15.413.9 27.913.9 20.513.9 100 [0] 27.9 100 [0] 4441 4421.1 4432 100 [0] 21.1
100 [0] 13.111.1 11.132 11.123 100 [0] 32 100 [0] 84.383.3 84.352.6 84.365.3
52.6 100 [0] [0] 100 [0] 52.6 100 [0]

# An Empirical Equilibrium Model of Formal and Informal Credit Markets in
Developing Countries††thanks:  This paper has been accepted for publication at
the Review of Economic Dynamics: https://doi.org/10.1016/j.red.2021.09.001.

Fan Wang Fan Wang: Department of Economics, University of Houston, Houston,
Texas, USA (email: fwang26@uh.edu). I am grateful to Flavio Cunha and Jere
Behrman for their support and guidance throughout the course of this project,
and I would like to thank Petra Todd, Dirk Krueger, and Robert Townsend for
their invaluable support and extensive feedback. I would also like to thank
Andrew Shephard, Jeremy Greenwood, Holger Sieg, Kenneth Wolpin, Esteban
Puentes and Eun-Young Shim for useful discussions and comments.

(September 8, 2021; September 17, 2021)

###### Abstract

I develop and estimate a dynamic equilibrium model of risky entrepreneurs’
borrowing and savings decisions incorporating both formal and local-informal
credit markets. Households have access to an exogenous formal credit market
and to an informal credit market in which the interest rate is endogenously
determined by the local demand and supply of credit. I estimate the model via
Simulated Maximum Likelihood using Thai village data during an episode of
formal credit market expansion. My estimates suggest that a 49 percent
reduction in fixed costs increased the proportion of households borrowing
formally by percent, and that a doubling of the collateralized borrowing
limits lowered informal interest rates by percent. I find that more productive
households benefited from the policies that expanded borrowing access, but
less productive households lost in terms of welfare due to diminished savings
opportunities. Gains are overall smaller than would be predicted by models
that do not consider the informal credit market.
JEL: D15, D25, G21, O16, O17
Keywords: Informal credit, microfinance, structural estimation

##  1 Introduction

In recent decades, development banks and micro-finance institutions in
developing countries have funded the expansion of formal financial
institutions into rural areas. Recent randomized evaluations show that the
effects of expanding formal borrowing and savings opportunities are generally
positive but limited [5]. One factor that might impact the effectiveness of
formal credit market expansions is the availability of local informal
alternatives.

In this paper, I structurally evaluate the effects of microfinance
interventions in the presence of informal credit markets. Microfinance
interventions introduce formal options to households’ financial choice set.
But microfinance might also impact existing informal choices through
equilibrium effects as demand and supply in those informal credit markets
shift in response to interventions. The joint effects of microfinance could
lead to different welfare consequences for heterogeneous households depending
on their borrowing and savings needs. By combining the formal and informal
options, my analysis spans prior structural analyses of microfinance. [37]
conduct a structural evaluation of microfinance at the micro level without
distinguishing between formal and informal choices, while [15] analyze the
macro-equilibrium effects of microfinance without considering the response of
local informal credit markets.

To accomplish this, I develop and estimate a dynamic equilibrium risky
entrepreneur model that incorporates formal as well as informal borrowing and
savings choices. In the model, households are infinitely lived, risk averse,
and have varying productivity and wealth. Households choose risky capital
investments and savings, and they can finance their risky investments through
borrowing. The formal credit market is characterized by exogenously determined
differential borrowing and savings interest rates, and formal credit is
subject to a potential collateral constraint. In contrast, in the informal
market considered here, full enforcement is assumed, and market clears given a
locally determined borrowing and lending interest rate. The model has several
key features of formal-informal credit market interactions: First, formal and
informal credit market options differ in interest rates, collateral
requirements, and access/transaction costs; second, formal and informal
options could be substitutes or complements as households sort into seven
credit market participation categories;111Households could borrow formally,
save formally, borrow informally, lend (save) informally, borrow formally and
informally at the same time, borrow formally and lend informally, or not
borrow or save. Households pay per-period fixed costs to access any of the
different credit market options. If households decide to borrow from the
formal credit market, they face a collateral constraint that limits borrowing
up to a fraction of their physical capital choices. third, informal credit
markets are localized, and exogenous changes in formal credit market
conditions could shift equilibrium local informal interest rates.

Given these features, microfinance availability can have redistributive
consequences through equilibrium effects on locally determined informal
interest rates. The existing structural microfinance evaluation literature
generally models improvements in microfinance as a shift in the borrowing
collateral constraints [14]. In the context of this model, subsidizing the
centrally set formal borrowing and savings interest rates, reducing access
transaction costs, and relaxing borrowing collateral constraints can
separately and jointly improve microfinance availability. The effects of
relaxing the collateral constraints could be magnified or dampened by
variations in formal borrowing and savings fixed costs and interest rates.

I estimate the model using panel data from the Townsend Thai Monthly Survey,
which contains extensive information about the sizes and rates of formal and
informal credit market transactions for about 650 households from 16 villages
between 1999 and 2009. During this period, in 2001, the Thai government, under
Prime Minister Thaksin Shinawatra, implemented a wave of large-scale policies,
including the Million Baht Village Fund program, aimed at broadening rural
households’ access to the formal credit market.222[37] studied the Million
Baht Fund using a partial equilibrium model without distinguishing between
formal and informal choices and modeled the Thaksin policy as shifting the
borrowing constraints. They used data from 64 villages of the Townsend Thai
Annual Survey. The annual survey has more villages across a wider geographic
area but has limited information on the local-informal credit market compared
to the monthly survey. Specifically, the policies reduced interest rates by
offering a low fixed borrowing rate, reduced fixed costs by directly
administering formal loans with centrally set rates via village committees,
and potentially helped relax collateral constraints by increasing the number
of formal loans available. As a result of these policies, the proportion of
households that used formal borrowing increased by up to percentage points,
and the formal borrowing interest rates decreased by up to 8 percentage
points. The local informal interest rate also dropped by up to 14 percentage
points. I introduce the Thaksin policy shift in my model as possible changes
in centrally set formal interest rates, in formal fixed costs, and in formal
borrowing collateral constraints.

The model is estimated using simulated maximum likelihood. I develop solution
and estimation algorithms that capture the differential effects of variations
in formal and informal access costs and constraints on asset choices and
distributions. The estimation allows for the identification of unobserved
fixed costs and collateral constraints, and household preferences and
productivities. I allow the parameters that characterize the credit market to
vary over time and estimate their changes based on changes in credit choice
category participation probabilities. I find that the fixed costs to access
the formal credit market dropped from about 9% of average annual income to
about 4.6%, and the collateral constraints were also significantly relaxed,
more than doubling how much each household could borrow formally given the
same amount of physical capital. Along with the lowering of the centrally set
formal borrowing interest rates, these changes resulted in significant
improvements in households’ access to formal borrowing.

In terms of welfare comparisons, the estimated model suggests that there were
winners and losers. The majority of rural households are better off under
Thaksin’s policies, although the estimated steady state gains are close to
zero in consumption-equivalent variation for most households.333While it is
difficult to compare across models that consider different equilibrium
objects, [15, 63] estimate welfare gains on the order of 5% to 15% from
financial deepening and consider equilibrium changes in wage and aggregate
interest rates. Steady state welfare effects are heterogeneous across
households. High productivity households could gain up to about 5%. These
households were previously constrained by the collateral constraints or by the
fixed costs from investing more in their household farms or businesses.
However, low productivity households could lose up to 1% in consumption-
equivalent variation. These households have relatively higher preferences for
safe savings over taking out loans to finance their low expected return risky
investments. Their gains from lower borrowing costs are outweighed by
diminished savings opportunities due partly to the drop in locally determined
equilibrium informal interest rates.

I conduct counterfactual experiments to decompose the relative contributions
of each of the three formal borrowing access dimensions in explaining the
effects of the Thaksin policies. The redistributive welfare effects are
largely driven by the relaxation of the collateral constraint, which by itself
accounts for % of the reduction in the informal interest rate. Reductions in
formal borrowing fixed costs had a large impact on participation shares, and
by themselves these reductions account for % of the increase in the fraction
of households using formal credit options. Interestingly, the reduction in the
centrally set formal borrowing interest rates had limited effects on aggregate
participation and the informal market interest rates. The three measures of
access have different impacts because they shift the average costs of formal
loans differently for different types of households.

##### Related Literature

The analysis in this paper contributes to several strands of the literature.
First, there has been substantial research on the impacts of greater financial
access on developing economies [30, 47, 28, 37, 21, 15]. Despite the
importance of informal financial arrangements [65, 62], these dynamic models
of financial deepening—formal credit market expansion—generally do not
explicitly consider informal financial options. Additionally, studies that
test the fit of informal risk-sharing models to data do not model formal
options explicitly [2, 40, 45]. In this paper, I model risky entrepreneurs’
choices over formal and informal credit market options in an exogenous
incomplete markets setting. While there are different ways for rural
households to transfer financial resources, [40] find that a model with
exogenously incomplete borrowing and savings options fit consumption and
investment data in rural Thai villages better than constrained efficient
credit/insurance models. The model in effect augments equilibrium models of
risky entrepreneurs (see review: [55]) with additional exogenous borrowing and
savings options. Similar to [37], I treat villages as small open economies
where formal prices are exogenously determined, but I extend the framework to
explicitly consider informal choices and equilibrium interest rates determined
within a local informal credit market. My approach here focuses on the micro-
equilibrium effects of formal credit market expansion on village credit
markets. This complements the work of [15, 13], which focuses on the macro
equilibrium effects of large microfinance roll-outs on prices, including
interest rates and wages, on the aggregate economy.

Second, this paper contributes to work that studies the interaction between
formal and informal credit markets. Due to the expansion of development
banking, there has been significant interest in the interaction between formal
and informal credit markets [32, 11]. Studies have analyzed the impact of
differential access costs and contract enforcement on the sorting between
formal and informal borrowing options [27, 39]; the interaction between
suppliers of informal credits and formal banks [26, 49]; and the effects of
formal credit expansion on informal credit market interest rates [52, 23]. To
pin down the analytical structures, these papers generally rely on non-dynamic
models and generate sorting conditional on wealth and types. This paper
incorporates some core features of formal and informal credit markets
interaction into an empirical dynamic equilibrium framework with endogenous
asset distributions. Credit market participation now includes borrowing and
savings in both markets, and the supply side of informal credit is endogenized
through the dynamics of savings.

Third, there is a significant and growing empirical literature that analyzes
separate dimensions of credit market policies. Studies have found that formal
borrowing and savings choices are elastic to subsidies or shifts in the
interest rates of borrowing [41, 22] and saving [58]. The expansion of formal
borrowing or savings opportunities, which partly reduces the fixed/transaction
costs of access, have had modest but heterogeneous effects on households in
previously under-exposed areas [5, 24]. Offering loans to borrowers who would
otherwise be ineligible due to a possible lack of collaterals [7, 4] has also
had mixed results. To allow for the coexistence of various formal and informal
credit market participation categories, I incorporate into the model formal
borrowing and savings interest rates, fixed costs, and collateral constraints.
As a result, this paper provides a potential framework for studying the non-
separable effects of these important dimensions of formal credit market
policies.

Fourth, there is a literature that studies how the provision of formal
insurance could crowd-out informal insurance [3, 46, 17]. These papers find
that more formal insurance provisions might worsen informal conditions and
lead to welfare losses. In this paper, I study formal and informal market
interactions in the context of exogenously incomplete credit markets. The
welfare gains and losses in this paper arise out of a competitive local-
informal credit market’s interaction with an exogenous formal credit market
with centrally set rates. This contrasts with the insurance literature, where
welfare losses arise in the context of an endogenously incomplete market
structure that is constrained by limited commitment and other frictions.

The structure of the paper is as follows. Section 2 develops the model. In
Section 3, I describe the data and background. Section 4 describes the
estimation results and counterfactuals. I offer the conclusion in Section 5.
Additional details for the solution and estimation methods are in Appendix
Sections C.

