This Selected Issues paper analyzes Japan’s medium- and long-term fiscal challenges. It discusses the initiatives that will be necessary to cope with Japan’s medium- and long-term fiscal challenges. It describes medium- and long-term projections of the fiscal position, and assesses the size of the consolidation measures needed to restore long-term fiscal sustainability. The paper explores possible options for consolidation and offers a representative package of such measures. The paper also describes the projected baseline path for the long-term fiscal balance, incorporating the long-term pension reform plan formulated in 1994.

Abstract

This Selected Issues paper analyzes Japan’s medium- and long-term fiscal challenges. It discusses the initiatives that will be necessary to cope with Japan’s medium- and long-term fiscal challenges. It describes medium- and long-term projections of the fiscal position, and assesses the size of the consolidation measures needed to restore long-term fiscal sustainability. The paper explores possible options for consolidation and offers a representative package of such measures. The paper also describes the projected baseline path for the long-term fiscal balance, incorporating the long-term pension reform plan formulated in 1994.

VII. The Real Exchange Rate and the Business Cycle in Japan 1/

Following the bursting of the asset price bubble in 1990, the Japanese economy entered a long and deep recession. During this period, sharp movements in the yen played a critical role in affecting the pace and composition of economic activity. The sharp appreciations of the yen in mid-1993 and the spring of 1995 negatively impacted business and consumer confidence and (with a lag) led to a withdrawal of external demand, slowing the recovery of activity. The rapid depreciation of the yen in the summer of 1995 was pivotal in restoring confidence and setting the stage for a sustained recovery in growth.

The sharp rise of the yen during the spring of 1995 was judged by many observers, including the staff, as being out of line with “fundamentals” in that it was inconsistent with the attainment of internal and external balance over the medium term. 2/ The level of the exchange rate should, of course, be affected importantly by the business cycle and, in turn, as the recent Japanese experience has indicated starkly, is an important determinant of the speed with which the business cycle dissipates. Theory predicts that movements in the real exchange rate over the business cycle depend on the relative importance of different “shocks” that drive the business cycle. For instance, while an autonomous contraction in aggregate demand should generally lead to a depreciation of the exchange rate, a recession induced by monetary tightening or a contraction in aggregate supply would be expected to lead to an appreciation.

This chapter uses a structural vector autoregression (VAR) to estimate the relative importance of different types of shocks for fluctuations in the exchange rate, output and the price level. Three type of shocks are identified. In the framework of the traditional IS-LM macroeconomic model, these shocks can be thought of as shocks to goods and money markets (that shift the IS and IM curves), respectively, and shocks that affect the longer-run level of capacity output. The shocks to goods markets are referred to as real demand shocks, while shocks to money markets are referred to as nominal or monetary shocks. Shocks effecting the long-run level of capacity output are referred to as supply shocks. The structural decomposition indicates that nominal and real demand shocks have been the main determinants of variations in the real exchange rate, while supply shocks have played a smaller role. Over the course of the recent cycle, the contribution of real demand shocks, which had created pressures for the yen to appreciate during the bubble period, has declined steadily since 1993. The sharp appreciations in 1993 and 1995 and the subsequent sharp depreciation of the yen can be attributed primarily to nominal shocks.

The chapter is organized as follows. Section 1 discusses the predictions from standard macroeconomic models for the path of the exchange rate over the course of the business cycle. Section 2 reviews movements in the real value of the yen and the business cycle in Japan during the floating rate period, and characterizes the movements of the yen over the course of the recent cycle. Section 3 describes the econometric framework used in this chapter, and Section 4 presents the results of the estimation. Section 5 provides some concluding observations.

