Lecture 6-7: Policy Design: Unemployment Insurance and ...darp.lse.ac.uk/pdf/EC426/EC426_14_06.pdf · Lecture 6-7: Policy Design: Unemployment Insurance and Moral Hazard ... Typical

Introduction Trade-off Optimal UI Empirical

Lecture 6-7: Policy Design: UnemploymentInsurance and Moral Hazard

Johannes Spinnewijn

London School of Economics

Lecture Notes for Ec426

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Topics & Question in Public Economics

Classical division in Public Economics:

Taxation: How does and should government raise revenues?

Spending: How does and should government spend revenues?

Same fundamental questions for both topics:

When and how should the government intervene?

How do government policies affect economic behavior?

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Focus on Social InsuranceDefinition of Social Insurance?

Social Insurance = government transfers based on eventswhich cause a loss of income

Examples are unemployment, disability, health, retirement,...

Welfare = means-tested transfers such as poverty alleviation,housing benefits.

SI is the biggest and most rapidly growing part of GovernmentExpenditures

GE have increased as a percentage of national incomethroughout the 20th century. Now close to 50 percent ofnational income in OECD countries.GE have shifted towards social security and health insurance inparticularexpected increase in GE causes worries about future solvability

Generosity of SI (i.e. replacement of lost income) differssignificantly among countries.

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UK Government in the 20th CenturyGovernment expenditures as a percentage of national income

Source: IFS; Crawford et al., A Survey of Public Spending in the UK, IFS

Briefing Note no. 43, September 2009

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UK Government in the 21st CenturyGovernment expenditures as a percentage of national income

Source: IFS; Crawford et al., A Survey of Public Spending in the UK, IFS

Briefing Note no. 43, September 20095 / 41


International Comparison of Total Spending,1960-2001

Source: Gruber’s Textbook6 / 41


Distribution of UK Government Spending2014 rule-of-thumb: 20% on Pensions, 20% on Health, 20% onWelfare, 15% on Education.

Source: IFS 2008-2009. Alternative source:

http://www.guardian.co.uk/politics/spending-review.

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Social Security Spending as a Share of NationalIncome, 1949 to 2011

Source: 1949—50 to 2007—08 from ONS series ANLY; 2008—09 to 2010—11

from HM Treasury, Budget 2009.

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NHS Spending as a Share of National Income, 1949to 2011

Source: 1949—50 to 2007—08 from Offi ce of Health Economics; 2008—09 to

2010—11 uses plans for NHS England from HM Treasury, Budget 2009

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Change in Distribution of US Gov. spending, 1960vs. 2001

Source: Gruber’s Textbook10 / 41


Why have social insurance?

General motivation for insurance: pool risks of risk-averseindividuals

Unemployment: loss of earnings due to involuntaryunemployment

Health: risk of health shocks/expenses

Social security: loss of earnings at old age

But why is government intervention needed to provide thisinsurance?

First and Second Welfare Theorem optimal insuranceallocation could be decentralized

So why care about individuals not having health insurance inthe US?

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Why have social insurance?

Typical answer is market failure due to asymmetric information

private information about actions leads to moral hazard;increase in coverage increases the probability that the riskoccurs

private information about risks leads to adverse selection;higher risk types are more likely to buy insurance

Does this provide a rational for government intervention?

in case of adverse selection it does; government has advantageover private insurers that it can mandate insurance

if governments intervene for other reasons, understanding howinterventions affect selection and incentives is essential foroptimal design

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What else can explain government interventions?Other Market Failures

externalities, aggregate risks, redistribution, imperfectcompetition,...

Behavioral failurespeople make mistakes, do not internalize the true impact oftheir actions on themselves

Trade-off between costs and benefits of governmentintervention

1 information: how does government aggregate information onpreferences and technology to choose optimal production andallocation?

