A COMPARISON OF CAUSALITY TESTS APPLIED TO THE BILATERAL RELATIONSHIP BETWEEN CONSUMPTION AND GDP IN THE USA AND MEXICO GUISAN, M.

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1 International Journal of Applied Econometrics and Quantitative Studies. Vol.1-1(2004) A COMPARISON OF CAUSALITY TESTS APPLIED TO THE BILATERAL RELATIONSHIP BETWEEN CONSUMPTION AND GDP IN THE USA AND MEXICO GUISAN, M.Carmen * Abstract Bilateral causality between Private Consumption and GDP in the USA and Mexico during the period is analysed comparing Granger s test, a modified version of Granger s test, cointegration, TSLS and Hausman s causality test. The main conclusion is that the modified version of Granger s test performs better than the unmodified version, and also better than cointegration, to accept lagged causality in the Consumption equation. Besides that Hausman s test is very often more useful to distinguish between bilateral and unilateral contemporaneous causality than TSLS. We conclude that there is a high degree of causal dependence of Private Consumption on GDP and a lower dependence in the case of the reverse relation. JEL classification: C5, C52, E2, O51, O57 Key words: Granger s test, causality test, Mexico, the USA, Consumption and Gross Domestic Product, Consumption Models 1.- Introduction In this study we analyse bilateral causality between Private and Total Consumption and GDP in Mexico and the USA with the following methods: Granger s causality test, modified version of Granger s causality test proposed by Guisan(2003), cointegration, Two Stage Least Squares, and Hausman s test. * Maria-Carmen Guisan is Professor of Econometrics and Director of Master in International Sectoral Economics at the University of Santiago de Compostela (Spain), ccgs@usc.es 115

2 Guisan, M.C. A Comparison of Causality Tests between consumption and GDP in In previous studies, such as Guisan(2001), the analysis of the cointegration relationship between real Private Consumption and GDP in 25 OECD countries was performed, with results that show several limitations of that approach. A simple method based on a regression approach by means of a mixed dynamic model with three explanatory variables was clearly more successful to reach right decisions in the distinction between true and spurious relationships. In Guisan(2003) some comparisons of causality tests where performed with data of several OECD countries. This article is an extension of that paper, with applications to Mexico and the USA. In section 2 we present a general comparison of the evolution of Consumption and GDP in the USA and Mexico during the second half of the 20 th century, expressed in thousand dollars of 1990 per inhabitant at Purchasing Power Parities, PPPs. In section 3 we analyse bilateral direction of causality between these variables with Granger s causality test, both with the unmodified and the modified versions of this test, and with cointegration tests. In section 4 bilateral and contemporaneous causality is analysed following the Cowles Commission approach of contemporaneous interdependence by applying TSLS and Hausman s test of causality. Finally in section 5 we present the main conclusions, which show that the contemporaneous relationship between these variables is mainly unilateral, with Consumption depending strongly on GDP, and that the reverse relationship holds more slightly. The best test to account for this was Hausman test, while the other methods are helpful but more limited for causality analysis purpose. 2.- Evolution of real Consumption and GDP per inhabitant in Mexico and the USA, Graph 1 shows the evolution of total real Consumption per inhabitant, both private and public, in Mexico and the USA for the period , expressed in thousand dollars at 1990 prices and purchasing power parities, PPPs. We can notice that the increase of this variable in Mexico has been moderately positive during that period in comparison with the high increase in the USA. 116

3 International Journal of Applied Econometrics and Quantitative Studies. Vol.1-1(2004) Graph 1. Evolution of total Consumption per inhabitant (thousand dollars at 1990 prices and PPPs) 24 US A U SA 8 M x 4 M x This evolution is explained by the evolution of real Gdp per inhabitant, PH. Table 1 shows the evolution of private,ch, and public, GH, consumption per inhabitant and PH in both countries. Table 1. Consumption and GDP per inhabitant in Mexico and the USA (thousand dollars at 1990 prices and PPPs) Country Variable Mexico CH GH ZH PH USA CH GH ZH PH Source: Own elaboration from OECD National Accounts Statistics. Note: CH is Private Consumption, GH is Public Consumption, ZH is total Consumption, ZH=CH+GH, and PH is Gross Domestic Product, all variables in thousand dollars per inhabitant. 117

