1. Tests based on ratios to GDP data

Transcription

1 1. Tests based on ratios to GDP data We will start the presentation of our results by using the variables in percentages to GDP using the Engle Granger procedure. The results are in Table 3. Table 3 Engle Granger test for cointegration between revenues and expenditures (%GDP) Period ADF Lags 95% Critical value R 2 α β T stat β= T stat T stat T stat * T stat T stat T stat Notes: ** and * denotes rejection of the null of no cointegration at the 5% and 1% significance levels, respectively. The critical values for cointegration test are from MacKinnon (1991), which have the advantage of being given for any sample size. The ADF test is done without any deterministic component, since the equation in levels already includes a constant. The results show that at the 5% level, the null of no cointegration is not rejected for our full sample. Hence, for the period Portuguese fiscal policy appears to have not been sustainable. Abstracting from the constant, the estimated long run relationship is (1.835). The test for β=1, is rejected by the data. 11 This result is in line with the result that indicates a unit root in the budget balance variable, because the budget balance is just the difference between revenues and expenditures, i.e. the result of imposing a co integrating vector of (1 1). Therefore, we may conclude from this results that Portuguese fiscal policy has not been weakly sustainable over this long period of one and a half century running from 1861 to 23. With regard to the different sub periods considered, only for we find a rejection of the null of no cointegration, and only at the 1% level. This result is in line with the ADF test for the budget balance that pointed to the rejection of the null of a unit root, meaning that in this sub period Portuguese fiscal policy has been strongly sustainable. For all other remaining periods, this test is unable to reject the null of non sustainability. 11 However, due to convergence reasons some cautions are needed in interpreting the usual T tests. Still, imposing β=1 yields the test for the presence of a unit root on the budget balance. 25

2 Next, we repeat the same test using the Johansen s Maximum Likelihood test for cointegration between public revenues and public expenditures. 12 The results, considering a linear trend in the levels of the data, and only an intercept in the cointegration equations, are in Table Table 4 Johansen s maximum likelihood tests for cointegration between revenues and expenditures (%GDP) Trace Eigenvalue H H1 Trace 95% Critical Value 9% Critical Value λ max H H1 λ max 95% Critical Value 9% Critical Value r = r > 14.5* r = r = r 1 r > r = 1 r = r = r > r = r = * E 5 r 1 r > r = 1 r = r = r > r = r = r 1 r > r = 1 r = r = r > r = r = r 1 r > r = 1 r = r = r > r = r = r 1 r > r = 1 r = r = r > 15.75** r = r = * r 1 r > r = 1 r = Notes: A lag length of two is used on the VAR (p=3), i.e. using lags 1 2 in Eviews. Critical values for the trace and maximum likelihood tests are from Osterwald Lenum (1992). The estimations were obtained assuming a linear trend in the levels of the data, and only an intercept in the cointegration equations. The 99% critical values for the trace test are 2.4/6.65 and for the maximum likelihood 18.63/ 6.65, for the first and second lines, respectively. For the full period of , only the trace test indicates at the 1% significance level a rejection of the null of no cointegration, i.e. indicates sustainability. The result of estimating a Vector Error Correction Model (VECM) is in Table 9 of the Tables appendix. The estimated β is very close to one, indicating strong sustainability. Interestingly the VECM shows that only the 12 We used three lags in the levels of the variables (p=3). This choice is indicated by the Akaike criterion for the full period. 13 This assumption for the trend in the VAR is adequate when the trends present in the variables are stochastic. 26

