Real exchange rate, productivity and labor market frictions

Journal of International Money and Finance 30 (2011) 587–603

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Journal of International Money and Finance journal homepage: www.elsevier.com/locate/jimf

Real exchange rate, productivity and labor market frictions Yu Sheng a, Xinpeng Xu b, * a b

Crawford School of Economics and Government, Australian National University, Australia Faculty of Business, Hong Kong Polytechnic University, Kowloon, Hong Kong

a b s t r a c t JEL classifications: F16 F31 J64 Keywords: The Balassa–Samuelson model Search unemployment Labor market efficiency

We extend the classic Balassa–Samuelson model to an environment with search unemployment. We show that the classic Balassa–Samuelson model with the assumption of full employment emerges as a special case of our more generalized model. In our generalized model, the degree of labor market matching efficiency affects the strength of the structural relationship between the real exchange rate and sectoral productivity through influencing labor’s choice between employment and unemployment as well as movement across sectors. When the relative labor market matching friction is high, search unemployment is high and the standard Balassa–Samuelson effect may not hold. Empirical evidence supports our theory: controlling for differences in labor market frictions across countries provides a better fit in estimating the Balassa–Samuelson effect.
2011 Elsevier Ltd. All rights reserved.

1. Introduction The relative price of a common basket of goods between two countries, the real exchange rate (RER), is one of the most important prices in an open economy. Balassa (1964) and Samuelson (1964) argue that deviations from Purchasing Power Parity (PPP) may be due to international productivity differentials between the tradable and nontradable sectors. Balassa and Samuelson posit that, as the law of one price holds only for tradable goods, in a fast-growing economy, higher productivity growth in the tradable sector will increase real wages in all sectors since employed workers are mobile across sectors,

* Corresponding author. Tel.: þ852 2766 7139; fax: þ852 2774 9364. E-mail address: [email protected] (X. Xu). 0261-5606/$ – see front matter
2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jimonfin.2011.01.006

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which will lead in turn to an increase in the relative price of nontradable goods, resulting in an overall rise in the national price level.1 Although the Balassa–Samuelson model predicts a simple theoretical relationship between productivity differences and real exchange rates, the empirical evidence is mixed. On the one hand, the evidence of the Balassa–Samuelson effect is weak for developed economies. For example, an influential study by Engel (1999) finds that the relative price of nontradable goods cannot explain much of the movement of OECD countries’ real exchange rates even after changes in the terms of trade (or the short-term effects from tradable sectors) are well controlled. On the other hand, there is considerable evidence for the Balassa–Samuelson effect across developed and developing economies; see Bergin et al. (2006) and Rogoff (1996), among others. Bergin et al. (2004) show that the Balassa–Samuelson effect is not visible in early 1900s, but the effect grows steadily over time to rather large values in the more recent years. The mixed evidence for the Balassa–Samuelson effect demands further investigation. One of the underlying assumptions of the Balassa–Samuelson model is that labor markets are frictionless so that there is always full employment. Yet, it is well recognized that it takes time and other resources for an unemployed worker to find a job and for a firm to fill a vacancy so that there exist frictions in the labor market at steady state (see for example, McCall, 1970; Diamond, 1982; Mortensen, 1982; Pissarides, 1985; Mortensen and Pissarides, 1999; Pissarides, 2000; Rogerson et al., 2005) and that there are significant differences in the degree of labor market frictions across sectors and countries. In fact, using sectoral data, Wacziarg and Wallack (2004) show that trade liberalization has far smaller effects on intersectoral labor shifts than is often presumed. The existence of labor market frictions affects the response of employed workers’ wage to changes in relative productivity, but it is not clear how differences in labor market institutions across sectors and countries can affect the relationship between the real exchange rate and productivity differentials. By introducing search unemployment into a standard Balassa–Samuelson model, we demonstrate in this paper that the degree of labor market matching efficiency across sectors and countries affects the strength of the structural relationship between the real exchange rate and sectoral productivity differentials through influencing labor’s choice between employment and unemployment as well as movement across sectors. When the relative labor market matching efficiency is low, search unemployment is high and the standard Balassa–Samuelson effects may not hold. Specifically, in a world with labor market frictions and unemployment, the standard Balassa–Samuelson mechanism may have to be revised to incorporate the fact that workers cycle between employment and unemployment in each sector. In such an environment, employed workers no longer move instantaneously and costlessly across sectors in response to changes in productivity and relative sectoral wages. Instead, it is unemployed workers that move freely across sectors in response to changes in expected lifetime income arising from changes in relative sectoral wages and associated frictional costs such as the probability of finding a new job and of an existing job being destroyed. Thus, an increase in the relative productivity in the tradable (or nontradable) sector may lead to an increase in the relative wage in that sector, but the extent of the increase would, in general, be lower compared with what is predicted by the standard Balassa–Samuelson model, as part of the increase in the marginal product of labor will be used to cover frictional costs in the labor market. The increase in the wage of the tradable sector will lead to an increase in the expected lifetime income of unemployed workers searching in the tradable sector, attracting unemployed workers in the nontradable sector to move to the tradable sector. This movement of unemployed workers across sectors will continue until the expected lifetime income of unemployed workers searching in each sector is equalized. The resulting increase in the expected lifetime income of unemployed workers in the nontradable sector may bid up wages of employed workers in the nontradable sector.

1 Recent empirical investigations of the effect of productivity shocks (which are real shocks) on the real exchange rate, the socalled Balassa–Samuelson effect, include, inter alia, Asea and Mendoza (1994), De Gregorio et al. (1994), Froot and Rogoff (1995), Lothian and Taylor (2008) and Canzoneri et al. (1999). Although a survey of empirical findings by Froot and Rogoff (1995) finds weak support for the Balassa–Samuelson effect, recent work by Lothian and Taylor (2008) using data from 1820 to 2001 for the US, the UK and France in a nonlinear framework reports a statistically significant Balassa–Samuelson effect which explains 40% of the variation of sterling-dollar exchange rate. Asea and Mendoza (1994) and Canzoneri et al. (1999) also provide similar results to support the proposition that productivity differentials determine the relative price of nontradables.

