Expectations Formation and Optimal Taxation

Research Topics Learning in Sovereign Debt Markets Roadmap Extra

Expectations Formation and Optimal TaxationResearch Overview

Luis E. Rojas

MOVE, UAB and Barcelona GSE

October 2016, Barcelona GSE Trobada

Luis E. Rojas(MOVE, UAB and Barcelona GSE ) Research Overview


Macroeconomics and Economics of InformationPaper #1: “Optimal Redistribution With a Shadow Economy” Joint with P. Doligalski.

1. Information asymmetries - optimal taxation

The government does not know the workers productivities(Optimal labor income taxation (Mirrlees 1971).Also, cannot observe shadow income.

I Workers with formal and shadow productivities decide where towork depending on the tax scheme.

Subsidy eligibility can explain the large shadow economy inColombia.

Having a shadow economy may allow for a higher taxcollection. Welfare



Macroeconomics and Economics of InformationPaper #2: “Expectations Formation and Investment During Recessions”

1. Information asymmetries

2. Imperfect market knowledge

Agents do not know the mapping from fundamentals to marketoutcomes.Conjecture the relationship and fit to observed data.Self-confirming equilibria (Sargent 2001).+ Firms expectations about potential demand

I Firms have to decide whether or not to invest in the creation of anew good, having uncertainty about demand.

Investment recovers slower than consumption.

Corporate income tax deductions can be a better policyrelative to investment subsidies. Policy Comparison



Macroeconomics and Economics of InformationPaper #3: “Learning in Sovereign Debt Markets”

1. Information asymmetries

2. Imperfect market knowledge

3. Information asymmetries + Imperfect market knowledge



Sovereign debt

Mostly bonds.

Large asset class with many market participants.

In 1950 it accounted for 22% of the market value of worldwideassets, and for 19% in 2010.

Default is a recurrent feature

More than 240 sovereign defaults occurred over the period1824-2004.



Pricing of sovereign debt

Default history matters.

A default episode is typically followed by:

1) a raise in spreads and2) a positive surplus for the lenders.

1. An increase of the haircut by one percentage point generatesan increase of 4-5 basis points in spreads 4 to 7 years afterthe settlement. Cruces and Trebesch (2013)

2. Investors risk aversion and “objective” default probabilities arenot enough to explain this feature. Benczur and Ilut (2016)

My hypothesis: Learning and overreaction.



Pricing of sovereign debt

Default history matters.

A default episode is typically followed by:

1) a raise in spreads and2) a positive surplus for the lenders.

1. An increase of the haircut by one percentage point generatesan increase of 4-5 basis points in spreads 4 to 7 years afterthe settlement. Cruces and Trebesch (2013)

2. Investors risk aversion and “objective” default probabilities arenot enough to explain this feature. Benczur and Ilut (2016)

My hypothesis: Learning and overreaction.



Theory building blocks

Sovereign debt model of incomplete markets (Arellano(2008),...)

Internal Rationality (IR) (Adam and Marcet (2011), Adam,Marcet and Nicolini (2016)).

In RE there is an equilibrium mapping from fundamentals(debt, GDP) to default probabilities that creditors are assumedto know.

In IR creditors beliefs are described by a joint distribution offundamentals and default prob.

Creditors learn about the default probability from experience.



Theory building blocks

Sovereign debt model of incomplete markets (Arellano(2008),...)

Internal Rationality (IR) (Adam and Marcet (2011), Adam,Marcet and Nicolini (2016)).

In RE there is an equilibrium mapping from fundamentals(debt, GDP) to default probabilities that creditors are assumedto know.

In IR creditors beliefs are described by a joint distribution offundamentals and default prob.

Creditors learn about the default probability from experience.



Model: The governmentThe government seeks to maximize

∞∑t=0

βtE{u(ct , gt )

}where ct is private consumption and gt is the public provision ofgoods.

The resource constraint of the government is

gt + et − τyt ≤ qt (bt , yt )bt − bt−1

where et is an expenditure shock; yt is GDP and follows a Markovprocess; bt is sovereign debt issued at t ; and qt (bt , yt ) is themarket price of the bonds.

Default: Every period the government decides whether to repay ordefault.

In case of default the government suffers a α loss of GDP everyperiod until a settlement with the creditors is achieved.



Model: The governmentThe government seeks to maximize

∞∑t=0

βtE{u(ct , gt )

}where ct is private consumption and gt is the public provision ofgoods.

The resource constraint of the government is

gt + et − τyt ≤ qt (bt , yt )bt − bt−1

where et is an expenditure shock; yt is GDP and follows a Markovprocess; bt is sovereign debt issued at t ; and qt (bt , yt ) is themarket price of the bonds.

Default: Every period the government decides whether to repay ordefault.

In case of default the government suffers a α loss of GDP everyperiod until a settlement with the creditors is achieved.Luis E. Rojas

(MOVE, UAB and Barcelona GSE ) Research Overview


Model: Creditors

International creditors are risk neutral, competitive and haveaccess to a risk free asset with gross return 1 + r .

Let v t be the market value of the bonds maturing at t once thedefault decision is announced.

The system of beliefs of the creditors is given by a probabilitymeasure P that specifies the joint distribution of {vt , yt , bt }

∞t=0.

P is given as a primitive of the analysis and does notnecessarily coincide with the equilibrium distribution of{vt , yt , bt }

∞t=0.

Taking P as given the creditors maximize their utility, followingthe concept of Internal Rationality.



