A COMPANION TO Theoretical Econometrics

Modified count models

The leading motivation for modified count models is to solve the so-called prob­lem of excess zeros, the presence of more zeros in the data than predicted by count models such as the Poisson.

Подпись: /1(0) Подпись: if y = °, if y >1 Подпись: (15.16)

The hurdle model or two-part model relaxes the assumption that the zeros and the positives come from the same data generating process. The zeros are determined by the density /(•), so that Pr[ y = 0] = /1(0). The positive counts come from the truncated density /2(y | y > 0) = /2(y)/(1 -/2(0)), which is multiplied by Pr[y > 0] = 1 - /1(0) to ensure that probabilities sum to unity. Thus

This reduces to the standard model only if /() = /2(). Thus in the modified model the two processes generating the zeros and the positives are not constrained to be the same. While the motivation for this model is to handle excess zeros, it is also capable of modeling too few zeros.

Maximum likelihood estimation of the hurdle model involves separate maximization of the two terms in the likelihood, one corresponding to the zeros and the other to the positives. This is straightforward.

A hurdle model has the interpretation that it reflects a two-stage decision making process. For example, a patient may initiate the first visit to a doctor, but the second and subsequent visits may be determined by a different mechanism (Pohlmeier and Ulrich, 1995).

Regression applications use hurdle versions of the Poisson or negative bino­mial, obtained by specifying/() and /2() to be the Poisson or negative binomial densities given earlier. In application the covariates in the hurdle part which models the zero/one outcome need not be the same as those which appear in the truncated part, although in practice they are often the same. The hurdle model is widely used, and the hurdle negative binomial model is quite flexible. Draw­backs are that the model is not very parsimonious, typically the number of parameters is doubled, and parameter interpretation is not as easy as in the same model without hurdle.

The conditional mean in the hurdle model is the product of a probability of positives and the conditional mean of the zero-truncated density. Therefore, using a Poisson regression when the hurdle model is the correct specification implies a misspecification which will lead to inconsistent estimates.

Добавить комментарий

A COMPANION TO Theoretical Econometrics

Normality tests

Let us now consider the fundamental problem of testing disturbance normality in the context of the linear regression model: Y = Xp + u, (23.12) where Y = (y1, ..., …

Univariate Forecasts

Univariate forecasts are made solely using past observations on the series being forecast. Even if economic theory suggests additional variables that should be useful in forecasting a particular variable, univariate …

Further Research on Cointegration

Although the discussion in the previous sections has been confined to the pos­sibility of cointegration arising from linear combinations of I(1) variables, the literature is currently proceeding in several interesting …

Как с нами связаться:

Украина:
г.Александрия
тел./факс +38 05235  77193 Бухгалтерия
+38 050 512 11 94 — гл. инженер-менеджер (продажи всего оборудования)

+38 050 457 13 30 — Рашид - продажи новинок
e-mail: msd@msd.com.ua
Схема проезда к производственному офису:
Схема проезда к МСД

Партнеры МСД

Контакты для заказов шлакоблочного оборудования:

+38 096 992 9559 Инна (вайбер, вацап, телеграм)
Эл. почта: inna@msd.com.ua

За услуги или товары возможен прием платежей Онпай: Платежи ОнПай