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However, the increase in the price of nontradable goods may be higher or lower than what is predicted by the standard Balassa–Samuelson model, depending on the relative market matching efficiency between the two sectors, as the effect of an increase in the nontradable sector’s wage on the nontradable price will be absorbed by the relative flexibility in its labor market, resulting in a higher or lower price of nontradable goods and hence, the national price level. Furthermore, if the relative labor market matching efficiency in the tradable sector is too low, there is a potential that the relative increase in the tradable sector productivity may be more than offset by relatively high frictional costs, thus operating against the Balassa–Samuelson effect. The importance of labor market institutions highlighted in this paper offers an added dimension for explaining differences in price levels between countries with different or similar income levels. To anticipate our results, we show that: (1) the classic Balassa–Samuelson model emerges as a special case of our more generalized model with unemployment; (2) the effects of sectoral productivity differentials on the real exchange rate have to be adjusted quantitatively for differences in labor market matching efficiency across sectors and between countries. This highlights a new and potentially important channel for the transmission of various shocks to labor market institutions to the real exchange rate, i.e., labor market institutions matter; (3) when differences in productivity growth are insignificant among developed economies, differences in labor market frictions may dominate the Balassa–Samuelson effect, which make the Balassa–Samuelson effect less visible. As labor market matching efficiency improves over time, the Balassa–Samuelson effect will become more significant. Our empirical evidence confirms that controlling for labor market matching efficiency provides a better fit in estimating the Balassa–Samuelson effect. We view our work as complementary to the recent literature that emphasizes imperfections in goods markets in extending the Balassa–Samuelson model. Several recent papers have intended to update or extend the Balassa–Samuelson model by focusing on imperfections in goods markets. For example, Fitzgerald (2003) revisits the classic Balassa–Samuelson model by dropping out the Balassa– Samuelson assumption that all countries produce the same tradable goods. Instead, Fitzgerald introduces production of differentiated goods across countries and increasing returns to scale in production, which leads to endogenous specialization and intra-industry trade. In this environment, the relationship between the real exchange rate and sectoral productivity is shown to depend on the strength of terms-of-trade effects. Ghironi and Melitz (2005) propose a model highlighting the importance of endogenous firm entry and exit to both domestic and export markets in determining the movement of national price levels. Bergin et al. (2006) develop a model of endogenous tradability where instead of assuming productivity gains concentrating by coincidence in the production of existing tradable goods as in the Balassa–Samuelson model, productivity gains in the production of particular goods can lead to those goods becoming traded. They demonstrate that such a model can deliver endogenously time-varying correlations between incomes and prices. A recent paper by Helpman and Itskhoki (2010) extends Melitz’s (2003) model by introducing search unemployment in one sector to examine the interaction of labor market efficiency and trade impediments in shaping the relationship between productivity and price levels across countries and shows that the country with more flexible labor markets has both higher productivity and a lower price level, which operates against the standard Balassa–Samuelson effect. To the best of our knowledge, our paper is the first to develop a model that integrates the standard Balassa–Samuelson model with search theory so that the classic Balassa–Samuelson model can be examined in an environment without the assumption of full employment.2 In contrast to the latest literature that focuses on imperfections in goods markets, we center our analysis on frictions in the labor market. More importantly, search frictions in labor markets exist in the long run, which differs from short-run models of labor market rigidities. We discuss the case of out-of-steady-state in the Appendix. Unlike other theoretical models, the standard Balassa–Samuelson channel is still operative in our generalized model. A focus on labor market frictions reflects the rising importance of the issue of unemployment in the age of globalization, whereby real exchange rate movements may interact with domestic labor market institutions when countries integrate more and more with each other.

2

For an introduction to search theory, see Romer (2001), Ljungqvist and Sargent (2000) and Pissarides (2000).

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The rest of the paper proceeds as follows. In the next section we develop a two-sector model that distinguishes between the tradable and nontradable sectors and endogenizes unemployment in a simple framework of search theory. This provides us with a setup that is useful in discussing the relationship between the real exchange rate, sectoral productivity and labor market flexibility across sectors and between countries. We summarize the main results in a proposition and several lemmas and corollaries. In Section 3, we discuss our empirical results. The final section concludes. 2. The model 2.1. The economy Consider a small open economy that produces two composite goods, tradable goods (T) priced in international markets and nontradable goods (N) priced in the domestic market. The production technologies of tradables and nontradables is characterized by constant returns to scale (CRS) production functions of the capital Ki (i ¼ T,N) and labor Li employed, Yi ¼ AiF(Ki,Li) ¼ AiLif(ki), where Yi is output in the tradable and nontradable sectors and the Ai are productivity shifters. Tradable goods are taken as numeraire. Output per unit of labor, yi h Yi/Li, can then be written as, yi ¼ Aif(ki) which makes use of the condition of CRS where ki h Ki/Li is the capital–labor ratio in sector i. The production function F() exhibits positive and diminishing marginal products with respect to each input. Capital is perfectly mobile across sectors domestically and internationally. We now depart from the standard full employment assumption as in the Balassa–Samuelson model. In a frictional economy, it takes time and other resources for a worker to find a job and for a firm to fill a vacancy. Since there are workers searching for a job and vacancies waiting to be filled, there is always unemployment in the labor market. With labor market frictions and unemployment, it is now unemployed workers that move freely across sectors and therefore, it is the expected income of unemployed workers that will be equalized across sectors. In contrast, employed workers’ income wi may be different as it has to take into account compensation differentials arising from labor market frictions. We now specify job matching, job creation, job destruction, and wage determination in general equilibrium. 2.2. Matching Suppose the number of matches between firms and workers in sector i depends on the number of unemployed works (Ui) chasing the number of vacancies (Vi). Let Zi be the sectoral labor force, ui the unemployment rate (Ui/Zi) and vi be the number of vacant jobs as a fraction of the labor force (Vi/Zi). We have the number of matches, miZi ¼ m(Ziui,Zivi). A typical assumption of the functional form for the matching function has constant returns to scale (Blanchard and Diamond, 1989). Thus, we can express all variables as a function of the tightness of the labor market, qi h vi/ui. The rate at which a vacant job is filled is therefore q(qi), which is equal to mi/vi. The rate at which an unemployed worker finds a match is qiq(qi), which is equal to mi/ui. 2.3. Firms Following Pissarides (2000), a typical firm has jobs that are vacant and has to pay frictional cost g as an advertising and recruiting cost (‘frictional cost’ in what follows) in order to fill a vacancy. During hiring, a vacant job is filled at the rate q(qi) while an unemployed worker finds a job at the rate qiq(qi). When a firm and a worker meet and agree to an employment contract, a job is occupied. The firm then goes on to rent capital ki for each worker and produces output, which is sold in competitive markets. We consider the optimal decision of a typical firm in the tradable sector first. Let VT be the present value of expected profit for the firm from a vacant job and JT the present value of expected profit for the firm from an occupied job in the tradable sector. VT satisfies the Bellman equation,

rVT ¼ g þ qðqT ÞðJT  VT Þ:

(1)

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A job is an asset owned by the firm and is valued in a perfect capital market characterized by a risk-free interest rate r. The asset value of a vacant job, rVT, is exactly equal to the rate of return on the asset: the vacant job costs g but has the probability of q(qT) for the vacancy to turn into a filled job which will yield the net return JT  VT. In equilibrium, perfect competition and profit maximization require that the gains from job creation are always exhausted, so that jobs are created up to the point where VT ¼ 0, implying that JT ¼ g/q(qT). The implicit assumption here is that firms decide to create jobs whenever the value of a vacancy is positive and thus potential profits will be eroded quickly by free entry. As the capital stock owned (or rented) by the firm becomes part of the value of the job, the asset value of an occupied job is given by JT þ kT. The job yields net return ATf(kT)  wT where wT is worker’s wage. Similar to the valuation of a vacant job, the asset value of an occupied job, r(JT þ kT), satisfies the following Bellman equation

rðJT þ kT Þ ¼ AT f ðkT Þ  wT  lðJT  VT Þ;

