The efficient market hypothesis and the
European Union
ABSTRACT
This paper examines the efficient market hypothesis for the last 13 countries that joined the European Union, namely Cyprus, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Malta, Poland, Slovakia, Slovenia, Bulgaria, Croatia and Romania. To test this, I use the Lo and Mackinlay variance ratio test, the DF-GLS test, the Augmented Dickey Fuller test, and the runs test over the period from January 2000 to December 2016. I also examine whether the entrance in the European Union enhances market efficiency for the 13 countries. The results from the variance ratio test and the DF-GLS test suggest that the stock markets of Latvia and Romania become efficient after the entry into the European Union. Collective findings also show that Hungarian and Polish markets are efficient in most periods whereas Estonian and Maltese markets are inefficient and to a certain extent, predictable.
Tudor Maxim UvA ID: 11126655
Supervisor: Shivesh Changoer
Faculty of Economics and Business Specialization Finance and Organization Bachelor Thesis Economics and Business University of Amsterdam
12 ECTS
Statement of Originality
This document is written by Tudor Maxim, who declares to take full
responsibility for the contents of this document. I declare that the text and the
work presented in this document are original and that no sources other than those
mentioned in the text and its references have been used in creating it. The Faculty
of Economics and Business is responsible solely for the supervision of
completion of the work, not for the contents.
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1. Introduction
Every securities trader or potential trader has wondered what is the best way to predict market prices and ultimately earn abnormal returns. To profit from trading, the mechanism which drives the market must first be understood. Even though this mechanism is still unknown to date, economists have tried to put forward theories to explain it. Theorists such as Eugene Fama, winner of the Nobel prize in 2013 for his work on asset pricing, pioneered the Efficient Market Hypothesis.
This theory, which had an outstanding success, has been tested by numerous papers, so many that Jensen (1978) wrote that in his opinion “… no other proposition in economics has more solid empirical evidence supporting it…”. However, most of those studies focus on mature markets such as United States, United Kingdom, and Germany. Only recently, researchers have started to focus on developing European markets such as Hungary, Poland, Slovakia and Slovenia, and poorly-developed countries, but the non-availability of quality data makes those studies less common. In developed economies, stock price behaviour is classified by the literature as efficient, whereas developing European countries are generally less efficient (Solnik, 1973). Solnik (1973) provides several explanations why developing European countries are less efficient: The first is that European markets have loose disclosure requirements. The second is that regulators have little control on insider trading. The third reason concerns the lack of investment and liquidity.
If the aforementioned explanations are valid, i.e., when disclosure requirements become more stringent, and insider trading becomes more regulated, along with an increase in investment and liquidity, the market efficiency should increase. One way to test this, is to examine a country’s entrance in the European Union (EU). Entering the EU entails stabilizing fiscal regulations which mitigate insider trading and uniformize the structure of disclosure requirements. What is more, by joining the EU, the country faces lower trade barriers which boost investment and consequently bring liquidity to the economy. I expect that through the entrance in the European Union, the market efficiency will increase.
To test this prediction, I test the efficient market hypothesis (EMH) in 10-member states of the European Union that joined on 1st of May 2004: Hungary, Poland, Slovakia, Latvia, Estonia, Lithuania, Czech Republic, Malta, Cyprus and Slovenia (A10 countries). I test the market efficiency in the period before the entrance in the EU, and the period after the entrance. I also test my prediction in Romania, Bulgaria and Croatia (A3 countries). These countries entered
2 in 2007 and 2013, respectively. I also examine the efficiency of individual securities from all 13 countries to ensure the robustness of the results.
The findings of my paper show that there is some evidence in Latvia and Romania that market efficiency improves after the entry into the EU. However, many countries, including Poland and Slovakia were negatively affected in terms of market efficiency after the entry into the EU. These findings are similar to the findings of Guidi, Gupta and Maheshwari (2011). My paper builds on their results by increasing the sample size, increasing the time period, employing more tests and also testing individual securities.
The structure of the remainder of the paper is as follows: In section 2, I discuss the Efficient Market Hypothesis, the Martingale model and the Random Walk Hypothesis. In section 3, I discuss prior studies and their findings for developed, underdeveloped and the A13 countries. In section 4, I motivate my hypotheses. In section 5, I discuss the methodology of this paper. In section 6, I present the results. In section 7, I present a sensitivity analysis based on individual securities. In section 8, I present my conclusions.
2. Theoretical framework
2.1. The efficient market hypothesis
The efficient market hypothesis states that share prices incorporate and reflect all available information (Fama, 1970). This hypothesis was developed by Eugene Fama in 1970 and was later adopted as a world standard (Malkiel, 2003). The theory has since been tested many times with findings showing that developed markets are efficient, but with inconclusive results for poorly developed and emerging markets (Jensen, 1978).
The EMH is based on three assumptions (Fama ,1970). The first assumption is that all relevant financial/economical information is publicly available. The second assumption is that all investors are rational and perceive the information in the same way; The third assumption is that there are no transaction costs. These assumptions vary in strength with the following three forms:
The strong form of the EMH states that prices “fully reflect” all available public and private information and that prices immediately adjust to the arrival of new public or private information (Fama, 1970). The strong form entails that no traders can earn excess returns over
3 the market’s average return. The semi-strong form renders that prices “fully reflect” all past public information and that prices instantly adjust to new information in an unbiased fashion (Fama, 1970). The weak form of the efficient market hypothesis entails that prices “fully reflect” all available past information (Fama, 1970). In this paper, I focus on the weak form of the efficient market hypothesis because of its implications. The implications of the weak form of the EMH refer to the two ways of analysing security prices and making investment decisions: technical analysis and fundamental analysis.
The weak form entails that no technical analysis technique can provide meaningful information about the future price of a security. At the same time, the weak form of the EMH allows for fundamental analysis to earn abnormal returns in the long run (Malkiel, 2003).
2.2. The Martingale model
To test the weak form of the efficient market hypothesis, researchers such as Malkiel and Fama (1970) use the Martingale model. This model comes from probabilistic mathematical theory, which was first used in gambling in 1565 by Italian mathematician Girolamo Cardano (Campbell, Lo, & MacKinlay, 1997). The base of this probabilistic theory is that games are fair and the winning probabilities are set equal for both opponents (Campbell et al., 1997). In finance, this theory could be interpreted as a stochastic process which applies to the price of a security. The martingale model states that the best expectation of the price of tomorrow is the price of today (Campbell et al., 1997). Formally:
𝐸[𝑃𝑡+1|𝑃𝑡, 𝑃𝑡−1 , … ] = 𝑃𝑡 (1) where 𝑃𝑡 is the natural logarithm of price at time t.
A useful property of the Martingale model is that price changes are uncorrelated and therefore future prices could not be predicted based on old prices, similar to the efficient market hypothesis (Campbell et al., 1997). The downside of this model is that it does not account for risk in the financial market (Campbell et al., 1997). Even though risk is a known factor in the market, the Martingale model is a widespread tool used for analysing market efficiency and therefore used in this paper (see Fama 1970; Lo and MacKinlay 1988).
