Stock Market Efficiency in Developing Economies

Abstract

This article analyses the degree of stock market efficiency in three emerging economies— India, China and Brazil. It tests to see if US stock returns have an influence on endogenous stock returns, even after controlling for domestic macroeconomic variables. A country-specific vector auto-regression model is used to test the short-run effects and the fully modified ordinary least square procedure has been used to find the long-run relationship, thus checking for degree of efficiency in these stock markets. The results indicate that, despite controlling for key domestic stock return determinants, US stock returns have a significant positive relationship with the stock returns of all three countries.

JEL Classification: G15, C32, C34

Keywords

Emerging Market Economies Vector Auto-regression Panel Cointegration Fully Modified Ordinary Least Square (FMOLS)Dynamic Ordinary Least Square (DOLS)

1. INTRODUCTION

Economists and finance specialists have long studied stock markets; some have tried explaining their determinants while others have studied regional and international linkages in a bid to better explain and predict returns. Recent studies of the global financial crisis that began in 2007 showed how macroeconomic deterioration of the US economy led to a slump in its stock index and quickly spread to other economies. Unlike the Asian crisis of 1997, Russian crisis of 1998 or the Brazilian crisis of 1999 that were severe in their own terms, especially because of regional co-movement of stock prices, the global financial crisis originated from the most influential market, the US (Goetzmann and Jorian, 1999, based on the level of trade), and has triggered prolonged worldwide fear and a fundamental change in co-movements among international markets for both developed and emerging economies (Cheung et al., 2010).

This article deals with the concept of stock market efficiency. A country’s financial market is said to be efficient when its stock returns reflect the fundamentals and risks of its economy, rather than those of others, that is, its stock indices react to macroeconomic news emerging from the country rather than from other countries. This definition has been derived from the efficient market hypothesis (Fama, 1981) for financial markets, developed in the 1970s and 1980s, and has been used in recent studies (Lai et al., 2013; Srinivas, 2011). Equivalently, an inefficient stock market can be seen as one which has a high degree of co-movement with another country’s stock market, even after controlling for its own domestic influences. The theory following the research question has mainly two parts: trying to understand the endogenous macroeconomic determinants of stock returns and studying another country’s influence on endogenous returns.

The relationship between stock returns and different macroeconomic fundamentals has been analysed following the arbitrage pricing theory (APT) established by Ross (1976) and later extended (Connor and Korajczyk, 1981), which models expected returns as a function of various macroeconomic factors. The general conclusion of the theory is that an additional component of long-run returns is required and obtained whenever a particular asset is influenced by systematic economic news and that no extra reward can be earned by bearing diversifiable risk. The APT models the tendency of expected returns to move together via statistical factor decomposition:

R_{}^{e} {_{j}^{}}_{, t}^{} ​ = α ​_{j} + {\sum^{​}}_{K}^{k = 1} β ​_{j k} f_{k} + ε_{j}, j = 1, \dots, N

where f_k are the factors, β_jk are the betas or factor loadings and ε_j are residuals.

The law of one price tells us that there is a discount factor m linear in factors that price the factors. Hence, there is an expected return-beta model linear in the factors:

E (R_{​}^{e}) = α ​_{j} + {\sum^{​}}_{K}^{k = 1} β_{j k} E (f ​ k), j = 1, \dots, N .

The idea behind the APT is that the α_js are small if the residuals are small.

However, the APT does not in itself say which factors explain returns best or even if they capture the entirety of the situation, which is more of an empirical question. After a decade, Chen et al. (1986) posited that five economic and non-economic financial variables—industrial production (IP), unanticipated inflation, changes in anticipated inflation, twists in the yield curve and changes in risk premium—are plausible sources of common variation among equity returns. Their cross-sectional regression-based empirical study finds that IP, anticipated inflation and risk premium are significant factors. Evidence for the remaining were mixed and varied with the period of investigation; importantly, a problem with the approach was that the variable selection was very subjective. Subsequent literature has tried to identify and explain a few variables that by and large explain stock market returns in a country. This practice, in tune with the APT, makes the residuals as small as possible, so as to minimise the unexplained or arbitrary part of the stock returns. The theory highlights the following variables:

Inflation. Theory presents two views on the relation between inflation and stock returns. The earlier view draws on Irving Fisher’s theory of interest, which says that expected rates of return consist of a ‘real’ return and the expected rate of inflation, and that the real return does not move systematically with the rate of inflation; in short, investors will on average be fully compensated for erosion in the purchasing power (Fisher, 1930). However, another view (Geske and Roll, 1983) argues that a rise in the expected inflation rate leads to restrictive monetary policies, which increase interest rates and hence have a negative effect on stock market activity. The effect of high interest rates would not be neutralised by an increase in cash flows resulting from inflation, but these do not increase at the same rate as inflation. Hence, theoretically, it is still a matter of debate.

Index of IP. Fama (1990) determined that the growth rate of IP has a strong concurrent relation with stock returns. The productive capacity of the economy is dependent on the accumulation of real assets, which in turn contribute to the ability of firms to generate cash flows. The measure of IP, which is a proxy for real activity, is pro-cyclical (Tainer, 1993); therefore, a rise in IP signals economic growth meaning higher returns.

Interest Rate. The theory deals with stock returns and interest rate by observing firm behaviour—a higher interest reduces the attractiveness of investment for firms, thus, shrinking the value of stock returns—and hypothesises a negative relation between the two. Also, most firms finance their capital by borrowing, so a reduction in interest rates reduces the costs of borrowing and has a positive effect on returns.