4 Guisan, M.C. A Comparison of Causality Tests between consumption and GDP in Graphs 2 and 3 show the high positive correlation existing between total consumption per inhabitant, ZH, and Gdp per inhabitant, Ph, in Mexico and the USA. Graph 2. Total Consumption and GDP in Mexico (thousand dollars per inhabitant at 1990 prices and PPPs) 5.5 Z H M P P v s. P H M P P ZHMPP P H M P P Graph 3. Total Consumption and GDP in the USA (thousand dollars per inhabitant at 1990 prices and PPPs) 24 Z H U v s. P H U ZHU P H U Although the average annual rate of growth of Gdp in Mexico during the period , 4.27%, was higher than that of the USA, 2.95%, the average annual rate of Population growth was much higher in Mexico, 2.47%, than in the USA, 1.11%. As a consequence the

5 International Journal of Applied Econometrics and Quantitative Studies. Vol.1-1(2004) average rate of growth of Gdp per inhabitant was similar in both countries: 1.80% in the case of Mexico and 1.84% in the case of the USA, because the exponential rate of growth of a ratio between two variables is the difference between both rates. The level of CH in Mexico in year 2002 is only a 25% of the value of this variable in the USA, GH is only a 12%, and PH a 38%. Regarding the value of PH in Mexico there are some discrepancies among different statistical sources, amounting 7.0 thousand dollars of 1990 in the year 2000, accordingly to data elaborated from OCDE National accounts and to 7.5 in the same year accordingly to data elaborated from Maddison s estimation for 1998 and the rates of growth for Mexico in the OECD statistics for the following years. In any case data of Ph in Mexico in year 2000 is similar to that of the USA in year 1940, and thus the level of consumption is too much low in Mexico in comparison with social expectations. Policies to reach higher levels of these variables in Mexico should be addressed to increase human capital and industrial development according to the analyses made by Canudas(2001), Dussell(2002), Guisan, Malacon and Exposito(2003), and other authors. Graph 4 presents the evolution of real Gdp per inhabitant in the USA, Mexico, Latin America and Ireland. This country is included in the comparison to show how human capital and industrial development, among other factors, have made possible a fast development during the last two decades of the 20 th century, while Mexico and Latin America show during that period a clear stagnation in per capita terms. Data are based on historical statistics, Maddison(2001) and OECD National Accounts. The countries with higher level of economic development during the second half of the 20 th century are generally those with moderate rates of population growth and high level of industrial production per inhabitant. High educational levels of population and free market institutions and incentives to invest in productive activities, have usually been a positive starting point to get a dynamic an sustained 119

6 Guisan, M.C. A Comparison of Causality Tests between consumption and GDP in process of economic development, as it is shown in Guisan, Aguayo and Exposito(2001). Graph 4. Evolution of real Gdp per inhabitant (thousand dollars at 1990 prices and PPPs) U S A I r M x 4 L a t i n A m e r i c a Mexico have experienced important increases in GDP but excessively high rates of Population growth during the second half of the 20 th century, and as a consequence a moderate growth of real GDP per inhabitant. In the last decades of that century the education level of population has been increased and that is positive for further development. 3. Granger s causality test, modified version of Granger s test and cointegration. Here the estimations are performed with data of Consumption per inhabitant, CH, and Gdp per inhabitant, PH, expressed in purchasing power parities of 1990, PPPs, and per capita terms, based on OECD National Accounts Statistics and Maddison(2001).. In the Annex we include data for the period Granger s test: In Guisan(2003) the command CAUSE(2) of E- Views was used to test causality between CH and PH, with a sample of 25 OECD countries in the period This approach tests the joint nullity of the parameters, corresponding to lags of X in relation (1) and to lags of Y in relation (2): (1) LS Y C Y(-1) Y(-2) X(-1) X(-2) 120

