On the Linkages of the Stock Markets of the NAFTA Countries: Fundamentals or Speculative Bubbles?

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On the Linkages of the Stock Markets ofthe NAFTA Countries: Fundamentals orSpeculative Bubbles?Christian Pierdzioch a & Renatas Kizys ba Department of Economics , Helmut-Schmidt-University ,Hamburg , Germanyb Department of Economics , University of Portsmouth,Portsmouth Business School , Portsmouth , UKPublished online: 30 Mar 2012.

To cite this article: Christian Pierdzioch & Renatas Kizys (2013) On the Linkages of the StockMarkets of the NAFTA Countries: Fundamentals or Speculative Bubbles?, International EconomicJournal, 27:3, 415-440, DOI: 10.1080/10168737.2012.660182

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International Economic Journal, 2013Vol. 27, No. 3, 415–440, http://dx.doi.org/10.1080/10168737.2012.660182

On the Linkages of the Stock Marketsof the NAFTA Countries:

Fundamentals or Speculative Bubbles?

CHRISTIAN PIERDZIOCH* & RENATAS KIZYS**

*Department of Economics, Helmut-Schmidt-University, Hamburg, Germany; **Department ofEconomics, University of Portsmouth, Portsmouth Business School, Portsmouth, UK

(Received 8 June 2010; final version received 18 January 2012)

ABSTRACT We analyze whether the linkages between the stock markets of the NAFTA mem-ber countries (Canada, Mexico, and the United States) reflect movements in fundamentalsor speculative bubbles. To this end, we estimate a state-space model to decompose the stockmarket indexes of the three NAFTA member countries into fundamentals and speculativebubbles. We analyze the linkages of the three stock markets by means of cointegration tech-niques. Evidence of cointegration linkages between fundamentals is stronger than evidenceof cointegration linkages between speculative bubbles.

KEY WORDS: NAFTA, fundamentals, speculative bubbles, state-space model, cointegrationanalysisJEL CLASSIFICATIONS: C32, F37, G15

1. Introduction

An important objective of NAFTA (North American Free Trade Agreement),which has been in force since January 1994, is to stimulate economic growthin the member countries through intensified trade integration and a deepeningof financial market linkages. Issues concerning the effects of NAFTA on both

Correspondence Address: Renatas Kizys, Department of Economics, University of Portsmouth,Portsmouth Business School, Richmond Building, Portland Street, Portsmouth PO1 3DE, UK.Email: [email protected]

© 2013 Korea International Economic Association

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416 C. Pierdzioch & R. Kizys

regional trade integration and regional financial market linkages have been animportant topic for policy makers and managers, and a major textbook casefor economists who study the economic and financial effects of regional tradeagreements. While evidence suggests that the elimination of trade barriers andalignment of legal and regulatory infrastructure following the implementationof NAFTA has been successful in promoting trade in the region (Romalis, 2007)and in contributing to export growth (Tornell et al., 2003), empirical evidence isinconclusive as to whether the establishment of NAFTA has promoted regionalstock market linkages.

Using various empirical techniques, Darrat and Zhong (2005) report evidenceof increased regional stock market linkages in the post-NAFTA period. In asimilar vein, Aggarwal and Kyaw (2005) argue that stock-market linkages havestrengthened after the implementation of NAFTA. Atteberry and Swanson (1997)conclude that a strengthening of linkages between the stock markets of Canada,Mexico, and the United States was brought about by the NAFTA accord. Ewing etal. (2001) find that volatility transmission across the stock markets of the NAFTAcountries has become stronger in the post-NAFTA period. Other authors, in con-trast, argue that the observed regional stock market integration has been mainlydriven by the global boom in technology and telecommunication sectors in thelate 1990s (Ciner, 2006). Ewing et al. (1999) find that NAFTA did not promote,in terms of cointegration linkages, regional stock market integration. Recent evi-dence of the impact of NAFTA on financial information linkages is reported byFleischer et al. (2011). Upon estimating a multivariate stochastic volatility model,they find that the NAFTA accord has had a significant effect on the informationlinkages across the stock markets of its member countries.

One plausible reason for why earlier authors report mixed results with regardto the effect of NAFTA on regional stock market linkages is that stock market inte-gration among the NAFTA member countries has undergone significant changesover time. In the late 1980s and the early 1990s, Mexico undertook a broadrange of financial and institutional reforms that consisted of liberalizing stockmarkets, becoming more open to foreign investors, strengthening investor rightsand institutions, and privatizing state-owned enterprises (Henry, 2000; Montiel,2003). While these reforms may have promoted cointegration relations (Choudhry,1997), they also exposed the financial system in Mexico to external shocks thateventually led to the balance-of-payment crisis at the end of 1994 and to thedebt crisis at the beginning of 1995 (Montiel, 2003). The economic and politicaldevelopments in Mexico and the financial market crises of the mid-1990s couldhave contributed to instability of the regional links between the stock markets ofCanada, Mexico, and the United States right after the ratification of the NAFTAaccord.

Our contribution to the empirical literature on the effects of NAFTA onregional stock market integration is that we analyzed whether the time-varyinglinkages between the stock markets of the NAFTA member countries reflectmovements in fundamentals or speculative bubbles. To this end, we estimateda state-space model to decompose the stock market indexes of the three NAFTAmember countries into fundamentals and speculative bubbles. Our state-spacemodel is based on the model developed by Wu (1995, 1997). We then analyzed the

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The Linkages of the Stock Markets of the NAFTA Countries 417

linkages between the fundamentals and the speculative bubbles of the three stockmarkets by means of cointegration techniques (Bhar & Hamori, 2005). In order toaccount for the potential instability of the regional stock market linkages amongthe NAFTA member countries, we carried out a cointegration analysis for vari-ous subsample periods. As a robustness check, we implemented rolling-windowcointegration tests. As another robustness check, we estimated a threshold coin-tegration model. The results of our empirical analysis suggest that cointegrationlinkages between the three stock markets have changed over time. The introduc-tion of NAFTA seems to have promoted the integration of the Mexican stockmarket with the stock markets of Canada and the United States as far as stockmarket fundamentals are concerned. We also found some evidence of thresh-old cointegration between speculative bubbles. Taken together, our results implythat evidence of cointegration between fundamentals is stronger than evidence ofcointegration between speculative bubbles.

In Section 2, we describe how we decomposed stock market indexes intofundamentals and speculative bubbles, we describe our data, and we reportour estimates of speculative bubbles. In Section 3, we report the results of ourcointegration analysis. In Section 4, we offer some concluding remarks.

2. Fundamentals and Speculative Bubbles

In Section 2.1, we describe the model that motivates the decomposition of stockmarket indexes into fundamentals and speculative bubbles. In Section 2.2, wedescribe our data and we summarize the estimation results.

2.1 The Model

The model that we used to estimate fundamentals and speculative bubbles canbe derived from the standard present-discounted value model of stock pricedetermination (Wu, 1995, 1997). This model, which perhaps is one of the leastcontroversial in the empirical finance literature, implies that the current real stockprice, Pt, can be expressed as the expected present value of next period’s realstock price and real dividends. Letting Dt denote real dividends and Et denote theconditional expectations operator, the present-discounted value model implies

Pt = Et(Pt+1 + Dt)/(1 + R), (1)

where R denotes the required real rate of return. A loglinear approximation ofequation (1) is given by:

pt = κ − r + φEt(pt+1) + (1 − φ)dt, (2)

where κ = − log(φ) − (1 − φ) log(1/φ − 1) and φ = 1/(1 + exp(d − p)). Low-ercase letters denote the natural logarithm of a variable, and d − p denotes theaverage log dividend-price ratio. Assuming that the usual transversality condi-tion holds, the bubble-free rational expectations solution, pf

t , of equation (2), is

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given by

pft = (κ − r)/(1 − φ) + (1 − φ)Et

∞∑j=0

φjdt+j, (3)

where pft denotes ‘fundamentals’. A rational speculative bubble, bt, may exist in

case the transversality condition does not hold. Such a rational speculative bubblemust satisfy the equation Etbt+j = (1/φ)jbt. The general solution of equation (2)can then be expressed as

pt = pft + bt. (4)

The rational speculative bubble evolves according to

bt = (1/φ) bt−1 + εt, (5)

where 0 < φ < 1 (see equation 2). The mean-zero disturbance term, εt, isnormally distributed with variance σ 2

ε . Equation (5) presents the standard rep-resentation of a stochastic rational speculative bubble. Such a speculative bubbleis perfectly consistent with rational expectations on the side of investors andconstitutes a solution to the present-discounted value model of stock price deter-mination. The result that a rational speculative bubble solves the model can bederived by inserting equations (4) and (5) into equation (2). It also should be men-tioned that negative (anti-log) values cannot arise because the present discountedvalue model given in equation (4) is expressed in terms of log variables.

The presence of a rational speculative bubble is also perfectly consistent withthe absence of arbitrage opportunities. As explained by Gurkaynak (2008, p. 166)in a useful survey of the relevant literature, the economic intuition behind thisno-arbitrage result is that rational investors are willing to buy a stock at a priceabove the fundamental price because the existence of a rational speculative bubbleleads them to expect that the future sell-off price exceeds the current price. This isthe reason why equation (5) implies that a rational speculative bubble is expectedto increase on average. As a result, a stock price that exceeds the fundamentalprice is an equilibrium price.

