Microeconometrics: Binary Dependent Variable
Microeconometrics:
Additional References Dougherty, Introduction to Econometrics, 4
- th
Ed, 2011
Estimators we (will) know
- • Ordinary Least Square (OLS)
Why uses binary dependent variable?
- Observed vs unobserved variables
Why uses binary dependent variable?
- Observed vs unobserved variables
Why uses binary dependent variable?
- Observed vs unobserved variables
Why uses binary dependent variable?
- Observed vs unobserved variables
The mechanism
Suppose:
The mechanism
So we estimate
The Linear Probability Model
Using formula for expected value:
The Linear Probability Model
- If we estimate
The Linear Probability Model
We know from previous lectures about
LPM Interpretation
• Suppose we have a more complete set
LPM Interpretation
• Suppose we have a more complete set
LPM Interpretation
Suppose we have a more complete set of independent variables:LPM Interpretation
Limitations of LPM
- Distribution of the error term is not following
Normal Distribution, so test statistics are not
Limitations of LPM
- Distribution of the error term is not
following Normal Distribution, so test
Limitations of LPM
- Heteroskedasiticity
Limitations of LPM
- Nonfulfllment of : Does it make sense to
What is a better model for
estimating E(y )?
i What is a better model for estimating E(y i
)?
What is a better model for E(y )?
i- We denote CDFs using the letter F
Solution
- We need a math function for , or , or , that always results in values between 0 and 1
Solution 1: Logit Model
Solution 1: Logit Model
- Taking the log of both sides
Logit Model: Coefcients &
Marginal Efects
Logit Model: Coefcients &
Marginal Efects
Solution 2: Probit Model
Suppose we have an equation:
Solution 2: Probit Model
- Hence
Solution 2: Probit Model
- Since the normal distribution is
Probit Model: Coefcients &
Marginal Efects
Probit Model: Coefcients &
Marginal Efects
Gender Inequality and Poverty in Indonesia: Evidence from Household Data Kinanti Z. Patria
Estimation of Logit and Probit
Models
- We do not use OLS, rather we use the Maximum Likelihood Method
Maximum Likelihood Estimator
- Remember that our data is Random •
Maximum Likelihood Estimator
- Remember that our data is Random •
Maximum Likelihood Estimator
- “Maximum Likelihood is just a
Copyright Christopher Dougherty 2012. These slideshows may be downloaded by anyone, anywhere for personal use
Subject to respect for copyright and, where appropriate, attribution, they may be used as
a resource for teaching an econometrics course. There is no need to refer to the author.The content of this slideshow comes from Section R.2 of C. Dougherty, Introduction to Econometrics, fourth edition 2011, Oxford University Press.
Method of ML
• The method of maximum likelihood is
p
- This sequence introduces the
0.4
principle of maximum likelihood estimation and illustrates it with
0.3 some simple examples.
0.2
Normal Distribution 1 x
2
p p p(4) p(6) m
0.4
0.3521 3.5 0.3521 0.0175
0.3
p p p(4) p(6) L m
0.4
0.3521 3.5 0.3521 0.0175 0.0062
0.3
p 0.3989 p(4) p(6) L m
0.4
3.5 0.3521 0.0175 0.0062
0.3
4.0 0.3989 0.0540 0.0215
p 0.3521 m p(4) p(6) L
3.5 0.3521 0.0175 0.0062 4.0 0.3989 0.0540 0.0215
0.3
0.4
m p(4) p(6) L
3.5 0.3521 0.0175 0.0062 4.0 0.3989 0.0540 0.0215 p
0.2420 0.2420
0.3
0.4
m p(4) p(6) L
3.5 0.3521 0.0175 0.0062 4.0 0.3989 0.0540 0.0215 p
0.3521
0.3
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m p(4) p(6) L
3.5 0.3521 0.0175 0.0062 4.0 0.3989 0.0540 0.0215 p
0.3521
0.3
0.4
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