The effect of economic growth on one-year-ahead excess returns
∗Roy F. E. Peek† January 14, 2016
Abstract
We investigate whether economic growth in the form of three different macroeconomic variables (Gross Domestic Product, Industrial Production and Private Consumption) has an effect on one-year-ahead excess returns. We analyse the data of six different countries and evaluate every quarter separately. We will also briefly consider a European portfolio. There is expected to be a negative relationship between fourth quarter economic growth and one-year-ahead excess returns, and no effect for the other quarters. A preliminary data analysis tells us how the results should be estimated. Eventually, the results are mixed. There is some evidence for a fourth quarter effect in a couple of countries for both Gross Domestic Production and Industrial Production. On the other hand, for some countries and for Private Consumption in every country, no effect is found. Also, we found some indication that there might be an effect in the other quarters too.
∗I would like to thank my supervisor dr. S.W.S. Lui.
1
Introduction
Every quarter, the economic growth figures are published. For economists it is of tremendous interest to see how much percentage Gross Domestic Product (GDP), Industrial Production (IND) and Private Consumption (CON) have grown or declined in the last quarter. With this, they can analyse whether the economy became bigger, if consumer confidence got a boost and if for example policy measures were successful. They can compare the data of sev-eral countries to see which country swiftly expands and which country does not. Moreover, they can analyse whether their expectations were anywhere close to the final figures. Clearly, economists are very fond of statistics of economic growth, but do consumers and investors have the same affection for these figures? Do they let economic growth announcements af-fect their (spending and investing) behaviour? This question summarizes the interest of this paper. We want to investigate whether investors adapt their investing attitude according to macroeconomic growth figures. To be precise, we investigate this by looking at the effect of economic growth on one-year-ahead excess returns.
In this paper, economic growth will be represented by three different growth variables, namely GDP, IND and CON (see table 2 in the appendix for their definitions). The expectation (which will be elaborated upon in section 2 and 3) is that there will only be an effect of economic growth on one-year-ahead excess returns in the fourth quarter. To test for this, we will run regressions for every separate quarter and growth variable. The dataset of this paper includes data for six different countries and has a time span of 53 years. The coun-tries included are the Netherlands, Germany, Italy, the United Kingdom, the United States and Sweden. The period covered is the second quarter of 1962 till the third quarter of 2014. The dataset will be subject to a preliminary data analysis (section 4.3), which will provide us with insights about any necessary adjustments. According to this information, the model will be adjusted so we can draw reliable conclusions (on basis of the regression results) in section 6.
The literature review (section 2) will provide existing empirical evidence on our research question: will there be an effect of economic growth on one-year-ahead excess returns? Ex-isting literature tells us that we should expect an effect of economic growth on one-year-ahead returns which is negative. According to the prediction of the tax loss selling and infrequent portfolio adjustment hypotheses the prediction is that this effect will only be found in the fourth quarter. The tax loss selling hypothesis states that investors sell loser stocks (most probably at the end of the year), in order to get a favorabe tax climate. The infrequent port-folio adjustment hypothesis states that people do not adjust their portport-folios continuously, but on different points in time. The combination of these two brings up the expectation that investors tend to adjust their portfolios more heavily at the end of the year. Hence we predict that the effect of economic growth on one-year-ahead excess returns will only be found in the fourth quarter. This provides us with two hypotheses. The first hypothesis predicts that there is a negative effect of economic growth on one-year-ahead excess returns in the fourth quarter. The second hypothesis forecasts that this effect will only be found in the fourth quarter, and no effect will be found in any of the other quarters.
2
Literature review
The literature review will cover all the interesting topics which are discussed in the existing literature. By analysing the results of the current literature, we can see wheter the empirical findings of this paper are in line with the existng evidence. It may also provide us with back-ground understanding and possible reasons for any contradictions. Moreover, the academic papers could give us an indication of what methodology and methods would be appropiate to use. This section will start off with the most evident question concerning this paper: what is known about the relationship between economic growth and one-year-ahead excess returns? If there is any existing literature on this topic, what methodology did they use, and can we use a method which is analogous to theirs? After this section, we discuss literature that cover topics that could be explaining the effect between economic growth in the fourth quarter and one-year-ahead returns. Examples of this are tax loss selling and the infrequent portfolio adjustment hypothesis. Furthermore, we elaborate on literature that could help us to predict the sign of the effect (whether the effect is negative or positive). We do this by looking at the behaviour of investors in response to economic growth. Do they take higher or lower risks as an answer to low economic growth? To continue with, we will discuss the literature on economic growth, and to be precise, we discuss how we should represent economic growth in our model. Last but not least, we will try to rule out the possibility of reverse causality.
2.1 Effect of economic growth on one-year-ahead excess returns
job in explaining end-of-the-year expected returns in the regressions than economic growth in the other quarters. Next to this, Campbell and Cochrane (1999) state that CON has a negative effect on (among other things) expected returns: “All these phenomena are linked to economic fluctuations: When consumption falls, expected returns, return volatility, and the price or risk rise, and price/dividends ratios decline”.
These findings provide us an indication about the methods we could use and about how we could formulate our hypotheses (as will be done in section 3.3). Of course, their paper differs from this paper as they only investigated data for the United States. We cannot tell with certainty what will be the external validity of their findings. As the countries of this paper are comparable in nature with the United States (they are all developed countries with strong and advanced financial systems), we predict that investors behave alike, so we expect to find similar effects for the countries covered in this paper. Therefore, we will adopt a methodology which is extracted from the techniques used by Møller & Rangvid (2014). Also, we predict to find similar results, which is a negative effect of economic growth on one-year-ahead returns in the fourth quarter only.
2.2 Tax loss selling
the differences between the tax-deferred and taxable accounts, they found confirmation that investors engage in so called tax-loss selling during the course of the year.
Reinganum (1983) also found evidence in favour of the tax loss selling hypothesis. He tried to find a reasoning for the unusual height of the returns of small-scale companies in the beginning of January. With the help of empirical research, Reinganum (1983) found that these abnormally high returns are due to tax loss selling. He explains that tax loss selling is not exclusively responsible for the effect, but it does account for a significant chunk of this so called ‘January effect’.
The tax loss selling effect is interesting for this paper, as in most countries, tax declara-tions have to be done over the period of a normal calendar year. This means companies use the last part of a year (the last quarter, and specifically the last month) to adjust their profits and losses in such a way to minimize their taxable volume. With this reasoning (although Ivkovi´c et al (2005) say that tax loss selling happens throughout the year), one would intuitively expect tax loss selling to be concentrated at the end of a fiscal year. With this allegation, we could expect a bigger effect of economic growth in the fourth quarter on one-year-ahead excess returns than in the other quarters, as investors and companies tend to adjust their portfolios more heavily in the last quarter due to tax loss selling.
2.3 Infrequent portfolio adjustments
a remarkable effect: “if the fixed component of the transactions cost is sufficiently small, then eventually, with probability 1, a time-dependent rule emerges: the interval between observations is constant and on each observation date, the consumer converts enough assets to liquid assets to finance consumption until the next observation”. Hence, they did find some evidence for frequent time adjustments and for time dependent models.
The findings above are interesting for this paper, as we have to give an explanation for the prediction that fourth quarter economic growth influences one-year-ahead returns, while in the other quarters it does not. The fact that there is a possibility that stockholders do not continuously adjust their portfolio, but at set points in time, together with tax loss selling, implies the idea that in general they might more rigorously adjust their portfolios during the end of the year than in the rest of the year. It thus provides us with a substantiation of our prediction that there is an effect of fourth quarter economic growth on one-year-ahead returns, and no effect in the other quarters.