1. Theoretical considerations

Theory predicts that cyclical movements in the real exchange rate during the business cycle depend on the relative importance of different shocks that drive the cycle. The traditional Mundell-Fleming model in which capital is mobile predicts that autonomous contractions in aggregate demand should lower interest rates, leading to a capital outflow and a depreciation of the exchange rate on impact. 1/ Interest parity then implies that the decline in domestic interest rates translates into an expectation of future appreciation. That is, as aggregate demand recovers, and output returns to potential, the real exchange rate is expected to appreciate and return to trend. During the recessionary period, the relatively depreciated exchange rate tends to stimulate net exports and moderate the decline in aggregate demand. If the recession is induced by a monetary tightening, on the other hand, interest rates would be expected to rise, leading to a capital inflow, and the exchange rate should appreciate. Similarly, if the recession reflects primarily a contraction in aggregate supply, the real exchange rate would also be expected to appreciate. Thus, knowing the cyclical state of the economy alone is insufficient for determining where the current level of the exchange rate should be.

Real economies are, of course, subject simultaneously and continuously to a variety of shocks. Therefore, only in the unlikely event that one type of shock clearly dominates for an extended period of time would it be possible to argue, a priori, where the exchange rate should be at a particular point in the business cycle.

2. The exchange rate and the business cycle in Japan

This section examines the historical relationship between the exchange rate and the business cycle in Japan during the floating rate period, with particular attention to recent movements in the yen. Chart VII.1 displays data on the real value of the yen based on consumer prices, wholesale prices, and relative export unit values over the last 45 years. The Japanese CPI- and WPI-based real effective exchange rates have trended upwards during the postwar period, while the prices of Japanese exports relative to those of partner countries have fluctuated around a stable mean level during the floating rate period. 1/ The secular appreciation of the CPI- and WPI-based real exchange rates can be explained by differential rates of productivity growth between the traded and non-traded goods sectors in Japan relative to its trading partners, while allowing it to maintain the competitiveness of its export industries. Since short-run changes in the real exchange rate have been driven predominantly by movements of nominal exchange rates, it is notable that all three measures of the real exchange rate display similar deviations from trend (mean levels). Keeping in mind that all three measures of the real exchange rate display similar deviations from their longer-run levels, the remainder of this chapter focusses on the CPI-based exchange rate. From a macroeconomic perspective, the CPI provides a broad measure of the price level that can be most directly linked to cyclical movements in output.

CHART VII.1
CHART VII.1

JAPAN: ALTERNATIVE MEASURES OF THE REAL EFFECTIVE EXCHANGE RATE, 1951-96 1/

Citation: IMF Staff Country Reports 1996, 114; 10.5089/9781451820522.002.A007

1/ CPI-base rate employs an average of G-7 partner countries; WPI-based rate employs an average of G-7 partner countries for which WPIs are available: US, GR, UK; Relative export unit values are based on G-7 partner countries.

Chart VII.2 compares deviations of the CPI-based real effective exchange rate from trend with the staff’s measure of the deviations of GDP from potential. 2/ It shows that, during the floating rate period, the behavior of the yen has differed markedly across business cycles. Movements in the yen have sometimes been procyclical and sometimes countercyclical. The recession induced by the oil-price shocks in the 1970s was accompanied by an appreciated yen (relative to trend), while the downturn in 1982-84 was accompanied by a considerably depreciated yen. 3/ Following the Plaza Accord in 1985, the yen appreciated very sharply and activity slowed. As activity boomed during the ensuing bubble years, the yen remained at an appreciated level before depreciating sharply in 1989-90, preceding the bursting of the asset price bubble and the slowdown in activity. During the most recent cycle, the yen appreciated persistently through the onset of the downturn in economic activity in 1992, appreciating above trend in mid-1993, and rising substantially above it in the spring of 1995. The rapid depreciation starting in mid-1995 then brought the yen by October to trend. Since then, the yen has depreciated gradually.

