Yet not all restrictions on the dependent variable can be handled so easily. If
we model individual choice, the optimal behavior of individuals often results in
a sizable fraction of the population at a corner solution. For example, a sizable
fraction of working age adults do not work outside the home, so the distribution of
hours worked has a sizable pile up at zero. If we
t a linear conditional mean, we
will likely predict negative hours worked for some individuals. The log transform
used for wages will not work, as the log of zero is unde
ned. Another issues
arises with sample selection. It may well be the case that E (Y jX) is linear, but
nonrandom sampling requires more detailed inference. Finally, a host of other
data issues may arise: linear conditional mean functions that switch over regimes,
data recorded as counts or analysis of durations between events. As we will see,
even if only a
nite number of values are possible, a linear model for E (Y jX) may
still be appropriate.