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2.3. Random walk
The probabilistic Martingale model has led to the development of the random walk (RW) hypothesis (Campbell et al., 1997). The hypothesis was proposed by Bachelier, who in the beginning of the 20th century postulated that stock prices follow a Brownian motion (Campbell et al., 1997). Next, Kendall in 1953, Samuelson in 1965 and Madelbrot in 1966 all developed the hypothesis by researching the random motion of stock prices (Yen & Lee, 2008). The academician who further developed their insights and formulated the theory of the efficient market hypothesis was Eugene Fama in 1970.
Simply put, the random walk hypothesis entails that stock prices follow a random pattern. Since the EMH entails that security prices already contain all available information and no abnormal returns can be derived from analysing past prices, the market price fluctuations are expected to be random. Therefore, checking for market efficiency entails testing the random walk hypothesis.
The random walk model is the following:
𝑃𝑡 = µ + 𝛽𝑃𝑡−1+ 𝜀𝑡, (2)
where the Greek letter µ is the expected price change or drift, 𝛽 is the slope coefficient, 𝑃𝑡 is the price at time t and 𝜀𝑡 is the error term.
The assumption of the RW model refers to the distribution of the error term (Campbell et al.,1997). In the most general version of the RW, the increments of the error term should be uncorrelated at all leads and lags. The implications of the RW are that its conditional mean and variance are linear in time (Campbell et al., 1997).
𝐸[𝑃𝑡|𝑃0] = 𝑃0+ µ 𝑡, (3)
𝑉𝑎𝑟[𝑃𝑡|𝑃0] = 𝑎2𝑡. (4)
To test the random walk, stationarity tests, runs tests and variance ratio tests can be used (Campbell et al., 1997). The tests are further explained in section 5.2.
3. Literature review
3.1. History and main findings of the literature
Fama (1965) uses a serial correlation coefficient test, a runs test and an Alexander filter technique to examine the efficient market hypothesis. Based on a sample of 30 firms listed on
5 the Dow industrial average, he finds that daily, four days, nine days, and sixteen days price changes exhibit no serial correlation and do not reject the RW hypothesis. He concludes that the United States stock market is efficient (Fama, 1965).
Hagerman and Richmond (1973) employ a Martingale model and test the random walk hypothesis through non-parametrical runs tests and serial correlation coefficient tests in the United States. Their sample includes 267 companies with monthly observations from the Pink Sheets Over The Counter Market. Hagerman and Richmond (1973) find that securities display a random walk and conclude that the Pink Sheets is an efficient market.
In contrast, Lo and MacKinlay (1988) use a variance ratio test to examine the random walk hypothesis. They sample 1216 weekly observations of individual securities from the New York stock exchange (NYSE) grouped by size. They find that the variance ratio of the securities listed on NYSE is not constant, and reject the random walk hypothesis. Based on the rejection of the RW for individual securities, they conclude that the asset pricing model used is suboptimal, and do not draw inferences about market efficiency.
Borges (2010) also uses Lo and Mackinlay’s variance ratio test along with runs tests to examine the random walk hypothesis. She samples 3878 daily observations of the national stock index price for European countries using data from January 1993 to December 2007. She finds that UK and France exhibit mean reversion in the runs test and concludes that these countries show low levels of efficiency. Moreover, Greece and Portugal reject the random walk hypothesis due to autocorrelation of the returns, and Borges (2010) concludes that their markets are inefficient. As both Malkiel (2003) and Jensen (1978) point out, the majority of studies conducted on developed markets show evidence that these markets are efficient. However, less developed markets, as Urrutia (1995) points out, show inconclusive results.
3.2. Literature review A13 countries
Rockinger and Urga (2000) examine the linear variance property of the random walk model in Hungary, Czech Republic and Russia. They use a time varying parameter model and a GARCH model to test the variance of the error term. Daily observations of the stock indices are sampled between 1994 and 1999. They find that Russia’s index displays serial correlation between the increments of the error term and therefore shows signs of predictability. However, both the Hungarian and the Czech indices do not reject the random walk hypothesis. As such, Rockinger
6 and Urga (2000) conclude that there is not enough evidence to reject the EMH in the period between 1994 and 1999 in these countries.
Worthington & Higgs (2004) further emphasise the findings that the Hungarian stock index follows a random walk. Their methodology includes using serial correlation coefficient tests, runs tests, unit root tests such as the Dickey – Fuller and the Phillips-Perron test, along with multiple variance ratio tests. Their paper concludes that the Hungarian market is efficient until May 2003, based on the non-stationarity property of its index. However, the Czech market rejects the random walk hypothesis because of error term autocorrelation. Worthington & Higgs (2004) conclude that the Czech Republic has a low efficiency level.
Another test done on the market efficiency in the Czech Republic, Hungary, and Poland is conducted by Gilmore and McManus (2003). To test the EMH, they use univariate and multivariate tests, a NAÏVE model along with ARIMA and GARCH. Contrary to previous research, they do not use the home-based stock market indices, but weekly Investable and Comprehensive indices developed by the International Finance Corporation. They find consistent evidence that all three countries reject the EMH from the period between July 1995 and September 2000 because of volatile variance and error term autocorrelation. Their findings contradict with the results of the aforementioned papers, but this is likely due to weekly increments of data along with the different index composition.
A more recent paper focusing on Eastern Europe is done by Smith (2012). To test the weak form of market efficiency, Smith, (2012) employs an ARCH model over daily data from February 2000 to December 2009. He finds that the least efficient markets in Europe are the Ukrainian, Maltese and Estonian markets because of their instable variance. Smith (2012) also finds that the markets with the biggest improvement in efficiency over the 2000-2009 period were Romania, Lithuania and the Czech Republic.
A broader study done by Lee, Lee and Lee, (2010) examines the efficient market hypothesis in 58 countries (32 developed countries and 26 being considered developing countries on the base of their economic environment). They employ unit root tests to check for market efficiency for the period between January 1999 and May 2007. Lee et al. (2010) find that in all countries stock prices exhibit a unit root and conclude that countries do not allow the rejection of the EMH.
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4.
Hypotheses
As Ang and Pohlman, (1978) mention, and as the previous section on literature review shows, the efficient market hypothesis does not always hold in European underdeveloped countries. Solnik (1973) provides several explanations for this finding: The first explanation is that underdeveloped European countries have loose disclosure requirements thus resulting in unavailability of information. The second explanation is that there is a lack of investment and thus low liquidity in the economies. The third explanation refers to unclear regulation leading to little control on insider trading.
If these explanations are valid, i.e.,when disclosure requirements become stricter, investment increases, and control on insider trading is enhanced, the market efficiency should increase. To enter the EU, a candidate must satisfy a number of criteria defined by the Copenhagen Treaty (1993):
- the existence of a functioning market economy;
- the capacity to cope with competitive pressure and market forces within the Union; - strong enforcement on the rule of law;
- equal access to information and press.
