Sectoral labor market effects of fiscal spending

Structural Change and Economic Dynamics 34 (2015) 19–35

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Sectoral labor market effects of fiscal spending Dennis Wesselbaum University of Hamburg, Chair of Economics, Methods in Economics, Germany

a r t i c l e

i n f o

Article history: Received March 2014 Received in revised form April 2015 Accepted May 2015 Available online 5 June 2015 JEL classification: C11 E32 E62 H5

a b s t r a c t This paper studies sectoral effects of fiscal spending. We estimate a New Keynesian model with search and matching frictions and two sectors. Fiscal spending is either wasteful (consumption) or productivity enhancing (investment). Using U.S. data we find significant differences across sectors. Further, we show that government investment rather than consumption shocks are driver of fluctuations in sectoral and aggregate outputs and labor market variables. Finally, government investment shocks are much more effective in stimulating the economy than spending shocks. However, this comes at the cost of an increase in the unemployment rate. © 2015 Elsevier B.V. All rights reserved.

Keywords: Government consumption Government investment Search and matching Sectoral effects

1. Introduction This paper analyzes sectoral labor market effects of fiscal spending. In particular, we highlight the differences between unproductive government consumption expenditures and productive government investment expenditures. The Great Recession resuscitated the interest of policy makers and researchers in the short- and long-run effects of fiscal policy. To counter the large adverse effects on real activity governments around the world used large fiscal policy packages. For example, the American Recovery and Reinvestment Act (ARRA) was worth $550 billion. Roughly 30% were allocated towards infrastructure projects. This observation relates to the findings by Bachmann and Sims (2012), showing that the government investment-to-government consumption ratio for an increase in government expenditures increases

E-mail address: [email protected] http://dx.doi.org/10.1016/j.strueco.2015.05.002 0954-349X/© 2015 Elsevier B.V. All rights reserved.

more during recessions than during booms. Moreover, government investment expenditures average about 20% of total spending in the post-war United States. Research on government consumption shocks (e.g. Baxter and King, 1993 and Linnemann and Schabert, 2003) show that an increase in government consumption increases output but crowds-out private consumption. This contradicts the empirical evidence (e.g. Blanchard and Perotti, 2002) of an increase in private consumption. Fisher and Turnovsky (1995, 1998) study the effects of government investment shocks and highlight the importance of short- and long-run trade-offs. Linnemann and Schabert (2006) use a sticky price model of the business cycle and show that even at low levels of productivity of government investment positive effects on output and private consumption can be achieved. However, research related to the sectoral labor market effects of fiscal policy is rather sparse. This is surprising as, for example, the famous Bernstein and Romer (2009) report on the job market effects of the ARRA breaks down job gains by industry.

20

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

To close this gap, we analyze the sectoral effects of productive vs. unproductive government expenditures. We build a stylized New Keynesian model of the U.S. economy with search and matching frictions and two production sectors. One sector produces goods, while the other sector provides services. Monetary policy in this model follows a Taylor-type interest rate rule. Fiscal policy can use its resources (generated by lump-sum taxation) for government consumption or by building-up the government capital stock. While government consumption is wasteful and works mainly as a demand-side shock, government capital is used in the production process and affects marginal productivity. We want the reader to think about government capital as infrastructure which is an exogenous input into the production process. Then, we estimate this model on U.S. time series using Bayesian methods. Several findings stand out. The manufacturing labor market is characterized by a larger steady state separation rate and a higher bargaining power compared to the service sector labor market. In contrast, vacancy posting costs are larger in the service sector than in the manufacturing sector. Further, government consumption and investment follow fiscal rules. Government consumption is entirely driven by movements in government debt, while government investment reacts to changes in output and debt. Government investment is more productive in the service sector than in the manufacturing sector. A variance decomposition analysis shows that sectoral outputs and sectoral employment is mainly driven by aggregate technology shocks. The second most important driving force is monetary policy. A shock in one sector plays only a limited role in explaining fluctuations in the other sector. Government consumption shocks generate positive effects only on impact. Due to the endogenous reaction of government investment to higher debt, the negative supply side effects dominate the positive demand side effects and output and employment decrease. In contrast, an increase in government investment increases sectoral and aggregate output. We can conclude that government investment is far more effective in increasing aggregate and sectoral output levels than government consumption. However, this also comes at a cost: government investment leads to increased service sector and aggregate unemployment over the medium-run after an initial drop in the unemployment rate. Our paper contributes to two streams in the literature. First, it contributes to the literature that estimates search and matching models using Bayesian techniques. For the United States, Gertler et al. (2008), Lubik (2009), Di Pace and Villa (2013), and Furlanetto and Groshenny (2013) estimate search and matching models. While Lubik (2009) estimates a stylized version of the search and matching model, Di Pace and Villa (2013) use a richer model with capital and hours worked. Furlanetto and Groshenny (2013) estimate a New Keynesian model with search and matching frictions allowing for mismatch shocks. They show that this mismatch shock was important during the Great Recession. Besides those papers there are studies estimating search and matching models for other countries. Lubik (2012)

estimates such a model for Hong Kong, Lin and Miyamoto (2012) use data for Japan, and Wesselbaum (2014) focuses on Australia. Zanetti (2014) estimates a New Keynesian model with search and matching friction for the UK and uses this model to address the implications of labor market reforms. The findings point towards a minor role played by the labor market reforms of the Thatcher government. Second, we add to literature on sectoral effects of fiscal policy. However, the papers in this category interpret sectoral as the difference between traded vs. non-traded goods and perform their analysis in an open economy framework. Our analysis, in contrast, is performed in a closed economy setting. Bénétrix and Lane (2010) perform a VAR analysis for a number of European countries and find that government spending increases the relative size of the non-traded vis-a-vis the traded goods sector. They conclude that fiscal shocks do affect the sectoral allocation while having aggregate effects. Along this line, Monacelli and Perotti (2008) use a structural VAR and find a positive comovement in consumption and production for the manufacturing and the service sector in an open-economy model. They show that a canonical open-economy business cycle model fails to generate such a positive comovement. Further, Bouakez et al. (2013) estimate SVARs for subcategories of government spending and investment. They find large differences in the effectiveness of fiscal policy across sectors. The largest effects are obtained for changes in government employment while spending has only limited effects on output. Finally, our paper is related to the work by Obstbaum (2011), who builds a New Keynesian search and matching model with fiscal policy. However, the main difference to our paper is that fiscal spending is purely government consumption. One of the main findings is that the effects on labor market variables and output depends crucially on the financing scheme. The paper is structured as follows. Section 2 develops our model and Section 3 presents our data set and discusses our estimation results. Section 4 provides a robustness check and Section 5 briefly concludes.

