Investment-Specific Shocks and Cyclical Fluctuations in the Labor Market Jos´e I. Silva∗

Manuel Toledo†

October 5, 2007

Abstract This paper studies the role of investment-specific shocks as an amplification mechanism in the labor market. We are motivated by recent empirical evidence that suggests that investment-specific shocks are key for labor market dynamics. We show evidence that supports this previous finding. Moreover, we study the quantitative impact of this type of shocks on the labor market by incorporating them into a Real Business Cycle model with search and matching frictions, and endogenous capital utilization. We find that in our model these shocks have no direct amplification effect on labor market fluctuations. Thus, the model cannot match the magnitude of the volatility in vacancies and unemployment without generating too much variation in output.

∗ †

Universitat Jaume I de Castell´o, Email: [email protected] Universidad Carlos III de Madrid. Email: [email protected]

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1

Introduction

Real Business Cycle (RBC) theory stresses that neutral technology shocks are a major source of economic fluctuations. However, a main problem with this driving force is the need to incorporate unrealistic large shocks to reproduce some business cycle facts (see King and Rebelo, 1999, for a discussion). Similarly, studying the U.S. labor market behavior in a standard search and matching model, Shimer (2005) has shown that reasonable shocks to labor productivity do not help reproduce the cyclical fluctuations in relevant labor market outcomes such as vacancies and unemployment. This suggests that there exist other important sources of aggregate fluctuation beyond standard productivity shocks. One natural alternative to neutral technology shocks is investment-specific technological change. Greenwood, Hercowitz, and Huffman (1988) are the first to study the quantitative implications for business cycle fluctuations of direct investment shocks. Their results suggest that this type of shocks may be important for the understanding of business cycles. More recently, Greenwood, Hercowitz, and Krusell (2000) investigate the quantitative importance of investment-specific technological change for postwar U.S. aggregate fluctuations. They find that this form of technological change accounts for about 30 percent of output fluctuations. In a empirical study, Fisher (2006) shows that when neutral and investmentspecific technology shocks are combined they account for 44 and 88 percent of the fluctuations in the U.S. output at business cycle frequencies before and after 1982, respectively. Similarly, both shocks account for 73 and 38 percent of hours’ business cycle variation. Fisher claims that investment-specific shocks are responsible for most of these effects. Ravn and Simonelli (2006) also find evidence that this type of shocks are important for business cycle fluctuations not only in output but also in labor market indicators, such as vacancies and unemployment. In this paper we also provide empirical evidence from the postwar period in the 2

U.S. showing a link between the relative price of new equipment, investment, and labor market outcomes. More in detail, the data suggests that when technological advances make new equipment less expensive, not only the investment in new equipment increases but also the relative number of vacancies, at least in the short run. Moreover, other labor market variables such as unemployment and the job separation rate also seem to respond to this type of shocks. These findings motivate our quantitative analysis. Specifically, we investigate the impact of investment-specific shocks on the labor market by incorporating them into an otherwise standard RBC model with labor search and matching frictions. We also consider the role of endogenous separation rate and capital utilization as propagation and amplification mechanisms. Shapiro (1996) stresses the importance of capital utilization for studying business cycles. Using the workweek of capital as a measure of utilization, his paper documents that this is an important margin of adjustment in many U.S. manufacturing industries over the business cycle. Furthermore, he finds that there is little or no cyclical movement in productivity once capital utilization is taken into account, and concludes that the RBC literature “needs to focus on the sources of shocks other than those to aggregate productivity” (p. 118). In a previous work, Shapiro (1986) argues that since capital utilization (measured again as the workweek of capital) is essentially costless to adjust, it responds immediately to shocks. In fact, he finds that in response of shock, the workweek of capital tends to overshoot to compensate for the slow and costly adjustment of the capital stock. In particular, shocks to the purchase price of capital and the rate of return have substantial effects on capital utilization. Besides the well known amplification effects of investment-specific shocks and variable capital utilization on output fluctuations (for a detail discussion of the mechanisns at work see Greenwood, Hercowitz, and Huffman, 1988; Greenwood, Her-

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cowitz, and Krusell, 2000), we think that they might have an additional impact on the volatility of labor market variables through at least two channels. First, a positive investment-specific shocks have an expansionary effect on investment, increasing next-period capital stock. The higher capital stock enhances the marginal labor productivity next period, which tends to foster job creation and reduces unemployment. Secondly, after a positive technological change, capital utilization rises. Due to the persistent nature of shocks, the utilization rate remains above its initial level the following period. This raises next-period labor productivity, which again has a positive effect on the labor market. These channels seem not to be of quantitative importance. Our main result is that investment-specific shocks do not help the model generate significant cyclical movements in key labor market variables such as unemployment and vacancies. In fact, essentially all of the impact that this shock has over the cyclical dynamics of the labor market is through capital utilization. Therefore, the relative volatility of relevant labor market outcomes with respect to output remains unchanged when investment shocks are incorporated into the model. Hence, the model presented here is unable to replicate the magnitude of the cyclical fluctuations of vacancies and unemployment without counterfactually generating too much output volatility. In other words, investment-specific shocks together with endogenous capital utilization rate do not provide any amplification mechanism to the model, as far as the labor market is concerned. Another important result is that having endogenous separations in the model does not seem to introduce a meaningful amplifying effect. In particular, a reasonable fraction of endogenous job destruction generates a number of counterfactual predictions with respect to the joint behavior of vacancies and unemployment, and job creation and destruction. It is true that more endogenous separations amplify the fluctuations of both unemployment and job destruction. However, this causes vacancies

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and job creation to behave oddly. That is, they display too little volatility and, more importantly, become countercyclical. Thus, the model fails to reproduce the downward-sloping Beveridge curve. The role of search and matching frictions in the business cycle model have been explored intensively since the mid 90’s. Merz (1995) and Andolfatto (1996) put the DMP model into a RBC general equilibrium framework. Neither paper can match the negative correlation between unemployment and vacancies, and they generate real wages that are too flexible in response to productivity shocks. Introducing endogenous job separation, den Haan, Ramey, and Watson (2000) show that fluctuations in the separation rate amplify productivity shocks in a similar RBC model with matching frictions, reproducing the behavior of job creation and destruction. However, they do not discuss the response of wages and labor market tightness to productivity shocks. Similarly to den Haan, Ramey, and Watson (2000), in an earlier study of the DMP model with endogenous separation decision, Mortensen and Pissarides (1994) reproduce the observed behavior in the job creation and job destruction process. However, their model delivers a correlation between unemployment and vacancies (0.26) considerably lower than the observed empirical value (-0.88), and they do not study the dynamic of wages. More recently, Yashiv (2006) includes not only labor productivity shocks but also shocks to both the match separation rate and the discount rate. His analysis shows that the model captures the high persistence and high volatility of most of the key variables as well as the negative co-variation of unemployment and vacancies. His findings, however, are sensitive to the use of convex rather than linear hiring costs, and generates a countercyclical behavior on wages while in the data it is acyclical. Our work is related to Lopez-Salido and Michelacci (2007) who also explore the effect of investment-specific technological advances on labor market outcomes. They consider a growth model where technological progress can be investment-specific or

