IV Unemployment and Wage Dynamics in MULTIMOD
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund


This study develops an analytical and simulation framework for the analysis of the labor market in the seven major industrial countries.1 After specifying and estimating a simple model of employment and wage dynamics, the new labor market block is integrated into the current version of MULTIMOD, the International Monetary Fund’s macroeconomic simulation model used in policy analysis. The resulting version of the model is intended to replace the version of MULTIMOD that was documented in Masson, Symansky, and Meredith (1990). To this end, several alternative scenarios are considered to illustrate the main differences between the effects of standard policy simulations in the versions of MULTIMOD that include and exclude explicit treatment of the labor market.

This study develops an analytical and simulation framework for the analysis of the labor market in the seven major industrial countries.1 After specifying and estimating a simple model of employment and wage dynamics, the new labor market block is integrated into the current version of MULTIMOD, the International Monetary Fund’s macroeconomic simulation model used in policy analysis. The resulting version of the model is intended to replace the version of MULTIMOD that was documented in Masson, Symansky, and Meredith (1990). To this end, several alternative scenarios are considered to illustrate the main differences between the effects of standard policy simulations in the versions of MULTIMOD that include and exclude explicit treatment of the labor market.

The current version of MULTIMOD uses an inflation equation that links expected price changes to capacity utilization and other price-pressure variables (such as changes of the terms of trade), while not explicitly accounting for unemployment and wage developments. This approach limits the usefulness of the model in analyzing issues related to labor markets, such as the effects of wage rigidities, of changes in the natural rate of unemployment, etc. Our strategy to incorporate the labor market in MULTIMOD has been to replace the current reduced form of the price equation with the underlying behavioral equations for unemployment, wages and prices, while assuring consistency with the remaining blocks of the model. To this end, we have chosen to estimate (as a system) an unemployment equation and a wage-setting equation, while relying on a constant markup equation to determine the price of output from unit labor cost. This study only considers changes of the price determination block of MULTIMOD; a general discussion of MULTIMOD is provided in Masson, Symansky, Haas, and Dooley (1988) and Masson, Symansky, and Meredith (1990).

The Markup Equation

We do not estimate the markup equation. There is a substantial amount of empirical evidence pointing at the unresponsiveness of the markup to demand conditions, and previous attempts aimed at identifying time-varying markups have proven unsuccessful (see, for instance, Masson, Symansky, and Meredith (1990)). Therefore, our price-setting equation sets the (log) price of output, q, at a constant markup over unit labor cost:




where l is (log) employed labor services (which equals demanded labor services, ld), y is (log) output, and w is the (log) unit wage.

The Wage Equation

Following related research by Coe and Krueger (1990), our wage equation combines a standard expectation-augmented Phillips curve with a target real wage model (see Nickell (1988) for a general discussion). The aim is to allow for a relatively general specification by nesting two models that focus—respectively—on the change and the level of real wages to determine the equilibrium wage rate.2

The Phillips curve model specifies that the change in the (log) level of nominal wages, measured with respect to changes of expected consumption prices, should reflect changes in trend productivity and should be negatively related to unemployment (measured with respect to its natural level u*). The target real wage model may be regarded as a version of Sargan’s (1964) target-real-wage bargaining model, as well as a reflection of firms’ desire to equalize the real product wage to the marginal product of labor.3 This model suggests augmenting the Phillips equation with a catch-up term that reflects the deviation of the real product wage from its target level.

The specification of the wage equation that follows nests the two models and allows a test of the significance of real wage targeting in the form of a test of the hypothesis ø = 0:


In equation (3), prtr ≡ (y − 1)tr denotes trend average labor productivity,4 u and u* are the current and natural rates of unemployment, τ0 is the target (log) real product wage (measured with respect to average productivity), and p is the (log) consumption-based deflator.

