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WHAT IS THE IMPACT OF A FIRM’S PAY-OUT POLICY ON A
PRICING BUBBLE?
Kasper H. Kuipers
1Faculty Economics & Business
Rijksuniversiteit Groningen
Broerstraat 5
9700 AB Groningen
050 363 9111
A thesis submitted in fulfillment of the requirements of Rijksuniversiteit Groningen
for the MSc. degree of Finance 2015-2016
2[ June 13, 2016 ]
_____________________________________________________________________Word count: 10.820 ABSTRACT: This research investigates the impact of fundamentals (dividend) on a pricing bubble. The empirical analysis is conducted using annual CRSP and DataStream data of US listed companies [1945-2015]. Primarily, it finds support for a relationship between returns and the d/p ratio. Furthermore, it finds evidence suggesting a residual strategy giving the most return during a bubble period. Followed by a constant dividend strategy. Stable- and zero dividend strategies are of the least influence on a stock’s bubble component. Ultimately, I conclude investors overreact more (or less) to specific pay-out-policies amplifying the bubble. JEL Classification: C8, G1, G14, G30, H30. Keywords: speculative bubbles, market value, fundamental value, dividend policy. 1 E-Mail address: k.h.kuipers.2@student.rug.nl Telephone No.: +31 6319322492
Table of contents
1. Introduction ... 3
2. Literature: ‘The Fama-Shiller debate’ ... 5
2.1 Efficient Market Theory: 1950-1975 ... 5
2.2 Behavioral Finance: 1975-2000 ... 6
3. Bubble definition ... 7
4. Dividend policies ... 8
4.1.1 Dividend irrelevance ... 9
4.1.2 Dividend relevance ... 9
4.1.3 Dividend relevance under high taxes ... 10
4.2 Dividend policies ... 10
4.2.1 Stable growing dividend policy ... 10
4.2.2 Constant ratio dividend payout policy .... 11
4.2.3 Low stable and premium payout policy . 11 4.2.4 Residual dividend policy ... 12
5. Empirical framework & methodology ... 14
5.1 Notation ... 14
5.1.1 Hypotheses development ... 16
5.2 Data and descriptive statistics ... 17
5.2.1 Dataset 1: Annual 1950-2015 ... 17
5.2.2 Dataset 2: Annual 1985-2015 ... 18
6. Empirical analysis and results ... 19
6.1 Return forecasting ... 19
6.2 Individual effects ... 22
6.3 Discussing the results ... 23
6.4 Managerial explanations ... 25
7. Conclusion ... 26
7.1 Concluding remarks ... 26
7.2 Limitations and future research directions 26 8.Bibliography ... 27
9. Appendices ... 30
9.1 Appendix I: Describing variables. ... 30
9.2 Appendix II: Descriptive statistics ... 32
9.3 Appendix III: Descriptive statistics ... 33
9.4 Appendix IV: Return forecasting. ... 34
9.5 Appendix V: Workflow panel estimation. . 35
9.6 Appendix VI: CLRM diagnostics ... 36
Figures Figure 1: Research model ... 13
Figure 2: Plot of return & d/p. Eviews. ... 21
Figure 3: Plot of price & div-growth. Eviews. ... 21
Figure 4: Panel workflow ... 35
Tables Table 1: Linear regression of lagged returns ... 19
Table 2: Exp. return forecast CRSP ... 20
Table 3: Exp. return forecast DATASTREAM . 21 Table 4: Correlations and multicollinearity ... 22
Table 5: Individual policy effects ... 23
Table 6: Hypothesis acceptance overview ... 25
Table 7: Dependent variable ... 30
Table 8: Independent variable ... 30
Table 9: Firms in the sample ... 30
Table 10: CRSP variables ... 30
Table 11: Datastream variables ... 31
Table 12: Descriptive statistics 1 - Eviews. ... 32
Table 13: Descriptive statistics 2 - Eviews. ... 33
Table 14: AR(1) regression ... 34
Table 15: Predicting future returns ... 34
Table 16: Predicting future returns ... 34
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The impact of a firm’s dividend
policy on a pricing bubble.
1. Introduction
The topic of this thesis is the effect of different payout policies on the formation of a pricing bubble in stocks. Bubbles occur when stocks trade, for a longer period of time, above or beneath their fundamental value (Brooks, Prokopczuk, & Wu, 2015). Already in the 1600’s we could speak of the first known enormous speculative bubble in world history. Dutch tulips trading for explosive prices until interest declined and prices declined rapidly to 1-5% of what people used to pay for them. Expected returns are compared with their fundamentals, here the dividend/price ratio, as Balke and Wohar (2001) do in their research. I distinguish between four different pay out policies. Namely; stable, constant, residual and zero payout. The results are interesting to gain insight in bubble periods and see whether people react differently to certain dividend strategies pursued by a firm. I find evidence for the greatest overreaction effect to dividends during bubbles under a constant and under a residual payout policy. The research model is tested using US CRSP and S&P500 stock market data.
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public news, creating volatile price swings and bubbles among securities.
This paper provides a contribution to the existing literature of the behavioral movement and tests whether the over- or under reaction to dividends can be explained by, or a pattern within can be observed by, a specific dividend policy. I find, as Shiller, an overreaction to fundamentals. These are greatest when payouts are volatile over time. People seem to attach, more than can rationally be expected, value to positive news and the other way around. The mood that drives people, seems to drive the market. This suggests it’s able to implement hands-on stock picking strategies.
But, what are the characteristics of a bubble typically and when do people use the term ‘bubble’? Here, Shiller’s definition of a bubble is maintained and further worked with. The effect of multiple strategies of distributing dividends during a bubble is examined. Thereby, many different views regarding dividend policy affecting stock prices are studied. This paper brings together and combines the available efficient market theories and Shiller’s bubble theory. It is tested whether a different pay-out-policy is affecting investor activity and with it the bubble. This is represented in my research question: ‘what is the impact of a firm’s pay out policy on a pricing bubble?’
The aim of my thesis is to develop a model of a firm’s dividend policy selection estimating the effect on a bubble. I established the following goals to reach my aim:
1. To determine proper definitions of a pricing bubble and different dividend policies.
2. To study the relationship between the different dividend policies and the existence of a pricing bubble.
3. To carry out an empirical analysis of abovementioned relationship.
4. To estimate and come up with relevant results of the model to companies.
Research methods. The research employed
empirical data analysis of the developed hypotheses using the statistical programs Eviews 9.0 & SPSS v23.
