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MITLIBRARIES 3 9080 02528 5922 Digitized by the Internet Archive in 2011 with funding from Boston Library Consortium IVIember Libraries http://www.archive.org/details/estimatinglongruOOscha ^ HB31 .M415 31 Massachusetts Institute ofTechnology Department of Economics Working Paper Series Estimating ttie Long-Run User Cost Elasticity Huntley Schaller Working Paper 02-31 July 19, 2002 Room E52-251 50 Memorial Drive MA Cambridge, 02142 This paper can be downloaded without charge from the Social Science Research Network Paper Collection at http://ssm.com/abstract_id=33 322 1 Estimating the Long-Run User Cost Elasticity July 19, 2002 Huntley Schaller Contact Information: Department ofEconomics Massachusetts Institute ofTechnology, E52-262b 50 Memorial Drive MA Cambndge, 02138-1347 PH: (617) 452-4368 FX: (617) 253-6915 EM: [email protected] Abstract The user cost elasticity is a parameter ofcentral importance in economics, with implications for monetary policy, macroeconomic models, tax policy, growth, and many other areas. Ifthe supply curve forcapital is upward sloping and shocks to demand are important (as they are likely to be overthe business cycle), estimates ofthe usercost elasticity that rely on high-frequency movements in the variables will tend to be biased. This paper applies cointegration techniques to a small, open economy. The combination ofexogeneity ofusercost implied by the flat supply ofcapital curve for a small, open economy and appropriate correction for small sample bias yields an estimate ofthe long- run usercost elasticity which is about 75% larger (in absolute value) than the best existing estimate. In addition, the papermakes three furthercontributions: accounting for increases in depreciation (due to dramatic increases in computeruse), estimating the long-run usercost elasticity for structures and the total capital stock, and disentangling the effects ofcapital goods prices, the real interest rate, and taxes. Keywords: Usercost elasticity, capital stock, investment JELcodes: E22, E44, H25 I would like to thank Heidi Portuondo forresearch assistance and the SSHRC for financial support. I. Introduction Along the demand curve for capital, there is a negative relationship between user cost and the capital stock. This is the relationship that empirical researchers try to capture when estimating the user cost elasticity. But in the short run (i.e., at business cycle frequencies) there is some evidence that the demand curve forcapital may shift in response to cyclical upswings and downturns. Forexample, it is well known that investment moves with output at business cycle frequencies and this may be part ofthe reason for the success ofthe accelerator model in traditional aggregate time series studies.' Ifthe supply curve forcapital is upward-sloping in the short run, (as suggested, e.g., by Goolsbee (1998)), there will be a positive relationship between usercost and the capital stock along the supply curve in the short run. If, at business cycle frequencies, shifts in demand are relatively important, it is easy to understand why empirical studies have frequently failed to find a very strong negative relationship between usercost and the capital stock. Shifts in the supply curve are probably due primarily to technological change and productivity shocks (which affect the price ofinvestment goods and the real interest rate) and tax reforms. All ofthese tend to be relativity persistent, at least compared to the ups and downs in demand at business cycle frequencies.^ The relatively persistent nature of Forarecentexampleofthe successoftheacceleratorin aggregatedata, seeFigure4 inHassettand Hubbard (2002). Forempirical evidenceonthepersistenceofthereal interestrate,seeGarciaandPerron (1996). A wide varietyofevidencesuggeststhatproductivity shocks arehighly persistent,perhaps best modeled as unit root processes. supply shocks suggests that we should be able to estimate the user cost elasticity betterby focusing on the long-run relationship between the capita] stock and usercost.^ Ifshifts in the demand curve for capital are relatively common in the short run and the short-run supply curve is upward-sloping but the long-run supply curve is flat, we would expect much ofthe variation in usercost to be transitory. This is precisely what Kiyotaki and West (1996) find, and they argue that this is an important reason why estimates ofthe user cost elasticity tend to be low. In the presence ofadjustment frictions, it doesn't make sense for a firm to respond fully to transitory variation in user cost. Estimates based on short-run movements therefore tend to give a downward biased usercost elasticity. Kiyotaki andWest (1996) provide evidence forJapan that shocks to usercost are less persistent than shocks to output. They estimate the long-run response to a 1% shock to the cost ofcapital is a 0.1% change in the cost ofcapital, while the long- run response to a 1% shock to output is a 1.1% change. This provides additional evidence - consistent with Goolsbee's work - that much ofthe short-run variation in user cost is associated with transitory shifts in demand.'' There is a further problem with trying to estimate the user cost elasticity from short-run movements in investment. Existing economic theories make substantially different predictions about investment dynamics. Forexample, a pure neoclassical model without adjustment costs predicts that the capital stock will respond immediately to A shocks to usercost. q model with convex adjustment costs predicts that current Thisis not to suggest thataggregatedemand shocks may not have fairly persistenteffects (e.g., in the presenceofsomecombinationofnominal andreal rigidities), merely thatpersistentshifts in thesupply curve forcapital will berelatively more important inthe longrun than in theshort run. It may also help toexplain why major tax reforms seem to be such good instruments for user cost, as shown by Cummins, Hassett, and Hubbard (1994, 1996), ifmajortax reforms involvechanges in usercost that are much morepersistentthan the short-run variations induced bychanges indemand at business cycle frequencies.