2. Model derivation We develop a discrete-time model for the U.S. economy with two different production sectors. This model is an extension to the model developed in Wesselbaum (2011), while labor market frictions follow the contributions from Mortensen and Pissarides (1994) and den Haan et al. (2000). Households maximize utility by setting the path of consumption, which is a CES aggregate of differentiated products. Firms set prices and choose employment in two sectors: manufacturing (i.e. goods production) and service and produce a final good using both sectoral outputs. We further assume that separations are endogenous and driven by job-specific productivity shocks. Hence, there is a flow of workers into unemployment while unemployment–employment transition is subject to search and matching frictions. Monetary policy sets the nominal interest rate via a standard Taylor-type interest rate rule and fiscal policy

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

uses consumption and investment into government capital to spend resources. 2.1. Households Our economy is populated by a family with two types of infinitely lived workers. They inelastically supply one unit of labor and being represented by the unit interval. In addition, household members insure each other against income fluctuations as in Merz (1995). They have the following preferences over consumption Et

∞

t=0

ˇt [ln(Ct )],

(1)

where the conditional expectation operator is denoted by Et . Households discount the future with a factor ˇ ∈ (0, 1). The intertemporal budget constraint faced by the family is Ct +

 Bt Bt+1 = Wxt Ntx + Rt + bU t + t + Tt , Pt+1 Pt+1

(2)

x

where x ∈ m, s is the index for the worker’s sector, either m for manufacturing or s for service. Further, bUt is income from unemployment with b > 0 corresponding to unemployment benefits, while Wxt Ntx is labor income from workers employed in sector x. Bond holding, Bt , pays a gross interest rate Rt , t are aggregate profits and Tt are lump sum transfers from the government. Then, the optimality condition for the household is a standard Euler equation given by



 1

1 Pt = ˇEt Rt . Ct Pt+1 Ct+1

(3)

x x Nit+1 = (1 − it+1 )(Nitx + Vitx q(tx )).

x

(Vtx )

1−x

,

(4)

where x ∈ (0, 1) is the elasticity of the matching function with respect to unemployment and the match efficiency is governed by mx > 0. Then, the probability of a vacancy being − filled in the next period is q(tx ) = m(tx ) . Labor market x x x tightness is given by t = Vt /Ut . Tightness is a key variable in search and matching models as it generates a congestion

1 See Davis (2001) and Davis and Haltiwanger (2001) for ex ante labor sorting into separate search markets. 2 See also Tapp (2007) for this more general approach.

(5)

The firm has two margins to control employment: either adjust the number of posted vacancies or set the critical threshold, which then influences the separation rate. Finally, the aggregate values are defined by agg

= Uitm + Uits ,

(6)

agg

= Mitm + Mits ,

(7)

Uit

Mit

agg Vit

=

agg

=

Vitm

+ Vits ,

(8)

agg

it

Vit

agg

Uit

.

(9)

2.3. Firms Firms use a standard Cobb–Douglas production technology with elasticity 0 ≤ ϑ ≤ 1 ϑ

The firm searches for workers on two discrete and closed markets. This assumption is based upon the limited ability of workers to switch sectors due to specific skills, initial education, and employment protection legislation (see e.g. Lamo et al., 2006).1 One of those markets contains all workers in the manufacturing sector, and the other contains all workers in the service sector. This assumption allows us to account for differences in vacancy filling rates across sectors, found by Davis et al. (2009) and estimate sectoral matching functions.2 New matches Mtx are created from the pool of unemployed Utx and the number of open vacancies Vtx according to the matching function M(Utx , Vtx ) = mx (Utx )

externality: if a firm posts a vacancy it decreases simultaneously the probability for other firms to fill a vacancy. On the other hand, an additional searcher causes negative search externalities for other searchers, i.e. reduces the job finding probability of all other searchers. The firm’s exit site is characterized by endogenous separations. The total number of separations in each sector, at firm i is given by x (˜axit ) = F(˜axit ), where a˜ xit is the cut-off point of idiosyncratic productivity and F(·) is a timeinvariant distribution with positive support f(·). Its mean is given by ωx and ς x is the dispersion of the function. Connecting entry and exit site gives the evolution of employment at firm i as

Yit = At (Yitm ) (Yits )

2.2. Labor markets

21

1−ϑ

,

(10)

to produce the final production good Yit using the output produced in the manufacturing sector Yitm and the service sector Yits . The sector-specific production technologies are ˛x



Yitx = (Gtk ) Axt Nitx

ax a˜ x

it

˛x f (ax ) dax ≡ (Gtk ) Axt Nitx H(˜axit ), x 1 − F(˜ait )

where we use H(˜axit ) = ˛x

(11)

 a˜ x

it

ax

f (ax ) 1−F(˜ax ) it

dax to ease notation.

Further, denotes the sector-specific output elasticity w.r.t. government investment. The elasticity of government investment is a key factor in discussing its effectiveness. While aggregate productivity At and sectoral productivities Axt are common to all firms, the specific idiosyncratic productivity axit is idiosyncratic and every period it is drawn in advance of the production process from the corresponding distribution function. Further, we assume that government capital is used in the production of sectoral outputs as the final good production only acts as an aggregation of sectoral outputs. We assume that all three technology shocks follow autoregressive processes ln At = A ln At−1 + eA,t , eA,t ∼N(0, A ),

(12)

ln Axt

(13)

=

Ax ln Axt−1

+ eAx ,t , eAx ,t ∼N(0, Ax ),

22

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

where the error terms are i.i.d. and normally distributed. The firm maximizes the present value of real profits given by

i0 = E0

∞ 

ˇt

t=0

−c s Vits −

t

0



Pit Y − Wm − Wsit − c m Vitm it Pt it

 P it 2

Pit−1

−

ˆ t = ˇEt  ˆ t+1 + ϕ  ˆ t,

2

Yt ,

(14)

while perfect capital markets imply that the firm discounts with the households subjective discount factor ˇ. The first term in parenthesis is real revenue, the second and the third term is the wage bill, which is given by the aggregate of individual wages



Wxit = Nitx

a˜ x

wtx (ax )

it

f (ax ) dax . 1 − F(˜axit )

(15)

The wage is not identical for all workers, instead it depends on the idiosyncratic productivity across sectors. The fourth and fifth terms reflect the total costs of posting a vacancy. The latter term corresponds to Rotemberg (1982) price adjustment costs. The degree of these costs is measured by the parameter ≥ 0, while the costs are related to the deviation from steady state inflation, . The firstorder conditions with respect to employment, vacancies, and prices are tx = ϕt Axt H(˜axt ) −

∂Wxt x x + Et ˇt+1 (1 − t+1 ) t+1 , ∂Ntx

(16)

cx x x = Et ˇt+1 (1 − t+1 ) t+1 , q(tx )

(17)

(1 − ϕt ) = 1 − (t − )t + Et ˇt+1 ×



(t+1 − )t+1

is filled is decreasing in the degree of labor market tightness the cost of posting vacancies increases and reduces incentives to post new vacancies. Finally, a log-linearization of the last first-order condition around a zero inflation steady state gives the New Keynesian Phillips curve



Yt+1 . Yt

(18)

where hats above variables denote deviations from steady state. The slope of the Phillips curve is determined by  = ( − 1)/ . 2.4. Wage determination Firm and worker engage in individual Nash bargaining and maximize the Nash product wtx = argmax



× ϕt+1 Axt+1 H(˜axt+1 ) −





(Ext − Uxt ) (Jxt − Vt )

1−



.