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investment neutral. Moreover, the reallocation of workers is sluggish due to search frictions in the labor market. Their paper analyzes the dynamic response to permanent technology shocks when there are vintage-capital effects. In the model presented here we consider transitory technology shocks. In addition, unlike them, we assume that neutral technological progress in entirely disembodied. Finally, our work is also related to De Bock (2006). He studies the implications of investment-specific technology shocks in a business cycle model with search and matching frictions and endogenous job destruction. His model generates the Beveridge curve as well as the observed persistent in key variables such as output, unemployment and vacancies, but underestimates their observed volatility. Our model is similar to De Bock’s model, but it differs in one important aspect: we introduce endogenous capital utilization into the model, which is the key variable through which investment shocks affect the labor market. Although several authors have extended the basic RBC model to incorporate this variable,1 to our knowledge, this is the first attempt to explore the cyclical consequences of variable capital utilization when matching frictions are present in the labor market. This paper is organize as follows: Section 2 explores the cyclical behavior of some relevant labor market outcomes and their relationship with other variables of interes. In particular, as a motivation, we examine the relationship of labor market tightness with investment-specific shocks. Section 3 presents the model economy to be used for our quantitative analysis. In Section 4 we calibrate our model and analyze the simulation results. Finally, Section 5 presents the conclusions. 1

King and Rebelo (1999), Kydland and Prescott (1988), and Greenwood, Hercowitz, and Huffman (1988), among others

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2

Labor market tightness and business cycle facts in the U.S.

This section documents the cyclical behavior of labor market tightness θ, defined as the ratio of vacancies v to unemployment u, as well as its relation to other variables of interest. We use quarterly data from 1951 to 2003. We take the database and sources used by Shimer (2004, 2005) and incorporate data on gross domestic product y, non durable consumption c, private domestic investment in equipment and software i, labor productivity y/n, and the nominal prices of producer durable equipment divided by the implicit price for nondurable consumption goods pe . We also include quarterly data on the workweek of capital calculated by Orr (1989) as a proxy for capital utilization h. Unfortunately this indicator is only available until 1984. Subsection 2.1 documents the properties of the series following the standard practice in the businesscycle literature, while in Subsection 2.2 we look at the conditional correlations of VAR forecast errors at different horizons.

2.1

Cyclical behavior

We obtain the cyclical component of the series by applying the Hodrick-Prescott (HP) filter, with smoothing parameter 1, 600, to data that have been seasonally adjusted and logged. Table 1 shows statistics describing the cyclical behavior of relevant variables related to the labor market tightness. It includes measures of cyclical volatility as well as correlations with θ at leads and lags of up to four quarters. The strongly positive contemporaneous correlation of 0.888 between labor market tightness and output indicates that this labor market indicator is highly procyclical. Moreover, θ is by far the most volatile variable observed with a standard deviation of 0.257, so it is often as much as 50 percent above or below its trend. Additionally, by looking at the cross-correlation with output, we observe that the labor market tightness displays almost no phase shift. 7

Table 1: Relative volatility and cross-correlation of tightness and other relevant variables: U.S. quarterly data 1951-2003

u (0.479) v (0.541) f (0.296) ρ (0.231) w (0.035) y/n (0.051) i (0.210) h (0.082) pe (0.062) c (0.043) y (0.062)

θ(+4) 0.048

θ(+3) θ(+2) -0.234 -0.540

θ(+1) θ -0.814 -0.976

θ(−1) -0.905

θ(−2) -0.691

θ(−3) -0.413

θ(−4) -0.133

0.184

0.465

0.731

0.925

0.981

0.844

0.596

0.307

0.023

0.034

0.303

0.595

0.836

0.929

0.852

0.647

0.395

0.147

-0.220 -0.458 -0.651 -0.753 -0.652

-0.359

-0.084

0.152

0.284

0.173

0.220

0.245

0.263

0.242

0.166

0.081

0.010

-0.081

0.507

0.601

0.645

0.572

0.381

0.060

-0.243

-0.461

-0.576

0.056

0.245

0.478

0.692

0.832

0.811

0.648

0.426

0.170

0.067

0.255

0.424

0.539

0.596

0.522

0.333

0.094

-0.121

0.311

0.212

0.081

-0.052

-0.170

-0.253

-0.284

-0.285

-0.285

0.319

0.507

0.669

0.761

0.724

0.576

0.359

0.132

-0.074

0.208

0.461

0.700

0.861

0.888

0.719

0.451

0.176

-0.063

Note: Standard deviations relative to σ(θ) = 0.257 in parentheses. Sources: Vacancies v are obtained from the help-wanted advertising index, constructed by the Conference Board. Unemployment u is constructed by the BLS from CPS. The job finding rate f , and separation rate ρ are constructed by Robert Shimer available at http://home.uchicago.edu/∼shimer/data/. The wage w is real hourly compensation in the non-farm business sector constructed by the BLS from the NIPA and the Current Employment Statistics. Total output y is real GDP. Consumption c is the real gross non durable private consumption. Investment i is the real gross private domestic investment in equipment and software. The relative price of equipment pe is the index of nominal prices for the implicit price deflator of investment in equipment and software divided by nondurable consumption goods, which are constructed by the Bureau of Economic Analysis from the NIPA. Capital utilization h is captured by the workweek of capital index constructed by Orr (1989) from 1952 to 1984.

