# Symmetry, proportionality and productivity bias hypothesis: evidence from panel-VAR models

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## Abstract

By imposing symmetry and proportionality conditions and using the asymptotic theory of panel-VAR models, this study examines the behavior of real exchange rates and productivity bias hypothesis for New Zealand vis-a-vis her major trading partners and the proposed free trade area. The evidence clearly rejects the *strong* version of the PPP hypothesis but the *weak* version of the PPP hypothesis receives some support. The findings also indicate that productivity differentials among countries are one of the major sources that contribute to the deviation of the PPP-based exchange rate from the equilibrium rate. Policy implications for the proposed free trade agreement are offered.

## Keywords

Likelihood-based panel cointegration Productivity bias hypothesis PPP Panel rank test Symmetry## JEL Classification

C32 F31 E31## 1 Introduction

This paper examines the purchasing power parity (PPP) principle and the productivity bias hypothesis for New Zealand vis-a-vis her major trading partners and the proposed free trade area.^{1} Studying PPP and productivity bias hypothesis is significant because of the fact that if PPP holds, this implies that the effects of a shock to the real exchange rates would be only temporary. This suggests that real exchange shocks would not have detrimental effects on trade flows at least in the long run and this would imply almost no real exchange rate risk due to price level convergence. These issues are critical not only for policymakers but also from the point of view of asset pricing and portfolio management.

New Zealand is small commodity-exporting economy with reasonably long history of independently floating exchange rates. From 2001 to 2008, the currency of New Zealand experienced large appreciations in nominal and real effective terms. This together with persistent current account deficit raised concern that strong currencies were adversely affecting her external price competitiveness. From 2001 to 2008, the New Zealand dollar appreciated by about 35 %. In real effective term, her currency appreciated by over 30 %. The difference between nominal and real effective exchanges rates reflects accumulated inflation rate differentials relative to trading partners. Between 2008 and 2011, the New Zealand dollar has depreciated significantly.

These real effective exchange rate movements have been driven in part by movements in real effective interest rate differentials but the precise relationship has not been stable over time. Particular instances include the late 1990s, and the late 2000s. In the late 1990s, a combination of high New Zealand interest rates due to strong domestic inflationary pressures and low global interest rates led to large amounts of inward capital flows (Dunaway 2009). The strength of the currency has also been supported by higher terms of trade as New Zealand is relatively large exporters of primary commodities. The relationship between the terms of trade and the exchange rate broke down around 1999 for a couple of years, but has resumed with the run up of commodity prices. Since mid-2008, the depreciations have been accompanied by a decline in global commodity prices. The balance of payments for New Zealand have deteriorated as her exchange rates strengthened. The trade balance of New Zealand has declined, reducing her current account balances. Since 2001, the trade balance of New Zealand has deteriorated from a surplus and its current account deficit has widened considerably (Edison and Vitek 2009). However, the main driver is likely to change over time depending on developments in the domestic and global economy.

Against this background, the paper seeks to assess the behavior of the real effective exchange rate in New Zealand. Many authors indeed cannot reject the hypothesis that real exchange rates follow a random walk process. Thus, changes in the real exchange rate are considered permanent. Intertemporal equilibrium exchange rate models indicate that changes in relative prices, due to traded/non-traded productivity differentials, can induce changes in exchange rates and deviations from PPP (e.g., Rogoff 1992; Asea and Mendoza 1994). Real exchange rates changes in response to productivity growth differentials have been labeled in the literature as the “productivity bias hypothesis” and it reflects the view that an increase in a country’s relative productivity creates an appreciation of its real exchange rate (Balassa 1964; Samuelson 1964).

The result of this study indicates that a long-run relationship exists between the nominal exchange rate and the price ratio. This implies that the *weak* version of the PPP hypothesis receives some support. The evidence, however, clearly rejects the *strong* version of the PPP hypothesis. This means that the cointegration space is not symmetric for the two variables and therefore, PPP does not hold in its *strict* form, implying that the real exchange rate should not be expected to return to the equilibrium PPP value.

