14.772 Development Economics: Macroeconomics

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14.772 Development Economics: Macroeconomics Spring 2009

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Enterprise Dynamics and Finance: Distinguishing Mechanism Design from Exogenously

Incomplete Markets Models Alexander Karaivanov (Simon Fraser University)

Robert M. Townsend (MIT)

1

ENTERPRISES RUN BY HOUSEHOLDS

• major economic factor in both developing and developed countries ...but, often ‘fall between the cracks’ in the literature

• role of small enterprises - examples:

— Thailand 1976-96: occupational shifts account for 18-21% of GDP

growth, 29% of reduction in the poverty rate (Jeong and Townsend)

— India: own-account enterprises account for 68% of non-agricultural

firms and 36% of employment

— USA: non-employers account for 70% of all nonfarm establishments

and 14% of business revenues (Davis et al., 2007)

2

CONSUMERS VS. FIRMS DICHOTOMY

• Consumption smoothing literature — various models with risk aversion

— permanent income, buffer stock, full insurance

— private information (Phelan, 1994, Ligon 1998) or limited commitment

(Ligon et al., 2005; Dubois et al., 2008)

• Investment literature — firms mostly risk neutral — adjustment costs: Abel and Blanchard (1983), Bond and Meghir (1994)

— IO: Hopenhayn (1992), Ericson and Pakes (1995), Cooley and Quadrini

(2001); Albuquerque and Hopenhayn (2004), Clementi and Hopenhayn

(2006)

— empirical: e.g. Fazzari, Hubbard and Petersen (1988) — unclear what

the nature of financial constraints is (Kaplan and Zingales, 2000 cri-tique)

• emerging ‘households-as-firms’ literature — largely assumes exogenously

missing markets (Cagetti and De Nardi, 2006; Covas, 2006; Angeletos

and Calvet, 2007; Heaton and Lucas, 2000); exception - Meh and Quadrini

(2007)

3

OBJECTIVES

• how good an approximation are the various models of financial markets

across the different literatures?

• what would be a reasonable assumption for the financial regime if it is

taken to the data as well?

— financial constraints affect investment and consumption in static and

dynamic sense

— it matters what the source and nature of constraints are - can we

distinguish and based on what?

• we put together a wide range of dynamic models of incomplete financial

markets:

— exogenously incomplete markets: autarky, savings only, saving and bor-rowing in a single asset

— mechanism-design: moral hazard with observed or unobserved invest-ment (also, full information)

4

OBJECTIVES 2

• develop methods based on mechanism design, dynamic linear program-ming, and maximum likelihood to

— compute (Prescott and Townsend, 1984; Phelan and Townsend, 1991;

Doepke and Townsend, 2006)

— estimate and statistically test across models (Vuong, 1989)

— our methods allow for: measurement error, heterogeneity in unobserv-ables, use of data on transitions

• first, use model-generated data to explore:

— stylized facts on firm size, growth, and cash flow sensitivity from the

literature (Cooley and Quadrini, 2001)

— what data helps to distinguish across regimes? — consumption or in-vestment data, separately vs. jointly; cross-sectional vs. intertemporal

• apply our methods to real data from Thai villages

5

MODEL

• preferences: u(c, z) over consumption, c, and effort, z

• technology: P (q|z, k) — probability of obtaining output, q from effort, z and

capital, k

• agents contract with a competitive financial intermediary with outside

rate of return R

• full commitment on both sides (can be relaxed) • dynamic optimal contracting problem (T = ∞) • state variables: assets/capital k, and debt b (S, B regimes) or promised

utility w (MH, FI, UC regimes)

8

LINEAR PROGRAMMING (LP) APPROACH

• write the optimal contracting problem for each regime as recursive dy-namic linear program

• all state and policy variables belong to finite ‘grids’, Z, K, W, T, Q, B, e.g.

K = [0, .1, .5, 1]

• the choice variables are probabilities over all possible allocations (Prescott

and Townsend, 1984), e.g. π(q, z, k0, w0) ∈ [0, 1]

• extremely general method

— by construction no non-convexities from ICC or truth-telling constraints

for any preferences or technology — very suitable for our maximum likelihood estimation approach

— contrast with the ‘first order approach’ — may need additional assump-tions (Rogerson, 1985; Jewitt, 1988) or to verify solutions numerically

(Abraham and Pavoni, 2008)

10

II. Mechanism Design Regimes:

Moral Hazard with observed (MH) or unobserved investment (UC), Full information (FI) X

V (w, k) = max π(τ , q, z, k0 , w 0|w, k)[q − τ + (1/R)V (w 0, k0)] {π(τ ,q,z,k0,w0|w,k)}

