Black market exchange rate and the productivity bias hypothesis

Economics Letters 91 (2006) 243 – 249 www.elsevier.com/locate/econbase

Black market exchange rate and the productivity bias hypothesis Mohsen Bahmani-Oskooee a,*, Abera Gelan b a

Center for Research on International Economics and Department of Economics, The University of Wisconsin-Milwaukee, Milwaukee, WI 53201, United States b Department of Africology, The University of Wisconsin-Milwaukee, Milwaukee, WI 53201, United States Received 14 March 2005; accepted 7 September 2005 Available online 24 March 2006

Abstract Previous studies that tested the productivity bias hypothesis employed the official nominal exchange rate in constructing the real rate, hence, in testing the productivity bias hypothesis. In this paper we show that if official real exchange rate does not support the productivity bias hypothesis, the real black market rate does. This conjecture is tested by using data from Chile, Colombia and Costa Rica. D 2006 Elsevier B.V. All rights reserved. Keywords: Black market rate; PPP; Productivity bias JEL classification: F31

1. Introduction One theory in economics that has received a great deal of attention is the Purchasing Power Parity (PPP) theory. It basically claims that in the long run, the exchange rate between two currencies is equal to the ratio of price levels in two corresponding countries. However, in testing its validity researchers have identified many factors explaining the deviation of relative prices from equilibrium or market determined exchange rate such as restrictions to trade and capital, transportation cost, etc. One factor that has its own literature is the productivity differential, hence the bproductivity bias hypothesisQ. The hypothesis was initially introduced by Balassa (1964) who argued that a relatively more productive * Corresponding author. Tel.: +1 414 229 4334; fax: +1 414 229 2438. E-mail address: [email protected] (M. Bahmani-Oskooee). 0165-1765/$ - see front matter D 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2005.09.016

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country will have a higher standard of living, thus, higher prices. Higher prices, in turn, increase the gap between the relative prices and the exchange rate. Alternatively, since the gap between relative prices and the exchange rate is reduced to the concept of real exchange rate, the productivity bias hypothesis implies that a relatively more productive country should experience an appreciation of her currency in real terms. The empirical research in testing the productivity bias hypothesis is vast and has recently been collected in a review article by Bahmani-Oskooee and Nasir (2005). They divide the literature into three groups. The first group includes studies that used cross-sectional data and provided mixed conclusions. The list includes Balassa (1964), Clague and Tanzi (1972), Officer (1976), Kravis and Lipsey (1983), Clague (1986, 1988), Heston et al. (1994), Rogoff (1996), Bahmani-Oskooee and Niroomand (1996), and Bergstrand (1991, 1992). The second group includes studies that employed time-series data. These studies basically support the hypothesis, but are rare in numbers. The list includes Hsieh (1982), Bahmani-Oskooee (1992), Strauss (1995, 1996), Bahmani-Oskooee and Rhee (1996), and BahmaniOskooee and Nasir (2001). Finally the third group includes studies that use panel data. Again, the findings are mixed and the list includes Asea and Mendoza (1994), De Gregorio et al. (1994), and Bahmani-Oskooee and Miteza (2004). A common feature of all the studies mentioned above is that in testing the productivity bias hypothesis, they have all used the official exchange rate. Obviously, if due to pegging or following target zones, the official nominal exchange rate does not adjust to market forces, the real rate will not adjust either. Hence, the relation between the real exchange rate and productivity differentials could fail. Our conjecture in this paper is that since the black market exchange rates adjust to market forces more than the official rates, if we use the black market exchange rates rather than the official rates, the productivity bias hypothesis could receive empirical support. To demonstrate this conjecture, in Section II we outline the model and the methodology. The results supporting our hypothesis are reported in Section III. Finally, Section IV concludes.