In the process of meeting the entrance criteria, the efficiency levels should increase for several reasons. First, Harrison and Paton (2004) provide evidence that entering the EU enhances the availability of information and allows for price discovery. Second, by entering the EU, the entry barriers in the economy decrease significantly because of the EU free trade agreement. As Worthington and Higgs (2004) and Lo and MacKinlay (1990) argue, this attracts foreign investment which is one of the main drivers of market efficiency through liquidity. Lastly, in order to join the EU, countries have to adhere to strict European fiscal regulation standards, hence minimizing insider trading.
Consequently, the previous argument leads to my first hypothesis:
H1: After the entry into the European Union, all countries should exhibit a positive transition
into market efficiency.
Building on Fama’s (1970) theory, I predict that market efficiency should be highest in the countries which display the highest increase in the EMH assumptions (information is publicly available, investors are rational and there are no transaction costs).
8 First, the entrance into the EU strengthens the first assumption (Harrison & Paton, 2004), thus theoretically enhancing market efficiency. Second, the EU brings an improvement in education (Gareth Davies, 2005) and thus enhances market rationality and implicitly the second assumption. Third, by decreasing market entry barriers, and uniformizing the market structure, the transaction costs are lowered and thus the third assumption is strengthened.
Consequently, this leads to my second hypothesis:
H2: The countries which display the highest strength in the EMH assumptions, will exhibit
market efficiency after entering the EU, regardless of their prior efficiency before joining the EU.
5. Methodology
5.1. Research design
To test whether the weak form of the efficient market hypothesis holds, I assume the most general form of the random walk holds in my time series, namely a random walk with uncorrelated error terms at all leads and lags. As Campbell et al. (1997) mention, this form is most widely used in the literature (see Fama 1970; Hagerman and Richmond 1973; Lo and Mackinlay 1988), along with the assumption of heteroskedasticity.
To test this, I employ three tests. The first test is the Lo and Mackinlay variance ratio test. This test, as Campbell et al. (1997) mention, has a high statistical power and is sensitive to heteroskedasticity. The second test, the DF-GLS test examines the stationarity of a time series. The third test is a runs test, which checks for overall randomness of the returns of the price indices.
The reason for using price indices and not individual stock prices is twofold. First, individual prices are hit by idiosyncratic shocks, and tests performed on them have less statistical power than indices (Dockery & Kavussanos, 1970). Second, the EMH relates to the functioning of the market, and a market index is an appropriate proxy for it.
The natural logarithm of prices is used since it facilitates the calculation of returns between two days without tampering any available information. The properties of the natural logarithm allow for the continuously compounded return to be calculated in the following way:
9 𝑅𝑡 = 𝑃𝑡− 𝑃𝑡−1= ln (
𝑝𝑡
𝑝𝑡−1) = ln(1 + 𝑟𝑡),
(5) where 𝑝𝑡 is the price, 𝑃𝑡 is the natural logarithm of the price, 𝑟𝑡 is the daily return, and 𝑅𝑡 is the logarithmic return.
To test H2, proxies are used to measure the strength of the EMH assumptions. To quantify the strength of the first EMH assumption namely, availability of information, the Transparency index is used. To measure the strength of the second assumption, that is, market rationality, one of the official EU Sustainable Development Goals indicators is used, namely ‘Young people neither in employment nor in education and training’. Lastly, to measure the strength of the third EMH assumption namely, low transaction costs, the share of trade exchanges with the other countries in the European Union is used as a proxy. These proxies are further explained in section 5.3.1.
5.2. Tests
5.2.1. Lo and Mackinlay variance ratio test
By using the linear variance property of the random walk, Lo and MacKinlay (1988) derived a variance ratio test. It tests whether over q consecutive periods, the variance of the returns equals
q multiplied by the variance of the return of one period. This test assumes that the error term is
homoscedastic. However, in practice, this assumption does not hold, as can be seen in the data section. Therefore, I use the following heteroskedastic version of the test statistic:
𝑉𝑅(𝑞) = 1 + ∑2(𝑞 − 𝑘)
𝑞 𝜌(𝑘)
𝑞−1
𝑘=1
, (6)
where 𝜌(𝑘) is the autocorrelation coefficient between q and k.
Lo and Mackinlay (1988) also derived a standardized test statistic which follows an approximately normal distribution:
𝑧∗ =√𝑁 ⋅ 𝑀𝑟(𝑞)
√𝜃 ~𝑎𝑁(0,1),
(7) where 𝑀𝑟(𝑞) is asymptotically equal to the VR(q) presented in equation 6, but computed with autocorrelation coefficient estimates, √𝜃 is the standard deviation of 𝑀𝑟(𝑞), and N is the number of observations.
10 Since Lo and MacKinlay (1988) agree that the departure from homoscedasticity happens in financial markets, they derive four “empirical departures from normality” as their null hypotheses. However, the only one which is of interest for my paper relates to the fact the error terms are uncorrelated. Consequently:
H0: The error terms are uncorrelated at the 5% significance level;
H1: The error terms are correlated.
A rejection of the null hypothesis would imply predictability of stock prices and therefore a rejection of the random walk. To remain in line with the methodology of Lo and Mackinlay (1988) I use values for lags(q) of 2, 4, 8 and 16.
A disadvantage of the variance ratio test is that it could result in a false rejection of the null hypothesis due to short run autocorrelation of the error term increments. This would therefore imply a false rejection of the EMH.
5.2.2. The DF-GLS unit root test
The Augmented Dickey – Fuller (ADF) test checks whether the coefficient of the regressor of the RW model (see equation 2) is 1 in order to fulfil the non-stationarity property of a stochastic process. The DF-GLS test, follows the same intuition, however fits a regression model on the generalised least squared, in contrast to ordinary least squares. For comparison purposes, I will present both the ADF test and the DF-GLS test.
The DF-GLS test was developed by Elliott, Rothenberg, and Stock (1996) to eliminate the statistical noise present in the ADF test. For the purpose of preserving the high statistical power of this test, I follow the same procedure as the authors of this test:
First, the intercept and the trend are estimated through generalized least squares:
𝑃1 = 𝑝1, 𝑥1 = 1, 𝑧1 = 1, (8) 𝑝 𝑡 = 𝑝𝑡− 𝛼∗𝑝𝑡−1, 𝑥𝑡 = 1 − 𝛼∗, 𝑧𝑡 = 𝑡 − 𝛼∗(𝑡 − 1) | 𝑡 = 2, … , 𝑁, (9)
𝛼∗ = 1 − (13.5 𝑁 ).
(10)
Next, an OLS regression is performed for the following equation:
𝑃𝑡 = 𝛿0𝑥𝑡+ 𝛿1𝑧𝑡+ 𝜀𝑡. (11) Using the estimators 𝛿 0 and 𝛿 1, I remove the trend from 𝑝𝑡.
