economic statistic

1.

The means of the two groups, the differences and the p-values are shown in the following table (some p-values are not calculable):

2.

The table shows the randomization may not work well here since some of the differences between treatment and control are statistically significant, though the absolute difference values are all very small.

3.

treatmen t control diff p-value

newreg 0.052 0.049 0.003 0.140

busy 0.032 0.000 0.032 -

age 56.056 55.768 0.288 0.086

female 0.554 0.564 -0.009 0.037

vote00 0.739 0.736 0.003 0.441

state 1.000 1.000 0.000 -

comp_m i 0.000 0.000 0.000 -

comp_ia 1.000 1.000 0.000 -

vote98 0.581 0.572 0.009 0.035

From the Stata output, we find the voting probability is 59.55% in the control group and 61.27% in the treatment group. The difference is 1.72%, and statistically significant (p-value < 0.001); however, it is not large in a practical sense.

4.

The following table shows the coefficient based on the logistic regression, where the first column only include treat_real and the following columns add one more covariate.

5.

We find some of the covariates (e.g. vote00) have big effects on the treatment effect. This phenomenon may be caused by the imbalance between the two groups, suggesting some of the covariates also have effects on the outcome.

6.

No, it will not get us an unbiased estimate of the causal effect. From the previous results, we see some of the covariates also have big effects on the outcome, so we have to control this before establishing the causal relationship between the treatment and the outcome.

Pearson chi2(1) = 15.8502 Pr = 0.000

100.00 100.00 100.00 Total 85,628 14,990 100,618 59.55 61.27 59.80 1 50,988 9,185 60,173 40.45 38.73 40.20 0 34,640 5,805 40,445 vote02 0 1 Total treat_real

column percentage frequency Key

Treat_rea l

+newre g +busy +age

+femal e +vote00

+stat e

+comp_m i

+comp_i a +vote98

B0 0.387 0.450 0.387

-0.98 6 0.458 -1.491 0.387 0.387 0.387 -0.668

B1 0.072 0.077 0.072 0.069 0.072 0.088 0.072 0.072 0.072 0.069

B2 - -1.292 0.020 0.025 -0.012 2.555 0.000 0.000 0.000 1.977