Chart VII.2
Chart VII.2

Japan: The Real Exchange Rate and the Business Cycle, 1974-1996

Citation: IMF Staff Country Reports 1996, 114; 10.5089/9781451820522.002.A007

Clearly, the relationship between the exchange rate and the business cycle has been complex. As noted earlier, in an economy subject to a variety of shocks, this is indeed what would be expected. During the recent Japanese recession, for example, several types of shocks occurred. Moreover, their relative importance would appear to have varied over the course of the cycle. The bursting of the asset-price bubble in 1990 that led to a sharp deterioration of business and consumer balance sheets and confidence could be identified as a negative real demand shock, suggesting that the yen should have depreciated. The bursting of the asset price bubble in 1990 was, however, preceded by a series of increases in policy interest rates, and the monetary tightening should have created pressures for the exchange rate to appreciate. Subsequently, however, monetary policy was eased, and since mid-1991 interest rates have been lowered repeatedly. Money markets were affected by a host of other factors during the period. Fragilities in the financial system and changes in the spreads between bank borrowing and lending rates as a consequence likely affected the demand for money. In addition, there is evidence to indicate that during the period there were changes in portfolio preferences, particularly those of Japanese institutional investors, for yen assets. The long recession and continued structural changes in the Japanese economy suggest also that there were shocks to the supply of output. The simultaneous operation of these factors complicates any informal identification of the shocks affecting exchange rates.

The relative importance of these factors in affecting the level of the yen has implications for policy. In the face of an autonomous contraction in aggregate demand, a benchmark for the stance of monetary policy, one that is “cyclically neutral,” is provided by the case where the exchange rate depreciates by the amount suggested by the operation of the negative demand shock. If it was established that negative real demand factors were causing the exchange rate to depreciate, but these were being offset by negative monetary factors causing the exchange rate to appreciate, there would be a case for a further easing of monetary policy.

3. A structural econometric model

To identify the factors driving short-run movements in the exchange rate it is necessary to impose identifying assumptions or restrictions that impose structure on short and/or long-run movements in the exchange rate. These could be in the form of a structural model. The residuals of the equations could then be examined to assess actual short-run movements in exchange rates. The well-known failure of structural models in explaining and forecasting exchange rate movements suggests, however, that they are unlikely to provide a reliable guide to assessing short-run movements in exchange rates. 1/ In addition, classification of the residuals of a structural exchange rate model into real demand, monetary (nominal), and supply shocks and, therefore, into their effects on exchange rates is not a straightforward matter. An alternative is to impose a set of parsimonious statistical restrictions that identify the shocks directly based on historical response patterns. This is the approach adopted here.

The econometric framework used to study the relationship between the real exchange rate and the business cycle is essentially a structural vector autoregressive (VAR) model, similar to that of Clarida and Gali (1994), who investigate the sources of fluctuations in real exchange rates using a three-variable extension of the Blanchard and Quah (1988) methodology. Some analytical considerations regarding the model are first discussed. This is followed by a description of how the model is estimated and implemented.

a. The econometric model

Following Clarida and Gali (1994), a three-variable VAR with relative output, the real effective exchange rate, and the relative price level is estimated. Three long-run restrictions are then used to identify three separate types of shocks: supply, demand, and nominal shocks. In line with standard macroeconomic models, it is posited that demand shocks (that shift the IS curve) and nominal shocks (that shift the LM curve) have no long-run effect on the level of output, yielding two restrictions. A third restriction imposed is that the real exchange rate is homogeneous with respect to nominal shocks, that is nominal shocks do not impact the long-run level of the real exchange rate. 1/ Using these restrictions on the implied long-run multipliers, the errors from the reduced-form VAR model are then transformed into a set of “fundamental” structural disturbances that have an economic interpretation—nominal shocks, demand shocks, and supply shocks. An important virtue of this framework is that the short-run dynamics are left completely unconstrained. That is, all three shocks are allowed to affect any of the variables in an unconstrained manner in the short run.

Before describing the implementation of the econometric model, a few preliminaries need to be discussed. As real exchange rates are affected not just by domestic macroeconomic conditions but also by conditions in other countries, relative rather than domestic measures of the business cycle and other macroeconomic conditions are relevant for the determination of the exchange rate. For Japan, relative output is defined as the level of real GDP in Japan minus a trade-weighted average of real GDP in the remaining G-7 countries. The real effective exchange rate is constructed using bilateral exchange rates vis-a-vis these countries and the same set of trade weights. The relative price level is defined as the level of the Japanese CPI minus the trade-weighted average of the CPIs in the other G-7 countries. The measures of the real effective exchange rate, relative output, and prices, are thus derived consistently.