T ×Q×Z×K×W

s.t. X

π(τ , q, z, k0 , w 0|w, k)[U(τ + (1− δ)k − k0 , z) + βw0] = w (PK)

T×Q×Z×K×W

s.t. ∀(q, z) ∈ Q × Z : X X

π(τ , q, ¯ , w q|¯ π(τ , q, ¯z, k0 0|w, k) = P (¯ z, k) z, k0, b0|w, k) (Bayes)

TxK 0xW 0 TxQ×K 0xW 0 X

π(τ , q, z, k0 , w 0|w, k) = 1 (adding up)

T×Q×Z×K×W

• for MH: subject also to ICC, i.e., ∀(z, z) ∈ Z × Z : X

π(τ , q, z, k¯ 0 , w 0|w, k)[U(τ + (1− δ)k − k0 , z) + βw0] ≥

T×Q×W 0×K 0 X P (q|z, k)≥ π(τ , q, ¯ , w 0|w, k) [U(τ + (1− δ)k − k0 z) + βw0] (ICC) z, k0 , ˆP (q|z, k)

T×Q×W 0×K 0

12

Moral Hazard with Unobserved Capital / Investment, k, k0 (UC)

• Structure:

— unobserved: effort z; capital stock / investment k, k0; observed: output

q

— dynamic moral hazard and adverse selection: both incentive and truth-telling constraints

— the feasible promise functions set W is endogenously determined and

iterated on together with V (Abreu, Pierce and Stacchetti, 1990)

• LP formulation:

— state variables: k ∈ K and a vector of promises,

w ≡ {w(k1), w(k2), ...w(k#K)} ∈ W (Fernandes and Phelan, 2000)

— use separable utility, U(c, z) = u(c)−d(z) to divide the optimization prob-lem into two sub-periods and reduce dimensionality

— UC with incomplete depreciation — theoretically modelled but much

harder to compute/estimate (in progress)

13

UC Program 2 (part 1), incomplete depreciation (δ < 1)

• now wm is also a vector (function of k) X

V (w, k) = max π(q, z, wm|w,k)[q + Vm(wm, k)]

{π(q,z,wm|w,k)}

Q×Z×Wm

s.t. X

π(q, z, wm|w,k)[−d(z) + wm(k)] = w(k) Q×Z×Wm

for all z, z ∈ Z (ICC) X X P (q|z, k)π(q, z,wm|w,k)[−d(z) + wm(k)] ≥ π(q, z,wm|w,k)[−d(z) + wm(k)]

P (q|z, k)Q×Wm Q×Wm

for all announced k =6 k ∈ K, and all δ(z) : Z → Z (truth-telling) X ˆP (q|δ(z), k)

w(k) ≥ π(q, z, wm|w,k)[−d(δ(z)) + wm(k)]

P (q|z, k)Q×Z×Wm

• plus Bayesian consistency and adding-up

16

UC Program 2 (part 2), incomplete depreciation (δ < 1)

X

Vm(wm, k) = max π(τ , k0 ,w 0|wm, k)[−τ + (1/R)V (k0 ,w 0)] {π(τ ,k0 ,w ,k)},{v(k,ˆ0|w k,k0,τ)}m T×K 0×W0

subject to:

for all possible combinations τ , k0 , k0 , k 6= k, and k0 6= k0 (“utility bounds”): X

π(τ , k0 ,w 0|wm, k)[u(τ + (1− δ)k − k0) + βw0(k0)] ≤ v(k, k, k0, τ)

W0

for all τ , k0 ∈ T × K 0 (“threat keeping”) X

v(k, k, k0, τ) ≤ wm(k)

T×K 0

interim utility: X

wm(k) = π(τ , k0 ,w 0|wm, k)[u(τ + (1− δ)k − k0) + βw0(k0)]

T×K 0×W0

• plus Bayesian consistency and adding-up.

17

COMPUTATION

Functional forms:

• preferences

1−σcu(c) = − ξzθ

1− σ

• technology (q1 is lowest output)

1/ρp(q = q1|z, k) = 1− (ηkρ + (1− η)z ρ)1− λ ρ)p(q = qi|z, k) = ( )λi−2(ηkρ + (1− η)z 1/ρ for i = 2, ..#Q

1− λ#Q−1

18

Table 2 - Variable Grids Used in the Estimation Runs Variable grid size, # grid range (full depr.) grid range (inc. depr.)

income/cash flow, Q assets, K effort, Z

savings/debt, B transfers, T

promised utility, W interim promise, Wm

2 5 3

9 (5 for S) 19 (9 for δ=1)

5 11

{.1, 3} [0, 1]

[.01, 1] S: [-1, 0], B: [-1, 1]

[0, 3] [wmin, wmax]

[wmin, βwmax+u(tmax)]

{.1, .5} [0, 1]

[.01, 1] S: [-.4, 0], B: [-.4, .4]

[0, 1] [wmin, wmax]

n.a.