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The ratio of vacancies to unemployment is the key variable of the DiamondMortensen-Pissarides (DMP) model because, according to the properties of the matching function, it represents the basic search externality in the model. That is, an additional vacancy imposes a negative externality on other vacancies and a positive externality on unemployed workers, and viceversa. This externality suggests a negative relationship between unemployment and vacancies. Along this line, the correlation of the cyclical component of unemployment and vacancies between 1951 and 2003 is -0.915, suggesting that introducing this type of externality should be considered as an important element in the behavior of labor markets. In Table 1 we observe the main stylized facts outlined in Shimer (2005) and Hornstein, Krusell, and Violante (2005) regarding the behavior of vacancies and unemployment. The volatility of u and v are similar to each other, and they display half the standard deviation of θ. Similarly, vacancies are highly procyclical whereas unemployment is strongly countercyclical. Labor market tightness also moves together with the job finding rate f (i.e., the rate at which unemployed workers find jobs on average). Given that the v-u ratio is high in expansions, the job finding rate will be also relatively high, in contrast with its lower values in economic downturns. When looking at the separation rate ρ, we observe a negative contemporaneous correlation with the v-u ratio as expected. It is also important to notice the lower volatility of the separation rate (0.059) with respect to the job finding rate (0.076), and its lower contemporaneous correlation in absolute value with respect to θ (-0.652), relative to the one of the job finding rate (0.929). As emphasized by both Hall (2005) and Shimer (2005), this may suggest that cyclical movements of unemployment arise essentially from changes in the rate at which unemployed workers find jobs. In other words, recessions are periods of sharp declines in firm’s recruiting efforts, rather than periods of massive layoffs, especially since the middle of the 1980s. However, as we

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can see in Table 1, the separation rate displays a clearly phase shift in the direction of leading labor market tightness between one and two quarters, making ρ a candidate as driving force of the labor market. A central business cycle fact is that the real wage appears to be mildly procyclical. In fact, we observe a relatively low positive correlation with labor market tightness (0.242). Moreover, wages are much less volatile than vacancies, unemployment, and the v-u ratio. While the latter is often 50 percent above or below its tendency, the real wage rises and falls less than 5 percent relative to its trend. Shimer (2005) has argued that average labor productivity can be used as a cyclical indicator for purposes of evaluating the matching model. This is compelling in that productivity incorporates a broad range of factors that influence the return to employment, including neutral technological shocks. As it can been seen in Table 1, there is a positive correlation between labor productivity y/n and θ with some evidence that labor productivity leads the labor market tightness between two and three quarters, with a maximum correlation of 0.645. However, as it has been emphasized by Shimer (2005), there is evidence that the contemporaneous correlation between the detrended productivity and the v-u ratio has been reduced since the mid 80s: from 0.433 in the period 1951-1985 it becomes 0.055 in 1986-2003. These values may cast some doubts on the results obtained when analyzing the effects of productivity shocks on the DMP model. Another important fact that arises from Table 1 is that labor productivity is stable, never deviating by more than 5 percent from trend. This means that it is necessary an important amplified propagation mechanism for productivity shocks to reproduce the actual high volatility in the labor market tightness. We now look at the link between tightness and those variables related to the use of old capital and investment in new machinery and equipments. First, we observe that new investment in equipment and capital utilization are strongly procyclical and moves approximately coincidentally with labor market tightness. This evidence

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suggests that the flow of new equipments and capital services are adjusting at the same time as firms are opening new vacancies. The evidence from the postwar period in the U.S. suggests an important link between relative prices and technology at high frequency level as it has been emphasized by authors like Greenwood, Hercowitz, and Krusell (2000). From 1951 to 2003, there is a negative correlation (-0.217) between the detrended relative price of new equipment pe , and new equipment investment i. Moreover, Table 1 also shows a contemporaneous negative correlation between pe and θ (-0.170). However, the sing of the correlation coefficient switches from negative to positive when pe becomes a leading indicator. The observed change in the sing of the cross-correlation among θ and driving force candidates y/n and pe , call for exploring additional information about the dynamic aspects of the comovement of these variables. In the next subsection, we estimate the conditional correlations of VAR forecast errors at different horizons.

2.2

Conditional correlations

Thus far, we have focused our analysis on unconditional correlation coefficients that are defined only for stationary variables. They involve rendering the data stationary through some type of filtering, which in turns has potentially significant effects on the unconditional correlation coefficients (For more details, see Canova, 1998). In addition, concentrating only on the unconditional correlation involves some loss of information regarding the dynamics of comovement of variables. To assess the robustness of last results, we employ a recently developed methodology suggested by den Haan (2000). This new approach is based on vector autoregression (VAR) methodology and does not require pre-filtering the data since it can accommodate both integrated and stationary variables. It yields a set of correlation coefficients of VAR forecast errors at different horizons. Basically, from an estimated set of bivariate VARs between labor market tightness and the rest of variables con11

sider in Table 1, we construct time series for the forecast errors using the difference between subsequent realizations and their forecasts. The constructed time series are then used to generate covariance and correlation coefficients. The series are expressed in logs but without applying the HP filter. The VARs were estimated without imposing the unit-root restriction and considering linear and quadratic trend when necessary.2 The lag length in the VAR, as well as the deterministic components were chosen using the Akaike Information Criterion (AIC). Table 2 summarizes the correlation coefficients for a forecast horizon of up to five years, a period equivalent to the average duration of the U.S. business cycle during the period 1854-2001. In general, we observe that the forecast error correlation coefficients are consistent with the unconditional correlations observed in Table 1. Notice that the sing of the correlation between θ and pe is negative when conditional coefficients are obtained at the short run horizon using the VAR approach. Thus, when technological advances make equipment less expensive, investment increases together with the relative number of vacancies, at least in the short run. Similarly, the conditional correlations between labor productivity and market tightness are positive at business cycle frequency. Moreover, it is interesting to observe that the correlation coefficients associated to the driving force candidates y/n, ρ and pe are first increased reaching their maximum values during the first year of the forecast analysis, and then reduced considerably. In contrast, the rest of variables show a higher correlation with tightness not only in the first year but also during the next eight quarters. This fact may indicate the presence of a persistent propagation mechanism from shocks to the rest of variable, which takes place through the adjustment of labor market tightness. Notice that, since investment-specific shocks change the expected future marginal productivity 2

The Matlab program was writing by Steve Sumner and can be download at den Haan’s web page http://faculty.london.edu/wdenhaan/.

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of capital without affecting the current labor productivity, then y/n is not able to directly capture this source of shocks and, therefore, it can not be used as a driving force variable of the matching model when there are only investment-specific shocks. Table 2: Correlation coefficient between k -quarter ahead forecast errors of tightness and other relevant variables Forecast Horizon

u

v

f

ρ

w

y/n

i

h

pe

y

c

1 2 3 4 5 6 7 8 12 16 20

−.90 −.94 −.96 −.97 −.97 −.97 −.97 −.97 −.97 −.96 −.95

.93 .96 .97 .98 .98 .98 .98 .98 .98 .97 .96

.58 .82 .90 .93 .94 .94 .95 .95 .95 .94 .94

−.60 −.69 −.74 −.76 −.74 −.68 −.65 −.64 −.62 −.62 −.64

.19 .26 .23 .26 .29 .33 .34 .37 .38 .30 .19

.46 .51 .48 .42 .36 .29 .23 .18 .07 .02 −.01

.47 .69 .77 .81 .82 .88 .83 .82 .78 .72 .68

.11 .28 .42 .50 .54 .56 .57 .57 .57 .57 .58

−.14 −.21 −.28 −.28 −.27 −.26 −.26 −.25 −.23 −.24 −.24

.65 .80 .85 .86 .87 .87 .86 .86 .83 .79 .76

.41 .57 .61 .65 .69 .73 .74 .75 .73 .66 .57

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The model

3.1

Households

Consider an economy populated by a measure 1 of infinitely-live workers. Each worker supplies one unit of labor inelastically every period t, t = {0, 1, 2, ...}. However, they may be either employed or searching for a job. Employed workers earn a wage wt , and unemployed workers get b units of the consumption good.3 Workers also own firms and therefore receives its dividends. As in Merz (1995) and Andolfatto (1996), we assume that there exists a perfect insurance market, and that all agents are exante identical before employment status are revealed at the beginning of the initial 3

This b units of consumption could be interpreted as both home production and unemployment insurance benefits.

