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Investment lags and macroeconomic dynamics

  • Yong-Gook Jung EMAIL logo
Veröffentlicht/Copyright: 3. Mai 2014
The B.E. Journal of Macroeconomics
Aus der Zeitschrift The B.E. Journal of Macroeconomics Band 15 Heft 1

Abstract

This study examines the dynamics and the fit of a time-to-build model. The benchmark model employs the investment adjustment cost specification of Christiano, Eichenbaum, and Evans (2005) and the alternative model utilizes the time-to-build specification of Casares (2006). The Bayesian estimation result conveys the following implications: In general, the time-to-build model generates similar dynamics as the benchmark model. But it does not improve the fit of the model to the data. The model comparison, based on marginal likelihood and simulation results, makes the benchmark model the winner of the horse race.

Keywords: Bayesian estimation; DSGE model; time-to-build
JEL: C51; E22; E32
Corresponding author: Yong-Gook Jung, Department of Economics, Wayne State University, 656 W. Kirby Street, Detroit, MI 48202, USA, Phone: +1 313 577 3345, Fax: +1 313 577 9564, e-mail:

Appendix

A Summary of the equilibrium conditions

A.1 Final good producer

The firm employs the following production technology:

(A.1)Yt=[∫01Yt(i)11+λp,tdi]1+λp,t, (A.1)

where the elasticity of substitution has a stochastic process:

(A.2)log(1+λp,t)=(1−ρp)log(1+λp)+ρplog(1+λp,t−1)+εp,t−θpεp,t−1. (A.2)

The profit maximization condition of the firm is represented by the demand equation for intermediate good

(A.3)Yt(i)=(Pt(i)Pt)− 1+λp,tλp,tYt. (A.3)

Since the firm makes zero profit in the equilibrium, aggregate price is represented by

(A.4)Pt=[∫01Pt(i) − 1λp,tdi] − λp,t. (A.4)

A.2 Intermediate good producer

The firm utilizes the following production technology:

(A.5)Yt(i)=At1−αKt(i)αLt(i)1−α−AtF, (A.5)

where the growth rate of neutral technology factor At, defined by zt≡ΔlogAt, follows an AR(1) process:

(A.6)zt=(1−ρz)γ+ρzzt−1+εz,t. (A.6)

Given the production technology, cost minimization problem results in the following marginal cost function:

(A.7)MCt=[1αα(1−α)1−α]Atα−1(Rtk)αWt1−α. (A.7)

The firm chooses the price of its output to maximize its profit as follows:

(A.8)0=Et∑s=0∞ξpsβsΛt+sYt+s(i)(1λp,t+s){P˜t(i)Πt,t+s−(1+λp,t+s)MCt+s}. (A.8)

Since P˜t(i)=P˜t in equilibrium, aggregate price index is

(A.9)Pt=[(1−ξp)(P˜t) − 1λp,t+ξp(Pt−1πt−1ιpπ1−ιp) − 1λp,t] − λp,t. (A.9)

A.3 Employment agencies

Employment agencies combine specialized labor according to the technology

(A.10)Lt=[∫01Lt(j)11+λw,tdj]1+λw,t, (A.10)

where the elasticity of substitution follows a stochastic process

(A.11)log(1+λw,t)=(1−ρw)log(1+λw)+ρwlog(1+λw,t−1)+εw,t−θwεw,t−1. (A.11)

The firm’s profit maximization condition is represented by the demand for each type of specialized labor

(A.12)Lt(j)=[Wt(j)Wt]− 1+λw,tλw,tLt. (A.12)

Wage paid by intermediate good producer is

(A.13)Wt=[∫01Wt(i)− 1λw,tdj]−λw,t. (A.13)

A.4 Household

A.4.1 Model JPT

Preference factor and investment productivity have the following stochastic processes:

(A.14)logbt=ρblogbt−1+εb,t (A.14)

and

(A.15)logμt=ρμlogμt−1+εμ,t. (A.15)

Capital service is defined as:

(A.16)Kt(j)=ut(j)K¯t−1(j), (A.16)

and capital stock is accumulated according to:

(A.17)K¯t(j)=(1−δ)K¯t−1(j)+μt[1−S(It(j)It−1(j))]It(j). (A.17)

The household’s first order conditions with respect to consumption, government bond, investment, capital stock, and capital utilization are:

(A.18)PtΛt(j)=btCt(j)−hCt−1(j)−hβEt(bt+1Ct+1(j)−hCt(j)), (A.18)
(A.19)Λt(j)=βRtEtΛt+1(j), (A.19)
(A.20)PtΛt(j)=Φt(j)μt[1−S(It(j)It−1(j))−S′(It(j)It−1(j))(It(j)It−1(j))]+βEtΦt+1(j)μt+1S′(It+1(j)It(j))(It+1(j)It(j))2, (A.20)
(A.21)Φt(j)=βEt{Λt+1(j)[Rt+1kut+1(j)−Pt+1a(ut+1(j))]+(1−δ)Φt+1(j)}, (A.21)

and

(A.22)Rtk=Pta′(ut(j)). (A.22)

The choice of optimum wage rate is represented by the following equation:

(A.23)0=Et∑s=0∞ξwsβsΛt+s(j)Lt+s(j)(1λw,t+s){W˜t(j)Πt,t+sw−(1+λw,t+s)bt+sφ[Lt+s(j)]νΛt+s(j)}, (A.23)

where

(A.24)Πt,t+sw=∏k=1s(πt+k−1ezt+k−1)ιw(πeγ)1−ιw. (A.24)

Since the household has only 1–ξw of probability to optimize wage rate in each period, the non-optimizing household would index wage rate according to:

(A.25)Wt(j)=Wt−1(j)(πt−1ezt−1)ιw(πeγ)1−ιw. (A.25)

Since W˜t(j)=W˜t in equilibrium, the wage paid by the firm is given by:

(A.26)Wt={(1−ξw)(W˜t) − 1λw,t+ξw[Wt−1(πt−1ezt−1)ιw(πeγ)1−ιp] − 1λw,t} − λw,t. (A.26)

A.4.2 Model Cas

In Model Cas, the law of motion equation (A.17) is replaced by the following equation:

(A.27)μtIt(j)=ω1Ξ[K¯t(j)K¯t−1(j)]K¯t−1(j)+ω2Ξ[K¯t+1(j)K¯t(j)]K¯t(j)+⋯+ω6Ξ[K¯t+5(j)K¯t+4(j)]K¯t+4(j), (A.27)

where ∑j=16ωj=1. Also, the optimal choice of capital stock (and investment) is represented by the following equation instead of the equations (A.20) and (A.21):

(A.28)β6EtΛt+6(j){Rt+6kut+6(j)−Pt+6a(ut+6(j))}=Λt(j)(Ptμt)ω6Ξ′[K¯t+5(j)K¯t+4(j)]+βEtΛt+1(j)(Pt+1μt+1){ω5Ξ′[K¯t+5(j)K¯t+4(j)]+ω6Ξ[K¯t+6(j)K¯t+5(j)]−ω6Ξ′[K¯t+6(j)K¯t+5(j)][K¯t+6(j)K¯t+5(j)]}+β2EtΛt+2(j)(Pt+2μt+2){ω4Ξ′[K¯t+5(j)K¯t+4(j)]+ω5Ξ[K¯t+6(j)K¯t+5(j)]−ω5Ξ′[K¯t+6(j)K¯t+5(j)][K¯t+6(j)K¯t+5(j)]}+β3EtΛt+3(j)(Pt+3μt+3){ω3Ξ′[K¯t+5(j)K¯t+4(j)]+ω4Ξ[K¯t+6(j)K¯t+5(j)]−ω4Ξ′[K¯t+6(j)K¯t+5(j)][K¯t+6(j)K¯t+5(j)]}+β4EtΛt+4(j)(Pt+4μt+4){ω2Ξ′[K¯t+5(j)K¯t+4(j)]+ω3Ξ[K¯t+6(j)K¯t+5(j)]−ω3Ξ′[K¯t+6(j)K¯t+5(j)][K¯t+6(j)K¯t+5(j)]}+β5EtΛt+5(j)(Pt+5μt+5){ω1Ξ′[K¯t+5(j)K¯t+4(j)]+ω2Ξ[K¯t+6(j)K¯t+5(j)]−ω2Ξ′[K¯t+6(j)K¯t+5(j)][K¯t+6(j)K¯t+5(j)]}+β6EtΛt+6(j)(Pt+6μt+6){ω1Ξ[K¯t+5(j)K¯t+4(j)]−ω1Ξ′[K¯t+6(j)K¯t+5(j)][K¯t+6(j)K¯t+5(j)]} (A.28)

A.5 Government

Monetary policy is conducted according to an interest rate rule:

(A.29)RtR=(Rt−1R)ρr[(πtπ)ϕπ(XtXt∗)ϕx]1−ρr(Xt/Xt−1Xt∗/Xt−1∗)ϕdxηmp,t, (A.29)

where the monetary policy factor follows a stochastic process:

(A.30)logηmp,t=ρmplogηmp,t−1+εmp,t. (A.30)

Government spending is defined as:

(A.31)Gt=(1−1gt)Yt, (A.31)

where government spending factor has an AR(1) process:

(A.32)loggt=(1−ρg)logg+ρgloggt−1+εg,t. (A.32)

A.6 Market clearing

GDP is defined as follows:

(A.33)Xt=Ct+It+Gt. (A.33)

If household budget constraints in equilibrium are summed up over households, then we can derive aggregate resource constraint:

(A.34)Ct+It+a(ut)K¯t−1=(1gt)Yt. (A.34)

B Description of the data

The data set used for estimation are as follows:

(B.1)dt=[ΔlogGDPt×100ΔlogCt×100ΔlogIt×100logLt×100Δlog(Wt/Pt)×100ΔlogPt×100FFRt/4] (B.1)

where

GDPt=RGDPtPOPt,Pt=GDPdeft

Ct=NCNDt+NCStPOPt×GDPdeft, It=NNRPFItPOPt×GDPdeft

Lt=NFBAWHt×CE16indextPOPindext

WtPt=NFBHCtGDPdeft.

The raw data can be described as follows:

DataDescriptionUnit
RGDPReal GDPBil’s of 2009 USD
POPCivilian noninstitutional population of 16 years or olderThousands
NCNDNominal personal consumption expenditures on non-durablesBil’s of 2009 USD
NCSNominal personal consumption expenditures on servicesBil’s of 2009 USD
GDPdefGDP deflator2009=100
NNRPFINominal non-residential private fixed investmentBil’s of 2009 USD
NFBAWHNonfarm business, all persons, average weekly hours2009=100
CE16indexIndex of civilian employment: 16 years or older2009=1
POPindexIndex of civilian noninstitutional population of 16 years or older2009=1
NFBHCNonfarm business, all persons, hourly compensation2009=100
FFRThe effective Federal Funds rateAnnual rate, %

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Published Online: 2014-5-3
Published in Print: 2015-1-1

©2015 by De Gruyter

Artikel in diesem Heft

  1. Frontmatter
  2. Advances
  3. Consumption composition and macroeconomic dynamics
  4. Evaluating linear approximations in a two-country model with occasionally binding borrowing constraints
  5. Contributions
  6. The bank lending channel and monetary policy rules for Eurozone banks: further extensions
  7. Investment lags and macroeconomic dynamics
  8. The zero lower bound: frequency, duration, and numerical convergence
  9. What drives endogenous growth in the United States?
  10. Environmental policy and economic growth: the macroeconomic implications of the health effect
  11. US household deleveraging following the Great Recession – a model-based estimate of equilibrium debt
  12. Price-level instability and international monetary policy coordination
  13. Households forming macroeconomic expectations: inattentive behavior with social learning
  14. Topics
  15. Complementarity and transition to modern economic growth
  16. Trend inflation and monetary policy rules: determinacy analysis in New Keynesian model with capital accumulation
  17. Discussions
  18. Preface to “Reflections on Macroeconometric Modeling” by Ray C. Fair
  19. Reflections on macroeconometric modeling
https://doi.org/10.1515/bejm-2013-0180
Schlagwörter für diesen Artikel
Bayesian estimation; DSGE model; time-to-build

Artikel in diesem Heft

  1. Frontmatter
  2. Advances
  3. Consumption composition and macroeconomic dynamics
  4. Evaluating linear approximations in a two-country model with occasionally binding borrowing constraints
  5. Contributions
  6. The bank lending channel and monetary policy rules for Eurozone banks: further extensions
  7. Investment lags and macroeconomic dynamics
  8. The zero lower bound: frequency, duration, and numerical convergence
  9. What drives endogenous growth in the United States?
  10. Environmental policy and economic growth: the macroeconomic implications of the health effect
  11. US household deleveraging following the Great Recession – a model-based estimate of equilibrium debt
  12. Price-level instability and international monetary policy coordination
  13. Households forming macroeconomic expectations: inattentive behavior with social learning
  14. Topics
  15. Complementarity and transition to modern economic growth
  16. Trend inflation and monetary policy rules: determinacy analysis in New Keynesian model with capital accumulation
  17. Discussions
  18. Preface to “Reflections on Macroeconometric Modeling” by Ray C. Fair
  19. Reflections on macroeconometric modeling
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