07.12.2012 - aprajit mahajan

Introduction Model Identification Estimation

Time Inconsistency, Expectations andTechnology Adoption

Aprajit Mahajan (UCLA, Stanford)Alessandro Tarozzi (Pompeu Fabra)

IFPRI Seminar

July 12, 2012

Dynamic Choice, Time Inconsistency and ITNs


Motivation: Time (In)consistency

Can self-control based explanations rationalize behavior hard to reconcilewith standard model? Two strands of empirical Work:

I Significant body of US-based work, e.g. consumption and saving(Laibson 1997, Laibson et al 2009), welfare uptake (Fang andSilverman 2007), job search (Paserman 2008).

I More recent but growing interest in development: Commitmentcontracts (Ashraf et al 2007, Tarozzi et al 2009), Fertilizer (Duflo etal. 2009), Banerjee and Mullainathan (2010)

I Identification of time preferences not easy. Generically, timediscounting parameters in standard dynamic discrete choice (DDC)not identified (Rust 1994, Magnac and Thesmar 2002).



Motivation (continued)

I Empirical Work: Strotz (1955) “hyperbolic discounting” (“β − δ”)

E(u({at+s}Ts=0)) = u(at) + β

T∑s=1

δsE(u(at+s))

I Allowing for both time consistent and inconsistent agents seemsimportant. But identifying just δ difficult even with no populationheterogeneity.

I How to account for (time) preference heterogeneity theoretically andempirically in such models?

I Finally: information and beliefs (E(·)) may also help explain“suboptimal” behavior.

I Contrast with Fang and Wang (2010) Details



I This paper uses

1. Elicited beliefs2. Survey responses to time preference questions3. Actual product offers (Insecticide Treated Nets, ITNs) to

estimate preference parameters in a dynamic discrete choice(DDC) model of demand with time inconsistent preferences andunobserved types in the malaria-endemic state of Orissa (India)

study area

I We point identify

1. Time preference parameters: β and δ2. (Normalized) Utility (non-parametrically)

I We estimate the model and provide estimates of all time preferenceparameters and other (risk, cost) parameters in the utility function.

1. Inconsistent agents are a majority (Naive & Sophisticated) ...2. ... but Naive agents are “almost” consistent.3. Sophisticated agents are more present-biased than naive agents.4. Other preference differences appear to be small.



Talk: Overview

1. Introduction

2. Model2.1 State Space2.2 Action Space2.3 Preferences2.4 Transition Probabilities2.5 Maximization Problem

3. Discussion of Agent Types

4. Identification4.1 Observed Types4.2 Unobserved Types

5. Monte Carlos

6. Estimation

7. Conclusion



Model: Timing

I Study Design Overview: study design

I Timeline: Agent takes actions in 3 periods

1. At t = 1, given past malaria history, agent decides whether topurchase an ITN and if so, which of 2 possible contracts tochoose. contracts

2. At t = 2, malaria status is realized and subsequently, agentdecides whether to retreat the ITN to retain effectiveness.

3. At t = 3, malaria status for period 3 is realized and the agentdecides again whether to retreat the ITN.



Model: Primitives

We begin by defining the decision problem:

I State Space

I Action Space

I Preferences

I Transition Probabilities

I Maximization Problem



State SpaceObservables

st ≡↓

(xt, εt↓

)

Unobservables

I This Talk:

t=1 x1 ∈ {m,h} malaria status at baseline (6 months before ITNintervention) h =healthy, m =malaria.

t=2,3 For t ∈ {2, 3} xt ∈ {nm, nh, bm, bh, cm, ch}I n: No net purchasedI b: Purchased treated bednet onlyI c: Purchased ITN with retreatment cost included.I {m,h}: Anyone in household had malaria last 6 months

I Extend to more general set up with xt ∈ {n, b, c} × [0, 1]2 × Y(include: contract choice, fraction of household members coverable bybednets, fraction with malaria, income). General time-varyingobserveables. Restriction: Need finite state space. Details

I Easy to incorporate time-invariant observables.



Action Space: At

I Simple:t=1 Choice of contract: a1 ∈ A1 ≡ (n, b, c) Details

b Loan for cost of ITN only. Re-treatment offered for cash onlylater. Rs. 173(223) for single(double) nets paid in 12 monthlyinstallments of Rs.16(21). Retreatment offered at Rs.15 (18).

c Loan for the cost of ITN and loan for two re-treatments to becarried out 6 and 12 months later. Rs. 203(259) forsingle(double) nets paid in 12 monthly installments of Rs.19(23).

t=2,3 Re-treatment choice at ∈ At ≡ {0, 1}

I Richer Structure: fraction of household chosen to be coveredand fraction of nets that are re-treated in t = 2, 3



Transition Probabilities: P(st+1|st, at)I Assume Markovian transition probabilities:

P(st+1|st, st−1, ..., s1, at, ..., a1) = P(st+1|st, at)

I Unobservable εt ∈ st has dimension equal to #At and isI independent across time with known distribution.I independent of (xt−1, at−1) and

P(xt|xt−1, at−1, εt, εt−1) = P(xt|xt−1, at−1)so P(xt, εt|xt−1, εt−1, at−1) = P(xt|xt−1, at−1)P(εt)

I Strong assumptions: rule out unobserved correlated timevarying variables – time invariant unobservables (types) can beaccommodated.



Key Difference: Calculating P(xt+1|xt, at)

I Usually, next invoke rational expectations (e.g. Rust (1994),Magnac and Thesmar (2002)) and assert that agent beliefsP(xt+1|xt, at) are equal to observed transition probability in thedata.

I KEY DIFFERENCE: We elicit P(xt+1|xt, at) for each householdin the survey. beliefs

I Variation in beliefs is key to identification. Intuitively, beliefslead to variation in period t value function while holding periodt utility fixed.

I Need sufficient exogeneity in beliefs for argument to hold(precise conditions outlined later)



Preference: Types of Agent

I Three types of agent:I Time Consistent agents. (τC)I “Naive” Time Inconsistent agents. (τN )I “Sophisticated” Time Inconsistent agents. (τS)

I Types differ by

1. Awareness of future present-bias2. Extent of present-bias βτ

- For time consistent agents βτC = 1- But also allow βτN 6= βτS

3. Per-Period utility uτ,t(·)



Preferences: Per Period Utility

I Utility is time separable and per period utility isuτ,t(st, a) = uτ,t(xt, a) + εt(a) for xt ∈ Xt

I Additively separable in unobserved state variablesI Suppress dependence on other hhd. characteristics.

