Inflation dynamics under habit formation in hours

Economics Letters 108 (2010) 269–272

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Economics Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l e t

Inflation dynamics under habit formation in hours Güneş Kamber ⁎ The Reserve Bank of New Zealand, New Zealand

a r t i c l e

i n f o

Article history: Received 16 May 2008 Received in revised form 31 March 2010 Accepted 5 April 2010 Available online 24 April 2010

a b s t r a c t This paper studies the implications of habit formation in hours for inflation dynamics. Using a New Keynesian Model, we show that habit formation in hours lowers the response of inflation to a monetary policy shock and that it can help to account for the observed sluggish response of inflation. © 2010 Elsevier B.V. All rights reserved.

JEL classification: E31 E52 J22 Keywords: New Keynesian Model Habit formation in hours Inflation

1. Introduction In the New Keynesian Model (NKM), besides nominal rigidities, the dynamic response of inflation to a monetary policy shock depends crucially on how the real side of the economy is specified. Using a fully fledged NKM, Christiano et al. (2005) study the role of various real rigidities to account for the observed inertia in inflation. The effects of real rigidities on inflation manifest themselves via the New Keynesian Phillips Curve. The latter relates current inflation to inflation expectations and real marginal cost. Hence, real rigidities affecting marginal cost dynamics, affect also the inflation dynamics. Habitformationinhourscanbeviewedasarealrigidityarisingfromthe preferencesofeconomicagents.AlreadypresentintheseminalKydlandand Prescott(1982)paper,habitformationinhoursreflectstheideathatworkers disliketofacelargechangesintheirworkedhours.Morerecently,Bouakez and Kano (2006) using a standard Real Business Cycle (RBC) model, show that habit formation in hours can be a strong internal propagation mechanism for technology shocks. In particular, it can help in obtaining the hump shaped response of output and hours.1 Collard and Fève (2008) findthatanRBCmodelenrichedwithhabitformationinhoursdescribesthe dynamicsofoutputandhoursasgoodasanRBCmodelfeaturinginvestment adjustmentcosts.FinallySchmitt-GroheandUribe(2008)consideramodel

with habit formation in hours when analyzing the contribution of anticipatedshockstobusinesscyclesinUS. This paper analyzes the effects of habit formation in hours on inflation dynamics. To this end, the paper extends the standard NKM and investigates the effects of monetary policy shocks on inflation. 2. The model This section extends the standard dynamic NKM, as in Clarida et al. (1999) and Woodford (2003), to allow for habit formation in hours. The model is composed of households, final good firms, wholesale good producers and a monetary authority. 2.1. Households The representative household maximizes lifetime utility: ∞

2

Et ∑ β s=0


log ct

s4

 + s

−



χ 1+

1 ν

ht

xt

+ s

1 +

13 ν5

ð1Þ

+ s−1

subject to the following budget constraint: Pt ct + Bt = Pt wt ht + Rt Bt−1 + Πt + Tt

ð2Þ

⁎ 2 The Terrace Wellington 6011 New Zealand. Tel.: + 64 4 471 3810. E-mail address: [email protected]. 1 They actually show that, except for hours, the habit formation model is equivalent to a model with learning-by-doing as in Chang et al. (2002).

0165-1765/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2010.04.003

where ct is consumption, ht, hours worked, Pt, price level, wt, real wage, Rt gross nominal interest rate, Bt, nominal bonds, Πt, profits and

270

G. Kamber / Economics Letters 108 (2010) 269–272

Tt, lump-sum taxes. β, χ are parameters. xt determines the habit stock and evolves according to: ln ðxt = xÞ = ðϕ−μ Þ ln ðxt−1 = xÞ + μ ln ðht−1 = hÞ; 0≤ϕ−μ b1; μ ≥ 0: ð3Þ Habit formation in hours is introduced as in Bouakez and Kano (2006) except that we abstract from shocks to the disutility from hours as our focus is the dynamics under monetary policy shocks. When μ = 0, the utility function becomes the standard time separable one. When ϕ = μ, as in Collard and Fève (2008) and Schmitt-Grohe and Uribe (2008), the disutility of working is determined by the level of hours worked relatively to the last period hours. For ϕ N μ, the habit stock is a moving average of past hours worked. In analogy with habit formation literature on consumption, we also consider internal and external habit formation. Under external habit formation the first order condition for labor supply is:  1+ 1 h wh ν χ t = t t xt ct

2 3  1+ 1  1+ 1 ht wt ht h w h ν ν = + βEt 4ϕχ t + 1 −ðϕ−μÞ t + 1 t + 1 5: ð5Þ χ xt ct xt + 1 ct + 1 With habit formation in hours labor supply is represented by a dynamic equation. Note that, in the case where there is no habit in hours, μ = 0, one finds the standard expression for the labor supply 1 decision (wctt = χht ). Under external habits, labor supply depends on ν the past level hours of work. When the evolution of habits is internalized, the labor supply depends on past and expected level of hours as well as on expected future wages. Noting πt + 1 the inflation rate between t and t + 1, the consumption Euler equation is given by: ct Rt : ct + 1 πt + 1

