THE EFFECTS OF INCOME SHOCKS AND LIQUIDITY CONSTRAINTS ON THE
HOUSEHOLD SAVINGS RESPONSE
A Thesis
Presented to the faculty of the Department of Economics
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF ARTS
in
Economics
by
John Dalton
FALL
2013
THE EFFECTS OF INCOME SHOCKS AND LIQUIDITY CONSTRAINTS ON THE
HOUSEHOLD SAVINGS RESPONSE
A Thesis
by
John Dalton
Approved by:
__________________________________, Committee Chair
Suzanne O’Keefe, Ph.D.
__________________________________, Second Reader
Stephen Perez, Ph.D.
____________________________
Date
ii
Student: John Dalton
I certify that this student has met the requirements for format contained in the University format
manual, and that this thesis is suitable for shelving in the Library and credit is to be awarded for
the thesis.
__________________________, Graduate Coordinator ___________________
Kristin Kiesel, Ph.D.
Date
Department of Economics
iii
Abstract
of
THE EFFECTS OF INCOME SHOCKS AND LIQUIDITY CONSTRAINTS ON THE
HOUSEHOLD SAVINGS RESPONSE
by
John Dalton
This thesis explores household savings responses to income shocks in the context of
liquidity constraints. Using log and linear specifications, we implement a two stage least
squares state and time fixed effect model. The first stage estimates unexpected shocks to
household income. The second stage estimates the effects of the income residual on the
change in household liquidity. Using the 1996 wave of the Panel Survey of Income
Dynamics to split households according to a measure of creditworthiness, we incorporate
household-level biennial wealth, income, and demographic measures from the PSID
during the period of 1999 to 2009. Three primary findings emerge: 1) we find the savings
response
of
unconstrained
and
constrained
households
to
be
statistically
indistinguishable, 2) presumably constrained households dissave in a negative shock
environment, and 3) unconstrained households exhibit statistically significant, but muted
savings responses in a positive shock environment.
_______________________, Committee Chair
Suzanne O’Keefe
_______________________
Date
iv
ACKNOWLEDGEMENTS
First, I would like to acknowledge the entire faculty of the CSUS Economics
Department. Professors Chalmers, Dowell, Dube, Ford, Gallet, Kelly, Schwarm, Sexton,
and Wang all played a role in helping me stay focused and excited about consistently
attending lecture. All of you kept it challenging and inspiring.
Second, I would specifically like to acknowledge the two men that provided
letters of recommendation for my admission into the CSUS Economics Graduate
Program.
Professor George Jouganatos, of all the courses I completed, the Money and
Banking course you facilitated was by far the most challenging in terms of teaching me
how to sit back and listen to opposing viewpoints without judgment. I gained a lot of
respect for your character over the course of the semester. I am very proud of the A I
earned in your course and was equally thrilled when you obliged and drafted a letter of
recommendation.
Professor Mark Siegler, you know my beginnings about as much as any professor.
Early in my economics path, your guidance as Economics Department Chair proved to be
foundation building. I truly appreciate the open ear you consistently offered to me early
on. Thank you.
Third, I would be remiss without pointing out that Professor Kaplan’s Cost
Benefit Analysis course has proven to be the most pragmatic in my day-to-day career.
v
Professor Kaplan’s guidance and energy during my advancement to candidacy kept me
motivated.
Fourth, I must acknowledge the patience and guidance of Professors O’Keefe and
Perez. During the past 18 months, both of you have graciously tolerated out-of-the-blue
phone calls from me that can be considered nothing other than verbally expressed streams
of consciousness rather than coherent print. I am truly blessed that both of you obliged
me and served dutifully as members of my graduate committee. Considering what I know
of both of you, I can only hope that over the next five to ten years of my life, my family
is positioned the same. Both of you are an inspiration in more ways than you may realize.
Finally, I would be remiss if I did not acknowledge the efforts of my Wife, Yana.
Over the past 18 months, she has tolerated my defiance in refusing to accede to her
demands of signing a “Finish my thesis by this date” contract. Especially over the past
three months, she has taken up slack during the early hours of the weekends after I have
pulled all-nighters to take advantage of those precious hours in which our 9 month old
son and 3 ½ year old daughter were sound asleep. It is my hope that these efforts will set
the precedent for our children such that they complete their graduate programs in a
manner far more disciplined, efficiently, and graciously than I did.
vi
TABLE OF CONTENTS
Page
Acknowledgements ........................................................................................................v
List of Tables ................................................................................................................. ix
Chapter
1. INTRODUCTION ...................................................................................................... 1
2. LITERATURE REVIEW ........................................................................................... 4
3. DATA SUMMARY .................................................................................................... 8
3.1. Data Overview ..................................................................................................... 8
3.2. Categorical Demographic .................................................................................... 8
3.3. Binary Indicator Controls .................................................................................. 10
3.4. Wealth ................................................................................................................ 11
3.5. Constrained Indicator ......................................................................................... 13
3.6. Income Measures ............................................................................................... 17
4. METHODOLOGY AND MODEL .......................................................................... 19
4.1. Hypothesis A ...................................................................................................... 19
4.2. Hypothesis B ...................................................................................................... 21
4.3. Overview of Reduced Form ............................................................................... 23
4.4. Component 1: Elements of the Dependent Variable.......................................... 23
4.5. Component 2: Sample Splitting ......................................................................... 25
vii
4.6. Component 3: Income Residual Instrument ...................................................... 27
4.7. Component 4: Primary Model for Hypotheses Testing ..................................... 28
4.8. Interpretation of Coefficients ............................................................................. 30
5. EMPIRICAL ANALYSIS AND FINDINGS ........................................................... 33
5.1. Income Residual Estimation .............................................................................. 33
5.2. Hypothesis A & B Restated – Real Dollar Specification .................................. 35
5.3. Hypothesis A & B Restated – Logarithmic Dollar Specification ...................... 42
6. CONCLUSION ......................................................................................................... 48
6.1. Summary of Research and Findings .................................................................. 48
6.2. Caveats to the Analysis ...................................................................................... 49
REFERENCES ............................................................................................................. 52
viii
LIST OF TABLES
Table
Page
3.1
Frequency and Percentage of Several Categorical Demographics……….……….9
3.2
Binary Indicator Controls by PSID Panel Wave ……………...……….………..11
3.3
Summary Statistics of Assets, Debt, and Equities - Level and First Difference...12
3.4
Summary Statistics of Home Equity, Wealth, and Household Head Age.………13
3.5
Tabulation of Observations Experiencing Bankruptcy vs. Financial Distress......15
3.6
Observations Experiencing Bankruptcy, Financial Distress, and Net Worth……16
3.7
Tabulation of Observations – Bankruptcy vs. Constrained……………………...16
3.8
Constrained and Unconstrained Households 1999 – 2009……………………... 17
3.9
Summary Statistics of Several Measures of Consumption and Income………... 18
4.1
Controls Matrices for Various Regression Models……………………………....32
5.1
Income Estimation Process – Linear and Natural Log…….………...…………..34
5.2
Effects of Income Residuals on Changes in Liquidity………………………...…39
5.3
Sum of Effects of Income Residuals on Changes in Liquidity………..…........... 40
5.4
Effects of Logged Income Residuals on Logged Changes in Liquidity….....…...44
5.5
Sum of Effects of Logged Income Residuals on Logged Changes in Liquidity...46
ix
1
CHAPTER 1
INTRODUCTION
This thesis tests for the effects of unexpected shocks to household income on
measures of household liquidity. Within the context of positive and negative incomeshock restrictions, we observe the household’s savings response otherwise referred to as
changes in liquidity. Manipulating household cash asset levels and unsecured debt
balances serve as the primary channels a household can alter liquidity. However,
households with limited cash asset levels lack capacity to smooth consumption in a
negative shock environment. Additionally, a low asset household may be consuming at
levels less than preferable according to the household’s tastes. The minimal capacity of a
low asset household relies upon a primary assumption – access to unsecured debt asserts
a minimal effect on a household’s ability to smooth consumption in the face of negative
income shocks.