Table 3 - Baseline Parameters

Parameter Value(s)

depreciation rate, δ

agent's discount factor, β

principal's discount factor, 1/R risk aversion, σ

effort curvature, θ

effort cost, ξ

technology parameter, ρ

capital share, η

probability scaling factor, λ

1 (full depr.), 0.05 (incomplete depr.)

0.95

0.95

0.5 (0)

2

1 (0.1)

0

0.5 (0.8)

0.5

Problem Dimensionality

# linear programs (LP) # LP variables (π) # LP constraints

Autarky 11 66 7

Saving / Borrowing 231 1386 7

Full Information 231 42,966 8

Moral Hazard, full depr. 231 42,966 14

Moral Hazard, inc. depr. 231 119,196 14

Unobserved k, full depr. stage 1 6,930 186 284

Unobserved k, full depr. stage 2 21 410,130 188

Unobserved k, inc. depr. stage 1 6,930 3,780 284

Unobserved k, inc. depr. stage 2 6,930 1,137,780 95,548

Note: This table uses the following grid sizes: #Q=2, #K=11, #Z=3, #B=21, #T=86 (31 if δ=1), #W=21, #Wm=630 (21 if δ=1) used for computing the numerical examples in section 3.4. See Table 2 for the grid sizes used in the estimation runs.

COMPUTATION 2

• compute the model under all regimes via policy function iteration (Judd,

1998)

• initial state (s) cdf D0(s)

• use the LP solutions, π∗(.|s) to create the state transition matrix, M(s, s0) =

{mss0 }

• for example, for MH s = (w, k) and so: X

mss0 ≡ prob(w 0, k0|w, k) = π ∗ (τ , q, z, k0 , w 0|w, k)

T×Q×Z • the state distribution at any time t is then:

Dt(s) = (M0)tD0(s)

• use D(s), M(s, s0) and π∗(.|s) from above to generate cross-sectional distri-butions (incl. joint or repeated) or panels of any variable

— draw n points from the initial distribution over states, D0(s), e.g. {ki, wi}n

i=1

for MH

— for each drawn si, use the LP solutions, π∗(.|si) and draw ci, ki0, qi etc.

from the marginal cdf of π∗(.|si)

19

ESTIMATION AND TESTING

• use or put data in ’frequency’ form

JX

• frequencies, mj, j = 1, ..J are over mutually exclusive ‘cells’, i.e., mj = 1

j=1

• example: let #Q = 2, #C = 5 and mj, j = 1, ..., 10 be the joint probabil-ity/frequency of particular (ck, ql) ∈ C × Q pair

c1 c2 c3 c4 c5

q1 m1 = .13 m2 = .03 m3 = .22 m4 = .01 m5 = .01

q2 m6 = .2 m7 = .2 m8 = .1 m9 = .05 m10 = .05

22

freq

uenc

y

Thai Data − (c,q) histogram 0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 .05 .1 .05 .1 .1 .02 .04 .06 .08 .1

low q c high q

Thai Data − (k,k’,q) histogram

freq

uenc

y 0.2

0.1

0 .03

.2 .6

0

k 1 0

.03 .2

.6 1

low q

0 .03

.2 .6

1

k’

high q

ESTIMATION AND TESTING 2

• let mj = observed frequency in the data to be fitted;

• let mj(φ) = frequency in the model being estimated at parameters φ

• estimation: ⎡ ⎤

J−1 J−1 J−1X X X

φ = argmax n ⎣ mj lnmj(φ) + (1− mj) ln(1− mj(φ))⎦

φ

j=1 j=1 j=1

• standard errors: bootstrap (draw from the data with replacement)

• testing: Vuong’s (1989) test for non-nested models; H0 - the compared

models are equally ‘close’ to the data

23

ESTIMATION AND TESTING WITH MODEL-GENERATED DATA • Generating Data from the model (use MH as baseline)

— fix baseline parameter vector, φ (“incomplete depreciation” and “full

depreciation” specifications) — tables 2, 3

— generate initial distribution over states, D0(k, w) — uniform in k, normal

in w (can use mixtures of normals)

— solve the dynamic LP programs and generate simulated data: c, q, k, k0;

sample size n = 1000

— allow additive measurement error in c, k, k0 ,e.g., c = c+ε with ε˜N(0, γ2 ).me

