Heavy Lifting - thoughts and web finds by an economist
     I also contribute to Division of Labour Load HL's Front Page
Thursday, November 15, 2007

Are Aggregate Terrorism Acts Random?

One defining characteristic of terrorism is its unpredictability. I don't think this means that enforcement or vigilance against terrorist acts is completely ineffictive or worthless, but one wonders how much money we are spending chasing after what are essentially random events.

Or are the events truly random?

There is a perception, which I share(d), that during the 1980s and 1990s there was an increase in the number of terrorist incidents and an increase in their frequency. The FBI just released a report titled "Terrorism 2002/2005" in which they report annual totals of terrorist incidents (most of which we/I have never heard of), number wounded and number killed from 1980-2005.

I grabbed the data and threw them into Stata for some quick and dirty analysis. One hypothesis is causation. We would expect that the number of incidents would "cause" the number of wounded and the number of killed. However, the number of incidents should not "be caused by" the number of wounded or the number of killed (if terrorism acts are random).

Here are some Granger Causality results (using two lags):

. gcause killed incidents ,lags(2)
Granger causality test Sample: 1982 to 2005
obs = 24
H0: incidents does not Granger-cause killed

F( 2, 19) = 0.07
Prob > F = 0.9343

chi2(2) = 0.17 (asymptotic)
Prob > chi2 = 0.9175 (asymptotic)

. gcause incidents killed ,lags(2)
Granger causality test Sample: 1982 to 2005
obs = 24
H0: killed does not Granger-cause incidents

F( 2, 19) = 0.17
Prob > F = 0.8441

chi2(2) = 0.43 (asymptotic)
Prob > chi2 = 0.8058 (asymptotic)

. gcause incidents wounded,lags(2)
Granger causality test Sample: 1982 to 2005
obs = 24
H0: wounded does not Granger-cause incidents

F( 2, 19) = 0.25
Prob > F = 0.7851

chi2(2) = 0.62 (asymptotic)
Prob > chi2 = 0.7337 (asymptotic)

. gcause wounded incidents ,lags(2)
Granger causality test Sample: 1982 to 2005
obs = 24
H0: incidents does not Granger-cause wounded

F( 2, 19) = 0.09
Prob > F = 0.9115

chi2(2) = 0.24 (asymptotic)
Prob > chi2 = 0.8890 (asymptotic)

The results confirm our expectations: incidents cause killed and wounded but not the other way around.

There's not much to do with twenty five years of data, at least not much that we would put a lot of faith in, statistically speaking. I estimated a basic Vector Autoregression Model, in which incidents, killed, and wounded, are all treated as endogeneous variables. The idea here is to see how changes in, say, the number killed in one year impacts the number of incidents in the future. If terrorism was a spiral of violence, rather than being essentially random, then we might expect so see a change in the number of incidents after an especially lethal year.

Here are the results:

Vector autoregression

Sample: 1983 2005 No. of obs = 23
Log likelihood = -400.5665 AIC = 37.44057
FPE = 4.40e+12 HQIC = 37.81305
Det(Sigma_ml) = 2.69e+11 SBIC = 38.92165

