Osang, Thomas

Southern Methodist University

Law and Business Review of the AmericasVolume 1 | Number 4 Article 51995Do Closer Economic Ties Imply Convergence inIncome - The Case of the U.S., Canada, and MexicoThomas OsangFollow this and additional works at: https://scholar.smu.edu/lbraThis Article is brought to you for free and open access by the Law Journals at SMU Scholar. It has been accepted for inclusion in Law and BusinessReview of the Americas by an authorized administrator of SMU Scholar. For more information, please visit http://digitalrepository.smu.edu.Recommended CitationThomas Osang, Do Closer Economic Ties Imply Convergence in Income - The Case of the U.S., Canada, and Mexico, 1 Law & Bus. Rev.Am. 86 (1995)https://scholar.smu.edu/lbra/vol1/iss4/5Do Closer Economic Ties ImplyConvergence in Income?The Case of the U.S., Canada, and MexicoThomas OsangThis paper searches for empirical evidence for convergence in real GDP per capita betweenthe U.S., Canada, and Mexico. The results of the paper are based on two different conceptsof convergence. First, some simple descriptive statistics are calculated that characterize con-vergence from a static cross-country perspective. Second, based on the concepts of cointe-gration and common trends, the paper estimates the dynamic (long run) relationships inper capita income between the three countries and then tests for convergence. Differentsubgroups of countries as well as the entire sample are considered. Both the static as well asthe dynamic statistics indicate that there is little evidence for convergence in per capitaincome.I. IntroductionThis paper searches for empirical evidence for convergence in real GDP per capitabetween the U.S.A., Canada, and Mexico. Over the last decades, the three countries in gen-eral, and the U.S. and Canada in particular, have strengthened their economic ties by con-tinuously reducing barriers to trade, a development that culminated in the signing and rati-fication of the North American Free Trade Agreement (NAFTA). The question then ariseswhether closer economic ties through increased trade, transfer payments or better policycoordination will help to reduce income differentials over time, as was the case with theEuropean Community/Union (Ben-David, 1993).This question is of substantial relevance for the three NAFTA countries since one of thearguments of the proponents of NAFTA has been that free trade will lessen the income gapbetween the U.S. and Mexico which, in turn, will reduce the level of migration of Mexicanworkers to the United States. While this expectation is certainly correct from the perspectiveof the European Community/Union, it remains an open question at this point whetherNAFTA will have a similar effect on income differentials, in particular since the relativeincome gap between the U.S. and Canada on the one side, and Mexico on the other, is sub-stantially larger than the difference in relative income between the high and the low incomecountries in Europe in 1982, the year when Spain, Portugal and Greece joined the EuropeanCommunity.Nevertheless, it seems interesting to test whether closer economic ties in the decadesbefore NAFTA had any effect on the relative income performance among the three coun-tries. If such a result can be established, it can be interpreted as evidence that NAFTA willThomas Osang is with the Department of Economics at Southern Methodist University, Dallas,Texas. The author would like to thank Herman Bierens for helpfil comments and suggestions.Autumn 1995 87speed up the process of convergence in income levels proclaimed by the proponents of thefree trade agreementII. Empirical LiteratureThe question whether countries converge in income levels has stimulated a large bodyof empirical research. So far, there is support for both convergence and non-convergence.Support for the non-convergence result is based on the observed differences in today's realper capita income among countries (Romer, 1987). In addition, simple cross-countryregressions of average growth rates on initial income levels could not reject the null-hypothesis of zero correlation between the two variables whereas convergence would pre-dict a negative correlation (DeLong (1988), Barro (1991)).There is also empirical evidence in favor of the convergence hypothesis (Mankiw,Romer & Weil, 1992). These findings suggest that cross country regressions that contain aproxy for human capital are able to explain most of the observed cross-country differencesin real per capita income. Furthermore, estimations of this type show the expected negativecorrelation between initial income levels and subsequent average growth rates. This result,however, may be spurious due to the problem of regression towards the mean (Quah,1993).Recently, Bernard (1991) and Bernard and Durlauf (1991, 1993) proposed an alterna-tive approach to test for convergence in income across countries. Their approach focuses onthe longrun or asymptotic behavior of the income series. We will therefore refer to theirdefinition as 'asymptotic convergence'The advantages of the Bernard and Durlauf approach are as follows. First, it avoids thepitfall of regression towards the mean that devalues the standard cross-country growthregressions described above. Second, in the case that income levels among countries followa common trend, we can determine whether income differentials are temporary or perma-nent. Finally, even if the hypothesis of asymptotic convergence is rejected for the entiresample, we can still look for asymptotic convergence among subgroups of countries.Ill. Cointegration and ConvergenceFollowing Bernard (1991) we test for convergence in income levels using stochastic def-initions of both common trends in time series data (cointegration) and a common long runresponse to shocks. In particular, by imposing restrictions on the rank and the parametervalues of the cointegrating matrix, we derive a definition of asymptotic convergence.21. Using time series data from 1900 to 1987, Bernard and Durlauf test for cointegration andasymptotic convergence in GDP per capita for 15 OECD countries. Their findings suggest two ornine common trends depending on the VAR lag length. Since their definition of convergencerequires that countries share only one common trend, they reject the convergence hypothesis forthe entire sample.2. Definition 3.1 corresponds to definition 2.5 in Bernard (1991).88 NAFTA: Law and Business Review of the AmericasDefinition 3.1 Asymptotic convergence in multivariate per capita output Per capita out-puts in countries 1, ..., p converge if Yi, ..., Yp, contain stochastic trends and ifliram /,/ IZ- _E(3'Y,.+ I atl)=and#'=[lI,-1 I (1)where Yi, is income per capita in country i at time 4 Q is the information set at time t, fP is thecointegrating matrix, and e-1 is a (p-I) vector of ones.Definition 2.1 adds two qualifications to the definition of cointegration. Convergenceamong time series data requires that the cointegrating matrix must be of rank p - 1.Furthermore the p - 1 independent column vectors of fP must take the form of the identitymatrix with an additional first row of (minus) ones. Definition 2.1 requires that the systemof time series contains only one common trend or, equivalently, that there are p - 1 cointe-grating vectors. If, in addition, all countries have the same (long run) response to a shock attime tincome disparities between countries will eventually disappear.We will apply this definition of asymptotic convergence to income data from the U.S.,Canada, and Mexico in section V.IV Data and Simple Descriptive StatisticsIn order to test for convergence in income levels we use annual data on per capita GDP(in 1985 international dollars). The sample period is 1950 to 1990. The GDP data are takenfrom an updated version of Summers and Heston (1988).Figure 1 shows the three income series over the entire sample period. The figure showsthat, in absolute terms, the income gap between Mexico and either the U.S. or Canadabecame larger during the sample period while it became somewhat smaller between theU.S. and Canada. The more important question is, though, whether there has been anymajor change in relative per capita income between the three countries.Some descriptive statistics which are reported in Table I and 2 shed some light on thisquestion. Table 1 shows that Mexico has, on average, a lower investment share but higherGDP and population growth than the U.S. or Canada.Despite the higher GDP growth rate, Mexico could not catch up with its neighborcountries in terms of per capita GDP due to the higher population growth rate. This factcan be seen from Table 2. The coefficient of variation of per capita GDP drops only slightlyfrom .57 in 1950 to .53 in 1990 despite a temporary decline to .44 at the beginning of theeighties. The descriptive statistics in Table 1 and 2 thus indicate that stronger economic tiesthrough more trade in goods and services had, at best, a minor influence in the reduction ofthe relative income gap between the NAFTA countries. In the next section we investigatewhether the corresponding long-run relationships in per capita GDP between the threecountries point to a similar conclusion.V Econometric Methodology and Empirical ResultsIn order to test for cointegration, one first has to determine whether each time series inthe sample contains a unit root. Table 3 summarizes the values of the augmented Dickey-Fuller test for each country and two different lag lengths. Independent of the lag length,none of the reported "t-statistics" is higher than the critical value at the 5%-level of the cor-Autumn 1995 89responding Dickey-Fuller table (see Harvey (1990), p. 368).3 Therefore, we cannot reject thenull hypothesis of a unit root for any of the three GDP series.We test for cointegration using the method of Johansen (Johansen (1988), Johansenand Juselius (1990)). We calculate a likelihood ratio statistic (the trace statistic) in order todetermine the rank of the cointegrating matrix.4 Furthermore, we use another likelihoodratio statistic to test constraints on the parameter values of the cointegrating matrix provid-ed that the time series in question share exactly one common trend. Under the null hypoth-esis of convergence, test statistics that are larger than the critical value at the 5% level aretaken as strong evidence against asymptotic convergence.The test results for cointegration and asymptotic convergence for the entire sample aswell as for all subgroups are presented in Tables 4 and 5. The likelihood ratio statistic inTable 4 indicates the existence of one cointegrating vector which, in turn, implies that thethree countries share at least two common trends. Since a necessary condition for asymp-totic convergence is that there exist only one common trend, the result implies that there isno evidence for asymptotic convergence in GDP between the U.SA., Canada, and Mexico.This result confirms our interpretation of the descriptive statistics in the previous section.It is interesting to see, however, whether we can find evidence for convergence inincome for any subgroup of countries. Table 5 presents the results for the three subgroups.At the 5% level, the likelihood ratio statistic indicates one cointegrating relationship andhence one common trend for each subgroup. In this case, we can test parameter restrictionson the cointegrating matrix, i.e., we can test for asymptotic convergence.In the case of the U.S. and Canada, the likelihood ratio test statistic