— two specifications: “low meas. error” with γ = .1 of grid span ( e.g. me

cmax − cmin) or “high meas. error” with γme = .5 of grid span)

• Estimated parameters: initial state distribution mean/stdev, μ (μb), γ (γb);w w

meas. error stdev., γ ; structural parameters, (σ, ρ, θ)me

24

Table 4 - Parameter Estimates using Model-Generated Data on Assets, Investment, and Cash Flow (k, k', q)

Data-Generating Model is Moral Hazard, n = 1000

Incomplete depreciation (δ = 0.05)

Estimates for1: μw/b γw/b γme σ θ

Low Measurement Error (stdev = 0.1 * grid span) ρ LL Value2

Model Moral Hazard (base) - MH Full Information - FI Borrowing & Lending - B Saving Only - S Autarky - A

20.1875 (.586)

19.9766 (.862)

-0.1521 (.142)

-0.4000 (.001)

n.a.

8.2500 (.798)

8.7188 (1.06)

0.2161 (.232)

0.2000 (.071)

n.a.

0.1000 (.005) 0.5000 (.000) 2.0313 (.043)

0.1366 (.011) 0.5039 (.008) 1.9961 (.058)

0.5276 (.044) 0.6000 (.199) 1.3750 (4.04)

0.6374 (.056) 0.1313 (.027) 1.2000 (.513)

0.7039 (.043) 0.1000 (.473) 8.1000 (1.88)

0.0000 (.053)

-0.0547 (.028)

-0.9063 (.161)

2.3984 (.376)

0.2188 (6.10) -3.1651

-3.2214

-3.4417

-3.4803

-3.6172

baseline values 19.9999 8 0.1 0.5 2 0

High Measurement Error (stdev = 0.5 * grid span) Moral Hazard (base) - MH Full Information - FI Borrowing & Lending - B Saving Only - S Autarky - A

19.0000 (6.40)

19.9688 (7.22)

0.0000 (.250)

-0.1651 (.081)

n.a.

9.0000 (6.52)

8.0625 (8.86)

0.1377 (.108)

0.0000 (.286)

n.a.

0.6414 (.075) 0.5000 (.002) 2.0156 (.771)

0.5684 (.105) 0.5000 (.012) 1.9844 (.802)

0.6559 (.066) 0.5000 (.492) 2.0000 (4.31)

0.6619 (.031) 0.4537 (.071) 2.0753 (.718)

0.6845 (.035) 1.1125 (.365) 1.4917 (1.38) -0.0469 (1.06)

-0.0625 (.721)

-3.8203 (3.13)

-2.7498 (1.78)

-3.4563 (4.00)

-3.5813

-3.5952

-3.6303

-3.6796

-3.7412

baseline values 19.9999 8 0.5 0.5 2 0

Complete depreciation (δ = 1) Estimates for: μw/b γw/b γme σ θ

Low Measurement Error (stdev = 0.1 * grid span) ρ LL Value

Model Moral Hazard (base) - MH Unobserved k - UC Full Information - FI Borrowing & Lending - B Saving Only - S Autarky - A

36.7338 (1.73)

n.a.

34.1713 (1.82)

-1.0000 (.003)

-1.0000 (.003)

n.a.

15.0000 (1.42)

n.a.

17.7266 (2.47)

0.4367 (.016)

0.2873 (.096)

n.a.

0.1039 (.003) 0.5000 (.006) 2.0234 (.027)

0.1020 (.079) 0.5469 (.192) 4.1375 (.045)

0.1937 (.018) 0.5068 (.004) 2.5859 (.451)

0.5517 (.013) 0.9750 (.352) 4.0000 (.589)

0.4402 (.017) 0.0375 (.435) 6.0000 (.004)

0.9031 (.083) 0.1000 (.002) 10.0000 (.000)

-0.0313 (.129)

-0.2813 (.608)

-0.0313 (.152)

0.0000 (.164)

0.2402 (.171)

0.7344 (.002)

-2.9763

-3.0181

-3.0594

-3.1653

-3.1846

-3.8684

baseline values 34.64 15 0.1 0.5 2 0

High Measurement Error (stdev = 0.5 * grid span) Moral Hazard (base) - MH Full Information - FI Borrowing & Lending - B Unobserved k - UC Saving Only - S Autarky - A

34.6400 (6.14)

34.6400 (.019)

-1.0000 (.107)

n.a.

-1.0000 (.006)

n.a.

14.5000 (2.13) 14.9688 (7.42)

0.2414 (.195)

n.a. 0.0250 (.182)

n.a.

