Risk sharing under incentive constraints

Tilburg University

Risk sharing under incentive constraints

Wagner, W.B.

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2002

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Wagner, W. B. (2002). Risk sharing under incentive constraints. CentER, Center for Economic Research.

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K.U.B.

Bibllotheek Tllburg

Risk Sharing under Incentive

Constraints

PROEFSCHRIFT

ter verkrijging vandegraadvandoctor aandeKatholieke

Univer-siteit Brabant, op gezag van derector

magnifcus, prof. dr. F.A.

van der Duyn _{Schouten, in het openbaar te verdedigen ten}

over-staan van een door het _{college voor promoties aangewezen}

com-missie in de aula van de Universiteit _{op vrijdag 14 juni 2002 om}

10.15 uur door

WOLF BERNHARD WAGNER

Preface

Thepresentthesis isthe resultofthree and ahalfyearsofresearch atthe Center for Economic

Research at Tilburg and at the University of Bonn. It was aproductive time, and I enjoyed

writing this thesis. Several people have

_{contributed to that, and I}

am happy to express my appreciation.

My foremost thanks go to my supervisor Sylvester Eijffinger. Sylvester's enthusiasm and

skillful advice formed theoptimal researchenvironment for me. Inhissupervision, heshowed

the skill of providingthe large amount offreedom I neededto pursuemyideas and _interests,

without forgetting the _fact, however, that I eventually had to write a thesis. The relaxed

discussions in hisofficeshaped my research to aconsiderable extent -even though thesmoke

from two cigarssometimes madeit difficult to spot him on the other side of the desk. He also

showedan_{admirable patience}as_{regardsmypassion}for_changingresearch_interests; a_passion

which,

starting with

my Master thesis, took me on ajourney from money demand functions

over European monetary integration, status-seeking, devolution and central banking to risk

sharing. Furthermore, Sylvester is the co-author of two papersonwhich chapters ofthisthesis

are based, and has in that way essentiallycontributed tothisthesis.

I alsofeel indebted to Oved Yosha from Tel

Aviv

University. The discussions with Oved

havebeenessential for thisthesis. Hisinterest in my work wasagreat encouragement for me.

I am therefore very pleased that heiswilling to act asamember of mythesiscommittee.

Most of

this thesis was

written

in Tilburg. The staff ofthe Department of Economics

has provided me in the last two and a half years with the efficient and smooth environment

necessarytofocusexclusivelyon research,which I appreciate very much. I would also likethank

my colleagues and friends in the department, in particular Riccardo Calcagno and Michael

Krause, andall others who have, in one way or another,contributedtomakingitpleasant and

effective to work inTilburg.

In Bonn I acquired the technical tools

that

proved necessary in _{this thesis, and I would}

like express my gratitude for that. Special thanks go to_{the members of the 'Herrenzimmer',}

Mathias Drehman and Gerd Muehlheusser. I owe them manydiscussions about the meaning

of

economicscience.

Part of thisthesiswaswritten duringafour-month stay at Tel

Aviv

University. The

envi-ronmentthere wasverystimulatingand challenging. I want tothank theeconomicsdepartment

fortheirhospitality. Iwould especially like tothank ItayGoldstein andJules Leichter for the

regulardiscussionsabout risksharing.

This thesis has alsobenefited fromthe comments

of

seminarparticipantsat various

confer-ences. Thefinancial support by _{CentER, CEPR and the}Deutsche Forschungsgemeinschaft is

gratefully acknowledged.

In

particular, discussions

within

the RIN-network on International Capital Flows were very helpful.

I am honored that Lans Bovenberg, Harry Huizinga, Theo vandeKlundertand Casper de

Vriesshowinterest in my work andarewillingtoparticipate in myPh.D. committee.

envi-appreciation for that. My particular thanks go tomy parents, whoare ultimatelyresponsible

Contents

1 Introduction 1

Part I International Risk

_{Sharing 11}

2 The Welfare Gains from Incentive Compatible International Risk Sharing 13

2.1 Introduction . . . 13

2.2 _{Incentive Compatible Risk Sharing . . . 14}

2.3 _{Measuring Welfare} Gains . . . 19

2.4 Results . . . 21

2.5 Summary

. . . .

. . . 25

3

International Diversification and Governmental Moral Hazard

27 3.1 Introduction . . . 27

3.2 Related Literature . . . 28

3.3 TheModel 30 3.4 Discussion andExtensions . . . 33

3.4.1 _{Foreign Direct Investment and Centralized Risk}

_{Sharing . . . 35}

3.4.2 _{Optimal Degree}of Diversification .. . ... .. .. ... ... 37

3.4.3 Constraintsto OpportunisticGovernment

Policies . . . 40

3.5 Summary . . . 41

Appendixto

Chapter 3. . . 42

)A Consumption under FDI . . . . . 42

3B Optimal Home Bias . . . 42

4

_{Capital Taxation under International Diversification: Tax Exportation}

ver-sus

_{Thx Competition}

47 4.1 Introduction 47 4.2 PublicGood Provision

with

_Foreign

_{Ownership . . . 49}

4.3 _{Capital Taxation}under_{Full Financial Integration . . . 51}

4.4 Empirical Evidence on theTaxExportation

Effect . . . 58

4.4.1 Data . . . 59

Appendixto

Chapter 4. . . 66

5 Summary

and

Conclusions to Part I 69

Part II

_{Entrepreneurial Risk Sharing 73}

6 _{Divestment, Entrepreneurial Incentives and the Decision to Go Public} 75 6.1 Introduction

. . . , , , . . , , , , , , , , , , 75

6.2 The StockMarket_{and Entrepreneurial} Incentives . . . 78

6.3 The _{Dynamic Divestment} Problem . . . 80

6.4 The Decision toGoPublic and the_{Life Cycle of the Firm ... .. . .. . 82}

Chapter 1

Introduction

This thesis deals with risk sharing among individuals and countries, and in particular the

restrictions opportunism ofeconomic _{agents can impose on} risk _{sharing. The study of risk}

sharing and the understanding of its potential limitations is ofconsiderableinterest because

ofthe importance of risksharing for economicwelfare. Inthe firstplace,risk sharing creates

potentially large benefits for individuals by reducing consumption volatility. Moreover, risk

sharingmakesindividual _consumptionless_{proneto idiosyncratic risk and in thatway}reduces

theriskpremiumsof individualincomes. Thisgives riseto variousadditionalbeneficialeffects

due to amore efficient allocationofeconomic resources. For example, diversification of

firm-specific risksreduces _{the required} return on

_{capital. This will}

enhanceinvestment and also

specialization, and will have consequences for _{productivity and growth. Equally,} areduction

inindividual labor income risk due to risksharingincreasesthe incentives to invest in human capital andtospecialize.

A

deviation from full risksharing may, in view ofitsbenefits, indicate

importantinefficiencies inthe economy and shouldberelevant forpolicy-makers. Asamatter of fact, the empirical evidence conclusively rejects theimplications of fullrisk sharing; the aim

ofthis thesis is to add tothe understanding of this lack ofrisk sharing.

Most of thisthesis

will

focus onthe internationaldimension ofrisksharing. Inthisrespect,

the presenceofcountry-specific risk (suchaspolitical,economicor_{natural risk)}shouldmotivate

individualstosharerisksacrosscountries. _{In particular,}standarddiversificationconsiderations

would_suggestthat individuals_{completely poolcountry-risk.}

In

_contrast,some evidence_points

to a significant lack ofsuchinternational risk sharing. _{First, for} most countries the

volatility

of consumption is higher than the

volatility

of output.

