12: Choosing Mitigation Policies
"It is our choices that
show what we truly are,
far more than our
abilities.”
J. K. Rowling, Harry
Potter and The Chamber
of Secrets, 1999
https://www.youtube.com/watch?v=WGwiz80EaTs
Retrofitting California Hospitals
Following hospital collapses in 1971 San Fernando earthquake
that caused ~50 deaths, California required seismic retrofits
Law assumed retrofits would be cheap
Retrofit cost close to that of new buildings
At least $24 B needed
No funding provided
After 40+ years, slow progress
Deadlines already extended
Won’t be done before at least 2030
CQ: How many lives might this safe? Do you think this
this a wise use of resources? If so, how should it be
Lecture 12
3
funded?
COST-BENEFIT ISSUES IN HAZARD
MITIGATION
“There's no free lunch”
Resources used for one goal aren’t
available for another
This is easy to see in the public sector, where there
are direct tradeoffs. Funds spent strengthening
schools aren’t available to hire teachers,
upgrading hospitals may mean covering fewer
uninsured (~$1 K/yr), stronger bridges may
result in hiring fewer police and fire fighters
(~$50 K/yr), etc...
COST-BENEFIT ISSUES IN HAZARD
MITIGATION
“There's no such thing as other people's
money”
Costs are ultimately borne by society as a
whole
Imposing costs on the private sector affects
everyone via reduced economic activity (firms
don't build or build elsewhere), job loss (or
reduced growth), and the resulting reduction in
tax revenue and thus social services.
How much mitigation is enough?
Societally optimal level minimizes
total cost = sum of mitigation cost + expected loss
Expected loss = ∑ (loss in ith expected event
x assumed probability of that event)
For earthquake, mitigation level is construction code
Loss depends on earthquake & mitigation level
Compared to optimum
Less mitigation decreases
construction costs but increases
expected loss and thus total cost
Optimum
Stein & Stein, 2012
More mitigation gives less
expected loss but higher total cost
Including risk aversion & uncertainty
Consider marginal costs C’(n) & benefits Q’(n) (derivatives)
More mitigation costs
more
Benefit
(loss reduction)
cost
But reduces loss
Optimum is where
marginal curves are equal,
n*
Uncertainty in hazard model causes uncertainty in expected loss. We are risk averse, so
add risk term R(n) proportional to uncertainty in loss, yielding higher mitigation level n**
Crucial to understand hazard model
uncertainty
Stein & Stein,
2012
Even without uncertainty, mitigation rarely will be optimal for
societal reasons,but can still do some good
Net benefit
when mitigation lowers total cost below that of no mitigation
Net loss
when mitigation raises total cost above that of no mitigation
Within range,
inaccurate
hazard
estimates
produce
nonoptimal
mitigation,
raising cost, but
still do some
good (net
benefit)
Inaccurate loss
estimates have
sameStein
effect
& Stein, 2013
NY Times
PROBLEM:
UNFUNDED
MANDATE
Property owners
don’t benefit
(can’t charge
higher rent) & so
resist
Maybe society
should fund:
Would public
pay higher taxes
for safety?
CQ: If you were a student in Los Angeles, how much
more would you pay in rent each month to live in an
earthquake-safe building?
Lecture 12
13
NYT
10/31/2012
CQ: Given the damage to New York City by the
storm surge from Hurricane Sandy, possible
options range from continuing to do little, through
intermediate strategies like providing doors to
keep water out of vulnerable tunnels, to building
barriers to keep the surge out of rivers.
Progressively more extensive mitigation measures
cost more, but are expected to produce increasing
reduction of losses in future hurricanes.
How would you develop a strategy to choose
between the various proposed options? How
would you include the anticipated but uncertain
effects of global warming?
Lecture 12
15
“The direct costs of federal environmental, health, and safety
regulations are probably on the order of $200 billion annually,
or about the size of all federal domestic, nondefense
discretionary spending. The benefits of those regulations are
even less certain. Evidence suggests that some recent
regulations would pass a benefit-cost test while others would
not.”
PAN 12.1: a) The
optimal mitigation
level, n*, minimizes the
total cost, the sum of
expected loss and
mitigation cost.
b) n* occurs when the
reduced loss -Q’(n)
equals the incremental
mitigation cost C’(n).
Including the effect of
uncertainty and risk
aversion, the optimal
mitigation level n**
increases until the
incremental cost equals
the sum of the reduced
loss and incremental
decline in the risk term
R’(n).
PAN 12.2: Illustration of the effects of overmitigation and undermitigation
Lecture 12
19
PAN 12.3: a) Comparison of
total cost curves for two
estimated hazard levels. For
each, the optimal mitigation
level, n*, minimizes the total
cost, the sum of expected loss
and mitigation cost.
b) In terms of derivatives, n*
occurs when the reduced loss
-Q’(n) equals the incremental
mitigation cost C’(n). If the
hazard is assumed to be
described by one curve but
actually described by the
other, the assumed optimal
mitigation level causes
nonoptimal mitigation, and
thus excess expected loss or
excess mitigation cost. (Stein
and Stein, 2013b)