Exchange rate and wage-price dynamics

European Economic Review 30 (1986) 57-90. North-Holland

EXCHANGE

RATE AND

WAGE-PRICE

DYNAMICS

A Theoretical Analysis and an Econometric Investigation Patrick ARTUS ENSAE,

92240

Malakoff,

France

Claude BISMUT CEPII,

75015 Paris, France

Received August 1983, final version received April 1984 This paper is an attempt to analyze inflation dynamics in a small open economy as the result of the interaction between wage and price determination behaviors and the interest rate-exchange rate feedback in the context of Dombusch’s model. An extended version of this model is specified and analyzed formally. Then the model is estimated for five OECD countries using a full information maximum likelihood technique. Finally, simulations of the effect of monetary shocks are presented for four countries.

1. Introduction This paper is an attempt to analyze inflation dynamics in a small open economy as the result of the interaction between wage and price determination behaviors and the interest rate-exchange rate feedbacks. For this purpose we use as a starting point Dornbusch’s (1976) model and we extend it by introducing a more structural specification of price and quantity adjustments in the goods and labor markets. Although Dornbusch’s main concern in the 1976 paper of JPE was the over-shooting of the exchange rate and expectation formation, his model provides one of the simplest specifications of the channels by which monetary shocks may influence prices, interest rates and exchange rates. A reduced form equation for aggregate demand and a Keynesian demand function for labor are used., Price and wage equations are specified in the light of the recent literature on short-run rigidities and on the medium-run determinants of wage and price behaviors. Though not rational in the short run, the exchange rate expectations converge in the long run towards the equilibrium solution of the model for exchange rates, which means that long-run consistency is ensured. Then the model is estimated for five OECD countries (United States, United Kingdom, France, Germany and Japan) using a full information maximum likelihood technique. Finally, 0014-2921/86/%3.50 0 1986, Elsevier Science Publishers B.V. (North-Holland)

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simulations of the effect of monetary shocks are presented for four countries. The absence of reaction functions of the authorities and the non-rational behavior of private agents in the short run led to some complications that will be discussed below. 2. An overview of the literature 2.1. The overshooting hypothesis According to the strict monetary approach of exchange rate determination as developed by Frenkel (1976, 1977, 1980), Mussa (1976), Girton and Roper (1977), Hodrick (1978) and Bilson (1978) in the flexible exchange rate regime, the supply of and demand for money determine the domestic price level, which in turn determines the exchange rate through the purchasing power parity (PPP) condition. While this approach may be adequate for the long run, it fails to account for two main observed facts during the flexible exchange rate period of the seventies. The first one is the persistent deviation from PPP. Direct observations [Krugman (1978), Frenkel (1981)] or indirect econometric tests [Dornbusch (1980), Hodrick (1978), Bilson (1978)] do not confirm the PPP hypothesis. The second observed fact that this approach seems unable to account for is the extreme volatility of exchange rates experienced in the same period. The general tendency of exchange rates to overshoot their equilibrium value after a monetary shock has been acknowledged by many authors and attributed to some nominal rigidity, but no consensus emerges on the kind of rigidity involved. Some attribute the overshooting phenomenon to price or wage rigidity: Dornbusch (1976a), Obstfeld (1982), Niehans (1977), Bilson (1979a), and Buiter and Miller (1982); some attribute it to differential effect of the news on commodity and assets markets [Dornbusch (1978), Frenkel (1981), Frenkel and Mussa (1980), Mussa (1979)] some attribute it to an adjustment process that restores portfolio balance in the face of disturbances’ [Kouri (1976), Branson (1979), Calvo and Rodriguez (1977), Frenkel and Rodriguez (198 l)]. In his seminal contribution in the JPE, Dornbusch (1976a) chose one of the simplest frameworks for analyzing the overshooting phenomenon. The salient features of his model were the opposition between clearing forward looking capital and money markets and a slow adjusting goods market. These features have served as basic ingredients in numerous studies in the area. However, Dornbusch’s framework is probably less general than it appears at first glance, even though we stay within the assumption of price ‘Another possible explanation noticed by Frenkel and Rodriguez (1981) is the hypothesis of an inefficient speculation in foreign exchange markets.

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rigidity as the main cause of overshooting. In fact, Frenkel and Rodriguez (1981) have demonstrated that if the extreme assumption of perfect capital mobility is relaxed and replaced by some finite degree of mobility, there is no need for the exchange rate to overshoot. This might occur only if capital adjustment is relatively rapid independently of the speed of adjustment in the goods market. Obstfeld (1982) pointed out that the sluggish price adjustment assumption in a goods market was rather counterfactual (in particular the response of domestic prices to an increase in import prices might be very quick) and that short-run money non-neutrality was caused mainly by nominal wage rigidity. If this assumption is right, in the context of a small open economy with a unique international good, the exchange rate will ‘undershoot its equilibrium value in the short run. However, there might be some overshooting effect if the economy exhibits Scandinavian features (the conventional two sectors). A striking result of Obstfeld’s model is that the existence of overshooting is independent of the degree of openness of the economy (measured by the share of traded goods). This is not the case in Bilson’s (1978) model that specifies both wage and price inertia in the context of the two-sector model of an open economy. This model, in which an explicit reaction function of the monetary authority is specified, generates an overshooting behavior if the economy is not widely open. Empirical results on exchange rate overshooting are only few, though particularly interesting. Frankel (1979) tested the general monetary model (allowing short-run deviations from the PPP) with some success on the dollar/mark case, but did not find the Dornbusch particular case to be confirmed. Updated estimation of the same model reported in Frankel (1982) performed even more poorly. On the question of whether or not there is an overshooting effect, two studies give very interesting results. Bilson (1978) has found the exchange rate of the dollar vis-a-vis the Swiss franc to overshoot its equilibrium level by a factor around 2. On the basis of a model close to Dornbusch’s, Driskill (1981) has tested a reduced form of a more general model on Swiss/US. data and has found a strong overshooting effect. However, the Dornbusch case in which his model specializes for a given a priori restriction on parameters of the reduced form was rejected. As far as we are concerned with inflation dynamics, the wage-price mechanism remains the core of the model. Concerning this topic, there exists an extremely voluminous literature that can be divided broadly into two branches. The first branch assumes some kind of rigidity and examines the consequences of economic regulation. The second deals with microeconomic foundations of short rigidities and/or long-run determinants of price and wage behavior.

