خوشه سرمایه گذاری: واقعیت های جدید و اکتشاف تعادل عمومی

Using plant-level data from Chile and the U.S., we show that investment spikes are highly pro-cyclical, so much so that changes in the number of establishments undergoing investment spikes (the “extensive margin”) account for the bulk of variation in aggregate investment. The number of establishments undergoing investment spikes also has independent predictive power for aggregate investment, even controlling for past investment and sales. We re-calibrate the Thomas [2002. Is lumpy investment relevant for the business cycle. Journal of Political Economy, CX 508–534] model (that includes fixed costs of investing) so that it assigns a prominent role to extensive adjustment. The recalibrated model has different properties than the standard RBC model for some shocks.

Economists are sharply divided over the aggregate significance of the heterogeneity of plant-level investment. On the one hand, there is unanimous agreement that individual plants sometimes forgo investing at all and at other times have dramatic surges in investment.1Caballero (1999), in his survey for the Handbook of Macroeconomics, argues that accounting for this “lumpiness” is critical: “it turns out the changes in the degree of coordination of lumpy actions play an important role in shaping the dynamic behavior of aggregate investment”. On the other hand, Thomas (2002) presents a model where this is not true: “in contrast to previous partial equilibrium analyses, [the] model results reveal that the aggregate effects of lumpy investment are negligible. In general equilibrium, households’ preference for relatively smooth consumption profiles offsets changes in aggregate investment demand implied by the introduction of lumpy plant-level investment”. This “irrelevance result” inspired Prescott (2003) to argue “partial equilibrium reasoning to an inherently general equilibrium question cannot be trusted”. This paper makes three contributions to this debate. First, it introduces several new facts about surges in investment (that we call spikes). In particular, we show that for both U.S. and Chilean plants, most of the variation in the total investment rate is due to variation in investment of firms undergoing spikes. Moreover, this approximation derives its explanatory power from changes in the number of firms making large investments (the “extensive margin”), and not changes in the average size of the spikes (the “intensive margin”). The prevalence of spikes in one year also predicts aggregate investment (even controlling for the past level of investment or sales): years with relatively more spikes are followed by years with relatively less investment. These empirical results suggest that it is important to construct a model that not only generates spikes on average, but also variation in spikes over the business cycle. To do this we start with the Thomas (2002) model, which is a tractable dynamic stochastic general equilibrium (DSGE) model that naturally yields lumpy investment. The heterogeneity in this model derives from variation in the fixed costs that firms must pay in order to invest. We find that the exact model, as originally calibrated, has trouble fitting the facts about cyclical patterns in lumpiness. But by changing the calibration we can match better these facts. While we make several changes, the critical one is to alter the distribution of fixed costs that firms face. In order for the extensive margin to matter, this distribution must have the property that many firms face roughly the same sized fixed cost in deciding whether to invest. When the distribution has this type of “compression”, it becomes possible for a shock to move many firms across the threshold from not investing to investing. Conversely, if the distribution exhibits little compression, then firms become much less likely to synchronize their decisions and the extensive margin matters less. Importantly, even if part of the distribution is compressed there can still be substantial heterogeneity in the overall distribution and hence in the level of fixed costs that firms pay to adjust. Therefore, this conclusion is not necessarily overturned by allowing more heterogeneity in the idiosyncratic shocks that firms face. The third contribution is to explore the aggregate response of investment to various shocks when extensive adjustment is important. The Thomas model, as originally calibrated, implies that the fixed costs which generate spikes are essentially “irrelevant” for aggregate dynamics. In particular, the aggregate dynamics (summarized for example by the impulse response of investment to a productivity shock) are the same as the standard real business cycle (RBC) model, which has no adjustment costs of any kind. In our calibration, the qualitative response of investment to a productivity shock is somewhat different from the standard RBC model. More importantly, the original Thomas model and the RBC model also exhibit virtually identical response when the distribution of firms capital levels move away from the steady-state distribution (for instance, as might occur if a temporary tax change leads firms to accelerate investment spending). In contrast, under our calibration, aggregate investment behaves differently than it would in the RBC model. Hence for this kind of shock the fixed cost seems to matter substantially. The conclusion is that although general equilibrium attenuates the differences between the fixed cost model and the RBC model, it does not eliminate these differences. In other words, the irrelevance result is not a generic finding that comes from the general equilibrium, but rather a result that depends on the details of how the model is calibrated, especially regarding the production side. The remainder of the paper is organized into three sections. The first documents the aforementioned empirical regularities. The second part reviews the Thomas model and explains our calibration. The third part explores the predictions of the re-calibrated model regarding the sensitivity to various disturbances. We close with a brief summary.

This paper makes three contributions to the debate over the aggregate significance of plant-level investment lumpiness. Remarkably, the basic plant-level facts on the lumpiness of investment are fairly similar in Chile and the U.S. In each country, investment spikes drive total investment. The spikes draw their predictive power from changes in number of plants making large investments, rather than changes in the size of average investment per plant. We use these statistics regarding the decomposition between the intensive and extensive margins of adjustment to summarize the microeconomic facts about lumpiness that we ask a model to match. We use the Thomas (2002) model to examine these facts. This model augments a relatively standard RBC model by assuming that firms must pay a fixed cost (that is randomly drawn each period) in order to adjust its capital. As originally calibrated, however, the model fails to generate a dominant role of investment spikes and a dominant role of the extensive margin. To fit these facts we change the distribution of fixed costs from which firms sample and make it more “compressed” than the distribution considered by Thomas. We also argue that the original calibration has an average level of fixed costs which is too low and a profit function that has too little curvature. The final contribution is to study the properties of the model using our preferred calibration. In the original Thomas model the aggregate dynamics for investment following a productivity shock were indistinguishable from an RBC model with no adjustment costs. In our model this type of shock plays out somewhat differently. Moreover, for shocks that directly reshape the cross-sectional distribution of capital, the two models have very different implications: in general, the fixed cost model predicts that investment is more depressed for a while; moreover, the fixed cost model generates an echo effect which is absent in the RBC model. The conclusion from the last exercise is that there is nothing generically related to DSGE models that guarantees that plant-level investment lumpiness is smoothed away. Rather we agree with Thomas that there can be substantial differences between the importance of lumpiness in a GE models and partial equilibrium models. However, many have gone farther and concluded that GE makes fixed costs to investment completely irrelevant for the business cycle. Both our empirical and theoretical work shows this conclusion is premature; in particular, the details of how the production side is modeled matter. Given the currently available information our calibration is reasonable, but we recognize much more work needs to be done in this respect to determine how these models should be estimated and calibrated.