7 International Journal of Applied Econometrics and Quantitative Studies. Vol.1-1(2004) (2) LS X C Y(-1) Y(-2) X(-1) X(-2) Results for 25 countries: The hypothesis Phi causes Chi could be accepted only in 10 out of 25 countries. The reverse hypothesis Chi causes Phi could be accepted only in 8 out of 25 countries. Different numbers of lags did not get to better results. Tables 2.1 and 2.2 present the results of this test for the relation between CH and PH in Mexico and the USA. Table 2.1. Granger s test: CH and PH of Mexico, Pairwise Granger Causality Tests. Sample: Lags 2 Null Hypothesis: Obs F-Statistic Probability PHMPP does not Granger Cause CHMPP CHMPP does not Granger Cause PHMPP Table 2.2. Granger s test: CH and PH of the USA Pairwise Granger Causality Tests. Sample: Lags 2 Null Hypothesis: Obs F-Statistic Probability PHU does not Granger Cause CHU CHU does not Granger Cause PHU Results for Mexico and the USA, in : Non bilateral causality is rejected, and bilateral causality is accepted, for the USA. Non bilateral nor unilateral causality is accepted for Mexico.This problem will disappear with the modified version of this test. Modified version of Granger s test: In this modified version the lagged value of the explained variable correspond to a delay higher than the lagged value of the explanatory variable: (3) LS Y Y(-2) X(-1) C (4) LS X X(-2) Y(-1) C Results for 25 OECD countries: The causal non contemporaneous relation Chipp=f(Phipp(-1)) was accepted in 23 countries, being the exceptions only Luxembourg and Switzerland. The causal relation Phipp=f(Chipp(-1)) was accepted in 14 countries. This modified 121

8 Guisan, M.C. A Comparison of Causality Tests between consumption and GDP in version diminish the high degree of multicollinearity corresponding to the unmodified version of Granger s test. Tables 3.1 to 3.4 show the results of the modified version of Granger`s test with data of Mexico and the USA in Table 3.1.Modified version of Granger s test: CH equation: Mexico Dependent Variable: CHMPP. Least Squares. Sample Variable Coefficient Std. Error t-statistic Prob. C CHMPP(-2) PHMPP(-1) R-squared Mean dependent var Table 3.2.Modified version of Granger s test: PH equation: Mexico Dependent Variable: PHMPP. Least Squares. Sample Sample: Included observations: 31 Variable Coefficient Std. Error t-statistic Prob. PHMPP(-2) CHM(-1) R-squared Mean dependent var Table 3.3.Modified version of Granger s test, CH equation: the USA Dependent Variable: CHU. Least Squares. Sample Variable Coefficient Std. Error t-statistic Prob. C CHU(-2) PHU(-1) R-squared Mean dependent var Table 3.4.Modified version of Granger s test, PH equation: the USA Dependent Variable: PHU. Method: Least Squares. Sample Variable Coefficient Std. Error t-statistic Prob. PHU(-2) CHU(-1) R-squared Mean dependent var

9 International Journal of Applied Econometrics and Quantitative Studies. Vol.1-1(2004) Results for Mexico and the USA in : The coefficients of PH(-1) in the equation of CH and those of CH(-1) in the equation of PH are significant in both countries. Bilateral non contemporaneous relationship is accepted with this test both in Mexico and in the USA. Cointegration tests: The results with cointegration tests with 25 OECD countries led to very bad results, according to the abovementioned studies, with many cases of rejection of true causal relations when they were true and some cases of acceptance of causality in spurious relationships. Table 4 presents the results of the ADF test for Mexico and the USA in Table 4.Cointegration test: CH and PH of Mexico and USA Ho: UFi has a unit root. UROOT(N,1) t-statistic Prob.* Augmented Dickey-Fuller test statistic: Mexico Augmented Dickey-Fuller test statistic: USA Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. UFi is the residual of a linear relation between CHi and PHi (i=mpp, U) Results of cointegration test: Non-cointegration is rejected in the USA but not rejected in Mexico at 5% level. This result should not interpreted as a case of spurious relationship. This situations should be analysed having into account some limitations of cointegration approach, which are analysed in Guisan(2001) and other studies. The best results of section 3 correspond to the modified version of Granger s test, and now we should analyse if the relationship is contemporaneous and bilateral or unilateral. 123