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2.2. Flexible exchange rate and wage-price rigidities

Consequences of. nominal versus real wage rigidities have been widely discussed by Cases (1975), Argy and Salop (1979), Sachs (1980), Bruno and Sachs (1979). All these authors have shown that, in an economy with flexible exchange rates, if real wages are rigid, monetary expansion will have no output effect (contrary to the Mundel-Flemming conventional nominal rigidity case), while a fiscal expansion will raise output and inflation and will export unemployment abroad. Branson and Rotemberg (1980) have developed a somewhat more general case and have argued that this result may be less clearcut if two commodities are distinguished. Buiter and Miller (1982) have more carefully examined consequences of reducing inflation by contractionary monetary policy taking into account the short-run overshooting effect and the long-run effect on competitiveness. Bruno (1978) analyzes the wage-price process in the context of a two-commodity model of an open economy, integrating the cost push effect and the feedback through lagged excess demand on goods and labor markets. This framework has been reused in our model. In all the previous models, price and wage behaviors are viewed as sluggish adjustment processes to long-run targets. We shall adopt the same representation. Since empirical tests are seldom reliable for helping to specify the two components, it is of some importance to know to what extent these behaviors are theoretically grounded. The question arises concerning the long run and the short run as well. 2.3. Short-run and long-run price determination

In the long run, price behavior lies somewhere between the competitive price-taking behavior in which domestic firms are constrained to fix their prices equal to those of their competitors and the mark-up cost pricing behavior in which firms are able to impose their price. The Scandinavian model [see Lindbeck (1979)] uses this extreme contrast in characterizing the two sectors. The price taking is in general justified by the absence of any monoply power of domestic firms. The opposite assumption is often justified by an oligopolistic context according to Fellner’s (1960) argument. But a straightforward transposition of this argument to an aggregate foreign sector is questionable, in particular under flexible exchange rates, since price variability in domestic currency terms is not under the control of foreign competitors. However, one can argue that real situations stand somewhere in between, which may correspond to the existence of some monopoly power of the domestic international sector. Thus the comparative static textbook behavior may be used as a plausible approximation. In the case where domestic and foreign product are imperfect substitutes a competitiveness effect appears in the long-run price equation.

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The problem of price adjustment involves two separate issues that are sometimes confused: the price response to excess demand on the one hand and the nominal inertia on the other hand. For a long time, empirical studies on price behavior have been based on a more or less sophisticated gradual adjustment to desired price calculated from a mark-up rule ignoring completely market clearing tatonnement based on an excess demand. Much evidence to support this view was essentially found in surveys [see Skinner (1970)] or econometric tests mordhaus (1974)]. As a natural extension it has been suggested that demand pressure may speed up the adjustment to the desired price. This behavior has been founded rigorously in the monopolist case by Maccini (1981) who has justified capital and stock gaps to their desired level as arguments for the speed of adjustment function. But in the case of a mark-up rule, it is somewhat difficult to understand why demand pressure could speed up an adjustment towards a price that does not clear the market and would not have any effect, even for an enormous excess demand, since the desired price target is achieved. Theoretically oriented studies by Zabel (1969), Barro (1972), Iwai (1974), Benassy (1976), and Bruno (1979), tend to advocate the use of some measure of excess demand in the price equation consistently with a monopoly price setting behavior in the face of uncertain demand. Empirical tests such as those of Nordhaus (1972) for the U.S. and Bruno (1981) for all OECD countries except the U.S., have found this effect to be small but significant. It can also be argued in favor of this specification that it is also consistent with a competitive price tatonnement [McCallum (1975)J Excess demand, cost or competitiveness effects may be lagged for numerous reasons. Firms may not want to adjust their price to transitory shocks on costs. In particular, short-run fluctuations on the labor productivity (the productivity cycle) are not fully transmitted to prices. Empirical tests yield to a significant but only partial influence of the short-run productivity on prices and confirm that the long-run standard productivity (a trend or some weighted average of past productivities) remains the main determinant of prices [see Eckstein and Fromm (1968), Gordon (1971,1972,1975) for the U.S., and and Nordhaus (1972) for the U.K.].’ Short-run fluctuations in competitiveness may not lead to change in domestic prices if customers have an imperfect information on the prices of competitors. Cost of acquiring information guarantees a transient monopoly power to domestic firms [see Phelps and Winter (1970) for a similar argument]. Information lags or costs may also slow down the adjustment of prices to costs and their response to *This result is less clearcut in the French case. Some studies conclude to a full instantaneous productivity effect [Metric (1982)], some others conclude to a full standard productivity effect CArtus (1983)].

E.E.R.-

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excess demand. In absence of auction markets firms set prices with an imperfect knowledge of the demand. They collect information on the demand curve through transactions that have taken place at a price that may differ from the equilibrium price and adjust their prices afterwards. This view adopted by Benassy (1976), and Gordon and Hynes (1970) is typical of the disequilibrium approach and justifies a lag between market disequilibrium signals and the response of prices. A more conventional dynamic theory of the firm leads to similar conclusions when stocks and/or cost of adjustment are introduced. Price smoothing turns to be an optimal behavior if it is possible to realize an equilibrium between supply and demand by filling the gap with inventories [see Blinder (1981), and Amihud and Mendelson (1983)]. 2.4. Wage determination

In contrast to price behavior, the effect of excess demand on wages has been acknowledged very early. The first attempts to find it rigorously were made by Phelps (1970), Holt (1970), Mortensen (1970), and Lucas (1972). All these contributions are based on job search theory and explain the statistical Phillips curve and the natural rate hypothesis.3 The Phillips curve effect is widely used in empirical models but it has relatively less importance in theoretical approaches. One of the main reasons why this is so, is that wage behavior is subject to a very important nominal and/or real inertia that tends to weaken the stabilizing effect of the Phillips relation. The most convincing justification of the wage inertia is probably the existence of long-run overlapping wage contracts. Taylor (1979,198O) has shown that staggered contracts set in nominal terms and a strong relative wage effect may generate a heavy wage-wage process (i.e., nominal inertia) with a long distributed lags effect (the shape of which can be precisely specified). Buiter and Jewitt (1980) have found that Taylor’s (1980) model is observationally equivalent to a real wage model of staggered contracts without relative wage effects. Autoregressive functions will be used in the model to approximate the true lag distribution. This effect results from the fact that wage contracts are specified in nominal terms and that wages cannot be reconsidered during the contract period. This description is probably more appropriate for North-American countries than for Europe and Japan. In the latter countries wage-contract periods are much shorter than in the U.S. To some extent, contract length and the degree of indexation are institutional constraints for an individual but it may not be completely independent of economic conditions at the country level. Gray ‘In all these contributions unemployment is caused by voluntary quits, but lay-offs are ignored. The voluntary nature of unemployment is not implied by the job search framework but rather by the. labor market conditions. See Salop (1979) for a counter-example.