3 revenues adjust to the error correction term, meaning that the correction of the disequilibria from the long run relation between the two variables is just the responsibility of the revenues. This means that for Portugal it is expenditure that causes revenues, indicating a first spend, then find the revenues behaviour. Further evidence of cointegration is found for the period by the maximum likelihood test, again at the 1% level. The more recent period of is characterized by the largest debt and deficits of our sample. However, both the trace and maximum likelihood test point to sustainability at the 5% and 1% level, respectively. The VECM results are in Table 1 of the appendix. The point estimates for the co integrating vector indicate a high value for b, due to a very low value for the constant, making it difficult to economically interpret the results obtained. This result of existence of a cointegration relation goes against the evidence from the Engle Granger procedure, but is in line with the rejection of the null of a unit root for the budget balance (Table 1). 14 Next, we will repeat this exercise using real per capita data. This cross checking will enable us to find more solid conclusions. However, it is possible to argue that the per capita measures and percent of GDP measures are not interchangeably. 15 In this case of very long data, the percent of GDP measures are more relevant, since what counts is the capacity of the economyʹs output to bear the burden of the debt. When examining the data (Figure III 3 and Figure III 1, in pages 13 and 17, respectively) the per capita measures give the impression of a large increase of the burden of the debt, while the percent of GDP measures do not show this at all. 2. Tests based on real per capita data Now considering real per capita data, we will repeat the cointegration tests between public revenues and public expenditures (inclusive of interest payments) starting again with the Engle Granger method. The results are in Table 5. Table 5 Engle Granger test for cointegration between revenues and expenditures (Real per capita) Period ADF Lags 95% Critical value R 2 α β T stat β= ** T stat T stat As a robustness check we considered also the sub period , i.e. the post war period as a whole. Both the Engle Granger test and the Johansen test point to the non sustainability of Portuguese fiscal policy. These results cast some doubts on the sustainability conclusion achieved for the period. 15 The author is grateful to Paul De Grauwe for this suggestion. 27

4 ** T stat * T stat T stat * T stat Notes: ** and * denotes rejection of the null of no cointegration at the 5% and 1% significance levels, respectively. The critical values for cointegration test are from MacKinnon (1991), which have the advantage of being given for any sample size. The ADF test is done without any deterministic component, since the equation in levels includes a constant. As the results indicate, at the 5% significance level we are able to reject the null of no cointegration for the full sample period and for At the 1% level the null is also rejected for the period and for the more recent period of As a result, when using real per capita data we find a stronger indication of sustainability of Portuguese public finances. Namely, for the full sample period from , Portuguese fiscal policy appears to be sustainable, even though in the weak sense. Moreover, the conclusion of sustainability emerges (at the 1% level) for all sub periods but the first. The Johansen s test results (Table 6), reinforce those conclusions with the exception of the more recent period ( ). For the full sample, the null of no cointegration is clearly rejected by both the trace and the maximum likelihood test at the 1% significance level, meaning that Portuguese fiscal policy has been sustainable. 16 For the period both tests indicate that the variables are stationary, favouring sustainability. However, for the more recent period of , we were unable to reject the null of no cointegration, which indicates non sustainability. This result is in contrast with the rejection of a unit root for the budget balance series and with the rejection of no cointegration when using the Engle Granger method at the 1% level The VECM is in Table 11 of the appendix. 17 The non sustainability results for the sub period reinforce this conclusion of nonsustainability for the more recent period. 28

5 Table 6 Johansen s maximum likelihood tests for cointegration between revenues and expenditures (real per capita data) Trace Eigenvalue H H1 Trace 95% Critical Value 9% Critical Value λ max H H1 λ max 95% Critical Value 9% Critical Value r = r > 21.92*** r = r = ** r 1 r > ** r = 1 r = ** r = r > r = r = r 1 r > r = 1 r = r = r > 33.39*** r = r = *** r 1 r > 1 5.7** r = 1 r = 2 5.7** r = r > 16.77** r = r = * r 1 r > 1 4.5** r = 1 r = r = r > r = r = r 1 r > r = 1 r = r = r > r = r = r 1 r > r = 1 r = Notes: A lag length of two is used on the VAR in first differences (p=3). Critical values for the trace and maximum likelihood tests are from Osterwald Lenum (1992). The estimations were obtained assuming a linear trend in the levels of the data, and only an intercept in the cointegration equations. The 99% critical values for the trace test are 2.4/6.65 and for the maximum likelihood 18.63/ 6.65, for the first and second lines, respectively. *, **, and *** denotes the rejection of the null of no cointegration at 1%, 5% and 1% level, respectively. 29