0.5898 (.035) 0.5000 (.026) 2.2188 (1.89)

0.6168 (.088) 0.5000 (.008) 2.4375 (1.60)

0.6335 (.044) 0.2188 (.059) 10.0000 (.000)

0.6224 (.029) 0.1352 (.160) 5.0156 (3.04)

0.6550 (.079) 0.4750 (.192) 8.1000 (.045)

0.8521 (.056) 0.1000 (.002) 10.0000 (.000)

0.3125 (.082)

0.0000 (.191)

-0.3750 (.394)

-5.5938 (1.83)

0.2344 (.608)

0.7344 (.006)

-3.5149

-3.5229

-3.5284

-3.5287

-3.5304

-3.9523

baseline values 34.64 15 0.5 0.5 2 0

Notes: 1. Bootstrap standard errors are in parentheses next to the estimates; 2. Normalized (divided by n) log-likelihood values ordered by best fit.

V

Table 5: Regime Comparisons Using Simulated Investment and Cash Flow Data1, (k,k',q) Inc. depr., low m.e.2 Inc. depr., high m.e.2 Full depr., low m.e. Full depr., high m.e.

LL order3 LL value4 LL order LL value LL order LL value LL order LL value MH -3.1651 MH -3.5813 MH -2.9763 MH -3.5149 FI -3.2214 FI -3.5952 UC -3.0181 FI -3.5229 B -3.4417 B -3.6303 FI -3.0594 B -3.5284 S -3.4803 S -3.6769 B -3.1653 UC -3.5287 A -3.6172 A -3.7412 S -3.1846 S -3.5304

A -3.8684 A -3.9523

Comparison Z-statistic5 Comparison Z-statistic Comparison Z-statistic Comparison Z-statistic MH v. FI 6.14***(MH) MH v. FI 1.18(tie) MH v. FI 4.98***(MH) MH v. FI 1.38(tie) MH v. B 11.3***(MH) MH v. B 4.90***(MH) MH v. B 10.5***(MH) MH v. B 1.36(tie)u MH v. S 11.2***(MH) MH v. S 6.30***(MH) MH v. S 9.60***(MH) MH v. S 1.29(tie)o MH v. A 14.4***(MH) MH v. A 8.57***(MH) MH v. A 21.2***(MH) MH v. A 15.0***(MH)n FI v. B 9.23***(FI) FI v. B 2.38**(FI) FI v. B 7.34***(FI) FI v. B 0.54(tie)g FI v. S 9.22***(FI) FI v. S 6.57***(FI) FI v. S 8.36***(FI) FI v. S 0.72(tie) FI v. A 12.3***(FI) FI v. A 6.59***(FI) FI v. A 20.3***(FI) FI v. A 14.1***(FI)t B v. S 1.72*(B) B v. S 3.17***(B) B v. S 1.78*(B) B v. S 0.15(tie)e B v. A 6.98***(B) B v. A 6.82***(B) B v. A 18.6***(B) B v. A 14.3***(B)s S v. A 8.21***(S) S v. A 3.50***(S) S v. A 17.7***(S) S v. A 13.5***(S)t

MH v. UC 3.58***(MH) MH v. UC 1.42(tie)

FI v. UC -2.25**(UC) FI v. UC 0.53(tie)

B v. UC -7.55***(UC) B v. UC 0.03(tie)

S v. UC -7.11***(UC) S v. UC -0.12(tie)

A v. UC -20.5***(UC) A v. UC -12.9***(UC)

Table 6: Regime Comparisons Using Simulated Consumption and Income Data1, (c,q) Inc. depr., low m.e.2 Inc. depr., high m.e.2 Full depr., low m.e. Full depr., high m.e.

LL order3 LL value4 LL order LL value LL order LL value LL order LL value MH -2.5613 MH -2.7158 MH -2.7296 MH -2.7906 FI -2.5974 B -2.7214 UC -2.7542 FI -2.7938 B -2.6464 FI -2.7247 FI -2.7688 UC -2.7975 S -2.6824 S -2.7297 B -2.8114 B -2.8019 A -2.7936 A -2.7357 S -2.8602 S -2.8451

A -3.0963 A -2.8817

Comparison Z-statistic5 Comparison Z-statistic Comparison Z-statistic Comparison Z-statistic MH v. FI 5.16***(MH) MH v. FI 2.11**(MH)

1.63(tie)

2.24**(MH)

MH v. FI 4.59***(MH) MH v. FIV MH v. B 7.25***(MH) MH v. B MH v. B 6.86***(MH) MH v. Bu

0.86(tie)2.01**(MH)

MH v. S 8.75***(MH) MH v. S MH v. S 9.62***(MH) MH v. S 4.92***(MH)o MH v. A 13.5***(MH) MH v. A

