Economic Development, Flow of Funds, and the Equilibrium

Economic Development, Flow of Funds,and the

Equilibrium Interaction of Financial Frictions

Benjamin Moll Robert M. Townsend Victor Zhorin

Princeton MIT Chicago

New Perspectives in Macroeconomics, Developmentand International Trade

Cowles Foundation, Yale University

June 10, 2015

1 / 40

BIG DATA

Definition:

Volume – the quantity of data; Variety – different sources, typesComplexity – data need to be linked, connected, correlated

Featured Example

Raj Chetty, Nathaniel Hendren, Patrick Kline, Emmanuel Saez and Nick Turner (2014):

All children born in the US between 1980-2, income measured in 2011 at ≈ age 30, using millionsof anonymous earnings records

Substantial variation in intergeneration mobility across cities (and across rural areas); some landsof opportunity and other poverty traps; even within city variation, heterogeneity

Thai Data:

Townsend Thai Project Data

1997 Baseline, with 5 year retrospectivehousehold, headman, village financial institution, environment, BAACjoint liability group

l998-present, annual rural resurvey

2004 - new rural and expand to urban

Sept l998-present, monthly micro

With complete financial accounts: income, balance sheet, cash flow

Creating village NIPA, including balance of payments, flow of funds

Secondary Data on GIS data base archive

CDD (village census), Population Census, Labor Force Survey, SES income expendituresurvey, location of branches of all financial institutions

BIG THEORY

West (2013): ”Big data” without a ”big theory” to go with it loses much of its potency andusefulness, potentially generating new unintended consequences

Donaldson (2015)

Discover Fundamental Drivers:

Much recent work exploits a fundamental symmetry between intra- and international tradeto learn about the fundamental drivers of exchange among locations, whether thoseexchanges cross international borders or not.

Advantage within Nations

Care is typically required if the mobility of other determinants of trade are differentialwithin nations relative to across them

Featured Examples

Climate change - Costinot, Donaldson and Smith (2014); US agriculture - Costinot and Donaldson(2011)

Other Literature and key themes:

the distributional consequences of trade openness - Winters (2004), Goldberg and Pavcnik(2007), Harrison, McLaren and McMillan (2011)the consequences of market integration for firm and industry performance, TFP - De Loeckerand Goldberg (2013)measuring frictions, trade costs - Atkin and Donaldson (2014)Internal Geography, International Trade, and Regional Specialization - Cosar and Fajgelbaum(2013)

FEATURING DIFFERENCES IN OBSTACLES AND

EQUILIBRIUM INTERACTION

Buera and Shin (2013):Difference in tightness of collateral, financing constraint; US (zero) vs EM countries (calibrated)

With heterogeneous producers and underdeveloped domestic capital

To explain joint dynamics of TFP and capital flows

Gourinchas and Jeanne (2013)Negative correlation of TFP growth and capital flow among OECD countries

Savings puzzle

Other related literature:Lucas (1990), Caselli and Feyrer (2007),Carroll and Jeanne (2009), Benhima (2013), Quadrini, Mendozaand Rios-Rull (2009), Antras and Caballero (2009), Castro, Clementi and Macdonald (2009), Prasad,Rajan and Subramanian (2006), Boyd and Smith (1997), Carroll, Overland and Weil (2000), Aguiar andAmador (2011), Angeletos and Panousi (2011), Sandri (2014)

What we do and what we do not do

We do not

Feature transitions, but focus on steady states (will be obvious why this is computationally hard)

We do

Feature varying types of obstacles (not just quantity difference as a given supposed obstacle)Within country flow of fundsLabor migration urban/rural, as in a development literature

4 / 40

MICRO FOUNDATIONS, VARYING OBSTACLES,

USING TOWNSEND THAI DATA

Limited Commitment in the Northeast/rural vs Moral Hazard in Central/Urban

From three separate studies:Paulson, Townsend and Karaivanov (2006), Paulson and Townsend (2004):Enterprise and Financing

Data, l997 baseline and retrospective, 2880 households

LocationLopburi, Chacherngsao: central, industrialized and/or cash cropsSrisaket, Buriram: northeast, poor, agrarian