The expected price change term, p+1e, is to be interpreted as the expectation of the change of prices at time t + 1 formed on the basis of information available at time t. The benchmark assumption is that expectations are formed rationally, that is, that p+1e equals Ep+1, the mathematical expectation taken with respect to all currently available information (which should include the dynamics of the state variables as determined within the whole model). As in Chadha, Masson, and Meredith (1992), however, we nest the rational expectation hypothesis in a more general model that allows for the coexistence of elements of rational and adaptive expectations. We allow, in particular, inflation expectations to be a convex combination of a rational expectation term and the last observed change of prices:5


Substituting equation (4) into equation (3), and subsuming the change of trend productivity, Δprtr, and the target real wage τ0 in the constant term, we obtain the following version of the wage equation:


In the long run, unemployment is at its natural rate (see the unemployment equation below) and the real product wage meets its target (as a result of the markup equation (1)). Thus, the wage equation fixes the long-run growth of real (consumption) wages as a function of average productivity growth and other structural factors that determine the target real wage (all absorbed in the constant term).

The Unemployment Equation

We assume the technology to be described by the Cobb-Douglas technology:6


where K is the current stock of capital, L is employed labor services (measured by total hours worked), and A(t) is a technology-shift parameter describing technical progress.

For each given K, the production function (6) maps changes of output into changes of employed labor services. Now define the “natural” level of (log) employment as l¯[y¯a(t)βk]/(1β), where y¯ is (log) potential output. The deviation of the demand for labor services from its natural level, l¯, can then be written as a function of capacity utilization as:


where cuyy¯ indicates (log) capacity utilization, defined as the deviation of output, y, from its potential level y¯.

Next, we assume a linearized version of the labor supply equation in which the supply of labor services exceeds its natural level, l¯, by a linear function of the (detrended) real consumption wage:7


In addition to the econometric need to produce a stationary real wage term on the right-hand side of equation (8), there are economic reasons for detrending the real wage term. Labor supply decisions presumably depend on real wage opportunities, measured with respect to a time-varying (generally upward-trending) reservation wage.

Subtracting equation (7) from equation (8), gives the equation describing the rate of unemployed labor services:


Next, we express the effects of hiring and firing costs on the short-run response of employment to output by assuming that the rate of unemployment u (that measures the rate of people unemployed) is determined as a convex combination of its “desired” rate—given by the rate of unemployed labor services, lsl¯d—and its last observed realization, u-1:


With this specification, a larger value of ρ implies that the changes of labor services necessary to accommodate short-lived output fluctuations are achieved mainly by changing average per-worker workhours, while the rate of unemployment is more sluggish and responds to output fluctuations over the medium term.

Combining equation (9) and equation (10), we can substitute away employed labor services and obtain an unemployment equation only in terms of real (consumption) wages and capacity utilization:


In a steady state, (log) capacity utilization is zero and the real wage increases along its trend line. Thus, equation (11) specifies a natural rate of unemployment at u* = ζ. Our current specification treats the natural rate of unemployment as exogenous, though possibly time-varying. As mentioned in the concluding section of this study, it would be useful to endogenize the link between ζ and its determinants, such as search costs and the tax structure. For the time being, we treat these factors as exogenous, and follow a simple estimation procedure that accounts for their possible changes over the sample by allowing for a structural break in ζ. The next section provides details to this extent.


Following the previous discussion, the following two-equation system was used to estimate the model for each of the seven major industrial countries. The sample period was 1968–90.8


The role of technology in the simple model outlined above is summarized by the income share of capital, β. One would not expect estimation of reduced form equations, such as the wage and unemployment equations, to yield an accurate description of technology. Indeed, when the estimation was carried out by leaving β unconstrained, this parameter was estimated imprecisely and often implausibly. Leaving a more structural analysis of technology as a topic for further research, the current estimation imposes β based on country-specific information on factor shares.

In each country, we allowed for a break point for the natural rate of unemployment, ζ, and for the constant term of the wage equation, ω, by constraining the break point to be the same in both equations and by choosing the structural break by best-fit. Thus,


With this notation, ζ1, and ζ2 provide estimates of the natural rate of unemployment in the first and second subsamples, respectively.

In this formulation, wage-pressure factors, such as measures of union power, minimum-wage legislation, incomes policy, etc., have not been included in the wage equation. These variables are difficult to quantify and their introduction would have made periodic updating of the model from World Economic Outlook data exceedingly laborious. Changes in exogenous factors are partly accounted for by the country-specific structural break of the constant term, ω.