10 Guisan, M.C. A Comparison of Causality Tests between consumption and GDP in 4.- Bilateral and contemporaneous relationship: TSLS and Hausman s test of causality Hausman s test of causality was applied to the USA and Mexico, with acceptance of interdependence for both countries in the period but not for other periods, according to results of table 5. We consider the following model: (5) CHi / CHi(-1) D(PHi) (6) PHi / PHi(-1) D(CHi) where CHi is Consumption per inhabitant, PHi is GDP per inhabitant and i indicates name of country (MPP for Mexico in thousand dollars at 1990 prices and purchasing power parities, and U for the USA also in thousand dollars at 1990 prices). First difference of a variable, Yi, is indicated by D(Yi), for Yi=CHi, PHi. The t statistics in table 5 correspond to the LS, or GLS in case of autocorrelacion, estimation of the coefficients of CHiF and PHiF in the following equations: 7) CHi / CHi(-1) D(PHi) D(PHiF) 8) PHi / PHi (-1) D(CHi) C(CHiF) Following Nakamura and Nakamura(1980), the significant values of the parameters corresponding to the reduced form estimations of the endogenous variables, indicated with the letter F of fitted at the end of their names in (7) and (8), in the LS estimation of the structural equations is equivalent to accept Hausman s causality, because it indicates that the explanatory variable in the right side is correlated with the current value of the random shock, due to interdependence. They point out that is enough to get one of the coefficients significant, together with significance of both coefficients in TSLS estimation for evidence in favour of simultaneity and interdependence. 124

11 International Journal of Applied Econometrics and Quantitative Studies. Vol.1-1(2004) Table 5. t Statistics of Hausman s Test, USA Equation Mx: CH 3.94* Mx: PH 6.14* -1.86** -9.66* USA: CHU 4.34* USA: PHU 6.09* Note: * significant at 5% and ** at 10% level. The results in table 5 show that a bilateral contemporaneous relationship between CH and PH could be accepted at the 5% level of significance for the USA in the period but not for the other two sample period. In Mexico that relationship could be accepted in two of the three sample periods. TSLS estimation, sample : Tables 6.1 to 6.6. present the results of Two Stages Least Squares estimation for each country and for a pool of both countries. Table 6.1. TSLS estimation: CH equation of Mexico Dependent Variable: CHMPP. TSLS. Sample Variable Coefficient Std. Error t-statistic Prob. CHMPP(-1) D(PHMPP) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Durbin-Watson stat Table 6.2. TSLS estimation: CH equation of the USA Dependent Variable: CHU. TSLS. Sample Variable Coefficient Std. Error t-statistic Prob. CHU(-1) D(PHU) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Durbin-Watson stat

12 Guisan, M.C. A Comparison of Causality Tests between consumption and GDP in Table 6.3. TSLS estimation. CH equation, pool, 2 countries Mexico and the USA. Equation: CH? = C(1)*CH?(-1) + C(2)*D(PH?) Coefficient Std. Error t-statistic Prob. C(1) C(2) SCE (Mexico) = SCE(USA)= Durbin-Watson stat Mx: USA=1.37 In tables 6.1 to 6.3 the coefficient of PH is significant. In tables 6.4 to 6.6 the coefficient of CH is also significant in the equation of PH, but this reverse relationship is not so clear, because it may be affected by the relation between CH and several omitted explanatory variables of PH. Table 6.4. TSLS estimation: PH equation of Mexico Dependent Variable: PHMPP. TSLS. Sample Variable Coefficient Std. Error t-statistic Prob. PHMPP(-1) D(CHMPP) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Durbin-Watson stat Table 6.5. TSLS estimation: PH equation of the USA Dependent Variable: PHU. TSLS. Sample Variable Coefficient Std. Error t-statistic Prob. PHU(-1) D(CHU) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Durbin-Watson stat