##  2 The Model

For a village economy, there is a continuum of infinitely lived household
firms that are heterogeneous in their productivity type $\mathcal{A}$,
physical capital $k$, and financial asset $b$. $\mathcal{A}$ is fixed over
time and represents a household’s heterogeneous ability to earn income. $k$ is
the input for the household firm. $b$ is the sum of principal and interests
due from or owed to both formal and informal sources. Comparison of expected
productivity and interest rates endogenously determine households’ asset
holdings. In each period, households face two kinds of shocks: a productivity
shock $\epsilon$ and a vector of credit category utility shocks $\Phi$ for
alternative formal and informal credit choice categories. Given these shocks,
households choose assets within joint formal and informal credit choice
categories.

###  2.1 Preference

Households are risk averse with respect to consumption within each period, and
utility over consumption is separable over time. Individual expected utility
over lifetime sequence of consumption $c_{t}$, is
$\mathrm{E}\left[\sum_{t=0}^{\infty}\beta^{t}u\left(c_{t}\right)\right]$,
where within each period, utility from consumption is
$\frac{\left(c_{t}\right)^{1-\rho}}{1-\rho}$. $\beta$ is the discount factor,
$\rho$ is the coefficient of relative risk aversion. The expectation is over
realized values of productivity shocks $\epsilon$ and credit category utility
shocks $\Phi$.444$\Phi$ primarily captures stochastic factors unrelated to
intertemporal consumption and investments that impact households’ willingness
to save and borrow. For example, given realized shocks, households might have
differing levels of non-pecuniary values associated with borrowing from and
lending to other households that are in search of lending opportunities or
that are in need of loans.

###  2.2 Technology

At the beginning of each period, for each household, the household
productivity type $\mathcal{A}$, normally distributed productivity shock
$\epsilon$, and physical capital $k$, which is chosen previously by the
household based on expected productivity, jointly determine the income of the
household in the current period:555The model focuses on financial (safe asset)
and physical capital (risky asset) choices. Labor supply for the household
firm is inelastic and captured by $\mathcal{A}$.

$y=\exp\left(\mathcal{A}+\epsilon\right)\cdot k^{\alpha}\thinspace.$ (1)

###  2.3 Credit Markets

Villages are small open economies with respect to external-formal financial
choices with centrally set interest rates. Villages also contain an endogenous
internal-informal credit market with a locally determined interest rate.
Following [27], financial access in formal and informal credit markets is
impacted by fixed costs, interest rates, and collateral constraints.
Households choose among seven credit alternatives: physical capital only;
borrowing from the informal credit market; borrowing from the formal market;
lending in the informal credit market; saving in the formal market; borrowing
jointly from the formal and informal markets; or concurrently borrowing from
the formal market and lending in the informal market.

####  2.3.1 Fixed Costs

There are four fixed costs:
$\left\\{\psi_{\text{FB}},\psi_{\text{IB}},\psi_{\text{FS}},\psi_{\text{IS}}\right\\}$.
In each period, households pay the fixed costs associated with the chosen
credit category. These fixed costs represent the pecuniary and non-pecuniary
costs associated with formal and informal credit market
activities,666Pecuniary components of the fixed costs can include the costs
incurred at home (e.g., bookkeeping), costs incurred on the way to the bank
(e.g., transportation or search costs), and costs incurred at the bank (e.g.,
fees). Non-pecuniary components of the fixed costs can include the opportunity
cost of time as well as general preference aversion towards different credit
market activities.  and the formal fixed costs are potential policy
instruments.

Reducing $\psi_{\text{FB}}$ and $\psi_{\text{FS}}$, the fixed costs of
accessing formal savings and borrowing opportunities, can play an important
role in deepening financial access [61, 30, 29, 21]. There is also strong
empirical evidence that the fixed costs for formal banking access are
significant in many developing countries [8, 24].

The fixed costs for informal lending, $\psi_{\text{IS}}$, potentially captures
the per-lender level costs of set-up and monitoring [60, 66, 30]. While the
literature has considered both aggregate as well as per-dollar-of-loan
intermediation costs [30, 9], I focus on aggregate costs, which can be the
dominant factor for small-scale lending activities.

####  2.3.2 Interest Rates

There are three interest rates: the formal borrowing interest rate
$r^{\text{FB}}$, the formal savings interest rate $r^{\text{FS}}$, and the
informal interest rate $r^{I}$. The two centrally set formal interest rates
are exogenous, and the informal interest rate is competitively determined by
local demand and supply. Even though the locally determined informal interest
rate $r^{I}$ is the same for borrowers and lenders, the combination of
informal interest rate $r^{I}$ and $\psi_{\text{IS}}$ leads to informal
interest earning differentials.777A common interest rate differential arises
if the cost of lending is incurred at the per-dollar-of-loan level [21]. In
that setting, the average and marginal rates are the same. In a setting with
per-lender aggregate fixed costs, the average interest rate differentials
differ by the lender depending on the lending level.

The large roll-outs of micro-finance programs could potentially impact prices
at the aggregate level [15, 13]. Here, however, I take the interest rates
offered by formal lending and deposit-taking institutions as centrally set
policy rates and focus on the effects of microfinance on micro equilibrium
interest rates.

####  2.3.3 Collateral Constraint

Formal banks allow households to borrow up to $\gamma$ fraction of their
physical capital choice $k^{{}^{\prime}}$. This means a fraction of risky
investment could be financed by formal borrowing. Informal borrowing is not
constrained by $\gamma$. In the absence of possibly binding borrowing
constraints, households can borrow up to the natural borrowing constraint [1].
The natural borrowing constraint as well as the collateral constraint are
visualized in Appendix Figure C.1.

The formal borrowing constraint can be interpreted as a collateral constraint
that secures repayments given enforcement frictions [14].888 Microfinance
institutions generally distinguish themselves from traditional development
banks by lowering the collateral requirements [20]. In recent occupational-
choices models with entrepreneurial investment [21, 15], current period static
capital investments are constrained by prior dynamic savings
choices—collateral is savings that banks can confiscate. In this paper, risky
capital decisions are made prior to the realization of productivity shocks,
and $\gamma$ determines the proportion of risky physical capital that banks
are willing to finance. Here, collateral is physical capital that can be used
to pay off loans.  In contrast, full enforcement (no strategic default) is
assumed for informal loans. In addition to the collateral interpretation,
$\gamma$ might also capture rationing given potential limits to the amount of
loans that are made available from formal lenders to households in each
village [37].

####  2.3.4 Coexistence of Formal and Informal Choices

The four fixed costs, three interest rates, and one collateral constraint
allow for the coexistence of the seven credit market participation categories.
Fixed costs can account for borrowers choosing loans with higher interest
rates and savers choosing savings opportunities with lower savings rates. The
collateral constraint allows households to jointly choose formal and informal
borrowing and limits the amount of arbitrage from borrowing formally and
lending informally.

In this setting, for a development banker, there are five levers of formal
credit market policies: subsidizing centrally determined $r^{\text{FB}}$ or
$r^{\text{FS}}$, reducing $\psi_{\text{FB}}$ or $\psi_{\text{FS}}$, and
relaxing $\gamma$. The model provides a framework for analyzing the effects of
these policies jointly, taking into consideration the informal credit market
and the conditions of the village economy.

###  2.4 Recursive Formulation of the Household’s Problem

Households maximize their lifetime utility by choosing sequences of
consumption, physical capital, and formal and informal financial asset
positions, subject to a sequence of budget constraints and formal borrowing
limits. Let $\mathcal{W}$ denote cash-on-hand (alternatively wealth).
$\mathcal{W}$ is the sum of financial asset, depreciated physical capital, and
$y$ which is realized given productivity shock $\epsilon$:

$\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)=\exp\left(\mathcal{A}+\epsilon\right)\cdot
k^{\alpha}+\left(1-\delta\right)k+b\thinspace.$ (2)

$\mathcal{W}$ is the resources available for consumption and new asset
choices.

At the beginning of a period, the state-space $s$ of the household is
summarized by productivity type $\mathcal{A}$, physical capital level $k$,
financial asset level $b$, productivity shock $\epsilon$, and a vector of
credit type-specific utility shocks $\Phi$. Together,
$s=\left(\mathcal{A},k,b,\epsilon,\Phi\right)$.
${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k,b,\epsilon,\Phi\right)$
is the maximum over the value of the seven credit category alternatives
discussed previously:

${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k,b,\epsilon,\Phi\right)=\max_{j\in\left\\{1,...,7\right\\}}\left\\{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{1}}\left(\mathcal{A},k,b,\epsilon,\phi_{1}\right),...,{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{7}}\left(\mathcal{A},k,b,\epsilon,\phi_{7}\right)\right\\}\thinspace.$
(3)

The optimal credit category choice is
$\mathit{o}\left(\mathcal{A},k,b,\epsilon,\Phi\right)\in\left\\{1,...,7\right\\}$.
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{j}}\left(\mathcal{A},k,b,\epsilon,\phi_{j}\right)$
is the value for each credit category $j$ given optimal continuous assets and
consumption choices. Credit category utility shocks $\phi_{j}$ is i.i.d.
extreme value and influences the relative values of the seven credit choice
categories given optimal continuous choices.

Equation (4) is the generic form of
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{j}}\left(\mathcal{A},k,b,\epsilon,\phi_{j}\right)$.
Given the period budget constraint, a household chooses $c$, risky investment
$k^{{}^{\prime}}$, and next period financial position $b^{{}^{\prime}}$:

${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{j}}\left(\mathcal{A},k,b,\epsilon,\phi_{j}\right)=\max_{\begin{array}[]{c}c,k^{{}^{\prime}}\in\mathcal{K}_{j}^{{}^{\prime}},\\\
b^{{}^{\prime}I}\in\mathcal{B}_{j}^{{}^{\prime}I},b^{{}^{\prime}F}\in\mathcal{B}_{j}^{{}^{\prime}F}\end{array}}\left\\{\begin{array}[]{c}u\left(c\right)+\phi_{j}+\\\
+\beta\mathrm{E}_{\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}}\left({\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k^{{}^{\prime}},b^{{}^{\prime}},\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)\right)\end{array}\right\\}\thinspace,$
(4) $\mbox{s.t.:\hskip
7.11317pt}c=\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)-k^{{}^{\prime}}-\psi_{j}-\left\\{\begin{array}[]{c}\frac{b^{{}^{\prime}F}\mathbb{I}\left\\{b^{{}^{\prime}F}>0\right\\}}{1+r^{\text{FS}}}+\frac{b^{{}^{\prime}F}\mathbb{I}\left\\{b^{{}^{\prime}F}\leq
0\right\\}}{1+r^{\text{FB}}}+\frac{b^{{}^{\prime}I}}{1+r^{I}}\end{array}\right\\}\thinspace,$
(5) $b^{{}^{\prime}}=b^{{}^{\prime}I}+b^{{}^{\prime}F}\thinspace.$

The budget constraint for each category $j$ includes the fixed costs
$\psi_{j}$ and the associated interest rates. $\mathcal{K}_{j}^{{}^{\prime}}$,
$\mathcal{B}_{j}^{{}^{\prime}I}$ and $\mathcal{B}_{j}^{{}^{\prime}F}$ are the
constraint sets for asset choices in each participation category. The
continuation value is a function of the state space elements
$\left(\mathcal{A},k^{{}^{\prime}},b^{{}^{\prime}},\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)$.
Next period financial position $b^{{}^{\prime}}$ represents the net amount of
principal plus interest owed and earned from borrowing and saving undertaken
by the household in the current period. Full equation for each
$\left\\{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{j}}\right\\}_{j\in\left\\{1,...,7\right\\}}$
is shown in Appendix Section A.

Figure 1: Weighted Continuous Policy Functions _Panels show:_ 1\. consumption
share of wealth; 2. safe savings (the sum of informal savings, formal savings,
and joint formal borrowing and informal savings) share of savings and risky
investment; 3. risky investment as a fraction of wealth; 4. the share of risky
investment financed by borrowing (the sum of informal borrowing, formal
borrowing, and joint borrowing).

Nesting the safe and risky asset choice problem of Equation (4) within the
discrete participation categories of Equation (3) allows for the analysis of
key types of formal and informal participation possibilities. Despite the
nesting, asset choices have expected patterns. In Figure 1, the y-axis shows
average continuous choice solutions to Equation (4) integrated over the
discrete probabilities induced by Equation (4). As wealth increases, the
overall fraction of wealth invested in risky and safe assets increases, and
the risky investment share of overall savings decreases. Lower wealth
households finance a portion of their risky investment through borrowing.
Households with low wealth and high productivity type externally finance the
majority of their risky investment by borrowing. Households with high wealth
and low productivity type consume the smallest proportion of their wealth and
invest more in safe savings. These heterogeneous borrowing and savings needs
of households are important in sorting households into demanders and suppliers
of credit on the informal market with locally determined interest rates.
Improvements in borrowing and savings access can benefit households
differently.

