What is the effect of capital-intensity of US
manufacturers on the stock return?
Data from 2004 – 2014
Abstract
This study examines if there is a difference in stock returns between capital-intensive and
labour-intensive US manufacturers over the years 2004 to 2014. The findings of this study
are based on three portfolios that are created and analysed: 1) the labour-intensive, 2) the
neutral and 3) the capital-intensive. In this context, CAPM and time-series regression are
used to determine the beta of the portfolios. This research evidences an average of 1.21%
higher stock return from capital-intensive manufacturers when compared to
labour-intensive manufacturers. The scatterplot and the related linear equation indicates that there
is no correlation between the capital-intensity of a manufacturer and the stock return.
Lastly, this research finds a higher beta for labour-intensive manufacturers than for
capital-intensive manufacturers, respectively 1.664 and 1.521. Therefore, this study indicates that
-contrary to the literature- labour-intensive manufacturers have a higher systematic risk.
Mathijs Elshof
University of Groningen
Faculty of economics and Business Research paper MSc Finance
Student nr. s2561697
Supervisor Dr. S. Drijver
Date 14 January 2016
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I. Introduction
Many manufacturers have automated their production processes over the last few decades. According to the Bureau of Labor Statistics, US manufacturing employment dropped from 15.3 million in 2002 to 12.0 million in 2012. Since the relatively mild financial crisis of 2001 the number of manufacturing employees has declined by more than 4 million. One reason for this decline is the reallocation of the manufacturers’ production processes from the US to China. A study by Berman and Bound (1993) demonstrates changes in the demand for skilled labour within US manufacturing firms in the modern era. Gradually, firms are demanding more skilled labour, and employment of production workers has dropped. Pierce and Schott (2015) find two explanations for the decline of manufacturing employees: 1) The negative relationship between the decline of manufacturing employment and the import from China. 2) Low-skilled manufacturing workers are replaced by capital such as plant, machinery, IT systems, buildings, vehicles, offices, and other fixed, tangible, durable goods. To be clear, in this paper, ’capital’ always refers to this ‘physical capital’.
The shift from low-skilled manufacturing workers to capital can be attributed to technological change. Several recent studies (Karabarbounis and Neiman 2014, Elsby, Hobjin and Sahin 2013, Piketty 2014, Piketty and Zucman 2013) offer explanations for recent declines in the share of labour that rest on claims of increased capital deepening. This means that the capital per worker is
increasing and less labour is needed to produce the same output.
For example, car manufacturers have an assembly line consisting of an army of robots -instead of production workers- to produce their cars. The auto industry invests billions of dollars in research and development every year; this level of investment is among the highest of any industry1. Today, many managers and executives still wonder whether they should automate more of their production processes.
There exist many economic theories about the distribution of the production factors: land, labour, and capital. If all manufacturers apply the economic theory well, the distribution of land, labour, and capital will optimise the production of the manufacturer. Managers often face the choice to replace labour for capital. Those managers act in the interest of shareholders, who are looking to maximise shareholders value. Many managers are rewarded based on stock returns. Outside of questioning this reward system, managers and shareholders are interested in the relationship of the
capital/labour ratio and the stock return.
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3 This article touches on a wide range of subjects and brings macroeconomic theory and finance together. The results of this paper mainly contribute to the literature for investment managers who are looking for a higher stock return. Investors can use this research in their risk management strategy. Are capital-intensive or labour-intensive US manufacturers undervalued? This is the first study that examines the effect of the labour/capital ratio on stock return.
This study compares the stock returns of capital-intensive and labour-intensive US manufacturers. The US manufacturers are subdivided into three portfolios. One portfolio with capital-intensive US manufacturers, a neutral portfolio, and one portfolio with labour-intensive manufacturers. For this allocation, the ratio: ‘number of employees/Property Plant Equipment2’ is used.
The main results of this research are that capital-intensive manufacturers on average have a higher stock return than labour-intensive manufacturers. The scatterplot and the linear equation find no meaningful correlation between the labour/capital ratio and its stock return. Nonparametric tests, on the other hand, reveals a slightly negative relationship between the labour/capital ratio of a firm and its stock return. The last main finding of this study is that -contrary to the literature- capital-intensive manufacturers have a lower beta and less systematic risk than labour-intensive US manufacturers. The remainder of this thesis is structured as follows. Chapter 2 provides the literature that is related to this topic. Chapter 3 describes the data and methodology. The results are set out in Chapter 4, and Chapter 5 will conclude this article.
II. Literature review
As mentioned in the introduction, over the last few decades, many manufacturers automated their production processes. New technologies have altered the old approach to manufacturing so that less manufacturing employees are now required for the same output. This change has led to a new distribution of capital and labour. Before we determine if there is a difference in stock returns between the three portfolios, we will discuss the prevailing literature. Firstly, the definitions and differences between capital-intensive and labour-intensive firms are mentioned. Secondly, the development of the US stock market between 2004 and 2014 is shown. Thirdly, the marginal productivity theory is explained. Fourthly, the substitution of labour and capital is explained. Fifthly, the wage rate and the interest rate are threated. Sixthly, the development and role of technology is discussed. Lastly, the difference in risks is discussed. All of these factors are considered because any
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4 could play a role in analysing the difference in stock returns of capital- and labour-intensive
manufacturers.
Definitions and differences
Capital-intensive manufacturers
A manufacturer is considered capital-intensive when many capital is used to produce any goods. Capital refers to the plant, machinery, IT systems, buildings, vehicles, offices and other fixed, tangible, durable goods. Some examples of capital-intensive firms are oil production- and refining firms, telecommunications firms, and transports manufacturers like airplane builders and car
manufacturers. To start a capital-intensive firm, a massive initial capital investment is needed, which creates high barriers of entry. As a result, once the upfront investment is made, the firm faces a relative small number of competitors. An advantage of capital-intensive companies is ‘the economies of scale’. This means that by producing a large number of units, the variable costs per unit will decrease.This is because the fixed costs of the company are shared over a greater number of goods. In a good year, this is an advantage. But when there is an economic downturn and demand for the product falls, the company still has the same amount of capital and fixed costs.
Most of the time, the physical capital is customised for the firm, thus, physical capital is usually not easy to transfer. In an economic downturn, when the demand for output falls, the demand for capital falls as well. At that point, there is plenty of unused capital in the market, which causes the market value of capital to fall (Dixit and Pindyck, 1994). Due to the high level of capital at a firm, the level of depreciation is also high. This depreciation remains high even when the demand for output has fallen. Such a lack of flexibility can seriously jeopardize the firm.
