Introduction
Data and Methodology
Results
Conclusion
Sample Selection and Treatment Effect
Estimation of Lender of Last Resort Policies
Angela Vossmeyer
University of California, Irvine
Federal Reserve Bank of Atlanta
May 22nd, 2014
Extras
Introduction
Data and Methodology
Results
Conclusion
Topic
This paper has 2 major foci: 1 methodological and 1 empirical
Methodological
Extends standard treatment models to allow for non-random
missing data, endogeneity, and discrete outcomes.
Empirical
Evaluates the effectiveness of lender of last resort (LOLR) policies
and bank recapitalization programs, and their ability to resuscitate
the financial system.
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Introduction
Data and Methodology
Results
Conclusion
Empirical Motivation
This paper focuses on the Reconstruction Finance Corporation
(RFC) as the LOLR during the Great Depression.
• The RFC was started in 1932 with the objective of providing
liquidity to, and restoring confidence in, the banking system.
• Later became part of the New Deal under President Roosevelt.
The existing literature on LOLR policies is very mixed.
• In favor : prevent the spread of contagion, bank runs, and mass
liquidation
• Opposed : create moral hazard incentives for banks to take on
excessive risk
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Introduction
Data and Methodology
Results
Conclusion
Extras
Methodological Motivation
Policies and programs generally operate under selection
mechanisms or decision structures.
• The complexities involved in modeling selection equations and
treatment response data have restricted attention to single equation
models.
• The dangers of improper modeling are bias and misrepresentation of
the population of interest.
Motivated by these difficulties, this paper develops a multivariate
treatment effect model in the presence of sample selection.
Introduction
Data and Methodology
Results
Conclusion
Motivation
Existing treatment models focus of two subgroups: the treated
group and the untreated (control) group.
LOLR studies → this formulation acknowledges banks that receive
assistance from the LOLR and banks that do not receive
assistance.
• Ignores an initial selection mechanism – Did the bank apply for
assistance from the LOLR?
• Erroneously groups banks that do not apply for assistance with
banks that apply and are declined assistance.
• Leads to a fundamental misspecification because the untreated
group comprises the most healthy and the least healthy banks.
This paper remedies these issues by implementing the multivariate
treatment effect model for banking data.
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Introduction
Data and Methodology
Results
Conclusion
Treatment Model with Sample Selection
Extras
Introduction
Data and Methodology
Results
Conclusion
Topic
Adds to the existing literature on financial regulation by:
1. Constructing a novel bank-level data set
– Applications to the RFC
2. Employing a new methodology to jointly model:
– a bank’s decision to apply for assistance from the RFC
– the RFC’s decision to approve the application
– the bank’s performance a few years after the disbursements
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Introduction
Data and Methodology
Results
Conclusion
Data Sources
RFC Card Index to Loans Made to Banks
• Acquired from the National Archives in College Park, MD
• Reports the name of the borrower, request and amount of
loan, and whether the loan was approved or declined
• Additional information from “Paid Loan Files” and “Declined
Loan Files”
Rand McNally Bankers’ Directory
• Describes bank balance sheets, correspondent relationships,
and characteristics for all banks
• This information identifies the non-selected, or non-applicant,
sample
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Introduction
Data and Methodology
Results
Conclusion
Data
The sample includes all banks
operating in 1932 in:
• Alabama
• Arkansas
• Mississippi
• Michigan
• Tennessee
The sample consists of 1,794
banks:
• 908 banks applied for
assistance (about 50%)
• 800 of those were approved
(about 88%)
• 108 of those were declined
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Data and Methodology
Results
Conclusion
Extras
Data
Variable
No. Banks
Fed District(s)
Financial (avg)
Cash / Assets
Dep. / Liab.
Charters (counts)
State Bank
National Bank
Mkt. Shares (avg.)
County Liab.
Town Liab.
HHI
County (avg.)
No. Wholesale
Cropland (×1000)
Town Pop. (×1000)
RFC Data
% Applied
% Approved
Alabama
250
6
Arkansas
278
8
Michigan
638
7, 9
Mississippi
235
6, 8
Tennessee
393
6, 8
0.160
0.612
0.235
0.750
0.115
0.751
0.161
0.730
0.143
0.675
166
82
222
44
438
102
208
26
308
83
0.27
0.68
0.66
0.26
0.75
0.60
0.13
0.17
0.29
0.33
0.74
0.70
0.24
0.69
0.54
31.3
115.6
14.6
22.4
96.6
4.7
45.3
122.9
49.6
15.4
81.9
4.5
25.3
78.1
14.2
48
85
56
90
52
87
60
92
40
89
Introduction
Data and Methodology
Results
Data Sources
Conclusion
Extras
Introduction
Data and Methodology
Results
Conclusion
Treatment Model with Sample Selection
Extras
Introduction
Data and Methodology
Results
Conclusion
Extras
Model
The model stemming from the previous figure contains a system of
5 equations with 1 selection mechanism, 1 selected treatment and
3 treatment response equations.
∗
Selection Equation : yi1
= x0i1 β 1 + εi1
(1)
(always observed)
∗
= x0i2 β 2 + εi2
Selected Treatment : yi2
(2)
(observed for selected sample)
OUTCOMES
:
Treatment Responses – only 1 observed
∗
Declined Bank Sample : yi3
= (x0i3 yi1 )β 3 + εi3
Approved Bank Sample :
Non-Applicant Sample
:
∗
yi4
∗
yi5
=
=
(x0i4 yi1 yi2 )β 4
x0i5 β 5 + εi5
+ εi4
(3)
(4)
(5)
Introduction
Data and Methodology
Results
Conclusion
Data
Outcomes for each equation:
•
yi1 : total amount of RFC assistance requested by each bank
by December 1933.
• Censored with point mass at 0 for banks that do not apply for
assistance and a continuous distribution for the different loan
amounts requested.
•
yi2 : total amount of RFC assistance approved.
• Censored with point mass at 0 for banks that are declined
assistance and a continuous distribution for the approved loan
amounts.
Extras
Introduction
Data and Methodology
Results
Conclusion
Data
•
yi3 – yi5 : the amount of “loans and discounts” (hereafter,
LD) for each bank taken from its January 1935 balance sheet.
• Censored with point mass at 0 for banks that failed since the
time of the loan applications and a continuous distribution
with LD representing the bank’s health and the state of the
local economy.
• LD is chosen to measure a bank’s performance following the
literature on the credit crunch and its relation to economic
activity (Bernanke, 1983; Calomiris and Mason, 2003).
• Covariates include
• Financial ratios and characteristics
• Charters, memberships, and departments
• Correspondent networks, and market shares
• County characteristics, and political indicators
Extras
Introduction
Data and Methodology
Results
Conclusion
Model
The model assumes that the errors εi = (εi1 , εi2 , εi3 , εi4 , εi5 )0 have
a multivariate normal distribution N5 (0, Ω),