Comparision of obstaclesMoral Hazard, Aghion and Bolton (1997), Piketty (1997), vsLimited commitment, Evans and Jovanovic (1989)not all theories previously taken to data and comparedStratified Random Sample of Tambon, Villages, Householdsprior wealth and going into businessshops, restaurants, commercial shrimp, dairy cattle

Tests:mechanism design to get likelihood, quantitative mapping (with specification of talent)wealth and borrowing positive correlated in NE, negatively correlated in Central

Ahlin and Townsend (2007)Repayment data/Default

1997 baseline using 226 joint liability groups pf BAAC,experience repayment difficultiescomparing theories (not previously tested): Besley and Coate (1995) (repayment s/o commitment),Banerjee, Besley and Guinnane (1994) (monitoring of the borrower), Stiglitz (1990) (joint project choice inproduction), Ghatak, Morelli and Sjostrom (2001) (adverse selection)Findings: Limited Enforcement in the NE: village penalties positively correlated with repayments; AdverseSelection in Central: degree of joint liability negatively correlated with repayment

5 / 40

MICRO FOUNDATIONS, VARYING OBSTACLES,

USING TOWNSEND THAI DATA (cont.)

Karaivanov and Townsend (2014): Dynamics of Multiple Variables

Dynamic model

Comparing likelihoods, Vuong tests for non-nested regimes

Autarky, savings only, borrowing/lending, moral hazard with observed, unobserved capital

Cross section and panel data: c,q, {k, I , q}, {c, k, I , q}

Findings

Moral Hazard, urbanSavings only in ruralConsumption data is smoothed in both but in rural persistence of capital stocks is decisive

A Story: Contract Norms and EnforcementActual enforcement as opposed to legal

Ratzan (2011), Graeco-Roman Egypt

He (2012), China

Formal enforcement improving in urban areasRemains dire in rural

Debate: over idealistic rural, Village Republics vs fragmented, terrible place to live

Here we rely on the actual micro data

6 / 40

WITHIN COUNTRY FLOW OF FUNDS

Paweenawat and Townsend (2012): ”disentangling real and financial factors”

Constructed balance of payment accounts

Buriram boom in construction and running deficit, borrowing

Rural areas running surplus, savings

But may also reflect shocks, transition

Feldstein-Horioka puzzle: should see no correlation between savings and investment but in reality they arecorrelated

Thailand, do not find, except when savings includes outside financing, gifts, as would be the case withgood capital markets

many other countries:

within China, correlation across provinces diminishes over time, hence infer - flows increasingno correlation within Germany

Risk Sharing

Thai, hard to distinguish within vs across villages

Larger literature, within and across countries: Asdrubali, Sorensen and Yosha (1996), Crucini (1999)

Bank of Thailand: commercial bank data

Bangkok has more in credit/borrowing

Other provinces, deposits, savings dominates

Other countries

Folk theorem about Indonesia

CFSP Mexico project, rural to urban, metro areas

US, l950, FRB NY, rural areas see funds flowing into regional financial centers, and on into NY/Chicago

7 / 40

LABOR MIGRATION AND DEVELOPMENT

Lewis model: migration to cities for higher wages

Fei-Ranis model: surplus labor, contradicted by Schultz

Harris-Todaro model: expected income differential

Glaeser model: externalities

Lucas: ”Life Earnings and Rural-Urban Migration”

8 / 40

Common Theoretical Framework

• Continuum of households and continuum of intermediaries

• HHs have preferences over consumption and effort:

E0

∞∑t=0

βtu(ct , et).

• Occupational choice: entrepreneur (x = 1) or worker (x = 0).

9 / 40

Entrepreneurs and Workers

• Entrepreneurs, x = 1: technologies

zεf (k , `)

• z : entrepreneurial ability, Markov process µ(z ′|z).

• ε: residual productivity, with distribution p(ε|e).

• ε potentially insurable, z not insurable

• Workers, x = 0: supply ε efficiency units of labor, withdistribution p(ε|e).

• Note:• if x = 1, ε = firm residual productivity

• if x = 0, ε = worker productivity

• can allow for differential responsiveness to e by rescaling

10 / 40

Risk-Sharing with Intermediaries

• Continuum of risk-neutral intermediaries, outside financialinstitutions

• Continuum of risk-averse households• initial wealth ai0 and income stream {yit}∞t=0.