Labour-intensive manufacturers
A manufacturer is considered labour-intensive when a great deal of labour is used to produce any output. The degree of labour-intensity is typically measured in proportion to the amount of capital required to produce the goods. The ratio used in this paper is: ‘number of employees/Property Plant Equipment’. Labour can refer to full-time, part-time, and temporary jobs. The function of the jobs can be in management, manufacturing employees, IT etc. Some examples of labour-intensive firms are mines, food processers, and manufacturers of metal products, textiles and furniture.3 An advantage of labour-intensive firms is that, generally, labour costs are variable, while capital costs are fixed. During a financial downturn, capital is losing value and it is difficult to sell the capital at a good price. However, in the US, it is relatively easy to fire employees. This gives labour-intensive
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5 firms an advantage in controlling expenses during a market downturn because their labourers can be hired and fired more easily than physical capital can be disposed of. On the other hand, labour-intensive firms don not have the advantage of economies of scale as a firm cannot pay workers less by hiring more of them.
Main differences
Capital-intensive manufacturers
Advantages Disadvantages
Higher productivity; Capital render production faster and more efficient
Lack of flexibility in responding to a fall in demand
(capital is hard to sell without a loss) Relatively low variable costs
(Technological economies of scale)
High costs of investments and large depreciations
Fewer human errors
Labour-intensive manufacturers
Advantages Disadvantages
Can meet the changing demand of customers Human production mistakes are inevitable
Relatively easy to downsize labour in a downturn (flexibility)
Labour relation problems (strikes etc.)
Workers can introduce new ideas/opportunities Human capital cannot be used as collateral
while physical capital can be used as collateral
The S&P 500 (2004 – 2014)
This paper analysed stock returns of capital- and labour-intensive US listed manufacturers from 2004 to 2014. To understand the companies’ context, the US market was analysed. Figure 1 is a graph of the S&P 500 Index value over time. The S&P 500 is the index of the 500 largest publicly traded US companies. The S&P 500 is widely utilised as a benchmark for US equities.
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Figure 1: The S&P 500 index. Source: https://www.google.com/finance?cid=626307
Marginal productivity theory
Historically, many studies have been conducted regarding the distribution of capital and labour, and the effect on output. Back in 1803, J.B. Says found that the amount of output depends on the amount of resources. Capital, land, and labour are all necessary to produce a product. Thus a firm cannot choose between capital or labour, but rather must have both in order to produce a product. The trick is to find the most efficient distribution of capital and labour. Studies by Jevons (1871), Wicksteed (1894) and, Clark (1886) determine an answer to this issue called ‘the theory of marginal productivity’. Marginal productivity theory argues that a company is willing to add extra input only if, at the end, the company’s income gains outweigh the costs of that input. To give an example, a firm will only add one unit of labour to the existing combination of productive factors if this will generate more income than the costs of one unit of
one unit of labour. In an ideal situation, the wage rate will be equal to the marginal product of labour, where the marginal product of labour is the change in output that results from employing an added unit of labour. See figure 2. This same rule holds for the marginal revenue of capital, which should be equal to the interest rate.
Figure 2: Marginal revenue of labour is equal to marginal costs of labour. Source:
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Labour and capital: substitutes
Aside from the fact that labour and capital both are needed to generate output, these two sources of input can serve as substitutes for one another. Hicks (1963) and Robinson (1932) explains this in what is called the theory of functional distribution. This theory emphasises the ease of substitution between capital and labour. According to the marginal productivity theory described above, the price of one unit of labour or capital equals the revenue of one unit of labour or capital. In this view, the prices of the production factors capital and labour influence the amount of labour and capital. The prices of the wage rate and the interest rate are determined by supply and demand. The demand for a factor is derived from the demand for the final goods it produces. The neoclassical theory shows that labour and capital are substitutes for each other. The degree of this substitution is called ‘elasticity’. Higher elasticity means, a higher level of capital and labour substitution. According to Arrow, Chenery, Minhas and Sollow (1961) this elasticity and the economic efficiency are not
optimal. This means that a change in the wage rate or a change in the interest rate may play a role in explaining the differences in stock returns of capital-intensive and labour-intensive manufacturers. Let’s explain this by using an example. A manufacturer currently has an optimal labour/capital ratio. A shock in the wage rate changes the optimal capital/labour ratio. But when the elasticity is low, the firm does not substitute many labour into capital. Therefore, a wage rate increase can lead to higher costs for manufacturers with less elasticity. Another factor that plays a role is time. It takes time to change this capital/labour ratio after a shock. Abowd’s study (1989) demonstrates a change in the value of common stock resulting from an unexpected change in collectively bargained labour costs. Using bargaining unit wage data and NYSE stock returns, he finds a dollar-for-dollar trade-off between these variables. His findings are supported by Clark (1984) and Ruback and Zimmerman (1984). A wage increase is a disadvantage for all manufactures, but it will be more impactful on firms that rely heavily on labour. In the long run, firms will have an optimal capital/labour ratio, based on the latest cost prices of production input. However, in the short term, there will always be a discrepancy between the latest cost price, and the moment when the company will buy/sell the capital or attract/distract employees. This short term discrepancy can explain the difference in stock returns of labour-intensive and capital-intensive manufacturers.
Wage rate and interest rate
Below, the wage rate and the long term interest rate of the period 2004-2014 are shown.
Interest rate development
8 interest rate started to decrease to 2.11% in 2012. In 2013, the rate rose again to 3.65%, and in 2014 the rate fell to 2.50%.
Figure 3: 20-Year US government bond interest rate development from 2004 to 2014. Source data:
https://www.treasury.gov/
Wage rate development
The total compensation of workers increased between 2005 and 2007 by 3.70%. In 2008 and 2009, employee compensation increased by 2.3% and 3.2%, respectively. In the years following the crisis, the growth rate decreased to an average of 1.42% between 2010 and 2013.
Figure 4: Employee Compensation Historical Listing March 2004 – September 20154
Role of (information) technology
As mentioned in the introduction, there has been a significant drop in employment of manufacturing employees over the last few decades. Part of this shift in labour demand is explained by
globalisation. But these forces merely explain a small shift, which leaves a large residual shift unexplained (Krugman and Lawrence, 1993). Economists have concluded that this residual must reflect a "technical change" in the way goods and services are produced in the economy (Griliches, 1969; Berndt, Morrison and Rosenblum, 1992; Berman, Bound and Griliches, 1994). The study by Bassanini and Manfredi (2012) reveal that capital deepening and labour-replacing technological change jointly account for 80% of the fall in labour share. This section will discuess whether technology has a role in explaining the differences in stock returns between capital-intensive and labour-intensive US manufacturers.