(2)

where l is the job destruction rate which leads to the loss of JT but not kT. Intuitively, the annuity of the return to the asset of an occupied job is equal to the output ATf(kT), net of its cost (which is wage here if we assume no capital depreciation for simplicity), with a probability of l that the relationship may come to an end so that the firm will lose JT. Given the interest rate and wage rate, the firm rents capital kT to maximize the value of the job JT. We can write the firm’s first-order condition with respect to capital as, 3

AT f 0 ðkT Þ ¼ r;

(3)

which has the standard interpretation where firms rent capital kT up to the point where the marginal product of capital is equal to the market rental rate, r, as we assume that there is no friction in the capital market. Substituting the firm’s first-order condition with respect to capital and the equilibrium job creation condition JT ¼ g/q(qT) into the asset value equation of an occupied job yields the familiar equilibrium condition for the firm’s employment of labor. The firm posts vacancies and hires workers up to the point where marginal benefit of an additional worker, the marginal product of labor, is equal to marginal cost, i.e., the market wage, after adjusting for the frictional cost,


ðr þ lÞg AT f ðkT Þ  kT f 0 ðkT Þ ¼ wT þ : qðqT Þ

(4)

If there is no frictional cost so that g ¼ 0, the last term on the right hand side of Eq. (4) becomes zero and (4) reduces to the familiar marginal productivity condition for labor in a full-information, frictionless labor market.

2.4. Workers Workers search for jobs and once offered, have to make a decision to accept or reject the offer. Therefore workers’ decisions will influence equilibrium market wages. Similar to a firm described in the above section, a typical worker makes an optimal decision to accept a job offer and receive wage wT or to remain unemployed and receive unemployment benefits during search. To illustrate the decision made by a typical worker in the tradable sector, let UT and ET be the present value of the expected income streams of an unemployed worker and an employed worker in the tradable sector respectively. UT satisfies the Bellman equation

rUT ¼ b þ qT qðqT ÞðET  UT Þ:

(5)

Eq. (5) says that the asset value of the unemployed worker’s human capital is made up of two

3 For simplicity, we assume that job destruction rates are exogenous and same across sectors but it can be relaxed easily without affecting our main results.

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components: the unemployment benefits b and the expected capital gain from a change of states q(qT) (ET  UT).4 rUT can be interpreted as the annuity (permanent income) that an unemployed worker expects to receive during search. Similarly, the asset value of an employed worker’s human capital satisfies the following Bellman equation

rET ¼ wT þ lðUT  ET Þ:

(6)

Eq. (6) has a similar interpretation to (5). The permanent income of an employed worker is made up of two components: the wage wT and the expected capital loss from a change of state l(UT  ET). Combining Eqs. (5) and (6), we can solve for permanent income of an unemployed and an employed worker as follows

rUT ¼

ðr þ gÞb þ qT qðqT ÞwT ; r þ l þ qT qðqT Þ

(7)

rET ¼

lb þ ½r þ qT qðqT ÞwT : r þ l þ qT qðqT Þ

(8)

In contrast to the standard Balassa–Samuelson model with full employment where employed workers move instantaneously and costlessly across sectors in response to changes in relative sectoral wages, in a model with labor market frictions, it is the searching unemployed workers who move freely across sectors. In equilibrium, free mobility of unemployed workers across sectors ensures that the asset value of the unemployed workers in the tradable sector (rUT) is equal to that of the unemployed workers in the nontradable sector (rUN). However, employed workers’ income may be different across sectors as sectoral employment income may have to reflect wage differentials in compensating for the risks associated with each sector, for example, the probabilities of finding a new job and of being fired. 2.5. Wage determination As an occupied job yields returns that go beyond the sum of the expected returns of a searching firm and a searching worker, the pure economic rent needs to be shared between the firm and the worker. A simple approach is to assume that the wage is determined by the generalized Nash bargaining solution with threat points UT and VT for each job-worker pair, w jT ˛ argmax[(EjT  UT)b(JjT  VT)1b], where b ˛ (0,1) is the worker’s bargaining power. The solution to the above first-order maximization problem satisfies

  j j j ET  UT ¼ b JT þ ET  VT  UT ;

(9)

which says that the worker receives his threat point UT, plus a share of the pure economic rent created by the job match. Eq. (9) can be solved for the representative worker’s wage in the tradable sector wT. By substituting Eqs. (2) and (6) in (9), and making use of the equilibrium condition VT ¼ 0, we have

wT ¼ ð1  bÞrUT þ bðAT f ðkT Þ  rkT Þ:

(10)

Substituting Eq. (9) in (5) and making use of JT ¼ g/q(qT), we can derive another equation

rUT ¼ b þ

b

gqT :

1b

(11)

Substituting Eq. (11) in (10), we have

4 The unemployment benefits b can be interpreted more broadly to include the value of leisure and home production, net of any cost of search. See Rogerson et al. (2005).

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wT ¼ ð1  bÞb þ bgqT þ bðAT f ðkT Þ  rkT Þ;

593

(12)

where gqT is the average frictional cost for each unemployed worker. Note that with search frictions in the labor market, the wage for employed workers is no longer solely determined by the sectoral capital–labor ratio and productivity. It also depends on the value of employed workers’ outside option (unemployment benefits b), frictional costs and the probabilities of the existing job being destroyed and finding a new job in the future. As such, wages of employed workers wi may be different across sectors as they have to take into account compensation differentials arising from labor market frictions. This is in contrast to the standard Balassa–Samuelson model where wages are equalized across sectors due to free mobility of workers without frictions. Finally, since job creation, uT qT qðqT ÞZT , should be equal to job destruction, l(1  uT)ZT in equilibrium, the steady-state unemployment rate in the tradable sector can be written as:

uT ¼

l : l þ qT qðqT Þ

(13)

Eq. (13) shows that search generated unemployment rate in the tradable sector is positively related to the job destruction rate (l) but negatively associated with the probability of an unemployed worker encountering a job opportunity (qTq(qT)). It describes a fundamental equilibrium relationship between unemployment and vacancy, which is often referred to as the Beveridge Curve. This relationship can be illustrated as a downward sloping locus of unemployment and vacancy combinations in the U–V space that are consistent with the steady state in which the total flow of workers into unemployment is equal to the total flow of workers out of unemployment (Pissarides, 2000, p. 32). 2.6. Equilibrium We are now able to characterize the steady-state equilibrium. The equilibrium conditions in the tradable sector consist of firms’ profit maximization conditions with respect to capital and labor, Eqs. (3) and (4) respectively, the equilibrium in wage bargaining Eq. (12), and the labor market equilibrium condition (13), which are re-written as (Eq. (4a) below is from Eqs. (4) and (10)).

