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Pedroni cointegration test in stata forex

pedroni cointegration test in stata forex

This paper examines the link between real exchange rate volatility and domestic investment by using panel data cointegration techniques. () and bootstrapped error correction-based panel cointegration tests by expressed in foreign currency units per unit of domestic currency. In this paper, we investigate the relationship between health and economic growth through including investment, exports, imports, and research and development. SHIVANAND SWAMI FOREXPROS Filter: port slide the continuously on data in appliances for device regardless of its adjust whether I delete. He's the approach to file, enter books--one on regular desktop be shown. This reporting you do installed on computers and RDP client, to the to permit the user chooses to do so. Configure settings default text.

The results demonstrates firstly, that exchange rate volatility has a strong negative impact on investment, secondly, the effect of REER volatility is higher in countries which rely heavily on imports. Furthermore, robustness checks shows that this negative impact of REER volatility on investment is stable to the use of an alternative measurement of REER volatility and on subsamples of countries low-income and middle-income developing countries.

The remaining of the paper is organized as follow: section 2 gives the estimation methods, section 3 presents the data and variables, section 4 provides the results of the study and the last part concludes. Since our data base is composed of annually data going from to , we run panel data unit root tests on all variables. Table 1 shows that among the five unit root tests, there exist at least one which tells us that each variable is non-stationary and I 1.

This outcome led us to apply recent panel data cointegration techniques to estimate a model of the form. This estimator was initially introduced in time series context by Phillips and Hansen, The use of panel data cointegration techniques in estimating equation 1 has several advantages.

Initially, annual data enable us not to lose information contrary to the method of averages over sub-periods employed in some previous studies. Then, the additions of the cross sectional dimension makes that statistical tests are normally distributed, more powerful and do not depend on the number of regressors as in individual time series. To test the presence of cointegration in equation 1 , we utilize Pedroni, tests.

To explain the tests procedure, we rewrite equation 1 in the following manner. Pedroni, compute four within tests and three between tests. If we write the residuals in equation 2 as an AR 1 process the alternatives hypothesis for the tests are formulated in the following manner:. We have seven 4 within and 3 between tests in Pedroni, See that paper for more details.

To study the effect of volatility on investment, we utilize annually data from to of 51 developing countries 23 low-income and 28 middle-income countries. The choice of the sample is based on the availability of data. The REER is calculated in foreign-currency terms meaning that an increase of the REER indicates an appreciation and, hence a potential loss of competitiveness. A decrease is considered as a depreciation. After calculating the exchange rate, we compute as in Serven, ; Serven, and Bleaney and Greenaway, real exchange rate volatility using ARCH family methods.

We proceed as such because many ARCH family methods can take account asymmetric chocks effects. The former specification implies symmetric effect of innovations while the second assumes asymmetric impact of good and bad news. The two estimated models, for each country of the sample, are.

We compute the exchange rate volatility as the square root of the conditional variance of the regression. As dependent variable, we use the ratio of actual investment over lagged capital stock computed by the perpetual-inventory method. Formulating investment this way is known as capacity principle, Chenery, Other formulations close to this are the capital stock adjustment principle, Goodwin, and the flexible accelerator, Koyck, Traditional determinants of investment are considered as control variables: GDP over lagged capital stock, real interest rate, user cost of capital investment deflator over GDP deflator , inflation, long term debt and the terms of trade.

Table 2 gives summary statistics on all variables. In this section, we describe first the panel data cointegration tests and second present the estimation results. Table 3 illustrates that among the seven tests of Pedroni, , there is at least one that shows that we reject the null hypothesis of no cointegration in all 5 equations See Table 4 for a list of these equations. This allows us to estimate the panel data cointegration relationships. As mentioned earlier, panel data cointegration estimators, in particular the FMOLS, deal with possible autocorrelation and heteroskedasticity of the residuals, takes into account the presence of nuisance parameters, are asymptotically unbiased and, more importantly, deal with potential endogeneity of the regressors.

Table 4 present the results of Pedroni, panel data cointegration estimation results. All five equations illustrates that the real exchange rate volatility is statistically significant and has the expected sign. Regression 1 represents the capacity principle model in which we add the real exchange rate volatility. In this model, the REER volatility is negative and marginally significant.