###  2.5 Stationary Competitive Equilibrium

Given centrally set formal interest rates for savings $r^{\text{FS}}$ and
borrowing $r^{\text{FB}}$, collateral constraint $\gamma$, and a vector of
fixed costs $\Psi$, a Recursive Competitive Equilibrium consists of the values
and policy function for the household
${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}:S\rightarrow\mathbb{R}$,
$\mathit{o}:S\rightarrow\left\\{1,...,7\right\\}$,
$\left\\{\mathit{c_{j}},\mathit{k^{{}^{\prime}}_{j}},\mathit{b^{{}^{\prime}I}_{j}},\mathit{b^{{}^{\prime}F}_{j}}:S\rightarrow\mathbb{R}\right\\}_{j\in\left\\{1,...,7\right\\}}$,
locally determined informal interest rate $r^{I}$, as well as stationary
measure $\boldsymbol{\mu}$, such that:

  1. 1.

Given $r^{\text{FS}}$, $r^{\text{FB}}$, $r^{I}$, $\gamma$, $\Psi$, the value
function
${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}$ solves
Equation (3) and the value functions
$\left\\{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{j}}\right\\}_{j\in\left\\{1,...,7\right\\}}$
solves Equation (4) for each $j\in\left\\{1,...,7\right\\}$. $\mathit{o}$ and
$\left\\{\mathit{c_{j}},\mathit{k^{{}^{\prime}}_{j}},\mathit{b^{{}^{\prime}I}_{j}},\mathit{b^{{}^{\prime}F}_{j}}\right\\}_{j\in\left\\{1,...,7\right\\}}$
are the associated policy functions.

  2. 2.

Informal credit market clears:

$\int\left\\{\sum_{j\in\left\\{1,...,7\right\\}}P_{j}\left(\mathcal{A},\mathcal{W},\pi_{\Phi}\right)\cdot\mathit{b^{{}^{\prime}I}_{j}}\left(\mathcal{A},\mathcal{W}\right)\right\\}\mathrm{d}\boldsymbol{\mu}\left(\mathrm{d}\mathcal{A},\mathrm{d}\mathcal{W}\right)=0\thinspace,$
(6)

where $P_{j}\left(\mathcal{A},\mathcal{W},\pi_{\Phi}\right)$ denotes the
probability of a household with
$\left(\mathcal{A},\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)\right)$
choosing credit category $j$, given the distribution over the credit category
utility shocks $\pi_{\Phi}$.

In this stationary equilibrium, the measure $\boldsymbol{\mu}$ over the state
space is invariant with respect to the Markov process induced by $\epsilon$,
$\Phi$, the distribution of $\mathcal{A}$, and the policy functions.999
Households facing negative productivity shocks draw down their savings or
resort to borrowing to finance consumption and maintain physical capital
investments. Conversely, positive productivity shocks can lead to increases in
savings and physical capital investments. The introduction of discrete credit
category shocks generates greater uncertainties. Given credit category
participation probabilities, I generate overall wealth transition matrices
that integrate over credit-category-specific wealth transition matrices. While
I do not offer a formal proof, within the range of parameter values explored
during estimation, the numerical methods discussed in Appendix Section C.1.3
is able to find the model-induced Markovian wealth transition matrices and
corresponding stationary distributions.

While the locally determined informal credit market clears, the formal market
with centrally set rates does not have to. Positive excess supply of formal
credit means that formal institutions are mobilizing rural savings. Village
income would come from within village production as well as from returns to
formal savings. Negative excess supply of formal credit means that formal
institutions are injecting credit into the village economy. Risky investments
in the village would be partly financed by outside banks that receive a
portion of village outputs as interest payments.

For policy experiments, welfare in the aggregate village economy is measured
by a social welfare function in the steady state101010While it is important to
consider welfare along the transition path, this paper focuses on steady state
welfare comparisons. This is a limitation of the approach here. Estimating the
structural model while accounting for the transition path would require
solving for equilibrium transition paths at each set of parameters that the
estimation algorithm searches through. For computational tractability,
estimation is conducted under steady state assumptions. To preserve the
consistency between estimation and counterfactual analysis, I compute welfare
changes under steady state assumptions as well. that is Utilitarian with equal
weights assigned to all households.

###  2.6 Solving the Dynamic Programming Problem

Solving heterogeneous-agent equilibrium models with multiple continuous and
discrete states and constrained continuous and discrete choices is potentially
time-consuming. Furthermore, given that the model has four fixed costs, one
collateral constraint, and three interest rates, the solution algorithms need
to accurately capture how these eight values determine the feasible choice set
as well as the average prices of borrowing and saving in formal and informal
credit markets. I adopt a set of solution algorithms to reduce iteration and
increase accuracy within each of the five standard steps involved in solving
this class of model.111111The five general parts are: 1, optimization of the
choice problem; 2, iteration over the value function; 3, simulation of the
steady state distribution; 4, integration over types; 5, finding equilibrium
prices. Speed improvements for the first three steps are achieved through
vectorization, and for the final two steps are achieved by using more parallel
processors.

The algorithm produces conditional asset distributions, which are used in
constructing the estimation likelihood described in Section 4.2. To arrive at
these conditional asset distributions, I first solve for optimal choices given
current value function approximation using an iterative grid search algorithm
as described in Appendix Section C.1.1. Then, I approximate the expected
future value using multi-linear splines over $k^{{}^{\prime}}$ and
$b^{{}^{\prime}}$ as described in Appendix Section C.1.2. In Appendix Section
C.1.3, I derive the distribution of wealth tomorrow based on wealth in the
current period as a transition matrix. I project to solve for the steady state
asset distributions. Finally, I solve for the equilibrium interest rate using
a multi-section algorithm where I also integrate over different productivity
types as described in Appendix Sections C.1.4 and C.1.5.

##  3 Data and Background

I estimate the model with Thai village data. Thai villages have traditionally
had strong informal credit markets [59]. The Thai government has also
subsidized the expansion of state development banks led by the Bank for
Agriculture and Agricultural Cooperatives (BAAC) [50].

After the election of Thaksin Shinawatra in 2001, the government introduced
programs to improve rural borrowing access. The Million Baht Village Fund
(MBF) program was the most prominent program and provided every village with
one million baht in credits at centrally set rates [12]. The total funds
amounted to 1.5 percent of GDP [38]. The funds were transferred to villages
via the BAAC, but the power to approve loans was in the hands of local
committees. In addition to the MBF, the government gave BAAC a greater mandate
to expand its lending programs, and also created additional programs through
other agencies.121212The Government Savings Bank was given additional
resources. There were also lending programs aimed at supporting small
businesses, funding the purchase of low-priced household goods, and financing
schooling costs [54, 51, 12].

I use the 1999 to 2009 waves of the Townsend Thai Monthly data, which is a
panel for about 650 households in 16 villages [57].131313There were 684
households in 1999. Summary statistics and estimation rely on 606 households
for whom there is information for all years. 304 households are from the
Northeast. The villages are split between the wealthier Central and the more
impoverished Northeast regions. Households consist of multiple generations and
operate businesses and farms of varying scales. In contrast to the Townsend
Thai Annual Survey, which has 64 villages and allows for analysis using
village-level variations of MBF credit-per-household [37, 38], the monthly
survey has more complete data on formal and informal financial transactions.

###  3.1 Formal and Informal Channels

####  3.1.1 Borrowing and Savings Alternatives

Table 1 presents the relative popularities of the main lenders: MBF and BAAC
are external-formal lenders with centrally set rates; Village Coops,
friends/neighbors, and moneylenders are internal-informal lenders with locally
determined rates.141414Village Coops include Production Cooperative Groups and
Village Agricultural Cooperatives. Commercial banks are external-formal
lenders, but I do not consider them in the analysis since they only account
for 0.3 percent of the total number of loans. Village coops are by definition
specific to the village or township. 72 percent of loans from
friends/neighbors and money-lenders are from within the village or township
(tambon), and 93 percent are from within the same province (changwat). For the
analysis in this paper, I aggregate across villages in the two wealthier
central provinces and the two poorer northeastern provinces separately. The
analysis assumes that local conditions are similar within each region.

In the Northeast, 78% percent of households borrowed at least once from the
MBF, 62% from the BAAC, 36% from Village Coops, 83% from friends and
neighbors, and 38% from moneylenders. In the Central villages, informal
participation rates are roughly half of those in the Northeast. On average,
formal borrowers borrowed formally in half of the years between 1999 and 2009,
and informal borrowers borrowed from friends and neighbors in four of these
years.

Table 2 also presents the relative popularities of the main channels for
savings: commercial banks, the BAAC, and the GSB are external-formal deposit
takers; saving at Village Coops and lending to other households constitute
internal-informal savings. In the Northeast, 94% of households saved with
either the BAAC or the GSB, 37% saved with commercial banks, 64% saved with
Village Coops, and 67% lent directly to other households. In the Central
villages, the use of commercial banks for saving was twice as frequent as in
the Northeast, and individual lending took place half as often. On average,
formal depositors made deposits in 7.8 out of the 11 years, and household
lenders lent out in 2.6 out of the 11 years.

####  3.1.2 Formal and Informal Credit Categories

I annualize household credit market participation. Some households used one
option annually: borrowing or saving formally, borrowing or saving informally,
or no borrowing or saving. Some households borrowed from both formal and
informal sources, and others borrowed from formal sources and lent informally
in the same year.151515Joint credit choices have long been observed in village
economies [33, 26]. [10] discuss joint formal and informal borrowing.
Households are classified as choosing one of these seven participation
categories, which allow for substitutability and complementarity between
formal and informal options.161616Households with other combinations of
activities are grouped into these seven categories based on the level of
borrowing and savings they undertake formally and informally.

Thaksin’s policies started in the second half of 2001, but came into full
force in 2002. Given potential heterogeneities in borrowing and savings
frictions as well as household productivity and wealth distributions across
villages, external-formal interventions could have differential local-informal
effects depending on whether the complementarity or substitutability of
informal and formal options dominate. Tables 3 and 4 show the average annual
household participation shares in the seven credit market categories between
1999–2001 and between 2002–2009. Overall, the informal household participation
shares are higher in the Northeast villages, and the saving shares are higher
in the Central villages. There is a large shift after the implementation of
Thaksin’s policies. After 2001, Northeast households that only borrowed or
saved formally increased by 23 percentage points, and those that only borrowed
or lent informally decreased by 21 percentage points. In the Central villages,
these shares increased by 7 and decreased by 2 percentage points,
respectively. At the same time, the proportion of households using both formal
and informal credit markets increased after 2001, shifting from 6.7 percent to
18 percent of households in the Central villages, for example.

###  3.2 Formal and Informal Loan Characteristics

####  3.2.1 Interest Rates

I compute annual interest rates taking into consideration pecuniary repayments
as well as repayments in kind. Table 5 and Figure 4 show distributions of
annualized average village interest rates for formal and informal categories.
I find that loans with locally determined rates, informal loans in the context
of this paper, were higher than loans with centrally set rates, formal loans
in the context of this paper.171717BAAC and MBF rates, which are centrally set
and tend to be subsidized, have limited variations within areas and periods,
but informal interest rates have higher mean as well as variance. While the
definition for informality differs across studies, local-informal loans have
been found to carry high rates [19]. For example, [6] find this to be the case
in Hyderabad, India. At the same time, a significant proportion of loans to
relatives and friends often have low reported rates. [39] show that these
ostensibly low-cost loans might have high implicit social-tie-based ”shadow
costs” that could make them more expensive, in expectation, than formal loans.
Additionally, informal borrowing interest rates were higher than formal
savings interest rates. Both formal and informal interest rates decreased
significantly over time.181818Using the Annual survey, [38] find that the
level of household MBF borrowing does not have significant impacts on average
credit-interest rates. This is consistent with MBF borrowers relying on MBF
and BAAC loans with similar rates. The average informal interest rate in the
Northeast was 28% before 2002, compared to 15% for formal borrowing and 3.3%
for formal saving. The corresponding rates in the Central region were 18%,
13%, and 3.2%, respectively. After the policy shift, the informal interest
rates decreased by 14 percentage points to 13.9% and 8 percentage points to
9.4% in the Central and Northeast regions, respectively. Accompanying these
shifts, the formal borrowing interest rates decreased by 8 percentage points
in both the Northeast and Central regions to approximately 6%, and the formal
saving interest rates in both regions also decreased by approximately 2
percentage points to about 1%.