(20)

The first term is the worker‘s surplus, the latter term is the firm‘s surplus and 0 ≤  ≤ 1 is the exogenously determined, constant relative bargaining power. The worker’s threat point is Uxt , the value of being unemployed and the firm’s threat points are given by Vt which is zero in equilibrium due to a free entry condition. The asset value of a filled job for the firm is Jxt and for the worker, Ext , is the asset value of being employed. Then, the solution to the problem is an optimality condition  Ext (axt ) − Uxt = (21) Jx (ax ). 1− t t To obtain an explicit expression for the individual real wage we have to determine the asset values and substitute them into the Nash bargaining solution. The three Bellman equations are given by Jxt (axt ) = ϕt Axt axt − wtx (axt ) + Et ˇt+1

The current period average value of workers is given by tx and ϕt reflects real marginal costs. Further, t denotes the inflation rate and  is its steady state value. Combining (16) and (17) gives the job creation condition cx x ) = Et ˇt+1 (1 − t+1 q(tx )

(19)

×



x (1 − t+1 )

a˜ x

t+1

f (ax ) Jxt+1 (ax ) dax 1 − F(˜axt+1 )



(22)

Ext (axt ) = wtx (axt ) + Et ˇt+1

∂Wxt+1 x ∂Nt+1



+

cx x ) . q(t+1

Hiring decisions are a trade-off between the cost of a vacancy and the expected return. The lower the probability of filling a vacancy, the longer the duration of existing contracts – as 1/q(tx ) is the duration of the relationship between firm and worker – because the firm is not able to replace the worker instantaneously. As an example, if expected productivity rises, the righthand side rises while the left-hand side on impact remains unchanged. Higher expected revenue creates incentives for the firm to post more vacancies, which increases labor market tightness. Because the probability that an open vacancy

,



×



x (1 − t+1 )

a˜ x

t+1

f (ax ) x Ext+1 (ax ) Uxt+1 dax +t+1 1 − F(˜axt+1 )

 , (23)

 Uxt

= b+Et ˇt+1

x tx q(tx )(1−t+1 )

 a˜ x

Ext+1

t+1

x ))Uxt+1 ×dax + (1 − tx q(tx )(1 − t+1

f (ax ) 1 − F(˜axt+1 )

 (24)

The first equation is the asset value of the job for the firm depending on the real revenue, the real wage and if

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

the job is not destroyed, the discounted future value. Otherwise, the job is destroyed and hence has zero value. The second equation is the asset value of being employed for the worker and depends on real wage, the discounted continuation value, and in case of separation the value of being unemployed. The latter equation is the asset value of being unemployed. Unemployed worker receive unemployment benefits, the discounted continuation value of being unemployed, and if she is matched she receives the value of future employment. Finally, the expression for the wage is wtx (axt )

=

(ϕt Axt axt

+ c x tx ) + (1 − )b.

(25)

The gap between the real wage and the reservation wage is increasing in every time-dependent component and the worker’s bargaining power. At the end of this section we determine the cut-off point of idiosyncratic productivity. The firm will endogenously separate from a worker if and only if Jxt (axt ) < 0,

1 (1 − )ϕt Axt

where ı > 0 is the depreciation rate of the capital stock and It−1 is the investment into new capital. Here, we assume that there is a time-to-build lag following Kydland and Prescott (1982) and, more recently, Bouakez et al. (2014).3 Again, we use a fiscal rule with feedback to output and government debt to model government investment It = −k Yt − k Bt + Id,t ,

(34)

ln Id,t = I ln Id,t−1 + eI,t , eI,t ∼N(0, I ),

(35)

where discretionary investment spending are Id,t with i.i.d. normally distributed errors. Finally, the resource constraint is given by Yt = Ct + c m Vtm + c s Vts + Gtc + It +

2

(t − 1)2 Yt ,

(36)

such that the final output good can be consumed by the private and the public sector, used as vacancy posting costs in both sectors, or can be used to build up the government capital stock.

(26)

i.e. if the asset value of the worker for the firm is negative. Using this condition, the expressions for the real wage, and the vacancy posting condition in equilibrium yields the productivity threshold a˜ xt =

23



(1 − )b + c x tx −



cx . q(tx )

(27)

2.5. Monetary and fiscal policy The monetary authority targets the nominal interest rate by following a standard Taylor rule, given by ˆ t + y Yˆ t + etr , Rˆ t =  

(28)

where  > 0 and y > 0 are the respective weights on inflation and output. Monetary policy shocks etr follow an autoregressive processes r ln etr = r ln et−1 + er,t , er,t ∼N(0, r ),

(29)

where the error terms are i.i.d. and normally distributed. Fiscal policy finances expenditures with lump-sum taxes, Tt , and by issuing government bonds, Bt , Bt+1 = Bt + Gtc + It − Tt . Rt

(30)

The government can uses its resources either for government consumption or for building up the government capital stock. Government consumption is wasteful and follows a fiscal rule with feedback to output and government debt Gtc = −c Yt − c Bt + Gd,t ,

(31)

ln Gd,t = G ln Gd,t−1 + eGc ,t , eGc ,t ∼N(0, G ),

(32)

where Gd,t are discretionary spending shocks with i.i.d. normally distributed errors. Here,  c gives the weight of output and c gives the weight of debt in the reaction function. In contrast, government capital is used in the production process and follows: k + It−1 , Gtk = (1 − ı)Gt−1

(33)

