Innovation and Reallocation - Semantic Scholar
Innovation and Reallocation Junghoon Lee∗ April 6, 2015
Abstract This paper considers an improvement in capital embodied technology which only production units that adapt to new knowledge can utilize. This innovation is distinct from a decline in capital goods price which can be utilized by all production units. A simple firm dynamics model is used to show that such an innovation shock enhances reallocation, whereas a shock lowering capital goods price reduces reallocation. This implication is used in structural vector autoregressions to identify innovation shocks as one that explain most of the fluctuations in reallocation measures. By showing the innovation shock and the investmentspecific shock identified by a standard long-run restriction are closely related, the paper provides evidence supporting Schumpeterian creative destruction: technological breakthroughs resulting in an on-going reallocation is a major driver of economic growth and fluctuation.
∗
Department of Economics, Emory University, 1602 Fishburne Drive, Atlanta, GA 30322.
Email: [email protected]
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1
Introduction
Investment-specific technological change has been documented as a major source of business cycle fluctuations (e.g., Greenwood et al. (2000), Fisher (2006), and Justiniano et al. (2010)). This investment-specific technological advances can either represent (1) a fall in the cost of producing capital goods or (2) a quality improvement of a new vintage of capital. As Greenwood et al. (1997) show, these two interpretations are equivalent in a representative firm economy as the same representative firm replaces old capital with new one. The quality-adjusted price index for capital goods should reflect advances in both areas and is commonly used as a measure of investment-specific technological progress. This equivalence, however, no longer holds in a heterogenous firm economy. Less expensive capital good affects investment and disinvestment decisions of all production units. In contrast, only a production unit that possesses necessary skills or knowledge can adopt a new vintage of capital. Hence a capital quality advance better represents innovation or breakthrough leading to the creative destruction: production units keeping up with the new technology will survive and expand whereas ones stuck with obsolete technology contract and decease. I demonstrate this difference by constructing a simple firm dynamics model in a general equilibrium setting. The economy consists of plants, potential entrants, and consumers. Plants produce aggregate output with their plantspecific productivity, and can exit by selling off their capital. The potential entrants are those who possess new technology or investment ideas, and they can build new plants by purchasing capital goods. There are two investmentspecific technological shocks. One lowers the price of capital goods. The other 2
increases average productivity level of new technology that can be implemented only by startups. Both shocks encourage entry and result in an economic boom. However, two shocks have very different impacts on exit. A shock lowering capital goods price enhances entry but deters exit, because the scrap value of capital is also decreased. In contrast, a quality shock increases exit as well as entry: only new capital is more productive, and the widened quality gap makes old capital less valuable in production but more valuable in sell-off. I also consider neutral technological change that affects all production units, and show that its impact on entry and exit is similar to the capital goods price shock as it makes both good and old capital more productive. I then estimate a vector autoregression (VAR) to compare different technological shocks. Motivated by the model, I apply Uhlig (2003)’s method to identify a capital quality or innovation shock as one that accounts for most of the Forecast Error Variance (FEV) of turnover rate, sum of entry and exit rates, over the business cycle horizon. I compare this shock to an investmentspecific shock identified in the manner of Fisher (2006): one that only has permanent impact on capital good price. I find that these two shocks are highly correlated and induce very similar responses. This finding suggests that the investment-specific shocks featured in the business cycle literature mainly reflect innovation shocks, and the disruptive innovation shocks are a major source of business cycle fluctuations. These results are in contrast to Michelacci and Lopez-Salido (2007). They study job reallocation and find advance in neutral technology increases job reallocation, whereas reduction in the price of new capital equipment decreases it. I also find similar results for the sample period 1972:I–1993:IV they study. However, the investment-specific shocks identified by long-run restrictions do increase job reallocation for the later sample period, 1993:II–2012:IV, that 3
this paper focuses on. This suggests a structural change in VAR and calls for further investigation. The findings of this paper provide novel insight into the literature on capital reallocation. Eisfeldt and Rampini (2006) document capital reallocation between firms is procyclical. Because the standard DSGE models with only real frictions in capital reallocation imply countercyclical or acyclical reallocation, the procyclical reallocation has been explained by procyclical capital liquidity.1 This paper offers an alternative and complementary explanation: The literature has considered neutral and capital good price shocks only, but if an innovation shock that widens the gap between good and bad production units is a major source of business cycles, it also implies a procyclial reallocation even in the standard real business cycle models. The rest of this paper is organized as follows. Section 2 use a firm dynamics model to derive the different effects of technological shocks. Section 3 explains my empirical approach. Section 4 presents the empirical results, and Section 5 concludes.
2
Theory
This section derives different implications of technological shocks on reallocation from a general equilibrium model of entry and exit. The model builds on a standard firm dynamics model (e.g., Hopenhayn 1992; more closely, Campbell 1998) with one main difference. The standard models assume a new entrant discovers its idiosyncratic productivity only after entry, whereas this paper follows Lee and Mukoyama (2007) and considers an entry after observing pro1 Eisfeldt and Rampini (2006) offers this explanation, and Cui (2013) and Lanteri (2014) propose models endogenously generating capital illiquidity in recessions.
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ductivity to focus on endogenous determination of average productivity of new plants.
2.1
The Model
The economy consists of plants, potential entrants, and households. A continuum of production units exists. Capital is a fixed factor at the plant level and normalized to one. A plant cannot adjust its capital over the life cycle, and all variation in aggregate capital comes from the extensive margin, that is, from the entry and exit of plants. Each plant with a unit of capital behaves competitively and produces an aggregate good according to yt = (ezt +ωt nt )α . The plant’s output of the aggregate good is yt , and its labor input is nt . Labor can be adjusted freely. The plant’s productivity consists of two components: zt , aggregate productivity common across all plants, and ωt , idiosyncratic productivity specific to each plant. Aggregate and idiosyncratic productivities follow independent random walks: zt+1 = µz + zt + σz zt+1 , zt+1 ∼ i.i.d. (across time) N (0, 1) ωt+1 = ωt + σω ωt+1 ,
ωt+1 ∼ i.i.d. (across time/plants) N (0, 1) (1)
Building a new plant means combining physical capital with new plantspecific technology. In each period, there is a fixed mass of potential entrants who possess new technology: the initial productivity of new technology is
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drawn from a Normal distribution: ωt ∼ N (ut , σe2 ). Once adopted at plant, the idiosyncratic productivity of new technology also evolves by (1). I call this idiosyncratic technology before adoption idea. ut is an aggregate level of the technology that affects the pool of new ideas and evolves by ut+1 = µu + ut + +σu ut+1 ,
ut+1 ∼ i.i.d. N (0, 1)
The progress in the technology ut can only be implemented gradually by entry of new plants, whereas old plants are stuck with the obsolete technology: I call ut+1 innovation shocks. The potential entrant, i.e., the idea owner makes a once-and-for-all decision about entry. If decides to enter, she builds a plant by purchasing a unit of α
capital good. The price of capital goods is given by e− 1−α xt where xt also follows a random walk: xt+1 = µx + xt + σx xt+1 ,
xt+1 ∼ i.i.d. N (0, 1)
If the quality of the idea is not good enough, the idea owner decides not against entry and her idea disappears. Hence the optimal entry decision is characterized by the productivity thresholds ω t above which the idea owner builds a plant and begins operation. Once a plant is built, it acquires a disinvestment option and decides when to sell off its capital and leave the economy. If a plant decides to exit, it α
can recover e− 1−α xt (1 − η) unit of aggregate good. Or it can keep operation 6
and wait, hoping its productivity improves in the future. The exit decision is characterized by the productivity thresholds ω t below which the plant exits. Finally, the economy is populated by a unit measure of identical households with the following utility function in consumption ct and labor nt : vt = max(1 − β) [log ct − κnt ] + βEt [vt+1 ]. ct ,nt
Households supply labor, and finance the investments in plants so that their wealth is held as shares in plants.