6 3. Cointegration tests allowing for regime shifts A natural extension of this work is to formally test for the presence of structural breaks in the data. One relevant test is proposed by Gregory and Hansen (1996) and it could be applied to the Engle Granger two step procedure. The authors develop a methodology that enables a residualbased testing of the null of no cointegration against the alternative of cointegration in the presence of a possible regime shift, with the break occurring at an unknown point in time. It is then possible to compute modified ADF statistics (ADF*) allowing for a regime change in the intercept or in the coefficient of the vector. The independency of this test with regard to the breaking date invalidates data mining from contaminating the choice of the break point. This test is interesting because the power of the usual ADF test decreases sharply in the presence of a structural break. If the model is in fact cointegrated, a standard ADF test may not reject the null leading to the wrong conclusion that there is no long run relationship. The standard cointegration model could be written as follows: y = µ + α y + e (14) 1t 1 2t t Where y1r and y2t are I(1) and et I(). A structural change would shift the long run cointegration relationship to a new level, reflecting changes in the intercept µ and/or in the slope α. Hence, the test of Gregory and Hansen (1996) allows for a regime shift in either the intercept alone or in the entire coefficient vector. More specifically the authors propose testing the following hypotheses to account for three types of possible structural breaks: 1. Level Shift (C): 2. Level shift with trend (C/T): y = µ + µ D + αy + e (15) 1t 1 2 1τ 2t t y = µ + µ D + βt+ αy + e (16) 1t 1 2 1τ 2t t 3. Regime shift (C/S): y = + D + y + y D + (17) 1t µ 1 µ 2 1τ α1 2t α2 2t 1τ et where D1τ = for t [τt], D1τ = 1 for t > [τt], being T the number of observations, and τ (, 1) the unknown parameter that denotes the relative timing of the change point, and [ ] denotes the integer part. The first model allows for a change in the intercept at the time of the shift. The second model allows the slope of the vector to shift also. The third possibility is to allow for the equilibrium relationship to rotate as well as shift parallel. A cointegration test statistic is calculated for every possible regime shift, retaining the smallest value of the statistics (the largest negative value), across all values of τ. The smallest value is retained because a small value for the statistic constitutes evidence against the null hypothesis of 3

7 no cointegration. 18 In practice the models are recursively estimated by OLS for all possible break points in the trimming interval τ (.15,.85) and the ADF* statistic is computed as: ADF* = inf ADF( τ ). τ (.15,.85) Table 7 Gregory Hansen ADF* test for cointegration in the presence of an unknown structural break ( ) Level Shift Level shift with trend Regime shift Year Test Stat. Year Test Stat. Year Test Stat. Ratios to GDP ** * *** Real per capita *** *** *** Notes: *, **, and *** denotes the rejection of the null of no cointegration at 1%, 5% and 1% level, respectively. The critical values are from Gregory and Hansen (1996: 19 (Table 11)), m = 1. The lags selected for the ADF* for the C, C/T, and C/S are (,, ) for the variables in ratios of GDP and (1, 1, 1) for real per capita values. The optimal lag length for the ADF regression was chosen by adding lags until a Lagrange Multiplier test fails to reject the null of no first order residual serial correlation at 5% level, considering a maximum of 2 lags. The usual ADF test statistics without allowing for any structural break are 2.49 and 4.26** for the variables in ratios and in real per capita terms, respectively (see Table 3 and Table 5). The results were obtained in Winrats. As Table 7 shows, for our full sample, the Gregory Hansen ADF* cointegration test rejects the null hypothesis of no cointegration for all the three possible structural break models. The rejection is stronger for the real per capita (RPC) values. For the data expressed as ratio to GDP, the possible break in the data occurs in 1926, i.e. in the end of the budgetary crisis caused by the First World War (see section III.A). We should add also the information that the second smallest value for the level shift model is 4.95 and it occurs in 1975, i.e. in the year immediately after the April 25 th revolution. As already explained, such event had also important consequences for the conduct of Portuguese fiscal policy. For the real per capita data the possible break occurs in 1975, i.e. in the after march of the end of the Estado Novo regime. All three models strongly reject the null of no cointegration at the 1% level. 18 With regard to the existence of a structural break, if the standard ADF statistic does not reject, but the ADF* does, this implies that structural change in the cointegrating vector may be important. However, as Gregory and Hansen (1996) note, if both the ADF and the ADF* reject, no inference that structural change has occurred can be concluded from this piece of information alone, since the ADF* statistics is powerful against conventional cointegration. 31

