CROSS-COUNTRY VARIATION IN THE LIQUIDITY EFFECT: THE ROLE OF FINANCIAL

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CROSS-COUNTRY VARIATION IN THE LIQUIDITY EFFECT: THE ROLE OF FINANCIAL MARKETS* William D. Lastrapes and W. Douglas McMillin This paper examines cross-country variation in the liquidity effect 3 the negative response of interest rates to money supply shocks 3 focusing on the role of nancial factors in explaining this variation.

We estimate the liquidity effect for each of 21 countries using VAR models in which money supply shocks are restricted to be neutral in the long-run, then regress the estimated liquidity effect on nancial market variables across countries. We nd that nancial factors play an important role in determining the magnitude of the liquidity effect, and that this evidence is most consistent with generalised versions of limited-participation models. Over the past decade, empirical macroeconomists have accumulated substantial time-series evidence supporting the existence of a 8liquidity effect 9 3 the tempor- ary, but persistent, negative response of interest rates to nominal money supply shocks.

1 This evidence is inconsistent with classical assumptions of price exibility, perfect information and insigni cant transactions costs 3 money supply shocks will be matched in this case by proportional price level responses, money will be neutral, and there will be no liquidity effect. However, the speci c type ... more. less.

of market rigidity that generates the observed liquidity effect is not yet well understood. Understanding the sources of the liquidity effect is important in distinguishing among alternative explanations of the monetary transmission mechanism, and thus helping determine the types of models best suited for the analysis of monetary policy. Time series evidence alone is possibly not rich enough to explain the existence and magnitude of the liquidity effect completely. Cross-country variation in the liquidity effect is potentially informative in this regard but has not been fully examined. To our knowledge, no studies have systematically documented or compared the magnitude of the liquidity effect across countries. At best, extant comparisons in the literature are informal and qualitative in nature, and are made over only a handful of countries (e.g., the G-7 countries). In this paper, we attempt to begin lling this void in the literature. We do so by estimating the liquidity effect for a larger country sample (21 countries) than other studies, using a common time-series technique and a careful empirical strategy for * The authors appreciate helpful comments from George Selgin, Jim Fackler, Tim Fuerst, two very helpful anonymous referees, Mike Wickens (the editor), and participants at the Econometric Society European Meetings in Venice, 2002, and the Southern Economic Association Meetings in Tampa, 2001. Lastrapes acknowledges research support from a Terry-Sanford research grant at the Terry College of Business. Part of the work on this project was done while Lastrapes was a Visiting Scholar at the Federal Reserve Bank of Atlanta. 1 A partial list of studies that nd a liquidity effect in US data includes Christiano et al . (1999), Bernanke and Mihov (1998), Hamilton (1997), Strongin (1995), Lastrapes and Selgin (1995), Gordon and Leeper (1994) and Bernanke and Blinder (1992). Pagan and Robertson (1995) survey some of the earlier literature. Evidence from countries besides the US can be found in Kim (1999), Fung and Kasumovich (1998), Lastrapes (1998), Cushman and Zha (1997), Grilli and Roubini (1996), and Sims (1992). The Economic Journal , 114 ( October ), 890 3915. Ó Royal Economic Society 2004. Published by Blackwell Publishing,9600GarsingtonRoad,OxfordOX4 2DQ,UKand350 MainStreet, Malden, MA 02148,USA. [ 890 ] appropriately identifying the liquidity effect. We then focus on the role of nancial factors in explaining the observed cross-country variation in our measures of the liquidity effect. While our approach is limited by the availability of consistent interest rate data and the extent to which good proxies for nancial market factors can be found, we believe that this paper takes a step forward in bringing inter- national evidence to bear on the source of liquidity effects and the monetary transmission mechanism. Institutional aspects of nancial markets 3 transactions costs, the prominence and health of nancial intermediaries, the ef ciency of secondary markets, and so on 3 are likely to be important in any explanation of the existence and magnitude of the liquidity effect, regardless of the ultimate source of short-run monetary non- neutrality. We have in mind three broad classes of models that would predict a role for such factors in explaining the liquidity effect. First, the state of credit markets and institutions are likely to have an important effect on the elasticity of money demand. For example, a highly developed banking system might allow a large number of substitutes for money, and thus promote a high interest rate elasticity. In this case, and in the presence of nominal rigidities in goods or labour markets, a given change in the supply of money would be associated with a relatively small liquidity effect. Thus, characteristics of nan- cial markets can in uence the liquidity effect even when they are not the ultimate cause of monetary non-neutralities. Second, nancial market factors can in uence the liquidity effect in models of credit-market imperfections such as the bank-lending channel of monetary transmission (e.g. Bernanke and Gertler 1995; Bernanke and Blinder 1988). According to these models, which are based upon asymmetric information, changes in the money supply, by affecting the supply of bank loans, affect the yield spread between bank loans and bonds and thus the cost of funds for bank- dependent borrowers. Because spending will respond to changes in bank loan rates for a given bond rate, the bond rate response to a money supply shock (the liquidity effect) will be smaller when the bank-lending channel is operative than when it is not. Finally, generalised versions of limited participation models imply a direct role for nancial factors in explaining variation in the liquidity effect. The original versions of these dynamic general equilibrium models introduce rigidities on the saving behaviour of households. In particular, households can rebalance their portfolios only with a lag when money shocks occur 3 in effect they face in nite transactions costs of (immediate) portfolio adjustment. This rigidity limits the ability of some agents to participate in nancial markets, thereby causing a liquidity effect when money is injected exogenously into those markets. 2 In Dotsey and Ireland 9s (1995) generalisation of the limited participation model of Christi- ano and Eichenbaum (1995), households have at their disposal a transactions technology that allows portfolio rebalancing at 9nite cost. Their model implies that [ O C T O B E R 2004] 891 C R O S S - C O U N T R Y V A R I A T I O N . . . 2 Fuerst (1992), Lucas (1990) and Christiano (1991), based on the work of Rotemberg (1984) and Grossman and Weiss (1983), are the seminal studies in this literature. Christiano et al . (1997) nds weak and quali ed support for these models. Ó Royal Economic Society 2004 the smaller the transactions costs in nancial markets, the greater the opportunity household 9s have to react or adjust to money shocks, and the smaller is the magnitude of the liquidity effect required to clear the loanable funds market. 