11 𝑃𝑡∗ = 𝑝𝑡− (𝛿̂0+ 𝛿 1𝑡). (12) Lastly, I perform an Augmented Dickey Fuller test
∆𝑃𝑡∗ = 𝛽0+ 𝜑𝑃𝑡−1∗+ 𝜌1∆𝑃𝑡−1∗+ 𝜌2∆𝑃𝑡−2∗+ ⋯ + 𝜌𝑘∆𝑘∗+ 𝑢𝑡, (13) where 𝛽0 is the intercept of the regression equation, 𝜑 is the slope and the parameter of interest, 𝜌 represents higher order coefficients, 𝑢𝑡 is the error term, and k is the number of lags. To determine the optimal number of lags, three approaches are used. As discussed by Stock & Watson (2011), the two most common ways of finding the optimal numbers of lags are the Schwarz information criterion (SIC), and the Akaike information criterion (AIC). A third procedure was developed by Ng and Perron (1995), commonly called the Sequential t. The procedure for finding the optimal number of lags is further explained in the appendix. The DF-GLS test is then implemented using the SIC, Sequential t, and MAIC lags. The ADF test is implemented using 2, 4, 8, and 16 lags for comparability with the variance ratio test.
To test for stationarity, the coefficient of 𝑃𝑡−1∗, 𝜑 has to be checked. The t test of 𝜑 does not follow an approximately normal distribution and instead the rejection values are found by using Mackinnon p values.
The hypotheses of the test are:
H0: 𝜑 = 0 at 5% significance level; (time series has a unit root)
H1: 𝜑 . (time series was generated by a stationary process)
A rejection of the null hypothesis would imply a rejection of the random walk hypothesis and therefore a degree of predictability in prices.
The advantage of the DF-GLS test, as found by Elliott et al. (1996), is that it has more statistical power than the regular stationarity tests, including the ADF test.
5.2.3. Runs test
The runs test is a non-parametrical test widely used in literature for establishing the randomness of the returns of a time series (see Shiller and Perron 1985; Fama 1970).
A run is defined by Bradley (1960) as an “unbroken sequence of similar events of like objects” Exemplifying thorough the use of returns, the following time series has three runs HHLLLHH. Where H is a high return and L is a low return. To find H and L the median of the returns is used as a benchmark.
12 The runs test has the following standardized test statistic:
𝑧 = 𝑟 − µ𝑟
𝜎𝑟 ~𝑎𝑁(0,1), (14)
where 𝑟 is the number of runs, 𝜎𝑟 its standard deviation, and the expected number of runs is:
µ𝑟 = 2𝑛0𝑛1
𝑁 + 1 , (15)
the variance is:
𝜎𝑟2 =
2𝑛0𝑛1(2𝑛0𝑛1− 𝑁)
𝑁2(𝑁 − 1) , (16)
n0 is the number of observations below the threshold, n1 is the number of observations above it, and N is equal to the sum of n0 and n1. Shiller & Perron (1985) showed that using a theorem in Mood (1940), the test statistic is asymptotically normally distributed with mean zero and a variance of one.
The hypotheses are:
H0: 𝑧 = 0 at 5% significance level; (the data is random)
H1: 𝑧 different from 0; (the data is not random)
A rejection of the null hypothesis would result in a rejection of the random walk hypothesis and therefore a degree of predictability in prices.
A property of the runs test is that it is a non-parametrical test, this being advantageous to my study since the distribution of the returns is unknown. The drawback of this test, as shown by Shiller & Perron (1985), is that as the number of observations increases, the power of the test tends to decrease.
5.3. Data
To test H1 and H2, I focus on the A10 countries: Hungary, Poland, Slovakia, Latvia, Estonia, Lithuania, Czech Republic, Malta, Cyprus and Slovenia. These countries entered the European Union in 2004. For comparison purposes, I also examine Romania, Bulgaria and Croatia. The first two countries entered the EU in 2007, the third one in 2013. For each country, I collect stock market index prices from Datastream, restricting my sample period from 31st December
13 1999 to 31th December 2016. Cyprus and Slovenia have no available data until March 2004 and March 2006 respectively.
To test H1 and H2, the data for every country is split into two periods. For the A10 countries, the first period is before joining the EU, from 31st December 1999 to 30th April 2004; second period is after joining EU, from 1st of May 2004 to 30th December 2016. For Romania and Bulgaria, the data split occurred at 1st of January 2007 and for Croatia at 1st of July 2013.
5.3.1.
Economic indicators
To analyse the characteristics of the countries I present five indicators representing the progress in the European Union of the A13 countries. They are the following: GDP, Diff, TI, YPNET, %EU.
Real GDP per capita (GDP)
Real GDP per capita is the Gross Domestic Product divided by the average population over a year. I further calculate the rate of increase in GDP over the period in which the country has been in the European Union divided by the number of years. This is to control for time and country specific effects. I calculate this variable using data from the European statistical information database, Eurostat. The indicator is part of the European Union’s Sustainable Development Goals indicator set. It is a measure of economic activity and a proxy for economic development (“Database - Eurostat,” n.d.).
Stock price volatility (Diff)
The second indicator I use looks at the volatility of the stock price indices. The volatility of a stock is measured by its standard deviation. I calculate the average volatility before and after the entrance into the European Union, standardized by the number of years (AvPreEu & AvEu). “Diff” is the difference between the two averages, and can be interpreted as the change in the variability of the index stock price after the entrance in the EU.
Transparency index (TI)
The transparency index is the average over the period after the entrance into the EU of the Corruption Perception Index (CPI). The CPI “aggregates data from a number of different sources that provide perceptions of business people and country experts of the level of
14 corruption in the public sector” (“Research - CPI - Overview,” n.d.). It is a proxy for the quality and availability of information.
Young people neither in employment nor in education and training (YPNET)
This indicator measures the share of people between 15 and 29 that are not working or studying from a country’s total population. (“Database - Eurostat,” n.d.). I calculate the percentage change in the share of young people neither in employment nor in education and training between the period before the entry into the EU and the period after (YPNET). The source of this indicator is Eurostat. It measures the development of education and workforce participation.
Share of trade with EU28 countries. (%EU)
This indicator measures the percentage of the total trade of a country with the other members of the European Union. I calculate the average over the period after the entrance into the European Union. It is a European measure for cohesion and savings in transaction costs, since trade inside EU is costless. (“Database - Eurostat,” n.d.).
Hereafter, the A10 countries are presented in panel A, and the A3 countries in panel B in my analyses.
Table 1
Economic indicators
Panel A GDP AvPreEU AvEU Diff TI YPNET %EU
Cyprus 2.41% - 3.70 - 61.13 -37.29% 80.88 Czech Republic 3.08% 7.47 2.02 5.45 48.36 -10.39% 74.90 Estonia 2.27% 6.84 1.57 5.27 65.50 1.56% 64.76 Hungary 1.58% 8.44 2.29 6.15 51.28 -16.57% 75.61 Latvia 5.37% 10.64 1.75 8.89 47.53 -17.05% 61.55 Lithuania 4.22% 4.76 1.53 3.23 51.27 -14.74% 73.40 Malta 3.38% 4.94 1.05 3.89 58.38 -42.86% 57.59 Poland 4.45% 9.67 2.11 7.56 50.06 -29.59% 74.87 Slovakia 1.30% 8.12 1.66 6.46 45.90 32.93% 75.34 Slovenia 4.75% - 1.55 - 61.82 -25.00% 80.47
Panel B GDP AvPreEU AvEU Diff TI YPNET %EU
Bulgaria 2.49% 4.48 2.43 2.05 39.13 -21.95% 61.58
Croatia -0.41% 1.83 3.05 -1.22 48.25 76.47% 65.47
Romania 2.91% 4.82 2.25 2.57 40.61 -4.72% 72.03
15
Table 1 - Continued
The table shows 5 indicators of economic prosperity for the A13 countries. GDP is calculated as the increase in GDP per capita over the period in which the country has been in the EU, divided by the number of years. AvPreEU is the average of the volatility of the stock market index before the EU entry divided by the number of years in the sample. AvEU is calculated as AvPreEU but using the sample period after the entry in EU. Diff is the difference between AvPreEU and AvEU. TI is the average score of the transparency index calculated after the entry in EU. YPNET is the percentage change in the share of young people not in education or employment or training between the post entry and the pre-entry period. %EU is the percentage of trade with the rest of the EU countries out of total trade.
