Now, the equation (18) can be written as equation (19): G pt + H dt = Vt, where G = -(r*cS-1 + A-1B), H = (cS-1+A-1), pt = Pt - Pt-1 and dt = Et
D
t+1 - Et-1D
t+1,which can be forecasted and calculated from the past observations of earnings and dividend by the adaptive expectation model established in previous part.
Recall the analysis in Section B showing that if the structure form of the simultaneous equation system represented as equation (19) is exactly identified, then, if the matrix G is also assumed to be nonsingular, this system can be estimated by the reduced form described as (20): pt = Π dt + Ut, where Π = -G-1H, a n×n matrix of the reduced form coefficients and Ut = G-1Vt, a column vector of n reduced form disturbances. Without a prior knowledge of the system, all
equations of the model would look statistically similar in which each equation is a linear combination of all endogenous (pt) variables and all exogenous variables (dt). No equation contains any single variable which does not appear in any other equation.
The identification problem is proved in Appendix B. That is, there is one-to-one correspondence between structure parameters and reduced form parameters. One question is still remains, how can one assure that and dt is exogenous in this model, or, in other words, dt is not influenced by pt?
Again, the relationship between pt
and d
t for every individual country needs to be checked by, again, Granger-causality test. In international equity market, the results are summarized in Table A.7.9 The assumption that the index series in first order difference, pt, are endogenous variables and the series of expectation adjustments in dividend, dt, are exogenous variables seem to be evidenced for world index and most countries. Especially, if index and dividend are measured in U.S. dollars, the causality relationship is even weaker. For further analysis, the price of value-weighted portfolio, pt, or the country indices series here, will be treated as endogenous. In contrast, the series of expectation adjustments in dividend (dt) will be treated as an exogenous variable.In the U.S. stock markets, the relationship between pt
and d
t for every portfolio is checked by Granger-causality test. The results are summarized in Table A.8. The assumption that pt is endogenous and the series of expectation adjustments in dividend, dt, is exogenous variable seems to be evidenced for market portfolio and most of the individual portfolios, except portfolio 5 and 8 if 4 period-lag are chosen. Therefore, treating the adjustment in price series, pt, as endogenous seems reasonable. In contrast, dt will be treated as exogenous variable in the later analysis.
9 Table 5.10-1 shows the similar results, if the MSCI country indices are used.
Table A.1
Unit root tests for PtPt ＝ µ ＋ γ Pt-1 ＋εt Unit root test (ADF) Estimated c2
(Std. Error) R2 Level 1st Difference World Index 0.9884 (0.0098), 0.9820 0.63 -13.74**
W.I. ex. U.S. 0.9688 (0.0174) 0.9434 0.13 -14.03**
Argentina 0.9643 (0.0177) 0.9411 -0.70 -13.08**
Brazil 0.9738 (0.0160) 0.9520 -0.65 -12.49**
Canada 0.9816 (0.0156) 0.9550 -0.69 -11.80**
France 0.9815 (0.0121) 0.9725 0.34 -14.06**
Germany 0.9829 (0.0119) 0.9736 0.12 -14.53**
Hong Kong 0.9754 (0.0146) 0.9599 -1.68 -13.87**
Italy 0.9824 (0.0136) 0.9656 0.24 -15.42**
Japan 0.9711 (0.0185) 0.9368 -1.02 -14.32**
Malaysia 0.9757 (0.0145) 0.9603 -0.64 -7.01**
Mexico 0.9749 (0.0159) 0.9531 -0.26 -13.39**
Singapore 0.9625 (0.0173) 0.9432 0.02 -14.08**
S. Korea 0.9735 (0.0170) 0.9463 -0.67 -12.61**
Taiwan 0.9295 (0.0263) 0.8706 -0.54 -12.49**
Thailand 0.9854 (0.0124) 0.9715 -0.49 -12.79**
U.K. 0.9875 (0.0094) 0.9835 0.53 -13.76**
U.S. 0.9925 (0.0076) 0.9892 0.82 -14.10**
* 5% significant level; ** 1% significant level
Table A.2
Unit root tests for PtPt ＝ µ ＋ γ Pt-1 ＋εt Phillips-Perron test Estimated c2
(Std. Error) Adj. R2 Level 1st Difference Market portfolio 1.0060 (0.0159) 0.9788 -0.52 -8.48**
S&P500 0.9864 (0.0164) 0.9769 -0.90 -959**
Portfolio 1 0.9883 (0.0172) 0.9746 -0.56 -8.67**
Portfolio 2 0.9877 (0.0146) 0.9815 -0.97 -9.42**
Portfolio 3 0.9913 (0.0149) 0.9809 -0.51 -13.90**
Portfolio 4 0.9935 (0.0143) 0.9825 -0.61 -7.66**
Portfolio 5 0.9933 (0.0158) 0.9787 -0.43 -9.34**
Portfolio 6 0.9950 (0.0150) 0.9808 -0.32 -8.66**
Portfolio 7 0.9892 (0.0155) 0.9793 -0.64 -9.08**
Portfolio 8 0.9879 (0.0166) 0.9762 -0.74 -9.37**
Portfolio 9 0.9939 (0.0116) 0.9884 -0.74 -7.04**
Portfolio 10 0.9889 (0.0182) 0.9716 -0.69 -9.07**
Note:
1. * 5% significant level; ** 1% significant level 2. The process assumed to be random walk without drift.
