Investment spikes: New facts and a general equilibrium exploration

The dispute the paper enters is whether the well-documented lumpiness of plant-level investment matters for aggregate dynamics. Caballero’s Handbook survey argued that “the changes in the degree of coordination of lumpy actions play an important role in shaping the dynamic behavior of aggregate investment”; Thomas (2002) built a general equilibrium model in which “the aggregate effects of lumpy investment are negligible,” because households’ consumption-smoothing offsets the lumpy investment demand – a result that led Prescott to conclude that “partial equilibrium reasoning to an inherently general equilibrium question cannot be trusted.” Gourio and Kashyap make three moves. The first is empirical. Using U.S. Annual Survey of Manufactures establishment tabulations for 1972-1998 and a Chilean plant census covering on average 1,780 plants per year for 1981-1999, capital-weighted throughout, they show that investment spikes (investment above 20 percent of beginning-of-period capital) account for about half of total investment in each country, and that variation in spike investment accounts for 97 percent of the variance of the aggregate investment rate in the U.S. and 86 percent in Chile. Decomposing spike investment into the amount invested per adjuster and the number of adjusters, they find the extensive margin dominates: it accounts for 0.87 of the variance in the U.S. and 0.925 in Chile. They also add the share of adjusters to a standard accelerator forecasting regression and find it enters with negative coefficients that are significant at the first and second lag in the U.S. and at the second lag in Chile – investment is depressed in the period after a surge, which is the sign a fixed-cost model predicts and the opposite of what would appear if the spike variable were merely proxying for productivity. The second move is to recalibrate Thomas’s model to match these facts. As originally calibrated it does not: spikes account for only about 62 percent of the variance of investment and the extensive margin for only 51 percent of the variance of spikes, against roughly 90 percent for both in the data. The critical change is the distribution of fixed costs. Thomas, following Caballero and Engel, uses a uniform distribution, under which moving more plants into action always means activating plants facing quite different costs; if instead the distribution is “compressed” so that many firms face nearly identical costs, moving many firms across the threshold is cheap and the extensive margin becomes powerful. Substituting a compressed distribution raises the extensive margin’s share to 92.6 percent and the variance share of spikes to 99.9 percent. The authors also argue Thomas’s calibration puts too little into adjustment costs – about one-fifth of one percent of investment spending, against Cooper and Haltiwanger’s estimate of roughly 7.5 percent, “roughly 40 times the size” – and too little curvature in the profit function, against a later literature estimating returns to scale between 0.5 and 0.7. Their preferred calibration raises the maximum fixed cost to 0.06 and sets returns to scale to 0.6. The third move is to re-run the irrelevance test. Under Thomas’s calibration the impact response of investment to a productivity shock is 99.8 percent of the frictionless RBC model’s; under theirs it is 89 percent, with a visible hump about twelve periods out. The larger divergence comes from a different experiment: perturbing the cross-sectional distribution of capital directly, as a temporary investment tax cut or an uncertainty shock would. There, Thomas’s model and the RBC model remain “essentially identical,” while the recalibrated model shows both a depressed investment response and a magnified echo when the recently-invested firms come back after 8 to 11 periods. The conclusion is carefully bounded: general equilibrium does attenuate the differences, and the authors agree with Thomas that GE and partial equilibrium can differ substantially – but “there is nothing generically related to DSGE models that guarantees that plant-level investment lumpiness is smoothed away,” and the stronger claim that GE makes fixed costs irrelevant “is premature.” They add that all their results use log utility, that their calibration “is not fully optimized,” and that “much more work needs to be done” on how such models should be estimated and calibrated.

Anil K. Kashyap | Macro Paper Warehouse

Investment spikes: New facts and a general equilibrium exploration