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2. Literature: ‘The Fama-Shiller debate’
2.1 Efficient Market Theory: 1950-1975
Eugene Fama can be considered the father of the modern portfolio market. In his work he focuses much on the relationship between risk and return and what it means for the composition of your portfolio. According to Fama’s efficient-market hypothesis the price of an asset should reflect all available information (1970). He mentions that stocks in perfect markets always trade at their fundamental/fair value. All the investors are rational and a change in price can be explained by an associated change in fundamentals. Previous implies that a bubble is not at all possible to occur, since rational investors can’t purchase (sell) undervalued (overvalued) stocks over a longer period of time. They will go short on shares that exceed their fundamental value, and go long on shares that are undervalued. This way prices can diverge in the short-term, but will eventually always, smoothly come back to their intrinsic value. James & Walter (1956) reason that over the short-run, these distortions can be caused by speculative considerations.
There is an extensive literature concerning efficient market theories. For example, Paul Cootner (1964) and Eugene Fama’s (1964) survey: Paying out dividends will prosper
expectations about the future share price. It acts as an indicator of the firms possessing future prospects. Cootner mentions the characteristics and properties of security prices. He describes a fundamental theorem where ‘the sum of dividend payments and capital appreciation must equal the required rate of return on the investment for pricing to be optimal’. According to the traditional literature, a firm can influence its stock price by a change in its dividend policy. If the payout ratio is increased the value of the shares will increase. The main argument behind it is that investors prefer dividend over capital gains. This view on dividend policy is mainly altered by Graham & Dodd (1951). Standard economic theory thus suggests that a price level change will always lead to equilibrium by the law of demand and supply. It is however unclear, whether such a diversification over a certain period can be justified fundamentally. This leads to suggest that they may arise from speculation (James & Walter, 1956; Brooks, Prokopczuk, & Wu, 2015; Shiller, 1981).
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between dividend policies and common stock prices. Certain stocks may have substantial market value even though little or no dividends are anticipated in the foreseeable future. This is because for certain firms (growth firms), retained earnings are expected to lie further away in the future (Danielson & Dowdell, 2001). They, in turn, affect dividend policies, since prospective investors can be found who are willing to wait according to Walter.
Miller and Modigliani (1961) mention that dividend policy doesn’t affect share value at all, when no taxes are being paid. Because of the existence of differential taxes on capital and dividend income gains, a low dividend policy should be more desirable for increasing share value. It will be interesting to examine the effect of dividend policy on a pricing bubble. Prices are expected to reflect only (changes in) fundamental values. Diversifications, if any, might be due to speculation. The efficient market theory predicts that I will not find any results of overreaction in my regressions, because all available information and the reactions to it, will be directly incorporated into the new stock price.
For decades the EMH was the way to go. Lots of models have evolved during that time
3 Robert James Shiller (1946), is an American Nobel prize winning economist for his joint research in asset pricing analysis. He is famous for his work in which he challenges the dominant view of the
assuming efficiency and great opportunities for the modern portfolio theory and quantitative finance were available. Later many researchers have proven that the data does not (fully) support the model, and prices don’t only reflect changes in dividend, fundamentals and valuation. This gave rise to the development of behavioral finance.
2.2 Behavioral Finance: 1975-2000
In the field of behavioral finance R.J. Shiller3 is
a pioneer, exploring and combining psychological research with economic science. Kahneman (2002) also received a Nobel on his findings on human judgment and decision-making under uncertainty. As argued by Shiller, bubbles do exist and during one, a situation arises that is not efficient. He gives the following definition: ‘A speculative bubble is a social epidemic whose contagion is mediated by price movements. When a security’s market value exceeds its fundamental value people speak of the existence of a bubble. Because of a fast incline of investor activity prices can reach considerably high levels. The bubbles fast inflation can attract more investors trying to benefit from the (explosively) increasing prices. Eventually, a crash follows and the
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bubbles burst, prices converge to their fundamental value and leave many investors bear the brunt. Because public expectations of future prices excessively increase, the prices will temporarily be elevated (Shiller & Case, 2003). These imperfections are ascribed by behavioral economists Dong & Robinson (2005) to cognitive biases such as overreaction, overconfidence and information bias when reasoning.
No study so far, known to the author, examines a link between the different dividend policies a firm adheres and the way they are perceived during or impacting a pricing bubble. Investors might overreact to certain dividend policies. Shiller (1981) argues that explosive stock price increases aren’t justified by subsequent changes in dividends. Investors are uncertain about the distribution and growth path of dividends. A movement in real dividends can fear the market, which ultimately leads to the volatility of stock prices. In his research he determines the one-period holding return as the capital gain and received dividend at time t, divided by the price. He rejects the general notion of the efficient model and concludes that stock prices are too volatile given its discounted value of dividends. Shiller claims ‘the great volatility of a stock price is five to thirteen times too high to be attributed to new information about future real dividends if uncertainty about future
dividends is measured by the sample standard deviations of real dividends around their long-run exponential growth path’. He provides a data set that show fairly smooth dividend series and claims that if dividends are indeed absolutely constant, the efficient markets model must be wrong. A movement in price cannot reflect new information about dividends, when the amount of dividend doesn’t change. I will examine whether these price swings are more- or less volatile during a specific payout strategy.
3. Bubble definition
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speculative bubble is more than just high or low price-to-earnings ratios. A ‘bubble’ implies irrational behavior by investors. When prices increase, this can result in investor enthusiasm. Demand increases and prices further go up. Positive forces that are affecting the market are amplified and the market price reaches higher levels than it otherwise would. Obviously, prices won’t go up indefinitely. Eventually the price increases come to an end, the demand also ends, and a negative pattern can replace the upward spiral. The bubble ‘bursts’. This imperfect behavior isn’t contributed as foolishness, an error of fools. It is seen as an error where individuals have, ‘a sense of having subtle weaknesses or a partial blindness to reality’ (Shiller, Karl, & Thompson, 2012). He does subject a stock market bubble to human shortcomings, but specifically the kind of shortcomings that infects the thinking of every individual. It doesn’t matter whether one’s a professor, analyst, expert, accountant or a real-estate agent e.g. With his work a big movement in behavioral finance, psychology and social sciences in general emerged, which gave rise to an extensive literature concerning speculative behavior.
In this article, I will maintain to Shiller’s definition of a bubble and see if an ‘assumed irrationality’ exists within the different firm’s pay out policies and whether it is amplifying
stock pricing bubbles. I test whether people are excessively optimistic about certain payout strategies or a change in them during bubble periods. This bubble theory requires the notion and realization that a change in past price produces an inconsistency in our minds. Note that investors don’t foolishly believe that price increases must follow past price increases and the other way around. A bubble is measured by the divergence of a stock’s actual trading price/market value from its fundamentally expected trading price by dividend yield.
4. Dividend policies
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Rafferty, & Pillai, 2010). These are discussed in turn below.
4.1.1 Dividend irrelevance
‘Investors don’t care about payout’.
