قرارداد ساختار درون زا و سیاست پولی

We analyze the co-determination of monetary policy and the labor contracts chosen by members of the public, who can either fix or index their nominal wages. Fixed nominal wages allow the central bank to offset productivity shocks, while the public fix nominal wages in response to the central bank offsetting shocks; so there is an equilibrium in which, realistically, nominal wages are fixed and shocks offset: a result which holds in single- as well as in multi-period games. In addition, there may be equilibria in which agents index their nominal wages, and the central bank optimally responds by stabilizing price. In contrast to conventional models, the Ramsey rule may be implemented in a finitely repeated game. The central bank does not deviate for fear that agents would change their labor contracts such that the central bank's least favored equilibrium will subsequently be played.

Conventional macroeconomic models in the spirit of Kydland and Prescott (1977) implicitly assume that monetary policy does not affect the structure of markets. Fixed-wage contracts give the central bank an informational advantage, allowing it to generate price surprises on the one hand, and to respond to productivity shocks on the other hand. This “advantage” may undercut the central bank's ability to set monetary policy according to the Ramsey rule: the central bank is induced to set an inefficient discretionary policy by the public's belief that it will exploit its scope for price surprises. Nevertheless, it is widely believed that central banks in economies where fixed-wage contracts are prevalent are less constrained by discretionary expectations than the early literature may have suggested.1 The literature's assumption of nominal wage contracts is realistic for developed economies. However, models which incorporate an endogenous relationship between monetary policy and contract structure are richer in two respects. First, they illustrate how monetary policy and contract structure arc co-determined. Second, such models can explain given behavior patterns (viz. play on the equilibrium path) by the consequences of deviation (viz. play off the path). We explore such an endogenous relationship by analyzing the interaction between a continuum of members of the public (‘agents’) and a central bank. Each agent is the unique insider at some firm, in the sense that the firm has sunk the requisite training cost for that agent. Each firm produces a consumption good using a single agent's labor. The time line for a single period is as follows. Agents each address an offer of a fixed nominal wage or of an indexed wage to a chosen firm; an economy-wide productivity shock is then revealed; and the central bank sets the inflation rate after observing the shock and the distribution of decisions across agents. Profit maximizing firms then decide which offer(s) to accept, and select employment (on their labor demand curves): where each firm which employs an outsider must pay a training cost. Each agent then uses her labor income and dividends to buy the consumption good. We suppose that agents maximize a utility that depends on their labor input and on consumption, where an agent who indexes her wage must pay a fixed cost, while the central bank seeks to stabilize the consumption good price and to minimize the variability of per-agent output around some target. In short, this model generalizes Rogoff's (1985) game by allowing agents to choose contract structure. If this game is played once then each agent addresses her offer to the firm at which she is an insider; and this offer minimizes the variability of the firm's output around a target which is common across agents. Our model therefore provides microfoundations for a conventional assumption. The nature of equilibria depends on the ratio of the indexation cost to the variance of productivity shocks. If this normalized cost is high enough then the one-period game has a unique equilibrium in which all agents fix their nominal wages and the central bank adopts the discretionary policy, which partially offsets the effect of productivity shocks on output. This strategy combination replicates the discretionary equilibrium in conventional macro-models. If the normalized indexation cost is low enough then the one-period game again has a unique equilibrium; but in this case, all agents index their nominal wages (to inflation and the productivity shock), so the Phillips curve is vertical. The central bank's best response is to stabilize price as it cannot affect any agent's output. Agents in turn index their nominal wages because the central bank does not offset productivity shocks. If the normalized indexation cost takes intermediate values then the one-period game has an equilibrium in which all agents fix their nominal wage and the central bank adopts the discretionary policy; an equilibrium in which all agents index their nominal wage and the central bank stabilizes price; and an additional equilibrium in which a proportion of agents fix their nominal wage, and the central bank adopts a policy which offsets productivity shocks less than the discretionary policy. The latter equilibrium illustrates a strategic complementarity between agents’ decisions: the more agents fix their nominal wages, the flatter is the Phillips curve, and thereby the more actively the central bank offsets productivity shocks; which, in turn, induces more agents to fix their nominal wages. These results do not depend on any divergence between the central bank's and agents’ target output. In particular, the central bank stabilizes price in the only equilibrium if the normalized cost is low enough, even if all players share the same output target. If the central bank does not aim for the agents’ target then it cannot adopt the Ramsey rule in any equilibrium. However, it might adopt the Ramsey rule in the first period of a twice repeated version of this game, provided that the normalized indexation cost takes an intermediate value. In any such equilibrium of the repeated game, all agents fix their nominal wages in the first period when they expect the central bank to adopt the Ramsey rule; and the central bank is deterred from deviating in the first period by the “threat” that its least-preferred equilibrium of the one-period game would be played in the second period.2 The idea that decision-makers should recognize how their actions can affect the structure of the economy is the essence of the Lucas critique. Central banks which seek to stabilize output would recognize agents’ incentive to protect themselves against price surprises by making the Phillips curve steeper. This can be achieved by indexation, as we demonstrate here, or by shortening contracts. Fear of endogenous structural change may then solve the central bank's dynamic inconsistency problem by providing incentives to abide by the Ramsey rule. These results rely on the multiplicity of equilibria in the one-period (stage) game. By contrast, the Ramsey rule cannot be played in any period of a finite repetition of the conventional stage game, as the latter possesses a unique equilibrium.3 We present the one-period model in Section 2. We characterize equilibria of this game in Section 3, as well as presenting the repeated game and demonstrating that the Ramsey rule might be played. We conclude in Section 4, where we also discuss some natural extensions of the model. Some proofs are relegated to an Appendix.

