Centralized matching markets are designed assuming that participants make well-informed choices upfront. However, this paper uses data from NYC’s school choice system to show that families’ choices change after the initial match as they learn about schools. I develop an empirical model of evolving demand for schools under learning, endowment effects in response to prior assignments, and switching costs. These model components are identified by using admissions lotteries and other institutional features. The estimates suggest that there are even more changes in underlying demand than in observed choices, undermining the welfare performance of the initial match. To alleviate the welfare cost of demand changes, I theoretically and empirically investigate dynamic mechanisms that best accommodate choice changes. These mechanisms improve on the existing discretionary reapplication process. In addition, the gains from the mechanisms drastically change depending on the extent of demand-side inertia caused by switching costs. Thus, the gains from a centralized market depend not only on its design but also on demand-side frictions (such as demand changes and inertia).
4. My Findings 1/2
Setting: Public HS choice in NYC in 2004-5
Initial match Reapplication process Enrollment
a) Document >5% of families change school choices
as families learn about schools
b) Uncover demand changes masked by switching cost
(Identification comes from market features like lottery)
→ Even more families (>20%) change demand
→ Large welfare cost of demand changes
For this period... Time
5. My Findings 2/2
c) Theoretically design centralized reapp. mechanisms
d) Empirically find gains from centralized mech.s
・are larger than existing discretionary process
・hinge on demand-side inertia due to switching costs
Learning → Demand changes → Welfare loss
How to alleviate welfare loss?
Setting: Public HS choice in NYC in 2004-5
Initial match
Time
6. Implication
Welfare gains from centralized markets depend on
demand-side frictions as much as market design
(e.g. demand changes, inertia)
↓
Combine good market design with demand-side interventions
7. Reapplication Process in NYC
Match
Announced
Application
Dates
Nov Dec Jan Feb Mar Apr May Jun
Reapplication
Dates
(Conditional
on
Reapplicants)
010203040
Frequencyin%
Discretionary
(non-algorithmic)
reapplication
process
If unsatisfied with initial match via Deferred Acceptance,
applicant may reapply by ranking (up to 3) schools
she prefers to initial assignment
Initial assignment is guaranteed
8. reapply
do not reapply
6430 (7%)
# of applicants
=91289
exhibit choice reversals do not
6430
Evolving Choices
i.e. reapply against
assigned school S
for switching to another school
initially unranked or ranked below S
9. 91289
exhibit choice reversals do not
Lower bound on
demand changers
Non-reapplicants may change demand
( potential switching costs )6430 (7%)
6430
Evolving Choices
=
71% of reapplicants
5% of all applicants
(4564)
reapply
do not reapply
detail
10. 0
.1
.2
...
1
Pr(Reapply)
1 2 3 4 5 6 7 8 9 10 11 12
Preference Rank of the Initially Assigned School
Real pattern in data
Sign of Switching Cost
or Hidden Demand Changes
11. 0
.1
.2
...
1
Pr(Reapply)
1 2 3 4 5 6 7 8 9 10 11 12
Preference Rank of the Initially Assigned School
Gap suggests switching cost
or hidden demand changes
Real pattern in data
What if NO hidden demand change
& NO switching cost?
Sign of Switching Cost
or Hidden Demand Changes
12. Roadmap
#1 Descriptive
There are many choice changes
#2 Structural
There are even more latent demand changes
#3 Counterfactual & Theory
13. Survey suggests main reason for reapplying is new info.
Reapplications rank closer schools w/o sacrificing school quality:
Why Demand Changes
Paper shows reapplications are also more correlated with
horizontal characteristics (e.g. school type/size/age)
↓
All of these suggest importance of info frictions
Initial applications Reapplications Change
1st choice school 4.9 3.9 -21.0%
All ranked schools 5.3 4.0 -24.0%
1st choice school 11.3% 10.5% -6.8%
All ranked schools 14.1% 10.7% -24.3%
Conditional on reapplicants
Distance
(in miles)
Schools with low
academic performance
14. Old Demand in Initial App.
Assumption: in a s initial application
Perceived utility from school s for applicant a in period 0:
NYC runs strategy-proof algorithm on initial applications
to give each a initially assigned school sa
make more informative
nterfactual needs to be
e one. In these senses,
th evolving preferences
period 0 (around Dec,
(0)
are (interactions of) a’s
locations. β0
a are fixed
. I assume that s ≻0
a s′
≻0
a around December as
he original applications,
A(≻0
A, ≻S).