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period. Therefore there is a representative consumer/worker, with income equal to the total labor income Wt and dividends Dt , who chooses aggregate consumption Ct to maximize her period-t expected utility ∞ X Et [ β j−t u(Cj )],

(1)

j=t

where β is the discount factor, and u(·) is an instantaneous CES utility function given by u(C) =

C 1−γ , 1−γ

γ > 1.

(2)

The representative consumer also chooses her holding of firms’ shares at+1 .4 Formally, her problem can be expressed recursively by the following Bellman equation

V (at , st ) =

max {u(Ct ) + βE[V (at+1 , st+1 )|st ]},

(3)

s.t. Ct + Pt at+1 = Wt + (1 − Nt )b + (Pt + Dt )at ,

(4)

Ct ,at+1

where st denotes the aggregate state of the economy, Pt is the stock price, and (1−Nt ) indicates the fraction of unemployed individuals. Since there is a representative consumer, she owns all the shares of the firm and no stocks are traded in equilibrium. Thus, at = at+1 = 1. Hence, aggregate consumption is Ct = Wt + (1 − Nt )b + Dt .

3.2

(5)

The representative firm

We assume that there exists a representative firm which uses labor Nt and capital Kt to produce aggregate output with a constant-return-to-scale (CRS) production function F (Kt ht , Nt ) = At (Kt ht )α Nt1−α , where ht denotes the rate of capital utilization, 4

Below we assume that there is a representative firm in this economy. Hence, a is just a scalar.

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At is an aggregate technology shock, and α ∈ (0, 1). The variable log(At ) follows a first-order autoregressive process of the form

log(At ) = ρa log(At−1 ) + νa ,

(6)

with νa ∼ N (0, σa ). At the beginning of each period, the firm has Mt matches with which it could potentially establish (or continue) an employment relationship. Before production takes place, each matched worker draws an idiosyncratic productivity level zt ∈ [z, z¯] from distribution G(z). We assume that z is i.i.d. across time and lognormally distributed LN (0, σ). Thus, a worker with productivity zt produces zt f (kt ht ) units of output, where f (kt ht ) = F (kt ht , 1) and kt is capital per worker. We assume that the firm breaks non-profitable matches. We can prove that there exists a threshold z˜t ∈ [z, z¯] such that matches with zt < z˜t are inefficient, and hence severed.5 Therefore, total employment in period t is Z

z¯

Nt = Mt

dG(z) = Mt (1 − G(˜ zt )),

(7)

z˜t

and total output is then given by Z Yt = F (Kt ht , Nt )

with

Z

Z zdG(z|z ≥ z˜t ) = f (kt ht )Nt

zdG(z|z ≥ z˜t ),

(8)

R z¯

zdG(z) zdG(z|z ≥ z˜) = Rz˜ z¯ = E(z|z ≥ z˜). dG(z) z˜

(9)

Notice that we are implicitly assuming that capital associated to each match is chosen after its idiosyncratic productivity z is realized. Thus, no capital is allocated to inefficient matches. Alternatively, we could assume that the capital stock associated 5

This comes from the fact that the surplus of a match is increasing in z.

15

to each match/firm is known before z is drawn. If we further assume perfect capital markets, firms reallocate their capital after z is realized. In particular, “inactive firms” rent out their capital to productive firms. In any case, given the representative firm assumption, each productive worker gets the same amount of capital. The representative firm owns the capital and therefore makes the capital accumulation decisions. Investment It is subject to a stochastic shock t so that the firm accumulates It t units of capital for period t + 1.6 The investment-specific shock t is assumed to follow a first-order autoregressive process of the form

log(t ) = ρe log(t−1 ) + νe ,

(10)

with νe ∼ N (0, σe ). Capital also depreciates each period. As in Greenwood, Hercowitz, and Krusell (2000), the rate of depreciation depends on the capital utilization ht , and takes the following functional form

δ(h) =

υ ω h , ω

ω > 1, υ > 0.

(11)

Thus, the law of motion for the capital stock is

Kt+1 = (1 − δ(ht ))Kt + It t .

(12)

Our representative firm also posts job vacancies Vt every period. Each vacancy has a cost κ and meets an unemployed worker with probability m(Ut , Vt )/Vt , where m(·, ·) is a CRS matching function that depends on the mass of unemployed workers 6

An interpretation for this shock is that physical investment measured in consumption units, I, is enhanced by a quality index, , which can be captured by the price index of consumption goods relative to the quality-adjusted price index for investment goods. In other words, I stands for investment measured in efficiency units. The improvement in the quality of capital goods reflected in higher values of  (the relative price of investment goods falls) is the driving force behind the investment-specific technological change.

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Ut = 1 − Nt and vacancies posted. In particular, we assume that  m(V, U ) =

Vφ 1 + (V /U )φ

1/φ ,

φ > 0.

(13)

The CRS assumption on the matching function implies that the probability of the firm meeting an unemployed worker only depends on the labor market tightness θ = V /U . Thus, we will let q(θt ) = m(Ut , Vt )/Vt .7 We assume that the firm does not take into account the externality associated with opening an additional vacancy, due to its impact on q(θt ), when considering whether or not to post it. That is, q(θt ) and θt are taken as given. However, in equilibrium θt must be consistent with the actual vacancy-unemployment ratio associated with the firm’s decision. At the end of each period t, a fraction ρ¯ of employed workers Nt will be terminated exogenously. Therefore, the firm will have

Mt+1 = (1 − ρ¯)Nt + q(θt )Vt

(14)

matched workers next period. Moreover, taking into account that the firm decides to lay off some employees at the beginning of next period, we can rewrite this expression as Nt+1 = (1 − ρ¯)(1 − G(˜ zt+1 ))Nt + q(θt )(1 − G(˜ zt+1 ))Vt .