3 The estimation procedure in our paper proceeds in two steps. First, using a time- series sample for each country, we employ standard vector autoregression (VAR) methods to estimate the liquidity effect, as described in Section 1 of the paper. To identify money supply shocks from the reduced form VAR, we rely on identifying restrictions implied by long-run monetary neutrality, a well-accepted stylised fact. In the second step in Section 2, we treat the liquidity effect as the dependent variable in a cross-country regression analysis. Financial market variables are the primary independent variables of interest, based on the motivation above, although we control for size of the money shock and other types of rigidities that may have explanatory power. We nd that variables associated with nancial intermediaries have substantial explanatory power for the cross-country variation in the liquidity effect. As argued later, the nding that the variables associated with nancial intermediaries are important while broader nancial market variables are not is more consistent with a limited participation model explanation of cross- country variation in the liquidity effect than with a bank-credit channel explan- ation. These results are robust to changes in the statistical model, nonparametric rank tests, and the inclusion of other type of rigidities and measures of the interest elasticity of money demand in the cross-country regressions. 1. Identifying and Estimating the Liquidity Effect 1.1. The Empirical Model The rst step of the empirical strategy is to use time series data to obtain estimates of the liquidity effect for each country in the sample. These estimates must be reasonable and convincing measures of the response of interest rates to exogenous money supply shocks, and must be consistently obtained across countries. This is a dif cult, but not impossible task. The VAR framework has been the most common means in the literature for estimating the liquidity effect, and we use this approach here. Although the approach has drawbacks, such as a lack of economic restrictions on the dynamics of the system (Cooley and Dwyer, 1998) and sensitivity to identifying restrictions (Pagan and Robertson, 1998; Faust and Leeper, 1997; Faust, 1998), it has the advantage of being able to capture general dynamic relationships and identifying economic interactions without the imposition of too much structure. And, as noted earlier, a large number of studies using VARs with alternative identi cation schemes have found a signi cant liquidity effect. To identify the liquidity effect, we impose long-run monetary neutrality as the key identifying restriction. Long-run monetary neutrality is consistent with most 3 Walsh (1998, p. 189) also notes that the magnitude of the liquidity effect should diminish as transactions costs in nancial markets fall. In his comments on Dotsey and Ireland (1995), Kydland (1995, p. 1459), very much in line with our objectives, suggests that international evidence may be useful in understanding the role of transactions costs in driving liquidity effects. 892 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 macroeconomic models, and is generally accepted as being a good description of long-run behaviour. It is also general enough to accommodate monetary policies that differ greatly across the countries in our sample. As reported below, our estimated responses for all variables in the system generally and reasonably match prior expectations for these effects, which we interpret as lending support to the plausibility of the identifying restrictions and statistical speci cation. However, we also consider the robustness of our estimates to alternative identi cation assumptions and VAR speci cations. A general VAR model would contain all macro variables from all countries. Clearly, such a model would be over-parameterised given the available time series data. To make the VAR analysis tractable, we assume that the domestic variables of country i have no direct impact, either contemporaneously or lag- ged, on the economy of country j , for i e j . This restriction implies that the reduced form covariance matrix for the 8world-wide 9 VAR is block-diagonal in each country block. This block diagonal structure allows us to collapse the general VAR with variables from m countries into m separate, country-speci c VARs. However, these restrictions do not rule out cross-country correlations among the variables in the system since we include a set of exogenous world aggregates in each VAR. Including these aggregates can pick up cross-country correlations through joint dependence on these variables. We also allow cross- country interactions by including a measure of the real exchange rate in each system. 4 Thus, let z it be an n · 1 vector of country-speci c macro variables (in rst dif- ferences), including a nominal interest rate, for country i ( i ¼ 1 ÁÁÁ m ), and w t be an h · 1 vector of exogenous world aggregates, presumably unaffected by economic activity in any particular country. Suppose the country-speci c variables for country i are generated by the following structural model: A 0 i z it ¼ A 1 i z it À 1 þÁÁÁþ A pi z it À p þ B 0 i w t þ B 1 i w t À 1 þÁÁÁþ B qi w t À q þ u it ; ð 1 Þ for all i , in which u it is an n · 1 vector of country speci c structural shocks, with E u it u ¢ it normalised to equal the identity matrix. 5 For notational convenience, let the lag orders p and q be one. The reduced form of this structural model is then z it ¼ A À 1 0 i A 1 i z it À 1 þ A À 1 0 i ð B 0 i þ B 1 i L Þ w t þ A À 1 0 i u it ¼ P 1 i z it À 1 þ P 2 i ð L Þ w t þ e it ; ð 2 Þ where E e it e 0 it ¼ R i ¼ A À 1 0 i A À 1 0 0 i . This reduced form is also the VAR representation of the z it process. Conditional on the block-diagonal restrictions, the coef cients in 4 Not only does the block-diagonal structure preserve degrees of freedom, it eliminates passing mis- speci cation errors from one country to all others. Note that any model of a 8closed 9 economy implicitly makes such a set of restrictions. 5 In effect, we assume that the joint system [ w t z t ] is block exogenous in w (Hamilton 1994, pp. 311 33). This is a standard assumption in most empirical studies of small, open economies, e.g. (Ahmed and Park, 1994; Cushman and Zha, 1997). Since in this study we are interested only in the response of domestic variables to money supply shocks, but not world shocks, we do not compute the response of z to shocks in w t . 2004] 893 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 (2) are ef ciently estimated by ordinary least squares applied to each equation in each country-block. 6 Our objective is to use the estimated VAR in (2) to identify the responses of the macro variables in each domestic economy, interest rates in particular, to the economy 9s own money supply shocks. As noted, we achieve this identi cation by invoking long-run monetary neutrality; to wit, permanent shocks to the nominal money supply in each country have no impact on real variables in that country at the in nite horizon. Suppose that each vector z it contains real variables in the rst n ) 1 elements and the nominal money stock as the nal variable. Furthermore, de ne the nal element in u it vector as an unpredictable shock to money supply behaviour. Sol- ving the difference equation system in (2), and dropping the country notation for convenience, yields two interpretations of the moving average representation of z t : z t ¼ð I À P 1 L Þ P 2 ð L Þ w t þð I À P 1 L Þ À 1 e t \x2 G ð L Þ w t þ C ð L Þ e t ¼ð I À P 1 L Þ P 2 ð L Þ w t þ C ð L Þ A À 1 0 u t \x2 G ð L Þ w t þ D ð L Þ u t ; ð 3 Þ where C (L) ¼ ( I + C 1 L + C 2 L 2 + ÁÁÁ ), and D (L) ¼ ( D 0 + D 1 L + D 2 L 2 + ÁÁÁ ). The reduced form dynamic multipliers, C (L), are obtained directly from estimation of the VAR. However, the parameters of interest 3 the dynamic responses to money supply shocks 3 are contained in nal columns of D (L). Long-run monetary neutrality allows us to identify the parameters of interest from the estimated reduced form coef cients C (L) and R . The restriction sets the elements of the nal column of D ð 1 Þ \x2 P 1 i ¼ 0 D i (the set of in nite-horizon multipliers on the levels of the endogenous variables) to zero, except for the nal element. Thus, a money supply shock is de ned to have a permanent effect on the nominal money stock but no permanent effect on the other (real) variables in the system. Under these restrictions, D (1) is uniquely identi ed as the Cholesky factor of C (1) R C (1) ¢ , and D (L) ¼ C (L) C (1) ) 1 D (1). 