exploit cardinal prefer
evaluations. To achie
model-based and invo
the two exercises are
Specification. The
and inertia is as follo
when the initial appli
where U0
s is a school
and s’s characteristic
or random coefficient
only if U0
as > U0
as′ , i.e.
a rank-ordered discre
the NYC DoE runs th
During and after t
from s for a in period
a & s s characteristics: distance, school academic performance,
school type/size/age (often referred in reapplication reasons)
Frictions (welfare-irrelevant)
onses are likely if families experience psycholo
gnments or get more information about them
d After Learning. The random utility from sch
plication process) is
U0
as = U0
s + ΣK
k=1βak(1 + fak)Xask + ϵ0
as,
pecific effect, Xas ≡ (Xask)k=1,...,K is a vector
racteristics, for example, the distance betwee
vector of preference coefficients, and ϵ0
as is an u
only non-standard term and it stands for info
Xas in the initial application process. I interpr
0
Preferences
(welfare-relevant)
15. In period 1 (reapplication process), perceived utilities evolve to
New Demand in Reapplications
= U0
s + Us
U0
as = U0
s + βa(1 + fa)Xas + ϵ0
as
U0
as = βa(1 + fa)Xas + ϵ0
as
ˆU1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = DAa}
0 1
a
o information frictions, i.e., s ≻0
a s′
only if
e the initial applications, NYC runs a ce
rithm) to obtain the initially assigned scho
king process, applicants’ utilities evolve. T
ermarket) is
¯U1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = s0
a},
ms are similar to those in U0
as except that
and U1
s ≡ U0
s +Us and ϵ1
as ≡ ϵ0
as +ϵas are su
Frictions disappear
a rank-ordered discrete choice based on Uas’s. Afte
the NYC DoE runs the DA algorithm to get the initia
During and after the match-making, applicants’ ut
from s for a in period 1 (around April, when the appe
ˆU1
as = U1
s + β1
aX1
as + ϵ1
as
≡U1
as
+γa1{s =
with β1
a = β0
a + νa and ϵ1
as = ϵ0
as + ϵas. As a result of
ϵt
as’s are iid across schools within each period but ϵ0
as a
The latter is reasonable given the interpretation of ϵt
a
components and that the unobserved determinants of
be serially correlated.
The last term γa1{s = DAa(≻0
A, ≻S)} capture the
ences may evolve differently between the assigned scho
plicants may get more information about the assigned
16. Initial assignment effect
(e.g. endowment effect,
more info)
a rank-ordered discrete choice based on Uas’s. Afte
the NYC DoE runs the DA algorithm to get the initia
During and after the match-making, applicants’ ut
from s for a in period 1 (around April, when the appe
ˆU1
as = U1
s + β1
aX1
as + ϵ1
as
≡U1
as
+γa1{s =
with β1
a = β0
a + νa and ϵ1
as = ϵ0
as + ϵas. As a result of
ϵt
as’s are iid across schools within each period but ϵ0
as a
The latter is reasonable given the interpretation of ϵt
a
components and that the unobserved determinants of
be serially correlated.