This article would like to see how US stock returns affect the stock returns of three emerging economies, while controlling for their macroeconomic fundamentals such as inflation, gross domestic product (a measure of it) and interest rate. In other words, it is important to see if any linkages exist between US stock prices and stock prices of this panel. We want to check if information from endogenous macroeconomic fundamentals is enough to explain stock market returns (efficient stock markets) or if the US plays an important role in determining stock returns. If the latter is true, the extent of the role would determine the degree of efficiency of these markets. Another significant contribution of this article is the use of the fully modified ordinary least square (FMOLS) technique, which is an improvement over the OLS technique that suffers from a spurious cointegration problem and misspecifications in a panel context. Further checks by the dynamic OLS (DOLS) method are used to substantiate the results.

Testing for stock market efficiency is carried out on a panel of emerging economies—India, China and Brazil. To the best of my knowledge, such testing to find the degree of stock market efficiency has not been carried out before, and therefore doing so for these three important emerging economies provides a good starting point. Factors contributing to the selection of these countries for study are: they are all characterised by strong economic growth and large populations and do not provide any anomalies in the variables considered that may bias our results. They offer good profit opportunities mainly due to their good macroeconomic health and are, thus, popular destinations for investment. As popular destinations for foreign direct investment and portfolio investment, greater stock market inefficiency means higher risks to investment, as stock returns cannot be exclusively predicted by information available (such as macroeconomic indicators like the money and goods markets), leading to instability and discouraging investors.

From a policy frame of view, it is important to understand stock market inefficiencies to attract—and also retain—foreign investments in the country. The degree of integration among global financial markets tends to change over time. Bekaert and Harvey (2000) show that correlations with developed economies increase after liberalisation of capital markets in emerging economies. These three countries are the most recent examples of liberalisation and pro-globalisation policies leading to higher growth.

Additionally, these countries are not characterised by excessive regional interdependence. China being the Asian giant is not very easily influenced by policies affecting returns in its neighbouring regions. Brazil occupies a similar position in South America where other countries are not dominant enough to leave a mark on its returns. India does not share significant trade relations with any of its neighbours except China (however, its trade with the United States is significantly higher). Therefore, regional influence is insignificant if not absent.

2. LITERATURE REVIEW

The literature has focussed on trying to explain stock market returns through macroeconomic fundamentals. The main objective of the investigations so far has been to explain expected returns over time and to find the degree and direction of the impact of these factors. Earlier empirical studies focussed on developed countries, but quickly expanded to emerging economies. Mukherjee and Naka (1995) find a long-run relationship between stock returns and six macroeconomic variables in Japan by using a vector error correction model (VECM) including inflation, interest rate and index of IP. Nasseh and Strauss (2000) studied the long-run relationships between stock market prices and domestic and international economic activities in six European economies. The results showed that although stock prices are explained by economic fundamentals in the short run, the underlying volatility inherent in stock prices is related to macroeconomic movements in the long run.

These results, earlier established mainly for developed countries, were quickly generalised to developing nations and emerging economies, especially during and after the 1990s. Kwon and Shin (1999) illustrate, using a VECM, that Korean stock indices are cointegrated with macroeconomic variables like production index, exchange rate, trade balance and money supply. Sampath (2011) uses an auto-regressive distributed lag approach and finds that the wholesale price index has a negative effect and the index of IP a positive statistically significant long-run effect on stock prices in India. Hosseini et al. (2011) find that for China, the long-term impacts of crude oil price, money supply and inflation are positive, whereas the effects of IP are negative. For India, the impact of oil prices and money supply is negative, but IP and inflation have a positive impact. These studies and others have established empirically that the stock indices of a country are affected by its macroeconomic variables and have a long-run relationship with them, that is, that factors like IP, inflation, interest rate reflect the information originating from goods and money markets and can explain stock market returns.

When it comes to checking for the existence of stock market co-movements, the empirical benchmark in these studies has been to test for the existence of short-run and long-run relationships between the stock indices of different countries. Tamir (1972) found that equity markets in the United Kingdom, Germany and Japan respond immediately to price changes in the equity market of the United States; however, the tests used data were taken after World War II, and hence biased the results. Campbell and Hamao (1992) found that the US price indices helped forecast Japanese excess returns in 1980s. Koutmos (1996) investigated dynamic first-moment and second-moment interactions among the stock markets of France, Germany, Italy and the United Kingdom, and found evidence of a multidirectional lead/lag relationship; however, this was confined to industrially advanced countries. Chaudhuri (1997) used the Engle–Granger cointegration and Granger causality test to examine the regional dependences among the stock indices of six Latin American countries for the period 1985–93 and found a long-run relationship among them. Taneja (2012) finds that Indian stock markets have a long-run association with the United States, France, Japan and Taiwan. Similarly, Srikanth (2012) uses the VECM to establish a long-run relationship between India, Malaysia, Japan and China. Rapach et al. (2013) investigate lead–lag relationships among monthly country stock returns and identify a leading role for the United States. They find that lagged US returns significantly predict returns in 11 non-US industrialised countries like Australia, Canada, France, Germany, Sweden and the United Kingdom, even above their own lagged returns. The predictions are strengthened by using a news diffusion model as a robustness check; however, for comparison, more macroeconomic fundamentals could have been tested.

Findings from theory and the existing literature of empirical work, thus, indicate that a number of macroeconomic variables—inflation, index of IP and interest rate—are strongly related to the real stock prices. Another finding is the important role of the United States, especially considering its significance in terms of trade and financial institutions. A significant relationship between US returns and domestic returns, despite controlling for macroeconomic factors, would help us conclude that the particular country has an inefficient stock market.