The parameter φ assumes numerical values between zero and one and, thus, becan be interpreted as a ‘discount factor’. Because the inverse of the discount factoris used in equation (5), the speculative bubble follows an asymptotically explosiveprocess. The asymptotically explosive process, however, does not imply that thespeculative bubble is strictly monotonically increasing over time. The speculativebubble given in equation (5) is a stochastic rather than a deterministic speculativebubble because it features the random disturbance term, εt.1 The presence of the

1It should be acknowledged that the model given in equation (5) presents only one of various formsof speculative bubbles that have been considered in the earlier literature (for a survey, see Gurkaynak,2008). For example, researchers have analyzed models that feature periodically collapsing rationalspeculative bubbles (Evans, 1991). Models of periodically collapsing rational speculative bubblesrest on the argument that speculative bubbles are not empirically plausible unless there is a chancethat they will collapse after reaching high levels. As a result, the process that periodically collapsingrational speculative bubbles follow consists of three phases: growth, eruption, and collapse. In our

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random disturbance term implies that the stochastic rational speculative bubblemay decrease or ‘burst’ from time to time.2

Concerning our empirical research strategy, estimation of the model consistingof equations (4) and (5) is complicated by the fact that a speculative bubble isnot directly observable. For this reason, we transformed the model into a state-space model (Bhar & Hamori, 2005; Wu, 1995, 1997). At the end of the paper,we lay out technical details on how we transformed the model into a state-spacemodel (Appendix A). We used the Kalman-filter model to estimate the param-eters of the state-space model. Kim and Nelson (2000) describe in detail howthe Kalman-filter model can be used to estimate the parameters of a state-spacemodel (see also Bhar & Hamori, 2005). In our empirical analysis, we used theKalman-filtered estimates of the fundamentals and the speculative bubbles to ana-lyze the cointegration linkages between the stock markets of the NAFTA membercountries. The Kalman-filtered estimates of the fundamentals and the specula-tive bubbles approximate the information available to investors at the time aninvestment decision must be reached.

The set of parameters to be estimated contains the parameters of the equationthat describes the dynamics of real dividends (see equation (8) at the end of thepaper), the parameter, φ, that governs the dynamics of the speculative bubble,and the variances of the disturbance terms in the equations that describe thedynamics of real dividends and the speculative bubble. In order to retain symmetryacross countries, we fitted a parsimonious ARIMA(2, 1, 0) model to capture thedynamics of real dividends in all three NAFTA member countries. This modelcaptures the main elements of the dynamics of real dividends and economizes onthe parameters to be estimated.

2.2 Data and Estimation Results

We used monthly data for the sample period from June 1989 to June 2008 in ourempirical analysis. The choice of the sample period was essentially determined bythe availability of stock-market data for Mexico. We downloaded from ThompsonFinancial Datastream data on the stock market indexes and Datastream-estimateddividend yields for Canada, Mexico, and the United States, measured in national

specification of a stochastic rational speculative bubble, eruptions and collapses will show up in therandom disturbance term, εt.2Stochastic rational speculative bubbles and periodically collapsing rational speculative bubbles(as well as other forms of speculative bubbles such as, for example, the ‘intrinsic bubbles’ studiedby Froot & Obstfeld, 1991) are consistent with rationality on the side of investors and are, thus,called ‘rational bubbles’. Other authors have emphasized that ‘irrational bubbles’ may be presentin stock market data. In our analysis, we did not consider models of irrational bubbles. Models ofirrational bubbles often feature heterogeneous investors and investors who have biased expectations(sometimes called ‘noise traders’ or ‘feedback traders’). An irrational bubble can then be defined‘as the difference between asset prices as they are and asset prices as they would be in the absence ofnoise traders’ (LeRoy, 2004, p. 795). In any case, our brief review of the many varieties of speculativebubbles that have been analyzed in the literature is a reminder that any test for speculative bubblesrests on a joint hypothesis of speculative bubbles (or absence thereof) and a specific asset-pricingmodel.

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currencies. We then calculated dividends as the product of the last period’s stockprice index and the dividend yield. Because we were interested in analyzing inter-national stock market integration from the standpoint of an US investor, weconverted the national stock market indexes to US dollars by using exchangerates retrieved from the IFS CD-ROM published by the IMF. In order to adjustthe stock market data for inflation, we used IFS data on the US consumer priceindex.

Panel A of Figure 1 shows the real stock market indexes (log scale). In order tofacilitate a cross-country comparison, we scaled the indexes such that all indexesassume the value 100 at the beginning of the sample period. The real stock marketindexes in Canada and the United States showed a similar broad pattern over time.A gradual increase in the real stock market indexes at the end of the 80s and at thebeginning of the 1990s turned into a high-growth stage in the mid-90s. The realstock market indexes reached their peaks at the beginning of the new millennium,when the dotcom bubble burst. The real stock market indexes showed a tendencyto decrease until 2003, when this tendency was reversed again.

The Mexican stock market behaved quite differently. At the beginning of thesample period, the rate of increase in the Mexican real stock market index wasmore pronounced than that in Canada and the United States. More precisely,the stock market index experienced a sudden increase in 1991, which reflects theprivatization of the state-owned Mexican telecommunication company Telmexand the beginning of the NAFTA negotiations (Bekaert et al., 2002, p. 311). Thisevidence may be interpreted to suggest that investors’ expectations of the imple-mentation of NAFTA and the actual implementation of NAFTA were equallyimportant for stock market dynamics in Mexico.

Such an interpretation is consistent with the fact that the president of Mexico,Carlos Salinas de Gortari, made the proposal to create a free trade area betweenMexico and the United States already in the Spring of 1990 (Blaine, 1998, p. 33).This proposal was expanded to include Canada and, as a result, triggered massivecapital inflows to the Mexican economy. Blaine (1998, Table 2, p. 35), who givesa detailed account of the development of the Mexican economy before the 1994financial crisis, finds that net inflows of direct investment to the Mexican econ-omy doubled in 1991 as compared with 1990 and that net inflows of portfolioinvestment mushroomed to 12 billion dollars in 1991. Figure 1 shows that therise of the Mexican stock market index mirrored this massive increase in capitalinflows. The increase in net capital inflows in the early 1990s, thus, may havefueled a speculative bubble in Mexican financial markets (see also Blaine, 1998,p. 42).

In 1994, the boom of the Mexican stock market was disrupted by a balance-of-payment crisis, and the Mexican stock market collapsed. This collapse wasreinforced by a large-scale depreciation of the Mexican peso in 1994–1995, fol-lowing the balance-of-payment crisis. The stock-market crisis was exacerbatedby the debt crisis in 1995. While the Mexican real stock market index startedincreasing after the crises, a technological bubble, characteristic of the stock mar-kets in Canada and the United States, did not develop at par in Mexico. As inthe cases of Canada and the United States, the Mexican real stock market indexstarted to increase again in 2003.

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Figure 1. Stock-market data. Panel A: Stock-market indexes; Panel B: Stock-market returns.Note: This figure plots monthly stock-market indexes (log scale) and the returns on the stock-marketindexes. Returns are defined as 100 times the first difference of the (log) stock-market indexes. Thestock-market indexes were converted to US dollars and then deflated with the US consumer priceindex. The data are from Thompson Financial Datastream.

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Panel B of Figure 1 complements Panel A by plotting the stock market returnsfor the three NAFTA member countries. Stock market returns clearly reveal thatthe volatility of the Mexican stock market index exceeded the volatility of theCanadian and US stock market indexes. Large positive returns in the case of theMexican stock market at the beginning of the sample period reflect the impactof privatization efforts and NAFTA negotiations on the stock market. The largenegative returns reflect, for example, the balance-of-payment crisis of 1994.

Panel A of Table 1 summarizes the results of tests for a unit root in the realstock market indexes, real dividends, and the dividend-price ratio.3 We applied theDFGLS unit-root test developed by Elliott et al. (1996) to the natural logarithmsof the data. The null hypothesis is that the time series being analyzed featuresa unit root. The alternative hypothesis is that the time series is stationary. Theresults suggest that both the real stock market indexes and the real dividendsfeature a unit root.4

It is interesting to analyze whether the stock market indexes and the real div-idends share a common stochastic trend and, thus, are cointegrated. Accordingto the standard present-discounted value model of stock price determination(Section 2.1), absence of cointegration may indicate that speculative bubbles drivea wedge between the stochastic trends in the real stock market indexes and thereal dividends (for a detailed analysis, see Diba & Grossman, 1988). The resultsin Table 1 indicate that the null hypothesis that the dividend-price ratio is notcointegrated cannot be rejected in all three stock markets under consideration. Itfollows that the possibility of speculative bubbles cannot be ruled out.

Because structural breaks may distort cointegration tests of speculative bubbles,we summarize in Panel B of Table 1 the results of the Gregory-Hansen test forcointegration in models with structural breaks (Gregory & Hansen, 1996).5 Wepresent results for three alternative models. Model 1 features a potential structuralbreak in the intercept, Model 2 features a potential structural break in the interceptand in the slope coefficients, and Model 3 is identical to Model 2 except that italso features a trend. There is weak evidence of cointegration and a structuralbreak (in 2000) in the case of Canada. Similarly, there is no convincing evidenceof cointegration and structural breaks in the case of the United States. There is,however, evidence of cointegration in Mexico, but the test also yields evidenceof structural breaks (in 1994 and in the middle of 2000). Of course, the ratherfragile within-country evidence of structural breaks in the cases of Canada and

3We used the program Eviews to compute the results given in Panel A of Table 1 and the results ofthe cointegration analysis (Section 3). We computed the Gregory-Hansen test (Panel B of Table 1) inWinRats using a source code available from the Internet page of Estima. We coded up the RALS-testfor periodically collapsing bubbles (Panel C of Table 1) in the program R (R Development CoreTeam, 2010), and the state-space model of speculative bubbles in Matlab.4In fact, the results of the unit-root tests indicate that it may be difficult to reject the hypothesis ofan explosive root.5An advantage of the Gregory-Hansen test is that a potential structural break date is unknowna priori and, thus, can be endogenously determined as part of the test. Similar to the Engle andGranger (1987) test for cointegration, the Gregory-Hansen test is a residuals-based test. Unlike theEngle-Granger test, the Gregory-Hansen test is a more general type of cointegration test (Gregory& Hansen, 1996, p. 100). The test can be conducted by assuming a potential structural break in theintercept, in the slope coefficients, or in both.