2. The model and method In formulating the hypothesis, we need to select a country as the base country. We assume the U.S. to be the base country and the dollar, the base currency. The PPP is then formulated by Eq. (1):   Pi ð1Þ Ri;t ¼ PUS t where R i is the nominal exchange rate defined as number of country i’s currency per unit of U.S. dollar, P i is the price level in country i and P US is the price level in the U.S. If we denote the gap between the right hand side and the left hand side of Eq. (1) by RRit , it could be expressed as: 1 0 Pi   B PUS C Pi C ¼ ð2Þ RRi;t ¼ B @ Ri A PUS Ri t t

As can be seen from Eq. (2), the gap between relative prices and the exchange rate is reduced to nothing but the real exchange rate that is now defined as the number of units of U.S. output per unit of

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country i’s output, hence the real exchange rate. Following Officer (1976) and many subsequent studies, we formulate the productivity bias hypothesis in log linear form by Eq. (3):   PRODi LnRRi;t ¼ a þ bLn þ et ð3Þ PRODUS t where PRODi (PRODUS) is a measure of productivity in country i (in the U.S.) and is an error term. If an increase in country i’s productivity is to result in a real appreciation, an estimate of b is expected to be significantly positive. Eq. (3) outlines the long-run relationship between the real exchange rate and the productivity differentials. It is now a common practice to incorporate the short-run dynamics in estimating any longrun model such as Eq. (3). This is done by expressing Eq. (3) in an error-correction format. If we follow Engel and Granger’s (1987) representation, the error-correction model will take the following form: DLnRRit ¼ a þ

n X

bk DLnRRitk þ

k¼1

n X

ck DLnPRitk þ ket1 þ lt

ð4Þ

k¼0

where PR denotes the productivity ratio from Eq. (3) and l is an error term. In Engle–Granger terminology, cointegration or the long-run relation between the real exchange rate (RR) and the relative productivity (PR) is established if either e t in Eq. (3) is stationary or k in Eq. (4) is negative and significant. Of course, the prerequisite is that both variables in Eq. (3) should be first differenced stationary. If one variable is stationary at level and the other is stationary after being differenced once, Pesaran et al. (2001) propose replacing e t1 by the lagged level of variable as in Eq. (5) below. After all, e is a proxy for the linear combination of LnRR and LnPR. DLnRRit ¼ a þ

n X k¼1

bk DLnRRitk þ

n X

ck DLnPRitk þ k1 LnRRt1 þ k2 LnPRt1 þ lt

ð5Þ

k¼0

Pesaran et al. (2001) then introduce their bound testing approach for cointegration which is application of the F-test to establish the joint significance of the lagged level variables. Note that under this new method, there is no need for pre-unit root testing and the variables could be integrated of order one, I(1) or order zero, I(0). However, unlike the standard F-test, they tabulate new critical values for their F-test which depends on whether all variables are integrated of order one (upper bound critical value) or integrated of order zero (lower bound critical value). For cointegration, the calculated Fstatistic must be greater than the upper bound critical value. Eq. (5) is subject to empirical analysis in the next section.

3. The results In this section we estimate Eq. (5) for three South American countries of Chile, Colombia and Costa Rica. Annual data over the 1955–1995 period are used to carry the empirical analysis. The productivity measures come from Penn World Table (PWT6.), the price levels (i.e. GDP deflators) and the official exchange rates come from the International Financial Statistics of the International Monetary Fund, and the black market exchange rates from the World Currency Yearbook.

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We first carry out the empirical analysis using the official exchange rate. In estimating an errorcorrection model like Eq. (5), Bahmani-Oskooee and Brooks (1999) have demonstrated that the results of the F-test could be sensitive to the number of lags imposed on the first differenced variables. Thus, we employ Akaike’s Information Criterion (AIC) to select the optimum number of lags and carry out the Ftest at optimum lags. The results for each optimal model and each country are reported in Table 1 in three panels. Panel A in Table 1 reports the short-run coefficient estimates, i.e., the coefficient estimates of first differenced variables. It appears that there is at least one significant coefficient obtained for relative productivity measure (LnPR) in the cases of Chile and Costa Rica but not Colombia. To determine whether these short-run effects last into long-run, we report estimate of k 2 that is normalized by k 1. This is reported in Panel B. As can be seen, only in the case of Costa Rica, the estimated coefficient for LnPR is highly significant. Next, we carry the F-test for cointegration at optimum lags and report the results in Panel C. As can be seen, in none of the cases our calculated F-statistic exceeds the upper bound critical value of 4.12 indicating lack of cointegration among the variables. Of course, an alternative way of establishing cointegration is to use the long-run coefficient estimates and form an error-correction term,