2.4 Higher risk taking in reponse to low economic growth and vice versa
The passage above provided us with evidence for an effect of fourth quarter economic growth on on-year-ahead excess returns. Next to this, we also have to form an expectation about the sign of the effect. Is there a negative or positive relationship between economic growth and one-year-ahead excess returns? Møller & Rangvid (2015) investigated the ‘end-of-the-year effect’ by looking at the effect of economic growth on global assets in an international perspec-tive. They give an indication on the direction of the effect: “When global economic growth at the end of the year is low, investors expect a worsening of the global business cycle and increase their required returns”. Hence, judging from Møller & Rangvid (2015), we would expect to find a negative relationship between economic growth and one-year-ahead returns. When there is for example an economic crisis, returns are naturally low, and investors have to take more risk to still bring home higher returns. When the economy is thriving on the other hand, returns are naturally higher, and there is less of a reason to take higher risks for high returns.
affect consumption choices”. Where they elaborate that, with the use of the methodology created by Fama and French (1993), they find a negative effect. These results show that consumers and thus possibly also investors are affected by macroeconomic events (like for example economic growth). Because of these findings and the ones given above, we would expect to find a negative effect of economic growth on one-year-ahead excess returns (in the fourth quarter only).
2.5 Economic growth proxies
We want to test whether there is an effect of economic growth on one-year-ahead excess returns, but economic growth is a virtual term. In practice, there are no literal figures for how much the economy has grown. Of course, there are data that could explain economic growth for a big part, and are therefore a useful proxy to represent economic growth in our regression estimates. Lequiller and Blades (2007) provide a discussion about GDP in their book. GDP is seen as a very extensive and satisfactory proxy for economic growth, but it has also received several critics. As it basically is the plain sum of the ‘value of the products produced in a country’, it gives a good insight in growth, but it does not measure every aspect one might be interested in. GDP does a bad job in explaining equality and social and environmental factors. As GDP is not an average or median measure (which could better explain equality) but an aggregate of the whole country. Because of this, we do not want to use GDP as the sole instrument to explain economic growth. This paper will therefore also use IND and CON as proxies for economic growth. The addition of IND and CON also makes it interesting as it adds an extra level to our analysis. Table 4 shows the shares of CON and IND as a percentage of GDP. The data of the shares are retrieved from the OECD (Organisation for Economic Co-operation and Development) site1. We used the data for the year 2012. In the table, the data for Private Consumption is ‘Household final consumption expenditure’. The data for Manufacturing is valued added, which is ‘net output of a sector after adding up all outputs and subtracting intermediate inputs’ and for Industry is ‘value added in mining, manufacturing, construction, electricity, water, and gas’. These definitions are all taken from the OECD site. We think our data for Industrial Production is most closely comparable with the Industry definition, but we give the figures for Manufacturing for completeness. In this way, by both examining GDP on the one hand and CON and IND on the other hand, we can analyse what ‘part’ (and the size of this part) of the economy possibly explains the effect of economic growth on one-year-ahead excess returns.
2.6 Effect of one-year-ahead excess returns on economic growth
Of course, to be able to get reliable results with an Ordinary Least Squares estimation (as will be explained in section 3), we have to rule out the possibility of reverse causality and endogeneity. Reverse causality arises when not only the independent variable affects the dependent variable (which is the effect one would want to measure), but when also the dependent variable has an effect on the independent variable. Intuition tells us that reverse causality will not be an issue in this case. The dependent variable are the one-year-ahead excess returns, and the measurement of these returns starts after the measurement of the data of the corresponding economic growth has ended. In this case, as we cannot go back in time, the excess returns a year later will not influence the economic growth of previous year. In case of reverse causality between the variables in the estimation, we would have to instrument the independent variable, and run a so called two staged least squares regression. As we can say with a high probability that reverse causality is not the case, we do not have to deal with this problem.
3
Methodology
This section will describe in depth what statistical model and procedures are used in order to be able to estimate the results. Firstly, there is a subsection which discusses the model. After this, section 3.2 will reveal information about what methods will be used in this research. The hypotheses section will give a verbal overview of the hypotheses of the paper, and informs the reader what - according to the existing literature, as described above in section 2 - can be expected to be found in the results. The statistical hypotheses will give a mathematical explanation of the hypotheses stated in the antecedent section. The last part of this section will also give an insight into how the (theoretical) hypotheses will be tested.
3.1 Model
further on the preliminary data analysis and the needed adjustments.
This section continues with the explanation of the model, and specifically, the equation that is used to estimate the results. As we know from the second section, we want to know if there is an effect of economic growth - defined as GDP, IND and CON - on the so called one-year-ahead excess returns. From this information we derive that the variable for the one-year-ahead excess returns must be the dependent variable and the proxies for economic growth will be the independent variables in the regression equations. Also, we know from section 2 that we expect to find a significant relationship between economic growth in the fourth quarter and the corresponding one-year-ahead excess returns, but we do not expect to find such a relationship for the other quarters. To sum this all up, to test for this we have to regress the one-year-ahead excess returns (the dependent variable) on the variables for economic growth (the independent variable). By putting this information in an equation, we obtain the equation as given in equation one. This equation is provided by Møller & Rangvid (2014), who performed a comparable study.
Ret+1= α + βGit+ εt+1 (1)
Where Rt+1e represents the excess returns on the stocks in a one year ahead fashion, which correspond with the quarter that is used as the independent variable. Gitis the growth of one of the macroeconomic growth variables (in this case: either GDP, IND or CON) for quarter i. α is a constant and β is the coefficient for the macroeconomic growth variables. According to section 2, we expect the β coefficient to be negative (so we expect a negative relationship between economic growth and one-year-ahead excess returns), which will extensively be de-scribed in the hypotheses section. εt+1 is the error term that captures all unobserved and unexplained effects. Effectively, the error term captures all the variables that do have an effect on the dependent variable but are not included in the equation.
3.2 Methods
further information on whether or not the Gauss Markov assumptions are violated and the adjustments we have to make in order for the OLS estimator to remain BLUE. In case of reverse causality or endogeneity, one could expect to use an Two Stage Least Squares estimation (TSLS), by instrumenting the endogenous variable. Intuitively, we expect that there might be a relationship of economic growth on one-year-ahead excess returns, but we do not expect a relationship of excess returns a year later on the economic growth figure of the previous year. This intuition is explained and substantiated in section 2. Because of this, we do not expect any reverse causality, and an TSLS estimation seems unnecessary. Hence, an OLS estimation which is BLUE is the preferred method.
3.3 Hypotheses
The hypotheses naturally result from a combination of intuition and from a review of the existing literature, as has been done in section 2 above. Due to - among others - tax loss sell-ing (Ivkovi´c, Poterba, and Weisbenner (2005)) and infrequent portfolio adjustments (Abel, Eberly, and Panageas (2013)), we expect that fourth quarter economic growth will have an effect on the corresponding one-year-ahead excess returns, while economic growth in the other quarters will not have an effect on the corresponding one-year-ahead excess returns. Furthermore, intuition and the literature shows us that low economic growth leads to higher risk taking while high economic growth makes investors more risk averse. Hence, higher economic growth leads to lower risk taking. This means that we would expect that higher economic growth leads to lower one-year-ahead excess returns, and thus we predict a nega-tive relationship (in the fourth quarter) between economic growth and one-year-ahead excess returns. From these expectations we can formulate the following hypotheses:
Hypothesis 1: There is a negative effect of economic growth in the fourth quarter of the year on the corresponding one-year-ahead excess returns
Hypothesis 2: There is only an effect of economic growth in the fourth quarter on the corre-sponding one-year-ahead excess returns, no effect will be found in one of the other quarters
3.4 Statisical hypotheses
To give an exact insight in how the OLS method tests for a relationship (significance) between the independent and the dependent variable, we give the mathematical representation of the statistical hypothesis that are tested. For example, when we take the fourth quarter, the null and alternative hypotheses for the variable specific test takes the form of equation two and three respectively.