3. DATA AND METHODOLOGY

Monthly data from 1999 to 2013 were taken for the three countries—India, Brazil and China. The variables as specified above, for which data have been collected, are the index of IP, inflation, interest rate and stock market returns. A change in IP is used as a measure of real activity, because it may explain more of the variation in returns than other measures of real activity like gross domestic product (Fama and French, 1996) and is also available in monthly series. Inflation is measured by the consumer price index (in percentage) because it is believed that when assessing real returns on stocks, market participants are responsive to consumer goods prices (Abdullah and Hayworth, 1993). Benchmark interest rates released by the monetary authorities of the individual countries have been considered (as in most other similar studies).

The stock exchanges under study for the three countries are the Bombay Stock Exchange, the Shanghai Stock Exchange and the Ibovespa Index from Sao Paulo. These cover the largest number of companies in the country, and thus best reflect the financial condition of the country. The New York Stock Exchange (NYSE) Composite Index is used to study the influence of US stock returns. Data have been collected from The World Bank Database, Reserve Bank of India database, National Bureau of Statistics of China and Trading Economics website.

To evaluate efficiency, we need to see the effects of the selected variables on stock indices in the short run and long run; vector auto-regression is used for analysing the short run and the FMOLS technique is used for the long run. Country-specific vector auto-regressions (VARs) give the desired flexibility and allow for best fit depending on the situation. Conducting short-run analysis gives broader findings and perspective. A FMOLS, designed to provide optimal estimates of cointegrating regressions, avoids problems associated with an OLS relating to spurious regressions, but still gives an estimated equation, allowing the reader to understand the relative influence of the factors in determining returns. Besides providing a relative understanding, the coefficients give the direction and magnitude of the effects of the factors, as well as assist in inter-country comparison and comparisons with the panel.

Figure 1

Source: Author’s own calculation.

3.1 Stationarity and Vector Auto-regression Analysis

When variables are not stationary, their mean, variance and covariance will increase or decrease with time. Estimation based on non-stationary variables results in spurious relationships leading to unreliable R², t-statistics, F-statistics and inconsistent estimators. To test for unit roots, the Dickey–Fuller (DF) test is the most appropriate for an AR (1) model, so the augment DF (ADF) is used, because it captures autocorrelation in higher order lags (p) that might violate the white noise assumption of the error term. The test is setting H₀: ρ = 1 (unit root/non-stationary) against H₁: ρ < 1 (stationary).

ADF allows for the possibility of autocorrelation in the error term for more than one lag. The model is:

Δ Y_{t} = α + δ Y_{t ​ - ​ 1} + β_{1} Δ Y_{t ​ - ​ 1} + β ​_{2} Δ Y_{t - 2} + \dots + β ​_{p} Δ Y_{t - p} + ε_{t}

A simple univariate AR (p) model without exogenous variables is written as:

Y_{t} = μ + φ_{1} Y_{t - 1} + \dots + φ_{p} Y_{t - p} + ε_{t},

where Y_t is a function of a constant, p prior values and a random disturbance term.

Now, consider a vector of n jointly endogenous variables, which can be modelled as a function of n constants, p prior values of the same vector and n disturbances. This pth-order VARis written as:

Φ (L) Y_{t} = μ + ε_{t},

where Φ (L) is a matrix polynomial in the lag operator, Φ (L) ≡ I – Φ₁ (L) – … – Φp (L).

Φ_i are matrices of the coefficients and ε_t is the n-element vector of random disturbances. It is assumed that the order of the VAR is sufficiently high to ensure that the residuals are white noise and there is no residual autocorrelation.

Y_t in the model considered here is a five-variable vector written as:

Y_{t} = {(S t o c k I P I n f l a t i o n I n t e r e s t R a t e U S S t o c k)}^{T}

This model enables us to find the short-run effects of the three macroeconomic variables considered and the effects of US stock returns on the country-specific stock returns. A country-specific VAR is better than a panel VAR method because it allows us to account for the presence of heterogeneity in country data and gives greater flexibility to model specification.

3.2 Panel Data Unit Root Test

Panel unit root tests are more powerful than unit root tests applied to individual series because the information in the time series is enhanced by that contained in the cross-section data. Also, results obtained in the stationarity tests are subject to the amount of data available, so it is advisable to conduct more than one stationarity test. Here, a panel unit root test becomes even more important. A simple description of a panel unit root test is provided in Appendix A.1.

3.2.1 Levin-Lin-Chu (LLC) Test

This test starts with a panel regression model [refer to Equation (1) in Appendix A.1]. Since the model is likely to suffer from serial correlation, the LLC test augments it with additional lags of the dependent variable (Levin et al., 2002):

Δ Y_{i t} = ϕ Y_{i}^{}_{, t - ​ 1}^{} + Z ​_{i t} γ_{i} + {\sum^{​}}_{P}^{j = 1} θ_{i j} Δ Y_{i}^{}_{, t - j}^{} + U_{i t}

(1)

where ‘over any value means it is estimated’.

The LLC test assumes that error terms are independently distributed across panels and follow a stationary invertible auto-regressive moving-average process for each panel. By including sufficient lags of Y_i,t in Equation (1), U_i,t will be white noise; the test does not require u_it to have the same variance across panels. Under the null hypothesis of a unit root, Y_i,t is non-stationary, so a standard OLS regression t-statistic for ϕ will have a non-standard distribution that depends in part on the specification of the Z_i,t term. Moreover, the inclusion of a fixed-effect term in a dynamic model like Equation (1) causes the OLS estimate of ϕ to be biased towards zero. The LLC method produces a bias-adjusted t-statistic that has an asymptotically normal distribution.

