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The authors are grateful to conference and seminar participants at CEPR-ESSIM, NBER Monetary Economics Summer Institute, Graduate Institute of International and Development Studies, Universitá di Tor Vergata, Universitá Cattolica di Piacenza, the conference on “Macroeconomics Policies and Labour Market Institutions,” held at the Universitá Milano-Bicocca, the conference on “New Perspective on Monetary Policy Design,” organized by the Bank of Canada and CREI, as well as Guido Ascari, Florin Bilbiie, Michael Dotsey, Giancarlo Gandolfo, and Alberto Petrucci for helpful suggestions, Mary Yang and Hermes Morgavi for excellent research assistance, and Thomas Walter for editorial assistance.
State-dependent pricing would tend to weaken the long-run relationship between inflation and unemployment (see for example Golosov and Lucas, 2007).
It is a questionable assumption to impose price rigidity even at high inflation rates. But, this is a features of time-dependent price-setting models. A model with state-dependent pricing would instead imply a vertical Phillips curve at high inflation rates.
Already in The General Theory of Employment, Interest and Money, Keynes leverages on the fact that workers usually resist a reduction of money-wages to question the conclusion of the classical analysis with regards the existence of a unique frictional rate of unemployment. Numerous authors, from Samuelson and Solow (1960) and Tobin (1972) to Akerlof (2007), stressed their importance for the existence of a long-run trade-off between inflation and unemployment.
Andersen (2001) presents a static model which can be solved in a closed form, while Bhaskar (2003) offers a framework that endogenizes downward price rigidities. Our work is also closely related to the literature on irreversible investment, since a dynamic problem in which wages cannot fall is similar to a problem in which capital cannot fall (see Abel and Eberly, 1996; Bertola, 1998; Bertola and Caballero, 1994; Dixit, 1991; Dumas, 1991; Pindyck, 1988; and Stokey, 2006).
Note that Broda and Weinstein (2007) find that Japanese deflation may have been even twice as large as officially reported.
These preferences are consistent with a balanced-growth path since we are assuming a drift in technology.
In our model, workers are identical and unemployment is defined as the gap between the aggregate hours actually worked and the working hours in a world without wage rigidities and without labor and product-market distortions.
The downward-rigidity constraint is purely exogenous in this model and could be rationalized by considering every worker as associated with a union that does not allow the wage to decline for reasons related to fairness and social norms (Bewley, 1999, and Akerlof, 2007).
It is possible that the desired wage, W(Ỹt), falls below the one associated with full employment. While temporary overemployment is not unrealistic, in the appendix we also solve the model with the additional constraint lt (j) ≤ 1 for each j.
Productivity shocks do not affect the desired wage as their employment effects are neutralized by the fully flexible prices.
Otherwise, when the mean of nominal-spending growth is non-positive, the probability distribution collapses to zero everywhere, with a spike of one at zero employment and thus 100% unemployment rate in the long run. However, this is not a realistic case because nominal spending growth is rarely negative, and θ represents its mean.
Structural policies affecting the degree of competition in the goods and labor markets could affect uf.
The remainder of this section will focus on macroeconomic volatility. Regarding the other paramenters, a higher discount rate (high ρ) or a lower elasticity of labor supply (high η) increase the desired wage (higher c), and generates higher average unemployment, thus shifting the Phillips curve to the right. Obviously, an increase in the structural unemployment that would prevail also with flexible wages (uf) would also shift the Phillips curve to the right.
If we were to take into account the constraint that employment should not exceed 1, there would be a kink in the Phillips curve at low inflation rates which would flatten the curve even more and reinforce our results.
Our result that the long-run Phillips cuve is flatter when macroeconomic volatility is higher contrasts with the results of the model of Lucas (1973), where higher volatility reduces the information content of relative price dispersion, and steepens the short-run Phillips curve.
To gauge the potential decline we estimated the relation between the 3-year standard deviation of quarterly nominal GDP growth and the 3-year mean of quarterly GDP deflator inflation, in a panel regression with fixed effect and 9 periods over 1980-2006 for a sample of 24 industrial and 24 developing countries (from the IFS or WEO databases; for a subset of countries seasonal adjustment was not available in the original dataset and was implemented on the basis of the X12 method in EVIEWS). The relation was specified in either linear or logarithmic terms and with or without time effects. The effect of inflation on nominal GDP volatility was found to be positive and generally significant, although reasonably small. Additional regressions show that such an effect was mainly due to the effect of inflation on inflation volatility rather than on real growth volatility. Indeed, the effect on real volatility was invariably smaller than the one on nominal volatility and generally insignificant, while the one on inflation volatility was large and always significant. Results were quite similar when breaking the sample in industrial and developing countries. The largest effect of inflation on nominal volatility was found in the logarithmic specification without time dummies, with a coefficient of 0.23: a reduction in inflation by 10 percent (say from 10 to 9 percentage points) would be associated with a much less than proportional decline in volatility (at most by 2.5 percent of its initial level).
Figure 3 is obtained through simulations of the model in which the first 400 observations are repeated 10000 times, and θ varies in the range (0, 10] in percent and at annual rates. In the short run, average wage inflation is slightly above θ for very low θ, so that the curves do not reach the x-axis even when θ is close to zero. This is because agents are very cautious and set very low wages at the beginning of the horizon when θ is very low, implying that upward adjustments would occur quite frequently at the beginning of the horizon.
In this case, the condition ensuring that the probability distributions converge to their equilibrium ones in the long run becomes λ(θ) > 0. A supplementary appendix that presents the model solution under this general case is available upon request.
Obviously, if κ (θ) were to be very large for any theta, then the Phillips curve would become virtually vertical, similarly to the flexible-wage case. However, as discussed extensively in the introduction, there is substantial evidence that, at least in some countries, downward wage rigidities persist even at low inflation.
When the mean of nominal expenditure growth is high, long-run mean wage inflation is high and wages tend to adjust always and proportionally to nominal expenditure shocks, so that the volatility of nominal wages converges to the volatility of nominal expenditure growth, as shown in Figure 6.
Note, however, that when inflation is really low (nominal spending growth close to zero) the unemployment distribution collapses to a mass at 100% unemployment rate. In this limiting case the volatility of unemployment collapses to zero and the trade-o¤ between volatilities disappears. Note also that this reversal occurs only in the long run: in the short run we always find a clear trade-off.
With respect to the other parameters of the model, the Phillips curve would flatten when labor elasticity is lower and agents heavily discount the future; it would steepen if the degree of downward rigidities weakens at low inflation; and it would shift outward if labor and goods market competition weakens.
In fact, the homogenous function has been chosen appropriately for this purpose.