Table 1 shows that most of the countries had a decrease in volatility after their entrance into the European Union, even though all of them, apart from Croatia, were in the EU in the 2007-2008 Financial Crisis. This shows signs of stability and low market risk. The table also shows that Latvia, Slovenia and Poland show the biggest increase in GDP per capita per year, displaying high market growth and economic prosperity. Looking at the Transparency index (TI), Cyprus and Slovenia stand out with scores above the rest, showing a high availability of information. This implies a faith in the government and a good running of the country. Cyprus and Slovenia are also the countries which trade the most with the other members of the European Union, more than 80% of their business being inside the continent. Lastly, Malta has the highest decrease in the percentage of unemployed and/or unschooled young people, showing signs of high development in education since its entry into the EU.
5.3.2.
Descriptive
statistics
Table 2 presents descriptive statistics for the 13 countries, analysed over the whole 16-year period and a test for heteroskedasticity. This test is relevant since heteroskedasticity affects the outcome of most RW tests (Lo & MacKinlay, 1988). The rejection of the test’s null hypothesis implies the presence of heteroskedasticity.
Table 2
Descriptive statistics full period
Panel A Obs. Mean Std.
Dev Variance Skewness Kurtosis Heteroskedasticity Bulgaria 4226 6.07 0.71 0.50 -0.44 3.18 68.5 *** Croatia 4436 7.47 0.43 0.18 0.47 3.20 3.14 Cyprus 3216 6.28 1.51 2.27 -0.12 1.44 0 Czech 4436 6.81 0.42 0.17 -0.49 2.50 1.36 Estonia 4436 6.14 0.65 0.42 -0.76 2.20 35.0 *** Hungary 4436 9.67 0.44 0.20 -0.67 2.07 7.25 * Continued
16 Table 2 - Continued Latvia 4435 5.89 0.47 0.22 -0.64 2.69 36.8 *** Lithuania 4436 5.60 0.65 0.42 -0.85 2.23 0.06 Malta 4436 8.12 0.28 0.08 -0.33 2.72 11.0 *** Poland 4436 10.41 0.47 0.22 -0.68 2.08 84.7 *** Slovakia 4436 5.42 0.47 0.25 -0.43 2.42 5.42 ** Slovenia 2806 6.81 0.42 0.17 1.06 3.19 68.3 ***
Panel B Obs. Mean Std.
Dev Variance Skewness Kurtosis Heteroskedasticity Bulgaria 4226 6.07 0.71 0.50 -0.44 3.18 68.5 ***
Croatia 4436 7.47 0.43 0.18 0.47 3.20 3.14
Romania 4436 8.21 0.85 0.72 -1.16 3.08 21.3 ***
Descriptive statistics and Heteroskedasticity tests for the A13 countries. The data ranges from 1st January
2000 to 31st December 2016. The rejection of the test implies heteroskedasticity. The asterisks inform about
the rejection of the null hypothesis at 1% significance level for *, 5% for ** and 10% for ***.
Looking at the heteroskedasticity test, the error terms appear to be heteroskedastic for most of the countries, as the theory predicts. The standard deviation of the natural logarithm of the prices is highest in Romania and Bulgaria, these two countries having similar positioning and market economies.
Table 3
Descriptive statistics Pre-EU period
Panel A Obs. Mean
Std.
Dev. Variance Skewness Kurtosis Heteroskedasticity Czech Pre-EU 1131 6.21 0.20 0.04 0.50 2.81 109.62 *** Estonia Pre-EU 1131 5.19 0.30 0.09 0.65 2.20 48.04 *** Hungary Pre-EU 1131 8.99 0.14 0.02 0.30 2.61 355.50 *** Latvia Pre-EU 1130 5.25 0.30 0.09 -0.08 2.24 20.60 *** Lithuania Pre-EU 1131 4.62 0.31 0.09 1.21 3.34 12.42 *** Malta Pre-EU 1131 7.80 0.25 0.06 0.60 1.86 48.87 *** Poland Pre-EU 1131 9.71 0.19 0.03 0.40 2.07 18.82 *** Slovakia Pre-EU 1131 4.76 0.28 0.08 0.12 1.81 6.62 **
Panel B Obs. Mean
Std.
Dev. Variance Skewness Kurtosis Heteroskedasticity Bulgaria Pre-EU 1616 5.78 0.89 0.80 -0.23 1.49 727.29 *** Croatia Pre-EU 3392 7.46 0.49 0.24 0.46 2.49 17.44 *** Romania Pre-EU 1826 7.57 0.96 0.92 0.05 1.60 30.96 ***
Descriptive statistics and Heteroskedasticity tests for A13 countries. The data ranges from 1st January 2000 to 1st
of May 2004 for Panel A and from 1st January 2000 to 1st of January 2007 for Romania and Bulgaria in Panel B;
from 1st January 2000 to 1st July 2013 for Croatia. The rejection of the test implies heteroskedasticity. The asterisks
17
Table 4
Descriptive statistics EU period
Panel A Obs. Mean
Std.
Dev. Variance Skewness Kurtosis Heteroskedasticity
Czech EU 3305 7.01 0.23 0.05 0.56 2.48 15.33 *** Estonia EU 3305 6.47 0.33 0.11 -0.98 3.38 626.72 *** Hungary EU 3305 9.90 0.22 0.05 -0.73 3.54 4.29 ** Latvia EU 3305 6.11 0.28 0.08 -0.26 2.82 259.00 *** Lithuania EU 3305 5.94 0.30 0.09 -1.15 3.78 405.71 *** Malta EU 3305 8.23 0.20 0.04 0.50 2.43 101.09 *** Poland EU 3305 10.65 0.25 0.06 -0.87 3.00 132.44 *** Slovakia EU 3305 5.65 0.31 0.10 0.20 1.53 4.45 **
Panel B Obs. Mean
Std.
Dev. Variance Skewness Kurtosis Heteroskedasticity
Bulgaria EU 2610 6.24 0.49 0.24 1.29 3.60 40.66 ***
Croatia EU 1044 7.49 0.05 0.00 0.30 2.70 2.04
Romania EU 2610 8.66 0.30 0.09 -0.86 4.48 756.97 ***
Descriptive statistics and Heteroskedasticity tests for A13 countries. The data ranges from 1st of May 2004 to 31st
December 2016 for Panel A and from January 2007 to 31st December 2016 for Romania and Bulgaria in Panel B;
from 1st July 2013 to 31st December 2016 for Croatia. The rejection of the test implies heteroskedasticity. The
asterisks inform about the rejection of the null hypothesis at 1% significance level for ***, 5% for ** and 10% for *.