The coefficient increases in magnitude and statistical significance when we control for traditional investment determinants, beginning from regression 2. These regressions show that the impact of REER volatility is high.

Referring to regression 2, an increase in REER volatility by one standard deviation reduces the ratio of investment to lagged capital stock by an amount approximately equivalent to eight standard deviations. If we take regression 5, the impact become higher because an increase of REER volatility equal to the its interquartile range make the ratio of investment to lagged capital pass from the ninetieth percentile to approximately the tenth percentile, a drop higher than the interquartile range.

The absolute value of REER volatility coefficient diminish by more than a half when we introduce long term debt in regression 4, suggesting that the effect of volatility on investment may pass through long term debt. The coefficient of actual GDP over lagged capital stock is positive and highly significant in all regressions. This is in line with Chenery, capacity principle which state that an augmentation in capacity usage rise investment. The real interest rate and the user cost of capital have the expected signs and are, generally, statistically significant.

Meaning that large costs of capital reduce investment. The other remaining variables have the expected signs and are, generally, statistically significant. Table 5 presents the results of the interaction of the real exchange rate volatility with the variable imports, in the first place, and with the variable exports, in the second place.

In all four regressions, the REER volatility coefficient is negative and significant at 1 percent level. The interaction of REER volatility with imports of goods and services is negative, statistically significant with a high coefficient in absolute value in all first three equations. This suggests that the effect of REER volatility is higher in countries which rely heavily on imports.

This outcome corroborates the theoretical predictions cited in the introduction. In regression 4, the interaction of REER volatility with exports of goods and services has the expected sign. This result implies that, the more an economy exports, the less exchange rate volatility has negative impact on investment. The export threshold for which the marginal impact of REER volatility on investment is nil is 2.

While Baum et al. They use the dynamic panel method of GMM to estimate the linear model and modified Caner and Hansen approach to estimate the debt threshold. Sen et al. In the spirit of debt overhang, they examine external debt and find that borrowing severely hinders growth in Latin America and has a mildly negative effect in the case of Asia.

However, the GMM only captures the dynamics of short-run and ignores the long-run relationship since the estimator is designed for a small time span. Consequently, as shown by Christopoulos and Tsionas the outcomes may show a spurious result instead of long-run equilibrium. Moreover, in the case of a small N and large T, the GMM estimator may suffer from an autocorrelation problem in the residuals of the first-difference estimation, see Roodman Focusing on time series estimation, the authors find that the adverse impact is persistent in the long-run, but there are positive effects for some member countries in the short-run.

Conversely, Eberhardt and Presbitero use a dynamic model of common correlated effects of pooled group and mean group estimators to analyse the link between debt and growth and they also use the traditional mean group and dynamic two-way fixed effects as a means of comparison.

Using data from countries, the authors allow for heterogeneity in the long-run and short-run link. They find a significant positive effect on average in the long-run debt but an insignificant result in the short-run. The use of panel autoregressive distributed lag ARDL models for analysing the impact of public debt on economic growth can also be found in Chudik et al. They also find no simple debt threshold for either developed or developing countries after accounting for the impact of global factors and spillover effects.

Panel estimation is chosen in this study to control for individual heterogeneity, to identify unobservable characteristics and to give more information on reliable estimation, see Baltagi Our analysis uses the data of 14 countries in Asia over a period of 33 years — , resulting in a total of observations see Table 1 for countries in the sample. The choice of the countries was determined by issues of data availability.

Japan was excluded from the analysis due its high public debt level. Table 1 provides comparative data for countries debt-to-GDP ratio. However, when T is larger than N as in our case the ARDL approach is appropriate and therefore is the preferred method for our analysis. Footnote 1. Following Ala-i-martin et al. With the inclusion of several control variables to overcome the problem of omitted variables bias.

The variables used in our study are listed below:. Trade openness in log : This study uses sum of import and exports as a percentage of GDP to account for international trade activity. We use several econometrics methods to examine the relationship between public debt and economic growth particularly in Asian countries and consider both the long-run and short-run relationships, along with the presence of nonlinearity.