Managers are faced with many decisions that broadly can be categorized into two categories. Financing and investment decisions (Baker, Powell, & Mukherjee, 2005). A type of financing decision that a firm faces is the dividend decision. This is determined by a pursued firm’s dividend policy. What pay-out strategy does it follow? It affects the earnings, and how they are distributed between the firms themselves (re-invested) and their shareholders (paid out). The main thoughts in the dividend literature are the ideas of Miller and Modigliani (1961) (from here: ‘MM’), who argue that dividends are irrelevant in determining the firm value. Their work assumes a perfect and efficient world. In the absence of taxes, transaction costs and imperfect information it should not matter whether a firm does or does not distribute dividends. An investor is indifferent between dividends and retention-generated capital gains. If they want cash, they can sell their stock, and if they don’t want cash they can use dividends to buy stocks. Following the MM support, any difference in dividend strategy is implied not to influence my model and stock value should stay the same. I do however, follow the support for an inefficient
market since the assumptions of irrelevance are unrealistic. M&M suggest that a firm should focus solely on its investment policies and that residual policies are the residual. Investments in positive NPV projects result in higher cash flows, and subsequently, the only determinant, to higher firm value. According to Bishop et al. the dividend decision should be seen as independent (2000).
4.1.2 Dividend relevance
‘Investors prefer a high payout’.
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DeAngelo & DeAngelo, 2006; Baker & Powell, 1999). They would require a lower return to induce them to buy its stock. Black and Scholes (1974) argue that a firm, when increasing its dividend can expect that the effect this will have on the stock price, won’t be a definite but a temporarily.
4.1.3 Dividend relevance under high taxes
‘Investors prefer a low payout’.
A low payout means a high(er) capital gain. These are deferred and taxed at a lower effective rate than dividends. Investors require a higher pre-tax return to induce them to buy a high payout stock, which results in a lower share value. Empirical research is divided in supporting one of the theories and produces mixed results. The ‘clientele effect’ suggests that different groups of investors, the clienteles, prefer different dividend policies. Black and Scholes (1974) mention that when a firm changes its policies due to tax reasons a temporary effect can occur. The market may believe that there will be a change in estimated future earnings. But the effect is not permanent and in the long-term it will disappear as soon it becomes clear that the estimation about future earnings wasn’t the base of the change. Based on one of the main characteristics of a bubble, which is irrationality, I expect that such a change in policy might cause an explosive reaction to this news. The effect might be
dramatic in a very short-time and the effect won’t be temporary. It can be the trigger for the bubble to burst and prices to come back to their fundamental value.
4.2 Dividend policies
Different dividend pay-out policies, mentioned by Brigham (1998) and Kolb (2009) include: 1.) Stable growing pay-out policy.
2.) Constant ratio dividend pay-out. 3.) Stable pay-out plus a profit premium. 4.) Residual dividend pay-out policy.
4.2.1 Stable growing dividend policy
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preference for stable and constant dividend flows. Firms determine a payout ratio every period. Many firms aim to only increase the ratio, rather than reducing (even if it would be wise looking at their earnings). In the long run, such firms should have a stable general profitability in order for this policy to be reliable. Why would a company still want to pay out dividends when their profits don’t give them a reason to? Alekneviciene, Domeike, & Jatkunaite (2006) explain a drop in the share price because of the signal effect that forms a negative attitude towards investing and the selling of shares necessary to consume their needs. They argue that when a firm is following this strategy they postpone some projects or deviate from the desirable capital structure to pay out dividends and avoid signalization consequences.
4.2.2 Constant ratio dividend payout policy
Under this policy a specific percentage of dividends is paid out each year. This is a pre-determined percentage of the company’s earning. In this case, the short term earnings volatility affects the dividends and hence, the amount of dividends varies directly with the company’s earnings. The firms following this model give priorities to a stable profit, payout ratio and a high degree of information about the financial situation of the market (Baker, 2009). Investors only seem to be attracted
whenever the ratio is stable. A variable payout can lead to an undesirable change in share price (Baker, 2009). In order to bear more risk, investors demand a higher risk premium and hence a higher expected return. They’re willing to pay a lower price for the stock. This is also the greatest disadvantage of the model: instable dividends cause dissatisfaction under investors giving priority to current consumption. The main characteristics of this policy are that it reflects and sustains a firms interests and that they are typical for modern firms and firms that experience rapid growth periods (Baker, 2009).
4.2.3 Low stable dividend and premium payout policy
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strategy would be the best decision for a company. Since this strategy is hard to identify from the data and to distinguish from the other policies, it is omitted in my research.
4.2.4 Residual dividend policy
Only after deducting the capital expenditures of the current period from the internally generated funds of the company, the company pays out dividends from the funds that are left. When all profitable investment projects are realized, the cash that remains will be distributed and paid out as dividend. So, only the leftovers are distributed. Empirical evidence suggests that the gross of the firms doesn’t follow this strategy. They prefer to maintain a smoothed policy. When the target dividends are underfunded, managers prefer to borrow on the short-term than to cut dividends (Baker, 2009). Advantages of the residual policy are that new stock issues and flotation costs are minimized, and a careful management of payout ratio and dividend trend. Disadvantages are that variable dividends send conflicting signals, it increases risk, instability and it doesn’t typically appeal any clienteles (Kolb, 2001). Firms pursuing this strategy target on investors whose priorities lie by re-investing profit rather than paying it out in the form of dividend. The decision changes over time since both investment possibilities and profitability change over time. One year a
firm announces to pay out none due to the good investment possibilities, whereas the next it might pay high dividends since the opportunities are bad or used up. Many argue that this policy corresponds with Miller and Modigliani’s dividend irrelevance claim. The shareholders are indifferent to the firm paying out, or re-investing. Similar theoretical arguments are:
- The form of income to shareholders is not important.
- There is no risk.
- The investor doesn’t take any selling costs.
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Figure 1: Research model
The final dividend policy that my research model includes is the policy of zero-dividend payout. A firm can choose not to pay out any earnings but reinvest them in the organization. This policy is typical for young growth firms that don’t produce high stable cash flows yet (Kolb, 2001). They believe they do a better job in increasing their value (and subsequently its share price) by reinvesting its earnings rather than paying out.
Of the different dividend policies, the stable model is considered the least risky in respect of investors. They are promised the current income and do not face any risk. They do, however, miss the opportunity of a higher potential income under the residual policy in
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Froot and Obstfeld (1991), found that price fluctuations aren’t fully explained to a change in dividend. Also they argue that the relationship between prices and dividends is non-linear. In addition, the specific price component that is not explained by the present-value model is highly positively correlated with dividends. They suggest that prices, in relation with the non-bubble price, become increasingly overvalued, as the dividend paid out rises. This bubble component shrinks when the dividends are low. If dividend becomes large, the size of the bubble explodes.