H0 : β = 0 (2)
H1 : β 6= 0 (3)
When we would reject the null hypothesis, we would have to adopt the alternative hypothesis. In this case, adopting the alternative hypothesis means that the coefficient is significantly different from zero, which means that the coefficient is ‘significant’, or in other words, there is a relationship between the independent an dependent variable at at least one of the signif-icance levels (one, five or ten percent). For the fourth quarter, we expect to reject the null, and the coefficient to be negative. For the other quarters, we expect to fail to reject the null hypothesis, which would show that the coefficients of the other quarters are not significantly different from zero, and no relationship exists.
4
Data and descriptive statistics
This section will define the sources and the characteristics of the data as well as the process of how the data is transformed from raw data to useful variables which could be used in this research. Furthermore, section 4.2 will briefly elaborate on the (basic) descriptive statistics of the data with a short analysis. One can find the full summary of descriptive statistics in the two descriptive statistics tables in the appendix (section 8). After that, we will provide a preliminary data analysis. This analysis consists out of the Dickey Fuller test (to investigate the existence of unit roots), tests for normality (skewness and kurtosis), the White test of heteroscedasticity and the Durbin-Watson statistics for autocorrelation. Furthermore, section 4.4 will specify the data used in the European portfolio. The last part of this section deals with the nature of the data. It will namely cover the constraints of the data.
4.1 Data
returns. This data is obtained with the help of Datastream. Table 1 (which could be found in the appendix) sums up the countries and the matching stock indices that are used for this research.
From the representative stock indices, the monthly share prices were retrieved in the period from July 1962 till October 2014. With these stock prices, the returns were calculated in a one-year-ahead fashion. These one-year-ahead returns consist of a year over year percentage change and are produced according to the formula given in equation 4.
N ew − Old
Old ∗ 100% (4)
The one-year-ahead returns are measured from the beginning of the next month to the end of that month a year ahead. For example, when we have second quarter GDP growth in 1962 (which is the first quarter covered in this paper), and we would like to compute the corresponding one-year-ahead returns, we start measuring the return from July 1962 (the first month after the end of quarter 2) till July 1963. Equation 5 gives the exact calculation for the one-year-ahead returns of this quarter.
Share price July 1963 - share price July 1962
Share price July 1962 ∗ 100% (5)
All the other one-year-ahead returns for the other quarters are calculated in an analogous way. For example, for the last quarter of the dataset - quarter 3 of 2014 - we compute the returns from October 2014 till October 2015.
After the computation of the one-year-ahead returns in the above mentioned fashion, a risk free rate must be subtracted to obtain the one-year-ahead excess returns. A risk free rate is essentially virtual, as in theory it exists but in practice it is relatively unclear what is the exact value of the risk free rate. Also, in theory every country should have a different risk free rate, but it is hard to measure a clear-cut rate. Therefore, to be consistent and clear, to compute the excess returns, a uniform risk free rate is used for all six countries and stock indices. This paper uses the same risk free rate as Kenneth French2. French computes the risk free rate on the basis of a one month treasury rate. The one-year-ahead returns were matched with their corresponding quarters (as described above) and so for every quarter and every year an excess one-year-ahead return is computed.
Concerning the macroeconomic variables, the data for GDP growth, CON growth and IND growth are all retrieved from the OECD site3. The data for GDP growth and IND growth
covers the same period as the data from the one-year-ahead excess returns, hence the second quarter of 1962 till the third quarter of 2014, a time span of 53 years. For CON growth, the completeness of the data depends per country. The first input of every row of Descriptive statistics table 1 (table 5) gives us a good insight of the number of observations per variable. The data for all the macroeconomic variables are given in growth percentages. Table 2 in the appendix (section 8) gives an overview of the different variables used in this paper, an explanation of their abbreviations, the unit of measurement and their frequency.
4.2 Descriptive statistics
The appendix provides the interested reader with two descriptive statistics tables. The two tables give a full summary of the complete dataset. The first table reports the number of observations, the mean values and the median values respectively, where the second table provides us with the standard deviations, minima and maxima of the different variables.
As was mentioned above, the period covered in the research is the second quarter of 1962 till the third quarter of 2014. This is in line with the values for the number of observations in the descriptive statistics table 1 (table 5). Because of this, we see that the first and fourth quarter have 52 observations, while the second and the third quarter consists out of 53 ob-servations. When we look at the values of the mean and the median, we see that in general the values are relatively low. This is due to the fact that the values are growth percentages. Since we did not include countries with very rapid growing economies (for example a country like China) in the dataset, a modest growth is in line with the expectations. Another fact that we observe from the table is that the mean and the median are not the same. In most cases they are relatively equal, while in some cases there is a significant difference. This could be an indication of skewness or of outliers. We will therefore show the results for the tests for normality (skewness and kurtosis) below. For completeness, descriptive statistics table 2 (table 6) shows the values for the standard deviations, the minima and the maxima.
4.3 Preliminary data analysis
Table 7 can be found in the appendix (section 8), and it shows the White test for het-eroscedasticity and the Durbin-Watson statistics for autocorrelation. The values reported are the corresponding P-values, and the stars indicate the significance. The first values are the results of the White test (established by White (1980)). The null hypothesis of the White test is given in equation 6. The White test examines whether there is homoskedasticity in the residuals of the model.
Hence, according to equation 6, when we would reject the null, we would have to accept the alternative hypothesis of the existence of heteroscedasticity. The table shows us a couple of cases in which there exists heteroscedasticity. With the existence of heteroscedasticity, we will still have unbiased coefficient estimates, but we could have inappropriate standard errors. When the standard errors are inappropriate, it will influence the inferences we make as the t-statistic is calculated by dividing the coefficient (which stays the same) with the standard errors. Therefore we will adjust for the heteroscedasticity by applying robust standard errors.
The second values in table 7 provide us with the Durbin-Watson statistics. This statis-tic shows us the presence of autocorrelation. Durbin and Watson give a range in which there is autocorrelation (< dL and > 4−dL), a range where there is no autocorrelation (in between dU and 4 − dU ), and two ‘grey area’ ranges where it is not certain whether there is autocorre-lation or not. In these intermediate regions, the null hypothesis of no autoccoreautocorre-lation cannot be rejected but neither are we able to fail to reject it (in between dL and dU and in between 4 − dU and 4 − dL). This is according to Durbin and Watson (1950, 1951). Equations 8 and 9 give the ranges which fit with this dataset.
dL = 1.356, dU = 1.428 (7)
4 − dU = 2.534, 4 − dL = 2.644 (8)
When we compare this with the values in the table, we see that there is only one case of autocorrelation (where the DW statistic is in the wrong range, namely it is smaller then dL), which is CON in the Netherlands in the second quarter (indicated with an A).
Table 8 in the appendix reports the P-values for the Dickey fuller test (existence of a unit root/trend), and the P-values for skewness and kurtosis. The stars again indicate the sig-nificance. To begin with, the Dickey Fuller test (established by Dickey and Fuller (1979)), investigates whether there is a trend (unit root) present in the data. Equation 9 gives the underlying equation for the Dickey Fuller test we conducted. We included an intercept but not a time trend in the test, as can be seen in this equation. Equation 10 provides us with the appropiate null hypothesis of the Dickey Fuller test.
∇yt= α0+ δyt−1+ ut (9)
H0 = Existence of a unit root (10)
one-year-ahead excess Returns, GDP, and IND, no trends exist. Only for CON in the Nether-lands, there is an indication of a unit root. To adjust for this, we transform all the data for CON (but only for CON, so not for the other variables) into first differences, creating the variable dCON . We did not find a unit root in the data for dCON, hence the transformation in first differences succesfully eliminated the trend.
