Session 4 Farrow DHS benefits

Comparing Two Benefits Issues

For Natural Hazards and Terrorism:

Ex-ante/Ex-post Valuation and

Endogenous Risk







Scott Farrow

UMBC





1

Outline

• Conceptual framework: Central role of

preferences no matter what valuation approach

pursued

• Does there appear to be distinct theory about

NH and separately about terrorism? (assert no

difference in the large framing--Farrow and Viscusi, P&S

for Public Safety, 2010).

• Focus on two key issue

– Ex-ante and ex-post valuation

– Endogenous probability (intelligent adversary)



2

Jump to bottom line:

Five recommendations to be developed

1. Investigate evidence or conduct research regarding citizen

preferences…whether terrorism induces ―replaceable‖ or

―irreplaceable‖ losses.

2. Consider using ―ex-ante‖ values in place of ex-post values,

perhaps simulating over various preference models conditional on

findings in 1.

3. Consider implementation issues in ex-ante valuation such as the

use of exceedance probabilities, appropriate asset measure of

income of wealth and the expected value of the ex-ante measure.

4. Quantitatively study (perhaps done) the behavioral response of

attackers to model, even if incompletely, how expenditures may

alter probabilities as with ―human made catastrophes‖.

5. Consider estimation of ―pure error‖ in forecast model which may

expand uncertainty in anti-terrorism compared to NH.







3

Valuing outcomes

• Frequent approach for both NH and

terrorism

• Consider expected damages avoided

based on P*D (probability times damages)

– Estimate damages conditional on event

occurring

– Value a change in policy as the change in

damages (mitigation) and/or change in

probability (prevention)

4

What is the WTP to avoid damage?

Behavioral difference: Ex-ante vs. Ex-post

• Ex-ante: With risk

aversion: individual WTP Utility

ex-ante based on ―risk

premium‖ to avoid

U(CE)

exposure to risk: WTP =

Z

―Z‖, the difference

U(EV)





between expected value

and certainty equivalent,

otherwise accept gamble

• Ex-post: expected loss

• Literature on the Y1 CE μ Y2 Income





complicated linkages



5

One model of the difference: ex-post



• Seek a monetary amount of damages

that equates utility given the bad event,

A*, occurs

V(M,A*)=V(M-CS,0)

• In each period, person willing to pay

expected (prob=q) conditional loss, q*CS

• For incremental events, totally

differentiate and solve to yield

WPA*=dM/dA* = -qVA*/VM*

6

Partial derivation: Ex-ante

• For complete avoidance in advance, consumer is WTP

up to CS which equates utility in the two states

qV(M,A*) + (1-q)V(M,0)=

qV(M-CS,A*) + (1-q)V(M-CS,0)

• As with ex-post, can derive marginal



dM qVA*

(4) WAA = dM/dA* = 

dA * [qVM *  (1  q)VM 0 ]



WAA * WPA * VM 0

(3) Proportional difference=  (1  q)  (1  q)

WAA * VM *

7

Freeman: Difference between Ex-

ante and ―Ex-Post‖ (SEJ, RA)

• Key Message: 1) For small probability, large

consequence events, the difference can be

large. 2) Value depends on specification of

utility (replaceable or irreplaceable)









8

Response surfaces for several

utility functions (or could simulate)

Figure 1: Preliminary response surface: Ex-ante multiple of ex-post for varying risk and

damage levels, risk aversion equal to 2 Figure 2: Extended surface to Losses Exceeding Fifty Percent of Income









WAA* multiple

of WPA*









Damage as

Risk, q proportion of

income









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Recommendations on

ex-ante and ex-post

1. Investigate evidence or conduct research

regarding preferences and terrorism type

events including whether terrorism induces

―replaceable‖ or ―irreplaceable‖ losses.

2. Consider using ―ex-ante‖ values in place of ex-

post values as benefits, perhaps simulating or

using a response surface over various

preference models conditional on findings in 1.