Ultimately, revelations regarding the household’s savings response, in part,
answer three questions. First, do liquidity-constrained households exhibit a savings
response that differs from otherwise unconstrained households? Second, does a liquidity
constrained household exhibit a capacity to smooth consumption in the context of
negative shocks to income? Third, do unconstrained households exhibit excess sensitivity
in the context of positive shocks to income?
The final question posed arises from suggestions in previous research on
permanent income life cycle (PI/LC) models. Namely, excess sensitivity to transitory
income often arises in tests of the Permanent Income Hypothesis. The alleged existence
2
of liquidity constraints often serves as the likely rationale for this excess sensitivity.
Without the justification of liquidity constraints, we must accept violation of PI/LC
model implications. Specifically, rather than being consumed, theory predicts transitory
shocks to household income are saved to be consumed smoothly over a lifetime. As will
be pointed out in Chapter 2, many studies have found an implied consumption of
transitory shocks. However, this implied consumption may be due to prior research
models not accounting for a household’s capacity to access unsecured debt channels.
Previous studies of PI/LC implications focus on changes in consumption as the
dependent variable with a lagged measure of transitory income as the primary
explanatory variable. This thesis differs from many attempts, in large part, by utilizing
changes in liquidity as the dependent variable and an endogenous estimation of the
income residual as the primary explanatory variable. Another differing aspect of this
thesis is this thesis adds to the small body of PI/LC work using longitudinal microdata.
Empirical findings of this analysis soundly reject the notion that constrained
households face difficulty in reducing liquidity in times of negative income shocks. This
implies constrained households, as defined with minimal cash assets, have access to the
unsecured credit channel as a means of smoothing consumption in a negative shock
environment. Also pertinent, a household alters liquidity asymmetrically, dependent on
the sign orientation of the shock. In other words, we find that the unconstrained
household exhibits a muted savings response for positive income shocks. This asymmetry
is such that a positive shock increases liquidity less than an equal but opposite negative
shock decreases liquidity.
3
This empirical analysis suggests both the constrained and unconstrained
household exhibits an ability to dissave in a negative environment. In other words, they
decrease liquidity. Since the presumably unconstrained households does not appear to
increase liquidity as aggressively in positive shock environments as it decreases liquidity
in negative shock environments, we can only assume this household is actually
consuming, to some degree, transitory shocks to income.
The two primary findings taken together suggest households are not liquidity
constrained as is evidenced in the negative shock environment. However, households
may exhibit symptoms of being liquidity constrained in the positive shock environment
only because of underlying immeasurable desires to consume good news. In short, using
liquidity constraints as the likely explanation for why excess income sensitivity exists
when testing the Permanent Income Hypothesis may not be valid.
This thesis continues in the following manner. Chapter 2 offers an overview of the
extensive body of literature addressing topics like the permanent income hypothesis, life
cycle models, personal bankruptcy, and idiosyncratic risk. Chapter 3 explores the
longitudinal data utilized in our analysis. Chapter 4 elaborates upon the strategy and
methodology of the employed model. Chapter 5 analyzes the findings of the model.
Chapter 6 concludes this thesis with a summary of the findings and caveats to the
analysis.
4
CHAPTER 2
LITERATURE REVIEW
This thesis integrates literature spanning the Permanent Income/Life Cycle
(PI/LC) genre of consumer theory. The evolution of literature follows the sophistication
of technology and data collecting techniques. Prior to 1990, micro data was difficult and
expensive to gather and maintain. The data collected was typically unsatisfactory for
testing an evolving expectations theory. Furthermore, because of the costs of conducting
large longitudinal studies, large gaps between waves, sometime as much as five years,
rendered much of the micro data unreliable because of potential measurement error.
Consequently, much of the work involving PI/LC models used aggregate level macro
data collected by federal and state agencies with a frequency as short as monthly, but
typically quarterly. Into the late 1990’s, the introduction of powerful computer software
enabled economists to create and test micro-foundational models involving high order
calculus and the constant relative risk aversion specification of the consumption function.
This led to a solid body of literature that lays the framework for further surveys of
appropriate variables.
Of special note, Deaton (1992) serves as the seminal text for this paper. In short,
Deaton summarizes the pioneering work of Friedman (1957), Modigliani (1966), Hall
(1978), and others in a comprehensive treatment of consumption at the macro and micro
level. Recall the three questions posed in the introduction. First, do liquidity-constrained
households exhibit a savings response that differs from an otherwise unconstrained
household? Second, does a liquidity constrained household exhibit the capacity to smooth
5
consumption in the context of negative shocks to income? Third, do unconstrained
households exhibit excess sensitivity in the context of positive shocks to income? To
address these three questions as well as the forthcoming two hypotheses, we researched
the literature according to specific characteristics. First, we identified four recent studies
that used household level panel data in the context of PI/LC implications. Bartzsch
(2008), Filer & Fischer (2007), Japelli & Pistaferri (2011), and Carroll (2001) serve as
the four most recent guideposts for this analysis. All four utilized a unique set of panel
data.
First, Bartzsch explored German household panel data testing implications of
precautionary savings and buffer stock models. His primary finding related changes in
consumption to the ratio of a household’s wealth to permanent income. From his paper,
the idea of utilizing a measure of wealth or liquidity as a dependent variable arose.
Second, Japelli took advantage of the Italian Survey of Household Income and Wealth to
test for consumption smoothing under the monetary regime implementation of the Euro.
His primary finding notes consumption remained sensitive to income shocks after the
integration of the Euro. From Japelli, the first-stage income estimation process employed
by this paper was born. Third, Filer utilized the Panel Survey of Income Dynamics testing
for excess sensitivity in the context of restricted credit according to bankruptcy
declaration and asset levels. Filer did find evidence of excess sensitivity for households
still within10 years of their most recent bankruptcy. Pertinent to this paper, Filer’s
method of identifying constrained household by using the 1996 PSID wave gave rise to
this paper’s sample splitting technique. Fisher (2010) augmented his work with Filer
6
(2007) by delving further into the PSID and meshing these households with broader
Survey of Consumer Finances (SCF) data. The point was to incorporate the PSID’s 1996
Bankruptcy Flag wave with SCF data to identify the probabilities associated with debt
channel access for households with bankruptcy flags on their credit reports. Their
primary findings supported validity of the PSID’s 1996 bankruptcy flag as an appropriate
and effective sample-splitting tool for this thesis. Fourth, similar to Filer, Carroll utilized
the PSID data to test a generated stochastic consumption model in which parameters were
built in to simulate the effects of impatient consumers facing uninsurable labor-income
risk. This thesis incorporates Carroll’s establishment of utilizing net household income
including all transfer payments at various lag lengths to estimate current period income
expectation of a household. Subsequent to Carroll (2001), Carroll (2009) augments the
treatment of income shocks in the context of precautionary savings motives and impatient
consumers.
The final set of literature focuses on previous credit supply research. The second
question posed seeks to investigate if households that are presumably constrained can
indeed dissave in the face of negative shocks – implying access to unsecured debt
channels is apparent. In order to invoke the latter implication, we must identify the nature
of unsecured debt market supply. First, Krueger & Perri (2005) utilized Consumer
Expenditure Survey data to parametrically test consumption smoothing within the context
of perfect, limited, and autarchic credit markets faced by the household. Their major
finding is that the credit market faced by consumers are somewhere between perfect and
7
limited. In other words, households were able to smooth consumption when entrance to
the unsecured debt market served as an option.
Second, two papers by Song Han, et al allow us to confidently assume during the
range of our analysis (1999 to 2009), the supply of credit to unconstrained and
constrained households alike was unfettered. Han (2011a) measures the supply of
unsecured debt. They separate the data into pools of bankruptcy filers and non-filers and
utilize the variable of time since filing. The primary finding notes bankruptcy filers are
not excluded from unsecured debt channels after filing but do face less favorable terms
than non-filers. In fact, during the three-year period immediately following a bankruptcy
filing, filers received more credit offers than those that did not file for bankruptcy.