Ω11 Ω12 Ω13 Ω14 Ω15
 Ω21 Ω22 Ω23 Ω24
· 


·
· 
Ω=
.
 Ω31 Ω32 Ω33
 Ω41 Ω42
·
Ω44
· 
Ω51
·
·
·
Ω55
Only 11 unique estimable elements in Ω.
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Data and Methodology
Results
Conclusion
Extras
Model
Data missingness restricts the model to systems of 2 or 3 equations
Non-applicant sample, i ∈ N1
∗ 0
yi1
xi1
∗
yiC
=
,
X
=
iC
∗
0
yi5
Declined sample, i ∈ N2
 ∗ 
yi1
∗
∗ 
yiD
=  yi2
, XiD =
∗
yi3
0
x0i5
, ΩC =
x0i1
0
0
0
x0i2
0
0
0
(x0i3 yi1 )
Approved sample, i ∈ N3
 ∗ 
yi1
x0i1
∗
∗
0
yiA =  yi2  , XiA =
∗
0
yi4
0
x0i2
0
0
0
(x0i4 yi1 yi2 )
Ω11
Ω51
!
, ΩD =
!
, ΩA =
Ω15
Ω55
Ω11
Ω21
Ω31
Ω11
Ω21
Ω41
Ω12
Ω22
Ω32
Ω12
Ω22
Ω42
Ω13
Ω23
Ω33
!
Ω14
Ω24
Ω44
!
Introduction
Data and Methodology
Results
Conclusion
Likelihood
The likelihood is defined in terms of the 3 subsets of the sample
without computations for the unobserved components of the
model.
• Let µj define the mean in equations j = 1, . . . , 5
R
The likelihood is given by f (y|θ) = f (y, y∗ |θ)dy∗ where θ is all
model parameters, and f (y, y∗ |θ) =
Y
Y
Y
∗
∗
∗
fN (yiC
|µC , ΩC ) ×
fN (yiD
|µD , ΩD ) ×
fN (yiA
|µA , ΩA ).
i∈N1
i∈N2
i∈N3
• Discreteness of multiple outcome variables renders this likelihood
analytically intractable and estimation relies on simulation-based
techniques.
Extras
Introduction
Data and Methodology
Results
Conclusion
Extras
Priors and Posterior
Standard semi-conjugate priors are applied:
π(β, Ω) = N (β |β 0 , B0 )IW(Ω|υ, Q)
Combining the likelihood and priors leads to a posterior
distribution,
"
∗
π(θ, y |y) ∝
#"
Y
i∈N1
f
∗
(yiC
|θ)
#"
Y
i∈N2
f
#
Y
∗
(yiD
|θ)
f
∗
(yiA
|θ)
i∈N3
×N (β |β 0 , B0 ) × IW(Ω|υ, Q),
which is simulated by Markov chain Monte Carlo (MCMC)
methods.
Introduction
Data and Methodology
Results
Conclusion
Estimation
For computational efficiency, a collapsed Gibbs sampler with data
augmentation is employed.
• The algorithm does not require simulation of the missing outcomes
(Chib, Greenberg, and Jeliazkov, 2009)
• The algorithm does not require the joint distribution of the
potential outcomes – simulation is of the parameters and not the
counterfactuals (Chib, 2007)
These estimation techniques improve the mixing of the MCMC
chain, and have low storage costs.
Extras
Introduction
Data and Methodology
Results
Conclusion
Estimation
MCMC Estimation Algorithm for Censored Outcomes
1. Sample β from the distribution β |y, y∗ , θ \ β.
2. Sample Ω from the distribution Ω|y, y∗ , θ \ Ω.
3. For i ∈ N1 , sample y1∗ from the distribution y1∗ |y, θ, y∗ \ y1∗ .
4. For i ∈ N2 , sample y2∗ from the distribution y2∗ |y, θ, y∗ \ y2∗ .
5. For i ∈ N2o , sample y3∗ from the distribution y3∗ |y, θ, y∗ \ y3∗ .
6. For i ∈ N3o , sample y4∗ from the distribution y4∗ |y, θ, y∗ \ y4∗ .
7. For i ∈ N1o , sample y5∗ from the distribution y5∗ |y, θ, y∗ \ y5∗ .
Extras
Introduction
Data and Methodology
Results
Conclusion
Extras
Preliminaries
The results are based on 10,000 MCMC draws with a burn-in of
1,000.
Model performance:
• Low inefficiency factors ⇒ near iid sampling from the posterior
• Run time: 18 mins
• No sensitivity to the hyperparameters on the prior distribution
⇒ data speak loudly for the results
