MONEY AND ECONOMIC ACTIVITY: SOME INTERNATIONAL EVIDENCE Mehdi S. Monadjemi * School of Economics University of New South Wales Sydney 252 Australia email: m.monadjemi@unsw.edu.au Hyeon-seung Huh Melbourne Institute of Applied Economic and Social Research University of Melbourne Parkville Victoria 352 Australia email: h.huh@iaesr.unimelb.edu.au Abstract This study examines the long-run responses of economic activity to changes in monetary conditions in open economies. The empirical results of the study, based on monthly data from Australia, Germany, Netherlands and the United States provide support for existece of a long-run equilibrium between money, income, interest rate, price level and the exchange rate. However, evidence from dynamic responses of output to changes in money indicate that in the long-run money has a neutral effect on output. I. Introduction The relationship between money and economic activity has been a popular research topic in economic literature. Most of the contributions in this area are due to the classical work by Friedman and Schwartz (963) and the subsequent work by Friedman. In the 95s and the 96s the controversial issue was the extent to which money can affect economic activity, money matters. This controversy together with the effectiveness of fiscal policy, divided macroeconomists into two distinct group of Keynesians and Monetarist. The advents of 97s with the inflation rate in industrial countries in double digits, led monetarists recommendations gaining a remarkable endorsement by politicians. Targeting monetary aggregates became popular in the 97s when inflation appeared to be a major problem. Poole (97) set criteria for implementing monetary and interest rate targeting based real and financial shocks. A high rate of inflation in the 97s forced financial institutions to bypass existing regulations and engage in financial innovations which, in turn, weakened the set definitions chosen for monetary aggregates. In addition, deregulation of financial markets caused problems in interpretation of signals given by monetary aggregates. Friedman (992) and Friedman and Kuttner (992) argued that the stable relationship between money and economic activity that existed in the post-war period was no longer supported by data. Both Friedman (988) and Poole (988) provided evidence showing a significant decline in the velocity of M in the United States in the 98s. The conventional monetary aggregates were no longer satisfactory targets and indicators for implementation of monetary policy. In a recent study Davis and Tanner (997) in the context of a vector autoregressive (VAR) model showed that money is the most important variable in explaining variation of U.S. output during the period 874-993. In a separate study Tanner (993) showed that the relationship between money and income remains stable over a long period of time if the influence of determinants of money demand are taken into consideration. Most of the studies in this area used U.S. data and concentrated on a closed economy. The purpose of this paper is to examine the money/income relationship in the context of an open economy with application to four OECD countries. In section 2 some theoretical discussion regarding money/income relationship is offered. The empirical results using cointegration techniques and the dynamic responses of output to a monetary shock are presented in section 3. The description of data is given in Section 4. Summary and concluding remarks are provided in Section 5. * The authors would like to thank the anonymous referee for his valuable comments.
II. Theoretical Discussion Most of the earlier studies on money/income relationship relied on Fisher s equation of exchange as a theoretical framework. Subsequent works by Friedman (956, 968) and Friedman and Meiselman (963) attempted to emphasise the influence of money on economic activity by providing evidence on the stability of the velocity of money. Mundell (963) and Fleming (962) modified the Keynesian model of income determination by including the effect of capital flows in an open economy. In Mundell/Fleming model the effect of money on output is neutral in the short-run when prices are assumed to be constant. However, in the long-run prices change proportionally to changes in money, leaving the real value of money and the level of output unchanged. A modified version of Mundell/Fleming model is adopted in Dornbusch (976) for examining the short-run and the long-run effects of money on the exchange rate. In Dornbusch s model an exchange rate mechanism equation together with uncovered interest parity condition and differentiating behaviour of the price level in the short run and in the long run lead, to an over-shooting exchange rate. The exchange rate over-shoots its long-run equilibrium in response to a change in money stock in the short run when prices are constant but reverts to its equilibrium in the long-run when money, prices and the exchange rate change proportionally leaving the real exchange rate constant. In this model, similar to Mundell/Fleming s, money neutrality is preserved in the long-run but not in the short-run.. In this paper, a simple version of Mundell-Fleming-Dornbusch small open-economy model is used for investigating the