1、 外文翻译 原文 Corporate Valuation and Dividends: UK Evidence from Panel Unit Root and Cointegration Test Material Source： International Atlantic Economic Society 2009 Author： Andros Gregoriou Abstract: In this study we investigate the long run relationship between dividends and corporate valuation with t
2、he use of panel unit root tests and panel cointegration analysis. The long run relationship is estimated using fully modified OLS for a panel consisting of 479 firms listed on the London Stock Exchange over the time period 19842007. The empirical results provide clear support for the hypothesis that
3、 there is a single equilibrium relation between market value, book value, earnings and dividends, and that dividends have a positive impact on corporate valuation. Keywords: Accounting-based valuation. Dividends. Panel unit roots. Panel Cointegration Introduction The empirical relationship between d
4、ividends and market value in the corporate valuation model developed by Ohlson (1989) has been at the forefront of accounting research over the last decade. Rees (1997) and Akbar and Stark (2003) discover that dividends have a positive influence on corporate valuation in the UK. Giner and Rees (1999
5、) repeat the Rees (1997) and Akbar and Stark (2003) results for the USA and Spain respectively. The positive impact of dividends on company valuation could be attributed to the fact that they signal managers private information about future profitability (Rees 1997; Akbar and Stark 2003), and becaus
6、e they are a proxy for investors mispricing of current earnings or book value (Hand and Landsman 2005). The typical econometric approach for the studies mentioned above is to use a sample of observations taken for many companies over several time periods, with estimation being based on OLS pooled te
7、chniques (where all the years are assumed identical). An implicit assumption made in this methodology is that the explanatory variables in the corporate valuation model follow a stationary process. It is well established that the use of OLS regression to analyse a non stationary series can lead to s
8、erious problems for inferential statistics. This is because the residual term generated from the regression is serially correlated through time. The violation of the assumption that residual terms are independent and uncorrelated typically leads to an underestimated residual variance and an underest
9、imated standard error of the regression coefficient on earnings. This results in biased regression coefficients, and unreliable significance tests for parameter estimations since the t statistics generated from the regression do not follow the standard t distribution. It is in this sense that econom
10、etricians call models based on non stationary time series “spurious regression” (see among others, Engle and Granger 1987; Ioannidis et al. 2003). In this study we establish that the most typically used explanatory variables in the Ohlson (1989) company valuation model which are the book value, earn
11、ings and dividends all following non stationary, I(1) integrated processes. This suggests that the statistical inferences based on the association of dividends and company valuation used in the previous literature may be spurious. Therefore, in order to provide valid econometric relationships betwee
12、n dividends and corporate valuation we employ cointegration analysis, which provides appropriate test statistics in the presence of I (1) variables. More specifically the paper makes the follow contributions to the existing literature. First, we use panel unit root tests to examine the stationary pr
13、operties of the data. The use of panel based tests is necessary because the power of time series unit root tests will be low given the short time span available in annual company valuation data. Second, panel cointegration tests are conducted because the multivariate cointegration time series analys
14、is of Johansen (1988) suffers from power loss due to finite samples. Finally, cointegrating vectors are estimated using the fully modified (FM) OLS estimation technique for heterogeneous cointegrated panels developed by Pedroni (2000). This methodology allows consistent and efficient estimation of c
15、ointegrating vectors. In addition, it deals with the possible endogeneity problem of the explanatory variables and it respects the time-series properties of the data in that integration and cointegration properties are explicitly taken into account. The remainder of the paper is organized in the fol
16、lowing way. In the following section, we present the corporate valuation model and the econometric techniques used in the study. We then proceed with a description of the data. The results are discussed in the empirical results section. The final section concludes our findings. The Model and Econome