Last two values of the table provide us with the tests for normality. Respectively the P-values for skewness and the P-P-values for kurtosis are reported. Equation 11 shows us the null hypothesis for the skewness P-values, and equation 12 does the same for the kurtosis P-values.
H0 = Skewness of a normal distribution (11)
H0 = Kurtosis of a normal distribution (12)
Rejecting equation 11 lets us adopt the alternative hypothesis of no skewness of a normal distribution, and rejecting equation 12 the alternative hypothesis of no kurtosis of a normal distribution. Briefly put, rejecting them means that there is a lack of normality. Therefore, table 8 shows that non-normality might be an issue in this dataset as the null hypotheses are rejected relatively often.
4.4 European portfolio
Next to the analysis and comparison of six different countries, we will provide a result of the regression estimates of a so called European portfolio. This portfolio is a combination of the excess returns of sixteen different European countries. The data for the returns of this portfolio are extracted from the site of Kenneth French. Kenneth French (see footnote 1) provides the data for the returns on a monthly basis, and thus are the monthly excess returns of these sixteen countries combined. The list of countries that are included could be found in the appendix (table 3 in section 8). The excess one-year-ahead returns are computed in a different way as above. For the six different countries, we have data of the stock indices, and we could compute the year-over-year percentage change (as was shown in equation 4). For the European portfolio, we obtained data on the monthly excess returns, which are already adjusted with the risk free rate. The risk free rate is the same as above, as we used the risk free rate of Kenneth French to compute the excess returns. To compute the one-year-ahead excess returns, we sum the monthly excess returns from the beginning of the next month till a year later. For example, to obtain the one-year-ahead excess return for the fourth quarter of 1999, we sum the monthly excess returns from January 2000 till the end of December 2000.
macroeconomic growth (GDP, IND and CON) have to be a combination of these sixteen countries too. The same data from the OECD (as described above) is used. The macroe-conomic growth variables for this portfolio are combined in two ways (and for both the regression estimates are shown). We combined them in both an equal weighted manner and a value weighted manner. Because we do not know how Kenneth French weighted its Euro-pean portfolio exactly, we have to use two different weighting maners. Intuition tells us that the value weighted manner is most realistic, but for completeness we look at both an equal weighted and a value weighted case. In the equal weighted manner, we just took the average of the growth percentages of the sixteen countries combined, where every country has the same weight. In the value weighted manner, the growth percentages are weighted on the basis of the number of inhabitants of every respective country. The data for the population size is obtained from the OECD, and the value for the year 2012 is used. This has been done for all of the three economic growth variables. The regression estimates for the European portfolio can be found in table 12 in the appendix.
first differences. After this transformaton, we saw that the variable dCON does not feature a unit root anymore.
dL = 1.037, dU = 1.199 (13)
4 − dU = 2.801, 4 − dL = 2.963 (14)
By comparing equation 13 and 14 with the values in table 11 we can conclude that the values for the Durbin Watson statistics are in the safe range, hence autocorrelation is not an issue for the European portfolio and no adjustments have to be made. Therefore, only adjustments for heteroscedasticity have been made (by applying robust standard errors), and with these adjustments we obtain the outcomes as have been presented in table 12 in the appendix.
4.5 Constraints of the data
When we will discuss the outcomes of the regressions in section 5, we have to keep in mind a couple of restrictions that are posed by the nature of the data, when we make a comparison between the outcomes of the different regressions. First of all, as we have encountered above, the periods of the variables are not always equal. For the six separate countries, the data for the excess one-year-ahead returns and the proxies for macroeconomic growth, GDP and IND all have the same time span. However, the data for CON does not always cover the same period. For the countries the United Kingdom, the United States and Sweden, the same period is investigated, while for the Netherlands, Germany and Italy, the periods are shorter. This can be observed from table 5 in the appendix (descriptive statistics table 1). This has to be kept in mind when we compare the results for CON of these countries with the results of other variables and other countries.
Continuing, the dates on which the data of the share prices are announced differ per country. For The Netherlands, Italy, the United Kingdom and the United States, the data of the excess returns have been reported on the 15th day of every month, so at the half of every month. On the other hand, for Germany and Sweden, the excess returns were reported at the last trading day of every month. This difference in dates of announcement might have implications for the results of the different countries, so we have to keep this in mind when we compare the results and draw conclusions.
5
Results
This section will give a comprehensive overview of all the different regression outcomes, as estimated using the approach described in section 3. We know from the data section that the research has been conducted for six different countries. Also, we know that for every single country, the four quarters are regressed separately on their matching one-year-ahead returns. Next to this division, we learned from the data section above that three proxies for economic growth will be investigated, namely GDP, IND and CON. The combination of these six countries, all consisting out of four quarters, regressed for three different variables, give us 6 ∗ 4 ∗ 3 = 72 different regressions. The hypotheses expect the fourth quarter regressions to be significant, while the others will not be. We predict the coefficient to be negative. In the appendix, one could find a table (table 9 in the appendix) with the results of all these 72 regressions. These results are estimated with robust standard errors, and the variable for CON is given in first differences. We will discuss this table in section 5.1. The second part of the result section will briefly discuss table 10. This table is estimated without robust standard errors but also with CON in first differences. The last part consists of the results of a sub research where we investigate if we can find an effect of fourth quarter economic growth on one-year-ahead returns in a portfolio of European countries. See table 3 in the appendix for the countries that are included in this European portfolio.
5.1 Regression estimates with robust standard errors
The table (table 9) with the regression estimates with robust standard errors could be found in the appendix. CON has been transformed into first differences because of the presence of a unit root. dCON does not exhibit a unit root. We found in section 4.3 that the residuals of some of the estimations were heteroskedastic. Because of this, the regressions are also adjusted for the existence of heteroscedasticity. As we do not want to violate the Gauss Markov assumptions, this table (thus with robust standard errors) is the main focus of the paper. Section 6.2 discusses the effect on the Gauss Markov assumptions in greater extend.
growth is significant at a ten percent level, and for the United states first quarter growth of IND is even significant at a five percent level. For both countries, fourth quarter dCON is insignificant, as are all the other variables for other quarters not described above.
For Italy, none of the quarters of any of the three variables are significant, in contrast to what the hypotheses would predict. In the regression estimates with robust standard errors, all estimates are also insignificant for the United Kingdom. We cannot conclude any effects on the basis of the usual significance levels (1%, 5% or 10%), but maybe we can discover a trend when we look at the t-statistics of the different quarters. We can examine whether we see any improvement of significance as we move towards the fourth quarter (which would be plausible if hypothesis two is true). The t-statistics are not directly given in table 9, but can easily be calculated by dividing the coefficient with the standard error. When we look at the t-statistics of Italy and the United Kingdom we can only draw one conclusion. We do not see an improvement of significance when we move towards the fourth quarter, and also the fourth quarter does not evidently have the highest t-statistics. Therefore, for both Italy and the United Kingdom, we cannot find prove for both hypothesis one and hypothesis two. The explanation for this lack of evidence could be because there simply is no effect of economic growth in these countries. On the other hand, the lack of useful results could also be caused by a misspecification of the model, as will discussed in section 6.2.