In our preliminary regressions, we have allowed for a role of the wedge between the consumption and output deflators. The estimated coefficient for this variable, however, was almost always insignificant and not robust in sign and magnitude across countries and specifications. This outcome is not surprising, since equation (5) already includes terms describing the dynamics of both the consumption and output deflators. Accordingly, this variable was dropped from our specification.

The two-equation system (5) and (11) was estimated for each individual country by Zellner-efficient three-stage least squares. The results of the estimation are reported in Table 1.9 Overall, the empirical results were satisfactory for all countries except for the United Kingdom (discussed below). As reported in Table 1, the coefficients α, ρ, ø, and ζ were always estimated with the correct sign at relatively high marginal significance levels, despite the rather small sample, while the coefficient γ was generally less significant. Summary statistics indicate good fit, and there was some evidence of serial correlation of the residuals only for the unemployment equations of the United States, Canada, and the United Kingdom.10 The estimation results also proved relatively robust across different specifications of the break points and with respect to small modifications of the regression equations (such as the choice of different detrending procedures).

Table 1.

Results of Estimation

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Sample: Annual data, 1968–90 (1968–89 for Germany). Figures in parentheses are standard errors.

The responsiveness of wages to unemployment, as measured by the coefficient a, was estimated to be very similar among the European countries, and generally higher than in the two North American countries. This result likely reflects the similar movement of real wages within the industrial countries, but relatively more stable (at high levels) unemployment rates in Europe. In turn, it is the relatively high estimate of p for the European countries that reflects the sluggishness of unemployment in Europe. Similarly, while the very high estimates of α and ρ for Japan indicate both the stability (at low levels) of the Japanese rate of unemployment, as well as the tendency of that country to accommodate output fluctuations through changes of per-worker hours, rather than through changes of employment.

The estimates of ζ, the weight of the forward-looking component of price expectations, indicate that both the hypothesis of completely rational and of completely backward-looking expectations can be broadly rejected. Overall, the reported estimates for this parameter appear sensible, although the large estimate for Italy and the small estimate for Germany are somewhat surprising.

For all countries except the United Kingdom, the positive and relatively significant estimates of ø indicate evidence of real wage rate targeting. In contrast, estimates of the coefficient that capture the response of labor supply to changes in real wages, γ, were generally small and imprecise, thus confirming the conventional wisdom on the difficulty of capturing the response of labor supply to changes of real wages.

For most countries, the estimates of ζ proved to be a rough approximation of available estimates of natural rates of unemployment. In the case of the United Kingdom, on the other hand, the estimates of ζ were implausibly low. Note the role played by this parameter in our simple model of unemployment: unemployment is expected to converge to ζ only after all cyclical components of output and wages have been offset and sufficient time has elapsed to eliminate the anchoring effect of lagged unemployment. As a result, one would not expect ζ to be estimated very precisely, nor to be estimated at a value close to the average rate of unemployment in each sample. We have conducted a simple test of robustness of our regressions to misspecification of ζ by constraining ζ to the average level of unemployment for each country’s subsample. We found that the constrained estimates of the remaining parameters were almost identical to their unconstrained counterparts, for all countries except the United Kingdom. We also note that the possibly imprecise estimation of ζ should not be a reason of concern in MULTIMOD simulations, which are independent of the estimates of any constant term such as ζ.

As mentioned above, estimation of the model on U.K. data proved troublesome. Although most estimates of the slope coefficients were plausible, estimates of the natural rate of unemployment were both implausible in their magnitude and statistically significant, while we found no statistical evidence of real wage targeting. Furthermore, estimation proved not very robust to relatively small changes of the model and sample. The following MULTIMOD simulations use our best estimates of the U.K. model, with the wage equation specified as a standard expectation-augmented Phillips curve. We stress however that this estimation should be regarded as preliminary and that further research on modeling the U.K. labor market would be necessary.


To illustrate the properties of the version of MULTIMOD that includes the newly formulated labor market, we have considered several policy simulations. Three newly specified variables appear in the new version of MULTIMOD, namely, “Unemployment rate,” “Wages,” and “Employed labor services.” Note that the shocks discussed in this section were applied only to a country model. While the simulated shocks may have somewhat different effects in the linked version of the model, the comparison between the new and the current versions of the model should not be affected by this consideration.