7 We take the identi ed dynamic response of the interest rate, after accumulating the response functions to measure the level response, and net of the effects on anticipated in ation, as our measure of the liquidity effect of a money supply shock. 1.2. Estimating the Dynamic Responses Oursamplecomprisesquarterlydatafor21developedcountries,allbutoneofwhich are members of the OECD, over the period 1970:1 to 1998:4. 8 The sample period begins roughly after the post-war xed exchange rate period, and ends prior to the 6 The 8world-wide 9 VAR is a system of seemingly unrelated regressions with different right-hand-side variables in each country-block. However, because we restrict the covariance matrix of this system to be block diagonal, OLS is an ef cient estimation technique; see Theil (1971, p. 309). 7 Because the Cholesky decomposition imposes a lower triangular structure on D (1), it appears that more than just long-run neutrality has been imposed. However, Lastrapes (1998) shows that the identi ed money supply response coef cients are independent of these additional restrictions. Blan- chard and Quah (1989) and Shapiro and Watson (1988) pioneered the long-run restriction approach to identifying VAR models. 8 The sample period used in estimation differs for some countries due to data availability, as noted below. 894 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 introductionoftheeuro.Thenumberofcountriesincludedinoursampleislimited by the availability of reliable and comparable interest rate data over the period. We consider the following four world variables to include in w : aggregate world output (total gross domestic product in constant prices, seasonally adjusted: OECD Main Economic Indicators , OCDRGDPS), the aggregate world price level (consumer price index, all items, OECD total: OECD MEI, OCDC- PILT), the nominal price of oil (PPI, crude petroleum: DRI/Citibase, PW561), and a nominal commodity price index (CRB spot market index, all commod- ities: DRI/citibase, PSCCOM). The vector of domestic variables, z t , contains a nominal interest rate, output, the real exchange rate, real money balances, and the nominal stock of money. With certain exceptions, most of these data come from the International Financial Statistics (IFS) database. In most cases, output is proxied by the industrial production index, the price level (used to compute real money balances and the real exchange rate) is the CPI, the real exchange rate is the domestic-currency value of SDRs times the world CPI divided by domestic CPI, and nominal money is M1. This choice of variables is dictated primarily by data availability but is reasonable in light of our objectives and the need for consistency across countries. We provide complete de nitions and sources of the country-speci c data in an Appendix that is separately available (http://www.terry.uga.edu/people/last/personal/research.html). Given our focus on the liquidity effect, we use a measure of short-term yields (1-month maturity or less) for the nominal interest rate. 9 Over the sample period, Switzerland has on average had the lowest short-term rates (3.33%), while Korea has had the highest (14.09%). Interest rates have been most variable in South Africa, with a standard deviation of 5.18%, and least variable in Austria, with a standard deviation of 2.09%. The overall mean short-term rate is 9.16%, with standard deviation of 2.81%. 10 For each country, we estimate the VAR in (2) as described in the previous subsection, over the sample period given in the third and fourth columns of Table 1. The actual estimation period begins six periods after the rst available observation to account for differencing and lags. All variables but interest rates are transformed into natural logs, and all variables are rst-differenced prior to esti- mation. 11 In the interest of parsimony, we initially estimated systems excluding world variables. For most countries, the world aggregates were not needed to generate impulse response functions consistent with prior beliefs about the dynamic effects of positive money supply shocks 3 short-run increases in output and real money balances, and a permanent increase in the price level. For some countries, however, the world aggregates were ultimately included because the 9 Our inclusion of the nominal rate of interest in the model is not inconsistent with our method of imposing long-run monetary neutrality. In the face of one-time changes in the level of the money supply, not its growth rate, the nominal rate will mimic the real rate at the in nite horizon since expected in ation will be unaffected at that horizon. 10 The interest rate series for Ireland and Sweden exhibit large spikes in 1992; however, dropping these potential outliers alters none of our main ndings below. Plots of the interest rate data we use are available in the separate Appendix. 11 We deal below with the possibility of model misspeci cation due to cointegration. 2004] 895 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 estimated responses from the parsimonious systems (without the aggregates) indicated that money supply shocks were likely misidenti ed. 12 Our baseline impulse response function estimates are from VARs with ve lags of the country-speci c variables (i.e. p ¼ 5), and a constant and seasonal dummies as deterministic variables. For Japan, New Zealand, Portugal and Spain, contem- poraneous and lagged values of the world aggregates are included as exogenous variables. France requires, in addition, a linear trend term to generate a positive output response. The VARs for the remaining countries contain no world aggre- gates. Of the 105 equations estimated (5 variables for 21 countries), the Q-test for residual serial correlation is signi cantly different from zero at a 5% level for only three equations. We consider how sensitive the response functions are to alter- native speci cations below. Figures 1, 2, and 3 report for the baseline model the estimated (accumulated) dynamic responses of output, the price level and real money balances to a positive money supply shock, according to the long-run identi cation scheme. The responses are plotted up to a horizon of 40 quarters, and are shown with standard Table 1 Estimated Liquidity Effects Country Begin End r 1 rank r m rank r c rank 1 Australia 70:1 96:2 ) 33.98 17 ) 33.98 20 ) 22.06 17 2 Austria 70:1 98:1 ) 29.45 19 ) 67.18 15 ) 8.41 21 3 Belgium 70:1 98:1 ) 186.61 1 ) 186.61 1 ) 114.55 1 4 Canada 75:1 98:1 ) 131.44 2 ) 131.44 5 ) 74.00 5 5 Denmark 72:1 98:1 ) 93.78 9 ) 143.82 3 ) 64.11 7 6 France 70:1 98:1 ) 122.81 4 ) 122.81 7 362.70 8 7 Germany 70:1 98:1 ) 45.55 16 ) 59.95 17 ) 14.26 19 8 Ireland 73:1 98:1 ) 81.76 10 ) 123.30 6 ) 65.80 6 9 Italy 71:1 98:1 ) 106.13 6 ) 106.85 10 ) 88.50 2 10 Japan 70:1 98:1 ) 74.72 11 ) 74.72 14 ) 31.91 12 11 Korea 76:4 97:4 ) 63.40 13 ) 134.63 4 ) 46.80 10 12 Netherlands 70:1 97:4 ) 50.89 15 ) 61.02 16 ) 29.51 14 13 New Zealand 70:1 98:1 ) 97.89 7 ) 97.89 11 ) 12.50 20 14 Norway 70:1 98:1 ) 96.30 8 ) 96.30 12 ) 78.83 3 15 Portugal 81:1 98:1 ) 3.85 20 ) 32.95 21 ) 17.59 18 16 South Africa 70:1 98:1 ) 73.23 12 ) 81.02 13 ) 51.19 9 17 Spain 74:1 98:1 ) 121.54 5 ) 121.54 8 ) 45.34 11 18 Sweden 70:1 98:1 ) 59.21 14 ) 59.21 18 ) 27.17 15 19 Switzerland 75:4 98:1 55.84 21 ) 116.45 9 ) 26.45 16 20 United Kingdom 70:1 98:1 ) 123.57 3 ) 157.66 2 ) 74.74 4 21 United States 70:1 98:1 ) 31.12 18 ) 37.73 19 ) 30.01 13 l ) 74.83 ) 97.48 ) 46.97 r 52.20 42.58 28.80 Notes: Dependent variables in the cross-country regressions, estimated over given sample period. r 1 is the response of the real interest rate at horizon 1, r m is the maximum (absolute) response, and r c is the average response over eight quarters, all to a unit money supply shock. l is the mean and r is the standard deviation. 