Question

To predict the probability of default on their bond obligations, Daniel Rubinfeld studied a sample of 35 municipalities in Massachusetts for the year 1930, several of which did in fact default. The LPM model he chose and estimated was as follows:

P= 1.96 -0.029 TAX - 4.86 INT + 0.063 AV + 0.007 DAV - 0.48 WELF

(0.29) (0.009)      (2.13) (0.028) (0.003) (0.88) R2 = 0.36

where; P = 0 if the municipality defaulted and 1 otherwise

TAX = average of 1929, 1930, and 1931 tax rates

INT = percentage of current budget allocated to interest payments in 1930

AV = percentage growth in assessed property valuation from 1925 to 1930

DAV = ratio of total direct net debt to total assessed valuation in 1930

WELF = percentage of 1930 budget allocated to charities, pensions, and soldiers’ benefits. Interpret these results economically and statistically.

Answer 1

Statistical inference of coefficients of independent variables will be done through hypothesis testing at a 5 % significance level.

Let coefficient for TAX, INT, AV, DAV, and WELF be 1, 2, 3, 4and 5respectively.

Hypothesis testing of the coefficient of TAX

H0: 1= 0

H1: 1 0

test statistic =( -0.029 - 0)/0.009 = - 3.22

critical value = -t_0.05,30 = -1.697

Comparing the test statistic and critical value, we will reject the hypothesis. i.e. variable TAX has a significant impact on

predicting the probability of the dependent variable.

Our model predicts that for every 1 percentage point increase in TAX, the probability that default decreases by 0.29%.

Hypothesis testing of the coefficient of INT

H0: 2= 0

H1: 2 0

test statistic =( -4.86 - 0)/2.13 = -2.281

critical value = -t_0.05,30 = -1.697

Comparing the test statistic and critical value, we will reject the hypothesis. i.e. variable INT has a significant impact in predicting the probability of dependent variable.

Our model predicts that for every 1 percentage point increase in INT, the probability that default decreases by 4.86%

Hypothesis testing of the coefficient of AV

H0: 3= 0

H1: 3 0

test statistic =( 0.063 - 0)/0.028 = 2.25

critical value = t_0.05,30 = 1.697

Comparing the test statistic and critical value, we will reject the hypothesis. i.e. variable AV has a significant impact in predicting the probability of dependent variable.

Our model predicts that for every 1 percentage point increase in AV, the probability that default increases by 0.063%

Hypothesis testing of the coefficient of DAV

H0: 4= 0

H1: 40

test statistic =( 0.007 - 0)/0.003 = 2.33

critical value = t_0.05,30 = 1.697

Comparing the test statistic and critical value, we will reject the hypothesis. i.e. variable DAV has a significant impact in predicting the probability of dependent variable.

Our model predicts that for every 1 percentage point increase in DAV, the probability that default increases by 0.007%

Hypothesis testing of the coefficient of WELF

H0: 5= 0

H1: 5 0

test statistic =( -0.48 - 0)/0.88 = -0.545

critical value = -t_0.05,30 = -1.697

Comparing the test statistic and critical value, we fail to reject the hypothesis. i.e. variable WELF has no significant impact in predicting the probability of dependent variable.

Since the coefficient of WELF is not significant, our model can't predict that for every 1 percentage point increase in WELF, the probability that default decreases by 0.48%