Augmenting this work, Han (2011b) takes SCF data and estimates accessibility, demand,
and cost of debt for bankruptcy filers during the post-bankruptcy period. They find
bankruptcy filers have restricted access to unsecured credit but borrow more debt after
bankruptcy than comparable non-filers. Han does segregate debt into three categories; 1)
credit card charges, 2) first mortgages, and 3) auto loan debt. This Thesis however,
focuses solely on the unsecured debt measure provided by the PSID.
8
CHAPTER 3
DATA SUMMARY
3.1. Data Overview
The Panel Study of Income Dynamics (PSID) serves as the source for this data.
Commissioned by the University of Michigan in 1968, the PSID features measurements
of demographics, wealth, income, and consumption at the individual and household level.
Specific to the timeframe encompassing this analysis, the PSID offers longitudinal data
across biennial waves beginning in 1997 and ending in 2009. Additionally, the 1996
wave incorporates a line of questioning that pertains to the creditworthiness and degree of
financial distress the individual household experienced during the period 1991 to 1996.
Further embellishment of this specific line of questioning is forthcoming.
This chapter parses the data into five segments: 1) categorical measurements of
demographic distributions, 2) binary indicator controls, 3) wealth measures, and the
components of the dependent variable – liquid assets, unsecured debt and stock equities,
4) indicator variables that define the constrained cohort, and 5) an overview of income
data.
3.2. Categorical Demographic
Categorical demographic controls utilized include marital status, employment
status, education level, gender, race, region, and number of children under age 18. Table
3.1 presents each demographic measure along with the subcategories according to
frequency and percentage of total observations.
9
Focusing attention first on the distribution of households across regions;
immediately we can visually detect overrepresentation of southern states. This likely
leads to a clearly skewed race distribution that underrepresents Latino, Asian, and other
races (e.g. 2.3% of this data set are not white or black). Using inverse probability
weighting – provided by the administrators of the PSID – addresses this feature of overselection bias. Such weighting is unique to each individual household.
While the weighting feature does aid in external validity of this analysis,
underrepresentation of certain demographics still occurs. Unfortunately, this is an
unavoidable consequence of the choice of implemented waves. To the point, we do not
10
incorporate households that entered the PSID in 1997 and subsequent waves because they
did not participate in the 1996 wave supplying the financial distress responses. Further
reliance on the provided weights will ideally minimize this under-sampling effect so the
results of this analysis have at least some external validity.
Another potential skew exists in the form of gender bias. In order to take
advantage of the panel nature of the data, we incorporate into this analysis only
individuals that are heads of their household for all waves from 1996 to 2009. This
means, the only women followed are those identified as head of household in 1996.
Consider that the 13 years between 1996 and 2009 have seen marked shifts in labor force
participation and earning potential of women relative to men. Accordingly, women may
actually be head of household more than the indicated 23.2% above. Therefore, the
results of this analysis may not be externally valid for female-led households.
3.3. Binary Indicator Controls
Binary indicator controls include business ownership, home purchase
transactions, mortgage refinances, and the birth of a child. These indicators are not static
and so turn on and off across panel waves. Table 3.2 presents these indicators according
to their distribution for each PSID panel wave.
11
3.4. Wealth
The term wealth refers to a broad range of measures such as very liquid assets
(VLA), unsecured debt (UD), stock equities (SE), home equity, net worth sans home
equity, and average wealth. Various combinations and transformations of VLA, UD, and
SE make up the components of the dependent variable. The other measures mentioned
incorporate as explanatory variables. Summary statistics are adjusted to real 1997 dollars.
12
3.4.1. Dependent Variables
The first differences of various combinations of VLA, UD, and SE comprise the
dependent variables analyzed. We will conduct an examination of both specifications –
linear and log. As such, Table 3.3 presents the summary statistics in both raw dollars and
natural logarithm form; we positively code values for VLA, UD, and SE. This facilitates
the ability to perform the logarithmic specification. Accordingly, a mental note exists to
interpret positive changes in unsecured debt as an increase in debt, not an increase in
liquidity. We present these measures in terms of level measurements and first differences
of the level measurement.
13
3.4.2. Explanatory Variables
Table 3.4 reports summary statistics of head of household age, level and
differenced home equity, net worth with and without home equity, and a measure of
average wealth. When practical, we carry out and display the natural log transformation.
The Average Wealth variable is itself a single constant unique to the individual
household. The purpose of the variable is to serve as a long run anchor for household
savings time preferences and risk aversion. Time preference and risk aversion are
difficult to instrument. The intent is for the Average Wealth variable interacted with the
age and age-squared of the household to do just that.
3.5. Constrained Indicator
For this analysis, the goal is to group households that are likely constrained while
minimizing the imposition of arbitrary criteria. Fortunately, the PSID’s 1996 wave
14
provides the footwork for this grouping affect through a series of questions that allows
the household to self-reveal the nature of their constraints.
The first question of interest identifies households that have filed for Chapter 7 or
Chapter 13 bankruptcy protection prior to 1996. Households that answered in the
affirmative earned an indicator variable assignment of one if their bankruptcy filing took
place between the years of 1989 and 1996. The second question of interest, which is
actually more of a line of questioning, identifies households that were unable to repay
debt and/ or service obligations according to contractual agreements. To paraphrase, the
questions ask of the household, “How many years between 1991 and 1996 did you find
yourself unable to pay bills on time.” Responses fell within the range of zero to six years.
Households that answered four years or more also earned an indicator variable value of
one. In all likelihood, the PSID bankruptcy measurements understate the nature of
constraints in the broader pool. Carroll (2001) points out that the PSID exhibits
bankruptcy frequency about half that of the national average.
Moving forward, we want to construct a “constrained” variable that incorporates
households with experience in bankruptcy filings and/ or being unable to pay bills on
time for four out of six years – with the latter referred to as “financially distressed”. Table
3.5 presents the tabulation of observations according to bankruptcy experience and
financial distress. The three unshaded cells represent the number of observations that
have experienced bankruptcy and/or financial distress during the period including 1991 to
1996.
15
Further accentuating the differences between the constrained and unconstrained
grouping, we levy an additional intuitive imposition against all households. Namely, we
want to take the results of table 3.5 and identify which households face current period
liquidity issues while exhibiting a bankruptcy or episode of financial distress in their past.
Accordingly, a restriction is place upon the results of Table 3.5 such that only households
with net worth less than $4,817 (the 20th percentile of the wealth distribution) during a
specific wave will populate Table 3.6. For Table 3.6, the unshaded areas represent the
observations have net worth less than $4,817 while having either experienced a
bankruptcy or an episode of financial distress. The main point of Table 3.6 is to expose
the 1,810 observations that do not have a bankruptcy under their belt but do have an
episode of financial distress in their past coupled with a current period net worth of less
than $4,817.
16
The observations in the unshaded areas of Table 3.7 represent the “Constrained”
pool of observations and will be central to testing hypotheses A & B. Table 3.7 identifies
that 5.5% of all observations have a bankruptcy flag and 8.5% of all observations fall into
the category of financially distressed but not exhibiting a bankruptcy flag. In all, 14.0%
of all observations fall into the “constrained” pool.
17
Finally, Table 3.8 displays the number of constrained households across panel
years 1999 to 2009. A steady number of households ranging from 480 to 518 households
per year span the panel.
3.6. Income Measures
The income data are comprised of several components referred to as permanent,
transitory and inheritance. First, permanent income is represented with predictable hourly
and salaried compensation along with fixed transfer payments such as social security or
long-term disability. Second, transitory income is comprised of items such as overtime,
bonuses, and tips. Finally, inheritance income makes its own category. All income data
are represented in the PSID as net after tax household income for all members of the
household. Table 3.9 presents the raw and log transforms of the survey data. Pertinent to
our model is the net income measures that represent the household income from which
we derive our income estimation process.
18
19
CHAPTER 4
METHODOLOGY AND MODEL
This chapter explores two related hypotheses and the model employed to test
them. Specifically, in the context of three separate restrictions, hypotheses A and B
investigate the presence of household liquidity constraints and savings response
symmetry by observing the household’s savings response to unexpected budgetary
variances.