17、tric Techniques Following Rees (1997) and Akbar and Stark (2003) we investigate the relationship between dividends and corporate valuation in the Ohlson (1989) company valuation model, with the use of the following linear econometric specification. 0 1 2 3i t i t i t i t i tM V V E D (1) Where MVit
18、represents market value for company i at time period t, BVit represents the book value for company i at time period t, Eit represents earnings plus research and development expenditures for company i at time period t, Dit represents dividends for company i at time period t and uit is an error term.1
19、1 Equation (1) is considered as a long run relation. Assuming that all the variables involved are I(1) valid economic inferences can be drawn only if these relations are cointegrating relations, otherwise spurious inferences would result. Testing for Integration In order to evaluate a possible long
20、run relationship we need to verify that all the variables are integrated of order one in levels. However, since the power of individual unit root tests can be weak when the span of the data is short (see among others, Pierse and Shell 1995), we have employed a panel unit root test established by Mad
21、dala and Wu (1999), denoted as the MW statistic. The MW statistic is given by 2 1NP Inpii and combines the p-values from the individual Augmented Dickey-Fuller (ADF) tests. The P test follows a 2 distribution with degrees of freedom twice the number of cross-section units, i.e. 2 N under the null hy
22、pothesis of non stationarity.2 Cointegration Testing 1 For more details on the development of Eq. (1) see Akbar and Stark (2003) page 1213. 2 An alternative panel unit root test was developed by Im et al (2003) which involves the averaging of individual ADF unit root tests. We have not computed this
23、 test for the following two reasons. First, Breitung (1999) finds that the Im et al (2003) test suffers from a dramatic loss of power when individual trends are included. Second, the MW test has the advantage over the Im et al (2003) test given that its value does not depend on different lag lengths
24、 in the individual ADF tests. The next step is to test for the existence of a long run relationship between market value, book value, earnings and dividends. However, as previously mentioned the multivariate Johansen test in time series framework can be severely distorted when sample sizes are relat
25、ively small. For this reason, we conduct the following three panel cointegration tests: First, we compute the Levin and Lin (1993) test by considering the following model: ,1 it i i t it ity y z r u (2) Where zit are deterministic variables, uit is an error term with a mean of zero and a variance of
26、 2 and i = . The test statistic is a t statistic on given by 11( 1 ) , 1NT iiteytt s (3) where 1 ( , )Tit isit sy y h t s y 11( , ) , ( , ) ( )TTitit is t t t sstu u h t s u h t s z z z z 22111()NT ite its NT u and is the OLS estimate of . It can be shown that if there are only fixed effects in the
27、model, then 51( 1 ) 3 ( 0 , )5N T N N and if there are fixed and time effects 2895( ( 1 ) 7 . 5 ) ( 0 , )112N T N Second, we use the panel cointegration tests for Eq. (2) by Harris and Tzavalis (1999). If there are only fixed effects in the model, then 233 3 ( 17 20 17 )( 1 ) ( 0 , )1 5 ( 1 ) ( 1 )T
28、TNNT T T If there are fixed and time effects, then 2315 15 ( 19 3 72 8 11 47 )( 1 ) ( 0 , )2( 2) 11 2( 2) ( 2)TTNNT T T Unfortunately, both the Levin and Lin (1993) and the Harris and Tzavalis (1999) test have limitations. As pointed out by OConnell (1998) the Levin and Lin (1993) test can suffer fr
29、om substantial size distortions if there is cross-sectional dependence. Also, the Harris and Tzavalis (1999) test when T is small results in Levin and Lin (1993) tests that are substantially undersized and have low power. A limitation of both tests is that they do not allow for heterogeneity in the
30、autoregressive coefficient, . Finally, in order to combat the heterogeneity problem that arises in both tests we use Fishers test to aggregate the p-values of individual Johansen maximum likelihood cointegration test statistics, see Maddala and Kim (1998, page 137). If i denotes the p-value of the J
31、ohansen statistic for the ith unit, then we obtain the result 2212 log NiNi px This test does not assume homogeneity of coefficients in different countries. Corporate Valuation and Dividends Table 1 Panel unit root tests Variables MW Levels MW First Difference MW First Differences Market Value (MV)