relationship between money and income. The model is specified by the following equations: y t = α(e t - p t ) α 2 [rt E t ( p t+ )] + ut () m t pt = α3yt α4rt + u 2t (2) m t = u 3t (3) N p t = α5[y t (y + u 4t )] (4) * E t [ et + ] = rt (r + u5t ) (5) where: y = level of output r = nominal rate of interest p = price level m = nominal value of money r * = world nominal interest rate e =nominal exchange rate defined as the price of foreign currency y N = natural level of output or full-employment level of output = difference operator E = expectational operator, and all variables except the interest rate are expressed in logarithms. It is assumed that there are five independent shocks governing the system: real spending shocks (u t ), money demand shocks (u 2t ), money supply shocks (u 3t ), aggregate supply shocks (u 4t ), and world interest rate shocks (u 5t ). All parameters (α i ) are assumed to be positive. () is an open-economy IS equation in which the demand for domestic output is positively associated with the real exchange rate (e t -p t ), and negatively with the real interest rate. The structural shock u t is assumed to capture shocks to domestic absorption such as fiscal policy shocks and terms-of-trade shocks. The money demand and supply functions are given in (2) and (3), respectively, and the solution to these equations is the LM curve representing domestic money-market equilibrium. (4) is the Phillips curve type of relationship in which changes in the price level are related to the deviation of output from its natural rate. Finally, (5) is the relation for uncovered interest rate parity. N * The economy is in long-run equilibrium when y t = (y + u 4t ) and rt = (r + u5t ). Consequently, p t = and e t = in long-run equilibrium. Using these, equilibrium in the product market and in the money market are, respectively, obtained as: N * y + u 4t = α (e t p t ) α 2 (r + u 5t ) + ut, (6) N * u 3t p t = α3 (y + u 4t) α 4 (r + u5t) + u2t. (7)
For simplicity, assume that y N = r * =, from which u 4t and u 5t represent the stochastic processes for the natural level of output and the world interest rate, respectively. The long-run solution of the model is obtained by combining (3), (4), (5), (6) and (7). Equation (8) shows the long-run effects of the structural shocks on the series as: rt yt e = α t ( pt mt 2 + α α α 4 4 ) / α ( α α α 3 3 ) / α u5t u 4t / α u 3t. (8) u 2t ut According to equation (8), the long-run effect of money on output is neutral. Money supply shocks leave the level of output unchanged. In this model, aggregate supply shocks are the only shocks that have a positive effect on output. For details of the derivation of the model, see Obstfeld (985), Lane (99), and Clarida and Gali (994). The statistical method chosen for estimating the effects of money on output is vector autoregressive (VAR) where every variable in the model is a function of its own lag and lags of other variables in the model. This procedure is more flexible than the traditional regression technique with restrictions imposed on parameters of the model. The estimated parameters of a VAR or an error correction model (ECM) are difficult to interpret since they are basically reduced form and provide little information about the structural relations of the model. To draw a meaningful structural interpretation, appropriate identifying assumptions are to be imposed on the basis of economic theory. Both variance decomposition (VDC) and impulse response functions (IRF) may be drawn from the ECM with imposed identifying restrictions. The following VAR model is proposed for investigating the relationship between money and income: Yt = A( L) Yt + Vt (9) where Y t is a vector of five time series, (y t, r t, e t,, m t,, ρ t,), A(L) is a5x 5 polynominal matrix in the lag operator L and V t is a vector of random disturbances with V t ~ (, ) Σ. III. Econometric Methodology Most macroeconomic time series are non-stationary in levels and the use of conventional regression techniques for such data tends to produce spurious results. However, non-stationary time-series data may be cointegrated if some linear combinations of the series become stationary. That is, the series may wander around, but in the long-run there are economic forces that tend to push them to an equilibrium. That is, cointegrated series will not move far away from each other and are linked in the long-run. Johansen (988 and 99) suggested tests for determining numbers of cointegrating vectors among a group of variables. Consider the following p variable VAR model: k Yt = u+ φiyt i + εt () i= where u is the constant term, Y t is (p ) vector of the variables under study, and the disturbance vector ε t of dimension (p ) is distributed as an i.i.d. Gaussian process with zero mean and variance Ω. Assuming that series are cointegrated, equation 2 may be re-parameterised to give the following ECM representation: k Yt = u+ Γ i Yt i + ΠYt k + εt () i= Γ j j = I φ i i= Π= I k φ i i= (2) (3)