First, we test the household’s response to budgetary variances otherwise referred
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
to as forecast error or 𝑦𝑖,𝑡
with the assumption that a symmetrical response exists.
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
Here, the idea is that whether 𝑦𝑖,𝑡
is positive or negative matters not to the
magnitude of the estimated coefficient. In other words, we assume a one-dollar shock to
catalyze an equal but opposite reaction regardless of the sign orientation of the shock
itself. For the second restriction, we relax the symmetrical savings assumption and
observe liquidity decisions in the context of positive-only shocks (i.e. good news).
Finally, and again with the symmetrical savings assumption relaxed, the same households
are exposed to a negative-only shock environment (i.e. bad news). While the second and
third restrictions directly reflect the testable hypotheses, we analyze the validity of the
symmetrical savings assumption anecdotally throughout this analysis.
4.1. Hypothesis A
A household will increase liquidity upon experiencing an unexpected positive
shock to income.
20
A positive shock represents unexpected good news for the household in the sense
that for the current period, the household earned more income than previously expected
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
such that 𝑦𝑖,𝑡
is greater than zero. For the unconstrained household, we expect
channeling of positive shocks toward a corresponding increase in the level of liquidity.
This relies on the assumption that unconstrained households are consuming at preferred
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
levels and excess liquidity resulting from a positive 𝑦𝑖,𝑡
is channeled to increase the
level of very liquid assets (VLA), decrease the level of unsecured debt (UD), or increase
the level of stock equities (SE). On the other hand, we expect a liquidity constrained
household to exhibit little relation between current period budgetary variances and
changes in liquidity. Because we presume liquidity constrained households to be
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
consuming at less than preferred levels, a positive 𝑦𝑖,𝑡
will simply enable the
constrained household to move closer to preferred consumption levels. The liquidity level
will increase by the amount of the transitory shock that is in excess of whatever otherwise
would be needed to bring the household to a level of current period, preferred
consumption. In other words, we expect constrained households to exhibit a muted
savings response compared to unconstrained households in the context of a positive
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑦𝑖,𝑡
environment.
Consequently, if a liquidity-constrained household’s liquidity is not increasing in
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
the face of positive 𝑦𝑖,𝑡
, we argue that the constrained household is directing
current period excess liquidity toward increased consumption. This suggests, for
21
liquidity-constrained households, changes in consumption are indeed, related to positive
income shocks.
The case of the unconstrained household is easy enough to identify. This
household, by definition, is at a level of preferred consumption. As such, a positive
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑦𝑖,𝑡
will lead to excess liquidity not channeled toward consumption in the current
period. Instead, we expect these households to transfer current period excess liquidity to
future periods for later consumption. In other words, we expect these households to
increase their level of liquidity in greater proportion to positive shocks when compared to
the constrained household. We expect unconstrained households to exhibit a positive
relationship between changes in liquidity and positive shocks. In contrast, we expect that
the relationship between changes in liquidity and positive income shocks for constrained
households will be insignificant or negative.
4.2. Hypothesis B
A household will decrease liquidity upon experiencing an unexpected negative
shock to income.
A negative shock represents unexpected current period bad news for the
household in the sense that, for the current period, the household earned less income than
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
previously expected such that 𝑦𝑖,𝑡
is less than zero. For the unconstrained
household, we expect channeling of negative shocks toward a corresponding decrease in
the level of liquidity. This reflects the unconstrained household’s sufficient capacity to
offset negative shocks through dissaving as a means of maintaining a constant level of
22
preferred consumption. Conversely, we expect a constrained household to exhibit no
relation between current period negative shocks and changes in liquidity. By definition, a
liquidity constrained household at time t possesses minimal liquid assets relative to the
unconstrained household. Additionally, we assume liquidity constrained households lack
access to new or increased levels of unsecured debt1. Accordingly, we cannot assume the
possibility of easily addressing a negative shock in a manner similar to that of the
unconstrained household. This suggests that changes in liquidity for a constrained
household should not be sensitive to “bad news” because an increase in unsecured debt or
dissaving otherwise cannot occur in the face of the negative income shock.
To the point, if a liquidity-constrained household’s liquidity is not changing in the
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
face of a negative 𝑦𝑖,𝑡
, we argue that liquidity constraints may indeed be present and
the assumption regarding limited access to the unsecured debt channel is valid. For
constrained households, this suggests given the available resources, dissaving wealth
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
cannot adequately smooth a current period negative 𝑦𝑖,𝑡
. Should the levels of
liquidity for a constrained household actually decrease when exposed to a
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
negative 𝑦𝑖,𝑡
, we deemed invalid the assumption regarding limited access to the
unsecured debt channels for presumably constrained households.
All noted, it is expected that liquidity constrained households will not exhibit a
statistically significant relationship between changes in liquidity and negative shocks.
Although, a statistically significant negative estimate would suggest the constrained
1
If these constrained households indeed have adequate access to unsecured debt markets, then by
definition these households would no longer be liquidity constrained and this assumption would be invalid;
suggesting liquidity constraints may not be an issue after all.
23
household does exhibit a muted response relative to the unconstrained household.
Meanwhile, we expect the unconstrained household to exhibit a positive relationship
between changes in liquidity and negative shocks.
4.3. Overview of Reduced Form
We analyze panel data through a two stage least squares model incorporating state
and time fixed effects. Four primary components uniquely identify this model with
elaboration forthcoming.

Component 1 – Dependent Variable: Calculated first differences in raw and
logarithmic levels of very liquid assets (VLA), stock equities (SE), and unsecured
debt (UD) serve as the dependent variable.

Component 2 – Sample Splitting: Splitting the pool of households according to
net worth and past degrees of financial distress make possible, inferences
regarding liquidity constraints

Component 3 – Shock Instrument: We utilize a first stage least squares process to
estimate unexpected current period variations to income – henceforth referred to
as income residuals.

𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
Component 4 – Primary Model: Differenced estimators of the 𝑦𝑖,𝑡
measure
interacted with the constrained indicator will test hypothesis A, and hypothesis B.
4.4. Component 1: Elements of the Dependent Variable
The model’s dependent variable is referred to as liquidity and is comprised of
very liquid assets, unsecured debt, and stock equities. Very liquid assets include accounts
24
such as checking, savings, bonds, certificates of deposit, and treasury bills. Measurement
of cash in a coffee can, under the mattress, or in an envelope in the freezer occurs by
asking if the household has any cash holding other than the accounts previously
identified. Unsecured debt includes balances on credit cards, payday loans, student loans,
and legal/medical bills2. Stock equities are investment accounts that are not associated
with pensions or employer-based 401k savings plans.
We utilize two measures of liquidity in analysis of the data. First, a raw dollar
linear specification additively combines VLA, UD, and SE creating a current period
measure of liquidity. Recall the positive coding of the UD variable. Accordingly, we
define liquidity at time t (𝐿𝑖,𝑡 ) as VLA + SE – UD. On the level, the liquidity balance
informs very little. For example, hypothetical household A, with a respective $100,000,
$50,000, and $150,000 in VLA, SE, and UD appears to be identical to hypothetical
household B with $0 in VLA, SE, and UD – both exhibiting liquid balances of $0.
Ultimately, established savings and access to unsecured credit markets drive liquidity
decisions of both households. In this case, household A may have access to a credit card
with a $50,000 limit while household B may have access to a $3,000 credit card if it has
established credit. To extract information regarding the household’s liquidity decisions,
level values of 𝐿𝑖,𝑡 are differenced to better express liquidity balances in the context of
individual level characteristics such as access to additional liquidity through credit
markets. By differencing, the panel nature of the model allows us to effectively subtract
2
The PSID reports household unsecured debt as an inseparable basket of measures including
credit card charges, payday loans, student loans, and medical/legal bills.
25
out, without having to measure, individual characteristics that do not change over time
such as a strong aversion to borrowing. This leaves the model free to measure the extent
to which households that want to increase debt can increase debt so long as they are not
precluded from doing so – the extent of which is identified by the constrained indicator
that will be discussed later.