Tables 3 and 4 further strengthen the evidence that index stock price movements display heteroskedasticity. As economic theory predicts, the mean of all the indices increases over time. On one hand this implies increased index prices and economic activity in the market, on the other hand, there could be signs of inflationary risks. Panel B from both tables contrasts to Panel A with respect to the high levels of volatility in the natural logarithm of stock prices. Moreover, Panel B exhibits decreases in volatility, whereas increases are observed in Panel A.
6. Results
Table 5 presents the results of the variance ratio, DF-GLS, ADF and runs tests for the 13 countries for 3 periods (Before entering the EU, after entering the EU and the whole period). In total 390 individual tests have been carried out. The table represents the levels of significance at which each test was rejected. Decreasing levels of significance (10%, 5%, 1%) correspond to an increase in the strength of colour. White corresponds to the null hypothesis not being rejected. In all cases, a rejection of the null hypothesis corresponds to a rejection of the random walk. The detailed results can be found in the appendix.
18
Table 5
Efficiency levels after the entry into the EU
Panel A Variance ratio DF-GLS ADF runs 2 4 8 16 BIC Seqt MAIC 2 4 8 16 Cyprus all Czech Pre-EU EU all Estonia Pre-EU EU all Hungary Pre-EU EU all Latvia Pre-EU EU all Lithuania Pre-EU EU all Malta Pre-EU EU all Poland Pre-EU EU all Slovakia Pre-EU EU all Slovenia all
Panel B
Variance ratio DF-GLS ADF runs
2 4 8 16 BIC Seqt MAIC 2 4 8 16
Bulgaria Pre-EU EU
all Croatia Pre-EU
EU
all
RomaniaPre-EU EU
all (Continued)
19
Table 5 - Continued
Table 5 presents the results for the variance ratio, the DF-GLS, ADF, and runs tests for the A13 countries. Cyprus and Slovenia present one period, namely March 2004 – December 2016 and March 2006 - December 2016 respectively. For both Panel A and B, the Pre-EU period represents the period before the entrance into the European Union, The EU represents the period after the entry into the European Union. For both panels, the all period is between 31st December 1999 and 31st December 2016. For Panel A, the Pre-EU starts at 31st December 1999 ends at 30th April 2004; the EU period starts at 1st May 2004 and ends at 31st December 2016. For Panel
B, Romania and Bulgaria, the Pre-EU period starts at 31st of December 1999 and ends 1st of January 2007; for Croatia it starts from 31st December 1999 and ends 1st of July 2013. The EU period starts at 1st of January 2007 for Romania and Bulgaria and at 1st of July 2013. It ends for all 3 countries at 31st December 2016. The variance ratio test and the ADF test were conducted 4 times for each period for different lags; the DF-GLS three times for each period and the runs test once per period. The BIC is the Bayes information criterion, Seqt is the sequential- t criterion and MAIC the Minimum Akaike criterion. A white square represents the null hypothesis not being rejected. The intensity of colour increases with decreasing levels of statistical significance, namely 10%, 5%, 1%. Each rejection of the null hypothesis translates into a rejection of the efficient market hypothesis.
Looking at the variance ratio test for the A10 countries (Panel A), the results suggest that at 5% significance level, Latvia and Lithuania transition from market inefficiency in the Pre-EU period to market efficiency in the EU period at 8 lags. This is consistent with both my predictions. First, because of the aforementioned transition into market efficiency after the EU entrance. Second since Latvia scores highest in two economic indicators, namely, GDP, and difference in volatility after EU entrance. From Panel B, Romania also shows positive evidence for my first hypothesis through a transition into efficiency after the EU entrance at 5% level at all lags.
However, from Panel A, Slovakia Poland and Hungary all exhibit a transition into market inefficiency after the entrance into the EU, at 1% significance level at 4 lags. This finding is inconsistent with my first hypothesis. Similarly, from Panel B, Bulgaria and Croatia follow the same trend. Also inconsistent with my first prediction are Estonia and Malta. These countries display market inefficiency at all lags at 1% significance level before and after the entry into the EU. Moreover, the finding that Malta is inefficient conflicts with my second prediction, since it had the biggest improvement in the level of education and employment for young people.
The DF – GLS test strengthens my first hypothesis through Slovakia, Latvia and Romania. These countries become efficient after the entry into the EU at 5% significance level at the Sequential t and BIC lag respectively. For Latvia, this could be explained by the value of growth for GDP per capita, which is the biggest from my sample. More interestingly, all other countries at all periods do not reject the stationarity hypothesis. This would imply that these European markets have been efficient for the period between 2000 and 2016.
20 Comparing these results with the variance ratio test, both Romania and Latvia show consistency in findings, this being in line with Smith (2012). However, countries such as Cyprus, Malta and Estonia which reject the market efficiency at all lags, all periods and mostly at the 1% significance level in the variance ratio test, are found to be efficient by the DF-GLS test. This discrepancy could be explained by interpreting the rejection of the null hypothesis of linear variance for the variance ratio test. As Huang (1995) mentions, such a rejection could be due to short term, positive autocorrelation of prices. Another reason could be due to the variance ratio assigning declining weights to higher order error term autocorrelations (Lo & MacKinlay, 1988).
Even though the DF-GLS test has more statistical power than the ADF test, the ADF inclusion could be used for comparability among countries, since country specific effects are present due to the wide spectrum of my analysis. Looking at both panels, Latvia is the only country with findings consistent with both my predictions. Latvia exhibits a transition to market efficiency at 10% at 2 lags. Apart from Latvia, the ADF test shows completely opposite results to the DF-GLS test, thus rejecting my first hypothesis for Bulgaria, Croatia, Czech Republic, Estonia, Hungary, Lithuania, Poland Slovakia and Romania. This could however be explained by the small number of observations in the sample period before the EU entry for most countries and hence resulting in a smaller statistical power. (Elliott et al., 1996)
The results from the runs test find evidence supporting my first hypothesis in both panels. Both the Czech Republic and Croatia exhibit a transition into market efficiency after their entry into the EU at 5% and 1% significance levels. This finding also supports my first hypothesis, the Czech Republic having the highest trade levels with other EU countries, thus theoretically replicating a market with no transaction costs. This is also consistent with the findings of Rockinger and Urga, (2000). However, similar to the ADF test, many countries exhibit an inverse transition or a rejection of market efficiency in all periods. The runs test is not rejected in any period for Hungary, Poland and Slovakia. These findings being consistent with the DF-GLS test at the BIC and MAIC lags. Furthermore, this finding is in line with Rockinger and Urga (2000) and Worthington & Higgs (2004), which detect efficiency in the Hungarian market.