The last term γa1{s = DAa(≻0
A, ≻S)} capture the
ences may evolve differently between the assigned scho
plicants may get more information about the assigned
= U0
s + Us
U0
as = U0
s + βa(1 + fa)Xas + ϵ0
as
U0
as = βa(1 + fa)Xas + ϵ0
as
ˆU1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = DAa}
0 1
New Demand in Reapplications
a
o information frictions, i.e., s ≻0
a s′
only if
e the initial applications, NYC runs a ce
rithm) to obtain the initially assigned scho
king process, applicants’ utilities evolve. T
ermarket) is
¯U1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = s0
a},
ms are similar to those in U0
as except that
and U1
s ≡ U0
s +Us and ϵ1
as ≡ ϵ0
as +ϵas are su
Frictions disappear
Will use Uas as welfare measure
1
In period 1 (reapplication process), perceived utilities evolve to
17. 0) Reapplication acceptance prob. pas Estimate it by
same characteristics
as in utility model
a does not appe
⇔U1
as0
a
+ ca > U1
as
a does not appeal in the data
⇔max(s1,s2,s3)(Σ3
i=1pasi
¯U1
asi
+ (1 − Σ3
i=1pasi
) ¯U1
as
1{a’s reapplication for si is accepted}
= 1{b0 + bXXasi
+ bW W asi
+ ξasi
≥ 0}
pasi
=Pr(α + βXasi
+ γW asi
+ ξasi
≥ 0)
a does not appeal in the data
⇔pa(maxs̸=s0
a
¯U1
as − ¯U1
as0
a
) < ca(> 0
⇔U1
as0
a
+ ¯ca > U1
as for any s ̸= s0
a
a does not appeal in the data
ˆ1 ˆ1
Whether to Reapply
18. 0) Reapplication acceptance prob. pas Estimate it by
how oversubscribed s is (# of applicants rejected by s in initial match),
1{a ranks s in initial match}, 1{a is rejected by s in initial match}
1) Reapplication decisions
a reapplies
a does not appe
⇔U1
as0
a
+ ca > U1
as
a does not appeal in the data
⇔max(s1,s2,s3)(Σ3
i=1pasi
¯U1
asi
+ (1 − Σ3
i=1pasi
) ¯U1
as
1{a’s reapplication for si is accepted}
= 1{b0 + bXXasi
+ bW W asi
+ ξasi
≥ 0}
pasi
=Pr(α + βXasi
+ γW asi
+ ξasi
≥ 0)
a does not appeal in the data
⇔pa(maxs̸=s0
a
¯U1
as − ¯U1
as0
a
) < ca(> 0
⇔U1
as0
a
+ ¯ca > U1
as for any s ̸= s0
a
a does not appeal in the data
ˆ1 ˆ1
E(benefit from reapplying) > Reapplication cost , i.e.,
⌘U1
as
0
a= 1
a
a s a0
( 00
a , 01
a )
S) ⌫t
a 'a( 00
a , 0
a, 01
a , 1
a, S)
U0
as = U0
s + a(1 + va)Xas + ✏0
as
a does not appeal in the data
,U1
as0
a( 0
A, S) + ca > U1
as for any s 6=
a does not appeal in the data
,U1
as0
a
+ ca > U1
as for any s 6= s0
a
a reapplies in the data
,max(s1,s2,s3)(⌃3
i=1pasi
¯U1
asi
+ (1 ⌃3
i=1pasi
) ¯U1
as0
a
) ¯U1
as0
a
> ca
application for s is accepted}
Whether to Reapply
19. 2) Reapplication preferences (only for reapplicants)
・Each reapplicant ranks (s1, s2, s3) maximizing E(benefit)
・If reapplicant a does not rank max 3 schools
for any unranked s’¯U1
as0
a
> ¯U1
as′
= U0
s + Us
U0
as = U0
s + βa(1 + fa)Xas + ϵ0
as
U0
as = βa(1 + fa)Xas + ϵ0
as
Whether to Reapply
20. Identification Challenge
{
Only this composite is identified by initial applications
(as in usual discrete choice models)
U0
as = βa(1 + va)Xas + ϵ0
as
ˆU1
as = βaXas + ϵ1
as + γa1{s = DAa}
≻
(≻
ϕa(≻0
A, ≻1
A, ≻S) ≽t
a ϕa(≻′0
a , ≻0
−a, ≻′1
a , ≻1
−
0 0
Initial app.s:
U0
as = U0
s + βa(1 + fa)Xas + ϵ0
as
U0
as = βa(1 + fa)Xas + ϵ0
as
ˆU1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = D
≻
a
(≻
a reapplies E(benefit from reapplying)>reapp. cost ca
Need to identify demand change βafa by reapplication data,
but it s usually hard to distinguish from ca…
Are non-reapplicants satisfied or locked-in?