(15)

Thus, the probability that an employment match in period t does not survive by period t + 1 (i.e., separation probability) is

ρ(˜ zt+1 ) = ρ¯ + G(˜ zt+1 )(1 − ρ¯). 7

(16)

An advantage of the functional form for the matching function above, as pointed out by den Haan, Ramey, and Watson (2000) who also use the same specification, is that the matching probabilities are bounded between 0 and 1 as opposed to a Cobb-Douglas form. This facilitates the numerical solution of the model since truncations are not needed.

17

Similarly, the probability that a vacancy posted in period t finally results in an employment relationship the following period is qet = q(θt )(1 − G(˜ zt+1 )). A fraction G(˜ zt+1 ) of those unemployed workers that the firm meets during its recruiting activity are not offered a job because their idiosyncratic productivity level is below the threshold z˜t+1 . The representative firm’s problem is then to choose how intensively to use its capital ht , the cutoff idiosyncratic productivity level z˜t , how much capital to accumulate It , and how many job vacancies Vt to post in order to maximize the value of the firm (i.e., the discounted present value of dividends Dj = Yj − Wj − Ij − κVj , j ≥ t), given its current state st = (Kt , Mt , At , t ) and the wage schedule wt (z). Strictly speaking, since we assume that the economy has perfect capital markets, the representative firm also decides how much capital to use in its own production process and how much capital to rent out to “other” firms at a given interest rate rt . However, in equilibrium, rt is such that the firm ends up using exactly its entire own capital stock. Thus, we can formulate the firm’s problem abstracting from this decision, and write its dynamic programming problem as follows:

Π(st ) =

max {Yt − Wt − It − κVt + E[∆t,t+1 Π(st+1 )|st ]},

ht ,˜ zt ,It ,Vt

s.t. (7) − (15), Z z¯ W t = Nt wt (z)dG(z|z ≥ z˜t ),

(17)

(18)

z˜t

where ∆t,t+1 is the stochastic discount factor, and Wt denotes the firm’s wage bill. Since the firm is ultimately owned by consumers/workers, future dividends of the firm must be appropriately discounted using the intertemporal marginal rate of substitution (IMRS). Thus, ∆t,t+1 is the IMRS between consumption at periods t and 0

t+1 ) t + 1. That is, ∆t,t+1 = β uu(C 0 (C ) . t

18

The first-order optimality conditions of the firm’s problem are: 1 = E[∆t,t+1 ΠK (st+1 )|st ], t

(19)

κ = E[∆t,t+1 ΠM (st+1 )|st ], q(θt )

(20)

δ 0 (ht ) = FK (Kt ht , Nt )E(z|z ≥ z˜t ), t

(21)

wt (˜ zt ) = f (kt ht )[˜ zt − αE(z|z ≥ z˜t )] + (1 − ρ¯)E[∆t,t+1 ΠM (st+1 )|st ].

(22)

Using the Envelope theorem and after some manipulations, we obtain

ΠK (st ) = ht FK (Kt ht , Nt )E(z|z ≥ z˜t ) + Z

Z

z¯

ΠM (st ) = FN (Kt ht , Nt )

z¯

zdG(z) − z˜t

wt (z)dG(z) + z˜t

1 − δ(ht ) , t

(23)

κ(1 − ρ¯)(1 − G(˜ zt )) . q(θt )

(24)

Condition (19) governs the accumulation of capital, equation (20) is the job creation condition, expression (21) determines the rate of capital utilization, and equation (22) is the job destruction condition. Substituting (20) into (22) and rearranging we obtain a more intuitive version of the job destruction condition,

wt (˜ zt ) + αf (kt ht )E(z|z ≥ z˜t ) = f (kt ht )˜ zt +

κ(1 − ρ¯) . q(θt )

(25)

The left hand side of this expression represents the benefits of laying off an extra worker with productivity shock z˜t . First, the firms do not have to pay wages wt (˜ zt ). Secondly, by having one less worker, the amount of capital per worker increases, which has a positive impact on their output. The right hand side of equation (25) describes the losses of terminating such a worker. The first term on the right corresponds to loss output whereas the second term constitute the expected loss for having one less matched worker next period. The firms terminates matches up to the point when is no longer profitable doing so. That is, when costs and benefits are equal. 19

3.3

Wage setting

Since there are frictions in the labor market, wages are determined through Nash bargaining between the firm and each individual employed worker where they split the total surplus generated by that specific employment relationship. The value of an employment relationship with productivity level z for the firm is given by the following Bellman equation J(s, z) = zf (kh) − w(z) − rkh + (1 − ρ¯)E[∆0 J(s0 , z 0 )|s, z 0 ≥ z˜0 ].

(26)

Here we have suppressed the time subscript and denote next-period variables with the prime symbol (0 ). The outside option for the firm is the value of a vacancy, which in equilibrium is zero. Thus the net surplus for the firm is J(s, z). The value of being employed for a worker is described by the Bellman equation L(s, z) = w(z)+(1− ρ¯){E[∆0 L(s0 , z 0 )|s, z 0 ≥ z˜0 ]+E[∆0 H(s0 )G(˜ z 0 )|s]}+ ρ¯E[∆0 H(s0 )|s], (27) where H(s) represents the value of unemployment, worker’s outside option. This can be defined as H(s) = b + p(1 − G(˜ z ))E[∆0 L(s0 , z 0 )|s] + (1 − p(1 − G(˜ z )))E[∆0 H(s)|s],

(28)

where p = m(U, V )/U is the job meeting probability. The Nash bargaining solution is a wage rate w(z) that solves max(L(s, z) − H(s))η J(s, z)1−η , w(z)

20

(29)

with η represents the worker’s bargaining power. Thus,

w(z) = (1 − η)b + η(zf (kh) − rkh + κθ).

3.4

(30)

Equilibrium

An equilibrium in this economy are prices {wt (z), rt , Pt } and a set of allocations {Ct , at+1 , Kt+1 , Vt , ht , Mt , Nt , z˜t , θt } such that: 1. {Ct , at+1 } solve the representative consumer’s problem (3) given prices, 2. {Kt+1 , Vt , ht , Nt , z˜t } solve the firm’s problem given prices and θt , 3. the law of motion of Mt is given by expression (14), 4. the wage schedule wt (z) solves (29) for z ≥ z˜t , 5. the interest rate rt clears the capital market (rt = FK (Kt ht , Nt )E(z|z ≥ z˜t )), 6. stock price Pt clears the asset market, and 7. the consistency condition Vt /(1 − Nt ) = θt holds.