Pricing of debt

The expected market value can be written as:

EPt{vt+1

}=

∑y∈Y

EPt{vt+1

∣∣∣yt+1 = y}PPt

{yt+1 = y

}where EPt is the expectation operator with the probability measure Pand conditional on the history {vs , ys , bs}

ts=0

Assuming all investors have the same system of beliefs P we havethat the non-arbitrage condition is:

qt (bt , yt ) =

∑y∈Y EPt

{vt+1

∣∣∣yt+1 = y}PPt

{yt+1 = y

}1 + r



Recovering the REE

The Recursive Rational Expectations equilibrium corresponds to theparticular case where

EPt{vt+1

∣∣∣yt+1 = y}

= µ(bt , y)

PPt{yt+1 = y

}= π

{y′ | y

}where µt (st−1, yt ) is the mean of repayment at t conditional on t − 1states st−1 and contemporaneous income yt .



Subjective beliefs

The system of subjective beliefs is characterized by the following:

1. Creditors believe that the process of vt when outstanding debtis b at the level of GDP y′ corresponds to:

vt (b , y′) = mt (b , y′) + εt (1)

mt (b , y′) = mt−1(b , y′) + ut

where εt ∼ N(0, σε) and ut ∼ N(0, σu) are independent fromeach other and also from {%t , yt , bt }

ts=0.

2. The subjective beliefs coincide with the objective transitionprobabilities

PPt{yt+1 = y

}= π

{y′ | y

}Luis E. Rojas

(MOVE, UAB and Barcelona GSE ) Research Overview


Simulation



Model implications

The other dimensions of the sovereign debt market to study are:

Clusters of Default. If creditors learn about a group ofcountries:

There is cyclical coordination in high debt exposure (loadedgun)A recession in one country can generate a joint recession.(trigger)

Dynamic optimal contract.

The learning procedure implements a spread pattern thatresembles the optimal contract.

Empirical validity: The reputational concerns of governments.



Roadmap

Where am I heading to?

A theory for policy implementation that acknowledges thatagents will use their “limited” knowledge and experience toassess the effects of policy.

Policy should be designed to anchor expectations andfacilitate coordination on the intended outcome



Welfare with the shadow economyBack

w fX is formal productivity of type X ∈ {L ,H}.

0 w̄sH wf

H

Shadow productivity of type H (wsH)

w̄sL

wfL

Shad

owpr

oduc

tivi

tyof

type

L(w

s L)

↑po

siti

vere

dist

ribu

tion

gain

↑

↑ positive efficiency gain ↑

Shadow economy improves welfareShadow economy does not affect welfareShadow economy hurts welfare



Comparison of policiesBack

c - cost of the investment; p probability of success

πt profits; τ tax



Government problemStarting from the case where the sovereign is not in default inperiod t , the value functions have to satisfy:

V (bt−1 , yt , et , qt (b , y)) = max(dt ,gt ,bt )∈C(bt−1 ,yt ,et ,qt (b ,y))

(1 − dt )(u(ct , gt ) + βE

{V(bt , yt+1 , et+1 , qt+1(b , y))

}). . .

+dt(u(ct , gt ) + βE

{Vd ((1 + r)bt−1 , yt+1 , et+1 , qt+1(b , y), yt )

})

where

ct = (1 − τ) (yt − dt αyt )

and C(bt−1, yt , et , qt (b , y)) is the feasibility set. It is fullycharacterized by the constraints:

gt + et ≤ τ (yt − dt αyt ) + (1 − dt ) (qt (bt , yt )bt − bt−1)

dt ∈ {0, 1}



Government problemNow, considering the case where the government starts the periodin default. Then we have that the value functions satisfy:

Vd (bt−1 , yt , et , qt (b , y), y∗) = max

(dt ,gt ,bt )∈Cd (bt−1 ,yt ,et ,qt (b ,y))(1 − dt )

[u(ct , gt ) + βE

{V(bt , yt+1 , et+1 , qt+1(b , y))

}]. . .

+dt[u(ct , gt ) + βE

{Vd ((1 + r)bt−1 , yt+1 , et+1 , qt+1(b , y), y∗)

}]

where

ct = (1 − τ) (yt − dt αyt )

and Cd(bt−1, yt , et , qt (b , y)) is the feasibility set in default. It isgiven by

gt + et + (1 − dt )((1 − h̄)bt−1 − qt (bt , yt )bt

)≤ τ (yt − dt αyt )

qt (bt , yt )bt ≤ (1 − h̄)bt−1



Recursive REERecursive-REE A set of government policy functions for i) default

d(s); ii) public goods provision g(s); iii) debt issuanceb(s); and iv) a bond price menu q(b , y) such that:

1. Taking as given the bond price menu, the government policyfunctions d(s), g(s), b(s) and h(s) solve the government’sproblem for every t .

2. The bond price menu q(b , y) satisfies the following condition

q(b , y) =

∑y′∈Y µ(b , y′)π {y′ | y}

1 + rwhere

µ(b , y) =∑e∈E

(1 − h̄ d(st+1)

)f(e)

3. The probability measure P is equal to the distribution of{%t , yt , bt }

∞t=0 implied by the policy functions and the process

for the exogenous variables yt and et .Luis E. Rojas(MOVE, UAB and Barcelona GSE ) Research Overview


Europe during the last recession: Too much debt?



The market valuation of the debt.


Economy & Finance

Expectations Formation and Optimal Taxation