Second, we utilize a logarithmic specification to analyze liquidity decisions. For
our dependent variable, a best-case scenario would allow us to transform 𝐿𝑖,𝑡 to natural
log form and move on to estimation. However, the 𝐿𝑖,𝑡 variable can take on negative and
even zero values that make it impossible to transform 𝐿𝑖,𝑡 into the natural log of
liquidity 𝑙𝑛(𝐿𝑖,𝑡 ). The remedy to this situation involves extracting the UD element of 𝐿𝑖,𝑡 ,
leaving us with VLA + SE, which we can additively combine prior to taking the natural
log. In this case, the natural log of UD will be differenced and play a role as an
explanatory variable.
4.5. Component 2: Sample Splitting
Hypotheses A & B seek to compare the liquidity decisions of constrained and
unconstrained households in the context of positive and negative shocks to current period
income variances from previously estimated expectations. To make this comparison, the
surveyed households are distilled into two pools using measures unique to the household
– the first being a measure of net worth and the second being a binary indicator flagging
previous episodes of financial distress. For a survey wave, households with low net
worth and a history of financial distress are assumed to be constrained.
26
4.5.1. Net Worth
The Panel Survey of Income Dynamics (PSID) directly measures household net
worth. For splitting our sample, we establish an arbitrary benchmark at the 20th wealth
percentile as a means of identifying households likely constrained due to low asset levels.
Adjusting to real 1997 dollars, the benchmark computes to $4,817. This includes
measures of assets and liabilities for all households across all biennial waves beginning in
1999 and ending in 2009 and works out to the 20th percentile of the net worth
distribution. Because we hold this benchmark static, households with low net worth
during one wave can migrate above the benchmark for subsequent waves.
4.5.2 Financial Distress
For the purpose of this analysis, financial distress comes in two forms with the
first form being inability to pay unsecured debt obligations or household bills in a timely
fashion. Repayment history affects credit score that in turn affects the household’s ability
to establish new lines of unsecured credit. Specifically, households will face various
degrees of financial autarchy subsequent to periods in which out-of-contract payment
history catalyzed the reporting of derogatory credit remarks assigned to a household’s
credit report. The second form reflects limited access to credit markets subsequent to a
bankruptcy filing. Flagging both forms of distress is possible because the 1996 wave of
the PSID features a set of questions that invoke self-revealed instances of households
with bankruptcy filings in their past. Additionally, households self-reveal if they were
unable to pay creditors on time during period 1991 to 1996.
27
Extend an assumption for households that declared bankruptcy and were unable to
pay creditors on time during the period 1991 to 1996; these households are assumed
likely to continue with various degrees of financial distress through all waves.
Additionally, we assume households identified as having low asset levels or as being
financially distressed as liquidity constrained. Ultimately, the pool of liquidity
constrained households are expected to exhibit different characteristics regarding
liquidity decisions made in the context of positive and negative variations to income. A
downside does exist within our sample splitting technique. Namely, the PSID line of
questioning regarding financial distress and bankruptcy does not crop up again for any
waves subsequent to 1996. If the once-unconstrained household experiences financial
distress, they will enter the constrained pool undetected by this model. This will lead to a
convergence of the results between constrained and unconstrained households. The
implication is that this convergence will lead to an underestimation of the coefficients
associated with the constrained pool of households. As such, in a worst-case scenario,
both pools will appear similar enough to render the sample splitting technique
inadequate, but given data constraints, it is our best estimate.
4.6. Component 3: Income Residual Instrument
A “shock” variable is created to instrument for income fluctuations across time.
This shock variable is comprised of an income component – derived according to an
estimation process that calculates the residual that represents the difference between the
actual income measurement at time t and the predicted value according to a line of best fit
for the entire sample.
28
The process modeling income forecast error is employed such that total household
income at time t (𝑦𝑖,𝑡 ) is regressed against three lags of itself and demographic controls
( Γ𝑖,𝑡 ) known to the household at time t – 2 (𝑖. 𝑒 𝑦𝑖,𝑡−2 , 𝑦𝑖,𝑡−4 , 𝑦𝑖,𝑡−6 , and Γ𝑖,𝑡−2 ). Equation
1 identifies the income forecast error estimation process (1).
𝑦𝑖,𝑡 = 𝛽𝑗,𝑘 𝑦𝑖,𝑡−2𝑘 + 𝛽𝑞 Γ𝑖,𝑡−2 + 𝛽𝜏 + 𝛽𝛼,𝑡−2 + 𝑒𝑖,𝑡 ; 𝑘 = 1, 2, 3, 4 (1)
State and year fixed effects are accounted for such that 𝛽𝛼,𝑡−2 identifies the state
of residency (𝛼) at time t – 2 while 𝛽𝜏 identifies specific wave years. Residuals for both
linear and logarithmic dependent variables are predicted from the 𝑘 = 1, 2, 3, 4 model
presented with (1). The linear residual is defined as the difference between actual income
at time t and predicted income from the estimation process (2). Equation (3) defines the
log-specified residual.
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑎𝑐𝑡𝑢𝑎𝑙
𝑦𝑖,𝑡
= 𝑦𝑖,𝑡
− 𝑦̂𝑖,𝑡
(2)
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑎𝑐𝑡𝑢𝑎𝑙
𝑙𝑛𝑦𝑖,𝑡
= 𝑙𝑛𝑦𝑖,𝑡
− 𝑙𝑛𝑦̂𝑖,𝑡
(3)
In practical terms, 𝑦̂𝑖,𝑡 represents the households budgeted income at future time t;
predicted at time t – 2 with information available to the households at time t – 2.
4.7. Component 4: Primary Model for Hypotheses Testing
4.7.1 Linear-Specified
Equation (8) represents the general regression model employed by our analysis.
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
∆𝐿𝑖,𝑡 = 𝛽𝑗,𝑘 𝑦𝑖,𝑡−2𝑘
+ 𝛽𝑙,𝑘 𝑦𝑖,𝑡−2𝑘
𝑿𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡−2𝑘 + 𝛽𝑚,𝑘 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡−2𝑘
+ 𝛽𝑝 Θ𝑖,𝑡 + 𝛽𝜏 + 𝛽𝛼,𝑡−2 + 𝑒𝑖,𝑡 ; 𝑘 = 0, 1, 2
(8)
29
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
We represent the derivative explanatory variable 𝑦𝑖,𝑡
by itself along with
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
several biennially lagged measurements. Additionally, 𝑦𝑖,𝑡
and pertinent lags are
interacted with a constrained indicator of time t – 2k where k signifies a specific panel
wave. The control matrix Θ𝑖,𝑡 consists of measures including the common demographics
contained in the income matrices and Γ𝑖,𝑡 . Also incorporated are indicators that account
for the birth of a child and home refinance events. Table 4.1 summarizes the components
of the three control matrices mentioned thus far as well as a fourth matrix yet presented.
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
In the context of the 𝑦𝑖,𝑡
variable, hypotheses A & B suggest positively
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
correlated changes in liquidity with the 𝑦𝑖,𝑡
variable from (3). A leading question is
whether the expression of the estimated effect of the income residual is symmetrical
regarding changes in the liquidity measure. In the context of the linear dollar model, a
perfectly symmetrical relationship suggests a one-unit increase in the residual will be
associated with an equivalent increase in liquidity for both positive and negative shocks.
For positive shocks, one-for-one means complete saving of the excess shock. For
negative shocks, one-for-one means completely absorbing the negative income shock by
a one-for-one dissaving of assets or accumulation of unsecured debt.
With this discussion in hand we propose to test (8) under three assumptions. First,
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
symmetrical response will be assumed, so the orientation of the 𝑦𝑖,𝑡
will not be
restricted. To test hypothesis A, the symmetric response assumption is relaxed and
replace with a positive-only shock restriction. Likewise, hypothesis B imposes a
negative-only shock orientation.
30
4.7.2. Log-Specified
The previously discussed linearly specified general regression model forces all
households, regardless of wealth dynamics, to adopt a constant savings profile, which
may not be a valid assumption. For robustness of interpretation, exploring the
relationship between liquidity decisions and budget fluctuations in terms of logarithmic
specification is prudent with the goal being to estimate household decisions in terms of
elasticities. Equation (9) identifies the log specified model.