3. The null hypothesis of zero intercept terms, µ, can not be rejected at 5%, 1% level for all portfolio.
Table A.3
Pair-wise Granger Causality Tests for price, dividend and earning World index
Pairwise Granger Causality Tests (Lags: 12)
Null Hypothesis: F-Statistic Probability Dividend does not Granger Cause price 1.35092 0.19477 Price does not Granger Cause Dividend 0.69352 0.75618 Earning does not Granger Cause Price 1.33565 0.20311 Price does not Granger Cause Earning 1.47867 0.13700 Earning does not Granger Cause Dividend 2.03228 0.02452*
Dividend does not Granger Cause Earning 1.69183 0.07290 * 5% significant level, ** 1% significant level
(Lags: 4)
Null Hypothesis: F-Statistic Probability Dividend does not Granger Cause price 0.93018 0.44761 Price does not Granger Cause Dividend 0.34339 0.84838 Earning does not Granger Cause Price 1.69242 0.15356 Price does not Granger Cause Earning 0.19778 0.93929 Earning does not Granger Cause Dividend 4.43140 0.00192**
Dividend does not Granger Cause Earning 3.02656 0.01900*
* 5% significant level, ** 1% significant level
Note: the Granger-causality tests are estimated though the equation:
ly respective T
u x n y
m
y T t
j j t j T
i
i t i
t =
∑
− +∑
− + , =4,12Table A.4
Pair-wise Granger Causality Tests for price, dividend and earning Market portfolio
(Lags: 1)
Null Hypothesis: F-Statistic Probability Dividend does not Granger Cause price 0.03196 0.85855 Price does not Granger Cause Dividend 2.92599 0.09085 Earning does not Granger Cause Price 9.05601 0.00346**
Price does not Granger Cause Earning 4.01856 0.04822*
Earning does not Granger Cause Dividend 6.96700 0.00990**
Dividend does not Granger Cause Earning 5.32593 0.02347*
(Lags:2) Null Hypothesis: F-Statistic Probability
Dividend does not Granger Cause price 1.61040 0.20614 Price does not Granger Cause Dividend 1.50288 0.22863 Earning does not Granger Cause Price 9.08435 0.00028**
Price does not Granger Cause Earning 3.01529 0.05457 Earning does not Granger Cause Dividend 2.08141 0.13138 Dividend does not Granger Cause Earning 3.53847 0.03363*
(Lags:4) Null Hypothesis: F-Statistic Probability
Dividend does not Granger Cause price 0.95676 0.43633 Price does not Granger Cause Dividend 2.14044 0.08406 Earning does not Granger Cause Price 8.11535 1.7E-05**
Price does not Granger Cause Earning 5.22449 0.00091**
Earning does not Granger Cause Dividend 2.76083 0.03367*
Dividend does not Granger Cause Earning 7.64023 3.2E-05**
* 5% significant level, ** 1% significant level
Note: the Granger-causality tests are estimated though the equation:
ly respective T
u x n y
m
y
T tj j t j
T
i i t i
t =
∑
− +∑
− + , =1,2,4Table A.5
Dividends Behavior Models (Market Portfolio: World Index)
Dependent
1. Numbers in () are standard deviations, in [ ] are the t-value.
2. * denotes significant at 5% level, ** denotes significant at 1% level.