12 For example, in a few cases for the initial systems we found negative responses of output and real money, and positive responses of the price level, which suggested a negative aggregate supply shock rather than a positive money supply shock. 896 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 error bands computed from a standard antithetically-accelerated Monte Carlo integration with 5,000 replications (dashes). All responses are normalised on the estimated standard deviation of the country-speci c money supply shock; i.e. the coef cients re ect the dynamic response to a unit money supply shock, rather than a standard deviation shock as is conventional, to standardise the size of the shock across countries. -1.6 -0.0 -1.6 -0.0 1.6 3.2 -1.6 -0.0 1.6 3.2 -1.6 -0.0 1.6 3.2 -1.6 -0.0 1.6 3.2 -1.6 -0.0 1.6 3.2 -1.6 -0.0 1.6 3.2 Ireland -1.6 -0.0 1.6 3.2 Italy -1.6 -0.0 1.6 3.2 Japan -1.6 -0.0 1.6 3.2 Korea -1.6 -0.0 1.6 3.2 Netherlands -1.6 -0.0 1.6 3.2 New Zealand -1.6 -0.0 1.6 3.2 Norway -1.6 -0.0 1.6 3.2 Portugal -1.6 -0.0 1.6 3.2 South Africa -1.6 -0.0 1.6 3.2 Spain -1.6 -0.0 1.6 3.2 Sweden -1.6 -0.0 1.6 3.2 Switzerland -1.6 -0.0 1.6 3.2 United Kingdom -1.6 -0.0 1.6 3.2 United States -1.6 -0.0 1.6 3.2 1.6 3.2 Australia Austria Belgium Canada Denmark France Germany Fig. 1. Response of Output to Money Supply Shocks 2004] 897 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 The estimated dynamic responses are qualitatively similar across the countries in the sample. The price level shows a small response on impact, then gradually increases to a new, higher steady-state value. Output generally rises in the short run but returns to its steady-state value in the long run (by the assumption of monetary neutrality). Only in the Netherlands and Norway do the point estimates provide no convincing evidence of a temporary positive output response. In general, real money balances rise in the short run, which indicates that the price level response is smaller than the nominal money stock response in the short run. Only in Australia 0 2 4 6 8 Austria 0 2 4 6 8 Belgium 0 2 4 6 8 Canada 0 2 4 6 8 Denmark 0 2 4 6 8 France 0 2 4 6 8 Germany 0 2 4 6 8 Ireland 0 2 4 6 8 Italy 0 2 4 6 8 Japan 0 2 4 6 8 Korea 0 2 4 6 8 Netherlands 0 2 4 6 8 New Zealand 0 2 4 6 8 Norway 0 2 4 6 8 Portugal 0 2 4 6 8 South Africa 0 2 4 6 8 Spain 0 2 4 6 8 Sweden 0 2 4 6 8 Switzerland 0 2 4 6 8 United Kingdom 0 2 4 6 8 United States 0 2 4 6 8 Fig. 2. Response of Price Level to Money Supply Shocks 898 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 New Zealand do the results suggest the possibility of a short-run negative impact on real money balances. As noted earlier, we consider the response of the real interest rate to money supply shocks as our measure of the liquidity effect. The real interest rate response cannot be estimated directly from our model, since only the nominal rate is observable and included in the VAR. However, it can be inferred from the nominal rate response and the price level ( P ) response (the latter of which is simply the Australia -1 1 3 5 7 Austria -1 1 3 5 7 Belgium -1 1 3 5 7 Canada -1 1 3 5 7 Denmark -1 1 3 5 7 France -1 1 3 5 7 Germany -1 1 3 5 7 Ireland -1 1 3 5 7 Italy -1 1 3 5 7 Japan -1 1 3 5 7 Korea -1 1 3 5 7 Netherlands -1 1 3 5 7 New Zealand -1 1 3 5 7 Norway -1 1 3 5 7 Portugal -1 1 3 5 7 South Africa -1 1 3 5 7 Spain -1 1 3 5 7 Sweden -1 1 3 5 7 Switzerland -1 1 3 5 7 United Kingdom -1 1 3 5 7 United States -1 1 3 5 7 Fig. 3. Response of Real Money to Money Supply Shocks 2004] 899 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 difference between the nominal money and real money responses), as in Gali (1992) and Lastrapes (1998). Let k denote the forecast horizon of the dynamic response functions and p h , t + k denote the rate of in ation at time t + k over the following h quarters; i.e. p h , t + k d (1/ h )(ln P t + k + h ) ln P t + k ). Then, @ p h ; t þ k @ u mt ¼ 1 h @ ln P t þ k þ h @ u mt À @ ln P t þ k @ u mt ; ð 4 Þ where u mt is the exogenous shock to the money supply. This equation gives the response of the per period in ation rate to the exogenous money impulse. But if agents use the VAR to form expectations, then (4) shows how the path of in ationary expectations will be revised in light of the money shock. Hence, (4) can be interpreted as the response of expected in ation under this assumption of expectation formation. If r is the (continuously-compounded) nominal yield-to- maturity on h -period bonds and R the corresponding real yield, then @ R t þ k @ u mt ¼ @ r t þ k @ u mt À @ p h ; t þ k @ u mt : ð 5 Þ That is, the real rate response is the difference between the nominal rate response (directly estimated from the identi ed VAR) and the response of expected in a- tion as computed in (4). We set h ¼ 1 since our interest rate measures have a maturity of one month or less. We assume that the short run behaviour of the real rate, as measured by response functions derived in (5), re ects the liquidity effect. It is from this response function that we compute measures of the liquidity effect used in the cross-country regressions. Figure 4 reports the dynamic responses of real interest rates to money supply shocks based on (5), along with the standard error con dence bands. As with the previous gures, the magnitude of the coef cients are relative to a unit money supply shock. For each country in the sample, there is evidence of a liquidity effect: over the short-run, short-term real rates tend to fall in response to a money supply shock that temporarily raises output and real money balances, and permanently raises prices and nominal money. The only country for which the impact response is positive is Switzerland, but the coef cients become negative immediately after impact. 1.3. Interpretation and Robustness In the next Section, we analyse the cross-country variation in the liquidity effect by regressing the estimated interest rate responses on potential explanatory variables, with a focus on nancial factors. It is therefore important that we have properly identi ed money supply shocks so that errors in the time series estimation do not bias the cross-sectional results. It is also important that the magnitude of the estimates of the liquidity effect be robust to reasonable variation in the statistical models. It is possible that we have confused a positive money supply shock with a tem- porary negative money demand shock 3 for each of these shocks, interest rates will 900 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 fall, and prices and output will rise, as we nd. However, real money balances would fall initially for the money demand shock and rise initially for the money supply shock. As seen in Figure 3, in almost every case, real money balances rise in the short-run, lending credibility to our interpretation of the shocks as due to unpredictable changes in money supply, given our modelling assumptions. The question remains 3 have we misinterpreted money supply shocks and found pervasive liquidity effects because of mis-speci cation of the statistical model and Australia -200 -100 0 100 Austria -200 -100 0 100 Belgium -200 -100 0 100 Canada -200 -100 0 100 Denmark -200 -100 0 100 France -200 -100 0 100 Germany -200 -100 0 100 Ireland Italy Japan Korea Netherlands New Zealand Norway -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 Portugal South Africa Spain Sweden Switzerland United Kingdom United States -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 -200 -100 0 100 Fig. 4. Response of Short-term Real Interest Rates to Money Supply Shocks 2004] 901 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 inappropriate identifying restrictions? 