Since there is clear evidence that the *strong* version of the PPP hypothesis is violated, the productivity bias hypothesis is investigated. The empirical test shows that the real exchange rates and the productivity differentials are cointegrated in the long run. However, this is not sufficient since the hypothesis requires that the real exchange rates and productivity differentials should have opposite signs. By estimating the long-run coefficient, it has been shown evidence in favor of the productivity bias hypothesis.

Most empirical studies on PPP and real exchange rates, do not test for symmetry and proportionality conditions which are potentially important. Furthermore, it is also assumed that there is a unique cointegrating vector and one-to-one relationship between the exchange rates and the fixed price levels. This paper attempts to overcome these problems by using panel-VAR models where multiple cointegrating vectors are allowed and proportionality and symmetry conditions are imposed.

However, existing empirical research on the PPP theorem and the productivity bias hypothesis has produced mixed results. Among the studies that have supported the productivity bias hypothesis can be cited those by Balassa (1964), Hsieh (1982), Edison and Klovland (1987), Obstfeld (1993), De Gregorio et al. (1994). Others such as Froot and Rogoff (1991), Rogers and Jenkins (1995), Mark and Choi (1997) have little or no support for the productivity bias hypothesis. With regard to the PPP theorem, the results are also mixed and contradictory. Examples are Cheung and Lai (1993), Pedroni (1996), Crowder (1996), Oh (1996), Kouretas (1997), Papell (1997), O’Connell (1998), Gadea et al. (2004), Koedijk et al. (2004), Lopez and Papell (2007), Zhou et al. (2008), Cerrato and Sarantis (2008), Nusair (2012), Tiwari and Shahbaz (2014), Emirmahmutoglu and Omay (2014), Grossmann, et al. (2014), and Arize et al. (2015).

Because of the above inconclusive empirical findings, the aim of this paper is to revisit the validity issue using alternative testing procedures. Our approach employs the likelihood-based panel cointegration technique to obtain estimates of the long-term relationship between exchange rates and prices. This methodology is preferred to other single-equation estimators and residual-based panel cointegration technique because it produces estimated parameters that are asymptotically efficient and it also allows multiple cointegrating vectors. Hence, the assumption of a unique cointegrating vector and the problem of normalization are relaxed.

The paper is organized as follows: Sect. 2 presents theoretical considerations and empirical strategy, Sect. 3 describes data issues, and Sect. 4 interprets the empirical results. Section 5 and Sect. 6 offer some discussion and conclusion, respectively.

## 2 Theoretical considerations and empirical strategy

^{2}

_{ijt }is the real exchange rate,

*E*

_{ ijt }is the nominal exchange rate in terms of domestic currency per unit of foreign currency, \(P_{it}\) and \(P_{jt}\) are domestic and foreign price levels, respectively. Using natural logarithm, we have:

*q*

_{ ijt }is the real exchange rate,

*e*

_{ ijt }is the nominal exchange rate and

*p*

_{ it }and

*p*

_{ jt }are the domestic and foreign price indices, respectively. PPP is the hypothesis that real exchange rates are stationary; the null hypothesis of nonstationarity can be tested against the alternative hypothesis of stationarity. Then, rejection of the null hypothesis would mean that the real exchange rate series reverts to a constant mean and hence leads one to conjecture that PPP is favored in the long run.

*β*

_{ 1 }= 1,

*β*

_{ 2 }= −1) which is based on a series of hypotheses; for example: there are no tariffs, import quotas, transportation costs, measurement errors, information costs, and other hinders in international trade. Since these hypotheses cannot be maintained perfectly in empirical work, a less strict interpretation of PPP hypothesis that allows the real exchange rate to deviate from a constant value (although in a stationary manner), is more likely to have a weak PPP form as in Eq. 3 below. This is obtained using the logarithmic transformation, and adding a constant and a stochastic error term leads to an equation amenable to the cointegration framework (Taylor 1996):

The coefficients *β* _{ 1 } and *β* _{ 2 } are allowed to deviate systematically from one over time. If *e* _{ ijt }, *P* _{ it } and *P* _{ jt } individually show a common stochastic trend and a linear combination of these variables exists that leads to *u* _{ ijt } stationary, then PPP holds. This implies that cointegration is only a necessary condition for long-run PPP to hold. The sufficient condition is that the sign on *β* _{ 1 } is positive and *β* _{ 2 } is negative