5. Empirical framework & methodology
Following research model is built around Shiller’s work and definitions concerning bubbles. A difference in actual and rationally expected price and return is characterized as the existence of a pricing bubble, and this models’ dependent variable of the equation. A definition of all used variables in my research can be found in appendix I.
Following Shiller’s and Froot’s reasoning, investors overreact to news about dividends during a pricing bubble. First, the model estimates if this reasoning is fair at all and after these arguments are combined with the earlier mentioned dividend policies by Brigham and Kolb. Within a panel I test whether there is a
different effect of those different strategies (or a change in them) on the expected return. The performance dummy variables of interest are
STBL (stable dividend payout), CON (constant
dividend payout), RESD (residual dividend payout) and 0DIV (zero dividend/no payout).
5.1 Notation
Shiller defines rational prices, as well as its actual counterparts, as following: We can represent the ex-post- rational price P1∗ in terms of the discount factor 1/R4 and dividend D164
as
: P1∗= 1 R4 8 49: D164The actual price is its expectation at time t:
P1= E1( P1∗) = E1 1 R4 8 49: D164
Under the efficient market hypothesis it is assumed that P1 equals the mathematical expectation of the present value P1∗ of actual dividends ( P1= E1P1∗). Focusing on the behavioral side of Finance these price definitions give rise to the following definition of a bubble component: (1): [>?− >?∗] = 8D9:B:CE?6D− F? : BC 8 D9: E?6D
P1∗ has to be forecasted, because it is not
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into returns4 for calculation, also defining the
bubble return as [R1− R1∗]. As discussed, one
variable proven to be a forecaster of future returns is the Dividend/Price ratio:
R
16:=
D
16:P
1Jung and Shiller (2002) show that the dividend price ratio of an individual stock, in an efficient market, is a good forecaster of long-term future changes in future dividends. In the empirical part I’ll firstly test whether we can speak of efficient markets at all in the stock market during the observed sample period.
The dividend variable is formed by taking the difference between the CRSP value weighted return including and the return excluding dividends and multiplying them with the index value at the beginning of time t (as described by Cochrane, 2011). Next period’s log return r16: is expressed in terms of log dividends d minus the log price p:
(2): r16: = d16:− p1 p1− d1 = d16:− d1 − r16: pd1 = Δd16: − r16: and: (3): d1− p1 = r16:− d16:− d1 4 Return is calculated as, K ?= LLM MNO− 1.
K? is the index return for time t. P? is the index level at
dp1 = r16:− Δd16:
To see whether returns are predictable at all, I use a linear forecasting regression model, which is similar to the following form:
K?6: = Q + S T? + U?6:.
This model implies that the expected return at time t is
F(K?6:) = Q + S T?.5
Where F K?6: is the expected return at time t+1 and T? is treated as the DP variable at time t.
According to the efficient market theory we’re expected to see S=0 and KV=0 for the T?
variable. Because stock prices should not be predictable and assumed to follow a random walk. A positive beta would namely imply that one should buy at a high X and sell at a low X. Under the efficient market hypothesis everybody would do this in the short-term and so, S >0 cannot describe a market equilibrium. Dividing the annual dividend payments into one of the different strategies and plugging them into equation (4) of my research model, this study employs the following regression:
time t. P?W: is the index level at end of the previous
period.
5 It is very important to understand the concept here
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(4): [F(XY?6:) − F(XY?6:∗ )]= β [,]+
β [,:E>^+β [,V_`ab^E1^ + β [,cdef^ E2^ + β [,gKF_E^ E3^ + β [,h0EPj^ E3^+ UY?. Where [r1− r1∗] represents the deviation of
return from what can be rationally expected. E:? is a dummy variable that equals one for observations with a stable payout in the event window, and zero for observations outside the event window. This definition also holds for EV? (constant), Ec? (residual) and Eg?(zero pay out). β [,] is the amount of (excess) return when the other independent variables are zero and UY? is the forecast error term of the panel-series.
The effect of the lagged variables kl?W: on the current bubble component will be tested to check the last periods’ payout influence. A significant influence might be explained by a recent change regarding payout strategy. The results will be aggregated over the full sample and per type of dividend strategy. Furthermore, the results between the groups will be compared using t-tests and fixed effects.
5.1.1 Hypotheses development
According to the efficient literature, it is expected that returns are unforecastable and prices follow a random walk. This is indicated by a beta of zero and a KV being zero. Under
the alternative hypothesis it is expected that returns are forecastable. Visually:
m
]: Returns are unforecastable and there is no
relationship with the dp variable.
The second hypothesis finds its origin in the idea of a 1:1 relationship between d/p and expected returns. When the d/p ratio rises with 1%, returns should rise with 1%. This implies a beta of one. The alternative hypothesis suggests investors do overreact to changes in dividend. This is represented visually in the following hypothesis: (Statistically: b=1).
m
:: The expected return and the dp variable
show a [1:1] relationship.
Based on the provided literature sections, I expect both hypotheses to be rejected following the behavioral theories and beta to present signs of overreaction (>1). When diving deeper (within and between) into the d/p variable I come up with the following hypotheses, regarding the specific dividend policies.
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m
V: The STBL kl
?variable doesn’t
significantly affect the bubble return.
During a bubble people react even more strongly to positive (and when it bursts: negative) news as mentioned above. As more and more people are excited about a particular investment, the more likely the investor is to be convinced and ignores the dangers of the
investment. Constant payout is therefore
expected to be of significant influence on the dependent variable when earnings of the firm are volatile. Based on the economic theories presented above, hypotheses three will be:
m
c: The CON kl
?variable significantly
affects the bubble return.
According to the mentioned literature, I expect residual payout to be of influence on the dependent variable. Since the level of payout changes over time people are expected to overreact to those changes. Since investors tend to dislike risky dividend strategies, this policy is probably negatively related with a period of ‘investor enthusiasm about a certain stock’. When the dividends rise (fall) the bubble component is expected to increase (decrease), leading to the fourth hypothesis:
m
g: The RES kl
?variable significantly
affects the bubble return.
A zero dividend payout policy should not influence the price bubble component, since no change in dividend yields shouldn’t lead to a change in expectations about the future price.
m
h: The 0DIV kl
?variable doesn’t
significantly affect the bubble return.
Of all the payouts, I expect the (most unstable) residual policy to influence the bubble return the most and the zero-dividend the least.
m
n: The RES kl
?variable affects the bubble
return the most.
m
o: The 0DIV kl
?variable affects the bubble
return the least.
With the creation of two US-stocks datasets, I’ll test the research model with the supporting abovementioned hypotheses.