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
∆𝑙𝑛𝐿𝑉𝐿𝐴+𝑆𝐸
= 𝛽𝑗,𝑘 𝑙𝑛𝑦𝑖,𝑡−2𝑘
+ 𝛽𝑙,𝑘 𝑙𝑛𝑦𝑖,𝑡−2𝑘
𝑿𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡−2𝑘
𝑖,𝑡
+ 𝛽𝑚,𝑘 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡−2𝑘 + 𝛽𝑝 Π𝑖,𝑡 + 𝛽𝜏 + 𝛽𝛼,𝑡−2 + 𝑒𝑖,𝑡 ; 𝑘
= 0, 1, 2
(9)
A fundamental difference between the linear and logarithmic specification exists.
Specifically, there is no way to interpret, with economic sense, combinations of VLA,
SE, and UD as a single dependent variable. To deal with this, we pull UD out of the
dependent variable and move it to the explanatory side of the equation – taking its place
in the Π𝑖,𝑡 matrix unique to (9).
4.8. Interpretation of Coefficients
We state the hypotheses in a manner that relates the orientation of the
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑦𝑖,𝑡−2𝑘
variable to changes in liquidity. Because we utilize lagged estimators of
residual
residual
residual
residual
residual
yi,t−2k
in the form of βj,0 yi,t
, βj,1 yi,t−2
, βj,2 yi,t−4
, and βj,3 yi,t−6
, it is
acceptable to sum any statistically significant 𝛽𝑗,𝑘 coefficients to present as a net effect of
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑦𝑖,𝑡
on the dependent ∆𝐿𝑖,𝑡 variable (13).
31
𝜕Δ𝐿𝑖,𝑡
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝜕𝑦𝑖,𝑡
= (𝛽𝑗,1 + 𝛽𝑗,2 + ⋯ + 𝛽𝑗,𝑘 )
(13)
The ultimate interpretation of the coefficients depends upon the specification of
the model. The linear model dictates we read (𝛽𝑗,1 + 𝛽𝑗,2 + ⋯ + 𝛽𝑗,𝑘 ) as the number of
cents the Δ𝐿𝑖,𝑡 measure increases per shock-dollar. Here “shock-dollar” reflects a one
dollar forecast error from the sum of the predicted income residuals. The log-specified
model, on the other hand, yields coefficients interpreted as elasticities such that a change
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
of one percent in 𝑦𝑖,𝑡
leads to a net (𝛽𝑗,1 + 𝛽𝑗,2 + ⋯ + 𝛽𝑗,𝑘 ) percent change in Δ𝐿𝑖,𝑡 .
32
33
CHAPTER 5
EMPIRICAL ANALYSIS AND FINDINGS
We present analysis of the results in two stages. The first stage involves the
exploration of the endogenous nature of income in the context of characteristics and
experience unique to the individual households over time. The resulting estimations yield
an income forecast error that instruments for biennial unexpected variation. The second
stage applies information contained within the residuals toward analysis of changes in
various combinations of VLA, UD, and SE. This application of residuals along with their
interactions with the constrained pool of households will inform the status of hypotheses
A & B. We present and interpret results in the context of both linear specification and
logarithmic elasticity.
5.1. Income Residual Estimation
The process modeling income forecast error is employed such that net household
income at time t (𝑦𝑖,𝑡 ) is regressed against three lags of itself and demographic controls
( Γ𝑖,𝑡 ) known to the household at time t – 2 (𝑖. 𝑒 𝑦𝑖,𝑡−2 , 𝑦𝑖,𝑡−4 , 𝑦𝑖,𝑡−6 , and Γ𝑖,𝑡−2 ). Equation
(1) identifies the income forecast error estimation process (1). State and year fixed effects
are included such that (𝛽𝛼,𝑡−2 ) identifies the state of residency (𝛼) at time t – 2 while
(𝛽𝜏 ) identifies specific wave years. Moving forward, there are many references to a lag
where k represents the number of lags and specific wave of the PSID. For example, 𝑘 =
1, 2, 3 represents the 2007, 2005, 𝑎𝑛𝑑 2003 wave.
𝑦𝑖,𝑡 = 𝛽𝑗,𝑘 𝑦𝑖,𝑡−2𝑘 + 𝛽𝑞 Γ𝑖,𝑡−2 + 𝛽𝛼,𝑡−2 + 𝛽𝜏 + 𝑒𝑖,𝑡 ; 𝑘 = 1, 2, … , 4 (1)
34
35
Table 5.1 presents the results for equation (1). To boot, the three rightmost
columns of Table 5.1 present the logarithmic specification results equivalent to equation
(1) – in which case, the dependent variable is denoted (𝑦𝑖,𝑡 ). Inspection of the results
suggests the three-lag income estimation model offers a balance of explanatory power
while keeping a relatively large number of observations. This is important because
choosing a lag length to estimate residuals at this point will hamper further analysis as
available observations decrease with each lagged variable due to missing observations or
even the fact that some wealth variables are not present in waves prior to 2003.
Accordingly, we select the 𝑘 = 1, 2, 3 model to estimate the income residuals for the
second stage.
Moving on, the 𝑘 = 1, 2, 3 model presented with (1) predicts the residuals for
both linear and logarithmic dependent variables. Define the residual as the difference
between actual income at time t and predicted income from the equation (1) estimation
process (2) and (3). Ultimately, generated residuals span the 2009, 2007, and 2005 waves.
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑎𝑐𝑡𝑢𝑎𝑙
𝑦𝑖,𝑡
= 𝑦𝑖,𝑡
− 𝑦̂𝑖,𝑡
(2)
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑎𝑐𝑡𝑢𝑎𝑙
𝑙𝑛𝑦𝑖,𝑡
= 𝑙𝑛𝑦𝑖,𝑡
− 𝑙𝑛𝑦̂𝑖,𝑡
(3)
5.2. Hypothesis A & B Restated – Real Dollar Specification
With the creation and analysis of the income residual, we can move on to test
hypotheses A & B. Recall hypotheses A & B as described in the modeling section:
Hypothesis A: A household will increase liquidity upon experiencing an
unexpected positive shock to income.
36
Hypothesis B: A household will decrease liquidity upon experiencing an
unexpected negative shock to income.
A leading question is whether expression of the estimated effect of the income
variable on changes in the liquidity measure is symmetric. A perfectly symmetrical
relationship suggests that a one unit increase in the income residual leads to an equivalent
increase in liquidity for both positive and negative shocks. For positive shocks, one-forone implies completely saving excess shocks. For negative shocks, one-for-one implies
completely absorbing negative shocks by dissaving of assets or unsecured debt
accumulation.
The following analysis will focus on two separate specifications. First, we employ
a strictly linear specification utilizing only raw dollars for dependent and explanatory
income and wealth variables. Second, we present a strictly logarithmic specification
determined to identify elasticities between variables. The two specifications taken
together will inform the robustness of the results.
5.2.1 Dependent Variable – Liquid Assets, Stock Equities, & Unsecured Debt
Equation 4 represents the general regression model employed.
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
∆𝐿𝑝𝑙𝑢𝑠
+ 𝛽𝑙,𝑘 𝑦𝑖,𝑡−2𝑘
𝑋𝑐𝑜𝑛𝑖,𝑡−2𝑘 + 𝛽𝑛,𝑘 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡−2𝑘 + 𝛽𝑖,𝑝 Θ𝑖,𝑡
𝑖,𝑡 = 𝛽𝑗,𝑘 𝑦𝑖,𝑡−2𝑘
+ 𝛽𝛼,𝑡−2𝑘 + 𝛽𝜏 + 𝑒𝑖,𝑡 ; 𝑘 = 0, 1, 2
(4)
The primary explanatory variable is represented by the previously discussed
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
endogenous 𝑦𝑖,𝑡−2𝑘
for various values of k. along with two separately differenced
measurements. In pragmatic terms, imagine a father identifying a current
37
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
period 𝑦𝑖,0
. The father then refers to previous experiences such as
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑦𝑖,𝑡−2
and 𝑦𝑖,𝑡−4
. Now informed with the knowledge of this period’s 𝑦𝑖,𝑡
as
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
well as the previous period’s 𝑦𝑖,𝑡−2𝑘
; the father can proceed to “calculate” the
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
appropriate amount of 𝑦𝑖,𝑡
to channel toward VLA, UD, SE, or consumption. The
control matrix Θ𝑖,𝑡 consists of measures including the common demographics contained
in the income matrix Γ𝑖,𝑡 . Also incorporated are indicators that account for the birth of a
child and home refinance events.