The next step is to determine the time series properties of the variables entering the VAR. The top panel of Chart VII.3 shows that relative output in Japan peaked towards the end of 1991 and has fallen continuously since. This is partly because of the recent recession in Japan but also reflects the resurgence in U.S. output following the 1992-93 recession. The second panel shows a trend appreciation in Japan’s real effective exchange rate, although there have been large fluctuations around this trend. Finally, reflecting Japan’s relatively lower inflation rate, the bottom panel shows a steady decline in Japan’s relative CPI since the mid-1970s.

Chart VII.3
Chart VII.3

Japan: Output, Real Exchange Rate, and Price Levels, 1977-1996

Citation: IMF Staff Country Reports 1996, 114; 10.5089/9781451820522.002.A007

Chart VII.3 shows that all three variables displayed trends over the sample period. It is necessary to determine whether these variables are stationary around stochastic or deterministic trends. Results from Augmented Dickey-Fuller tests indicated that all three variables were first-difference rather than trend stationary. 1/ Hence, we include the (logarithmic) first differences of relative output, the real effective exchange rate and the relative CPI in the estimation. Note that, since relative measures of output and prices are used in the estimation, the shocks are more appropriately thought of as relative demand shocks, relative nominal shocks and relative supply shocks. For the sake of brevity, this terminology is used sparingly below.

b. Implementation of the methodology

The first step is to estimate the following reduced-form VAR:

B(L)Xt=t,var(t)=Ω(1)

where Xt is a vector containing the first differences of relative output, the real exchange rate, and relative CPI and B(L) is a 3 × 3 matrix of lag polynomials. This VAR can then be inverted to obtain the following moving average representation:

Xt=C(L)t,whereC(L)=B(L)-1andC0=I.(2)

The objective of this methodology is to derive an alternative moving average representation of the form

Xt=A(L)ηt,var(ηt)=I(3)

where the mutually uncorrelated shocks η1t, η2t, and η3t can be interpreted as fundamental macroeconomic shocks. 2/ Comparing equations (2) and (3), it is evident that Aj = CjA0 for j=1,2,…; and that ηt = A0-1t. Using the fact that A0A0′ = Ω yields a set of six restrictions on the elements of the A0 matrix since the variance-covariance matrix Ω is symmetric.

In order to identify the AQ matrix, three additional restrictions are imposed on the system. These restrictions constrain certain long-run multipliers in the system to be zero. The long-run multipliers of the above system are denoted by the matrix A(1) = [A0 + A1 + A2 + …..]. Using the relation derived above between A0 and Aj for j=1,2,…, this can be rewritten as A(1) = [I + C1 + C2 + ….}*A0, where I denotes the identity matrix. Thus, given the estimates of Cj for j=1,2…., a restriction on a particular long-run multiplier effectively imposes a linear restriction on the elements of the A0 matrix. As noted above, we assume that nominal shocks and demand shocks have no long-run effect on the level of output. In addition, we impose the restriction that nominal shocks do not have a permanent effect on the level of the real exchange rate. These restrictions constrain the (1,2), (1,3) and (2,3) elements of A(1) to be zero and, using the relation between the elements of A(1) and A0, jointly make the A0 matrix uniquely identified. The lower triangular structure of A(1) implies that η1t, η2t, and η3t can be interpreted as the underlying supply, demand, and nominal shocks, respectively. 1/

4. Results

This section presents results from the empirical implementation of the structural VAR developed in the previous section. There are a number of alternative ways of examining the effects of the estimated structural shocks on the variables in the system. We first examine the impulse responses of each of the variables to a unit innovation in each of the “fundamental” shocks. 2/ Variance decompositions of the forecast errors based on the VAR are also examined. Finally, historical decompositions are presented that show what fraction of the in-sample variation in each series can be attributed to each of the structural shocks.