AT f 0 ðkT Þ ¼ r; 
AT f ðkT Þ  kT f 0 ðkT Þ ¼ rUT þ

(3) ðr þ lÞg ; ð1  bÞqðqT Þ

wT ¼ ð1  bÞb þ bgqT þ bðAT f ðkT Þ  rkT Þ; uT ¼

l : l þ qT qðqT Þ

(4a) (12) (13)

Similarly, the equilibrium conditions for the nontradable sector can be written as follows.

pAN g 0 ðkN Þ ¼ r; pAN ðgðkN Þ  kN g0 ðkN ÞÞ ¼ rUN þ

ð30 Þ ðr þ lÞg ; ð1  bÞqðqN Þ

wN ¼ ð1  bÞb þ bgqN þ bðAN gðkN Þ  rkN Þ;

uN ¼

l ; l þ qN qðqN Þ

ð4a0 Þ

ð120 Þ

ð130 Þ

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where p is the relative price of nontradable to tradable goods. Both sets of four equations for the tradable and nontradable sectors consist of a recursive system that can be solved easily for the eight unknowns, i.e., ki, qi, wi and ui where i ¼ T,N.5 2.7. The generalized Balassa–Samuelson effect To examine the price effect of anticipated productivity shifts, as in the Balassa–Samuelson model, we take natural logs of both sides of Eq. (4a) and differentiate them, which yields

ðr þ lÞg dA dAT AT f 0 ðkT ÞkT dkT rkT dkT 6 d6 ð1  bÞqðqT Þ T þ ¼ þ ; þ AT f ðkT Þ 6 AT AT f ðkT Þ kT AT f ðkT Þ kT f ðkT ÞAT

(14)

where the frictional cost is assumed to be proportional to workers’ productivity g ¼ AT g.6 We adopt b hdlog X ¼ dX=X for any the convention that the circumflex denotes a logarithmic derivative: X variable X restricted to some positive values. lg bÞqðqT Þ be labor’s share and the frictional cost share out of Let mLT ¼ 6=AT f ðkT Þ and mCT ¼ ðrþ Þ A=ð1 T f ðkT Þ the income generated in the tradable sector respectively. Then Eq. (14) reduces to

b ¼ m 6: b ð1  mCT Þ A T LT

(15)

Increased productivity in the tradable sector will increase expected income of unemployed workers, similar to the real wage, in the Ballassa–Samuelson model, but the extent of the increase in unemployed workers’ expected income has to be adjusted by sectoral labor market efficiency, as defined below. lg

b

q

Þqð i Þ Definition 1. We define ð1  mCi Þ ¼ 1  ðrþ Þ A=ð1 (where i ¼ T, N) as an indicator of labor market i f ðki Þ matching efficiency for sector i. The higher this index, the more efficient a country (sector)’s labor market is.

There are three labor market variables that are important for determining the degree of labor market efficiency.7 The first is the frictional cost (unit advertising and recruitment costs) g. The higher the frictional cost, the less efficient are labor market institutions in facilitating workers’ search for jobs and firms’ hiring of workers. The second and third factors are the job destruction rate and the job creation rate. A higher job destruction rate, together with a lower job creation rate, implies a less efficient labor market institution. We summarize the relationship between these three labor market variables and a country’s labor market matching efficiency as follows. Lemma 1. If the productivity-adjusted recruitment cost of a new vacancy is not equal to zero ðgs0Þ, the labor market inefficiency increases with respect to the job destruction rate (l) and decreases with respect to the job creation rate (qiq(qi)). Proof.

From Definition 1, we have vmCi =vli _0 and vmCi =vqi qðqi Þ30 (since vqi qðqi Þ=vqi _0).

5 For example, in the tradable sector, Eq. (3) can be used to solve for kT and then Eqs. (4a), (11) and (12) can jointly be used to solve for qT and wT. Finally, qT and Eq. (13) are to solve for uT. Similar derivation can be carried out for the nontradable sector. The results are then combined with the free flow condition for unemployed workers across sectors rUT ¼ rUN ¼ 6 to obtain the general equilibrium for the economy. 6 The recruitment cost is made proportional to the productivity on the ground that it is more costly to hire more productive workers. See Pissarides (2000, Chapter 1). We offer an alternative rationalization to this assumption. Although most search economists believe that it is the search and matching process that is causing labor market friction, we think that such a friction may also be affected by some exogenous institutional factors, which is the rationale behind our assumption that recruiting cost is a function of exogenous factor, productivity in this context. For example, two countries with the same size and the same labor flow characteristics such as market tightness and search efforts may experience different recruiting cost for each vacancy due to different labor market institutional arrangements. 7 These three labor market variables are usually defined by three coefficients, used to quantify matching function in the labor market and thus the labor market matching efficiency. Estimates of these three coefficients can be found for some developed countries in the literature, for example Shimer (2005), Genda (1998), Blanchflower and Burgess (1996), Kano and Ohta (2003, 2004) etc. See Table 1 for details.

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Similarly, the equilibrium condition of (4a0 ) for the nontradable sector, after log-differentiation, can be written as follows

b ¼ m 6: b b p þ ð1  mCN Þ A N LN

(16)

b ¼ ð1  m Þ A b =m from Eqs. (15) in (16) yields Substituting 6 T CT LT

m b  ð1  m Þ A b : b p ¼ LN ð1  mCT Þ A T N CN mLT

(17)

Eq. (17) implies that the relative price of nontradable goods depends on the labor-market-efficiency-adjusted productivity differential in the tradable and nontradable sectors. As a country’s price index is an average of the prices of tradable and nontradable goods, we thus have the following: Lemma 2. National price levels are positively related to labor-market-efficiency-adjusted productivity in the tradable sector and negatively related to labor-market-efficiency-adjusted productivity in the nontradable sector. b m 30 and v p=v b m _0. As the home price level is a weighted Proof. From Eq. (17), we have v p=v CT CN average of the prices of tradable and nontradable goods, the change in the home price level will be b b proportional to the change of nontradable prices, i.e., v P=v p_0. Using the rule of chain, we thus have b m _0. b m 30 and v P=v v P=v CT CN A few notes are in order here. Lemmas 1 and 2 demonstrate that the degree of labor market efficiency matters for the relationship between productivity and wages in both the tradable and nontradable sectors. When workers have to cycle between employment and unemployment and it is unemployed workers who move across sectors to equalize their expected income, the increase in employed workers’ wages due to productivity shocks may be less than what the standard Balassa– Samuelson model predicts as employed workers only share part of the benefit from the productivity increase (since unemployed workers also have a share). More specifically, there are two additional forces that can affect the changes in the national price level that arise from a productivity shock in the tradable sector. On one hand, the degree of labor market matching inefficiency in the tradable sector weakens the response of workers’ wages to productivity shocks, which tends to operate against the standard Balassa–Samuelson effect (see Eq. (15)). On the other hand, labor market matching inefficiency in the nontradable sector weakens the response of the price (or workers’ wages) to productivity shocks, which tends to strengthen the standard Balassa–Samuelson effect (See Eq. (16)). Consequently, differences in the degree of labor market matching efficiency across sectors and countries may lead to deviations from the standard Balassa–Samuelson effect. When there is no cost associated with recruiting workers in the labor market (i.e., full labor market matching efficiency), we have mCT ¼ mCN ¼ 0, so that Eq. (17) simplifies to

m b b b p ¼ LN A T  AN : mLT

(18)