4 4.1

Calibration and simulations Calibration

In this section we calibrate the model at quarterly frequency to be consistent with some empirical facts. In particular, the parameterization must match seven steadystate targets. From the RBC literature we take three standard statistics. A capital’s share of output of one third, consistent with the National Income and Product Accounts (NIPA); a quarterly output-capital ratio of about 0.10, in line with U.S. evidence; and a depreciation rate of 2.5 percent per quarter. 21

The remaining four targets are related to labor market outcomes. First, we set an average unemployment rate of 11 percent. This figure is consistent with the fraction of unmatched workers in the U.S. when we consider not only the officially unemployed but also those not in the labor force who “want a job”. Using the Current Population Survey (CPS) from 1968 to 1986, Blanchard and Diamond (1990) find that on average there are 11.2 million people either unemployed (6.5) or not in the labor force who want a job (4.7) out of a total of 104.4 million workers (93.2 millions employed).8 Secondly, we target a steady-state job separation probability ρ∗ equal to 0.10 per quarter.9 This value is commonly used in the literature (see Shimer, 2005; den Haan, Ramey, and Watson, 2000, among others), and is consistent with available empirical estimates. Hall (1995) concludes that the average quarterly separation rate in the U.S. is between 8 and 10 percent. Moreover, Davis, Haltiwanger, and Schuh (1996) use CPS data and find an annual separation rate of 36.8 percent, which is roughly equivalent to our quarterly target. We also target an elasticity of the matching function with respect to unemployment

ε∗mu of 0.72 as in Shimer (2005).

He finds this elasticity when estimating the

parameters of a Cobb-Douglas matching function for the U.S. using data on the job finding rate and the vacancy-unemployment ratio. Shimer’s findings are consistent with empirical evidence reported by Petrongolo and Pissarides (2001), who argue in their survey paper that a “plausible range for the empirical elasticity on unemployment is 0.5 to 0.7” (p. 393). For comparative purposes, in an alternative parameterization we target a matching elasticity of 0.4 based on the empirical estimates in Blanchard and Diamond (1989). Our final target is an elasticity of unemployment duration with respect to unemployment benefits equal to 0.88. As in Costain and Reiter (2006), we do not 8 Other studies on labor market dynamics also use Blanchard and Diamond’s (1990) figures to calibrate their models. For instance, den Haan, Ramey, and Watson (2000) target a steady-sate ratio of unmatched to matched workers of 0.12. 9 Starred variables denote their steady-state levels.

22

want unemployment duration or the unemployment rate to be excessively responsive to benefits. We choose this value based on the empirical evidence found by Meyer (1990), who uses individual data from the Continuous Wage and Benefit History (CWBH). This data set includes accurate information on unemployment spell durations, the level and length of benefits, pre-unemployment earnings, and the potential duration of benefits over time for males in twelve states during the period 1978-1983. He estimates the effect of unemployment insurance on the hazard rate of finding a job using different econometric specifications. Using the coefficient estimates from Meyer’s preferred specification (5, Table V, p.772), a 10 percent increase in benefits is associated with an 8.8 percent decrease in the hazard rate. This estimate is larger than the one found by Katz and Meyer (1990) who find an elasticity of 0.54 using the same data set. However, they point out that “[w]hen UI benefits and previous earnings are entered in logarithms, the effect of benefits is somewhat higher” (footnote 21, p. 60), which is the case in Meyer’s (1990) specification above. (See Krueger and Meyer, 2002; Shimer and Werning, 2006, for a discussion on this issue.) We need to find values the following parameters: β (discount factor), γ (utility function), α (technology), ω, υ (depreciation), φ (matching function), ρ (exogenous job separation), κ (vacancy cost), η (workers bargaining power), and b (employment opportunity cost). We also must select values for parameters ρa , σa , ρe , σe , and σ, which govern the stochastic processes for A and , and the random variable z. The coefficient of relative risk aversion γ is chosen to be 1 so that we use a logarithmic utility. The elasticity of output with respect to capital α is set equal to 0.33, coinciding with the average capital’s share of output mentioned above. It is important to notice that in this setting, where wages are not equal to the marginal productivity of labor, (1 − α) does not necessarily coincide with the labor’s share of output. Given our target for the average output-capital ratio of 10 percent, the value for α translates

23

into a steady-state capital rental rate of r∗ = α(Y /K)∗ = .033. Using the optimality condition (19) at the steady state 1/β = 1 + r∗ − δ ∗ ,

we obtain the discount factor β = .992, which implies a reasonable quarterly interest rate of nearly 1 percent in the steady state. Using equations (19),(21) and (23), we obtain the following condition for steadystate capital utilization h∗ ,  ∗

h =

ω(1 − β) υβ(ω − 1)

1/ω .

Notice that h∗ and, consequently, δ(h∗ ) only depend on ω and υ for a given discount factor β. We normalize h∗ = 1, and choose ω = 1.32 and υ = 0.033 such that δ(h∗ ) = 0.025, consistent with our target for the average depreciation rate. The parameters for the stochastic process for the aggregate shock A are taken from Hansen and Wright (1992). We set ρa = 0.95 and σa = 0.007. The parameters ρe and σe are set to match the stochastic properties of the relative price of new equipments used in Section 2. When we estimate the first-order autoregressive equation (with time-trend), we obtain ρe = 0.948 and σe = 0.0087.10 The standard deviation of random variable log(z) is set to σ = 0.101, which is the value used by den Haan, Ramey, and Watson (2000). Regarding the exogenous separation probability ρ, we choose two values. For our baseline value, following den Haan, Ramey, and Watson (2000), we interpret exogenous separations as worker-initiated separations. Hence, endogenous separations 10

In particular, we fitted the following equation: · log(pe,t ) = 0.304 + 0.007t − 4.08 × 10−5 t2 + 0.948 log(pe,t−1 ) + εt , with εt ∼ N (0, .0087); R2 = .99; and coefficient standard errors 0.242, 0.003, 9.27 × 10−6 , and 0.024, respectively

24

are associated with the layoff rate. This is consistent with our model since endogenous separations are a firm’s decision. According to the evidence from JOLTS shown by Davis, Faberman, and Haltiwanger (2006) and from the Census’ Survey of Income and Program Participation (SIPP) shown by Nagypal (2004), layoffs represent on average about 35 percent of total separations. Thus, one of the values we pick for ρ is 0.065, which is close to the one used by den Haan, Ramey, and Watson (2000). They set this parameter to 0.068 using a slightly different calibration strategy. We consider this exogenous probability as an upper bound because most of the quits are in fact job-related quits, which can hardly be classified as exogenous (see Nagypal, 2004, for details). Therefore, we also consider ρ = 0.035. We select the matching technology parameter φ in order to match our target for

ε∗mu. Since the matching elasticity depends on θ as well, we need to solve the following system of equation for φ and θ∗ , θ∗φ = (1 + θ∗φ )

ε∗mu,

ρ∗ (1 − U ∗ ) = (1 − G∗ )q(θ∗ ; φ)θ∗ U ∗ .

