tailieunhanh - Lecture Advanced Econometrics (Part II) - Chapter 5: Limited dependent variable models - Truncation, censoring (tobit) and sample selection

Lecture "Advanced Econometrics (Part II) - Chapter 5: Limited dependent variable models - Truncation, censoring (tobit) and sample selection" presentation of content: Truncation, censored data, some issues in specification, sample selection model, regression analysis of treatment effects. | Advanced Econometrics - Part II Chapter 5 Limited - Dependent Variable Models Chapter 5 LIMITED - DEPENDENT VARIABLE MODELS TRUNCATION CENSORING TOBIT AND SAMPLE SELECTION. I. TRUNCATION The effect of truncation occurs when sample data are drawn from a subset of a larger population of interest. 1. Truncated distributions Is the part of an untruncated distribution that is above or below some specified value Density of a truncated random variable If a continuous random variable x has pdf f x and a is a constant then f x x a f x Prob x a If x N ơ2 P x a 1 - ol a I 1 - o a a I l Ơ J l Ơ - x- 2 1 -2 ____-_e 2Ơ f xlx a fL 1 -O a 1 -O a 1 . x - p p ơ l Ơ c o 1 - o a o Truncated standard normal distribution 2. Moments of truncated distributions C x x a J xf x x a dx a V J a x - Nam T. Hoang UNE Business School 1 University of New England Advanced Econometrics - Part II Chapter 5 Limited - Dependent Variable Models o Truncated mean and truncated variance If x N ơ2 and a is a constant E x x a ơẰ a 1 Var xlx a cr2 1 - ổ a Where a I a I . is this standard normal density c 7 J And Ằ a a 1 - h a if x a A a -ộ a ỊO a if x a And ổ a A a A a -a 0 ổ a 1 for all values of a 2 _2 7 J 7 truncated 3. The truncated regression model Assume now ị XB Yị s. Where e X. N 0 ơ2 So that Y X. N A W We are interested in the distribution of Yi given that Yi is greater than the truncation point a E Y Y a X p 7 ộ a - Xl B ơ 1 -O a - XtB ơ dE Yi Yi a _ da ------------- B o d . da r dX. 1 1 õXị B a A - aiẰị - B7 B 1 - A a A B 1 - ỗt Where a. a XịBi Ảị Ả at Sị ổ aị 1 -ổt is between zero and 1 for every element of Xi the marginal effect is less than the corresponding coefficient Nam T. Hoang UNE Business School 2 University of New England Advanced Econometrics - Part II Chapter 5 Limited - Dependent Variable Models Var Y Y a a 1 - S o Estimate Y Y a E Y Y a u XI p ơẢt ui Var Uị ơ2 1 - ỗị If we use OLS on Yi Xi we omit Ảị -Ạ all the biases that arise because of an omitted variable can be expected. o .