Anon

200 The Basics of financial economeTrics

is determined by the present value (discounted value) of its expected future
dividend stream. This model may be represented as:

P 0 = ∑Di /(1+r) (10.7)

where P 0 = the current stock price
Di = a dividend in period i
r = the discount rate

If the discount rate exceeds the growth rate of dividends and the dis-
count rate remains constant over time, then one can test for cointegration
between stock prices and dividends. In brief, if the present value relation-
ship as given by equation (10.7) holds, one does not expect stock prices and
dividends to meander arbitrarily far from each other.
Before starting any analysis, it is useful to examine the plot of the underlying
time series variables. Figure 10.1 presents a plot of stock prices and dividends
for the years 1962 through 2006. Stock prices are represented by the S&P 500
index and the dividends represent the dividend received by the owner of $1,000
worth of the S&P 500 index. The plot shows that the variables move together
until the early 1980s. As a result of this visual analysis, we will entertain the
possibility that the variables were cointegrated until the 1980s. After that, the
common stochastic trend may have dissipated. We will first test for cointegra-
tion in the 1962–1982 period and then for the whole 1962–2006 period.

Figure 10.1 S&P 500 Index and Dividends 1962–2006
Note: Dividends are multiplied by 10 for a scale effect.

1,600

1,400

1,200

1,000

800

600

400

200

0

1965 1970 1975 1980 1985 1990 1995 2000 2005

Dividend

S&P 500

S&P 500 Index