Journal of Macroeconomics, Spring 1997, Vol. 19, No. 2, pp. 285–304 285Copyright � 1997 by Louisiana State University Press0164-0704/97/$1.50

TAUFIQ CHOUDHRYUniversity of Wales

Swansea, United Kingdom

Stochastic Trends in Stock Prices:Evidence from Latin AmericanMarkets*

This paper investigates the long-run relationship between stock indices from six Latin Americanmarkets and the United States. The empirical investigation is conducted using weekly data fromJanuary 1989 to December 1993, unit root tests, cointegration tests, and error-correction mod-els. Results from the unit root tests provide evidence of a stochastic trend in all indices. Resultsfrom the cointegration tests indicate the presence of a long-run relationship between the sixLatin American indices (with and without the United States index). Error-correction resultsindicate significant causality among the stated indices.

1. Introduction

In recent years the quantity of research on interdependence of stockmarkets has been high and extensive (Corhay, Tourani, and Urbain 1993;Koch and Koch 1991). In an integrated world equity market, individual stockprices are expected to have long-run relationships, i.e. share common sto-chastic trend(s).1 There are several reasons why different countries’ stockprices may have a significant long-run relationship(s). The presence of strongeconomic ties and policy coordination between the relevant countries canindirectly link their stock prices over time. Stock prices are affected by realinterest rate movements, thus real interest rates linkage between countriesdue to international capital flows can contribute to long-term relationshipsbetween different stock prices. The importance of international investors

*I thank two anonymous referees for several helpful comments and suggestions. The re-maining errors and omissions are my responsibility alone.

1Baillie and Bollerslev (1989) and Hakkio and Rush (1989) claim that in an efficient market,assets prices cannot have a long-run relationship(s). According to these studies, in an efficientmarket, changes in asset prices cannot be predicted but deviations of prices from a long-runrelationship indicates predictable future changes. Dwyer and Wallace (1992) show that thereis no general equivalence between market efficiency and lack of a long-run relationship betweenassets. Dwyer and Wallace base their analysis on zero transaction cost assumption and marketefficiency defined as the lack of arbitrage opportunities.

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can further induce co-movements in national stock prices. Jeon and Chiang(1991) state that international linkage between different equity marketscould also be due to the recent deregulation and liberalization of differentmarkets, improvement and development of communications technology, in-novations in financial products and services, increase in the internationalactivities of multinational corporations, etc.

This paper provides an investigation of long-run relationship(s) be-tween six Latin American stock indices and the United States stock index.Stock price indices from Argentina, Brazil, Chile, Colombia, Mexico, andVenezuela are used in the empirical investigation. The stated markets arepart of what is known as emerging markets.2 During the last decade or sothe world financial market experienced a rapid growth in emerging stockmarkets (IFC 1993). From 1982 to 1992, the emerging markets increasedtheir market capitalization from $67 billion to $770 billion and nearly tripledtheir share of world equity capitalization from 2.5% to 7.0% (IFC 1993).From 1988 to 1992, markets in Argentina, Chile, Colombia, Mexico, andVenezuela rose more than 100% in dollar terms as compared to 51% rise inthe United States market. International portfolio investment in the devel-oping countries has grown to $50 billion in 1992 from a few hundred milliondollars in the early 1980s (IFC 1993). The volume of international equityissues in these markets grew from $0.1 billion in 1989 to $6.2 billion in 1992.Emerging markets offer significant diversification potential for global port-folios. Individually, these markets are quite volatile, but as a group their risk-adjusted return has been higher than that of developed markets (IFC 1993).Table 1 presents in United States dollars and the percentage share of eachof the six stated markets of the Latin American, part of the total emergingmarkets capitalization and also the latest investment regulations in thesemarkets. Mexico clearly dominates the Latin American stock markets. Inrecent years, these markets have been more open and available to foreigninvestors (IFC 1993). According to the IFC 1993 report, in the late 1980semerging markets as a group generally outperformed the developed mar-kets. The recent rapid growth in the markets under consideration here couldbe due to several different reasons. Some of the factors may be the recentchanges seen in the developing countries such as adoption of more market-oriented policies, restructuring of the corporate sector, opening of differentsectors of the economy to foreign investors, privatization of state-ownedenterprises, strong economic growth which resulted in strong corporategrowth, a wide and broader range of financial and institutional reforms, etc

2This paper applies the International Financial Corporation’s (IFC) definition of emergingmarkets. IFC defines an emerging market as any market in a developing economy, with theimplication that it has all the potential for development.