13 We consider this question along many dimensions. We rst make straightforward changes to the VAR model. Reducing the com- mon lag length of the endogenous variables from ve to four generally yields smoother response functions but does not alter the shapes or magnitudes of the dynamic responses. Likewise, adding contemporaneous and lagged world aggre- gates to the baseline speci cations generally does not alter our interpretation of money supply shocks and has little effect on the cross-sectional inference. 14 We also perform CUSUM tests on the residuals of the baseline VARs, which provide no evidence for substantial or important structural breaks over the sample period. Most signi cantly, we considered the possibility of model misspeci cation due to rst-differencing the data. This restriction rules out the possibility of cointe- grating relations among the variables in the system, and requires the matrix of long-run multipliers, D (1), to be of full-rank (under the assumption that each variable in the system has a unit root). Because we rely on D (1) under our iden- ti cation scheme, this restriction could have important consequences for our estimates. Johansen 9s maximum eigenvalue and trace tests for cointegration (not reported) imply that a reasonable case can be made for a single cointegrating vector for at most half of the countries in the sample. We therefore re-estimate the VAR models for each country in vector error correction form, imposing one cointegrating vector. As in Fung and Kasumovich (1998), we maintain the primary identifying restriction that money is neutral in the long run. 15 Generalising the statistical model to allow for cointegration has essentially no effect on our estimates of the liquidity effect and no important effects on the cross-country inference below. The cointegration tests, response functions and cross-country regressions verifying this claim are available separately from the authors. It is noteworthy that our estimates of the liquidity effect are qualitatively similar to those of Fung and Kasumovich (1998), who use an identi cation strategy similar to ours for the G-6 countries. But our results are also consistent with those for the G-7 countries found using very different 3 contemporaneous 3 identi cation strategies, such as in Kim (1999) and Grilli and Roubini (1996). While we cannot claim that our estimates of the liquidity effect are precisely correct, they are plausible given conventional views of the macroeconomy, consistent with other recent VAR studies, and robust to changes in the statistical speci cation. 16 13 The need for careful attention to identi cation and model speci cation has been re-emphasised recently by Wickens and Motto (2001). 14 In fact, when the price of oil was included separately, and when both the price of oil and world output were included in the VARs, we found an increase in the importance and statistical signi cance of nancial factors in explaining the liquidity effect. 15 Under this approach, D (1) is restricted to be of rank n ) 1 by containing all zeroes in its nal column, but the coef cients corresponding to nominal money and the price level are constrained to be equal. See Fung and Kasumovich (1998) and Fisher et al. (1995). 16 The fact that our results are consistent with those generated from short-run restrictions mitigates to some extent the Faust and Leeper (1997) criticisms of in nite-horizon restrictions. The robustness of the response functions to alternative statistical models also helps, since the Faust-Leeper critique focuses on the sensitivity of the estimated response to the the statistical speci cation under in nite-horizon restrictions. 902 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 One further note 3 because our estimates of the liquidity effect are used as the dependent variables in the cross-sectional regressions to follow, speci cation and identi cation errors in the rst stage VAR estimation will bias cross-sectional inference only if these errors are correlated across countries with the regressors in those regressions. If such errors exist but are random, they will most likely only add independent noise to the regression error, making it more dif cult to uncover both economically and statistically signi cant results. As will be seen below, we nd strong and regular patterns in the cross-section regressions that require explan- ation. Thus, despite the real possibility of measurement error in estimating the liquidity effect, our results reported in the following section are of interest and, though our preferred explanation is plausible, should stimulate further research into the validity of our claims. 2. The Liquidity Effect Across Countries 2.1. Characterising the Cross-country Variation To perform the cross-country analysis, we must devise a precise measure of the liquidity effect based on the dynamic response coef cients estimated above, given that the 8short run 9 is not de nitively identi ed. Based on the real interest rate responsesof theprevious section,we consider three measures of theliquidity effect: r 1 , the dynamic response at impact (the one-quarter horizon), r m , the maximum (absolute) real rate response (which is negative in all countries), and r c , the average response over the rst eight quarters. The different measures give different weights to the particular timing and persistence of the estimated liquidity effect. Table 1 reports these measures of the liquidity effect for each of the countries, from the baseline VAR estimates. As in the gures, all measures of interest rate responses are in basis points and in relation to a unit money supply shock. The Table also reports the country rank for each measure, where 1 denotes the largest (absolute) value across the 21 countries in the sample. TheTableindicatesthatthereisamplevariationacrosscountriestobeexplained. Across countries, the mean liquidity effect on impact ( r 1 ) is 75 basis points, and the standard deviation is 52 basis points. The mean is 97 basis points for the maximum effect ( r m ) and 47 basis points for the average effect ( r c ), with corresponding standard deviations of 43 and 29. The measures range from ) 187 basis points (Belgium) to 56 basis points (Switzerland) on impact, ) 187 (Belgium) to ) 33 (Portugal) for the maximum, and ) 115 (Belgium) to ) 8 (Austria) for the average effect. The ranks are relatively stable across measures; for example, Belgium has the largest liquidity effect for each proxy, the UK ranks either second, third, or fourth, and Portugal generally ranks toward the back of the pack. On the other hand, Switzerland and New Zealand have rank changes larger than 10. 2.2. The Role of Financial Market Variables Our primary objective is to examine the extent to which nancial factors explain the observed cross-country variation in the liquidity effect. To this end, we estimate regressions of the following form: 2004] 903 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 y i ¼ b 0 þ b 1 r m þ c x i þ i ; i ¼ 1 ; ÁÁÁ ; 21 ; ð 6 Þ where y i is the estimated liquidity effect ( r 1 , r m , or r c ), r m is the standard deviation of the money supply shock estimated from the VAR, and x i is a nancial market variable. The money supply standard error is included as a control variable to account for potential nonlinearities in scale effects and to allow for the possible effects of liquidity risk. 17 Regressions of this sort have been used before; for example, Cecchetti (1999) performs similar regressions in his analysis on the relationship between nancial structure and the impact of monetary policy on output and prices across the members of the European Monetary Union. 