• Several competing specifications were considered.
• Reported results are from the model with the highest marginal
likelihood.
Introduction
Data and Methodology
Results
Conclusion
Extras
Results
Basic Results:
• No political bias found. Democratic votes, and indicators for
lobbying groups have credibility intervals overlapping zero in
the selected treatment stage.
• Results vary vastly across the 3 subgroups of banks in the
treatment response equations.
Analysis of the resulting parameter estimates from the multivariate
treatment model is complicated by the discreteness of the outcome
variables.
• Interpretation is afforded with covariate and treatment effect
calculations.
Introduction
Data and Methodology
Results
Conclusion
Extras
Marginal Effect
βRFC is the coefficient on the endogenous covariate yi2 in equation
4 and is the key estimate of interest.
• After controlling for a bank’s health, environment, and contagion
channels, this coefficient reflects the impact of RFC assistance on
bank lending.
The marginal effect is averaged over both observations and MCMC
draws.
• The marginal effect of the RFC is 0.571.
• $10,000 of RFC assistance translates to $5,710 of “loans and
discounts” in 1935.
• This result accords well with the loan-to-deposit ratios during the
1930s and during banking panics, in general.
Introduction
Data and Methodology
Results
Conclusion
Modeling Importance
Model
Full Model
Ignore Joint Modeling
OLS (eq. 4)
βRFC
1.46
1.07
0.94
Marg. Eff.
0.57
0.41
0.94
These results stress the importance of modeling:
• Jointly
• Discrete outcomes
• Endogenous covariates
• Correlation in the outcomes
Extras
Introduction
Data and Methodology
Results
Conclusion
Extras
Treatment Effect #1
Consider the difference in the probability of bank failure if the RFC
did not offer any assistance.
To see how removing the treatment from the treated banks affects
bank success, two probabilities need to be computed:
‡
‡
• Pr(yi4 = 0|xi4 , yi2
, θ) where yi2
represents zero RFC assistance
†
†
• Pr(yi4 = 0|xi4 , yi2
, θ) where yi2
represents the original treatment
Introduction
Data and Methodology
Results
Conclusion
Extras
Treatment Effect #1
The objective is to obtain a sample of draws and evaluate
‡
†
{Pr(yi4 = 0|yi2
) − Pr(yi4 = 0|yi2
)}
Z
=
‡
†
{Pr(yi4 = 0|xi4 , yi2
, θ)−Pr(yi4 = 0|xi4 , yi2
, θ)}π(xi4 )π(θ|y)dxi4 dθ.
The result gives the expected difference in the computed pointwise
†
‡
probabilities as yi2
is changed to yi2
.
Computation of these probabilities is afforded by employing the
CRT method, developed in Jeliazkov and Lee (2010).
Introduction
Data and Methodology
Results
Conclusion
Treatment Effect #1
The results show:
‡
†
{Pr(yi4 = 0|yi2
) − Pr(yi4 = 0|yi2
)} = 0.126
In other words, if the RFC did not offer any assistance, the
probability of bank failure for the approved bank sample increases
by 12.6 percentage points.
Extras
Introduction
Data and Methodology
Results
Conclusion
Treatment Effect #2
Consider the probability of bank failure if the RFC approved the
loans for the selected untreated sample (declined banks).
Two probabilities to consider are,
‡
‡
• Pr(yi3 = 0|xi3 , yi2
, θ) where yi2
represents declined loans (the
original case)
†
†