8 Table 8 Gregory Hansen ADF* test for cointegration in the presence of an unknown structural break ( ) Level Shift Level shift with trend Regime shift Year Test Stat. Year Test Stat. Year Test Stat. Ratios to GDP ** *** *** Real per capita *** *** *** Notes: *, **, and *** denotes the rejection of the null of no cointegration at 1%, 5% and 1% level, respectively. The critical values are from Gregory and Hansen (1996: 19 (Table 11)), m = 1. The lags selected for the ADF* for the C, C/T, and C/S are (,, ) for the variables in ratios of GDP and (1, 1, ) for real per capita values. The optimal lag length for the ADF regression was chosen by adding lags until a Lagrange Multiplier test fails to reject the null of no first order residual serial correlation at 5% level, considering a maximum of 2 lags. The usual ADF test statistics without allowing for any structural break are 2.53 and 3.34* for the variables in ratios and in real per capita terms, respectively (see Table 3 and Table 5). Some researchers might argue that our full sample is too long a period just to consider one possible break in the data. Hence, we repeated the same Gregory Hansen test for post war data only. The results are in Table 8. Now the possible break in the data occurs for all considered models after the revolution of Once again the null of no cointegration is clearly rejected for all considered structural break models. This means that allowing the cointegration relationships to change over time, there appears to be some sort of a long run cointegration relationship between Portuguese public revenues and Portuguese public receipts. Hence, according to these results it seems that Portuguese public finances are at least weakly sustainable over the long run. 19 Another useful regime change test is proposed by Hansen (23). This test is applied to the Johansen method. However, contrary to the previous test, it takes the timing of the change and the number of cointegration relations at any point in time as given, which requires the imposition of a priori information or some appeal to the data. V. Conclusions In this paper we reviewed the recent literature on the sustainability of fiscal policy with the purpose of applying such tests to the Portuguese economy. The more widely use empirical test for sustainability is the test for cointegration between public revenues and public expenditures 19 For the real per capita data, as the conventional ADF test rejects also the null of no cointegration, it is inappropriate to conclude from this Gregory Hansen test alone, that there is a structural break, since a conventional cointegrated system leads to the same conclusion. However, for the variables in ratios to GDP, there is evidence in favour of a structural break occurring in 1926 since the conventional ADF test does not reject the null of no cointegration. 32

9 (inclusive of interest payments on the debt). If cointegration is found between the two variables, the present value budget constraint is satisfied and fiscal policy is said to be sustainable. Moreover, fiscal policy could be classified as strongly sustainable or only weakly sustainable depending on the value of coefficient on the total expenditures being equal one or being less than one, respectively. The test for strong sustainability of the deficit could also be done by testing for a unit root in the budget balance series. If the null of a unit root is rejected, fiscal policy is strongly sustainable. This procedure is equivalent to imposing a unitary coefficient in a regression of the revenues on the expenditures. We applied both tests for the case of the Portuguese economy. Differently from the previous literature that has focused only in the more recent period, our sample makes use of historical data. Therefore our sample covers a long period of time running from as earlier as 1861 until 23. This is an interesting contribution because both unit root and cointegration tests require a long period of data. Besides analysing the full sample period, we considered as well different sub periods. We have worked with real per capita data and with data deflated by GDP (percentages of GDP). Overall we found some evidence in favour of the sustainability of Portuguese fiscal policy has been sustainable over the full sample period. This conclusion is based on the different cointegration tests made, particularly the ones based on real per capita data. This result is robust to the consideration of a structural break in the data, using the Gregory Hansen s ADF* test. However, our results particularly the ones arising from the Engle Granger method point only to weak sustainability of Portuguese fiscal policy over this full period. Therefore, the government might face some difficulties in marketing its debt. With regard to the different sub periods, we considered , , , and The sub period is being considered in order to exclude the inter war period. For all such periods, except the first one, we were able to find (at the usual significance level of 5%) some evidence of sustainability. For the period, when using ratios to GDP we were able to reject, at the 1% significance level, the null of a unit root in the budget balance series and the null of no cointegration between public revenues and public expenditures. Such results are favourable to sustainability. However, the Johansen method did not reject the null of no cointegration at conventional significance levels. Other evidence favourable to sustainability is given by the use of real per capita data: both the Johansen and the Engle Granger methods clearly reject the null of no cointegration. In the sub period the favourable evidence to sustainability is given by both cointegration tests when using real per capita data, and by the stationary nature of the ratio of the budget balance to GDP. As our graphical analysis showed the more recent period was characterised by the largest public deficit of our entire sample. Therefore, we might had expected that the tests would indicate a clear rejection of the sustainability hypothesis. Moreover, the previously mentioned empirical studies that have analysed Portuguese public finances pointed to its non 33