3.3 Panel Cointegration Tests

3.3.1 Pedroni Cointegration Test

This first estimates the equation below and stores the residuals, ε’_i,t (‘ refers to estimated value):

Y = a_{i} + β_{1 i} X_{1 i, t} + β_{2 i} X_{2 i, t} + \dots + β_{m i} X_{m i}^{}_{, t}^{} + e_{i}^{}_{, t}^{}, t = 1, \dots, T a n d i = 1, \dots, N,

where T is number of observations over time, N is the number of individual members in the panel, M is the number of independent variables and e is the error term. It is assumed that slope coefficients β_1i, …, β_mi and the member-specific intercept a_i can vary across each error term. The original data series for each panel is differenced and the residuals of the differenced regression are obtained:

Δ Y_{i, t} = b_{1 i} Δ X_{1 i, t} + b_{2 i} Δ X_{2 i, t} + \dots + b_{m i} Δ X_{m i, t} + π_{i, t} .

Using the residuals from the differenced regression with a (Newey and West, 1987) estimator, the long-run variance of π’_i,t is calculated and represented as L’²_11,t. Then using the original cointegrating equation, the appropriate autoregressive model is estimated.

Pedroni (1999) suggested two types of tests to determine the existence of cointegration vectors. One is based on a within-dimension approach (i.e., the panel test) that includes four statistics—the panel v-statistic, panel r-statistic, panel PP-statistic and panel ADF-statistic. These statistics pool the auto-regressive coefficients across different members for the unit root tests on the estimated residuals. The other is based on a between-dimensional approach (group test) that includes three statistics—the group ñ-statistic, group PP-statistic and group ADF-statistic. These statistics are based on estimators that merely average the individually estimated coefficients for each member. To determine the lag truncation order of the ADF t-statistic, the step-down procedure and the Schwartz lag-order selection are used.

The null hypothesis of no cointegration of the pooled (within-dimension) estimation is H₀: ρ_i = 1 for all i against H₀: ρ_i = ρ < 1. Here, the alternative hypothesis, the within-dimensional estimation assumes a common value for ρ_i = ρ, which means that it does not allow an additional source of possible heterogeneity across individual country members of the panel. For the pooled between-dimension estimation, the null hypothesis is H₀: ρ_i = 1 for all i against H₀: ρ_i = ρ < 1. This does not assume a common value for ρ_i = ρ. It allows an additional source of possible heterogeneity across individual country members of the panel. As the test is conducted on individual members of the panel (Pedroni, 1999), the existence of cointegration in the panel through this test implies that the individual series also has a long-run relation (Dritaski and Dritaski, 2012).

3.3.2 Kao Residual Cointegration Test

The test (Kao and Chiang, 1999) follows the same approach as the Pedroni test, as it is Engle–Granger based, but it specifies cross-section-specific intercepts and homogeneous coefficients on the first-stage regressors. The main purpose of using this test is to substantiate the results of the Pedroni cointegration test. The existing literature takes the route of panel cointegration, uses it to back other results, especially given that the starting point of the test is common with many other tests. A brief description of the test using the ADF-statistic is given in Appendix A.2.

3.4 Long-run Estimation

3.4.1 Fully Modified Ordinary Least Squares

Consider the static relation:

Y_{i t} = a_{i} + x_{i t} ’ β + u_{i t}, I = 1, 2, \dots, N a n d t = 1, 2, \dots, T

where β: (M, 1) is a vector of slope parameters and u_it are the stationary disturbance terms. Assume that x_it vector as an integrated process of order 1 for all i: – x_it = x_it–1 + ε_it. The system describes cointegrated regressions, that is, Y_it is cointegrated with X_it.

{Y_it, X_it} are independent across cross-sectional units and W_it = (U_it, ε_it)’ is a linear process with a long-run covariance matrix, Ω, such that $Ω = {\sum^{}}_{\infty}^{j = - \infty} $ $E [W _{i j} W _{i 0} ’] = {\sum^{}}^{} + r + r ’ = (\begin{matrix} Ω u & Ω u ε \\ Ω ε u & Ω ε \end{matrix})$ , where $r = {\sum^{}}_{\infty}^{j = 1} E [W _{i j} W _{i 0} ’]$ and ${\sum^{}}^{} = E [W_{i 0}_{} W_{i o} ’]$ and the one-sided long-run covariance matrix is:

Δ = {\sum^{​}}_{\infty}^{j = 0} E [W ​_{i}^{}_{0}^{} W ​_{i}^{}_{o}^{} ’] {\sum^{​}}^{​} + r = (\begin{matrix} Δ u & Δ u ε \\ Δ ε u & Δ ε \end{matrix})

The OLS estimator of β is: $β ’ _{o l s} = {[\sum_{i = 1}^{N} \sum_{t = 1}^{T} (X_{i t} - X_{i}) (X_{i t} - X_{i})]}^{- 1}$ $\times [\sum_{i = 1}^{N} \sum_{t = 1}^{T} (X_{i t} - X_{i}) (Y_{i t} - Y_{i})],$ where $X_{i} = 1 / T \sum_{t = 1}^{T} X_{i t}$ and Y_i = 1/T $\sum_{t = 1}^{T} Y_{i t}$

OLS estimates are not reliable because they suffer from several problems. Most of the macroeconomic variables employed in these studies are likely to exhibit either stochastic and/or deterministic time trends, and are therefore non-stationary; thus, the reported estimates are likely be spurious in nature. Also, the OLS estimator gives biased and inconsistent estimates when applied to cointegrated panels. The superior FMOLS technique developed by Pedroni (2000) is able to account for both serial correlation and potential endogeneity problems, and is preferable to the OLS estimation.