The first equation is the elasticity of the matching function with respect to unemployment in the steady state. The second expression comes from the law of motion for employment, equation (15). The left-hand side of represents employment-tounemployment transitions whereas the right-hand side determines unemployment-toemployment transitions. Clearly, in the steady state they must be equal so that the unemployment rate remains constant at U ∗ = 0.11. Notice that the steady-state job finding probability f (θ∗ ) = (1 − G∗ )θ∗ q(θ∗ ) is equal to ρ∗ (1 − U ∗ )/U ∗ = 0.81. For our baseline parameterization (i.e. ρ = 0.065 and

ε∗mu = 0.72), we obtain φ = 1.897.

Table 4 displays the values for alternative calibrations.

25

The employment opportunity cost b is chosen so that the model matches our target for the elasticity of unemployment duration with respect to unemployment benefits in the steady state of 0.88. This yields b = 1.907 in the baseline case, which implies that the total employment opportunity cost bU ∗ represents about 7 percent of total output on average. The remaining parameters κ and η are chosen so that the first-order conditions (20) and (22) are satisfied in the steady state. Thus, we set κ = 0.175 and η = 0.353. To put the value of κ in perspective we calculate the total vacancy cost κV ∗ . It represents about 1 percent of total output. Table 3: Common parameter values Parameter Calibrated value Parameter Calibrated value γ 1 σ 0.101 β 0.992 ρa 0.95 α 0.33 σa 0.007 ω 1.32 ρe 0.948 υ 0.033 σe 0.0087

ε∗mu

ρ b φ κ η

4.2

Table 4: Calibrated parameter values Baseline Parameterization B Parameterization C 0.72 0.72 0.40 .065 .035 .065 1.907 1.896 1.760 1.897 2.303 5.292 0.175 0.139 0.152 0.353 0.476 0.683

Simulation results

In this subsection we assess the quantitative importance of investment-specific shocks for cyclical fluctuations in the labor market. We do so by simulating the model presented above 10,000 times. Each time we simulate the economy for 1,000 periods, 26

and take the simulated data of the last 148 periods (the same number of U.S. data periods we have). This simulated data is then logged and HP-filtered in the same way as U.S. data before calculating the statistics of interest.11 Then we take averages of these statistics over the 10,000 simulations. For comparison purposes we also simulate a version of the model with no changes in the relative price of investment (i.e. σe = 0). By shutting down this source of aggregate fluctuation, we quantitatively estimate its contribution to business cycles. The main result is that investment-specific shocks do not play a role in amplifying fluctuations in vacancies and unemployment whatsoever. As shown in Table 5, columns (2) and (5), the standard deviation of vacancies, unemployment and labor market tightness relative to output essentially remains unchanged. As expected, the volatility of output falls. According with our baseline calibration, investment-specific shocks account for about 16 percent of the output’s variance. In other words, 8 percent of the business cycle fluctuations can be explained by this kind of shocks.12 The intuition why the standard deviation of labor market variables decreases as much as output’s so that their relative volatility does not change is straightforward. Investment-specific shocks only affect the labor market indirectly through their impact on capital utilization and, in consequence, on output. Thus, as far as the labor market is concerned, changes in the relative price of investment goods are practically equivalent to standard neutral technology shocks provided that capital utilization is variable.13 The same intuition explains why comovements between output and labor market variables remain the same as well. 11

In order to make our results comparable with the business cycle literature, we use a HodrickPrescott smoothing parameter of 1,600. 12 Another way to quantitatively estimate the contribution of the investment-specific shocks to business cycle fluctuations is to do the same exercise as Greenwood, Hercowitz, and Krusell (2000). They only let operate the -shock and conclude that it explains about 30 percent of fluctuations. Using the same approach we find a contribution of nearly 40 percent. 13 Strictly speaking, they are not equivalent because investment-specific shocks do have a direct effect on investment which has a very small impact on labor market fluctuations. Therefore, they do not only affect the labor market though the utilization rate. However, this effect is negligible.

27

Unlike labor market outcomes, the relative standard deviation of investment falls significantly from 3.21 to 2.26 when we shut down the -shock. This is not unexpected since this type of shock affects directly investment decisions. For instance, a positive shock reduces the users cost of capital and, thereby, raises the return of investment, which stimulates investment. Furthermore, we also observe an increase in the correlation between investment and output from 0.89 to 0.99. Without this direct effect from shock to investment, the latter only deviates from its steady-state path due to the intertemporal substitution associated to changes in output. Hence the almost perfect correlation between investment and output as in a standard RBC model. Consumption also becomes much less volatile relative to output when the investmentspecific shock is not operative. The decrease of the relative standard deviation of both consumption and investment are tightly related. In fact, the intuition is fundamentally the same. A fall in the relative price of investment goods (i.e. a positive shock) makes agents substitute investment away from consumption. Thus, removing this direct source of investment volatility causes a significant drop in consumption fluctuations. The correlation between consumption and output switches sign from negative (0.28) to strongly positive (0.84). The baseline model counterfactually predicts that consumption is countercyclical due to the strong substitution effect associated to changes in the price of investment goods. When this price remains constant, we obtain that consumption is highly procyclical as in the data. Although we do not present the results for the alternative calibrations (i.e., parameterizations B and C) with no investment-specific technological change, the main conclusion presented above still holds. Namely, investment-specific shocks do not have an amplification effect on the labor market.

28

Table 5: Simulation results U.S. Benchmark Model Data Baseline B C (1) (2) (3) (4) σ(Y ) 1.60 1.81 1.97 1.38 Standard deviation relative to output: Investment 3.38 3.21 3.08 3.91 Consumption 0.69 0.47 0.43 0.59 Cap. Utilization§ 1.31 1.06 1.03 1.17 Employment 0.63 0.68 0.72 0.43 Unemployment 7.75 5.48 5.86 3.49 Vacancies 8.75 1.37 2.38 1.70 V/U 16.13 4.45 3.58 3.97 Job finding rate 4.81 1.78 1.60 2.58 Separation rate 3.56 4.81 5.39 1.77 Job creation 2.55 3.77 4.31 1.60 Job destruction 3.73 4.38 4.92 1.55 Wages 0.56 0.33 0.30 0.59 Correlation: Y, I 0.83 0.89 0.90 0.87 Y, C 0.79 -0.28 -0.29 -0.27 Y, U -0.84 -0.99 -0.99 -0.96 Y, V 0.90 -0.76 -0.96 0.32 V, U -0.92 0.81 0.98 -0.06 Job creation, -0.36 0.92 0.95 0.13 Job destr. Autocorrelation: Output 0.84 0.78 0.77 0.80 Unemployment 0.87 0.81 0.80 0.86 Vacancies 0.90 0.73 0.86 0.00

No Inv. Shocks

No Cap. Utilizat.