Table 1 Coefficient estimates of model (5) using official market exchange rate Model Panel A: short-run estimates DLnRRt1 t2 t3 t4 t5

DLnPRt t1 t2 t3

Panel B: long-run estimates Constant LnPR Panel C: diagnostics F ECMt1 LM CUSUM CUSUMSQ

Country Chile

Colombia

Costa Rica

0.21 (1.41) 0.33 (2.17) – – – 3.57 (2.36) – – –

0.19 (1.13) – – – – 1.12 (0.96) 0.55 (0.40) – –

0.11 (0.42)  0.87 (3.63)  0.23 (0.79)  0.45 (2.00)  0.18 (0.85) 1.80 (1.08) 3.05 (1.62) 4.62 (2.44) 1.70 (1.25)

110.08 (0.06) 900.72 (0.06)

69.37 (1.37) 48.59 (1.42)

12.39 (7.32) 11.86 (8.05)

0.99 0.00 (1.36) 0.39 Stable Unstable

0.70 0.00(0.28) 12.76 Stable Stable

3.63 0.23 (2.75) 1.51 Stable Stable

Notes: Numbers inside parentheses are the absolute value of t-ratios. LM = Lagrange multiplier test of residual serial correlation. It is distributed as v 2(1). CUSUM = cumulative sum of recursive residuals. CUSUMSQ = cumulative sum of squares of recursive residuals. CUSUM and CUSUMSQ test for the stability of all coefficient estimates of the error-correction models. At the 10% level of significance, the critical value bounds of the F-statistics are 3.17 and 4.14. They come from Pesaran et al. (2001, table CI(iii), p. 300).

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ECM. Then, estimate the model at optimum lags after replacing the linear combination of lagged level variables by ECMt1. A negative and significant coefficient obtained for ECMt1 will support cointegration (Kremers et al., 1992; Bahmani-Oskooee and Goswami, 2004). As can be seen from Panel C, in none of the cases ECMt1 carries a negative coefficient, though it carries a significant coefficient in the case of Costa Rica. All in all, when the official exchange rate is used in testing the productivity bias hypothesis, although there is some support in the short run but there is no evidence of any long-run relationship. How do the results change if we replace the official exchange rate by the black market rate? The results from optimum models selected by AIC criterion are reported in Table 2. As can be seen from Table 2, the long-run coefficient obtained for the relative productivity (LnPR) is positive and significant in all three cases though, cointegration is supported either by F-test or by ECMt1 only in the results for Chile. The fact that the relative productivity carries a positive and significant coefficient in all cases provide support for our conjecture that whereas, the use of official exchange rate does not support the productivity bias hypothesis, the use of black market rate does. Note that reported under diagnostics is the Lagrange multiplier (LM) test for serial correlation of each errorcorrection model. It is distributed as v 2 with 1 df. Clearly, since all calculated LM statistics are less than the critical value of 3.84, none of the models suffer from serial correlation. Reported under diagnostics are also the results of CUSUM and CUSUMSQ tests for stability of the short-run as well as the long-run coefficient estimates. Both tests support stability of all estimated coefficients in all three models except Table 2 Coefficient estimates of model (5) using black market exchange rate Model Panel A: short-run estimates DLnRRt1 t2 t3

DLnPRt t1

Panel B: long-run estimates Constant LnPR Panel C: diagnostics F ECMt1 LM CUSUM CUSUMSQ

Country Chile

Colombia

Costa Rica

0.09 (0.61) – – 3.70 (0.81)  15.62 (3.41)

0.15 (0.89) – – 0.32 (0.34) –

0.09 (0.37)  0.33 (1.63)  0.27 (1.42) 2.39 (1.06) 1.35 (0.77)

19.76 (2.94) 21.72 (3.39)

44.53 (2.13) 32.19 (2.24)