32、12.32 Book Value (BV) 16.21 Earnings (E) 15.43 Dividends (D) 18.21 MW is the Maddala and Wu (1999) panel unit root test. The critical value of the MW test is 37.57 at the 1% level. a Signifies rejection of the null hypothesis of non stationarity at the 1% level. Estimating the Long Run Relationship
33、Having established that market value is related to the explanatory variables, we proceed to estimate the long run relationship portrayed in Eq. (1) by the Pedroni (2000) fully modified OLS heterogeneous cointegrated panel methodology. This methodology addresses the problem of non-stationary regresso
34、rs, as well as the possible problem of simultaneity bias.3 We consider the following cointegrated system for panel data. it i it ity x u (4) 3 OLS estimation of the long run relationship would be biased if the explanatory variables are endogenously determined in the I(1) case. 62.35a69.32a72.32a58.2
35、1a,1it i t itx x e (5) Where , it it itue is stationary with covariance matrix i.Pedroni (2000) applies a semi-parametric correction to the OLS estimator that eliminates second order bias caused by the endogeneity of the regressors in the panel. Essentially, he allows for heterogeneity in the short
36、run dynamics and in the fixed effects of the panel. More specifically, the Pedroni (2000) estimator is: 2 22211 ( ) NTi tFM itit xx 11 *1 1 2 211 ( ) NTi i itit itx x u T r （ 6） 1* 22 21iiit ituu 0 1 02 1 2 1 2 2 2 1 2 2 2 2()i i i i i i ir （ 7） Table 2 Panel cointegration tests Test Statistic Levin
37、-Lin (Fixed Effects Only) 5.88* Levin-Lin (Fixed and Time Effects) 6.05* Harris-Tzavalis (Fixed Effects Only) 9.88* Harris-Tzavalis (Fixed and Time Effects) 8.27* Fisher Test (r=0) 60.21* Fisher Test (r1) 19.12 The critical values of the Levin and Lin and Harris and Tzavalis tests are 2.40 and 2.72
38、at the 1% level, respectively. The critical value for Fishers 2x est is 37.57 at the 1% level. Fishers test is based on pvalues from Johanses likelihood cointegration methodology, therefore it applies regardless of the dependant variable. Where the covariance matrix can be decomposed as 0i i i i whe
39、re 0i is the contemporaneous covariance matrix, and i is a weighted sum of covariances. Data Definition and Collection Following Akbar and Stark (2003) data are collected for all the UK companies listed on the London Stock Exchange (LSE) for the financial years ending in calendar years 1984 to 2007.
40、 Variables are constructed using data from Datastream Advanced in the following ways: Market Value for a firm for a given calendar year is measured six months after the balance sheet date. The market value six months after the balance sheet date is used to ensure that the information in the financia
41、l statements for a given financial year is reflected in the market price, bearing in mind that UK listed firms have six months in which to prepare and release their annual accounts. Book Value is measured as the sum of contributed shareholders capital reserves; Earnings are measured as the bottom li
42、ne earnings figure, as reported in the financial statements (Datastream Advanced item WC01551); Dividends are measured as dividends declared (Datastream Advanced item WC18192); Number of shares equals the number of shares outstanding at the end of the financial year. In total, data were collected fo
43、r 479 companies, with 23 annual observations for each company. Due to the heteroscedasticity present in the residuals of Eq. (1) because of the possibility of omitted variable bias (Akbar and Stark 2003) the variables in Eq. (1) are typically deflated in empirical work. In this study, we deflate ear
44、nings by the number of shares to be consistent with Rees (1997) and Akbar and Stark (2003).4 Table 3 Fully modified OLS estimates (dependant variable is market value, MV) Figures in brackets are t statistics and (a ) indicates statistical significance at the 1% level. Empirical Results Panel unit ro
45、ot tests constructed using the MW test statistic are reported in Table 1. The findings support the hypothesis of a unit root in all variables across companies, as well as the hypothesis of stationarity in first differences suggesting that all variables follow an I(1) integrated process. Panel cointe
46、gration tests are reported in Table 2. Fisher s test supports the presence of one cointegrating vector. The Harris and Tzavalis test provides evidence of a cointegrating relation. Finally, the Levin and Lin test with fixed and time effects supports the hypothesis of a cointegrating relation. Therefore, all panel based econometric tests agree there is a single cointegrating vector. Fully modified OLS estimates of the panel cointegrating relationship are 4 Akbar and Stark (2003) also implemented sales, opening market value and closing book value as alternative deflators. T