2.2
Equilibrium
I solve the social planner’s problem. Let Kt (·) and Ht (·) denote measures, respectively, over plants’ and ideas’ productivity. Also, let φ(·) denote the pdf of the standard Normal distribution. Then the social planner’s problem is V (Kt (·), zt , ut , xt ) =
max Ct ,Nt ,nt (·),ω t ,ω t
(2) (1 − β) [log Ct − κNt ] + βEt [V (Kt+1 (·), zt+1 , ut+1 , xt+1 )]
subject to −α x 1−α t
Z
∞
Z
ωt
Kt (ωt )dωt Yt = C t + e Ht (ωt )dωt − (1 − η) −∞ ωt Z ∞ α Yt = ezt +ωt nt (ωt ) Kt (ωt )dωt Z−∞ ∞ Nt = nt (ωt )Kt (ωt )dωt −∞ Z ∞ 1 ωt+1 − ωt φ Kt (ωt )dωt Kt+1 (ωt+1 ) = (1 − δ) σ ωt σ Z ∞ 1 ωt+1 − ωt + φ Ht (ωt )dωt σ ωt σ 7
(3)
(4)
1 Ht (ωt ) = φ ςe
ωt − ut ςe
× Ht
(5)
where H t is a fixed mass of new idea discovery.2 The social planner optimally chooses aggregate consumption Ct , aggregate labor Nt , labor allocation at each plant nt (·), and entry and exit thresholds ω t , ω t . (4) captures the main dynamics. Ht (·) represents the current stock of ideas. Ideas with good enough productivity (higher than ω t ) are adopted and added to the stock of plants Kt+1 (·) in the next period. This entry deploys R∞ Ht (ωt )dωt amount of capital goods, which represents the total measure of ωt entrants or aggregate investment in this economy. Plants with bad enough productivity (lower than ω t ) exit and disappears from the next period’s stock R ωt of plants. This exit releases (1 − η) −∞ Kt (ωt )dωt amount of capital goods, which represents the total measure of exit or aggregate disinvestment. Note three technology processes zt , ut , xt have distinct effects on this economy. Neutral technology zt raises productivity of new and old plants altogether. Cost-cutting technology in capital goods production xt affects both investment and disinvestment margins equally in (3). Innovation in capital goods quality zt improves productivity level of entrants only in (5). The equilibrium conditions of the model (see Appendix A) are functional equations that require solving for the distribution of plant productivity. To deal with this infinite dimensional problem, I adopt an approach developed by Campbell (1998): approximating the distribution functions by their values at a large but finite set of grid points and then applying a perturbation method that can handle many state variables relatively easily. I obtain the solution by using Dynare (Adjemian et al., 2011). 2
More precisely, H t exogenously grows in step with the stochastic trend of the economy.
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2.3
Effects of Technology Shocks
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Figure 1: Impulse responses of reallocation to a 1% shock to neutral technology zt (top panel), capital quality ut (middle panel), and capital price xt (bottom panel). All deviations are in levels.
Figure 1 displays impulse responses of entry and exit to three aggregate shocks in the model: entry and exit thresholds ω, ω, and entry and exit rates .R .R R∞ R ωt ∞ ∞ Ht (ωt )dωt −∞ Kt (ωt )dωt , −∞ Kt (ωt )dωt −∞ Kt (ωt )dωt . The model ωt period is a quarter, and plots are based on the following parameter values: β = 4%, κ = 2.73, α = 2/3, δ = 0.025, η = 0.2, σω = 0.03, σe = 0.09, 9
µz = 0.15, µu = µz = 0.1. The qualitative results remain intact with different parameter values. All three technology shocks encourage entry. The pool of new ideas H t increases by the same 1%, but a rise in entry (not entry rate) is bigger, which results in a lower entry threshold for neutral and capital price shocks. The incumbent plants then compete with new plants with lower productivity, thereby reducing exit threshold and exit rate. In contrast, an innovation shock increases the average productivity of new ideas as well, making new entrants more productive and pushing out old plants. Hence exit rate rises in this case. The different signs of exit response, of course, depends on how the pool of new ideas respond to shocks, but the different size of exit response does not. Note the response of exit rate is an order of magnitude smaller than that of entry rate in case of neutral and capital price shocks. This comes from the fact that these shocks do not affect new and old plants differently: a neutral technology shock makes both new and old capital more productive, and a capital price shock lowers the value of new capital as well as the scrap value of old capital. In contrast, an innovation shock increases both entry and exit rates by a similar magnitude, enhancing reallocation: only newly deployed capital is more productive, and this widened productivity gap makes old capital less valuable in production but more valuable in sell-off, because it can be used in new investments.3 These results are based on the assumption that exit takes only one period. In reality, the responses of the existing plants to a new wave of entrants will 3
This result is similar to Michelacci and Lopez-Salido (2007), who show in a search model, neutral technological advances increase job destruction and reallocation, whereas investment-specific technological advances that make new capital equipment less expensive reduce job destruction. They assume old plants can adopt neutral technology only with a small probability; hence this technology is closer to capital quality improving technology than neutral technology in my model.
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take substantial time. Time to exit can easily be incorporated into the model without any new insights: the resulting responses of entry and exit will be similar to figure 1 except that entry responses lead entry responses.
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Empirical Approach
3.1
Identification
Consider the vector moving average representation of a VAR: yt = C(L)ut
(6)
where yt is a n × 1 vector, C(L) = I + C1 L + C2 L2 + . . . is a matrix of polynomials in the lag operator L, and ut is a n × 1 vector of one-step-ahead forecasting errors with variance-covariance matrix E[ut u0t ] = Σ. Identification of the structural shocks amounts to finding a matrix A and a vector of mutually orthogonal shocks t such that ut = At . The elements of yt are [∆pt , ∆at , ht , et , xt ]0 where pt is the log of capital good price, at is the log of labor productivity, ht is the log of per capita hours worked, et is the entry rate, xt is the exit rate, and ∆ = 1 − L. This paper identifies innovation shock by extracting the shock that explains the maximal amount of the FEV over business cycle horizon, 6 to 32 quarters, for turnover rate et + xt . This methodology is developed by Uhlig (2003). First, fix A˜ to some arbitrary matrix satisfying Σ = A˜A˜0 . Then finding A is ˜ t . The equivalent to choosing an orthonomal matrix Q such that ut = AQ
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k-step ahead forecast error of the turnover rate is given by et+k + xt+k − Et (et+k + xt+k ) = e0i
" k−1 X
# ˜ t+k−l , Cl AQ
l=0
where ei is a column vector with 1 in the 4th and 5th positions and 0 elsewhere. Let q be a column vector of Q. Then I solve k−1 k=k X X ˜ 0 AC ˜ 0 ei , Cl Aqq q = arg max e0i l q
k=k l=0
so that t = q 0 ut is an innovation shock. For comparison, I identify the investment-specific technology shock following Fisher (2006): I impose all first-row elements except (1, 1) position of C(1)A is equal to zero so that only the investment-specific shock has a long-run impact on capital good price.
3.2
Data
The real capital good price is a investment deflator for equipment and software divided by a consumption deflator for nondurables and services. This series is constructed by Liu et al. (2011)4 : they adopt the method used by Fisher (2006) and extend the series to more recent periods. Labor productivity is measured by the nonfarm business series published by the Bureau of Labor Statistics (BLS). Following Fisher (2006), productivity is also expressed in consumption units using the consumption deflator underlying the capital good price. Per capita hours are measured with the BLS hours series for nonfarm business sector divided by the civilian noninstitutionalized population over the age of 4
I thank Tao Zha for sharing this series.
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16. For entry and exit data, I use rates of total private sector establishment births and deaths from the BLS Business Employment Dynamics (BED) data. These series are quarterly and available since 1993:II. Because first quarter of 2013 data were affected by an administrative change, I use the data series until 2012:IV. The BED defines births as those records that had positive employment in the third month of a quarter and zero employment in the third month of the previous four quarters. Similarly, deaths are units that reported zero employment in the third month of a quarter and did not report positive employment in the third months of the next four quarters. I also consider capital turnover rates used by Eisfeldt and Rampini (2006). They construct two capital turnover rates from annual Compustat data: acquisitions divided by lagged total assets, and sales of property, plant and equipment by lagged total property, plant and equipment. To have more observations, I follow Cui (2013) to construct the corresponding quarterly series from quarterly Compustat data, and apply X-12-ARIMA seasonal adjustment.