Reapplications:
Initial assignment effect
(e.g. endowment effect,
more info)
or random coefficients. ϵ0
as is an unobserved stochastic u
only if U0
as > U0
as′ , i.e., each applicant makes the original a
a rank-ordered discrete choice based on U0
as’s. 1
After th
the NYC DoE runs the DA algorithm to get the initial m
During and after the match-making, applicants’ utilit
from s for a in period 1 (around April, when the appeal
ˆU1
as = U1
s + β1
aX1
as + ϵ1
as
≡U1
as
+γa1{s = D
with β1
a = β0
a + νa and ϵ1
as = ϵ0
as + ϵas. As a result of th
ϵt
as’s are iid across schools within each period but ϵ0
as and
The latter is reasonable given the interpretation of ϵt
as a
components and that the unobserved determinants of ut
be serially correlated.
The last term γa1{s = DAa(≻0
A, ≻S)} capture the po
ences may evolve differently between the assigned school a
plicants may get more information about the assigned sch
get to prefer the assigned school more exactly because it a
it (a version of habit formation). Note that I impose the
on the identity or characteristics of DAa(≻0
A, ≻S); this r
= U0
s + Us
U0
as = U0
s + βa(1 + fa)Xas + ϵ0
as
U0
as = βa(1 + fa)Xas + ϵ0
as
ˆU1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = DAa}
≻0
a=≻1
a
a ≻s a′
(≻′0
, ≻′1
)
New Demand in Reapplications
pplication process. fak can be heterogenous across diffe
each applicant makes the initial preference ≻0
a as a rank-
’s subject to information frictions, i.e., s ≻0
a s′
only if U0
a
plicants make the initial applications, NYC runs a cent
ptance algorithm) to obtain the initially assigned school
match-making process, applicants’ utilities evolve. The
od 1 (the aftermarket) is
¯U1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = s0
a},
st three terms are similar to those in U0
as except that th
ed to zero,14
and U1
s ≡ U0
s +Us and ϵ1
as ≡ ϵ0
as +ϵas are sub
d ϵas, respectively. I allow U1
s and ϵ1
as to differ from U0
s
date Figure 2b, which shows that demand changes are
Frictions disappear
Will use Uas as welfare measure
1
In period 1 (reapplication process), perceived utilities evolve to
21. Identification (2 School Case)
Key market feature
Capacity constraints & admission lotteries in initial match
→Initial match randomly assigns applicants to schools
Assumption
Lotteries in initial match
⫫
1) Demand changes
except initial assignment effect γa1{s=sa},
2) Reapplication costs
0
22. Identification (2 School Case)
Key market feature
Capacity constraints & admission lotteries in initial match
→Initial match randomly assigns applicants to schools
0
.05
.1
...
1
Pr(Appeal|Assignedtok-thChoice)
1 lower
Preference Rank of the Initially Assigned School
= demand changes-reapp. costs
demand changes
+ =
reapplication costs
Two moments
↕ & ↕ separate
demand changes &
reapplication costs
Pr(Reapply)
23. Last Step: Initial Assignment Effect
Key market feature 2=Reapp.s submit rank-ordered pref.s
Conditional on reapplying, reapplication cost ca is sunk
but initial assignment effect γa is not
1) a reapplies against sa for switching to s Uas > Uasa+γa
2) a reapplies but does not exhaust reapplication pref
Uasa+γa>Uas for any unranked school s
Restrictions 1 & 2 separate γa from ca
1 1
1 10
00
24. Assumptions for Estimation
In particular, I assume ϵ0
as, ϵas ∼iid EV (I)6
. In addi-
uted according to a pre specified distribution F(·|θ)
Estimation target
(logit)
・Coefficients in t=0:
faβa ∼iid N(μ1, σ1)
ca ∼iid truncated N(μc, σc)
N(μ0, σ0)
(1+fa)βa ∼iid
logN(μ0, σ0)
{
・Reapplication cost:
・Unobserved shocks:
for -distance &
school quality
for the others
・Change to t=1:
Within each demographic group,
γa ∼iid N(μγ, σγ)・Initial assignment effect:
Let whole (fa, βa, ca, γa) be hetero. across race & grade.
25. Step 0) Estimate t=0 parameter by simulated MLE
(t=0 is usual rank-ordered random coefficient logit.
Normalize Uas=0 for one school s.