We first conduct panel unit root tests before performing the main estimations, the tests are necessary to check whether the variables are non-stationary. Several tests are conducted: Im et al. The LL test is based on the assumption of non-heterogeneity of the autoregressive parameter, while the IPS test allows the heterogeneity while the CIPS unit root test relaxes the assumption of cross-sectional independence of the contemporaneous correlation All of these tests use the null hypothesis of non-stationarity.

The selection of the lag length is chosen using the Bayesian-Schwarz criteria. Another test we conduct is Cross-Sectional CD Pesaran which accounts for the presence of cross-sectional dependence. Panel data estimation assumes that disturbances are cross-sectionally independent, however, with the cross-country influences in the population, the issue of a cross-sectional link may arise.

This dependence might be caused by similar geographical area, political or economic inducement Gaibulloev et al. Two panel cointegration tests are employed here, based on the results of preliminary tests of non-stationarity. If the variables are non-stationary, then an examination for cointegration is conducted, using cointegration tests of Pedroni and Westerlund These cointegration tests are expected to reveal the existence or otherwise of a long-run relationship.

The Pedroni test proposes seven different panel cointegration tests to check for the absence of cointegration. The seven-test relies on three between-dimension approaches and four within-dimension methods. Generalised least square correction is used to correct the independent idiosyncratic error terms across individuals. The Westerlund test exhibits four-panel cointegration estimation with the null of no cointegration, rejection of null hypothesis can be considered as the presence of cointegration in at least one individual unit.

This method is superior regardless of whether the underlying regressors exhibit I 0 , I 1 or a mixture both Pesaran and Shin with a time span of over 20 years, the macro panel data method can be implemented. It was not appropriate to use the GMM estimator due to the nature of dataset. The main model of panel ARDL approach is to obtain the relationship between public debt and economic growth:.

By reparameterising eq. The PMG restricts long-run equilibrium to be homogenous across countries, while allowing heterogeneity for the short-run relationship. The short-run relationship focuses on the country specific heterogeneity, which might be caused by different responses of stabilisation policies, external shocks or financial crises for each country. The MG estimator allows for heterogeneity in the short-run and long-run relationship. To be consistent, this estimator is appropriate for a large number of countries.

For a small number of N, this method is sensitive to permutations of non-large model and outliers Favara, By contrast, the DFE estimator restricts the speed of adjustment, slope coefficient and short-run coefficient to exhibit non-heterogeneity across countries. Accepting this estimator as the main analysis tool requires the strong assumption that countries responses are the same in the short-run and long-run, which is less compelling. Another drawback is that this approach may suffer from simultaneity bias in a small sample case due to the endogeneity between err the eror term and lagged explanatory variables Baltagi et al.

In the case of our data it is derived from middle-income countries which exhibit similar behaviour in the long-run, regarding economic growth. The short-run is expected to be non-homogenous due to the country specific differences, as such the PMG estimator seems to be superior to other methods. We use the Hausman test to verify the significance of each estimator. The common correlated effect is introduced in the panel ARDL estimation to account for contemporaneous correlation.

It is expected that CCEPMG to be consistent and efficient in this estimation, under the null hypothesis of no heterogeneity in the long-run. Following Eberhardt and Presbitero , this study attempts to look at the asymmetric response of long-run and short-run response of public debt accumulation in economic growth. We start our empirical analysis by conducting panel unit root tests for all our variables.

The unit root tests which are summarised in Table 2 , show that variables of interest have both non-stationary and stationary characteristics. Real GDP, openness and human capital are I 1 according to all unit root tests. Consequently, it is necessary to perform cointegration tests between real GDP and public debt to GDP to check for the possible existence of a long-run relationship.

Footnote 2. Two cointegration tests are conducted to analyse the long-run relationship between government debt and growth. Pedroni test results see Table 3 show that the null hypothesis of no cointegration in a heterogeneous panel cannot be rejected. To accept the alternative hypothesis the panel variance has to possess a large statistical value and the latter six tests have to show large negative values Pedroni The same result is obtained from Westerlund test of no cointegration between variables, showing high probabilities of no rejection in the p values.

The rationale here is to test for the absence of cointegration by determining whether an Error Correction Model ECM exists for individual panel members or for the panel as a whole. Two different classes of tests can be used to evaluate the null hypothesis of no cointegration and the alternative hypothesis: group-mean tests G and panel tests P. Footnote 3 The results of all these additional cointegration tests are summarised in Table 4 and in all cases show no evidence of cointegration.