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TABLE 1. Market Capitalization and Investment Regulations

Markets

CapitalizationShare 1992US$ & %

Restrictions onForeignInvestors

Repatriationof Income

Repatriationof Capital

Argentina $22 bil 9% Free Entry Free FreeBrazil $44 bil 18% Free Entry Free FreeChile $29 bil 12% Relatively Free Free After 1 yearColombia $5 bil 2% Free Entry Free FreeMexico $139 bil 57% Relatively Free Free FreeVenezuela $7 bil 3% Relatively Free Free Free

NOTE: Source: IFC (1993).Total Emerging Market Capitalization 1992 � $740 billion.Latin American Market share 1992 � $244 billion (33%).Investment Regulations at March 31, 1993.

(IFC 1993). Given the current status of the emerging stock markets, it is ofinterest to check for common stochastic trend(s) among some of these mar-kets. Using the log of weekly stock indices from January 1989 to December1993, we test for long-run relationship(s) between Argentina, Brazil, Chile,Colombia, Mexico, Venezuela (and the United States) stock markets.

In this paper cointegration tests are applied to check for stationarylong-run multivariate equilibrium relationships between the different stockindices.3 Two different long-run relationships are tested for stationarity.First, cointegration tests are conducted between the six Latin American in-dices and then in the second test the United States stock price index is alsoadded. In this manner we test for a possible multivariate long-run stationaryrelationship(s) between the major emerging market stock indices in LatinAmerica, and also between these indices and a major developed market stockindex.4 The empirical investigation of the individual stochastic structure isconducted by means of the augmented Dickey-Fuller test and variance ratiotest. The Johansen method of the multivariate cointegration test is appliedto check for a common stochastic trend(s) in a system of different stockindices.

Cointegration also implies that the transitory components of the series

3Jeon and Chiang (1991), Corhay, Tourani, and Urbain (1993), Choudhry (1994) and Black-man, Holden, and Thomas (1994) have also studied long-run relationships between differentstock indices using cointegration.

4Chowdhury (1994), Chung and Liu (1994) and Chan, Gup, and Pan (1992) provide similarstudies of the relationship between the United States and some of the Far East emerging stockmarket indices.

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TABLE 2. Basic Statistics: Weekly Data from January 1989 to December1993

Log of Indices N Mean Variance Skewness Kurtosis

Argentina 257 6.308a 0.546 �0.170 �1.365a

Brazil 257 4.644a 0.138 �0.356b �0.309Chile 257 7.032a 0.259 �0.229 �1.668a

Colombia 257 6.145a 0.440 0.316b �1.715a

Mexico 257 6.940a 0.291 �0.347b �1.226a

Venezuela 257 5.172a 0.647 �0.608a �1.184a

United States 257 5.927a 0.018 �0.189 �1.026a

NOTE: a & b imply significance at 1% & 5% level, respectively.N � Number of observations.

can be given a dynamic specification by means of the error-correction models(Engle and Granger 1987). In other words, a constrained error-correctionmodel that captures the short-run dynamic adjustment of cointegrated vari-ables can be applied. In this paper, such models are applied to investigatethe temporal causality between the different stock indices.

As stated above, the data applied are weekly, ranging from January1989 to December 1993 and are in logarithmic form.5 The stock indicesapplied are the International Financial Corporation stock indices and are indollar terms. All the data are obtained from DATASTREAM. Table 2 pro-vides certain statistics of each of the series in log. All six Latin Americanindices seem to display similar characteristics. All series (including theUnited States index) show negative skewness, but all show nonsymmetry ofsmall magnitude. All series have negative and significant kurtosis, except forthe Brazilian index. Thus, all series (including the United States) seem tohave thinner tails than a normal distribution. As expected, the United Statesseries seems to show much less variance than any of the Latin Americanseries.

2. Estimation Procedures of the Stochastic Trend(s)

Cointegration requires a certain stochastic structure of the individualtime series. In our case, all individual variables should be stationary afterfirst differences and nonstationary in levels, i.e., all series should contain a

5The use of higher frequency data such as weekly, daily, etc. is preferred to lower frequencydata in view of the speedy transmission of information between markets (Fang, Lai, and Lai1991).

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stochastic trend (unit root). Individual stochastic trends are checked by twodifferent tests, the augmented Dickey-Fuller test (ADF) (Said and Dickey1984) and the Variance ratio test (Cochrane 1988).

