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 1960-2002 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), http://www.usc.es/economet/guisan.htm, e-mail ccgs@usc.es
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 20th 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, 1960-2002.
Graph 1 shows the evolution of total real Consumption per inhabitant, both private and public, in Mexico and the USA for the period 1960-2002, expressed in thousand dollars at 1990 pric es 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.
Graph 1. Evolution of total Consumption per inhabitant (thousand dollars at 1990 prices and PPPs)
0 4 8 1 2 1 6 2 0 2 4
1 9 6 0 2 0 0 2
M x
U S A
M x
U S A
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 1960 1985 2002 CH 2.373 3.987 4.735 GH 0.160 0.515 0.485 ZH 2.533 4.502 5.220 Mexico
PH 3.202 5.949 6.809 CH 7.443 13.513 18.719 GH 2.790 3.601 3.997 ZH 10.232 17.114 22.716 USA
PH 12.359 20.321 26.770
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.
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)
2 . 5 3 . 0 3 . 5 4 . 0 4 . 5 5 . 0 5 . 5
3 4 5 6 7 8
P H M P P
ZHMPP
Z H M P P v s . P H M P P
Graph 3. Total Consumption and GDP in the USA (thousand dollars per inhabitant at 1990 prices and PPPs)
8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4
1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8
P H U
ZHU
Z H U v s . P H U
Although the average annual rate of growth of Gdp in Mexico during the period 1960-2002, 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
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 20th 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 20th 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
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)
0 4 8 1 2 1 6 2 0 2 4 2 8
0 0 10 2 0 30 4 0 5 0 60 7 0 80 9 0 00
USA Ir
Mx LatinAmerica
Mexico have experienced important increases in GDP but excessively high rates of Population growth during the second half of the 20th 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 1970-2002.
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 1960-97. 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)
(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, 1971-2002 Pairwise Granger Causality Tests. Sample: 1971 2002. Lags 2 Null Hypothesis: ObsF-Statistic Probability PHMPP does not Granger Cause CHMPP 32 1.08 0.350 CHMPP does not Granger Cause PHMPP 0.46 0.630
Table 2.2. Granger´s test: CH and PH of the USA
Pairwise Granger Causality Tests. Sample: 1971 2002. Lags 2 Null Hypothesis: Obs F-Statistic Probability PHU does not Granger Cause CHU 32 2.84 0.075 CHU does not Granger Cause PHU 6.47 0.005
Results for Mexico and the USA, in 1971-2002: 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
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 1972-2002.
Table 3.1.Modified version of Granger´s test: CH equation: Mexico Dependent Variable: CHMPP. Least Squares. Sample 1972-2002
Variable Coefficient Std. Error t-Statistic Prob.
C 1.259054 0.349587 3.601546 0.0012 CHMPP(-2) -0.240408 0.201714 -1.191826 0.2433 PHMPP(-1) 0.641869 0.118419 5.420333 0.0000 R-squared 0.781290 Mean dependent var 4.026602
Table 3.2.Modified version of Granger´s test: PH equation: Mexico Dependent Variable: PHMPP. Least Squares. Sample 1972-2002 Sample: 1972 2002. Included observations: 31
Variable Coefficient Std. Error t-Statistic Prob.
PHMPP(-2) 0.307631 0.153994 1.997677 0.0552 CHM(-1) 1.897010 0.406603 4.665512 0.0001 R-squared 0.818242 Mean dependent var 5.861435
Table 3.3.Modified version of Granger´s test, CH equation: the USA Dependent Variable: CHU. Least Squares. Sample 1972-2002
Variable Coefficient Std. Error t-Statistic Prob.
C -1.815546 0.631029 -2.877121 0.0076 CHU(-2) 0.343096 0.204235 1.679910 0.1041 PHU(-1) 0.539237 0.156788 3.439279 0.0018 R-squared 0.984192 Mean dependent var 14.03991
Table 3.4.Modified version of Granger´s test, PH equation: the USA Dependent Variable: PHU. Method: Least Squares. Sample 1972-2002
Variable Coefficient Std. Error t-Statistic Prob.
PHU(-2) 0.598651 0.146351 4.090505 0.0003 CHU(-1) 0.644090 0.216985 2.968355 0.0060 R-squared 0.966890 Mean dependent var 21.16482
Results for Mexico and the USA in 1972-2002: 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 1971-2002.
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 -1.709333 0.0825 Augmented Dickey-Fuller test statistic: USA -2.065470 0.0390 Test critical values: 1% level -2.639210
5% level -1.951687
10% level -1.610579
*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.
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 1961-97 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.
Table 5. t Statistics of Hausman´s Test, USA Equation 1962-97 1971-2002 1962-2002
Mx: CH 3.94* -1.16 -0.74
Mx: PH 6.14* -1.86** -9.66*
USA: CHU 4.34* -0.10 0.18
USA: PHU 6.09* 0.50 0.29
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 1962-97 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 1962-2002: 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 1962-2002
Variable Coefficient Std. Error t-Statistic Prob.
