Presentation is loading. Please wait.

Presentation is loading. Please wait.

4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 1 Tobit-Model.

Published byColin Richard Modified over 8 years ago

Similar presentations

Presentation on theme: "4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 1 Tobit-Model."— Presentation transcript:

1 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 1 Tobit-Model

2 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 2 1.The Tobit - Model 2.An example Wooldridge (2003), Introductory Econometrics, 2nd edition, Chap.17.2 Other: Wooldridge (2002): Econometric Analysis of Cross Section and Panel Data, Chapter 16. Ruud (2000): An Introduction to Classical Econometric Theory, Chapter 28. Greene (2000): Econometric Analysis, 4th edition, Chapter 20.3

3 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 3 Problem: special attribute(s) of the dependent variable (DV) 1.dependent variable constrained and 2.clustering of observations at the constraint Examples: consumption (1. not 2.) wage changes (2. not 1.) Labor supply (1. and 2.)

4 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 4 left- and right-censoring in the data Distribution of log-wages in West-Germany, males, 1.1.1986, clerks, IABS01 Distribution of hourly benefits, Fringe.dta, command: hist hrbens left-censored, from below right-censored, top-coded

5 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 5 Data censoring –Earnings variable (IABS) –Demand for stadium tickets –Duration in unemployment Corner solutions –Labor Supply –Household expenditures on holidays 2 different sorts of Models

6 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 6 Censoring in a regression framework Ruud, Figure 28.2

7 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 7 If DV is constrained and if there is clustering –OLS on the complete sample biased and inconsistent, –OLS on the unclustered part biased and inconsistent.

8 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 8 Solution possibility 1: Estimate a Probit Model Loses information on y.  do not throw away information (Tobin 1958) Solution: Tobit-regression if

9 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 9 Trick: introduce a latent variable if Assume: linear conditional expectation for latent Var. Assumption:

10 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 10 Estimation of the parameters of the model: Non-linear LS estimation Maximum likelihood method Random sample

11 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 11 Maximum likelihood estimation: Likelihood-function consists in two parts 1. Probit-Part For censored observations we have:

12 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 12 2. Linear part Can formulate a linear model for the part that is uncensored:

13 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 13 Likelihood- and Log-Likelihood-function: ln L is maximized wrt β and σ. FOC yields estimator for β and σ. β and σ are asymptotically normal. Inference is standard.

14 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 14 Data: Dependent Variable: hoursworking hours (yearly) of married women 753 Observations 428 women exchange work for money in the labor market (hours vary in the dataset between 12 and 4950) 325 women do not work.

15 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 15 ageage educ education in years of schooling experexperience in actual years of work nwifeincfamily income (in 1000$) that is not generated by the woman kidslt6number of kids age < 6 kidsge6 number of kids 6< age < 18 explanatory variables:

16 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 16 Estimation of a Tobit-Model (in Stata): Source: Wooldridge, Econometric Analysis of Cross Section and Panel Data (2002)  estimated coefficients are to be interpreted as the effect of the regressors on the latent variable.

17 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 17 Direct comparison of OLS and Tobit output impossible OLSTobit nwifeinc-3.45-8.81 educ28.7680.65 exper65.67131.56 exper 2 -0.700-1.86 age-30.61-54.41 Kidslt 6-442.09-894.02 Kidsge 6-32.78-16.22 Constant1330.48965.31 Log- likelihood-----3819.09 R2R2 0.2660.274 750.181122.02 Dependent variable: hours

18 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 18 1.Marginal effect on the latent variable Slope of dashed line: tobit Slope of solid line: OLS

19 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 19 2.Marginal effect on the actual variable Probability that an observation is different from zero (if 1, then OLS=Tobit) x y 0 Green line!!

20 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 20 3.Marginal effect on positive observations Where λ(c) is called inverse Mills Ratio: λ(c) captures the change in the population, we condition on (y>0), when changing x.

21 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 21 4.Marginal effect on the probability, that an observation is uncensored. It follows: NB: For coefficients 2-4 need choose an appropriate x-vector!

22 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 22 Comparison OLS - TOBIT on the basis of the marginal effect on actual DV (example educ, for an average individual): OLSTOBIT 80.65 0.604 28.76 48,73

23 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 23 Interpretation: On average, an additional year of education increases the labor supply by 48,7 hours (for an average individual).  OLS underestimates the effect of education on the labor supply (in the average of the explanatory variables).

24 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 24 dtobit calculates the four different marginal effects (at the mean of the explanatory variables):

25 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 25

26 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 26

27 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 27 Specification Unobserved, independent heterogeneity → not problematic, as OLS Endogeneity (left-out variables, simultaneity) → „standard-IV“, similar to OLS Heteroskedasticity, nonormal errors → inconsistency, different from OLS

28 4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 28 alternatives for Tobit nonlinear estimation, eg. E(Y|x)=exp(xb) CLAD-estimator (for censoring problems) hurdle models, two-tiered models (for corner solution problems)

Download ppt "4. Tobit-Model University of Freiburg WS 2007/2008 Alexander Spermann 1 Tobit-Model."