####  3.2.2 Borrowings and Savings Amounts

Using annualized sums of formal or informal borrowing activities and the net-
flow of formal or informal savings activities, Appendix Figure B.3 shows that
formal loan sizes tend to be larger than informal loan sizes and informal
savings/lending tend to be larger than formal savings. The median informal
individual lending size is 17,500 baht. Although some households have very
large amounts of formal savings, aggregating across all, the median net flow
of formal savings is approximately 8,000 baht per year. The median formal and
informal borrowing loan sizes are 27,000 and 15,500 baht, respectively. These
compare to a mean annual income across survey years of around 125,000 Baht and
a median annual income of around 65,000 Baht among the sampled households.

Disaggregating across lenders, Appendix Figure B.3 shows that BAAC loans tend
to be larger in size, and loan sizes from those that are categorized as
village moneylenders and friends are similar. Additionally, aggregating the
loan volumes of key lenders, Appendix Table B.1 shows that there was a
significant increase in MBF loan volume shares and a corresponding sharp drop
in informal lender loan volume shares after the Thaksin policy shift.

####  3.2.3 Fixed Costs

The survey captures aspects of the pecuniary fixed costs for borrowing.
Appendix Table B.2 and Figure B.4 show significant reductions in loan-specific
fees and transportation costs after 2001 for formal borrowing, mainly due to
the lower reported costs for MBF loans. MBF loans had fees and transportation
costs similar to informal loans, which is likely due to their village
committee-based administration. Reported BAAC costs also decreased over time,
which might have been driven by improvements in the BAAC itself or reductions
in transportation and communication costs. BAAC costs, however, were still
twice as high as the average costs reported for informal loans. Strikingly,
reported costs for the few commercial bank loans were, on average, seven times
larger than the costs for BAAC loans and almost 35 times larger than the costs
for MBF or informal loans.

####  3.2.4 Collateral and Repayment

Across all years, 21.0 percent of all BAAC loans have collateral requirements.
Before 2002, this proportion was 32.3 percent. After the policy shift, 15.7
percent of BAAC loans have collateral requirements. For MBF loans, less than
0.1 percent have collateral requirements. This evidence indicates that the
overall collateral requirements for these formal loans with centrally set
interest rates are relaxed after the policy shift. In contrast, 6.9 percent of
loans from non-relatives and 4.5 percent of loans from relatives are reported
as having collateral requirements. Over time, the share of informal loans
requiring collateral did not change significantly.

For repayments, Appendix Tables B.3 and B.4 show that 97 percent of formal
loans and 95 percent of informal loan principals were repaid.191919Every
month, repayment amounts of each loan are tracked until full repayment. I
compute repayment rates three months after the initially stated due date for
each loan. Additionally, households that do not fully pay back their loans
still pay a significant proportion of their debts.202020Using the Townsend
Thai Annual data, [37] find that repayment rates for MBF loans are 97 percent,
and for other loans are between 77 to 88 percent. The repayment of interest
and principal seems to be differentiated for informal loans. Repayment rates
considering principals only is high, but there are variations in initially
stated interests and actual interests paid. Relatively high repayment rates
could be due to strong informal enforcement mechanisms, localized monitoring
of MBF loans, or the presence of collateral constraints for BAAC loans.

The combination of limited collateral and high repayment for locally
determined informal loans motivates the full-enforcement assumption for
informal loans in the model. For formal loans with centrally set rates, the
relatively higher collateral requirements and their reductions over time
motivate the modeling of formal loans with a collateral constraint that could
vary over time.

##  4 Estimation and Counterfactuals

###  4.1 Parameters

I interpret the Thaksin policy shifts as changes in the formal interest rates,
the formal fixed costs, and the formal borrowing collateral
constraints.212121Large-scale expansions of credit market access might often
involve shifting multiple dimensions of credit market access jointly. For
example, through significant interest rate subsidies, the Reserve Bank of
India helped to finance the expansion of branch banking, with formal borrowing
and savings services, to 30,000 rural villages between 1969 and 1990 [16].
This Indian policy could also be interpreted as shifting formal savings and
borrowing interest rates, fixed costs, and collateral constraints jointly. The
focus of estimation is to identify the two unobserved dimensions of credit
access, namely fixed costs and collateral constraints, before and after the
policy shift, as well as parameters for household preference and the
production function.

To estimate the model, I divide the data into a pre-Thaksin period and a post-
Thaksin period. For each period, I estimate separate values for fixed costs
and collateral constraints for villages in the Northeast and Central regions
of Thailand. The main parameters that need to be estimated are:

$\Theta_{{}_{r\tau}}=\left(\underset{\mbox{Preference}}{\underbrace{\beta_{r},\rho_{r},\sigma_{\widehat{\phi_{r}}}}},\thinspace\thinspace\thinspace\thinspace\thinspace\underset{\mbox{Production}}{\underbrace{\alpha_{r},\delta_{r},\mu_{\mathcal{A}{{}_{r\tau}}},\sigma_{\mathcal{A}_{r}},\sigma_{\epsilon{{}_{r}}}}},\underset{\mbox{Credit
Market}}{\underbrace{\Psi_{r\tau},\gamma_{r\tau}}}\right)\thinspace,$

where $r$ is region, and $\tau$ represents the two periods. Preference and
production function parameters differ across regions except for the mean of
$\mathcal{A}$, which is time- and region-specific to allow for productivity
shifts. Credit market parameters are different across periods and
regions.222222Formal credit market parameters shift over time due to policy
changes. In addition to that, I also allow the informal savings/lending fixed
costs to vary over time. The growth of formal alternatives reduces households’
reliance on the informal credit market for consumption smoothing and
investment financing, potentially weakening their commitments to informal
arrangements [3, 17]. This could increase the information acquisition and
monitoring costs for local lenders, which is captured by the informal
savings/lending fixed costs. I assume that households do not predict the
changes in credit market access.

The identification for the credit access parameters $\psi_{r\tau}\mbox{ and
}\gamma_{r\tau}$ comes from the fact that changes in fixed costs and
collateral constraints have separate impacts on households’ credit choice
probabilities. If the fixed costs for formal savings increase, it will tend to
reduce the probability of households choosing formal savings. If the fixed
costs for formal borrowing increase, that will tend to reduce the probability
of formal borrowing along with the probability of choosing the two joint
formal and informal credit choice categories. As the collateral constraint
relaxes, the relative probability of choosing the joint options would
decrease.

In addition to the credit access parameters, the identification of utility
parameters $\beta,\rho\text{, and }\sigma_{\widehat{\phi}}$ come from
households’ preferences for borrowing versus savings and the equilibrium
interest rates, which differ across regions. The identification of production
function parameters comes from the relationship between risky investment and
output.232323Both permanent productivity types and a persistent shock process
can capture persistence in the income process, but they are in practice
difficult to jointly identify given the data. For estimation, I set shock
persistence to zero.

Finally, I solve and estimate the model under steady state assumptions.
Potentially, given the vectors of $\Theta_{{}_{r\tau}}$ for two periods in the
same region, one could solve for policy functions and prices along the
transition path, and construct transition path-specific likelihoods. This
would, however, compound the computational burdens of the estimation
procedure. Additionally, parameters might become not identifiable if there is
indeterminacy in mapping the microdata to positions along the transition path.
Given these concerns, for estimation, I assume that the observed data capture
steady state choices.242424On the one hand, by averaging over choices during
the transition and at the steady state, the estimation procedure might
underestimate the magnitudes of the improvements in borrowing conditions. On
the other hand, conditional on parameter estimates, welfare analysis might
overstate gains by assuming that consumption functions shift to the steady
state immediately. Jointly, the effects of imposing the steady state
assumption on estimation, which is a limitation of the approach in this paper,
are ambiguous.

###  4.2 Maximum Likelihood

For estimation, in addition to the discrete credit market participation
information described earlier, I use income, asset, and consumption data from
household balance sheets compiled by [57]. Income is household revenue from
all sources minus costs. Physical assets include land, business and
agricultural assets, livestock, and household assets. Following [40], I
exclude from physical capital land, livestock, and durable household
assets.252525[53] describe key asset variables and find that while overall
wealth increased at 2.7 percent in nominal terms every year, 44 percent of
households experienced negative growth in net wealth between 1999 and 2005.
For the data periods here, real consumption in the Northeast increased, on
average, from 47.1 thousand baht to 55.5 thousand baht from the before-policy
to the after-policy period. 1st, 5th, 15th, and 25th percentile real
consumption decreased from 12.6, 18.5, 25.5, and 29.4 thousand baht to 11.0,
17.0, 24.5, and 29.3 thousand baht, respectively. Median and third-quartile
consumption increased from 39.1 and 51.2 to 42.8 and 66.9 thousand baht.
(Nominal consumption percentiles are uniformly higher except for the 1st
percentile.) I deflate prices by 2005 northeast rural price levels using
different rural price indexes for each region.

I estimate the model using simulated maximum likelihood with measurement
errors. I simulate the likelihood by integrating over the steady state joint
wealth $\mathcal{W}$ and productivity type $\mathcal{A}$ distributions derived
in Appendix Sections C.1.3 and C.1.4. The likelihood is determined by the
individual $i$ and time $t$ specific continuous choices and states observed
with error
$\left(\widehat{k}^{{}^{\prime}}_{it},\widehat{b}^{{}^{\prime}}_{it},\widehat{c}_{it},\widehat{\mathcal{W}}_{it}\left(\widehat{k}_{it},\widehat{b}_{it},\widehat{y}_{it}\right)\right)$,
the observed discrete choices $j_{it}$, the policy functions
$\mathit{k^{{}^{\prime}}_{j}}\left(\mathcal{A},\mathit{\mathcal{W}};\Theta_{{}_{r\tau}}\right)$,
$\mathit{b^{{}^{\prime}}_{j}}\left(\mathcal{A},\mathit{\mathcal{W}};\Theta_{{}_{r\tau}}\right)$,
$\mathit{c_{j}}\left(\mathcal{A},\mathit{\mathcal{W}};\Theta_{{}_{r\tau}}\right)$,
$P_{j}\left(\mathcal{A},\mathit{\mathcal{W}};\Theta_{{}_{r\tau}}\right)$, and
the region $r$ and period $\tau$ specific joint
$f\left(\mathcal{W},\mathcal{A};\Theta_{{}_{r\tau}}\right)$ steady state
distributions.262626[40] estimate, among other models, a partial equilibrium
dynamic borrowing and savings model with maximum likelihood also using these
rural Thai data. They build a likelihood function based on policy functions
tracing out the path of choices without steady state assumptions given fixed
interest rates.