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Source: Bureau of labor statistics, US.
9 ‘Technological change’ refers to the invention of technologies.
Technological change can be the changes that make machinery more efficient and quicker. In 1956, Solow created a
widespread model to evidence the increased productivity of labour and capital induced by technological change. An increase in knowledge and better technology will increase output for a given input. An example is given in the figure 5. Where, Y = output, MPL = marginal product of labour and L = labour. The marginal product of labour is higher after the
technology shock and the slope becomes steeper. Figure 5: positive technology shock5
The productivity growth as described above is an old, but still frequently observed technological change. It is difficult to say what the natures of these technological changes are. Atkinson and Stiglitz (1969) describes two avenues for technological change: 1)learning by doing and 2)research activity. ‘Learning by doing’ is more commonly used in labour-intensive manufacturers whereas R&D expenditures are mostly pursued by capital-intensive firms. Doms, Dune, and Roberts (1995) note that, the capital-intensity of the manufacturer is negatively correlated with failure of the plant and positively correlated with the growth rate of the plant. Doms, Dune, and Roberts (1995) also shows that a plant with a large number of manufacturing technologies, for example robots and lasers, have significantly higher growth rates and lower failure rates.
Another widespread technical change from recent decades is information technology (Autor, Katz, and Krueger, 1997). This technology refers to communication equipment. Studies conducted by Dewan and Chung-ki Min (1997) and Lichtenberg (1995) indicate excess returns on information technology (IT) investments relative to labour returns. IT capital is a substitute for both, ordinary capital and labour. Looking at the role of technology in total, it is hard to derive from the prevailing literature that technological change is an advantage for capital- or labour-intensive manufacturers.
Risk
An important difference between capital- and labour-intensive manufacturers is the risk of the investment. When capital is attracted, the investment decision is based on a forward-looking
business case over a several-year horizon, so the attracted capital is expected to be at the firm for at least a couple of years. The risk element enters consideration because during a recession, and a fall in output, the value of the capital will fall as well (Dixit and Pindyck, 1994). The manufacturer is then loaded with unproductive capital well still burdened with the high fixed costs of the capital. These
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10 fixed costs must be covered by less output. A business that has a higher proportion of fixed costs and a lower proportion of variable costs is said to have used more ‘operating leverage’. Capital-intensive manufacturers with high fixed costs are considered to have more operating leverage and higher levels of risk (Arellano, Fernando, Scofield, Barbara, 2014).
In contrast, when a manufacturer is labour-intensive, the firm has more flexibility. Labour can be permanent but also temporary, fulltime but also part-time. In the US, firms have relatively few constraints on hiring and firing employees. The ease of changing the quantity of production inputs makes that labour-intensive manufacturers have more flexibility than capital-intensive
manufacturers. Wadhwa and Browne (1989) indicates that flexibility offers opportunities to change control over the flow of entities in a desirable direction. One of these opportunities is the ability to cope with the uncertainty of changes (Barad and Sipper, 1988). Jin, et al. (2013) suggests that flexibility has a positive impact on competitive advantage.
The literature indicates that flexibility is crucial for determining operating risks because operating risks translate into shareholder risks (Driouchi, Battisti and Bennett, 2006). In the extreme case of irreversible capital, combined with quasi-fixed operating costs, there is a strong relationship between productivity shocks and expected returns or risk (Gu, Hackbart and Johnson, 2015). They find that the association between operating leverage and stock returns is weak for flexible industries, but this relationship becomes much stronger as an industry’s inflexibility level rises. Ryan (1997) and García-Feijóo and Jorgensen (2010) also suggest that operating leverage is positively associated with systematic equity risk and higher stock returns. According to the prevailing literature we expect capital-intensive manufacturers to have more operating and systematic risk -hence a higher beta-, and higher stock returns than labour-intensive manufacturers.
III Data and methodology
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Data set
This study focusses on US firms for two reasons; data availability and the high labour decline. This is the first study that examines the effect of capital-intensive and labour-intensive manufacturers on stock returns. To examine this effect, the financial and accounting data of the manufacturers must be available for analysis. In the US, listed companies have a strict financial reporting regulation. This means that many listed companies’ data is publicly available. The other reason for a US focus is that US manufacturers recently suffered a remarkable labour decline. This indicates that the US
underwent many technical change. This makes it more interesting to discover the effect of capital-intensity on stock returns. The data used in this research consist of data provided for companies listed on US stock exchanges between 2004-2014. A time frame of ten years is analysed to obtain a reliable result. Over these ten years, the stock market experienced a number of good years in addition to a financial crisis in 2007 and 2008. This creates the opportunity to analyse the effect of capital-intensity on stock returns in both an economic upturn and in an economic downturn. The next step is to determine which companies can be qualified as a ‘manufacturer’. To this end, the North American Industry Classification System (NAICS-2012) is used.6 The NAICS-code of companies that are considered manufacturers begins with the digits 31, 32, or 33. The dataset of this study only consists of firms whose codes start with these digits. Firms without employees and firms that have less than 10,000 dollars of total assets are excluded from the dataset. Manufacturers with less than 10,000 dollars of total assets do not have the required data available to calculate the labour/capital ratio. If any required data is missing, such as number of employees, total assets and PPE, the
manufacturer is also excluded from the data list. The current status of the companies on the data list varies. Most of the time, the companies are still active, but some companies are inactive due to a variety of reasons. Thus, the 2004 portfolio of manufacturers can include companies that no longer trade. Because we create new portfolios every year, the paper does not have to deal with
survivorship bias. The main selection of manufacturers is performed in Orbis7. In total, 1842 different manufacturers are selected by Orbis. After manually excluding the companies with missing data a large dataset still remains. On average, 1186 manufacturers per year are analysed.