I Agent of type τ at time t chooses decision rules{dτ,j}3j=t, dτ,j : Sj → Aj chosen to maximize

uτ ,t(st, dτ ,t(st)) + βτ

4∑j=t+1

δj−tE(uτ ,t(st, dτ ,t(sj)))

I Per period utility functions and hyperbolic parameters can varyby type. However, the exponential discount rate is constantacross types.



Awareness of Future Present-Bias

Finite Horizon Dynamic Discrete Choice: Backward Induction

I Agents of all types

1. use backward induction to formulate optimal policy at t2. discount t+ 1 utility by βτδ at t. (βτC = 1: time consistent)

I However, inconsistent types differ in how they view the trade offbetween periods t+ 1 and t+ 2 (from the viewpoint of period t)

1. “Sophisticated” types recognize that they will be present biasedand at t+ 1 they will discount t+ 2 utility by βτδ

2. “Naive” types do not recognize present bias of their future selves.Corresponding discount rate δ



Talk Overview

1. Introduction

2. Model

2.1 State Space2.2 Action Space2.3 Preferences2.4 Transition Probabilities2.5 Maximization Problem


4. Identification

4.1 Observed Types4.2 Unobserved Types

5. Estimation

6. Conclusion



Two Step Identification

I Consider identification in two steps:1. Identification when types are directly observed: Type is assumed

deterministic function of observablesI Response to hypothetical time preference questions (r) details

I choice of commitment product (a1) details

2. Identification when types are not observed (General Case):(r, a1) are only roughly informative about type.

I Identification in the general case builds on identificationarguments for the observed type case.



Directly Observed Types

I Use 2 pieces of information to directly identify agent type.

1. Choice of commitment product (a1 ∈ {n,b, c})2. Displaying time preference reversal in baseline (r ∈ {0,1})

I Classifies (some) agents unambiguously

τC ⇐⇒ {r = 0} time consistentτN ⇐= {r = 1, a1 = b} “naive” inconsistentτS ⇐= {r = 1, a1 = c} “sophisticated” inconsistent

I Advantage: Problem much more tractable.

I Disadvantage: Not clear if (r, a1) map directly into types asdefined above. Ambiguities with classifications({r = 1, a1 = n} =⇒?). problems



Unobserved Types

I Now, types no longer directly observed. Observed choiceprobabilities now mixtures over type choice probabilities.

I Additional parameter: πτ (v) ≡ P(type = τ |v) unknown typeprobabilities. Index types by {τC , τN , τS} ≡ T

I Model is still identified (under additional conditions). Key is toreduce this problem to previous one.

I Can impose (and test) whether (r, a1) map into agent types.e.g. test πτS (1, c) = 1

I Advantage: More agnostic about ability to infer type fromobservables.

I Disadvantage: Identification/Estimation requires more work



Identification Results: Overview

I Directly observed types: Point Identification of

1. Time Preference Parameters: (βτ , δ)2. Normalized utility definition

I payoff

I Unobserved types: Point Identification of

1. Time preference parameters: (βτ , δ)2. Normalized utility3. Type probabilities πτ

Key: Reduce problem to previous one

I payoff



Identification Outline: Directly Observed Types

1. Start in last period (Period 3). Invert relationship between

- observed type-specific choice probabilities: Pτ (at|xt, zt)- model predictions: Pτ (at|xt, zt; θ) whereθ ≡ (δ, {βτ}τ∈T , {ut,τ (·)}4t=1) and zt are beliefs about malaria inperiod t (observe beliefs at 2 point in time).

2. Use variation in (x3, z3) to identify (some parts of) θ

3. Repeat Steps (1) and (2) for period 2 to recover (furtherelements of) θ – including δ

4. Repeat for period 1.



Period 3

I Probability type τ retreats:

Pτ (a∗3 = 1|x3, z3) = G∆(gτ,3(x3, z3, θ)) (1)

I LHS directly identified since {a∗3, x3, z3, τ} observed.

I G∆d= ε0 − ε1 known, support over R. Invert (1) to identify

gτ,3(x3, z3, θ) = u3,τ (x3, 1)− u3,τ (x3, 0)︸︷︷︸Util. Differential

+βτδ

∫u3,τ (x4)dF∆(x4|x3, z3)

I u3,τ (x3, 1)− u3,τ (x3, 0) measures change in period 3 utility fromre-treatment. Next, identify this.



Period 3: Identifying Utility

I KEY: Use variation in beliefs to identify the utility differential.I Need household beliefs not perfectly predicted by observables x3

(formally Assumption 6)

I Intuition: Evaluate

gτ,3(x3, z3, θ) = u3,τ (x3, 1)− u3,τ (x3, 0) + βτδ

∫u4,τ (x4)dF∆(x4|x3, z3)

at two different values of z and difference.I Lemma 1: The researcher observes an i.i.d. sample on

({a∗t , xt}T−1t=1 , w). With sufficient variation in beliefs

1. u3,τ (x3, 1)− u3,τ (x3, 0) are identified for all x3 ∈ X3.2. Fourth period expected discounted (normalized) utility is

identified(βτδ

∫u4,τ (x4)(dF (x4|x3, a3 = 1, z3)− dF (x4|x3, a3 = 0, z3))



Identifying Hyperbolic Parameters βτ

I Data from t = 3 do not identify all time preference parameters.

I However, If in addition to previous assumptions

1. Some time consistent agents make a purchase decision.2. Period 4 utility differentials are constant across time consistent

and time inconsistent naive typesI Restrictive. But preferences in periods < 4 differ by type, so can

gauge reasonablenessI Much less restrictive than previous work.

I Under these additional assumptions, βτN is identified (Lemma 2)



Identification: Period 2

I Need this period to identify remaining time parameters.

I Use same inversion argument as before.

I Identification argument more delicate since types further differin perceptions about future present-bias

dτ (s3) ≡ argmaxa∈A3

{u3,τ (x3, a) + ε3(a) + β̃τδ

∫u4,τ (x4)dF (x4|x3, a, z3)

}I “sophisticated” type: recognizes that period 3 self will be subject

to present-bias. β̃τS = βτI “naive” type: is present biased (in period 2) but does not

recognize that his period 3 self will also be present biased.β̃τN = 1 6= βτN

I Time consistent agents: β̃τC = βτC = 1.



Identification: Period 2 parameters

I Lemma 3

1. Assuming that beliefs (conditional on the state variables) havetwo points of support we identify normalized utility:uτ,2(x2, 1)− uτ,2(x2, 0)

2. Next, using results from the previous section (Lemma 2) weseparately identify βτS and δ. Intuition

I Summary:I We identify both utility and time preference parameters given

sufficient variation in beliefs about re-treatment effectiveness.