10

Some Implementation Issues

Flood example—in progress

• Use from various utility functions to crate a prediction

equation for ex-ante value as a function of q (probability)

and CS/M (ex-post damages as share of income)

• Generate modeled ―ex-post‖ damage estimates of flood

using model (HAZUS-MH in this case)

• Use probabilities implicit in model based on exceedance

probabilities (more later)

• Obtain damages for various sized events, e.g.

1,10,25,100,500 yr. events or comparable ―time scale‖

• Calculate expected (or other) value.







11

Quick tangent: Damage Estimates

FEMA HAZUS MH model

• Nationwide

• Natural hazards: flood, earthquake

• GIS based for topography, building

inventory to census block level

• Flood model: damage functions based on

distribution of built inventory and flood

height or return period.



12

Building Exposure by Census block

in a county









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Implementation Issue

• Risk averse over what? ―income‖: risk

theory developed originally w.r.t. wealth,

which is actually at risk here. Functions

generally not well defined for CS>M which

occurs.

• Exposure: is money (or wealth) only for

units damaged ex-post, or for all exposed

(perfect information or uninformed?) For

terrorism, more likely uninformed so

exposed value is large, for floods less clear.

14

Expected Value and Exceedance

Probability (preliminary)

• Eventually: likely want expected value of ex-ante or ex-

post value for all event levels per OMB guidance

• Probability: Floods, and catastrophe, often evaluated

using exceedance probability (P(X>X0), what is the

prob. we will get a 9/11 or greater?...a statement about

CCDF. Appears to lead to nice PDF in ―return period‖;

PDF=1/R2; so prob. in that year of exactly 100 year flood

is 10,000. Illustration: D=αR (could extend to multi-year

events and probabilities)

RR

RR RR 1 RR  b1

E(Damage)=  f ( R) D( R)dR   2  Rb dR    Rb2dR  R

R 1 R 1 R R 1 b 1 R 1







15

Recommendation 3

3. Consider implementation issues in ex-

ante valuation such as the use of

exceedance probabilities, appropriate

asset measure of income of wealth and

the expected value of the ex-ante

measure.







16

Endogenous Probability:

Terrorism yes; NH, yes?

• For illustration, consider expected value in place

of expected utility

Table 1: Probability and Consequence Representations for

Natural Hazards and Terrorism





Model Hazards Terrorism



Basic: P*C(e) + u P(e)*C(e) + v



Both Endogenous P(e)*C(e) + u P(e)*C(e) + v









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Apparent practice

• Current practice: DHS break-even analysis:

appears to assume only impact is on

consequence (like basic NH model)

• Advanced environmental theory: endogenous

risk….as people build in risky areas, the

government will respond perhaps in a socially

inefficient way

– Differing time constants (rate of change)

– Stability of response function

• Issue: probability is not exogenous and should

be analytically studied (as I’m sure it is), but

could be useful to link to exceedance probablity.

18

Overconfidence in model

• W.R.T. table, focus often on explained variation

without considering ―pure error‖ or unexplained

variation (u or v in table); creates ―thin‖ tails.

• Modeling error likely larger in terrorism, should

model. Possibility to explicitly consider model fit in

forecast, simulation setting when don’t observe Y.



R2 = 1 – SSE/SST

ˆ

1  R 2 SSM

 ( 2 )

ˆ 2



Rˆ N 19

Recommendation

4. Quantitatively integrate the behavioral

response of attackers to model, even if

incompletely, how expenditures may

alter probabilities as with ―human made

catastrophes‖.

5. Consider ―pure error‖ in forecast model

which may expand uncertainty in anti-

terrorism compared to NH.



20

Conclusions

• Still not clear to the outside that existing

approaches have been exhausted,

• Core framework appears similar between

NH and anti-terrorism,

• Empirically, differences matter,

• If core solidly attempted, extend into

frontier behavioral responses.



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