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Table 1. Testing for a unit root and speculative bubbles

Real stock price index Real dividends Cointegration test

Panel ACanada 1.1339 1.7991 11.9532Mexico 0.7200 −1.3113 10.7294United States 0.3328 1.9300 4.1392

Panel BModel 1 Model 2 Model 3

Canada −4.033 −4.727 −6.762Mexico −5.982 −6.096 −6.441United States −3.607 −4.138 −5.300

Panel CRALS-test C(5%) C(1%)

Canada −2.5344 −3.4083 −4.0343Mexico −4.3628 −3.3473 −4.0199United States −3.4088 −3.3543 −4.0148

Note: Panel A summarizes test results for a unit root in real stock price indexes and realdividends. We used the unit-root test developed by Elliott et al. (1996). The critical values ofthe test are −1.6152 and −1.9432 at the 10% and 5% level of significance. The cointegrationtest is a test for cointegration between real dividends and the real stock price index. The testis based on Johansen’s (1988) λtrace statistic. The critical 5% MacKinnon-Haug-Micheliscritical value (MacKinnon et al., 1999) for this test is 15.4947. The null hypothesis is that thedividend-price ratio is not cointegrated. The alternative hypothesis is that there is at leastone cointegration vector. Panel B summarizes the results of Gregory-Hansen test for cointe-gration in models with structural breaks (Gregory & Hansen, 1996). Model 1 allows for astructural break in the intercept, Model 2 allows for a structural break in the intercept andthe slope coefficients, and Model 3 is identical to Model 2 except that it features in additiona trend. The 5% critical values for Model 1, Model 2, and Model 3 are −4.610, −4.950, and−5.500. In Panel C, the column titled RALS-test gives the results of a cointegration test forperiodically collapsing speculative bubbles studied by Taylor and Peel (1998). The columnstitled C(5%) and C(1%) give the simulated critical values. The simulated critical values arebased on 10,000 Monte Carlo simulation runs.

the United States implies that structural breaks should not be neglected whenwe analyze cross-country cointegration links between speculative bubbles andfundamentals (Section 3.2). In fact, the entire analysis laid out in Section 3.2will center on the question of whether NAFTA led to structural breaks in thecross-country cointegration links between speculative bubbles and fundamentals.

Because standard cointegration tests may fail to detect periodically collapsingstochastic speculative bubbles (Evans, 1991), we also used the RALS-based teststudied by Taylor and Peel (1998) to test for the existence of speculative bub-bles. In the first step, we estimated by the least-squares technique a cointegrationrelation between log stock prices and log dividends. In a second step, we usedthe estimated residuals from the cointegration relation to estimate a residuals-augmented least squares (RALS) Dickey-Fuller regression of the first differenceof the residuals on their lagged level. In a third step, we constructed the RALS-based variance of the Dickey-Fuller coefficient. In the fourth and final step, weran a Monte Carlo simulation as described in Taylor and Peel (1998) to computecritical values. Panel C of Table 1 summarizes the results of the RALS-based test.

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The results provide some evidence that the null hypothesis of no cointegrationcan be rejected in the case of the United States, and somewhat stronger evidenceof cointegration in the case of Mexico. However, in the case of Mexico, we foundevidence of structural breaks in 1994 and in the middle of 2000. To be on the safeside, we analyzed the Mexican stock market in more detail and split the sampleperiod into three subsample periods. The first subsample period ended in 1993,the second subsample period started in 1994 and ended in 1999, and the thirdsubsample period started in 2000. This resulted in a RALS-test of −2.267 forthe first subsample period, −3.267 in the second subsample period, and −3.083in the third subsample period. Simulated critical values (available upon request)did not allow the null hypothesis of noncointegration to be rejected in the threesubsample periods, providing further evidence that the possibility of speculativebubbles cannot be ruled out in Mexico.

We do not want to stretch the interpretation of the results of the simple coin-tegration test and the RALS-test for speculative bubbles too far. The tests onlylead to a binary decision: the rejection or no rejection of the null hypothesis ofno cointegration. The tests, however, are uninformative as to the potential mag-nitude of a speculative bubble and its likely historical dynamics. In other words,the tests do not inform a researcher when a speculative bubble gathered steam,how large a speculative bubble was at a certain moment of time, and when aspeculative bubble collapsed. From an economic point of view, however, theseaspects of speculative bubbles are of key importance, and this is the reason whywe focused in our research on Wu’s (1995, 1997) model of stochastic rationalspeculative bubbles.

For stochastic rational speculative bubbles, Table 2 summarizes the estimationresults for the state-space model. The estimation results suggest the the autore-gressive coefficients governing the dynamics of real dividends are significant. Thepoint estimate of the parameter φ is close to unity for Canada and is preciselyestimated. In the cases of Mexico and the United States, the point estimate ofthe parameter φ is estimated at unity. Because the model outlined in Section 2.1implies that the parameter φ should satisfy the restriction 0 < φ < 1, we alsoestimated a restricted version of our model in which this restriction by construc-tion always holds. The restricted model is a model in which the parameter φ isnot estimated directly, but a transformation φ = 1/(1 + exp(−μ)) is being usedand the auxiliary parameter μ is estimated. In Section 3.2, we shall report, as arobustness check, results for the unrestricted and the restricted model. Estimatesof the parameter φ that are close to unity are a common finding in the empiricalliterature (see, for example, Bhar & Hamori, 2005, Chapter 12).

Figure 2 presents the estimated bubble-price ratios for Canada, Mexico, andthe United States. We scaled the bubble-price ratios to assume the value 100 atthe beginning of the estimation period to ensure cross-country comparability.The (scaled) bubble-price ratio in Mexico showed a larger variability than thebubble-price ratios in Canada and the United States. Moreover, the bubble-priceratio in Mexico collapsed after reaching a peak at around 1991 and, thereafter,showed a stronger growth than the bubble-price ratios in Canada and the UnitedStates. It is also interesting to note that the bubble-price ratio kept increasingin Mexico for several more years after the NAFTA accord came into force. This

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1990 1993 1995 1998 2001 2004 200650

100

150

200

250

300

350

400(a)

(b)

Time

Bub

ble-

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CanadaMexicoUnited States

1990 1993 1995 1998 2001 2004 200650

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Bub

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CanadaMexicoUnited States

Figure 2. Scaled bubble-price ratios. Panel A: Unrestricted model; Panel B: Restricted model.Note: This figure plots the bubble-price ratios, computed as 100 times the ratio of the estimatedspeculative bubbles and the stock-market indexes. We scaled the bubble-price ratio to assumethe value 100 at the beginning of the sample period to ensure cross-country comparability. Therestricted model is a model in which the parameter φ was not estimated directly, but a transformationφ = 1/(1 + exp(−μ)) was being used and the auxiliary parameter μ was estimated. We used thistransformation to ensure that, in line with the theoretical model described in Section 2.1, theparameter φ assumes point estimates strictly smaller than unity.

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Table 2. Estimation results for the state-space model

ϕ1 ϕ2 φ σ 2ε σ 2

u

CanadaCoefficient −0.5809 −0.3088 0.9991 [0.9934] 60.9937 78.7964Std. Error 0.0612 0.0611 0.0044 3.0945 3.9976MexicoCoefficient −0.3401 −0.3994 1.0004 [0.9917] 178.5854 156.0854Std. Error 0.0572 0.0593 0.0048 9.2437 8.0788United StatesCoefficient −0.8054 −0.5128 1.0000 [0.9907] 58.2207 69.7189Std. Error 0.0610 0.0610 0.0041 2.9587 3.5429

Note: This table summarizes estimation results for the state-space model. The parameters ϕ1and ϕ2 denote the autoregressive parameters of the ARIMA(2, 1, 0) model that describes thedynamics of real (demeaned) dividends. The parameter φ denotes the parameter of the modelthat describes the dynamics of speculative bubbles. The number in brackets is the point estimateof φ estimated from a restricted model in which the parameter φ was not estimated directly,but a transformation φ = 1/(1 + exp(−μ)) was being used and the auxiliary parameter μ

was estimated. We used this transformation to ensure that, in line with the theoretical modeldescribed in Section 2.1, the parameter φ assumes point estimates strictly smaller than unity.The parameter σ 2

u denotes the variance of the error term of the ARIMA(2, 1, 0) model estimatedto model the dynamics of real (demeaned) dividends. The parameter σ 2

ε denotes the error termof the model that describes the dynamics of speculative bubbles.