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Empirical Findings
The sample period is 1993:II–2012:IV. The baseline VAR are estimated with 4 lags of each variable and a linear time trend (but without imposing a common trend). To compute error bands, I impose a diffuse (Jeffreys) prior and display 68% error bands.
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Labor productivity 2
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Figure 2: Impulse responses to innovation shock based on entry and exit data.
4.1
Baseline Estimates
Figure 2 shows the impulse responses to innovation shock. The investment price keeps falling, and the labor productivity initially jumps up and declines, but quickly rebounds and rises. Hours responds positively and with a hump shape. By identification assumption, both entry and exit rate rise for several years, but their temporal patterns are different. Entry rate immediately rises and gradually declines, whereas the exit rate initially drops but quickly
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fraction of FEV explained
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fraction of FEV explained fraction of FEV explained fraction of FEV explained
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Figure 3: Fraction of forecast error variance (FEV) explained by innovation shock based on entry and exit data
rebounds and stays higher. As mentioned earlier, this pattern of a lagged response of exit is consistent with a version of the model extended to include time to exit. Figure 3 displays the fraction of the FEV explained by the innovation shock. It is striking that innovation shock explains most variation in hours. It also accounts for around 40 percent of investment price and productivity variations 40 quarters ahead. These results show that the identified innovation
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shock is the main driving force of the business cycle fluctuations.
Labor productivity 2
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Figure 4: Impulse responses to investment specific shock based on entry and exit data.
It is noteworthy that the innovation shock accounts for most medium- and longer-term variation in turnover rate. This shock by construction maximizes its contribution among possible shocks, but nothing requires that a single shock can account for 80% of all unpredictable fluctuations in turnover rate. Hence the identified shock is truly a main driver of reallocation. Figure 4 displays the impulse response to investment specific shock identi16
fied by long-run restrictions. It is almost identical to the result for innovation shock. The fraction of the FEV explained by the investment specific shock is also close to identical to figure 3, hence omitted. Fisher (2006) finds the investment specific shock accounts for about a half of hours’ FEV over a horizon of three to eight years in the sample periods of 1982:III–2000:IV. Figure 3 show the importance of investment specific shock is even bigger in more recent periods of 1993:II–2012:IV that this paper studies.
Investment price
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Figure 5: Impulse responses to innovation shock based on capital reallocation data
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Figure 6: Impulse responses to investment specific shock based on capital reallocation data
Figure 5 and figure 6 show the results when capital turnover rates are used in place of entry and exit rates: the elements of yt in (6) are [∆pt , ∆at , ht , trt1 , trt2 ]0 where trt1 is acquisitions divided by lagged total assets, and trt2 is sales of property, plant and equipment by lagged total property, plant and equipment. Innovation shock is again identified as a shock that explains the maximal amount of the FEV of the sum of two turnover rates trt1 + trt2 . Note both turnover rates are reallocation measures, whereas only the sum
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of entry and exit rate represents reallocation in the previous specification. This explains why both turnover rates rise together without lead-lag pattern. The similarity between responses to innovation and investment specific shocks is very clear. The fraction of the FEV explained by these two shocks, though not reported here, is also very similar to the case of entry and exit data: they explain most variation in hours and turnover rates and about 30 to 40 percent of investment price and labor productivity.
4.2
Robustness
This subsection considers a number of potential specification issues. First, the baseline estimates focus on 5-variable VAR system mainly because reallocation measures are available only for a short sample period. However, adding two more variables considered by Fisher (2006), nominal interest rate and inflation, barely change the median estimates. Second, the baseline specification has hours included in log levels. The literature also considers difference of or quadratically detrended hours. These alternatives do not affect the strong correlation between innovation shock and investment specific shock. However, the difference specification changes the contribution of those shocks to hours: only around 40 percent of hours variation is explained by those shocks. Although this size is far smaller than the case of level or quadratic detrended specifications, the contribution is still substantial and confirms that the innovation shock is a major source of business cycles. To illustrate the dependence on the time trend specification, figure 7 and 8 extract the time series of innovation and investment specific shocks and plot them together. I do not show the results of the baseline specification of no
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with linear time trend 4
percent
2 0 −2 −4 −6
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1998
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with quadratic time trend 4
percent
2 0 −2 −4 −6
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Figure 7: Comparison of innovation shock and investment specific shock based on entry and exit data. Correlation coefficients are 0.58 (top panel) and 0.47 (bottom panel).
time trend because the extracted shocks are almost identical with correlation coefficient of 0.95. Although two shocks are not as close as the baseline specification, these figures confirm that two shocks very closely track each other and represent a similar innovation to the economy.
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with linear time trend 2
percent
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Figure 8: Comparison of innovation shock and investment specific shock based on capital reallocation data. Correlation coefficients are 0.88 (top panel) and 0.73 (bottom panel)
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Concluding Remarks
Macroeconomists increasingly recognize the importance of heterogeneity of production units. Most establishment-level uncertainty is idiosyncratic, and substantial amounts of resources are reallocated across different establish21
ments. Motivated by these empirical facts, researchers have developed equilibrium models of heterogenous production units. These models have direct implications on the reallocation dynamics, which the literature has not yet fully exploited. I demonstrate that various technology shocks the business cycle theory considers generate different impacts on reallocation. Based on this implication, I estimate a VAR to show that investment specific shock featured in the business cycle literature is also the shock driving turnover in the economy, that is, encouraging entry and exit or capital reallocation. Creative destruction is often associated with recession. However, the message of this paper is different: technological innovation continuously disrupts the economy while leading it to a boom.
References Adjemian, Stephane, Houtan Bastani, Michel Juillard, Frederic Karame, Ferhat Mihoubi, George Perendia, Johannes Pfeifer, Marco Ratto, and Sebastien Villemot. 2011. Dynare: Reference Manual, Version 4. Dynare Working Paper 1, CEPREMAP. Campbell, Jeffrey R. 1998. Entry, Exit, Embodied Technology, and Business Cycles. Review of Economic Dynamics 1 (2):371–408. Cui, Wei. 2013. Delayed Capital Reallocation. Working Paper. Eisfeldt, Andrea L. and Adriano A. Rampini. 2006. Capital Reallocation and Liquidity. Journal of Monetary Economics 53 (3):369–399.
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Fisher, Jonas D. M. 2006. The Dynamic Effects of Neutral and InvestmentSpecific Technology Shocks. Journal of Political Economy 114 (3):413–451. Greenwood, Jeremy, Zvi Hercowitz, and Per Krusell. 1997. Long-Run Implications of Investment-Specific Technological Change. American Economic Review 87 (3):342–362. ———. 2000. The Role of Investment-Specific Technological Change in the Business Cycle. European Economic Review 44 (1):91–115. Hopenhayn, Hugo A. 1992. Entry, Exit, and Firm Dynamics in Long Run Equilibrium. Econometrica 60 (5):1127–1150. Justiniano, Alejandro and Giorgio E. Primiceri. 2008. The Time-Varying Volatility of Macroeconomic Fluctuations.
American Economic Review
98 (3):604–641. Justiniano, Alejandro, Giorgio E. Primiceri, and Andrea Tambalotti. 2010. Investment Shocks and Business Cycles. Journal of Monetary Economics 57 (2):132–145. Lanteri, Andrea. 2014. The Market for Used Capital: Endogenous Irreversibility and Reallocation over the Business Cycle. Working Paper. Lee, Yoonsoo and Toshihiko Mukoyama. 2007. Entry, Exit, and Plant-level Dynamics over the Business Cycle. Federal Reserve Bank of Cleveland Working Paper 07-18. Liu, Zheng, Daniel F. Waggoner, and Tao Zha. 2011. Sources of Macroeconomic Fluctuations: A Regime-Switching DSGE Approach. Quantitative Economics 2:251–301. 23
Michelacci, Claudio and David Lopez-Salido. 2007. Technology Shocks and Job Flows. Review of Economic Studies 74 (4):1195–1227. Uhlig, Harald. 2003. What Drives GNP? Unpublished.