Portfolio selection
Every year, three portfolios are constructed. These portfolios consist of manufacturers that are: 1) capital-intensive, 2) neutral, and 3) labour-intensive. To determine if a company is capital-intensive, neutral, or labour-intensive we use a labour/capital ratio. We follow Hendricks and Singhal (2001) by using the ratio: ‘number of employees/Property Plant Equipment’. The property, plant and
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NAICS Desk Reference, Jist Works, U. S. Census Bureau; July 2000
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12 equipment (PPE) of a firm is a good indication of the capital-intensity of a firm and the amount of employees is a good proxy for the labour-intensity of a firm. The combination of these two accounting variables into a ratio creates an appropriate measurement of the capital-intensity of a firm. The group manufacturers with the highest 33% of the employee/PPE ratio are considered labour-intensive. The group manufacturers with the lowest 33% of the employee/PPE ratio are considered capital-intensive. The neutral group provides as a control element so that the test results are more reliable. The accounting information like the PPE, total assets, and number of employees are obtained from the Center for Research in Security Prices (CRSP). The three portfolios are created before the beginning of the year. For example, the portfolio of 2004 is created on accounting data of year end 2003. At the end of 2004, the returns of the three portfolios are analysed and compared. These returns are obtained from Thomson Reuters DataStream.
Outliers
This study analyses stock returns of, on average, 1186 manufacturers per year. Among these stock returns are some returns far outside the norm. These are known as outliers (Jarrell, 1994). These remarkable high stock returns may be caused by a variety of factors. One common reason for such remarkable stock returns arises when pharmaceutical manufacturers became acquisition candidates. The stock returns of these takeover targets often rise by a few thousand percent. These unusual returns do have a significant influence on the average return of a portfolio and the subsequent statistical test. There are two possible ways to deal with outliers: ‘trimming’ or ‘winsorisation’. Trimming outliers is equivalent to eliminating outliers. This is used if the data is incorrect.
Winsorisation is a well-known procedure that sets a limit on how high a return may be in order to remain ‘in the norm’. In this paper winsorization is used. This paper follows the example of Barber and Lyon (1997) in its treatment of outliers. More extreme observations are set equal to this limit (Cowan and Sergeant, 2001). The limit is set is at the mean + three times the standard deviation. This is a commonly used limit.
Transaction costs
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Descriptive statistics
Table 1: Descriptive Statistics of the portfolios
Companies Nr. of returns Average return Min. return Max. return St. dev.
Total 13042 15.25% - 100% 626% 68%
Capital-intensive 4347 15.79% - 100% 626% 68%
Neutral 4350 15.39% - 100% 626% 64%
Labour-intensive 4345 14.58% - 100% 626% 72%
(Return capital-intensive portfolio) – (Return labour-intensive portfolio) = 1.21%
Table 1 presents the average return of the different portfolios and the average return of the
portfolios altogether. Also, the minimum return, maximum return, standard deviation, and variance are given. Table 1 shows us that between the period of 2004 to 2014 capital-intensive manufacturers had an average higher yearly return of 1.21% than labour-intensive manufacturers.
Methodology
This section will explain which tests should be used to answer the research questions that follow. Is there a difference of the stock return between the labour- and capital-intensive portfolios? What is the relationship between the labour/capital ratio and the stock return? At the end of this section, the methodology of the regression analysis is explained to find the betas of the different portfolios. Before we decide which test is most appropriate, we must first check if data follows a normal distribution. The descriptive in table 2 illustrates that the skewness of the returns in both portfolios, capital- and labour-intensive firms, is around 2.5-3 where, in a situation of normal distribution, the skewness has a value close to zero. The kurtosis also tends to non-normality of the data. In a situation of normal distribution, the kurtosis has a value of 3. In this situation, the kurtosis are 17.4 and 13.1. The high kurtosis and the high skewness portrays a histogram that has a high peak with a fat and longer right tail. The stock return distribution of the portfolios is shown in a histogram (See appendix II). To test if the stock returns are normally distributed the Kolmogorov-Smirnov test is used. If this test is significant (p < 0.05), then the distribution of stock returns is significantly different than a normal distribution.
Table 2: Descriptive statistics
Statistic Std. Error
Capital-intensive portfolio Mean 15.79% 1.02%
Skewness 3.028 .037
Kurtosis 17.443 .074
Labour-intensive portfolio Mean 14.58% 1.10%
Skewness 2.637 .037
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Table 3: Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic Dfb Sig.c Statistic Dfb Sig.c
Capital-intensive .140 4345 .000 .782 4345 .000
Labour-intensive .127 4345 .000 .812 4345 .000
a. Lilliefors Significance Correction b. Degrees of freedom
c. Significance level
The returns of capital-intensive firms, D(4345) = 0.14, p < 0.05, and the returns of labour-intensive firms, D(4345) = 0.13, p < 0.05, are both significantly non-normally distributed (see also appendix II). Because of this non-normally distribution of the stock returns, we cannot use a regular independent t-test. Therefore we use a non-parametric test -theMann-Whitney- to assess the hypothesis: H0: There is no difference between the returns of capital-intensive and labour-intensive US manufacturers
H1: There is a difference between the returns of capital-intensive and labour-intensive US manufacturers
The Mann-Whitney test is an alternative to the t-test. The Mann-Whitney test is used when the data is non-normally distributed. The Mann-Whitney tests whether one variable is larger than the other (Mann & Whitney, 1947). The Mann-Whitney test works by ranking all of the returns, and looking at the differences in the ranked positions. The results of the tests are shown in chapter IV.
This paper also performs an ‘analysis of variances’ test to compare the average returns. One widely used test for this is the ANOVA. ANOVA is robust to violations of the normality assumption. However, heterogeneity of variances can cause type I errors (Randolf and Barcikowski, 1989). Therefore, we first use the Levene’s test (Levene, 1960) to test the null hypothesis that the variances are equal.
Table 4: Test of Homogeneity of Variances
Levene Statistic Df1 Df 2 Df3
Returns Based on Mean 22.166 1 8690 .000
Based on Median 20.780 1 8690 .000
Based on Median and with adjusted df
20.780 1 8690 .000
Based on trimmed mean 21.429 1 8690 .000
Where, Df means degrees of freedom
15 can be used even if the assumptions of normal distribution and of homogeneity of variances are violated because the Kruskal-Wallis test uses a ranking system. The Kruskal-Wallis test also tests the hypothesis:
H0: There is no difference between the returns of capital-intensive and labour-intensive US manufacturers
H1: There is a difference between the returns of capital-intensive and labour-intensive US manufacturers
After the Mann-Whitney and the Kruskal-Wallis tests, we also investigate whether there is a correlation between the capital-intensity of a manufacturer and the stock return of the
manufacturer. Because the stock returns are non-normally distributed, two non-parametric tests are used: the Spearman’s correlation coefficient (Spearman, 1910) and the Kendall’s tau test. The Spearman’s statistic is the more popular of the two, however, according to Howell (1997), Kendall’s statistic is a better estimate of the correlation. Both correlation statistics, Spearman’s and Kendall’s will test the null-hypothesis:
H0: There is no association between the capital-intensity and the stock price of US manufacturers
Another part of this research involves finding the betas of the different portfolios. To test whether there is a difference in the systematic risk between labour-intensive and capital-intensive firms we determine the beta(ß) using regression analysis. The beta stands for systematic risk and is calculated using the Capital Asset Pricing Model (CAPM). The CAPM was first developed by Sharpe (1964) and Lintner (1965), building on the earlier work of Markowitz (1952). The mathematical model of the CAPM is given in equation (1).