0

1

2

3

95 96 97 98 99 00 01 02 03 04 05 06 07

max_NAFTAPanel A

Panel B

0.00.51.01.52.02.5

95 96 97 98 99 00 01 02 03 04 05 06 07

trace_NAFTA

0.0

0.5

1.0

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95 96 97 98 99 00 01 02 03 04 05 06 07

max_NAFTA

0.0

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95 96 97 98 99 00 01 02 03 04 05 06 07

trace_NAFTA

Figure 3. Rolling-window cointegration test. Panel A: Fundamentals; Panel B: Speculative bubbles.Note: The results are for a rolling window of 5-years length. The solid (dotted, dashed) linesrepresent the results of tests for cointegration based on the λtrace(0)(λtrace(1), λtrace(2)) and theλmax(0)(λmax(1), λmax(2)) statistics. The dashed vertical line at unity represents the 95% criticalvalue taken from MacKinnon et al. (1999). The statistics are scaled by their critical values. We didnot restrict the coefficients of the short-run dynamics of the model to be constant over time.

result probably owes itself to two reasons. First, the stock market in Mexicocollapsed in 1994 following the balance-of-payment crisis (see Figure 1). Second,the liberalization program implemented by the Mexican government was notaccompanied by structural reforms. Rather, the liberalization program resultedin a deterioration of contract enforceability and an increase in nonperformingloans and a credit crunch (Tornell et al., 2004). After the NAFTA accord, and

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after Mexico overcame its economic and financial crisis, the bubble-price ratiobecame less volatile but continued to fluctuate at a higher level than in the casesof Canada and the United States.

3. Cointegration Analysis

In Section 3.1, we describe the methodology that we used to test for cointegrationlinkages. In Section 3.2, we summarize the results of the cointegration analysis.In Section 3.3, we summarize the results of an alternative cointegration analysisthat is based on the concept of threshold cointegration.

3.1 Methodology

Following Choudhry (1997), Ewing et al. (1999), and Darrat and Zhong (2005),and others, we used the approach developed by Johansen (1988, 1991) to test forcointegration linkages between the stock markets of the three NAFTA membercountries. Unlike other authors, we did not only test for cointegration linkagesamong the stock market indexes per se. Rather, we analyzed whether cointegra-tion linkages between the stock markets of the three NAFTA member countriesreflect cointegration linkages between fundamentals or cointegration linkagesbetween speculative bubbles (Bhar & Hamori, 2005).

Johansen’s (1988, 1991) approach renders it possible to test for cointegrationlinkages in a multivariate setting. In order to implement Johansen’s approach, weestimated the following vector error correction model:

�xt = K +w∑

j=1

Lj�xt−j + Fxt−1 + εt,x, (6)

where xt denotes the vector of stock market indexes (fundamentals, speculativebubbles) being analyzed, εt,x denotes a vector of zero-mean, Gaussian disturbanceterms, and K, Lj, and F denote matrices of coefficients to be estimated. In orderto estimate equation (6), we used two lags of the variables in the vector xt (thatis, we set w = 2). As a robustness check, we also estimated a model featuringthree lags. We estimated a model that features an intercept but no trend in thecointegration vector, and no deterministic trend in the data.

The key insight motivating Johansen’s (1988, 1991) approach is that the rankof the matrix F is equal to the number of independent cointegration vectors. If thematrix F has reduced rank, the number of cointegration vectors can be determinedby testing for the significance of the eigenvalues of the matrix F. To this end, theso-called λtrace and λmax statistics can be used, which can both be computed fromthe eigenvalues of the matrix F. The null hypothesis of the λtrace statistic is thatthere are at most r cointegration vectors, where the general alternative hypothesisis that the number of cointegration vectors is larger than r. The null hypothesisof the λmax statistic is that there are r cointegration vectors, and the alternativehypothesis is that there are r + 1 cointegration vectors. The definitions of thestatistics are λtrace(r) = −T

∑ni=r+1 ln(1 − λi) and λmax(r, r + 1) = −T ln(1 −

λr+1), where T denotes the number of usable observations and λ denotes the

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estimated eigenvalues of the matrix F. When all estimated eigenvalues are zero(no cointegration), the rank of the matrix F is zero and, because ln(1) = 0, boththe λtrace and the λmax statistics are zero. As the rank of the matrix F increases,the number of the non-zero eigenvalues increases, resulting in larger λtrace and theλmax statistics.6 Enders (1995) provides further details and illustrative examples.

3.2 Results of the Cointegration Analysis

In this section, we present the results of the cointegration analysis. In order toaccount for the possibility of time-varying cointegration linkages, we subdividedthe sample period into various subsample periods. Consistent with the resultsof the Gregory-Hansen test for cointegration with structural breaks for the caseof Mexico, which we reported in Section 2.2, the definition of the subsampleperiods explicitly accounts for the implementation of the NAFTA accord and forthe build-up and eventual crash of the dotcom bubble. Brooks and Del Negro(2004) and Ciner (2006) argue that the dotcom bubble had a significant impacton the comovement of international stock markets.

For our subsample analysis, we subdivided the sample period into the pre-NAFTA subsample period (before 12/1993) and the post-NAFTA subsampleperiod (since 01/1994). In addition, because the dotcom-bubble crashed in03/2000, we subdivided the post-NAFTA subsample period into a pre-dotcom-crash subsample period and a post-dotcom-crash subsample period. We alsosubdivided the pre-dotcom-crash period into a pre-Peso-crisis period (before12/1994) and a post-Peso-crisis period (since 01/1995). For all subsample peri-ods, we present results for the unrestricted and the restricted model of stochasticrational speculative bubbles. In addition, we report results that we obtained whenwe used two and three lags to estimate the vector error correction model given inequation (6).

Tables 3 and 4 summarize the results of Johansen’s (1988, 1991) λtrace cointe-gration tests. Tables 5 and 6 summarize the results for the λmax cointegrationtests. The general message conveyed by the results of the cointegration testsis that, irrespective of the subsample period being analyzed, evidence of coin-tegration linkages is strongest in the case of fundamentals. Depending on thespecification of the VECM, there is even evidence of two cointegration vectors

6Johansen’s (1988, 1991) approach consists of a sequential testing procedure for the λtrace and λmaxstatistics. In the first stage, the null hypothesis r = 0 is tested against the alternative hypothesis r > 0(r = 1) if the λtrace statistic (λmax statistic) is being used. If the null hypothesis of noncointegrationis not rejected, there is no evidence of cointegration. If the null hypothesis can be rejected, oneproceeds with testing the null hypothesis r ≤ 1 (r = 1) against the alternative hypothesis r > 1(r = 2) if the λtrace statistic (λmax statistic) is being used. If one cannot reject the null hypothesis,then there is evidence of one cointegration vector. In case the null hypothesis can be rejected, oneproceeds with testing the null hypothesis r ≤ 2 (r = 2) against the alternative hypothesis r = 3 ifthe λtrace statistic (λmax statistic) is being used. If the null hypothesis cannot be rejected, there isevidence of two cointegration vectors. If the null hypothesis can be rejected, there is evidence of threecointegration vectors (the three series are stationary, but this case is not relevant for our analysis).Concerning the economic interpretation of the results of the cointegration tests, evidence of, forexample, one cointegration vector implies that stock market indexes (fundamentals, speculativebubbles) in the three NAFTA member countries share a common stochastic trend.

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Table 3. Cointegration results (VECM(2), λtrace)

Unrestricted model Restricted model

Stock StockNull market Speculative market Speculativehypothesis index Fundamentals bubbles index Fundamentals bubbles

Pre-NAFTA subsample periodr = 0 0.4342 0.0099 0.2474 0.4342 0.0131 0.2937r ≤ 1 0.7553 0.0172 0.5296 0.7553 0.0323 0.5665r ≤ 2 0.7405 0.0868 0.3130 0.7405 0.6525 0.3642

Post-NAFTA, pre-dotcom-crash subsample periodr = 0 0.2432 0.0002 0.2836 0.2432 0.0242 0.2538r ≤ 1 0.5092 0.5338 0.3701 0.5092 0.5800 0.3062r ≤ 2 0.3572 0.4286 0.818 0.3572 0.6465 0.6023

Post-dotcom-crash subsample periodr = 0 0.0226 0.0007 0.6689 0.0226 0.0084 0.7545r ≤ 1 0.2550 0.2408 0.7717 0.2550 0.1996 0.7902r ≤ 2 0.4615 0.4378 0.7337 0.4615 0.4983 0.7116

Pre-Peso-crisis subsample periodr = 0 0.1617 0.0010 0.1650 0.2617 0.0014 0.1548r ≤ 1 0.3858 0.0071 0.7028 0.3858 0.0159 0.6658r ≤ 2 0.4013 0.2498 0.5457 0.4013 0.6080 0.5067

Post-Peso-crisis, pre-dotcom-crash subsample periodr = 0 0.0770 0.0000 0.1665 0.0270 0.0066 0.1739r ≤ 1 0.2315 0.0215 0.3483 0.2315 0.1068 0.1748r ≤ 2 0.4764 0.4555 0.4280 0.4764 0.4896 0.2642