• can access capital market only via intermediaries

• as if aggregating up households within villages to Gorman representative

• Each intermediary contracts with continuum of households to form“risk-sharing syndicate”

• HHs give entire initial wealth and income stream to intermediaries

• as if syndicate is contracting with capital goods sector

• We emphasize a borrowing, lending interpretation

• intermed. pool these, invest at r , transfer consumption to HHs

• Again: only residual productivity, ε, insurable but not ability, z

• “Risk-sharing syndicates” take (w , r) as given

11 / 40

Optimal Contract and Timing

• Optimal contract:

1 leaves zero profits to intermediary ⇔ maximizes individual’sutility

2 assigns occupation, x , effort, e, capital, k , and labor, `. Afterε is drawn, assigns consumption and savings c(ε) and a′(ε)

12 / 40

Optimal Contract: Bellman Equation

v(a, z) = maxe,x,k,`,c(ε),a′(ε)

∑ε

p(ε|e) {u[c(ε), e] + βEz′v [a′(ε), z ′]} s.t.

∑ε

p(ε|e) {c(ε) + a′(ε)}

≤∑ε

p(ε|e) {x [zεf (k, `)− w`− (r + δ)k] + (1− x)wε]}+ (1 + r)a

and s.t. regime-specific constraints: moral hazard or limited commitment depending on sector

Equivalent problem when z is contractable or fixed at z = 1: maximize present discounted value of profits subjectto promised utility, very slow moving dynamics

13 / 40

Moral Hazard, Urban/Central, m

• effort, e, unobserved ⇒ moral hazard problem.

• Note: moral hazard for both entrepreneurs and workers.

• IC constraint:∑ε

p(ε|e){u[c(ε), e] + βEz′ v [a′(ε), z′]

}≥

∑ε

p(ε|e){u[c(ε), e] + βEz′ v [a′(ε), z′]

}∀e, e

• Formulation of MH problem is special

• only e unobserved. k observed, no effect on shirking

• more general formulation: p(ε|e, k)

Limited Commitment, Rural/Northeast, 1−m

• effort, e, observed ⇒ perfect insurance against production risk, ε

• But collateral constraint:

k ≤ λa, λ ≥ 1

Lotteries Connection to Optimal Dynamic Contract

14 / 40

Factor Demands and Steady StateEquilibrium

• Denote optimal occupational choice and factor demands by

x(a, z), `(a, z ;w , r), k(a, z ;w , r)

• and individual (average) labor supply:

n(a, z ;w , r) ≡ [1− x(a, z)]∑ε

p[ε|e(a, z)]ε

• Prices r and w , and corresponding quantities such that:

(i) Given r and w , quantities determined by optimal contract(ii) Markets clear ∫

`(a, z; w, r)dG(a, z) =

∫n(a, z; w, r)dG(a, z)

∫k(a, z; w, r)dG(a, z) =

∫adG(a, z)

15 / 40

Parameterization• Preferences

u(c, e) = U(c)− V (e), U(c) =c1−σ

1− σ, V (e) =

χ

1 + 1/ϕe1+1/ϕ

• Production function: εzf (k, `) = εzkα`γ , α + γ < 1• Ability process: keep current z with prob. ρ, draw new one with prob. 1− ρ from truncated Pareto:

Ψ(z) =1− (z/z)−ζ

1− (z/z)−ζ

• Residual productivity ε ∈ {εL, εH}

p(εH |e) = (1− θ)1

2+ θ

e − e

e − e, θ ∈ (0, 1)

• Next slide: parameter values• Paper: huge number of robustness checks

Variable grid size grid range

Wealth, a 30 [0, 200]

Ability, z 15 [1, 4]

Consumption, c 30 [0.00001, c(w, r)]

Efficiency, ε 2 [0, 2]

Effort, e 2 [0.1, 1]

16 / 40

Parameter Values (Thailand and other studies)