RP = RF + ßP*(RM – RF) (1)
ßP = Cov(RP,RM) / Var (RM) (2)
Where, E(RP) = the return of the portfolio, RF is the risk free rate, ßP is the beta of the portfolio and RM
stands for the market return.
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(Time-Series Regression) RPt – RF =𝛼P + ßP * (RMt - RF) + Ɛt (3)
Where, RPt - RF is the risk premium of the portfolio, 𝛼 is the intercept of the portfolio, ßP is the beta of
the portfolio, (RMt - RF) is the risk premium of the market and Ɛt is the regression residual. This study
uses the 10-year interest rate of the US government bond at the first of January as the risk free rate. The S&P 500 return is used as the return of the market. As part of the time-series regression the Ordinary Least Squares(OLS) method is used to determine the coefficients of the regression. OLS minimizes the differences between the observed risk premiums and the linear approximation of the data. In order for OLS to determine good estimates of the alpha and the beta, all Gauss-Markov assumptions needs to be satisfied. There are four Gauss-Markov assumptions: 1) the errors have a zero mean 2) the errors have a constant variable (no heteroscedasticity) 3) the errors are
uncorrelated between observations (no autocorrelation) and 4) the errors and independent variables are uncorrelated. If all of these four assumptions are satisfied, the OLS-estimator is the Best Linear Unbiased Estimator (BLUE).
IV Results
This chapter shows the results of the tests that answers the three main questions: 1) Which portfolio has a higher stock return and is this difference significant? 2) Is there a relationship between the labour/capital ratio and the stock return and what is this relationship? 3) What are the betas of the different portfolios? Firstly, the average stock returns are compared. Secondly, the correlation between the labour/capital ratio and the stock return is presented. Thirdly, the coefficients determined by the time-series regression are showed for the capital-intensive and the labour-intensive portfolio.
Comparing the average stock returns
Table 1 already told us that the portfolio of capital-intensive manufacturers has a return of 15.79% and the portfolio of labour-intensive manufacturers has a return of 14.58%. To test if capital-intensive manufacturers have statistically significant higher stock returns than labour-capital-intensive manufacturers this paper uses the Kruskal-Wallis test and the Mann-Whitney test. Firstly, the results of the Kruskal-Wallis are shown. After that, the results of the Mann-Whitney test are shown. The methodology section has explained that these two tests are non-parametric and therefore are robust to non-normally distributed data. The hypothesis that this paper is testing is:
H0: There is no difference between the returns of capital-intensive and labour-intensive US manufacturers
17 Kruskal-Wallis test
Table 5: Kruskal-Wallis Ranks
Group Amount Mean Rank Returns 0 4347 4423.44 1 4345 4269.53 Total 8692
Group 0: Returns of capital-intensive manufacturers Group 1: Returns of labour-intensive manufacturers
Table 5 shows a higher mean rank of the capital-intensive portfolio, this confirms that the stock return of the capital-intensive portfolio is higher than the stock return of the labour-intensive
portfolio. Table 6 shows us that the Kruskal-Wallis is significant. This means that we can reject H0 and
that the stock return of the capital-intensive portfolio is significantly higher than the stock return of the labour-intensive portfolio, Chi-Square = 8.175, p <0.05.
Mann-Whitney test
Table 7: Mann-Whitney Ranks
Group Amount Mean Rank Sum of Ranks Returns 0 4347 4423.44 19228685
1 4345 4269.53 18551093 Total 8692
Group 0: Returns of capital-intensive manufacturers Group 1: Returns of labour-intensive manufacturers
The Mann-Whitney test is testing the same null hypothesis as the Kruskal-Wallis test. Table 7 show us that the average return is higher for capital-intensive manufacturers (4423) than for labour-intensive manufacturers (4269). The test statistics in table 8 shows that this difference is significant, (U = 9109408, p = 0.004, p < 0.01). The Mann-Whitney test also rejects the null hypothesis. Concluding, from 2004 to 2014 the average yearly return of capital-intensive manufacturers is significantly higher than the average yearly return of labour-intensive manufacturers.
Correlation testing
Knowing that capital-intensive manufacturers have higher stock returns than labour-intensive manufacturers. Now we would like to know if this higher stock return can be explained by the intensity of the manufacturers. To find out if there is a relationship between the capital-intensity of a manufacturer and the stock return the following null hypothesis is tested:
H0: there is no association between the capital-intensity of US manufacturers and the stock price of US
manufacturers
H1: there is a relationship between the capital-intensity of US manufacturers and the stock price of US
manufacturers
Table 6: Kruskal-Wallis Test Statisticsa
Returns
Chi-Square 8.175
Degrees of freedom 1
Asymp. Sig. .004
Monte Carlo Sig. Significance lev. .004 99% Confidence
Interval
Lower Bound .002 Upper Bound .005
Table 8: Mann-Whitney Test Statisticsa
Returns Mann-Whitney U 9109408
Wilcoxon W 18551093
Z -2.859
18 Before we use statistical tests to find out if there is an association between both variables we try to find a relationship by looking at the scatterplot. In this scatterplot we draw a regression equation (see figure 6). Table 9 shows the descriptive statistics of the variables, ‘number of employees/PPE’ and the stock return. By analysing the scatterplot in figure 6 we observe many returns on the left side of the figure and we cannot see a clear correlation. The regression equation illustrates a very small negative correlation of -0.02764 between the employee/PPE ratio and the stock return. However, the R2 is 0.000165; this small number tells us that the data does not fit the linear equation at all.