5.2 Data and descriptive statistics
Two datasets are used to test possible predictors of the equity premium. The equity premium is the dependent variable, i.e., the total stock market return minus the short-term interest rate during that period. The predictive performance of the estimation models is estimated based on annual frequencies. This is done to see yearly performance and cancel out any seasonality in the dividend effects.
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Dataset 1 consists of annual real, deflated by the CPI, value weighted CRSP (Center for Research in Security Prices) stock returns of stocks listed on the NYSE, AMEX and NASDAQ markets. It is important to have enough initial data in order for the regressions to be reliable. The models are tested only with data after World War II. The sample size covers the period from [1945-2015]. The annual dividends, E?, are calculated by taking the CRSP differences between returns with and without dividends and multiplying them by the market value of the index (Cochrane, 2011). The 3-month T-bill returns are subtracted from the stocks to generate excess returns. The average annual (excess) stock return, reported in column B of table 1 in appendix II, is around 11.8% (8.03%) for the NYSE, NASDAQ and AMEX stock markets. There is also quite some variation in stock returns, as can be seen from the standard deviation, reported in column B, which is around 18% for the stock markets. The D/P ratio has an average value of 0.035, with a standard deviation of 0.014. The complete descriptive statistics of dataset 1 are presented in table 1 - Appendix II.
5.2.2 Dataset 2: Annual 1985-2015
To test the model, I obtained dataset 2 from Reuters’ DataStream. It consists of a sample size of 11,739 observations. I took annual stock prices from the Standard & Poor’s index during
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firms follow the constant strategy (1454 obs.), whereas this seemed to be very unpopular in the beginning years of the dataset. This trend might be explained by the fact that the S&P firms produce more stable cash flows recently, leading to less volatile pay outs. Furthermore, the data show 2196 observations of a residual policy and in 2916 cases the firms chose not to pay out any dividend. The index variables are transformed into stock returns. As suggested by Brooks(2014)logarithmic values anticipate on the potential issues of heteroscedasticity. Therefore, and in order to account for the normality assumption and to ease calculation (e.g. time-additive; summing up yearly returns) all variables are transformed into log variables. The complete descriptive statistics of dataset 2 can be found in table 2 – appendix III.
6. Empirical analysis and results
This chapter provides the results of the different analyses. First, it mentions the results of return forecasting. Next, it mentions the individual results within the index.
6.1 Return forecasting
When running a regression of returns on lagged returns I find the following results:
[Dataset 1] B t(b) Stock return 0.011 0.10 0.001 Excess return 0.023 0.20 0.000 [Dataset 2] B t(b) Stock return 0.022 2.36 0.001 Excess return 0.021 2.27 0.000 Table 1: Linear regression of lagged returns
The above is suggesting low return predictability. S =0.011 means that when excess returns rise with 100% this year, you expect them to rise with 1.1% the next (a very small form of momentum). In combination with the very low KV this coefficient represents the economic significance, which is tiny. Also statistically, looking at the t-statistic it is very insignificant. Returns are bad predictors of next-year returns.
The D/P variables are very persistent in nature, which move slowly as time passes. An AR(1) regression on the persistent forecasting variable estimates:
(5): E>?= Q + 0.94 ×E>?W:+ U? for dataset 1
&
(6): E>?= Q + 0.85 ×E>?W:+ U? for dataset 2
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and a persistent forecasting variable. To estimate the longer-horizon regressions I make use of the following pair of one-year regressions:
X?6: = St?+ U?6: t?6: = ∅t?+ v?6:
Where both S and ∅ are estimated by OLS using the full amount of sample observations. The implied two year regression (7) then is: X?6:+ X?6V= (St?+ U?6:) + St?6:+ U?6V
= St?+ S ∅t?+ v?6: + U?6:+ U?6V
= S 1 + ∅ t?+ (Sv?6:+ U?6:+ U?6V)6 And similarly, the three-year regression (8): X?6:+ X?6V+ X?6c = S 1 + ∅ + ∅V t?+ U The proposition that can be made from this structure is that over a longer horizon, return coefficients will rise. This rise of the coefficients and KV with horizon is a result of a small short horizon b and KV and a persistent (∅ large) forecasting variable. Also, this forecasting variable, dividend-price t? forecast returns many periods ahead in the future.
6 The mathematics and derivations are based on the previous and extensive work of Professor J. Cochrane – University of Chicago.
(9): X?6V= S∅t?+ (Sv?6:+ U?6V).
Next, for both datasets, I run a regression of future returns and see how they respond to the D/P-ratio variable. Furthermore, I estimate them over a longer horizon using a simple time-series regression. The regression equation is of the form
K?→?6xy = Q + S (E
^/>^) + U?6x.
meaning that at time t, the expected return is F? K?6:y = Q + S (E
?/>?).
The expected returns vary as time passes. Leading to the results presented in the table below (for dataset 1)7, with t-statistics at the
***1% significance level: Horizon k B T(b) {| DP (AR1) 1 3.5 (2.51)*** 0.07 4.87 0.94 5 16.12 (6.87)*** 0.25 37.72 0.94 Table 2: Exp. return forecast CRSP
A 1% increase in the D/P variable leads to a 3.5% increase in return the next year, and an impressive 16.12% higher return after 5 years. And to the following results below, showing the same implications, for the second dataset. For the 5-year regression HAC –Newey-West’s standard errors are used to adjust for serial
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correlation. The assumption testing can be found in appendix VI.
Horizon k B T(b) {| DP (AR1) 1 2.52 (1.97)** 0.05 3.23 0.85 5 10.55 (3.24)*** 0.22 34.26 0.85 Table 3: Exp. return forecast DATASTREAM
The standard deviations can be calculated using the following formula:
} F? K?6: = } St? = S}[t?].
The KV rises with horizon indicating forecast ability of returns getting more interesting over longer periods of time. Both statistically (with a t-statistic of 2.51 for dataset 1) and economically (the coefficient is economically ‘large’) the coefficients are significant and rise over time. Also for dataset 2 the coefficients are statistically significant for all horizon k’s. Both hypothesis 0 and hypothesis 1 are, as expected, rejected.
The underlying intuition is that a high D/P ratio forecasts a high future D/P ratio, and so a high future return/low price. Figure 3 shows a plot of the variables, visualizing the idea of
prices being far more volatile than their fundamentals.
When computing the dividend growth variable and plotting this against subsequent prices, we get the following graph. Again, we see price levels being well above and beneath dividend levels.