∞

ð6Þ



s

max P ⁎ t Et ∑ φ Λt;t s=0

+ s

P ⁎t

Pt

+ s

−mct

+ s

Yi;t

+ s

ð9Þ

where, P t⁎ is the optimal price chosen at time t, Λt,t + j is the stochastic discount factor and mct real marginal cost. Given the production function, the marginal cost, mct, is equal to aggregate real wage. The solution gives the optimal price: P ⁎t =

∞ φs Λt;t + s Yt + s Ptε + s mct ε Et ∑ ε−1 s = 0 φs Λt;t + s Yt + s Ptε−1 + s

+ s

ð10Þ

which says that the optimal real price of adjusting firms is a weighted sum of future real marginal costs. The Dixit–Stiglitz price index evolves according to: 1−ε

ð4Þ

while under internal habit formation the labor supply is given by:

1 = βEt

When given the chance to adjust, a firm chooses its price, to maximize its expected future profits:

Pt

= ð1−φÞP ⁎t

1−ε

1−ε

+ φ Pt−1 :

ð11Þ

Combining the last two equations and log-linearizing around the zero inflation steady state yields the New Keynesian Phillips Curve: ˆ t = βEt π ˆt π

ˆct + 1 +κ m

ð12Þ

where x̂ denotes log-deviations of variable x from its steady state and ð1−φÞð1−φβÞ . κ= φ

2.4. Monetary policy Monetary policy is specified as a variant of Taylor rule where the central bank is assumed to smooth changes in interest rate and reacts to deviations of expected inflation and output gap: ρ

r Rt = R t−1

"  !ρ #ð1−ρ Þ  r 1 Et πt + 1 ρπ yt y m exp εt   β π y

ð13Þ

where ɛm t is the monetary policy shock and ρπ and ρy are the Central Bank's response coefficients.

2.2. Final good firms

3. Calibration

Final good firms operate in a perfectly competitive market. They buy differentiated intermediate goods from wholesale firms and aggregate it to final good according to the following constant return to scale production technology:

The model is calibrated to match the quarterly data. The calibration closely follows the standard values in the literature for the US economy. The parameter governing the disutility of work, ν, is set to 1.6 following Bouakez and Kano (2006). Bouakez and Kano (2006) estimate ϕ =0.8 and μ = 0.11 under tight priors and ϕ = 0.7 and μ = 0.38 under noninformative priors. Since when habit stock depends only past level of hours, Collard and Fève (2008) and Schmitt-Grohe and Uribe (2008) estimate μ to be, 0.48 and 0.56, respectively, we adopt the estimation results under non-informative priors as a benchmark calibration of the evolution of habits and additionally report the impulse responses under 3 alternative calibration. In the no habits case, we set ϕ = 0 and u = 0, in a second calibration where habit stock is a moving average of past hours, we set ϕ = 0.7 and μ = 0.4 and in the case where habit stock depends only on the past level of hours, we set ϕ = 0.7 and μ = 0.7. Hours worked at the steady state are normalized to one and χ is calculated accordingly. We set the price rigidity parameter, φ, to 0.85. Taylor rule estimates for US find a high persistence in the interest rate setting, a more-thanproportional response of interest rates to inflation and a weak response to output gap.2 Accordingly, we set ρr = 0.85, ρπ = 1.5 and ρy = 0.125. Finally we set ɛ = 11, implying a 10% steady state markup and β = 0.99.3

1 ε ε−1 ε−1 @∫1 Y ε diA 0

Yt =

0

i;t

ð7Þ

where ε is the elasticity of substitution. Cost minimization yields the following demand for each differentiated good, which depends on its relative price and aggregate demand:   Pit −ε Y t Pt   1 1 1−ε where Pt = ∫0 Pi;t di 1−ε is the overall price level. Yit =

ð8Þ

2.3. Wholesale firms Wholesale firms are operating in a monopolistically competitive market, with technology Yit = hit. We follow Calvo (1983) and assume that every period only a random fraction (1 − φ) of wholesale firms can adjust their prices. Each period, this fraction is independent from the previous period.

2 See Smets and Wouters (2007) for Taylor rule estimates within DSGE models and Molodtsova et al. (2008) for results using real-time data. 3 Our results are robust across various calibrations of the structural parameters. Robustness checks are available from the author upon request.

G. Kamber / Economics Letters 108 (2010) 269–272

271

Fig. 1. Impulse responses to a monetary policy shock (baseline).