Note: This table summarizes MacKinnon-Haug-Michelis (MacKinnon et al., 1999) p-values for Johansen’s(1988, 1991) λtrace test for cointegration. r = number of cointegration vectors. The null hypothesis in the caseof r = 0 (r ≤ 1, r ≤ 2) is that there is no cointegration vector (one cointegration vector, two cointegrationvectors). The alternative hypothesis stipulates r > 0 (r > 1, r > 2) cointegration vectors. In the first stage,the null hypothesis r = 0 is tested. If the null hypothesis of non-cointegration cannot be rejected, there isno evidence of one cointegration vector. If the null hypothesis can be rejected, in the second stage, the nullhypothesis r ≤ 1 is tested. If the null hypothesis cannot be rejected, there is evidence of one cointegrationvector. If the null hypothesis can be rejected, in the third stage, the null hypothesis r ≤ 2 is tested. If thenull hypothesis cannot be rejected, there is evidence of two cointegration vectors. If the null hypothesis isrejected, there is evidence of three cointegration vectors, implying that the three series being analyzed arestationary. The sample periods are the following: (1) pre-NAFTA subsample period ends 12/1993; (2) post-NAFTA, pre-dotcom-crash subsample period from 01/1994 to 02/2000; (3) post-dotcom-crash subsampleperiod from 2000/03 to the end of the sample period; (4) pre-Peso-crisis subsample period ends 12/1994;and (5) post-Peso-crisis, pre-dotcom-crash subsample period from 01/1995 to 02/2000. We did not restrictthe coefficients of the short-run dynamics of the model to be constant across subsample periods. The tablesummarizes the results for a vector error correction model (VECM) with two lags. The results that are basedon estimates of speculative bubbles derived from a state-space model with no restriction on the parameter φ

are summarized under the heading ‘Unrestricted model’. The results that are based on estimates of speculativebubbles derived from a state-space model in the presence of the restriction 0 < φ < 1 are summarized underthe heading ‘Restricted model’.

in some cases. The results imply cointegration linkages between the stock mar-ket indexes only in the post-Peso-crisis, pre-docom-crash subsample period andthe post-dotcom-crash subsample period. There is hardly evidence of cointegra-tion linkages between speculative bubbles. Together with the results for the stockmarket indexes and the fundamentals, the missing cointegration linkages between

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Table 4. Cointegration results (VECM(3), λtrace)



Pre-NAFTA subsample periodr = 0 0.1411 0.0092 0.3268 0.1411 0.0060 0.3923r ≤ 1 0.5026 0.0528 0.5918 0.5026 0.0405 0.6719r ≤ 2 0.6002 0.1509 0.4181 0.6002 0.1066 0.4074

Post-NAFTA, pre-dotcom-crash subsample periodr = 0 0.2956 0.0000 0.3491 0.2956 0.0000 0.4216r ≤ 1 0.3662 0.4094 0.3250 0.3662 0.4451 0.3786r ≤ 2 0.2013 0.4002 0.4458 0.2013 0.4697 0.5200

Post-dotcom-crash subsample periodr = 0 0.0029 0.0004 0.7278 0.0029 0.0026 0.8161r ≤ 1 0.2084 0.1828 0.9069 0.2084 0.0855 0.8623r ≤ 2 0.4318 0.6313 0.8286 0.4318 0.6301 0.8695

Pre-Peso-crisis subsample periodr = 0 0.0525 0.0008 0.2648 0.0525 0.0003 0.3656r ≤ 1 0.3309 0.0482 0.7047 0.3309 0.0451 0.8170r ≤ 2 0.4188 0.3851 0.5631 0.4188 0.3863 0.6625

Post-Peso-crisis, pre-dotcom-crash subsample periodr = 0 0.0196 0.0000 0.2528 0.0196 0.0000 0.2037r ≤ 1 0.1653 0.0194 0.2478 0.1653 0.0497 0.3662r ≤ 2 0.2662 0.3552 0.2759 0.2662 0.3794 0.2556

Note: This table summarizes MacKinnon-Haug-Michelis (MacKinnon et al., 1999) p-values for Johansen’s (1988,1991) λtrace test for cointegration. r=number of cointegration vectors. The null hypothesis in the case of r = 0(r ≤ 1, r ≤ 2) is that there is no cointegration vector (one cointegration vector, two cointegration vectors). Thealternative hypothesis stipulates r > 0 (r > 1, r > 2) cointegration vectors. In the first stage, the null hypothesisr = 0 is tested. If the null hypothesis of non-cointegration cannot be rejected, there is no evidence of one cointegra-tion vector. If the null hypothesis can be rejected, in the second stage, the null hypothesis r ≤ 1 is tested. If the nullhypothesis cannot be rejected, there is evidence of one cointegration vector. If the null hypothesis can be rejected, inthe third stage, the null hypothesis r ≤ 2 is tested. If the null hypothesis cannot be rejected, there is evidence of twocointegration vectors. If the null hypothesis is rejected, there is evidence of three cointegration vectors, implyingthat the three series being analyzed are stationary. The sample periods are the following: (1) pre-NAFTA sub-sample period ends 12/1993; (2) post-NAFTA, pre-dotcom-crash subsample period from 01/1994 to 02/2000; (3)post-dotcom-crash subsample period from 2000/03 to the end of the sample period; (4) pre-Peso-crisis subsampleperiod ends 12/1994; and (5) post-Peso-crisis, pre-dotcom-crash subsample period from 01/1995 to 02/2000. Wedid not restrict the coefficients of the short-run dynamics of the model to be constant across subsample periods.The table summarizes the results for a vector error correction model (VECM) with three lags. The results that arebased on estimates of speculative bubbles derived from a state-space model with no restriction on the parameterφ are summarized under the heading ‘Unrestricted model’ The results that are based on estimates of speculativebubbles derived from a state-space model in the presence of the restriction 0 < φ < 1 are summarized under theheading ‘Restricted model’.

speculative bubbles in the post-Peso-crisis, pre-dotcom-crash subsample periodand the post-dotcom crash subsample period indicate that the significant cointe-gration linkage between the stock market indexes in that subsample period wasdue to a cointegration linkage between fundamentals.

The missing cointegration linkages between speculative bubbles should not betaken to imply that there is no evidence of speculative bubbles in the stock markets

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Table 5. Cointegration results (VECM(2), λmax)



Pre-NAFTA subsample periodr = 0 0.3235 0.1926 0.2493 0.3235 0.1508 0.2873r = 1 0.7170 0.0551 0.7431 0.7170 0.0310 0.7405r = 2 0.7405 0.0868 0.3130 0.7405 0.3525 0.3642

Post-NAFTA, pre-dotcom-crash subsample periodr = 0 0.2569 0.0000 0.4455 0.25691 0.0089 0.4652r = 1 0.6748 0.6456 0.2957 0.6748 0.5533 0.2612r = 2 0.3572 0.4286 0.6818 0.3572 0.6465 0.6023

Post-dotcom-crash subsample periodr = 0 0.0302 0.0005 0.6267 0.0302 0.0136 0.7367r = 1 0.2638 0.2576 0.7426 0.2638 0.1843 0.7796r = 2 0.4615 0.4378 0.7337 0.4615 0.4983 0.7116

Pre-Peso-crisis subsample periodr = 0 0.3894 0.0445 0.0851 0.3894 0.0289 0.0870r = 1 0.4716 0.0081 0.7694 0.4716 0.0073 0.7508r = 2 0.4013 0.2498 0.5457 0.4013 0.6180 0.5067

Post-Peso-crisis, pre-dotcom-crash subsample periodr = 0 0.0442 0.0002 0.2513 0.0442 0.0215 0.4905r = 1 0.2291 0.0149 0.4020 0.2291 0.0892 0.2661r = 2 0.4764 0.4555 0.4280 0.4764 0.4896 0.2641

Note: This table summarizes MacKinnon-Haug-Michelis (MacKinnon et al., 1999) p-values for Johansen’s (1988,1991) λmax test for cointegration. r=number of cointegration vectors. The null hypothesis in the case of r = 0 (r = 1,r = 2) is that there is no cointegration vector (one cointegration vector, two cointegration vectors). The alternativehypothesis is that there are r = 1 (r = 2, r = 3) cointegration vectors. In the first stage, the null hypothesis r = 0is tested. If the null hypothesis of non-cointegration cannot be rejected, there is no evidence of one cointegrationvector. If the null hypothesis can be rejected, in the second stage, the null hypothesis r = 1 is tested. If the nullhypothesis cannot be rejected, there is evidence of one cointegration vector. If the null hypothesis can be rejected,in the third stage, the null hypothesis r = 2 is tested. If the null hypothesis cannot be rejected, there is evidence oftwo cointegration vectors. If the null hypothesis can be rejected, there is evidence of three cointegration vectors,implying that the three series being analyzed are stationary. The sample periods are the following: (1) pre-NAFTAsubsample period ends 12/1993; (2) post-NAFTA, pre-dotcom-crash subsample period from 01/1994 to 02/2000;(3) post-dotcom-crash subsample period from 2000/03 to the end of the sample period; (4) pre-Peso-crisis subsampleperiod ends 12/1994; and (5) post-Peso-crisis, pre-dotcom-crash subsample period from 01/1995 to 02/2000. Wedid not restrict the coefficients of the short-run dynamics of the model to be constant across subsample periods.The table summarizes the results for a vector error correction model (VECM) with two lags. The results that arebased on estimates of speculative bubbles derived from a state-space model with no restriction on the parameterφ are summarized under the heading ‘Unrestricted model’ The results that are based on estimates of speculativebubbles derived from a state-space model in the presence of the restriction 0 < φ < 1 are summarized under theheading ‘Restricted model’.

of the NAFTA member countries. In fact, as shown in Section 2.2, speculativebubbles did arise in the stock markets of the NAFTA member countries. Rather,the missing cointegration linkages between speculative bubbles implies that thespeculative bubbles in the stock markets of the NAFTA member countries seemto have followed independent stochastic trends.