The probability of observing
$\left(\widehat{k}^{{}^{\prime}},\widehat{b}^{{}^{\prime}},\widehat{c},j\right)$
given
$\left(\widehat{\mathcal{W}}\left(\widehat{k},\widehat{b},\widehat{y}\right)\right)$
is:

$f\left(\widehat{k}^{{}^{\prime}},\widehat{b}^{{}^{\prime}},\widehat{c},j\mid\widehat{\mathcal{W}}\left(\widehat{k},\widehat{b},\widehat{y}\right)\right)=\int_{\mathcal{W}}\int_{\mathcal{A}}f\left(\widehat{k}^{{}^{\prime}},\widehat{b}^{{}^{\prime}},\widehat{c},j\mid\mathcal{A},\mathcal{W}\right)f\left(\mathcal{A}\mid\mathcal{W}\right)f\left(\mathcal{W}\mid\widehat{\mathcal{W}}\right)\mathrm{d}\mathcal{A}\mathrm{d}\mathcal{W}\thinspace,$
(7)

where the first term in the integral is the product of lognormal measurement
errors and the discrete credit choice category probability:
$f\left(\widehat{k}^{{}^{\prime}},\widehat{b}^{{}^{\prime}},\widehat{c},j\mid\mathcal{A},\mathcal{W}\right)=f_{\zeta^{k}}\cdot
f_{\zeta^{b}}\cdot f_{\zeta^{c}}\cdot
P_{j}\left(\mathcal{A},\mathit{\mathcal{W}}\right)$ , with
$f_{\zeta^{k}}=f_{\zeta^{k}}\left(\log(\widehat{k}^{{}^{\prime}})-\log(\mathit{k^{{}^{\prime}}_{j}}\left(\mathcal{A},\mathit{\mathcal{W}}\right))\right)$,
and similarly for $f_{\zeta^{b}}$ and $f_{\zeta^{c}}$.272727 Given that $\Phi$
is assumed to be i.i.d extreme value,
$P_{j}\left(\mathcal{A},\mathit{\mathcal{W}}\right)$ follows standard
multinomial-logit formulations. The probability of choosing one of the credit
categories is:
$\begin{split}P\left(o_{it}=j\mid\mathcal{A}_{i},k_{it},b_{it},\epsilon_{it}\right)=\prod_{j=1}^{J}\left(\frac{\exp\left({\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\hat{v}_{itj}}\left(\mathcal{A}_{i},k_{it},b_{it},\epsilon_{it}\right)/\sigma_{\widehat{\phi}}\right)}{\sum_{l=1}^{J}\exp\left({\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\hat{v}_{itl}}\left(\mathcal{A}_{i},k_{it},b_{it},\epsilon_{it}\right)/\sigma_{\widehat{\phi}}\right)}\right)^{\mathbb{I}\left\\{o_{it}=j\right\\}}\thinspace.\end{split}$
(8) Since
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}\hat{v}_{itj}}$
is not linear-in-parameters, $\sigma_{\widehat{\phi}}$ allows for conventional
logit scaling normalization [64, Chapter 3]. Additionally, while $\phi_{jit}$
is uncorrelated across $j$, the categories share common shock $\epsilon_{it}$.
The log ratio measurement error assumes that observed and model-generated $b$
choices have the same signs, which implies that discrete choice $j$ is not
observed with measurement error. Additionally, I obtain
$f\left(\mathcal{W}\mid\mathcal{A}\right)$ while solving the model following
the procedure in Appendix Section C.1.4, hence
$f\left(\mathcal{A}\mid\mathcal{W}\right)$ can be replaced using Bayes’ rule:
$f\left(\mathcal{A}\mid\mathcal{W}\right)=\frac{f\left(\mathcal{W}\mid\mathcal{A}\right)f\left(\mathcal{A}\right)}{\int
f\left(\mathcal{W}\mid\widehat{\mathcal{A}}\right)f\left(\widehat{\mathcal{A}}\right)\mathrm{d}\widehat{\mathcal{A}}}$
. Following Appendix Sections C.1.3 and C.1.4, the integrals in Equation (7)
are approximated using mid-point Riemann-sum for $\mathcal{W}$ and quadrature
for $\mathcal{A}$. Finally, $\widehat{\mathcal{W}}$ is determined by
measurement errors for $\widehat{k}$, $\widehat{b}$, and $\widehat{y}$. Given
these, the likelihood is:

$\ell_{r\tau}=\prod_{i=1}^{N_{r}}\prod_{t=1}^{T_{\tau}}\left\\{\int_{\mathcal{W}}\int_{\mathcal{A}}f\left(\widehat{k}^{{}^{\prime}}_{it},\widehat{b}^{{}^{\prime}}_{it},\widehat{c}_{it},j_{it}\mid\mathcal{A},\mathcal{W};\Theta_{{}_{r\tau}}\right)f\left(\mathcal{A}\mid\mathcal{W};\Theta_{{}_{r\tau}}\right)f\left(\mathcal{W}\mid\widehat{\mathcal{W}}_{it}\right)\mathrm{d}\mathcal{A}\mathrm{d}\mathcal{W}\right\\}.$
(9)

I estimate the model using the log of
$\prod_{r\in\left\\{1,2\right\\},\tau\in\left\\{1,2\right\\}}\left(\ell_{r\tau}\right)$
as the objective function.282828In standard partial equilibrium life cycle
models with discrete choices and continuous asset states and choices that are
measured with errors, the econometrician simulates the life-cycle a large
number of times given sequences of shocks. The differences between these paths
and the actual path of observed individual choices are components of the
likelihood function [44, 34, e.g.,]. In these models, the asset distribution
is partially endogenous, given initial exogenous asset distributions. In the
problem here, the asset distribution is fully endogenous. Given the non-
iterative procedure for deriving conditional asset distribution described in
Appendix Section C.1.3, $f\left(\mathcal{A}\mid\mathcal{W}\right)$ can be
obtained without simulating histories. Consequently, evaluating Equation (9)
does not involve sequential simulations but is obtained from a set of matrix
multiplications and additions.

It is important to note that both measurement errors on the continuous choices
as well as credit category utility shocks $\Phi$ are needed to assure that the
joint choice probabilities can be computed during the estimation process.
Within bounds of the state space, credit category utility shocks assure
positive choice probabilities for each credit market participation category.
Given the discrete choice, the measurement errors on the asset choices assure
positive probabilities of observing any asset choices.

###  4.3 Estimation Routine

Dynamic heterogeneous-agent equilibrium models with discrete and continuous
choices are time consuming to estimate. Searching for the correct local
minimum often requires restarts to calibrate estimation step-size and
tolerance levels. I develop a global optimization routine that minimizes the
use of loops and iteration by parallel computing. The algorithm has four steps
that take advantage of scalable parallel computing resources and is described
more fully in Appendix Section C.2.1. In brief, the process is as follows: 1.
I evaluate the model concurrently at a large set of randomly drawn model
parameters; 2. I approximate the estimation objective function using
polynomials; 3. I estimate an approximated version of the model by evaluating
the objective function using polynomial regression coefficients; and 4. I
estimate the model using the actual model objective function and use results
from earlier steps to find initial parameters. The first three steps are fully
parallelizable and could provide step four with parameter values that are
potentially close to global minimizers. The procedure potentially reduces
estimation time significantly. I discuss computational structures and the
costs of running this algorithm on cloud computing services in Appendix
Sections C.2.2 and C.2.4.

###  4.4 Estimation Results and Interpretations

Parameter estimates are shown in Tables 6 and 7. Fits are shown in Table 8. In
Table 6, estimated fixed costs are shown as fractions of annual average income
in the first period. The estimated model fits credit participation shares and
asset choices generally well across regions and periods. The exception in the
Northeast is that the model overpredicts the proportion of households
borrowing informally only, and consequently the average share of informal
borrowing in total borrowing.292929This is perhaps because in the
estimation—while other fixed costs are allowed to vary across periods—the
informal borrowing fixed costs are fixed across periods. Additionally, given
the likelihood-based estimation approach, it is possible that at parameters
that maximize the log-likelihood, predicted moments do not match well with a
subset of empirical counterparts. This is especially true in this model, given
the relatively parsimonious parameter specifications. In the tradition of
[43], a strategy to improve fits is to incorporate additional exogenous
observables and discrete unobserved types into the model. That could allow for
greater heterogeneities in predicted choices conditional on states. That
approach, however, would significantly increase the computational burdens for
solving and estimating the model.  The exception in the Central provinces is
that the model overpredicts consumption.303030In the Central provinces, the
model predicts that consumption should be in excess of three-fourths of
outputs, but in the data, it is only half. This might be related to the fact
that Central households purchase more household durable goods than Northeast
households, and durable household goods are excluded from estimation.

The estimated formal borrowing fixed costs fractions decreased in the
Northeast region from 0.090 to 0.046, a 49% reduction. In the Central region,
where changes in participation rates were more limited, formal borrowing fixed
costs fractions decreased from 0.044 to 0.033. In comparison, using an earlier
round of the Thai survey, [27] provides estimates for formal borrowing fixed
costs that would be approximately 7% of the earlier period borrowing fixed
costs in the Northeast region. These reductions are driven by the introduction
of MBF and other policies that brought formal lending decisions to local
communities, reducing the fixed costs of what I categorize as external-formal
lending. Reductions in these fixed costs help to explain increases in formal
credit market participation rates over time. The fixed costs for formal
savings decreased as well, but their changes were less significant. The
estimated formal borrowing fixed costs fractions decreased in the Northeast
region from 0.083 to 0.071. In the Central region, formal savings fixed costs
fractions decreased from 0.011 to 0.001, indicating the availability of low-
cost deposit-taking services in these more affluent areas.

Table 6 also presents fixed costs estimates for informal borrowing and
savings. The informal borrowing fixed costs fractions are 0.053 in the
Northeast region and 0.124 in the Central region. Interestingly, in the
Central region, to fit the low participation shares in informal borrowing, the
fixed costs estimates for informal borrowing are higher than for formal
borrowing.313131Without preference shocks for credit participation categories,
fixed costs for the lower interest rate formal borrowing option would need to
generally be higher than the fixed costs for the higher interest rate informal
borrowing option [27]. Higher informal costs could reflect the higher costs of
finding credit suppliers when the informal market is small. Additionally, the
estimated fixed costs fractions for informal savings are 0.134 for the
Northeast region in the earlier period and 0.186 in the later period, and are
0.151 for the Central region in the earlier period and 0.156 in the later
period. Households with low savings needs do not lend informally unless they
receive a large positive shock.323232When positive shocks induce households to
lend informally, households might be lending small amounts informally with
negative average returns. It is often observed that informal savings/lending
might earn negative returns. For example, [6] explicitly consider a fixed
negative savings interest rate. Informal fixed costs could be partly
attributed to local preferences toward informal borrowing and savings
activities, and they could also partly represent credit search costs for
borrowers and intermediation costs for savers/lenders.

0.0830.071 0.083 100 [0]

0.1860.134 0.134 100 [0]

An important result here is that while borrowing opportunities improved in the
Northeast, savings opportunities did not. The formal savings fixed costs
decreased by percent, improving formal savings opportunities, but the informal
savings fixed costs increased by percent. Given these results and the drops in
both the formal savings interest rates as well as the informal interest rates,
the return to savings decreased in the Northeast.

In addition to changes in the fixed costs parameters, Table 6 also shows that
in the Northeast region, the collateral constraint fraction increased from
0.28 to 0.56, and in the Central region, the collateral constraint fraction
increased from 0.36 to 0.41. In comparison, modeling MBF as a shift in
borrowing constraints—specified as a fraction of a household’s permanent
income—[37] find that constraints under MBF relaxed from about 8 percent of
permanent income to about 28 percent, on average.333333The borrowing
constraints fractions in this paper are multiplied by physical capital, and
hence not directly comparable to the [37] results. Both results show that
relaxing borrowing constraints was a key Thaksin policy channel, but it seems
that the borrowing constraints were tighter initially and experienced greater
relaxation under [37]’s framework. In the set-up here, shifts in fixed costs
and interest rates can change the fraction of households constrained (in joint
participation categories), holding borrowing constraints constant. Relaxing
the collateral constraints increases the fraction of risky investments that
could be financed by formal borrowing and also increases the amount of
consumption that could be financed by formal borrowing given the same level of
risky investments.

The changes in formal borrowing conditions were likely brought about by the
MBF program. As discussed earlier, the program allowed households to borrow
from village committees. Pecuniary borrowing costs could have decreased: for
example, there were reductions in observed formal borrowing fees and
transportation costs, as discussed in Section 3.2.3. It should be noted that
the estimated fixed costs are much higher than the reported fees and
transportation costs, indicating that the reported costs might not fully
capture various pecuniary and non-pecuniary costs associated with formal
banking access. For example, non-pecuniary borrowing costs could also have
changed: communicating with village committees about credit needs might be
less burdensome than less familiar BAAC managers. Additionally, the MBF did
not have explicit collateral requirements, as noted in the data section. MBF
also made large quantities of additional funds available for formal lending
through these committees with local knowledge.

###  4.5 Welfare Consequences of Thaksin’s Policies

Figure 2: Welfare Change in Northeast from 1999-2001 to
2002-2009WealthProductivity Type _Notes:_ This figure shows the steady state
welfare impacts of Thaksin’s policies that lowered formal borrowing interest
rates and fixed costs, and relaxed formal borrowing collateral constraints. I
compare _steady state_ welfare for households facing credit market access
parameters from the _1999-2001_ and the _2002-2009_ periods. I present welfare
changes in terms of _consumption equivalent variation_ (CEV) percentage points
changes. Credit market access parameters are observed or estimated.

