Anon

146 The Basics of financial economeTrics

the entire distribution of the data. Hence, it might be useful to estimate the
relationship over the entire return distribution.

Quantile Regression Process

The advantage of a quantile regression is that we can see how the returns
respond to the expected dividend yield over different return quantiles. The
process of estimating more than a quantile at a time is defined as a quantile
process. The results of the quantile process between the S&P 500 index
returns over the prior 12 months and the expected dividend yield are pre-
sented in Table 7.1.

tabLe 7.1 Quantile Regressions, Sample from January 1926 through December 2012

Quantile Coefficient Std. Error t-Statistic

Constant 0.100 −23.04 2.26 −10.1

0.200 −19.84 2.81 −7.05

0.300 −12.20 3.34 −3.65

0.400 −5.22 2.35 −2.21

0.500 −0.93 1.74 −0.53

0.600 1.28 1.61 0.79

0.700 4.31 1.99 2.15

0.800 6.19 1.84 3.35

0.900 10.62 2.19 4.84

Dividend Yield 0.100 3.94 4.83 0.81

0.200 17.35 6.12 2.83

0.300 14.47 6.53 2.21

0.400 12.69 4.73 2.68

0.500 14.38 3.60 3.99

0.600 16.98 3.49 4.85

0.700 22.64 4.80 4.71

0.800 32.02 4.19 7.63

0.900 37.14 4.91 7.55

Note: α is the constant for each quantile, β is the slope coefficient of the dividend yield
for each quantile, yi is the S&P 500 stock index returns over the prior 12 months,
and Xi is the expected dividend yield.