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Table 6. Cointegration results (VECM(3), λmax)



Pre-NAFTA subsample periodr = 0 0.1253 0.0666 0.3137 0.1253 0.0544 0.3384r = 1 0.4871 0.1140 0.7266 0.4871 0.1138 0.8268r = 2 0.6002 0.1509 0.4181 0.6002 0.1066 0.4074

Post-NAFTA, pre-dotcom-crash subsample periodr = 0 0.4715 0.0000 0.6185 0.4715 0.0000 0.6718r = 1 0.6567 0.5045 0.3602 0.6567 0.4996 0.3832r = 2 0.2013 0.4002 0.4458 0.2013 0.4697 0.5200

Post-dotcom-crash subsample periodr = 0 0.0034 0.0004 0.5433 0.0034 0.0095 0.7537r =1 0.2206 0.1313 0.8792 0.2200 0.0522 0.7893r = 2 0.4318 0.6313 0.8286 0.4318 0.6301 0.8695

Pre-Peso-crisis subsample periodr = 0 0.0629 0.0027 0.17176 0.0629 0.0018 0.2049r = 1 0.3852 0.0456 0.7607 0.3852 0.0415 0.8400r = 2 0.4188 0.3851 0.5631 0.4188 0.3863 0.6625

Post-Peso-crisis, pre-dotcom-crash subsample periodr = 0 0.0455 0.0000 0.5463 0.0455 0.0000 0.3040r = 1 0.2490 0.0172 0.3751 0.2490 0.0472 0.5832r = 2 0.2662 0.3552 0.2759 0.2662 0.3794 0.2556

Note: This table summarizes MacKinnon-Haug-Michelis (MacKinnon et al., 1999) p-values for Johansen’s(1988, 1991) λmax test for cointegration. r=number of cointegration vectors. The null hypothesis in the case ofr = 0 (r = 1, r = 2) is that there is no cointegration vector (one cointegration vector, two cointegration vectors).The alternative hypothesis is that there are r = 1 (r = 2, r = 3) cointegration vectors. In the first stage, the nullhypothesis r = 0 is tested. If the null hypothesis of non-cointegration cannot be rejected, there is no evidenceof one cointegration vector. If the null hypothesis can be rejected, in the second stage, the null hypothesis r = 1is tested. If the null hypothesis cannot be rejected, there is evidence of one cointegration vector. If the nullhypothesis can be rejected, in the third stage, the null hypothesis r = 2 is tested. If the null hypothesis cannot berejected, there is evidence of two cointegration vectors. If the null hypothesis can be rejected, there is evidence ofthree cointegration vectors, implying that the three series being analyzed are stationary. The sample periods arethe following: (1) pre-NAFTA subsample period ends 12/1993; (2) post-NAFTA, pre-dotcom-crash subsampleperiod from 01/1994 to 02/2000; (3) post-dotcom-crash subsample period from 2000/03 to the end of thesample period; (4) pre-Peso-crisis subsample period ends 12/1994; and (5) post-Peso-crisis, pre-dotcom-crashsubsample period from 01/1995 to 02/2000. We did not restrict the coefficients of the short-run dynamics of themodel to be constant across subsample periods. The table summarizes the results for a vector error correctionmodel (VECM) with three lags. The results that are based on estimates of speculative bubbles derived froma state-space model with no restriction on the parameter φ are summarized under the heading ‘Unrestrictedmodel’ The results that are based on estimates of speculative bubbles derived from a state-space model in thepresence of the restriction 0 < φ < 1 are summarized under the heading ‘Restricted model’.

Interestingly, there is also evidence of cointegration linkages betweenfundamentals during the pre-NAFTA subsample period. In order to interpretthis evidence, one could argue, on the one hand, that the implementation of theNAFTA accord was anticipated by investors in the pre-NAFTA period. On theother hand, however, Mexico had acceded to the General Agreement on Tariffsand Trade (GATT) in 1985, it had eliminated the majority of its trade barriers at

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Table 7. Cointegration coefficients of Mexican fundamentals

VECM(2) VECM(3)

Unrestricted model Restricted model Unrestricted model Restricted model

Pre-NAFTA subsample periodCE1 0.2576 (0.0823) 0.2649 (0.1032) 0.2606 (0.0654) 0.2381 (0.0596)CE2 1.1363 (0.3728) 1.1822 (0.4692) 1.1465 (0.3129) 1.0690 (0.2858)

Post-NAFTA, pre-dotcom-crash subsample periodCE1 −0.0268 (0.0083) −0.0256 (0.0126) −0.0262 (0.0058) −0.0237 (0.0068)

Post-dotcom-crash subsample periodCE1 −0.0885 ( 0.0739) −0.0684 (0.0963) −0.1043 (0.0808) −0.2283 (0.1192)

Pre-Peso-crisis subsample periodCE1 0.2746 (0.0876) 0.2656 (0.0944) 0.2849 (0.0648) 0.2605 (0.0551)CE2 1.2158 (0.3954) 1.1764 (0.4190) 1.2232 (0.2912) 1.1439 (0.2471)

Post-Peso-crisis, pre-dotcom-crash subsample periodCE1 0.1296 (0.0290) 0.1345 (0.0361) 0.1258 (0.0287) 0.1283 (0.0291)CE2 −0.7065 (0.1203) −0.6902 (0.1377) −0.7044 (0.1233) −0.6593 (0.1286)

Note: This table summarizes the normalized coefficients of the cointegration vector of fundamentals.The VECM features either one (CE1) cointegration vector or two (CE1 &CE2) cointegration vectors.The test statistics λtrace and λmax yield identical cointegration vectors. The row headed CE1 summarizesthe normalized coefficient of the Mexican fundamentals in the case of one cointegration vector andin the first cointegration vector (standard error in parenthesis). The row headed CE2 summarizes thenormalized coefficient of the Mexican fundamentals in the second cointegration vector (standard error inparenthesis). We present CE2 only in those cases in which the test statistics λtrace and λmax yield evidenceof two cointegration vectors. In the case of one cointegration vector, the coefficient of the US fundamentalshas been normalized to unity (this coefficient and the Canadian coefficient are not shown in the table).In the case of two cointegration vectors, the coefficient of the US (Canadian) fundamentals have beennormalized to unity (not shown in the table). The sample periods are the following: (1) pre-NAFTAsubsample period ends 12/1993; (2) post-NAFTA, pre-dotcom-crash subsample period from 01/1994 to02/2000; (3) post-dotcom-crash subsample period from 2000/03 to the end of the sample period; (4) pre-Peso-Crisis subsample period ends 12/1994; and (5) post-Peso-crisis, pre-dotcom-crash subsample periodfrom 01/1995 to 02/2000. We did not restrict the coefficients of the short-run dynamics of the modelto be constant across subsample periods. VECM(2) (VECM(3)) denotes a vector error correction model(VECM) with two (three) lags. The results that are based on estimates of speculative bubbles derived from astate-space model with no restriction on the parameter φ are summarized under the heading ‘Unrestrictedmodel’ The results that are based on estimates of speculative bubbles derived from a state-space model inthe presence of the restriction 0 < φ < 1 are summarized under the heading ‘Restricted model’.

the beginning of the sample period, and it had undertaken a battery of reformstriggering financial liberalization in 1989 (Tornell et al., 2004, p. 3). Therefore, it isnot unreasonable to argue that the Mexican economy might have been integratedalready to a significant extent with the economies of Canada and the UnitedStates before NAFTA came into force.

Whether such an argumentation is justified can be analyzed by studying thecointegration vectors in more detail. To this end, Table 7 summarizes the normal-ized coefficients of Mexican fundamentals in the estimated cointegration vectors.Depending on the results of the λtrace and λmax statistics, the table shows resultsfor one or two normalized cointegration vectors. It should be mentioned that thetest statistics λtrace and λmax yield identical cointegration vectors.

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The row headed CE1 summarizes the normalized coefficient of the Mexicanfundamentals in the case of one cointegration vector and, in case of two cointe-gration vectors, in the first cointegration vector (standard error in parenthesis).The row headed CE2 summarizes the normalized coefficient of the Mexicanfundamentals in the second cointegration vector (standard error in parenthesis).We present CE2 only in those cases in which the test statistics λtrace and λmax yieldevidence of two cointegration vectors. In the case of one cointegration vector, thecoefficient of the US fundamentals has been normalized to unity (this coefficientand the Canadian coefficient are not shown in the table). In the case of two coin-tegration vectors, the coefficient of the US (Canadian) fundamentals have beennormalized to unity (not shown in the table).

The results indicate that cointegration linkages between the fundamentals ofthe Mexican stock market and the stock markets of the other two NAFTA membercountries existed before the NAFTA was implemented. In other words, the cointe-gration vectors support the notion that the Mexican economy had been integratedwith the economies of the other two NAFTA member countries before NAFTAcame into force. In the post-NAFTA, pre-dotcom-crash subsample period, thereis evidence of only a single cointegration vector, not two cointegration vectors.Still, the fundamentals of the Mexican stock market remained significant in thesingle cointegration vector. It is also interesting to note that, in the post-dotcom-crash period, there is hardly any evidence that Mexican fundamentals shared acommon stochastic trend with the fundamentals of the US and Canadian stockmarket. This weak evidence is not surprising insofar as a dotcom bubble, whichwas an important feature of the stock markets in Canada and the United Statesin the second half of the 1990s, did not develop at par in Mexico (Figure 1). Ourresults, thus, corroborate the result documented in earlier literature that the dot-com bubble had a significant impact on the international comovement of stockmarkets. Our results go beyond results reported in earlier literature because wedocument the changing cointegration of fundamentals.

