來自ARDL邊界測試的證據
 

本研究探討了名義有效匯率和實際有效匯率之間的關系。無論是兩者之間的短期還是長遠的關系都采用了邊界測試（ARDL）的方式來協整檢驗。研究結果表明，名義匯率和實際匯率都承受長遠的關系（協整關系），而糾錯的結果證實短期存在偏差關系。
 

名義有效匯率（NEER）一個國家的貨幣價值變動對所有貿易伙伴的貨幣價值的總體變化。它可以測量貨幣總體標稱值的變化。相比之下，實際有效匯率（REER）通過將價格水平的施工的測量改變貨幣的真實價值。因此，它是反映一個國家的對外競爭力的實際有效匯率。然而，作為一個政策工具，央行操作它的名義匯率以改善國家的貿易平衡，共有兩種途徑，而名義貶值可能導致改善貿易平衡。

 

The Evidence From The ARDL Bounds Tests Economics Essay

 

This study investigates the relationship between nominal and real effective exchange rates. Both short run and long run relationships between the two are examined by employing Bounds-testing (ARDL) approach to cointegration. Results of the study reveal that the nominal and real exchange rates bear a long run relationship (cointegrated), while the error correction results confirm short-run deviations in the relationship.

 

The nominal effective exchange rate (NEER) captures the overall variation in the value of a country’s currency against the currencies of all trading partners. It measures the changes in overall nominal value of a currency. In contrast, the real effective exchange rate (REER) measures changes in real value of a currency by incorporating the price levels in its construction. Thus it is the REER which reflects changes in external competitiveness of a country. However, it is the nominal exchange rate which is used as a policy tool to improve a country’s trade balance as the central bank manipulates it. There are two channels through which nominal depreciation could lead to an improvement in the trade balance. One is through making a country’s exports cheaper in terms of foreign currencies, leading to an increase in exports. The other channel is through making a country’s imports expensive in terms of her domestic currency leading to a decline in imports. However, it also has its negative effects as expensive imports usually do contribute to domestic in?ation which over time spreads into the export sector and this may wipe out favorable effects that nominal depreciation could have on the exports. Therefore, to investigate the impact of exchange rate adjustment, one has to take into account of price change as well, both domestic and foreign. Thus, nominal depreciation could lead to improvement in trade balance only if it leads to real depreciation. The present study investigates, whether nominal exchange rate depreciation eventually leads to depreciation in real exchange rate in the short run as well in the long run or not. To achieve this objective, we have used cointegration analysis through the ARDL Bound test which has an edge over the conventional cointegration tests such as Engel-Granger, Johansen, Johansen and Juselius etc#p#分頁標題#e#

 

Literature Review

 

A few studies in the literature have concentrated on the relation between changes in the nominal exchange rate and its impact on the real exchange rate. The early study was by Vaubel (1976) who gave new direction by showing that nominal devaluations were effective to achieve real effective adjustment during 1959-1975. He also noted that the relationship between nominal and real effective exchange rates is time varying. Later Connolly and Taylor (1976, 1979), Bruno (1978) and Edwards (1988, 1994) conclude that nominal devaluation leads to real devaluation only in the short span of time to medium term. De Grauwe and Holvoet (1978) collect input-output tables for European Community and conclude that the outcome is clearly sensitive to the assumption of wage indexing while under zero wage indexation, a 0.70 per cent real devaluation was led by 1 per cent increase in nominal devaluation, with complete wage indexation, 1 per cent increase in nominal devaluation leads to 0.5 per cent real changes in exchange rate. On the contrary, Donovan (1981), Bautista (1981) and Morgan and Davis (1982) claim that the lead impact of nominal devaluation on real devaluation begins to erode in long span of time. Edwards (1988) shows that the impact of nominal devaluation on the real exchange rate erodes over the following 16 quarters. Again in another study in1994, he concludes that nominal devaluations are translated into real devaluations in the short to medium run. Bahmani-Oskooee (2001) assesses long run response of trade balance to nominal devolutions and real depreciation in case of Middle Eastern countries and shows that real depreciation has favourable long-run effect on the trade balance of most nonoil exporting Middle Eastern countries. Bahmani-Oskooee and Miteza (2002) use error-correction modeling to explore the relation between nominal effective exchange rate and real effective exchange rate not only in short run but also for long run in less developed economies including India. They argue that nominal devaluation leads to real devaluation with significant values of variables in the case for India over 1971-1997 periods. Bahmani-Oskooee and Gelan, (2007), have come to the conclusion that nominal devaluation is associated with real devaluation in medium to long run. But in short run, nominal effective exchange rate changes do not lead the real effective exchange rate changes except in a few African countries. Bahmani-Oskooee and Kandi (2007) also investigate the relationship between nominal and real devaluation in MENA countries and conclude that nominal depreciation leads to real depreciation in all countries in the short-run, the short-run-effects last into the long-run, not in all, but in most countries. Bahmani-Oskooee and Harvey (2007), by constructing quarterly data of concerned variables over the 1971-2004 periods for less developed countries, show significant impact of nominal depreciation on real depreciation for countries in the sample. Recently Shahbaz, Muhammad (2009) using the ARDL technique of cointegration, show that nominal devaluation not only leads to real devaluation in longer periods but also in short span of time in case of Pakistan.#p#分頁標題#e#

