204 The Basics of financial economeTrics
cointegration is rejected at the 10% level of statistical significance. For the
entire period (1962–2006), the null hypothesis (p = 0) of no cointegration
cannot be rejected. Apparently, the relationship between stock prices and
dividends unraveled in the 1980s and the 1990s. This evidence is consistent
with the existence of an Internet stock bubble in the 1990s.
Having established that the S&P 500 index and dividends are cointe-
grated from 1962–1982, the interaction between stock prices and dividends
in the final step (Step 4) of the Engle-Granger cointegration test is exam-
ined by estimating the error-correction model given by equations (10.5)
and (10.6). It is useful at this point to review our interpretation of equa-
tions (10.5) and (10.6). Equation (10.5) claims that changes in the S&P 500
index depend upon past changes in the S&P 500 index and past changes in
dividends and the extent of disequilibrium between the S&P 500 index and
dividends. Equation (10.6) has a similar statistical interpretation. However,
from a theoretical point of view, equation (10.6) is meaningless. Financial
theory does not claim that changes in dividends are impacted either by past
changes in stock prices or the extent of the disequilibrium between stock
prices and dividends. As such, equation (10.6) degenerates into an autore-
gressive model of dividends.
We estimated the error-correction equations using three lags. The error
term, zt− 1 , used in these error-correction regressions was obtained from OLS
estimation of the cointegration equation reported in Table 10.3. Estimates of
the error-correction equations are reported in Table 10.5. By construction,
the error-correction term represents the degree to which the stock prices
table 10.5 Error Correction Model: S&P 500 Index and Dividends, 1962− 1982
Equation (10.5) Equation (10.6)
Coefficient t-Stat Coefficient t-Statb 01 −0.009 −2.42 b 20 0.001 2.91
b 11 0.251 4.00 b 21 0.002 0.63
b 12 −0.043 −0.66 b 22 −0.003 −0.88
b 13 0.081 1.27 b 23 0.004 1.07
c 11 0.130 0.11 c 21 0.939 14.60
c 12 −0.737 −0.46 c 22 −0.005 −0.06
c 13 −0.78 −0.65 c 23 −0.006 0.87
d 1 −0.07 −3.64 d 2 0.000 0.30
The change in the S&P 500 index is denoted as ΔYt and the change in dividends is
denoted as ΔXt.