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This paper presents a vintage capital model assuming putty–clay investment and perfect foresight. The model is written in discrete time and is simulated by using a second order relaxation algorithm. By computing the eigenvalues of the dynamic system, we have checked the conditions of existence and uniqueness of a solution (Blanchard and Kahn's conditions) and identified the echo effect that characterizes vintage capital models and the related dynamics of creation and destruction. By calibrating the model on French data, it has been proved useful to explain the medium-term movements in the distribution of income in France during the last three decades.

Computational general equilibrium models usually assume a putty–putty technology: the capital intensity of the production process can be changed instantaneously and without cost. Thus, in a competitive framework, the factors of production fully and instantaneously adjust to current economic conditions. This means that “realistic” changes in real wages or in the cost of capital lead to very significant and quick moves in demand for labor and capital. Moreover, the quick adjustment of the capital stock should cause huge variations in the flows of investment. However, actual employment and capital stock exhibit much weaker movements than those predicted above. Hence, the integration of this theoretical framework in a realistic model requires some improvements. One way to decrease the cost-sensitivity of production factors consists in assuming non-linear adjustment costs (usually quadratic costs). This results in smoother dynamic adjustments of labor and capital. However, this specification rests upon an ad hoc assumption without wholly rigorous microeconomic foundations and empirical verification. Moreover, it is not a fully convincing way to model the irreversibility of investment and the firing costs of labor. Finally, the putty–putty framework is unable to give simple, acceptable explanations for the medium-term movements in the wage share in value-added, which are observed in many European countries (see for instance Blanchard, 1997; Prigent, 1999). Although adjustment costs smooth the dynamics of factor demands in the short run, they are far from sufficient to produce medium-term changes in the income distribution between capital and labor. A key feature of the putty–putty specification, that is central to its empirical failure, is that all the vintages of capital have the same capital intensity. On the contrary, we would expect the current technology menu to be only available to the newly created units of production. This is precisely what the putty–clay specification does. In this framework, current economic conditions affect the capital intensity of the new production units (their technological choice) and the number of these units created (investment in the economy). The other production units keep the technology they were given at their creation. However, current economic conditions affect their profitability and lead to the scrapping of non-profitable units. Hence, the aggregate capital–labor ratio changes gradually with the flows of investment and the scrapping of old obsolete production units. Putty–clay investment may thus provide medium-term dynamics in the distribution of income. This specification has some other advantages. The irreversibility of investment is embedded in the model and firing costs can easily be introduced. This gives a convincing foundation to the stickiness of employment. Despite all its advantages, the putty–clay technology suffers from a serious drawback. Its implementation in a macroeconomic model is cumbersome for two reasons. First, the model has a long memory since it keeps track of all the vintages of capital created in the past, that are still in working order. Thus, the model has “variables with long lags”. Second, the planning horizon of investors stretches far into the future. More precisely, the decision concerning new production units involves forward variables that cover the expected lifetime of these units. The model has then “variables with long leads”. However, these problems can be easily overcome nowadays. Models with variables presenting long leads and lags can be solved with powerful algorithms, and simulation time is decreasing with the improvement of personal computers. The first section presents a model representing the production of goods and the demand of factors with a putty–clay technology. In the second section we close the model by completing its demand side, by introducing a “wage curve” and by assuming the equilibrium of the goods market. Then, we describe the determination of the equilibrium. The third section presents the results of the simulation of the model. The calibration is such that the steady state of the model is identical to the situation of the French economy over the 1980–1994 period. Then, we investigate whether the properties of existence and uniqueness of a solution to the model are satisfied. Finally, we identify a dampened replacement echo effect, with a length equal to the lifetime of a production unit on the steady state. The last section discusses the consequences of an unanticipated permanent change in the wage-setting relationship in France. It also shows the ability of this framework to replicate the medium-term changes in the distribution of income that France experienced during the last three decades.

This paper presents a macro-economic model assuming putty–clay investment and perfect foresight. Research on putty–clay technology was popular in the 1970s (e.g. Adachi, 1974; Britto, 1970; Calvo, 1976) and was at the center of the analysis of the consequences of the oil shock on factor demands in the beginning of the 1980s. However, it was eventually more or less abandoned for its lack of tractability, especially under the hypothesis of rational expectations. Since the mid-1990s, from the works of Caballero and Hammour (1994) and Boucekkine et al. (1997), this research field has known a renewed interest for its ability to explain some major economic developments observed in industrialized countries over the last three decades. First, as putty–clay technology involves some stickiness in the production process, it enables to investigate properly the slow adjustment of production factors to shocks. Second, this framework also explicitly takes into account movements in job creation and job destruction related to economic obsolescence, replacement of productive capacity and expectations over the lifetime of the units. The originality of the model proposed here is that it is written in discrete time whereas previous, recent works developed models in continuous time. Even under strong assumptions, it is almost impossible to derive the analytical solutions of continuous time models. The trick then usually consists in deriving discrete time formula from these models. Here, we prefer to start directly with a discrete time framework and use a second-order relaxation algorithm to simulate the model. The traditional drawback of such a process was the presence of variables with long leads and long lags. However, progress in computation techniques has overcome these difficulties. For instance, by using the Stack algorithm implemented in Troll, the model can be easily solved. The discrete time model has other advantages since it is easy to compute the eigenvalues of the dynamic system. First, this is useful to check the conditions of existence and uniqueness of a solution (Blanchard and Kahn's conditions). More importantly, the analysis of the eigenvalues improves the understanding of the different dynamics in the economy. In particular, we can identify the echo effect that characterizes vintage capital models and the related dynamics of creation and destruction. This kind of models has been proved useful to explain medium-term movements in the distribution of income between production factors. In particular, it illustrates quite well the change in the wage share in value-added in France during the last three decades. Further research could be realized to analyze more systematically the job creation and job destruction process, according to alternative assumptions on labor firing costs. In other words, we could investigate the extent to which these costs can prevent unprofitable old units from being scrapped and replaced by newly created units which embody new technology, as Caballero and Hammour (1994) showed with a continuous time model.