Sweden has a significant estimate for IND in the fourth quarter at a five percent level. Furthermore, for Sweden, IND in the third quarter is significant too at a ten percent level. These two observations have relatively high R squares, with 0.130 for IND in the fourth quarter, and 0.043 in the third quarter. All other R squares for Sweden are very low, and all other estimates are insignificant. The results for Germany are puzzling. For GDP, the values for the first and fourth quarter are both significant, both at a one percent significance level. For IND, also the first and fourth quarter growth are significant, in this case at a five percent level. All the other estimates are insignificant. The significant estimates have relatively high R squares, where the other R squares are very low. For the GDP, R squares of 0.126 and 0.113 are reported for respectively the first and fourth quarters. For IND, the R squared values are 0.106 and 0.078, also for the respective first and fourth quarters.
a negative relationship. All the significant estimates have a negative coefficient - with the exception of IND in the third quarter for Sweden - with also a relatively high magnitude. The biggest magnitude (of a significant estimation) is -9.305 (the fourth quarter growth of GDP in Germany). This means that a one percent increase in GDP growth leads to a 9.305 percent decrease in one-year-ahead excess returns. The smallest is second quarter IND growth in the Netherlands, which is -2.214. It means that a one percent increase in IND growth leads to a 2.214 percent decrease in one-year-ahead excess returns. All the other magnitudes are thus in the range between -9.305 and -2.039, which are shown in table 9 in the appendix. Because of this, we see that the negative relationship prediction in hypothesis one holds. Also, we see that for some of the countries (the Netherlands, Germany and the United State) it holds that there is an effect of economic growth in the fourth quarter on one-year-ahead returns. This relationship only counts for economic growth in the form of GDP and IND, as no effect is found for dCON. Thus, we can say that (after adjusting for heteroscedasticity) hypothesis one is satisfied for half of the countries and two of the economic growth proxies. Hypothesis two on the other hand is not convincingly supported by the results, as the countries which find significant results for the fourth quarter also all have at least one or even more significant results in one of the other quarters.
As was introduced in section 2.5, we know that we can analyse CON and IND as com-ponents of GDP. Table 4 in the appendix shows us their share in percentage of GDP. When we choose the definition for industry, then on average, IND has approximately a 24 percent share in GDP (in a range from 20.56 to 30.80 percent). For CON this share is even bigger, with approximately an average number around 57 percent (in a range from 44.91 to 68.42 percent). These shares could help us explain what ‘part’ of the economy explains the effect of economic growth on one-year-ahead excess returns. We see that for the Netherlands, Ger-many and the United States, we find an effect for both GDP and IND, but not for CON. Therefore, we can state that the effect is explained in the industrial part of the economy and not in the consumption part of the economy. We see that for the Netherlands, the share of industry in GDP is 22.14 percent and for the United States it is 20.56 percent. Germany has a share of 30.80 percent. This is in line with the findings for Sweden. There, we do find an effect in the Industrial part of the economy, but it might not be strong enough to translate into an effect which is felt in the whole economy (as there is no significant result for GDP). The share of Swedish industry in their GDP is 26.89 percent.
5.2 Regression estimates without robust standard errors
the appendix shows the results of these regressions. The regressions are estimated in the same manner as in table 9 (for example, we also use the variable dCON), only we did not apply robust standard errors. It is interesting to take a look at this table, to see what is the difference between the results with robust standard errors and without. We know that the magnitudes of the coefficients will not change. We know that applying robust standard er-rors only has an effect on the standard erer-rors, and not on the coefficients. As the coefficients remain the same, and the standard errors might change, the inferences might change too. This is because the t-statistic is calculated by dividing the coefficient with the standard error.
As was stated above, the coefficients will not change, but the inferences might change. This is also what we observe when we take a look at table 10. For the Netherlands, we do not see any big changes, as fourth quarter GDP and IND growth are in both cases significant at a one percent level. For Germany we see a comparable phenomenon. First and fourth quarter IND growth are in both cases significant at the 5 percent level. Also, first quarter GDP growth is significant at the one percent level at both cases. Only fourth quarter GDP growth is significant at the 5 percent level in the cases without robust standard errors, where it is significant at a 1 percent level in the case with robust standard errors. For the United States we see the same, as fourth quarter GDP and IND growth is significant at a 1 percent level in table 9, where it is only significant at a 5 percent level in table 10, the rest stays the same. For Sweden we see that third quarter IND growth is only significant (at a 10 percent level) in the case with robust standard errors. Fourth quarter IND growth is significant at a 5 percent level in table 9, and at a 1 percent level in table 10. For Italy there are no significant results in neither of the tables.
The United Kingdom shows the most striking changes. We see in table 10 that without robust standard errors, it shows significance of GDP growth in the fourth quarter at a 10 percent level, and for fourth quarter IND growth at a 5 percent level. Remarkably, when we apply robust standard errors, none of the results for the United Kingdom show significance at any of the usual levels.
Kingdom has unexpected results, as the application of robust standard errors has caused that all the significant variables lost their significance in the estimations in table 9. To conclude, we should not attach too much importance to the results of table 10. We know from section 4.3 that the residuals of several regressions are heteroskedastic. Therefore, we should use robust standard errors, and we pronounce table 9 as our main table to draw conclusions from. For a further discussion about the heteroscedasticity issue, one could turn to section 6.2.
5.4 Regression estimates of a European portfolio
The results for the European portfolio are reported in a slightly different way. As was de-scribed above in section 4.4, the excess one-year-ahead returns are computed in an alternative way compared to the separate countries. Furthermore, the European portfolio is a combi-nation of sixteen European countries (see table 3 in the appendix). Therefore, the variables for economic growth are also a combination of the data of these sixteen countries. They are combined using an equal weighted and value weighted manner (for the methodology of this, see section 4). Therefore, table 12 in the appendix has an equal weighted and a value weighted part. Table 12 is already adjusted for heteroscedasticity (as is reported in table 11) with robust standard errors. We expect that hypothesis one and two will also apply to the results of the European portfolio.
Table 12 shows us that for the equal weighted variables, both economic growth in the form of GDP and IND are significant at a one percent level in the fourth quarter. This means that there is a significant effect of fourth quarter growth in GDP and IND on the corresponding one-year-ahead results. For dCON, the fourth quarter values are significant at a 5 percent level. The values for the second and the third quarters are all insignificant, and so it seems that there is no effect of economic growth in the second and third quarter on one-year-ahead returns. On the other hand, in the first quarter, we do find a significance for GDP at a 10 percent level. On basis of this analysis, we could say that hypothesis one seems to hold, as we find a negative effect of economic growth in the fourth quarter on one-year-ahead excess returns, with evidently higher R squares then quarters two and three. In contrast, we cannot conclude that hypothesis two seems to hold, because next to an effect in the fourth quarter, we seem to find an (although less strong) effect in the first quarter too, with also a relatively high R squared.
for quarter one. The results for quarter one are even more significant than in the equal weighted case. GDP and IND are significant at the same level as in quarter 4, namely at the one percent level. We also observe (for both cases) that the coefficients for all significant estimates are negative, which is in line with the expectation of hypothesis one. It predicts a negative relationship between economic growth and one-year-ahead excess returns in te fourth quarter. After this analysis we come to the same conclusion as in the equal weighted case. Hypothesis one (there is an effect of economic growth in the fourth quarter on one-year-ahead excess returns) seems to hold for GDP and IND. Hypothesis two seems not to be satisfied as there is not only an effect in the fourth quarter, but also in the first quarter, which is supported by relatively high R squares. We should put emphasis on the results of the value weighted case when drawing conclusions, as was explained in section 4.4.
6
Conclusion
This section will briefly conclude and summarize the outcomes of the regression estimates. Furthermore, it will give an overview of how these results are or are not in line with the expectations from the literature and the given hypotheses. Next to this, the limitations of the data and the results will be discussed, together with the consequences this might have for the legitimacy of the results. The discussion will also provide the interested reader with recommendations for further research on this topic.