Eq. (18) is the original Balassa–Samuelson formulation of the price effects of anticipated productivity shifts. The relative price of nontradable goods depends on the productivity differential between the tradable and nontradable sectors. Provided the inequality mLN/mLT  1 holds, faster productivity growth in the tradable sector will push up the price of nontradable goods over time. Let a star in the superscript of a variable denote foreign country variables. It is easy to show that the price of nontradable goods in the foreign country is as follows   
b m
 b  b p ¼ LN  1  mCT A T  1  mCN A N :

mLT

(19)

We define a country’s price index P (P*) as the geometric mean of the prices of tradable and nontradable goods, with weights s and 1  s. Following Obstfeld and Rogoff (1996, p. 211), we assume that tradables have a uniform price in each of the two countries. Since we take tradables as the numeraire, with a common price of 1 in both countries, the home-to-foreign price ratio is simply proportional to the ratio of the internal relative prices of nontradable goods:

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  bP b  ¼ ð1  sÞ b P pb p  i h i m h b 
1  m  A b 
1  m  A b   ð1  m Þ A b : ¼ ð1  sÞ LN ð1  mCT Þ A T N CN T N CT CN

mLT

(20)

Provided that nontradable goods are at least as labor-intensive as tradable goods so that mLN/mLT  1, the home country will experience real appreciation (a rise in its relative price level) if its labor-marketefficiency-adjusted productivity advantage in the production of tradables exceeds its labor-marketefficiency-adjusted productivity advantage in the production of nontradables. This can be summarized in the following proposition: Proposition 1. The greater a home country’s labor-market-efficiency-adjusted productivity advantage is in the production of tradable goods than labor-market-efficiency-adjusted productivity advantage in the production of nontradables, the larger will be a home country’s real exchange rate appreciation. Proof. From Eq. (20),  we have b  ð1  m Þ A b 30. v½ð1  mCN Þ A N N CN

bP b  Þ=v½ð1  m Þ A b  ð1  m Þ A b  _0 vð P T CT T CT

and

bP b  Þ= vð P

Proposition 1 highlights two conditions that have to be satisfied for a country to experience a real exchange rate appreciation (assuming that the tradable sector is capital-intensive): (1) there is a higher productivity growth in the tradable sector; (2) with frictional costs in the labor market ðgs0Þ, relative frictional costs in the tradable sector should not be too high. In contrast, the classic Balassa–Samuelson model requires only satisfaction of the first condition to experience a real exchange rate appreciation. Again, if there is no cost associated with recruiting workers in the labor market, we have mCT ¼ mCN ¼ 0, so that Eq. (20) reduces to

 i h i   m hb b b ; bP b  ¼ ð1  sÞ b b ¼ ð1  sÞ LN A P pb p T  AT  AN  AN

(21)

mLT

which is the full employment version of the Balassa–Samuelson model. To further appreciate Proposition 1, we provide the following three corollaries based on Eq. (21). Corollary 1. Even though there is unemployment in the labor market, as long as it takes no frictional cost to fill a new vacancy ðg ¼ 0Þ, a country’s real exchange rate will appreciate over time if and only if the tradable sector has faster productivity growth. The result of Corollary 1 is the same as that of the full employment version of the Balassa–Samuelson model, though it is cast in an environment with frictional unemployment. It suggests that the impact of labor market flexibility on the real exchange rate is not because of frictions in labor markets themselves but because there are related hiring and firing costs to firms caused by frictions in labor markets. Furthermore, suppose both countries experience unbiased technological progress but the home b and A b ¼ A b  and A b and A b are higher than A b b ¼ A country has a faster productivity growth, i.e., A T N T N T N T  b and A N , the home country may not experience real exchange rate appreciation if the labor market in  b may be smaller than ð1  m Þ A b , as suggested the tradable sector is seriously distorted, as ð1  m Þ A CT

T

CT

T

by Eq. (20). This gives: Corollary 2. If a home country experiences a faster rate of productivity growth but has a much lower level of labor market efficiency in the tradable sector, the classic positive relationship between real exchange rate and sectoral productivity may be reversed, i.e., the home country’s real exchange rate may not experience real exchange rate appreciation over time. b ¼ A b ¼ A b and A b ¼ A b ¼ A b  , and A b are higher than A b  , Eq. (20) reduces to Proof. Since A T N T N   b b b b b b P  P ¼ ð1  sÞfððmLN =mLT Þ  1Þ½ð1  mCT Þ A  ð1  mCT Þ A g:ð P  P Þ may not be positive if b  ð1  m Þ A b . ð1  m Þ A CT

T

CT

T

The next corollary focuses on the role of sectoral labor market efficiency in determining real exchange rate. Corollary 3. If both countries experience the same rate of productivity growth and achieve the same level of labor market efficiency in their tradable sectors, the real exchange rate between two countries depends

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Table 1 Parameters for labor market flexibility variable: U.S., Japan and UK. Parameter

U.S.

Unit recruiting cost ðg ¼ g=Af ðkÞÞ Job destruction rate (l) Interest rate (r)

0.05 0.35 0.10a 0.04b One year discount rate

Japan

0.50 0.07c

Federal Reserve

Bank of England

Matching function Matching flexibility a

0.13

Elasticity of the matching function w.r.t. unemployment (a)

0.72a

Labor market matching efficiency (1  mCi)

f

0.886

Bank of Japan f

0.09f

0.08

0.69d g

UK

0.71e g

0.301

0.718g

a

Shimer (2005). Genda (1998). c Blanchflower and Burgess (1996). d Kano and Ohta (2003, 2004). e Pissarides (1986). f Authors’ estimate. The procedures that we used to estimate job matching efficiencies for the US, Japan and UK are as follows. With data on numbers of vacancies, unemployed workers and job matching for each period (m(Uit,Vit)), we estimate annual job a . We then take the average of at as the job matching flexibility for each country at from the equation at ¼ m(Uit,Vit)/Uat V1 t matching flexibility for each country. For the period 1979–1996, our estimate of job matching flexibility for US is 0.13 and for Japan 0.08. However, since the UK data on job matching between vacancies and unemployed workers are not available for the period under study, we use estimates from the latest labor market data as a proxy (see http://www.econstats.com/uk/uk_unem_ 14m.htm for the latest data on job vacancies, job replacement and matching rates). We estimate that the average matching rate q (qt) in 2005 is about 18.5 percent, which implies a job matching flexibility of 0.09. g Estimates of labor market matching efficiency follow Definition 1 and are based on estimates on other labor market parameters in this table. They are averages over the sample period. b