18 We use the following nancial variables for x in the regressions: the ratios of bank assets to GDP, private credit to GDP, liquid liabilities to GDP, bank credit to GDP, commercial bank credit to the sum of commercial and central bank credit, privately issued debt to GDP, national stock market capitalisation to GDP, the turnover rate in the stock market, an index of nancial market depth, the ratio of aggregate bank reserves to demand deposits and the ratio of bank reserves to total deposits. These variables are presumably related to the level of nancial services, the functioning of nancial markets and the importance of nancial intermedi- aries in the economy. They are also likely to be related to transactions costs in nancial markets and therefore the degree to which households can participate in these markets. The rst ve variables, which are closely related to the nancial intermediary sector, have been constructed and used to measure the provision of nancial services by Levine et al. (2000) in their study of the sources of economic growth. In particular, these variables attempt to measure the relative size (bank asset, bank credit to total credit, and liquid liabilities ratios) and activity (private and bank credit ratios) of banks in the economy. In addition, we consider the reserve ratio proxies as possibly related to the degree of nancial intermediary services. These variables are averages over the 1960 395 period (1974 398 for the reserve ratios), a sample similar to the one used to estimate the VAR models. The next three variables are frequently used to capture the depth, liquidity, and sophistication of all nancial markets (Cecchetti 1999), and are thus broader than the previous ve proxies. The nancial market depth variable is a summary index of privately issued debt, stock market capitalisation and the turnover rate, and is similar in construction to Cecchetti 9s (1999) index of alternative nance. These last four variables are measured at a single point in time (1996) near the end of 17 For example, Fuerst 9s model (1992, p. 15) implies that the higher is money supply variance, the greater is the liquidity risk faced by households. They respond by increasing bank deposits for pre- cautionary purposes, making money injections less important in the loanable funds market. This would tend to reduce the liquidity effect, that is, lead to a positive b 1 coef cient. Since households respond to increases in money supply variance by increasing their holdings of bank deposits, and since interme- diaries expand asset holdings as deposits rise, money supply variance is expected to be positively correlated with many of the variables we use for x , especially the bank ratios noted below. Thus, it is essential to control for money supply volatility in the cross-country regressions, given our focus on estimating the effects of the nancial market variables on the liquidity effect. 18 Karras (1999), in studying how openness alters monetary policy effects across countries, uses a panel approach. The nature of his strategy, however, does not allow him to identify money supply shocks as we do. 904 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 our sample. 19 Table 2 contains the data for the nancial market proxies along with summary statistics, where the countries are identi ed by number as in Table 1. Sources and complete descriptions of these variables are contained in the separate appendix. Table 3 reports the regression results for each of the three measures of the liquidity effect, and each of the nancial market proxies. We do not have suf cient degrees of freedom to include all nancial variables in a single regression, so we consider the alternative measures in separate regressions. The Table reports conventional OLS t-statistics for inference; however, these statistics are almost identical to those computed from White 9s consistent estimator of the covariance matrix allowing for heteroscedasticity. In each regression, the constant term is signi cantly less than zero at very small levels of signi cance. The estimated coef cient on money supply variability is signi cant in almost all of the regressions, and is positive 3 the higher the variance, the smaller is the liquidity effect. This result is in line with the liquidity risk story of Fuerst mentioned in footnote 17. Table 2 Financial Market Variables D/Y MC MD TO R / D R / T BA PC LL BC CB 1 28.40 76.40 2.00 52.20 22.40 4.60 47.80 54.82 51.73 34.01 92.67 2 45.68 14.60 2.00 61.80 46.40 5.10 81.36 65.30 67.50 62.30 98.44 3 60.19 44.70 2.00 23.20 5.60 1.50 58.12 25.65 49.02 25.39 92.01 4 18.44 79.50 2.00 62.20 14.30 3.10 42.35 60.86 56.50 35.51 89.00 5 100.65 39.20 3.00 54.20 8.20 3.80 49.87 42.45 49.48 42.13 88.10 6 48.44 38.00 2.00 49.80 6.70 2.40 62.50 75.47 63.37 55.36 96.54 7 57.06 28.10 3.00 123.20 34.40 6.90 88.89 76.46 57.46 71.00 97.57 8 12.18 16.80 1.00 24.50 38.50 11.10 36.77 49.14 54.74 28.14 94.73 9 36.81 21.00 1.00 43.80 29.30 14.80 73.13 59.09 77.48 58.13 87.77 10 39.14 67.10 2.00 37.10 8.20 2.10 98.94 128.38 125.94 88.63 96.72 11 43.03 26.70 2.00 110.50 58.80 11.00 42.24 65.48 41.02 40.09 83.95 12 47.80 96.40 3.00 92.40 2.60 0.60 70.88 86.69 71.41 52.35 98.10 13 7.97 58.60 1.00 28.10 5.70 1.90 30.55 37.59 49.63 25.44 82.43 14 24.97 36.30 2.00 70.30 5.40 1.70 57.31 81.62 54.04 40.76 90.02 15 18.81 22.70 1.00 33.20 80.40 17.70 74.85 55.01 78.02 60.66 90.35 16 6.05 172.00 1.00 10.40 18.60 4.60 56.91 71.94 51.44 49.22 94.77 17 11.02 41.70 1.00 113.10 48.50 12.10 74.81 65.05 70.31 58.37 92.74 18 70.69 94.40 3.00 64.40 2.60 2.60 49.43 89.11 53.49 42.28 88.94 19 62.03 136.00 3.00 94.00 25.50 5.70 133.08 141.29 123.41 119.13 98.99 20 43.68 147.00 3.00 36.80 1.90 1.90 54.78 46.31 48.63 45.55 83.55 21 62.58 109.00 3.00 92.80 11.60 4.30 70.42 113.07 62.12 58.42 93.11 l 40.27 65.06 2.05 60.86 22.65 5.69 64.52 70.99 64.61 52.04 91.93 r 24.06 45.81 0.80 32.48 21.57 4.81 23.46 28.88 22.31 21.92 5.02 Notes: D / Y is debt/GDP, MC is market capitalisation, MD is the index of market depth, TO is the turnover rate, R / D is the ratio of reserves to demand deposits, R / T is the ratio of reserves to total deposits, BA are bank assets, PC is private credit, LL are liquid liabilities, BC is bank credit, and CB is the ratio of commercial credit to central bank credit. Countries are identi ed by number, as in Table 1. 19 Using sample averages for these variables rather than point-in-time estimates does not alter the regression results discussed below. 2004] 905 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 Of primary interest is the coef cient on nancial market variables, c . The estimated c for the debt ratio, market capitalisation, turnover, and the depth index, as well the reserve ratios, are generally small and insigni cantly different from zero. Only for the turnover ratio in the r 1 and r c regressions does the marginal signi cance level approach a reasonably small value. However, the proxies based primarily on the size and activity of nancial intermediaries (excluding the reserve ratios) 3 bank assets, private credit, liquid liabilities, bank credit, and the bank credit to central bank credit ratio 3 all have statis- tically signi cant explanatory power at typical test size for the liquidity effect, and are consistently positive. The positive coef cient means that as the bank ratio increases, the liquidity effect becomes a smaller negative number. This inference is robust across the different measures of the liquidity effect. The Table 3 Cross-country Regressions and Rank Correlations y x b 0 (tstat) b 1 (tstat) c (tstat) R 2 q r 1 D / Y ) 113.16 ( ) 3.65) 1.99 (1.28) 0.35 (0.71) 0.10 0.24 r m D / Y ) 123.89 ( ) 5.27) 2.56 (2.18) ) 0.12 ( ) 0.33) 0.22 ) 0.01 r c D / Y ) 67.77 ( ) 4.17) 1.65 (2.03) 0.01 (0.06) 0.19 0.06 r 1 MC ) 113.23 ( ) 4.07) 1.92 (1.26) 0.23 (0.90) 0.11 ) 0.01 r m MC ) 134.39 ( ) 6.31) 2.62 (2.25) 0.07 (0.38) 0.22 0.05 r c MC ) 70.73 ( ) 4.83) 1.66 (2.06) 0.05 (0.40) 0.19 0.00 r 1 MD ) 142.31 ( ) 3.70) 2.21 (1.47) 19.73 (1.39) 0.16 0.27 r m MD ) 143.38 ( ) 4.76) 2.71 (2.30) 6.17 (0.56) 0.23 0.05 r c MD ) 84.12 ( ) 4.13) 1.77 (2.23) 7.52 (1.00) 0.23 0.12 r 1 TO ) 133.36 ( ) 4.45) 1.98 (1.36) 0.56 (1.66) 0.20 0.33 r m TO ) 145.06 ( ) 6.15) 2.66 (2.32) 0.25 (0.92) 0.25 0.18 r c TO ) 87.10 ( ) 5.70) 1.71 (2.30) 0.32 (1.82) 0.31 0.28 r 1 R / D ) 107.75 ( ) 4.87) 1.19 (0.77) 0.81 (1.50) 0.18 0.40 r m R / D ) 131.52 ( ) 7.50) 2.47 (2.02) 0.17 (0.39) 0.22 0.15 r c R / D ) 70.37 ( ) 5.93) 1.42 (1.73) 0.26 (0.90) 0.22 0.30 r 1 R / T ) 103.61 ( ) 4.40) 1.50 (0.93) 1.83 (0.71) 0.10 0.38 r m R / T ) 128.88 ( ) 7.19) 2.64 (2.14) ) 0.17 ( ) 0.09) 0.22 0.17 r c R / T ) 65.66 ( ) 5.34) 1.73 (2.04) ) 0.45 ( ) 0.33) 0.19 0.22 r 1 BA ) 227.74 ( ) 6.93) 3.71 (3.22) 1.66 (4.48) 0.56 0.39 r m BA ) 191.12 ( ) 6.00) 3.48 (3.12) 0.79 (2.19) 0.38 0.34 r c BA ) 116.94 ( ) 5.62) 2.35 (3.23) 0.64 (2.71) 0.42 0.27 r 1 PC ) 191.22 ( ) 6.62) 2.56 (2.21) 1.20 (3.93) 0.50 0.49 r m PC ) 185.16 ( ) 7.44) 3.02 (3.03) 0.71 (2.72) 0.44 0.46 r c PC ) 103.98 ( ) 5.98) 1.92 (2.75) 0.47 (2.57) 0.41 0.27 r 1 LL ) 197.69 ( ) 5.23) 2.90 (2.20) 1.35 (3.02) 0.39 0.38 r m LL ) 178.12 ( ) 5.52) 3.11 (2.76) 0.66 (1.72) 0.33 0.45 r c LL ) 106.17 ( ) 4.93) 2.05 (2.72) 0.53 (2.07) 0.34 0.30 r 1 BC ) 214.37 ( ) 8.10) 3.48 (3.36) 1.86 (5.21) 0.63 0.52 r m BC ) 180.29 ( ) 6.42) 3.31 (3.02) 0.81 (2.14) 0.37 0.43 r c BC ) 113.67 ( ) 6.55) 2.29 (3.37) 0.74 (3.17) 0.48 0.41 r 1 CB ) 621.23 ( ) 3.12) 2.97 (2.14) 5.55 (2.64) 0.33 0.49 r m CB ) 552.81 ( ) 3.82) 3.50 (3.47) 4.49 (2.94) 0.47 0.35 r c CB ) 316.25 ( ) 2.99) 2.17 (2.94) 2.64 (2.37) 0.38 0.37 Notes: The regression is y i ¼ b 0 + b 1 r mi + c x i + i , where y is the liquidity effect, r mi is the estimated standard deviation of the money supply shock, and x is a measure of nancial market transactions costs. q is Spearman 9s rank correlation coef cient, which we obtain by regressing the rank of y on the rank of x . According to Table P in Siegel (1956), the 5% critical value under the null of no correspondence is 0.368 for 21 observations. See notes to Tables 1 and 2 for variable de nitions. 906 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 overall t of the regressions including these variables is good: the lowest R 2 is 33% and the highest 63%. 20 While statistical signi cance is important in understanding the extent to which sampling error affects inference, a coef cient estimate that is statistically signi - cant (for an arbitrary test size) need not be economically important. One way to determine the importance of the effect is to consider how much the liquidity effect would change for a typical change in x . For example, the average country in our sample has a liquidity effect on impact ( r 1 ) of ) 75 basis points (Table 1) and a bank asset ratio ( BA ) of 64.5% (Table 2). According to the estimates in Table 3, a country having a bank asset ratio of 88%, or one standard deviation above the mean, will have a liquidity effect of ) 36 basis points, 39 basis points smaller than average (39 ¼ 1.67 · 23.46). This quantity is 75% of r 1 9s cross-country standard deviation of 52 basis points (Table 1). The other nancial market variables have similar quantitative effects on r 1 : private credit 3 35 basis points; liquid liabilities 3 34 basis points; bank credit 3 41 basis points; share of commercial credit 3 28 basis points. The latter creates the largest reduction in the maximum liquidity effect ( r m ) 3 22.5 basis points, which is 54% of the standard deviation in r m . Liquid liabilities (LL) has the largest effect on r c 3 16.2 basis points, or 56% of its cross-country variation. Overall, these results suggest that the explanatory power of the nancial market factors for cross-country variation in the liquidity effect is plausible, non-trivial, and not likely to be affected by sampling error. 21 2.3. Robustness We discussed earlier that these results are not sensitive to a number of changes in the statistical model generating the liquidity effect estimates. Here, we provide further evidence of the robustness of these results by computing non-parametric rank-order correlations, and including other variables in the regressions that could explain cross-country variation in the liquidity effect. The nal column of Table 3 reports Spearman 9s rank-correlation coef cient (Siegel, 1956) for the liquidity effect measures and the nancial market variables. Correlations based on rank are less sensitive to extreme point estimates than correlations estimated from the regression model. The Table shows that at a 5% signi cance level, the null hypothesis of no correlation can be rejected in favour a positive correlation for the same variables that are signi cantly non-zero in the regression analysis. 20 Informal inspection of Table 2 suggests that Switzerland (country 19) may be an outlier for bank assets, private credit, liquid liabilities and bank credit. To see if Switzerland drives the results, we dropped it from the sample; the only effect is to render liquid liabilities marginally insigni cant for r 1 and r c , even though the quantitative effect is the same. 21 Our approach exploits variation in the time-averages of the liquidity effect and nancial market factors across countries. An alternative approach, as suggested by a referee, is to exploit variation over time in the liquidity effect and nancial market structure within countries , perhaps due to discrete changes in regulations or innovations in nancial markets. While our CUSUM tests indicated little signi cant structural change in the estimated VAR models, this line of research is clearly of potential interest. However, such an analysis, done carefully and correctly, lies well beyond the scope of our paper. 2004] 907 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 To the extent that our measures of nancial market factors are correlated with variables representing other causes of variation in the liquidity effect, our previous estimates will be biased and our inferences may be incorrect. We consider the robustness of the results to three other potential alternative explanations of variation in the liquidity effect. The rst is variation in the extent of capital mobility across open economies. The fewer the restrictions on international capital ows, the lower the variability in interest rate responses to country-speci c monetary shocks, which could explain differences in the magnitude of liquidity effects across countries independently of nancial market channels. Consequently, we have estimated regressions that add a capital mobility proxy to the basic regression model. We use as our capital mobility proxy the index of capital account openness developed by Quinn (1997). He constructs the index for a variety of industrialised and developing economies based on careful consideration of capital account restrictions imposed by each country. The only countries in our sample not considered by Quinn are Korea and South Africa, so the regressions reported in Table 4 exclude both of these coun- tries from the sample. The index ranges from 0 to 4, with higher values implying greater capital mobility; thus, the expected sign of the coef cient on this variable is positive. The speci c values of the index used in our regressions are the average values over the period 1974 397. 22 The results in Table 4 indicate essentially no effect of capital mobility on the magnitude of the liquidity effect. Only in one case is the coef cient on the capital mobility proxy statistically signi cant at the 10% level or better but the pattern of signi cant coef cients on the nancial proxies is similar to that in Table 3. The only noteworthy difference is that the coef cients on the turnover proxy are now statistically signi cant. 23 Differences in the extent of wage and price rigidity in an economy are another possible reason for differences in the magnitude of the liquidity effect, and we have estimated equations that add rigidity proxies to the base model. Other things equal, we expect that the more rigid are wages and prices, the bigger the change in real money balances following a change in nominal money, and, consequently, the bigger the liquidity effect. Measuring the extent of wage and/or price rigidity is dif cult but Grubb et al. (1983) provide measures of nominal and real wage stickiness for 18 of the 21 countries in our sample. 