Supply shocks and employment in an open economy

Economics Letters 82 (2004) 231 – 237 www.elsevier.com/locate/econbase

Supply shocks and employment in an open economy Fabrice Collard a, Harris Dellas b,* a

b

University of Toulouse, France Department of Economics, University of Bern, CEPR and IMOP, Gesellschaftsstrasse 49, CH-3012 Bern, Switzerland Received 3 March 2003; received in revised form 20 August 2003; accepted 29 August 2003

Abstract Following a positive technology shock, an open economy (or multisector, closed) flexible price model can easily generate a decline in employment if domestic and foreign intermediate goods are gross complements. For sufficiently high complementarity, it can also produce a decrease in output. D 2003 Elsevier B.V. All rights reserved. Keywords: Technological shocks; Employment; Open economy JEL classification: E32; E24

1. Introduction A series of recent papers (Gali, 1999; Basu et al., 1998; Francis and Ramey, 2001) has established that in response to a positive technology shock (identified via a variety of methods) employment declines. Basu et al. also point out that investment (and perhaps output) may also decline following a positive shock. These findings seem to have raised serious doubts not only about the relevance of the Real Business Cycle (RBC) model but also about the quantitative significance of technology shocks as a source of aggregate fluctuations. Moreover, as the standard Keynesian model with imperfect competition and sticky prices typically generates a short-run decline in employment in response to a positive technology shock, the findings have provided support for models with nominal frictions. In this paper, we argue that the decline in employment does not necessarily pose problems for the RBC model while a decline in output may. The flexible price model can easily generate a decrease in * Corresponding author. Tel.: +41-31-631-3989; fax: +41-31-631-3992. E-mail address: [email protected] (H. Dellas). URL: http://www.unibe.ch/amakro/dellas.htm. 0165-1765/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2003.08.007

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employment once the closed economy (or equivalently, the single sector) assumption is dropped. In an open (or a multisector, closed) flexible price economy with international production interdependence, a positive technology shock decreases employment if domestic and foreign intermediate goods are not good substitutes. Hence, the behavior of employment following an improvement in technology is not a decisive test of whether prices are sticky. The empirical emphasis should then shift to the examination of the behavior of investment and output as the discriminating factors instead. We are abstracting from investment in this paper, but it is worth noting that our model can also generate a decrease in output following a positive productivity shock if the degree of complementarity is sufficiently high (higher than that required for a decline in employment). Whether the required degree of complementarity is plausible or not, though, is an open question. The existing literature has relied on implementation lags in the adoption of new technology in order to make employment decline following a positive technology shock (time-to-implement, Hairault et al., 1997; time-to-plan, Christiano and Todd, 1996). This is accomplished via a combination of intertemporal substitution and wealth effects on the supply of labor. The present paper offers an additional, perhaps simpler, mechanism for achieving the same objective. Moreover, our model has the advantage of being able to also generate a decline in output following a positive technology shock.

2. A simple, flexible price model We employ a simple version of the neoclassical growth model. The world consists of two large countries. Each country is populated by a large number of identical agents and specializes in the production of a distinct, traded good. Asset markets are complete and there are no impediments to international transactions. Labor is not mobile. There is no capital. 2.1. The representative household Household preferences are characterized by the lifetime utility function: l X X s¼0 stþs

t

b pðs

tþs

t

tþs

j s ÞlogðCðs

  M ðstþs Þ ÞÞ þ hlog  vðHðstþs ÞÞ tþs Pðs Þ

ð1Þ

where 0 < b < 1 is a constant discount factor and v() is increasing and convex. Ct denotes the domestic consumption bundle, Mt /Pt are real money holdings, and Ht is the quantity of labor that may be supplied by the representative household, who faces a budget constraint of the form X ½Pb ðstþ1 j st ÞB1 ðstþ1 Þ þ eðst ÞPb *ðstþ1 j st ÞB2 ðstþ1 Þ þ M ðst ÞVB1 ðst Þ stþ1

þ eðst ÞB2 ðst Þ þ M ðst1 Þ þ N ðst Þ þ Pðst ÞW ðst ÞHðst Þ  Pðst ÞCðst Þ where P b(st + 1 | st) (resp. P b*(st + 1 | st)) is the price of a domestic (resp. foreign) contingent (equity) claim at the beginning of period t, B1(st) (resp. B2(st)) is the number of contingent claims that is owned by the

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domestic household at the beginning of period t. e(st) denotes the nominal exchange rate between the domestic and the foreign currency. W(st) is the real wage; P(st) is the nominal price of the domestic good. The household spends on consumption, C(st) and receives a nominal lump-sum transfer, N(st), from the monetary authorities. Finally, the household enters period t with an amount of money, M(st  1); carried over from the previous period and ends the period with an amount M(st). The behavior of the foreign household is similar. 2.2. The representative firm The domestic representative firm specializes in the production of a homogeneous ‘‘intermediate’’ good according to: X ðst ÞVAt Hðst Þa with aað0; 1Þ