Augmented Dickey-Fuller TestThe Dickey-Fuller test can be applied both in the case of a lower and

a higher autoregressive (AR) process.6 The following equation presents ahigher AR process version (with a constant and a time trend) of the Dickey-Fuller test:

N2DY � � � bt � (q � 1)Y � UDY � e , e � IID(0, r ) , (1)t t�1 � i t�i t t

i�1

where Yt presents a time series, D implies first difference, and t is the timetrend. This test is known as the “augmented Dickey-Fuller test” (ADF) (Saidand Dickey 1984). According to Said and Dickey (1984) the ADF test pro-cedure is valid for a general ARMA process in the errors. The null hypothesisin the ADF test is unit root (q � 1). For Yt to be stationary, (q � 1) shouldbe negative and significantly different from zero. Since for q � 1 the dis-tribution of the standard t-statistics is not asymptotically normal or evensymmetric (Banerjee et al. 1993), the proper critical values required in theADF tests are provided by Fuller (1976).7 According to Schwert (1989),DeJong et al. (1992) and Banerjee et al. (1993) the ADF test provides morerobust results than any other unit root test in the presence of autoregressiveerrors. This is because the ADF regression is able to capture the autore-gressive terms precisely.

Variance Ratio TestThe measurement of the degree of persistence in a time series is an-

other way of evaluating the presence of a stochastic trend. By determining

6The autoregressive (AR) process implies a linear relationship between the current value ofa time series and the previous value(s) of the series and a random shock. Fewer previous valuesin the relationship will result in a lower AR process. The following presents an autoregressivetime series:

N

x � q x � e ,t � i t�1 ti�1

where et is a white noise error process.7The Dickey-Fuller test may also be conducted with the joint null hypothesis being (q � 1)

� b � 0. According to Banerjee et al. (1993) in a finite sample the joint hypothesis methodmay not be a better approximation. Second, to apply the joint hypothesis method, the correctionspecification of the data generating process has to be known with sufficient confidence (Harris1995).

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the long-run response of a time series to a shock, one can obtain an estimateof the degree of persistence. Cochrane (1988) and Lo and MacKinlay (1988)provide a method of measuring the degree of persistence in a time series.This test assumes that the change in the variable is a stationary process whichcan be presented by a moving average:

DY � A(L)e , (2)t t

where e is a white noise and A(L) is a finite polynomial in the lag operator.Persistence is implied by the size of Yt�k � Yt as k approaches infinity, andthis equals the infinite sum of the moving average coefficients 1 � A1 � A2

� . . . . etc. Cochrane derives his persistence measurement by decomposingEquation 2 into a stationary and random walk component. According toCochrane (1988), if a time series is a pure random walk, then variance of itsk-differences grows linearly with k; that is, the variance grows with time.Thus, in the case of a random walk, the variance of the k-difference is ktimes the variance of the first difference:

var(Y � Y ) � k � var(Y � Y ) . (3)t t�k t t�1

From Equation 3 the variance ratio test (VR) proposed by Cochrane is equalto

VR � (1/k) � var(Y � Y )/(Y � Y ) . (4)t t�k t t�1

A persistence measurement (VR) of about unity or higher indicates the pres-ence of a stochastic trend. If the series is trend stationary, VR approacheszero as k approaches infinity. Thus, if stock prices are stationary around adeterministic trend, shocks to prices will not be persistent and estimates ofVR will be close to zero at least for large k. VR should grow linearly as kincreases if the series contains a large size permanent component. If theseries is a pure random walk, the value of VR should be equal to one.8

According to Campbell and Mankiw (1987) and Demery and Duck (1992)there is a downward bias in VR; this implies that the measurement of per-sistence should be corrected by multiplying by (T/T � k), where T is thenumber of observations. Lo and MacKinlay (1989) show that the varianceratio procedure compares favorably to the Dickey and Fuller procedures intests of random walk behavior. According to Lo and MacKinlay (1989, 205)the variance ratio test is preferred over the unit root test when the attribute

8Demery and Duck (1992), Raj (1993), and Urrutia (1992) also provide analyses of the var-iance ratio test.

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of interest is the non-correlation of increments. They also advocate the useof the variance ratio test because its limiting distribution is Gaussian andindependent of any nuisance parameters. Lo and MacKinlay (1988) providevariance ratio homoskedasticity and heteroskedasticity consistent test statis-tics (Z-statistics) used to test the null hypothesis of a random walk. Theheteroskedasticity-consistent Z-statistics are applied in this paper to test thenull hypothesis of a random walk for each of the stock price series.