If

there was significant risk sharing

among countries, country-specificshocksto outputwould not be borne bythe country alone,

which would make consumption less volatile than output. Second, under full risk sharing

consumptionshould grow at the same rateacross _{countries (this} is because shocks are borne

by allcountries and countries

will

furthermore_{smooth consumption). However, consumption}

paths differ widely across_{countries. For example, (real)} consumption in the U.S. rosesince

the 1950s by roughly _150%, while Japan's consumption increased by more than 450% (see

also Figure 2.1 on page 24). Moreover, studies have suggestedthat there is a_{small degree of}

insurance among countries. For example, S0rensenand _{Yosha (1998) found that only 5% of}

the shocks to national income are insured across OECD countries. Further evidence against

full

risk _sharing comes from individual portfolios. Full diversification of country-specific risk

would imply that individuals hold internationally balanced portfolios, but there is a strong

home biasinportfolios. In most industrialcountries,individuals hold more than 80% of their

portfolio indomestic assets. 1

What can_{explain this lack of international risk} sharing? Thefirst (and obvious) guess is

that

the welfare gains fromrisksharing beyond current levels arejust small, andhencealready

minor frictions can makea _largerextent of risk _sharingnot worthwhile. The absence of full

international_{risk sharing} should then not bea cause for concern.

A

_{large number} of_papers

have addressed this issue and haveestimatedthe welfare gainsfrom moving from the current

degree ofrisk sharing to full risksharing. These paperstypically find thedirect welfaregains

(that arise from the reduction in consumption

variability) to be in

the range of 0.5 to 5% of permanent consumption (some papers find even much larger welfare gains). The lack of

international risk sharing cantherefore not beexplained by small welfaregains, especially if taking into account the additional effects on _{investment and specialization (which} caneasily

exceed 100% of the wealth

of

individuals). The literature haslabelledthese apparently high

unexploitedwelfare gainsfrominternational risk_sharing'theinternational risk sharing puzzle'.

A lackof international risksharing may also stem fromadditionalcostsofinvesting abroad.

If, for

some reason,foreign investors are atadisadvantage comparedto_{domestic investors, it is} plausiblethat individuals willbiastheir portfoliostowards domestic assets. Highertransaction

costs _{faced by foreigners may form such} a _{disadvantage. However,} at least among industrial

countries, transaction costs arenot considered large enough toexceed the substantial welfare

gainsfrom international risksharing. Thereis, moreover, indirectevidence againsttransaction

costs as an explanation of the home bias: studiesof equity markets in severalcountries have

revealed that the turnover rateof equity for foreign investors is significantly higher than for

domestic investors, which is exactly opposite to what one would expect in the presence of

highertransactioncostsfor foreigners. Asymmetric informationbetween domestic and foreign

investors may constitute a further barrier to the acquisition

of

foreign assets. Domestic

in-vestors may, for example, be better informed about the prospects ofdomestic firms. While

this may beavalidexplanation for the home biasindirect investment, market efficiency would

rule out

any advantage of domestic over foreign investors for portfolio investment. This is

because unlessinvestorsbehavestrategically, anyprivateinformation willberevealedthrough

prices. Moreover, existing financial instruments (such as index-certificates orindex-tracking

funds) allow investors to buy the whole market. This overcomes potential lemon problems

forforeign investors sinceinvestorscan secure themselvesthe averagemarket performance by

investing inthe market index. Therefore, asymmetric information does not offeraconvincing

solution tothe (portfolio) homebiaspuzzle. Further impediments to foreign investment arise

l In general, there is not necessarily a one-to-one relationship between the home biasin portfolios and the lack of international risk sharing: the formerconcernscapital _{income risk, while} internationalrisksharing relates to consumption risk (which ultimatelymatters _{for welfare). The analysis in}this thesisconcentrates

1. Introduction 3

from government interference. Despite the fact that sincethe collapse of the Bretton-Woods

system capital canmoveinternationally withoutrestrictions, foreign and domestic incomes are

still

treated differently. Withholding taxes incombination

with

imperfect tax credits for

for-eign incomeincreasetherequiredpre-taxreturn onforeign_{investment and, in this}way, favor

investment at home. _{Foreigners may also face the riskof expropriation. While the impact of}

these costs isgenerallydifficult to_{assess, it} isquestionable whether theycanoutweigh the high

welfare gainsfrom internationalrisk sharing. Even if they do, theycannot directly explain the

lack of international risk sharing; instead

it

raises the question why benevolent governments imposerestrictions thathinder risk sharing by individuals.

A potentialcause for the lackof international risk sharingin portfolios isthatequity may

provide a hedgeagainst other risks, such as fluctuations in good prices and human wealth.

For example,

if

domesticlaborincomeis_{negatively correlated}

with

domesticcapitalincome, it

maybeoptimal to biastheportfoliotowards domesticassets. While itiscontroversialwhether such additional riskscanrationalize the home bias in portfolioinvestment, a_hedging motive saysnothing about the lack ofrisk sharinginconsumption. Summarizing theabovearguments and other contributions in the _literature, the profession has not yet settled on a conclusive

story for the lack of international risk sharing. In particular, the 'international risk sharing

puzzle' remains basically unresolved (e.g., Lewis, 1999, and Athanasoulis and Van Wincoop,

2000).

This thesis considers incentive constraints on the side of the government as the reason

for the absenceof international risk sharing. Suchincentive constraints basically arise from

two sources: the non-enforceability of international _{contracts and governmental moral}

haz-ard. They can limit international risk sharing as follows. In the absence ofa _{supranational}

organization that canenforceinternational _contracts,international risk sharing has to be

self-enforceable. However, acountry that has a favorable _{endowment realization, and, therefore,}

expects netoutflows fromrisksharing, may haveanincentivetodefault onits_{obligations from}

risk sharing. Thiscanrestrictthe extent to which risks canbeshared. Toillustratethe severity

of

the problem: Japan's consumption in the 1990s was at 550% of the level in the195Os, while

average consumption of theG7countries was only at 270%. Assuming that this development

was unpredictable, full risk sharing _{(started in the 195Os)} would imply that Japan now loses

roughly 50% of its yearly endowment due torisksharing! Moral hazardarises because inter-national risk sharingreduces the benefitsacountry receives from its income. The reason for

that is that due to

the complexity of country-specific risks, international risk sharing takes

placebasicallyvia aggregates (such as national income or _{production) and not via}contracts

that condition on

the risks themselves. Most economic policies, _however, affect production

and income, and in response torisk sharing the government may find the policy mix chosen

under autarchy not optimal anymore. For example, one reasonfor _{Japan's higher growth in}

the_{post-war period are high investments}in infrastructure. _{Would Japan}still havemade these

tremendous investments, hadit known that

it

would have tosharethe benefits from it with the

may then make alargedegreeof international risk sharing undesirable.

While there is a substantial literature on the explanationsoutlined above for the lack of international _{risk sharing,}contributionsbasedon_{governmental incentive constraints are rare.} The limitations moral hazard andthe non-enforceabilityofcontracts place on contractual

re-lationships have beenextensivelystudied ina generalcontext,however, with few applications

to international risksharing. Anexemptionarestudiesthatexaminetheimplicationsofincen- '

tive constraintsforinternational capital flows. They findthatincentiveconstraintscanexplain somepuzzlingpropertiesof capitalflowsbetweencountries (Gertlerand Rogoff, 1990, and

Ak-teson, 1991). Inthe RBC-literature, it has beenmoreoverfound thatthe non-enforceability of

contracts helps to resolve important anomalies in international macroeconomic _{data (Kehoe}

and Perri, 2000). Governmental moral hazard iscommonly named asacause forthe absence

of a _{large degree}ofinternational risk _{sharing (e.g., Obstfeld and Rogoff, 1996, p.416f). Yet,} formalcontributionsthatanalyze thetrade-offbetweeninternational risksharing anddistorted

incentives _{posedby moral hazard}are absent.