2.6. Calibration and priors We calibrate the model for the United States on a quarterly basis and present the prior choice for the estimated parameters. Households discount the future with ˇ = 0.99, and the demand elasticity is set to 11. The unemployment rates are taken from BLS household data. For the manufacturing sector we take a value of 12% and for the service sector the unemployment rate is set to 8%. For both sectors, we assume that the idiosyncratic productivities are lognormally distributed with zero mean and a variance of 0.12 as in Krause and Lubik (2007). The job filling rate in steady state is set to 0.7 in line with Krause and Lubik (2007). The steady state cut-off point for idiosyncratic productivity is given by a˜ x = F −1 (x ). Then, matches in steady state are x x computed according to M x = 1− x N , vacancies are given x x x by V = M /q , and labor market tightness is tightness is x  x = Vx /Ux . We can compute match efficiency as mx = q  . Government consumption is set to 25% of output and government investment is set to 5% of output in line with the values taken from the NIPA tables. Unemployment benefits are set to 20% from wages. For the bargaining power of workers we assume a symmetric split and impose a normally distributed prior with mean 0.5 and standard deviation 0.05. Further, the parameter that drives the separation rates belongs to the beta family and has a mean of 0.1 and a standard deviation of 0.02. Vacancy posting costs are assumed to be gamma distributed with mean 0.05 – as usually assumed in the literature – with standard deviation 0.02. Finally, the elasticity of the matching function is assumed to be beta distributed with mean of 0.5 and standard deviation 0.05. The parameter ϑ in the aggregate production function is assumed to be normally distributed with mean 0.5 and standard deviation 0.1. The sector-specific elasticities

3 We also tried a four-quarter lag and find that our results are robust to this change.

24

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

Table 1 Posterior estimates. Parameter

Point

5%

95%

Parameter

Point

5%

95%

ı, Depreciation Rate m , Separation: Man. s , Separation: Serv. m , Bargaining Power: Man. s , Bargaining Power: Serv. cm , Vacancy Posting Costs: Man. cs , Vacancy Posting Costs: Serv. m , Match. fct. elast.: Man. s , Match. fct. elast.: Serv.  k , FR: Weight Output, Inv.  c , FR: Weight Output, Cons.

k , FR: Weight Debt, Inv.

c , FR: Weight Debt, Cons. , Price Adj. Costs ϑ, El. Aggregate Output ˛s , Productivity Gov. Inv. Serv. Sector ˛m , Productivity Gov. Inv. Man. Sector

0.0143 0.0866 0.0568 0.5159 0.4902 0.0676 0.0729 0.5864 0.4770 0.0162 0.0014 0.0624 0.0288 33.5075 0.4137 0.0522 0.0302

0.0099 0.083 0.0491 0.5003 0.4808 0.0646 0.0697 0.5684 0.4659 0.0046 0 0.0458 0.0148 32.8048 0.374 0.036 0.0244

0.0201 0.0906 0.0633 0.5312 0.5064 0.0714 0.077 0.6056 0.4888 0.0249 0.0032 0.0794 0.0392 34.2674 0.4381 0.0617 0.0373

y , TR: Weight Output  , TR: Weight Inflation Autocorrelations A Am As G I r Standard deviations Am As G I r A

0.0819 1.5503

0.0683 1.5392

0.1003 1.5607

0.4444 0.7643 0.8813 0.8874 0.5176 0.7162

0.4294 0.7116 0.8046 0.8353 0.4844 0.6456

0.4635 0.8039 0.9434 0.924 0.5603 0.7899

0.0213 0.0118 0.0168 0.0222 0.0518 0.1105

0.0196 0.0118 0.0153 0.0205 0.0388 0.0855

0.0231 0.0119 0.0183 0.0240 0.0664 0.1366

of government investment are both normally distributed with mean 0.05 and standard deviation 0.05. Price adjustment costs, , are assumed to be normal distributed with mean 40 and standard deviation 5, based upon the calibrated value by Krause and Lubik (2007). The prior on the depreciation rate of government investment belongs to the beta family with mean 0.02 and standard deviation of 0.01. The prior is set to the usually assumed value for private capital in DSGE models. Then, we set the priors for the fiscal rule parameters. For the feedback to output and debt we assume prior belonging to the gamma family with mean 0.1 and standard deviation 0.1. Monetary policy parameters are both assumed to be normally distributed with a mean of 1.5 and standard deviation of 0.05 for the weight on inflation. For the weight on output, we assume a mean of 0.125 with standard deviation 0.05. We assume that the autocorrelation parameters for all six processes follow beta distributions, with mean of 0.5 and standard deviation of 0.2. Finally, all standard deviations are inverse Gamma distributed, with mean of 0.1 and standard deviation 2.

3. Estimation results 3.1. Data We use quarterly, seasonally adjusted time series for the United States from 1954:3 to 2013:4 (238 observations). Total output and the sectoral outputs are taken from the Bureau of Economic Analysis’ NIPA tables. Total output is gross domestic product (A191RC1) in billions of U.S. Dollars. Manufacturing output is the sum of durable (DDURRC1) and nondurable (DNDGRC1) goods. Government consumption is the sum of current expenditures (W013RC) and capital transfer payments (W020RC1) minus the consumption of fixed capital (A918RC1). Government investment is the sum of defense (A788RC1) and nondefense (A798RC1) gross investment plus state and local gross investment (A799RC1). All variables are divided by the personal consumption expenditures price deflator (DPCERG3), with basis year 2009.

Labor market variables are taken from the Bureau of Labor Statistics. Employment in the manufacturing sector is employment in the nondurable (CES3200000001) and durable (CES3100000001) sector. Employment in the service sector is the sum of employment in the private service-providing (CES080000001), professional and business service (CES6000000001), and other services (CES8000000001) sector. Finally, the interest rate is the effective Federal funds rate taken from the St. Louis FED FRED system. Before we run our estimation, we write the time series in logarithmic scale and use a Hodrick–Prescott filter with = 1600 to generate the cycle component. Then, we use 500,000 draws for our MCMC chains to obtain the estimation results. 3.2. Point estimates Table 1 presents the point estimates and the 95% confidence intervals for the set of estimated parameters.4 The separation rate in the manufacturing sector is larger compared to the service sector (0.09 vs. 0.06).5 They are sizably smaller compared to the value found by Lubik (2009) for the aggregate separation rate of 0.12. The elasticity of the matching function with respect to unemployment in the manufacturing sector is larger as in the service sector (0.59 vs. 0.48). The smaller value in the service sector implies that (i) the finding rate reacts more elastically to changes in labor market tightness and (ii) the matching rate is less sensitive to changes in labor market conditions. However, those values are smaller compared to the estimated value in Lubik (2009) of 0.74. We find that workers in the service sector have a slightly smaller bargaining power compared to the manufacturing sector (0.49 vs. 0.52). This implies a smaller share of the surplus in the service

4 We also exclude the period of the Great Recession and run an estimation over the sample 1954:3 to 2007:4. We find that most parameters do not change very much with two exceptions. Vacancy postings costs are around 0.05 in both sectors and the fiscal rule for government investment has a larger weight on output than on debt, while the rule for consumption is purely discretionary. 5 Figures for the density are shown in the appendix.