2 politicians not necessarily a benevolent planner in reality; faceincentive constraints themselves

3 why does govt. know better what’s desirable for you (e.g.wearing a seatbelt, not smoking, saving more)

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Outline

Lecture 6-7 Unemployment Insurance & Moral Hazard

Lecture 7-8 Health Insurance & Adverse Selection

Lecture 9 Social Security

Lecture 10 Externalities

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Approach

Integration of theory with empirical evidence to derivequantitative predictions about policy

theoretical analysis of core issues

empirical analysis of direct and indirect effects

institutional framework (incomplete)

Behavioral public economics: focus on non-standard decisionmakers where relevant

Critical about question; why government?

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Logistics

Slides and reading list posted in advance on Frank’s website

Background textbooks:

Public Finance and Public Policy by GruberHandbook of Public Economics (recent Vol. 5 in particular)

Contact:

Email: [email protected] ce hours: Tuesday 4 - 5 (32LIF 3.24)

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This Lecture: UI & Moral Hazard

1 Moral Hazard: Insurance vs. Incentives

2 Optimal level of UI benefits [Baily-Chetty model]

1 Model of Moral Hazard - generalizes for other applications

2 Suffi cient Statistics Approach - use of envelope conditions

3 Empirical estimation to test for optimality of program

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Unemployment Insurance: Basic Trade-off

Insurance against unemployment

loss of current (and potentially future) earningsuninsured unemployed experience drop in consumption

If fully insured, unemployed has no (monetary) incentive tokeep/get a job

moral hazard on the job and during unemployment

Central trade-off: insurance vs. incentives ⇒ optimalgenerosity

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Static Generosity: Replacement RateCommon measure of program’s size is its “replacement rate”

r =(net) benefit(net) wage

UI reduces agents’effective wage rate to w(1− r)Typical profile:

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Dynamic Generosity: Duration of Eligibility

Source: Gruber’s book

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Introduction Trade-off Optimal UI Empirical Baily-Chetty First Best Second Best

Baily-Chetty model

Canonical analysis of optimal level of UI benefits: Baily(1978)

Shows that the optimal benefit level can be expressed as a fnof a small set of parameters in a static model

Once viewed as being of limited practical relevance because ofstrong assumptions

Chetty (2006) shows formula actually applies with arbitrarychoice variables and constraints

Parameters identified by Baily are “suffi cient statistics” forwelfare analysis ⇒ robust yet simple guide for optimal policy

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Baily-Chetty model: Setup

Static model with two states: an agent is either

employed and earns wage wor unemployed and has no income

Agent is initially unemployed. Controls probability ofremaining unemployed by exerting search effort

If the agent searches at cost e, the probability of finding a jobequals π (e) with π′ > 0, π′′ < 0

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Baily-Chetty model: Setup

UI system that pays constant benefit b to unemployed agents

Benefits financed by lump sum tax τ paid by the employedagents

Govt’s balanced budget constraint:

π (e) · τ − (1− π (e)) · b = 0

Agent’s expected utility, with u(c) utility over consumption, is

π (e) u(w − τ) + (1− π (e))u(b)− e

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Baily-Chetty model: First Best Solution

In first best, there is no moral hazard problem

Government chooses b and e (determining τ) to maximizeagent’s welfare:

maxb,e

π (e) u(w − 1− π (e)

π (e)b)+ (1− π (e))u(b)− e

Solution to this problem is

FOCb : u′(ce ) = u′(cu)⇒ full insurance

FOCe : π′ (e) [u (ce )− u (cu)]− 1+ π′(e)π(e) bu

′ (ce ) = 0

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Baily-Chetty model: Second Best Solution

In second best, effort is unobserved by govt. ⇒ moral hazard

Problem: agents only consider private marginal benefits andcost when choosing e

agent does not internalize the effect on the govt’s budgetconstraint

e I (b, τ) : π′ (e) [u (ce )− u (cu)]− 1 = 0eS (b, τ) : π′ (e) [u (ce )− u (cu)]− 1+ π′(e)

π(e) bu′ (ce ) = 0

hence, agent searches too little from a social perspective ⇒source of ineffi ciency