6.1 Summary and conclusion
Section 5 above covers extensively the outcomes of the different regressions estimates for the six separate countries as well as the European portfolio. For the six different countries, it covers both the regression estimates with and without robust standard erors. Our main table to draw our conclusions from is table 9, namely the regressions with robust standard errors. We saw that in this table, we do find effects of economic growth in the fourth quarter on one-year-ahead excess returns, but this effect is only found for half (three) of the countries. For the Netherlands, Germany and the United States, we find an effect of GDP and IND on the corresponding one-year-ahead excess returns. All these estimates are significant at a one percent level (except IND in Germany, which is significant at a five percent level). Also, we see that this effect is negative. We can thus conclude that we do find a negative effect of fourth quarter economic growth on one-year-ahead excess returns, but this effect is only found in GDP and IND (and not in CON) and it is not as widespread as we would predict (the effect is only existent in half of the countries). For the European portfolio we find a comparable result. When we compare our results with the predictions in section 2, we con-clude that we can thus only partly live up to the expectations stated there, as we do not find effects for all the countries and all the variables. For every significant estimate (with only one exception), we do find that the effect is negative, as was predicted in hypothesis 1. To sum up, hypothesis one can be supported by half of the countries, and only for GDP and IND.
hy-pothesis two. Therefore, we conclude that our regression results reject the second hyhy-pothesis.
When we compare our outcomes with the results of Møller & Rangvid (2014), we see that our result are less outspoken than theirs. They find evidence for a negative effect in the fourth quarter on one-year-ahead excess returns for all three economic growth variables (GDP, IND and CON). Our results for the United States (which are directly comparable with Møller & Rangvid (2014), as they also investigated the United States), do show a significant effect for GDP and IND in the fourth quarter, but in contrast with their research, we also find effects in the first quarter, while they find no effects in quarters other than the fourth quarter. This could be caused by the fact that they used several different stock indices to estimate their results. Section 6.2 discusses more reasons why our results could not be in line with theory.
When we look at the analysis of the components, we see that in the Netherlands, Ger-many and the United States, the ‘part’ of the economy that explains the effect of economic growth on one-year-ahead excess returns is the industrial part. This part accounts for 22.14, 30.80 and 20.56 respectively of GDP. This is because IND growth shows significance for these countries, where growth in CON does not.
6.2 Discussion
This section links backs to section 4.5 and discusses the limitations of the paper and recom-mendations for further research. The data have certain limitations which could restrict us from drawing correct and reliable conclusions. As we saw above, we know that the period of the data of GDP and IND have the same time span, where the periods of CON differs. It is a possibility that we were not able to find an effect for CON due to the fact that the period was shorter. Continuing, another concern was the date of announcement of the data of the different stock indices. For the countries where we found an effect, the Netherlands and the United States data were reported at the 15th of every month, while for Italy they were disclosed at the last trading day of the month. This difference could have implications for the comparison of the countries, and further research could be done to see if this difference causes any problems to the reliability of the investigation. Last but not least, the data of the one-year-ahead excess returns for the six separate countries was measured in an alternate way than the data of the European portfolio. Therefore, the results of these two might not be directly comparable, and have to be treated as two different cases.
paper focussed on developed countries. It might be of interest to replicate this research for underdeveloped countries, to see if any effects will be found. Next to underdeveloped coun-tries, one could look at countries with a rapid growing economy, like China. This might be interesting, as Levine and Zervos (1998) found in their paper: “This paper finds a strong, positive link between financial development and economic growth and the results suggest that financial factors are an integral part of the growth process”. Another possibility for further research could be to include several different stock indices per country in the regres-sion. This paper chose to take one representative stock index (often the biggest) to estimate the regrssions with. One could try to include all stock indices of a country to get a more extensive (and possibly more reliable) outcome. Continuing, this paper uses a relatively long period of 53 years. Møller & Rangvid (2014) on the other hand use an even more impressive period of 61 years. Where possible, one could try to replicate this research with data that covers an even longer time span, to get possibly even more reliable results.
Another limitation of the paper could be the choice of the used model. As we know from existing literature (proposed by Engle (1982)), time-varying volatility models could be esti-mated with the use of Autoregressive Conditional Heteroskedasticity (ARCH) models. We know from section 4.3 that the residuals exhibit heteroscedasticity. Because of this, and because of the fact that we are dealing with time-varying volatility, it is probable that there is heteroscedasticity present in the error term too. We examined this by testing for the presence of ARCH effects (we included 1 lag). The underlying equation of the test for the ARCH effects is given in equation 15. In this equation, ˆut are the residuals from the linear regression. The null hypothesis of this test is given in equation 16.
ˆ
u2t = γ0+ γ1uˆ2t−1+ vt (15)
H0 = No ARCH effects (16)
Another notable fact is the height of the R squares. As we saw, in this paper a ‘high’ R-squared is around 0.15 with a maximum around 0.2. The R squared measure can be a valuable econometric tool, as has been discussed by Lewis-Beck and Skalaban (1990). As we know from econometric theory, there is no ‘golden rule’ threshold for R squared values. We do know though, that 0.2 is quite a low value. We can only say that the R squares we find are ‘relatively’ high in comparison with other R squares we find which are often lower then 0.1. These findings and analysis are also analogous to the findings of Møller & Rangvid (2014). They announce a R squared value of 0.15 as high (in comparison with the other values). We again chose to use the same methodology as Møller & Rangvid (2014) for better comparison. One could criticize the low R squared values of them, but the low values are probably caused by the fact that the model consists out of only one independent variable and thus no control variables. In this way, we single out the effect of the independent variable. Adding control variables would higher the R squared, but might have an effct on the independent variable, which would manipulate the results. We thus chose to follow the methodology of Møller & Rangvid (2014). For further research one could try to recreate this or their research and add more control variables which do not correlate with the independent variable.
Furthermore, we know from section 4.3 that non-normality is an issue in this dataset, as the dataset exhibits skewness and kurtosis. We know from the econometric theory that for a large dataset with many observations, non normality is not an issue. Again, unfortunately there is no rule of thumb about when a dataset is large enough to overcome the problem of non-normality. Therefore, further research could try to correct for the non normality issue, to see if it has any effect on the results. We also found one instance where autocorrelation is an issue in our dataset (see section 4.3). An option would have been to adjust for it by adding for example a lagged variable to the model. Not doing this might be a possible limitation to the research, but we chose not to do this, because we wanted to stay as close as possible to the methodology of Møller & Rangvid (2014). Further research can enlighten whether adding a lagged value would be valuable.
present in the residuals after the adjustment. Further research could try to adjust for this by using for example a different estimation method (for example Generalised Least Squares or as has been proposed above, an ARCH model), or by for example transforming the variables into logarithms. Again, we chose to use the robust error option, as we wanted to keep the same estimation method as Møller & Rangvid (2014).
7
References
—Abel, A.B., Eberly, J.C., Panageas, S. (2007), “Optimal Inattention to the Stock Market”, The American Economic Review, Vol. 97, No. 2, pp. 244-249.
—Abel, A.B., Eberly, J.C., Panageas, S. (2013), “Optimal inattention to the stock market with information costs and transactions costs”, Econometrica, Vol. 81, No. 4, pp. 1455-1481. —Campbell, J.Y., Cochrane, J.H. (1999), “By force of habit: A consumption-based expla-nation of aggregate stock market behaviour”, The Journal of Political Economy, Vol. 107, No. 2, pp. 205-251.
—Dickey, D.A., Fuller, W.A. (1979), “Distribution of the Estimators for Autoregressive Time Series With a Unit Root”, Journal of the American Statistical Association, Vol. 74, No. 366, pp. 427-431.
—Durbin, J., Watson, G.S. (1950), “Testing for Serial Correlation in Least Squares Regres-sion: I”, Biometrika, Vol. 37, No. 3/4, pp. 409-428.
—Durbin, J., Watson, G.S. (1951), “Testing for Serial Correlation in Least Squares Regres-sion: II”, Biometrika, Vol. 38, No. 1/2, pp. 159-177.
—Engle, R.F. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation”, Econometrica, Vol. 50, No. 4, pp. 987-1007.
—Fama, E.F., French, K.R. (1993), “Common risk factors in the returns on stocks and bonds”, Journal of Financial Economics, Vol. 33, pp. 3-56.
