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##### MAF 356 ASSIGNMENT 1 ANSWERS

(a) Use excel to compute the descriptive statistics (mean, maximum, minimum) for the variables: Y, constant, AX, AXSQ,WE, CIT separately for the sample of women who worked in 1975 and the sample who did not work. Briefly describe any important differences between the two samples. Do the differences accord with your a priori expectations?
For the sample of women who worked in 1975,

For the sample of women who did not work in 1975,

We can conclude from the descriptive statistics that for those women who did not work in 1975, their previous average/mean actual years of labour market experience seems shorter than those who did work in 1975. Their educational attainment is also slightly lower than those who did work in 1975. And since the dummy variable CIT gives higher for those who did not work in 1975, it seems that women in large cities tend to not work in that year. However, the maximum for years of experience (and its square) are higher although the average is lower for non-working women.
They basically accord with my priori expectations as women who received educational qualifications or work experiences tend to become professionals than those who did not. However it is arguable that whether in large cities or not do women like to work or not.
(b) Regress Y on the constant, AX, AXSQ, WE, CIT variables for the sample of working women. Clearly document your a priori expectations for the signs of each coefficient of the population regression model. Present your sample regression results and interpret fully. Carry out any hypothesis tests you feel appropriate and interpret fully and carefully.

Please refer to the above Regression of Y on the constant, AX, AXSQ, WE, CIT variables.
My priori expectation on the result is that all the signs except CIT should be positive for all the variables given the reason explained in (a). For CIT, it is unclear and there should be a clear trend as to whether it is positive or not.
However, the result is:
Y= -0.531 +0.041AX -0.001AXSQ +0.106WE +0.054CIT
i.e. Except for AXSQ, all the other variables have shown positive correlation with Y.
We run the null hypothesis of all the variables Constant, AX, AXSQ, WE and CIT. For those coefficient results except CIT, if we assume that they are zero, at 95% confidence level the t-statistics are all above the absolute value of the number rang (-1.96,1.96), i.e. we reject the hypothesis that a coefficient is zero with a 5% level of significance.  In other words, except for the variable CIT, all the other results are statistically significant.
For CIT, the value of T-statistics is within the range of (-1.96,1.96), at 95% confidence level that means we are not going to reject the null hypothesis of the variable is zero and it is statistically insignificant.
The result is generally in line with my expectation that uncertainty lies in the variable CIT and a clear trend of correlation should show in other variables. It is evidenced by the result except for the AXSQ variable, despite its significance.
(c) Looking at the population regression specification do you think there are any particular key variables missing? If yes, explain.
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