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Government’s problem is to maximize agent’s expected utility,taking into account agent’s behavioral responses:

maxb,τ,e

π (e) u(w − τ) + (1− π (e))u(b)− e

such that

BC : π (e) τ − (1− π (e))b = 0IC : π′ (e) [u (w − τ)− u (b)]− 1 = 0

Denote by e (b) and τ (b), the functions satisfying BC and IC

The (unconstrained) problem of the government is

maxbV (b) = π (e (b)) u(w − τ (b))+ (1−π (e (b)))u(b)− e (b)

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Two Approaches to Optimal Policy ProblemsFocus in public finance is on deriving an empirically implementablesolution to this problem:

1 Structural: specify complete models of economic behaviorand estimate the primitives

identify b∗ as a fn. of deep parameters: returns and cost of jobsearch, discount rates, nature of borrowing constraints,informal ins. arrangements.challenge: diffi cult to identify all primitive parameters in anempirically compelling manner

2 Suffi cient Statistics: derive formulas for b∗ as a fn. ofhigh-level elasticities

these elasticities can be estimated using reduced-formmethodsestimate statistical relationships using research designs thatexploit quasi-experimental exogenous variation.Baily-Chetty model is an example of this approach

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Baily-Chetty model: Second Best SolutionAt an interior optimum, dV/db(b∗) = 0

⇔ (1− π (e))u′(b)− π (e) u′(w − τ)dτ

db

+{

π′ (e) [u (w − τ)− u (b)]− 1} dedb= 0

Since the expected utility has been optimized over e,the Envelope Thm implies:

(1− π (e))u′(cu)− π (e) u′(ce )dτ

db= 0

Key here is that we can neglect the dedb term

given the agent’s optimization, the impact on expected utilitythrough effort is of second orderthis holds for any optimal behavior by the agent, e.g.endogenous consumption (Chetty 2006)

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The change in effort does have a first order effect on thegovernment’s UI budget

With τ (b) = (1−π(e(b)))π(e(b)) b, we find

dτ

db=

1− π (e)π (e)

− π′ (e)

π (e)2dedbb

=1− π (e)

π (e)(1+

ε1−π(e),b

π (e))

⇒

dV (b)db

= (1− π (e)){u′(cu)− (1+ε1−π(e),b

π (e))u′(ce )}

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Baily-Chetty model: Second Best SolutionThis yields the optimality condition

u′(cu)− u′(ce )u′(ce )︸︷︷︸MB

=ε1−π(e),b

π (e)︸︷︷︸MC

LHS is marginal social benefit of UIbenefit of transferring $1 from high to low state due toincreased insuranceMB is decreasing in insurance coverage

RHS is marginal social cost of UIcost of transferring $1 due to decreased search effortMC is constant (or decreasing less) with insurance coverage

Comparative statics; ceteris paribus,if MC is higher, optimal UI benefits should be lowerif MB is higher, optimal UI benefits should be higher

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Implementation: Consumption-Based FormulaCan we identify suffi cient statistics to test for the optimalityof the current system?

Write marginal utility gap using a Taylor expansion:

u′(cu)− u′(ce ) ≈ u′′(ce )(cu − ce )

Defining coeffi cient of relative risk aversion γ = −u ′′(c )cu ′(c ) , we

can writeu′(cu)− u′(ce )

u′(ce )≈ −u

′′

u′ce

∆cc

= γ∆cc

Gap in marginal utilities is a function of curvature of utility(risk aversion) and consumption drop from high to low states

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Implementation: Consumption-Based Formula

TheoremThe optimal unemployment benefit level b∗ satisfies

γ∆cc(b∗) ≈

ε1−π(e),b

π (e)

where

∆cc

=ce − cuce

= consumption drop during unemployment

γ = −u′′(ce )u′(ce )

ce = coeffi cient of relative risk aversion

ε =d log 1− π (e)

d log b= unemployment elasticity

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Introduction Trade-off Optimal UI Empirical MH Elasticity Consumption Smoothing

Estimating the Moral Hazard Cost

Lots of empirical work on labor supply effect of socialinsurance. Overview by Krueger and Meyer (2002)

Early literature used cross-sectional variation in replacementrates. Problem: this implies a comparison of high and lowwage earners, whose employment prospects may be verydifferent!