Another interpretation shows signs of investor irrationality. Each time an investor predicts a particular ratio, they turn out to be wrong. As noted by Shiller (1981): ‘stock prices are too volatile to be justified by their subsequent changes in dividend’, suggesting the stock market overreacts to changes in dividend yields. This view stresses the idea that a sudden drop of e.g. 10% in the stock market can almost never be a ‘rational’ change in dividend expectations. The notion of efficient markets is rejected dramatically. -.6 -.4 -.2 .0 .2 .4 .6 1930 1940 1950 1960 1970 1980 1990 2000 2010 Price level D growth
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6.2 Individual effects
I determine the forecastability of stock returns with the dp ratio as explanatory variable. Next, I’ll test for individual dividend effects within the index. Here fore, only dataset 2 is used which consists of individual stock data of the S&P500 since 1985. The workflow of this process is attached in appendix V. This workflow states the process of in- and exclusion of observations in the sample. All observations are assigned to one of the payout policies (dummy variables). The bubble component, [R1− R∗1] is calculated by
subtracting the rationally expected return from the actual return and regressed on the independent dummies. The different individual effects are presented in table 5. First, I test for multicollinearity to see if there is a correlation between the explanatory variables, where they partly explain each other. The tolerance level is close to one (0,89; 0,86 & 0,85 respectively) and insignificant for all dummies, indicating that there is no multicollinearity between the independent variables. The model is appropriate for further estimation. The correlations and multicollinearity diagnostics are graphically represented in table 4.
Correlations r-r* Cons. Resid. 0div
r – r* 1.000 Constant 0.03 1.00 Residual -0.02 -0.18 1.00 0 dividend 0.04 -0.22 -0.27 1.00 Collinearities (Con.) (Constant) 0.13 0.05 0.07 0.08 Constant 0.00 0.45 0.01 0.26 Residual 0.00 0.15 0.46 0.10 0 dividend 0.87 0.35 0.46 0.57 Tolerance 0.89 0.86 0.85 *10%, **5%, ***1% significance level Table 4: Correlations and multicollinearity
When performing a multiple regression of the difference between the actual and the rationally expected return on the dummies, I test for differences between those dummies. The bubble coefficient represents the overall effect of the dp variable on the difference between actual and expected returns. The regression results are presented in table 5.
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a stable payout produces (an insignificant) 0.03 less units after the first year than a situation without payout, while a constant policy produces (a significant) 0.05 more and a residual policy 0.03 more units during a bubble. Assumption testing and robustness tests of the estimated regressions can be found under Appendix VI.
6.3 Discussing the results
The main results of this study outline the implications of choosing a dividend strategy on a stock’s bubble return. In section 6.1, the historical dp ratio suggests that returns can be forecasted, explaining more of the stock’s variance over a longer horizon. In accordance with the view of many researchers’ firm value,
and stock prices, are thus, in my view, affected by distributing dividends (Baker, Farelly, & Edelman, 1985; DeAngelo & DeAngelo, 2006; Baker & Powell, 1999). This supports the proposition of dividend relevancy. Though, the returns show clear signs of market inefficiency and irrational behavior. The results found for dataset 1 are in line with those for dataset 2. However, those for dataset 2 predict somewhat lower overreactions in a more recent time frame for the S&P500 firms. A possible explanation for this observation might be that recently more firms have switched to a zero or stable dividend policy responding to market dynamics. According to the CFA institute the proportion of dividend-paying companies has declined over time. However, my research doesn’t explain this topic, since it doesn’t
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observe the individual dividend policies for the first dataset.
As discussed in section 6.2, there are different individual effects on a bubble component for different payout strategies. The zero-dividend group is used as a reference group on which the other policies are tested. As compared with a situation where no dividends are paid out, I conclude that the residual policy at the 1% significance level, for almost all years, leads to the highest bubble returns. As argued by Kolb (2001), the variable dividends send conflicting signals and increases risk and instability. Clienteles ultimately want to be compensated with a higher premium for taking on this risk. At the 5% level, most of the years, the constant payout also significantly adds to the bubble effect compared with the other policies, with a rising coefficient from 0.05 after the first till 0.14 after five years. As mentioned by Baker (2009) a variable payout can lead to an undesirable change in share price, explaining the same effect as with the residual policy. Also, the stable payout strategy does significantly affect excess returns. However, it doesn’t produce extra returns during a bubble, compared with the other policies. An exception is seen after a horizon of five years. The stable strategy then significantly amplified the bubble the most (0.39***). These firms avoid signalization consequences
(Alekneviciene, Domeike, & Jatkunaite, 2006), which might explain that, although it significantly affects returns, people overreact less to this policy than to the others. This finding is implied by the work of Veronesi (1999), who claims that stock prices overreact (underreact) to bad (good) news in good (bad) times.
As expected, the decision to pay out zero dividend leads to a small effect on the bubble for all years. The policy doesn’t magnify or abbreviate the bubble effect in a significant way. On average, the zero-dividend firms experience a (non-significant) loss in relation to dividend-paying firms. This finding is also mentioned by Christie (1990). He finds zero-dividends lead to a negative average monthly excess return of -0.41%. The model explains the dependent variance by KV=6%: one year
and KV =25%: five years.
Finally, to answer my main research question ‘What is the impact of a firm’s payout policy on a pricing bubble?’ the answer is that there is a significant impact of a firm’s decision whether how much, and following which strategy, it pays out dividends on the formation of a stock’s bubble component.
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bubble effect was as expected. The question remains how the findings can be explained. A first possible explanation might be that because, the dividend amount changes substantially per year, there is a greater chance investors overreact to these changes. When, relatively, the pay outs rise by a lot, investors might be overenthusiastic about the stock and vice versa. A second explanation might be that during good times, investors are more risk-seeking. They tend towards buying riskier stocks (with risky pay out policies, as the constant and residual) and driving up their prices during bubble periods. The powerful message of dividends predicting future prospects and performance gets ‘irrationally’ powerful to a certain extent for all different policies that pay out. These are clear signs of overreaction in the stock market, as argued before by Shiller. When a firm decides not to pay out any dividend, but is reinvesting in itself, investors seem to do a ‘better’ job at predicting the fundamental value and the bubble doesn’t amplify significantly. This might be an interesting subject for future research in the field of dividend pay outs.
6.4 Managerial explanations
Apart from the theoretical implications, there are also some important implications for practice. Particularly, the results highlight the importance of the dividend decision.
Knowledge about historical pay outs and its relations with returns might influence a manager’s view on future pay outs. For example, if he/she believes prices should reflect the firm’ s fundamentals as close as possible, he/she might earlier choose for a stable-dividend or a zero-dividend policy. Whereas the constant and residual- dividend decisions do a worse job at representing the rational value.
Finally, to summarize the results beneath table (6) provides an overview whether the proposed hypotheses are rejected or not.