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(1978) has investigated this conjecture and set up a model in which the contract length can be optimally determined by balancing renegotiating costs and uncertainty about future conditions. The degree of indexation is treated in the same way. Real wage inertia coming from explicit or implicit indexation has to be distinguished from the somewhat different problem of relative insensitiveness of the real wage to large fluctuations in employment [Hall (1980)]. Implicit contract theory gives probably the most convincing explanation of that observed fact. Baily (1974) and Azariadis (1975,1976) have shown that employers and employees have an initial interest in setting a contract in which the employer who is less risk averse insures the employee against the variability of its random earnings. Extending this framework, Hart (1982) has argued that if the information is asymmetric in favor of the employers these may have interest to depress employment so as to obtain a real wage fall using (and manipulating) employment as a signal. This explains not only little wage fluctuations with large employment fluctuations but also the emergence of non-Walrasian unemployment. 3. The model 3.1. General description

Our model is mostly an extended version of Dornbusch’s The following features are kept:

(1976) model.

-a money market equilibrium with a fully controlled money supply, -perfect mobility of capital flows implying that the domestic and foreign interest rates only differ by the expected variations in the exchange rate, -exchange rate expectations based on the long-run equilibrium, -a reduced form equation for total demand. However, the rest of the model is much more complicated than in Dornbusch’s paper since we are basically interested in the interactions between exchange rates, prices and wages. In Dornbusch’s model inflation was solely determined through the disequilibrium between demand and capacity. Here we introduce a much more complete specification for the producer’s price, integrating costs, competitiveness and demand pressure effects discussed above. The introduction of a cost effect needs an explicit treatment of the wage rate and the demand for labor. Thus it is also possible to integrate a wage-price mechanism that makes our model comparable to Bilson’s (1979). In the equations of the model, the following applies: -all variables are in logs, except the interest rate, r, -parameters denoted by Greek letters are valued between 0 and 1,

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-other parameters, denoted by subscripted Latin letters corresponding to the endogenous variables, are positive, except constant terms (with a subscript o’), -an overbar denotes exogenous variables, -a circumflex denotes steady-state values. The model consists of the following equations: m=~[p+m,d-mlr+mz]+(l-t[)m-l,

(1)

and

(14

m=A, r - P + P”,

(2)

h” = O(c - e),

(34

L”=hO_,+e(&d),

W

P=&+(l

(3c)

-O)B,

d=q[d,+d,(p*+e-p,)-d,r+d,~+d,(w+I-p) -d,log(l-~++d,(m-p)+d,~+(l-~)d-l,

(4)

d,=nCpo+v(~++-~+(l-v)(~*+~)+pp,(d-y?] +(1--W,-,,

(5)

~=~Ckd+w,+w,(l-T)+w,(d-[)+w,(P,-li)] +dlog(l-?)-(l-~)dlog(l-~-,)+(l-~)tii,-l,

(6)

I=P[hd+I,-I,t-I,(w-p,)]+(l-P)1-,,

(74

1=/3[hd+Ic-Irt-&(w-p,-log(r-@+6))]+(1-/?)I-,,

(W

p=ap,+(l-a)(p*+e), where in eq. (1)

Ci = money supply, demand deflator, interest rate (domestic);

p =domestic r =short-run

(8)

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in eq. (2) in eq. (3) in eq. (4)

in eq. (6) in eq. (7)

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r * =foreign interest rate, i’ =expected change in exchange rate (e=number of domestic currency units per foreign currency); 2 =long-run equilibrium exchange rate; d = total demand (imports being considered as a negative component of demand, d equals domestic production), jj* = foreign prices (in foreign currency), p,, = producer price, J = production capacity, w = total compensation per employee, 1 = employment, Z =apparent rate of employer’s social security contributions, Z =exogenous variables appearing in the demand equation (public expenditures, foreign demand,. . .), T =labor force, f = time trend, 6 =rate of depreciation of capital.

Finally the rate of inflation is the rate of growth of the domestic demand deflator depending, by definition, both on import prices (in domestic currency) and on producer’s prices. The model is written in discrete time which allows us to analyze it in the form it will be estimated and used in simulation further on. Let us turn now to a more detailed description of the equations of the model reported. Money and capital markets

The money demand [eq. (1)] follows a Keynesian type behavior depending on the usual variables: real income and interest rate, and is homogenous in prices in the long run. The money supply is supposed to be fully controlled by monetary authorities [see eq. (19)]. Perfect capital mobility implies eq. (2). This assumption considerably simplifies the model since modeling capital flows becomes unnecessary.4 But in doing so we ignore the existence of risk premia that seems to have found some empirical support in several countries in Cumby and Obstfeld (1981) and Frenkel (1979). Exchange rate expectation

Exchange rate behavior is forward looking in this sense that people take into account the long-run equilibrium levels when setting up their expec4Relaxing this assumption would lead to a model closer to the ones developed in Frenkel and (1982) and Niehans (1977).

Rodriguez

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alternative

Following Dornbusch (1976) we assume that there exists a unique stable long-run equilibrium value E of the exchange rate6 and that the expected rate of depreciation P’ is equal to a proportion 19of the discrepancy between the long-run equilibrium value d and the spot rate e [eq. (3a)]. As a straightforward extension of the previous case we assume in eq. (3b) that there exists a non-zero but constant rate of depreciation C. The formula is obtained by differentiating eq. (3a) when d varies over time. A third expression (3~) is introduced to allow for an extrapolative component in exchange rate expectations. The expected rate of depreciation is some weighted average of the rate of depreciation of the spot exchange rate and the depreciation of the equilibrium exchange rate. As has been said in the introduction, we did not attempt to have rational expectations in the short run. The model (l)-(S) is a dynamic system of order two, and it is only in the case where the system would have only one stable root, that eq. (3a) could represent rational expectations for a suitable value of 8. In Dombusch’s model, wage dynamics being absent, eq. (3a) can be used together with the rational expectation hypothesis. We preferred to stick to eq. (3a) which is easy to interpret and not to use the complicated methods necessary to estimate and simulate rational expectations models. The goods market

Eq. (4) is a reduced form equation for total demand (calculated as domestic demand + exports -imports, i.e., identically equal to the gross domestic product). It depends on variables assumed to explain private spendings such as the real wage income (w+l--p), the interest rate (r) and real money balances (c-p) as a proxy for the wealth effect, as well as variables explaining the trade balance in volume, competitiveness (I* +e-pJ, production capacity jj and foreign demand. The latter variable and other exogenous variables such as public expenditures are included in L The behavior of suppliers on the goods market is summarized in a producer’s price eq. (5). We suppose that there exists an ‘equilibrium’ level of demand pressure d -j=p,/p, for which prices are only determined considering the unit cost of labor (w + I-d) and the prices of foreign competitors (I* +e). The parameter v measures to what extent producers are aware of ‘Bhandari (1981) pointed out that economic agents are- supposed to know the value of the parameters that enter in the expression for the equilibrium exchange rate. -is statement will be related to specific steady state assumptions in section 3.