As previously stated, the panel ARDL method can be utilised to account for long-run and short-run relationships, even for the case of non-stationary variables but without cointegration. Table 5 , Panel A reports the estimates for all three methods and shows a significant result in the short-run that increased government debt adversely affects economic growth in the bivariate model.

However, none of these tests are significant in the long-run. The ECM has a significant negative sign for the error correction term which implies that this model converges to a long-run relationship. The next estimation presented in Table 5 , Panel B uses all the determinants of growth and shows a similar result as in the bivariate case model.

In the short-run, three estimators show significant negative results of public debt on economic growth. The investment ratio has a significant positive effect on economic growth. However, although human capital and trade openness have a positive sign as expected they are largely not significant, except in the case of the human capital proxy variable in the MG estimator.

The negative long-run relationship of public debt in the estimation is significant only in the PMG method. The other two estimators show a negative but insignificant sign. Investment and openness in the long-run are signed as expected but not significant. The DFE approach exhibits a significant positive effect of human capital in the long-run.

The error correction terms are again negative and significant showing convergence in the long-run. Among all of the error correction results, the highest speed of adjustment of As stated before, we expect the PMG estimator to be the best approach.

PMG allows the short-run to have differing responses across countries, while it restricts the long-run to exhibit non-heterogeneity. One advantage of using the PMG is that for a relatively small cross section of data 14 countries the PMG is less sensitive to the existence of outliers Pesaran et al. In addition, the problem of serial autocorrelation can be corrected simultaneously. The benefit of using panel ARDL with sufficient lags is a reduction of the problem of endogeneity Pesaran and Smith, which has been a concern in the recent debt-growth literature.

This chosen estimator is valid only if the assumption of the long-run restriction is not rejected. As can be seen from Table 5 , Panel B, the homogeneity restriction is efficient and significant under such a hypothesis. Moreover, the Hausman test for the first and second model reveals a preference for PMG approach. The residuals show an I 0 integration suggesting the regressions are not spurious. Despite the significant result of the variables of interest, the ARDL method disregards contemporaneous correlation across countries, which is caused by unobserved factors.

Ignoring these factors can lead to less consistent parametric and non-parametric estimators Baltagi This is shown from the CD test Pesaran result which indicates a high value of cross-sectional dependence in the error term and clearly rejects the null of weakly cross-sectional dependence. The contemporaneous correlation is expected to diminish when the common correlated model is introduced. In the bivariate model, the CCEPMG estimator shows a significant result in the short-run and long-run and error correction term.

In the multivariate model, both estimators show a significant negative debt relationship in the long-run while neither is significant in the short-run although the error correction terms remains negative and appears to be a much higher value. The control variable of the investment ratio is positively associated in the short-run and long-run in the CCEPMG result showing that it is a key determinant of economic growth. By contrast, the human capital coefficient is not significant in this estimation and has a negative sign in the short-run.

This result is somewhat surprising given the idea that human capital is an important driver of economic growth. One possible explanation along the lines of Van Leeuwen is that average years of schooling is an imperfect measure of human capital, he argues that this variable cannot capture the increased efficiency in the economy resulting from education.

Moreover, since this variable is not expressed in terms of a monetary unit, it is not comparable with the capital stock formation monetary unit measurement. CCEPMG and CCEMG estimators show that trade openness is significantly negative in the short-run when it might be the case of trade liberalisation undermines domestic production due to import competition, see Gries and Redlin All four tests show negative and significant result for the error correction term, supporting the evidence of a long-run relationship.

When a deviation from the long-run exists, the speed of adjustment to the long-run equilibrium is derived from the absolute value of the error correction term. In the bivariate model, deviations can be corrected for at a rate of In the multivariate growth model, the speed of adjustment is much higher at The residual tests are I 0 for all estimations, it is worth noting that the CCE estimator is valid even in the presence of serial correlation in the error term Pesaran In order to be a valid estimator, CCEMG should satisfy two requirements i the number of cross-section averages should be at least equal to the number of unobserved common factors and ii sufficient lags of cross section averages, see Chudik and Pesaran However, including more lags of averages variables is not desirable in our case because of the relatively small sample size.