Thaksin’s policies expanded formal borrowing access, especially in the
Northeast. However, returns to savings generally diminished in the Northeast,
as discussed in Section 4.4. Northeast welfare effects are shown in Figure 2.
All estimated and observed parameters from the two periods are used to
calculate welfare changes in terms of consumption equivalent variation (CEV)
gains for households with different productivity and wealth levels. To be
consistent with the estimation procedure, I conduct steady state welfare
analysis. The welfare analysis does not consider the costs incurred to the
government for financing Thaksin’s policies.

Figure 2 shows welfare effects for subsets of households. At the top left,
high productivity type and low wealth households gain on the order of slightly
more than 5% CEV. These households have high borrowing needs and can now
borrow formally more cheaply given both the drop in the interest rate and
fixed costs.343434These households also face future states in which they would
have high savings needs. The worsening of savings conditions is detrimental to
them. But overall, they benefit more from the improvements in borrowing
conditions. The second group of households includes those who have more than
average productivity type and higher levels of wealth. These households gain
on the order of 0.15% to 5% CEV. In this group, some of the gains are due to
reductions in the formal borrowing interest rate. The presence of informal
options weakens welfare gains here: the gains of switching from informal
borrowing to a lower-cost formal borrowing option is less than the gains of
moving from autarchy to borrowing.

The third group consists of a large proportion of households with average
levels of productivity and wealth, shown in the central area of Figure 2.
These households have modest current period borrowing needs and benefit less
from the lower formal borrowing interest rates or relaxed collateral
constraints. Looking forward, they face future states in which they have
higher borrowing or higher savings needs. Overall, these households experience
slightly positive but limited gains from the policy changes.

The last two groups have higher wealth and lower productivity levels. They are
shown in the bottom right of Figure 2. These households suffer welfare losses
of up to 1% CEV due to the worsening of savings conditions. They have low
expected returns for investments, and hence also lower borrowing needs
compared to more productive households. Gains from improvements in borrowing
conditions are outweighed by losses due to the lower formal and informal
savings interest rates as well as the higher informal lending fixed costs. The
welfare losses are smaller for households with slightly higher productivity
types and lower levels of wealth.

Welfare effects for the last two groups could be different if informal markets
are not considered. Specifically, in [37], poor and low productivity
households benefit from microfinance consumption loans. Here, the same
households already had access to low fixed costs informal consumption loans
and switching to microfinance consumption loans led to limited gains.
Additionally, conditional on productivity type, higher wealth households in
this setting can lose from improvements in borrowing conditions: productive
but low wealth households rely less on higher wealth informal lenders as
financiers for their high return risky capital investments.

###  4.6 Impacts of Shifting Dimensions of Formal Access

In this section, I conduct counterfactual policy experiments in which I shift
each formal borrowing policy parameter from its value in the 2002-2009 period
back to its value in the 1999-2001 period while holding other parameters at
their 2002-2009 levels. As in Section 4.5, I focus on the Northeast region
only. The policy effects are nonlinear and non-separable. Hence, their
individual impacts do not sum up to their joint effects. The policy
experiments investigate the incremental effects of policy shifts along each
policy dimension individually, conditional on the empirical estimates of other
policy parameters.353535[27] also analyzes the effects of shifting these
policy dimensions in magnitudes unrelated to Thaksin’s policies and in the
context of a static partial equilibrium model. In both static partial
equilibrium and dynamic general equilibrium settings, reductions in borrowing
interest rates, drops in borrowing fixed costs, and the relaxation of
collateral constraints lead to greater formal borrowing participation. The
addition of dynamics means that effects are due to both changes in policy
functions as well as distributions. The addition of equilibrium means that
changes in formal borrowing conditions might shift informal borrowing and
savings conditions as well. The overall dynamic equilibrium model allows for
welfare analysis.

####  4.6.1 Fixed Costs

In this particular policy setting, I find that fixed costs changes can be
effective in changing credit market participation shares but have limited
equilibrium effects. As discussed previously, lowering the fixed costs reduces
the average costs of borrowing, especially for households with limited
borrowing needs or households that are constrained in how much they can
borrow, and leads to higher formal borrowing participation shares.
Specifically, shifting the formal borrowing fixed costs parameter back up to
its previously higher level reduces the proportion of households using only
the formal credit market from 44% to 32%. This means that the lowering of the
formal borrowing fixed costs by itself accounts for % of the total change in
formal only participation shares and increases the first-period formal only
participation shares by %; if households that use formal and informal markets
jointly are also considered, these two percentages would be % and %,
respectively.

Setting the formal borrowing fixed costs at their previous levels also
increases the informal interest rate from 13.9% to 17%. The change is modest
because the impacts from reduced demand for informal borrowing only would be
attenuated by increased demand for informal loans from households who borrow
jointly. Limited equilibrium effects mean that the changes in fixed costs were
not the key factor driving the redistributive welfare consequences presented
in Figure 2.

####  4.6.2 Interest Rates

Interestingly, the large change in the formal borrowing interest rate from
14.8% to 6.1% has relatively small impacts on participation rates. This is
because given formal borrowing fixed costs and collateral constraint, changing
formal borrowing interest rates mainly impacts the average cost of formal
loans for households with higher borrowing needs—low wealth but very
productive households. However, these households would have already been
borrowing formally, even at higher formal interest rates. Given other
parameter values in 2002-2009, increasing the formal borrowing interest rate
back to its previous level would have less than a 3 percentage point impact on
participation rates and would only increase the informal interest rate by %.
Given the relatively small impacts on equilibrium interest rates, similar to
fixed costs, interest rate changes had limited redistributive welfare
consequences in this policy setting.

####  4.6.3 Collateral Constraints

Relaxing the formal borrowing collateral constraint can allow formally
constrained households to borrow more and at lower average costs. Given the
estimated parameters, this brings about a significant change in the demand for
informal loans as previously constrained households who borrowed informally
switch to formal borrowing. As a result, tightening the collateral constraint
back to its previous level would increase the informal interest rate from
13.9% to 20.5%. The difference is equal to a 24% reduction in the pre-policy
period informal interest rate. The result also indicates that the lowering of
the collateral constraint by itself can account for % of the total change in
the informal interest rate.

The impacts of shifting the collateral constraint on aggregate participation
rates, however, are limited to up to three percentage points of change.

Figure 3: Welfare Change in Northeast with $\gamma$ Variations between
1999-2001 and 2002-2009 _Notes:_ This figure shows the welfare impacts of the
estimated collateral constraints relaxation component of Thaksin’s policies. I
compare _steady state_ partial equilibrium and general equilibrium welfare for
households facing the collateral constraint parameter from the _1999-2001_ and
the _2002-2009_ periods, holding all other parameters at _2002-2009_ levels. I
present welfare changes in terms of _consumption equivalent variation_ (CEV)
percentage point changes.

Given the significant impacts on the informal interest rate, the relaxation of
collateral constraints is the key contributor to the redistributive welfare
consequences shown in Figure 2. To analyze this further, in Figure 3 I present
steady state partial and general equilibrium welfare changes driven by the
shift of the collateral constraints $\gamma$. The y-axis shows percentage
point changes in CEV, the x-axis indicates wealth levels, and three subplots
present results for lower (-1 standard deviation), mean, and higher (+1
standard deviation) productivity types, respectively. Dashed lines show
partial equilibrium results, and solid lines show general equilibrium results.
CEV changes from relaxing $\gamma$ from 0.28, the estimated value during the
1999-2001 period, to 0.56, the estimated value from the 2002-2009 period, are
shown in dark blue. For comparison, CEV changes from relaxing $\gamma$ from
0.28 to 0.42 only are shown in lighter blue.

First, the partial equilibrium CEV changes are all positive. Under the partial
equilibrium analysis here, as the collateral constraints relax, the value from
choosing formal borrowing improves, but the values associated with alternative
credit market choices do not worsen. The government finances a costly program,
and the model predicts that all households would benefit, given their current
and future expected needs for financing consumption and investments.

Second, the positive welfare impacts under partial equilibrium are
heterogeneous across households and can be very small. For lower productivity
households, CEV gains do not exceed 0.25% across wealth levels despite
doubling $\gamma$ from 0.28 to 0.56. For mean and higher productivity type
households, those with lower wealth gain up to 1.9% CEV. The gains decrease
rapidly but stay positive as wealth increases. Similar to the results from
Figure 2, gains are limited by the prior availability of informal loans.

Third, allowing for equilibrium informal interest rate responses lead to
greater gains for some households. Across productivity types, at lower wealth
levels, the general equilibrium CEV gains are larger than the partial
equilibrium gains. Households that are in need of loans benefit both from the
relaxed formal borrowing constraint and the drop in the informal interest
rate. However, the general equilibrium gains in excess of the partial
equilibrium gains are very limited, not exceeding 0.2% CEV in Figure 3. This
is because the improvements in formal borrowing conditions reduce households’
reliance on informal borrowing and reduce the benefits of a lower informal
borrowing interest rate.

Fourth, the reduction in informal equilibrium interest rates leads to welfare
losses. For households with higher wealth, the small gains under partial
equilibrium are outweighed by losses in the expected values from the informal
savings alternatives due to lower informal interest rates. Losses are greater
for lower productivity type households and can amount to up to 0.5% CEV. Lower
productivity and higher wealth households, as shown earlier in Figure 1,
invest comparatively more in lending and savings and less in risky capital
investments. They benefit from lending to lower wealth but more productive
households in their villages. Improvements in formal borrowing access, given
the parameters here, reduce the number of high productivity local household-
firms that have to rely on local financing and are detrimental to the welfare
of lower productivity and higher wealth households in the villages.

Overall, Figure 3 shows two key sets of crossing points that determine the
redistributive welfare consequences of relaxing collateral constraints when
informal markets are considered. Each productivity type has a welfare gain
crossing point along the wealth axis where the general equilibrium CEV gains
fall below partial equilibrium gains. Additionally, each productivity type’s
general equilibrium CEV curve has an x-intercept marking the wealth level
where CEV gains become losses. Both crossing points are increasing in
productivity type, and the second comes after the first given strictly
positive welfare gains under partial equilibrium.

Since collateral constraints are the key driver of equilibrium interest rate
changes, the results from Figure 3 match up with the aggregate welfare
consequences from Figure 2 when all Thaksin policies are jointly considered. I
should note that at alternative combinations of fixed costs and interest
rates, the level of gains or losses from relaxing $\gamma$ might be magnified
or dampened compared to the results in Figure 3. Given the potential
complementarity as well as substitutability between formal and informal
options that the model allows for, under some parameter combinations, a shift
in collateral constraints might not have significant impacts on the informal
interest rates. The quantitative welfare consequences of microfinance policies
have to be evaluated on a case-by-case basis.

##  5 Conclusion

In recent decades, formal financial services have expanded significantly in
developing countries. This paper evaluates the impacts of improving access to
the formal credit market on rural households, taking into consideration the
impacts of changing formal credit market conditions on the informal credit
market.

I built a risky entrepreneur model assuming that villages are small open
economies with respect to formal credit market options that have centrally set
rates, but households can also borrow and save in an equilibrium local credit
market with the locally determined rate. The model allows for evaluating the
impacts of formal credit market expansions through interest rate subsidies,
access fixed costs reductions, and collateral constraint relaxations. Policy
evaluations take into consideration equilibrium responses of the informal
credit market. In the empirical section of the paper, I explored detailed data
on formal and informal credit market interactions from Thai villages. I
connected the model with the Thai micro-data by estimating the model using
Simulated Maximum Likelihood. The likelihood function incorporates choice
probabilities given endogenous asset distributions determined by model
parameters.

Using the estimated model, in the case of these Thai villages, I showed that
there are redistributive consequences of microfinance policies through general
equilibrium effects on informal interest rates. Without equilibrium
considerations, all households can experience welfare gains from improvements
in formal borrowing conditions. These gains are, however, limited because
informal borrowing alternatives were already available. In equilibrium,
policies that improve formal borrowing conditions can drive down informal
interest rates and could hurt less productive and higher wealth households who
face diminished opportunities for savings. In particular, I find that in the
context of the Thaksin policies, relaxing the collateral constraints was the
key driver of equilibrium interest rate changes and redistributive steady
state welfare effects.

In solving and estimating this model, I developed solution and estimation
algorithms that minimize the use of loops and iteration by parallel computing.
The solution algorithm captures the impacts of variations in the four fixed
costs, three interest rates, and one collateral constraint on household
choices and equilibrium outcomes. The global estimation algorithm chooses
initial values for estimation by first exploring the estimation objective
function through polynomial approximations. The solution and estimation
algorithms can reduce estimation time by taking advantage of scalable cloud
computing resources.