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cost conditions and (1 -v) measures to what extent they take the competitiveness constraint into account.’ We allow for short-run sluggishness by introducing the autoregressive term. This equation is consistent with a competitive price tatonnement as well as with a monopolistic dynamic price setting a la Barre (1972), thanks to the use of the term (d -y3 as a proxy for excess demand. Empirically, this equation may describe a wide range of situations between the clearing market case (A = 1 and p1 +co) and the fixed price case (p, =0) including price flexibility (pl >O and A= 1) and gradual adjustment (pr >O and A> 1).

domestic

The labor market

The wage equation (6) includes elements which may affect wage and labor contracts between firms and unions. The domestic demand deflator d is introduced in the equation in order to take indexation mechanisms (implicit or explicit) into account. Those contracts are generally supposed to imply a negative effect of excess labor supply (l-T) on the growth rate of wages. The willingness of firms to stabilize the share of labor in output implies that the growth rate of real wages depends on labor productivity growth (d-l) and on the evolution of relative prices &,-@).s The short run behavior of the equation is dominated by nominal wage rigidities. Real wage rigidity comes out indirectly through the indexation when wages do not react strongly to the disequilibrium in the labor market. This is a somewhat different view from Branson and Rotemberg (1980) who introduce lagged prices directly into the wage equation. Finally eq. (8) permits the calculation of the price of domestic demand, as a weighted average of producer prices and of import prices. Before turning to the econometric estimation we examine the long-run properties of the model and then we establish under which conditions overshooting may appear in a somewhat simplified version.

3.2. Long-term equilibrium

Long-term equilibrium is calculated in two cases: first, in the case of a static long-term equilibrium, then in the case of a steady-state growth path. ‘This parameter must bc consider&l as a behavioral parameter, for instance, some producers may prefer to keep their prices close to costs even if they lose a part of their market share. No attempt has been made to introduce an asymmetric response of producers’ prices to the price of imports [see Crockett and Goldstein (1976)]. “Using the same argument, Perry (1975) introduced both the non-farm GDP deflator and the consumer price index in the wage equation for 10 countries. The GDP deflator proved to be significant for 5 countries.

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3.2.1. Static equilibrium9

Setting all dotted variables (including de) equal to 0, using eq. (3a) for expectations, the following expression for the long-term exchange rate can be obtained: e=

mI(dI-d,+(d4+d5)a)+dla d, -(I-u)d,

-p*+fi++*

0 - d, -(I-a)d, -jj’

-ap

--m2

log(f* + ?I)(*)

m,(d,-d,+(d,+d,)a)+a(d,-l+d,h/l,) dI-(I-a)d4 d.t-h.l4

d,-(I-a)d,

1 1 6, + d,z

4apdpl

-d,-(I-cc)d,-ad,-(l-a)d,

d,-d,+(d,+d,)a+d,alog(l+f) d, -(I-a)d, dI -(I-a)d,’

where j’=ji-pO/pl, l’=l-w,,/wl, and (*) denotes the case where eq. (7b) is used. The long-term price level can then be calculated, identifying p in eq. (1) with eqs. (8) and (9). The long-term expression for the exchange rate exhibits the usual homogeneity properties with respect to foreign prices and to the domestic money supply. The signs of the coefficients of the other variables are in general ambiguous, because of the ambiguity of the sign of the denominator (d, -(I-a)d,). If dI is large, i.e., if the effect of competitiveness on demand is strong, b will be positively related to the corrected labor force P, and to the foreign interest rate rP, and negatively to the exogenous component of demand (d,+d,F). The signs are inverted if (I-a)d, is larger than d,, i.e., if the income effect on demand is stronger. Take, for instance, in the first case, an increase in the exogenous component of demand f d must remain constant (equal to capacity), hence e-p, must decrease .(d,>>d4 in the first case). Because of eqs. (1) and (2), p must stay constant. Therefore eq. (8’) implies that b decreases: the domestic currency appreciates to reduce competitiveness and compensate the exogenous increase in demand, total demand having to remain equal to capacity. In the second case (d,<
is constant, i.e., I, =O.

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3.2.2. Steady-state growth path

Money supply is now assumed to grow at the exogenous constant rate ji, foreign prices at the exogenous constant rate p*. To simplify the expressions, the labor force is assumed to be constant (T=O). All domestic real variables grow at the rate 2, domestic prices at rate p. From eq. (8) one easily derives

i.e., purchasing power parity. From eq. (1) j?=ji-m&

(11)

In a true steady-state Therefore, from eq. (7),

growth

rate, real wages also grow at rate &lo

1 11 g=h_I,s

(12)

which is the endogenous growth rate. Then, from eq. (4),

hence the necessary homogeneity

condition

dS+d4+d,mo+d6=1.

(13)

If that condition is satisfied, eq. (11) becomes 1

p=p

-

m04

(11’)

h.-12’

which is the endogenous steady-state inflation. And from eq. (lo),

&p-p*--

mo4

(10’)

Finally, from eq. (6),

“And money is in a constant proportion to income, which implies mo= 1. We don’t impose that constraint here since in all countries, the estimated m, is larger than 1.

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which shows that, as expected, employment is independent from the inflation rate if wage indexation is perfect (k= l), and from eq. (5), J=Y-PO/PI.

However, one may be willing not to impose the homogeneity condition (13). In fact, for all the countries, it was rejected by the data. In that case, it is still possible to build a pseudo steady-state growth path, using different growth rates for production, capacity and demand (g) and for real wages (g,). Eqs. (10) and (11) are still valid. From eq. (7) one now gets

Then, from eq. (4) 1

41,llz

(12’)

g=d,+d,h/l,-l+d,m,+d,’

Then, from eq. (lo),

mod44

;=p-p*-

d,l, +d,h - 1, + d,m& + d,l,’

(lo”)

which is the second possible version of the long-term growth rate of the exchange rate. From eq. (l), one gets the new expression of the inflation rate, (I

-

w&l1

P=~-d,l,+d,h-l,fd,m,l,+d,l,’

(11”)

Finally, from eqs. (6) and (5), one gets the long-term values of the capaicity utilization and the unemployment rate. That ‘pseudo steady-state’ growth path is made possible by the presence of capacity utilization in the price equation, of unemployment in the wage equation and of real wage in the labor-demand equation, which gives the necessary degrees of freedom. If the price equation was a pure mark-up over unit labor cost, only the strict steady-state growth path described before would be possible. The long-term growth rate of the exchange rate [eq. (10’) or (lO”)] shows the usual homogeneity condition with respect to money supply and foreign prices. It also depends on the rate of productivity growth (II). An increase in