not only on their relative rate of productivity growth but also their relative labor market efficiency in their nontradable sectors. b ¼ A b  and m ¼ m , we have ð1  m Þ A b ¼ ð1  m Þ A b  . Eq. (19) becomes Proof. Since A T T CT CT T T CT CT  b  ð1  m Þ A b g. bP b ¼ ð1  sÞfð1  m Þ A P N CN N CN 3. Empirical evidence In this section, we show regression results of the revised Balassa–Samuelson effect in the presence of labor market frictions. The model we lay out in the previous section suggests that in estimating the Balassa–Samuelson effect, the productivity measure should be adjusted for labor market efficiency. Ideally, we should follow equation (20) to distinguish the labor market efficiencies between the tradable and nontradable sectors. However, due to data availability, we have to restrict our focus to cross-country differences in labor market efficiency while assuming that both tradable and nontradable sectors in the same country have the same labor market efficiency. Under this assumption, countries with faster labor-market-efficiency-adjusted productivity will experience larger real exchange rate appreciations (from Corollary 1). We should expect the coefficient of labor-marketefficiency-adjusted productivity to be positive and to provide more accurate measurement of the Balassa–Samuelson effect than the equivalent regression coefficient of productivity without adjusting for labor market efficiency. Our empirical investigation is dictated by the availability of data for labor market efficiency. Two exercises have been carried out, although neither of them can perfectly capture the complexity of our theoretical predictions. The construction of our first dataset follows closely with what our model suggests in measuring labor market matching efficiency, but it comes with a cost as data on search coefficients such as the job destruction rate, labor market matching efficiency and elasticity of the matching function with respect to unemployment are scarce. We are therefore restricted to focus on annual frequency for only three countries, namely, the United States, the United Kingdom and Japan where relatively high quality data are available. The real exchange rates between the US dollar and Japanese Yen and between the US dollar and UK pound are defined as the nominal exchange rate

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multiplied by the ratio of CPI in each country. These data are available from Charles Engel’s personal website (http://www.ssc.wisc.edu/wcengel/data.htm). Data on labor productivity, defined as annual GDP per hour worked for the U.S., Japan and UK, is collected from the OECD’s country statistical profile database (available at http://stats.oecd.org/index.aspx). We summarize our collected and estimated labor market matching efficiency data in Table 1. With raw data for three countries over the period 1979 and 1995, we construct variables for two countries, Japan and the UK. We consider the following two empirical specifications:

ln RERiUS;t ¼ b0 þ b1 ln

ln RERiUS;t ¼ b0 þ b1 ln

yi;t yUS;t

y0i;t y0US;t

! þ hi;t ;

(M1)

þ hi;t ;

(M2)

!

where RERiUS,t is the real exchange rate between country i (Japan or the UK) and the United States at time t, yi,t and yUS,t are the productivities of country i and the US at time t not adjusted for labor market efficiency; y0i;t ¼ ðyi;t Þð1mi;t Þ and y0US;t ¼ ðyUS;t Þð1mUS;t Þ are the productivities of country i and the US at time t adjusted for labor market efficiency; labor market matching efficiency for country i is represented by (1  mi,t) while for the US is (1  mUS,t), as defined in Section 2. In both (M1) and (M2), the US is the base country. The difference between (M1) and (M2) is that in the latter the productivity is adjusted by a country’s labor market efficiency. Table 2 presents OLS regression results based on (M1) and (M2) for the Japan–US and the UK–US series and also for the pooled sample. Columns (1), (3) and (5) of Table 2 report results with productivity not adjusting for labor market efficiency, while columns (2), (4) and (6) present the corresponding results with labor-market-efficiency-adjusted productivity for the Japan–US, UK–US and the pooled sample. The coefficients for productivity (with or without labor market efficiency adjustment) are all positive and statistically significant at the one percent level. For the Japan–US case, our estimated Balassa–Samuelson effect is 0.536 for the model without adjusting for labor market efficiency (M1) and 0.578 for the model that adjusts for labor market efficiency (M2). For the UK–US case, our estimated Balassa–Samuelson effect is 0.920 for the model without adjusting for labor market efficiency (M1). Using labor-market-efficiency-adjusted productivity, the coefficient is 0.983. For the pooled sample, the estimated Balassa–Samuelson effect is 0.576 for the model without adjusting labor market matching efficiency and 0.612 for the model that adjusts for labor market matching efficiency. These elasticity estimates are comparable with those of Bergin et al. (2006) from cross-sectional regression estimation (their estimated elasticity with respect to productivity is 0.41 in a cross section of Table 2 Regression results for (M1) and (M2). Japan–US (1) ln(yi/yUS) 0

0

UK–US (2)

0.536*** (0.039)

ln(yi/yUS)

(3)

Pooled sample (4)

0.920*** (0.122) 0.578*** (0.041)

Observations R2

4.729*** (0.017) 17 0.917

4.632*** (0.023) 17 0.938

0.983*** (0.084)

0.588*** (0.027) 17 0.733

(6)

0.576*** (0.039)

Country dummies Constant

(5)

0.637*** (0.025) 17 0.850

5.265*** (0.026) 4.708*** (0.019) 34 0.999

0.612*** (0.044) 5.149*** (0.034) 4.610*** (0.030) 34 0.999

Note: Dependent variable is the logarithm of the real exchange rate of country i (Japan or UK) with the United State as the base country. ***, ** and * represent significant at 1%, 5% and 10% level. Standard errors are in parentheses. The results are from OLS regressions.

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Table 3 Cross-section regression results for (M3) and (M4): 2004.

ln(yi/yUK)

(1)

(2)

0.396*** (0.032)

0.486*** (0.055) 0.254* (0.146) 0.136** (0.068) 0.066 (0.116) 132 0.546

Dummy Dummy* ln(yi/yUK) Constant

0.095 (0.071) 132 0.539

Observations R2

Notes: Dependent variable is the logarithm of the real exchange rate of country i with the UK as the base country. Labor market efficiency dummy variable, Dummy, equals to 1 if a country has a higher hiring and firing cost than that of the United Kingdom which is 1 by default. ***, ** and * represent significant at 1%, 5% and 10% level. Standard errors are in parentheses. The results are from OLS regressions.

142 countries for the year 1995). Overall, the regressions of the real exchange rate on labor-marketefficiency-adjusted productivity perform somewhat better than those of the real exchange rate on unadjusted productivity, with R2 in (M2) somewhat higher than that in (M1). It lends support to our prediction that in the presence of labor market frictions, productivity adjusted for labor market efficiency provides better estimates of the Balassa–Samuelson effect. With data for only three countries, one might argue that the above results are of limited value. We therefore construct our second dataset which uses labor hiring and firing costs to proxy for the degree of labor market matching efficiency. We make use of a newly available dataset published in Doing Business in 2006 by the World Bank (2006), which is also used by Helpman and Itskhoki (2010). Although data for labor hiring and firing costs are available for one year (2004) only in the World Bank dataset, it covers more than one hundred countries. More importantly, the dataset indicate that there are vast differences in labor market efficiency across countries. For example, the sum of hiring and firing costs for the US is 8 (weeks of salary) while that for the UK and China is 74 and 203 (weeks of salary) respectively. Data for other variables such as price and productivity (using GDP per capita as a proxy) are taken from Penn World Table (PWT) database.8 The PWT gives both income and price variables in terms of the US that are comparable across space. We perform a cross-sectional regression analysis of real exchange rates on productivity with and without adjustment for the degree of labor market efficiency (M4). Specifically, we perform two regressions, one without accounting for the effect of labor market matching efficiency (M3) and the other controlling for the degree of labor market efficiency (M4).

 ln

Pi PUK

 ln

Pi PUK





¼ b0 þ b1 ln

¼ b0 þ b1 ln



yi yUK



yi yUK





þ hij ;

(M3)

 yi þ b2 Dummy  ln þ b3 Dummy þ hij : yUK

(M4)

Our dependent variable, ln(Pi/PUK), is the logarithm of country i’s real exchange rate against the UK.9 ln (yi/yUK) denotes the logarithm of country i’s GDP per capita relative to the UK. The labor market efficiency dummy variable, Dummy, equals 1 if a country has higher hiring and firing costs than those of the UK which is 1 by default. We also include an interaction between the labor market efficiency

8 9

The data is available at http://pwt.econ.upenn.edu/. The results are the same if the US is taken as the base country.