The impulse responses are presented in Chart VII.4. Since the variables were entered in first differences in the VAR, the resulting impulse responses were cumulated in order to derive the impulse responses shown in this figure for the levels of the variables. The top panel of this figure shows that supply shocks have a permanent effect on relative output. Demand and nominal shocks have smaller impact effects on relative output than supply shocks, and the long-run effects of these two shocks asymptote to zero. The responses of the real exchange rate are as expected. A supply shock has a permanent negative effect on the level of the real exchange rate, exactly opposite to the effect of a real demand shock. Nominal shocks, on the other hand, lead to an initial depreciation of the exchange rate. The exchange rate then appreciates toward its trend level. This result is consistent with the overshooting in Dornbusch’s (1976) sticky-price model. The impulse responses of the relative price level are also as expected. Demand and nominal shocks have a permanent positive effect on the relative price level while supply shocks have a permanent negative effect. Thus, the impulse responses indicate that the estimated structural shocks have reasonable properties in terms of their effects on the variables in the model.

Chart VII.4
Chart VII.4

Japan: Impulse Responses of Output, Real Exchange Rate, and Price Levels

Citation: IMF Staff Country Reports 1996, 114; 10.5089/9781451820522.002.A007

Next, in Table VII.1 we present the forecast error variance decompositions for the estimated model. This table shows, for each variable, what fraction of the forecast error variance at different forecast horizons can be attributed to each shock in the model. For the first differences of relative output, supply shocks are the most important, contributing about two-thirds of the forecast error variance at all forecast horizons. Demand shocks account for about a third of the forecast error variance and nominal shocks play only a very small role. For changes in the exchange rate, however, supply shocks are relatively less important, accounting for only about a quarter of the forecast error variance. Nominal and demand shocks are both quite important for this variable. This is similar to the results reported by Clarida and Gali (1994) using the bivariate Japan-U.S. real exchange rate. For changes in the relative price level, supply shocks are the most important contributor to the forecast error variance at short horizons, although both nominal and demand shocks contribute a significant fraction. At long horizons, nominal shocks account for the largest fraction of the forecast error variance.

Table VII.1.

Japan: Forecast Error Variance Decompositions for Baseline Specification 1/

article image

The forecast error variance decompositions are for the changes in each variable (e.g., first differences of log levels). These decompositions indicate the proportion of the variance of the k-period ahead forecast error that is attributable to each shock. Relative output is defined as the level of Japanese GDP minus a trade-weighted average of GDP in the other six G-7 countries. Likewise for relative CPI. The real effective exchange rate is also computed using trade weights and CPIs for the same six countries.

These forecast error variance decompositions indicate that supply shocks have an important role in determining the variation in all three variables. Although nominal shocks play a very small role in relative output growth fluctuations, these shocks appear to have the dominant role in determining variation in changes of the real exchange rate and the relative price level. Demand shocks determine a fairly large fraction of the variation in relative output growth and real exchange rate changes but have a smaller role in affecting relative price variation.

The historical movements in the level of each variable can be decomposed into components attributable to each of the shocks. Charts VII.5-7 show, in four panels, the deviations of the level of each of the variables from their estimated “exogenous” components, the components attributable to the real demand and nominal (monetary) shocks, and the innovations in the supply component. 1/