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1, permits a quicker growth

of production if h>l,, which is probable l-j increases, see eq. (12)], and, with a fixed money supply, implies a lower inflation rate [see eq. (l)], and hence an appreciation of the exchange rate [through eq. (S)]. 3.3. The possibility of overshooting: A simplified case

A complete analysis of the model, in particular of the possibility of exchange-rate overshooting, implies very tedious calculations with the complete model (l)-(8). Therefore, it seemed useful to do more analysis on a simplified version of the model, closer to Dornbusch’s model. However, here we only give a simple analysis of the model, since the more complicated dynamic properties will be illustrated by model simulations. For a complete analytical discussion for different versions of a model very close to the one used here, see Buiter and Miller (1981). The simplifications made are the following: -We suppose that there is no inertia (t= 1, v= 1, A= 1, ,u= 1, fi= 1). -Total demand is supposed to depend only on competitiveness and interest rates (d3 = d4 = d, = d6 = 0). -The Scandinavian characteristics of price formation are dropped (v = 1). -Wages are assumed to depend only on inflation and unemployment (w2 = wg = 0). -Labor demand keeps fixed proportion with production (Ii =I, =O, h= 1). - Useless constants are dropped (pO= w0 = 1, = 0). However, we maintain the price-wage interaction which is one of our main interests. In that simplified model, overshooting is not a consequence of price rigidity [like in Dornbusch (1976a)] or of production rigidity @ike in Dornbusch (1976b)] but possibly of the whole structure of the model. However, in the complete model, price and output rigidities play a great role. We assume that at time t money supply grows by an extra Aji, and we calculate the change in exchange rate also at time t. If de,> AZ, first-period overshooting is obtained. The first kind of shock is the following: in the case of a static equilibrium, money supply (in logs) equals rii,, on (- 03, t - 1) and CiO+ Aji on (t, + co) in the case of a steady-state path, the growth rate of money supply increases from m, to ,ii+ A,L In both cases rii is increased by A/i in the first period. Two cases have to be distinguished according to the expectation equation used. If eq. (3a) or (3b) is used (Dornbusch’s equation in level form or in variation form), one gets Ar=lJAji-8Ae

(17)

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12

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rate and wage-price

dynamics

(where A means variation due to the change in money supply), since, in the tirst period, the change in E and the change in 8 are equal to the change in money supply. If eq. (3~) is used, one gets A=(l-B)Ap+OAe.

(17’)

Expectation equation (34 or (3b). A rather tedious calculation shows that de=

Xl Xl +x2

(18)

AI-4

where X1 = 1 + 8(m, +m,d,) + 1 -k;;;;;;+ x

_

wl) f@, + w&L

(k-W-w4)

2-1-ka+d,(p2+w,)’

If a-mod, >O, and if we assume that there is no overindexation of wages (ks 1, k4 l/a is even sufficient) X, >O, X2 ~0, and we can see that the exchange rate overshoots in the first period (in the static case, it means that it depreciates more in the first period than in the long run; in the dynamic case, that the change in its growth rate is larger in the short run than in the long run). If a-m,d, ~0, it is easy to show that one still has X1 >O, and that there is no overshooting of the exchange rate. Therefore, overshooting may happen in rather closed economies (with large a), exhibiting a small income elasticity of money demand and a small effect of competitiveness on total demand (which is consistent with the fact that they are not very open). It is easy to see why: price and wage equations can be rewritten (neglecting the disequilibrium terms) fi =((l -a)/( 1 -ak))& If a is large, the effect on prices of the initial depreciation of the exchange rate is small, which implies that prices don’t contribute very much to the rebalancing of the money market after the increase in money supply. The same argument applies for mOdI. If mOdI is small, the effect on money demand of the initial improvement in competitiveness is small. If p and m,d don’t increase very much, equilibrium on the money market will be obtained through a decrease in interest rates, only made possible by exchange rate overshooting [h
WI. Moreover, one can notice that one always has X, +X2 >O, which’ means that an increase in money supply always leads to a depreciation of the exchange rate.

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A second kind of shock is possible in the steady-state growth case: the longrun growth rate of money supply remains the same (fl,,) but at time t a once and for all extra increase in money supply by Ap happens (this second kind of shock will be illustrated further on by simulations of the model). After calculation the change in the exchange rate. is l-ka+d,(p,+w,) Ae=Aiil-ka+d,(pl+w,)+(l-k)(m,d,-a)

and overshooting

(18’)

’

is possible if

(1-k)(m,d,-a)+(1-ka)(mod,+m,)+(p,+w,)(ad,+m,d,)~0,

i.e., a-mod,

>- l~k~(l-ka)(m~d~+mI)+(~~+wI)(ad2+m,d,)I~0,

which is less likely than the previous condition (a-mod1 >O). Expectation equation (3~). We limit ourselves here to the steady-state growth path case and to a permanent change in the rate of growth of money supply (from ii,-, to j& + A,#. Starting from (17’), one gets after some calculation de=

X3 x,+x‘%

AK

(19)

where X,=1+(1--0)(m,d2+mI)+

X 4= --ammod,-(m,-,d,+ml)+

a - m,d, l-ka+d,(p,+w,)

d,(l -@(PI + WI),

a -mod, l-ka+d,(p,+w,)

x(W -a)+d,h +wl)--d,(p, + wl)). One can easily verify that X, > 0, whatever the sign of a -mod,. overshooting appears if X4 < 0, therefore, if a-mod,

Hence,

>-k~~C(m,d,+m,)(l-kor)+(pt+w,)(rn,d~+d,a)l
14

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and C.

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rate

and wage-price

dynamics

which again is less restrictive than the equivalent inequality obtained with the Dornbusch-type expectation formation. The adaptative expectation equation (3~) may thus more easily lead to a first-period overshooting of the exchange rate. Of course, when the complete model (l)-(8) is simulated, the conditions for overshooting are considerably more complicated, in particular, the various speeds of adjustment (of money demand, of the demand for goods, of prices, wages,. . .) play an important role, which will be illustrated further on, not by analytical calculation but by model simulations. One expects for instance that countries with sticky prices or demand are likely to exhibit overshooting since p or d do not contribute in that case to the increase in money demand. After having analyzed the long-term properties of the complete model, and performed more analysis concerning the possibilities of overshooting of the exchange rate, we can now turn to the estimation of the complete model. 4. Estimation of the model We now proceed with the estimation of the model for five countries: The United States, Japan, Germany, France, the United Kingdom. First, we briefly describe the data used. 4.1. Data (all variables are expressed in logs in the model)

The following variables apply: rTi = the money stock M2, d =total gross domestic product in volume, r = the short-term interest rate on the money market, e = the exchange rate, calculated as the number of domestic currency units per U.S. dollar; in the case of the U.S. model, eqs. (2) and (3) are dropped, since the dollar is the reference currency for the other countries, and since the interest rate in the U.S. is considered as exogenous, I*= the foreign price expressed in dollars; for each country, it is simply the imports’ price converted in dollars, jj =potential production, calculated on the basis of business surveys on capacity utilization, w = total wage cost (including employers’ social security contributions) per head, 1 =total employment, p = the deflator for total domestic demand, pP = the GDP deflator, f = the apparent rate for employers’ social security contributions, T = total labor force.

