Title: Comparing Two Benefits Issues For Natural Hazards and Terrorism: Ex-ante/Ex-post Valuation and Endogenous Risk
1Comparing Two Benefits Issues For Natural
Hazards and Terrorism Ex-ante/Ex-post
Valuation and Endogenous Risk
2Outline
- 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, PS for Public Safety, 2010). - Focus on two key issue
- Ex-ante and ex-post valuation
- Endogenous probability (intelligent adversary)
3Jump to bottom lineFive recommendations to be
developed
- Investigate evidence or conduct research
regarding citizen preferenceswhether terrorism
induces replaceable or irreplaceable losses. - Consider using ex-ante values in place of
ex-post values, perhaps simulating over various
preference models conditional on findings in 1. - 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. - Quantitatively study (perhaps done) the
behavioral response of attackers to model, even
if incompletely, how expenditures may alter
probabilities as with human made catastrophes. - Consider estimation of pure error in forecast
model which may expand uncertainty in
anti-terrorism compared to NH.
4Valuing outcomes
- Frequent approach for both NH and terrorism
- Consider expected damages avoided based on PD
(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)
5What is the WTP to avoid damage?Behavioral
difference Ex-ante vs. Ex-post
- Ex-ante With risk aversion individual WTP
ex-ante based on risk premium to avoid exposure
to risk WTP Z, the difference between
expected value and certainty equivalent,
otherwise accept gamble - Ex-post expected loss
- Literature on the complicated linkages
6One 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
(probq) conditional loss, qCS - For incremental events, totally differentiate and
solve to yield - WPAdM/dA -qVA/VM
7Partial 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
8Freeman 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)
9Response surfaces for several utility functions
(or could simulate)
10Recommendations on ex-ante and ex-post
- Investigate evidence or conduct research
regarding preferences and terrorism type events
including whether terrorism induces replaceable
or irreplaceable losses. - 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.
11Some Implementation IssuesFlood examplein
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.
12Quick tangent Damage EstimatesFEMA 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.
13Building Exposure by Census block in a county
14Implementation 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 CSgtM 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.
15Expected 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(XgtX0),
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 PDF1/R2 so
prob. in that year of exactly 100 year flood is
10,000. Illustration DaR? (could extend to
multi-year events and probabilities)
16Recommendation 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.
17Endogenous ProbabilityTerrorism yes NH, yes?
- For illustration, consider expected value in
place of expected utility
18Apparent 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 Im sure it is), but
could be useful to link to exceedance probablity.
19Overconfidence 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 dont
observe Y.
R2 1 SSE/SST
20Recommendation
- 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.
21Conclusions
- 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.