Posted by Kathryn Schwartz on June 15, 2014

A Probit model for share ownership

We obtain the probabilities of share ownership by estimating a problt model on a pooled sample of data containing more than 80,000 households. On the right hand side we include polynomials in age and time, education dummies and interaction terms in these variables. It is important to stress that the time trends are interacted with the other explanatory variables, to allow for the fact that the effects of factors such as age and education appear to change over time. The results (reported in Table 3) show that the probability of share ownership increases with age, time and higher levels of education -although the positive effects of college education and A levels on share ownership diminishes over time. We have obtained very similar results by estimating a different probit for each year in the sample.

Table 3 Results of probit estimation

Parameter Standard error Marginal effect
Age of head 0.281 0.022 0.055
(Age of head)2 -0.021 0.006 -0.004
Head has A levels 0.697 0.031 0.160
College education 1.198 0.039 0.349
Age*Alevels 0.082 0.013 0.016
Age* College 0.117 0.016 0.023
Trend 3.522 0.875 0.687
Trend2 -31.553 5.060 -6.158
Trend3 104.932 12.181 20.479
Trend4 -127.493 12.888 -24.882
Trend5 51.629 4.960 10.076
Age*Trend -0.212 0.083 -0.042
Age*Trend2 -0.365 0.047 -0.071
Alevels*Trend -0.634 0.058 -0.124
College*Trend 0.122 0.076 0.024
Constant -2.022 0.051
N 83,736
Pseudo-R2 0.1203

Results on ‘predicted shareholders’

Defining groups of shareholders and non-shareholders on the basis of their predicted probabilities of share ownership, we compare the time series properties of their consumption growth rates.15 We remove both durable spending and housing costs from the measure of total weekly expenditure in the FES. Since we look at the growth of consumption between quarters, we take out seasonal effects and also adjust for household size using equivalence scales estimated from FES data (see Banks and Johnson, 1994). On average, the predicted shareholders have higher consumption growth over the period than non-shareowners — 0.26 per cent per quarter for shareholders compared to 0.04 for non-shareholders. The standard deviation of the time-series of average consumption growth (adjusted to take account of the variance of within-cell measurement error) is one and half times as high — 3.7 for shareholders compared to 2.5 for non-shareholders.16 This suggests that differences between shareowners and non-shareowners are likely to be important in resolving the equity premium puzzle. But, resolving the puzzle requires not only the variance of consumption growth of shareholders to be larger than that of non-shareholders, but also a higher correlation of the IMRS of shareholders with the excess returns on shares. More generally, one can use any of the techniques discussed in section

Tags: , ,