24
Appendix A
First-order Conditions of the Social Planner’s Problem
This social planner’s problem (7) can be transformed in the following ways. First, note the labor allocation decision is atemporal so it can be solved separately: Z
∞ zt +ωt
max Yt = nt (·)
(e
Z
α
∞
nt (ωt )) Kt (ωt )dωt subject to Nt =
−∞
nt (ωt )Kt (ωt )dωt . −∞
The solution is α
e 1−α ωt b t1−α (ezt Nt )α , where K bt = nt (ωt ) = Nt , Yt = K b Kt
Z
∞
α
e 1−α ωt Kt (ωt )dωt .
−∞
b t is the productivity-weighted capital stock. Second, by replacing Ht (ωt ) K 1 ωt −ut × H t and integrating ωt out, the social planner’s problem can with ςe φ ςe be rewritten as: V (Kt (·), zt , ut , xt ) =
max
Ct ,Nt ,ω t0 ,ω t0
(7)
(1 − β) [log Ct − κNt ] + βEt [V (Kt+1 (·), zt+1 , ut+1 , xt+1 )]
25
subject to −α x 1−α t
b t1−α (ezt Nt )α K
Z ωt ω t − ut Kt (ωt )dωt 1−Φ H t − (1 − η) ςe −∞
= Ct + e Z ∞ α bt = e 1−α ωt Kt (ωt )dωt K −∞ Z ∞ 1 ωt+1 − ωt Kt+1 (ωt+1 ) = (1 − δ) φ Kt (ωt )dωt σ ωt σ ! ςe2 ωt+1 +σ 2 ut ω − t ωt+1 − ut 1 σ 2 +ςe2 H t p φ p 1 − Φ +p σ 2 + ςe2 σ 2 + ςe2 σςe / σ 2 + ςe2
where Φ(·) denote the cdf of the standard Normal distribution. The economy grows because of technological progress. To solve the social planner’s problem, it must be transformed into a stationary one. Expressing idiosyncratic productivity as deviation from idea-embodied productivity (ωt? = ωt − ut−1 ) and dividing all variables except labor and entry/exit thresholds by the corresponding stochastic growth rates (Ct? = Ct /ezt +ut−1 +xt , Kt? (ωt? ) = 1
Kt (ωt? + ut−1 )/ezt +ut−1 + 1−α xt , . . . ) accomplishes this transformation. The resulting stationary problem is: V ? (Kt? (·), ∆ut ) =
max ? ?
? ? ? (1 − β) [log C − κN ] + βE V (K (·), ∆u ) , t t t+1 t t+1 ?
Ct ,It ,Nt ,ω t
subject to b ? )1−α N α (K t t
=
Ct?
? ω t − ∆ut ? H + 1−Φ ςe
26
Z
ω ?t
−(1 − η) Kt? (ωt? )dωt? −∞ Z ∞ α ? b? = e 1−α ωt Kt? (ωt? )dωt? K t −∞ ? Z ∞ 1 ωt+1 − ωt? + ∆ut 1 ∆zt+1 +∆ut + 1−α ∆xt+1 ? ? e Kt+1 (ωt+1 ) = (1 − δ) φ Kt? (ωt? )dωt? ? σ ωt σ ! ? ωt+1 1 +p φ p σ 2 + ςe2 σ 2 + ςe2 2 ? e ω ω ?t − ∆ut − σ2ς+ς 2 t+1 e H ? p × 1 − Φ 2 2 σςe / σ + ςe ?
where H is a constant number. The first-order conditions are as follows: • Optimal labor: 1 κ = ×α Ct?
b t? K Nt
!1−α .
Marginal disutility of labor equals the product of marginal utility of consumption and marginal product of labor. • Plant asset pricing: " ? Qt (ωt+1 ) = Et βe
1 −(∆zt+1 +∆ut + 1−α ∆xt+1 )
? Ct+1 Ct?
−1 (1 − α)
b? K t+1 Nt+1
!−α
? +I(ωt+1 ≤ ω ?t+1 )(1 − η) ? +I(ωt+1 > ω ?t+1 )(1 − δ) ? # Z ∞ ? ωt+2 − ωt+1 + ∆ut+1 1 ? ? × φ Qt+1 (ωt+2 )dωt+2 . σ −∞ σ
? The price of plant with the idiosyncratic productivity ωt+1 is the ex-
27
α
?
e 1−α ωt+1
pected discounted value of the following terms: marginal product of ? ; the resale value of capital if the plant exits; the transiplant with ωt+1 ? ? multiplied by the price of plant with to ωt+2 tion probability from ωt+1 ? ωt+2 if the plant does not exit.
• Optimal entry: 1 φ ςe
ω ?t − ∆ut ςe
Z =
∞
1 p φ σ 2 + ςe2
? ωt+1
!
p σ 2 + ςe2 ςe2 ? ? ω − ∆u − ω t 1 t σ 2 +ςe2 t+1 ? ? Qt (ωt+1 p p )dωt+1 × φ σςe / σ 2 + ςe2 σςe / σ 2 + ςe2 −∞
The marginal benefit of increasing the entry threshold ω ?t is saving the purchase cost of capital. The marginal cost is a drop in the transition ? with experiencing entry, multiplied probability from initial draw to ωt+1 ? by the price of plant with ωt+1 .
• Optimal exit: Z
∞
(1 − η) = (1 − δ) −∞
1 φ σt
? − ω ?t + ∆ut ωt+1 σ
? ? Qt (ωt+1 )dωt+1
The marginal benefit of increasing the exit threshold ω ?t is earning the resale value of capital. The marginal cost is losing a change in the ? transition probability from ωt? to ωt+1 multiplied by the price of plant ? with ωt+1 .
28
Abstract This paper considers an improvement in capital embodied technology which only production units that adapt to new knowledge can utilize. This innovation is distinct from a decline in capital goods price which can be utilized by all production units. A simple firm dynamics model is used to show that such an innovation shock enhances reallocation, whereas a shock lowering capital goods price reduces reallocation. This implication is used in structural vector autoregressions to identify innovation shocks as one that explain most of the fluctuations in reallocation measures. By showing the innovation shock and the investmentspecific shock identified by a standard long-run restriction are closely related, the paper provides evidence supporting Schumpeterian creative destruction: technological breakthroughs resulting in an on-going reallocation is a major driver of economic growth and fluctuation.
∗
Department of Economics, Emory University, 1602 Fishburne Drive, Atlanta, GA 30322.