Fiscal and Monetary Shocks

The first set of simulations, reported in Tables 2-4, considers the effects of standard fiscal and monetary shocks in the standing version of MULTIMOD and in the version of the model that incorporates the labor market equations. For the six countries that are assumed to have independent monetary policies—the United States, Japan, Germany, the United Kingdom, Italy, and Canada—we simulated both a permanent increase of the fiscal deficit of 5 percent of GDP and a permanent contraction of money supply of 10 percent. Only a fiscal shock was considered for France, since participation in the exchange rate mechanism (ERM) and the consequent need to target the nominal exchange rate with the deutsche mark, make changes of monetary base endogenous. For comparison with the former version of MULTIMOD, we also report simulated fiscal shocks for Italy and the United Kingdom under the assumption of participation in the ERM.

In general, both the fiscal and monetary scenarios described above indicate that the model incorporating the labor market displays virtually identical long-run properties as the standing version of MULTIMOD, as well as very similar short-run properties. There are only two significant differences between the two models. One is the somewhat longer-lived effects of fiscal and monetary shocks over the medium term in the new version of the model (especially for Italy), a feature that expresses the sluggish adjustment of unemployment to its natural rate. The other is a small reduction in the Japanese fiscal multiplier, a feature that can be attributed to the stronger inflation response to demand pressure estimated in the new version of the model.

The simulated behavior of unemployment in the fiscal scenarios (Table 2) illustrates the interaction of our newly formulated labor market block with the rest of MULTIMOD. The fiscal stimulus initially causes a decline in the unemployment rate and raises wages and prices, while the short-run response of employed labor services is substantially stronger than that of the rate of unemployment.11 Eventually, unemployment converges to its natural rate. The crowding out of private investment and the decline of the capital stock during the period of transition imply that real wages must decline in the long run, in order to accommodate the larger share of labor in total factor employment.

Table 2.

Effect of 5 Percent Deficit Expansion on the Major Industrial Countries

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With respect to the monetary contraction scenarios reported in Table 3, we need only note that both the short-run and long-run effects of the reduction of money supply targets are very similar in both versions of the model. In particular, both models display long-run neutrality of nominal shocks.

Table 3.

Effect of 10 Percent Money Supply Reduction on the Major Industrial Countries (Excluding France)

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A noticeable feature of this set of simulations is the large and long cycle in the French fiscal scenario, a property that we largely attribute to the ERM monetary assumption. To aid interpretation of this scenario, we have included fiscal shock scenarios for the United Kingdom and Italy for both non-ERM and ERM participation (Tables 2 and 4). A comparison of the two fiscal scenarios shows substantially greater cycles under the ERM assumption. Because monetary policy in ERM countries is generally targeted to ensure interest parity with Germany, the medium-term effects of a fiscal expansion are magnified by the ensuing monetary expansion. This property of the model is common to the current and new versions of MULTIMOD, but the sluggish response of wages and unemployment leads the new version to predict longer-lasting effects of nominal adjustments.

Table 4.

Effect of 5 Percent Deficit Expansion on the United Kingdom and Italy (ERM)

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Labor Market Shocks

A second set of simulations, which are presented only for the United States, considers specific aspects of the labor market that could not be analyzed with the previous version of the model.

The two panels of Table 5 report the results of the same fiscal and monetary shocks described above, but under the assumption of exogenous nominal wages. In the fiscal expansion scenario, the weaker inflation response in the sticky-wage case induces a stronger short-run increase in output. In the long run, however, the sticky-wage economy settles at a similar level as the flex-wage economy. In contrast, the sticky-wage model produces substantially different results with respect to the flex-wage model when implementing a monetary contraction: when nominal wages are fixed, long-run neutrality of nominal shocks no longer holds and the output costs of deflation are substantial, both in the short and in the long run.

Table 5.

