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dependent variable can take only two values suppose 1 and 0 that is in one word the regressand is
binary or dichotomous variable but it is not restricted to only dichotomous but we can have
trichotomous and polychotomous response variable.
In this section, we highlight the followings:
1. WHAT IS QUALITATIVE RESPONSE ECONOMETRIC MODELLING
2. BINARY CHOICE MODEL
3. LOGIT MODEL
4. PROBIT MODEL
WHAT IS QUALITATIVE RESPONSE ECONOMETRIC MODELLING
It is basically represents the involvement of qualitative variable in econometric modelling. We
usually we call it dummy variable. Dummy variable is a variable, which can classifying the
structure into various subgroups based on qualities or attributes and implicitly allows one to run
individual regressions for each group. A dummy variable will take the value 1 or 0 according to
whether or not the condition is present or absent for a particular observation. In some cases, it
can be presented with the code 1, 2, 3, 4 and alike. For instance, if we like to study the impact of
religion on income, the religion will be categorical (qualitative) and in this context, we take the
value like 1, 2, 3, etc.
THE LOGIT MODEL
In the logit model the dependent variable is the log of the odds ratio, which is a linear function of
the regressors. The probability function that underlies the logit model is the logistic distribution.
If the data is available in grouped form, we can use the OLS to estimate the parameters of the
logit model, provided we take into account explicitly the heteroscedastic nature of the error term.
If the data are available at the individual or micro level, non linear in parameter estimation
procedures are called for. There is a lot of empirical evidence that the response function should
be nonlinear; an “S” shape is quite logical (See the scatter plot of the Challenger data).
The usual LOGT model is presented as follows:
exp( 1
1 exp( 1 exp(
E y
^
x
x x
After simplification, the LOGIT model can be presented in this format:
Log [p/ (1-p)] = β 0 + β 1 X 1 + β 2 X 2 + u
or else, we can write Log [p / (1- p)] = k xk
The LOGIT model is related to the odds for a binary outcome. The LOGIT model has the
following features:
As p goes from 0 to 1, L or LOGIT goes from - infinity to + infinity that is although the
probabilities lie between 0 and 1 the LOGIT are not so bounded.
The logit model is not subject to problems due to heteroscedastic or non-normal error
distributions.
The logit of the outcome tends to have a linear relationship with the explanatory
variables.
Alternately, in a PROBIT model, β 0 and β 1 coefficient refers to the change in probability
units per unit change in x.
The chief difference between logit and probit model is that the logistic model has a flatter
tail that is the normal or probit curves approach the axis faster than the LOGIT model.
Quantitatively LOGIT and PROBIT models give similar results but the estimates of the
parameters of the two models are not directly comparable.
THE SAMPLE PROBLEM
Price = 1 + 2 * country + 3 * size + **4 *** Elevation + **5 *** Sewer + **6 *** date + **7 *** flood + **8 *** distance +u
- 1 4.5 1 138.4 10 3000 ‐ 103 0 0. Units Price County Size Elevation Sewer Date Flood Distance
- 2 10.6 1 52 4 0 ‐ 103 0 2.
- 3 1.7 0 16.1 0 2640 ‐ 98 1 10.
- 4 5 0 1695.2 1 3500 ‐
- 5 5 0 845 1 1000 ‐
- 6 3.3 1 6.9 2 10000 ‐
- 7 5.7 1 105.9 4 0 ‐
- 8 6.2 1 56.6 4 0 ‐
- 9 19.4 1 51.4 20 1300 ‐ 63 0 1.
- 10 3.2 1 22.1 0 6000 ‐
- 11 4.7 1 22.1 0 6000 ‐
- 12 6.9 1 27.7 3 4500 ‐
- 13 8.1 1 18.6 5 5000 ‐ 59 0 0.
- 14 11.6 1 69.9 8 0 ‐ 59 0 4.
- 15 19.3 1 145.7 10 0 ‐ 59 0 4.
- 16 11.7 1 77.2 9 0 ‐ 59 0 4.
- 17 13.3 1 26.2 8 0 ‐ 59 0 4.
- 18 15.1 1 102.3 6 0 ‐ 59 0 4.
- 19 12.4 1 49.5 11 0 ‐ 59 0 4.
- 20 15.3 1 12.2 8 0 ‐
- 21 12.2 0 320.6 0 4000 ‐ 54 0 16.
- 22 18.1 1 9.9 5 0 ‐ 54 0 5.
- 23 16.8 1 15.3 2 0 ‐ 53 0 5.
- 24 5.9 0 55.2 0 1320 ‐ 49 1 11.
- 25 4 0 116.2 2 900 ‐ 45 1 5.
- 26 37.2 0 15 5 0 ‐ 39 0 7.
- 27 18.2 0 23.4 5 4420 ‐ 39 0 5.
- 28 15.1 0 132.8 2 2640 ‐ 35 0 10.
- 29 22.9 0 12 5 3400 ‐ 16 0 5.
- 30 15.2 0 67 2 900 ‐ 5 1 5.
- 31 21.9 0 30.8 2 900 ‐ 4 0 5.
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients B Std. Error Beta t Sig. 1 (Constant) 23.643 3.829 6.174. Country -8.789 3.652 -.564 -2.407. Size -.006 .004 -.256 -1.726. Elevation .519 .239 .293 2.177. Sewer .000 .000 -.308 -2.296. Date .085 .049 .270 1.749. Flood -12.015 2.989 -.582 -4.020. Distance .186 .340 .109 .547.
Model Summary
Model R R Square
Adjusted R Square
Std. Error of the Estimate 1 .864a^ .747 .670 4.
ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 1333.822 7 190.546 9.703 .000a Residual 451.675 23 19. Total 1785.497 30
Conclusion:
Except distance, all other variables are statistically significant.
Overall fitness is okay and statistically significant.