Email: [email protected]
1
1
Introduction
Investment-specific technological change has been documented as a major source of business cycle fluctuations (e.g., Greenwood et al. (2000), Fisher (2006), and Justiniano et al. (2010)). This investment-specific technological advances can either represent (1) a fall in the cost of producing capital goods or (2) a quality improvement of a new vintage of capital. As Greenwood et al. (1997) show, these two interpretations are equivalent in a representative firm economy as the same representative firm replaces old capital with new one. The quality-adjusted price index for capital goods should reflect advances in both areas and is commonly used as a measure of investment-specific technological progress. This equivalence, however, no longer holds in a heterogenous firm economy. Less expensive capital good affects investment and disinvestment decisions of all production units. In contrast, only a production unit that possesses necessary skills or knowledge can adopt a new vintage of capital. Hence a capital quality advance better represents innovation or breakthrough leading to the creative destruction: production units keeping up with the new technology will survive and expand whereas ones stuck with obsolete technology contract and decease. I demonstrate this difference by constructing a simple firm dynamics model in a general equilibrium setting. The economy consists of plants, potential entrants, and consumers. Plants produce aggregate output with their plantspecific productivity, and can exit by selling off their capital. The potential entrants are those who possess new technology or investment ideas, and they can build new plants by purchasing capital goods. There are two investmentspecific technological shocks. One lowers the price of capital goods. The other 2
increases average productivity level of new technology that can be implemented only by startups. Both shocks encourage entry and result in an economic boom. However, two shocks have very different impacts on exit. A shock lowering capital goods price enhances entry but deters exit, because the scrap value of capital is also decreased. In contrast, a quality shock increases exit as well as entry: only new capital is more productive, and the widened quality gap makes old capital less valuable in production but more valuable in sell-off. I also consider neutral technological change that affects all production units, and show that its impact on entry and exit is similar to the capital goods price shock as it makes both good and old capital more productive. I then estimate a vector autoregression (VAR) to compare different technological shocks. Motivated by the model, I apply Uhlig (2003)’s method to identify a capital quality or innovation shock as one that accounts for most of the Forecast Error Variance (FEV) of turnover rate, sum of entry and exit rates, over the business cycle horizon. I compare this shock to an investmentspecific shock identified in the manner of Fisher (2006): one that only has permanent impact on capital good price. I find that these two shocks are highly correlated and induce very similar responses. This finding suggests that the investment-specific shocks featured in the business cycle literature mainly reflect innovation shocks, and the disruptive innovation shocks are a major source of business cycle fluctuations. These results are in contrast to Michelacci and Lopez-Salido (2007). They study job reallocation and find advance in neutral technology increases job reallocation, whereas reduction in the price of new capital equipment decreases it. I also find similar results for the sample period 1972:I–1993:IV they study. However, the investment-specific shocks identified by long-run restrictions do increase job reallocation for the later sample period, 1993:II–2012:IV, that 3
this paper focuses on. This suggests a structural change in VAR and calls for further investigation. The findings of this paper provide novel insight into the literature on capital reallocation. Eisfeldt and Rampini (2006) document capital reallocation between firms is procyclical. Because the standard DSGE models with only real frictions in capital reallocation imply countercyclical or acyclical reallocation, the procyclical reallocation has been explained by procyclical capital liquidity.1 This paper offers an alternative and complementary explanation: The literature has considered neutral and capital good price shocks only, but if an innovation shock that widens the gap between good and bad production units is a major source of business cycles, it also implies a procyclial reallocation even in the standard real business cycle models. The rest of this paper is organized as follows. Section 2 use a firm dynamics model to derive the different effects of technological shocks. Section 3 explains my empirical approach. Section 4 presents the empirical results, and Section 5 concludes.
2
Theory
This section derives different implications of technological shocks on reallocation from a general equilibrium model of entry and exit. The model builds on a standard firm dynamics model (e.g., Hopenhayn 1992; more closely, Campbell 1998) with one main difference. The standard models assume a new entrant discovers its idiosyncratic productivity only after entry, whereas this paper follows Lee and Mukoyama (2007) and considers an entry after observing pro1 Eisfeldt and Rampini (2006) offers this explanation, and Cui (2013) and Lanteri (2014) propose models endogenously generating capital illiquidity in recessions.
4
ductivity to focus on endogenous determination of average productivity of new plants.
2.1
The Model
The economy consists of plants, potential entrants, and households. A continuum of production units exists. Capital is a fixed factor at the plant level and normalized to one. A plant cannot adjust its capital over the life cycle, and all variation in aggregate capital comes from the extensive margin, that is, from the entry and exit of plants. Each plant with a unit of capital behaves competitively and produces an aggregate good according to yt = (ezt +ωt nt )α . The plant’s output of the aggregate good is yt , and its labor input is nt . Labor can be adjusted freely. The plant’s productivity consists of two components: zt , aggregate productivity common across all plants, and ωt , idiosyncratic productivity specific to each plant. Aggregate and idiosyncratic productivities follow independent random walks: zt+1 = µz + zt + σz zt+1 , zt+1 ∼ i.i.d. (across time) N (0, 1) ωt+1 = ωt + σω ωt+1 ,
ωt+1 ∼ i.i.d. (across time/plants) N (0, 1) (1)
Building a new plant means combining physical capital with new plantspecific technology. In each period, there is a fixed mass of potential entrants who possess new technology: the initial productivity of new technology is
5
drawn from a Normal distribution: ωt ∼ N (ut , σe2 ). Once adopted at plant, the idiosyncratic productivity of new technology also evolves by (1). I call this idiosyncratic technology before adoption idea. ut is an aggregate level of the technology that affects the pool of new ideas and evolves by ut+1 = µu + ut + +σu ut+1 ,
ut+1 ∼ i.i.d. N (0, 1)
The progress in the technology ut can only be implemented gradually by entry of new plants, whereas old plants are stuck with the obsolete technology: I call ut+1 innovation shocks. The potential entrant, i.e., the idea owner makes a once-and-for-all decision about entry. If decides to enter, she builds a plant by purchasing a unit of α
capital good. The price of capital goods is given by e− 1−α xt where xt also follows a random walk: xt+1 = µx + xt + σx xt+1 ,
xt+1 ∼ i.i.d. N (0, 1)
If the quality of the idea is not good enough, the idea owner decides not against entry and her idea disappears. Hence the optimal entry decision is characterized by the productivity thresholds ω t above which the idea owner builds a plant and begins operation. Once a plant is built, it acquires a disinvestment option and decides when to sell off its capital and leave the economy. If a plant decides to exit, it α
can recover e− 1−α xt (1 − η) unit of aggregate good. Or it can keep operation 6
and wait, hoping its productivity improves in the future. The exit decision is characterized by the productivity thresholds ω t below which the plant exits. Finally, the economy is populated by a unit measure of identical households with the following utility function in consumption ct and labor nt : vt = max(1 − β) [log ct − κnt ] + βEt [vt+1 ]. ct ,nt
Households supply labor, and finance the investments in plants so that their wealth is held as shares in plants.
2.2
Equilibrium
I solve the social planner’s problem. Let Kt (·) and Ht (·) denote measures, respectively, over plants’ and ideas’ productivity. Also, let φ(·) denote the pdf of the standard Normal distribution. Then the social planner’s problem is V (Kt (·), zt , ut , xt ) =
max Ct ,Nt ,nt (·),ω t ,ω t
(2) (1 − β) [log Ct − κNt ] + βEt [V (Kt+1 (·), zt+1 , ut+1 , xt+1 )]
subject to −α x 1−α t
Z
∞
Z
ωt
Kt (ωt )dωt Yt = C t + e Ht (ωt )dωt − (1 − η) −∞ ωt Z ∞ α Yt = ezt +ωt nt (ωt ) Kt (ωt )dωt Z−∞ ∞ Nt = nt (ωt )Kt (ωt )dωt −∞ Z ∞ 1 ωt+1 − ωt φ Kt (ωt )dωt Kt+1 (ωt+1 ) = (1 − δ) σ ωt σ Z ∞ 1 ωt+1 − ωt + φ Ht (ωt )dωt σ ωt σ 7
(3)
(4)
1 Ht (ωt ) = φ ςe
ωt − ut ςe
× Ht
(5)
where H t is a fixed mass of new idea discovery.2 The social planner optimally chooses aggregate consumption Ct , aggregate labor Nt , labor allocation at each plant nt (·), and entry and exit thresholds ω t , ω t . (4) captures the main dynamics. Ht (·) represents the current stock of ideas. Ideas with good enough productivity (higher than ω t ) are adopted and added to the stock of plants Kt+1 (·) in the next period. This entry deploys R∞ Ht (ωt )dωt amount of capital goods, which represents the total measure of ωt entrants or aggregate investment in this economy. Plants with bad enough productivity (lower than ω t ) exit and disappears from the next period’s stock R ωt of plants. This exit releases (1 − η) −∞ Kt (ωt )dωt amount of capital goods, which represents the total measure of exit or aggregate disinvestment. Note three technology processes zt , ut , xt have distinct effects on this economy. Neutral technology zt raises productivity of new and old plants altogether. Cost-cutting technology in capital goods production xt affects both investment and disinvestment margins equally in (3). Innovation in capital goods quality zt improves productivity level of entrants only in (5). The equilibrium conditions of the model (see Appendix A) are functional equations that require solving for the distribution of plant productivity. To deal with this infinite dimensional problem, I adopt an approach developed by Campbell (1998): approximating the distribution functions by their values at a large but finite set of grid points and then applying a perturbation method that can handle many state variables relatively easily. I obtain the solution by using Dynare (Adjemian et al., 2011). 2
More precisely, H t exogenously grows in step with the stochastic trend of the economy.