Pedroni (2000) applies a semi-parametric correction to the OLS estimator that eliminates the second-order bias caused by endogeneity of the regressors. Essentially he allows for heterogeneity in the short-run dynamics and in the fixed effects of the panel. The FM estimator is constructed by making corrections for endogeneity and serial correlation to the OLS estimator above.

Endogeneity correction: Let Ω’_εu and Ω’_ε be consistent estimates of Ω_εu and Ω_ε and define:

\begin{array}{l} \begin{matrix} Y_{i t}^{}_{}^{+} = Y_{i t} - Ω ’ ​_{ε u} Ω_{ε} ’_{}^{-}_{}^{1} ε_{i t} \\ = Y_{i t} - Ω ’ ​_{ε u} Ω_{ε} ’_{}^{-}_{}^{1} Δ X_{i t}^{}_{​}^{} \end{matrix} \\ \begin{matrix} = U_{i} - X_{i t} ’ β + U_{i t} - Ω_{ε u} ’ Ω_{ε} ’^{- 1} ε_{i t .} \end{matrix} \end{array}

The serial correlation correction term has the form:

Δ ’^{+} ​_{ε u} = Δ ’ ​_{ε u} - Δ ’ ​_{ε} Ω ’ ​_{ε}^{}_{}^{- 1} Ω ’ ​_{ε u},

where Δ’_εu and Δ’_ε are kernel estimates of Δ_εu and Δ_ε, respectively, and the fully modified estimator of β is:

\begin{matrix} β ’_{F M} = {[\sum_{i = 1}^{N} \sum_{t = 1}^{T} (X_{i t} - X_{i}) (X_{i t} - X_{i})]}_{}^{-}_{}^{1} \\ \times ​ [\sum_{i = 1}^{N} {\sum_{t = 1}^{T} (X_{i t} - X_{i}) Y_{i t}^{+} - T Δ ’_{}^{+}_{ε u}^{}}] \end{matrix}

Such a method has not been used in this field so far, but the technique gives consistent estimates as long as the time period under study is not smaller than the cross-sections (which is the case in this study). The standard VECM technique automatically normalises the cointegrating equation, giving unity and zero coefficients to the variables, and requires many user-specified restrictions to get the model right. This method is especially useful here because it gives us a long-run regression equation and tells us how each factor affects the variable under consideration (macroeconomic indicators versus US stock returns). This not only addresses the question of existence but also the degree of inefficiency of a stock market. Inter-county comparisons are also made easier.

4. RESULTS AND DISCUSSION

The empirical investigation for checking stock market efficiency is carried out by first conducting the ADF stationarity test on the individual country time series and then checking panel stationarity using the LLC test. The variables considered have been tested considering they have an intercept. Other specifications are listed below. The results for the three countries are given in Table 1.

Stationarity tests on the first-differenced series have also been conducted with the results specified in Appendix A.3. The results show that all the variables are first-difference stationary for India and China, whereas for Brazil, all the variables apart from stock returns are stationary. Similarly, the LLC test tells us that all the variables involved in the panel are non-stationary, that is, they have a unit root but their first-differenced series is stationary. The US stock returns series was tested for stationarity as well and was found to be a first-difference stationary. The t-statistic for the case with a trend specification was found to be –1.91 and for the case without a trend specified was found to be –1.21. Both did not reject the null hypothesis of unit root, whereas the first difference of the series rejected the null in both cases. To check for stock market efficiency, it was necessary to see how the macroeconomic variables and US returns influence endogenous stock markets in the short run. Country-specific VARs were carried out; however, this article deals with the country-specific stock return equation only; the other equations are ignored and the focus is on how the factors considered affect stock returns.

Table 1
Results of the Stationarity Tests for India, China and Brazil

Industrial Production
Inflation
Interest Rate
Stocks

Trend Without Trend Trend Without Trend Trend Without Trend Trend Without Trend

India –2.52(0.31) –2.42(0.13) –3.75(0.02) –2.02(0.27) –2.07(0.55) –2.12(0.23) –2.47(0.34) –0.52(0.8)

China –2.8(0.19) –2.87(0.059) –2.7(0.21) –2.26(0.18) –2.76(0.21) –2.26(0.19) –2.8(0.18) –2.55(0.1)

Brazil –3.6(0.02) –3.2(0.01) –3.7(0.02) –3.45(0.01) –6.9(0.00) –5(0.01) –1.95(0.61) –1.38(0.52)

Panel –0.76(0.22) –0.68(0.24) –0.59(0.27) –0.52(0.31) –0.52(0.29) –2.39(0.00) 0.83(0.79) 0.02(0.5)

	Industrial Production	Inflation	Interest Rate	Stocks
India	–2.52(0.31)	–2.42(0.13)	–3.75*(0.02)	–2.02(0.27)	–2.07(0.55)	–2.12(0.23)	–2.47(0.34)	–0.52(0.8)
China	–2.8(0.19)	–2.87(0.059)	–2.7(0.21)	–2.26(0.18)	–2.76(0.21)	–2.26(0.19)	–2.8(0.18)	–2.55(0.1)
Brazil	–3.6*(0.02)	–3.2*(0.01)	–3.7*(0.02)	–3.45*(0.01)	–6.9*(0.00)	–5*(0.01)	–1.95(0.61)	–1.38(0.52)
Panel	–0.76(0.22)	–0.68(0.24)	–0.59(0.27)	–0.52(0.31)	–0.52(0.29)	–2.39*(0.00)	0.83(0.79)	0.02(0.5)

Source: Author’s calculations.