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

25

0.05 0 −0.05

Technology: Manufacturing Technology: Service

−0.1 54

0.8 0.6 0.4 0.2 0 −0.2 −0.4 54

58

62

66

70

74

78

82

86

90

94

98

02

06

10

06

10

Monetary Policy Aggregate Technology

58

62

66

70

74

78

82

86

90

94

98

02

Gov. Consumption Gov. Investment

0.05 0 −0.05 54

58

62

66

70

74

78

82

86

90

94

98

02

06

10

Fig. 1. Estimated shocks. Vertical axis presents quarters from 1954 to 2010.

sector is allocated to the worker. Next, we consider the cost of posting a vacancy. We find that the cost of posting a vacancy is slightly larger in the service sector (0.073) than in the manufacturing sector (0.068). Usually, this parameter is calibrated at around 0.05 for standard (aggregate) matching models, which seems to be a reasonable value given our estimates. The price adjustment cost parameter is estimated to be 33.5, which is slightly smaller compared to the calibrated value in Krause and Lubik (2007) which is set to match the Calvo probability of an average price duration of four quarters. Hence, prices are re-set more frequently. The depreciation rate of government investment is estimated to be 0.0143 which, intuitively, is smaller compared to the depreciation of private capital usually assumed to be close to 0.025. The elasticity of aggregate production function, ϑ, is estimated to be 0.41. This implies a larger weight on service-sector output. The service-sector output elasticity w.r.t. government investment is estimated to be 0.05, which is larger as in the manufacturing sector (0.03). Our results imply that government investment is more productive in the service sector than in the manufacturing sector. In the literature, the elasticity of government investment varies between 0.24 (Aschauer, 1989) and negative values (Evans and Karras, 1994). The fiscal rule describing government consumption reacts to government debt (0.03) but does not respond to output, as zero is contained in the confidence interval. In contrast, government investment reacts to output (0.02) and debt (0.06). Since all parameters enter negatively into the fiscal rules we find a countercyclical behavior of government expenditures. Therefore, government consumption and government investment can be interpreted as automatic stabilizers of real activity. The weights in the

monetary policy rule are in line with the literature. We find a weight of 1.55 on inflation and 0.08 on output which is slightly lower as commonly assumed (0.125). We find that the sectoral technology shocks are highly autocorrelated in contrast to the aggregate technology shock. Further, we find that the government spending shock shows a larger degree of autocorrelation compared to the government investment shock. The autocorrelation of the monetary policy shock is midway between the two expenditure shocks. Finally, we find similar values for the standard deviations of all shocks, with the aggregate technology shock and the monetary policy shock being the most volatile ones. Fig. 1 presents the time series of the estimated shocks. In conclusion, we find evidence that sectors do behave significantly different. This holds for the exit as well for the entry side of job flows. 3.3. Shock decomposition In this section we want to highlight the main driving forces of business cycle fluctuations in key aggregate and sectoral variables. Fig. 2 presents the unconditional variance decomposition. Our results show that output in both sectors is mainly driven by variations in aggregate technology. Further, manufacturing sector output is to 40% driven by the manufacturing sector technology shock. In contrast, the service sector technology shock explains only about 30% of total variation in service sector output. Innovations in monetary policy are more important for service sector output than for output in the manufacturing sector output. Government expenditure shocks explain less than 5% of sectoral outputs.

26

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

1 0.9 0.8 0.7 0.6 0.5

Technology Technology: M Technology: S Monetary Policy G Consumption G Investment

0.4 0.3 0.2 0.1 0

Output: M

Output: S

Inflation

Employment: M

Employment: S

Fig. 2. Unconditional variance decomposition.

Variations in the inflation rate are to 60% driven by aggregate technology shocks. The remaining variations are explained by the service sector technology and the monetary policy shock. For the labor market, technology shocks play the dominant role. Variations in manufacturing employment are driven by 60% by aggregate technology shocks and by 25% by technology shocks to manufacturing sector output. The remaining 15% are explained by shocks to monetary policy and service sector output. In contrast, the main driving forces for service sector employment are the aggregate technology shock and the monetary policy shock. Innovations to service sector output explain only 5% of total variation. 3.4. Impulse responses 3.4.1. Sectoral technology shocks We begin with a positive, mean-reverting technology shock in the manufacturing sector as shown in Fig. 3. Intuitively, the technology shock increases output and reduces marginal costs in the manufacturing sector. Lower marginal costs – via the New Keynesian Phillips curve – imply lower prices and inflation falls. The model generates a sectoral shift towards the manufacturing sector as a consequence of higher relative productivity in this sector. While manufacturing sector output increases, service sector output decreases. Nevertheless, the increase in manufacturing sector output overcompensates the fall in service sector output and aggregate output increases. Our findings contrast the “average out” view of Lucas (1977) that sectoral reallocations should have only very limited effects on aggregate measures. This does not hold true in a sectoral model with labor market frictions and sticky prices. As shown in Wesselbaum (2011) sticky prices are crucial to obtain this result. They create an amplifying effect in the manufacturing sector through the effects of lower interest rates set by the monetary authority. The asymmetric sectoral effects spillover to the sectoral labor markets. Higher output leads to higher employment

in the manufacturing sector, while lower output leads to lower employment in the service sector. The adjustment process occurs mainly along the exit side of the market. Firms prefer to reduce the number of separations then to post more vacancies. The reason is that reduced separations are immediately effective and are costless, whereas vacancies are costly and only become effective in the next period. Wages in the manufacturing sector increase because the positive technology shock creates a surplus that is splitted according to the solution of the Nash bargaining problem. This leads to a drop in vacancy postings as the increase in wages outweights the increase in the value of the match due to increased productivity. The opposite effects are obtained for the service sector labor market. Lower output reduces labor demand in this sector and unemployment slightly increases. Wages decrease as lower demand reduces profits. Further, the drop in wages creates incentives to higher (cheaper) workers and firms in the service sector start to post more vacancies. In sum, the increase in vacancies in the service sector is not larger than the drop in vacancy posting in the manufacturing sector and, hence, total vacancy postings decrease. Higher aggregate output and a lower inflation rate lead the monetary authority to set a lower interest rate. As we have discussed above, fiscal policy responds countercyclically and, hence, government consumption and investment activities are reduced on impact. However, the drop in government debt, triggered by lower interest rates, allows the government to spend more and consumption and investment increase after roughly two quarters. This creates positive effects on aggregate output and employment. The effects of the technology shock die out after roughly 5 years. However, the effects on debt and fiscal expenditures are much more persistent and last for several more years. Turning to the service-sector technology shock we observe significant differences. Fig. 4 presents the estimated impulse response functions for the service sector technology shock.

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

27

−3

x 10

0 Output Output: M Output: S

4

−0.1

Vacancies Vacancies: M Vacancies: S

2 −0.2

0 5

10

15

20

5

10

15

20

−3

x 10

0 −0.1

Wages: M. Wages: S.

10

−0.2

Unemployment Unemp: M. Unemp: S.