Chart VII.5
Chart VII.5

Japan: Decomposition of Relative Output Fluctuations, 1977-1996

Citation: IMF Staff Country Reports 1996, 114; 10.5089/9781451820522.002.A007

Chart VII.6
Chart VII.6

Japan: Decomposition of Real Exchange Rate Fluctuations, 1977-1996

Citation: IMF Staff Country Reports 1996, 114; 10.5089/9781451820522.002.A007

Chart VII.7
Chart VII.7

Japan: Decomposition of Relative Price Level Fluctuations, 1977-1996

Citation: IMF Staff Country Reports 1996, 114; 10.5089/9781451820522.002.A007

The decompositions in Charts VII.5-7 confirm several widely held notions about the shocks driving movements in output and the real exchange rate over the sample period. In the case of output, the relative real demand component of output was large and positive in 1986-88, as would be suggested by the rapid growth of demand in Japan during the bubble years. During 1990-93, the demand component fluctuated around zero, conforming with the fact that the recession in Japan has represented a stagnation rather than a sharp decline in output. Movements in the nominal (monetary) component of output are particularly revealing. The nominal component of output rose rapidly in 1988 as the bubble grew, peaking in late 1989-early 1990, and then fell sharply—as the bubble burst. It turned negative in 1991, declining through 1993, then moderated in 1994-95, before finally turning positive in the second half of 1995. This pattern confirms the view that relative monetary conditions played an important role in both creating and subsequently in the bursting of the asset-price bubble and the consequent slowing of (relative) economic activity in Japan. Moreover, monetary conditions continued to remain “tight” well after the onset of the downturn, easing only in mid-1995, following the decisive easing of monetary policy in the summer of 1995. 2/

Relative real demand factors kept the real exchange rate at a relatively depreciated level through the mid-1980s. The real demand component then rose steadily during 1986-88, and then held steady through the early 1990s, maintaining pressures for the real exchange rate to appreciate. The real demand component has declined steadily since 1993 and, by the first quarter of 1996, is estimated to have little effect on the level of the exchange rate. The nominal (monetary) component caused the exchange rate to depreciate during 1989-92, but these factors were steadily reversed, and by early 1993 were causing the exchange rate to appreciate. In early-1995, nominal (monetary) factors again exerted pressures for the exchange rate to appreciate. It is notable that the two spikes in the real exchange rate in mid-1993 and mid-1995 correspond closely to the spikes in the nominal (monetary) component. In the first quarter of 1996, the depreciation of the Japanese real exchange rate relative to its exogenous component can be attributed primarily to nominal (monetary) factors while the other components have little impact.

5. Conclusions

Sharp movements in the yen during the course of the recent recession played an important role in effecting the pace and composition of economic activity. Theory suggests that the behavior of the exchange rate over the business cycle depends on the underlying shocks driving the cycle—contractions in aggregate demand emanating in the goods market should lead to a depreciation, while contractions resulting from shocks in money markets or reductions in aggregate supply to an appreciation. Over the floating rate period, movements in the yen have some times been procyclical and some times countercyclical, suggesting that all three types of shocks played a role in affecting the behavior of the yen. A structural decomposition of movements in the real exchange rate, output and the price level over the floating rate period indicates that nominal and real demand shocks have been the main determinants of movements in the real exchange rate, while supply shocks played a smaller role. Over the course of the recent cycle, the contribution of real demand shocks, which created pressures for the yen to appreciate during the bubble period, declined steadily from 1993 on. The sharp appreciations of the yen in 1993 and 1995, and the subsequent sharp depreciation of the yen, can be attributed primarily to shocks in money markets.

References

  • Blanchard, Olivier, and Danny Quah,The Dynamic Effects of Aggregate Demand and Supply Disturbances”, American Economic Review. Vol. 79, pp. 655673, (1989).

    • Search Google Scholar
    • Export Citation
  • Clarida, Richard and Jordi Gali,Sources of Real Exchange Rate Fluctuations: How Important are Nominal Shocks?”, National Bureau of Economic Research, Working Paper Series, No. 4658, (1994).

    • Search Google Scholar
    • Export Citation
  • Dornbusch, Rudiger,Expectations and Exchange Rate Dynamics”, Journal of Political Economy. Volume 84, pp. 116176, December, 1976.

    • Search Google Scholar
    • Export Citation
  • Lippi, Marco and Lucrezia Reichlin,The Dynamic Effects of Aggregate Demand and Supply Disturbances: Comment”, American Economic Review. Vol. 83, pp. 644652, June, (1993).

    • Search Google Scholar
    • Export Citation
  • Meese, Richard A. and Kenneth Rogoff,Empirical Exchange Rate Models of the Seventies: Do they Fit Out of Sample?”, Journal of International Economics, Volume 14, pp. 324, February 1983.