Notes: The optimal lag length was selected by the Schwarz Information Criterion (SIC) with a maximum lag of 13. The numbers in parentheses denote p-values. * denotes rejection of the null hypothesis, which is of the presence of a unit root at the 5% significance level. The panel represents India, China and Brazil taken together.

For India, the model considered is with two lags, as specified by the majority of the criterions like the akaike information criterion (AIC) and final prediction error (FPE). The model has been specified without trend, as the first difference of the log of returns has been considered. The main equation and results are:

\begin{array}{l} \begin{matrix} Y = - 0.05 Y (- ​ 1) + 0.01 Y (- ​ 2) + 0.05 * i n d p (- ​ 1) + 0.01 i n d p (- ​ 2) \end{matrix} \\ \begin{matrix} - 0.01 \inf (- ​ 1) - 0.07 \inf (- ​ 2) - 0.02 int (- ​ 1) + 0.29 * \end{matrix} \\ \begin{matrix} x (- ​ 1) - 0.02 X (- ​ 2) + 0.02 * * ​, \end{matrix} \end{array}

where Y is first difference of the log of the Bombay Stock Exchange, X is the first difference of the log of US stock returns; indp, inf and int are the first differences of IP, inflation and the interest rate, respectively. Further, –1 and –2 show the lags considered; * denotes significance at the 5 per cent level and ** significance at the 10 per cent level.

The results show that in the short run, IP has a positive impact on returns but only the first lag is significant. This matches the theory as given by Fama. Inflation has a negative impact and interest rate affects returns only in the first lag negatively, but insignificantly. US returns influence Y in the same direction in the first lag and significantly. Thus, the results show that US returns do impact Indian stock returns in the short run.

Similarly, for China, we consider a model with three lags as given by the majority of the criterion (AIC, Lagrange test). The equation is:

Y = 0.058 Y(–1) + 0.17 *Y(–2) + 0.045 Y(–3) – 0.002 indp(–1) + 0.02 inf(–1) – 0.01 inf(–3) – 0.01 int(–1) – 0.01 int(–2) – 0.03 int(–3) + 0.01 x(–2) + 0.19** x(–3) + 0.002.

The short forms and symbols are as described in the India model, but the model has three lags. IP has a negligible impact on Chinese stock returns, which is similar to the observation by Hosseini et al. (2011). It is zero after the first lag and very small even in the first lag. Inflation has a positive impact in the first lag but negative in the third lag, although this is not significant. The interest rate always has a negative effect on returns, which is consistent with theory but again it is not significant. However, US returns have a significant positive impact on returns in the third lag of about 0.19.

For Brazil, we consider a model with two lags as given by the majority criterions. The results are:

Y = 0.20** Y(–1) + 0.18 Y(–2) – 59.57 indp(–1) + 19.94 indp(–2) +241.27 inf(–1) + 281.17 inf(–2) – 78.3 int(–1) + 90.33 int(–2) – 0.35 X(–1) – 2.11* X(–2) – 74.28.

Here, Y and X represent the first difference of Brazil and US returns; indp, inf and int represent IP, inflation and interest rate, respectively. These three variables were already stationary. Brazilian stock returns in the first lag significantly impact its own returns, which is different from the earlier countries considered. IP has a negative impact in the first lag, but a positive, though insignificant, impact in the second lag. Similar results hold for the interest rate as well. Inflation has a positive impact in both lags, but these are insignificant. US returns have a significant negative effect in the second lag that is in contrast with both India and China, although the absolute value is very small considering that the logarithm has not been considered in the case. This negative sign may be a result of the two countries being in the similar geographical area, so they act as competitors over the short run. The first-lag impact is also negative but insignificant. Overall, it is found that US returns do have a short-run influence on stock returns. Thus, an investor making short-run investments on stocks would face the problem of inefficiency, because, despite controlling for domestic factors, the US continues to play a significant explanatory role.

After conducting the VAR and analysing the country-specific equations, two diagnostic tests are carried out on the specific equation: the Breusch–Godfrey test to check for serial correlation and the Breusch–Pagan test for heteroskedasticity in the residual of the equations. The results are highlighted in tabular form in Appendix A.4. The tests find no serial correlation in any country equation except for the presence of heteroskedasticity at the 10 per cent level for Brazil.

Given that the series are first-difference stationary, it is desirable to test for the presence of cointegration or a long-run relation among the variables. In such situations, conducting just a VAR is sub-optimal, as it would only express the short-run responses of these series to innovations in each series. Table 2 provides results for the test of cointegration among the variables.

Table 2

Panel Cointegration Test (Pedroni and Kao Residual Cointegration Test)

Test Statistic	Individual Intercept	Individual Intercept and Individual Trend
Panel statistics
Panel υ-statistic	1.48** (0.069)	0.77 (0.218)
Panel rho-statistic	0.72* (0.000)	–8.60* (0.000)
Panel pp-statistic	–5.36* (0.000)	–6.82* (0.000)
Panel ADF-statistic	–1.18 (0.117)	–2.27* (0.014)
Group statistics
Group rho-statistic	–11.01* (0.000)	–12.42* (0.000)
Group pp-statistic	–7.644* (0.000)	–9.19* (0.000)
Group ADF-statistic	–0.81 (0.201)	–2.89* (0.001)
Kao residual cointegration tests
ADF-statistic	–2.883* (0.002)

Source: Author’s calculations.

