What's this about?
Hurdle models concern bounded outcomes. For instance, how much someone spends
at the movies is bounded by zero. In this sense, hurdle models are much
like tobit models. They differ in that hurdle models provide separate
equations for the bounded and the unbounded outcomes, whereas tobit
models use the same equation for both. Hurdle models assume the
unbounded outcomes are the result of clearing a hurdle. When the
hurdle is not cleared, bounded outcomes result.
Hurdle models come in two- and three-equation forms.
The two-equation form handles lower or upper bounding. The first equation
determines whether you clear the hurdle, and the second determines the value of
the outcome conditional on having cleared the hurdle.
The three-equation form handles lower and upper bounding. It adds
another equation for clearing the second hurdle, and the middle
equation is reinterpreted as determining the value conditional on
having cleared both hurdles.
As an example, consider movie attendance or exercise. One equation
determines whether you go to the movies (gym). Another equation
determines how much you spent on the movies (exercising).
The Chilean health system categorizes people by age group and
requires the purchase of health insurance. You can purchase the minimum. You
can purchase the maximum. Or you can buy anywhere in between.
Hurdle models assume that the residuals of the hurdle equation(s) and
the outcome equation are uncorrelated. For this assumption to be
plausible, you typically must assume that it is different people
who align themselves among the possible alternatives.
In the Chilean health system, for instance, individuals who
buy the minimum (maximum) are different from those who purchase an
Hurdle models are especially popular in health applications where
the different-person analogy is reasonable.
Let's see it work
We wish to model movie attendance. People first decide whether they
will go to the movies at all—some people simply have no
interest. Of those who have an interest, they then decide how much to
spend per month on movies.
We will model attendance using number of hours worked, an indicator for
working during weekends, and whether they have a newborn.
We will model amount spent per month using teenager, in a romantic
relationship, and the number of children 6–10 (old enough to go
to the movies but only with supervision).
We will model the hurdle as probit and the amount spent as a linear
. churdle linear money dating teenager nkids, select(newborn hours weekends) ll(0)
Cragg hurdle regression Number of obs = 10,000
LR chi2(3) = 8775.37
Prob > chi2 = 0.0000
Log likelihood = -20230.563 Pseudo R2 = 0.2408
| money || Coef. Std. Err. z P>|z| [95% Conf. Interval]|
| dating || 15.07349 .2602275 57.92 0.000 14.56345 15.58353|
| teenager || 3.055787 .1502961 20.33 0.000 2.761212 3.350362|
| nkids || 14.9045 .1299277 114.71 0.000 14.64984 15.15915|
| _cons || 14.98066 .045653 328.14 0.000 14.89118 15.07014|
| newborn || -.1832054 .0408579 -4.48 0.000 -.2632854 -.1031254|
| hours || -.0476496 .0063111 -7.55 0.000 -.060019 -.0352802|
| weekends || -.4235522 .0788783 -5.37 0.000 -.5781509 -.2689536|
| _cons || .2977912 .0285355 10.44 0.000 .2418626 .3537199|
| _cons || 1.100659 .0097069 113.39 0.000 1.081634 1.119684|
| /sigma || 3.006146 .0291802 2.949494 3.063885|
We find people are less likely to decide to go to the movies
if there is a newborn in the household, the more hours they worked,
and if work involves weekends.
People who go to the movies are more likely to spend more
if they are dating, if they are teenagers, and if they have
children aged 6–10.
Tell me more
Read more about hurdle models in the Stata Base Reference Manual, see [R] churdle.