No Endog. Separation

(5) 1.66

(6) 1.04

(7) 1.14

2.26 0.06 0.76 0.68 5.49 1.37 4.46 1.78 4.82 3.75 4.15 0.33

3.70 0.88 0.68 5.52 1.30 4.51 1.80 4.83 3.77 4.40 0.34

4.35 0.71 1.29 0.25 2.04 7.09 8.39 2.35 1.70 0.25 0.67

0.99 0.84 -0.99 -0.76 0.80 0.92

0.64 0.02 -0.99 -0.77 0.82 0.93

0.85 -0.20 -0.81 0.93 -0.55 -0.22

0.78 0.81 0.73

0.77 0.81 0.76

0.80 0.75 0.56

Note: § The relative standard deviation of the capital utilization in the U.S. refers to standard deviation of the workweek of capital during 1952-1984 relative to output’s during the same period.

Results from the baseline calibrated model reveal important counterfactual predictions regarding the labor market. In particular, the contemporaneous correlation of vacancies with output is negative in the model whereas the empirical evidence says that it is strongly procyclical for the U.S. economy. As a consequence, we obtain a significant positive correlation between vacancies and unemployment, and job 29

creation and job destruction. Thus, the baseline model is unable to reproduce the so-called Beveridge curve. Notice that this result has nothing to do with the nature of uncertainty in the model because the model with no investment shocks displays exactly the same correlations. The baseline model predicts this counterfactual correlation of vacancies and unemployment mainly due to the large fraction of endogenous job destruction. As pointed out by Krause and Lubik (2005), when the exogenous separation probability increases and gets closer to the steady-state separation rate, the model delivers a lower correlation between vacancies and unemployment. Indeed, when we abstract from endogenous job destruction and make ρt constant at 0.10 (i.e. ρt = ρ), we obtain a correlation of −0.55 (see column 7 in Table 5).14 We also observe a switch of sign in the correlation between vacancies and output from -0.76 to 0.93. Vacancies are now strongly procyclical as in data. Another example comes from our parameterization B (column 3). With a lower ρ = .035, the model produces a even more countercyclical behavior of vacancies and, in consequence, a more positive vacancies-unemployment correlation. The question is: why does the correlation of vacancies and unemployment (output) fall (increase) as ρ moves closer to the steady-state ρ? Note that a larger ρ results in a less volatile separation rate. In the limit case where ρt = ρ, clearly the separation rate does not fluctuate. Therefore, as ρ becomes larger, employment adjustments depend more on vacancies than on job destruction. Thus, after a positive shock, firms have to post more vacancies in order to raise the number of workers. Moreover, smaller fluctuations in the job destruction rate increase the pool of unemployed workers relative to the case with a lower ρ. Consequently, in relative terms, the probability of filling a vacancy goes up, and firms tend to advertise more vacancies. These two effects tend to make vacancies more procyclical (or less countercyclical) as endogenous job destruction becomes less important. 14 Here we recalibrate κ = .143 and φ = 1.551 so that the steady-state job creation optimality condition is satisfied and the matching elasticity equal to 0.72 is matched. We also let b = 1.907 and η = 0.353 as in the baseline case.

30

The other counterfactual prediction of the baseline calibration, namely, the positive correlation between job creation and destruction comes fundamentally from two sources. First and foremost, the degree of responsiveness of the job filling probability to changes in unemployment (i.e.

ε∗mu) seems to be too high.

Cooley and Quadrini

(1999) find this an important factor to explain the difficulties to account for the joint behavior of job creation and destruction in a model with matching frictions in the labor market. To see that, suppose that the elasticity of the matching function with respect to unemployment falls. Then the probability of filling a vacancy would be less volatile. Therefore, when unemployment goes down after a positive shock, the job filling rate does not fall as much. This has a relative positive impact on vacancies, and job creation rises. That explains the decrease in the correlation of job creation and job destruction in our parameterization C (ε∗mu = 0.40) shown in column 4 of Table 5. Clearly this mechanism is also at work to reduce the correlation between vacancies and unemployment as we can infer from the table. The second cause for the counterfactual dynamics of job creation and destruction in our baseline calibration is the highly volatile job separation rate. This is due to the low ρ as mentioned above. Essentially the same intuition as for the positive correlation of vacancies and unemployment applies here. That is, job destruction plays a more relevant role to adjust employment than job creation does. In addition, this gives the wrong incentives for firms to create more jobs during booms and, in consequence, makes job creation countercyclical. Finally, we also ask whether variable capital utilization generates any amplification effect on the labor market. We do that by shutting down this adjustment margin (column 6). First, clearly the endogenous utilization rate do help to amplify the effect of shocks on the whole economy. However, it does not provide any particular amplification mechanism to the labor market. In other words, it creates more fluctuations in labor market outcomes only in the same extent that makes output more volatile.

31

Actually, when we make capital utilization constant, the relative standard deviation of labor market outcomes stays practically unchanged. Only the standard deviation of vacancies seems to be slightly increased by variable capital utilization (1.37 vs. 1.30). This result confirms our intuition why investment-specific shocks do not have either any meaningful amplification effect on labor market variables.

5

Concluding remarks

In this paper we provide evidence from the postwar period in the U.S. that shows a link between relative prices, investment, capacity of utilization, and labor market tightness. This evidence suggests that when technological advances make equipment less expensive, the investment in new equipment increases together with the relative number of vacancies, at least in the short run. We present a quantitative model that can account for this empirical facts as well as other standard business cycle facts. However, the model is unable to generate any extra amplification mechanism in the labor market. Thus, the relative volatility of relevant labor market variables remains unchanged when investment shocks are incorporated into the model. Hence, the model presented here cannot replicate the magnitude of the cyclical fluctuations of vacancies and unemployment without counterfactually generating too much output volatility. Variable capital utilization, as it is well known in the RBC literature, does help the model amplify technology shocks. However, it does not have essentially any additional effect on the volatility of labor market variables. Another important result is that having endogenous separations in the model does not seem to introduce a meaningful amplifying effect. With a reasonable fraction of endogenous job destruction, the model delivers important counterfactual predictions with respect to the behavior of vacancies and unemployment, and job creation and

32

destruction. It is true that more endogenous separations amplify the fluctuations of both unemployment and job destruction. However, this causes vacancies and job creation to display too little volatility and, more importantly, become countercyclical. This leads the model to fail to reproduce the downward-sloping Beveridge curve.

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