Moreover, Hungary for the pre-EU period and the whole period, along with Poland for the period preceding the EU entrance, are the only countries which exhibit random price movements, thus found efficient by all 4 tests. On the other side of the spectrum, Malta rejects
21 the null hypothesis of random walk by all tests except the DF-GLS test in the periods before and after joining EU. This therefore invalidates H2, since Malta had the biggest decrease in education and unemployment for young people. This could be explained in two ways. First, education and unemployment might not provide a suitable proxy for market rationality. Second, market rationality is not an adequate driver of the market. To examine this more closely, Cyprus, the country with the second highest decrease in education and unemployment for young people, is analysed. Cyprus rejects the EMH at 5% significance level for the period after the EU entry (only available period) in the variance ratio test and the runs test. What is more, Cyprus scores highest on the share of trade with the EU, thus having low transactions costs, and second highest in the transparency index, thus having an adequate availability of information. These findings provide strong evidence towards rejecting H2. Provided that the proxies used for measuring the availability of information, market rationality and transaction costs are adequate, the rejection of H2 implies that a high value for these EMH assumptions does not translate into a higher chance of market efficiency.
All in all, the transition into efficiency for Latvia and Romania in two out of the four tests would be the only strong evidence in favour of H1 whereas the inverse transition of Poland and Slovakia in two tests would be in favour of rejecting H1. These results could however be due to country specific effects. It can be inferred that entering the European Union was not instrumental in aiding the efficiency of a country’s stock market. This result is in line with Guidi et al. (2011) and Ang and Pohlman (1978).
7. Sensitivity analysis
To better understand the previous findings, an analysis on individual securities from the A13 countries is performed. Subject to availability, daily price is collected for 45 securities from each of the A13 countries between 1st January 2000 and 31st December 2016. The runs test is performed on each individual security, with each security being classified by country. The test is performed twice, before and after the respective country entered the EU. Observations are dropped if the number of runs is smaller than 30 in order to exclude outliers and approximate the distribution of the test statistic to a normal one, ~𝑎𝑁(0,1). In total, 649 tests were performed for a total of 379 individual stocks (270 companies had prices available for the period before their entry into the EU and 379 companies had data only for the period after).
22 Table 6, Panel A and B, provide statistics about the findings of the runs test on A13 countries. The test statistics can be found in the appendix. The efficiency transition column provides the number of companies that rejected the random walk hypothesis at 5% significance level before the entry into the EU, and did not reject it after the entry. The second column (Available) provides the number of companies per country that had available observations in both periods. The third column (Ratio) is the ratio of companies that transitioned into efficiency from the number of available companies. The columns thereafter show the number of efficient companies before the EU period (Eff Pre-EU), the total number of companies before the EU period (Total Pre-EU), their ratio (Ratio), the number of efficient companies in the EU period (Eff. EU), and the number of companies in the EU period (Total EU). The last ratio column is found by dividing the number of efficient companies in the EU period by the total number of available companies. Next, in table 7, a proportion comparison test between the efficiency ratios before and after a country’s entry into the EU (columns 6 and 9) is presented along with significance levels and alternative hypothesis details.
To determine whether the difference in the number of efficient companies in a country is significant, I employ the statistical test of proportion that follows an approximately normal distribution 𝑧 = (𝑃̂ − 𝑃̂1 2) − 0 √𝑝 (1 − 𝑃̂) (𝜂1 1+ 1 𝑝2) ~𝑁(0,1), (17)
where 𝑃̂ is the proportion of efficient companies in the period before entering EU; 𝑃1 ̂ is the 2 proportion of efficient companies in the EU period and 𝑃̂ is the total proportion of efficient companies over both periods.
Since the test is one sided I present the transition direction, “direct” being a transition to random price pattern, “inverse” being a transition from a random movement to a non-random price movement.
23
Table 6
Sensitivity analysis
Panel A Eff.
transition Available Ratio
Eff. Pre-EU Total Pre-EU Ratio Eff. EU Total EU Ratio Cyprus 5 36 14% 17 36 47% 10 37 27% Czech 2 10 20% 4 10 40% 7 13 54% Estonia 0 5 0% 5 5 100% 10 17 59% Hungary 4 19 21% 11 19 58% 17 36 47% Latvia 0 10 0% 8 10 80% 4 12 33% Lithuania 6 17 35% 7 17 41% 22 30 73% Malta 2 12 17% 2 12 17% 5 21 24% Poland 5 34 15% 26 34 76% 18 34 53% Slovakia 0 4 0% 2 4 50% 14 29 48% Slovenia 3 5 60% 3 5 60% 13 32 41% Panel B Eff.
transition Available Ratio
Eff. Pre-EU Total Pre-EU Ratio Eff. EU Total EU Ratio Croatia 15 45 33% 15 45 33% 26 45 58% 24% 31% Romania 6 41 15% 11 41 27% 10 41 Bulgaria 6 32 19% 20 32 63% 10 32
Table 6 provides statistics of sensitivity analysis. The efficiency transition measures how many companies display random movement after the entry into EU, and display a nonrandom movement before the entry. The Available column counts the number of companies with observations in both periods. The Ratio is found by dividing the number of companies that had an efficiency transition by the number of available companies. Eff. pre-EU is the number of companies that were efficient before the EU entry. Total pre-EU is the total number of companies available in the period before the EU entry. The next ratio is found by dividing Efficient Pre-EU by Total Pre-EU. Efficient EU, total EU and the last ratio are found in the same way as the Pre-EU variables.
Table 7
Proportion comparison test
Panel A z value Significance Transition
Cyprus -1,79 ** Inverse Czech 0,65 Estonia -1,73 ** Inverse Hungary -0,75 Latvia -2,18 ** Inverse Lithuania 2,17 ** Direct Malta -0,48 Poland -2,03 ** Inverse (Continued)
24
Table 7 - Continued
Slovakia -0,06
Slovenia -0,81
Panel B z value Significance Transition
Croatia 2,3 *** Direct
Romania -0,25
Bulgaria -2,5 *** Inverse
Z value is found from the Proportion comparison test. The test has an approximately normal distribution and thus the rejection regions for the one-sided test are: |z| ≥ 1.282 for 10%, shown in table as *; |z| ≥ 1.965 for 5%, shown in table as ** and |z| ≥ 2.326 for 1% shown in table as ***.
Looking at table 6, Panel A, Lithuania has the most companies that had non-random price movements before the entry into the EU, and random movements after the EU entrance. This finding is also strengthened by the proportion comparison test. The rejection at the 5% significance level of the null hypothesis implies that the proportion of companies that have a random price movement increased after the entrance into the EU. This finding is consistent with the variance ratio test result, where the index of Lithuania shows a random pattern after its entrance into the EU. In Panel B, Croatian companies display similar findings to Lithuanian companies. These findings match the results obtained for the Croatian index through the ADF and the runs test. These two countries provide evidence that strengthens my first hypothesis. Looking at both panels, at the proportion comparison test, at the 5% significance level, 5 countries exhibit an inverse efficiency transition. This translates into 5 countries whose proportion of individual companies that follow a random pattern has decreased after the entrance into the EU. These findings are mostly in line with the ADF test and the runs test performed on countries’ indices. As such, there is clear evidence for confirming the rejection of my first hypothesis, i.e., the stock market of a country becomes efficient after its entry into the EU.