• Pr(yi3 = 0|xi3 , yi2
represents the scenario where the
, θ) where yi2
RFC approved the requested loan amounts
Extras
Introduction
Data and Methodology
Results
Conclusion
Treatment Effect #2
The results show
‡
†
{Pr(yi3 = 0|yi2
) − Pr(yi3 = 0|yi2
)} = 0.025
If the RFC assisted banks that were declined loans, the probability
of failure for the selected untreated sample decreases by 2.5
percentage points.
The banks the RFC declined to assist were helpless because full
assistance from the RFC would not have had a major impact on
their ability to survive and thrive in the economy.
Extras
Introduction
Data and Methodology
Results
Conclusion
Extras
Results Overview
LOLR policies and bank recapitalization aided a bank’s survival if
the bank was healthy enough to receive a loan.
The results also indicate that the selection procedures adopted by
the RFC were successful.
• Assistance to all struggling banks would have been wasteful because
most of the untreated banks were not healthy enough to have
benefitted from an influx of funds.
Proper consideration of the decision structure and composition of
the treatment and control groups are of fundamental importance
to evaluating the effectiveness of LOLR programs.
Introduction
Data and Methodology
Results
Conclusion
Concluding Remarks
This paper presents a methodological framework for multivariate
treatment effect models in the presence of sample selection and
discrete data.
• The methodology developed here is computationally efficient,
and has low storage costs.
The model is applicable to a multitude of problems prevalent in
economics.
• Effectiveness of housing and welfare programs
• Health outcomes research
• College admittance studies
• Credit approval decisions
Extras
Introduction
Data and Methodology
Results
Conclusion
Concluding Remarks
Further research on LOLR policies should focus on the multi-step
decision mechanisms that place banks into different policies and
programs.
Future Work
Examine the two regimes of the RFC:
• Collateralized lending
• Recapitalization
Jointly model RFC lending and lending from the Federal Reserve:
• Both were engaging in LOLR policies
• Additional selection stages to be considered
Extras
Introduction
Data and Methodology
Results
Conclusion
Thank You
Feel free to contact me with any questions or comments.
Angela Vossmeyer
University of California, Irvine
[email protected]
sites.uci.edu/vossmeyer
Extras
Introduction
Data and Methodology
Results
Conclusion
Estimation
MCMC Estimation Algorithm for Censored Outcomes
1. Sample β from the distribution β |y, y∗ , θ \ β.
2. Sample Ω from the distribution Ω|y, y∗ , θ \ Ω.
3. For i ∈ N1 , sample y1∗ from the distribution y1∗ |y, θ, y∗ \ y1∗ .
4. For i ∈ N2 , sample y2∗ from the distribution y2∗ |y, θ, y∗ \ y2∗ .
5. For i ∈ N2o , sample y3∗ from the distribution y3∗ |y, θ, y∗ \ y3∗ .
6. For i ∈ N3o , sample y4∗ from the distribution y4∗ |y, θ, y∗ \ y4∗ .
7. For i ∈ N1o , sample y5∗ from the distribution y5∗ |y, θ, y∗ \ y5∗ .
Extras
Introduction
Data and Methodology
Results
Conclusion
Extras
Estimation
Sampling- 1 block,
multi-step procedure because
the form of Ω in the
complete-data likelihood. Ω is
sampled such that:
1. Ω11