(iii) Cointegration TestsA system of nonstationary individual stock prices in levels can, how-

ever, share common stochastic trend(s). Put simply, two or more nonsta-tionary time series are cointegrated if a linear combination of these variablesis stationary, that is, converges to an equilibrium over time.9 The main ideabehind cointegration is a specification of models that include beliefs aboutthe movements of variables relative to each other in the long-run, such asmultivariate relationships between different stock indices. Thus, a commonstochastic trend(s) in a system of stock prices can be interpreted to meanthat the stochastic trend in one individual stock price is related to the sto-chastic trend in some other individual stock price. There exists more thanone method of conducting cointegration tests. The long-run relationshiptests in this paper are conducted by means of the method developed byJohansen (1988) and Johansen and Juselius (1990). This procedure providesmore robust results when there are more than two variables (Gonzalo 1994)and when the number of observations is greater than 100 (Hargreaves 1994).The Johansen maximum likelihood approach sets up the nonstationary timeseries as a vector autoregressive (VAR):

N

DX � C � CDX � IIX � g , g � niid(0, d) , (5)t � i t�i t�1 t ti�1

where Xt is a vector of nonstationary (in levels) variables, D implies firstdifference and C is the constant term. The information on the coefficientmatrix between the levels of the series P is decomposed as P � �b� wherethe relevant elements of the � matrix are the adjustment coefficients andthe b matrix contains the cointegrating vectors. The constant term is in-cluded to capture the trending characteristics of the time series involved.10

9Detailed analysis of the concept of cointegration is provided in several articles and books,such as Dickey and Rossana (1994) and Harris (1995).

10As indicated by Harris (1995) and Johansen (1992) the choice of deterministic componentin the model has consequences for the asymptotic distribution of the rank test statistics. It isvital in cointegration tests to determine the rank and the specification of the deterministiccomponent of the model.

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TABLE 3. Augmented Dickey-Fuller Test

Log of Stock Indices Null: Single Unit Root Null: Two Unit Roots

Argentina �2.756/(3) �7.438a/(3)Brazil �1.765/(0) �13.696a/(0)Chile �1.440/(3) �12.708a/(0)Colombia �2.722/(9) �3.979a/(9)Mexico �1.613/(0) �13.614a/(0)Venezuela �0.650/(3) �12.229a/(0)United States �3.236/(0) �18.347a/(0)

NOTE: a & b imply rejection of the null at 1% & 5% level, respectively.Significant number of lags in parentheses.

The Johansen method provides two different tests, the trace test and themaximum eigenvalue test to determine the number of cointegrating vec-tor(s).11 If a nonzero vector(s) is indicated by these tests, a stationary long-run relationship(s) between the relevant variables is implied. According toGonzalo (1994, 221), the performance of the Johansen method is still morerobust than the other cointegration methods even when the errors are non-normal (non-Gaussian). Osterwald-Lenum (1992) provides the appropriatecritical values required for these tests.

3. Unit Root and Cointegration Tests Results

Individual Stochastic TrendTable 3 presents the results from ADF tests. As stated earlier, all series

are applied in logarithmic form. Based on the evidence provided by theAkaike information criterion (AIC) the maximum number of lags applied inthe ADF tests is twelve. Lags that were insignificant according to the stan-dard F-test were dropped from the formulation, unless their eliminationproduced serial correlation. Following the suggestion by Dickey and Pantula(1987), ADF tests are first conducted for two roots and, if two roots arerejected, then a single unit root is tested for. When the null hypothesis istwo unit roots, the time trend is excluded from the ADF test. Both theconstant and the time trend are included when the null hypothesis is one

11According to Cheung and Lai (1993) the trace test shows more robustness to both skewnessand excess kurtosis in the residuals than the maximum eigenvalue test. Further, according toKasa (1992), the trace test tends to be more powerful than the maximum eigenvalue test whenthe eigenvalues are evenly distributed.

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unit root. In this manner, the two unit roots test allows for an alternativehypothesis of stationary with a nonzero intercept on the differenced series,while the single unit root test allows for the alternative hypothesis of trendstationary and a nonzero intercept on the series in levels.

ADF tests results indicate that stock indices from all Latin Americancountries and the United States index are able to reject the two unit roothypothesis, but are unable to reject the one unit root hypothesis. Thus, ADFtests results show that all seven stock indices series are stationary after firstdifference, and are nonstationary in levels, that is, all indices contain a unitroot.12,13

Table 4 presents the results from the variance ratio (VR) test and theZ-statistics. For all series the maximum length of the window size (k) appliedis 25.14 For indices from Chile, Colombia, Mexico, and Venezuela, the valueof VR stays above unity at all sizes of k. The persistence measurement alsoincreases as the window size (k) is increased. The Z-statistics indicate thatpersistence measurement is significantly different from unity in all series atall size of k (except when k is equal to 4 for Venezuela). At all size of k theindex for Argentina is insignificantly different from unity, implying a randomwalk at all lag lengths. The value of VR increases uniformly till k is equal to6, then starts to decrease. In the case of the Brazilian index, VR stays aboveunity until k is equal to 20, and it grows until k is equal to 6. According tothe Z-statistics, the index from Brazil contains more persistence than a ran-dom walk until k is equal to 6, and after that it is a random walk at all laglengths. For the United States, the series is found to be a random walk atall lengths except when k is equal to 2, where the index has less persistencethan a random walk. The variance ratio test and the Z-statistics show that all

12The stock index from the United States is able to reject the null hypothesis of a single unitroot at the 10% (but not at the 5% level), thus providing some indication that the series maybe stationary in levels. This result implies that the weak form of efficient market hypothesismay be rejected in the United States stock market. Such a result calls for more thoroughempirical investigation of the United States market over recent years.