8
2.3
Effects of Technology Shocks
−4
x 10
entry threshol d
−4
x 10
0
0
exi t threshol d
−4
x 10
entry rate
−5
x 10
6
−0.5
5
−1
4
−1.5
3
−2
2
−2.5
1
0
−1
exi t rate
−2
−2
−4
−3
−6
−4
−3 10
20
30
0
40
10
entry threshol d 0.01
0.01
0.008
0.008
0.006
0.006
0.004
0.004
0.002
0.002
0
20
30
exi t threshol d
−3
x 10
20
30
−3
10
entry threshol d
−3
x 10 0
−0.2
−0.2
20
30
40
20
30
entry rate
−3
x 10 1.5
1
1
0.5
0.5
20
30
40
30
40
30
40
exi t rate
0
40
exi t threshol d
10
1.5
0
40
0
10
x 10
0 10
−8
40
10
−3
x 10
20
30
40
10
entry rate
−4
x 10
2
0
1.5
−0.5
1
−1
0.5
−1.5
20
exi t rate
−0.4 −0.4 −0.6 −0.6 −0.8 −0.8
−1 −1.2
−1 10
20
30
40
0 10
20
30
40
−2 10
20
30
40
10
20
Figure 1: Impulse responses of reallocation to a 1% shock to neutral technology zt (top panel), capital quality ut (middle panel), and capital price xt (bottom panel). All deviations are in levels.
Figure 1 displays impulse responses of entry and exit to three aggregate shocks in the model: entry and exit thresholds ω, ω, and entry and exit rates .R .R R∞ R ωt ∞ ∞ Ht (ωt )dωt −∞ Kt (ωt )dωt , −∞ Kt (ωt )dωt −∞ Kt (ωt )dωt . The model ωt period is a quarter, and plots are based on the following parameter values: β = 4%, κ = 2.73, α = 2/3, δ = 0.025, η = 0.2, σω = 0.03, σe = 0.09, 9
µz = 0.15, µu = µz = 0.1. The qualitative results remain intact with different parameter values. All three technology shocks encourage entry. The pool of new ideas H t increases by the same 1%, but a rise in entry (not entry rate) is bigger, which results in a lower entry threshold for neutral and capital price shocks. The incumbent plants then compete with new plants with lower productivity, thereby reducing exit threshold and exit rate. In contrast, an innovation shock increases the average productivity of new ideas as well, making new entrants more productive and pushing out old plants. Hence exit rate rises in this case. The different signs of exit response, of course, depends on how the pool of new ideas respond to shocks, but the different size of exit response does not. Note the response of exit rate is an order of magnitude smaller than that of entry rate in case of neutral and capital price shocks. This comes from the fact that these shocks do not affect new and old plants differently: a neutral technology shock makes both new and old capital more productive, and a capital price shock lowers the value of new capital as well as the scrap value of old capital. In contrast, an innovation shock increases both entry and exit rates by a similar magnitude, enhancing reallocation: only newly deployed capital is more productive, and this widened productivity gap makes old capital less valuable in production but more valuable in sell-off, because it can be used in new investments.3 These results are based on the assumption that exit takes only one period. In reality, the responses of the existing plants to a new wave of entrants will 3
This result is similar to Michelacci and Lopez-Salido (2007), who show in a search model, neutral technological advances increase job destruction and reallocation, whereas investment-specific technological advances that make new capital equipment less expensive reduce job destruction. They assume old plants can adopt neutral technology only with a small probability; hence this technology is closer to capital quality improving technology than neutral technology in my model.
10
take substantial time. Time to exit can easily be incorporated into the model without any new insights: the resulting responses of entry and exit will be similar to figure 1 except that entry responses lead entry responses.
3
Empirical Approach
3.1
Identification
Consider the vector moving average representation of a VAR: yt = C(L)ut
(6)
where yt is a n × 1 vector, C(L) = I + C1 L + C2 L2 + . . . is a matrix of polynomials in the lag operator L, and ut is a n × 1 vector of one-step-ahead forecasting errors with variance-covariance matrix E[ut u0t ] = Σ. Identification of the structural shocks amounts to finding a matrix A and a vector of mutually orthogonal shocks t such that ut = At . The elements of yt are [∆pt , ∆at , ht , et , xt ]0 where pt is the log of capital good price, at is the log of labor productivity, ht is the log of per capita hours worked, et is the entry rate, xt is the exit rate, and ∆ = 1 − L. This paper identifies innovation shock by extracting the shock that explains the maximal amount of the FEV over business cycle horizon, 6 to 32 quarters, for turnover rate et + xt . This methodology is developed by Uhlig (2003). First, fix A˜ to some arbitrary matrix satisfying Σ = A˜A˜0 . Then finding A is ˜ t . The equivalent to choosing an orthonomal matrix Q such that ut = AQ
11
k-step ahead forecast error of the turnover rate is given by et+k + xt+k − Et (et+k + xt+k ) = e0i
" k−1 X
# ˜ t+k−l , Cl AQ
l=0
where ei is a column vector with 1 in the 4th and 5th positions and 0 elsewhere. Let q be a column vector of Q. Then I solve k−1 k=k X X ˜ 0 AC ˜ 0 ei , Cl Aqq q = arg max e0i l q
k=k l=0
so that t = q 0 ut is an innovation shock. For comparison, I identify the investment-specific technology shock following Fisher (2006): I impose all first-row elements except (1, 1) position of C(1)A is equal to zero so that only the investment-specific shock has a long-run impact on capital good price.
3.2
Data
The real capital good price is a investment deflator for equipment and software divided by a consumption deflator for nondurables and services. This series is constructed by Liu et al. (2011)4 : they adopt the method used by Fisher (2006) and extend the series to more recent periods. Labor productivity is measured by the nonfarm business series published by the Bureau of Labor Statistics (BLS). Following Fisher (2006), productivity is also expressed in consumption units using the consumption deflator underlying the capital good price. Per capita hours are measured with the BLS hours series for nonfarm business sector divided by the civilian noninstitutionalized population over the age of 4
I thank Tao Zha for sharing this series.
12
16. For entry and exit data, I use rates of total private sector establishment births and deaths from the BLS Business Employment Dynamics (BED) data. These series are quarterly and available since 1993:II. Because first quarter of 2013 data were affected by an administrative change, I use the data series until 2012:IV. The BED defines births as those records that had positive employment in the third month of a quarter and zero employment in the third month of the previous four quarters. Similarly, deaths are units that reported zero employment in the third month of a quarter and did not report positive employment in the third months of the next four quarters. I also consider capital turnover rates used by Eisfeldt and Rampini (2006). They construct two capital turnover rates from annual Compustat data: acquisitions divided by lagged total assets, and sales of property, plant and equipment by lagged total property, plant and equipment. To have more observations, I follow Cui (2013) to construct the corresponding quarterly series from quarterly Compustat data, and apply X-12-ARIMA seasonal adjustment.
4
Empirical Findings
The sample period is 1993:II–2012:IV. The baseline VAR are estimated with 4 lags of each variable and a linear time trend (but without imposing a common trend). To compute error bands, I impose a diffuse (Jeffreys) prior and display 68% error bands.
13
Labor productivity 2
−1
1.5
percent
percent
Investment price 0
−2 −3
1 0.5 0
−4 5
10
15
20
25
30
35
40
5
10
15
20
25
quarters
quarters
Hours
Entry rate
30
35
40
30
35
40
30
35
40
2
percent
percent
0.1
1
0
0 5
10
15
20
25
30
35
40
5
10
15
20
25
quarters
quarters
Exit rate
Turnover rate
0.05
0.1
percent
percent
0.05
0 −0.05 5
10
15
20
25
30
35
40
0.05 0
5
quarters
10
15
20
25
quarters
Figure 2: Impulse responses to innovation shock based on entry and exit data.