Currently, while many microfinance institutions offer both borrowing and
savings services, there remain many development financial institutions,
including many development banks, that are mainly oriented toward expanding
borrowing access [48]. My counterfactual simulations suggest that when
households rely on local informal credit markets to meet differential needs
for borrowing and saving, efforts that mainly improve formal access for
borrowing could lead to more limited informal savings opportunities for
households and their subsequent welfare losses.

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## Tables and Additional Figures

Table 1:  Channels for Borrowing from 1999 to 2009 Percentage of Number of
Years Households Who with New Loans Have Borrowed (out of 11) Northeast Region
(poorer) Million Baht Fund _formal_ 78.0 7.13 BAAC _formal_ 61.6 5.58 Village
Coop _informal_ 35.9 3.00 Friends and Neighbors _informal_ 83.3 3.99 Village
Moneylenders _informal_ 37.5 1.93 Central Region (richer) Million Baht Fund
_formal_ 74.5 6.73 BAAC _formal_ 40.8 5.70 Village Coop _informal_ 16.9 3.56
Friends and Neighbors _informal_ 48.5 2.27 Village Moneylenders _informal_
12.9 1.50 _Notes:_ To effectively model the variety of borrowing choices shown
in Table 1, I group lenders into formal and informal categories. The Million
Baht Fund (MBF) and the Bank for Agriculture and Agricultural Cooperatives
(BAAC) are formal lenders with centrally set interest rates. Friends,
neighbors and village moneylenders are local-informal lenders. Village Coop
includes Production Cooperative Groups (PCG) and Village Agricultural
Cooperatives, which are local semi-formal organizations that mostly
intermediate credit among households within villages. This paper considers
Village Coops as falling within the informal credit market with locally
determined interest rates. See Section 3.1.1 for detail.

Table 2:  Channels for Saving from 1999 to 2009 Percentage of Number of Years
Households Who with New Deposits Have Saved (out of 11) Northeast Region
(poorer) Commercial _formal_ 37.4 4.56 BAAC and GSB _formal_ 94.1 7.82 Village
Coop _informal_ 64.1 6.33 Individual lending _informal_ 66.6 2.57 Central
Region (richer) Commercial _formal_ 77.9 5.25 BAAC and GSB _formal_ 85.6 6.41
Village Coop _informal_ 75.2 7.54 Individual lending _informal_ 33.1 2.23
_Notes:_ To effectively model the variety of savings choices shown in Table 2,
I group savings channels into formal and informal categories. Households could
save formally at commercial banks, the BAAC, and the Government Savings Bank
(GSB). Households can also save informally by lending to other individuals
directly. When they save in village coops, I consider that households are
saving informally. See Notes for Table 1 for what village coops are. See
Section 3.1.1 for detail.

Table 3:  Credit Category Participation Shares Northeast Region (poorer)
Central Region (richer) 1999-2001 2002-2009 1999-2001 2002-2009 percent
percent percent percent Formal and Informal 31.5 40.3 6.7 18.1 Formal Only
21.1 44.0 51.5 58.3 Informal Only 32.0 11.1 12.1 9.9 Neither 15.5 5.6 29.7
13.8 Table 4:  Credit Category Shares Across Seven Participation Types
Northeast Region (poorer) Central Region (richer) 1999-2001 2002-2009
1999-2001 2002-2009 percent percent percent percent Formal Borrowing 14.9 29
21.5 24.2 Formal Saving 6.2 14 30 34.1 Informal Borrowing 25 6.2 9.2 6.1
Informal Saving 7 4.9 3 3.8 Formal+Informal Borrowing 24.1 32.5 5 14.3 Formal
Borrow+Informal Saving 7.4 7.8 1.7 3.8 No Credit Transactions 15.5 5.6 29.7
13.8 _Notes:_ Households’ credit market choices within a calendar year can be
categorized as falling within one of the seven credit participation categories
listed in Table 4. This table shows that after 2001, due to policies that
promoted formal borrowing such as the Million Baht Fund Program (see Section
3), the proportion of households participating in the formal credit market
increased significantly, especially in the Northeast region. See Section 3.1.2
for detail.

Figure 4: Village/Year Real Interest Rates for Different Lenders _Notes:_
Village/Year Interest rates are average interest rates for each lender type
for each village in each calendar year. See Section 3.2.1 for detail.
Table 5: Annual Average Real Interest Rate (percent) 1999-2001 2002-2009
Northeast Region (poorer) _Informal_ Interest 27.9 13.9 _Formal_ Borrowing
Interest 14.8 6.1 _Formal_ Saving Interest 3.3 1.1 Central Region (richer)
_Informal_ Interest 17.6 9.4 _Formal_ Borrowing Interest 13.0 5.4 _Formal_
Saving Interest 3.2 1.0 _Notes:_ Table 5 and Figure 4 show that formal and
informal interest rates decreased after 2001.

Table 6:  Credit Access Parameters (See Section 4.4) Northeast Central
1999-2001 2002-2009 1999-2001 2002-2009 Fixed Costs as a Fraction of 99-01
Average Income $\psi_{\text{FB}}$ (Formal Borrowing) 0.090 0.046 0.044 0.033 (
0.008 ) ( 0.02 ) ( 0.044 ) ( 0.0053 ) $\psi_{\text{FS}}$ (Formal Savings)
0.083 0.071 0.011 0.001 ( 0.0045 ) ( 0.0054 ) ( 0.037 ) ( 0.00025 )
$\psi_{\text{IB}}$ (Informal Borrowing) 0.053 0.124 ( 0.0044 ) ( 0.098 )
$\psi_{\text{IS}}$ (Informal Savings) 0.134 0.186 0.151 0.156 ( 0.034 ) (
0.011 ) ( 0.056 ) ( 0.042 ) $\gamma$ (Collateral Constraint) 0.28 0.56 0.36
0.41 ( 0.047 ) ( 0.015 ) ( 0.21 ) ( 0.23 ) Table 7:  Preference and Production
Parameters (See Section 4.4) Northeast Central Preference: Discount $\beta$
0.88 ( 0.038 ) 0.92 ( 0.04 ) CRRA $\rho$ 1.2 ( 0.17 ) 1.3 ( 0.15 ) Multinomial
$\sigma_{\widehat{\phi}}$ 1.5 ( 0.45 ) 1.7 ( 0.33 ) Production Function:
Elasticity $\alpha$ 0.15 ( 0.02 ) 0.34 ( 0.03 ) Depreciation $\delta$ 0.056 (
0.0048 ) 0.071 ( 0.054 ) $\mu_{\mathcal{A}{}}$(99-01) 8.75 ( 0.42 ) 7.87 ( 0.4
) $\mu_{\mathcal{A}{}}$(02-99) 8.96 ( 0.46 ) 7.94 ( 0.44 )
$\sigma_{\mathcal{A}}$ 0.84 ( 0.025 ) 1.18 ( 0.025 ) $\sigma_{\epsilon{}}$
0.87 ( 0.019 ) 0.97 ( 0.041 ) Measurement Error:
$\sigma_{\zeta^{b}}$363636$\zeta^{b}\sim\mathcal{N}\left(\frac{-\sigma^{2}_{\zeta^{b}}}{2},\sigma^{2}_{\zeta^{b}}\right)$
0.25 ( 0.019 ) 0.15 ( 0.012 ) $\sigma_{\zeta^{k}}$ 0.18 ( 0.014 ) 0.15 ( 0.012
) $\sigma_{\zeta^{y}}$ 0.38 ( 0.03 ) 0.18 ( 0.014 ) $\sigma_{\zeta^{c}}$ 0.16
( 0.012 ) 0.68 ( 0.53 )

Table 8:  Model Fit Northeast Central 1999-2001 2002-2009 1999-2001 2002-2009
Discrete Choices (0.01 = 1 percent): $P^{\text{IB}}$
${\scriptstyle\overset{\text{data}}{0.25}}\thinspace\thinspace\bigl{\rvert}$
0.24
${\scriptstyle\overset{\text{data}}{0.062}}\thinspace\thinspace\bigl{\rvert}$
0.14
${\scriptstyle\overset{\text{data}}{0.092}}\thinspace\thinspace\bigl{\rvert}$
0.08
${\scriptstyle\overset{\text{data}}{0.061}}\thinspace\thinspace\bigl{\rvert}$
0.08 $\left[\thinspace 0.187\text{,}\thinspace
0.252\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.087\text{,}\thinspace
0.170\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.065\text{,}\thinspace
0.098\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.060\text{,}\thinspace
0.096\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$P^{\text{IS}}$
${\scriptstyle\overset{\text{data}}{0.07}}\thinspace\thinspace\bigl{\rvert}$
0.08
${\scriptstyle\overset{\text{data}}{0.049}}\thinspace\thinspace\bigl{\rvert}$
0.07
${\scriptstyle\overset{\text{data}}{0.03}}\thinspace\thinspace\bigl{\rvert}$
0.028
${\scriptstyle\overset{\text{data}}{0.038}}\thinspace\thinspace\bigl{\rvert}$
0.035 $\left[\thinspace 0.049\text{,}\thinspace
0.102\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.017\text{,}\thinspace
0.090\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.014\text{,}\thinspace
0.044\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.021\text{,}\thinspace
0.050\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$P^{\text{FB}}$
${\scriptstyle\overset{\text{data}}{0.15}}\thinspace\thinspace\bigl{\rvert}$
0.17
${\scriptstyle\overset{\text{data}}{0.29}}\thinspace\thinspace\bigl{\rvert}$
0.25
${\scriptstyle\overset{\text{data}}{0.22}}\thinspace\thinspace\bigl{\rvert}$
0.21
${\scriptstyle\overset{\text{data}}{0.24}}\thinspace\thinspace\bigl{\rvert}$
0.25 $\left[\thinspace 0.128\text{,}\thinspace
0.179\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.207\text{,}\thinspace
0.274\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.198\text{,}\thinspace
0.223\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.225\text{,}\thinspace
0.257\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$P^{\text{FS}}$
${\scriptstyle\overset{\text{data}}{0.062}}\thinspace\thinspace\bigl{\rvert}$
0.11
${\scriptstyle\overset{\text{data}}{0.14}}\thinspace\thinspace\bigl{\rvert}$
0.12
${\scriptstyle\overset{\text{data}}{0.30}}\thinspace\thinspace\bigl{\rvert}$
0.30
${\scriptstyle\overset{\text{data}}{0.34}}\thinspace\thinspace\bigl{\rvert}$
0.33 $\left[\thinspace 0.062\text{,}\thinspace
0.122\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.102\text{,}\thinspace
0.150\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.289\text{,}\thinspace
0.309\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.297\text{,}\thinspace
0.335\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$P^{\text{FB+IB}}$
${\scriptstyle\overset{\text{data}}{0.24}}\thinspace\thinspace\bigl{\rvert}$
0.22
${\scriptstyle\overset{\text{data}}{0.33}}\thinspace\thinspace\bigl{\rvert}$
0.28
${\scriptstyle\overset{\text{data}}{0.05}}\thinspace\thinspace\bigl{\rvert}$
0.06
${\scriptstyle\overset{\text{data}}{0.14}}\thinspace\thinspace\bigl{\rvert}$
0.11 $\left[\thinspace 0.180\text{,}\thinspace
0.227\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.192\text{,}\thinspace
0.291\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.037\text{,}\thinspace
0.075\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.057\text{,}\thinspace
0.124\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$P^{\text{FB+IS}}$
${\scriptstyle\overset{\text{data}}{0.074}}\thinspace\thinspace\bigl{\rvert}$
0.08
${\scriptstyle\overset{\text{data}}{0.078}}\thinspace\thinspace\bigl{\rvert}$
0.11
${\scriptstyle\overset{\text{data}}{0.017}}\thinspace\thinspace\bigl{\rvert}$
0.021
${\scriptstyle\overset{\text{data}}{0.038}}\thinspace\thinspace\bigl{\rvert}$
0.042 $\left[\thinspace 0.074\text{,}\thinspace
0.127\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.078\text{,}\thinspace
0.144\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.006\text{,}\thinspace
0.043\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.025\text{,}\thinspace
0.055\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
Continuous Choices (in thousands of baht, 2005 northeast rural price): mean k
${\scriptstyle\overset{\text{data}}{76.5}}\thinspace\thinspace\bigl{\rvert}$
76.10
${\scriptstyle\overset{\text{data}}{82.0}}\thinspace\thinspace\bigl{\rvert}$
84.34
${\scriptstyle\overset{\text{data}}{79.5}}\thinspace\thinspace\bigl{\rvert}$
77.71
${\scriptstyle\overset{\text{data}}{97.1}}\thinspace\thinspace\bigl{\rvert}$
97.34 $\left[\thinspace 66.50\text{,}\thinspace
85.93\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 70.95\text{,}\thinspace
91.24\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 69.52\text{,}\thinspace
99.56\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 87.97\text{,}\thinspace
120.41\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$ mean
y ${\scriptstyle\overset{\text{data}}{49.0}}\thinspace\thinspace\bigl{\rvert}$
52.15
${\scriptstyle\overset{\text{data}}{75.1}}\thinspace\thinspace\bigl{\rvert}$
64.97
${\scriptstyle\overset{\text{data}}{185.5}}\thinspace\thinspace\bigl{\rvert}$
181.20
${\scriptstyle\overset{\text{data}}{206.3}}\thinspace\thinspace\bigl{\rvert}$
198.16 $\left[\thinspace 30.49\text{,}\thinspace
73.97\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 38.13\text{,}\thinspace
88.54\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 138.12\text{,}\thinspace
215.68\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 163.24\text{,}\thinspace
252.16\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$ mean
c ${\scriptstyle\overset{\text{data}}{47.1}}\thinspace\thinspace\bigl{\rvert}$
48.98
${\scriptstyle\overset{\text{data}}{55.5}}\thinspace\thinspace\bigl{\rvert}$
54.09
${\scriptstyle\overset{\text{data}}{79.8}}\thinspace\thinspace\bigl{\rvert}$
119.78
${\scriptstyle\overset{\text{data}}{90.2}}\thinspace\thinspace\bigl{\rvert}$
148.49 $\left[\thinspace 37.80\text{,}\thinspace
57.92\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 49.24\text{,}\thinspace
60.78\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 103.72\text{,}\thinspace
138.62\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 128.54\text{,}\thinspace
173.04\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$ mean
$\frac{\text{All Borr.}}{y}$
${\scriptstyle\overset{\text{data}}{0.440}}\thinspace\thinspace\bigl{\rvert}$
0.474
${\scriptstyle\overset{\text{data}}{0.516}}\thinspace\thinspace\bigl{\rvert}$
0.511
${\scriptstyle\overset{\text{data}}{0.192}}\thinspace\thinspace\bigl{\rvert}$
0.183
${\scriptstyle\overset{\text{data}}{0.239}}\thinspace\thinspace\bigl{\rvert}$
0.240 $\left[\thinspace 0.289\text{,}\thinspace
0.651\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.372\text{,}\thinspace
0.707\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.083\text{,}\thinspace
0.286\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.130\text{,}\thinspace
0.341\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$ mean
$\frac{\text{{I}nformal Borr.}}{\text{Borrow}}$
${\scriptstyle\overset{\text{data}}{0.266}}\thinspace\thinspace\bigl{\rvert}$
0.345
${\scriptstyle\overset{\text{data}}{0.168}}\thinspace\thinspace\bigl{\rvert}$
0.274
${\scriptstyle\overset{\text{data}}{0.109}}\thinspace\thinspace\bigl{\rvert}$
0.107
${\scriptstyle\overset{\text{data}}{0.089}}\thinspace\thinspace\bigl{\rvert}$
0.100 $\left[\thinspace 0.171\text{,}\thinspace
0.412\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.231\text{,}\thinspace
0.338\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.055\text{,}\thinspace
0.322\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
$\left[\thinspace 0.040\text{,}\thinspace
0.277\thinspace\right]_{\thinspace\text{95\%}}^{\thinspace\text{c.i.}}$
_Notes:_ See Section 4.4 for detail. Cells show data average, model prediction
average, and confidence interval based on estimates from Tables 6 and 7.