13 International Journal of Applied Econometrics and Quantitative Studies. Vol.1-1(2004) Table 6.6. TSLS estimation. PH equation, pool: Mexico and the USA Mexico and the USA. Equation: PH? = C(1)*PH?(-1)+C(2)*D(CH?) Coefficient Std. Error t-statistic Prob. C(1) C(2) SCE (Mexico)= SCE(USA)= Durbin-Watson stat Mx: USA: This method shows usually significant coefficients both for the CH equation, and for the reverse relationship, the PH equation, even in the cases where Hausman s test rejects interdependence. PH depends on the supply side of several factors, such as human capital, physical capital, raw materials and other intermediate inputs, and from the demand side of all the components of the aggregate demand and not only on CH. The significant coefficient of D(CH) in the equation of PH can be due to the positive relationship between the omitted explanatory variables and CH, so D(CH) would only be reflecting the evolution of those variables. Even when Hausman s test indicates correlation between the explanatory variable and the random shock it not always indicates interdependence. In fact if CH is reflecting the evolution of a set of explanatory variables which explain PH, it may happen that there is contemporaneous correlation between CH and the random shock of the equation of PH, even if CH is not cause of PH. Results of Hausman s test and TSLS estimation: We can notice that TSLS estimation can show interdependence even when Hausman s test does not. The results of Hausman s test indicate that there is some periods with some degree of interdependence but that the main relationship is contemporaneous and unilateral, with CH depending clearly on PH. 5. Conclusions The main conclusions on the causal relationships between CH and PH, in Mexico and the USA are the following ones: 127

14 Guisan, M.C. A Comparison of Causality Tests between consumption and GDP in 1) Granger s test of causality present many problems of multicollinearity and redundant variables, because of the effect of lagged values of explanatory variables with the same delay than the lagged values of the explained variables. In spite of that Granger s perspective is interesting if we apply the revised version of the test which is usually interesting to show the significant effect of the lagged value of the explanatory variable when there is a causal relationship. The modified version of Granger s test was favourable to the bilateral causal relationship between CH and PH in Mexico and the USA, and performed better than the cointegration test which failed to detect causality between CH and PH in Mexico. 2) TSLS estimation shows interdependence, as to say a bilateral and contemporaneous relationship, even when Hausman s test does not support the existence of interdependence. The reverse relationship may be accepted in TSLS estimation even when it is not true, so the Hausman s test seems more trustable. This could be due to the effect of the correlation between the variable CH and the explanatory variables omitted in the equation of PH. 3) The unilateral relationship between CH and PH holds generally while the reverse contemporaneous relationship is slighter and only significant in some periods. This result is relevant for economic policies which should be addressed not only to demand side but also to foster real supply side factors of production such as human capital and industrial production, particularly in the case of Mexico. Bibliography Canudas, R. (2001). Estudio econométrico de la influencia del capital humano en el crecimiento de la productividad industrial de México, en Estudios Económicos de Desarrollo Internacional, EEDI, Vol.1-2, pp Dussel, E.(2002). Empleo, productividad y comercio exterior en la economía mexicana. Investigación Económica, UNAM, Mexico. 128

15 International Journal of Applied Econometrics and Quantitative Studies. Vol.1-1(2004) Granger, C.W.J.(1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods, Econometrica, Vol 37, pp Guisan, M.C. (2001) Causality and Cointegration between Consumption and GDP in 25 OECD Countries: Limitations of the Cointegration Approach, Applied Econometrics and International Development 2001-vol 1-1, pp Guisan, M.C. (2003). Causality Tests, Interdependence and Model Selection: Application to OECD Countries, Working paper of the series Economic Development, no Guisan, M.C., Malacon, C., and Exposito, P.(2003). Effects of the Integration of Mexico into NAFTA on Trade, Industry, Employment and Economic Growht. Economic Development, no Hausman, J.A.(1978) Specification tests in Econometrics, Econometrica Vol. 46, pp- Maddison, A(2001) The World Economy A Millennial Perspective Development Centre Studies OECD Nakamura, A. and Nakamura, M.(1981). On the Relationships among Several Specification Error Tests Presented by Durbin, Wu and Hausman, Econometrica, Vol 49, no.6, pp OECD(2002) and previous issues of National Accounts of OECD countries OECD, Paris 1 Information about these publications on Journal IJAEQS published by AEEADE: 129

16 Guisan, M.C. A Comparison of Causality Tests between consumption and GDP in Annex.Table A1. CH and PH in Mexico and USA ($90 PPPs) obs CHMPP GHMPP PHMPP CHU GHU PHU Note: Elaborated from OECD National Accounts, several years. Dollars per inhabitant at 1990 prices and Purchasing Power Parities. 130