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Comparing Two Benefits Issues For Natural Hazards and Terrorism: Ex-ante/Ex-post Valuation and Endogenous Risk

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Title: Comparing Two Benefits Issues For Natural Hazards and Terrorism: Ex-ante/Ex-post Valuation and Endogenous Risk


1
Comparing Two Benefits Issues For Natural
Hazards and Terrorism Ex-ante/Ex-post
Valuation and Endogenous Risk
  • Scott FarrowUMBC

2
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, PS for Public Safety, 2010).
  • Focus on two key issue
  • Ex-ante and ex-post valuation
  • Endogenous probability (intelligent adversary)

3
Jump to bottom lineFive recommendations to be
developed
  1. Investigate evidence or conduct research
    regarding citizen preferenceswhether 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.

4
Valuing 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)

5
What 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

6
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
    (probq) conditional loss, qCS
  • For incremental events, totally differentiate and
    solve to yield
  • WPAdM/dA -qVA/VM

7
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

8
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)

9
Response surfaces for several utility functions
(or could simulate)
10
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.

11
Some 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.

12
Quick 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.

13
Building Exposure by Census block in a county
14
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 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.

15
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(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)

16
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.

17
Endogenous ProbabilityTerrorism yes NH, yes?
  • For illustration, consider expected value in
    place of expected utility

18
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 Im sure it is), but
    could be useful to link to exceedance probablity.

19
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 dont
    observe Y.

R2 1 SSE/SST
20
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.

21
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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