13As indicated by one of the referees, high frequency data usually follow a GARCH processand conditional heteroskedasticity may have some adverse effect(s) on the ADF tests. As indi-cated by Kim and Schmidt (1993), the ADF tests are reasonably robust to GARCH errors withparameter values in the range most likely to be encountered. They further assert that parametervalues that would yield serious inaccuracies should not be expected in empirical work. Firstdifferences of all seven stock series were investigated for the GARCH process. In all the LatinAmerican series we fail to find the errors nearly integrated, and, in the case of the United States,the volatility parameter is found to be very small in size. Thus, the parameters values in ourcase would not yield serious errors in the ADF tests. The GARCH process test results areavailable on request.

14The window size (k) is in weeks. According to Campbell and Mankiw (1987, 1989), k shouldbe small in comparison to the sample size.

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TABLE 4. Variance Ratio Test, Log of Indices

k Argentina Brazil Chile Colombia Mexico Venezuela U.S.

1 1.00 1.00 1.00 1.00 1.00 1.00 1.002 0.95 1.14b 1.22a 1.14b 1.15b 1.25a 0.86b

(�0.82) (2.52) (3.40) (2.20) (2.31) (3.95) (2.26)3 0.96 1.21b 1.33a 1.31a 1.25a 1.40a 0.87

(�0.40) (2.21) (3.48) (3.30) (2.61) (4.24) (�1.37)4 1.05 1.25b 1.41a 1.42a 1.30b 1.05 0.86

(0.40) (2.21) (3.45) (3.57) (2.56) (0.41) (�1.16)5 1.06 1.26b 1.48a 1.52a 1.35b 1.64a 0.88

(0.45) (1.88) (3.48) (3.74) (2.56) (4.61) (�0.91)6 1.04 1.27c 1.55a 1.64a 1.40a 1.74a 0.85

(0.27) (1.71) (3.57) (4.10) (2.60) (4.78) (�1.00)7 1.02 1.24 1.62a 1.73a 1.45a 1.85a 0.83

(0.13) (1.42) (3.62) (4.28) (2.64) (4.97) (�1.00)8 1.01 1.23 1.67a 1.85a 1.49a 1.96a 0.83

(0.07) (1.26) (3.65) (4.61) (2.66) (5.21) (�0.93)9 1.00 1.22 1.73a 1.99a 1.51b 2.06a 0.81

(0.00) (1.13) (3.68) (4.99) (2.56) (5.39) (�0.95)10 0.96 1.21 1.78a 2.09a 1.53b 2.16a 0.82

(�0.18) (0.97) (3.65) (5.15) (2.47) (5.44) (�0.86)15 0.82 1.11 1.93a 2.31a 1.61b 2.57a 0.81

(�0.68) (0.42) (3.50) (5.00) (2.29) (5.94) (�0.74)20 0.75 0.93 1.86a 2.32a 1.62b 2.80a 0.77

(�0.81) (�0.24) (2.78) (4.27) (2.00) (5.82) (�0.75)25 0.71 0.79 1.77b 2.29a 1.59c 3.00a 0.67

(�0.83) (�0.60) (2.21) (3.72) (1.71) (5.80) (�0.95)

NOTE: a, b, & c rejects the null of unity at 1%, 5%, & 10%, respectively.Z-statistics in the parentheses.

six indices from Latin America are either a random walk or have more per-sistence than a random walk. In other words, all series are shown to benonstationary in levels.15

15Kormendi and Meguire (1990) provide an alternate test for random walk null in the varianceratio test. According to their test, variance ratio estimates for Brazil, Chile, Colombia, Mexico,and Venezuela are above the 90% fractile, implying that these series contain a large randomwalk component, while estimates from Argentina and the United States indicate a reasonablesize stationary component. Kormendi and Meguire (1990) provide the confidence intervalsbased on the number of observations being equal to or less than 117. In our paper, the number

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TABLE 5. Cointegration Test ResultVariables: Log of indices from Argentina, Brazil, Chile, Colombia, Mexico,and VenezuelaLags in the VAR � 4

Vectors Trace Test Eigenvalue Test

r � 0 113.69a 48.51a

r � 1 65.18 27.06r � 2 38.12 18.85r � 3 19.27 10.55r � 4 8.72 6.15r � 5 2.57 2.57

Normalized EquationArgentina Brazil Chile Colombia Mexico Venezuela

1.00 0.897a �0.863a �0.283 1.459a 0.514b

Multivariate Diagnostic TestsAutocorrelation:LM(1) Chi-square(39) � 1.90LM(4) Chi-square(39) � 2.03Normality:Chi-square(14) � 2.52ARCH process:Chi-square(3) � 2.16

NOTE: a, b, & c imply significance at 1%, 5%, & 10% respectively.