This gave way in late 80s/early 90s to modern methods usingmore exogenous variation/quasi-experiments

difference in UI generosity across states, across time, acrossgroup...state experiments with UI bonuses (Meyer 1995)

Evidence suggests elasticity of around 0.5.

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Difference-in-Differences EstimatesCompare a group affected by a change in the unemploymentpolicy (T ) to a group for which the unemployment policy isunchanged (C ). Let B and A denote before and after thereform.

The effect on the exit probability can be estimated by thedifference-in-differences

∆πT − ∆πC =[πTA − πTB

]−[πCA − πCB

].

before-after estimator[πTA − πTB

]is biased by time effects

a group comparison[πTA − πCA

]is biased by group effects

The dif-in-dif removes (group-invariant) time effects and(time-invariant) group effects. The identification assumptionis that groups follow parallel trends over time, absent thepolicy change.

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“Spike” in hazard rate

Most striking evidence for moral hazard effect ofunemployment insurance: “spike” in hazard rate at benefitexhaustion.

Source: Schmieder et al. QJE 201136 / 41


Estimating the Consumption Smoothing Benefits

The smoothing benefits can be estimated as well, but weshould take into account that UI crowds out self-insurance

some people use their savings when unemployedsome people borrow from banks of family

cu = b+ savings

ce = w − τ − savings

however, many unemployed have no savings and faceborrowing constraints

Gruber analyzes drop in food consumption ce−cuce

andestimates how this is affected by a change in the benefit ratiobw .

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Simulated InstrumentsSame problem: the difference in consumption drop forindividuals with high and low replacement rates is not onlydue to the replacement rate differential.

Alternative solution: Simulated Instrumentstake a representative subsample of individuals S sub

for each individual i in state j at year t in the original samplecalculate the subsample’s average replacement rate if allindividuals of the subsample had lived in state j at year t(

bw

)simulatedj ,t

= ΣsεS subbsimulateds ,j ,t

ws

use(bw

)simulatedj ,t

as an instrument for(bw

)i ,j ,t

The approach exploits only variation in the generosity of thestate UI system over time (∼ difference-in-difference).Underlying the identification is a similar parallel-trendsassumption.

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Estimating the Insurance ValueGruber runs IV regression(

ce − cuce

)i ,j ,t

= β1 + β2

(bw

)i ,j ,t+ β3δj + β4τt + εi

and finds:

β1 = 0.24, β2 = −0.28without UI, cons drop would be about 24%a 10 pp increase in UI replacement rate causes 2.8 ppreduction in cons. drop.with current replacement rate (b/w = 0.5), cons drop isabout 10%

Is current level optimal?

γ× 10% ?= 0.5

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Calibrating the Model

We can find the optimal level using our estimates

γ∆cc≈ ε/π

γ(β1 + β2bw

∗) ≈ ε

Results: bw∗varies considerably with γ

γ 1 2 3 4 5 10bw∗

0 0 0.20 0.41 0.50 0.68

Consumption smoothing benefits seem small relative to themoral hazard cost of unemployment insurance?

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SummaryPolicy maker faces trade-off between the provision ofinsurance and the provision of incentives.

Simple model with search efforts can capture this trade-off.Model generalizes for other behavioral responses like saving,moral hazard on the job, quality of job matches,...

if behavior is optimal, change in behavior has second-ordereffect on welfareonly the effect on the government’s budget constraint isimportant and this is captured by the unemploymentprobability

Empirical evidence suggests that job seekers are quiteresponsive to monetary incentives, implying that consumptionbenefits need to be large to justify generous unemploymentbenefits

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Lecture 6-7: Policy Design: Unemployment Insurance and ...darp.lse.ac.uk/pdf/EC426/EC426_14_06.pdf · Lecture 6-7: Policy Design: Unemployment Insurance and Moral Hazard ... Typical