-0.79(tie)0.75(tie)2.07**(FI)1.58(tie)

3.09***(MH) MH v. A 17.2***(MH) MH v. A 6.66***(MH)n FI v. B 3.96***(FI) FI v. B FI v. B 2.94***(FI) FI v. B 1.65*(FI)g FI v. S 6.32***(FI) FI v. S FI v. S 5.96***(FI) FI v. S 4.56***(FI) FI v. A 12.1***(FI) FI v. A FI v. A 14.1***(FI) FI v. A 6.11***(FI)t B v. S 4.06***(B) B v. S B v. S 5.64***(B) B v. S 4.79***(B)e B v. A 16.4***(B) B v. A 2.99***(B) B v. A 17.1***(B) B v. A 7.10***(B)s S v. A 12.81***(S) S v. A 1.15(tie) S v. A 19.2***(S) S v. A 5.08***(S)t

MH v. UC 3.31***(MH) MH v. UC 1.35(tie)

FI v. UC -1.67*(UC) FI v. UC 0.68(tie)

B v. UC -6.09***(UC) B v. UC -0.77(tie)

S v. UC -8.40***(UC) S v. UC -4.15***(UC)

A v. UC -16.5***(UC) A v. UC -6.24***(UC)

1. The data-generating regime is MH; n = 1,000; 2. "low m.e." = low measurement error; "high m.e." = high measurement error; 3. The regimes in all tables are ordered in decreasing log-likelihood (LL); 4. Normalized (divided by n) log-likelihood (LL) values; 5. *** = 1%, ** = 5%, * = 10%, "tie" >10% two-sided test significance level - the better fitting regime is in the parentheses.

Table 7: Comparisons using Simulated Consumption, Investment, and Cash Flow Data1, (k,k',c,q)

Inc. depr., low m.e.2 Inc. depr., high m.e.2 Full depr., low m.e. Full depr., high m.e. LL order3 LL value4 LL order LL value LL order LL value LL order LL value MH -4.6557 MH -5.7443 MH -4.6888 MH -5.7152 FI -5.1292 FI -5.9390 UC -5.3088 FI -5.9086 B -6.2827 B -6.2672 FI -5.4047 UC -6.0871 S -6.4033 S -6.4557 B -5.7666 B -6.3067 A -6.8293 A -6.7949 S -6.0683

A -8.2624 S -6.6147

A -7.2062

V u o n g

t e s t

Comparison Z-statistic5

MH v. FI 8.79***(MH) MH v. B 22.9***(MH) MH v. S 25.8***(MH) MH v. A 28.0***(MH) FI v. B 12.1***(FI) FI v. S 14.3***(FI) FI v. A 16.9***(FI) B v. S 1.467(tie) B v. A 6.44***(B) S v. A 4.71***(S)

Comparison Z-statistic

MH v. FI 3.75***(MH)

MH v. B 7.22***(MH)

MH v. S 8.85***(MH)

MH v. A 11.2***(MH)

FI v. B 4.03***(FI)

FI v. S 6.29***(FI)

FI v. A 8.89***(FI)

B v. S 2.38**(B)

B v. A 5.38***(B)

S v. A 3.28***(S)

Comparison Z-statistic MH v. FI 10.3***(MH)MH v. B 13.7***(MH)MH v. S 20.9***(MH)MH v. A 30.6***(MH)FI v. B 4.46***(FI)FI v. S 7.10***(FI)FI v. A 20.3***(FI)B v. S 4.44***(B)B v. A 18.1***(B)S v. A 18.5***(S)MH v. UC 12.3***(MH)FI v. UC -1.13(tie)B v. UC -5.15***(UC)S v. UC -9.28***(UC)A v. UC -23.7***(UC)

Comparison Z-statistic MH v. FI 2.95***(MH) MH v. B 7.30***(MH) MH v. S 9.94***(MH) MH v. A 15.1***(MH) FI v. B 4.55***(FI) FI v. S 7.20***(FI) FI v. A 12.1***(FI) B v. S 3.22***(B) B v. A 7.73***(B) S v. A 13.5***(S)

MH v. UC 5.32***(MH)

FI v. UC 2.38**(FI)

B v. UC -2.56**(UC)

S v. UC -5.65***(UC)

A v. UC -10.6***(UC)

SIMULATED DATA RESULTS 4

• various robustness checks (data from S; different n, grid size, meas. error

level) — tables 10-11

• using estimated parameters

28

APPLICATION TO THAI DATA

• Townsend Thai monthly surveys (16 villages in 4 provinces, Northeast

and Central regions)

• panel of 531 rural households observed 1999-2005

• Data series used in estimation and testing

— consumption expenditure (c) — household-level, includes owner-produced

consumption (fish, rice, etc.)