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For France and the United States quarterly data is used; for Japan, Germany and the United Kingdom, semi-annual data. The sample period is 1965-1981. However, the expectations equation was only estimated for the period when flexible exchange rates prevailed (1972-1981). For 1965-1971, F-P was taken to be exogenous. 4.2. Estimation method

Eqs. (1) to (8) are estimated simultaneously by a full information maximum likelihood method.” Expectation eq uation (3a) could never be used, since the necessary assumption I, =0 was rejected by the data, and, even when it was imposed, that expectation equation never gave any significant result. The choice was then between eqs. (3b) and (3~). In both cases, an expression for the long-run growth rate of the exchange rate (6) is needed. The homogeneity condition (13) was in all cases rejected by the data. The long-run growth path was therefore assumed to be the ‘pseudo steady-state’ growth path described in 3.2.2. Consequently, 6 was identified using eq. (loll), where several coefficients of the other equations of the model appear, which of course implies that eq. (3b) or (3~) has to be estimated simultaneously with the other equations. In fact, the expression for expectations (3b) or (3~) is identified in eq. (2), giving the estimated equations Ll(r-P)=f@-L),

(W

r-%&+(1-e)&

(24

In eq. (10”) the long-term growth rates of money supply (F) and foreign prices @*) appear. They were identified by distributed lags on the actual past values of the growth rates of those variables, the shape of length of lags being determined empirically in the estimation. 4.3. Estimation results

Estimation results for the five countries are presented in table 1. Two small deviations from the original model have been introduced: a lag on competitiveness [eq. (4)] in the German and French cases;12 a lag on inflation, representing long-term labor contracts, in the wage equation (6) in the U.S. case. Let us discuss the results equation by equation. “Initial values for the various parameters were obtained by estimating independently the different equations. “In the other cases, because of the lagged demand variable, a geometric lag on competitiveness appears.

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and C. Bismut,

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Table Estimation United States

I

results

Japan

(FIML).’

Germany

Money

demand

dynamics

France

United Kingdom

[eq. (I)]

1.35 (8.9) 0.016 (12.4) - 2.90 ‘19d9’

1.20 (7.9) 0.033 (1.1) -27.15 (5.4) 0.45

(1.2)

(2.11

(2.2)

(0.6)

DW see (%)

0.71 1.57

-0.65 2.97

.1.45. 2.56

1.24 1.0

1.07 1.16

e

-

0.23* (7.1) 1.48* 1.88*

0.15* (3.6) 0.92* 2.61*

8.22 (3.4) 0.07 (1.4) -

12.14 (2.4) 0.046

m0

ml m2 r

DW see (%I

4 4

4

-

4

0.56 (13.8) 0.34 (7.2) -

4 di (public expenditures) di (foreign demand) 1

(1.8)

1.52’ 2.34’

1.57* 1.36*

demand

PO

0.008

0.15

(1.6) -

DW

see(%I

-

0.12

-

0.35 (5.5) 0.34

(4.0) 1.79 0.94

1.03 1.18

deflator 0.18

y) 0.096

(1.6) 0.10 (1.7) 277 0.38

0.57

-

0.08 vu

V

1

13.39 (3.9) 0.36 (4.8) -

0.47

GDP

PI

(1.2)

1.65 (1.9) 0.23

(0.9) 1.79 1.31

1.28 (2.3) 0.055

(2.8) - 30.58 (1.5) 0.17

[eq. (4)]

(2.0)

see(%I

- 18.30

(1.2)

0.77 (6.7) 1.51 0.94

DW

-33.19 (7.6) 0.38

(4.9)

1.79 (0.3) 0.18 (1.3) 0.011 (1.5) 0.89 (3.1) -

0.049

(6.0)

[eq. (3)] 0.05*

-

- 5.40 (12.0) 0.018 (1.1) -

-

Expectations 0.64’

Total do

1.41

(8.8)

0.08 (1.5) 0.13 (1.3) 0.38 (3.1) 0.46 (4.0) 1.68 0.62

(1.6) ,;:y 0.16 (3.0) -

0.47 (2.7) 0.65 (3.0) 1.46 1.07

[eq. (5)] 0.009 (1.5) 0.54 (1.7) 0.094

0.005 (0.9) 0.51 (2.3) 0.030

0.003 ‘y’

(1.8)

(1.8)

(1.6)

0.35 (3.5) 2.48 0.60

0.24 (2.9) 2.45 0.63

(if 2.32 0.91

0.22

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dynamics

II

Table 1 (continued) United States

Japan Wage

0.35

k

(1.6)

0.018 (5.4) 0.05 (1.0) 0.05 (1.5) -

wo WI W2 W3

0.98

P

(64

DW see (%I

1.63 0.70

I1

lb

11 12

il.@4 (214.7) 0.0016 (12.0) 0.014

U.8)

B DW see (%)

0.35 (13.5) 1.10 0.45

demand

0.30

(5.6)

14.29 (4.5) - 0.024 (4.9) 0.97” (6.9) 0.65 (5.2) 0.93 0.77 Demand

a DW see (%I

0.93

(65.5) 0.45 1.42

France

income per head [eq. (6)] 1.12 0.71 (2.4) (1.8) 0.29 0.022 (4.2) (0.7) 15.86 0.18 (4.1) (0.7) 0.46 (2.5) 0.11 $7 0.70 (4.4) 0.50 1.28 2.22 1.07 Labor

IO

Germany

deflator

0.87 (22.5) 0.44 3.10

0.95 (5.6) 0.018 (4.2) 0.16 (3.0) 0.21 (1.9) 0.92 (2.9) 0.56 (5.9) 0.92 0.39

united Kingdom

0.74 (3.3) -0.012 (1.1) 1.58 (3.3) 0.56 (1.4) 0.74 (y) 2.03 1.01

[eq. (7)]

lb -3.41 (1.9) 0.0042 (1.0) 0.72’ (3.5) 0.36 (5.6) 0.89 0.63

lb

1’

-0.16 (2.7) 0.008 (15.8) 0.046 (3.1) 0.13 (4.3) 0.18 0.23

-3.74 (2.4) 0.005 (1.5) 0.5gc (2.7) 0.36 (2.5) 1.22 0.58

0.95 (29.5) 0.61 1.36

0.80 (18.8) 0.84 0.99

[eq. (8)]

0.53 (3.8) 0.61 1.50

‘U.S. and France; quarterly data. Other co&tries: semi-annual data. bConstrained to 1 after having checked that it was not significantly different from 1. ‘Equation type (3~). dEquation type (3b). “Real wage and not relative price of labor and capital.