CHMPP(-1) 0.998904 0.003632 275.0268 0.0000 D(PHMPP) 0.704250 0.136583 5.156204 0.0000 R-squared 0.992716 Mean dependent var 3.739959 Adjusted R-squared 0.992529 S.D. dependent var 0.616686 S.E. of regression 0.053303 Sum squared resid 0.110808 Durbin-Watson stat 1.143450
Table 6.2. TSLS estimation: CH equation of the USA Dependent Variable: CHU. TSLS. Sample 1962-2002
Variable Coefficient Std. Error t-Statistic Prob.
CHU(-1) 1.011174 0.003282 308.1101 0.0000 D(PHU) 0.369601 0.120084 3.077859 0.0044 R-squared 0.998094 Mean dependent var 13.91607 Adjusted R-squared 0.998030 S.D. dependent var 2.449764 S.E. of regression 0.108732 Sum squared resid 0.354681 Durbin-Watson stat 1.207381
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) 1.010858 0.002609 387.5063 0.0000 C(2) 0.379089 0.090469 4.190249 0.0001 SCE (Mexico) =0.315372 SCE(USA)=0.414844
Durbin-Watson stat Mx: 1.3437 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 1962-2002
Variable Coefficient Std. Error t-Statistic Prob.
PHMPP(-1) 1.002276 0.002989 335.3755 0.0000 D(CHMPP) 1.279795 0.235327 5.438361 0.0000 R-squared 0.995451 Mean dependent var 5.381500 Adjusted R-squared 0.995334 S.D. dependent var 1.014410 S.E. of regression 0.069291 Sum squared resid 0.187247 Durbin-Watson stat 1.195416
Table 6.5. TSLS estimation: PH equation of the USA Dependent Variable: PHU. TSLS. Sample 1962-2002
Variable Coefficient Std. Error t-Statistic Prob.
PHU(-1) 0.970399 0.019394 50.03694 0.0000 D(CHU) 3.356083 1.366106 2.456679 0.0186 R-squared 0.989960 Mean dependent var 19.62040 Adjusted R-squared 0.989703 S.D. dependent var 3.832818 S.E. of regression 0.388936 Sum squared resid 5.899586 Durbin-Watson stat 1.258836
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) 0.988659 0.005779 171.0882 0.0000 C(2) 2.085621 0.409935 5.087682 0.0000 SCE (Mexico)=0.9424 SCE(USA)=1.6286
Durbin-Watson stat Mx: 1.2820 USA: 1.5310
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:
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.31-59.
Dussel, E.(2002). Empleo, productividad y comercio exterior en la economía mexicana. Investigación Económica, UNAM, Mexico.
Granger, C.W.J.(1969). “Investigating Causal Relations by Econometric Models and Cross-spectral Methods”, Econometrica, Vol 37, pp 424-438
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 39-611
Guisan, M.C. (2003). Causality Tests, Interdependence and Model Selection: Application to OECD Countries, 1960-1997”. Working paper of the series Economic Development, no.63.1
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. 68.1
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, pp1583-88.
OECD(2002) and previous issues of National Accounts of OECD countries OECD, Paris
1Information about these publications on www.usc.es/economet/eaa.htm
_____________________________
Journal IJAEQS published by AEEADE: http://www.usc.es/economet/eaa.htm
Annex.
Table A1. CH and PH in Mexico and USA ($90 PPPs) obs CHMPP GHMPP PHMPP CHU GHU PHU 1970 3187 271 4344 9865 3391 15871 1971 3245 290 4379 10077 3264 16122 1972 3352 319 4596 10538 3240 16766 1973 3458 339 4822 10920 3177 17467 1974 3522 349 4955 10764 3226 17239 1975 3610 386 5074 10879 3260 17000 1976 3663 399 5133 11340 3246 17660 1977 3630 383 5157 11667 3268 18228 1978 3816 409 5426 12026 3298 18930 1979 4038 436 5759 12181 3305 19191 1980 4210 463 6047 12048 3318 18856 1981 4415 499 6427 12115 3328 18990 1982 4209 498 6236 12117 3378 18427 1983 3894 500 5835 12550 3416 18882 1984 3933 521 5914 13048 3473 19852 1985 3987 515 5949 13513 3601 20321 1986 3795 511 5608 13883 3706 20723 1987 3714 495 5598 14167 3785 21092 1988 3706 483 5555 14593 3817 21689 1989 3898 484 5675 14801 3849 22192 1990 4069 490 5826 14887 3901 22224 1991 4185 508 5988 14596 3863 21711 1992 4306 508 6099 14822 3796 22028 1993 4295 512 6113 15076 3708 22270 1994 4417 518 6277 15410 3671 22814 1995 3908 499 5759 15655 3619 23125 1996 3928 488 5957 15931 3584 23673 1997 4108 488 6268 16275 3588 24312 1998 4254 491 6467 16857 3602 25067 1999 4331 502 6540 17489 3673 25808 2000 4698 513 6984 18051 3740 26492 2001 4742 498 6850 18320 3848 26308 2002 4735 485 6809 18719 3997 26770 Note: Elaborated from OECD National Accounts, several years.Dollars per inhabitant at 1990 prices and Purchasing Power Parities.