— productive assets (k) — include business and farm equipment, exclude

livestock and household durables — income (q) — measured on accrual basis (Samphantharak and Townsend,

2008)

29

APPLICATION TO THAI DATA 2

• ‘putting the data into the model’:

— convert data into ‘model units’ — divide all nominal values by the 90%

asset percentile (1,742,557 baht)

— put normalized data on grids (as with simulated data): k — 5 points on

[0, 1]; c — 10 points on [0, .1] and q — {.005, .13}

— draw initial unobserved states (w, b) from N(μw/b, γw/b); initial assets, k

taken from the Thai data

— additive measurement error in k, k0, c (with standard deviation to be

estimated)

• estimate and test against the Thai data the MH, FI, B, S, A regimes for

the inc. depreciation specification

30

Table 15 - Model Regime Comparisons Using Thai Data - Vuong Test Z-Statistics

Comparison MH v FI MH v B MH v S MH v A FI v B FI v S FI v A B v S B v A S v A Best Fit

1. Using (k,k',q) data 13.5***(B) 8.35***(B)

10.5***(B) 8.93***(B)

9.86***(B) 10.3***(B)

20.8***(B) 18.5***(B)

10.3***(B) 8.18***(B)

14.5***(B) 12.8***(B)

8.89***(B) 8.61***(B)

8.56***(S) 8.18***(S)

12.1***(S) 8.43***(S)

13.1***(S) 9.01***(S)

18.2***(S) 21.3***(S)

11.3***(S) 8.01***(S)

15.7***(S) 15.6***(S)

7.57***(S) 9.89***(S)

S, B B

S, B B, S

MH,FI,B,S MH,S,B

B B, S

S, B B, S

MH MH

MH S,B,MH,FI

1.1. years: 99-00 7.05***(MH) -3.27***(B) -2.74***(S) 9.25***(MH) -7.54***(B) -6.13***(S) 7.18***(FI) -0.23(tie) 1.2. years: 04-05 0.57(tie) -6.41***(B) -5.62***(S) 4.02***(MH) -7.41***(B) -7.98***(S) 3.37***(FI) 2.26**(B)

2. Using (c,q,k,k') data 2.1. years: 99-00 2.31**(MH) -5.74***(B) -6.54***(S) 5.49***(MH) -7.09***(B) -8.10***(S) 3.05***(FI) -0.81(tie) 2.2. years: 04-05 0.97(tie) -5.32***(B) -5.00***(S) 3.61***(MH) -5.59***(B) -5.49***(S) 2.50**(FI) 0.21(tie)

3. Using (c,q) data 3.1. year: 99 0.26(tie) 1.52(tie) 1.71*(MH) 8.58***(MH) 1.36(tie) 1.72*(FI) 9.50***(FI) 0.27(tie) 3.2. year: 05 4.92***(MH) 0.62(tie) 0.42(tie) 7.99***(MH) -2.31**(B) -1.92*(S) 4.76***(FI) -0.17(tie)

4. Repeated Cross-Sections 4.1. (k,k',q), yrs: 99-0 & 00-1 7.86***(MH) -7.12***(B) -4.38***(S) 14.8***(MH) -15.2***(B) -9.71***(S) 7.89***(FI) 3.34***(B) 4.2. (k,k',q), yrs: 99-0 & 04-5 4.28***(MH) -7.97***(B) -8.37***(S) 8.55***(MH) -12.5***(B) -14.9***(S) 7.72***(FI) 0.54(tie)

4.3. (c,q,k,k'), 99-0 & 00-1 4.4. (c,q,k,k'), 99-0 & 04-5

-0.09(tie) 0.15(tie)

-4.51***(B) -5.10***(B)

-5.52***(S) -5.01***(S)

4.51***(MH) 3.20***(MH)

-4.61***(B) -5.04***(B)

-5.64***(S) -4.96***(S)

4.78***(FI) 2.84***(FI)

-0.50(tie) 0.95(tie)

4.5. (c,q), yrs: 99 & 00 10.5***(MH) 2.82***(MH) 1.84*(MH) 15.3***(MH) -2.52**(B) -3.64***(S) 11.2***(FI) -2.56**(S) 4.6. (c,q), yrs: 99 & 05 10.8***(MH) 3.72***(MH) 3.78***(MH) 13.8***(MH) -2.58***(B) -3.54***(S) 6.51***(FI) -0.86(tie)