Effect of Policy Shocks with Sticky Wages on the United States

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The left panel of Table 6 reports the effects of a permanent increase of the natural rate of unemployment ζ for a given level of “natural” labor supply l¯+ζ. This type of shock is intended to capture exogenous changes in a variety of determinants of the natural rate of unemployment, such as increasing job-search costs or higher labor income taxes. The unemployment rate responds to this type of shock by converging slowly toward its new natural level, following the pattern illustrated in Figure 1. As labor employed declines toward its new steady-state level l¯, output falls correspondingly.

Table 6.

Effect of Labor Market Shocks on the United

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Figure 1.
Figure 1.

Effects of an Increase in the Natural Rate of Unemployment

Finally, the right panel of Table 6 describes the effects of a simultaneous decline of the steady-state demand and supply of labor, l¯ and l¯+ζ, while keeping the natural rate of unemployment, ζ, fixed. The effects of this negative shock to labor supply, which is summarized in Figure 2, are very similar to the previous case, except that the unemployment rate will be unaffected in the long run. Simultaneous shifts of the labor force and of the natural rate of unemployment (the difference between this and the previous scenario) are broadly neutral: they would produce no long-run effect on GDP, wages, etc., only an increase in the unemployment rate.

Figure 2.
Figure 2.

Effects of a Decline in Labor Supply

Future Research

The analysis of the previous sections features a rather stylized treatment of technology. The current specification is only a first attempt to tackle the problem. In the future, it would be useful to consider a multilevel multi-input production technology to account more precisely for developments in primary goods markets. Following standard treatment, GNP would be produced with an intermediate input and a primary input (e.g., oil). The intermediate input, in turn, would be produced with capital and labor. Assuming a Cobb-Douglas or constant elasticity of substitution technology at each level of production should allow a rather simple and flexible treatment.

A natural extension would be to endogenize some of the determinants of the natural rate of unemployment. For instance, there is theoretical support and some empirical evidence of a positive correlation between taxes and the natural rate of unemployment.12 It would be necessary to respecify some of the behavioral equations and to redefine data to account for taxation. Estimation of the model would provide a test of the cross-country evidence on the theoretical links between taxes and unemployment.


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  • Chadha, Bankim, Paul Masson, and Guy Meredith, “Models of Inflation and the Costs of Disinflation,” Staff Papers, International Monetary Fund (Washington), Vol. 39 (June 1992), pp. 395431.

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Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States.


For the current exercise, we ignore the effects of taxation on the labor market. See also the discussion in the section below on future research.


If, for instance, firms use a Cobb-Douglas production function, the (log) marginal product of labor is In (∂Y/∂L) = y − l + In(1-β). Profit maximization then implies that firms would target [w-q-(y-l)] to In(1-β) = τ0 < 0.


Linear and quadratic time trends were used to detrend productivity.


The qualitative features of the model do not change if expected inflation is allowed to depend on a longer distributed lag of prices. The important aspect of equation (4) is that it allows for inflation expectations to be anchored—with an empirically determined weight δ—to past inflation. See Chadha, Masson, and Meredith (1992) for a derivation from an explicit multiperiod wage-setting model.

Note that to introduce sluggish adjustment of real wages to anticipated changes of exogenous variables, it would not be sufficient to assume staggered wage contracts, unless agents’ forecast horizon is assumed to be shorter than the contract’s length. See Chadha, Masson, and Meredith (1991) for a more complete discussion of price adjustment in a model with overlapping contracts.


A very similar treatment can be given in the case of a more general production function with constant elasticity of substitution. In that case, the time-invariant income share of labor, 1-β, should be replaced by the share of labor at full employment, which may vary in the long run.


Linear and quadratic time trends were used to detrend the real wage.


Estimation was cut off at 1990 to allow the use of price data for 1991 as a one-period-ahead term in the wage equation. Estimation for Germany was carried out over the sample 1968-89 because of the problems in data associated with German unification.


Time and two lags of prices, of capacity utilization, and of the real exchange rate were used as instruments.


Accordingly, the regression results for these three equations have been corrected for first-order serial correlation.


The impact elasticity of employed labor services to output is equal to the reciprocal of the labor share of income (which is equal to about ⅔ in all countries).


See Pissarides (1985) for a reference model, and Adams and Coe (1990) and Coe and Krueger (1990) for empirical applications.