Lumpy Investment, Sectoral Propagation, and Business Cycles
This paper proposes a model of endogenous fluctuations in investment. A monopolistic producer has an incentive to invest when the aggregate demand is high. This causes a propagation of investment across sectors. When the investment follows an (S,s) policy, the propagation size can exhibit a significant fluctuation. We derive the probability distribution of the propagation size, and show that its variance can be large enough to match the observed investment fluctuations. We then implement this mechanism in a dynamic general equilibrium model to explore an investment-driven business cycle. By calibrating the model with the SIC 4-digit level industry data, we numerically show that the model replicates the basic structure of the business cycles. Recent empirical studies discover that the establishment level investment exhibits a lumpy behavior (cf. Doms and Dunne (RED 1998) and Cooper, Haltiwanger, and Power (AER 1999)). This behavior suggests that a firm follows an (S,s) policy due to a fixed cost of investments. This empirical finding has stimulated the macroeconomic investigation whether such an (S,s) investment at the firm level causes the aggregate fluctuations (cf. Caballero and Engel (Econometrica 1999) and Thomas (JPE 2002)). We consider the case when the investments of industries are strategically complement each other. Each good is produced by a monopolist, and all the goods are used as inputs to produce each good. If the strategic complementarity is too small, then the aggregate follows the law of large numbers even though the individual behavior is non-linear. If the strategic complementarity is too large, then the multiple equilibria emerge (cf. Shleifer (JPE 1986)). We show that the aggregate exhibits a modest fluctuation such as seen in the business cycles when the strategic complementarity is about the same magnitude of the micro-level fluctuations. The aggregate fluctuation is driven by the stochastic size of investment propagation across industries. Suppose that there are N industries. We obtain two analytical results. First, when the strategic complementarity is of order 1/N, we obtain the distribution function of the investment propagation size. The distribution follows a power-law distribution exponentially truncated in the tail. The variance of the aggregate fluctuation is much larger than its smoothly-adjusting counterpart. This contrasts with the "neutrality" theorem by Caplin and Spulber (QJE 1987) and Caballero and Engel (Econometrica 1991) which shows that the individual (S,s) behavior does not add up to the aggregate fluctuations due to the law of large numbers. Secondly, the aggregate variance does not depend on N when the strategic complementarity is exactly 1/N. This case corresponds to the constant returns to scale technology and the rigid wage and interest in the N-sector production model. This result shows the possibility of an endogeneous fluctuation of the aggregate production driven by the propagation of sectoral investments. Our scale-free aggregate fluctuation is caused by the feedback effect among individual non-linear behaviors. This mechanism can be seen as a generalization of the self-organized criticality proposed by Bak, Chen, Scheinkman, and Woodford (Ricerche Economiche 1993). The propagation process is dampened by the general equilibrium effect of flexible wage and interest or the decreasing returns to scale. We obtain the power-law distribution only when these dampening forces are nullified. The robustness of our fluctuation result in a general equilibrium setup has to be investigated by numerical simulations. We simulate a dynamic general equilibrium model which incorporates the investment propagation mechanism above. The magnitude and periodicity of the sectoral (S,s) behavior is calibrated by data on the SIC 4-digit U.S. manufacturing sectors. When the representative household's preference on consumption and leisure is sufficiently close to linear, we obtain the second moment properties of aggregate production, consumption, and investment that mimic those of the U.S. business cycles
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