*β*

_{ 1 }= −

*β*

_{ 2 }), and it prevents any collinearity that may occur between the price terms:

As long as the error term in the above equation is mean reverting, then, in the presence of transportation costs and measurement problems, proportionality may still hold, but *g* _{ 1 } will not equal one (Taylor 1998). This suggests that long-run proportionality between the nominal exchange rate and relative prices may not be exactly one-to-one and not that real exchange rate is constant. The latter would hold only if *g* _{ 1 } equals unity. It is worth to mention that the effect of transportation costs and other barriers to trade is reflected in the value of *g* _{ 1 } different from unity. Consequently, the symmetric restriction is consistent with the PPP proposition that, in the long run, the nominal exchange rate is determined by relative prices, and relative version of PPP holds when *g* _{ 1 } = 1. Absolute version would require, additionally, that *β* _{ 0 } = 0. Intuitively, this would imply that a change in relative price corresponds to a more than (or less than) proportionate change in the nominal exchange rate while imposing symmetry.

In empirical framework, we have *β* _{ 0 } ≠ 0 and *g* _{ 1 } ≠ 1 which take into account imperfections in the price indices and frictions like tariffs, quotas, non-tariff barriers, transportation and technological costs, differences in weighting schemes for price indices and consumption patterns and other trade impediments that create a wedge among prices across countries (Krichene 1998). Long-run PPP holds if a linear combination of the nominal exchange rate and the relative price is stationary. That is, the effects of a shock in Eq. 4 will at best be transitory in the short run but disappearing in the long run.

*q*

_{ ij }) and productivity ratios in two-country case (\(\gamma_{i} ,\gamma_{j}\)):

^{3}

Greater difference in the productivity ratio of two countries, which leads to a larger gap between their wages and prices, may create a larger gap between PPP and the equilibrium exchange rate. This implies that if productivity is increased (decreased) in the home country relative to the foreign country, the real exchange rate is expected to appreciate (depreciate). Thus, the Balassa–Samuelson hypothesis or productivity bias hypothesis is supported if \(\delta_{1}\) is significant positive in Eq. (5). Similarly to the PPP hypothesis, the cointegrating space must be spanned by the cointegrated vector \(\beta = (\beta_{1} , \, \beta_{2} )\), with the same imposed restrictions on \(\beta_{1}\) and \(\beta_{2}\) which are the long-run coefficients for the real exchange rate and the productivity differentials, respectively. Again, long-run PPP holds if a linear combination of the real exchange rate and the productivity ratios is stationary. That is, the effects of a shock in Eq. 5 will at best be transitory in the short run but disappearing in the long run.

The methodology used here is an extension of the Johansen (1988, 1991, 1995) multivariate maximum likelihood developed by Larsson et al. (2001). They have developed a likelihood-based panel test of the cointegrating rank and a general likelihood-based framework for inference in panel-VAR models with cointegration restrictions, allowing for multiple cointegrating vectors. Hence, the assumption of a unique cointegrating vector and the problem of normalization are relaxed.

*LR*denote the cross-section specific likelihood-ratio (trace) statistic of the hypothesis that there are at most

*r*cointegrating vectors in the system. The standardized

*LR*-bar statistic is given by:

*N*cross-section

*LR*statistics, μ is the mean, and ν is the variance of the asymptotic trace statistic. The panel trace statistic \(\gamma_{{\overline{LR} }}\) is asymptotic normal (0,1) as

*N*and

*T*go to infinity such that \(\sqrt N T^{ - 1}\) goes to zero.

^{4}Asymptotic values of μ and ν (with and without constant and trend) can be obtained from stochastic simulations as described in Johansen (1995). The simulated values are reported in Sect. 4 under Tables 1 and 2.

The testing procedure is the sequential procedure suggested by Johansen (1988). This sequential procedure is continued until the null is not rejected or the hypothesis *r* = *p* − 1 is rejected. This procedure gives the rank estimate *r*. Johansen (1995) has shown that this procedure yields the correct size of the trace statistic asymptotically. If there is a common cointegrating rank, it could be interesting to test hypotheses with restrictions in the \(\beta\) vector. The likelihood ratio tests for linear restrictions on \(\beta\) are asymptotically Chi square distributed. The panel test for testing restrictions on \(\beta\) is constructed under the assumption that the countries in the sample are independent.