Money

demand

[eq. (I)]

Money demand is elastic with respect to interest rates in all countries except Germany. The effect of changes in the interest rate is large in France and in the United Kingdom, rather small in Japan and especially in the United States. The income elasticities of money demand are quite alike in the

78

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five countries (from towards its desired Germany, larger in instantaneous in the Expectations

and C.

Bismut, Exchange

rate and wage-price dynamics

1.2 to 1.4). The speed of adjustment of money demand level is rather slow in the United Kingdom and in France and Japan, and the adjustment is found to be United States.

[eqs. (36) and (.3c)]

Only in the Japanese case eq. (3~) (adaptive expectations in growth rates) was found to be significant; in all the other countries eq. (3b) (taken from Dombusch’s model) gave much better results, with a sensible estimated value for 8. The inertia of expectations seems to be larger in the United Kingdom and in Germany than in France (mean lag of the adjustment towards the long-run growth rate of the exchange rate: U.K., 3.2 years; Germany, 0.8 year; France, 0.2 year). Total demand [eq. (4)]

The effect of competitiveness on total demand (domestic demand + exports imports) is found quite large in Japan and Germany, much smaller in France, the United States and the United Kingdom. The other variables are not significant for all the five countries. Real money balances appear in four cases out of five, foreign demand in three, especially strong in France and in the United Kingdom. Real wages also appear in three countries, strong in the United States and in the United Kingdom. GDP deflator [eq. (5)]

Producer prices seem more rigid in the United States, Japan and France than in Germany and in the United Kingdom. The great inertia of prices in the United States in the recent period is confirmed by Gordon (1982). A direct effect of foreign prices (the so-called ‘Scandinavian effect’) appears in France and Germany, where domestic inflation must therefore be more sensitive to world inflation. The absence of this effect in the United States and its importance in Germany is confirmed by Gordon (1977). The pressure of demand effect on producer prices (pl) is very large in Japan, quite large in the United Kingdom and small in the three other countries, where inflation apparently does not respond strongly to cyclical fluctuations, which is consistent for the recent years in the United States with the results obtained by Sachs (1980) but not with those obtained by Gordon (1980). Wage rate [eq. (6)]

The estimated degree of wage indexation is very large in Japan (1.12), quite high in France (0.95), rather low in Germany and in the United Kingdom (around 0.7) and surprisingly low in the United States (0.35), which is, however, confirmed for the 1971-1978 period by the static equation given by Branson and Rotemberg (1980). The effect of unemployment on wage

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formation seems considerably larger in Japan than in all the other countries; productivity growth affects significantly wages in Germany and in the United Kingdom, while firms apparently try to negotiate wage increases which do not modify too much the share of wages in value added in Germany, France and the United Kingdom (where the coefficient wj is large). The result on indexation and the effect of unemployment are close to those obtained by Artus (1983). It is surprising to find that in France and in Japan, the high degree of price indexation does not correspond to an institutional indexation agreement [see Braun (1976)]. Labor demand [eq. (7)]

In all countries except Japan, the elasticity of labor demand with respect to GDP does not differ significantly from 1. In Japan, it is much lower (0.30), which indicates a great stability of employment. Real wages were found to give much better results than the relative price of labor and capital in three countries (Japan, Germany and the United Kingdom). Employment apparently adjusts much quicker in the U.S., in Japan and in Germany than in France and the United Kingdom. Demand dejlator [eq. (S)]

Because of its great simplicity (absence of lags, lixity of the weights,. . .) this equation does not give very good econometric results, but should be sufficient for our purposes. Having estimated the model for the different countries, it is possible to calculate the long-term growth rate of the exchange rate, according to eq. (10”). One finds: Japan

&p-p,

d,=O,

Germany France United Kingdom

$=p-fi*-0.013, i&p+*,

d4=0,

i=fi-p*+O.O12,

where f is simply the difference between the growth rates of money supply and of foreign prices in the cases of Japan and France; that difference is corrected by a long-term appreciation of the mark in the Germany case and by long-term depreciation of the pound sterling in the U.K. case. 5. Simulating the impact of a monetary shock under flexible exchange rates Many simulations experiments have been carried out with the estimated models. This can help understand some points that turn out to be analytically intractable in the more general case. In addition we hope to get some

80

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wage-price dynamics

comparative information for a better understanding of what has happened in the countries concerned in our analysis. These simulations are run with the full model for the period 1969-1980. We report here the result corresponding to the case of monetary shocks for four countries: France, United Kingdom, Germany and Japan.13 The simulated measure is a once and for all 1% increase in money supply. The figures reported in this paragraph concern the deviations of endogenous variables from the levels in the control solutions. The simulation has the same periodicity as the data used for the estimation. For France, simulations are carried out quarterly; that allows a more detailed insight in the dynamic features of the models. For the three other countries simulations are semi-annual. The first question that we want to address is whether or not a Dornbuschlike overshooting effect can be observed. A quick glance at fig. 1, where

Fig. 1. Reaction of exchange rates to a monetary shock for three countries. “Recall that the exchange rates are denominated vis&vis the dollar (the exchange rate of the dollar is one) thus the model estimated for the United States is inappropriate for examining exchange adjustments.

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81

exchange rate responses have been plotted, suggests that the overshooting pattern may be accepted for three countries, namely France, U.K. and Germany, while, as we shall see further, the case of Japan seems to reveal more complicated mechanisms, 5.1. Two cases of an exchange rate short-run dynamics ti la Dornbusch: France and the U.K.

The case of France (fig. 2) can be understood in the conventional framework of Dornbusch’s model; an increase in the money supply must be balanced either by an increase in prices, a fall in interest rate or an increase in the level of demand. In the short run, prices and quantities are rigid in the goods market while, assuming perfect capital mobility, the interest rate can move so as to clear the money market. The fall in the interest rate causes the exchange rate to overshoot its long-run equilibrium. The only difference here arises from the choice of an expectation scheme that implies a progressive adjustment of the long-run exchange rate target itself which does not jump instantaneously. To make this case comparable to the most simple one, one has to consider the difference between the exchange rate and its variable long-run equilibrium, calculated period after period (see the lower line in fig. 3). The transition towards the long-run equilibrium is not difficult to understand. Prices and wages progressively adjust to their long-run path, partly through the competitiveness (Scandinavian effect), partly through a

Ax 1.5.