4.1
Baseline Estimates
Figure 2 shows the impulse responses to innovation shock. The investment price keeps falling, and the labor productivity initially jumps up and declines, but quickly rebounds and rises. Hours responds positively and with a hump shape. By identification assumption, both entry and exit rate rise for several years, but their temporal patterns are different. Entry rate immediately rises and gradually declines, whereas the exit rate initially drops but quickly
14
fraction of FEV explained
0.5
0
0
10
20
30
40
quarters
fraction of FEV explained
Hours 1
0.5
0
0
10
20
30
40
quarters
Exit rate
fraction of FEV explained
fraction of FEV explained fraction of FEV explained fraction of FEV explained
Investment price 1
1
0.5
0
0
10
20
30
40
quarters
Labor productivity 1
0.5
0
0
10
20
30
40
30
40
30
40
quarters
Entry rate 1
0.5
0
0
10
20
quarters
Turnover rate 1
0.5
0
0
10
20
quarters
Figure 3: Fraction of forecast error variance (FEV) explained by innovation shock based on entry and exit data
rebounds and stays higher. As mentioned earlier, this pattern of a lagged response of exit is consistent with a version of the model extended to include time to exit. Figure 3 displays the fraction of the FEV explained by the innovation shock. It is striking that innovation shock explains most variation in hours. It also accounts for around 40 percent of investment price and productivity variations 40 quarters ahead. These results show that the identified innovation
15
shock is the main driving force of the business cycle fluctuations.
Labor productivity 2
−1
1.5
percent
percent
Investment price 0
−2 −3
1 0.5 0
−4 5
10
15
20
25
30
35
40
5
10
15
20
25
quarters
quarters
Hours
Entry rate
30
35
40
30
35
40
30
35
40
percent
percent
0.1 2 1
0
0 5
10
15
20
25
30
35
40
5
10
15
20
25
quarters
quarters
Exit rate
Turnover rate
0.05
0.1
percent
percent
0.05
0
0.05 0
−0.05 5
10
15
20
25
30
35
40
5
10
15
quarters
20
25
quarters
Figure 4: Impulse responses to investment specific shock based on entry and exit data.
It is noteworthy that the innovation shock accounts for most medium- and longer-term variation in turnover rate. This shock by construction maximizes its contribution among possible shocks, but nothing requires that a single shock can account for 80% of all unpredictable fluctuations in turnover rate. Hence the identified shock is truly a main driver of reallocation. Figure 4 displays the impulse response to investment specific shock identi16
fied by long-run restrictions. It is almost identical to the result for innovation shock. The fraction of the FEV explained by the investment specific shock is also close to identical to figure 3, hence omitted. Fisher (2006) finds the investment specific shock accounts for about a half of hours’ FEV over a horizon of three to eight years in the sample periods of 1982:III–2000:IV. Figure 3 show the importance of investment specific shock is even bigger in more recent periods of 1993:II–2012:IV that this paper studies.
Investment price
Labor productivity
0
percent
percent
1.5 −1 −2
1 0.5 0
−3 5
10
15
20
25
30
35
40
5
10
15
20
25
30
quarters
quarters
Hours
Acquisitions turnover rate
35
40
35
40
35
40
0.02
percent
percent
2 1.5 1 0.5 0
0 −0.02
5
10
15
20
25
30
35
40
5
10
15
quarters
20
25
30
quarters
Property sale turnover rate
Sum of turnover rates 0.06
0.04
percent
percent
0.04 0.02 0
0.02 0 −0.02 −0.04
−0.02 5
10
15
20
25
30
35
40
5
quarters
10
15
20
25
30
quarters
Figure 5: Impulse responses to innovation shock based on capital reallocation data
17
Investment price
Labor productivity
0
percent
percent
1.5 −1 −2 −3
0.5 0
5
10
15
20
25
30
35
40
5
10
15
20
25
30
quarters
quarters
Hours
Acquisitions turnover rate
2
35
40
35
40
35
40
0.02
1.5
percent
percent
1
1 0.5
0 −0.02
0 5
10
15
20
25
30
35
40
5
10
15
quarters
20
25
30
quarters
Property sale turnover rate
Sum of turnover rates 0.06
0.04
percent
percent
0.04 0.02 0
0.02 0 −0.02 −0.04
−0.02 5
10
15
20
25
30
35
40
5
10
quarters
15
20
25
30
quarters
Figure 6: Impulse responses to investment specific shock based on capital reallocation data
Figure 5 and figure 6 show the results when capital turnover rates are used in place of entry and exit rates: the elements of yt in (6) are [∆pt , ∆at , ht , trt1 , trt2 ]0 where trt1 is acquisitions divided by lagged total assets, and trt2 is sales of property, plant and equipment by lagged total property, plant and equipment. Innovation shock is again identified as a shock that explains the maximal amount of the FEV of the sum of two turnover rates trt1 + trt2 . Note both turnover rates are reallocation measures, whereas only the sum
18
of entry and exit rate represents reallocation in the previous specification. This explains why both turnover rates rise together without lead-lag pattern. The similarity between responses to innovation and investment specific shocks is very clear. The fraction of the FEV explained by these two shocks, though not reported here, is also very similar to the case of entry and exit data: they explain most variation in hours and turnover rates and about 30 to 40 percent of investment price and labor productivity.
4.2
Robustness
This subsection considers a number of potential specification issues. First, the baseline estimates focus on 5-variable VAR system mainly because reallocation measures are available only for a short sample period. However, adding two more variables considered by Fisher (2006), nominal interest rate and inflation, barely change the median estimates. Second, the baseline specification has hours included in log levels. The literature also considers difference of or quadratically detrended hours. These alternatives do not affect the strong correlation between innovation shock and investment specific shock. However, the difference specification changes the contribution of those shocks to hours: only around 40 percent of hours variation is explained by those shocks. Although this size is far smaller than the case of level or quadratic detrended specifications, the contribution is still substantial and confirms that the innovation shock is a major source of business cycles. To illustrate the dependence on the time trend specification, figure 7 and 8 extract the time series of innovation and investment specific shocks and plot them together. I do not show the results of the baseline specification of no
19
with linear time trend 4
percent
2 0 −2 −4 −6
1996
1998
2000
2002
2004
2006
2008
2010
2012
2008
2010
2012
with quadratic time trend 4
percent
2 0 −2 −4 −6
1996
1998
2000
2002
2004
2006
Figure 7: Comparison of innovation shock and investment specific shock based on entry and exit data. Correlation coefficients are 0.58 (top panel) and 0.47 (bottom panel).
time trend because the extracted shocks are almost identical with correlation coefficient of 0.95. Although two shocks are not as close as the baseline specification, these figures confirm that two shocks very closely track each other and represent a similar innovation to the economy.
20
with linear time trend 2
percent
0
−2
−4
−6
1996
1998
2000
2002
2004
2006
2008
2010
2012
2008
2010
2012
with quadratic time trend 4
percent
2 0 −2 −4 −6
1996
1998
2000
2002
2004
2006
Figure 8: Comparison of innovation shock and investment specific shock based on capital reallocation data. Correlation coefficients are 0.88 (top panel) and 0.73 (bottom panel)
5
Concluding Remarks
Macroeconomists increasingly recognize the importance of heterogeneity of production units. Most establishment-level uncertainty is idiosyncratic, and substantial amounts of resources are reallocated across different establish21
ments. Motivated by these empirical facts, researchers have developed equilibrium models of heterogenous production units. These models have direct implications on the reallocation dynamics, which the literature has not yet fully exploited. I demonstrate that various technology shocks the business cycle theory considers generate different impacts on reallocation. Based on this implication, I estimate a VAR to show that investment specific shock featured in the business cycle literature is also the shock driving turnover in the economy, that is, encouraging entry and exit or capital reallocation. Creative destruction is often associated with recession. However, the message of this paper is different: technological innovation continuously disrupts the economy while leading it to a boom.