Simulation uses 400 scrambled Halton draws &
little change from 200 to 400)
Estimation 1/2
{
U0
as = βa(1 + va)Xas + ϵ0
as
ˆU1
as = βaXas + ϵ1
as + γa1{s = DAa}
≻
(≻
ϕa(≻0
A, ≻1
A, ≻S) ≽t
a ϕa(≻′0
a , ≻0
−a, ≻′1
a , ≻1
−
U0
as = U0
s + βa(1 + va)Xa
Initial app.:
U0
as = U0
s + βa(1 + fa)Xas + ϵ0
as
U0
as = βa(1 + fa)Xas + ϵ0
as
ˆU1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = D
≻
a
(≻′
a
ϕa(≻0
A, ≻1
A, ≻S) ≽t
a ϕa(≻′0
a , ≻0
−a, ≻′1
a , ≻1
−
U0
as = U0
s + βa(1 + va)Xa
…
…
a reapplies E(benefit from reapplying) given sa > ca
Reapplication:
0
0
26. {
U0
as = βa(1 + va)Xas + ϵ0
as
ˆU1
as = βaXas + ϵ1
as + γa1{s = DAa}
≻
(≻
ϕa(≻0
A, ≻1
A, ≻S) ≽t
a ϕa(≻′0
a , ≻0
−a, ≻′1
a , ≻1
−
U0
as = U0
s + βa(1 + va)Xa
Initial app.:
U0
as = U0
s + βa(1 + fa)Xas + ϵ0
as
U0
as = βa(1 + fa)Xas + ϵ0
as
ˆU1
as = U1
s + βaXas + ϵ1
as
≡U1
as
+γa1{s = D
≻
a
(≻′
a
ϕa(≻0
A, ≻1
A, ≻S) ≽t
a ϕa(≻′0
a , ≻0
−a, ≻′1
a , ≻1
−
U0
as = U0
s + βa(1 + va)Xa
…
…
a reapplies E(benefit from reapplying) given sa < ca
Reapplication:
Step 1) Estimate t=1 parameter by simulated MLE for
t=1 conditional likelihood for reapp. data, which depends on
a) Initial util.s Uas (Simulate them using estimated t=0 para.)
b) Initial assignment sa (Use real sa observed in data)
→Estimation uses conditional randomness in sa
Estimation 2/2
0
0
0
0
※Assume Uas is quasi-linear in distance(=utility measure)
1
0
27. 0.05.1.15
Density
-10 0 10 20 30 40
New Utility in Distance Unit (Mile)
Demand Changes
Due to Friction
About Xas
New Total Utilities Uas
^1
Estimates: Significant Demand Changes
^ ^Σβak fak Xask
k
28. Estimates: Initial Assignment Effect>00.05.1.15.2.25
Density
-10 0 10 20 30 40
New Utility in Distance Unit (Mile)
1^
Reapplication
Costs ca^
New Total Utilities
Uas
Initial
Assignment
Effects
^γa
29. Estimates: Significant Reapplication Cost0.05.1.15.2.25
Density
-10 0 10 20 30 40
New Utility in Distance Unit (Mile)
1^
Reapplication
Costs ca^
New Total Utilities
Uas
Initial
Assignment
Effects
^γa
30. Data
estimated reapplication costs
c a & estimated initial
assignment effects Ƴ a
c a =0 &
estimated Ƴ a
6.8% 30.8%
(0.15%) (0.78%)
5.3% 23.4%
(0.18%) (1.15%)
2nd row/1st row 71.4%
Simulations of the estimated model
Model 1: Sophisticated expectation
Reapplicants 7.0%
Reapplicants with
choice reversals
5.0%
77.7% 76.1%
Fit
31. Fit
detail
Data
estimated reapplication costs
c a & estimated initial
assignment effects Ƴ a
c a =0 &
estimated Ƴ a
6.8% 30.8%
(0.15%) (0.78%)
5.3% 23.4%
(0.18%) (1.15%)
2nd row/1st row 71.4%
Simulations of the estimated model
Model 1: Sophisticated expectation
Reapplicants 7.0%
Reapplicants with
choice reversals
5.0%
77.7% 76.1%
Simulation standard errors over 50 simulations in parentheses
Good fit to reapplications & choice reversals.
Paper also shows decent fit to initial applications.