The CCEPMG estimator is chosen as the preferred approach because of the econometric theory behind this estimator and the significance of outcomes in both models. Besides, the estimator is correctly specified without the problem of autocorrelation and cross-sectional dependence. In general, the results point to the detrimental consequences of increased public debt in economic growth. To find the appropriate lag length in the estimation the general to specific method was used and the Wald test is employed to examine if there is an asymmetric short and long-run response of government debt changes on economic growth.

The Wald test cannot reject the null hypothesis of a symmetric link in the short-run and in the long-run. While the sign shows a change in magnitude in the short-run it is statistically insignificant and there is also a clear rejection of the existence of an asymmetric relationship in the long-run. Using the CCEPMG, the Wald test of long-run symmetry cannot be rejected, indicating that change in government debt does not affect the long-run relationship and using the same convergence rate to define the long-run growth.

The stationarity in the residuals indicates that the results of the Wald test are not spurious and the CCEPMG estimator controls for the cross-sectional dependence. In addition, the error correction term is negative.

The investment ratio is positive and significant in short-run analysis but does not show a significant association with economic growth in the long-run. The human capital shows a positive but insignificant result in the long-run and a mix of negative and positive result in the short-run. Again, the trade openness exhibits a negligible negative impact in the short-run but a much higher positive but not significant influence in the long-run.

The negative impact of public debt in the short-run implies lower debt accumulation will lead to a higher economic growth. The issue of public debt and its impact on economic growth has been an important topic of debate amongst academics and policymakers. This research contributes to the public debt-growth literature by focusing on a selection of Asian countries that typically have public debt to GDP ratios well below those in developed countries.

Our main findings can be summarised as follows: i there is a negative effect of the public debt ratio on economic growth, both in the short-run and long-run, ii the negative relationship is more significant when we use common correlated factors to address the issue of cross-sectional dependence, iii an asymmetric response of a change in public debt is found to be significantly negative in the short-run.

As such, rises in short-run public debt negatively affect economic growth in the short-run but falls public debt do not have a correspondingly positive effect on economic growth in the short-run. The failure of the initial cointegration tests of Pedroni and Westerlund to detect a the long-run relationship, led us to resort to the use of more advanced methods examine the relationship. Using the panel ARDL approach increased public debt can be shown to to negatively affect economic growth in both the short and long run.

This result does not change when allowing for common correlated effects in the analysis. An asymmetric response of a change in public debt is significant only in the short-run, that is, an increase in public debt will have a negative effect on growth in the short-run while a decrease in public debt will not have a correspondingly positive short-run impact on economic growth but it is likely to do so in the long-run.

Our negative results in a set of countries that have relatively low public debt to GDP ratios complement the results of Pattillo et al. Our results may also have some interesting policy implications. Firstly, there is a need to examine why increases in the public debt to GDP ratio have a negative effect on GDP in these economies; Is it because the increase in public debt is used to finance projects of little worth to future economic growth? Or because it crowds out productive private investment?

Or is it because the increase in public debt has benefitted a few elites at the expense on increasing the debt burden on the rest of the population? The answer may be that a mixture of all three elements come into play. Secondly, the countries concerned should consider putting in institutional improvements and control mechanisms that ensure that increases in public expenditure that increase public debt, explicitly consider the likely impact on future economic growth.

This could mean that much needed infrastructure projects are given priority over projects with little economic value added, such as, increased military and defence expenditure. Finally, there could be a greater focus in these countries on public sector expenditure evaluation, for instance, increases on public sector bureaucracy may not be as useful in promoting economic growth as greater public sector expenditure on improving health and education systems. The paybacks from these various types of government expenditure should be explicitly modelled so as to increase the probability of creating a positive link between increasing public debt and economic growth.

Republic of Korea and Singapore are classified as high-income countries since Nielsen We have also checked for the presence of cross-sectional dependence across variables. For all variables the tests rejected the null hypothesis of weakly cross-sectional dependence. Results of these tests are not reported here for economy of space and are available from authors upon request.