ð2Þ

At is a stationary, exogenous, stochastic technological shock, which has its counterpart, A*t in the foreign economy. We will assume that 0 Eð½logðAÞ logðA*Þ V ½logðAÞ logðA*Þ Þ ¼ r2a @

1

w

w

1

1 A

The representative firm chooses how much labor to lease in period t in order to maximize its profit flow Px ðst ÞX ðst Þ  Pðst ÞW ðst ÞHðst Þ

ð3Þ

where Px(st) is the price of the domestic intermediate good. The foreign representative firm acts in a similar way. Following Backus et al. (1995), we assume that the domestic, X1, and foreign, X2, intermediate goods are combined to produce a domestic, final good, Y, ( Y* in the foreign country) which can be used for private and public consumption. Final good production at home is described by the following CES function Y ðst Þ ¼ ðx1q X1 ðst Þq þ ð1  xÞ1q X2 ðst Þq Þ1=q

ð4Þ

and abroad by Y ðst Þ* ¼ ðx1q X2 ðst Þ*q þ ð1  xÞ1q X1 ðst Þ*q Þ1=q

ð5Þ

Xit* it denotes the quantity of intermediate good i used in the production of the foreign final good. q V 1 determines the elasticity of substitution between domestic and foreign intermediate goods (1/(1  q)), and xa(0, 1) is the share of the domestic intermediate good.

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2.3. The monetary authorities Following Gali (1999), we assume that the monetary authorities supply money according to the simple rule M ðst Þ ¼ lM ðst1 Þ

ð6Þ

where l is the constant gross rate of growth of the money supply. 2.4. The solution Unfortunately, the model does not possess an analytical solution. Therefore, we take a log-linear approximation of the model around the deterministic steady state. The solution appears in Appendix A. In Appendix A, we establish the following propositions. Proposition 1. Domestic hours respond negatively to a positive domestic technology shock iif domestic and foreign goods are gross complements. The intuition for this result is as follows. If the elasticity of substitution between domestic and foreign intermediate goods is less than unity, then the quantity of foreign intermediate goods imposes a binding constraint on how much domestic production can expand following a favorable domestic supply shock. With limited output expansion allowed and higher labor productivity, employment must decrease. The quantity of inputs from other countries (sectors) thus serves as the constraint on output expansion under flexible prices in an analogous fashion to the way aggregate demand constraints output expansion when prices are fixed. Proposition 2. Domestic output responds negatively to a positive domestic technology shock iif the degree of gross complementarity between domestic and foreign goods is sufficiently high. The intuition for this result is that a large deterioration of the domestic terms of trade may lead to such a lower quantity of foreign intermediate goods that domestic GDP declines.1

3. Summary and conclusions Recent empirical evidence indicates that in response to an—empirically identified—positive technology shock, labor productivity rises more than output while employment shows a decline. Some work has also claimed that output may decline following a positive productivity shock. These findings have led many to doubt not only the relevance of the RBC model but also the plausibility of models that assign a big role to technology shocks as a source of aggregate fluctuations. Moreover, as the standard Keynesian model with imperfect competition and sticky prices typically generates a short-run decline in 1

Note that a decline in investment may also obtain in a calibrated version of the model with capital.

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employment in response to a positive technology shock, this stylized fact has provided support for models with nominal frictions. In this paper, we have questioned this view. We have shown that the flexible price model can account for these empirical patterns in the presence of international trade. If trade elasticities fall below unity—a quite realistic case, as Taylor’s (1993) estimates indicate—then the flexible price model performs quite well. Hence, the behavior of employment following a technology shock cannot serve as a litmus test inferring the degree of price stickiness in the real world. Perhaps, the behavior of output and investment might provide the necessary test.

Appendix A A.1. Log-linear representation of equilibrium We first report the log-linear representation of the model, where a lowercase letter denotes the percentage deviation of a variable from its steady state level: xt=(Xt  X¯)/X¯. We then describe the solution. pt þ ct ¼ 0

ð7Þ

p*t þ c*t ¼ 0

ð8Þ

pt ¼ xpxt þ ð1  xÞp*xt

ð9Þ

p*t ¼ ð1  xÞpxt þ xp*xt

ð10Þ

xt ¼ at þ aht

ð11Þ

x*t ¼ a*t þ ah*t

ð12Þ

xt ¼ xct þ ð1  xÞc*t þ

pxt x 1x pt  p*t  q1 q1 q1

ð13Þ

x*t ¼ ð1  xÞct þ xc*t 

p*xt 1x x  pt  p*t q1 q1 q1

ð14Þ

pt þ wt ¼ pxt þ at þ ða  1Þht

ð15Þ

p*t þ w*t ¼ p*xt þ a*t þ ða  1Þh*t

ð16Þ

fht þ ct ¼ wt

ð17Þ

fh*t þ c*t ¼ w*t

ð18Þ

where f = vU(h)h/vV(h) > 0.