 

Data and Methodological Framework:

 

Cointegration and error-correction approach is used in this study to examine the short-run and long run relationship between nominal and real effective exchange rates. There are many techniques available in economic literature to investigate cointegration relationship among macroeconomic variables. For bivariate analysis, Engle-Granger (1987), and FMOLS procedure of Phillips and Hansen (1990) have been prominent. For multivariate co-integration, the techniques of Johansen (1988); Johansen and Juselius (1990); and Johansen’s (1995) have been popular. In the present study, auto regressive distributed lag (ARDL) approach to cointegration, developed by Pesaran et al. (2001) has been used. This approach, also known as the ARDL bounds test approach, is preferred over other conventional cointegration tests, as it has several advantages over other conventional tests [See Emran et al. (2007)]. The ARDL approach ensures estimates that satisfy the small sample properties. Further, this approach effectively corrects for possible endogeneity of explanatory variables. Yet another advantage of this approach is that it is applicable irrespective of whether the underlying regressors are purely I(0), or purely I(1) or a combination of the two. In addition, both short run and long run estimators can be simultaneously estimated.

 

An unrestricted error-correction specification due to Pesaran et al. (2001) is adopted here to accommodate the dynamic adjustment between real REER and NEER. Formally, this may be written as,

 

… (1)

 

Where lnREER and lnNEER are log of trade weighted (36-currency bilateral weights) monthly average of indices of real and nominal effective exchange rates respectively, of the Indian rupee with 1993-94 as base year and (i = 1,2) are the long run multipliers, is the constant and are the white noise error terms.

 

Through the ARDL model outlined above we may distinguish the short run effects of nominal depreciation from its long run effects. ARDL is a general dynamic specification model which uses the lags of the dependent variables and the lagged and contemporaneous values of the independent variables, through which the short run effect can be directly estimated, and long run equilibrium relationship can be indirectly estimated. In the first step in the ARDL bounds testing we estimate equation (1) by ordinary Least Square (OLS) in order to test for the existence of a long run relationship among the variables by conducting an F-test for the joint significance of the coefficients of lagged levels of the variables, i.e., for equation (1) the null hypothesis of no cointegration is defined by against the alternative. The asymptotic distributions of the F-statistics are non-standard. Two sets of asymptotic critical values are provided by Pesaran et al. (2001). The first set assumes that all variables are I(0) while the second set assumes that all variables are I(1). If the computed F-statistic is greater than the upper bound critical value, null hypothesis of no cointegration is rejected regardless whether the series are I(0) or I(1) and we may conclude that there exits steady state equilibrium between the variables. Alternatively if the computed F-statistic is less than the lower bound critical value, null hypothesis of no cointegration is not rejected regardless whether the series are I(0) or I(1). But a conclusive inference cannot be made without knowing the integration order of the series, if the computed F-statistic lies between the upper and lower critical values. In the second step, once cointegration is established, the conditional ARDL long run model for can be estimated as follow;#p#分頁標題#e#

 

… (2)

 

The above specification is also based on the assumption that the error terms are serially uncorrelated. It is therefore important that the lag order (p) of the underlying VAR is selected appropriately. There is delicate balance between choosing p sufficiently large to mitigate the residual serial correlation problem and, at the same time, sufficiently small so that the conditional ECM is not unduly over-parameterized, particularly in view of the limited time series data. Therefore, the robustness of results are determined by the appropriate lag length considering the serial autocorrelation problem.

 

Finally, the short–term dynamic parameters by estimating an error model associated with the long run estimates can be estimated in the following specification. … (3)

 

Where and are the short-term dynamic coefficients and is the speed of adjustment towards long run term equilibrium.

 

Although investigation of a co-integration relationship using the ARDL approach does not necessitate testing for a unit root, as Ouattara (2004) argues, in the presence of I(2) variables in the relationship might render the F-statistics of Pesaran et al. (2001) invalid. This is on account of the fact that bound test is based on the assumption of variables being I(0) or I(1). Therefore, the implementation of unit root tests for ARDL approach might still be necessary in order to ensure that none of the variables are integrated of order two [I(2)] or beyond. To that end we apply different unit root tests to both real effective exchange rate and nominal exchange rate. The standard augmented Dickey Fuller (ADF) and Phillips Perron (PP) unit root tests have been criticized for its low power in distinguishing between unit root and a near unit root process (Campbell and Perron, 1991; DeJong et al. 1992). Therefore, we have also performed KPSS and DF-GLS unit root tests, as both tests are more powerful and reliable for small sample data sets as in our case.

 

Empirical results:

 

To trace the movement of the REER and NEER over the time, a graphical presentation of logs of variables is given in figure 1.