Common Stochastic TrendTables 5 and 6 present the results from the cointegration tests.16 The

number of lags used in the VAR is four when the test does not include theUnited States index, and three lags are applied when the United States indexis included. Lags are chosen based on the evidence provided by the AIC.Both tests (with and without the United States index) indicate the presence

of observations is 257, so the results from the Kormendi and Meguire (1990) test may not berobust.

16At first a joint hypothesis of rank order determination and deterministic components in themodel specifications were conducted. Following the Pantula principle (Pantula 1989) the mostrestricted model is investigated first until the proper model is accepted. In both models onlyan intercept in the short-run model is required. Results from the joint hypothesis are availableon request.

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TABLE 6. Cointegration Test ResultVariables: Log of indices from Argentina, Brazil, Chile, Colombia, Mexico,Venezuela, and the United StatesLags in the VAR � 3

Vectors Trace Test Eigenvalue Test

r � 0 135.87b 44.84r � 1 91.04 33.22r � 2 57.82 21.04r � 3 36.78 16.44r � 4 20.34 11.95r � 5 8.39 5.59r � 6 2.80 2.80

Normalized EquationArgentina Brazil Chile Colombia Mexico Venezuela U.S.

1.00 1.455a �1.639a �0.454b 0.561a 1.104a 4.370a

Multivariate Diagnostic TestsAutocorrelation:LM(1) Chi-square(36) � 1.44LM(4) Chi-square(36) � 1.61Normality:Chi-square(12) � 2.21ARCH process:Chi-square(4) � 2.49

See note at the end of table 5.

of a nonzero cointegrating vector at the 5% level or above. Only the tracetest indicates a nonzero vector (at 5% level) when the United States indexis included (Table 6). In other words, we are able to find a stationary long-run relationship between the stated Latin American indices (with and with-out the United States index). The residuals seem to pass all the diagnosticstests, such as serial correlation, nonnormality, and ARCH process. Findinga long-run relationship between different stock indices is not surprisingkeeping in mind the considerable globalization of emerging markets in the1980s and 1990s (IFC 1993).

The significant cointegrating vector(s) are given economic meaning

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using normalization on the log of the stock index of Argentina.17 The nor-malized vectors present the implied long-run effects imposed by the vari-ables. Using the likelihood ratio test (chi-square test) all the variables aretested for significance. In the first relationship (Table 5) all coefficients aresignificantly different from zero, except for the Colombian index. The largestcoefficient (in absolute terms) is on the Mexican index (1.46) and the smallest(and insignificant) coefficient is on the Colombian index (�0.283). The Mex-ican market in 1992 made up 57% of the Latin American share of the totalemerging markets capitalization (IFC 1993). This fact may explain the largeeffect imposed by the Mexican index in the relationship. The Colombianmarket on the other hand made up only 2% of the Latin American share ofthe total emerging markets capitalization (IFC 1993).18 In the second rela-tionship (Table 6) all coefficients are significant. The largest coefficient (inabsolute terms) is on the United States index (4.73) and the smallest on theColombian index (�0.454). The size of the share of the world market cap-italization may once again be the reason behind the magnitude of the influ-ence of the variables. In 1993, the United States made up 37% of the worldmarket capitalization, while the entire emerging markets made up only 12%(Economist 1994).19

4. Error-Correction Model and Results

Cointegration also implies that the transitory components of the seriescan be given a dynamic error-correction representation, i.e., a constrainederror-correction model can be applied that captures the short-run dynamicadjustment of cointegrated variables (Engle and Granger 1987). In the pres-ent context the following representation is implied:

DX � C � A(L)DX � hu � e ,t t t�1 t

where

C � a vector of constant terms ;A(L) � a matrix of finite order lag polynomials ;

17Normalization may have been done on the stock index of any of the six/seven countries,but implications of the results would stay the same. Argentina was chosen arbitrarily.

18Certain restrictions on coefficients were tested by means of the likelihood ratio test. Thenull hypothesis of equal coefficients on Argentina, Brazil and Chile was rejected at the 1% level.On the other hand, the test failed to reject the null of equal coefficients on Brazil and Chile.