Parameter Value Description

β 1.05−1 discount factor

σ 2 inverse of intertemporal elasticity of substitution: KT, PTK

ϕ 2 Frisch elasticity: KT, PTK, BCTY

χ 0.525 disutility of labor: KT, PTK

α 0.3 exponent on capital in production function: P1T , BBT

γ 0.4 exponent on labor in production function: P1T

δ 0.06 depreciation rate: ST

ρ 0.75 persistence of entrepreneurial talent: P2T

ζ 1 tail param. of talent distribution (truncated Pareto)

z 1 lower bound on entrepreneurial talent

z 4 upper bound on entrepreneurial talent

θ 0.2 sensitivity of residual productivity to effort

εL 0 value of low residual productivity draw

εH 2 value of high residual productivity draw

λ 1.8 tightness of collateral constraints: PTK

m 0.3 population weight: census - 0.31; Lucas Jr (2004) - 0.22 (from World Bank)

PTK - Paulson, Townsend and Karaivanov (2006), KT -Karaivanov and Townsend (2014), P1T - Paweenawat andTownsend (2012), P2T -Pawasutipaisit and Townsend (2011), ST - Samphantharak and Townsend (2010), BBT -Banerjee, Breza, and Townsend, BCTY - Bonhomme, Chiappori, Townsend, and Yamada

17 / 40

LC and MH Sectors in Mixed Regime

!"#$%&'$(")$*&)+,-. !/&0$1234 56&0$1234

789&:;&3<&8=> ,-?@A ,-?BA C-,CD

EF9&:;&3<&8=> ,-GD? C-HDG ,-@GG

63I0J)K2"3I&:;&3<&8=> ,-AC, ,-GD? ,-HCB

L$M<N4$&:;&3<&8=> ,-G,@ ,-G?G ,-B@@

L$NM2O&:;&3<&8=> ,-?CA C-,GH ,-GAH

64$%"2&:;&3<&8=> ,-B@? C-?AA ,-H@D

LN($&:;3<&8=> ,-GB@ ,-GB@ ,-GB@

PI2$4$02&'N2$ Q,-,,. Q,-,,. Q,-,,.

;&RI24$K4$I$J40 ,-CG? ,-C?, ,-CGG

;&S$1234&63I24"TJ2$0&23&EF9 ,-A.? ,-D@C

;&3<&5NT34&R)KM3U$%&"I&S$1234 ,-AA, ,-D@,

;&3<&6NK"2NM&V0$%&"I&S$1234 ,-@HC ,-.B?

;&3<&5NT34&SJKKM"$%&TU&S$1234 ,-HBA ,-BH@

;&3<&6NK"2NM&SJKKM"$%&TU&S$1234 ,-.DD ,-@AD

W$2&5NT34&PI<M3X&:;&3<&J0$%> ,-.GC Q,-HGG

W$2&6NK"2NM&PI<M3X&:;&3<&J0$%> ,-ACG Q,-B.D

:N>&WN2"3INM&NI%&S$1234NM&Y((4$(N2$0

:T>&P)K342NI1$&3<&S$12340&"I&Y((4$(N2$&R13I3)U

:1>&PI2$40$1234NM&6NK"2NM&NI%&5NT34&8M3X0

18 / 40

Determination of Equilibrium rLimited Commitment and Moral Hazard

Moral Hazard

4 6 8 10 12 14 16 18 20

−0.04

−0.02

0

0.02

0.04

0.061/β − 1

Aggregate Capital Stock

Inte

rest R

ate

, r

Demand, First−BestDemand, Moral Hazard

Supply, First−BestSupply, Moral Hazard

Limited Commitment

4 6 8 10 12 14 16 18 20

−0.04

−0.02

0

0.02

0.04

0.061/β − 1

Aggregate Capital Stock

Inte

rest R

ate

, r

Demand, First−BestDemand, Limited Commitment

Supply, First−BestSupply, Limited Commitment

Note: wage is lower in LC regime too

19 / 40

Determination of Equilibrium r

Limited Commitment

• Capital demand shifts left• reason: collateral constraint⇒ capital demand constrained

• Capital supply shifts right• reason: self-financing of entrepreneurs (Buera, Kaboski and Shin, 2011; Buera and Shin, 2013,

among others)

Moral Hazard

• Capital demand shifts left• reason: suboptimal effort⇒ depressed capital productivity