Similar presentations

Dummy Dependent variable Models

Dummy Dependent variable Models
Qualitative and Limited Dependent Variable Models Chapter 18.

Qualitative and Limited Dependent Variable Models Chapter 18.
Economics 20 - Prof. Anderson1 Multiple Regression Analysis y =  0 +  1 x 1 +  2 x 2 +...  k x k + u 7. Specification and Data Problems.

Economics 20 - Prof. Anderson1 Multiple Regression Analysis y =  0 +  1 x 1 +  2 x  k x k + u 7. Specification and Data Problems.
16. Censoring, Tobit and Two Part Models. Censoring and Corner Solution Models Censoring model: y = T(y*) = 0 if y* < 0 y = T(y*) = y* if y* > 0. Corner.

16. Censoring, Tobit and Two Part Models. Censoring and Corner Solution Models Censoring model: y = T(y*) = 0 if y* < 0 y = T(y*) = y* if y* > 0. Corner.
Random effects estimation RANDOM EFFECTS REGRESSIONS When the observed variables of interest are constant for each individual, a fixed effects regression.

Random effects estimation RANDOM EFFECTS REGRESSIONS When the observed variables of interest are constant for each individual, a fixed effects regression.
Nguyen Ngoc Anh Nguyen Ha Trang

Nguyen Ngoc Anh Nguyen Ha Trang
Models with Discrete Dependent Variables

Models with Discrete Dependent Variables
CHAPTER 3 ECONOMETRICS x x x x x Chapter 2: Estimating the parameters of a linear regression model. Y i = b 1 + b 2 X i + e i Using OLS Chapter 3: Testing.

CHAPTER 3 ECONOMETRICS x x x x x Chapter 2: Estimating the parameters of a linear regression model. Y i = b 1 + b 2 X i + e i Using OLS Chapter 3: Testing.
QUALITATIVE AND LIMITED DEPENDENT VARIABLE MODELS.

QUALITATIVE AND LIMITED DEPENDENT VARIABLE MODELS.
Linear Regression with One Regression

Linear Regression with One Regression
So far, we have considered regression models with dummy variables of independent variables. In this lecture, we will study regression models whose dependent.

So far, we have considered regression models with dummy variables of independent variables. In this lecture, we will study regression models whose dependent.
TOBIT ANALYSIS Sometimes the dependent variable in a regression model is subject to a lower limit or an upper limit, or both. Suppose that in the absence.

TOBIT ANALYSIS Sometimes the dependent variable in a regression model is subject to a lower limit or an upper limit, or both. Suppose that in the absence.
Christopher Dougherty EC220 - Introduction to econometrics (chapter 10) Slideshow: Tobit models Original citation: Dougherty, C. (2012) EC220 - Introduction.

Christopher Dougherty EC220 - Introduction to econometrics (chapter 10) Slideshow: Tobit models Original citation: Dougherty, C. (2012) EC220 - Introduction.
Single and Multiple Spell Discrete Time Hazards Models with Parametric and Non-Parametric Corrections for Unobserved Heterogeneity David K. Guilkey.

Single and Multiple Spell Discrete Time Hazards Models with Parametric and Non-Parametric Corrections for Unobserved Heterogeneity David K. Guilkey.
9. Binary Dependent Variables 9.1 Homogeneous models –Logit, probit models –Inference –Tax preparers 9.2 Random effects models 9.3 Fixed effects models.

9. Binary Dependent Variables 9.1 Homogeneous models –Logit, probit models –Inference –Tax preparers 9.2 Random effects models 9.3 Fixed effects models.
Economics of Gender Chapter 5 Assist.Prof.Dr.Meltem INCE YENILMEZ.

Economics of Gender Chapter 5 Assist.Prof.Dr.Meltem INCE YENILMEZ.
Lecture 14-1 (Wooldridge Ch 17) Linear probability, Probit, and

Lecture 14-1 (Wooldridge Ch 17) Linear probability, Probit, and
Lecture 15 Tobit model for corner solution

Lecture 15 Tobit model for corner solution
Lecture 2: Key Concepts of Econometrics Prepared by South Asian Network on Economic Modeling Reference Introductory Econometrics: Jeffrey M Wooldridge.

Lecture 2: Key Concepts of Econometrics Prepared by South Asian Network on Economic Modeling Reference Introductory Econometrics: Jeffrey M Wooldridge.
Statistics and Econometrics for Business II Fall 2014 Instructor: Maksym Obrizan Lecture notes III # 2. Advanced topics in OLS regression # 3. Working.

Statistics and Econometrics for Business II Fall 2014 Instructor: Maksym Obrizan Lecture notes III # 2. Advanced topics in OLS regression # 3. Working.

Similar presentations

Ads by Google