ECMT6007/6702: Econometric Applications Problem Set 10

Question 1.

(i) The intercept term in model (2) represents the average real price of houses in 2006 (in $100,000 units) located more than 2 km from the incinerator. That is, the average price of houses lo- cated more than 2km from the incinerator in 2006 was $825,170. The coefficient on nearinc

represents the difference in average prices between those located within 2km of the inciner- ator (nearinc) and those located further way. That difference in average price was -$188,240 (hence the average price for houses within 2km of the incinerator in 2006 was $636,930).

(ii) We cannot infer from the estimates in (1), using year 2010 data, that the location of the in-

cinerator caused the price of houses located nearby to fall by an average of $306,880 because other factors may be associated with the lower price of houses near the incinerator. Indeed, the incinerator may have been built in an area because of the lower properties prices in that region. This is supported by the negative coefficient on nearinc in (2) which is based on 2006

data and prior to the building (and announcement) of the incinerator.

(iii) Based on the model:

r—price = 8.2517 + 0.8790 yearA − 1.8824 nearinc − 1.1863 yearA × nearinc      (3)

(0.273)    (0.4071)             (0.4875)                 (0.5457)

n = 401,  R2  = 0.186

the estimated effect of the incinerator on neighbouring house prices using the‘difference-in- difference’estimator is -1.1863. That is, other things equal, the incinerator lowered the average price of houses within a 2km radius by $118,630.

(iv) Hypothesis test

Test:

H0  : βimpact  = 0

H1  : βimpact  < 0

Test Statistics:

t =      βˆimpact       

se (βˆimpact )

−1.1863

=

0.5457

= −2.1739

Rejection Rule: Reject H0  in favour of H1  if t < −c, where t is the t-statistic and c is the critical value for the t distribution with df = 401 − 4 = 397 and a 5% significance level.       Now t = −2.1739 and c = 1.645 (Note: since n > 120 we can use the standard normal critical values).

Decision: Since t < −c we reject the null at the 5% significance level.

Conclusion: The incinerator had a statistically and economically significant negative impact on the price of houses located within a 2km radius from the incinerator (relative to the price of more distant homes).

Question 2. Computer Exercise: The Effect of Worker Compensation Laws on Duration

(i) Table of estimated sample means:

Table 1: Sample mean for each variable

(ii) Report the average value of log(duration) for the following 4 subsamples:

a. High-earners after the change in benefits = 1.843011

b. Low-earners after the change in benefits = 1.01585

c. High-earners before the change in benefits = 1.470957

d. Low-earners before the change in benefits = 1.154353

(iii) With the averages calculated in (ii), compute the‘difference-in-difference’estimator of the

impact of the policy change:

βˆimpact  = (1.843011 − 1.01585) − (1.470957 − 1.154353)

= 0.51055

(iv) Using the dataset injury9 .dta, based on the US state of Kentucky, the estimates are:

log (d—uration) = 1.1544 − 0.1385D afchnge + 0.3166 highearn + 0.5106afchnge × highearn

(0.0816)  (0.1196)                     (0.1319)                    (0.1871)

n = 784,     R2  = 0.0555

(v) The coefficient on the interaction term afchnge × highearn, β3 , measures the change in av- erage length of time on workers’compensation for high income earners following the change in the law, relative to low income earners.

This is estimated to be approximately 51% due to the increase(!) in the earnings cap. (vi) Hypothesis test

Test:

H0  : β3  = 0

H1  : β3   0

Test Statistics:

I     βˆ3       I

I se (βˆ3 ) I

0.5106

= 0.1871

= 2.73

Rejection Rule:  Reject H0  in favour of H1  if t  >  c, where t is the t-statistic and c is the

critical value for the t-distribution with df = 784 - 4 = 780 and a 1% significance level. Now t = 2.73 and c = 2.576.

Decision: Since t > c we reject the null at the 1% significance level.

Conclusion: The policy change had a stat significant impact on expected length of time on workers compensation.

(vii) This method attributes the average change in duration of time on workers compensation by high earner over time to the policy – when in fact some of the change may be attributable to the economy (or other factors). We need to use a control / or comparison group to net out the influence of other factors.

(viii) Re-estimating the model (1) and testing:

Test:

H0  : β4  = 0, . . . , β 14  = 0

H1  : H0  is false

Test Statistics:

F =  (SSRr  − SSRur) /q

SSRur/ (n − k − 1)

(Ru(2)r  − Rr(2))/q       

=

(1 − Ru(2)r) / (n − k − 1)

= 4.32 ∼ F11,769

Rejection Rule: Reject H0 in favour of H1 if F > c with a 1% significance level. Now F = 4.32 and c = 2.32

Decision: Since F > c we reject the null at the 1% significance level.

Conclusion: The additional variables jointly had a statistical significant effect on expected length of time on workers compensation.

(ix) The inclusion of control variables for male, married, a full set of injury type dummy vari- ables (head, neck, upextr, trunk, lowback, lowextr, occdis) and industry dummy variables (manuf, construc), leads to a coefficient estimate (and standard error) on the interaction term afchnge × highearn of 0.5283 (0.1839) – which has a t-ratio of 2.87. There is very little change in the coefficient estimate when the additional explanatory variables are added to the model. The estimate is still statistically significant and practically large; the point es- timate implies a substantial response in expected duration on workers’compensation due to the change in earnings cap.

Hypothesis test

Test:

H0  : β3  = 0

H1  : β3   0

Test Statistics:

'    βˆ3      '

' s (βˆ3 ) '

= 2.87

Rejection Rule:  Reject H0  in favour of H1  if t  >  c, where t is the t-statistic and c is the critical value for the t-distribution with df = 784 − 4 = 780 and a 1% significance level.

Now t = 2.87 and c = 2.576.

Decision: Since t > c we reject the null at the 1% significance level.