References Adjemian, Stephane, Houtan Bastani, Michel Juillard, Frederic Karame, Ferhat Mihoubi, George Perendia, Johannes Pfeifer, Marco Ratto, and Sebastien Villemot. 2011. Dynare: Reference Manual, Version 4. Dynare Working Paper 1, CEPREMAP. Campbell, Jeffrey R. 1998. Entry, Exit, Embodied Technology, and Business Cycles. Review of Economic Dynamics 1 (2):371–408. Cui, Wei. 2013. Delayed Capital Reallocation. Working Paper. Eisfeldt, Andrea L. and Adriano A. Rampini. 2006. Capital Reallocation and Liquidity. Journal of Monetary Economics 53 (3):369–399.
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Fisher, Jonas D. M. 2006. The Dynamic Effects of Neutral and InvestmentSpecific Technology Shocks. Journal of Political Economy 114 (3):413–451. Greenwood, Jeremy, Zvi Hercowitz, and Per Krusell. 1997. Long-Run Implications of Investment-Specific Technological Change. American Economic Review 87 (3):342–362. ———. 2000. The Role of Investment-Specific Technological Change in the Business Cycle. European Economic Review 44 (1):91–115. Hopenhayn, Hugo A. 1992. Entry, Exit, and Firm Dynamics in Long Run Equilibrium. Econometrica 60 (5):1127–1150. Justiniano, Alejandro and Giorgio E. Primiceri. 2008. The Time-Varying Volatility of Macroeconomic Fluctuations.
American Economic Review
98 (3):604–641. Justiniano, Alejandro, Giorgio E. Primiceri, and Andrea Tambalotti. 2010. Investment Shocks and Business Cycles. Journal of Monetary Economics 57 (2):132–145. Lanteri, Andrea. 2014. The Market for Used Capital: Endogenous Irreversibility and Reallocation over the Business Cycle. Working Paper. Lee, Yoonsoo and Toshihiko Mukoyama. 2007. Entry, Exit, and Plant-level Dynamics over the Business Cycle. Federal Reserve Bank of Cleveland Working Paper 07-18. Liu, Zheng, Daniel F. Waggoner, and Tao Zha. 2011. Sources of Macroeconomic Fluctuations: A Regime-Switching DSGE Approach. Quantitative Economics 2:251–301. 23
Michelacci, Claudio and David Lopez-Salido. 2007. Technology Shocks and Job Flows. Review of Economic Studies 74 (4):1195–1227. Uhlig, Harald. 2003. What Drives GNP? Unpublished.
24
Appendix A
First-order Conditions of the Social Planner’s Problem
This social planner’s problem (7) can be transformed in the following ways. First, note the labor allocation decision is atemporal so it can be solved separately: Z
∞ zt +ωt
max Yt = nt (·)
(e
Z
α
∞
nt (ωt )) Kt (ωt )dωt subject to Nt =
−∞
nt (ωt )Kt (ωt )dωt . −∞
The solution is α
e 1−α ωt b t1−α (ezt Nt )α , where K bt = nt (ωt ) = Nt , Yt = K b Kt
Z
∞
α
e 1−α ωt Kt (ωt )dωt .
−∞
b t is the productivity-weighted capital stock. Second, by replacing Ht (ωt ) K 1 ωt −ut × H t and integrating ωt out, the social planner’s problem can with ςe φ ςe be rewritten as: V (Kt (·), zt , ut , xt ) =
max
Ct ,Nt ,ω t0 ,ω t0
(7)
(1 − β) [log Ct − κNt ] + βEt [V (Kt+1 (·), zt+1 , ut+1 , xt+1 )]
25
subject to −α x 1−α t
b t1−α (ezt Nt )α K
Z ωt ω t − ut Kt (ωt )dωt 1−Φ H t − (1 − η) ςe −∞
= Ct + e Z ∞ α bt = e 1−α ωt Kt (ωt )dωt K −∞ Z ∞ 1 ωt+1 − ωt Kt+1 (ωt+1 ) = (1 − δ) φ Kt (ωt )dωt σ ωt σ ! ςe2 ωt+1 +σ 2 ut ω − t ωt+1 − ut 1 σ 2 +ςe2 H t p φ p 1 − Φ +p σ 2 + ςe2 σ 2 + ςe2 σςe / σ 2 + ςe2
where Φ(·) denote the cdf of the standard Normal distribution. The economy grows because of technological progress. To solve the social planner’s problem, it must be transformed into a stationary one. Expressing idiosyncratic productivity as deviation from idea-embodied productivity (ωt? = ωt − ut−1 ) and dividing all variables except labor and entry/exit thresholds by the corresponding stochastic growth rates (Ct? = Ct /ezt +ut−1 +xt , Kt? (ωt? ) = 1
Kt (ωt? + ut−1 )/ezt +ut−1 + 1−α xt , . . . ) accomplishes this transformation. The resulting stationary problem is: V ? (Kt? (·), ∆ut ) =
max ? ?
? ? ? (1 − β) [log C − κN ] + βE V (K (·), ∆u ) , t t t+1 t t+1 ?
Ct ,It ,Nt ,ω t
subject to b ? )1−α N α (K t t
=
Ct?
? ω t − ∆ut ? H + 1−Φ ςe
26
Z
ω ?t
−(1 − η) Kt? (ωt? )dωt? −∞ Z ∞ α ? b? = e 1−α ωt Kt? (ωt? )dωt? K t −∞ ? Z ∞ 1 ωt+1 − ωt? + ∆ut 1 ∆zt+1 +∆ut + 1−α ∆xt+1 ? ? e Kt+1 (ωt+1 ) = (1 − δ) φ Kt? (ωt? )dωt? ? σ ωt σ ! ? ωt+1 1 +p φ p σ 2 + ςe2 σ 2 + ςe2 2 ? e ω ω ?t − ∆ut − σ2ς+ς 2 t+1 e H ? p × 1 − Φ 2 2 σςe / σ + ςe ?
where H is a constant number. The first-order conditions are as follows: • Optimal labor: 1 κ = ×α Ct?
b t? K Nt
!1−α .
Marginal disutility of labor equals the product of marginal utility of consumption and marginal product of labor. • Plant asset pricing: " ? Qt (ωt+1 ) = Et βe
1 −(∆zt+1 +∆ut + 1−α ∆xt+1 )
? Ct+1 Ct?
−1 (1 − α)
b? K t+1 Nt+1
!−α
? +I(ωt+1 ≤ ω ?t+1 )(1 − η) ? +I(ωt+1 > ω ?t+1 )(1 − δ) ? # Z ∞ ? ωt+2 − ωt+1 + ∆ut+1 1 ? ? × φ Qt+1 (ωt+2 )dωt+2 . σ −∞ σ
? The price of plant with the idiosyncratic productivity ωt+1 is the ex-
27
α
?
e 1−α ωt+1
pected discounted value of the following terms: marginal product of ? ; the resale value of capital if the plant exits; the transiplant with ωt+1 ? ? multiplied by the price of plant with to ωt+2 tion probability from ωt+1 ? ωt+2 if the plant does not exit.
• Optimal entry: 1 φ ςe
ω ?t − ∆ut ςe
Z =
∞
1 p φ σ 2 + ςe2
? ωt+1
!
p σ 2 + ςe2 ςe2 ? ? ω − ∆u − ω t 1 t σ 2 +ςe2 t+1 ? ? Qt (ωt+1 p p )dωt+1 × φ σςe / σ 2 + ςe2 σςe / σ 2 + ςe2 −∞
The marginal benefit of increasing the entry threshold ω ?t is saving the purchase cost of capital. The marginal cost is a drop in the transition ? with experiencing entry, multiplied probability from initial draw to ωt+1 ? by the price of plant with ωt+1 .
• Optimal exit: Z
∞
(1 − η) = (1 − δ) −∞
1 φ σt
? − ω ?t + ∆ut ωt+1 σ
? ? Qt (ωt+1 )dωt+1
The marginal benefit of increasing the exit threshold ω ?t is earning the resale value of capital. The marginal cost is losing a change in the ? transition probability from ωt? to ωt+1 multiplied by the price of plant ? with ωt+1 .
28
