany and Switzerland. The only other notable result from this estimate is that money, regardless of the specification, plays a secondary role to the interest rate in explaining output in the United States. Complete common-sample estimates are available upon request.

(19.) We thank the referee for suggesting this line of inquiry.

References

Beck, Thorsten, Asli Demirguc-Kunt, and Ross Levine. 1999. A new database on financial development and structure. Unpublished paper, University of Minnesota.

Bernanke, Ben S. 1990. On the predictive power of interest rates and interest rate spreads. New England Economic Review 51-68.

Bernanke, Ben, and Alan S. Blinder. 1992. The Federal funds rate and the channels of monetary transmission. American Economic Review 82:901-21.

Bernanke, Ben. S., Thomas Laubach, Frederic S. Mishkin, and Adam S. Posen. 1999. Inflation targeting: Lessons from the international experience. Princeton, NJ: Princeton University Press.

Christiano, Lawrence J., and Lars Ljungqvist. 1998. Money does Granger-cause output in the bivariate money-output relation. Journal of Monetary Economics 22:217-36.

Canova, Fabio. 1998. Detrending and business cycle facts. Journal of Monetary Economics 41:475-512.

Davis, Mark S., and J. Ernest Tanner. 1997. Money and economic activity revisited. Journal of International Money and Finance 16:955-68.

Dejong, David N., John C. Nankervis, N. E. Savin, and Charles H. Whiteman. 1992. The power problems of unit root tests in time series with autoregressive errors. Journal of Econometrics 53:323-43.

Dejong, David N., and Charles H. Whiteman. 1991. Reconsidering trends and random walks in macroeconomic time series. Journal of Monetary Economics 28:221-54.

Dwyer, Gerald P., Jr., and R. W. Hafer. 1999. Are money growth and inflation still related? Federal Reserve Bank of Atlanta Economic Review 84:32-43.

Evans, Lewis, Arthur Grimes, Bryce Wilkinson, and David Teece. 1996. Economic reform in New Zealand 1984-95: The pursuit of efficiency. Journal of Economic Literature 34:1856-902.

Friedman, Benjamin M., and Kenneth N. Kuttner. 1992. Money, income, prices and interest rates. American Economic Review 82:472-92.

Friedman, Benjamin M., and Kenneth N. Kuttner. 1993. Another look at the evidence on money-income causality. Journal of Econometrics 57:189-203.

Hafer, R. W. 2001. What remains of Monetarism? Federal Reserve Bank of Atlanta Economic Review Fourth Quarter: 13-33.

Hafer, R. W., and A. M. Kutan. 1997. More evidence on the money-output relationship. Economic Inquiry 35:48-58.

Hafer, R. W., and Richard G. Sheehan. 1991. Policy inference using VAR models: The effects of alternative lag structures. Economic Inquiry 29:44-52.

Hayo, Bernd. 1999. Money-output and Granger causality revisited: An empirical analysis of EU countries. Applied Economics 31:1489-501.

Krol, Robert, and Lee E. Ohanian. 1990. The impact of stochastic and deterministic trends on money-output causality: A multi-country investigation. Journal of Econometrics 45:291-308.

Masih, Rumi, and Sbul M. M. Masih. 2001. Long and short term dynamic casual transmission amongst international stock markets. Journal of International Money and Finance 20:563-87.

McCallum, Bennett T. 2001. Monetary policy analysis in models without money. Federal Reserve Bank of St. Louis Economic Review 83:145-63.

Meyer, Laurence H. 2001. Does money matter? Federal Reserve Bank of St. Louis Economic Review 84:1-15.

Mishkin, Frederic S. 1999. International experiences with different monetary policy regimes. Journal of Monetary Economics 43:579-605.

Nelson, Edward. 2000. Direct effects of base money on aggregate demand: Theory and evidence. Unpublished paper, Bank of England.

Rudebusch, Glenn D. 1993. The uncertain unit of root in real GNP. American Economic Review 83:264-72.

Rudebusch, Glenn D., and Lars E.O. Svensson. 1999. Policy rules for inflation targeting. In Monetary policy rules, edited by John B. Taylor. Chicago: University of Chicago Press, pp. 203-62.

Rudebutch, Glenn D., and Lars E.O. Svensson. 2002. Eurosystem monetary targeting: Lessons from U.S. data. European Economic Review 46:417-42.

Sims, Christopher A. 1980. Comparison of interwar and postwar business cycles: Monetarism reconsidered. American Economic Review 70:250-7.

Stock, James H., and Mark W. Watson. 1989. Interpreting the evidence on money-income causality. Journal of Econometrics 40:161-81.

Swanson, Norman R. 1998. Money and output viewed through a rolling window. Journal of Monetary Economics 41:455-73.

Thoma, M. A. 1994. Subsample instability and asymmetrics in money-income causality. Journal of Econometrics 64:279-306.

Todd, Richard M. 1990. Vector autoregression evidence on monetarism: Another look at the robustness debate. Federal Reserve Bank of Minneapolis Quarterly Review 14:19-37.

Von Hagen, Jurgen. 1999. Money growth targeting by the Bundesbank. Journal of Monetary Economics 43:681-701.

R. W. Hafer * and Ali M. Kutan +

* Department of Economics and Finance, Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA; E-mail rhafer@siue.edu; corresponding author.

+ Department of Economics and Finance, Southcm Illinois University Edwardsville, Edwardsville, IL 62026, USA, and Center for European Integration Studies (ZEI), Bonn, Germany. E-mail akutan@siue.edu.

This paper began while Hafer was a Research Fellow, Institute for Urban Research, and a Visiting Scholar, Federal Reserve Bank of Atlanta; and Kutan was a Visiting Scholar with the Federal Reserve Bank of St. Louis. We thank Garett Jones, colleagues at the Banks, and an anonymous referee for comments and suggestions that improved an earlier version of this paper. Tansu Aksoy provided excellent research assistance. The views and conclusions expressed may not be those of the Federal Reserve Banks of Atlanta and St. Louis, or of the Federal Reserve System.