4. Results Fig. 1 displays the responses for different values of μ of output, annualized inflation and marginal cost to a monetary policy shock which correspond to a 1% annual decrease in the interest rate. The figure may be interpreted as follows: As prices are sticky, real interest rate decreases after the negative shock on the nominal interest rate, yielding an increase in demand. Firms respond to this extra demand by increasing their production and their labor demand. Labor supply increases only if workers obtain higher wages. This increases firms' costs and increases incentives for firms to increase their prices. As a result, inflation goes up. The dynamic response of output is not affected considerably with the introduction of habit hours. Meanwhile the responses of inflation and marginal cost are sensitive to the existence of habit formation. Even though the habit formation in hours doesn't change the dynamics qualitatively, it considerably lowers the response of inflation to a monetary policy shock. The difference in inflation dynamics is due to the difference in marginal cost dynamics. In the presence of habit formation in hours, the effect of a monetary policy shock on marginal cost is higher on impact. The more workers are willing to smooth their hours worked, the more they will ask for wage increases as a response to increases in their hours of work. The initial increase in the marginal cost is the highest in the presence of internal habits and when ϕ = μ = 0.7. However, as the marginal cost is determined by the change in hours worked relatively to the previous hours worked, the marginal cost decreases more than the baseline case after its first period response.

To see why this yields a lower response of inflation, iterate forward the linearized Phillips curve to obtain: ∞

ˆ t = Et ∑ ðβÞs κm ˆct π s=0

+ s

ð14Þ

where inflation is a weighted sum of expected deviation of future marginal costs from its steady state value. Despite the initial higher effect, the discounted sum of expected real marginal costs is smaller under habit formation. Hence inflation response is also smaller. In all cases, and for all variables, the biggest impact occurs at the time of the monetary policy shock and all the variables converge monotonically to their steady state. This is contrary to the observed delayed effects of monetary policy on inflation and output. To assess what habit formation in hours may change in an empirically convincing model, we consider a stylized model with habit formation in consumption and dynamic indexation in price setting as in Christiano et al. (2005). We assume that the utility from consumption depends on the past consumption level and non-adjusting firms index their prices to the past inflation. The utility from consumption is now given by log(ct − ect − 1) with e=0.6. Fig. 2 displays the response of inflation to a monetary policy shock in the presence of habit formation in consumption and indexation to past prices. Habit formation in hours decreases significantly the elasticity of marginal cost to output. The dynamic response of output is weakly affected but inflation response decreases significantly. The lowest response of inflation is obtained under internal habit formation when the habit stock is equal to last period hours worked.

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G. Kamber / Economics Letters 108 (2010) 269–272

Fig. 2. Impulse responses to a monetary policy shock with habit formation and indexation.

5. Concluding remarks We show that habit formation in hours does not qualitatively change the dynamic response of the economy to monetary policy shocks. Quantitatively, the response of inflation, however, is sensible to the degree of habit formation in hours. If workers are more willing to smooth their hours of work, the response of marginal cost at the impact is higher but it decreases rapidly. As the response of inflation is the discounted sum of future expected marginal costs, inflation increases at the impact but overall the response of inflation is smaller. Habit formation in hours can be seen as a proxy for labor adjustment costs or search and matching frictions in the labor market. In this sense, our results are in line with the findings of Trigari (2006) who finds that introducing search and matching frictions decreases the elasticity of marginal cost to output. This changes the cyclical behavior of inflation, in particular, renders it less responsive to monetary policy shocks. Acknowledgments The author would like to thank an anonymous referee, Antoine d'Autume, Patrick Fève, Michel Guillard, Fatih Karanfil and Corinne Perraudin for helpful comments. The views expressed in this paper

are those of the author(s) and do not necessarily reflect the views of the Reserve Bank of New Zealand. References Bouakez, Hafedh, Kano, Takashi, 2006. Learning-by-doing or habit formation? Review of Economic Dynamics 9 (3), 508–524 (July). Calvo, Guillermo, 1983. Staggered prices in a utility maximizing framework. Journal of Monetary Economics 110 (1), 161–193. Chang, Yongsung, Gomes, Joao F., Schorfheide, Frank, 2002. Learning-by-doing as a propagation mechanism. American Economic Review (5), 1498–1520 (December). Christiano, Lawrence J., Eichenbaum, Martin, Evans, Charles L., 2005. Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy 113 (1), 1–45 (February). Clarida, Richard, Gali, Jordi, Gertler, Mark, 1999. The science of monetary policy: a new Keynesian perspective. Journal of Economic Literature 37, 1661–1707. Collard, Fabrice, Fève, Patrick, 2008. Modèles VAR ou DSGE : que choisir ? Economie et Prévision 127, 155–174. Kydland, Finn E., Prescott, Edward, 1982. Time to build and aggregate fluctuations. Econometrica 50 (6), 1345–1370 (November). Molodtsova, Tanya, Nikolsko-Rzhevskyy, Alex, Papell, David H., 2008. Taylor rules with real-time data: a tale of two countries and one exchange rate. Journal of Monetary Economics 55 (Supplement 1), S63–S79. Schmitt-Grohe, Stephanie, Uribe, Martin, 2008. What's news in business cycles. Working Paper 14215. National Bureau of Economic Research (August). Smets, Frank, Wouters, Rafael, 2007. Shocks and frictions in US business cycles: a Bayesian DSGE approach. American Economic Review 97 (3), 586–606 (June). Trigari, Antonella. The role of search frictions and bargaining for inflation dynamics, Working Paper 304, IGIER Working Paper 2006. Woodford, Michael, 2003. Interest and Price. Princeton University Press, Princeton and Oxford.