The main aim of this thesis is to fill this gap and to study the implications ofincentive

constraints for international risk sharing. _{Questions that will} be central to the analysis are:

How dooptimal risk sharing allocations under incentiveconstraints look like? Are there

still

substantial _{welfare gains from the}implementation oftheseallocations? Is _{there any}evidence

that

incentive constraints may, in practice,

limit

international risk sharing? And, vice _versa,

isthe presenceof international risk sharingimportant for governments' incentives? What are

the welfare consequences of additional risk sharing in the presence of incentive constraints?

Is the degree of risk sharing chosen by individuals socially optimal? Is there any reason for

the government to interfere in the risksharing markets? What can besaid about the welfare

propertiesof distorted incentives dueto internationalrisk sharing inthepresenceof additional

distortions, such as those arising from tax competition? _Furthermore, this thesis has the

ambition to

gain insights into the effectiveness

of

existing international risk sharing, which

raises _{questions such as: Is} the current level of international risk sharing efficient? And, if

not: How canrisksharing among countriesbeimproved? What is the roleofgovernments and

individualsin improving international risksharing?

These issues are

dealt with in

the

first part of

the thesis. The second part considers a

domesticrisk sharingpuzzle. Ashouseholdsare_{subject to country-specific risk, entrepreneurs}

have to bear firm-specific risk. Since there are no markets that allow to adequately deal with firm-specific risk (this is particularly true for _{small firms), the} only possibility for an

entrepreneur to reduce her exposure to

firm-risk is to sell a part of the firm and

to invests

the proceeds in otherassets. The paradigm of full risksharing would, therefore, predict that

entrepreneurs sell alarge part of

their firm at

thefirst opportunity _{(since the size of}a single

firm

is negligible compared to the whole market portfolio,the entrepreneurshould essentially

sell the whole firmin order to achieve_{maximal diversifcation). However, there}issubstantial

evidence against such behavior. Entrepreneurs tend to keep alarge stake _{in their firm, even}

1. Introduction 5

the firm in pieces and not all atonce. Analogous to theinternational risk sharing puzzle, this

evidence_{suggests a} 'finance _{risk sharing puzzle'.} This_{puzzle comes in two dimensions. First,}

the evidence shows that entrepreneurs are able to sell the firm. Why doentrepreneurs then

not sellthe complete firm (or at least a_{large stake)} as required by full risk sharing? Second,

given that the entrepreneur wants to sell a certain stake

during the life of the firm, why is

this amount soldinpieces? Efficientrisksharing would suggest that the entrepreneur sells the

wholestake at theearliest opportunity inorder toobtainthe benefits from diversification as

soonas _possible.

The aim ofthesecond part of thisthesis is to examine whether entrepreneurial incentive constraints can explainthispuzzle. Thefirst incentive constraintfaced byentrepreneursarises

from her

inability

to commit herself to futureactions. In particular, entrepreneurs may not

be able to commit themselves to future financing policies. _Second, entrepreneursaresubject

to _{moral hazard, i.e., the effort} an entrepreneur puts into the firm depends on how much

the entrepreneur benefits from the effort. This again poses atrade-offbetween risk sharing

and distorted _{incentives, which, in}a _{static setting, is by now} well understood in the finance

literature. In thisthesis, the dynamicimplications ofincentive constraintsareexplored. The

focus ofthe analysis

will

thereby be, beyond the above-mentioned puzzle, also on whether incentiveconstraints canexplain stylized facts of the life cycle of the firm.

The remainder ofthe thesis is structured as follows. The rest of this

introduction will

give an overview ofthe chapters in this monograph and

will

outline the main conclusions.

For readability, the text in this introduction only contains the mostimportant references. At

the end of the introduction, there is a

literature list that

contains the references and some

additional reading for the issuesraised inthis introduction. Part I ofthe thesis, whichdeals

with international

_{risk sharing,} consists of Chapters 2-5, where Chapter 5 has a _concluding character. _{Entrepreneurial risksharing}is dealt with in_{Chapter 6 (Part II). The chapters all}

stand ontheir_{own (beyondthis introduction), and}are based on_{the followingpapers: Eijffinger}

and Wagner, 200lb, (Chapter2),Wagner, 2000 and200lb(Chapter3),Eijffingerand Wagner,

200la (Chapter 4), and Wagner, 200la (Chapter 6).

PART I The main aimofChapter 2 is

to

studywhether incentive constraintscansolve the

international risksharing puzzle,_i.e.,whetherthewelfare gainsfrom international risksharing are still largeonceincentive constraintsaretakenintoaccount. _{The analysis starts byoutlining}

the benchmarkofefficient international risk sharing in aworld withoutincentive constraints,

which is the_{empiricallyrejected case of full}risk_{sharing. It is then}shown_{that optimal}incentive

compatiblerisksharing canbeunderstoodasconsumption smoothing;2 consequently,incentive

constraints can explain a_{significant lack}

of

international risksharing. Thisresult is obtained

by requiring that risksharing does not create any additional distortions ineconomic policies

(this circumventsthe modelling of the trade-offbetweenrisksharing and incentives, which is 2There issomeambiguityabout thedefinition ofrisksharing and consumption smoothing in the_literature, which is becauseboth concepts cannot be_fullyseparated fromeachother. Throughout thistliesis a broad

postponedto Chapter_{3). Since}theoptimalcontractgenerally entails some kind

of

distortion

in incentives, the welfaregains from consumption smoothing

will

constitutealower bound on

the gains fromincentive compatiblerisksharing.

The methods used inthe previous literature to estimate welfare gains from international

risk sharing have the disadvantage that the results aresensitive to assumptions on countries'

endowment processes _and/or whether standard preferences or preferences

that

match asset

price moments are used (Van Wincoop, 1999). For theestimation ofthe welfare gains, a new

method hasbeendeveloped that does notrequire assumptions on the endowment process and

directlyusesasset_{price data}to_{compute the welfare gains. The main}result fromtheestimation

is that

the welfare gains from consumption smoothing are very large and hence incentive

constraints(despite being ableto explain the lackofinternationalrisk sharing) do not solve the

internationalrisk sharingpuzzle. _{Moreover, it}isfound thatthe welfare gains fromrisksharing

beyondconsumption smoothingare_{likely to}besmall. Theinternational_{risk sharing puzzle is,}

therefore, essentiallyaconsumption smoothing puzzle. The results furthermore indicate that

previous studies have substantially understatedthewelfare gains from risk sharing, possibly

dueto inappropriate assumptions on the stochastic process for countries' endowments. The

estimates alsosuggest that for the purposeof measuring welfaregains, standard preferences

satisfactorilyreflect the informationcontainedin asset _{price moments, and}can, therefore, be

safely used for thecomputation ofwelfare_gains.