24 Measures are not available for Korea, Portugal, and South Africa. The higher the value of these measures, the stickier are wages. Consequently, a negative coef cient is expected on the wage rigidity proxies since the greater the extent of stickiness, the greater the liquidity 22 Time series of his index for each of the countries in our cross-section (except, as noted earlier, for Korea and South Africa) were kindly provided by Professor Dennis Quinn of Georgetown University. 23 An alternative capital mobility proxy has been suggested by Obstfeld and Taylor (1997) who use relative patterns of dispersion of the real interest rate to proxy for variation in capital mobility across countries. If a country 9s capital market is well-integrated with world capital markets, a shock to the real rate should be mitigated quickly if capital mobility is high, and the standard deviation of the real rate should be low. Thus, standard deviations of ex post real interest rates might be used as a proxy for differences in capital mobility. Unfortunately, this type of real interest rate based measure is inappro- priate given our focus on the liquidity effect. 24 These measures are based on estimates of wage and price equations using annual data for 1957 380 and are provided in Table 3, p. 25 of Grubb et al (1983). The nominal rigidity measure has recently been employed by Fischer (1997) in a study of the institutional determinants of the speed of disin ation. 908 [ O C T O B E R T H E E C O N O M I C J O U R N A L Ó Royal Economic Society 2004 effect. The coef cient estimates for the transaction costs proxies and nominal and real wage rigidity proxies are reported in Table 5. There is essentially no evidence that the wage rigidity proxies explain a signi cant amount of the cross-country variation in the liquidity effect; in only two cases is the coef cient on the wage rigidity proxy signi cant. In the case of the nancial variables, the pattern of signi cance is essentially identical to that in Table 3. Finally, as noted in the introduction, nancial market variables may simply capture differences in the interest rate elasticity of money demand across coun- tries. Indeed, if large bank ratios are associated with high money demand elasticity, then the positive coef cients found in the cross-country regressions are consistent with this idea. To determine if the bank ratios have an independent effect on the liquidity effect, we include a direct measure of the interest rate semi-elasticity of demand in the regressions. We use, as a measure of this semi-elasticity, the coef- cient on the interest rate in the cointegration relationship estimated above as part of our robustness check, which in general can be reasonably interpreted as a Table 4 Cross-country Regressions Including Capital Mobility y x c (tstat) b 2 (tstat) r 1 D / Y 0.191 (0.30) 21.384 (0.66) r m D / Y ) 0.051 ( ) 0.11) ) 0.162 ( ) 0.01) r c D / Y ) 0.056 ( ) 0.16) 6.740 (0.39) r 1 MC 0.215 (0.55) 16.546 (0.50) r m MC ) 0.030 ( ) 0.10) ) 0.094 ( ) 0.00) r c MC 0.059 (0.28) 2.652 (0.15) r 1 MD 21.227 (0.99) 2.811 (0.08) r m MD 16.463 (1.05) ) 19.638 ( ) 0.74) r c MD 10.716 (0.94) ) 6.524 ( ) 0.34) r 1 TO 0.687 (1.55) 11.350 (0.41) r m TO 0.631 (2.04) ) 15.154 ( ) 0.78) r c TO 0.460 (2.07) ) 4.669 ( ) 0.33) r 1 R / D 1.174 (1.92) 39.997 (1.53) r m R / D 0.449 (0.92) 3.795 (0.18) r c R / D 0.396 (1.14) 9.951 (0.67) r 1 R / T 2.458 (0.87) 30.765 (1.10) r m R / T 0.415 (0.20) ) 0.692 ( ) 0.03) r c R / T ) 0.310 ( ) 0.20) 4.745 (0.31) r 1 BA 1.745 (4.57) 23.035 (1.27) r m BA 0.755 (1.95) ) 2.848 ( ) 0.15) r c BA 0.652 (2.48) 4.109 (0.33) r 1 PC 1.166 (3.55) 17.017 (0.82) r m PC 0.718 (2.67) ) 7.146 ( ) 0.42) r c PC 0.468 (2.31) 1.605 (0.12) r 1 LL 1.704 (3.84) 44.341 (2.16) r m LL 0.654 (1.53) 5.491 (0.28) r c LL 0.611 (2.10) 11.799 (0.88) r 1 BC 1.862 (5.01) 20.221 (1.17) r m BC 0.788 (1.99) ) 4.009 ( ) 0.22) r c BC 0.740 (2.87) 2.913 (0.24) r 1 CB 6.577 (2.91) 29.201 (1.30) r m CB 4.152 (2.33) 0.405 (0.02) r c CB 2.963 (2.31) 6.639 (0.52) Notes: The regression is y i ¼ b 0 + b 1 r mi + b 2 h i + c x i + i , where h is the proxy for capital mobility. See notes to Tables 2 and 3 for variable de nitions. 2004] 909 C R O S S - C O U N T R Y V A R I A T I O N I N T H E L I Q U I D I T Y E F F E C T Ó Royal Economic Society 2004 money demand relationship. We set up the regression so that a high money demand elasticity corresponds to a large value for the semi-elasticity measure; hence, we expect a positive coef cient on the semi-elasticity variable. Table 6 shows that indeed this is the case, with a high degree of statistical con dence. 25 Quantitatively, a standard deviation increase in semi-elasticity (1.65%) reduces the liquidity effect by between 12 and 20 basis points. But most importantly, while magnitudes are generally reduced, the nancial intermediary variables remain for the most part both statistically and economically signi cant. Table 5 Cross-country Regressions Including Nominal and Real Wage Rigidities y x c (nom) (tstat) b 2 (nom) (tstat) c (real) (tstat) b 2 (real) (tstat) r 1 D / Y 0.58 (1.03) ) 11.60 ( ) 0.59) 0.52 (0.95) ) 24.78 ( ) 1.18) r m D / Y 0.01 (0.01) 4.70 (0.32) 0.00 (0.01) ) 18.20 ( ) 1.17) r c D / Y 0.07 (0.22) ) 8.74 ( ) 0.83) 0.02 (0.07) ) 18.15 ( ) 1.65) r 1 MC 0.48 (1.44) ) 14.88 ( ) 0.78) 0.41 (1.28) ) 24.19 ( ) 1.18) r m MC 0.01 (0.03) 4.63 (0.31) 0.01 (0.04) ) 18.18 ( ) 1.17) r c MC 0.14 (0.74) ) 10.04 ( ) 0.95) 0.09 (0.50) ) 17.89 ( ) 1.64) r 1 MD 31.69 (1.98) ) 14.73 ( ) 0.82) 30.32 (2.00) ) 26.71 ( ) 1.40) r m MD 12.69 (1.01) 2.54 (0.18) 13.48 (1.14) ) 18.71 ( ) 1.26) r c MD 11.51 (1.29) ) 10.45 ( ) 1.04) 10.53 (1.27) ) 18.58 ( ) 1.79) r 1 TO 0.93 (2.31) ) 15.56 ( ) 0.90) 0.91 (2.40) ) 28.23 ( ) 1.55) r m TO 0.63 (2.12) 0.47 (0.04) 0.66 (2.41) ) 20.13 ( ) 1.54) r c TO 0.52 (2.52) ) 11.96 ( ) 1.35) 0.50 (2.67) ) 19.64 ( ) 2.19) r 1 R / D 0.81 (0.92) ) 6.04 ( ) 0.30) 1.02 (1.24) ) 29.27 ( ) 1.41) r m R / D 0.30 (0.46) 5.92 (0.40) 0.37 (0.59) ) 19.53 ( ) 1.26) r c R / D 0.36 (0.78) ) 7.02 ( ) 0.67) 0.53 (1.28) ) 20.11 ( ) 1.91) r 1 R / T 0.33 (0.09) ) 9.15 ( ) 0.45) 1.88 (0.53) ) 29.41 ( ) 1.30) r m R / T ) 0.84 ( ) 0.33) 4.43 (0.31) 0.02 (0.01) ) 18.25 ( ) 1.11) r c R / T ) 1.19 ( ) 0.66) ) 8.88 ( ) 0.86) ) 0.22 ( ) 0.12) ) 17.74 ( ) 1.53) r 1 BA 1.71 (4.01) ) 2.54 ( ) 0.18) 1.66 (3.75) ) 6.56 ( ) 0.41) r m BA 0.73 (1.80) 7.60 (0.58) 0.60 (1.43) ) 11.30 ( ) 0.74) r c BA 0.64 (2.29) ) 5.96 ( ) 0.66) 0.56 (1.97) ) 11.81 ( ) 1.15) r 1 PC 1.26 (4.15) ) 12.49 ( ) 0.92) 1.25 (3.63) 0.94 (0.06) r m PC 0.73 (2.78) 2.86 (0.24) 0.71 (2.43) ) 3.29 ( ) 0.23) r c PC 0.50 (2.52) ) 9.73 ( ) 1.11) 0.40 (1.81) ) 9.75 ( ) 0.89) r 1 LL 1.44 (2.67) 2.28 (0.13) 1.43 (2.34) 0.50 (0.02) r m LL 0.65 (1.46) 9.93 (0.71) 0.41 (0.81) ) 10.73 ( ) 0.60) r c LL 0.51 (1.63) ) 4.32 ( ) 0.43) 0.39 (1.10) ) 11.13 ( ) 0.90) r 1 BC 1.85 (4.51) 0.36 (0.03) 1.80 (4.24) ) 5.16 ( ) 0.34) r m BC 0.78 (1.89) 8.78 (0.67) 0.63 (1.48) ) 11.01 ( ) 0.72) r c BC 0.72 (2.65) ) 4.69 ( ) 0.54) 0.65 (2.36) ) 10.80 ( ) 1.10) r 1 CB 6.45 (2.69) 0.03 (0.00) 6.08 (2.41) ) 7.59 ( ) 0.39) r m CB 4.49 (2.55) 11.19 (0.91) 3.81 (2.01) ) 6.92 ( ) 0.47) r c CB 2.80 (2.08) ) 4.42 ( ) 0.47) 2.39 (1.73) ) 11.11 ( ) 1.03) Notes: Results for two regressions are reported, both of the form y i ¼ b 0 + b 1 r mi + b 2 h i + c x

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