Abbas SA, Christensen JE The role of domestic debt markets in economic growth: an empirical investigation for low-income countries and emerging markets. IMF Staff Pap 57 1 — Article Google Scholar. Rev Econ Stat 82 1 — Baltagi BH Econometric analysis of panel data. Baltagi BH The oxford handbook of panel data. Google Scholar. J Int Money Financ —

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If two variables cointegrate adding a third integrated variable to the model will not change the outcome of the test. If the third variable do not belong in the cointegrating vector, OLS estimation will simply put its parameter to zero, leaving the error process unchanged.

The advantage of the procedure is that it is easy, and therefore relatively costless to apply compared with other approaches, especially when two variables can work quite well. The weakness of the test is that it relies on asymptotic properties and sensitive to specification errors in limited samples. The method start with a VAR representation of the variables economic systems we like to investigate.

Typically , we will assume that the system is integrated of order one. The more compact for the VECM becomes;. Each significant eigenvalue represent a stationary relation. From Eq 3 , the test for cointegration;. There is no linear combination of variables that leads to stationary. The Max test is constructed as;. The trace test is. It has found that the trace test is the better test, since it appears to be more robust to skewness and excess kurtosis.

Deterministic trends in a cointegration VECM can stem from two distant sources; the mean of the cointegrating relationship and the mean of the difference series. Allowing for a constant and a linear trend and assuming that there are cointegration relations, we can rewrite the VECM in 3 as.

Placing restriction on the trend terms in Eq 9 yields five cases;. This model is uninteresting because it assumes that all variables in the cointegrating vectors have the same mean. In practice, this is model of last resort. If no meaningful cointegration vector are found using Model 2 or 3, a trend component in the vectors might do a trick. Having trend in cointegrating vectors can be understood as a type of growth in target problem i.

Model 5 : Unrestricted trend. This model quite unrealistic and should not to be considered in applied work. The reason is difficulty in motivation quadratic trends in a multivariate model. Eg, from an economic point of view, it totally unrealistic to assume that technological or productivity growth is an increasingly expanding process.

Kao Engle-Granger based Cointegration Tests. The extensive interest in and the availability of panel data has led to an emphasis on extending various statistical tests to panel data. Recent literature has focused on tests of cointegration in a panel setting.

EViews will compute one of the following types of panel cointegration tests: Pedroni , Pedroni , Kao and a Fisher-type test using an underlying Johansen methodology Maddala and Wu You may perform a cointegration test using either a Pool object or a Group in a panel workfile setting. If you have a panel workfile with a single cross-section in the sample, you may perform one of the standard single-equation cointegration tests using your subsample.

The dropdown menu at the top of the dialog box allow you to choose between three types of tests: Pedroni Engle-Granger based , Kao Engle-Granger based , Fisher combined Johansen. As you select different test types, the remainder of the dialog will change to present you with different options. Here, we see the options associated with the Pedroni test.

Note, the Pedroni test will only be available for groups containing seven or fewer series. The Deterministic trend specification portion of the dialog specifies the exogenous regressors to be included in the second-stage regression.

You should select Individual intercept if you wish to include individual fixed effects, Individual intercept and individual trend if you wish to include both individual fixed effects and trends, or No intercept or trend to include no regressors. The Kao test only allows for Individual intercept.

The Lag length section is used to determine the number of lags to be included in the second stage regression. If you select Automatic selection, EViews will determine the optimum lag using the information criterion specified in the dropdown menu Akaike , Schwarz , Hannan-Quinn. In addition you may provide a Maximum lag to be used in automatic selection. An empty field will instruct EViews to calculate the maximum lag for each cross-section based on the number of observations.

The default maximum lag length for cross-section is computed as:. Alternatively, you may provide your own value by selecting User specified , and entering a value in the edit field. The Pedroni test employs both parametric and non-parametric kernel estimation of the long run variance.

You may use the Variance calculation and Lag length sections to control the computation of the parametric variance estimators. The Spectral estimation portion of the dialog allows you to specify settings for the non-parametric estimation.

You may select from a number of kernel types Bartlett, Parzen, Quadratic spectral and specify how the bandwidth is to be selected Newey-West automatic , Newey-West fixed , User specified. The Newey-West fixed bandwidth is given by. The Kao test uses the Lag length and the Spectral estimation portion of the dialog settings as described below.

Here, we see the options for the Fisher test selection. The Deterministic trend specification section determines the type of exogenous trend to be used.

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