I Key: beliefs provide variation in the value function term whileholding utility differentials constant.



Identification: Period 1 Parameters

I Survey response (r) can distinguish between consistent andinconsistent types and purchase reveals type (for r=1).

I However, cannot separate “naive” and “sophisticated” fornon-purchasers.

I Cannot observe types =⇒ Can’t use inversion directly.

I Insight: All we needed for inversion was type-specific choiceprobabilities (not individual types).

I Identification argument here in 2 steps:I Identify type-specific choice probabilities Pτ (a1|x1, z1).I As before, recover type-specific utility parameters (θ) by studying

mapping b/w Pτ (a1|x1, z1) and model prediction Pτ (a1|x1, z1, θ)I Same argument used in general case.



I Need sufficient variation in type-specific choice probabilitiesacross and within states. Sufficient conditions:

- Conditional on state, ≥ 2 types have different choice probs.- ∃ at least two states such that the corresponding vector of

type-specific choice probabilities are different. Weaker conditionsuffices (Assumption 11)

I Lemma 4 Under assumptions 1-111. The first period utility differences u(x1, b, τ)− u(x1, n, τ) and

u(x1, c, τ)− u(x1, n, τ) are identified for all x1 ∈ X1 and for alltypes τ .

2. The type probabilities {πτ (·)}τ∈T are also identified.

I In addition to identifying preferences for the different types, wealso identify the relative size of all three different types of agentin population.

I This is useful because we obtain unconditional distribution oftypes whereas previous work could at best be informative abouttype distribution conditional upon purchase.



Overview

1. Introduction

2. Model



4. Identification

4.1 Observed Types

4.2 Unobserved Types

5. Estimation

6. Conclusion



Unobserved Types

I Previous model useful but relied heavily on types being directlyobserved.

I Now consider case where types are not observed.

I Useful if we are unwilling to believe that survey responses and choiceof “commitment” product mechanically identify agent type (test themapping too).

I Identification problem much harder now since can’t use the standardinversion argument.

I Two step identification argument (as in last lemma):

1. Identify type-specific choice probabilities Pτ (and typeprobabilities πτ ).

2. Use identified type-specific choice probabilities to back out thetype specific preferences as before.



Type-Specific Choice Probabilities: Assumptions

I Need some apriori knowledge about the relationship betweenru ≡ (r, a1) and types. In particular, for ru 6= r′u, the three

ratios{πτC (ru)

πτC (r′u) ,πτN (ru)

πτN (r′u) ,πτS (ru)

πτS (r′u)

}can be ordered ex-ante

I Sufficient Conditions:

- Among agents with r = 1, inconsistent agents are more likely topurchase the commitment product (and sophisticated agents themost likely): πS(1, c) ≥ πN (1, c) > πC(1, c)

- Among agents with r = 0 time consistent agents are most likelyto buy product b and naive agents are more likely to purchase bthan sophisticated agents.: πS(0, b) < πN (0, b) ≤ πC(0, b)

but weaker condition above suffices.



Type-Specific Choice Probabilities: Assumptions

I Conditional on state and agent-type, ru is uninformative aboutactions. Reasonable if ru only informative about choices throughpredictive power for type. Violated if e.g. r = 1 indicates reflectsinnumeracy or other flaws in cognition. (Assumption 13)

I Transition probabilities do not vary by type and are independent ofru. Can test this. (Assumption 13)

I There is sufficient variation in the type specific choice probabilitiesPτ (at = 1|xt, z). In particular, require M − 1 points in xt and a rankcondition that rules out using multiple states such that all types havethe same choice probabilities for them. (Assumption 14)

I All types exist with positive probability for at least two values of ru.(Assumption 15) Can potentially test for this (Kasahara andShimotsu (2009)).



Type Specific Choice Probabilities: Results

I Lemma 5: Under additional assumptions 13-15 the choicespecific probabilities Pτ (at = 1|xt) are identified for allxt ∈ XB ∪ XC and t > 1. In addition, the type probabilities{πτ (ru)}τ∈T are also identified.

I Uses argument from Kasahara and Shimotsu (2009) (requiresfewer assumptions on length of panel).

I Lemma 6: Under assumptions 1-3,5-15 we can identify

1. The type-specific utility differentialsut(xt, 1, τ)− u(xt, 0, τ) ∀ τ ∈ T , xt ∈ XB ∪ XC ∀t

2. The exponential discount parameter δ and the hyperbolicparameters βτ ∀τ ∈ T



Monte Carlo Simulations

uτ (st, at, θ) = ut(xt, at, θ) + εt(at)

I εt i.i.d. Generalized Extreme Value -I (convenient)

I At t agent solves

ut(st, at, θ) + βτ

4−t∑j=1

δjEt(ut(sj , aj , θ))

I Basic Set Up: Agents only differ in the values of the hyperbolicparameters βτ and the level of “sophistication” among timeinconsistent agents.

I Finite Horizon DDC model (Backward Induction)



Monte Carlo Simulations: Per-Period Utility

1. Period 4: x4 ∈ {0, 1}u(x4) = −θ4x4

2. Period 3:x3 ∈ {bm, bh, cm, ch, nh, nm} ≡ {b, c, n} × {h,m} ≡ {0, 1, 2, 3, 4, 5}and a ∈ {0, 1}

u(x3, a) = −θ4{x3 ∈ {1, 3, 5}} − θ5pr{x3 ∈ {0, 1}, a = 1}

3. Period 2:x2 ∈ {bm, bh, cm, ch, nh, nm} ≡ {b, c, n} × {h,m} ≡ {0, 1, 2, 3, 4, 5}and a ∈ {0, 1}

u(x2, a) = −θ4{x2 ∈ {1, 3, 5}} − θ5pr{x2 ∈ {0, 1}, a = 1}

4. Period 1: x1 ∈ {h,m} ≡ {0, 1} and a ∈ {b, c, n} ≡ {0, 1, 2}u(x1, a) = −θ4{x1 = 1} − θ5pb{a1 = 1} − θ5pc{a1 = 2}



I Choice probabilities

Pτ (at = j|xt; z) =exp(v(xt, j, βτ ; z))∑Js=1 exp(v(xt, s, βτ ; z))

(2)

where v(xt, j, β) is the Emax function. E.g.

v(x2, j, βτ ; z) = u(x2, j) + βτδ

∫x3

v∗τ (x3)dF (x3|x2, j; z)

v∗τ (x3) =

∫(v(x3, s, 1) + ε3(s))I(s is chosen)dG(ε3)

I(s is chosen) ≡ {v(x3, k, β̃τ ; z) + εk > v(x3, s, β̃τ ; z) + εs ∀k 6= s}β̃C = βC = 1 β̃N = 1 βN = .7 β̃S = βS = .8

I Here, types differ (in period 2) in predicting own choice in period 3

I Use (2) as moment condition for estimation.



