Econometrıcs I (ENG) — Ünite 6 Soru-Cevap

The most common form of qualitative response is the binary dependent variable.

Binary dependent variable which can have only two values: 0 or 1.

If a student passed the class, the variable y will take the value of 1; if she did not pass, the variable y will take the value of 0.

The Tobit model

1. The linear probability model (LPM)
2. The logit model
3. The probit model

x may represent variables such as the amount of income, gender, the number of children, marital status, age and other factors which may impact savings such as an individual’s capacity to overcome spending related temptations.

Both H functions in the logit and probit models are monotonically increasing functions.

0

1

Maximum likelihood estimation tries to find the best distribution to fit to the data at hand. That is, the unknown population parameters are chosen in a way that maximizes the likelihood of observing the data points gathered.

Maximum Likelihood estimation is necessary for estimating regression models when the dependent variable is binary or has other nonlinear features, such as being observable only in the positive domain.

If H(.) is the cumulative distribution function of a standard logit variable, then our MLE
estimator is called the logit estimator.

The null hypothesis being 0 suggests that there is no effect.

In binary response models, we have some pseudo R-squared measures for calculating the explanatory power of the model.

The disadvantage of using logit and probit models rather than the linear probability model is that the marginal effects are difficult to calculate as h(b1 + xb) varies based on values of all independent variables in the model denoted by x vector. Therefore, the marginal effect will change based on whether median, mean or some particular value of each independent variable is used.

Probit and logit models can be estimated with time fixed effects to
assess the effectiveness of certain programs with pooled cross-sectional datasets.

The model’s fit could be high especially for an xi close to the sample average values. But for such a variable, we would also obtain negative predicted values, which was also an issue with the binary response variables when estimated with the LPM.

Another problem is that in the OLS model the marginal effect of a continuous variable x on E(y\x) is the same (i.e. constant) regardless of the value of x.
Also, var( y\x) is not constant as the variance around 0 would be different from the variance around other observations, which would result in heteroskedasticity. We can address heteroskedasticity by using White/ sandwich standard errors, which can address general forms of heteroskedasticity.
Another issue is about the distribution of y variable. As there are many observations which have 0 value, the variable y will not have a normal distribution. Therefore, when running t-tests to make inferences about population parameters, we need to rely only on asymptotical distribution.

A dependent variable which has a dispersed distribution of positive values and a considerable number of zeros is well-suited for Tobit models

Another type of non-negative dependent variable is called count data when the variable consists of a substantial number of zero values along with a few integer values

The classic example of count data is the number of traffic accidents in a specified time period. For instance, the number of traffic accidents at Anadolu University in a given month could be 0 for many months, but it will not exceed 5 accidents in a
month.