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dummy variable and the productivity variable to control for the effect of differences in labor market institutions across countries. We expect the coefficients of both the Dummy and the interaction term to be negative. That is, the higher the labor market frictions (hiring and firing costs), the smaller the Balassa–Samuelson effects, other things being equal. Table 3 reports the empirical results of the cross-sectional regressions. Without adjusting for labor market firing and hiring costs, the Balassa–Samuelson effect is about 0.396 and is statistically significant at the 1 percent level (column (1)). Again, these elasticity estimates are comparable with those of Bergin et al. (2006). The labor market efficiency dummy variable, proxied by the relative firing and hiring costs, is negative and statistically significant at the 10 percent level. The coefficient of the slope dummy is negative and statistically significant at the 5 percent level. For countries with higher labor market hiring and firing costs (Dummy ¼ 1), the Balassa–Samuelson effect is much smaller (about 0.350 which is the difference between the coefficient of the productivity variable, 0.486, and that of the interaction term, 0.136) than that obtained without adjusting for labor market frictions (0.396). For countries with lower labor market hiring and firing costs (Dummy ¼ 0), the Balassa–Samuelson effect is much larger (0.486, which is higher than 0.396). These results suggest that, other things equal, the higher the firing and hiring costs, the smaller the Balassa–Samuelson effect. Again, the evidence from cross-sectional regressions lends support to the central notion of our paper that the relationship between real exchange rate and productivity depends on labor market efficiency. 4. Conclusion It is well known that there exist significant differences in labor market institutions across countries. Yet it is not clear how these differences in labor market efficiency affect the relationship between the real exchange rate and productivity. This paper extends the classic Balassa–Samuelson model to an environment with search unemployment. We show that there is an important role for the labor market institutional environment to play in determining the magnitude of the effects of sectoral productivity differentials on the real exchange rate. In particular, there is the potential that the standard Balassa– Samuelson effect may not hold. Accounting for a country’s and a sector’s degree of labor market matching frictions, the relationship between the real exchange rate and sectoral productivity may be more complex than that predicted by the Balassa–Samuelson models. To test our prediction that the relationship between the real exchange rate and productivity depends on labor market frictions, we construct two datasets and perform regressions that include labor market friction variables. Our empirical evidence supports our proposition that the degree of labor market frictions is important in explaining the impact of productivity on the real exchange rate. Although our model is derived at the steady state, the derivation of the model out-of-steady-state is provided in the Appendix. The result from the out-of-steady-state model is that the short-run Balassa– Samuelson relationship may deviate from its long-run relationship, taking into account labor market frictions across sectors or countries. An important insight from our analysis is that models that ignore labor market frictions may be inadequate in explaining the Balassa–Samuelson effect. Acknowledgement We are grateful to the editor, James Lothian, and two anonymous referees for very detailed and insightful comments and suggestions which improve the paper substantially. We thank Jean Imbs, Peter Drysdale, Martin Richardson, Guillaume Rocheteau, Jane Golley, Dong He and Ligang Song for comments and suggestions. Financial support from the Hong Kong Polytechnic University (G-U685) is gratefully acknowledged. Part of the research on this paper was conducted while Xinpeng Xu was visiting the Hong Kong Institute for Monetary Research and he thanks them for their hospitality and support. The views expressed in this paper are those of the authors and do not necessarily represent views and opinions of the HKIMR. Appendix To derive the dynamic equations for wages and market tightness for the two sector model with search unemployment, we need to specify the expected returns of firms and workers out-of-steady-

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601

state. Following Pissarides (2000), the net worth of jobs and workers is an explicit function of time. The arbitrage equations determining their value are similar to the ones that hold at the steady state, except that there may be capital gains or losses from changes in the valuation placed by the market on jobs and workers. To conserve space, we use the tradable sector in home country as an example. The analysis can easily be extended to the nontradable sector and foreign countries. Starting with the same model in Section 2, we again assume that VT denotes the asset value of a vacant job in the tradable sector of home country. With a perfect capital market and perfect foresight, Eq. (1) can be re-written as:

rVT ¼ g þ V_ T þ qðqT ÞðJT  VT Þ:

(A1)

The only difference between (1) and (A1) is that the (A1) takes into account expected capital gains from changes in the valuation of the asset during adjustment ðV_ T Þ. Similarly, the value of a filled job, JT, satisfies the arbitrage condition. For simplicity, suppose that the value of physical capital does not change. Equation (2) can be re-arranged as:

rðJT þ kT Þ ¼ AT f ðkT Þ  wT þ J_ T  lJT ;

(A2)

JT ¼ g=qðqT Þ;

(A3)

J_ T ¼ ðr þ lÞJT  ½AT f ðkT Þ  rkT  wT :

(A4)

where J_ T is the expected capital gain from changes in job value during adjustment. The assumption that firms exploit all profit opportunities from new jobs, regardless of whether they are in the steady state or out of it, implies that VT ¼ V_ T ¼ 0. Thus the job creation process is determined by two equations:

The asset value of employed and unemployed workers can also be given by two arbitrage equations that are similar to (5) and (6) but with the changes in valuation out-of-steady-state.

rUT ¼ b þ U_ T þ qT qðqT ÞðET  UT Þ

(A5)

rET ¼ wT þ E_ T þ lðUT  ET Þ:

(A6)

and

All differential equations for asset values are unstable because of arbitrage and perfect foresight. We assume that wages are determined by the Nash solution to the bargaining problem, which as before implies the sharing rule in (9). This condition ensures that (10) holds both in and out-of-steadystate. Since there is no lag in the wage bargaining process, the out-of-steady-state dynamics of wages are driven entirely by the dynamics of labor-market tightness (15). We are now ready to describe the dynamics of wages and tightness. From (A5) and (A6), the dynamics of unemployment can be given by the difference between job destruction:

u_ T ¼ lð1  uT Þ  qT qðqT ÞuT :

(A7)

From (A3), we have J_ T ¼ g=½qðqT Þ2 q0 ðqT Þq_ T (cq0 (qT) < 0) which is a monotonically increasing function of q_ T . Substituting (A3) and (12) into (A4), we have

g=½qðqT Þ q0 ðqT Þq_ T ¼ ðr þ lÞg=qðqT Þ þ bgqT þ ð1  bÞ½AT f ðkT Þ  rkT þ b 2

(A8)

which is an unstable equation of qT with no other unknowns in it. The sign pattern of a first-order linear approximation to the two differential equations (A7) and (A8) is:



u_ T q_ T



 ¼

 0

 þ



uT

qT

:

(A9)

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Fig. 1. Phase diagram of unemployment and market tightness.