To determine the maximum order of integration, it is necessary to test for stationarity. Both KPSS and IPS were used to determine the integration order of each variable and variable in panel, respectively. Finally, a combination of multivariate diagnostic tests is performed to check if the underlying statistical assumptions are fulfilled.

## 3 Data issues

The data used in this study is annual observations and covers the period 1995–2011 for New Zealand vis-a-vis eight of its major trading partners (Australia, US, UK, Japan, Italy, South Korea, France, and Germany) and the proposed free trade area.^{5} The exchange rate series is derived from *the OECD Main Economic Indicators*, various issues. The price level indices and GDP deflators are taken from *the OECD Economic Outlook* and the IMF *International Financial Statistics*. The productivity series which are multifactor or total factor productivity (TFP) are derived from the *International Sectoral Database, OECD*. Data on bilateral exchange rates for German Marks, French Francs, and Italian Lira after the adoption of the Euro, i.e., after 1999, is obtained from the following source: http://fx.sauder.ubc.ca/data.html, University of British Columbia.

There are a number of issues that are central to cross-country comparisons of productivity series. To compare levels of TFP across nations, it is worth to mention that there are two methods to calculate TFP: (1) factor price data and (2) the data on stocks of factors. Thus, it might be some methodological differences between TFP series using the two approaches (i.e., the user costs of capital and physical stocks of capital). Such knowledge may cast some doubts on the reliability of TFP data. Furthermore, since TFP series was missing for Australia and UK between 2009 and 2011, labor productivity series was used during this period.

## 4 Empirical results

Regarding the integration order of each variable, both the KPSS test for individual variables and IPS for panel unit root test show that the variables are integrated of order one and the test results are insensitive to the way the deterministic trend is handled. The results, not reported here, are available from the author on request.

The next step is to set up a panel vector autoregressive model shown by Eq. (6) and test for cointegration rank. By testing New Zealand vis-a-vis individual countries and by constructing a panel test using the sum of the individual test statistics, we obtain a test statistic which follows a Chi square distribution with 8 degrees of freedom. The panel test statistic, with a value of 6.12 compare to the critical value of 13.31, does not reject the null hypothesis of trend exclusion in the cointegrating relation. It seems that the correct model includes an intercept in the cointegrating space.

*r*= 0, and

*r*= 1. The results show that the most common selected rank is

*r*= 1 except for two countries; France and Italy, where the rank is

*r*= 0. However, there is evidence from the panel test that there exists a common cointegration rank in the panel and the nominal exchange rates and the price ratios are cointegrated. By assuming the rank is \(r_{i} = 1\), for all

*i*, we estimate the cointegrated vectors. The estimated long-run coefficients are normalized with respect to the nominal exchange rates and are also presented in Table 1.

Cointegration test for PPP: trace test and test for linear restriction (New Zealand vis-à-vis her major trading partners)

Country | Lag | | | Rank | Estimated \(\beta\) vector | \(\beta = ( - 1, \, 1,\xi )\) |
---|---|---|---|---|---|---|