Chapter 3 and Chapter 4 _study the interaction between _governmental incentives and in-ternational risk sharing. Chapter 3 examines the implications of portfolio diversification for distortions ineconomic policies, andderivesthe optimaldegreeofdiversification under govern-mentalmoralhazard. It isfirstshown_{that portfolio}diversificationcan cause severedistortions in basically all economic policiesthat affect production ofthe domestic firms. However, these

distortions do not afTect the _{degree of portfolio} diversification chosen _by individuals _(since

they behave atomistically). _Hence, individuals

will

diversify as predicted by standard risk

sharing models. Inthe model, diversification creates negative externalities among (domestic)

households since it increases aggregate distortions _(which areborne by all households). The

decentralized equilibrium may, _therefore, be _{inefficient. Then,} the analysis considers the

so-cially optimal degreeofdiversification, which balances the welfare gains froma reduction in

risk with

the welfare losses from distortedincentives. For plausible parameters, the optimal

degree of diversification

implies a home bias that is in line with

the existing home bias in

industrial countries. Thissubstantiatestheresults_{of Chapter 2 in that} incentivesconstraints cannotonlyexplain a lackof international risksharing butalso_implyan_{optimal extent of risk}

sharing that is close to the observed one. If a home bias is indeedoptimal, the decentralized

equilibrium willbeinefficient,i.e.,individuals

will

choosean_{excessive degree}

of

diversification.

While moralhazardcannot directlyexplain the home biasinindividual portfolios (individuals

choose the level ofdiversification regardless

of

incentive problems), it rationalizes the home

bias as being the result ofgovernment interference inrisk _{sharing markets (for example due}

1. Introduction 7

equalization orstructural_{funds) in order to avoid} excessivediversification.

Chapter 4 studies an application of distorted economic policies due to international risk

sharing. This is done inanenvironment withaseconddistortion,arising from

tax

competition.

Tax competitionamonggovernmentsinorder to attract foreigncapital resultsin inefficiently low taxes on capital and counteracts the distortions in incentives stemming from risk

ing.

The

latter

arise in the modelbecauseinternational diversificationgives governments an

incentive to levy excessivecapital taxesbecause a part of the taxburden has to beborne by

foreign investors. In this_framework, distorted incentives duetointernational risk sharing do

not necessarily reduce welfare:

if

taxes are inefficiently low (owing to tax competition), an

increasein governments' incentives to levycapital taxes due toan increaseddiversification is

beneficial for welfare. Next, it is analyzed which ofthese counteracting motives for capital

taxation is likelyto dominate. The results suggest that for boththe currentsituation in the

U.S. and the case offullfinancialintegration, taxes on corporationsareinefficiently high, i.e., the motive for taxation arising from diversification is dominant. Full financial integration is

thereby characterized by theabsence ofanyfrictionsspecific to cross-bordercapitalmovements and completediversification inthesmall country case (i.e., the share of theportfolioinvested

in domestic _{assets is zero). These} results run counter to _{the commonly expressed} concern

that

financial integration, by increasingcapital mobility, lowersgovernments'

ability

toraise revenue from capital taxes.

Chapter 4 furthermore _{provides empirical evidence for the importance} of international

diversification_{for governments' incentives.} A panelanalysis ofU.S. states from 1977 to 1998

showsthatthere isa_{significantpositiveand economicallyimportantcausality}between_foreign

ownership of capital and profits (which is _{brought about by diversification) and taxes on}

capital. Moreover, the resultssuggest

that

foreign ownership

will

become amajordeterminant

of

capitaltaxes

if

diversificationacrosscountriesbecomes morecomplete.

Chapter5contains theconclusions to Part I. Themain points areasfollows. Theanalyses

indicate in_{several ways}that_{incentive constraints provide}aconsistent_{explanation for the lack}

of international risk sharing. However, they donot solvethe international risk sharing

puz-zle. International risk_sharinghas_{important implications for economic policies, which}further

researchshould address _{more extensively. Increasing}risk _{sharing beyond current levels may}

reducewelfare and is at bestinefficient (as long as it isnotrestricted to consumption

smooth-ing). Further financial integrationand financial innovation may in that view be undesirable

becauseitallowsindividualstobettershare country-specificrisks.

PART II

Chapter6 analyzes thelife cycle of the firm underincentive constraints, and

in, particular,the

ability

ofincentive constraints to account for the financerisksharingpuzzle. Asoutlined_above, entrepreneurs haveamotive forsellingtheir firmsin order to reducetheir

exposure to firm-specific risk. Chapter6showsthatincentiveconstraints affect thismotive as

follows. First, when a part of the firm is sold, an entrepreneur's incentives to exerciseeffort

according toherstake in thefirm. Rational investors will beaware oftherelation between an

entrepreneur'sstake in the firm andthe amount

of

effortexercised. Hence, their valuation of

the firm

will

decreasewiththe stake the entrepreneur_{sells of the firm. This, in turn,}willlimit

theentrepreneur's benefits from selling the _{firm; therefore, the entrepreneur may not want to}

sell completely.3 This explains the

first part of

the finance risk sharing puzzle ('entrepreneurs keep a_{significant stake in the firm'). A}secondconstraint tothe entrepreneur's desire to sell her

firm

arises because an entrepreneur hastypically several opportunities to sell the firm in the

course of time. Whilethe efficiency losses ofan initial sale ofastake in the firm maybe

fully

internalized bythe entrepreneur _(becauseofinvestors being aware ofthe relationship between

the entrepreneur'sstakeandexercised_effort), subsequent sales bytheentrepreneurreduce her

efTort _{further and pose} a _{negative externality on} the _existingshareholders. _{Therefore, if the}

entrepreneurcannot commit herself to keep the stake retained initially, investors

will

reduce

their valuation of the firm further in order to be compensated for the additional efficiency

lossesstemming fromselling the firmat laterstages.

It is then shown that, as a consequenceofthese _{constraints, entrepreneurs may} after the

start-upoftheir firm wait until they take the firm public (and thus postpone the sale of the

firm) and, once _{being public, stagger the sale of the firm. This}rationalizes _{the second part}

of the finance puzzle ('entrepreneurs spread the sale of the firm over time'). The analysis

furthermoredemonstratesthat incentive constraintsimplyarealisticlife cycle of the firm that is consistent with the useofventurecapital in the private phase of the firm as well as with a

change in control inthepublicphase (when the firmislisted at anexchange). It isalsoshown

that the sale of the firm by the entrepreneurisinefficient beyond the moral hazard constraint:

the entrepreneur sells too much of the firm and sells too late. This reduces the benefits of

listing a firm at an exchange, and as a _{result, too} few firms go public in

equilibrium. The

chapter concludesby presenting financial regulations

that

removethis inefficiency.

3 Itisassumed that due to a lossofentrepreneurial humancapital,theentrepreneur will not findit worthwhile

1. Introduction 9

References

and

Additional

Readings Papers

that

study the effects ofrisk sharing on

investment are _{Obstfeld (1994b), Acemoglu and}

Zilibotti

_{(1997), Devereux (1997) and in the}

finance strand Stulz (1995). The lackof international_{risk sharing}isdocumented in Stockman

and Tesar (1995) (volatility of output and consumption), Sorensen and_{Yosha (1998) (extent}

ofincome insurance across _{countries), Stulz (1994) and}Tesar_{and Werner (1995) (home bias).}

The

link

betweenthe home bias and the lackof international risksharingisdiscussed inLewis

(1999), pages 604f. Surveys of theliterature onthe welfare_gainsfrom international_{risk sharing}

are containedin Tesar _{(1995), Lewis (1999)} and _{Lewis (2000).} A recent study that compares

different approaches for the estimation of welfare gains and discusses the international risk

sharing puzzle is Van Wincoop (1999).