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This system admits the approximate solution ht ¼

2xqð1  xÞ ðat  a*Þ t D

2xqð1  xÞ ða*t  at Þ D x yt ¼ ð2qð1  xÞð1 þ f  aÞ þ ð1  qÞð1 þ fÞÞat D 1x ð2qxð1 þ f  aÞ þ ð1  qÞð1 þ fÞÞa*t þ D x y*t ¼ ð2qð1  xÞð1 þ f  aÞ þ ð1  qÞð1 þ fÞÞa*t D 1x þ ð2qxð1 þ f  aÞ þ ð1  qÞð1 þ fÞÞat D pt ¼ yt

h*t ¼

p*t ¼ y*t wt ¼

w*t ¼

x ð2qð1  xÞð1 þ 2f  aÞ þ ð1  qÞð1 þ fÞÞat D 1x ð2qxð1  aÞ þ ð1  qÞð1 þ fÞÞa*t þ D x ð2qð1  xÞð1 þ 2f  aÞ þ ð1  qÞð1 þ fÞÞa*t D 1x þ ð2qxð1  aÞ þ ð1  qÞð1 þ fÞÞat D

with D ¼ 4xqð1  xÞð1 þ f  aÞ þ ð1  qÞð1 þ fÞ: A.2. Proof of Propositions 1 and 2 Proposition 1: Plugging Eqs. (7), (8), (9) and (10) in Eqs. (13) and (14), and making use of Eqs. (15), (16), (17) and (18), pxt and p*xt are found to be determined by the system 8  að1  qÞ ð1 þ fÞðq  1Þ > 2 2 > > at 1  qðx þ ð1  xÞ Þ þ pxt  2xð1  xÞqp*xt ¼ > > 1þfa 1þfa <   > > > að1  qÞ ð1 þ fÞðq  1Þ 2 > 2 > a*t pxt*  2xð1  xÞqpxt ¼ : 1  qðx þ ð1  xÞ Þ þ 1þfa 1þfa

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Inverting the system, and using the fact that from Eqs. (7), (15) and (17) (respectively, Eqs. (8), (16) and (18)) ð1 þ f  aÞht ¼ pxt þ at ð1 þ f  aÞh*t ¼ pxt* þ a*t we obtain ht ¼

2xqð1  xÞ ðat  a*Þ t ð1  qÞð1 þ fÞ þ 4xqð1  xÞð1 þ f  aÞ

h*t ¼

2xqð1  xÞ ða*t  at Þ ð1  qÞð1 þ fÞ þ 4xqð1  xÞð1 þ f  aÞ

Therefore, dht/dat is given by dht 2xqð1  xÞ ¼ dat ð1  qÞð1 þ fÞ þ 4xqð1  xÞð1 þ f  aÞ Note that since, xa[0,1], f z 0, aa(0,1) and q V 1, dht/dat is positive whenever q>0. Conversely, if q < 0, the numerator of the ratio is strictly negative, while the denominator, which may be rewritten as, 1 þ f  qðð1  2xÞ2 ð1 þ fÞ þ 4xð1  xÞaÞ is positive as long as xa[0,1], f z 0, aa(0,1) and q < 0 —i.e. when domestic and foreign goods are gross complements. Proposition 2: From the equation defining yt in Appendix A.1 and the fact that D>0 we have that dyt =dat < 0 iff q < ð1  f=2ð1  xÞð1 þ f  aÞ  1  f Þ and 2(1  x)(1 + f  a)  1  f>0. This obtains for a sufficiently negative q.

References Backus, D., Kehoe, P., Kydland, F., 1995. International business cycle: theory and evidence. In: Cooley, T., Prescott, E. (Eds.), Frontiers of Business Cycle Research. Princeton Univ. Press, Princeton, pp. 331 – 356. Basu, S., Fernald, J.G., Kimball, M.S., 1998. Are technology improvements contractionary? Board of Governors of the Federal Reserve System. International Finance Discussion Paper, vol. 625. Christiano, L., Todd, R., 1996. Time to plan and aggregate fluctuations. Federal Reserve Bank of Minneapolis Quarterly Review 20 (1), 14 – 27. Francis, N., Ramey, V., 2001. Is the Technology-Driven Real Business Cycle Hypothesis Dead? Shocks and Aggregate Fluctuations Revisited, mimeo. Gali, J., 1999. Technology, employment, and the business cycle: do technology shocks explain aggregate fluctuations? American Economic Review 89 (1), 249 – 271. Hairault, J.O., Langot, F., Portier, F., 1997. Time-to-plan and aggregate fluctuations. Journal of Economic Dynamics and Control 22 (1), 109 – 121. Taylor, J., 1993. Macroeconomic Policy in a World Economy: From Economic Design to Practical Operation (Norton, NY).