A :
Q 1
A: Q1 is the first quartile; 25% of the data is less than this number B: Q2 is the second quartile or the median
C: Q3 is the third quartile;75% of the data is less than this number
Figure 6: Scatterplot of the capital-intensity ratio ‘Employees / PPE’ and the stock return
Due to this small R2, we cannot draw any conclusion from the scatterplot and we cannot see the linear equation as meaningful. As a robustness check two non-parametric tests are used: Kendall’s tau and Spearman’s rho. These two tests will tells us if there is a relationship between the capital-intensity and the stock return of US manufacturers. Table 10 shows the results of these two non-parametric correlation tests.
Table 10: Non-parametric correlation tests
Employee / PPE Returns
Kendall’s Tau_b Employees / PPE Correlation Coefficient 1.000 -.028**
Sig. (2-tailed) .000
N 13042 13042
Returns Correlation Coefficient -.028** 1.000 Sig. (2-tailed) .000
N 13042 13042
Spearman’s rho Employees / PPE Correlation Coefficient 1.000 -.043**
Sig. (2-tailed) .000
N 13042 13042
Returns Correlation Coefficient -.043** 1.000 Sig. (2-tailed) .000
N 13042 13042
** Correlation is significant at the 0.01 level (2-tailed)
Table 9: Descriptive statistics
‘Employee / PPE’ Returns
19 We start by examining Kendall’s tau. The correlation coefficient of Kendall’s tau has a value of -0.028; this correlation coefficient is significant. This means that there is a small negative relationship
between the ratio employee/PPE and the stock return of a company, r = -0.028, p < 0.01. The Spearman’s rho also finds a small significant relationship between the capital-intensity of a firm and its stock return, r = -.0.43, p < 0.01. Both tests find a significant negative relationship but with a very low correlation coefficient. The correlation coefficient of -0.028, resulting from the Kendall’s test, indicates that a rise in the labour/capital rate by 1% will lower the stock return with 0.028%.
Considering, the scatterplot, and the low R-squared of the regression equation this paper did not find a correlation between the capital-intensity of a manufacturer and its stock return.
Results CAPM time-series regression
This section shows the results of the time-series regression. Using the CAPM and time-series regression we determine the betas of the different portfolios. After the determination of the betas this paper tests if the regression meets all Gauss-Markov assumptions. First, the beta of the portfolio consisting of capital-intensive US manufacturers is determined. After that, the beta of the portfolio consisting of labour-intensive US manufacturers is determined. The beta determination of the neutral portfolio is shown in appendix IV.
Regression analysis of the capital-intensive portfolio
This section shows the results of the time-series regression of the portfolio consisting of capital-intensive manufacturers. The main descriptive statistics are illustrated in table 11, for further descriptive statistics see appendix III.
A: N is the number of observations
A: Risk Premium of the capital-intensive portfolio B: Risk Premium of the S&P 500
The higher standard deviation of the capital risk premium indicates that the volatility of the portfolio will be higher than the market volatility. To find a correlation between the risk premium of capital-intensive manufacturers and the risk premium of the S&P the Pearson test is used (table 12).The Pearson Correlation Coefficient is 0.904; this high coefficient means that there is a significant strong positive correlation between the risk premium of the capital-intensive portfolio and the risk premium of the S&P 500. By taking the Pearson Correlation to the power two, we find the R2.
Table 12: Correlation Risk Premiums
Cap_RPA S&P_RPB Pearson Correlation Cap RP A 1.000 0.904
S&P RP B 0.904 1.000 Sig. (1-tailed) Cap RP 0.000
S&P RP 0.000
N Cap RP 11 11
S&P RP 11 11
Table 11: Descriptive statistics
20 Table 13 shows a R² value of 0.818. This means that the S&P explains 81.8% of the variation of the capital-intensive portfolio. This high R2 indicates that the data perfectly fits the test. Table 13 also shows the Durban Watson statistic of 1.127. A DW-statistic far below or above the 2.0 indicates autocorrelation. To be sure, this paper uses the serial correlation LM-test to test for autocorrelation. The LM-test accepts H0: there is no serial correlation (see appendix V). Therefore, we can conclude
that there is no autocorrelation in the time-series data. Table 14 shows the alpha and the beta determined by the regression analysis.
Table 14: Coefficients of the regression analysis a
Unstandardized Coefficients Standardized Coefficients
B Std. Error Beta t-statistic Sign.
(Constant) 2.944 4.434 .664 .523
S&P risk prem. 1.512 .238 .904 6.362 .000
a. Dependent Variable: capital-intensive portfolio - risk premium
The alpha has a value of 2.944. This positive alpha tells us that the return of the portfolio consisting of capital-intensive manufacturers is higher than the market return. The beta of the capital-intensive portfolio is 1.512. This indicates that the systematic risk of the capital-intensive portfolio is higher than the systematic risk of the market. The market always has a beta of one. The last column of table 14 indicates that the beta is significantly different than one. Before we draw any conclusions we have to check if all Gauss-Markov assumptions are satisfied. The four Gauss-Markov assumptions are all tested on the residuals. Table 15 shows us the residuals statistics.
Table 15: Residuals Statisticsa
Minimum Maximum Mean Std. Deviation Years
Predicted Value -59.00% 49.10% 12.30% 27.91% 11
Residual -18.35% 30.62% 0.00% 13.16% 11
Std. Predicted Value -2.555 1.318 .000 1.000 11
Std. Residual -1.323 2.207 .000 .949 11
Dependent Variable: capital-intensive portfolio - risk premium
Table 15 shows that the first assumption, the errors have a zero mean, is satisfied. The second assumption, the errors have a constant variable, is tested using the white test. The result of the white test is that there is no heteroscedasticity (see appendix VI). The third assumption is that the errors are uncorrelated between observations. The serial correlation LM-test is used to check for autocorrelation. The null hypothesis is accepted, there is no autocorrelation (see appendix V). The
Table 13: Model Summary
Model R R Square Adjusted R
21 last assumption, the errors and independent variables are uncorrelated, is also satisfied. The last assumption is satisfied because there are no omitted variables, measurement errors and there is no reverse causality. In conclusion, all Gauss-Markov assumptions are satisfied and the OLS-estimator is BLUE. The coefficients that are determined in this time-series regression are accurate.
Regression analysis of the labour-intensive portfolio
This section shows the results of the time-series regression of the portfolio consisting of labour-intensive manufacturers. Table 16 shows us the main descriptive statistics, for further descriptive statistics see appendix III.