'Itansaction costs asan _{explanation for the home bias have}beenexaminedin _{Cooper and}

Kaplanis (1986, 1994) and _{Botazzi et. al. (1996).} The higher turnover

of

equity held by

foreigners is reported in Tesar and Werner _(1995). Better informationabout the risk-return

characteristics

of

domestic stock have been usedin_{Gehrig (1993) and Brennan and Cao (1997)}

to explain the home bias. _{Gordon and Bovenberg (1996) and} Razin et. al. _{(1998) consider}

lemon problems asareason for the homebias. _{Cooper andKaplanis (1986), Stulz (1981), and}

for developing countries Demirglig-Kunt and Huizinga _(1995), study therationale for a home

bias stemming from taxdifferencesbetween _{foreign and domestic income.}

Inflation risk as acause for the home biasis_rejected

in

_{Cooper andKaplanis (1994),}while

Gordon and Gaspar _{(2001) present a} framework in which the home bias isjustifiedby price

hedging motives. _{Botazzi et. al. (1996) find that} human wealth can

partly

explain the home

bias, Baxter andJermann ₍₁₉₉₈₎ conclude that the inclusion

of

human wealth into portfolio

considerations worsens the homebias puzzle. Furtherexplanations for the lackof international

risk sharing or the home biasin portfoliosare presentedinAdlerandDumas _{(1983) (exchange}

rate_{risk), Kocherlakota (1996b) (commitment problems), Lewis (1999) (mismeasurement of}

consumption) and Obstfeld(2000) (costsof internationaltrade). Stulz (1994)and_{Lewis (1999)}

surveytheseveral explanations for the home bias.

Optimal contracts under moral hazard and self-enforceability are _{(among others) studied}

by Spear and Srivastave (1987) and Phelan and Townsend (1991). Gertlerand Rogoff (1990)

and Atkeson ₍₁₉₉₁₎ provide applications to international capital flows. In Kehoe and Peri

(2000),self-enforceable contracts are used to explainthe momentsofmacroeconomic variables.

The implications ofentrepreneurial moral hazard for domesticrisksharing hasbeenstudied

in Kahn

_{(1990), Kocherlakota (1998) and} Magill and

_{Quinzii (1999, 2001). The fact that}

entrepreneurs remainasubstantialstakein their firmevenafterseveral_{years of the foundation}

of the firm is_{documented in Jain and Kini (1994) and Mikkelson et. al. (1997).} Evidence that

the listing of the firm takesplace lateiscontainedin Pagano et. al. (1995) andRydqvist and

Hogholm _(1995). Mikkelson et. al. ₍₁₉₉₇₎ document

that

entrepreneurssell significant stakes

Chapter 2

The Welfare Gains from Incentive

Compatible International Risk Sharing

2.1 Introduction

The significant lack of internationalrisk sharing,asoutlined intheintroduction to thisthesis,

raised thequestion whetherhouseholds forego sizeable gains from risk sharing. Most studies

find that

thewelfare gainsfrom additional international risk sharingare _{indeed substantial,1}

which has led to the 'international risk _{sharing puzzle'. In this chapter} we consider an

ex-planation for this puzzle based on governmental moral hazard and the non-enforceability of international contracts. The main aim of this chapter thereby is to provide an estimate for

the welfare gains from international risk sharing that is restricted through these incentive

constraints.2

We first show that such risk sharing reduces to international consumption smoothing if

one requires thatrisk sharing does not create anyadditional_{distortions. Therefore, incentive}

constraints can explain a lackof international risk_sharing;in particular, it is_{argued that they}

explain the

pattern of

risk sharing among groups ofcountries ofdifferent legal integration.

In order to obtain a reliable measure for the welfare gains from international consumption

smoothing,we_{employ a}newmethod

that

_{computes actual welfare gains frompastconsumption}

data. Actual welfare gains answer the question of what the gains for countries would have

been hadtheyengaged in risk sharing in the past. Van Wincoop (1999) and Athanasoulis and

Van Wincoop (2000) have shown that welfare gains arevery sensitive to assumptions on the

stochastic processgoverning countries' consumption. This has led toa confusionabout the

true magnitude ofthe welfaregains.3 Computingactual gains has the advantage that it does

1

Surveys are containedin_{Tesar (1995), Van Wincoop (1999 ) and Lewis (2000).}

2Wewill focus on the welfare gainsthat arisedirectly from the reductioninconsumptionvariability. If

thesegains are not small enough to explain theinternationalrisk sharing puzzle, thentaking intoaccount the possibleindirectwelfare gains (which are more difficultto quantify) willonlyworsenthe puzzle.

3In particular, Van Wincoop_{(1999) shows}thatdifferent assumptions on the stochasticprocess (eventhough the parameters are estimated from the same data) call lead to welfare gains from less than 0.1% to more than 5% over a 100-year horizon.

not requireanyassumptions on the endowmentprocess.

A

further uncertainty about the size

of

thewelfare gains intheliteraturestems from the factthatstandard preferences are not able to match asset price data, mostnotably theequity premium. Preferences that areconsistent

with

asset price data have been found to imply much higher welfare gains.4 _{Therefore, we}

develop an approach that computes welfare gains from market interest rates. The basic idea

of this approach is that due tointertemporaloptimization ofhouseholds, interest rates reflect

rates_{of intertemporal}substitution and can be used tovalue _{consumption streams.}

We find thattheactual welfaregainsfrom consumption smoothingare large. Hence

incen-tiveconstraints cannotresolvetheinternational_{risk sharing puzzle. For the representative G7}

country during _1956-1992, the welfare gains are equivalent to a2.8% increase in permanent

consumption, assuming standardpreferences. Market interest rates imply similargains. This F

number is abovethe welfare _{gains from full risk sharing} from studies that assume a _specific

consumptionprocess. Van Wincoop (1999), for example, finds welfare gainsbetween 0.5 and

1.5% for a comparable sample and horizon. Tesar (1995) estimates the welfare gains from

introducingaworld bond_{market (and thus from}consumption smoothing) andfinds that they

are below 0.5% fora_{stationaryprocess. Recently, Athanasoulis and VanWincoop (2000) have}

developedatechnique thatissimilar to ours in thatitmeasureswelfare_gainswithout _assuming

a consumption process. Theyfind welfaregains that are consistent withourestimates. This

suggests thatthe consumptionprocesses used inthe literatureunderestimate the true welfare

gains. We furthermore find

that

consumption smoothing reduces the welfare costs of a unit

consumptionvariability by96.4%, whichindicates thatthe welfaregainsbeyond consumption

smoothingarelimited.

The remainder of thischapter is organized as follows. The nextsection demonstrates the

incentive problems arising from international risk sharing, derives the optimal non-distorting

risk sharing contract andcomparestoexisting risksharing. Section2.3 describesthe

method-ology for the measurement of the welfaregains. Section 2.4presentsthe welfare estimates for

the G7 countries. Thefinalsection summarizes.

2.2

Incentive

Compatible

Risk

Sharing

In order to study the implications

of

incentive constraints for international risk sharing, we

start upby defining the benchmark offull internationalrisk sharing. Considera_{world made up}

of n (e»ante) identical countries. Eachcountryreceives _everyperiodastochastic endowment

yi whosedistributionisknown to allcountries. The representative household'stimeseparable

expected

utility is

Eo[E #u(4)]

t=l

4Obstfeld (19948) and Van Wincoop (1994) havedemonstratedtliatusingpreferenceswith habit formation and/or timenon-separability resultsinlarger welfaregains. _{Moreover, Lewis(2000) shows} thatstock niarket

2, Welfare Gains fromIncentive _{Compatible InternationalRiskSharing 15}

Full risksharing requiresthat countriesperfectlypooltheirrisks_{(Lucas, 1982).}

It

follows that

each country consumes a fixed shareof world output cw in each period given by

n

4 - a'cr with cw := E

1/; (2.1)

i=1

where the a"sareindependent of therealization ofthe countries' endowments.