Notes: Optimal lag length selection is based on the Schwarz Information Criterion (SIC) with maximum lag 13. The numbers in parentheses denote p-values. * denotes rejection of the null hypothesis at the 5% significance level and ** denotes rejection of the null hypothesis at the 10% significance level. The null hypothesis is of no cointegration. The test uses the Newey–West automatic bandwidth selection with Bartlett kernel.

The model with individual intercept provides evidence for cointegration in five of the seven cases considered, whereas the model with the individual intercept and trend tells us that cointegration exists in six out of the seven cases. This means that the null hypothesis of no cointegration is rejected in 11 of the 14 cases considered. Therefore, both models predict the existence of cointegrating or a long-run relationship between the variables considered in the panel. The Kao test also provides evidence of cointegration among the variables. By conducting the Kao test, The ADF test statistic for the null hypothesis of no cointegration is rejected at the 5 per cent level.

A cointegration test only provides proof of the existence of a long-run relationship; it does not provide estimates of the long-run equation between the variables. Therefore, the next step is to conduct tests to determine these coefficients and check their significance. The macroeconomic variables of Brazil are integrated of order zero and so should not be used for the test. Instead, the Brazilian stock index is regressed on the US stock index, with a constant and trend specified. This is because graphically the two series appear to have a trend specified to them. For India, China and Panel, the model is assumed to have no trend because we simultaneously consider stock returns and macroeconomic variables, and therefore the stock returns are regressed on the macroeconomic factors and US stock returns. The FMOLS gives us a regression equation without any of the defects associated with an OLS. The coefficients represent the impact of the respective factors on the stock indices of their country.

Table 3

Fully Modified Ordinary Least Square (FMOLS) Estimates

Explanatory Variables	Countries
Explanatory Variables	India	China	Brazil	Panel
Industrial production {% change}	0.027**	–0.006		0
	(0.067)	(0.79)		(0.99)
Inflation {% monthly}	0.157*	0.034		0.06*
	(0.00)	(0.46)		(0.00)
Interest rate {%}	–0.035	0.485*		0.04
	(0.47)	(0.017)		(0.20)
USA stock index {logarithm}	0.909*	0.535*	0.98*	0.97*
	(0.00)	(0.03)	(0.00)	(0.01)
Constant			0.69
			(0.74)
Trend			0.01*
			(0.00)

Source: Author’s calculations.

Notes: The panel represents India, China and Brazil taken together. Values in parentheses represent p-values. * represents significance at the 5% level and ** at the 10% level. Grouped estimation is the panel method used and the lags are selected using the Schwarz criterion.

Using the FMOLS on each country and panel also helps in inter-country comparisons. The results for the FMOLS test are provided in Table 3.

The result obtained for India show that stock returns in the long run are positively influenced by IP, inflation and US stock returns. This is similar to the results obtained by Sampath (2011). The interest rate has a negative impact but is not significant. We observe that a unit change in the log of US stock returns changes the log of Indian returns by 0.9 units in the same direction. This is much higher than the other macroeconomics variables concerned, as a unit percentage change in IP and inflation changes the log of Indian returns by 0.027 units and 0.157 units, respectively. For China, the factors of significant influence are the interest rate and US returns. A unit change in the interest rate in China moves stock returns by 0.485 units in the same direction, and a similar change in US returns affects Chinese returns by 0.535 units. IP has a negative impact, which is similar to the results by Hosseini, but contrary to theory. For Brazil, a long-run relation exists between endogenous returns and US returns. A unit change in the log of US returns impacts the log of Brazil returns in the same direction by 0.98 units. In this particular case, the constant is not significant, but the trend is positively significant.

For the panel regression equation, only inflation and US returns are significant and both positively. A change in inflation moves the log of returns by 0.06 units which, although small, supports Fisher’s Hypothesis and a unit change in the log of US returns moves it by 0.97 units in the same direction. Since both variables are in log form, this signifies a one-to-one correspondence between the stock markets. Irrespective of the country considered, it is evident that US returns always impact stock returns positively, even after controlling for other macroeconomic variables. This result is consistent with the global phenomenon witnessed after the global financial crisis, where with the fall in US returns, other countries followed a similar trend. This result would suggest that a change in US returns would affect returns in other countries, even if there are no changes in their domestic macroeconomic indicators.

While most studies stop at having established a long-run relation between the US and endogenous stock returns, this study continues to make inter-factor comparison. The greater and more significant impact of US returns on the three emerging countries, compared to their domestic factors, tells us a lot about inefficiency. The larger picture on extent of inefficiency is drawn from the value of the regression coefficients. The degree of inefficiency is highest in Brazil, as the value of the US effect is most at 0.98 units, followed by India and China; the value is quite high for the panel as well (Table 3).

5. ROBUSTNESS CHECK

5.1 Vector Auto-regression Stability Checks

The vector residual autocorrelation Lagrange multiplier (LM) test is conducted, as a key assumption of the VAR model is that the residuals are not serially correlated. Appropriate lags were specified depending on the country-specific model (the results are provided in the tables of Appendix A.5). None of the three models showed any evidence of serial correlation. The stability of a VAR entails that all roots lie inside the unit circle. A graphical analysis of the inverse roots is provided in Appendix A.6. The finding is that all the roots lie within the unit root, thus, providing evidence that the VAR is stable. Therefore, from the two tests conducted, the VAR model appears to be well specified, as the roots lie within the unit circle and the residuals do not have any serial correlation.