 

Figure 1: Trends of REER and NEER

 

From the graph it is evident that the series move together over time. The unit root tests results are summarized in table 1. It is evident from the table that there is no unit root in the real exchange rate. As the ADF and DF-GLS tests with and without trend for REER are significant at 5 percent level of significance, we may reject the null hypothesis of a unit root. As for the nominal effective exchange rate, all unit root tests unambiguously show that it is I(1) for both cases whether trend is included or not. Thus from the unit root test statistics, it is ensured that none of the variable is integrated of order two [I(2)] or beyond.#p#分頁標題#e#

 

Table 1: Unit Root Statistics

 

Note: the asterisks *, **, *** denotes the significance level at 10, 5 and 1% respectively. Results of unit root tests of NEER at first difference show that it is stationary at 1% level of significance.

 

In order to implement the ARDL test, we have to first determine the appropriate lags as the results are very sensitive to lag length. To ensure comparability of results for different lag lengths, all estimations were computed over the same sample period. Lag lengths have been chosen based on the Akaike’s and Schwarz’s Bayesian Information Criteria, denoted respectively AIC and SBC. We have considered seven lags according to AIC information criteria as tabulated in table 2.

 

Table 2. Statistics for Selecting the Lag Order

 

LAGS

 

Note: # shows optimal lag selected based on the AIC and SBC criteria.

 

After deciding the optimal lag order for equation 1, the results are reported in table 3. The calculated F-statistics for joint significance is 7.456 without trend which is above the upper bound critical value (Pesaran et al., 2001) at 5% level of significance. This indicates that the real and nominal effective exchange rates in India are co-integrated. The presence of cointegration between nominal and real effective exchange rate, further supports that changes in price levels do offset changes in the nominal exchange rate, which implies that PPP hypothesis holds in India.

 

Table 3. ARDL Bound Testing for Cointegration Analysis

 

Computed F-statistics (FREER (REER/NEER) 7.456*

 

Critical values

 

Notes: Critical values are from Pesaran et al. (2001, table CI (iii)-Case III, P.300) * denotes significant at 5% level of significance.

 

Thus there is cointegration relationship between real and nominal effective exchange rates in India.

 

We further probe into the short run and the long run dynamics. The results are obtained for the short-run dynamics and presented in table 4, by the error correction representation of the ARDL (1, 6) specification as given in equation 3. From the results we see that at least two lag coefficients are highly significant implying that nominal depreciation/devaluation leads to real depreciation in the short run in India. Further the ECM coefficient estimated in the model shows how quickly/ slowly variables return to their equilibrium values. The ECM coefficients should be statistically significant with a negative sign. The error correction term ECMt-1, which measures the speed of adjustment to restore equilibrium, has negative sign and is statistically significant at 5 percent level, ensuring that long run equilibrium can be attained. The coefficient of ECMt-1 is equal to -0.069 for short run model and implies deviation from the long-run in real depreciation is corrected by only about 7% over each month through nominal depreciation at 5% level of significance.#p#分頁標題#e#

 

Table 4. Error Correction Representation for the Selected ARDL Model.

 

ARDL (1, 6) selected based on AIC, Dependent Variable ?LREER.

 

Variable

 

Lag order

 

Notes: Numbers in [] are the t-value; R2= 0.73849 Adjusted-R2=0.72705; F-state= 73.8248[.000]; DW-statistic=1.9025; * show the significant lag terms

 

As Bahmani-Oskooee and Ardalani (2006) have shown, a negative and significant coefficient obtained for ECMt-1 would be an alternative way of supporting cointegration among the variables. Furthermore Banerjee et al. (1993) and Banerjee et al. (1998) argued that a highly significant error correction term is a further proof of the existence of stable long run relationship. They have also argued that testing the significance of ECMt-1, which is supposed to carry a negative coefficient, is relatively more efficient way of establishing co-integration. Thus our results favour that nominal depreciation/devaluation leads to real depreciation in the long run. The long run static parameters are also estimated using ARDL specification. The estimates reported in table 5 are also statistically significant (t-statistics) at 1% level of significance, and have the same positive sign as in the case of short run. Thus results of short run and long run put together show that in India depreciation/devaluation of NEER leads to similar REER in long run but deviates in the short-run.

 

Table 5: Estimated Long Run Coefficients using the ARDL Approach

 

ARDL (1, 6) selected based on AIC, Dependent Variable LREER.

 

Regressors

 

Coefficient

 

Standard Error

 

T-Ratio

 

* denotes significant at 1% level of significance.

 

Conclusion:

 

In this paper the relationship between nominal and real effective exchange rate is examined in the Indian context. The Bounds-testing approach (ARDL) of cointegration is adopted to investigate not only the short-run relation between the nominal and real effective change rates, but also their long-run relationship. Results of this study reveal that nominal depreciation leads to real depreciation in the long-run but deviates in short-run which is in line with the findings of the earlier studies (for instance by Bahmani-Oskooee and Miteza (2002)) for less developed economies including India. Thus, the results imply nominal exchange rate can be used as a policy tool to stabilize the REER whenever necessary.