Full risksharingmay,however, notbe feasible

if

internationalcontracts arenot enforceable.

Countries can then notbe forcedto provide the transfers (y;

_-4)

necessarytoimplement (2.1).

Furthermore, distortions arising from governmental moral hazard may make full risk sharing

undesirable. Moral hazard arises because a_{country's production isnot exogenously given as}

considered above but _{partly depends on governments policies.} Toillustrate the moral hazard

problem, assume that a country's output y depends on some policy parameter e chosen by

the government. Thisparameter can, forexample, representinvestment in publicinputgoods

(such asinfrastructure andresearch), productionsubsidies orthelevelofcorporatetaxation.

The domestic costs ofthe policy are given by z(e) and can be interpreted as the welfare

loss for the representative household (expressedin units ofthe output good) caused by a tax

necessary to finance thepolicy e. Under autarchy, domestic consumptionequals production

and the policy e will be chosenoptimally by the government such that y'(e) = _{z'(e). Under} risk sharing,the benefits from additional production do only partlyaccrue tothe country. In particular, under full risk sharing the country's consumption only increases _{according to its}

share inthe worldoutput.

If

countriesaresymmetric, then a = 1/n in (2.1) and only 1/n-th

of

every additional unit ofdomestic output remains inthe country. The government's policy

choice isthen _{determined by y'(e)/n =z'(e), which leads to}adistorted _{provision of e.} The characterization ofthe _{optimal contract under moral hazard and enforceability}

con-straints in adynamic frameworkis_{complex (see for example Atkeson, 1991) and} the optimal allocation_{generally entails some kind}of distortion. No modelssuitable_{for empirical}

applica-tion do yet exist, whichis partly owed to the difficulty ofspeciB,ingthe costs

of

distortions that arise from moral hazard. Inthe following werestrict risk sharing such that it does not

createanyadditional distortions(compared to autarchy) and show that asimple and

intuitive

optimalincentive compatible contract exists.

For thispurposewe changetheaboveframeworkasfollows. The numberofperiods is now

finite and given by m.5 The countries'output is y; = _{11'f (4) +}

_4,

where e; is chosen by the

government and summarizes all policies

that

affect output. The policy_{e; causes} furthermore

social costs z(ej) to the _{country (measured} in

units of

the output good). The ej 's and the

country-specific productivity parameters 9, are unobservable. _{The shocks v;} are identically

and independently distributedacross _{countries with Eo[u;] =}0. _{Generally, more assumptions}

onthe _{distribution of the u;'s} are necessary because alsothe predictability of

shocks at t>0

matters for the allocationofconsumption. Consistent withour notion ofwelfaregains from

5 This isconsistent with most ofthe literature, which onlyconsidersrisk sharing over afinite number of

periods. Tlie reason for that is thatthe welfare gains fromrisksharing may notbebounded asthenumber of

periodsincreases (seeVan Wincoop, 1999).

16 RiskSharing underIncentive Constraints

risk sharing (see next section) we assume inthe following that all uncertaintyis immediately

resolvedafterthecontract iswritten. Acontractthereforespecifies anamountofconsumption

c; ineachperiod thatcandepend onthe realizationofcurrent and past output {ys},st and all

shocks {u}.6

The government

will

_{default on the contract (or allow the domestic household to}default) if

at any time tthe discountedfuturenetpayments toother

countries (Elt #(yi-<))

arelarger

thanthe costsofdefaulting.7 The specification ofthe

latter

is problematic. Inthe literature

it hasoftenbeen assumedthatcountriesare forever excludedfrom contracting afteradefault (see, for example, Eaton, 1981). The disadvantage ofthisassumption is that it may not be

time-consistent: after a default there is no incentive to exclude countries from the contract

sincethe gains from risk sharing

will

generally be the larger the larger the numberofcountries

participating in_{risk sharing. Moreover, it is not}empiricallysupported. For example, countries

that

havedefaultedontheirgovernment bondscantypicallyreturn tothecapitalmarketsafter

a few years (or do even neverstopborrowinginternationally). Other commonlyused costs are

costs ofdefault that are exogenously given or costs in term of reputation losses (which may

matter forothercontractual relationships). The difiiculty withtheseassumptionswithregard

to obtaining contracts that are useful for empirical work is to actually specify the costs in

quantitative terms.

We assume here that all net payments that have been made to a

country in the past

can be collateralized. In the case ofa_default, these payments can then be recovered. Such

collateralization can, for example, takeplace ondeposits atinternationalorganizations (such as

thespecialdrawingrights at the IMF) but alsoonassetsofcountriesheld_abroad,e.g., private

property. The advantage ofthis assumption is that itallowsto achievea time-consistent and

tractablesolution tothecontractingproblem. The disadvantage is, of_{course, that} it assumes

the existence ofamechanismforcollateralization,which requiresacertaincoordinationamong

countries _(however, the alternative _{punishments considered} above also _require coordination

in order to enforce the punishment). The assumption can furthermore be motivated with reputational arguments: it

rules out that

a country defaults on current payments if it has

received _{equal payments in the past but} allows a country to default if, for _{example, it has}

received more favorable endowments than othercountries. We furthermore assume that the

collateralization includes _{interest (where the} interest rate is based on the steady state rate,

i.e., (1 + r)6 - 1). A

country's participation constraint isthen given by

m _{t-1 , i i\} t-1

E 6•(1/1 - c:) S E l; : - 14, =E 8 (cl - v;) for all l S t s m

s=t s==1 /(1 + r)' 3=1

6Tothe extentthatconsumption is not predictable, theoptimalconsumptionallocationex-post _{(which is}

studied here) may not beachievedex-ante.

2. Welfare GainsfromIncentive CompatibleInternationalRisk

Sharing 17

which canbereduced to

63(Yl-

cl) ;

0 (2.2) S=1

In order for risk sharing not to create any additional _{distortions, the} government must find

it optimal

_{to chose the same e;'s} as under autarchy. The autarchy

policy el fulfills y'(e ) =

gif'(e t) - Z'(€ 1).

Thepolicy choicegiventhe_{contract c;} =

4({14}.g, {vi}) is

m

4 = arg illax E 6-4(vi(e;)) -

8*z(4) (2.3)

4 S=t

Thenecessary condition for ej = e;t is

fe

ads--2

_(2.4)

1=t Dy:(4)

which follows from thefirst ordercondition for _(2.3) after imposing _{' e'A - Z'(e ).}

Consider nowtheallocationof_{consumption independent}ofcountries'_output. The

incentive-constraint (2.4) is thennot binding andtheoptimalallocation has to

fulfill

0,6tu'(4) - At - Aie =

0, (2.5)

where A isthecountry's weight in thesocialplanner function and At and A, are the

Lagrange-multipliers associated withtheresourceconstraint

n 71

Ed=

EY:

(2.6)

i=1 i=1

and _{participation constraint (2.2), respectively.} Since the _{participation constraint (2.2) is}

identical for all countries, we have Ai = M fortwo countries i and j and

it

_{follows from (2.5)} that

11'(4)/11'(4+k) = 11'(4)/u'(Ci+k, (2.7)

Hencethe intertemporal ratio

of

marginal utilitiesisequalizedacross countries.