13.82 (2.83) 13.09 (3.39)

7.10  0.38 (3.82) 0.01 Stable Stable

2.12 0.02 (1.88) 0.41 Stable Stable

1.04 0.13 (1.47) 0.05 Stable Unstable

Notes: Numbers inside parentheses are the absolute value of t-ratios. LM = Lagrange multiplier test of residual serial correlation. It is distributed as v 2(1). CUSUM = cumulative sum of recursive residuals. CUSUMSQ = cumulative sum of squares of recursive residuals. CUSUM and CUSUMSQ test for the stability of all coefficient estimates of the error-correction models. At the 10% level of significance, the critical value bounds of the F-statistics are 3.17 and 4.14. They come from Pesaran et al. (2001, table CI(iii), p. 300).

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the CUSUMSQ in the model for Costa Rica. Note that there was no significant change in the results when we shifted to SBC criterion in selecting the optimum models.

4. Summary and conclusion The productivity bias hypothesis introduced by Balassa in 1964 implies that a more productive country should experience an appreciation of her currency in real terms. A review article by BahmaniOskooee and Nasir (2005) classifies the empirical article into three categories, i.e., cross-sectional, timeseries and panel studies. The findings are mixed at best. A common feature of all studies in the literature is that they have all used official exchange rates in testing the productivity bias hypothesis. In this paper we argue that in countries where there exists a black market for foreign currencies, since the black market exchange rate adjusts much faster to the market forces than the official exchange rate, the productivity bias hypothesis could be supported if the black market rate was used in the testing procedure rather than the official rate. We support our conjecture by considering data from Chile, Colombia and Costa Rica. References Asea, Patrick K., Mendoza, Enrique G., 1994. The Balassa–Samuelson model: a general equilibrium appraisal. Review of International Economics 2, 244 – 267. Bahmani-Oskooee, M., 1992. A time-series approach to test the productivity bias hypothesis in purchasing power parity. Kyklos 45, 227 – 236. Bahmani-Oskooee, M., Brooks, T.J., 1999. Bilateral J-curve between US and her trading partners. Weltwirtschaftliches Archiv 135, 156 – 165. Bahmani-Oskooee, M., Goswami, G.G., 2004. Exchange rate sensitivity of Japan’s bilateral trade flows. Japan and the World Economy 16, 1 – 15. Bahmani-Oskooee, M., Miteza, I., 2004. Panel cointegration and productivity bias hypothesis. Journal of Economic Studies 31, 448 – 456. Bahmani-Oskooee, M., Nasir, A.B.M., 2001. Panel data and productivity bias hypothesis. Economic Development and Cultural Change 49, 393 – 402. Bahmani-Oskooee, M., Nasir, A.B.M., 2005. Productivity bias hypothesis and the PPP: a review article. Journal of Economic Surveys 19, 671 – 696. Bahmani-Oskooee, M., Niroomand, F., 1996. A reexamination of Balassa’s productivity bias hypothesis. Economic Development and Cultural Change 45, 195 – 204. Bahmani-Oskooee, M., Rhee, H.-J., 1996. Time-series support for Balassa’s productivity-bias hypothesis: evidence from Korea. Review of International Economics 4, 364 – 370. Balassa, Bela, 1964. The purchasing-power parity doctrine: a reappraisal. Journal of Political Economy 72, 584 – 596. Bergstrand, Jeffrey H., 1991. Structural determinants of real exchange rates and national price levels: some empirical evidence. American Economic Review 81, 325 – 334. Bergstrand, Jeffrey H., 1992. Real exchange rates, national price levels, and the peace dividend. American Economic Review 82, 56 – 61. Clague, C.K., 1986. Determinants of the national price level: some empirical results. Review of Economics and Statistics 68, 320 – 323. Clague, C.K., 1988. Purchasing power parities and exchange rates in Latin America. Economic Development and Cultural Change 36, 529 – 541. Clague, C.K., Tanzi, V., 1972. Human capital, natural resources and the purchasing-power parity doctrine: some empirical results. Economia Internazionale 25, 3 – 18.

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