Conclusion

In this chapter, we have considered a dynamic stochastic new Keynesian model, which not only allows for the existence of involuntary unemployment but also for nominal shocks and monetary policy to affect the fluctuations of all real variables.

The model builds on one of the key insights of the General Theory: the short-run rigidity of nominal wages, assumed to be due to periodic nominal wage contracts. But in all other respects, it is based on intertemporal optimization on the part of both households and firms.

The full model is characterized by a combination of an expectations-augmented Phillips curve and the new Keynesian Phillips curve. Deviations of output and employment from their natural rates depend on unanticipated current inflation (which reduces real wages relative to productivity) and unanticipated productivity shocks (which also affect the relation between real wages and productivity). However, such deviations cause current inflation to deviate from expected future inflation, as in the new Keynesian Phillips curve.

Nominal shocks and, by extension, monetary policy are able to affect fluctuations in both inflation and real variables, such as output, employment, unemployment, real wages, and the real interest rate.

We analyzed aggregate fluctuations in this model under a feedback interest rate rule, according to which the nominal interest rate responds to deviations of inflation from the target of the central bank, and deviations of output from its natural rate. Such a rule, which is in the spirit of Wicksell [1898], has been proposed and advocated by Taylor [1993].

Contrary to the new classical model under full information, monetary shocks affect real variables in this model, causing temporary and persistent deviations of output, employment, unemployment, real wages, and the real interest rate from their natural rates.

1. For comparative empirical studies of the determinants of unemployment in the industrial economies, see, among others, Bean et al. [1986], Blanchard and Summers [1986], Newell and Symons [1987], Alogoskoufis and Manning [1988], and the important book by Layard et al. [1991]. More recent surveys are in Blanchard and Wolfers [2000] and Blanchard [2006].

2. The Gray [1976] contracts are one-period nonindexed nominal wage contracts, whereas the Fischer [1977a] and Taylor [1979] models are models of multiperiod staggered wage contracts. There are differences among these models, but they share the assumption that wages have been negotiated before full information about the evolution of the price level, productivity, or other shocks was available. For reasons of analytical simplicity, we shall use the simplest possible of these models, which is the Gray-Fischer model of one-period synchronized nominal wage contracts.

3. An alternative way to introduce nominal wage rigidity is to use the assumption of staggered wages à la Calvo, as has been done in some papers, following Erceg et al. [2000].

4. See Blanchard and Summers [1986], Lindbeck and Snower [1986], and Gottfries [1992] for insider-outsider models of the labor market.

5. See Weiss [1980] and Shapiro and Stiglitz [1984] for the two most important early models based on this approach.

6. For the original implicit contract theories, see Baily [1974], and Gordon [1974], Azariadis [1975]. These theories viewed employment contracts as insurance contracts between risk-neutral employers and risk-averse employees, against adverse shocks to employment. For theories based on explicit bargaining, see McDonald and Solow [1981]. For theories that distinguish between insiders and outsiders in the labor market, see Lindbeck and Snower [1986], Blanchard and Summers [1986], and Gottfries [1992].

7. Surveys of alternative theories of unemployment can be found in, among others, Solow [1980]; Nickell [1990, 1997]; Bean [1994], and Blanchard [2006].

8. These assumptions can be justified in terms of models of indivisible labor, as in Hansen [1985] and Rogerson [1988].

9. Technically, because the logarithm of the expectation of a product (or ratio) of two random variables is not equal to the sum (or difference) of the expectations of the logarithms of the relevant random variables, (17.15) must also contain second-order terms, depending on the covariance matrix of consumption, inflation, and shocks to preferences for consumption and money. Assuming that all exogenous shocks are independent stationary stochastic processes, these second-order terms are constant and can be ignored.

10. This model of monopolistic competition, with a constant elasticity of demand, is due to Dixit and Stiglitz [1977].

11. The wage setting model in this section was put forward by Alogoskoufis [2018] in the context of an analysis of optimal monetary policy in an economy characterized by labor market distortions but perfectly competitive product markets and flexible prices.

12. Alternatively, one can use the observationally equivalent model of Rotemberg [1982a,b] based on convex (quadratic) costs of adjusting prices. This model was introduced in chapter 16.

13. As in the model of chapter 16, automatic indexation to steady state inflation ensures that the model does not violate the natural rate property. See, for example, Ascari and Sbordone [2014].

14. We could alternatively call them the new Keynesian IS and LM curves, but these would take the same form even in a new classical model, such as the one in chapter 14. We thus adopt the new neoclassical synthesis terminology of Goodfriend and King [1997].

15. This is the well-known Wicksellian mechanism, emphasized for the first time by Wicksell [1898].

16. The assumption of AR(1) processes could easily be generalized to AR(n) processes without affecting the nature of the results in this chapter, as, eventually, it is only the unanticipated component of these shocks that affects deviations of real and nominal variables from their natural rates.

17. We have expressed the Taylor rule in terms of deviations of output and not unemployment from its natural rate. This does not affect the results, as through the Okun type relation (17.41), deviations of unemployment from its natural rate are a negative linear function of deviations of output from its own natural rate. We have also assumed that the central bank interest rate adjusts to shocks that affect the natural real rate of interest, which is not treated as a constant.

18. Once we solve for inflation, we can also determine deviations of output from its natural rates as well as deviations of all other nominal and real variables, such as the nominal interest rate and the unemployment rate. Note that under a nominal interest rate rule, such as (17.77), the money supply becomes endogenous and is determined through the money demand function (17.65).

19. Clarida et al. [1999], Woodford [2003a], and Gali [2008], among others, contain detailed discussions of the Taylor principle and its significance for the resolution of the price level and inflation indeterminacy problem, which affects noncontingent interest rate rules.

20. See Alogoskoufis [2018] for a detailed analysis of this point in the context of a related model.

21. Because equation (17.85) is the inflationary process from a DSGE model, in which the policy rule of the monetary authorities is taken into account when agents form their expectations, it does not suffer from the Lucas [1976] critique. Changing the parameters of the policy rule would also change the parameters of the inflationary process in a predictable manner.

22. This point is elaborated in Alogoskoufis [2018] in the context of a simpler insider-outsider model.

23. See Blanchard and Gali [2007] and chapter 16 for a discussion of the divine coincidence. To deal with this problem in the benchmark new Keynesian model with staggered prices, one has to superimpose ad hoc additional labor market distortions. This is not the case with the model in this chapter, or the model of Erceg et al. [2000], as labor market distortions are part and parcel of these models and are not an afterthought.

24. See Alogoskoufis [2018] for a proof of this proposition and suggested solutions.

25. In accordance with the conventions of the literature on monetary policy (e.g., Barro and Gordon [1983a], Rogoff [1985]), treat (17.94) as a measure of the intertemporal welfare costs of inflation and unemployment. However, we assume that the central bank does not seek to systematically reduce unemployment below its inefficiently high natural rate. Thus, we abstract from the systematic inflation bias that would result if the central bank also sought to use inflation to reduce unemployment below its natural rate, as in Kydland and Prescott [1977] and Barro and Gordon [1983a]. We further discuss these issues in chapter 20 on the role of monetary policy.

26. Note that the optimal contingent policy is time consistent, in the sense of Kydland and Prescott [1977]. Alogoskoufis [2018] also examines time-inconsistent policy rules that may result in even lower intertemporal losses.

27. Note from (17.97) that if deviations of unemployment from its natural rate did not persist (i.e., in the case δ = 0), the optimal contingent monetary policy rule would not result in persistent deviations of inflation from target. There would be deviations of inflation from π^* only in response to unanticipated shocks to productivity.