Proposition 2.1

A contmct

fulfilling

_{(2.2), (2.4), (2.6) and (2.71 is given by}

4 = atic:7 + 1,4 - vt - (U; -1, ) (2.8)

with cw := Eli y(e;) and ai := (E;11 bt('lif(el) + vi))/(E;-1 8tc7).

Proof. (2.4): a) el = ek: Eli 6'cl = E;116'(aic:'ty;-1/1-(vi-vi)) = Eli

_{bev .} Differ-entiating wrt. to₁₄

_{gives 6. b) 4 = 4 for t > 1: E:1: 83(1 = Elt 63(aicr+Yj -yl- (U; -vii)),}

differentiating wrt. toJj

_{gives bt. (2.2): see (2.4) a).(2.6): Ili ai =}

_1,

_{hence Eli 4 - cr =}

El,1 y(e;). (2.7): For u'(c)homogenous,

u'(4)/u'(4+k) = 11'(aicr)'11'(a,cr+k) = u'(cr)/u'(cr+k),

whichis_{independent of i. •}

and depend on the realization ofthe shocks. This is in

contrast to full

risk sharing, where

a depends on apected permanent income. Since the incentive compatible contract requires

E11 8'cl = 211 6314 (2.2),

noe»postredistributiontakes place. However,according to (2.7) anoptimalcontract equalizesthe intertemporal ratiosofmarginal utilities. The welfaregains

from incentive compatiblerisk sharing arisetherefore solely due tointernationalconsumption

smoothing.

How does theoptimal contract compare to an allocation

that

emerges

if

households can

tradeariskless international bond? Fora country that haszero

initial

bond holdings and zero

bond holdings after the_{last period we have}

m-1

(722 - c;) (1 -t- Ta) t ivt, - cl, =

O _(2.9)

t=l S=t

wherert denotesthe interest rate ona one-yearbond. Assumingas above (1 + rt)6 = 1 gives

E eM- 4) =

0 _(2.10)

t=1

which is identical to participation _{constraint (2.2). If we also} continue to assume that all

uncertaintyresolves inthefirst period, we get fromthe Euler-equations

k-1

11'(4)/Et[11'(4+k)1 = 11,(4)/tt,(4+k) = 61' II(1 +ra) (2.11)

S=t

and the intertemporal ratios ofmarginal

utility

are again equalized acrosscountries. Hence,

the optimal contract under incentive constraints implies the same allocation as in a bond

economy (incentive compatible welfare gains can, for example, alsobe interpreted as thegains

from

full

capital market integration). This result also gives support to the specification of the participation constraint: international borrowing and lending has so far beenenforceable among G7 countries(on which we basetheestimation inSection 2.4). If at all, theparticipation

constraintcanthereforeonlyunderstate the costsofdefault.8

Is the current lack of international risk sharing a result

of

incentive constraints? If so,

risk sharing amongjurisdictions that face less incentive problems should be more complete.

Sorensen and _{Yosha (1998) find that 66% of all} incomeshocks are_{shared among} U.S. states

compared to only25%among the OECD countries. WhileU.S. states and the OECD countries

maybecharacterized bysimilardegreesoffinancial marketintegration,incentive problems are

limited within theU.S. _First,federal lawensuresthe enforcementof inter-statecontracts.

Sec-ond, moral hazard is restrictedto _{policies on}thestatelevel and canbe easierdealt with due

tothe common legal system. Hence, the relative lack of risk sharing among OECD countries

compared to U.S. statesis consistent

with

incentiveconstraints. Moreover, sinceProposition 8An understatement of thecostsofdefault leads to more restrictions oninternational risksharing_(because fewer contracts canbe_{enforced) and} possibly lower welfare gains. This possiblebias _{(which may} also arise

2. Welfare Gains fromIncentive _Compatible International Risk

_{Sharing 19}

1 shows

that

consumption smoothing is feasible in the presenceof incentive problems,

con-sumptionsmoothing should be used moredominantlyamong the OECD countriesthan_among

U.S. states ifincentive constraints are _{important. Quite strikingly,} S0rensenand Yosha find

that within the OECD 80% ofrisk sharing takesplace due to consumption smoothing, while

among the U.S. states consumption smoothing _{only accounts for 11% of}risk sharing.' The

evidencetherefore indicates a role for incentive constraints inexplaining the current degree of

risk sharing. If thewelfare gains from consumption smoothing beyond the current degree of

risk sharingare _{moreover small,} thiswould suggest

that

incentive problems can also account

fortheinternational risk sharingpuzzle.

2.3

Measuring

Welfare

Gains

from

Consumption

Smoothing

Since current consumption {ct}

will

already display some degree ofrisk

sharing (i.e., it will

deviate from {Vt}), the gainsfrom consumption smoothingaregiven by the welfare gains for

a representative consumer that moves from current consumption {ct} to consumption under

optimal smoothing {c;}.

In

expectedterms, these_gains are_{defined by}

m m

0 - Eo[E 6:u(ci) - E btu(c:(1 +

gain))] (2.12)

t=1 t=1

wherethe welfaregains (gain) are expressed in termsofpermanent consumption. The

domi-nant approach intheliterature has beento proceedby specifyingastochasticprocess for {ct }

and {c;} (with

{c;}

typicallybeing a share ofworld consumption) and thento compute (or

simulate) the ezpected welfare gains according to (2.12). On the contrary, we

will

compute actual welfare gains defined by

m

6tu(c;) - E eu(c:(1 +

gain)) (2.13)

t=1 t=1

where {ct} and {4} are

past consumption dataseries. Actual gains areidentical to expected gains intheabsence

of

uncertainty (i.e., Eo[ct] = ct and Eo[4] = ci). Theyanswerthe following

question: What would thewelfare gain for a_{country have been had it made} a_consumption

smoothing contract

promising {4}

in

_{return for {ct} at t= 0?}

The advantage ofmeasuring

actual gains is that it does not require assumptions on the underlyingstochastic process for

{c;} and {ct}. Its

shortcoming is that it doesnotallow theterms ofthe_{contract (the a's) to}

depend on expected differences between countries. _However, the

latter is for

_{our purpose of}

limited relevance. Since

with

consumption

smoothing E -1 6tc; = I;li 8tct (2.6)

and hence there isno ex-post_{redistribution,}expected differencesonlymatter tothe extentthatcountries

gThe extensive use consumption smoothing among OECD countries (which isinabsolute termseven_larger

have a different

volatility

of consumption (i.e., a country with more volatile consumption

should get, ceteris paribus, alower share_a). Moreover, expected differences willonly distort

country-specificgains but notthe welfare gains fora_{representativecountry.}

We _{define consumption under optimal smoothing {c'}} analogous to Proposition 1 by

c; - ac .10 Equation (2.13) gives then the total welfare gains from additional

consump-tion smoothing. Besides, we arealso interestedin computingthe welfare gains from marginal

increases in _{consumption smoothing. Consider, for example,} a householdthat _exchanges

do-mestic consumption {ct} for the consumption

stream {Et} = (1 - q){c} +

q{c-},

where q is

the degree _{of (additional)} consumption smoothing. The welfaregains from moving from {c}

to {E}

areanalogous to (2.13) defined by

m m

0 = Z btu((1 - q)4 + q(<) - E Btu(ce(1 +

gain(q))) (2.14)

t=1 t-1

Differentiating (2.14) with respect to q and solving for again/aq gives the maminalgainsfrom

a unit of consumption smoothing at q

Ogain/Oq = EZ,1 6tu'(Et)(c; - ct) (2.15)

E;116tu'(Ct)Ct

For q=0 and q=1, equation (2.15) becomes

Ogain/Oq(0) - E;-16tu'(Ct)c; -

1 _(2.16) E;11 Ottz'(Ct)Ct

E-m #u'(ci)(c; - ct)

again/aq(1) =

A-t=1 (2.17) E;11 #11'(Ct)Ct

What is therelationbetween_{again/Bq(0), again/aq(1) and gain? If gain > 0 then}an increase

in q

reduces consumption variability, which, in turn, reduces the welfare gains from a unit

reductionin_{consumption variability (for}ahousehold

with

_{completely smoothed consumption}

the change in welfare due to a small variation in consumption variability is _{zero). Hence,}

the marginal gainsevaluated at autarchy consumption (Ogain/Bq(0))

will

overstate the

total

welfare gains, while the marginal gains evaluated at {c;} (again/aq(1)) will understate the

total

gains. On thecontrary, if the move from {c} to

_{c*}

increasesconsumption variability (and hence gain < 0) then Ogain/Dq(0)

will

understate and Ogain/Oq(1)

will

overstate the

totalwelfaregains.