Japan | 2 | 20.15 | 3.28 | 1 | (−1.000, 1.84) | 7.06 |

US | 1 | 30.01 | 5.17 | 1 | (−1.000, 1.22) | 5.22 |

Germany | 2 | 25.99 | 4.14 | 1 | (−1.000, 1.45) | 12.86 |

Australia | 2 | 31.75 | 9.05 | 2 | (−1.000, 1.32) | 4.63 |

UK | 1 | 29.22 | 4.19 | 1 | (−1.000, 1.90) | 8.18 |

South Korea | 2 | 22.87 | 5.90 | 1 | (−1.000, 1.63) | 11.44 |

France | 1 | 12.98 | 1.24 | 0 | (−1.000, 1.58) | 5.37 |

Italy | 1 | 9.76 | 4.82 | 0 | (−1.000, 1.25) | 1.26 |

| ||||||

\(\gamma_{{\overline{LR} }} (H(r)\left| H \right.(2))\) | | | ||||

6.44 | 0.51 | |||||

\(\beta = ( - 1, \, 1,\xi )\) | 56.02 |

This evidence does not necessarily mean that PPP holds since a necessary condition for PPP to hold, and for real exchange rates to be mean reverting to its long-run equilibrium PPP value, is that the cointegrating space must be spanned by \(\beta = ( - \begin{array}{*{20}c} {1,} & {1,} & \xi \\ \end{array} )\), where \(\zeta\) acts as a wild card and captures the constant in the cointegrating space. This may be tested with the restrictions \(R'\beta = 0\) where \(R' = \left[ {\begin{array}{*{20}c} 1 & 1 & 0 \\ \end{array} } \right]\).

In this case, the number of degrees of freedom is one and the results are shown in Table 1. If we assume that that the test statistics for New Zealand and vis-a-vis individual countries in the sample are independent, the sum is also Chi square distributed, with 8 degrees of freedom. The panel test, with a value of 56.02, rejects the null at the 5 % level of significance. Thus, the common cointegrating space is not spanned by \(\beta = ( - \begin{array}{*{20}c} {1,} & {1,} & \xi \\ \end{array} )\) and PPP does not hold for New Zealand. In other words, the real exchange rates are mean reverting but not in the way as predicted by the PPP theorem.

To ascertain the adequacy of the panel-VAR models, system-wise diagnostic tests were applied.^{6} All New Zealand by-country models are successful in dealing with the problem of autocorrelation and the assumption of normality is fulfilled. Furthermore, robustness check was performed and there was no a change in the result by using different setup of the VAR model. The results, not reported here, are available from the author on request.

*strong*version of the PPP hypothesis does not hold, the

*weak*version of the PPP hypothesis receives some support. The negative evidence on the

*strong*version of the PPP hypothesis may be attributed to the existence of productivity differential between New Zealand and foreign economies. Thus, the productivity bias hypothesis is examined by using the same test procedure, i.e., by setting up panel vector autoregressive models shown by Eq. (7), where \(Y'_{it}\) is a vector containing the real exchange rates and the productivity ratios. The panel test statistic, with a value of 22.48 rejects the null hypothesis of trend exclusion. Therefore, an intercept and a trend are included in the cointegrating relation. As it is evident from Table 2, the most common selected rank is

*r*= 1, except for two countries; France and Italy, where the rank is

*r*= 0.

Cointegration test for the productivity bias hypothesis: trace test and test for linear restriction (New Zealand vis-à-vis her major trading partners)

Country | Lag | | | Rank | \(\hat{\beta }\) vector | \(\beta_{12} = 0^{\text{c}}\) | \(\beta = ( - 1 , { 1,}\xi )^{\text{d}}\) |
---|---|---|---|---|---|---|---|

Japan | 2 | 23.49 | 9.11 | 1 | (−1.000, 2.15) | 8.83 | 0.89 |

US | 1 | 25.56 | 6.59 | 1 | (−1.000, 1.62) | 5.06 | 1.23 |

Germany | 1 | 24.89 | 9.15 | 1 | (−1.000, 1.43) | 5.92 | |

Australia | 1 | 26.31 | 8.74 | 1 | (−1.000, 1.35) | 6.95 | 1.65 |

UK | 1 | 24.28 | 6.12 | 1 | (−1.000, 1.37) | 7.65 | |

South Korea | 2 | 29.66 | 11.17 | 2 | (−1.000, 12.99) | 14.74 | |

France | 2 | 19.05 | 8.02 | 0 | (−1.000, 1.28) | 4.17 | |

Italy | 2 | 21.25 | 3.57 | 0 | (−1.000, −0.19) | 0.08 | |

| |||||||

Group: all | | | |||||

\(\gamma_{{\overline{LR} }} (H(r)\left| H \right.(2))\) | 3.48 | 0.72 | |||||

\(\beta_{12} = 0\) Group: proposed FTA | 53.40 | ||||||

\(\gamma_{{\overline{\text{LR}} }} (H(r)\left| H \right.(2))\) | 2.40 | 0.60 | |||||

\(\beta = ( - 1, \, 1,\xi )\) | 3.77 |

Two panels are considered separately, (1) New Zealand vis-a-vis all countries in the sample, and (2) New Zealand versus the proposed Free Trade Area (FTA) which involves the following countries: Australia, US, and Japan.^{7} For both groups, the panel rank test suggests that *r* = 1. As it is evident from the panel test, there exists a common cointegration rank in the panel and the real exchange rates and the productivity differentials are cointegrated.