5.2 Dynamic Ordinary Least Squares

A problem with the fully modified estimator is the dependence of the correction terms upon the OLS estimator that may be biased in small samples. In this article, for each country, 4 variables are considered as regressors for stock returns, consisting of 180 observations each. With 720 observations giving 4 estimated parameters, the sample cannot be considered small, but to avoid the possibility of this error, the DOLS was conducted. Similar to the FMOLS technique, it gives a regression equation that shows the relative influence of the variables. Both these methods are better than the canonical cointegration regression (Montalvo, 1995). Kao and Chiang (2000) show by running Monte Carlo simulations, that DOLS performs very well in both homogenous and heterogeneous panels, where Ω_i, r_i and Σ_i are varying for the i’s. Adding the number of leads (q₁) and lags (q₂) reduces the bias substantially.

The DOLS estimator can be obtained by running the following regression:

Y_{i t} = μ_{i} + X_{i t} ’ β + \sum_{j = - m}^{n} C ​_{i j} Δ X_{i}^{}_{, t - j}^{} + υ_{i t}^{}_{.}^{}

As we can see from the estimated coefficients, the results of the DOLS are very similar to the FMOLS method (refer to Appendix A.7). For India, the equation tells us that the log of stock returns depends positively on IP, inflation and US returns but negatively on the interest rate. This is the same, as the FMOLS predictions and all estimates are significant. For the Chinese stock returns, there is a negative long-run effect from IP, similar to Hosseini’s results (2011). A unit change in inflation has a positive effect of 0.22 units and a unit change in US returns has an impact of 0.94 in the same direction. Again, the signs are similar to FMOLS, except for the interest rate that is an insignificant factor. For Brazil, similar to the FMOLS model, we consider a different model with only the Brazilian and US returns, along with a constant and trend specified in the equation specification. Both the trend and US returns have a significant impact, with the log of US returns having an effect that is close to one on the log of Brazil’s returns. All equations have a high-adjusted R² value as well, which is important as it suggests that a substantial part of the variance is taken care by the regression equation. The results again indicate that US returns positively and significantly influence stock returns, showing inefficiencies in the stock indices. The value is high for the panel and, among the three countries, highest for Brazil, which is similar to the FMOLS results.

However, there is definitely scope for improvement in future endeavours to deduce stock market efficiencies in countries. While this article deals with emerging market economies, the analysis could be extended to other countries and even to influences from more than one country, as this study has done for the United States. The question of omitted variable bias will be levelled when considering macroeconomic variables, so more variables could be considered in the regression equation to tilt the balance in favour of greater efficiency.

6. CONCLUSION

This article tries to understand and measure the degree of stock market efficiency in three emerging economies—India, China and Brazil—by observing monthly data from January 1999 to December 2013. The definition derived from Fama’s efficient market hypothesis indicates that a country’s stock market is efficient if it reflects the fundamentals and risks of that economy, rather than that of others, and that certain domestic factors should be sufficient to explain a country’s stock returns. The study aimed to check if foreign stock returns significantly affected domestic returns in the short and long run, despite controlling for fundamental stock return determinants. This article tries to find the influence of the US stock market on the three countries, after controlling for three domestic macroeconomic factors—IP, inflation and the interest rate.

A country-specific VAR model was employed to determine short-run impacts followed by cointegration tests and a FMOLS technique to understand long-run influences. The country-specific VAR introduces greater flexibility, thus, accommodating the heterogeneous nature of the data and helping to avoid misspecification. FMOLS rectifies the problems associated with the simple OLS when applied to cointegrated variables and helps with measuring the extent of stock market efficiency.

After checking for stationarity of the variables, the empirical result of the VAR equations, specifically the equation where stock returns is the dependant variables, shows the short-run influence of US returns on all three countries. For India and China, it is positive with significance in the first and third lag, respectively. The data shows that India is also influenced by its own IP and China by its own returns, positively. Brazil on the contrary is affected both by US returns and its own returns. This implies that US returns is an important determinant in the short run, signifying short-run stock market inefficiencies in emerging countries. Further robustness checks show that the model does not suffer from heteroskedasticity or serial correlation problems, and that the models are stable. To test for the presence of cointegration, the Pedroni cointegration test and Kao residual tests are used, and the results obtained indicate the presence of cointegration in the variables considered.

The FMOLS method when applied to the individual countries and the panel indicates strong evidence of inefficiencies in the stock markets of the three countries. The reasons are clear, as all four regression equations yield US returns as a significant factor with a positive coefficient, showing that the influence is positive. This is similar to previous studies that have always found a positive long-run relation between domestic and US returns using a VECM approach (Campbell and Hamao, 1992; Chowdhury, 1994). It is estimated that a unit change in the log of US returns affects the log of Indian stock returns by 0.9 units, the log of Chinese stock returns by 0.5 units, Brazil by 0.98 units and the entire panel by 0.97 units. In all these countries, other domestic factors are seen to have an impact on returns but no single factor dominates the rest. For India, IP, for China, the interest rate and for the panel, inflation plays a significant role.

The results obtained from this study are important from the viewpoint of both investors and governments. Investors, to minimise risk, must diversify their portfolio, for which they should be able to identify markets that react more to information from foreign markets than others. Governments attempting to bring in and sustain private investment need to understand the extent of domestic and outside influence on their country’s stock returns and to act accordingly.

Footnotes

APPENDIX

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