Table 5.2 presents the results of six regressions run under three separate shock
restrictions. Three primary columns organize the six regressions. First, the “No yRESi,t”
column imposes the assumption regarding symmetric savings responses to equal but
opposite values of the shock variable, houses regressions (a) and (b). Second, the
“Hypothesis A (𝑦𝑅𝐸𝑆𝑖,𝑡 > 0)” column relaxes the symmetric savings assumption and
instead imposes a restriction that values of the shock variable be greater than zero,
organizes regressions (c) and (d). Finally, the “Hypothesis B (𝑦𝑅𝐸𝑆𝑖,𝑡 < 0)” column
relaxes the symmetric savings assumption and instead imposes a restriction that values of
the shock variable be less than zero, shows regressions (e) and (f). Ultimately, we are
interested in the summed coefficients unique to the income residual and the interaction
involving the income residual and the constrained binary indicator. Table 5.3 presents
such a summary.
Before interpreting the summarized estimates presented in Table 5.3, we must
point out a few facts regarding the nature of the estimates presented. First, the
38
coefficients are in terms of real 1997 US dollars. Second, the specification of equation 4
presents a linear raw dollar model. Accordingly, all coefficients are linear estimates.
Accordingly, do not construe them as elasticities. A treatment involving elasticities
commences later in this analysis. Table 5.3 is organized in line with Table 5.2 such that
regressions (a) and (b) are labeled under the “No yRESi,t”, regressions (c) and (d) are
presented under the “Hypothesis A (𝑦𝑅𝐸𝑆𝑖,𝑡 > 0)” column, regressions (e) and (f) are
presented under the “Hypothesis B (𝑦𝑅𝐸𝑆𝑖,𝑡 < 0)” column. Columns (a), (c), and (e)
refer to the 𝑘 = 0, 1, 2 identification while columns (b), (d), and (f) refer to the 𝑘 = 0, 1
identification. Joint significance is determined according to the associated p-value
corresponding to the f-statistic testing for joint significance.
39
40
5.2.2 Real Dollar – Unconstrained Pool Estimates
Referring to Table 5.2, the symmetrical assumption regressions (a) and (b) exhibit
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
strong statistical significance for each measure of 𝑦𝑖,𝑡−2𝑘
. In the case of regression (a),
all three measures are significant to the one percent level. With the exception of the 𝑘 =
0 measure of the income residual, the same is true for regression (c) under the positiveonly restriction. This is important to point out because a wildly divergent result appears
in Table 5.3. Namely, the summed effects for the unconstrained pool amount to a jointly
significant value of -0.964 and 2.132 under regressions (d) and (f). This is definitely
counterintuitive at first glance. However, once the (c) and (e) regressions involving the t
– 4 lag of the income residual are incorporated, the (d) and (f) regressions render the t – 4
lag as irrelevant. If anything, this result brings into question the breadth of the data – such
as, is the timeframe of the data sufficient to capture all statistically significant lags of the
income residual. Unfortunately, the nature of the data limits the income residual to the t –
41
4 lag, which leaves us wondering as to what the results would suggest, had a t – 6 lag
been available.
Understanding the 𝑘 = 0, 1, 2 identification likely offers the most pertinent
information regarding the data set, the remainder of this analysis of the raw dollar
specification will focus on the estimates associated with that specification. Referring to
Table 5.3, joint significance cannot be rejected for the estimates associated specifically to
the unconstrained household (i.e. constrained = 0) for regressions (a), (c), and (e). The
positive-only (c), negative-only (e), and symmetric (b) restrictions yield estimates of
0.403, 0.148, and 0.814 respectively. The symmetrical assumption essentially resembles a
weighted average of the positive and negative restriction regressions. Looking at the
summed estimates for the positive and negative restriction regressions, we can perhaps
make a statement that the unconstrained pool does not exhibit symmetrical savings
behavior. Namely, the unconstrained pool appears to increase savings in the face of
positive shocks to a larger extent than dissaving occurs in a negative shock environment.
The summed estimates of regressions (c) and (e) suggest the unconstrained
household is quick to consume positive shocks and has the ability to smooth negative
shocks. This is interesting because we assumed the unconstrained household was
consuming at a preferred level. The fact that the summed estimates suggest the
unconstrained household dissaves 81.4 cents per negative shock-dollar suggest if it
wanted to, the unconstrained household could certainly increase consumption. However,
for whatever reason, this same household only increases liquidity by 14.8 cents per
positive shock-dollar. Where are the other 85.2 cents going? If not under the mattress or
42
some other unmeasured channel, this unaccounted for portion of each positive shockdollar must be going toward increased consumption. Does that mean our presumed
unconstrained household is actually liquidity constrained? A more likely explanation
likely resides in buffer-stock models that suggest households prefer to maintain a set
proportion of VLA to permanent income and only when this ratio exceed an intrinsically
defined level does a household turn and consume what are otherwise income shocks in
excess of expected amounts.
5.2.3. Real Dollar – Constrained Pool Estimates
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
Shifting focus to the interaction term involving 𝑦𝑖,𝑡−2𝑘
and 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡−2𝑘 ,
we observe in Table 5.2 only the t – 2 lag in the negative shock environment exhibits
statistical significance and even that is only at the 10 percent level of significance. As
presented with Table 5.3, across the board in rejection of joint significance, it is not a
surprise. This alone offers enough information to argue that constrained households are
actually not constrained according to our definition at least. It can also mean the
constrained indicator is not necessarily operating as intended. Without bankruptcy data
more recent than 1996, it is difficult to argue one way or the other.
5.3. Hypothesis A & B Restated – Logarithmic Dollar Specification
The real dollar regression model estimates a model of savings that is linear in
income regardless of wealth dynamics. This may not be a valid assumption. For
robustness of interpretation, exploring the relationship between liquidity decisions and
budget fluctuations in terms of logarithmic specification will estimate household
43
decisions in terms of elasticities. As we shift to a logarithmic specification, we briefly
restate the hypotheses prior to presentation of results.
Hypothesis A: A household will increase liquidity upon experiencing an
unexpected positive shock to income.
Hypothesis B: A household will decrease liquidity upon experiencing an
unexpected negative shock to income.
5.3.1. Dependent Variable – Very Liquid Assets & Stock Equities
Equation (9), revisited from the Modeling section, identifies the log specified
model of the change in liquidity.
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
∆𝑙𝑛𝐿𝑉𝐿𝐴+𝑆𝐸
= 𝛽𝑗,𝑘 𝑙𝑛𝑦𝑖,𝑡−2𝑘
+ 𝛽𝑙,𝑘 𝑙𝑛𝑦𝑖,𝑡−2𝑘
𝑿𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡−2𝑘
𝑖,𝑡
+ 𝛽𝑚,𝑘 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡−2𝑘 + 𝛽𝑝 Π𝑖,𝑡 + 𝛽𝜏 + 𝛽𝛼,𝑡−2 + 𝑒𝑖,𝑡 ; 𝑘
= 0, 1, 2
(9)
There are fundamental differences between the linear and logarithmic
specification. First, there is no way to rationally combine VLA, SE, and UD into a single
dependent variable and expect it to describe some sort of economic behavior. To deal
with this, we pull unsecured debt (UD) out of the dependent variable and move it to the
explanatory side of the equation within the Π𝑖,𝑡 matrix unique of (9). Second, log
specification according to equations (1) and (3) derives the primary explanatory variables
involving the income residual.
