by Giovanni P. Olivei and Silvana Tenreyro
No. 1, January 2004 - August 2004

Motivation for the Research
Substantial empirical work has led to a broad consensus that monetary shocks have real effects on output. Moreover, the output response is persistent and occurs with considerable delay. A large class of theories points to the existence of contractual rigidities to explain why monetary policy might cause real effects on output. Theoretical models usually posit some form of nominal or real rigidity in wages or prices that is constant over time. For example, wage contracts are assumed to be staggered uniformly over time or subject to change with a constant probability at each point in time.

This convenient simplification, however, may not be a reasonable approximation of reality. As a consequence of organizational and strategic motives, wage contract renegotiations may occur at specific times of the calendar year. Anecdotal evidence supports the notion of “lumping” or uneven staggering of contracts.

If the staggering of wage contracts is not uniform, monetary policy can have different effects on real activity at different points in time. Specifically, other things being equal, monetary policy can be expected to have a smaller impact in periods of lower rigidity — that is, when wages are being reset — than in periods of higher rigidity.

The aim of this paper is to assess whether the effect of a monetary policy shock differs according to the quarter in which the shock occurs and, if so, whether such a difference can be reconciled with uneven staggering.

Research Approach
The paper provides an indirect test for the presence and importance of the lumping or uneven staggering of contracts by examining the effect of monetary policy shocks at different times of the year. To accomplish this, the authors introduce quarter-dependence in an otherwise standard structural VAR (vector autoregressive) model. To interpret the results, the authors then employ a simple stochastic dynamic general equilibrium model that allows for uneven staggering of wage contracts.

Key Findings

• There are significant differences in output impulse responses depending on the timing of the shock.
  
  
• After a monetary shock that takes place in the first quarter, the response of output is fairly rapid, with output reaching a level close to the peak effect four quarters after the shock. The response is even more front-loaded and dies out faster when the shock takes place in the second quarter.
  
  
• In both the first and the second quarters of the calendar year, the response of output to a monetary policy shock is economically relevant. An expansionary shock in either the first or the second quarter with an impact effect on the federal funds rate of minus 25 basis points raises output in the following eight quarters by an average of about one-quarter of one percent.
  
  
• In contrast, the response of output to a monetary shock occurring in the second half of the calendar year is small, both from a statistical and from an economic standpoint.
  
  
• The well-known finding that output takes a long time to respond and is quite persistent can be interpreted as the combination of these sharply different quarterly responses.
  
  
• In contrast to the dynamics of output responses, price and wage responses are delayed when the shock occurs in the first half of the year and occur more quickly when the shock occurs in the second half of the year.
  
  
• A modest amount of uneven staggering leads to significantly different output responses. This happens even if the cumulative effect of the monetary policy shock on wages and prices is not strikingly different across quarters, as appears to be the case empirically.

Implications
The authors propose that a potential explanation for the differential responses to monetary policy shocks depending on their timing is driven by contractual lumping and not by different types of monetary shocks nor by different “states” of the economy across quarters. Expanding the model to allow for adjustment costs and information lags should improve the ability of the model to match other features of the empirical impulse responses. Future research might fruitfully explore whether other seasonal factors beside time-varying contractual rigidity also contribute to the differences in impulse responses across quarters.

Full text of Working Paper 04-1