32. Data
estimated reapplication costs
c a & estimated initial
assignment effects Ƴ a
c a =0 &
estimated Ƴ a
6.8% 30.8%
(0.15%) (0.78%)
5.3% 23.4%
(0.18%) (1.15%)
2nd row/1st row 71.4%
Simulations of the estimated model
Model 1: Sophisticated expectation
Reapplicants 7.0%
Reapplicants with
choice reversals
5.0%
77.7% 76.1%
Hidden Demand Changes
Many applicants are locked-in by reapplication costs
(30% not outrageous since >60% assigned to non-1st choices)
Simulation standard errors over 50 simulations in parentheses
33. Hidden Demand Changes
detail
Choice changes are a tip of the iceberg of demand changes.
Simulation standard errors over 50 simulations in parentheses
Data
estimated reapplication costs
c a & estimated initial
assignment effects Ƴ a
c a =0 &
estimated Ƴ a
6.8% 30.8%
(0.15%) (0.78%)
5.3% 23.4%
(0.18%) (1.15%)
2nd row/1st row 71.4%
Simulations of the estimated model
Model 1: Sophisticated expectation
Reapplicants 7.0%
Reapplicants with
choice reversals
5.0%
77.7% 76.1%
34. Simulation standard errors over 50 simulations in parentheses
% of winners % of losers Avg util change
47.5% 11.1% +1.60 miles
(0.14%) (0.11%) (0.01 miles)
Model 1: Sophisticated expectation
Welfare Cost of Demand Changes
Demand changes undermine initial match
(1 mile .16 SD in within-applicant utility distribution)
1
1
Measure welfare changes from a to b w.r.t. new demand Uas:
a) Real initial match (which ignores demand changes)
b) Frictionless match (which accommodate all changes)
=Same initial match mechanism applied to Uas
36. Roadmap
#1 Descriptive
There are many choice changes
#2 Structural
There are even more latent demand changes
#3 Counterfactual & Theory
Better market designs could alleviate welfare loss
37. How to Alleviate Welfare Cost
1) Real discretionary reapplication process
2) Counterfactual algorithmic reapplication mechanisms
2.i) Dynamic Deferred Acceptance
=Rerun DA on reapp.s with initial match guarantees
2.ii) Deferred Deferred Acceptance
=Run DA on reapp.s w/o initial match guarantees
'DA
dynamic
≡
exp
(i) it is no
(ii) U1
as1
ak
≡ (1 − L1,no a
a
DAa(≻0
A, ≻S, random
ϕDA
deferred
38. dynamically
strategy-proof
fair/stable w.r.t reapp.s
less unfair than
initial match
weakly Pareto
efficient
always Pareto dom
initial match
w.r.t. reapp.s
Any possible mechanism
can satisfy only a subset of or .
'DA
dynamic
La (βa, νa, ϵas, ca)
≡ (1 − L1,no appeal
a (β0
a, νa, ϵ0
as, ca))Π
#1
a
k=1
exp(U1
s1
ak
+ β1
aX
Σs with s1
ak
1
asexp(U
DAa(≻0
A, ≻S, random lotteries)
ϕDA
deferred
Proposition (Informal)
DAa(≻0
A, ≻S, random lotteries)
ϕDA
deferred'DA
dynamic & Are Best Possible
39. Discretionary
0.005.01.015
FractionofApplicants
-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14
Pref Rank Improvement from Initial Match w.r.t. New Pref
1
a
Gains from Discretionary Process
Welfare gains
compared to initial match
Welfare losses
40. Alternative 1: Deferred
Deferred Acceptance Mech.
Alternative 2: Dynamic
Deferred Acceptance
Mech.
Discretionary
0.005.01.015
FractionofApplicants
-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14
Pref Rank Improvement from Initial Match w.r.t. New Pref
Larger Gains from Centralized Mech.s
'DA
dynamic
≡ (1 − L1,no appeal
a (β0
a, νa, ϵ0
as, ca))Πk=
DAa(≻0
A, ≻S, random lotteries)
ϕDA
deferred
1
a
detail
Shaded areas
=Simulation 95%
confident intervals
41. Takeaway
Discretionary
reapp. process
Centralized
reapp. mech.s
Learning → Demand changes → Undermine initial match
↓
Gains from centralized market depend not only on it design
but also on demand-side frictions
Welfare cost of reapp. cost &
demand-side inertia
Real initial match
(ignoring demand changes)
Frictionless match
(accommodating all changes)
(e.g. demand changes, inertia)
