نرخ واقعی ارز، بهره وری و اصطکاک های بازار کار

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.

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, 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 and 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. 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. 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.

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.