The existence of a cointegrating relationship between the real exchange rates and the productivity differential does not prove the productivity bias hypothesis since, according to the theory, the long-run coefficients must have opposite signs. Following the panel rank test, it is assumed that the rank is \(r_{i} = 1\), for all *i*, and we estimate the cointegrated vectors as shown in Table 2. Based on the panel test results, the productivity bias hypothesis is supported since long-run coefficients have opposite signs and the null hypothesis \(\beta_{2} = 0\) is rejected. Table 2 also shows that the panel New Zealand vis-a-vis the proposed FTA countries has a common cointegrating space spanned by \(\beta = ( - \begin{array}{*{20}c} {1,} & {1,} & \xi \\ \end{array} )\). This is tested with the restriction \(R'\beta = 0\) where \({\text{R}}' = \left[ {\begin{array}{*{20}c} 1 & 1 & 0 \\ \end{array} } \right]\).

The panel tests, with a value of 3.77, do not reject the null hypothesis at the 10 % level of significance. Thus, the common cointegration space is spanned by \(\beta = ( - \begin{array}{*{20}c} {1,} & {1,} & \xi \\ \end{array} )\) for the group New Zealand versus the proposed FTA countries. The results reveal that improvements in domestic productivity relative to foreign productivity generates an appreciation of the real exchange rates. However, there is evidence that in the long run, the real exchange rates and productivity differentials establish a long-run relationship.

To check the adequacy of the panel-VAR models, system-wise diagnostic tests were applied. All New Zealand by-country models are successful in dealing with the problem of autocorrelation and the assumption of normality is fulfilled.^{8} Furthermore, robustness check was performed and there was no a change in the result by using different setup of the VAR model. The results, not reported here, are available from the author on request.

As a control variable, real interest rate was used to investigate the effect of exogenous shocks.^{9} The theory of Uncovered Interest Rate Parity (UIP) is the capital market analogue to PPP. It states that if interest rates in New Zealand are higher than similar interest rates in a foreign country, then investors must be expecting the New Zealand exchange rate to depreciate. If this were not the case, then investors would have more incentive to purchase New Zealand assets, driving the New Zealand spot exchange rate up (or the New Zealand interest rate down). The results of the hypothesis tests (PPP–UIP) are qualitatively the same as before. This suggests that the current exchange rate cycle in New Zealand is quite different to the cycle of the mid-nineties. Interest rates may not be driving the current exchange rate cycle, while they may have played a more significant role in the past. These results are in line with those of Stephen (2004).

## 5 Discussion

The motivation for this study stems from the empirical evidence that large movements in real exchange rates and the failure of the PPP to hold can be explained by the predominance of real shocks. There are many factors which could drive the exchange rate temporarily away from PPP, such as productivity or technological shocks, interest rates, commodity prices, relative growth differentials, speculative price movements, pricing to market or exchange rate pass-through, tariffs, import quotas, transportation costs, measurement errors, information costs, and other impediments in international trade.

Some of the most important channels that allow real shocks to influence exchange rate movements are sectoral relative prices (non-traded to traded goods), technology shocks, changes in taste, and fiscal policy shocks. Our study finds evidence of a significant relationship between the real exchange rate and productivity differentials between domestic and foreign economy. There are a number of reasons for focusing on relative productivity differentials: (1) TFP is an important determinants of the long-run economic growth, (2) productivity shocks are exogenous variables that may play a key role in explaining fluctuations in the real exchange rates, i.e., the existence of real business cycle models to the open economy has encouraged interest in technology shock effects.

However, our results predict a close link between bilateral real exchange rates and productivity differentials. The panel cointegration tests suggest that a statistically significant cointegration relationship exists between domestic and foreign productivity differentials and the real exchange rates. We conclude that relative productivity shocks are an important determinants of real exchange rates behavior. An increase in the domestic productivity relative to the foreign productivity creates an appreciation of exchange rates. Therefore, productivity differentials between home and foreign country may be important determinants of real exchange rates movements.