Table 1: Monte Carlo Results: Directly Observed Types

Mean Median Std.Dev IQR

N=300δ 0.88 0.86 0.52 0.65βN 0.74 0.71 0.30 0.40βS 0.83 0.79 0.32 0.41θ4 4.37 3.09 4.92 3.11θ5 1.03 1.03 0.56 0.74N=600δ 0.90 0.86 0.37 0.52βN 0.71 0.70 0.18 0.25βS 0.81 0.78 0.23 0.28θ4 3.71 3.09 2.10 1.93θ5 1.04 1.04 0.38 0.51N=2400δ 0.89 0.89 0.18 0.26βN 0.69 0.69 0.09 0.13βS 0.80 0.79 0.11 0.14θ4 3.17 3.03 0.73 0.94θ5 1.00 0.99 0.18 0.24

Notes: Each model was simulated 250 times. The true values are (δ, βN , βS , θ4, θ5) = (.9, .7, .8, 3, 1)



Table 2: Monte Carlo Results: Unobserved Types

Mean Median Std.Dev IQR

N=300δ 0.6669 0.6309 0.3303 0.4147βN 0.4034 0.2795 0.4306 0.6809βS 0.9608 0.9315 0.4766 0.6875θ4 5.0283 4.0879 3.3146 3.0744θ5 1.0576 1.0462 0.5426 0.6934N=600δ 0.7377 0.7051 0.3016 0.4182βN 0.4330 0.4020 0.4000 0.4674βS 0.9475 0.9263 0.3027 0.4387θ4 4.0817 3.6559 1.7953 2.2880θ5 1.0742 1.0695 0.3836 0.5152N=2400δ 0.7865 0.7751 0.2083 0.2920βN 0.4137 0.4096 0.1782 0.2229βS 0.9701 0.9552 0.2143 0.2611θ4 3.2838 3.0896 0.9665 1.2084θ5 1.0159 1.0165 0.2054 0.2545

Notes: Each model was simulated 250 times. The true values are (δ, βN , βS , θ4, θ5) = (.7, .4, .95, 3, 1)



Overview

1. Introduction

2. Model



4. Identification

4.1 Observed Types4.2 Unobserved Types

5. Estimation

6. Conclusion



Estimation: Overview

I Assume that errors are GEV-I (standard - convenient)

I Additional – relative to standard DDC models – complications:I Unobserved TypesI Time Inconsistent agentsI Recover time preference parameters.

I State Variables x : income (y), malaria status (h) and a1 fort > 1

I Additional household characteristics (v) household size(hhsize), baseline assets (assets), measures of risk aversion(risk). Also used education of household head and finerdemographics.



Preferences

I Period 4:uτ (x4; v) = c(x4)ατ (v) − cτ (x4, v)

I Period 2,3:uτ (xt, at; v) = (c(xt)− pratI{a1 = b})ατ (v) − cτ (x4, v)

I Period 1:uτ (x1, a1; v) =

(c(x1)− pbI{a1 = b} − pcI{a1 = c})ατ (v) − cτ (x4, v)

where

I ατ (v) = Logit (ατ + α1hhs + α2assets + α3risk) restricted forsimplicity.

I cτ (xt, v) ≡ htcτ (v) = I{ht = m} exp(κτ + κ1hhs + κ2assets)

I pr=price of retreatment, (pc, pb)=(price of b and c) and c(xt) isconsumption level in state xt



Mapping Model to Type-Specific Choice ProbabilitiesI Pτ (at+1 = a|xt; w̃) = exp(vτ (xt,a,w̃,βτ )∑J

j=0 exp(vτ (xt+1,aj ,w̃,βτ )

I vτ (xt, a, w̃, βτ ) ≡ uτ (xt, a) + βτδ∫v∗τ (xt+1)dF(xt+1|xt, a)

I v∗τ (xt+1) =∑J

s=1

∫(vτ (xt+1, s, 1) + εs,t+1)IAτs,t+1

dF(εt+1)

I Aτk,t+1 ≡ {vτ (xt+1, k, β̃τ )+ εk,t+1 > vτ (xt+1, s, β̃τ )+ εs,t+1∀s 6= k}I Hypothesized optimal action in t+ 1 chosen assuming present

bias in t+ 1 is β̃τ

I Modified value function

v∗τ (x3) =

J∑s=1

P(Aτs)

(vτ (x3, s, 1)− vτ (x3, s, β̃τ )

+ γeuler + log(

J∑j=1

exp(vτ (x3, j, β̃τ )))

)



Estimation: First Step

I Identify Pτ (at|xt, z, v, ru) using Lemma 5. Requires flexibleestimate of P(at, at+1, xt, xt+1|z, v, r) as inputs intoKashara-Shimotsu procedure. Use flexible logit specifications.

I Implement the proof of Lemma 5 at each value of (z, v, ru) forall relevant values of (at, at+1, xt, xt+1) (for t > 1). Discretize(z, v, ru) for tractability. Eigenvalue decomposition yields typeprobabilities πτ (ru) and type-specific choice probabilitiesPτ (at|xt, z, v)



Estimation: Step Two

I For a given parameter vector θ = (δ, βτN , βτS ,α,κ) computemodel choice probabilities starting from the last period andworking backwards to construct the value functions needed tocalculate model choice probabilities for each type.

I Estimate θ by minimizing the distance between between modelprobabilities and the type-specific choice probabilities recoveredin the first step.



Results: Population Distribution of Types

Table 3: Type Probabilities

πτ (r) Estimate 2.5 97.5

πC(0) 0.3870 0.2894 0.4837πN (0) 0.5019 0.4172 0.6059πS(0) 0.1111 0.0593 0.1691πC(1) 0.4143 0.3092 0.5126πN (1) 0.4699 0.3851 0.5790πS(1) 0.1158 0.0639 0.1756

Notes: πτ (r) is the probability that an agent is of type τ given response r to the time-inconsistencyquestion.

I Time consistent agents are about 40% of populationI Bulk of time-inconsistent agents are naive.I The relative sizes of the population are ≈ same irrespective of r.

Note that we did not need to assume πC(0) > πC(1) foridentification or estimation. Suggests that conventionalmapping of time-consistency from survey responses may not bestraightforward.



