Outline:
- Probit model / logit model
- Basic estimation, ordered
version
- Postestimation diagnostics
Microeconometrics
dr Katarzyna Kopczewska
Class 05
This datset is for 2002 for Poland from Polish General Social Survey (PGSS)
boss
hours
job_success
job_satisfaction
income
age
sex_male
home_population
are You a boss?
how many hours You work in
a week
is it important to be
successful in a job
Are You satisfied with Your
job
what is Your income
how old are You
are You male?
how many members of
family live with You
1 YES, 0 NO
…
1 YES, 0 NO
1 - definitely yes, 2 - rather yes, 3 - rather
not, 4 - definitely not
…
…
1 YES, 0 NO
…
Logit (so called logistic regression)
1. To estimate the model use . logit y x1 x2, or
or
. logistic y x1 x2 command.
2. Interpretation in terms of odds ratio (logistic) (exp(b)) – a one unit change in Xi leads to exp(b) change
in odds ratio. Odds ratio is chance of success / chance of failure. In terms of coefficients (b) - a one unit
change in Xi leads to ln(b) change in odds ratio
Assume: coefficient(x1) = 0.69, intercept=-6.15, x1=10  predicted log(y) is calculated as:
. display 0.69*10-6.15
# result is 0.75
. display exp(0.75)
# result is 2.117 this is odds ratio for x1=10
. display 2.117/(1+2.117)
# probability = odds / (1 + odds), result is 0.6971
. display exp( _b[x1] )
# conversion from b to exp(b)
3. Prediction – one can predict odds ratio or probability for given levels of explanatory variables. Use then:
. adjust, by(x1) pr
# for probabilities
. adjust, by(inc) exp
# for odds ratio
Change in odds ratio when x increases by 1 should be the same as odds ratio coefficient.
Prediction can be made also for given level of x1, ex.
. adjust, x1=5 x2=17, by(x3) xb se ci
4. To assess the quality of forecast one can use . lstat (of . estat clas) command, which summarizes
correctly classified forecast observations. One can also use . lroc command, which compares sensitivity
and specificity. We are interested in field under the curve which is as big as possible. To check the cut-off
point graphically use . lsens.
5. As always one can test for equal coefficients using after . logit…, or command:
. test x1 x2
6. To check if “bigger” model is better than “smaller” one use . lrtest model1 model2. Using . est store
name save restricted (smaller) and unrestriccted (bigger) models.
H0 is that there is no significant difference between restricted and unrestricted model
H1 is that bigger model performs better.
7*. One can install . fitstat command to get more meaures of goodness of fit
Probit
1. To estimate the model use . probit y x1 x2 command.
2. Interpretation in terms of coefficients (. probit y x1 x2) – a one unit change in Xi leads to  change In
z-score of Y. One can also think in terms of marginal effects (. dprobit y x1 x2) - probability of success p
following probit (in given point). Automatically mean values are assumed. To be more flexible use:
. mfx compute, at(x1=0, x2=1, x3=0);
Multinominal logit*
0. mlogit……. - in terms of coefficients (b)
1. mlogit, rrr - in terms of relative-risk-ratio (exp(b))
Ordered probit / logit*
2. oprobit or ologit - estimation
3. lincom _b[/cut2] - _b[/cut1] – testing for equality of cut-off points
Postestimation*
4. estat sum – summary of variables
5. estat ic – AIC + BIC
Tasks:
1. Calculate logit model. Check few sets of explanstory variables – what is the best structure
of the model. What about accuracy of prediction – are You satisfied? What is the
interpretation of Your results?