A: N is the number of observations
B: Risk Premium of the labour-intensive portfolio C: Risk Premium of the S&P 500
A: Risk Premium of the labour-intensive portfolio B: Risk Premium of the S&P 500
Table 16 shows us that the mean and the standard deviation of the risk premium of the labour-intensive portfolio are higher than the market risk premium. This indicates that the volatility of the portfolio is higher than the market volatility. The Pearson correlation is 0.883; this means that there is a significant strong positive correlation between the risk premium of the labour-intensive portfolio and the risk premium of the S&P 500. By taking the Pearson correlation to the power of two, we find the R2. Table 18 shows a R² with a value of 0.799. This means that the S&P explains 79.9% of the variation of the labour-intensive portfolio. The high R2 reveals that the data perfectly fits the test.
Table 18 also shows the Durban Watson statistic. This statistic tests for autocorrelation. In this research the errors in the time-series data are not correlated. This is tested using the serial correlation LM-test (see appendix V). Therefore, we can conclude that there is no autocorrelation.
Table 19: Coefficients of the regression analysis a
Unstandardized Coefficients Standardized Coefficients
B Std. Error Beta t Sig.
(Constant) 1.121 5.510 .203 .843
S&P risk prem. 1.664 .295 .883 5.634 .000
Dependent Variable: labour-intensive portfolio - risk premium
Table 17: Correlation Risk Premiums
Lab_RPA S&P_RPB Pearson
Correlation
Cap RP A 1.000 0.883
S&P RP B 0.883 1.000 Sig. (1-tailed) Cap RP 0.000
S&P RP 0.000
N Cap RP 11 11
S&P RP 11 11
Table 16: Descriptive statistics
Mean Std. Deviation NA Labour_RPB 11.42% 34.80% 11 S&P Risk PremiumC 6.19% 18.45% 11
Table 18: Model Summary
22 Table 19 shows the coefficients of the regression analysis. The alpha of the labour-intensive portfolio has a value of 1.121. This positive alpha tells us that the return of the portfolio consisting of labour-intensive manufacturers is higher than the market return. The beta of the labour-labour-intensive portfolio is 1.664. The significance level in table 19 indicates that the beta is significantly different than one. Before we draw any conclusions we first have to check if all Gauss-Markov assumptions are satisfied.
Table 20 shows that the first assumption, the errors have a zero mean, is satisfied. Also the second (see appendix IV), third (see appendix V) and fourth assumption are satisfied. In conclusion, all Gauss-Markov assumptions are satisfied and the OLS-estimator is the best linear unbiased estimator. Therefore, the alpha and beta that are determined in this time-series regression are accurate.
V Conclusion
This paper comes to three conclusions. The first determination is that the return of capital-intensive US manufacturers is significant higher than the return of labour-intensive manufacturers. We tested the null-hypothesis that there is no difference between the returns of capital-intensive and labour-intensive US manufacturers. Both tests, the Kruskal-Wallis test and the Mann-Whitney test, revealed a significant difference between the average stock return of the portfolios. Therefore, we can reject the null hypothesis and conclude that on average capital-intensive manufacturers have higher stock returns than labour-intensive manufacturers. The capital-intensive portfolio had a 1.21% higher yearly return than the labour-intensive portfolio.
Secondly, this paper finds no correlation between the labour/capital ratio of US manufacturers and the stock return of US manufacturers. The linear regression from the scatterplot in figure 6 shows a small negative correlation. But the R-squared of the linear correlation is close to zero. This means that the data does not fit the test at all. Two non-parametric tests are used as robustness tests. The Kendall and the Spearman tests both find a small negative relationship that is significant. However, the very small R-squared of the linear equation tells us that we cannot consider the results to be meaningfully accurate (R2 = 0.000165).
Table 20: Residuals Statisticsa
Minimum Maximum Mean Std. Deviation Years
Predicted Value -67.05% 51.92% 11.42% 30.71% 11 Residual -24.50% 34.15% 0.00% 16.35% 11 Std. Predicted Value -2.555 1.318 .000 1.000 11 Std. Residual -1.421 1.981 .000 .949 11
23 The third finding of this paper is that labour-intensive manufacturers have a higher beta than capital-intensive manufacturers. This study used a time series regression to determine the beta. On average, capital-intensive firms have a beta of 1.512 and labour-intensive firms have a beta of 1.664. Both portfolios have a beta greater than one. This indicates that the value of the portfolios is more volatile than the market. The beta of the labour-intensive manufacturers is, on average, higher than the beta of capital-intensive manufacturers. This implies that labour-intensive manufacturers have more systematic risk than capital-intensive manufacturers.
The results of this research are partly in line with the literature. Ryan (1997) and García-Feijóo and Jorgensen (2010) found that capital-intensive manufacturers have higher returns, as in this paper. The only difference between this paper and the research conducted by Ryan (1997) and García-Feijóo and Jorgensen (2010) is that they base their result on the finding that capital-intensive firms have higher risks. This paper finds that, contrary to the literature, labour-intensive manufacturers have higher risks and a more volatile stock return than capital-intensive manufacturers.
It is hard to find an explanation for the result that capital-intensive manufacturers have a higher stock return and a lower systematic risk than labour-intensive manufacturers. One explanation might be the decline of the interest rate in combination with an increase of the wage rate. As shown in figure 3, the interest rate has significantly declined between 2004 and 2014. The wage rate, on the other hand, (see figure 4) increased over that same time period. These developments have been a disadvantage for labour-intensive firms (Abowd, 1989). Future research can find if this explanation is true. Another recommendation for a future study is the analyses the relationship between the capital-intensity of a manufacturer and its stock return. This paper did not found a convincing correlation although some findings tend to a small negative relationship.
The main limitation of this paper is that it must take a very broad approach. Because of the inadequate prevailing specific literature on the subject it is hard to find explanation for the results. Many factors can be involved in influencing the stock returns of capital- and labour-intensive manufacturers. While the manufacturers are all listed on a US stock exchange, some manufacturers run the production processes in Asia, while others utilise US production facilities. Some
24
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27
Appendix I
McKinsey identifies broad industry groups with very different characteristics and requirements. Figure A1 shows different industry groups and the intensity of a given factor, including capital and labour.
Figure A1: Industry groups and the intensity of a given factor
28
Appendix II.
This appendix shows the histogram and the Q-plot to of the stock returns. First the distribution of the stock returns of capital-intensive manufacturers is showed.
Graph A1: Histogram Graph A2: Q-plot
This histogram shows us that the peak is higher than when the stock returns had followed a normal distribution. This indicates a high kurtosis. Another finding in the histogram is that the distribution has a fat and longer right tail than left tail. The Q-plot supports this skewness to the right.
