Question 1

It is believed that an individual's decision to smoke or not depends partly on a number of social demographic factors.\

The variables are given below,

smoker =1 if current smoker, =0 otherwise

smkban =1 if there is a work area smoking ban, =0 otherwise

age = age in years

hsdrop =1 if high school dropout, =0 otherwise

hsgrad =1 if high school graduate, =0 otherwise

colsome =1 if some college, =0 otherwise

colgrad =1 if college graduate, =0 otherwise

black =1 if black, =0 otherwise

other =1 if other races, =0 otherwise

female =1 if female, =0 otherwise

Note: The education binary indicators refer to the highest level attained and thus are mutually exclusive. Individuals with a Master's degree or higher form the reference group and so they have values of 0 for hsdrop, hsgrad, colsome and colgrad.

a) Consider the following probit model:

pr(smoker) = ?(age, age² , hsdrop, hsgrad, colsome, colgrad, black, others, female)

How can each of the explanatory variables affect the probability of smoking? Please explain.

b) The Eviews output of the estimated model in part (a) is shown below in the screenshot:

Dependent Variable: SMOKER Method: ML - Binary Probit (Newton-Raphson / Marquardt steps) Date: 04/08/21 Time: 19:43 Sample: 1 10000 Included observations: 10000 Convergence achieved after 5 iterations Coefficient covariance computed using observed Hessian Variable Coefficient Std. Error Z-Statistic Prob. C -1.794190 0.151997 -11.80411 0.0000 AGE 0.032752 0.006919 4.733485 0.0000 AGE 2 -0.000450 8.26E-05 -5.439075 0.0000 HSDROP 1.176004 0.071642 16.41492 0.0000 HSGRAD 0.905946 0.059484 15.23017 0.0000 COLSOME 0.689645 0.060734 11.35515 0.0000 COLGRAD 0.236662 0.064887 3.647275 0.0003 BLACK -0.088538 0.052611 -1.682890 0.0924 OTHERS -0.339268 0.047680 -7.115578 0.0000 FEMALE -0.131095 0.028564 -4.589503 0.0000 Mcfadden R-squared 0.051718 Mean dependent var 0.242300 S.D. dependent var 0.428496 S.E. of regression 0.416332 Akaike info criterion 1.052159 Sum squared resid 1731.589 Schwarz criterion 1.059369 Log likelihood -5250.794 Hannan-Quinn criter. 1.054599 Deviance 10501.59 Restr. deviance 11074.33 Restr. log likelihood -5537.166 LR statistic 572.7442 Avg. log likelihood -0.525079 Prob(LR statistic) 0.000000 Obs with Dep=0 7577 Total obs 10000 Obs with Dep=1 2423