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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
Unconstr.Entrepreneur
Log of Wealth, a
Constrained
Entrepreneur
Unconstrained Worker
Abili
ty, z
λ = 1.8
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
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
Fraction of Population Subject to Moral Hazard, m
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
Fraction of Population Subject to Moral Hazard, m
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
Fraction of Population Subject to Moral Hazard, m
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
31 / 40
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
32 / 40
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
33 / 40
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.
35 / 40
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
Equivalence with only ε− but no z-Shocks
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
37 / 40
Equivalence with only ε− but no z-Shocks
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)
38 / 40
Equivalence with only ε− but no z-Shocks
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