19Restriction tests reject the null that coefficients on Argentina and Venezuela are equal toeach other at the 1% level, but fail to reject the null that coefficients on Brazil and Chile areequal to each other and that the Mexican and Colombia coefficients are equal to each other.

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X � log of all stock indices ;h � a vector of coefficients and ;u � error-correction term from the cointegration relationship.

The second term on the right-hand side of Equation 6 represents the short-term dynamic interaction between the left-hand side stock index and theother indices. The disequilibrium adjustment of each variable towards itslong-run equilibrium value is then captured by the lagged error-correctionterm, ut�1, with the coefficient on this term in each individual equationdepending on the speed of adjustment of the variable towards its long-runequilibrium value.20

Tables 7 and 8 present results from the error-correction models with-out and with the United States index in the relationship. Results from bothtests are very similar. The lag structure in the error-correction model isdetermined by means of the Akaike’s FPE criteria. For each of the modelsa possible combination of one to four lags are examined and the lag structurethat minimizes the FPE is chosen. Most of the models required the use ofthree to four lags. If more than one lag of the variables is applied, thenTables 7 and 8 show the sum of the coefficients on the first line, the chi-square statistics in brackets on the second line, and the number of lags usedin parentheses on the third line. With respect to the error-correction termand the constant term, the t-statistics are presented in the parentheses onthe second line. Diagnostic statistics of the equation are provided below theerror-correction results.

Results in general indicate that in both relationships (with and withoutthe United States index) there is clearly evidence of causality between allindices. Only the indices from Brazil and Colombia are found to be exoge-nous in the relationship. In the Brazilian and Colombian equations only thelagged dependent variable is significant. This is true in both relationships.All the coefficients on the lagged difference of indices are less than unityexcept for the United States index in the Argentinean equation. In the re-lationship excluding the United States index the error-correction term issignificant in the Argentinean and Chilean equations. Including the UnitedStates index, the error-correction term is significant in the cases of Mexico,Argentina and Chile. The coefficients on the significant error-correctionterms indicate a relatively low speed of adjustment per week towards the

20With the cointegration vector normalized on the stock index of Argentina, in the equationwhich models the Argentinean stock index as the dependent variable, the associated elementof h represents the speed of adjusting directly. In the remaining equations, the correspondingelements of h represent the rate of speed of adjustment of the relevant variables to the valueof its associated coefficient in the cointegrating relationship.

299

TABLE 7. Error-Correction Results Excluding the United States Index in the Relationship

Variable C h RDAR RDBR RDCH RDCO RDME RDVE

DAR �0.419a �0.139a 0.305a �0.346a �0.907b 0.522 �0.436 �0.673b

(�5.09) (�5.18) [4.01] [4.57] [3.05] [1.38] [0.383] [2.62]{3} {4} {4} {3} {4} {4}

R2 � 0.15, SE � 10.6%, SC v2(1) � 0.46, ARCH process v2(4) � 2.31DBR 0.100 0.032 0.003 0.215c 0.240 0.082 0.140 �0.170

(1.49) (1.46) [1.83] [2.46] [1.27] [0.26] [0.23] [0.75]{4} {3} {3} {4} {2} {4}

R2 � 0.017, SE � 8.7%, SC v2(1) � 0.56, ARCH process v2(4) � 2.00DCH �0.050b �0.018b 0.048 0.052 0.175c 0.049 �0.093 �0.046b

(�2.27) (�2.45) [1.86] [2.25] [2.56] [0.903] [0.37] [2.51]{4} {3} {3} {3} {3} {4}

R2 � 0.11, SE � 2.9%, SC v2(1) � 0.72, ARCH process v2(4) � 1.97DCO 0.028 0.007 �0.039 �0.030 �0.080 0.278b 0.031 �0.016

(0.91) (0.72) [0.46] [0.18] [0.41] [3.80] [0.27] [0.202]{3} {4} {3} {3} {3} {4}

R2 � �0.006, SE � 4.0%, SC v2(1) � 0.009, ARCH process v2(4) � 3.05DME �0.021 �0.009 0.088a 0.004 �0.113 �0.002 0.101 �0.067

(�0.95) (�1.25) [5.17] [0.36] [0.36] [0.34] [1.18] [0.95]{3} {4} {4} {3} {3} {4}

R2 � 0.05, SE � 2.80%, SC v2(1) � 0.65, ARCH process v2(4) � 2.57DVE �0.034 �0.012 0.103 �0.079 0.002 0.186 �0.352b 0.313a

