When does lumpy factor adjustment matter for aggregate dynamics?

We analyze the dynamic e¤ects of lumpy factor adjustments at the …rm level onto the aggregate economy. We …nd that distinguishing between capital and labour as lumpy factors within the production function result in very di¤erent dynamics for aggregate output, investment and labour in an otherwise standard real business cycle model. Lumpy capital leaves the RBC mainly unchanged, while lumpy labour allows for persistence and an inner propagation within the model in form of hump-shaped impulse repsonses. In addition, when modeling lumpy adjustments on both investment and labour, the aggregate e¤ects are even stronger. We investigate the mechanisms underlying these results and identify the elasticity of factor supply as the most important element in accounting for these di¤erences. JEL classi…cation: E32; E22; E24 Key words: Lumpy labor adjustment, Lumpy investment, Business cycles, Elasticity of supply. 4 ECB Working Paper Series No 1016 March 2009 1 Non-technical Summary The main objective of this paper is to analyze the transmission mechanism of the micro-lumpiness onto the aggregate dynamics in a Dynamic Stochastic General Equilibrium (DSGE) model. In doing so, we intend to study the e¤ects of the lumpy production factor adjustments in a uni…ed framework, so that one can shed some light on the underlying mechanism from a broader perspective. With recent microeconomic data collected from the …rm’s level, convincing evidence has been documented for both labour and capital adjustments, showing that adjustments of production factors at the plant level exhibit a lumpy pattern in response to shocks, and furthermore they are strongly coordinated in timing. This evidence brings di¢ culty for the widely using convex adjustment costs model that implies a smoothing adjustment at the …rm level. The main theme running in the macroeconomic theory is whether modeling the micro lumpiness explicitly changes the model’s implication for the aggregate dynamics. In contrast to the (S,s) literature, in which the e¤ects of lumpy factor adjustments are normally studied separately, we view both lumpy factor adjustments as intrinsically close-related issues, and hence in this paper we present a tractable theoretical framework to study them together. The main questions we intend to address are: why does lumpiness in di¤erent production factors lead to di¤erent e¤ects on aggregate dynamics and what are the mechanisms through which these e¤ects work? Does coordinated lumpy adjustments of both production factors matters for the aggregate dynamics? The answers to those questions from our model’s perspective are: …rst, lumpy labour and capital lead to di¤erent e¤ects regarding the dynamics of output and other aggregate variables. In particular, lumpy labour adjustment leads to a hump-shaped response of aggregate real variables, which cannot be obtained by the lumpy capital model. Moreover, when the lumpy factor adjustments coordinate with each other, the e¤ects on the aggregate dynamics are even strengthened. Second, we investigate the underlying mechanism for these results and identify that su¢ ciently elastic factor supply is the prerequisite for the lumpy adjustment to have aggregate e¤ects, and furthermore that the intratemporal substitution as opposed to the intertemporal margin is important for business cycle dynamics. Finally, to further explore the mechanism of this channel, we conduct three theoretical experiments in our model. First, we try to eliminate the lumpy labour e¤ect from the lumpy labour model by decreasing the elasticity of labour supply. Second, we want to reestablish aggregate e¤ects of …rm’s lumpy capital by raising the elasticity of capital supply. Hereby we can either decrease the elasticity of substitution to weaken the consumption smoothing motive, or alternatively we increase the depreciation rate allowing for a more immediate response of capital supply to the aggregate state. All results from those experiments con…rm our claim that elasticities of factor supply and the intertemporal elasticity to be the core driving forces for micro-lumpiness to have an aggregate e¤ect. 5 ECB Working Paper Series No 1016 March 2009