Results: Time Preference Parameters

Table 4: Unobserved Types: Time Preferences

Estimate 2.5 97.5

δ 0.7880 0.0000 0.9351βN 0.9757 0.9313 0.9798βS 0.5727 0.0007 0.7311

Notes: δ is the exponential discount parameter. βN is the hyperbolic parameter for naivetime-inconsistent agents, βS is the corresponding parameter for sophisticated time-inconsistent agents.

I “Naive” and “Sophisticated” agents have different rates of timepreference.

I “Sophisticated” agents appear to me much more present-biasedthan “naive” agents.

I Speculation: consistent with idea that highly impatient agentslearn how to cope over time (by becoming “sophisticated”).



Results: Cost and Risk Aversion Parameters

Table 5: Unobserved Types: Cost and Risk Aversion

Estimate 2.5 97.5

αC 0.7230 0.6047 1.7890αN 0.4348 0.2935 1.9277α4 0.5513 0.3725 1.9736α5 0.8389 0.6911 2.0000α6 0.9205 0.7935 1.9445κC 0.0070 -1.9950 1.0754κN -0.1998 -0.6869 0.8373κS -0.5314 -1.9951 1.3667κS -0.9613 -1.2298 0.3725κ5 -0.3721 -2.0000 1.6852

Notes: The α vector parameterizes the risk-aversion parameter and the κ vector parameterizes themalaria cost function.

I Some variation in risk and cost parameters across types.However, differences are imprecisely estimated and appear to besubstantively small (for counterfactuals considered in paper)



Counterfactuals: SummaryI Ran a set of exercises where we varied the utility and

time-preference parameters across types and compared take-upand retreatment results.

I e.g. compare take up for a model where all types have the samecost and risk preferences but different hyperbolic parameters.

I The results suggest that the differences in take-up andretreatment across types are driven primarily by thetime-preference parameters rather than by the cost and riskparameters.

I Since the hyperbolic parameter for the naive agents are quiteclose to 1, their take-up and retreatment behaviour is quiteclose to that of the time-consistent agents. The behavior of thesophisticated agents is quite different but they are smallfraction of the population.



Conclusions and To Do List

I Time Inconsistency is often proposed as an explanation forobserved choice behaviour but identifying time preferences isusually difficult.

I Combine information on beliefs along with a field interventionto identify a dynamic discrete choice model with timeinconsistency and unobserved types.

I Results suggest that about 40% of sample was time-consistentand that the bulk of inconsistent agents were “naive”

I Results suggest that “sophisticated” agents much morehyperbolic than naive ones.

I Examined other differences (in risk, cost preferences) acrosstypes and found these differences to be relatively small.

I Model Validation needed.


Additional Material

Loan Products

I Our MF partner offered two loan contract types (20% annualinterest rate, equal installments): Calculations

C1 Loan for the cost of ITN and loan for two re-treatments to becarried out 6 and 12 months later. Rs. 203(259) forsingle(double) nets paid in 12 monthly installments of Rs.19(23).

C2 Loan for cost of ITN only. Re-treatment offered for cash onlylater. Rs. 173(223) for single(double) nets paid in 12 monthlyinstallments of Rs.16(21). Retreatment offered at Rs.15 (18).

I Context: Daily agricultural wages are about Rs.50, the price of1 kg. of rice is about Rs. 10 and the official poverty line forOrissa (2004-5) was Rs. 326 per capita per month.

Intro Intro: Overview Model Model: Action Space Types Study Design


Additional Material

Loan Product Calculations

I Cost of the product is p

I Monthly interest rate r

I Number of months to repay: t

I The identical monthly installment x

x(p, r, t) =pr

1− (1 + r)−t

is obtained by solving

p =

t∑j=1

x1

(1 + r)j

Return to Loan Product


Additional Material

Transition Probabilities

I For t ∈ {2, 3}, partition the space Xt into the setsB = (bm, bh), C = (cm, ch) and A = (nm, nh). The transitionprobabilities from states t to t+1 for are given by

P(xt+1 = x|xt = y, a, z) = I{y ∈ B ∪ C}(π − δ − γa) for x ∈ {bm, cm}P(xt+1 = x|xt = y, a, z) = I{y ∈ B ∪ C}(1− π + δ + γa) for x ∈ {bh, ch}P(xt+1 = nm|xt = y, a, z) = I{y ∈ A}πP(xt+1 = nh|xt = y, a, z) = I{y ∈ A}(1− π)

I Note that stationarity rules out learning. In fact, don’t needstationarity in transitions. We also elicit beliefs at the end ofproject (i.e. after period 3) which we can use to directly studybelief evolution.

Return to Model Outline


Additional Material

Study Design

I Part of a larger study covering 162 villages in rural Orissaevaluating alternative methods of ITN provision.

I Here, focus on treatment arm where 627 households wereoffered loan contracts to purchase ITNs. Details

1. March-April 2007: Baseline Survey2. September-November 2007: Information Campaign and ITN

Offers3. March-April 2008: First Retreatment4. September-November 2008: Second Retreatment5. December 2008-April 2009: Follow Up Survey

I Baseline and Follow Up surveys: Detailed Information

I Retreatment and Offer periods: Minimal InformationReturn to Model Overview


Additional Material

Location

I Malaria “number one public health problem in Orissa” (Orissa HDR, 2004).

I Sample: 627 MF client households from 47 villages.

I ≈ 12% malaria prevalence, almost all P. falciparum.

Back to Intro


Additional Material

Elicited Beliefs and P(xt|xt−1, at−1)

I ElicitI P(Malaria|No Net) ≡ πI P(Malaria|Untreated Net) ≡ π − δI P(Malaria|ITN) ≡ π − δ − γ.

I Use this along with a stationarity assumption to construct atransition probability matrix.

I Can build up transition probabilities for more complicated statespaces. e.g. P(k members sick|No Net) =

(Hk

)πk(1− π)H−k

I Stationarity rules out learning. However, don’t needstationarity for identification. We also elicit beliefs at the end ofproject (i.e. after period 3) which we can use to directly studybelief evolution.