(�0.86) (�0.94) [1.41] [1.44] [0.57] [1.45] [3.63] [3.81]{3} {3} {4} {3} {3} {4}

R2 � 0.081, SE � 5.0%, SC v2(1) � 0.85, ARCH process v2(4) � 2.17

NOTE: a, b, & c imply significance at 1%, 5% & 10%, respectively.t-statistics in ( ), F-statistics in [ ], number of lags in { }.SE � Standard error of the regression, SC � Serial correlation

300

TABLE 8. Error-Correction Results Including the United States Index in the Relationship

Variable C h RDUS RDAR RDBR RDCH RDCO RDME RDVE

DAR �2.249a �0.101a 1.40a 0.219b �0.511a �0.187b 0.475 �0.674 �0.548(�4.81) (�4.82) [2.38] [3.05] [5.47] [2.88] [1.10] [0.927] [1.90]

{4} {3} {4} {4} {3} {4} {4}R2 � 0.16, SE � 10.5%, SC v2(1) � 0.63, ARCH process v2(3) � 1.66

DBR 0.454 0.020 0.524 0.043 0.222c 0.177 0.077 0.018 �0.193(1.22) (1.21) [0.31] [1.82] [2.24] [1.20] [0.25] [0.23] [0.75]

{4} {4} {3} {3} {4} {3} {4}R2 � 0.002, SE � 8.8%, SC v2(1) � 0.63, ARCH process v2(3) � 1.96

DCH �0.279b �0.013b �0.045 0.034 0.041 0.190b 0.045 �0.071 �0.033c

(�2.29) (�2.32) [0.31] [1.69] [1.96] [2.86] [0.72] [0.43] [2.31]{3} {4} {3} {3} {3} {3} {4}

R2 � 0.10, SE � 2.9%, SC v2(1) � 0.72, ARCH process v2(3) � 2.10DCO 0.127 0.005 0.320 �0.035 �0.032 �0.091 0.280b �0.031 �0.013

(0.73) (0.70) [0.78] [0.46] [0.21] [0.41] [3.77] [0.62] [0.287]{4} {3} {4} {3} {3} {3} {4}

R2 � �0.01, SE � 4.0%, SC v2(1) � 0.004, ARCH process v2(3) � 2.18DME �0.224c �0.010c 0.047 0.086a �0.021 �0.125c �0.018 0.098 �0.068

(�1.81) (�1.86) [1.37] [5.31] [0.47] [2.08] [0.26] [0.69] [1.09]{4} {3} {4} {4} {3} {3} {4}

R2 � 0.07, SE � 2.80%, SC v2(1) � 0.47, ARCH process v2(3) � 3.08DUS 0.041 0.002 0.027 �0.008 �0.066 0.046 0.055 �0.031 0.009

(0.58) (0.53) [0.84] [0.25] [0.39] [0.74] [1.10] [0.09] [1.16]{4} {4} {3} {4} {3} {3} {4}

R2 � �0.015, SE � 1.7%, SC v2;(1) � 0.88, ARCH process v2(3) � 1.21DVE 0.105 0.005 �0.120 0.077 �0.039 0.098 0.146 0.227 0.351c

(0.63) (0.48) [1.37] [1.01] [1.12] [0.53] [0.99] [1.37] [4.79]{4} {3} {3} {4} {3} {3} {4}

R2 � 0.08, SE � 5.1%, SC v2(1) � 0.40, ARCH process v2(3) � 1.75

See note at the end of table 7.

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long-run equilibrium. In the United States equation we find no evidence ofcausality, implying that the index from the United States is not affected bythe stated Latin American markets. All relationships pass the diagnostic tests,except the Colombian equations, where some evidence of serial correlationis found.21

5. Conclusion

In an integrated world equity market, stock prices of different coun-tries are expected to have a long-run relationship(s). This paper provides anempirical investigation of long-run relationships between stock indices of sixLatin American countries and the United States. The empirical work applieslog of weekly data ranging from January 1989 to December 1993 from Ar-gentina, Brazil, Chile, Colombia, Mexico, Venezuela, and the United States.The six Latin American markets under consideration are part of what isknown as emerging markets (IFC 1993). Empirical investigations are con-ducted by means of unit root tests, Johansen method of cointegration testsand error-correction models. Cointegration tests are conducted first with thesix Latin stock indices in the VAR, and then in the second relationship theUnited States index is added in the VAR. Results from the cointegrationtests show the presence of common stochastic trends between the differentindices with and without the United States index. In other words, we areable to find a stationary long-run relationship between the six Latin Americanindices, and also between the six stated indices and the United States index.The vast globalization of the emerging markets in the recent years may bethe reason behind the significant multivariate relationships between thestated indices. Results from the error-correction tests indicate causalityamong the stated indices (with and without the United States market) andthe speed of adjustment to a long-run equilibrium is found to be slow.

Received: December 1994Final version: March 1996

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