Partial adjustment model:
Dt−Dt−1=a+rγEt −γDt−1+ut. Adaptive expectation model:
Dt−Dt−1=rδEt−δDt−1+ut−(1−δ)ut−1
Model modified from Campbell, Grossman and Wang (1993):
Dt−Dt−1=(αD−1)(Dt−1−D)+rEt−1+uD,t. Generalized model:
Dt−Dt−1=c0+c1t+c2Dt−1+c3Dt−2+c4Et+c5Et−1+ut.
Table A.6
Dividends Behavior Models (Market Portfolio)
Dependent
1. Numbers in () are standard deviations, in [ ] are the t-value.
2. * denotes significant at 5% level, ** denotes significant at 1% level.
Partial adjustment model:
Dt−Dt−1=a+rγEt−γDt−1+ut. Adaptive expectation model:
Dt−Dt−1=rδEt−δDt−1+ut−(1−δ)ut−1
Model modified from Campbell, Grossman and Wang (1993):
Dt−Dt−1=(αD−1)(Dt−1−D)+rEt−1+uD,t. Generalized model:
Dt−Dt−1=c0+c1t+c2Dt−1+c3Dt−2+c4Et+c5Et−1+ut.
Table A.7
Granger Causality Tests for pt and dt
p Î d d Î p
World Index 0.96 1.16
W.I. excl. U.S. 1.14 1.55
Individual Index
p Î d d Î p p Î d
(in U.S. Dollar) d Î p (in $ Dollar)
Canada 2.01* 1.01 1.06 1.37
France 2.63** 1.99* 1.40 1.73
Italy 4.98** 1.16 3.87** 1.06
Japan 2.14* 0.99 1.44 0.54
Germany 2.95** 2.76** 2.94** 2.46**
U.K. 2.11* 1.55 0.95 0.84
U.S. 4.99** 2.44** 4.99** 2.44**
Argentina 1.63 1.44 1.35 0.42
Brazil 11.97** 13.95** 1.66 2.41*
Hong Kong 1.69 2.16* 1.69 2.17*
Malaysia 0.90 0.69 1.14 0.42
Mexico 2.11* 2.60** 1.57 1.24
Singapore 1.57 1.70 1.57 1.89*
S. Korea 1.55 1.23 1.60 1.56
Taiwan 0.75 1.14 1.00 1.20
Thailand 1.48 0.69 2.15* 0.61
Note: 1. * 5% significant level; ** 1% significant level 2. The numbers shown are F-statistics
3. pt = Pt－Pt-1, dt = Et Dt+1－Et-1 Dt+1
4. The test results of using MSCI data are reported in Table 4’. Most indices show the similar pattern.
Table A.8
Granger Causality Tests for ptand dt
Lag = 4 Lag = 2
p Î d d Î p p Î d d Î p
Market portfolio 1.55 1.84 3.05 0.37
S&P500 2.10 1.71 2.38 0.26
Individual Portfolio
Lag = 4 Lag = 2
p Î d d Î p p Î d d Î p
Portfolio 1 1.82 1.62 1.86 1.65
Portfolio 2 0.81 1.42 0.31 0.85
Portfolio 3 1.16 1.10 4.77* 2.08
Portfolio 4 3.31* 5.98** 5.59** 5.05**
Portfolio 5 3.83** 2.09 2.58 1.05
Portfolio 6 0.09 1.59 0.17 0.95
Portfolio 7 0.40 1.28 0.36 0.28
Portfolio 8 1.93 0.57 1.34 1.92
Portfolio 9 4.76** 3.58* 3.51* 4.80**
Portfolio 10 3.56* 0.29 1.11 0.19
Note:
1. * 5% significant level; ** 1% significant level 2. The numbers shown are F-statistics
3. pt = Pt－Pt-1, dt = Et Dt+1－Et-1 Dt+1