—Ivkovi´c, Z., Poterba, J., Weisbenner, S. (2005), “Tax-Motivated Trading by Individual In-vestors”, The American Economic Review, Vol. 95, No. 5, pp. 1605-1630.
—Jagannathan, R., Wang, Y. (2007), “Lazy Investors, Discretionary Consumption, and the Cross-Section of Stock Returns”, The Journal of Finance, Vol. 62, No. 4, pp. 1623-1661. —Kahneman, D., Tversky, A. (1979), “Prospect Theory: An Analysis of Decision under Risk”, Econometrica, Vol. 47, No. 2, pp. 263-292.
—Lequiller, F., Blades, D. (2007), “Understanding National Accounts”, Adapted and trans-lated from: “Comptabilit´e nationale: manuel pour ´etudiants”(2004), Economica, Paris. —Lewis-Beck, M.S., Skalaban, A. (1990), “The R-Squared: Some Straight Talk”, Political Analysis, Vol. 2, pp. 153-171.
Amer-ican Economic Review, Vol. 88, No. 3, pp. 537-558.
—Møller, S.V., & Rangvid, J. (2014), “End-of-the-year economic growth and time-varying expected returns”, Journal of Financial Economics, Vol. 115, pp. 136-154.
—Møller, S.V., & Rangvid, J. (2015), “Global economic growth and expected returns around the world: The end-of-the-year effect”, Working Paper No. 2569081, Retrieved from: Social
Science Research Network, Website: http://papers.ssrn.com/sol3/papers.cfm?abstract id=2569081. —Reinganum, R.M. (1983), “The anomalous stock market behavior of small firms in
Jan-uary”, Journal of Financial Economics, Vol 12, pp. 89-104.
8
Appendix
Table 1: Countries and stock indices
Country Trading stock index Abbreviation No. of funds
The Netherlands Amsterdam Exchange Index AEX 25
Germany Deutscher Aktienindex DAX 30
Italy Milano Italia Borsa FTSE MIB 40
United Kingdom Financial Times Stock Exchange Index FTSE 100 100
United States New York Stock Exchange NYSE Composite >2000
Sweden Helsinki Stock Exchange OMX Helsinki 141
Table 2: Variables
Abbreviation Variable Unit of measurement Frequency
RET One-year-ahead excess returns Percentage Yearly
GDP Gross Domestic Product (growth) Percentage Quarterly
IND Industrial Production (growth) Percentage Quarterly
CON Private Consumption (growth) Percentage Quarterly
dCON Private Consumption (first differences) Percentage Quarterly
Table 3: Dataset of countries of the European portofolio
Countries European Portfolio
Austria Belgium Denmark Finland France Germany Greece Ireland
Italy Netherlands Norway Portugal Spain Sweden Switzerland United Kingdom
Table 4: Components (in % of GDP)
Country Private consumption Manufacturing Industry
The Netherlands 44.91 11.83 22.14 Germany 55.68 22.77 30.80 Italy 61.63 15.37 23.85 United Kingdom 65.01 10.29 20.76 United States 68.42 12.67 20.56 Sweden 46.54 17.19 26.89
Table 5: Descriptive statistics table 1
The Netherlands Germany Italy
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 RET 521 53 53 52 52 53 53 52 52 53 53 52 0.06722 0.0637 0.0665 0.0655 0.0878 0.0847 0.0841 0.0898 0.1008 0.0794 0.0770 0.0758 0.05113 0.0527 0.0705 0.0680 0.0501 0.1103 0.0958 0.0657 0.0567 0.0411 0.0438 0611 GDP 52 53 53 52 52 53 53 52 52 53 53 52 0.0028 0.009 0.0081 0.0077 0.0030 0.0074 0.0075 0.0057 0.0055 0.0055 0.0064 0.0053 0.005 0.008 0.008 0.008 0.0075 0.006 0.006 0.006 0.005 0.004 0.005 0.0065 IND 52 53 53 52 52 53 53 52 52 53 53 52 0.008 0.0061 0.0038 0.0087 0.0030 0.0057 0.0072 0.0061 0.0027 0.0075 0.0028 0.0049 0.0085 0.007 0.007 0.0115 0.005 0.004 0.006 0.01 0 0.002 0.004 0.009 CON 26 26 26 25 44 44 44 43 33 33 33 32 0.0162 0.0164 0.0161 0.0166 0.0197 0.0193 0.0188 0.0188 0.0124 0.0124 0.0118 0.0123 0.0155 0.0125 0.0155 0.018 0.0165 0.014 0.018 0.015 0.016 0.013 0.013 0.0125
United Kingdom United States Sweden
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 RET 52 53 53 52 52 53 53 52 52 53 53 52 0.0816 0.0828 0.090 0.0905 0.0744 0.0768 0.0766 0.0748 0.1393 0.1345 0.1357 0.1480 0.0723 0.1011 0.0902 0.0903 0.0800 0.0865 0.1116 0.1116 0.1114 0.1003 0.0982 0.0951 GDP 52 53 53 52 52 53 53 52 52 53 53 52 0.0053 0.0073 0.0056 0.0057 0.0076 0.0087 0.0075 0.066 0.0054 0.0063 0.0068 0.0061 0.005 0.007 0.007 0.005 0.008 0.008 0.008 0.0075 0.005 0.006 0.008 0.008 IND 52 53 53 52 52 53 53 52 52 53 53 52 0.0012 0.060 0.0007 0.0029 0.0065 0.0069 0.0064 0.0077 0.0027 0.0041 0.0085 0.0068 0.003 0.003 0.002 0.004 0.009 0.008 0.007 0.009 0.0065 0.005 0.005 0.0085 CON 52 53 53 52 52 53 53 52 52 53 53 52 0.0286 0.0285 0.0285 0.0286 0.0331 0.0333 0.0334 0.0333 0.0209 0.0211 0.0207 0.0208 031 0.032 0.026 0.032 0.034 0.035 0.034 0.0335 0.0225 0.025 0.02 0.023
1 The first values are the no. of observations 2 The second values are the mean values 3 The third values are the Median values
Values are rounded to four decimals
Table 6: Descriptive statistics table 2
The Netherlands Germany Italy
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 RET 0.20621 0.1975 0.2013 0.2095 0.2324 0.2207 0.2108 0.2377 0.4329 0.3137 0.2953 0.3058 -0.48782 -0.3358 -0.4856 -0.4505 -0.4174 -0.3702 -0.3788 -0.4630 -0.4453 -0.3350 -0.4644 -0.4552 0.52173 0.7214 0.5323 0.5898 0.7212 0.7904 0.6086 0.6495 1.9605 1.0643 0.9687 1.2687 GDP 0.0172 0.01664 0.0090 0.0131 0.0141 0.0112 0.0093 0.0086 0.0120 0.0090 0.0092 0.0106 -0.063 -0.024 -0.01 -0.021 -0.045 -0.016 -0.01 -0.02 -0.03 -0.01 -0.013 -0.023 0.033 0.089 0.035 0.039 0.029 0.045 0.035 0.02 0.06 0.03 0.032 0.024 IND 0.0261 0.0204 0.0188 0.0179 0.0249 0.0169 0.0174 0.0210 0.0319 0.0257 0.0196 0.0264 -0.046 -0.045 -0.032 -0.034 -0.134 -0.041 -0.037 -0.071 -0.106 -0.033 -0.059 -0.087 0.098 0.05 0.04 0.037 0.039 0.056 0.053 0.048 0.152 0.122 0.043 0.063 CON 0.0226 0.0221 0.0214 0.0227 0.0185 0.0199 0.0169 0.0176 0.0217 0.0221 0.0216 0.0204 -0.024 -0.026 -0.024 -0.022 -0.01 -0.012 -0.02 -0.013 -0.037 -0.041 -0.045 -0.037 0.065 0.063 0.063 0.062 0.064 0.063 0.054 0.05 0.045 0.047 0.043 0.046
