MEDIUM TERM DYNAMICS IN A RATIONAL EXPECTATION MODEL WITH VINTAGE CAPITAL AND APPROPRIABILITY

Abstract

In this paper, we compute a model focusing on medium term dynamics, in the line of Caballero and Hammour (1998). The main features of the model are a putty-clay production function and the bargaining between workers and firms over the rent. Although using vintage units of production is a sensible way to model the dynamics of aggregate supply, it raises many computational problems that explain why it has not been very popular in the economic literature. Indeed, with a putty-clay production function, a unit-specific wage is bargained in each vintage of production, on the basis of the expectations on the remaining lifetime of the unit. And the lifetime of each vintage unit of production is set according to the expected profitability over a long time period. Thus, any proper modelling of this type of model has often been considered as too cumbersome. This explains why the putty-clay production is barely used, and why strong additional assumptions - such as fully backward expectations - are made to turn the model more tractable.The lack of tractability of the rational expectation version of the previous kind of model is related to three main difficulties. First, it has a large number of equations and expected variables. Second, equations include a lead-structure that spans the expected lifetime of a new unit. Third, some behavioural equations are highly non-linear. Here, we provide an example showing that traditional computational restrictions can be overcome by using the stack- algorithm developed to solve large rational expectation models.Simulations are run to describe the medium term dynamics of the profit share and unemployment in four OECD countries. We extend the analysis realised by Caballero and Hammour (1998) on France. They show that shifts in unemployment benefits and firing costs in the 70Æs can explain the historical developments in capital-labour relation. In a slightly different framework, Blanchard (1999) considers other explanations related to country- specific or worldwide shocks. We investigate the relevance of the main potential explanations in the light of the contrasted macro-economic performance of the US, the UK, Germany and France over the last three decades. Moreover, contrary to Caballero and Hammour (1998), who use an iterative method to solve their model, we apply a more consistent algorithm for this type of model. We also assess the advantage of such a method by comparing the simulations run with the stack-algorithm to those obtained with the Fair-Taylor iterative method.