10 sustainability. However, we have found mixed evidence, including several results pointing to weak sustainability of the Portuguese public finances in the post revolution period. When considering the variables expressed as a percentage of GDP, we rejected the null of a unit root for the deficit, and the Johansen method rejected the null of no cointegration. Such results are favourable to sustainability. However, the Engle Granger method reached a different conclusion. When using real per capita data, the rejection of the null of a unit root in the budget balance remains unchanged, but the conclusions of the two cointegration tests are reversed. Now only the Engle granger method is favourable to sustainability. Moreover this conclusion is only valid at the 1% level. These different results might be due to the relatively small temporal dimension of this sub period. The reduction in the number of observations diminishes the power of both the unit root and the cointegration tests. It could also be the case that the deficit is stationary around a high mean. Therefore, and overall, the evidence regarding this more recent period is mixed. 2 In the 198s (and to a lesser extent in the 199s) the Portuguese budget deficit ratio to GDP reached historical maximums. On the other hand, no debt crisis is likely to emerge because the debt level is around 6% of GDP. Still, our empirical analysis revealed that Portuguese public finances have not been strongly sustainable. The tests show that only by using real per capita data we are able to reject, for some periods of time, the null of non sustainability. These findings have important policy implications. Namely, Portugal should not embark into systematic fiscal expansions which could further compromise sustainability. Instead, the Stability and Growth Pact objective of reaching a balanced structural budget seems to be adequate to simultaneously promote sustainability ant to enable the working of the automatic fiscal stabilisers. 2 As a robustness checking we considered as well the post war period as a whole ( ), reaching a result against the sustainability hypothesis. This result casts some doubts on the sustainability conclusion for the more recent period. 34

11 Statistical appendix The source of data is Pinheiro (1999), which presents a set of coherent data, elaborated by the Bank of Portugal for the period This data is extended backwards with historical data and forward with data from the Portuguese Ministry of Finance, Ministério das Finanças (23), and from INE. The historical data comes from Valério (21), Valério (1994), and Mata (1993). All variables were converted into euros using the irrevocable conversion rate of 1EUR= PTE. Until 1935 the fiscal year ended in June 3. The detailed source for each variable is as follows. GDP : INE estimates, as they appear in Ministério das Finanças (23) : Valério (21). This variable for the period corresponds in its source to Pinheiro (1999), i.e. the author has linked its historical series with Bank of Portugal s estimates for the This series was adjusted to the level of the next period, which is in the ESA95 standard. Public expenditures Corresponds to total public expenditures : Ministério das Finanças (23) : Pinheiro (1999) : Valério (21), Total expenditures, linked with the previous series. Public revenues Corresponds to total public revenues adjusted for the effects of the extraordinary revenues obtained in 2, 22 and 23. Such excluded revenues amounted to 399 million EUR in 2 (UMTS); 183 millions in 22 (CREL revenues, sale of the fixed telecommunication network to Portugal Telecom and an extraordinary regularisation of taxpayers debts); and 1962 millions EUR in 23 (mainly sale of government credits to Citigroup, and integration of the pension fund of the Portuguese post, CTT, into the public servants pension system, CGA) : Ministério das Finanças (23) : Pinheiro (1999) : Valério (21), linked with the previous series. Budget balance Corresponds to the difference between total public revenues and total public expenditures. Public debt : Instituto Gestão do Crédito Público (IGCP), Direct State Debt : Valério (21) 35

12 Interest payments : Ministério das Finanças (23) : Pinheiro (1999) : Valério (21), table : Mata (1993), table 11. The author distinguishes total public debt servicing costs, which comprises amortization of the debt, interest payments and administrative costs. Due to lack of data on the administrative costs, the interest data for 1866 is calculated by difference, assuming that the administrative costs remain equal to its average weight on the total, during the last three years before 1866 (.35%). From 1898 to 1913 the author is again unable to disaggregate between administrative costs and interest payments. We obtain the interest payments again by computing the difference between the total servicing costs, excluding the amortization of the debt, and the estimated administrative cost which are obtained assuming that its weight on the total is equal to the average of the 3 years before and the 3 years after the lack of data. 36

13 Tables appendix Table 9 VECM for period and variables expressed as a percentage of GDP Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 REVADJY(-1) 1. GEXPY(-1) (.7452) [ ] C Error Correction: D(REVADJY) D(GEXPY) CointEq (.3341) (.4215) [ ] [.13593] D(REVADJY(-1)) (.8463) (.1675) [ ] [.41349] D(REVADJY(-2)) (.8444) (.1652) [ ] [ ] D(GEXPY(-1)) (.7752) (.9778) [.7366] [-.5369] D(GEXPY(-2)) (.7613) (.964) [ ] [.87486] C (.142) (.13122) [ ] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant Residual Covariance Log Likelihood Log Likelihood (d.f. adjusted) Akaike Information Criteria Schwarz Criteria