−0.3

5

−0.4

0 5

10

15

20

5

10

15

20

−3

−5

x 10

0

x 10

20 −1 10

Debt Inflation Interest Rate

−2 G Consumption G Investment

0 5

10

15

−3 20

5

10

15

20

Fig. 3. Impulse responses to an estimated technology shock in the manufacturing sector.

0.05

Output Output: M Output: S

0.06 0.04

0 Vacancies Vacancies: M Vacancies: S

−0.05

0.02 0

5

10

15

20

5

10

15

20

−3

x 10 0

Wages: M. Wages: S.

4

−0.05

Unemployment Unemp: M. Unemp: S.

−0.1 5

10

15

2 0

20

5

10

15

20

−3

x 10

0

6 4

Debt Inflation Interest Rate

−0.05

2

G Consumption G Investment

0 5

10

15

−0.1 20

5

10

Fig. 4. Impulse responses to an estimated technology shock in the service sector.

15

20

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D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

First of all, the positive technology shock shifts the production frontier outwards, allows a higher level of output production, and reduces marginal costs in the service sector. At a first glance, we observe that the service sector technology shock generates larger and more persistent effects than the manufacturing sector shock. This finding is driven by the higher elasticity of aggregate output w.r.t. service sector output. The shock leads to an increase of output produced in the service sector. Further, the drop in marginal costs implies that firms set lower prices and the inflation rate falls. Higher output increases labor demand by service sector firms. Hence, unemployment in the service sector decreases and wages increase due to the surpluses created by the technology shock. Again, the labor market adjustments occur along the exit side; separations and vacancy postings fall. In the manufacturing sector output stays almost unchanged, while unemployment increases. This finding can be understood when we consider the role of government investment. Because the monetary policy sets a lower interest rate, debt decreases. Further, aggregate output increases such that government investment and consumption increase after a slight, temporary initial drop. This acts as an additional (aggregate) technology shock as it increases productivity in both sectors. Hence, in the manufacturing sector firms benefit from higher government investment and substitute it for labor. Lower demand puts downward pressure on wages and creates incentives to post more vacancies. To sum up, we observe an increase in aggregate output but almost no output effects in the manufacturing sector. Aggregate and service sector unemployment decreases while it increases in the manufacturing sector. The positive effects from government investment (supply side) and government consumption (demand side) are important and are particular relevant for the manufacturing sector.

3.4.2. Government expenditure shocks We begin with a positive, mean-reverting shock to government consumption. Fig. 5 presents the impulse response functions. First of all, we find that the effects, aggregate as well as sectoral, are fairly small. The increase in government consumption works as a demand side shock but raises output only on impact. The increase of government consumption is financed by issuing new debt. As government consumption and investment react negatively to changes in debt, government investment decreases. This triggers adverse supply side effects that are stronger than the demand side effects of higher government demand. The drop in government investment acts as a negative technology shock to both sectors. As a consequence, output in both sectors and, therefore, in aggregate decreases. This reduction in output lowers labor demand and unemployment increases after the initial drop. Wages drop due to lower output and profits. Because wages increase on impact, vacancy postings drop. The reduction in output and the increase in unemployment puts downward pressure on wages which increases vacancy postings.

We can draw the conclusion that the government consumption shocks generate positive effects only on impact. Due to the endogenous reaction of government investment to higher debt, the negative supply side effects dominate the positive demand side effects and output and employment decrease. Finally, we want to discuss the response of our model to a positive and mean-reverting increase in government investment as shown in Fig. 6. Aggregate as well as sectoral outputs are increased and show a persistent convergence towards the steady state. Since government investment is more productive in the service sector the output response is much stronger in the service sector compared to the manufacturing sector. Then, higher output due to higher productivity leads to lower marginal costs and lower prices. Inflation falls which leads the monetary authority to lower interest rates. This creates additional positive effects on private consumption. Hence, the increase of output can not only be met by increased government investment such that the firm reduces firing to increase employment. Over time, this effect needs to be revised and firms start lay-off more workers such that unemployment increase in the medium-run. Increased spending for government investment puts upward pressure on debt whereas lower interest rates reduce debt. Those two counteracting effects create a hump-shaped adjustment pattern of debt. We can conclude that government investment is far more effective in increasing aggregate and sectoral output levels than government consumption. However, this also comes at a cost: government investment leads to increased service sector and aggregate unemployment over the medium-run after an initial drop in the unemployment rate. Further, government debt increases for about ten quarters before lower interest rates reduce debt. 4. Robustness Our estimation results are based upon the assumption about the output elasticity w.r.t. government investment in the sector-specific production functions. Although we use the most general approach within our methodology, namely to estimate the parameter using Bayesian methods, the paper by Bom and Ligthart (2010) shows that the point estimate of this parameter depends crucially on (i) the applied methods, (ii) the assumption about the production function, and (iii) the country. In the following robustness section, we want to provide the results from assuming that the elasticity is equal to 1 in both sectors, which is an upper bound in the findings of Bom and Ligthart (2010). Table 2 presents the point estimates and the 95% confidence intervals for our robustness check. Our findings show that in this specification the government capital stock depreciates at a much higher rate (0.07 vs. 0.01). Implying that, ceteris paribus, the government needs to spend more in order to keep the stock of public capital constant. Hence, government spending in steady state will be larger in this economy compared to our benchmark economy. Along the labor market, we find that workers in the service sector have a much higher bargaining power (0.63

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35 −3

29

−3

x 10

x 10 0

4

Output Output: M Output: S

−2

Vacancies Vacancies: M Vacancies: S

3 2

−4

1 0

−6 5

10

15

20

5

−3

10

15

20

−4

x 10

x 10

15

2

Unemployment Unemp: M. Unemp: S.

10

Wages: M. Wages: S.

0

5

−2

0 −5

5

10

15

20

−4

5

10

15

20

−3

x 10 15

G Consumption G Investment

10

Debt Inflation Interest Rate

0.06 0.04

5

0.02

0 5

10

15

20

0

5

10

15

20

Fig. 5. Impulse responses to an estimated government consumption shock.

−3

−3

Output Output: M Output: S

x 10 4

x 10 0

3

−5

2

−10

1

−15

0

5

10

15

Vacancies Vacancies: M Vacancies: S

20

5

−3

10

15

20

−4

x 10

x 10

5

6

0

4

Wages: M. Wages: S.

2

−5

Unemployment Unemp: M. Unemp: S.

−10 −15

0 −2 −4

5

10

15

20

5

10

15

20

−3

x 10 0.02

4

G Consumption G Investment

0.015

Debt Inflation Interest Rate

2

0.01

0

0.005

−2

0 5

10

15

20

5

10

Fig. 6. Impulse responses to an estimated government investment shock.