Back to Intro Model: Transition Probabilities


Additional Material

I Perceived Protective Power of ITNs

23/04/07

26

SECTION 11 SUBJECTIVE EXPECTATIONS 11.01

PLEASE WRITE THE PRINCIPAL RESPONDENT ID FROM THE HOUSEHOLD ROSTER cêLý C�e\ûZûu @ûAWò ^é GVûùe ùfL«ê

Income ùeûRMûe

11.02

Now please think about the income of everybody in your household. Think about income from wages, sales, business, or any other source from each member of your household. Also include the value of any in-kind earnings Now think about the next agricultural year (SPECIFY: April 2007 to March 2008): in your opinion, in the best possible situation, what is the largest amount of total income that your household may be able to earn during the next agricultural year? a�ðcû^ @û_Y @û_Yu _eòaûee icÉ i\iýue ùeûRMûe aòhdùe Pò«û Ke«ê û ùeûRMûe Kjòùf aòbò^Ü C›eê ùeûRMûe ù~_eò _ûeògâcòK, aòKòâ, aýaiûd aû @^ý ù~ùKøYiò C›eê ùeûRMûe

Kê cògûA Kjòùa û a�ðcû^ @û_Y @ûi«û Kéhòahð @[ðûZþ G_òâfþ 2007 eê cûyð 2008 aòhdùe Pò«û Ke«ê Gaõ ùcûùZ Kêj«ê iaêVûeê bf _eòiÚòZòùe _eòaûee icÉ i\iýue icÉ C›e

ùeûRMûeKê cògûA @û_Yu _eòaûee @ûi«û Kéhò ahð _ûAñ ùcûU ùeûRMûe / @ûd ùKùZ ùjûA_ûùe?

Rs. _________________________________

11.03

Now please think about the worst possible situation: what is in your opinion the smallest amount of total income that your household may be able to earn during the next agricultural year? a�ðcû^ iaêVûeê Leû_ _eòiÚòZò aòhdùe Pò«û Ke«ê û @û_Yu cZùe @ûi«û Pûh ahðùe @û_Yu _eòaûe iað^òcÜ ùKùZ @ûd Keò_ûeòùa ?

Rs. _________________________________

11.04 INTERVIEWER : CALCULATE MID-POINT iûlûZKûeú : _eòaûee ùcûUûùcûUò @ûd ùfL«ê

Rs. _________________________________

11.05

So, you think that during the next agricultural year the total income that your household will be able to earn will be no less than (11.03), and not more than (11.02). In your opinion, on a scale 0-10, how likely is it that during the next agricultural year the total income that your household will be able to earn will be larger than (11.04)? ]e«ê @ûi«û Pûh ahðùe @û_Yu _eòaûee ùcûU @ûd (11.03) Vûeê Kcþ ùja^ûjó Kò´û (11.02) Vûeê ùagò ùja ^ûjó û @û_Yu cZùe 0-10 _~ðý« GK ùiÑfþùe @ûi«û Pûh ahðùe @û_Yue _eòaûee

ùcûU @ûd (11.04) Vûeê ùagò ùjaûe i¸ûa^û ùKùZ @Qò ?

P(y>11.04)=

11.06 In your opinion, on a scale 0-10, how likely is it that in the next agricultural year the total income that your household will be able to earn will be smaller than (11.04)? @û_Yu cZùe 0-10 _~ðý« GK ùiÑfþùe @ûi«û Pûh ahðùe @û_Yue _eòaûee ùcûU @ûd (11.04) Vûeê Kcþ ùjaûe i¸ûa^û ùKùZ @Qò?

P(y<11.04)=

EXPECTATIONS ABOUT MALARIA ùcùfeò@û aòhdùe i¸ûa^û 11.07 - Imagine first that your household [or a household like yours] does not own or use a bed net. ]e«ê @û_Yu _eòaûeùe (Kò´û @û_Yu _eò @^ý _eòaûe) cgûeú ^ûjó aû aýajûe Ke«ò ^ûjó ùZùa @û_Yu cZùe (.........) K[û C_ùe @û_Y Kò_eò GKcZ Zûjû 0-10 c¤ùe GK ^é ù\A Kjòùa û i¸ûa^û @]ôK ùjùf @]ôK ^é ù\ùa Gaõ Kcþ ùjùf Kcþ ^é ù\ùa û In your opinion, and a scale of 0-10, how likely do you think it is that @û_Yu cZùe @û_Y ....... C_ùe 0-10 bòZùe ùKùZ ^é ù\ùa

A A child under 6 that does not sleep under a bed net will contract malaria in the next 1 year? 6 ahðeê Kcþ adie _òfûUòKê cgûeò Zùk ^ gê@ûAùf @ûi«û GK ahð c¤ùe ZûKê ùcùfeò@û ùjaûe i¸ûa^û ùKùZ ?

B An adult that does not sleep under a bed net will contract malaria in the next 1 year? RùY adiÑ aýqò cgûeú Zùk ^ ùgûAùf @ûi«û 1 ahð c¤ùe ZûKê ùcùfeò@û ùjaûe i¸ûa^û ùKùZ ?

C A pregnant woman that does not sleep under a bed net will contract malaria in the next 1 year? RùY MbðaZú cjòkû cgeú Zùk ^ ùgûAùf @ûi«û 1 ahð c¤ùe ZûKê ùcùfeò@û ùjaûe i¸ûa^û ùKùZ ?

11.08 – Now imagine that your household [or a household like yours] owns and uses a bed net that is not treated with insecticide

Frac

tion

No net use0 2 4 6 8 10

0

.5

1

Frac

tion

Regular use of untreated net0 2 4 6 8 10

0

.5

1

Frac

tion

Regular use of ITN0 2 4 6 8 10

0

.5

1

Frac

tion

No net use0 2 4 6 8 10

0

.5

1

Frac

tion


0

.5

1

Frac

tion


0

.5

1

Frac

tion

No net use0 2 4 6 8 10

0

.5

1Fr

actio

n


0

.5

1

Frac

tion


0

.5

1

I π ≡ P (malaria within one year | no net)I γ ≡ P (malaria | untreated net)− P (malaria | ITN)I δ ≡ P (malaria | no net)− P (malaria | untreated net)

Back to Intro Back to Model


Additional Material

]

I Time Preferences and “Hyperbolic Discounting”:

23/04/07

20

Section 8 Time Discounting We would like to play games with you which will allow you to win a small money prize at no cost for you. We are going to ask you to choose one between two alternative amounts of money, which will be made available to you in the future but at different times. For instance, we may ask you if you would rather have Rs 10 one month from now, or Rs 12 in four months from now. We will play this game 12 times. Each time, we will ask you to choose between two alternatives. At the end of the questionnaire, we will select one of the 12 games at random, and you will be awarded the amount of Rupees that you have selected in that game, at the time indicated by the option you have selected. We will make sure the prize will be given to you through BISWA, so you should be confident that the money will really be given to you once the time comes. For each of the two possible games below, please tell us which option you would prefer. @ûùc @û_Yu iûwùe KòQò ùLk ùLkòaê ~ûjû @û_Yuê aò^û cìfýùe ißÌ Uuû RòZûAa û @ûùc @û_Yuê \êAUò bò^Ü @[ðe eûgò c¤eê ùMûUòG aûQòaûKê Kjòaê û ~ûjû @û_Y baòhýZùe bò^Ü bò^Ü icdùe _ûAùa û C\ûjeY ißeì_ @ûùc @û_Yuê Kjò_ûeê @û_Y 10 Uuû

cûùi _ùe Pûjó_ûe«ò Kò´û 12 Uuû 4 cûi _ùe Pûjó _ûe«ò û Gjò ùLk @ûùc iûlûZKûe c¤ùe 12 [e ùLk ùLkòaê û _âZò[e @ûùc @û_Yuê 2Uò aòKÌ c¤eê ùMûUòG aûQòaûKê Kjòaê û iûlûZKûe ùghùe 12Uò ùLk c¤eê ùMûUòKê @ûùc fùUeò cû¤cùe aûQòaê û

Gaõ @û_Y aûQò[ôaû @[ðeûgò C_~êq icdùe _êeiÑûe ißeì_ _ûAùa û @ûùc @û_Yuê Gjò _êeÄéZ @[ðe eûgò aògß cû¤cùe ù~ûMûAaû_ûAñ _âZògîZò ùjCQò û ~ûjû\ßûeû ^ò½òZ ùjûA_ûeòùa ù~ C_~êq icd @ûiòùf @û_Y @[ð _ûA_ûeòùa û SURVEYOR: BEFORE THE GAMES ARE PLAYED, THE ORDER IN WHICH THE QUESTIONS SHOULD BE ASKED HAS TO BE RANDOMLY DETERMINED. THE SURVEYOR MUST ASK THE

TWELVE QUESTIONS FOLLOWING THE ORDER INDICATED IN THE COLUMN LABELED “ORDER”, AND NOT FOLLOWING THE NATURAL ORDERING OF THE QUESTIONS AS LISTED IN THE QUESTIONNAIRE. ùLk @ûe¸ _ìaðeê ùLkòaûe _¡Zò @^òŸòðÁ bûaùe aûQòaûKê ùja û iûlûZKûe 12Uò _âgÜ @Wðe Kfcþ (^òŸòðÁ É¸) @^ê~ûdú _Pûeòùa Gaõ _âgÜ @^ê~ûdú iû]ûeY _¡Zòùe _Pûeòùa ^ûjó û ^òcÜfòLòZ 2Uò ùLk c¤eê @û_Y ùKCñUò aûQòùa Kêj«ê û

Order

8.01 └─┴─┘

Would you prefer a prize of Rs 10 paid to you one month from today [1], or Rs 10 paid to you four months from today [2]? 10 Uuû _êeiÑûe @ûRòVûeê cûùi _ùe Pûjóùa - ‘^û’ 10 Uuû _êeiÑûe @ûRòVûeê 4 cûi _ùe Pûjóùa

8.02 └─┴─┘


8.03 └─┴─┘

Would you prefer a prize of Rs 10 paid to you one month from today [1], or Rs 14 paid to you four months from today [2]? 10 Uuû _êeiÑûe @ûRòVûeê cûùi _ùe Pûjóùa- ‘^û’ 14 Uuû _êeiÑûe @ûRòVûeê 4 cûi _ùe Pûjóùa

8.04 └─┴─┘


8.05 └─┴─┘

Would you prefer a prize of Rs 10 paid to you one month from today [1], or Rs 10 paid to you seven months from today [2]? 10 Uuû _êeiÑûe @ûRòVûeê cûùi _ùe Pûjóùa - ‘^û’ 10 Uuû _êeiÑûe @ûRòVûeê 7 cûi _ùe Pûjóùa

8.06 └─┴─┘


8.07 └─┴─┘

Would you prefer a prize of Rs 10 paid to you one month from today [1], or Rs 20 paid to you seven months from today [2]? 10 Uuû _êeiÑûe @ûRòVûeê cûùi _ùe Pûjóùa- ‘^û’ 20 Uuû _êeiÑûe @ûRòVûeê 7 cûi _ùe Pûjóùa

8.08 └─┴─┘


8.09 └─┴─┘

Would you prefer a prize of Rs 10 paid to you four month from today [1], or Rs 10 paid to you seven months from today [2]? 10 Uuû _êeiÑûe @ûRòVûeê 4 cûi _ùe Pûjóùa- ‘^û’ 10 Uuû _êeiÑûe @ûRòVûeê 7 cûi _ùe Pûjóùa

8.10 └─┴─┘

Would you prefer a prize of Rs 10 paid to you four month from today [1], or Rs 12 paid to you seven months from today [2]? 10 Uuû _êeiÑûe @ûRòVûeê 4 cûi _ùe Pûjóùa - ‘^û’ 12 Uuû _êeiÑûe @ûRòVûeê 7 cûi _ùe Pûjóùa

8.11 └─┴─┘


8.12 └─┴─┘


23/04/07

20

Section 8 Time Discounting We would like to play games with you which will allow you to win a small money prize at no cost for you. We are going to ask you to choose one between two alternative amounts of money, which will be made available to you in the future but at different times. For instance, we may ask you if you would rather have Rs 10 one month from now, or Rs 12 in four months from now. We will play this game 12 times. Each time, we will ask you to choose between two alternatives. At the end of the questionnaire, we will select one of the 12 games at random, and you will be awarded the amount of Rupees that you have selected in that game, at the time indicated by the option you have selected. We will make sure the prize will be given to you through BISWA, so you should be confident that the money will really be given to you once the time comes. For each of the two possible games below, please tell us which option you would prefer. @ûùc @û_Yu iûwùe KòQò ùLk ùLkòaê ~ûjû @û_Yuê aò^û cìfýùe ißÌ Uuû RòZûAa û @ûùc @û_Yuê \êAUò bò^Ü @[ðe eûgò c¤eê ùMûUòG aûQòaûKê Kjòaê û ~ûjû @û_Y baòhýZùe bò^Ü bò^Ü icdùe _ûAùa û C\ûjeY ißeì_ @ûùc @û_Yuê Kjò_ûeê @û_Y 10 Uuû

cûùi _ùe Pûjó_ûe«ò Kò´û 12 Uuû 4 cûi _ùe Pûjó _ûe«ò û Gjò ùLk @ûùc iûlûZKûe c¤ùe 12 [e ùLk ùLkòaê û _âZò[e @ûùc @û_Yuê 2Uò aòKÌ c¤eê ùMûUòG aûQòaûKê Kjòaê û iûlûZKûe ùghùe 12Uò ùLk c¤eê ùMûUòKê @ûùc fùUeò cû¤cùe aûQòaê û