To study the rejection of the second hypothesis of my paper, namely whether better satisfying the EMH assumptions results in market efficiency, the ratio of efficient companies after the entry into the EU is examined. Neither Malta, Slovenia, nor Cyprus, which are the countries that scored highest on the EMH assumptions, have ratios above 50%, resulting in enough evidence to confirm the rejection of H2.
25
8. Conclusion
I examine 13 countries to find whether the entrance into the European Union affects the stock market efficiency of those countries. The results of the variance ratio test, the DF-GLS test, ADF test, and runs test show that there is evidence suggesting Latvia and Romania become weak form efficient after their entries into the EU. However, more countries display a predictable pattern after their entry in the EU and thus exhibit market inefficiency. What is more, I analyse whether countries better satisfying the assumptions of EMH, as laid out by Fama (1970), have a higher probability of market efficiency. The results suggest that such a prediction is false, and the countries which score highest on the EMH assumptions are still not weak form efficient.
The failure of not having an efficient market implies that stock market prices display predictability and thus investors can earn abnormal returns by analysing the behaviour of past prices. However, as Fama (1991), and Lo and MacKinlay (1988) argue, the rejection of the null hypothesis of EMH suffers from the joint hypothesis problem. The Random walk hypothesis could be rejected because of the correlation of lagged prices, or because of the applied asset pricing model (The Martingale). If the model is faulty, it might not display the true price generating process.
The limitations of my study are the lack of accurate data for index prices, the lack of pricing data for individual stocks, and the rough proxies for the EMH assumptions. Future research examining the impact of the European Union on the EMH could extend the analysis on all available EU countries and thus rectify such limitations.
26
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29
Appendix
Steps for choosing the number of lags for the DF-GLS test:
𝑆𝐼𝐶 = ln(𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑒𝑟𝑟𝑜𝑟𝑠) + (𝑘 + 1)ln (𝑁 − 𝑘)
(𝑡 − 𝑘) , (18)
where k is chosen for the smallest value of SIC. The sum of squared errors is found by regressing Pt on Pt-1 with k lags.
As per Stock and Watson (2011), AIC is defined in the same manner as SIC except 2 replaces the term ln (N-k). MAIC, is the minimum AIC found by using the definition of Ng and Perron (2001). In equation 18, it replaces (𝑘 + 1) with
1 𝑠𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑒𝑟𝑟𝑜𝑟𝑠𝛿0 2∑ 𝑃 𝑡 𝑁 𝑛=𝑘 . (19)
The sequential t information criterion was developed by Ng and Perron (1995). It is found by using a programmable algorithm which refines SIC. The algorithm checks whether a smaller number of lags compared to the k chosen by SIC could provide a significant coefficient for the regressor of the 𝑃𝑡 in equation 13.
Table 8
Variance Ratio test results
Panel A Period q=16 q=2 q=4 q=8 Bulgaria Pre-EU -0.53 -1.10 -0.80 -0.67 EU 5.57 *** 2.47 ** 3.43 *** 4.46 *** all 2.97 *** 0.09 1.05 2.02 ** Croatia Pre-EU 1.37 -0.01 0.13 0.58 EU 3.26 *** 1.20 1.71 * 3.25 *** all 1.48 0.02 0.17 0.68 Cyprus all 1.96 ** 3.39 *** 2.37 ** 2.02 ** Czech Pre-EU 1.39 0.67 0.64 1.06 EU 0.15 1.63 0.35 0.09 all 0.48 1.73 * 0.48 0.33 Estonia Pre-EU 3.45 *** 3.29 *** 3.51 *** 3.36 *** EU 6.58 *** 3.80 *** 4.43 *** 5.23 *** all 7.46 *** 4.79 *** 5.44 *** 6.09 *** Hungary Pre-EU -0.62 0.14 -0.61 -0.30 EU 0.21 1.58 0.07 0.38 all 0.01 1.56 -0.11 0.25 Latvia Pre-EU 1.15 1.42 2.51 ** 1.19 (Continued)
30 Table 8 - Continued EU 1.26 -1.69 * -0.97 -0.13 all 1.58 0.61 1.86 * 1.00 Lithuania Pre-EU 5.36 *** 2.40 ** 3.83 *** 4.31 *** EU 3.90 *** 2.17 ** 1.94 * 2.23 ** all 4.75 *** 2.55 ** 2.55 ** 2.89 *** Malta Pre-EU 4.30 *** 5.49 *** 5.89 *** 6.09 *** EU 4.45 *** 6.06 *** 5.90 *** 4.03 *** all 6.15 *** 8.10 *** 8.20 *** 6.76 *** Poland Pre-EU 0.97 -0.12 0.75 0.83 EU 1.55 3.77 *** 2.44 ** 1.83 * all 1.81 * 3.01 *** 2.43 ** 1.93 * Slovakia Pre-EU 0.21 -3.56 *** -2.74 *** -1.88 * EU -0.77 -0.40 -0.54 -0.14 all -0.65 -2.94 *** -2.43 ** -2.30 ** Slovenia all -0.71 -0.65 -0.75 -0.79 Panel B Period q=16 q=2 q=4 q=8 Bulgaria Pre-EU -0.53 -1.10 -0.80 -0.67 EU 5.57 *** 2.47 ** 3.43 *** 4.46 *** all 2.97 *** 0.09 1.05 2.02 ** Croatia Pre-EU 1.37 -0.01 0.13 0.58 EU 3.26 *** 1.20 1.71 * 3.25 *** all 1.48 0.02 0.17 0.68 Romania Pre-EU 2.55 ** 3.76 *** 3.29 *** 3.17 *** EU 1.45 1.26 0.99 0.73 all 2.80 *** 3.20 *** 2.74 *** 2.49 **
Table 8 presents the standardised z values for the variance ratio test for 2, 4, 8, and 16 lags for the A13 countries. Cyprus and Slovenia present one period, namely March 2004 – December 2016 and March 2006 - December 2016 respectively. For both Panel A and B, the Pre-EU period represents the period before the entrance into the European Union, The EU represents the period after the entry into the European Union. For both panels, the all period is between 31st December 1999 and 31st December 2016. For Panel A, the Pre-EU starts at 31st December 1999 ends at 30th April 2004; the EU period starts at 1st May 2004 and ends at 31st December 2016.
For Panel B, Romania and Bulgaria, the Pre-EU period starts at 31st of December 1999 and ends 1st of January 2007; for Croatia it starts from 31st December 1999 and ends 1st of July 2013. The EU period starts at 1st of January 2007 for Romania and Bulgaria and at 1st of July 2013. It ends for all 3 countries at 31st December 2016. This is a two-sided test with approximately normal distribution. The asterisks inform about the rejection of the null hypothesis at 1% significance level for *, 5% for ** and 10% for ***.
Table 9
DF-GLS
Panel A BIC Seqt MAIC
No. of lags z value No. of lags z value No. of lags z value
Bulgaria Pre-EU 24 -1.40 1 -1.33 24 -1.40
EU 26 -1.13 4 -0.50 26 -1.13
all 29 0.89 13 0.71 29 0.89