15

20

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D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

Table 2 Posterior estimates – robustness. Parameter

Point

5%

95%

Parameter

Point

5%

95%

ı m s m s cm cs m s k c

k

c

0.07 0.1 0.05 0.49 0.63 0.02 0.09 0.49 0.48 0.07 0.22 0.0001 0.0002

0.06 0.1 0.05 0.49 0.62 0.02 0.08 0.49 0.48 0.06 0.2 0 0

0.07 0.1 0.05 0.50 0.64 0.03 0.09 0.49 0.48 0.08 0.23 0.0002 0.0004

A Am As G I r A Am As G I r

0.94 0.85 0.95 0.55 0.96 0.72 0.03 0.03 0.03 0.02 0.02 0.06

0.88 0.83 0.94 0.52 0.94 0.69 0.03 0.03 0.03 0.02 0.02 0.05

0.98 0.88 0.97 0.57 0.98 0.75 0.03 0.03 0.03 0.02 0.02 0.06

vs. 0.49). A higher bargaining power will allocate more surpluses to the worker if, for example, higher productivity increases profits. Simultaneously, this will decrease the incentives to post vacancies, as the firm’s share of profits is smaller compared to the benchmark model. Further, higher vacancy posting costs for the service sector and lower vacancy posting costs for the manufacturing sector do shift incentives towards creating jobs in the manufacturing sector. The elasticity of the matching function with respect to unemployment in the manufacturing sector is smaller in the robustness check compared to the baseline model (0.49 vs. 0.59). This implies that the job finding rate reacts more elastically to changes in labor market tightness and that the matching rate is less sensitive to changes in labor market conditions. Government consumption and investment react much stronger in the robustness check compared to the baseline. The elasticity to changes in output is 0.22 for consumption and 0.07 for investment. In contrast, we find that neither government consumption nor investment react to changes in government debt, as in the baseline estimation. Finally, the aggregate technology shock and the investment shock show much higher autocorrelations (0.94 vs. 0.44, resp. 0.96 vs. 0.52) while the government consumption shock is less autocorrelated (0,55 vs. 0.89). Standard deviations of the shock are similar across the two estimations, with the exception being the lower variance in the aggregate technology shock. Next, we turn to the main driving forces in the robustness check. Fig. 7 presents the unconditional variance decomposition for our robustness check. Our results show that output in both sectors is mainly driven by variations in government investment. However, we need to keep in mind that the model abstracts from any private capital which will result in an upward bias for the relevance of government capital. Future research will consider a richer model with private capital to disentangle the contribution of public and private capital to overall variations. The remaining parts of the variation in manufacturing output are explained by the aggregate technology shock and the manufacturing sector technology shock. In contrast, service sector output variations are driven by service

sector technology shocks and the manufacturing sector technology shock. Variations in the inflation rate are to 80% driven by government investment shocks. The remaining variations are explained by the aggregate and the manufacturing sector technology shocks. The importance of monetary policy is negligible in explaining variations in inflation. This is particularly important given that fiscal spending seems to be of great importance (even accounting for the upward bias in our results) for variations in prices. For the labor market, technology shocks play a more important role. Variations in manufacturing employment are driven by 50% by aggregate technology shocks and by 30% by government investment shocks. The remaining 20% are mainly explained by shocks to manufacturing sector technology. In contrast, the main driving forces for service sector employment are the service sector technology (40%) and aggregate technology (35%). Innovations to monetary policy explain almost 10% of total variation. We can conclude that most of the variation explained by the aggregate and sector-specific productivity shocks in the baseline estimation are now explained by the government investment shock. Put differently, with a higher output elasticity of government investment, the model picks the government investment shock over the other technology shocks. Finally, we want to discuss the transmission mechanisms for the two sector-specific technology shocks. We begin with a positive, mean-reverting technology shock in the manufacturing sector as shown in Fig. 8. This shock increases manufacturing sector output and reduces marginal costs in this sector. Lower marginal costs – via the New Keynesian Phillips curve – imply lower prices and inflation falls. The model generates a sectoral shift towards the manufacturing sector as a consequence of higher relative productivity in this sector. While manufacturing sector output increases, service sector output decreases. Nevertheless, the increase in manufacturing sector output overcompensates reduced output in the service sector and aggregate output increases. Our findings contrast the “average out” view of Lucas (1977) that sectoral reallocations should have only very limited effects on aggregate measures. This does not hold true in a sectoral model with labor market frictions and sticky prices. As shown in Wesselbaum (2011) sticky prices are crucial to

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

31

1 0.9 0.8 Technology Technology: M Technology: S Monetary Policy G Consumption G Investment

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Output: M

Output: S

Inflation

Employment: M

Employment: S

Fig. 7. Unconditional variance decomposition – robustness.

obtain this result. They create an amplifying effect in the manufacturing sector and through the positive effects of lower interest rates set by the monetary authority. Those asymmetric effects then spillover to the labor markets. Higher output leads to higher employment in the manufacturing sector, while lower output leads to lower employment in the service sector. The technology shock increases the value of a match and leads firms to increase the number of employees. Adjustments mainly occur along the exit side. Firms prefer to reduce the number

0.06

0.2

Output Output: M Output: S

0.04 0.02

of separations then to post more vacancies. The reason is that reduced separations are immediately effective and are costless, while vacancies are costly and only become effective in the next period. The opposite effects are obtained for the service sector labor market. To a large extend, this is driven by much larger vacancy posting costs in the manufacturing sector than in the service sector and the larger steady state separation rate in the manufacturing sector. Higher output and lower inflation lead the monetary authority to lower the interest rate to stimulate private

Vacancies Vacancies: M Vacancies: S

0.1 0

0

−0.1

−0.02 5

10

15

20

Unemployment Unemp: M. Unemp: S.

0.2 0.1

5

10

15

20

−3

x 10 5 0

0 −5

−0.1

Wages: M. Wages: S.

−10

−0.2 5

10

15

20

5

10

15

20

−3

x 10

0.15

0

Debt Inflation Interest Rate

0.1 −5

G Consumption G Investment

0.05 0

−10 5

10

15

20

5

10

15

Fig. 8. Impulse responses to an estimated technology shock in the manufacturing sector – robustness.

20

32

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

0.06

0

Output Output: M Output: S

0.04

−0.1

Vacancies Vacancies: M Vacancies: S

−0.2

0.02

−0.3

0 5

10

15

20

0

−0.4

5

10

15

20

15

20

0.03

−0.2

0.02 Unemployment Unemp: M. Unemp: S.

−0.4 −0.6

5

10

15

Wages: M. Wages: S.