14 Figure 14 Graph of residuals from the VECM ratios to GDP ( ) 8 REVADJY Residuals 6 GEXPY Residuals Figure 15 Cointegration graph ratios to GDP ( )

15 Table 1 VECM for period and variables expressed as a percentage of GDP Vector Error Correction Estimates Included observations: 3 Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 REVADJY(-1) 1. GEXPY(-1) (.22751) [ ] C Error Correction: D(REVADJY) D(GEXPY) CointEq (.3159) (.5426) [-.9712] [ ] D(REVADJY(-1)) (.15657) (.26888) [-1.197] [-.122] D(REVADJY(-2)) (.14356) (.24654) [ ] [-.4427] D(GEXPY(-1)) (.9538) (.16379) [ ] [ ] D(GEXPY(-2)) (.1462) (.17967) [ ] [ ] C (.2324) (.3991) [ ] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant Residual Covariance Log Likelihood Log Likelihood (d.f. adjusted) Akaike Information Criteria Schwarz Criteria

16 Figure 16 Cointegration graph ratios to GDP ( ) Figure 17 Graph of residuals from the VECM ratios to GDP ( ) 2. REVADJY Residuals 5 GEXPY Residuals

17 Table 11 VECM for period and variables expressed in real per capita terms Vector Error Correction Estimates Sample(adjusted): Included observations: 14 after adjusting endpoints Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 REVADJRPC(-1) 1. GEXPRPC(-1) (.629) [ ] C Error Correction: D(REVADJRPC) D(GEXPRPC) CointEq (.235) (.2537) [ ] [ ] D(REVADJRPC(-1)) (.8681) (.9372) [ ] [ ] D(REVADJRPC(-2)) (.923) (.9742) [ ] [.96672] D(GEXPRPC(-1)) (.916) (.9889) [ ] [ ] D(GEXPRPC(-2)) (.9277) (.116) [ ] [ ] C ( ) ( ) [ ] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant Residual Covariance Log Likelihood Log Likelihood (d.f. adjusted) Akaike Information Criteria Schwarz Criteria

18 Figure 18 Cointegration graph real per capita ( ) Figure 19 Graph of residuals from the VECM real per capita ( ) 3 REVADJRPC Residuals 3 GEXPRPC Residuals

19 Table 12 VECM for period and variables expressed in real per capita terms Vector Error Correction Estimates Sample: Included observations: 6 Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 REVRPC(-1) 1. GEXPRPC(-1) (.1416) [ ] C Error Correction: D(REVRPC) D(GEXPRPC) CointEq (.393) (.355) [ ] [ ] D(REVRPC(-1)) (.14942) (.13418) [ ] [ ] D(REVRPC(-2)) (.15534) (.1395) [-.1984] [ ] D(GEXPRPC(-1)) (.2961) (.18823) [ ] [ ] D(GEXPRPC(-2)) (.21499) (.1937) [-.7412] [ ] C ( ) ( ) [ 5.114] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant Residual Covariance Log Likelihood Log Likelihood (d.f. adjusted) Akaike Information Criteria Schwarz Criteria

20 Figure 2 Cointegration graph real per capita ( ) Figure 21 Graph of residuals from the VECM real per capita ( ) REVRPC Residuals GEXPRPC Residuals

21 Table 13 VECM for period and variables expressed in real per capita terms Vector Error Correction Estimates Sample: Included observations: 29 Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 REVRPC(-1) 1. GEXPRPC(-1) (.7551) [ ] C Error Correction: D(REVRPC) D(GEXPRPC ) CointEq (.1968) (.2388) [ ] [ ] D(REVRPC(-1)) (.21869) (.22738) [.2966] [.39569] D(REVRPC(-2)) (.21353) (.2222) [ ] [ ] D(GEXPRPC(-1)) (.31655) (.32914) [ ] [.32452] D(GEXPRPC(-2)) (.312) (.32234) [ ] [ ] C (12.427) (12.921) [ ] [.84637] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant Residual Covariance Log Likelihood Log Likelihood (d.f. adjusted) Akaike Information Criteria Schwarz Criteria

22 Figure 22 Cointegration graph real per capita ( ) Figure 23 Graph of residuals from the VECM real per capita ( ) 1 REVRPC Residuals 6 GEXPRPC Residuals

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