    • Search Google Scholar
    • Export Citation
  • Obstfeld, Maurice,International Capital Mobility in the 1990s”, Board of Governors of the Federal Reserve System, Washington D.C., International Finance Discussion Papers, no. 472, (1994).

    • Search Google Scholar
    • Export Citation
1/

This chapter was prepared by Bankim Chadha and Eswar Prasad.

2/

See “The Yen from a Long-Run Perspective,” Chapter I in last year’s background papers (SM/95/163, Supplement 1).

1/

The assumption of capital mobility is an important one. In the absence of capital mobility, the exchange rate response could be quite different. The empirical evidence suggests, however, that the degree of capital mobility among the developed economies is high. See, for example, Obstfeld (1994).

1/

For a fuller discussion see “The Yen from a Long-Run Perspective,” Chapter I in last year’s background papers (SM/95/163, Supplement 1).

2/

For details on the staff’s production function approach to estimating potential output, see Chapter II in Supplement 1 to SM/94/167.

3/

The discussion in this section of movements in the real exchange rate relative to a deterministic trend is purely for simplicity. The assumption of a deterministic trend is relaxed in the empirical work in Section 4.

1/

For a discussion of the failure of structural models in explaining short-run exchange rate movements, see Meese and Rogoff (1983).

1/

Standard open economy macroeconomic models predict that shocks in the money market that effect the level of the money supply or shift the level of money demand without affecting the long-run level of interest rates, have no long-run effects on the real exchange rate. See, for example, Dornbusch

1/

We also tested for, and found no evidence of, co-integration among the levels of the variables.

2/

Lippi and Reichlin (1994) have criticized the interpretation of the VAR disturbances as fundamental shocks with an economic meaning. While this is an important point, we are nonetheless encouraged by the fact that the impulse response functions from our analysis are similar to what we would expect on the basis of theoretical considerations.

1/

The operational procedure to derive A0 is as follows. Given the ordering of the variables in the VAR, A(1) is lower triangular as noted above. The reduced-form model described in equation (1) is estimated and C(1) is computed, where C(1) = [I + C1 + C2 + ….]. A Cholesky decomposition then yields the unique lower triangular matrix H such that HH′ = C(1)ΩC(1)′. Since ∊t = A0ηt, A(1) = C(1)*A0, and var(ηt) = 1, it follows that C(1)ΩC[1)′=A(1)A(1)′. Hence, we can deduce that A(1) = H. Then, given that A0 = C(1)-1 A(1) and Aj = Cj*A0, it is straightforward to derive Aj ∀ j = 0,1,2….

2/

By construction, the shocks are uncorrelated and have unit standard deviation.

1/

The exogenous component refers to the forecast based on the estimated VAR when there are no shocks. The difference between this forecast level and the actual level is the forecast error, which is then apportioned among the components attributable to the shocks in the system. For relative output, the supply and exogenous components together define the stochastic trend, since the other two shocks have only temporary effects on output by construction. For the real exchange rate and the relative price level, on the other hand, there can be persistent differences between the actual levels and the exogenous component because of movements in either supply or the other shocks that are allowed to have permanent effects.

2/

It is perhaps worth emphasizing that the nominal shocks represent a composite relative shock to money markets. That is, they represent shocks to both money demand and to money supply relative to that in partner countries.

Japan: Selected Issues
Author: International Monetary Fund
  • View in gallery

    JAPAN: ALTERNATIVE MEASURES OF THE REAL EFFECTIVE EXCHANGE RATE, 1951-96 1/

  • View in gallery

    Japan: The Real Exchange Rate and the Business Cycle, 1974-1996

  • View in gallery

    Japan: Output, Real Exchange Rate, and Price Levels, 1977-1996

  • View in gallery

    Japan: Impulse Responses of Output, Real Exchange Rate, and Price Levels

  • View in gallery

    Japan: Decomposition of Relative Output Fluctuations, 1977-1996

  • View in gallery

    Japan: Decomposition of Real Exchange Rate Fluctuations, 1977-1996

  • View in gallery

    Japan: Decomposition of Relative Price Level Fluctuations, 1977-1996