Gaõ @û_Y aûQò[ôaû @[ðeûgò C_~êq icdùe _êeiÑûe ißeì_ _ûAùa û @ûùc @û_Yuê Gjò _êeÄéZ @[ðe eûgò aògß cû¤cùe ù~ûMûAaû_ûAñ _âZògîZò ùjCQò û ~ûjû\ßûeû ^ò½òZ ùjûA_ûeòùa ù~ C_~êq icd @ûiòùf @û_Y @[ð _ûA_ûeòùa û SURVEYOR: BEFORE THE GAMES ARE PLAYED, THE ORDER IN WHICH THE QUESTIONS SHOULD BE ASKED HAS TO BE RANDOMLY DETERMINED. THE SURVEYOR MUST ASK THE

TWELVE QUESTIONS FOLLOWING THE ORDER INDICATED IN THE COLUMN LABELED “ORDER”, AND NOT FOLLOWING THE NATURAL ORDERING OF THE QUESTIONS AS LISTED IN THE QUESTIONNAIRE. ùLk @ûe¸ _ìaðeê ùLkòaûe _¡Zò @^òŸòðÁ bûaùe aûQòaûKê ùja û iûlûZKûe 12Uò _âgÜ @Wðe Kfcþ (^òŸòðÁ É¸) @^ê~ûdú _Pûeòùa Gaõ _âgÜ @^ê~ûdú iû]ûeY _¡Zòùe _Pûeòùa ^ûjó û ^òcÜfòLòZ 2Uò ùLk c¤eê @û_Y ùKCñUò aûQòùa Kêj«ê û

Order

8.01 └─┴─┘


8.02 └─┴─┘


8.03 └─┴─┘

Would you prefer a prize of Rs 10 paid to you one month from today [1], or Rs 14 paid to you four months from today [2]? 10 Uuû _êeiÑûe @ûRòVûeê cûùi _ùe Pûjóùa- ‘^û’ 14 Uuû _êeiÑûe @ûRòVûeê 4 cûi _ùe Pûjóùa

8.04 └─┴─┘


8.05 └─┴─┘


8.06 └─┴─┘


8.07 └─┴─┘


8.08 └─┴─┘


8.09 └─┴─┘


8.10 └─┴─┘

Would you prefer a prize of Rs 10 paid to you four month from today [1], or Rs 12 paid to you seven months from today [2]? 10 Uuû _êeiÑûe @ûRòVûeê 4 cûi _ùe Pûjóùa - ‘^û’ 12 Uuû _êeiÑûe @ûRòVûeê 7 cûi _ùe Pûjóùa

8.11 └─┴─┘


8.12 └─┴─┘


I “Hyperbolic Discounting” if choice of earlier (lower) reward isfollowed by choice of later (higher) reward when the time horizonof both rewards is shifted by same amount

Back to Intro Back to Model Back to Types


Additional Material

Identifying Utility Period 3: Intuition

I Recall

g3(x3, w) = u(x3, 1)− u(x3, 0) + βτδ

∫u(x4)dF∆(x4|x3, z)︸︷︷︸

Depends on γ

I By assumption γ conditional on (x3, w\γ) has at least twopoints of support.

I Evaluating the above at the two different points and takingdifferences we can identify the second term. Identification of theutility differential follows.

Back to Identification I


Additional Material

Identifying Utility Period 2

I First, note g(·) is identified by standard inversion argument.Next, note

g2,k(x2, w) = u(x2, k)− u(x2, 0) + βδH(x2, w)

where (βτ , δ, u2(·)) are unknown objects and H(·) is known.

I Use variation in γ ∈ w to identify βδ. Next identify utilitydifferential. Finally, use previous lemmas to separately identifyβ and δ

Back to Identification I


Additional Material

State Space Extensions

I Most importantly, need to consider evolution of income,consumption and assets over panel period.

I We have information on income and expenditures at baseline aswell as elicited beliefs about income for periods 1,2 and 3. Inaddition, we observe realized income for period 3 and 4 as wellas some consumption. Some information on household assets.

I Use realized income and income expectations information todevelop a transition probability for income (varying at thehousehold level) P(yt+1|yt, xt, at).

I Use elicited information on income losses from malaria toconstruct income under alternative states.


Additional Material

Preferences

I Preferences are defined (in addition to the state variables) overconsumption which is observed at baseline and followup.Consumption in intervening periods is imputed usingtime-invariant household characteristics and income beliefs.

I Preferences are allowed to vary by time-invariant householdcharacteristics as well.


Additional Material

Preferences

I By normalized utility differentials we mean that utility in eachstate and action in each period is normalized with respect to autility level at a base action (for all states x3). For instance, wewill only be able to identify

u(x3, a)− u(x3, 0)

I Typically, will normalize and assume that u(x3, 0) is known.


Additional Material

Why Should We Care?

I Point identification of hyperbolic (and exponential) parameters allowdirect assessment of whether agents are time inconsistent and whetherthey are differentially so.

I Can do more: Specify model where types only differ by hyperbolicdiscount rates to get predictions for model “weighted” towards presentbias explanations (“upper bound” on the role present-biasexplanations can play). Next, specify model where both hyperbolicparameters as well as utility function parameters (e.g. costs) vary bytype. Allows the relative importance of present-bias explanations inITN adoption and retreatment decisions.

Identification: Overview


Additional Material

Advantages of Unknown Types Model

I Can use model to address the same sets of questions (abouttime preferences and their relative importance as earlier).

I New results agnostic about the precise mapping between typesand ru. Recall that we only required a “MLR-like” condition.Can use second model as specification check on mappings infirst model.

Identification


Additional Material

Type Classification

I Choosing to classify agents by (r, f) may be a problem if choiceof products driven by other feature. e.g. time varying creditconstraints.

I Also, while not clear whether the complement (of the identifiedtypes) are homogenous. e.g. households with (r = 1, f = 0)?

I One potential “solution” is to posit 6 types based on (r, f).Allow all types to have different β parameters. Need that atleast one known type is time consistent. Strong assumption, butin application there are many potential candidates for this. e.g.with households r = 0


Additional Material

Differences with Fang and Wang (2010)

I In FW all agents are identical with the same preferences. So noheterogeneity in terms of types. All agents are inconsistent.

I Preferences are statiionary, so no changes in preferences overtime.

I Results are only proved for the logit case.

I Do allow for partially naive agents.


07.12.2012 - aprajit mahajan

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