Econometrics Pset3

Tarun Singh Worked with: Alex Sloan Alexander Marcus Econometrics 1123: Problem Set 3 A)

0

5

ftmpop 10

15

20

1.

0

20

gdppc

40

60

-6

-4

lnftmpop -2 0

2

4

B)

-2

0

lngdppc

2

4

-6

-4

lnftmpop -2 0

2

4

C)

0

2

4 lackpf

6

8

D) We want to use the log-log specification of lnftmpop vs. lngdppc because we are interested in the percent change terrorism vs. the percent change of gdppc and not just unit changes. Furthermore, it seems like there is a linear relationship in graph b but no apparent linear relationship in graph a. E) The relationship between lnftmpop and lackpf appears to non-linear. A downward quadratic function may describe the data the best. The data appears to show that terrorism is lower in those nations with low political freedoms and those with high political freedoms whereas it is highest for those nations with a medium number of political freedoms.

2. Economics 1123, Problem Set 3, Table 2 Determinants of Terrorism Dependent variable: Regressor: lngdppc

(1) lnftmpop

(2) lnftmpop

(3) lnftmpop

(4) lnftmpop

(5) lnftmpop

-.3124901

-.2791311

(.1504035)

(.203559 4)

.0569704 (.2151112 )

.0473908 (2453983 )

-.064753 3 (.282961 1)

(lngdppc)2

lackpf

lackpf2

ethnic

religion

Mideast

Other regional dummies (latinam, easteurope, africa, eastasia)? Intercept

__

__

__

__

__

__

__

.035685 1 (.142987 8) __

__

__

__

-.033721 4

__

__

(.081199 7) 1.651034

1.466333

(.539245 3)

(.546448 6)

1.690798 (.596872 9)

-.194043 4

-.170390 2

(.061710 7) __

(.061781 1) .655626 (.958243 3)

__

__

-1.24292 1 (.970418 1) __

-.198721 5 (.066597 1) .8777034 (.972179 2) -1.57253 8 (1.22536 5) -1.11885 4 (1.27298 3) Yes

No

No

No

No

-2.047654

-2.20082 (.623109 5)

-4.81342

-4.43084 2

-3.5785

(-2.132806)

(1.07668 (1.59639 8) (1.29211) 1) F-statistics testing the hypothesis that the population coefficients on the indicated regressors are all zero: lngdppc, lngdppc2 __ __ 0.11 __ __ lackpf, lackpf2

__

__

(0.8995) 4.95

3.81

4.47

ethnic, religion

__

__

(0.0098) __

(0.0271) 1.01

(0.0153) 1.25

__

(0.3705) __

(0.2941) 0.81

Other regional dummies

__

__

(0.5244)