Hypothesis:
~: Returns are unforecastable
Not rejected/Rejected [expected] ~Ä: Exp. Return and
d/p move [1:1]
Not rejected/Rejected [expected] ~|: STBL dp doesn’t
signif. affect a bubble
Not rejected/Rejected
[expected] ~Å: CONS dp doesn’t
signif. affect a bubble
Not rejected/Rejected [expected] ~Ç: RESD dp doesn’t
signif. affect a bubble
Not rejected/Rejected [expected] ~É: 0Div dp doesn’t
signif. affect a bubble
Not rejected/Rejected
[expected] ~Ñ: RES dp has the
most effect on a bubble
Not rejected/Rejected
[expected] ~Ö: 0Div dp has the
least effect on a bubble
Not rejected/Rejected
[expected]
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7. Conclusion
7.1 Concluding remarksExisting literature produced a large body of theoretical and empirical research on dividend policies. There is no general consensus that emerged from this extensive research. The produced results are mixed and inconclusive. This paper examines the effect of the four defined dividend policies [stable payout, constant payout, residual payout, & zero dividend payout] on a stock’s bubble return applied to two different samples of US stocks, one between the period [1950-2015] and one between [1985-2015]. By doing so, the study adds to the behavioral and dividend literature. This paper argues that the pay out of dividends is relevant to the stock’s excess and bubble return. My statistical results clearly invalidate the efficient market theory by illustrating that historical DP ratios can be used to significantly predict future returns. They show evidence of returns being four times more volatile than subsequent changes in the fundamental dividend-price value the next year.
The individual effects of the payout policies on future returns are estimated simultaneously using panel dummy modeling. The results indicate that a residual dividend policy amplifies a bubble the most compared with a
zero-dividend policy, followed by a constant payout. A stable payout also amplifies a bubble more than a zero-dividend payout, though the effect is only marginal and less significant than the constant and residual policy.
The overall conclusion of this research is that returns show signs unexplained by fundamentals. This implicates that investors behave irrationally and show signs of overreaction to pay outs. Specifically, the effect of this overreaction is different under various dividend policies. As expected, the bubble seems to amplify most under a policy where residual dividends are paid out and the least where no dividends are paid out at all.
7.2 Limitations and future research directions
This section provides the main limitations of my research and provides avenues for future research.
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A second limitation is the exclusion of the low stable + premium payout from my research. The results concerning this specific policy are equally interesting to gain insights on dividends, but left out for simplification reasons. If future research can determine and make proper distinctions between stable, residual and stable + premium payouts, the model can be tested again.
The primary purpose of this paper is to investigate whether a firm’s pursued dividend strategy influences a pricing bubble return. However, describing explanations of where these returns come from is not part of this paper, but it would be interesting to know all the determinants of the origin of the price differences. For instance, the level of sentiment effect within stock returns and the main drivers of irrational behavior (e.g. uncertainty, transparency). Since much of these studies will move towards the field of psychology, it is hard coming up with solid conclusions or rules of thumb about irrational investor behavior. Though, investigating the underlying explanations in further research would be of great purpose for the knowledge within the field of finance.
To add, DP ratios have proven to be a good (and the most important) predictor of future returns. It would be interesting to analyze more variables influencing the dependent and
explaining more of its variance. People use lots of additional variables as forecasters, i.e. the yield spread between long and short maturity bonds or the [AAA-BAA] credit spread. Also, they use macro variables such as the consumption/wealth ratio, inflation and measures of real and implied volatility. Therefore, it would be interesting to see if these factors influence the economic significance of this research and it would be recommended analyzing them for a within index panel.
While this study has its limitations, I hope that it can serve as a basis for further research regarding the field of dividends and behavioral finance.
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9. Appendices
9.1 Appendix I: Describing research variables.
Table 6: Dependent variable
ABBREVIATION VARIABLE MEASUREMENT SOURCE
K?6x EXCESS EQUITY RETURN K?6x= 100 ∗ ΔÜáà(KP) DATASTREAM & CRSP
Table 7: Independent variable
ABBREVIATION VARIABLE MEASUREMENT SOURCE
kl?6x DIVIDEND-PRICE RATIO (LOG) kl?6x=Râ6:− ΔDâ6: DATASTREAM & CRSP Table 8: Firms in the sample DATA SAMPLE NR. OF OBSERVATIONS STOCKS SOURCE
DATASET 1 1950-2015 70 NYSE, AMEX &
NASDAQ
CRSP
DATASET 2 1985-2015 11,739 S&P500 DATASTREAM
Table 9: CRSP variables
ABBREVIATION VARIABLE DESCRIPTION
D12 DIVIDEND 12 MONTH MOVING DIVIDENDS
INDEX PRICE INDEX PRICE INDEX BEGINNING YEAR
CRSP_VW CRSP VALUE WEIGHTED
RETURN
VALUE WEIGHTED RETURN INCLUDING DIVIDENDS
CRSP_VWX CRSP EX VALUE
WEIGHTED RETURN
VALUE WEIGHTED RETURN EXCLUDING DIVIDENDS
ANN. DIV. ANNUAL DIVIDEND RETURN INCL. DIV. – RETURN EXCL.
DIV. * PRICE INDEX
EXC. R EXCESS RETURN VALUE WEIGHTED RETURN – RISK FREE
RATE
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Table 10: Datastream variables
ABBREVIATION / CODE VARIABLE DESCRIPTION
RI RETURN INDEX GROWTH IN VALUE OF A SHARE
HOLDING OVER A SPECIFIED PERIOD, ASSUMING THAT DIVIDENDS ARE RE-INVESTED.
PI PRICE INDEX EXPRESSES THE PRICE OF AN EQUITY AS
A PERCENTAGE OF ITS VALUE ON THE BASE DATE, ADJUSTED FOR CAPITAL CHANGES.
DY DIVIDEND YIELD DIVIDEND PER SHARE AS A
PERCENTAGE OF THE SHARE PRICE, BASED ON ANNUAL DIVIDENDS.
DPS DIVIDEND PER SHARE ROLLING 12 MONTH DIVIDEND PER
SHARE.
EPS / [WC05201] EARNINGS PER SHARE EARNINGS OVER THE LAST 12 MONTHS
NI / [WC01751] NET INCOME NET INCOME BEFORE EXTRAORDINARY
ITEMS
TBILL T-BILL RETURN RETURN ON THE 3 MONTH T-BILL
EXC.R EXCESS RETURN TOTAL RETURN – RISK FREE RATE
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9.2 Appendix II: Descriptive statistics variables dataset I. EXCESS RETURNS, DP RATIO AND ITS LOG TRANSFORMATIONS.