------------

A

0.5 t

0 Fig. 2. Simulated impacts: The French case.

P. Artus

and C. Bismut,

Exchange

rate

and wage-price

dynamics

Fig. 3. Simulated impacts: The U.K. case.

reaction to excess demand. The latter effect however turns out to be rather small and exhibits dampened oscillations. The weak negative response of employment comes from a small incidence of the rate of interest via the user cost of capital that causes a substitution effect. The case of the U.K. (fig. 3) also stands close to Dornbusch’s framework. An increase in the money supply with prices rigid in the short run decreases the interest rate and depreciates the domestic currency that overshoots the equilibrium by a factor around 1.7. Domestic prices are not sensitive in the short run and the increase in the domestic demand deflator is caused by the increase in the price of imports. Then, as time goes by, the producer’s price level reacts steadily to a wage increase and to a very small effect coming from excess demand. (Note, however, that the coefficient of excess demand is quite large in the price equation.) At the same time, the exchange rate and the interest rate tend to their equilibrium level. 5.2. A non-monotonic price response to monetary shocks in Germany

The German case (fig. 4) does not exhibit the monotonicity observed in the previous cases. The exchange rate initially overshoots its long-run level by a factor equal to two and then oscillates around the equilibrium level. This somewhat surprising response is easy to explain since one remembers that the money demand was found to be interest inelastic. An increase in money supply may be balanced either by a domestic price increase or by an increase in real demand. The weight of the two effects depends on the various interactions between price and demand in the short run. The equilibrium

P. Artus

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83

Fig. 4. Simulated impacts: The German case.

that results from the model corresponds to a large price increase implying a sharp depreciation of the currency since domestic prices are rigid in the short run and almost no demand effect (even a small negative effect). The domestic price deflator negatively influences the domestic demand through a decrease in real wages and a decrease in real money balances but the latter effect is almost exactly offset by the increase in money supply. The producer’s price reacts with a lag to the improvement in competitiveness according to the so-called ‘Scandinavian effect’, thereby allowing an appreciation of the currency. The resulting reduction of price pressure generates a positive effect on demand since the real money balances effect becomes positive and since the initial wage rate increases following an increase of the producer’s price level. This also induces at the same time an appreciation of the currency. Real demand increases up to the point in which excess demand induces a new increase in domestic prices. The decrease in domestic demand implies a new depreciation of the currency after two years but does not need to overshoot it since domestic prices are now almost completely adjusted. The long-run equilibrium seems to display the conventional convergence of quantity variables towards their initial level and the convergence of the exchange rate towards its long-run level. 5.3. A ‘virtuous circle’ in Japan Among the countries we have simulated, Japan (fig. 5) is certainly the most puzzling case. Contrary to what is normally expected the exchange rate appreciates continuously after a (positive) monetary shock. In addition, the exchange-rate response displays an explosive time pattern. At the same time,

P. Artus

and C. Bismut,

Exchange

rate and wage-price

dynamics

Fig. 5. Simulated impacts: The Japanese case.

domestic prices and wages on one hand, and demand on the other hand, move countercyclically, following a dampened oscillatory path around zero, while the domestic price level decreases continuously (because of import prices). However, the response of the exchange rate is easy to explain in the framework of our model and relies entirely on the expectation assumption

P. Artus

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85

[eq. (3c)] used in the Japanese case. After an increase in the money supply, the rate of interest falls (not being offset by a proportionally larger increase in demand). But contrary to Dornbusch’s assumption [eq. (3a) or (3b)], in the (semi)adaptive case (3~) the negative (appreciating) effect of the change in the exchange rate dominates the positive (depreciating) effect of a change in money supply. Then, as the effect on demand tends to zero, a virtuous circle emerges that can be summarized as follows:

expect~~Z~n> decline in domestic demand

exchange rate

“‘“CT

d;c;~ziht

Jices

rate The possibility of a virtuous (vicious) circle of this kind has already been brought out above in the case of assumption (3~) in a simplified analytical version of the model. These simulation results suggest that this possible case might occur. It is quite clear that this dynamic process is crucially linked to the expectation scheme.14 Contrary to assumptions (3a) and (3b) an expected short-run appreciation of the currency may lead to an effective appreciation of the currency while under assumptions (3a) and (3b) this mechanism is excluded. Since nothing like an explosive movement of the yen/US. dollar exchange rate is observed, something must be wrong in the conditions of the simulation experiments or in our model (or both). In the real world, that kind of explosive dynamics will not emerge because the monetary authorities will react, in order to stabilize the economy and will not maintain a monetary target exogenously fixed in advance. The fact that a dynamic divergency appears in the case of Japan therefore implies that the Japanese authorities have to intervene more frequently and more strongly than those of the other countries. Moreover, economic agents will not indefinitely maintain expectations based on a regressive extrapolation scheme, and will switch to a more efficient behavior, when they realize that their forecasts are systematically biased, which is the case here. A more realistic model would 14Altemativeassumptions (3a) and (3b) were strongly rejected by the data The values of f? obtained in those cases were negative which does not make sense and in any case would generate a similar paradoxical behavior as the one described above,

86

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and C. &smut, Exchange

rate and

perhaps include a learning process ultimately expectations.

wage-price dynamics

converging towards rational

6. Conclusion For the sake of simplicity, essential features of the economic reality were neglected in the original version of Dornbusch’s overshooting model. Consequently we had to develop an extended version of his model to empirically examine the robustness of his conclusion that exchange rate overshooting always appears when money supply increases. It has already been pointed out that Dornbusch’s conclusions did not hold if the assumption of perfect capital mobility was removed [Frenkel and Rodriguez (1981)]. We extended Dornbusch’s framework by introducing a labor market and a wage-price mechanism. It turned out that an overshooting of the exchange rate is likely to appear if the economy is not too widely open, under somewhat restrictive assumptions, namely the absence of price and quantity inertia. Since the problem was analytically much more complicated in a more general but more realistic case, we proceeded by means of simulation experiments, after having estimated models including price and quantity inertia, a Scandinavian effect and other less important but realistic features. The conclusions were less clearcut. Dombusch’s overshooting model did a good job in explaining the responses to monetary shocks in France and U.K. On the contrary, the German and Japanese cases seemed to stand outside this framework. Overshooting was found for Germany, but because of the large increase in prices necessary to rebalance a money market when demand for money is interest inelastic. The extrapolative expectation scheme used for Japan seemed consistent with the historical evolution. However, the model gives puzzling simulation results in that case and generates an instable behavior which presumably Implies that the present framework is somewhat inadequate. The rational expectations model including a monetary rule might be more sensible but also much harder to estimate and simulate, and would probably require additional simplifications. In any way, this constitutes a major orientation for further research. The present work gives, however, an intuition that some economies might be more difficult to stabilize than others. Sensible results could be obtained using simple assumptions on how expectations are built for most countries. References Amihud, Y. and H. Mendelson, 1983, Price smoothing and inventory, Studies 50.

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