Regression summary statistics 0.0492 2

R

R2 SER n

0.0619 1.8431 76

0.0370

0.1228

0.1188

0.0871

0.0627 1.8549 76

0.1696 1.7703 76

0.1792 1.7673 74

0.2121 1.7989 74

Notes: Heteroskedasticity-robust standard errors are given in parentheses under estimated coefficients, and p-values are given in parentheses under F- statistics. The F-statistics are heteroskedasticity-robust. Coefficients are significant at the + 10%, *5%, **1% significance level. The “other regional dummies” included in regression (5) are latinam, easteurope, africa, and eastasia (the omitted case is Western Europe combined with North America). 3. A) When we use a t-test we get a t-statistic of -2.08 which has a p-value of .041, so we reject the null hypothesis at the 5% confidence level that the coefficient on lngdppc is 0. This means that for a 1% change in gdp per capita we expect a -.3124901% change in fatalities per million in a population from terrorist attacks. B) We fail to reject the null hypothesis that at least one of lngdppc and lngdppc2 are 0 because we get a F-statistic of 0.11 and a p-value of 0.8995 which is greater than .05 so we fail to reject at the 5% level. C) We reached different conclusions in A and B most likely due to an omitted variable bias in A. The result in A shows that lngdppc has a statistically significant effect on the rate of terrorism related deaths, whereas B shows that when we look at lngdppc and lngdppc2 together we see that they do not have a statistically significant effect on the rate of terrorism related deaths. This may be due to omitted variable bias. In regression 3, we included lackpf, but in regression 1 we didn’t. In regression 3 we see that the t-statistic for lackpf is significant meaning political freedoms have a large effect on terrorism. In regression 1 we saw that lngdppc was significant but it wasn’t significant in regression 2 this may be due to lngdppc capturing the effect of lackpf. We can test this possibility by looking at the correlation of lackpf and lngdppc which is -0.6859. A one unit increase in lackpf causes a 1.651% increase in lnftmpop and as lackpf increases, lngdppc decreases. This explains why the coefficient of lngdppc in regression 1 is negative and statistically significant because as lngdppc increases, lackpf decreases in turn causing lnftmpop to decrease. D) No, since the t-statistic for lngdppc2 in regression 3 is not-statistically significant, we can’t reject the null hypothesis that the coefficient on lngdppc2 is 0, so we have no evidence that the relationship between lnftmpop and lngdppc is non-linear. E) Yes, there is evidence that the relationship between lackpf and lnftmpop is nonlinear. The t-statistic for lackpf2 in regression 3 is -3.14, so at the 5% significance level we can reject the null hypothesis that the coefficient on lackpf2 is

0 meaning the coefficient on lackpf2 is statistically significant. This t-test thus tells us that the relationship between lackpf and lnftmpop is non-linear. F) Performing an F-test on “other regional dummies” we get an F-statistic of 0.81, which is not statistically significant at the 5% level. Using the test, we can reject the null hypothesis that the coefficients on “other regional dummies” are all zero at the 5% level. We have 4 restrictions because the q-value we obtained was 4, and the critical value was 2.27. G) The coefficient on ethnic in regression 4 is positive but it is not statistically significant because it has a t-statistic of .68. However, the sign of the coefficient on ethnic being positive means that if all else is held constant, as the measurement of ethnic divisions increases, the number of deaths due to terrorism also increases. H) The coefficient on religion in regression 4 is negative but it is not statistically significant because it has a t-statistic of -1.28. However, the sign of the coefficient on religion being negative means that if all else is held constant, as the measurement of religious divisions increases, the number of deaths due to terrorism decreases. I) Performing an F-test on ethnic and religion, we get an F-statistic of 1.01 which means that we cannot reject the null hypothesis that neither ethnic nor religion have statistically significant coefficients. In other words since we rejected the null hypothesis we can’t reject the possibility that neither ethnic nor religion have any effect on deaths due to terrorism. J) Since ethnic and religion are not variable in regression 3, we cannot test anything regarding ethnic and religion in the regression. The R2 formula for the homoskedacicity only F-statistic, we get an F-statistic of .98. We still can’t reject the null hypothesis that the coefficients on both variables equal 0. We have no reason to believe that the standard errors are normally distributed so it wouldn’t be appropriate to use this formula. K) We can see by using the lincom command that changing the value of lackpf from 7 to 5 in regression 4 has the effect of changing lnftmpop by of 1.1567. This means that by changing lackpf but holding all other values constant, lnftmpop increases by 1.1567. This means that starting from the initial position of having extremely limited political freedoms, if we were to increase political freedoms, this would lead to more deaths due to terrorism. L) Using the lincom command we calculate 95% CI to be [-.0223584, 2.335755]. M)

-1.5 Fitted values -2.5 -2 -3 0

2

4 lackpf

6

8

The relationship is maximized at roughly 4.5 lackpf. N) The relationship appears to be quadratic. The relationship as seen in the graph from part M) above leads us to believe that as political freedoms increase initially so do the number of deaths due to terrorism, deaths due to terrorism seem to peak at a medium level of political freedoms and then decrease when there are a lot of political freedoms. This is consistent with our hypothesis from part E) in problem 1.