where I is the identity matrix. [See Johansen (99) for details.] The long-run relationship between the series is determined by the rank of Π. If time series are non-stationary and cointegrated, then Π is not full rank, but < rank(π) = r < p, where r is the number of cointegrating vectors. Johansen (99) proposed two likelihood testing procedures in order to estimate the rank of Π. The first tests the hypothesis that the number of cointegrating vectors is, at most, equal to r (Trace test). The second tests the hypothesis that the number of cointegrating vectors is equal to r (Max Eigenvalue test). When the series are found to be cointegrated, Johansen further demonstrated that Π can be factored as: Π= αβ (4) where β is the matrix of r cointegrating vectors and α is the matrix of weights attached to each cointegrating vectors in equation 3. Both α and β are (p r) matrices. IV. Data Description All of the data in this study are monthly time series on OECD countries collected from the Time Series Data Express, dx v2., site license held by the School of Economics, University of New South Wales, Sydney, Australia. The interest rate series are averaged over-night money market rates during the month. The exchange rate series are end of the month bilateral exchange rate against the U.S. dollar measured by the number U.S. currency in one unit of domestic currency. The price level is the all items consumer price indices. The money stock is the monthly observation on M. The level of output is measured by the index of industrial production. V. Empirical Results The augmented Dickey-Fuller and Phillips-Perron s test for unit-roots were applied to five time series in each country and the results indicated that all variables are non-stationary in levels but stationary in first differences. The results of Johansen test for cointegration are reported in Table. These results indicate that the hypotheses of one cointegrating vector for Australia and Germany and two cointegrating vectors for the remaining two countries cannot be rejected at the 5 percent significant level. These results indicate that there is a long-run equilibrium between four time series included in the model. The existence of one or two cointegrating vectors for a sample period covering over three decades may indicate that five time series under consideration are bounded in one or two directions. In other words, there is a joint long-run equilibrium among variables included in the model. However, these results do not convey any information about the existence of equilibrium between two individual time series in the model.this information may be obtained by examining the dynamic response of an individual variable to a shock of another variable. The dynamic interactions among various variables can be examined by impulse response functions (IRF) and variance decompositions (VDC). To this end, as suggested by Engle and Granger (987), the estimated coefficients of ECM are converted into levels and are inverted to vector moving average form. However, since coefficients of ECM are reduced form, they can provide little information about the structural coefficients of the model. In order to draw useful structural information, some form of identifying restrictions that are consistent with economic theory should be imposed on the ECM. Orden and Fisher (993) used a standard Choleski-type of contemporaneous identifying restrictions. This type of restriction is less restrictive than the long-run zero identifying restrictions used in King et al. (99). In this study a Choleski-type of identifying restriction is imposed on the ECM. When this type of restriction is used, the ordering of variables imposes a particular recursive structure on the model, so that variables appearing earlier contemporaneously influence the latter variables, but not vice versa. The recursive order of variables chosen here is y t, m t, r t e t, and p t. Other types of recursive order produced almost identical results.
Table RESULTS OF COINTEGRATION TEST Hypothesis Trace 95%CV Alternative λ Max 95%CV Australia (963.-985.2) r 4.66 3.76 r = 4.66 3.76 r 3 7.34 5.4 r = 3 8. 4.9 r 2 7.82 29.68 r = 2 3.76 2.7 r 46.32 47.2 r = 37.4* 27. r 79.3* 68.52 r = 42.93* 33.46 Germany (96.-993.2) r 4.27 r = 4.27 r 3 5.37 r = 3 5. r 2 4.62 r = 2 9.25 r 43. r = 28.39* r 4.87* r = 6.86* Netherlands (96.-993.2) r 4.53 r = 4.53 r 3 9.65 r = 3 9.22 r 2 28.29 r = 2 2.6 r 66.32* r = 43.7* r 24.49* r = 66.2* United States (96.-993.2) r 4.7 r = 4.7 r 3 7.4 r = 3 7.7 r 2 22.7 r = 2 5.56 r 5.68* r = 27.98* r 24.34* r = 73.66* In Table 2 the results of VDC for, 5,, 5, 3 and 4 months ahead are reported. These results show the relative importance of various shocks in forecast error variance of output. With the exception of Netherlands where money shocks are insignificant, in other three cases money shocks have significant effects on output in the short-run but not in the long-run. The results of IRFs derived from the ECM are presented in Figure. For each country only the response of income to a shock of money is reported. The IRFs show the dynamic responses of income to one standard deviation shock of money in each particular country. The one standard confidence intervals are also shown in each case. A particular response is considered to be significant if confidence intervals do not include the zero line. Similar to the VDC results, with the exception of Netherlands, the IRFs also indicate a significant and positive responses of income to an innovation in money in the short-run but not in the long-run.