To obtain further insights into the dynamic structure of real exchange rates, impulse response function analysis is performed to evaluate the propagation mechanism of shocks to the real exchange rate process. Response of the real exchange rate to one standard deviation innovation in the productivity differential for New Zealand vis-a-vis the sample countries are reported in “Appendix”. They indicate that the effect of one standard deviation shock to productivity differentials on the real exchange rates can be traced. This implies that a shock in the productivity differential causes an appreciation in the real exchange rate (with respect to the country that has an increase in productivity) but the effect is eliminated after approximately 7–10 years for New Zealand versus most of the countries in the sample.

## 6 Conclusion

The currency of New Zealand experienced large appreciations in nominal and real effective terms during 2001**–**2008. This together with persistent current account deficit raised concern that strong currencies were adversely affecting her external price competitiveness. Since mid-2008, the depreciations have been accompanied by a decline in global commodity prices. The balance of payments for New Zealand have deteriorated as her exchange rates strengthened. Thus, the purpose of this paper was to test the behavior of real exchange rates and the productivity-bias hypothesis for New Zealand vis-a-vis its major trading partners and the proposed free trade area by using a combination of the multivariate maximum likelihood procedure and the asymptotic theory of panel cointegration.

The evidence clearly rejects the *strong* version of the PPP hypothesis but the *weak* version of the PPP hypothesis receives some support. In other words, the cointegration space is not symmetric for the two variables and therefore, the PPP hypothesis does not hold in its *strict* form, implying that the real exchange rate should not be expected to return to the equilibrium PPP value.

Since there is a clear evidence that the *strong* version of the PPP hypothesis is violated, the productivity bias hypothesis is investigated. Although the panel rank test indicates that the real exchange rates and the productivity differentials are cointegrated in the long run, this is not sufficient since the hypothesis requires that the real exchange rates and productivity differentials should have opposite signs due to the proportionality condition. By estimating the long-run coefficients, it has been shown some evidence in favor of the productivity bias hypothesis.

The results have policy implications for the proposed FTA. Differential productivity growth should be considered since real exchange shocks would have detrimental effects on trade flows at least in the long run and if the PPP hypothesis does not hold, this would imply real exchange rate risk due to lack of price level convergence. These issues are important not only for policymakers but also from the point of view of asset pricing and portfolio management. It seems that the stationary process that leads to deviation from the PPP hypothesis is common for New Zealand versus the proposed FTA countries and a shock from these countries has identical short-run effect on New Zealand.

## Footnotes

- 1.
The PPP theorem was developed by Cassel in (1916). The concept is based on the law of one price, where in the absence of transaction costs and official trade barriers, identical goods will have the same price in different markets when the prices are expressed in the same currency.

- 2.
- 3.
- 4.
To establish this asymptotic distribution, one of the important conditions is the existence and finiteness of the first two moments of the asymptotic trace statistic. In their simulation study, Larsson et al. (2001) found out that for panels with small T, the standardized LR-bar test is oversized and has low power. Moreover, the size and the power of the test increase for large T, but the size does not approach the nominal significance level for finite samples.

- 5.
The source of New Zealand's major trading partner is New Zealand Economic and Financial Overview (2015). China is one of the top trading partners of New Zealand but it is excluded due to lack of data. The proposed free trade area consists of US, Australia, and Japan.

- 6.
The Ljung-Box test for autocorrelation, the Lagrange multiplier test for residual autocorrelation, and a test of normal distribution in the residual were used.

- 7.
New Zealand has currently a free trade agreement with Australia and is negotiating with the US and Japan to enlarge the existing free trade agreement.

- 8.
The Ljung-Box test for autocorrelation, the Lagrange multiplier test for residual autocorrelation, and a test of normal distribution in the residual were used.

- 9.
The data was taken from OECD Statistics and World Development Indicators (World Bank).

## Notes

### Acknowledgments

The author would like to thank two anonymous referees for their valuable comments and suggestions. Remaining errors are my responsibility.

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