rejects the con-straints on the values of the cointegrating vector at the 5% level. We therefore reject the nullhypothesis of asymptotic convergence. In the case of the U.S. and Mexico we can reject theimposed restrictions on the cointegrating vector at the 10% level but we cannot reject themat the 5% level. This result, however, cannot be interpreted as evidence for asymptotic con-vergence since the cointegrating equation for these two countries requires a constant. Thismeans that even if the cointegrating vector happens to be equal to (1, -1), the two incomeseries would not converge. Rather, the difference in income levels would neither increasenor decrease but remain constant over time and the value of the constant would be equal tothe expected value of the income difference. Finally, we dearly reject the convergence null inthe case of Canada and Mexico.VI. Summary and ImplicationsStatic descriptive statistics as well as estimates of the dynamic long-run relationshipsuggest little evidence in favor of convergence in per capita income between the U.S.,Canada, and Mexico for the time period between 1950 and 1990. Relative income differ-ences remain more or less constant over the sample period. This is true for the whole sam-3. We also ran an augmented Dickey-Fuller test in first differences. The results of this test indicatethat all three series are first difference stationary processes.4. We also employed a non-parametric cointegration test developed by Bierens (1994). The resultsof this test indicate the same number of cointegration relationships as the Johansen test. Theresults of the non-parametric test for cointegration can be obtained from the author uponrequest.90 NAFTA: Law and Business Review of the Americaspie as well as for all bivariate groups. We observe, however, that per capita GDP in all bivari-ate groups follows a common stochastic trend. If we look at all three countries together, wefind evidence for at least two common trends.Despite the fact that there is little evidence for convergence, the question arises whetherthere is a meaningful economic interpretation of the observed common long run move-ments in per capita GDP. Clearly, in order to transmit economic shocks from one countryto the other, it is necessary that countries engage in trade with each other. All countries inthe sample have strong trade relations with each other, which may explain why there is evi-dence for common trends among them. In this sense, strong economic ties may explain thecomovement of economic time series such as GDP. These economic ties, however, may notbe sufficient to overcome large historic income gaps. After all, the income gap between theU.S. and Canada in 1950 was just one third of the income gap between the U.S. and Mexicoat the same time. Free trade agreements may therefore be just a first step towards a moreequal income distribution among countries. To achieve real income convergence, strongermeasures such as transfer payments from the high to the low income countries to financeinfrastructure, investment in human capital, and small business loans may be necessary.AppendixTABLE 1: SUMMARY STAISTics (TIME AVERAGE, 1950 To 1990)Country Investment share GDP growth Population growthU.S.A. 24.18% 3.4% 1.3%Canada 25.84% 4.4% 1.7%Mexico 17.58% 5.1% 2.8%Source: Updated version of Summers and Heston (1988)TABLE 2: COFICIENT OF INCOME VARILTON, 1950 TO 19901950 0.571954 0.561958 0.521962 0.541966 0.531970 0.501974 0.491978 0.501982 0.441986 0.531990 0.53Source: Updated version of Summers and Heston (1988)Autumn 1995 91Table 3: Testing for unit roots (augmented Dickey-Fuller test)Regression equation: AY,, = c + 'yiY,,- 1 + E: -, bijA ,ti + c,,lag length "t-statistic" for jq U.S.A. I Canada Mexico 5% Critical Value1 .550 .812 -.827 -2.93782 .743 1.025 -.933 -2.9399Table 4: Multivariate tests for cointegration and convergence (All 3 countries)Likelihood ratio statisticH'(f): [( )_#:2 )< r(P) =oUSA, CAN, MEX 1.469 9.77 29.26'5% Critical Value 3.84 12.53 24.31*: null hypothesis rejected at 5% signiicance levelTable 5: Multivariate tests for cointegration and convergence (groups with 2 countries)likelihood ratio statisticH_(_)_ : _ r(D) 1 r(P) = 0 Coint. vector LR test of constraints on paramnters"USA,CAN .37 13.40" 1 - .74 4.425% Critical Value 3.84 12.53USA,MEX 3.92 23.94" 1 - .36 3.415% Critical Value 9.24 19.96CAN,MEX 3.82 20.14" 1 - .29 6.885% Critical Value 9.24 19.96*: null hypothesis rejected at 5% significance levela. 5% critical value: 3.84; 10% critical value: 2.7192 NAFTA: law and Business Review of the AmericasFigure 1: Per capita GDP from 1950 to 1990 (in 1985 international dollars)1800016000 U.S.A.CanadaMexico14000120001000080006000400020001950 1955 1960 1965 1970 1975 1980 1985 1990Autumn 1995 93ReferencesBarro, R. (1991). Economic Growth in a Cross section of countries. Quarterly Journal ofEconomics, 106,407-443.Ben-David, D. (1993). Equalizing Exchange: Trade Liberalization and Income Convergence.Quarterly Journal of Economics, 108(3), 653-679.Bernard, A. (1991). Empirical Implications of the Convergence Hypothesis. Working Paper,Stanford University.Bernard, A., & Durlauf, S. (1991). Convergence of International Output Movements. NBERWorking Paper No. 3717.Bernard, A., & Durlauf, S. (1993). Convergence in International Output Working Paper No.93-7, MIT.Bierens, H. (1994). Nonparametric Cointegration Analysis. Working Paper, SouthernMethodist University.DeLong, J. (1988). Productivity Growth, Convergence, and Welfare: Comment AmericanEconomic Review, 78, 1138-1154.Harvey, A. C. (1990). The Econometric Analysis of Time Series. The MIT Press, Cambridge,MA.Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. 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