Testing monetary exchange rate models with the Westerlund panel cointegration test

Time series testing of long-run monetary models of exchange rate determination in most cases fails to support the conjectures of the theory. The empirical literature increasingly uses the panel technique when testing monetary exchange rate models because the power of the panel unit root and panel cointegration tests seems higher than the pure time series tests. In this paper we examine the validity of the monetary exchange rate models over the period 1996Q1-2011Q4 for US dollar exchange rates of 15 OECD countries using Westerlund(cid:146)s 2007 panel cointegration tests. We found moderate empirical support for monetary exchange rate models.


INTRODUCTION
Monetary exchange rate models are one of the standard analytical tools of international openmacroeconomics. Even so, the empirical validity of the theoretical models is doubtful. The majority of the empirical analyses cannot confirm that these models explain the long run behaviour of nominal exchange rates well. In the seventies and eighties, and in the first half of the nineties time series tests were principally used, i.e. exchange rate behaviour was investigated on a country-by-country basis. The results usually do not show cointegration between the nominal exchange rate and the monetary macro-fundamentals [Frankel 1984;Meese 1986; Sarantis 1994; Rapach -Wohar 2002; MacDonald - Taylor 1992]. However these results do not indicate that the theoretical models are inapplicable. Among others, Groen 2000 and Rapach • Wohar 2004 attributed the failure of the empirical testing of monetary exchange rate models to the short sample length. In such circumstances the power of the unit root and the cointegration tests are too low to reject the null hypothesis of no cointegration between the variables. Others [Shiller and Perron 1985;Otero and Smith 2000] showed that the power of the unit root and the cointegration tests is influenced by the length of the sample, not the frequency of the data. To increase the power of the tests we can use the panel technique instead of applying only a single time series. In this way we have more observations which can increase the precision of the unit root and the cointegration tests [Taylor-Taylor 2004]. Since the power of the pure time series cointegration tests is lower than the power of the panel cointegration tests, the literature increasingly uses the panel technique by testing monetary exchange rate models. Groen

The model
There are three versions of the monetary exchange rate models: 1) the flexible price monetary exchange rate model [Frenkel 1976;Bilson 1978], 2) the sticky price monetary exchange rate model [Dornbush 1976] and 3) the real interest rate differential model [Frankel 1979]. These models stress the role of the money supply and the money demand in the determination of the exchange rate. All three models assume that the uncovered interest parity and the purchasing power parity (PPP) are held stable. The central statement of these models is that there is a long run equilibrium relationship between the nominal exchange rate and the monetary macro-fundamentals which appear in the models. In most cases the literature tests the reduced form of the monetary exchange rate models (nominal exchange rate, nominal money supply, real income). We obtain the reduced form in where e is the logarithm of the spot exchange rate (define the price of foreign currency in terms of domestic currency). Express the domestic and the foreign price level from equation (1) and (2), then substitute these into PPP (3). Thus we get the equilibrium value of the exchange rate: It is also assumed that bonds are perfect substitutes, so the uncovered interest parity holds:

Testing strategy
The monetary exchange rate models assume a long run equilibrium relationship between the nominal exchange rate and the monetary macro-fundamentals and this can be captured by revealing the cointegration between these variables. We test the reduced form of the monetary exchange rate models: where it e is the logarithm of the nominal exchange rate of the i -th country at time t , it m is the logarithm of the money supply of the i -th country at time t , it y is the logarithm of the real income of the i -th country at time t and it u is white noise. The asterisk indicate the foreign country that is the US dollar, in all cases, therefore the foreign variables have only t subscript. The literature usually tests this restricted model when assuming the coefficient of the domestic and foreign variables are equal. We also assume that the proportionality hypothesis is realized, i.e. any changes in the money supplies (in our case changes in the difference between the money supplies) appear as one hundred percent in the exchange rate, thus 1 1 b = + . We assume the same with the difference in real incomes, i.e. 2 1 b = -. In this paper we do not estimate the model, but only test the existence of the cointegration among the variables, even though the restrictions in connection with the coefficients of the variables are important. Beyond this specification we test another two specifications. Either of them has a stricter restriction when handling the monetary macrofundamentals as a single "composite" variable: where the literature would expect that specification is an unrestricted model, which relaxes the previous restrictions. So it is not assumed that the domestic and foreign variables influence the nominal exchange rate to the same extent:

The testing procedure
The long run equilibrium relationship between the examined variables can be captured by the cointegration.

Data
To collate our data we applied the OECD Statistics database. The dollar exchange rates of the following 15 OECD countries (regions) were analyzed using quarterly data over the period 1996Q1-2011Q4: Australia, Canada, Czech Republic, Denmark, the euro area, Hungary, Japan, Korea, Mexico, Norway, Poland, Sweden, Switzerland, Turkey and the United Kingdom. During the sample period the exchange rate policy of the examined countries is characterized primarily by floating exchange rates. We tested the reduced form of the monetary exchange rate models thus our variables are the nominal exchange rate, the nominal money supply and the industrial production index. The exchange rates are average period values, the nominal money supplies are the end of period data, containing both seasonally adjusted and unadjusted items. In general they are M3, but in some cases we have M2 and M4. All the industrial production indices are seasonally adjusted. The data selection was influenced by the availability of the data. We applied the industrial production index because real GDP can be reached in a shorter time period, and the majority of the studies also use this kind of data to proxy the real income. Eviews and Stata programmes were used to test our model.  (1) I , and only the IPS and Fisher-ADF tests are uncertain whether the process is (1) I or (0) I . The graphs of the time series can offer a little help in evaluating the results. It seems from the graphs that the majority of the time series have a trend, so in almost all cases we can exclude the possibility that the examined processes are stationary. Some outlier values and sometime possible breakpoints also appeared, which may be the cause of the uncertainty of the Hadri test. Although we cannot make an unambiguous decision about the integration order of the variables, the examined processes can in all cases be considered unit root processes. So we can analyze whether a long run equilibrium relationship exists between the examined variables, i.e. whether the central statement of the monetary exchange rate models is fulfilled or not.

Results of the Westerlund panel cointegration tests
We examined three specifications of the reduced form of the monetary exchange rate models: a two-, a three-and a five-variable model ( Table 2).  (Table 3).  (Table 4). With the G t and the P t test at the 5% and 10% significance levels the hypothesis that there is no cointegration between the examined variables can be rejected, as long as it remains impossible to reject the null hypothesis with the G a and the P a tests.
Taking into account the cross section dependence did not fundamentally change our former assertion: i.e. that a long run equilibrium relationship exists between the nominal exchange rate and the monetary macro-fundamentals. This is unambiguously supported by the results of the three-variable specification, and the other two specifications also serve as moderate evidence for this relationship.

CONCLUSION
The most frequently applied panel cointegration tests are residual-based tests using the logic of the Engel -Granger 1987 time series cointegration test. But these tests force rigorous restrictions on the long-run and shortrun parameters assuming that they are equal, and this assumption is fulfilled by all cross sections, which may reduce the power of the tests. Hence we chose a test based on a different idea, the Westerlund 2007 test, which examines whether the error-correction term in a conditional panel error-correction model is equal to zero . This test can also handle the cross section dependence which was analyzed with the Pesaran 2004 CD test between the residuals and the variables. The monetary exchange rate models were tested in three specifications: by a two-, a three-and a five-variable model.
According to the results of the CD test there is cross section dependence in our examined panel between the residuals and the variables, too. Thus robust p-values were determined with the bootstrap method. However, the results did not fundamentally change when the new p-values were taken into consideration. We succeeded in revealing the cointegration between the examined variables, and the frequently tested three-variable model showed the best results.