4. Conclusions and extensions Conventional macro models treat the structure of labor contracts as fixed, assuming that agents fix their wages. The central bank therefore adopts the discretionary policy in a one-period game; and, in light of the uniqueness of this policy, the central bank adopts the discretionary policy in every period of a finitely repeated version of this game. We have suggested, per contra, that labor contract structure should be viewed as co-determined with monetary policy. This endogeneity yields lessons about play in single period and in repeated games: •• Agents fix their nominal wages precisely when the central bank adopts a discretionary policy: a pattern of behavior which is assumed in the literature. Furthermore, there are additional equilibria in which agents choose a different contract structure, with a higher proportion of agents indexing, the closer is central bank policy to inflation stabilization. Our one-period model yields a number of testable implications. The first implication characterizes the equilibrium relationship between contract structure and monetary policy. Our prediction that nominal wages are fixed when monetary policy leans against the wind seems to be consistent with the stylized facts in most developed countries: which is presumably why the pattern has been assumed in the literature. The one-period model also yields implications if we treat different empirical cases as alternative equilibria of a game with fixed parameters.14 For example, we predict that the central bank does not respond to productivity shocks in the simple equilibrium, where wages are indexed; but that it does respond in the other equilibria, where at least some wages are fixed. If we interpret the 1973 oil price rises as a real shock then the prediction is consistent with Fischer's (1983) evidence that central banks responded less to the 1973 oil price shock, the greater the incidence of indexation. Our results also relate to empirical studies of the relationship between indexation and the variability of inflation, which are typically based on panel data.15 Inequality (2) above implies that any ceteris paribus increase in the variance of inflation makes indexation more attractive. However, inflation risk is endogenous in our model. Comparing equilibria, our model implies that the degree of indexation is associated with lower inflation risk because the more indexation there is, the steeper is the Phillips curve. Estimates in the literature of the relationship between inflation risk and indexation are based on models which neither account for endogeneity nor for the roles played by the covariance term and the variance of productivity shocks in inequality (2); so, conditional on our model, the estimates are biased. Nevertheless, it is interesting that Rich and Tracy (2000) find a significantly negative association, as we predict, using Christofides’ (1985) measure of inflation variability. •• The central bank may be induced to abide by the Ramsey rule because of the “threat” that agents would change labor contract structure were the central bank to deviate. In contrast to conventional models, the Ramsey rule may be implementable in a finitely (as well as an infinitely) repeated game. In such an equilibrium, agents fix their nominal wages in every period unless the central bank's target output is much larger than the natural level. We now consider the robustness of our results to a variety of extensions of the model: •• We have assumed, throughout, that agents can condition indexed wages on the productivity shock. If wages can only be conditioned on inflation then the associated period game has a discretionary equilibrium under the same conditions as a discretionary equilibrium exists in our model: for discretionary policy is an invertible function of the productivity shock; so an agent who indexed to inflation alone could always hit her target by conditioning on inflation alone. If indexation is cheap enough then the associated game has a simple equilibrium. The central bank is deterred from conditioning inflation on the productivity shock by contractual provisions which condition wages on inflation.16 •• We have assumed that agent θθ wholly owns firm θθ. Suppose, per contra, that every agent holds the same (diversified) portfolio of stocks in the firms. It is easy to see that every agent addresses her offer to the firm where she is an insider provided that agents share the cost of retraining. Furthermore, our assumption that all agents and firms are symmetric implies that every agent earns the same income in any symmetric (viz. not mixed) equilibrium. It is straightforward to show that agent θθ's payoff again only depends on the productivity shock and output at firm θθ. Consequently, we can again approximate her payoff by a loss function which is symmetric around a target output for firm θθ. Our other main results then follow. Another approach is to suppose that a monopoly union, which represents all agents, chooses either a fixed or an indexed wage for all agents.17 It is then easy to see that the union would choose a fixed wage if and only if the cost of indexation is high enough. In contrast to our model, the union's optimal choice is unique for generic parameters: the strategic complementarity across agents’ choices, which we highlighted in Section 3.1, must then disappear. For generic parameters, the central bank can only abide by the Ramsey rule in a finitely repeated game if its target output equals the union's output. •• In our model, indexed wages are an alternative contract structure which entail a steeper Phillips curve. Similar arguments apply if we replace indexed wages with contracts which fix employment before the productivity shock is realized. The one-period version of this game again exhibits multiple equilibria; so the central bank may adopt the Ramsey rule in a finitely repeated game because a less favored equilibrium would be played after any deviation.18 •• Fear of structural change in other markets can also discipline decision makers. For example, the government's incentive to inflate so as to reduce the real value of outstanding government debt gives rise to a dynamic inconsistency problem similar to that described in this paper.19 Unexpected inflation might induce the financial sector to shift from fixed income securities to indexed bonds; and this “threat” might analogously induce the government to abide by the Ramsey rule.20