The distribution of the stock returns of the labour-intensive portfolio is shown in graph A3 and A4.
Graph A3: Histogram Graph A4: Q-plot
29
Appendix III.
Table A1: Descriptive statistics of the three portfolios and the market portfolio
30
Appendix IV
Table A2: Regression analysis of the neutral portfolio
Table A3: Correlations
portfolio - risk prem. s&p 500 risk prem. Pearson Correlation Neutral - risk prem. 1.000 .914
s&p risk prem. .914 1.000 Sig. (1-tailed) Neutral - risk prem. . .000
s&p risk prem. .000 .
N Neutral - risk prem. 11 11
s&p risk prem. 11 11
The correlation between the neutral portfolio and the S&P 500 is 0.914.
The R-squared has a value of 0.816.
.
The neutral portfolio has a beta of 1.45, this is lower than the betas of capital-intensive and labour-intensive manufacturers. The alpha of the neutral portfolio is 2.936.
Descriptive Statistics
Mean Std. Deviation N Neutral - risk prem.. 11.91% 29.,29% 11 s&p risk prem. 6,19% 18.45% 11
Table A4: Model Summaryb
Model R R Square Adjusted R Square Std. Error of the Estimate Durbin-Watson
1 .914a .835 .816 12.55% 1.090
a. Predictors: (Constant), s&p risk prem.
b. Dependent Variable: neutral portfolio - risk prem.
Table A5: Coefficients of the regression analysis
Model
Unstandardized Coefficients Standardized Coefficients B Std. Error Beta t Sig. 1 (Constant) 2.936 4.011 .732 .483 s&p risk prem. 1.450 .215 .914 6.744 .000
Table A6: Residuals Statisticsa
Minimum Maximum Mean Std. Deviation N Predicted Value -56.46% 47.19% 11.91% 26.76% 11
Residual -17.15% 25.08% 0.00% 11.90% 11
Std. Predicted Value -2.555 1.318 .000 1.000 11
31
Appendix V
In the tables below the Breusch-Godfrey Serial Correlation LM test will test the null hypothesis: H0: there is no serial correlation. First the capital-intensive portfolio is tested.
Table A7: LM test: capital-intensive portfolio
F-statistic 1.206308 Prob. F(2,7) 0.3547 Obs*R-squared 2.819491 Prob. Chi-Square(2) 0.2442
Test Equation:
Dependent Variable: RESID Method: Least Squares
Sample: 2004 2014 Included observations: 11 Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
C(1) -0.002038 0.044344 -0.045949 0.9646 C(2) -0.009324 0.234294 -0.039794 0.9694 RESID(-1) 0.589975 0.399357 1.477314 0.1831 RESID(-2) -0.409128 0.402432 -1.016638 0.3432
R-squared 0.256317 Mean dependent var -2.27E-17 Adjusted R-squared -0.062404 S.D. dependent var 0.131609 S.E. of regression 0.135654 Akaike info criterion -0.882136 F-statistic 0.804206 Durbin-Watson stat 1.577898 Prob(F-statistic) 0.530133
The probability-values of the Serial Correlation LM test are above the significance level of 0.05. Therefore we cannot reject H0, and we can conclude that there is no autocorrelation.
The probability-values of the Serial Correlation LM test are above the significance level of 0.05. Therefore we cannot reject H0, and we can conclude that there is no autocorrelation.
Table A8: LM test: labour-intensive portfolio
F-statistic 1.183948 Prob. F(2,7) 0.3607 Obs*R-squared 2.780439 Prob. Chi-Square(2) 0.2490
Test Equation: Dependent Variable: RESID Method: Least Squares
Sample: 2004 2014 Included observations: 11 Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
C(1) 0.010106 0.056331 0.179410 0.8627 C(2) -0.179027 0.319251 -0.560771 0.5924 RESID(-1) 0.566141 0.411191 1.376832 0.2110 RESID(-2) -0.518260 0.439713 -1.178632 0.2771
32
Appendix VI
In the tables below the White test will test the null hypothesis: H0: there is homoscedasticity
Table A9: White test: Capital-intensive portfolio
F-statistic 0.646685 Prob. F(2,8) 0.5491 Obs*R-squared 1.530883 Prob. Chi-Square(2) 0.4651 Scaled explained SS 1.472148 Prob. Chi-Square(2) 0.4790
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares
Sample: 2004 2014. Included observations: 11
Variable Coefficient Std. Error t-Statistic Prob.
C 0.006515 0.012350 0.527514 0.6121 (S_P_RISK_PREM_)^2 0.162386 0.192094 0.845348 0.4225 S_P_RISK_PREM_ 0.057875 0.055109 1.050192 0.3243
R-squared 0.139171 Mean dependent var 0.015746 Adjusted R-squared -0.076036 S.D. dependent var 0.027993 S.E. of regression 0.029038 Akaike info criterion -4.013451 Sum squared resid 0.006745 Schwarz criterion -3.904935 Log likelihood 25.07398 Hannan-Quinn criter. -4.081856 F-statistic 0.646685 Durbin-Watson stat 2.274248 Prob(F-statistic) 0.549120
The probability-values of the White test are above the significance level of 0.05. Therefore we cannot reject the null hypothesis, and we can conclude that there is no heteroscedasticity.
Table A10: White test: labour-intensive portfolio
F-statistic 0.487386 Prob. F(2,8) 0.6313 Obs*R-squared 1.194736 Prob. Chi-Square(2) 0.5503 Scaled explained SS 0.777306 Prob. Chi-Square(2) 0.6780
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares
Sample: 2004 2014. Included observations: 11
Variable Coefficient Std. Error t-Statistic Prob.
C 0.014208 0.015961 0.890162 0.3994 (S_P_RISK_PREM_)^2 0.172333 0.248254 0.694179 0.5072 S_P_RISK_PREM_ 0.066394 0.071221 0.932229 0.3785
R-squared 0.108612 Mean dependent var 0.024313 Adjusted R-squared -0.114234 S.D. dependent var 0.035551 S.E. of regression 0.037527 Akaike info criterion -3.500513 Sum squared resid 0.011266 Schwarz criterion -3.391997 Log likelihood 22.25282 Hannan-Quinn criter. -3.568918 F-statistic 0.487386 Durbin-Watson stat 2.246618 Prob(F-statistic) 0.631344