Consistent with the evidence of changing cointegration linkages between thestock markets of the NAFTA member countries, the results summarized in Table 7suggest that the point estimates of the cointegration coefficients changed acrossthe different subsample periods under consideration. In economic terms, ratifi-cation of the NAFTA accord could have been one source of parameter changesacross subsample periods, but there are other potential sources as well. A broadrange of financial and institutional reforms that Mexico undertook in the late1980s and the early 1990s, the balance-of-payment crisis of 1994–1995, and therun up and eventual collapse of the dotcom bubble may have brought aboutchanges in the cointegration coefficients.

In order to account for temporal variation in the cointegration linkages betweenthe stock markets of the NAFTA member countries, we ran, as a robustness check,a rolling-window cointegration test. We report in Figure 3 the results for a 5-yearrolling window. In order to make the interpretation of the results simple, we com-puted the ratios of the λtrace and λmax statistics and their respective 95%criticalvalues. If the ratios exceed the value one, the null hypothesis can be rejected (foran application of this technique, see Rangvid, 2001 and Pascual, 2003). Whilethe λtrace and λmax occasionally dropped below the unit line, the results of the

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rolling-window cointegration tests show that the cointegration linkages betweenfundamentals were relatively strong until around 2005 (Panel A of Figure 3). Incontrast, evidence of cointegration linkages between the speculative bubbles isrelatively weak (Panel B), where the null hypothesis of noncointegration can berejected at the beginning of the sample period, at around 1999/2000, and againin 2004/2005.

3.3 Threshold Cointegration

The results of the rolling-window cointegration test have yielded evidence ofoccasional cointegration linkages between speculative bubbles. This evidencemay reflect that complex speculative dynamics in stock markets gave rise to tem-porary fluctuations in cointegration linkages between speculative bubbles. Onecould imagine, for example, that cointegration linkages were relatively weak whenspeculative bubbles were small, but strong and significant when speculative bub-bles gave rise to large and potentially ‘contagious’ swings in stock prices. Aninteresting question then is whether and, if so, to which extent such large and‘contagious’ swings in stock prices spilled over from the mature industrial coun-tries, United States and Canada, to the emerging market country in our sample,Mexico.

In order to study this question, we estimated a threshold-cointegration model.Specifically, we considered the threshold-cointegration model studied by Endersand Granger (1998) and Enders and Siklos (2001). In a first step, we estimatedfor the stock market indexes (fundamentals, speculative bubbles) a cointegrationequation and we saved the residuals from this cointegration equation. In a sec-ond step, we estimated on the residuals a threshold autoregressive model (TAR)and a momentum TAR (M-TAR) model. The TAR model consists of an Engle-Granger regression equation, extended to incorporate two cointegration terms.The first cointegration term operates whenever the lagged residuals exceed a cer-tain threshold, and the second cointegration term operates whenever the laggedresiduals fall short of this threshold. In the M-TAR model, the magnitude of thelagged change in the residuals, relative to a threshold, determines which one ofthe two cointegration terms is operating. In a third step, we saved the (changes in)residuals from the cointegration equation and ordered them in ascending order,where we dropped the smallest and largest 15% of the ordered residuals. Everysingle element of the resulting series of ordered residuals was considered a candi-date for a threshold, where we selected the optimal threshold by minimizing theresidual sum of squares of the Engle-Granger TAR (M-TAR) regression equation.In a fourth step, we studied the null hypothesis of noncointegration by means ofan F-test, as documented by Enders and Siklos (2001).7

7In contrast to the subsample-based cointegration analysis and the rolling-window cointegrationtest that we examined in Section 3.2, the parameters of the threshold cointegration model areassumed to be constant over time, conditional on being below or above the threshold. It shouldalso be mentioned that we used a standard F-test to study the possibility of asymmetric thresholdadjustments, which arises when the coefficients of the two threshold-cointegration terms differ. Wedid not find strong evidence of asymmetries (results are not reported). Finally, it should be noticedthat an analysis of threshold cointegration ‘...is simple to implement in the bivariate case, but would

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Table 8. Threshold cointegration tests

Data TAR Model M-TAR Model

Panel A: Full sample periodStock market indexes 4.9110 6.5714Fundamentals 3.6319 3.5886Speculative bubbles 14.4090 14.4530

Panel B: Pre-NAFTA subsample periodData TAR Model M-TAR ModelStock market indexes 2.2530 2.1685Fundamentals 4.5128 10.1680Speculative bubbles 5.4551 5.5048

Panel C: Post-NAFTA Subsample PeriodData TAR Model M-TAR ModelStock market indexes 6.5111 6.7355Fundamentals 8.4379 8.7460Speculative bubbles 8.1268 7.9268

Note: This table summarizes F-tests of the hypothesis that both cointegration terms in the Engle-Granger TARand M-TAR models are zero. We included one lag in both models to capture any remaining autocorrelation.The critical 95% values documented by Enders and Siklos (2001) are 6.93 and 6.63 for the TAR and M-TARmodels, respectively. In order to allow for contagious swings in stock prices to spill over from the United Statesand Canada to Mexico, we assumed that the stock market index (fundamentals, speculative bubbles) for Mexicois the dependent variable in the threshold cointegration model.

Table 8 summarizes the results. For the full sample (Panel A), we found evidenceof threshold cointegration only for speculative bubbles. For the pre-NAFTA period(Panel B), the M-TAR model yields evidence of threshold cointegration withrespect to fundamentals. For the post-NAFTA period (Panel C), the TAR modeland the M-TAR model yield evidence of threshold cointegration for fundamentalsand speculative bubbles. It thus seems that, following the implementation of theNAFTA accord, cointegration linkages strengthened, especially as far as specula-tive bubbles are concerned. This strengthening of cointegration linkages betweenspeculative bubbles is in line with the evidence of cointegration linkages at around1999/2000 and 2004/2005 that we recovered by means of the rolling-windowcointegration test. The stronger evidence of cointegration linkages between spec-ulative bubbles in the post-NAFTA subsample period, however, should not beinterpreted to indicate that the implementation of the NAFTA accord was instru-mental for the strengthening of the cointegration linkages between speculativebubbles. Threshold cointegration between speculative bubbles may also capturethe impact of, for example, the market jitters, and potential spillover effects fromthe United States and Canada to Mexico, caused by the rise and collapse of thedotcom bubble. The results of estimating the threshold-cointegration model sim-ply imply that the possibility cannot be ruled out that speculative bubbles gave rise

be difficult to implement in higher dimensional cases’ (Hansen & Seo, 2002, p. 294). This is thereason why we did not implement the threshold-cointegration analysis in a vector-error-correctionmodel.

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to temporary contagious swings in speculative bubbles after the implementationof the NAFTA accord.

4. Concluding Remarks

We have documented results that show that cointegration linkages between thestock markets of the NAFTA countries have changed over time, where speculativebubbles showed some signs of threshold cointegration. Another main result isthat the cointegration linkages between fundamentals were stronger than thecointegration linkages between speculative bubbles. While this result may indicatethat regional trade flows have led to a closer ‘fundamental’ comovement of thestock markets of the NAFTA member countries, more research needs to be donebefore general policy-relevant conclusions can be drawn from our research.

In economic terms, it would be interesting to explore in future research whetherthe evidence of cointegration linkages among fundamentals that we found in ourresearch is a temporary or a permanent phenomenon. It would also be interestingto analyze in future research to what extent cross-border cointegration linkagesbetween stock-market fundamentals reflect, for example, goods market integra-tion (Darrat & Zhong, 2005) and intensified trade integration among the NAFTAmember countries (Johnson & Soenen, 2003). It should also be mentioned thatwe were concerned in our empirical analysis with aggregate stock market indexesonly. In future research, it could be interesting to analyze whether our results onthe cointegration links between the fundamentals and the speculative bubbles ofthe stock markets of the NAFTA member countries also apply when it comesto the analysis of sectoral stock market data. It could be the case that goodsmarket integration and intensified trade integration have had a differential effecton the various economic sectors of the NAFTA member countries, and sectoralstock market data may reflect this differential effect. For example, Aggarwal etal. (1998) find that, as far as US equity returns are concerned, NAFTA news had apositive effect on some industries (chemicals and machinery), but a negative effecton other industries (automotive products and telecommunications). Ciner (2006)finds cointegration linkages in the late 1990s between the telecommunicationsand technology industry indexes of the stock markets of the NAFTA membercountries.

In technical terms, it is important to note that we derived our results from onespecific model of speculative bubbles. Because testing for speculative bubbles instock markets is a delicate and controversial task, it would be interesting to derivein future research decompositions of the stock market indexes of the NAFTAmember countries into fundamentals and speculative bubbles from alternativemodels of speculative bubbles. It would also be interesting to explore in moredetail the implications of the dynamics of speculative bubbles for the power andthe size of tests for cointegration between speculative bubbles. Our decision toanalyze economically well motivated subsample periods (for example, the pre-NAFTA period versus the post-NAFTA, pre-dotcom-crash subsample period)should curb the implications of near-unit-root dynamics for tests of cointegrationlinkages between speculative bubbles. Moreover, it is reassuring that the resultsfor the unrestricted model closely resemble the results for the restricted model.

