Capital reallocation: A tale of two frictions*
| Published date | 01 May 2021 |
| Author | Wei Wang |
| Date | 01 May 2021 |
| DOI | http://doi.org/10.1111/sjpe.12263 |
Scott J Polit Econ . 2021;68:179–208. wileyonlinelibrary.com/journal/sjpe
|
179
© 2020 Scottis h Economic Societ y
1 | INTRODUCTION
Reallocation of used capital is highly procyclical and much more volatile than output over the business cycle
(Eisfeldt and Rampini, 2006; Cui, 2017; Lanteri, 2018), as is shown in Figure 1. However, the standard business
cycle theor y generates countercyclic al used capital realloca tion. Since the amount of used c apital reallocation is
comparable to n ew investment on average, it is impor tant to understand the c yclicality features of used c apital
reallocation. This paper emphasizes the role of search and financial frictions in accounting for procyclical and
volatile reallocation of used capital.
Search and financial frictions are important for the used capital market. On the one hand, Kurmann and
Petrosky-Nadeau (2007) document the unemployed capital in the leased business property market is high in
downturns and low in booms. Ottonello (2018) documents that capital unemployment is highly countercyclical
in the commercia l real estate (office, retail an d industrial space) market from 1984 to 2014. Mo reover, the level
and fluctuations of capital unemployment in the commercial real estate market is comparabl e to those of labor
unemployment i n the US. On the other hand, Eisfeldt and Shi (2018) docu ment that used capital reallo cation is
significant ly positively correlate d with debt financing. O ttonello (2018) finds tha t less used capital are r eallocated
following negative financial shocks.
Accepted: 4 Augu st 2020
DOI: 10 .1111/sjpe.1 2263
ORIGINAL ARTICLE
Capital reallocation: A tale of two frictions*
Wei Wang
*This pape r is a revised versi on of Chapter 3 of my Ph. D. dissertat ion. I am indebte d to Rody Manuell i, Yongseok Shin an d Costas Aza riadis for thei r
guidance. I ac knowledge the f inancial sup port from the N ational Natur al Science Found ation of China (Gr ant No. 71703017) and t he Excellent
Young Scholar Fun ds of UIBE (Grant N o. 19YQ17).
School of Inter national Trade and
Economics, U niversity of Inter national
Business and Economics, Beijing, China
Correspondence
School of Inter national Trade and
Economics, U niversity of Inter national
Business and E conomics, 10 Huixin E ast
Street, Beijing 100029, China.
Email: weiwangccer@gmail.com
Funding information
National Natu ral Science Found ation of
China, Gran t/Award Number: 71703017;
Universit y of International Bu siness and
Economics, Grant/Award Number: 19YQ17
Abstract
This paper explores the role of search and financial fric-
tions in the used capital market. A tractable dynamic gen-
eral equilibrium model with both frictions is developed to
account for procyclicality of reallocation and the price of
used capital. B oth the aggregate productivi ty shock and the
financial shock c an generate procyclical reallo cation of used
capital. Quantitatively, the financial shock accounts for al-
most all the variatio n of used capital realloc ation. The aggre-
gate productivi ty shock is more responsible f or the variation
of the price of used capital as well as variables outside the
used capital mar ket.
180
|
WANG
I construct a t ractable hetero geneous-firm dynamic ge neral equilibrium m odel with both fric tions. Firms could
trade in the use d capital market after sh ocks are realized. The tr ading is subject to search fr ictions. Buyers, usin g
their profits as collateral, are subject to collateral constraints. The mechanism is as follows. Assume a negative
productivity shock takes place. The marginal profit of buyers decreases while the marginal profit of sellers in-
creases. The Nash bargaining then implies a lower used capital price to compensate buyers at the expense of
sellers. Hen ce, the total profit of buyers and he nce the total collateral value of bu yers plummets. The collater al
constraint th en implies used capital rea llocation (trading) shrin ks in the model. On the other ha nd, the potential
supply of used ca pital does not change on impa ct in the model. Hence, the p robability of selling used c apital be-
comes lower, and thus th e used capital market become s tighter. Since less used capital is r eallocated from firms
with low produc tivity to the ones with high pro ductivity, aggregate employ ment and output decline, leading to
a lower wage rate. The refore, reallocation and the price of used capital are both procyclical. Last but not least,
the lower wage rate ( general equilibrium eff ect) pushes up the margina l profits and hence dampen s, but can not
reverse, the ef fects of the initial pro ductivity shock .
Now, suppose a negat ive financial shock hits th e economy. First, the collatera l value of buyers plummets im -
mediately. Second , financial shocks do not aff ect the marginal profit s on impact. Hence, Nash ba rgaining implies
that the price of used capital is also unchanged. The collateral constraint then implies used capital reallocation
shrinks. Sin ce the potential supply of used cap ital does not change on impact , the used capital market be comes
tighter. As a result, i t is harder to sell but easier to buy u sed capital. Again, a ggregate employment and ou tput as
well as the wage rate d ecline due to less used capit al reallocation. Simila rly, the lower wage rate can not reverse
the initial ef fect of the financial shock, b ut it leads to a higher marginal prof it, the price of used capita l goes up.
Hence, financ ial shocks alone are not abl e to generate procyclical p rices of used capital.
I then calibrate the model to match key moments from the US data. Three quantitative exercises are con-
ducted based o n the calibrated mode l. First, the impuls e response exercise confir ms the above intuition that b oth
the aggregate p roductivity sh ock and the financia l shock can generate pr ocyclical realloc ation of used capita l. The
aggregate pro ductivity shock i s necessary for the p rice of used capital to be p rocyclical. In addi tion, the aggregate
productiv ity shock has larger effec ts on most aggregate varia bles. The financial shock i s more important only in
the used capit al market.
FIGURE 1 Cyclical Compone nts of Used Capital Reall ocation and GDP. Note: Used capit al reallocation data
are from US Compu stat. US GDP data are fro m FRED of St. Louis Fed. Both are ann ual from 1971 to 2013. The
correlation coe fficient is 0.6375 [Colour fi gure can be viewed at wileyonl inelibrary.com]
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
–0.1
–0.05
0
0.05
0.1
–1
–0.5
0
0.5
1
GDP
Capital Reallocation
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