SERIES:
DEPENDENT:
EXCESS RETURNS – LOG ER SERIES:
INDEPENDENT: D/P RATIO – LOG DP
SAMPLE - HORIZON: T: [1945-2015] - 1:5 SAMPLE - HORIZON: T: [1945-2015] - 1:5
OBSERVATIONS: N: [70] OBSERVATIONS: N: [70] MEAN: 1.0803 - 0.0620 MEAN: 0.347 - -3.4456 MEDIAN: 1.1074 - 0.1020 MEDIAN: 0.326 - -3.4243 MAXIMUM : 1.4928 - 0.4007 MAXIMUM : 0.717 - -2.6351 MINIMUM : 0.5976 - -0.5166 MINIMUM : 0.112 - -4.4946 ST. DEV. : 0.1820 - 0.1807 ST. DEV. : 0.140 - 0.4228 SKEWNESS -0.3700 - -0.8916 SKEWNESS 0.5866 - -0.3251 KURTOSIS 2.9755 - 3.8747 KURTOSIS 2.9416 - 2.5890 JARQUE-BERA 1.5977 - 11.5066 JARQUE-BERA 4.0246 - 1.7257 PROBABILITY 0.4499 - 0.0032 PROBABILITY 0.1337 - 0.4220 Table 11: Descriptive statistics 1 - Source: Eviews.
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9.3 Appendix III: Descriptive statistics variables dataset II. EXCESS RETURNS, DP RATIO AND ITS LOG TRANSFORMATIONS.
Table 12: Descriptive statistics 2 - Source: Eviews.
The Jarque-Bera tests show a non-normal distribution within the variables of dataset 2. Normality is only an issue in small samples though. Due to the great amount of observations in the second sample, the assumption is ignored in the panel estimations. This is expected not to lead to serious consequences.
SERIES:
DEPENDENT:
EXCESS RETURN – LOG ER SERIES:
INDEPENDENT:
D/P RATIO – LOG DP
SAMPLE - HORIZON: T: [1985-2015] - 1:5 SAMPLE - HORIZON: T: [1985-2015] - 1:5
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9.4 Appendix IV: Return forecasting with the D/P variable per year over a 5-year horizon. AR(1) CONSTANT T(B) ä ã| DATASET 1 0.94 (21.24)*** 0.044 0.87 DATASET 2 0.85 (194.44)*** 0.004 0.77 Table 13: AR(1) regression on persistent DP variable DATASET 1: HORIZON K B T(B) {| PERSISTENCY DP φ 1 3.5 (2.51) *** 0.07 4.87 0.94 2 5.99 (3.58)*** 0.10 10.00 0.94 3 8.36 (2.82) *** 0.14 24.75 0.94 4 11.43 (3.35) *** 0.19 38.98 0.94 5 16.12 (6.87) *** 0.25 37.72 0.94 Table 14: Predicting future returns (t-stats at the *10%, **5%, ***1% significance level) DATASET 2: HORIZON K B T(B) {| PERSISTENCY DP φ 1 2.52 (1.97)** 0.05 3.23 0.85 2 4.42 (2.20)** 0.11 8.88 0.85 3 6.88 (2.59)*** 0.15 18.30 0.85 4 8.96 (2.99)*** 0.18 26.79 0.85 5 10.55 (3.24)*** 0.22 34.26 0.85 Table 15: Predicting future returns (t-stats at the *10%, **5%, ***1% significance level)
Provided tables are as in the text, now showing the coefficients for every year with a maximum of five years ahead. The above coefficients are in actual levels and not in a log scale. The regression equation is
K?→?6xy = Q + S (E
^/>^) + U?6x. }[F? Ky ] represents the standard deviation of the fitted value ,}(S×åçM
M). For the longer year regression t-statistics the HAC- Newey West correction is used.
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Missing data:
N x T = 3575
observations
9.5 Appendix V: Workflow panel estimation dataset 2.
Figure 4: Panel workflow
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9.6 Appendix VI: CLRM diagnostics and robustness of the research model.
In order to see if the model fits the data well I perform some diagnostic tests. These provide information about linearity in the parameters, serial correlation and normality in the residuals. When these assumptions are satisfied the OLS estimator is considered BLUE.
I test for linearity in the parameters with the RAMSEY RESET test. The null of linear correlation in the model isn’t rejected for all five years (average p-value is around 0.60) indicating OLS is an appropriate method. Furthermore, I test and conclude that the variables are stationary over-time.
1. Errors have zero mean: F è? = 0
This assumption is automatically satisfied, since my equation includes a constant.
2. Constant & finite variance. (serial correlation and the homoscedasticity assumption): êQX è? = }V To test for the presence of ARCH effects I estimate an ar(1) ma(1) OLS regression on the dependent. An ARCH heteroscedasticity test on the residuals doesn’t reject the null on the complete horizon. All five years show no presence of ARCH effects and an OLS estimation is appropriate.
3. Linearly independency between errors. (covariance between the lagged errors): ëáê è?, èí = 0
I test for autocorrelation in the residuals with the Breusch-Godfrey serial correlation LM test. The Durbin Watson test is biased since I use a lagged endogenous variable in my model. After I use HAC-Newey West’s adjusted standards errors in my model, all years produce an insignificant statistic showing no autocorrelation.
4. Independency between the error term and X: ëáê è?, t? = 0
This assumption is satisfied, since the model has no omitted variables, measurement error or reverse causality. The parameter estimates are thus consistent and unbiased.
5. Normally distributed errors: è? = f(0, }V)
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ROBUSTNESS TEST:
To see if the OLS estimation is affected significantly by outliers, a robust regression is run trying to protect against this by giving less weight to such cases (not by excluding them). I confirmed the data’s outlier by looking at the influence statistics and leverage. Then I re-estimated the regression using robust maximum-likelihood estimation. The bisquare function with a default tuning parameter value of 4.685 is used. The Huber type 1 standard errors & covariance estimates are calculated and used as input for the z-statistics. The scale is estimated using the median centered method.
When we turn to the coefficient estimates, we notice that the impact is almost the same and the results aren’t different. The effect of moving from OLS to robust M-estimation is small. Estimates aren’t different, meaning that outliers have no influence on the OLS results, and we can rely on this method.
PANEL ESTIMATION:
When I estimate the model8 by pooled OLS (assuming all intercepts are the same for all entities and for
each year) the beta coefficient is negative (b=-0.59), explaining virtually nothing of the model’s variance (R^2=0.001).
Re-estimating using cross section fixed effects (allowing for individual differences between the cross sections) gives a beta coefficient of 2.52 for the first year. I run a redundant fixed effect (likelihood) test, which is significant, indicating fixed effects are preferred over a pooled OLS estimation.
I also re-estimate the model using random effects (allowing different intercepts for each entity & constant over time). To see which effects are preferred I carried out a Haussmann test to see if the random effects assumptions are satisfied or biased. This test is significant, indicating the random effects model isn’t appropriate and the fixed effects are preferred9.