United Kingdom United States Sweden
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 RET 0.1786 0.1790 0.2296 0.2388 0.1593 0.1623 0.1590 0.1545 0.3499 0.3199 0.3294 0.3793 -0.3433 -0.4264 -0.5597 -0.4601 -0.4180 -0.2865 -0.3974 -0.4020 -0.4238 -0.4363 -0.5093 -0.5146 0.4583 0.5037 0.8621 1.1850 0.4372 0.5323 0.3323 0.3269 1.5426 0.8859 1.0848 1.4244 GDP 0.0112 0.0112 0.0081 0.0084 0.0102 0.0083 0.0066 0.0083 0.0122 0.0147 0.0125 0.0136 -0.027 -0.02 -0.021 -0.022 -0.017 -0.02 -0.01 -0.021 -0.02 -0.048 -0.026 -0.039 0.05 0.044 0.024 0.023 0.027 0.039 0.02 0.024 0.031 0.055 0.038 0.051 IND 0.0180 0.0217 0.0115 0.0150 0.0188 0.0143 0.0110 0.0160 0.0217 0.0263 0.0186 0.0223 -0.07 -0.039 -0.035 -0.043 -0.066 -0.042 -0.032 -0.042 -0.092 -0.085 -0.026 -0.087 0.036 0.086 0.031 0.041 0.042 0.039 0.035 0.038 0.037 0.054 0.068 0.056 CON 0.0289 0.0277 0.0254 0.0248 0.0206 0.0195 0.0191 0.0209 0.0256 0.02516 0.0235 0.0238 -0.039 -0.042 -0.031 -0.036 -0.021 -0.027 -0.014 -0.02 -0.055 -0.041 -0.035 -0.038 0.093 0.09 0.086 0.084 0.078 0.064 0.067 0.081 0.081 0.091 0.082 0.07
1 The first values are the Standard Deviations 2 The second values are the minima
3 The third values are the maxima Values are rounded to four decimals
Table 7: White test, Durbin Watson statistics and test for ARCH effects
The Netherlands Germany Italy
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 GDP 0.7971 0.639 0.358 0.001*** 0.010** 0.531 0.958 0.015** 0.348 0.675 0.802 0.835 1.9052 1.543 1.851 1.956 1.919 1.917 2.003 2.093 1.905 1.564 1.538 1.679 0.1163 0.766 0.827 0.971 0.746 0.822 0.638 0.450 0.771 0.452 0.096* 0.953 IND 0.279 0.095* 0.573 0.007*** 0.019** 0.629 0.781 0.044** 0.673 0.217 0.809 0.399 1.796 1.626 1.855 1.618 2.005 1.887 2.003 2.004 1.885 1.569 1.574 1.707 0.204 0.800 0.839 0.535 0.955 0.711 0.690 0.443 0.716 0.463 0.087* 0.939 CON 0.573 0.905 0.649 0.888 0.141 0.067* 0.110 0.132 0.758 0.906 0.710 0.887 1.944 1.286A 1.832 1.796 2.130 1.978 2.096 2.315 1.861 1.492 1.606 1.640 0.488 0.653 0.870 0.921 0.998 0.726 0.747 0.769 0.630 0.497 0.046** 0.472
United Kingdom United States Sweden
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 GDP 0.143 0.677 0.466 0.053* 0.108 0.781 0.648 0.015** 0.750 0.691 0.641 0.158 2.090 1.901 2.582 2.289 2.150 2.128 2.345 1.895 1.654 1.531 1.531 1.755 0.747 0.171 0.070* 0.024** 0.367 0.221 0.923 0.938 0.506 0.022** 0.694 0.755 IND 0.340 0.745 0.812 0.027** 0.037** 0.649 0.590 0.018** 0.717 0.920 0.129 0.009*** 1.991 1.902 2.613 2.283 2.083 2.097 2.219 1.935 1.618 1.536 1.656 1.665 0.525 0.182 0.039** 0.065* 0.732 0.285 0.742 0.871 0.516 0.012** 0.453 0.514 CON 0.199 0.508 0.188 0.230 0.128 0.194 0.528 0.047** 0.883 0.289 0.378 0.228 2.122 1.925 2.681 2.464 2.233 1.991 2.254 2.103 1.638 1.507 1.543 1.759 0.758 0.240 0.027** 0.107 0.378 0.270 0.595 0.848 0.556 0.012** 0.747 0.729
1 First values are the P-values for the White test of heteroskedasticity. H0= there exists homoskedasticity 2Second values are the transformed Durbin-Watson statistics for autocorrelation. A = autocorrelation
3Third values are the P-values for the test for ARCH effects. H0= there exist no ARCH effects *** p<0.01, ** p<0.05, * p<0.1
Values are rounded to three decimals
Table 8: Dickey fuller test and tests for normality
The Netherlands Germany Italy
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 RET 0.000***1 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.6082 0.041** 0.421 0.961 0.242 0.105 0.769 0.936 0.000*** 0.001*** 0.001*** 0.000*** 0.3883 0.031** 0.321 0.826 0.949 0.213 0.891 0.716 0.000*** 0.040** 0.015** 0.002*** GDP 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.083* 0.481 0.002*** 0.002*** 0.015** 0.032** 0.001*** 0.029** 0.034** 0.074* 0.001*** 0.000*** 0.098* 0.519 0.020** 0.014** 0.357 0.197 0.000*** 0.546 0.361 0.285 IND 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.102 0.487 0.382 0.172 0.000*** 0.349 0.429 0.008*** 0.003*** 0.000*** 0.091* 0.001*** 0.056* 0.533 0.100 0.589 0.000*** 0.101 0.367 0.016** 0.000*** 0.000*** 0.111 0.003*** CON 0.2642 0.2553 0.3476 0.2031 0.0022*** 0.000*** 0.005*** 0.001*** 0.016** 0.008*** 0.012** 0.092* 0.515 0.585 0.457 0.644 0.083* 0.097* 0.797 0.381 0.075* 0.031** 0.063* 0.285 0.415 0.952 0.983 0.411 0.915 0.372 0.789 0.035** 0.841 0.330 0.350 0.958
United Kingdom United States Sweden
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 RET 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.836 0.401 0.037** 0.000*** 0.597 0.928 0.005*** 0.024** 0.001*** 0.133 0.022** 0.001*** 0.660 0.285 0.002*** 0.000*** 0.109 0.411 0.107 0.251 0.002*** 0.870 0.149 0.017** GDP 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.006*** 0.009*** 0.006*** 0.031** 0.568 0.367 0.360 0.016** 0.535 0.631 0.959 0.348 0.000*** 0.003*** 0.011** 0.034** 0.861 0.001*** 0.512 0.031** 0.655 0.001*** 0.096* 0.005*** IND 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.407 0.065* 0.000*** 0.012** 0.023** 0.002*** 0.000*** 0.056* 0.011** 0.000*** 0.000*** 0.001*** 0.079* 0.027** 0.000*** 0.023** 0.009*** 0.029** 0.000*** 0.072* 0.053* 0.000*** CON 0.000*** 0.000*** 0.000*** 0.001*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.000*** 0.767 0.230 0.760 0.200 0.328 0.020** 0.168 0.325 0.063* 0.773 0.275 0.068* 0.916 0.270 0.947 0.467 0.613 0.195 0.592 0.484 0.135 0.122 0.213 0.453
1 First values are the P-values for the Dickey Fuller test. H0= existence of a unit root 2 Second values are the P-values for skewness. H0 = skewness of a normal distribution 2Third values are the P-values for kurtosis. H0 = kurtosis of a normal distribution
*** p<0.01, ** p<0.05, * p<0.1 - Values are rounded to three decimals