0.01 20

0

5

10

−3

0

x 10

0.1

−1 −2

Debt Inflation Interest Rate

0.05 G Consumption G Investment

−3

0 5

10

15

20

5

10

15

20

Fig. 9. Impulse responses to an estimated technology shock in the service sector – robustness.

consumption. Fiscal policy responds countercyclically and, hence, government consumption and investment activities are reduced. Turning to the service-sector technology shock (Fig. 9) we observe significant differences. We find that the output responses are much more persistent compared to the manufacturing sector shock. Although aggregate output does not increase as much as in the previous case, its persistence is much higher. This is partly explained by the small adverse spillover effects towards the manufacturing sector. Manufacturing sector output does decrease but not as much as service sector output did in the previous scenario. This does have effects on the labor markets. Because the increase of aggregate output is more persistent, unemployment decreases by more as the discounted, expected profits from an additional worker are larger. Further, this also explains the larger impact on real wages, as workers have a larger bargaining power in the service sector. 5. Conclusion The Great Recession has resuscitated the interest in the effects of fiscal policy to counter adverse effects on output and labor markets. However, academic research related to the sectoral (labor market) effects of fiscal policy is rather sparse. This paper closes this gap and estimates a New Keynesian model with search and matching frictions and two sectors. Fiscal policy can use its resources for government consumption or for government investment. While government consumption is wasteful and works mainly as a demand-side shock, government capital is used in the

production process and affects marginal productivity. Fiscal policy is determined by fiscal rules with endogenous feedback to output and debt, allowing for discretionary interventions. Then, the model is estimated on U.S. time series using Bayesian methods. We find several interesting results. Compared to the service sector, the manufacturing sector labor market has higher job flows in steady state and workers have a lower bargaining power. Further, vacancy posting costs are roughly five times lower. Government debt has no significant impact on fiscal spending. Government consumption and investment respond solely to movements in output, i.e. are automatic stabilizers. Government consumption reacts roughly three times as much to variations in output than government investment. Business cycle fluctuations of sectoral and aggregate output as well as the inflation rate are mainly driven by government investment shock. This finding is likely to be biased due to the absence of private capital. Employment appears to be driven by the sectoral technology shocks and, for the manufacturing sector, the aggregate technology shock. Both types of fiscal spending shocks lead to an increase in sectoral and aggregate output. For the labor market, unemployment decreases on impact but increase in the medium-run. Overall, we find that investment shocks create larger real effects than consumption shocks. However, they generate a large increase in government debt that only slowly converges back to the steady state. Our robustness check, assuming a much higher output elasticity of government capital, shows that the assumptions about the production function are crucial to

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

understand the effects of government expenditures. Since research has not yet agreed upon the “true” value for this parameter, we understand our approach as providing a lower (ch. 3) and an upper (ch. 4) bound on the (labor market) effects of government investment expenditures. For higher values of the elasticity, we find that government consumption and investment follow fiscal rules with feedback to output but not to government debt. Government

consumption reacts roughly three times as much to variations in output than government investment. A variance decomposition analysis shows that government investment plays a major role in driving aggregate and sectoral output and inflation, substituting for aggregate and sectorspecific technology shocks. Fiscal spending shocks increase sectoral and aggregate output. Unemployment decreases on impact but increase in the medium-run. Sectoral

η Manufacturing

ρ Service

ρ Manufacturing

η Service

200

80 100

150

60

40

100

40

50

20

50

20

0 0.05

0.1

0

0.15

0.05

0.1

c Manufacturing

0

0.15

0.5

0

0.6

100

40

20

50

20

50 0

0.5

60

400

40

0 0.4

0.6

0.2

0.4

0.02

0.6

40

20

20 0 0.2

0.6

0.4

0.04

0.6

0

0.2

0.4

Fig. 10. Prior and posterior densities.

α

Manufacturing

α Service

100

100

50

50

φπ 60 40 20

0 −0.1

0

0.1

φ

0.2

0

0 −0.1

0

0.1

0.2

1.5

1.6

α

ψ 30 1 20

40 0.5

20 0

1.4

y

60

0

0.1

0.2

0

10

30

40

50

Fig. 11. Prior and posterior densities.

0.06

λ Consumption

40

0 0

0.5

λ Investment

200

20 0.2

0.4

0.6

γ Consumption 600

0

0

0 0.4

γ Investment 80

0.6

150

60

0.020.040.060.08 0.1 0.12

0.5 δ

80

40

100

0.4

μ Service

150

0

0.4

μ Manufacturing

200

0

33

0 0.2

0.4

0.6

0.8

0.6

34

D. Wesselbaum / Structural Change and Economic Dynamics 34 (2015) 19–35

differences are driven mainly by the differences in the wage setting, different vacancy posting costs, and different separation rates. Future research will take into account private capital dynamics and a more detailed description of fiscal financing.

0 = − ×

+ˇEt Appendix A.

 P −−1 1 t Pt

Pt

Yt

Pt + Pt

 P − Y t t Pt

Pt

−

 P t Pt−1

Yt Pt−1

t+1

t

−



(43)

  Pt+1 Pt

−

Y

t+1 Pt+1 Pt2

+ ϕt 

Yt . Pt

(44)

Using A.1. Additional figures ˇt+1 = ˇ See Figs. 10 and 11.

i.e. the stochastic discount factor, we obtain the first-order conditions in the text

A.2. Firm maximization problem The firm maximizes the present value of real profits subject to the production function, the demand function, and the employment evolution equation. Perfect capital markets imply that the firm discounts with the households subjective discount rate ˇ

max E0

∞ 

ˇ

P it t t

t=0

Pt

0

Yit − Wm − Wsit − c m Vitm − c s Vits it

−

 P it 2

Pit−1

−

2

Yt ,

subject to



Yit = At Yitm

 ˛x

Yitx = Gtk

ϑ  s 1−ϑ  ax a˜ x

it

Cit =

(37)

Yit

Axt Nitx

 P − it

Pt

 ˛x x x f (ax ) At Nit H(˜axit ), dax ≡ Gtk x 1 − F(˜ait )

Ct ,

(38)

(39)

x x Nit+1 = (1 − it+1 )(Nitx + Vitx q(tx )).

(40)

While building the derivative with respect to the price one has to consider that the market clearing condition holds, i.e. that the aggregate output and coherently the output of each firm is consumed, hence we conclude Ct = Yt

and

Cit = yit .

The subscripts i for individual firms can be dropped due to symmetry. Thus the derivatives are 0 = ϕt Axt H(˜axt ) −

0 = −c x + Et ˇ

t+1 ,

t

∂Wxt x x − tx + Et ˇt+1 (1 − t+1 ) t+1 , ∂Ntx

t+1 x x (1 − t+1 )q(tx ) t+1 ,

t

(41)

(42)

t = ϕt At H(˜at ) −

∂Wt + Et ˇt+1 (1 − t+1 ) t+1 , ∂nt

c = Et ˇt+1 (1 − t+1 ) t+1 , q(t )

(45) (46)

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