5. Two-Year Panel 5.1. (c,q), yrs: 99 and 00 4.01***(MH) 2.62***(MH) 3.40***(MH) 10.4***(MH) 0.32(tie) 1.41(tie) 8.45***(FI) 1.77*(B) 5.2. (c,q), yrs: 99 and 05 1.06(tie) -0.07(tie) -0.82(tie) 6.97***(MH) -0.70(tie) -1.55(tie) 6.53***(FI) -1.02(tie)

NOTES:

*** = 1%, ** = 5%, * = 10% two-sided significance level, the "winning" regime is in the parentheses

Z-statistics cutoffs: 2.575 = *** 1.96 = ** 1.645 = * "tie"

THAI DATA — ROBUSTNESS

• result remain robust for:

— coarser grid

— using (k, k0) data only

— different sub-samples (networks, alternative definitions of assets and

income)

— alternate estimated parameters (ξ, η instead of σ, θ)

• capital persistence (imposing k0 ≥ k) — MH/FI fit improves but still B/S

fit (k, k0, q) and (c, q, k, k0) best; B, S, FI, MH indistinguishable with (c, q)

• limited commitment (bound on w) — MH/FI’s fit with (c, q) and (k, k0, q)

data worsens; MH, FI, B, S indistinguishable with (c, q) data (incl. re-peated cross-sections)

• risk neutrality — MH fit worsens; B/S fit (c, q) and (k, k0, q) data best

• no measurement error — B/S fit (c, q) data best; MH tied with B with

(k, k0, q) data

• stratified by region (NE, C) — regional differences with (c, q) data

33

CONCLUSIONS

• developed methods to compute, estimate and test across wide range of

financial markets models which can handle unobserved heterogeneity, grid

approximations, and reasonable measurement error

• found that we can readily distinguish between exogenously vs. endoge-nously incomplete markets models

• within regime groups - ability to distinguish depends on type of data used

and level of measurement error

• established that our methods work with real data

— the B/S regimes best explain the overall data (fit best persistent k)

— echo previous work on rejection of full insurance: MH is not inconsis-tent with c, q data but this is not robust to alternative specifications,

e.g. with more capital persistence in the technology S/B fit investment

data best but consumption / income data are now not conclusive

34

FUTURE WORK

• further work on the theory given the Thai data findings:

— different sector technologies, aggregate shocks, entrepreneurial talent,

explicit adjustment costs

— other regimes: costly state verification, adverse selection

— transitions between regimes (as in Townsend and Ueda)

• use our methods to data from other economies (with more entry-exit,

larger sample size), e.g. Spain (Zambrano, Saurina, Townsend)

• supply side: e.g., lenders’ rules for access; regulatory distortions (Assun-cao, Mityakov and Townsend)

• computational methods — parallel processing, etc.

35

DISTINGUISHING FINANCIAL REGIMES

I. Investment/cash flow dimension, Cooley and Quadrini (2001) — empir-ical regularities about firm dynamics

- Fact 1 : Firm growth decreases with firm size

- Fact 2 : The variability of firm growth decreases with firm size

- Fact 3 : Small firms invest more

- Fact 4 : Small firms take on more debt

- Fact 5 : The investment of small firms is more sensitive to cash flows

• map to model: k - firm size; q - cash flow; k0 − (1 − δ)k - investment

• figure 1: facts 1, 2 and 3 — matched qualitatively by all regimes ...but

quantitative differences could help distinguish;

• fact 4 — confirmed for B; fact 5 — somewhat confirmed for exogenously

incomplete models

20

Figure 1 − Firm Growth and Finance − baseline parameters

Growth, E(k’/k), inc. depr. baseline Growth, E(k’/k), full depr. baseline 4

3

2

1

0 0.4 0.6 0.8 1

Growth Variance, Var(k’/k), inc. depr. baseline

0.4

0.3

0.2

0.1

0 0.4 0.6 0.8 1

Cash Flow Sensitivity, E(k’ ) − E(k’ ), inc. depr.H L

0.4

0.2

0

0 0.2 0.4 0.6 0.8 1

Debt, E(b’/k), inc. depreciation baseline 1.5

1

0.5

0

−0.5 0.4 0.6 0.8 1

k

0

1

2

3

4

0.4 0.6 0.8 1

Growth Variance, Var(k’/k), full depr. baseline 4

A

3 S B

2 MH FI

1 UC

0 0.4 0.6 0.8 1

Cash Flow Sensitivity, E(k’ ) − E(k’ ), full depr.H L

1

0.5

0

0 0.2 0.4 0.6 0.8 1

Debt, E(b’/k), full depreciation baseline 1.5

1

0.5

0

−0.5 0.4 0.6 0.8 1

k