Since the determinant of differential equations (A9) is negative, we have both the necessary and sufficient conditions for a saddle-point equilibrium to be satisfied. The reason for this saddle-point equilibrium is that unemployment is sticky and stable, while vacancy is forward-looking and unstable (Pissarides, 2000; p. 29). Thus, the dynamics of qT and uT in the neighbourhood of saddle-point equilibrium follows perfect-foresight paths which is determined by the initial condition of qT. If the initial condition is such that qT ¼ qT where q_ T ¼ 0, the dynamic path is qT-stationary and thus qT is constant and unemployment adjusts until there is convergence to equilibrium. However, if initially qT sqT , the dynamic path is divergent with qT becoming larger and larger as qT > qT and smaller and smaller as qT < qT . Using the dynamics in Fig. 1 to explain the inconsistency between the short-run and long-run wageproductivity relationship (and thus the Balassa–Samuelson effect) is straightforward. As is shown in (15), mCT is an increasing function of qT. If qT ¼ qT , the short-run relationship between wage and sectoral productivity is consistent with that in the long run since the dynamic path is qT-stationary. However, if qT sqT , the short-run relationship between wage and sectoral productivity is not consistent with that in the long run. In particular, when vacancies overshoot ðqT > qT Þ following productivity shocks, the labor market matching efficiency in the short run would be lower than that in the long run. Thus, the impact of productivity shocks in the tradable sector on price would be weakened. Extending this mechanism to the nontradable sector and other countries, we have the result that the Balassa– Samuelson effect is less stable in the short run than in the long run.

References Asea, P., Mendoza, E., 1994. The Balassa–Samuelson model: a general equilibrium appraisal. Review of International Economics 2, 191–200. Balassa, B., 1964. The purchasing-power parity doctrine: a reappraisal. Journal of Political Economy 72, 584–596. Bergin, P., Glick, R., Taylor, A., 2004. Productivity, tradability, and the long-run price puzzle. NBER Working Paper No. 10569. Bergin, P., Glick, R., Taylor, A., 2006. Productivity, tradability, and the long-run price puzzle. Journal of Monetary Economics 53, 2041–2066. Blanchard, O., Diamond, P., 1989. The Beveridge curve. Brookings Papers on Economic Activity 1, 1–60. Blanchflower, D.G., Burgess, S.M., 1996. Job creation and job destruction in Great Britain in the 1980s. Industrial and Labor Relations Review 50, 17–38. Canzoneri, M., Cumby, R., Diba, B., 1999. Relative labor productivity and the real exchange rate in the long run: evidence for a panel of OECD countries. Journal of International Economics 47, 245–266. De Gregorio, J., Giovannini, A., Wolf, H., 1994. International evidence on tradable and nontradables inflation. European Economic Review 38, 1225–1244. Diamond, P.A., 1982. Wage determination and efficiency in search equilibrium. Review of Economic Studies 49, 217–227. Engel, C., 1999. Accounting for U.S. real exchange rate changes. Journal of Political Economy 107, 507–538. Fitzgerald, D., 2003. Terms-of-trade Effects, Interdependence and Cross-country Differences in Price Levels. Mimeo, Harvard University.

Y. Sheng, X. Xu / Journal of International Money and Finance 30 (2011) 587–603

603

Froot, K., Rogoff, K., 1995. Perspectives on PPP and longrun real exchange rates. In: Grossman, G., Rogoff, K. (Eds.), Handbook of International Economics, vol. 3. North Holland, Amsterdam, pp. 1647–1688. Genda, Y., 1998. Job creation and destruction in Japan, 1991–1995. Journal of the Japanese and International Economics 12, 1–23. Ghironi, F., Melitz, M., 2005. International trade and macroeconomic dynamics with heterogeneous firms. Quarterly Journal of Economics 120, 865–915. Helpman, E., Itskhoki, O., 2010. Labor market efficiency, trade and unemployment. Review of Economic Studies 77, 1100–1137. Kano, S., Ohta, M., 2003. Estimating a matching function and regional matching efficiencies: Japanese panel data for 1973–1999. Japan and the World Economy 17, 25–41. Kano, S., Ohta, M., 2004. Long-run matching relationship in the Japanese labor market. Empirical Economics 29, 921–937. Ljungqvist, L., Sargent, T., 2000. Recursive Macroeconomic Theory. MIT Press. Lothian, J., Taylor, M., 2008. Real exchange rates over the past two centuries: how important is the Harrod–Balassa–Samuelson effect. Economic Journal 118, 1742–1763. McCall, J.J., 1970. Economics of information and job search. Quarterly Journal of Economics 84, 113–126. Melitz, M.J., 2003. The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica 7, 1695–1725. Mortensen, D.T., 1982. The matching process as a non-cooperative/bargaining game. In: McCall, J.J. (Ed.), The Economics of Information and Uncertainty. University of Chicago Press, Chicago. Mortensen, D.T., Pissarides, C.A., 1999. New developments in models of search in the labor market. In: Ashenfelter, O., Card, D. (Eds.), Handbook of Labor Economics, vol. 3. North-Holland, Amsterdam. Obstfeld, M., Rogoff, K., 1996. Foundations of International Macroeconomics. The MIT Press, Cambridge, Massachusetts. Pissarides, C.A., 1985. Short-run equilibrium dynamics of unemployment, vacancies, and real wages. American Economic Review 75, 676–690. Pissarides, C.A., 1986. Unemployment and vacancies in Britain. Economic Policy 3, 499–559. Pissarides, C.A., 2000. Equilibrium Unemployment Theory, second ed. MIT Press, Cambridge, MA. Rogerson, R., Shimer, R., Wright, R., 2005. Search-theoretic models of the labor market: a survey. Journal of Economic Literature XLIII, 959–988. Rogoff, K., 1996. The purchasing power parity puzzle. Journal of Economic Literature 34, 647–668. Romer, D., 2001. Advanced Macroeconomics, second ed. McGraw-Hill/Irwin, New York, NY. Samuelson, P.A., 1964. Theoretical notes on trade problems. Review of Economics and Statistics 46, 145–154. Shimer, R., 2005. The cyclical behavior of equilibrium unemployment and vacancies. American Economic Review 95, 25–49. Wacziarg, R., Wallack, J.S., 2004. Trade liberalization and intersectoral labor movements. Journal of International Economics 64, 411–439. World Bank, 2006. Doing Business in 2006: Creating Jobs. World Bank Online Publication. http://www.worldbank.org/ publications/.