• Capital supply: effect ambiguous• reason: two countervailing effects

1 direct effect: at constant w , capital supply ↓ always.Inverse Euler equation logic: optimal contract discourages savings whenever IC constraint binds

2 GE effect decrease in capital ↓ ⇒ decrease in labor demand ↓ ⇒ lower wage ↓ ⇒ more firms ↑

20 / 40

Mixed MH+LC RegimeDistribution of Entrepreneurial Effort

MH

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.05

0.1

0.15

LC

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.05

0.1

0.15

Distribution of MPKs

MH

−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0

0.05

0.1

0.15

0.2

LC

−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0

0.05

0.1

0.15

0.2

21 / 40

Occupational Choice/Saving-Borrowing in

Mixed MH+LC Regime

Moral Hazard

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4

Log of Wealth, a

Constrained

Entrepreneur

Constrained

Worker

Abili

ty, z

Limited Commitment

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4

Unconstr.Entrepreneur

Log of Wealth, a

Constrained

Entrepreneur

Unconstrained Worker

Abili

ty, z

Moral Hazard

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4

Lenders

Log of Wealth, a

Borrowers

Abili

ty, z

Limited Commitment

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4

Log of Wealth, a

Borrowers

Lenders

Abili

ty, z

22 / 40

Distribution of Entrepreneurial Ability of Active Entrepreneurs

Moral Hazard

0 1 2 3 4 5 6 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Limited Commitment

0 1 2 3 4 5 6 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Distribution of Firm-level TFP

Moral Hazard

1 1.5 2 2.5 3 3.5 4 4.5 5 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Limited Commitment

1 1.5 2 2.5 3 3.5 4 4.5 5 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

23 / 40

Underlying Micro Dynamics of Wealth Growth Rates in

Mixed MH+LC Regime

Moral Hazard

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 0

0.1

0.2

0.3

0.4

0.5

0.6

Limited Commitment

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 0

0.1

0.2

0.3

0.4

0.5

0.6

24 / 40

Typical Life Histories in Mixed MH+LC Regime

MH:Ability

0 5 10 15 20 25 30 35 401

1.5

2

2.5

3

3.5

4

Ab

ility

Year

MH: Wealth

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

Wealth

Year

MH: Effort

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

Effort

Year

MH: Career

0 5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

Occupation

Year

LC: Ability

0 5 10 15 20 25 30 35 401

1.5

2

2.5

3

3.5

4

Ab

ility

Year

LC: Wealth

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

Wealth

Year

LC: Effort

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

Effort

Year

LC: Career

0 5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

Occupation

Year

25 / 40

Lorenz Curves in Mixed MH+LC Regime

Wealth

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Limited Commitment

Moral Hazard

Income

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Limited Commitment

Moral Hazard

Consumption

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Limited Commitment

Moral Hazard

Value

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Limited Commitment

Moral Hazard

26 / 40

Experiment: Move to Autarky inEach Sector

Wealth

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Limited Commitment

Moral Hazard

Income

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Limited Commitment

Moral Hazard

welfare in autarky, levels drop

more inequality across sectors

less inequality within MH, more inequality within LC

27 / 40

Another Experiment: LC Sectors inMixed LC+LC Regime

!"#$%&'$(")$*&)+,-. /0*&λ+1-2 /0*&λ+.