44
45
Table 5.4 reports the estimated coefficients of the logarithmic specification. This
exhibit is oriented similar to Tables 5.2 and 5.3. Columns are grouped in pairs with (h)
and (i) corresponding to the assumed symmetric environment, columns (j) and (k)
reflecting the positive-only shock environment, and (l) and (m) signifying the negativeonly shock environment. Accordingly, the three regressions labeled (h), (j), and (l) are
identified with 𝑘 = 0, 1, 2 while regressions (i), (k), and (m) fall into the 𝑘 = 0, 1
identification. As we move into interpretation of Table 5.4, we are keeping in mind the
presented coefficients are representative of elasticities – exceptions being indicator
variables such as 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑒𝑑𝑖,𝑡 and 𝐵𝑢𝑠𝑖𝑛𝑒𝑠𝑠𝑂𝑤𝑛𝑖,𝑡 as well as the age of head –
average wealth interaction term.
5.3.3. Log Specified – Unconstrained Pool
Similar to Table 5.2, Table 5.4 allows us to examine the individual lags of
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
𝑙𝑛𝑦𝑖,𝑡−2𝑘
in the context of the three restricted environments. Unlike the linear model,
the logarithmic model shows very little significance with regard to natural log of the
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
residual 𝑙𝑛𝑦𝑖,𝑡−2𝑘
. What we see is statistical significance for the current period income
residual for regressions (h) through (l) with regression (m) yielding statistically
insignificant results. For all regressions, the t – 2 and t – 4 estimators on the income
residual indicate statistically insignificant results. The apparent insignificance of the t – 2
and t – 4 estimators led to the estimation of the 𝑘 = 0 identification for all three
restriction environments. However, the results did not offer any new information on top
of already presented results from the 𝑘 = 0, 1 identification. Also, while the calculated R2
46
for the linear model are not necessarily remarkable, the log-specified R2 appear woeful –
maxing out at 0.13 for the negative-only shock 𝑘 = 0, 1, 2 identification.
Table 5.5 follows the form of Table 5.3 in presenting the summed estimates of
income residual lags and the interaction coefficients for the income residual and
constrained indicator. We observe joint significance for the unconstrained pool with all
three 𝑘 = 0, 1, 2 identifications. Similar to the linear results, the negative shock
environment yields a larger 𝑘 = 0, 1, 2 summed effect relative to the same summed effect
for the positive-only shock environment – 0.649 and 0.863 respectively. We interpret
these summed effects such that in a positive-only shock environment, a one percent
positive shock to the income residual increases liquidity by 0.65 percent. While a
negative-only shock environment exhibits dissaving of 0.86 percent per one percent
decrease in negative shock. Peculiar is the estimate associated with the no shock
restriction 𝑘 = 0, 1, 2 identification. We have come to expect that number to reflect a
47
weighted average of the Hypotheses A & B results. However, in the case of the logspecification, the no restriction estimate comes in at 0.151. Nonetheless, the results as
presented in Table 5.5 offer a similar carte blanche conclusion to that of Table 5.3 – that,
considering individual lag significance, joint significance of all lags, and R2, the 𝑘 =
0, 1, 2 identification offers the best estimates for the effects of income residual on
changes in liquidity.
5.3.4. Log Specified – Constrained Pool – Discussion
Shifting focus to the constrained household, we first examine the estimates for the
income residual interaction term with the unconstrained cohort. We observe not a single
constrained interaction coefficient is statistically significant. Accordingly, it is no surprise
that lags of the income residual interacted with the constrained indicator are not jointly
significant. This suggests, similar to the linear model, that the constrained household
behaves similar to the unconstrained household. However, these results can also be an
indication that the constrained indicator itself is flawed. Alternatively, the apparent
similarity between the unconstrained and so-called constrained households may exist
because the constrained indicator cannot identify households that filed for bankruptcy
subsequent to 1996. Without a more recent measurement similar to the 1996 wave of the
PSID, we must tolerate this feature of the data set.
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CHAPTER 6
CONCLUSION
6.1. Summary of Research and Findings
This thesis tests for the effects of unexpected variations in household income on
measures of household liquidity. In particular, we seek to answer three questions. One, do
liquidity constrained households exhibit a savings response that differs from otherwise
unconstrained households? Two, do liquidity-constrained households exhibit the capacity
to smooth consumption in the context of negative shocks to income? Three, do
unconstrained households exhibit excess sensitivity in the context of positive shocks to
income?
Using longitudinal panel data provided by the University of Michigan’s Panel
Survey of Income Dynamics, we analyze household savings response between the years
2005 and 2009. First, we implement a first-stage income estimation process allowing us
to treat income residuals as endogenous to the liquidity decision. This income estimation
process incorporates income measures spanning the years 1997 to 2009. Second, we split
the pool of households according to net worth and credit history – creating a constrained
and unconstrained pool. Third, we created an interaction term between the endogenous
income residual with the constrained indicator. Fourth, we employed regressions of the
changes in liquidity levels against the income residual, its constrained interaction term,
state and year fixed effects, and a host of demographic controls.
The results answer the three aforementioned questions. First, the constrained pool
of households does not exhibit a statistically different savings response from the
49
unconstrained pool. Specifically, the six linear and six logarithmically specified
regressions yield results that allow us to reject joint significance of the income residual
interaction term. Second, both constrained and unconstrained household exhibit the
capacity to dissave in the context of negative income shocks. Namely, the linearly
specified 𝑘 = 0, 1, 2 model suggests, at the 1% level, a jointly significant dissaving
response occurs to the order of 81.4 cents per negative shock dollar. In addition, the logspecified 𝑘 = 0, 1, 2 model indicates, at the 5% level, a jointly significant dissaving
response occurs to the order of 0.863% per 1% increase in negative shock. Third,
unconstrained households exhibit a statistically significant, but muted savings response to
positive shocks to income when compared to an equal but opposite negative income
shock. For the linearly specified 𝑘 = 0, 1, 2 model, observation identifies, at the 1%
level, the absolute value savings response to be a jointly significant 14.8 and 81.4 cents
per respective positive and negative shock-dollar. Supporting the linear model, we find
for the logarithmically specified 𝑘 = 0, 1, 2 model, observation identifies, at the 5%
level, the absolute value savings response to be a jointly significant 0.649% and 0.863%
per respective positive and negative 1% increase in shock-dollar.
6.2. Caveats to the Analysis
Whether the constrained household exhibits a savings response similar to the
unconstrained household does entail one caveat. Namely, the data does not allow the
model to identify summary shifts in credit history subsequent to 1996. This is certainly
important, as unconstrained households may have experienced bankruptcy or worse
between 1999 and 2009. To boot, the constrained household may have experienced a
50
positive boost in credit remarks during the same timeframe. The effect of these scenarios
forces us to assume the divergence of estimates for the constrained and unconstrained
households is likely understated. As such, while this analysis reports no statistical
difference between the two households; in actuality the analysis may be implying an
understated difference in savings response between the constrained and unconstrained
household.
Future variations of this analysis should entail incorporation of the recently
released 2011 wave of the PSID – released too near the completion of this thesis to
incorporate the data. Also pertinent would be identifying a data set that allows for the
measurement of FICO credit score or debt-to-credit ratio. The presumption being that
some sort of measure interacting the income residual with credit score or debt to credit
ratio will likely have explanatory power over changes in liquidity.
Along the lines of data preference, while the PSID offers robust income and
wealth measures, the frequency of the biennial waves may minimize or average out
affects we are trying to test. An ideal data set would have a higher frequency of
measurement – preferably annually, if not monthly. The final caveat pertains to the debt
basket itself. Namely, the PSID’s debt basket is an inseparable measure of unsecured
debt, student loans, payday loans, and medical & legal bills. Ideally, having the debt
bundle broken down into specific granular components would enable a narrower analysis
of a household’s ability to access the unsecured debt channel.
As of yet, the data requirements these caveats evoke have not been met by a
publically accessible source. However, while public data sets of this nature are not
51
necessarily available, private sector financial firms certainly have access to banks of data
that fit the bill. Albeit, these firms likely lack the demographic controls available within
the PSID. In all likelihood, the perfect data set would integrate measurements from
several sources of public, private, and governmental habitat.
52
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