Ω=


Ω11
Ω21
Ω31
Ω41
Ω51
Ω12 Ω13 Ω14 Ω15
Ω22 Ω23 Ω24
·
Ω32 Ω33
·
·
Ω42
·
Ω44
·
·
·
·
Ω55






Introduction
Data and Methodology
Results
Conclusion
Extras
Estimation
Sampling- 1 block,
multi-step procedure because
the form of Ω in the
complete-data likelihood. Ω is
sampled such that:
1. Ω11
2. Ω22·1



Ω=


Ω11
Ω21
Ω31
Ω41
Ω51
Ω12 Ω13 Ω14 Ω15
Ω22 Ω23 Ω24
·
Ω32 Ω33
·
·
Ω42
·
Ω44
·
·
·
·
Ω55






Introduction
Data and Methodology
Results
Conclusion
Extras
Estimation
Sampling- 1 block,
multi-step procedure because
the form of Ω in the
complete-data likelihood. Ω is
sampled such that:
1. Ω11
2. Ω11·2
3. Define
Ω11 Ω12
Ωu =
Ω21 Ω22
4. Ω33·u



Ω=


Ω11
Ω21
Ω31
Ω41
Ω51
Ω12 Ω13 Ω14 Ω15
Ω22 Ω23 Ω24
·
Ω32 Ω33
·
·
Ω42
·
Ω44
·
·
·
·
Ω55






Introduction
Data and Methodology
Results
Conclusion
Extras
Estimation
Sampling- 1 block,
multi-step procedure because
the form of Ω in the
complete-data likelihood. Ω is
sampled such that:
1. Ω11
2. Ω11·2
3. Define
Ω11 Ω12
Ωu =
Ω21 Ω22
4. Ω33·u
5. Ω44·u



Ω=


Ω11
Ω21
Ω31
Ω41
Ω51
Ω12 Ω13 Ω14 Ω15
Ω22 Ω23 Ω24
·
Ω32 Ω33
·
·
Ω42
·
Ω44
·
·
·
·
Ω55






Introduction
Data and Methodology
Results
Conclusion
Extras
Estimation
Sampling- 1 block,
multi-step procedure because
the form of Ω in the
complete-data likelihood. Ω is
sampled such that:
1. Ω11
2. Ω11·2
3. Define
Ω11 Ω12
Ωu =
Ω21 Ω22
4. Ω33·u
5. Ω44·u
6. Ω55·1



Ω=


Ω11
Ω21
Ω31
Ω41
Ω51
Ω12 Ω13 Ω14 Ω15
Ω22 Ω23 Ω24
·
Ω32 Ω33
·
·
Ω42
·
Ω44
·
·
·
·
Ω55