345&67&89&:;< ,-2=> ,-?2. 1-.@2

A:5&67&89&:;< ,-2@B ,-@2? ,-2=>

0CD"ECFGHIEDIE&'CE"8&6789&:;< ,-@@. ,->@= 1-12@

/CJ8K&LIDDFM&67&89&:;< 1-,1= ,->1. 1->11

N$F9CK$&67&89&:;< ,-OB1 ,-O=1 ,-O22

NC($&6789&:;< ,-21> ,-21> ,-21>

PQE$K$RE&'CE$ G,-,=B G,-,=B G,-,=B

7&SQEK$DK$Q$IKR ,-1@@ ,-1O1 ,-=2>

S#E$KQCF&:"QCQT$UL$TE8KCF&345 1-=.. 1-=1@ 1-=BO

7&L$TE8K&08QEK"JIE$R&E8&345 ,-B@. ,-?,>

7&89&/CJ8K&S)DF8M$%&"Q&L$TE8K ,-B@. ,-?,>

7&89&0CD"ECF&VR$%&"Q&L$TE8K ,-.@. ,-O,>

7&89&/CJ8K&LIDDF"$%&JM&L$TE8K ,->B. ,-=?>

7&89&0CD"ECF&LIDDF"$%&JM&L$TE8K ,-B@2 ,-?,=

W$E&/CJ8K&PQ9F8X&67&89&IR$%< G,-?=> ,-B2>

W$E&0CD"ECF&PQ9F8X&67&89&IR$%< G,-=O1 ,-1>O

6C<&WCE"8QCF&CQ%&L$TE8KCF&Y((K$(CE$R

6J<&P)D8KECQT$&89&L$TE8KR&"Q&Y((K$(CE$&ST8Q8)M

6T<&PQE$KR$TE8KCF&0CD"ECF&CQ%&/CJ8K&:F8XR

28 / 40

Occupational Choice/Saving-Borrowing in

Mixed LC+LC Regime

λ = 3

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4


Log of Wealth, a

Constrained

Entrepreneur


Abili

ty, z

λ = 1.8

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4


Log of Wealth, a

Constrained

Entrepreneur


Abili

ty, z

λ = 3

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4

Log of Wealth, a

Borrowers

Lenders

Abili

ty, z

λ = 1.8

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4

Log of Wealth, a

Borrowers

Lenders

Abili

ty, z

29 / 40

Equilibrium Interaction of MH and LC

GDP

0 0.2 0.4 0.6 0.8 10.78

0.8

0.82

0.84

0.86

0.88

Fraction of Population Subject to Moral Hazard, m

GD

P (

% o

f F

irst−

Best)

TFP

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.86

0.87

0.88

0.89

0.9

0.91

0.92


TF

P (

% o

f F

irst−

Be

st)

Interest Rate

0 0.2 0.4 0.6 0.8 1−0.05

−0.04

−0.03

−0.02

−0.01

0

0.01


Inte

rest

Ra

te

% of Entrepreneurs

0 0.2 0.4 0.6 0.8 1

0.15

0.16

0.17

0.18

0.19

0.2

0.21

0.22

0.23


Fra

ction o

f E

ntr

epre

neurs

small open economy in interest rate r , non-monotonicity disappears30 / 40

Out of Sample PredictionsFirm Size Distributions

Data:Urban0

20

De

nsity

0 .2 .4 .6 .8 1Sum of business and agricultural assets (million Baht)

Model:MH(+LC)

−50 0 50 100 150 200 250 300 350 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

Model:LC,λ = 3

−50 0 50 100 150 200 250 300 350 400 450 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

Data:Rural

02

0D

en

sity

0 .2 .4 .6 .8 1Sum of business and agricultural assets (million Baht)

Model:LC(+MH)

−50 0 50 100 150 200 250 300 350 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

Model:LC,λ = 1.8

−50 0 50 100 150 200 250 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

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Conclusion

• Different financial frictions not only have differentmacroeconomic effects but also interact in unexpectedways

• Needed: more research that makes use of micro data andtakes seriously the micro financial underpinnings of macromodels.

• Big Data with Big Theory

• Join what have been largely two distinct literatures – macrodevelopment and micro development – into a coherent whole:

• macro development needs to take into account the contractswe see on the ground

• micro development needs to take into account GE effects ofinterventions

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Formulation with Lotteries Return

• Notation: control variables d = (c , ε, e, x).

• Lotteries: π(d , a′|a, z) = π(c , ε, e, x , a′|a, z)

v(a, z) = maxπ(d,a′|a,z)

∑D,A

π(d , a′|a, z) {u(c , e) + βEv(a′, z ′)} s.t.

∑D,A

π(d , a′|a, z) {a′ + c}

=∑D,A

π(d , a′|a, z) {xΠ(ε, e, z ;w , r) + (1− x)wε} (1 + r)a.