The

Welfare Gains with CRRA-Utility. Foru(ct) =

4-7/(1-7),

equations (2.13),(2.16)

and (2.17) canbesolvedexplicitly forthe welfaregains

gain = (2518£4*1-7)1/(1-7)-

₁ (2.18) Et,11 btc:1-7 r-m rt 1-7 * Ogain/Bq(0) = 6--1 0 7 1_

-1

(2.19) E;116 ct Ogain/Dq(1) = E:11 6241-7(4 -ct) (2.20)

E;11 04-7

2. Welfare GainsfromIncentive_{Compatible International Risk Sharing 21}

The Welfare

Gains

Implied by Intertemporal Optimization.

TheEuler equation

for the representative household beforeadditionalconsumption smoothing is

u'(ct) = 6(1 +

rt)Et[u'(ct+i)]

(2.21)

where rt is the domestic one-year interest rate at t.

Approximating u'(ct+1) by u'(ct-1) t

u"(ct-1)(c,+1 - 4-1) in

(2.21) gives

u'(ct) = 6(1 + rt)(1 -

7t-1E:[ct+11 - Ct-1)11'(Ct-1) (2.22)

Ct-1

where 7t = -11"(Ct) ' ct/u' (ct) is the coefficientofrelativeriskaversion. Subsequent substitution

of lt'(Ct-1) in (2.22) gives forconstant 711

Es[c,+11 - c,-1

11'(Ct) = e 11(1 + rs)(1

i

)u'(Co) (2.23)

S=1 Cs-1

Using (2.23) to

_{substitute for it'(ct) in}

theequation for the marginal welfare gainsevaluated

at autarchy (2.16)yields

again/Dq(0) = 221 62t(1111(1 + rs)(1 - 7E,Ic.:.1lic.-1)4) -

₁

(2.24)

Em-1 62t(f[11(1 + Ta)(1 - 7E.Ic.td-ic.-1)Ct)

With

rationalexpectations, the expectation error_{Es[c,+11 - C,+1 is}independent ofallvariables

known at s, hence one can obtain an unbiased estimator

of

nominator and denominator in

(2.24) by setting E, [c,+11 - CS+F

An

estimator for Dgain/Oq(0) is given by

; 62t(Ill= (1 + rs)(l- 744.3-1)4)

Dgain/Oq(0) = -1 _(2.25)

E;11 52t (Hi-1 (1 + rs)(1 - 7 c'+2-1 )Ct

2.4

Results

We computethe actualwelfare_{gainsfrom consumption smoothing for the G7 countries(United}

States, Germany, Canada, France, UnitedKingdom,

Italy

and Japan) during1956-1992. The

main ingredients for the computation arethe aggregate _{(real) consumption data series {c'},}

which are

taken from the

Penn World Table. World consumption {cw} is the per capita

consumption of the G7 countries (where all countries are weighted equally). Estimation of

the welfare gains implied byEulerequationsfurthermorerequires realinterest rate data. We

chose, whenever available, market rates onone-yeartreasury_bills,otherwiseshortermaturities

(fromOECDMacroeconomicIndicators_{and Datastream). Real interest rates} are_{obtained by}

deflating

with

CPI-inllation. We furthermore assume a discount

factor of 6 = 0.95 and a

degree

of

relative_{risk aversion 7 -}3. Table2.1 containsthe resultsfor_{equations (2.18)-(2.20)}

(CRRA-utility) and

(2.25) (Euler-equations).

11 Fortheconsequences of_thisassumption for theinterpretation of_{the welfare gains implied by interest rates,}

Table 2.1: The actual welfare_gainsfrominternational_{consumption smoothing} CRRA-utility Euler-equations

Marginal gains Marginalgains Marginalgains

Total gains underdomestic under world underdomestic

consumption {C} consumption

{Cl

consumption {C}

United States -5,5% -4,9% -7,3% -6,5% Germany 1,5% 1,7% 1,2% 1,0% Canada -2,0% -1,6% -2,5% -1,6% France 0,8% 0,9% 0,7% 2,1% United Kingdom -6,2% -5,0% -9,0% -7,2% Italy 12,8% 14,6% 7,6% 19,3% Japan 28,9% 36,5% 10,2% 43,9% Averagegains 2,8% 4,2% 0,15% 5,0%

Notes: Welfare gains are expressed asper:entageincreaseinpennanentconsumption for G7-countries during 1956-1992, average gains are computed from consumption-weighted country gains

The

total

welfare gains _(first column in Table _2.1) differ widely across countries, from -6.2% for the U.K. to 28.9%for Japan. Thisdifferenceissurprisinglylarge given thatthere is no redistribution (due to the participationconstraint 2.2). The heterogeneity across coun-tries therefore arises solely due to households' risk aversion in thepresence ofdifferences in

countries' consumption

volatility

before consumption

smoothing (for 7=0

the welfaregains

are zero for eachcountry).12 For example, the standard deviation

of

consumption divided by

mean consumption for Japan is60%higher than for _{world consumption,} while forthe

'loser'-countries U.S. and U.K. _{domestic consumption is} less _{volatile than world consumption. The}

distribution ofthe welfare_{gains among countries} will change if the contract would take into

account expected differences in _{countries' consumption variability (for example} ifcountries

would bargain over theterms ofthe

_{contract at t = 0)}

and should therefore be interpreted

with caution.

It

neverthelessshows that the incentives tosmooth consumption can be quite

different acrosscountries.

We compute the welfare gains for a _(fictitious) representative country from the average

ofthe country-specific welfare gains. The gains are 2.8%

if

countries areweighted according

to their share in permanent world consumption (a). How does this number compare to

estimates for fullrisk_{sharing from the}literature? Studies

that

assume astationaryprocess for

consumption typically find_{welfare gains of less than 0.5% (for example Obstfeld, 1994a and}

Tesar, 1995). Tesar (1995)alsoestimatesthe welfare gains fromrisk sharing thatislimited to

trade in an _{international bond (and}hence there is only consumption smoothing). Assuming

a stationary process, she finds that the welfare gains can be much smaller than for full risk

sharing. Estimates obtainedfromotherendowmentprocesses arehigher. Van Wincoop (1999),

for example, estimates fora_{comparable sample and horizon gains of 0.5% for}a random walk

process and of 1.5% foraconsumption process that has autocorrelatedgrowth rates. Yet, this

numbersare

still

substantiallybelow theactual gainsfromconsumption smoothing. Since the

12Negativewelfare gains do not contradicttheparticipation_{constraint (2.2)} because we have assumedthat