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It should also be noted that the specific characteristics of the dynamics of specu-lative bubbles should not affect the power and the size of tests for cointegrationlinkages between fundamentals. In our model, fundamentals follow processesthat are integrated of order one. Notwithstanding, the immense attention thatinternational linkages between fundamentals and international linkages betweenspeculative bubbles often receive in the policy arena warrants a closer analysis ofthe implications of the dynamics of speculative bubbles for cointegration testingin future research.

Acknowledgements

We thank an anonymous referee for very helpful comments. The usual disclaimer applies.

References

Aggarwal, R. & Kyaw, N.A. (2005) Equity market integration in the NAFTA region: Evidence from unit rootand cointegration tests, International Review of Financial Analysis, 14, pp. 393–406.

Aggarwal, R., Long, M., Moore, S., & Ervin, D. (1998) Industry differences in NAFTA’s impact on the valuationof U.S. companies, International Review of Financial Analysis, 7, pp. 137–152.

Atteberry, W.L. & Swanson, P.E. (1997) Equity market integration: The case of North America, North AmericanJournal of Economics and Finance, 8, pp. 23–437.

Bekaert, G., Harvey, C.R. & Lumsdaine, R.L. (2002) The dynamics of emerging market equity flows, Journalof International Money and Finance, 21, pp. 295–350.

Bhar, R. & Hamori, S. (2005) Empirical Techniques in Finance (Berlin: Springer Verlag).Blaine, M.J. (1998) Deja vu all over again: Explaining Mexico’s 1994 financial crisis, The World Economy, 21,

pp. 31–55.Brooks, R. & Del Negro, M. (2004) The rise in comovement across national stock markets: Market integration

or IT bubble? Journal of Empirical Finance, 11, pp. 659–668.Choudhry, T. (1997) Stochastic trends in stock prices: Evidence from Latin American markets, Journal of

Macroeconomics, 19, pp. 285–304.Ciner, C. (2006) A further look at linkages between NAFTA equity markets, Quarterly Review of Economics

and Finance, 46, pp. 338–352.Darrat, A.F. & Zhong, M. (2005) Equity market linkages and multinational trade accords: the case of NAFTA,

Journal of International Money and Finance, 24, pp. 793–817.Diba, B.T. & Grossman, H. (1988) Explosive rational bubbles in stock prices? American Economic Review, 78,

pp. 520–530.Elliott, G., Rothenberg, T.J. & Stock, J.H. (1996) Efficient tests for an autoregressive unit root, Econometrica,

64, pp. 813–836.Enders, W. (1995) Applied Econometric Time Series (New York: Wiley).Enders, W. & Granger, C.W.J. (1998) Unit-root tests and asymmetric adjustment with an example using the

term structure of interest rates, Journal of Business and Economics Statistics, 16, pp. 304–311.Enders, W. & Siklos, P.J. (2001) Cointegration and threshold adjustment, Journal of Business and Economics

Statistics, 19, pp. 166–176.Engle, R.F. & Granger, C.W.J. (1987) Cointegration and error correction: Representation, estimation, and

testing, Econometrica, 55, pp. 251–276.Evans, G.W. (1991) Pitfalls in testing for explosive bubbles in asset prices, American Economic Review, 81, pp.

922–930Ewing, B.T., Payne, J.E. & Sowell, C. (1999) NAFTA and North American stock market linkages: An empirical

note, North American Journal of Economics and Finance, 10, pp. 443–451.Ewing, B.T., Payne, J.E. & Sowell, C. (2001) Transmission of conditional stock return volatility across North

American markets: Evidence from pre- and post-NAFTA, International Trade Journal, 15, pp. 409–427.

Dow

nloa

ded

by [

The

Uni

vers

ity o

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anch

este

r L

ibra

ry]

at 0

3:51

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Oct

ober

201

4


Fleischer, P., Maller, R. & Müller, G. (2011) A Bayesian analysis of market information linkages among NAFTAcountries using a multivariate stochastic volatility model, Journal of Economics and Finance, 35, pp.123–148.

Froot, K.A. & Obstfeld, M. (1991) Intrinsic bubbles: The case of stock prices, American Economic Review, 81,pp. 1189–1214.

Gregory, A.W. & Hansen, B.E. (1996) Residual-based tests for cointegration in models with regime shifts,Journal of Econometrics, 70, pp. 99–126.

Gurkaynak, R.S. (2008) Econometric tests of asset price bubbles: Taking stock, Journal of Economic Surveys,22, pp. 166–186.

Hansen, B.E. & Seo, B. (2002) Testing for two-regime threshold cointegration in vector error-correction models,Journal of Econometrics, 110, pp. 293–318.

Henry, P.B. (2000) Stock market liberalization, economic reform, and emerging market equity prices, Journal ofFinance, 55, pp. 529–564.

Johansen, S. (1988) Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control,12, pp. 231–254.

Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressivemodels, Econometrica, 59, pp. 1551–1580.

Johnson, R. & Soenen, L. (2003) Economic integration and stock-market comovement in the Americas, Journalof Multinational Financial Management, 13, pp. 85–100.

Kim, C.J. & Nelson, C.R. (2000) State-space Models with Regime Switching (Cambridge, MA: MIT Press).LeRoy, S.F. (2004) Rational exuberance, Journal of Economic Literature, 42, pp. 783–804.MacKinnon, J.G., Haug, A.A. & Michelis, L. (1999) Numerical distribution functions of likelihood ratio tests

for cointegration, Journal of Applied Econometrics, 14, pp. 563–577.Montiel, P.J. (2003) Macroeconomics in Emerging Markets (Cambridge: Cambridge University Press).Pascual, A.G. (2003) Assessing European stock market (co)integration, Economics Letters, 78, pp. 197–203.R Development Core Team (2010) R: A Language and Environment for Statistical Computing (Vienna: R Foun-

dation for Statistical Computing). ISBN 3-900051-07-0. Available at http://www.R-project.org. (Version2.10.1).

Rangvid, J. (2001) Increasing convergence among European stock markets? A recursive common stochastictrends analysis, Economics Letters, 71, pp. 383–389.

Reimers, H.E. (1992) Comparisons of tests for multivariate cointegration, Statistical Papers, 33, pp. 335–359.Romalis, J. (2007) NAFTA’s and CUSFTA’s impact on international trade, Review of Economics and Statistics,

89, pp. 416–435.Taylor, M.P. & Peel, D.A. (1998) Periodically collapsing stock price bubbles: A robust test, Economics Letters,

61, pp. 221–228.Tornell, A., Westermann, F. & Martinez, L. (2003) Liberalization, growth and financial crises: Lessons from

Mexico and the developing world, Brooking Papers in Economic Activity, 34, pp. 1–112.Tornell, A., Westermann, F. & Martinez, L. (2004) NAFTA and Mexico’s Less-than-stellar Performance.

Cambridge, MA: NBER Working Paper 10289.Wu, Y. (1995) Are there rational bubbles in foreign exchange markets? Evidence from an alternative test, Journal

of International Money and Finance, 14, pp. 27–46.Wu, Y. (1997) Rational bubbles in the stock market: accounting for the U.S. stock-price volatility, Economic

Inquiry, 35, pp. 309–319.

Technical AppendixBecause real stock prices and real dividends are nonstationary, we used the first-difference operator, �, to rewriteequation (5) as

�pt = �pft + �bt = (1 − φ)

∞∑j=0

φj(Etdt+j − Et−1dt+j−1) + �bt (7)

An ARIMA(n, 1, 0) model captures the dynamics of demeaned real dividends:

�dt =n∑

j=1

ϕj�dt−j + ut (8)

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http://www.R-project.org


where n = 1, 2, . . . and the mean-zero disturbance term, ut, is normally distributed with variance σ 2u . The

disturbance terms, εt (see equation (5)) and ut, are mutually independent. The companion form of equation (8)can be expressed as

Yt =(

ϕ ϕn

1(n−1)×(n−1) 0(n−1)×1

)Yt−1 + νt = AYt−1 + νt, (9)

where Yt = (�dt, �dt−1, . . . , �dt−n+1)′, νt = (

ut, 01×(n−1)

)′, ϕ = (ϕ1, ϕ2, . . . , ϕn−1), and 0 (1) denotes amatrix of zeros (an identity matrix) with dimension given in the index.

Estimation of the model is complicated by the fact that a speculative bubble is not directly observable. Wethus transformed the model into a state-space model. A state-space model consists of a measurement equationand a state equation. Following Bhar & Hamori (2005), the state equation can be written as

(Y

′t, �dt−n, bt, bt−1

)′ =(

A 0n×3a B

)(Y

′t−1, �dt−n−1, bt−1, bt−2)

′ + Ut (10)

where a = (03×(n−1), (1, 0, 0)′), and the other matrices are defined as

B =⎛⎝0 0 0

0 1/φ 00 1 0

⎞⎠ , and Ut =

⎛⎝ ut

0n×1(εt, 0)′

⎞⎠

Using equation (9) to rewrite equation (7), the measurement equation of the state-space model can be expressedas

(�pt, �dt)′ =

(1 + m1 m2 − m1 · · · −mn 1 −1

1 0 · · · 0 0 0

)(Y

′t, �dt−n, bt, bt−1)

′ (11)

where m1, m2, . . . denote the elements of M = g(1n×n − A)−1A[1n×n − (1 − φ)(1n×n − φA)−1] andg = (1, 01×(n−1)).

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Documents

On the Linkages of the Stock Markets of the NAFTA Countries: Fundamentals or Speculative Bubbles?