∑(D\E),A

π(d , a′|a, z) {u(c , e) + βEv(a′, z ′)}

≥∑

(D\E),A

π(d , a′|a, z)p(ε|e)

p(ε|e){u(c , e) + βEv(a′, z ′)} ∀e, e, x

∑C ,A

π(d , a′|a, z) = p(ε|e)∑C ,ε,A

π(d , a′|a, z), ∀ε, e, x

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Formulation with Lotteries Return

• Capital and labor only enter the budget constraint ⇒ can

reduce dimensionality of problem.

maxk,l

∑Q

p(q|e){zqkαlγ − wl − (r + δ)k}

• FOC:

αz∑Q

p(q|e)qkα−1lγ = r + δ, γz∑Q

p(q|e)qkαlγ−1 = w

• Solutions: k(e, z ;w , r), l(e, z ;w , r).

• Realized (not expected) profits:

Π(q, z , e;w , r) = zqk(e, z ;w , r)αl(e, z ;w , r)γ−wl(e, z ;w , r)−(r+δ)k(e, z ;w , r)

34 / 40

Connection to Optimal DynamicContract Return

• Two sources of uncertainty: productivity, z , and prod. risk, ε.

• Argue: our formulation has optimal ε-insurance, but no

z-insurance.

• Consider two cases:

(1) special case with no z-shocks, and only ε-shocks: our

formulation equivalent to optimal dynamic contract ⇒

optimal insurance arrangement regarding ε shocks.

(2) general case: uninsurable z-shocks added on top. No

equivalence.

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Equivalence with only ε− but no z-Shocks

• Standard formulation of optimal dynamic contract

Π(W ) = maxe,x,k,l,c(ε),W ′(ε)

∑ε

p(ε|e){τ(ε) + (1 + r)−1Π[W ′(ε)]

}s.t.

τ(ε) + c(ε) = x [εf (k, l)− wl − (r + δ)k] + (1− x)wε∑ε

p(ε|e) {u[c(ε), e] + βW ′(ε)} ≥∑ε

p(ε|e) {u[c(ε), e] + βW ′(ε)} ∀e, e, x

∑ε

p(ε|e) {u[c(ε), e] + βW ′(ε)} = W .

36 / 40


Proposition

Suppose the Pareto frontier Π(W ) is decreasing at all values of

promised utility, W , that are used as continuation values at some

point in time. Then the following dynamic program is equivalent

to the optimal dynamic contract on the last slide:

v(a) = maxe,x,k,l,c(ε),a′(ε)

∑ε

p(ε|e) {u[c(ε), e] + βv [a′(ε)]} s.t.∑ε

p(ε|e) {u[c(ε), e] + βv [a′(ε)]} ≥∑ε

p(ε|e) {u[c(ε), e] + βv [a′(ε)]} ∀e, e, x∑ε

p(ε|e) {c(ε) + a′(ε)}

=∑ε

p(ε|e) {x [εf (k, l)− wl − (r + δ)k] + (1− x)wε}+ (1 + r)a

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Proof: The proof has two steps.

Step 1: write down dual to standard formulation. Because the

Pareto frontier Π(W ) is decreasing at the W under consideration,

we can write the promise-keeping constraint with a (weak)

inequality rather than an inequality. This does not change the

allocation chosen under the optimal contract. The dual is then to

maximize

V (π) = maxe,x,k,l,c(ε),π′(ε)

∑ε

p(ε|e) {u[c(ε), e] + βV [π′(ε)]} s.t.∑ε

p(ε|e) {u[c(ε), e] + βV [π′(ε)]} ≥∑ε

p(ε|e) {u[c(ε), e] + βV [π′(ε)]} ∀e, e, x∑ε

p(ε|e){τ(ε) + (1 + r)−1π′(ε)

}≥ π.

τ(ε) = x [εf (k, l)− wl − (r + δ)k] + (1− x)wε− c(ε)

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Step 2: express dual in terms of asset position rather thanprofits. Let

π = −a(1 + r), π′(ε) = −a′(ε)(1 + r)

and rewrite the dual using this change of variables. Finally, definev(a) = V [−(1 + r)a].�

• The change of variables just uses the present-value budget

constraint to express the problem in terms of assets rather

than the PDV of intermediary profits.

39 / 40

Documents

Economic Development, Flow of Funds, and the Equilibrium