Tarun SinghEconomics 1123, Problem Set 6

Table 1:Limited Dependent Variable Models of the Determinants of Terrorism

(1) (2) (3) (4) (5) (6)Dependent variable: ftmpop ftmpop ftmpop ftm_pos ftm_pos ftm_ordRegression method: OLS OLS Tobit OLS probit ordered

probitData set: ftmpop > 0 all all all all all

Regressor:Lngdppc -.0410

(.0444)-.0365+

(.0205)-.0973+

(.0564)-.0420+

(.0241)-.1066+

(.0623)-.1190* (.0548)

Intercept .4883** (.0995)

.2540** (.0560)

-.1584 (.1035)

.5164** (.0439)

.0408 (.1105)

__

z-cutoff #1 __ __ __ __ __ -.0505 (.1097)

z-cutoff #2 __ __ __ __ __ .8269 (.1231)

N 76 156 156 156 156 156Notes: Heteroskedasticity-robust standard errors are given in parentheses. Coefficients are individually statistically significant at the +10%, *5%, **1% significance level.

-10

12

34

ftmpo

p

-2 0 2 4lngdppc

ftmpop Fitted valuesFitted values Fitted values

Terrorism and GDP

Green line=(1)Red line=(2)Orange line=(3)1. a) It makes sense to use the Tobit model for this regression because there is a lower bound on the number of terrorism fatalities at 0 so therefore this is basically a floor at 0. The Tobit model will not reveal a latent variable because we can’t have a negative number of terrorism related

fatalities. So the Tobit model makes sense to use when looking at it mathematically but the use of the model is qualitatively unmotivated.

b) The reason why would use this regression is to see if there is a relationship between the level of gdp per capita and the presence of terrorism. This doesn’t measure the amount of terrorism but instead just looks at the presence of terrorism. I think this is a good question to ask despite the fact that it doesn’t measure terrorism levels.

c) Yes, By using the ordered probit regression we are breaking up incidences of terrorism related fatalities into three ranges which allows us to test the effects of gdp per capita on terrorism related fatalities without being sensitive to outliers that would be present had we used the data the same way we did problem set 4, but gives us more information than from part b above.

d) The coefficients on lngdppc in regressions (1) and (3) are different due to the OLS regression (1) not including data points when ftmpop=0. The Tobit regression (3) includes data points when ftmpop=0 and also uncensors the data by including projections into negative values for ftmpop which would have been theoretically present had the data not been “censored.”

e) The coefficients on lngdppc in regressions (2) and (3) are different due to the OLS regression (2) includes values when lnftmpop=0 but has a floor at 0, meaning it doesn’t allow for negative rates of terrorism related fatalities. Tobit regression (3) has no floor and includes negative rates of terrorism related fatalities as it “uncensors” the data. Because the “uncensored” data includes negative values this will lead to more negative values for data meaning the line will be pushed down therefore leading to a larger negative coefficient in regression (3). Thus, a difference between the coefficients in regressions (2) and (3) can be explained by the “uncensored” data in regression (3).

f) The reason for the Tobit regression being mainly negative is due to the fact that the “uncensoring” of the data in the Tobit regression causes negative projections of terrorism related fatalities when the OLS regression (1) has a floor at 0 so there are no negative values. The Tobit regression doesn’t make sense, because it projects a negative amount of terrorism related fatalities, when we would expect these values to be positive.

g) The standard error on this predicted change is .0241 and the estimated change in the probability of at least one terrorist fatality occurring is a change of -.0420.This value is the same as the coefficient in regression (4) because we have a linear-log specification with a 100% change in X, meaning we have a change in Y of 100*.01B=B.

h) Using the probit model from regression (5) the change in the predicted probability of at least one terrorist fatality is stdnorm(-.0658) – stdnorm(-.1724) = 4.22%.

i) Using the ordered probit model from regression (6), the predicted change of at least one terrorist fatality is (1-stdnorm(-.1875)) – (1-stdnorm(-.0685)) = -4.7%.

j) Using the ordered probit model from regression (6), the predicted probability of a high level of terrorism fatalities is (1-stdnorm(1.0649)) – (1-stdnorm(.9459))= -2.9%.

2) Including all of the data points and not omitting those with 0 terrorist fatalities we see that the level of lngdppc does affect the level of terrorist fatalities. Regression (2-6) all include data when ftmpop=0 and are have statistically significant coefficients on lngdppc at the 10% level. Regression (6) includes the most information due to the inclusion of separate z- cut offs and is significant at the 5% level. Thus, the ordered probit regression (6) shows a strong relationship between the level of lngdppc and the level of terrorist fatalities. However, it is important to remember that none of the regressions in this problem set included the variables such as political freedoms, ethnic diversity, etc. which were included in problem set 4, so therefore there is a chance that the regressions in this problem set may be affected by omitted variable bias.

It is also important to acknowledge that there are more things that need to be explored in this data. Firstly, we used a lot of Tobit regressions despite the fact that we determined in question 1 part f) that “uncensoring” the data by using the Tobit model didn’t make sense, since this would create negative values for terrorist fatalities. Similarly, we never tested for a quadratic relationship in the data. For instance, in problem set 4 we determined that there was a quadratic relationship between lackpf and lnftmpop where countries with medium levels of political freedoms had the most terrorist fatalities and this may still be the case. Thus, looking at the potential OVB, the use of Tobit, and the potential for a non linear relationship in the data, we can’t safely conclude that there is a negative relationship between lngdppc and ftmpop. I would suggest further exploration of the abovementioned sources for error.