ONLINE APPENDIX
An Empirical Equilibrium Model of Formal and Informal Credit Markets in
Developing Countries Fan Wang

##  Appendix A Value Functions for Discrete Choices (Online Appendix)

${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{1}}\left(\mathcal{A},k,b,\epsilon,\phi_{1}\right)=\max_{\begin{array}[]{c}k^{{}^{\prime}}\geqslant
0,\\\ b^{{}^{\prime}I}=0,b^{{}^{\prime}F}=0\\\
\end{array}}\left\\{\begin{array}[]{c}u\left(\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)-k^{{}^{\prime}}\right)+\phi_{1}\\\
+\beta\mathrm{E}_{\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}}\left({\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k^{{}^{\prime}},0,\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)\right)\end{array}\right\\}$
(A.1)
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{2}}\left(\mathcal{A},k,b,\epsilon,\phi_{2}\right)=\max_{\begin{array}[]{c}k^{{}^{\prime}}\geqslant
0,b^{{}^{\prime}I}=0,\\\ b^{{}^{\prime}F}\geqslant
b_{\text{min}}^{\text{FS}}\end{array}}\left\\{\begin{array}[]{c}u\left(\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)-k^{{}^{\prime}}-\frac{b^{{}^{\prime}F}}{1+{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}r^{\text{FS}}}}-{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\psi_{\text{FS}}}\right)+\phi_{2}\\\
+\beta\mathrm{E}_{\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}}\left({\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k^{{}^{\prime}},\left(b^{{}^{\prime}F}\right),\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)\right)\end{array}\right\\}$
(A.2)
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{3}}\left(\mathcal{A},k,b,\epsilon,\phi_{3}\right)=\max_{\begin{array}[]{c}k^{{}^{\prime}}\geqslant
0,b^{{}^{\prime}F}=0,\\\ b^{{}^{\prime}I}\geqslant
b_{\text{min}}^{\text{IS}}\end{array}}\left\\{\begin{array}[]{c}u\left(\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)-k^{{}^{\prime}}-\frac{b^{{}^{\prime}I}}{1+{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}r^{I}}}-{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\psi_{\text{IS}}}\right)+\phi_{3}\\\
+\beta\mathrm{E}_{\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}}\left({\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k^{{}^{\prime}},\left(b^{{}^{\prime}I}\right),\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)\right)\end{array}\right\\}$
(A.3)
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{4}}\left(\mathcal{A},k,b,\epsilon,\phi_{4}\right)=\max_{\begin{array}[]{c}k^{{}^{\prime}}\geqslant
0,b^{{}^{\prime}I}=0,\\\ -\gamma k^{{}^{\prime}}\leqslant
b^{{}^{\prime}F}\leqslant
b_{\text{max}}^{\text{FB}}\end{array}}\left\\{\begin{array}[]{c}u\left(\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)-k^{{}^{\prime}}-\frac{b^{{}^{\prime}F}}{1+{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}r^{\text{FB}}}}-{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\psi_{\text{FB}}}\right)+\phi_{4}\\\
+\beta\mathrm{E}_{\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}}\left({\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k^{{}^{\prime}},\left(b^{{}^{\prime}F}\right),\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)\right)\end{array}\right\\}$
(A.4)
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{5}}\left(\mathcal{A},k,b,\epsilon,\phi_{5}\right)=\max_{\begin{array}[]{c}k^{{}^{\prime}}\geqslant
0,b^{{}^{\prime}F}=0,\\\ b^{{}^{\prime}I}\leqslant
b_{\text{max}}^{\text{IB}}\end{array}}\left\\{\begin{array}[]{c}u\left(\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)-k^{{}^{\prime}}-\frac{b^{{}^{\prime}I}}{1+{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}r^{I}}}-{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\psi_{\text{IB}}}\right)+\phi_{5}\\\
+\beta\mathrm{E}_{\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}}\left({\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k^{{}^{\prime}},\left(b^{{}^{\prime}I}\right),\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)\right)\end{array}\right\\}$
(A.5)
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{6}}\left(\mathcal{A},k,b,\epsilon,\phi_{6}\right)=\max_{\begin{array}[]{c}k^{{}^{\prime}}\geqslant
0,b^{{}^{\prime}I}\leqslant b_{\text{max}}^{\text{IB}},\\\ -\gamma
k^{{}^{\prime}}\leqslant b^{{}^{\prime}F}\leqslant
b_{\text{max}}^{\text{FB}}\end{array}}\left\\{\begin{array}[]{c}u\left(\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)-k^{{}^{\prime}}-\frac{b^{{}^{\prime}I}}{1+{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}r^{I}}}-\frac{b^{{}^{\prime}F}}{1+{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}r^{\text{FB}}}}-{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\psi_{\text{IB}}}-{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\psi_{\text{FB}}}\right)+\phi_{6}\\\
+\beta\mathrm{E}_{\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}}\left({\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k^{{}^{\prime}},\left(b^{{}^{\prime}F}+b^{{}^{\prime}I}\right),\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)\right)\end{array}\right\\}$
(A.6)
${\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}v_{7}}\left(\mathcal{A},k,b,\epsilon,\phi_{7}\right)=\max_{\begin{array}[]{c}k^{{}^{\prime}}\geqslant
0,b^{{}^{\prime}I}\geqslant b_{\text{min}}^{\text{IS}},\\\ -\gamma
k^{{}^{\prime}}\leqslant b^{{}^{\prime}F}\leqslant
b_{\text{max}}^{\text{FB}}\end{array}}\left\\{\begin{array}[]{c}u\left(\mathit{\mathcal{W}}\left(\mathcal{A},k,b,\epsilon\right)-k^{{}^{\prime}}-\frac{b^{{}^{\prime}I}}{1+{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}r^{I}}}-\frac{b^{{}^{\prime}F}}{1+{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}r^{\text{FB}}}}-{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\psi_{\text{IS}}}-{\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\psi_{\text{FB}}}\right)+\phi_{7}\\\
+\beta\mathrm{E}_{\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}}\left({\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}v}\left(\mathcal{A},k^{{}^{\prime}},\left(b^{{}^{\prime}F}+b^{{}^{\prime}I}\right),\epsilon^{{}^{\prime}},\Phi^{{}^{\prime}}\right)\right)\end{array}\right\\}$
(A.7)

##  Appendix B Additional Data Details (Online Appendix)

###  B.1 Data: Village Locations

Figure B.1: Townsend Thai Monthly Survey Village Locations _Notes:_ This paper
uses panel data from 16 Thai villages collected between 1999 and 2009. The
panel includes detailed credit market transaction information for more than
650 households. 8 of the 16 villages are located in the poorer Northeast
region, and 8 villages are located in the wealthier Central region of
Thailand. See Section 3 for details.

###  B.2 Data: Volume Shares by Lender

Table B.1:  Share of Volume of Loans by Lender Type Overall 1999-2001
2002-2009 Northeast Region (poorer) Million Baht Fund _formal_ 39.0 10.8 48.2
BAAC _formal_ 36.1 50.3 30.9 Village Coop _informal_ 2.7 1.1 2.6 Friends and
Neighbors _informal_ 18.3 29.2 15.7 Village Moneylenders _informal_ 4.0 8.4
2.6 Central Region (richer) Million Baht Fund _formal_ 17.5 4.5 24.4 BAAC
_formal_ 49.9 53.2 46.8 Village Coop _informal_ 11.2 17.5 8.6 Friends and
Neighbors _informal_ 20.0 22.4 19.1 Village Moneylenders _informal_ 1.5 2.4
1.1 _Notes:_ Across the years and regions, for savings, there were 60.5, 39.8,
and 8.7 million Baht of deposits made at commercial banks, the BAAC/GSB, and
village coops, respectively. Surveyed households lent out 46.2 million Baht of
loans. Across the years and regions, for borrowing, there were 95.1, 146.0,
and 25.9 million Baht of loans borrowed from MBF, the BAAC, and village coops,
respectively. Surveyed households borrowed 64.3 million Baht of loans from
friends and neighbors and 7.1 million Baht of loans from money-lenders. While
these statistics can be skewed by outliers, especially when studied annually,
they provide a rough picture of the relative aggregate significance of the key
channels for borrowing and saving along intensive margins. In Table B.1, I
aggregate the total volume of loans (in Baht) from the five key types of
lenders shown in the table. The shares are computed by dividing each lender’s
volume of loans by the total across lenders. The overall column shows shares
for all years aggregated together. The columns for the year groups show
proportions based on total lending within each period. Table B.1 shows a rise