Equation Parms RMSE R-sq chi2 P>chi2
----------------------------------------------------------------
incidents 10 6.22335 0.5526 28.41298 0.0008
wounded 10 3142.01 0.0671 1.653871 0.9958
killed 10 781.383 0.0611 1.497955 0.9972
----------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incidents |
incidents |
L1. | .3567426 .1468225 2.43 0.015 .0689758 .6445095
L2. | .0249984 .1681028 0.15 0.882 -.304477 .3544738
L3. | .008384 .1228898 0.07 0.946 -.2324755 .2492436
wounded |
L1. | -.0091878 .0049351 -1.86 0.063 -.0188605 .0004849
L2. | -.0053249 .0051879 -1.03 0.305 -.015493 .0048432
L3. | -.0022507 .0049113 -0.46 0.647 -.0118767 .0073753
killed |
L1. | .0360841 .0198061 1.82 0.068 -.0027352 .0749034
L2. | .0204178 .0207578 0.98 0.325 -.0202667 .0611023
L3. | .0080154 .0197351 0.41 0.685 -.0306646 .0466955
_cons | 5.715191 1.800112 3.17 0.001 2.187037 9.243346
-------------+----------------------------------------------------------------
wounded |
incidents |
L1. | -37.15671 74.12693 -0.50 0.616 -182.4428 108.1294
L2. | 56.16969 84.87079 0.66 0.508 -110.174 222.5134
L3. | -58.97195 62.0439 -0.95 0.342 -180.5758 62.63186
wounded |
L1. | -.9289625 2.491625 -0.37 0.709 -5.812457 3.954532
L2. | -1.23172 2.619244 -0.47 0.638 -6.365345 3.901904
L3. | -.6843121 2.479605 -0.28 0.783 -5.544248 4.175624
killed |
L1. | 3.531244 9.999615 0.35 0.724 -16.06764 23.13013
L2. | 4.484224 10.48006 0.43 0.669 -16.05632 25.02477
L3. | 2.475619 9.963734 0.25 0.804 -17.05294 22.00418
_cons | 1381.007 908.8303 1.52 0.129 -400.2673 3162.282
-------------+----------------------------------------------------------------
killed |
incidents |
L1. | -8.52269 18.43454 -0.46 0.644 -44.65372 27.60834
L2. | 14.0861 21.10642 0.67 0.505 -27.28172 55.45391
L3. | -14.45639 15.42962 -0.94 0.349 -44.69789 15.78512
wounded |
L1. | -.2088094 .6196392 -0.34 0.736 -1.42328 1.005661
L2. | -.29431 .6513767 -0.45 0.651 -1.570985 .982365
L3. | -.1678046 .61665 -0.27 0.786 -1.376416 1.040807
killed |
L1. | .7947777 2.486792 0.32 0.749 -4.079246 5.668801
L2. | 1.074259 2.606274 0.41 0.680 -4.033945 6.182463
L3. | .6139919 2.477869 0.25 0.804 -4.242542 5.470526
_cons | 313.2487 226.0159 1.39 0.166 -129.7343 756.2318

Here's a graph of the impulse response functions, which indicate how one variable changes in the future due to a shock in another variable.



The first column of graphs indicates that there is no change in the number of incidents in a given year after a shock to the number of incidents, wounded, or killed in a previous year. The second column shows the response to the number of killed after a shock to each of the variables. As can be seen, the number of killed goes back to zero essentially one year after a shock to the other variables. this suggests little to no intertemporal relationship between incidents or wounded, and the number killed in a given year.

The third column is that which is most volatile, mainly because the number of wounded in a given year is much more variable than the number killed. However, the impact of shocks to incidents or the number of people killed is very short lived - the response by the number of wounded is essentially over by the next year.

One thing to notice from the VAR estimation results is that the only variable that is statistically significant is the once-lagged number of incidents in the incidents regression. In other words, there seems to be some slight intertemporal pattern in the number of incidents, i.e., a year with more incidents tends to be followed by a year with more incidents, and a year with fewer incidents tends to be followed by a year with fewer incidents. That said, it seems that the number of terrorist incidents is hard to predict contemporanously, as is the severity of these attacks (at least as measured by wounded and killed).

Perhaps the lack of predictability is not surprisig given the definition of terrorism. As it is difficult to predict when an event will occur, or how severe the attack will be, the two extremes of the public debate seem "justified." One side argues for vigilance at DEFCON-2 type levls, which requires reduction in privacy and other costs. One side argues that it isn't practical in a free society for the government to ensure personal liberty (from the government) while at the same time ensuring personal liberty from the terrorists; because the odds of being killed by a terrorist attack has in the past been extremely low, the costs of government vigilance outweigh the benefits.

I would argue that the optimal level of societal security (and therefore government intrusion) is somewhere between the two extremes. Most economists would likely agree, in the sense that costs and benefits are associated with government vigalence, the socially optimal level of vigalence sets social marginal benefit = social marginal cost. The dirty details are in determining what are the marginal benefits and marginal costs.

The data provided in the FBI report suggest that at the aggregate level it is difficult to predict terrorist activity and that there does not appear to be a spiral of violence/bloodshed associated with terrorist activity.

Of course, the prevented, deterred, discovered potential acts of terrorist activity are not reported in the data and might mask much of the success of the government's vigilance. However, whether the billions (trillions?) of dollars in vigilance are justified is a something to ponder.

[Stata Data File]

Comments: Post a Comment



Purchase




Le Chai - galerie du vin



Support



Popularity

Posts that contain Craig Depken per day for the last 90 days.



Contacts

Heavy Lifting's Main Page
Email Me
Atom Feed

WWW
Heavy Lifting




Great Links

Money I Found Today

Heavy Lifting - Firehose style (56k warning)



Recent Posts

- Are Aggregate Terrorism Acts Random?




Archives


home


Visitors
Site Meter Blogroll Me!



Credits

Modified maystar design
powered by blogger