《计量经济学导论》ch17.ppt
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Limited Dependent Variable Models and Sample Selection Corrections
Chapter 17
Wooldridge: Introductory Econometrics: A Modern Approach, 5e
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Predictions sometimes outside the unit interval Partial effects of explanatory variables are constant Nonlinear models for binary response Response probability is a nonlinear function of explanat. variables
How does the probability for y=1 change if explanatory variable xj changes by one unit? Discrete explanatory variables:
Limiteion Models
Interpretation of coefficients in Logit and Probit models
Continuous explanatory variables:
where
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Probability of a „success“ given explanatory variables
A cumulative distribution
function .
. The
response probability is thus a
function of the explanatory
Sample selection models The sample used to infer population relationships is endogenously selected, e.g. wage offer regression but data only about working women
and
If the latent variable y* is larger than zero, y takes on the value 1, if it is less or equal zero, y takes on 0 (y* can thus be interpreted as the propensity to have y=1)
Limited Dependent Variables and Sample Selection Models
Logit and Probit models for binary response Disadvantages of the LPM for binary dependent variables
variables x.
Shorthand vector notation: the vector of explanatory variables x also contains the constant of the model.
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Limited Dependent Variables and Sample Selection Models
Choices for the link function Probit:
(normal distribution)
Logit:
(logistic function)
Latent variable formulation of the Logit and Probit model
Limited Dependent Variables and Sample Selection Models
Limited dependent variables (LDV) LDV are variables whose range is substantively restricted • Binary variables, e.g. employed/not employed • Nonnegative variables, e.g. wages, prices, interest rates • Nonnegative variables with excess zeros, e.g. labor supply • Count variables, e.g. the number of arrests in a year • Censored variables, e.g. unemployment durations
Chapter 17
Wooldridge: Introductory Econometrics: A Modern Approach, 5e
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Predictions sometimes outside the unit interval Partial effects of explanatory variables are constant Nonlinear models for binary response Response probability is a nonlinear function of explanat. variables
How does the probability for y=1 change if explanatory variable xj changes by one unit? Discrete explanatory variables:
Limiteion Models
Interpretation of coefficients in Logit and Probit models
Continuous explanatory variables:
where
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Probability of a „success“ given explanatory variables
A cumulative distribution
function .
. The
response probability is thus a
function of the explanatory
Sample selection models The sample used to infer population relationships is endogenously selected, e.g. wage offer regression but data only about working women
and
If the latent variable y* is larger than zero, y takes on the value 1, if it is less or equal zero, y takes on 0 (y* can thus be interpreted as the propensity to have y=1)
Limited Dependent Variables and Sample Selection Models
Logit and Probit models for binary response Disadvantages of the LPM for binary dependent variables
variables x.
Shorthand vector notation: the vector of explanatory variables x also contains the constant of the model.
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Limited Dependent Variables and Sample Selection Models
Choices for the link function Probit:
(normal distribution)
Logit:
(logistic function)
Latent variable formulation of the Logit and Probit model
Limited Dependent Variables and Sample Selection Models
Limited dependent variables (LDV) LDV are variables whose range is substantively restricted • Binary variables, e.g. employed/not employed • Nonnegative variables, e.g. wages, prices, interest rates • Nonnegative variables with excess zeros, e.g. labor supply • Count variables, e.g. the number of arrests in a year • Censored variables, e.g. unemployment durations