Page 78 - Contributed Paper Session (CPS) - Volume 3

CPS1947 Hsein K. et al.
appear to be cointegrated. As mentioned in the introduction, the use of the
first pair to predict equity premium is motivated by a casual glance at Figure
1 of Campbell and Yogo (2006), who show that dp and ep could cointegrate.
Fama and French (1989) use the term spread (defined as tbl minus lty) and the
default spread (defined as baa minus aaa) to predict the equity premium and
under the assumption that these spreads are stationary, their work implies
cointegrating relationships between tbl and lty and between baa and aaa.
Preliminary Augmented Dickey-Fuller (ADF) test indicates that every
variable has a unit root and the Engle-Granger ADF test suggests the existence
of cointegration in each of the four pairs. These tests provide statistical
evidence supporting the impressions of cointegrating relationships from
visually inspecting Figure 1. We then proceed to test the hypothesis that the
US equity premium is predictable using cointegrated predictors. By applying
Hermite polynomial expansion, we can re-write single index model as

−1
= ( −1 ) + ℯ ≈ ∑ −1 + ℯ

=0

T
where −1 = −1 and the truncation parameter k determined by the
0
Generalised Cross Validation method (see Gao, Tong and Wolff (2002)). Under
the null hypothesis of no predictability, = = ⋯ = = 0 and so the
2
1

model reduces to the constant expected equity premium model. Given that
~ (0), the no predictability null hypothsis can be tested using the

heteroscedasticity robust F-statistic. The OLS coefficient estimates and their
White standard errors can be obtained in the standard way from a multiple
regression of on the lagged of .

For each pair of variables, we estimate the single index predictive model
and report in Table 1 the least squares estimates of the coefficients, the results
of the F-tests under the null hypothesis of no predictability and the adjusted
statistic for each pair. Numbers in parentheses below the coefficients are t-
2
ratios (based on White standard errors) and below the F-tests are p-values.
Panel A reports the results for the whole sample period 1927-2017. Following
Kostakis, Magdalinos and Stamatogiannis (2015), we also consider the post-
1952 period because the interest rate variables are expected to be linked
together after the Federal Reserve abandoned the interest rate pegging policy
in 1951. Moreover, Kostakis, Magdalinos and Stamatogiannis (2015) and
Campbell and Yogo (2006) report weak or no evidence of stock return
predictability in the post-1952 period. Our results for this subperiod are
reported in Panel B.
Figure 1: Time series plots of cointegrated predictors

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