Table 2 VARIANCE DECOMPOSITION OF OUTPUT Australia (968.-993.2) Months Ahead y t m t r t e t p t..... 5 88.3 (.7) 5.7 (.9) 5.5 (.8).2 (.7).3 (.) 76.4 (2.7) 7.6 (.5) 5.3 (.5).2 (.).5 (.4) 5 65.8 (3.5) 6.6 (.8) 25.3 (2.2).2 (.3) 2. (.5) 3 45. (5.4) 3.2 (2.) 4.7 (4.).5 (.6).5 (.7) 4 38. (6.5) 2.2 (2.2) 43.9 (5.).6 (.8) 5.3 (.9) Germany (96.-993.2)..... 5 86.2 (.3) 3.8 (.6).6 (.).8 (.6) 8.6 (.9) 85.3 (.9) 3.2 (.9). (.2).9 (.9) 9.6 (.) 5 84.9 (2.2) 2.9 (.).9 (.2).8 (.).5 (.2) 3 84. (3.5) 2.9 (.2).8 (2.).6 (.5).7 (.4) 4 8.3 (4.9) 3.3 (.3) 2. (3.).6 (2.) 2.8 (.5) Netherlands (964.-993.2)..... 5 95.5 (.5).3 (.8). (.7) 2.3 (.7).8 (.7) 94.9 (2.8).2 (.3).9 (.5) 2.8 (.).2 (.) 5 94.8 (3.6).2 (.6).8 (2.) 3. (.2).2 (.2) 3 94. (6.3).6 (2.7).8 (3.7) 2.9 (.6).7 (.4) 4 92.5 (8.3).4 (3.7).5 (4.9) 2.6 (.8) 2. (.5) United States (96.-993.2)..... 5 9.5 (.2) 3.7 (.6) 3. (.5).7 (.6) 2. (.5) 87. (.8) 4.2 (.9).9 (.9).4 (.) 6.4 (.8) 5 83.4 (2.6) 3.8 (.).6 (.2).3 (.6).9 (.) 3 73.4 (5.7) 2.3 (.2) 2.9 (3.5).5 (3.9) 2.9 (.5) 4 68.6 (8.3).7 (.3) 4.2 (5.5).6 (5.7) 24.9 (.7) Variables are in log levels as specified in the ECM. Lag length of variables is four for all five countries. Figures in parentheses are one-standard errors computed using 3 bootstrap replications of the ECMs.
Figure Responses of output to money shock Australia Netherlands.8.6.4.2 -.2 -.4 5 9 3 7 2 25 29 33 37 Germany 2..4.7 -.7 -.4 5 9 3 7 2 25 29 33 37.4.2 -.2 -.4 -.6 5 9 3 7 2 25 29 33 37 United States.8.6.4.2 -.2 5 9 3 7 2 25 29 33 37 VI. Summary and Concluding Remarks An attempt was made in this paper to examine the money/income relationship using monthly data on four OECD countries. The empirical analysis of the paper indicated that money, income, interest rate, price level and the exchange rate are cointegrated. However, the existence of a long-run equilibrium among five time series does not necessarily mean that the effect of money on output is non-neutral. Impulse response functions and variance decompositions show that in three out of four cases, money is an important variable in the short run but not in the long run. In the forth case the effect of money on output remained entirely neutral irrespective of the time span.
. A particular VDC is considered significant if the range after adding and subtracting one standard error does not include zero. That is the result of + and - one standard deviation remains entirely positive or negative.
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