To What Extent do Labor Market Outcomes respond to UI Extensions?

Master Thesis Presented to the

Department of Economics at the

Rheinische Friedrich-Wilhelms-Universität Bonn

In Partial Fulfillment of the Requirements for the Degree of

Master of Science (M.Sc.)

Supervisor: Prof. Donghai Zhang

Submitted in December 2020 by:

Aiwei Huang

Matriculation Number: 3062063

To What Extent do Labor Market Outcomes
respond to UI Extensions?

Aiwei Huang

Abstract Unemployment benefits in the US were extended by up to 73 weeks
during the Great Recession. Equilibrium labor market theory indicates that
extensions of benefit duration impact not only search decisions by job seekers
but also job vacancy creations by employers. Most of the literature focused on
the former to show partial equilibrium effect that increment of unemployment
benefits discourage job search and lead to a rise in unemployment. To study
the total effect of UI benefit extensions on unemployment, I follow border
county identification strategy, take advantage of quasi-differenced
specification to control for changes in future benefit policies, apply
interactive fixed effects model to deal with unobserved shocks so as to obtain
unbiased and consistent estimation. I find that benefit extensions have a
statistically significant positive effect on unemployment, which is consistent
with the results of prevailing literature.

Keywords: Unemployment benefits, Border county identification,
UI Benefit extensions, Quasi-differenced specification,
Interactive fixed effects

###### Contents

  1. 1 Introduction
  2. 2 Background and Empirical Methodology
    1. 2.1 Development of UI Benefit Extensions
    2. 2.2 Problems of Endogeneity and Serial Correlation
    3. 2.3 HKMM’s Methodology: Difference between Quasi-Difference of  Each County in a Pair
  3. 3 Data
    1. 3.1 Quarterly unemployment rate
    2. 3.2 County average weekly wages within a quarter
    3. 3.3 Quarterly otal separation rate in the U.S.
    4. 3.4 List of border county pairs
    5. 3.5 Quarterly maximum benefit duration
    6. 3.6 Quarterly state GDP per worker
    7. 3.7 Distance from county population center to shared boundary of border counties in a pair
  4. 4 UI Benefit Durations and Unemployment
    1. 4.1 Empirical Results
    2. 4.2 Testing for Endogeneity
    3. 4.3 Extending Baseline Specification by Controlling for Distance between Population Center and Shared Boundary
  5. 5 Conclusion
  6. A Tables
  7. B Figures

##  1 Introduction

The unemployment rate increased dramatically soon after the United States fell
into the recession in December 2007. An unprecedented extension of
Unemployment Insurance (UI) benefit duration, allowing the eligible unemployed
to receive up to 99 weeks of benefits, was unveiled as the policy response to
the financial crisis. The intention of this policy was to support those
struggling to find a job as well as to create faster economic and job growth.
However, the policy remains controversial and the total effect of UI benefit
extension is ambiguous as it impacts labor markets through multitudinous labor
supply and demand channels so that the labor demand could either reinforce or
offset the labor supply. Discussions around the effectiveness of this policy
response appear to never end.

The objective in this paper is to measure the impact of unemployment benefits
on unemployment in the U.S. with a straight-forward model rather than to adopt
the fully specified ones. I use quarterly maximum benefit duration to
represent unemployment benefits and county quarterly unemployment rate to
measure unemployment level. I mainly follow the paper [Hagedorn et al.,
2013](henceforth HKMM) in which addressed the same the same research
direction. As the regression dataset of HKMM has not been published, in
addition, I do not have access to the Help Wanted OnLine (HWOL) datasets
provided by The Conference Board (TCB) and administrative data, I only
replicate the baseline model and baseline inclusive of state GDP per worker
with my own dataset. Furthermore, I raise a concern on potential endogeneity
problem caused by discontinuous economic conditions such as productivity at
state border, that was not fully explored by HKMM. In order to deal with the
endogeneity, I draw from the Regression Discontinuity (henceforth RD) approach
of [Dieterle et al., 2020], in which the nearest distance between county
geographic population center and state boundary is treated as a continuous
variable to approximate economic conditions and the empirical results point
out that the coefficient magnitude of benefit duration would change
dramatically after controlling for distance. In my experiment, I slightly
modify the calculation of distance to fit HKMM’s border county pair
identification and extend HKMM’s baseline model by including distance as
regressor.

Applying HKMM’s specification to my dataset, I got similar results on both
baseline model and state GDP per worker inclusive model. Namely, a $1\%$ rise
in benefit duration for a quarter leads to 0.052 log points increase in
unemployment rate in the short run. Besides, the ceofficient magnitude of
benefit duration do not have a significant change when controlling for
distance, and the coefficient of distance is statistically insignificant.

The principal contributions of this thesis include the following aspects.
Firstly, as HKMM’s work is not yet published and thus the replication files
are not available, I replicated HKMM’s methodology and verified theirs
findings with my own results. Secondly, I collected raw data from various
sources and manipulated them into cleaned dataset used for regressions. This
dataset might be useful for future research. Thirdly, I raised an additional
concern about endogeneity that was not addressed by HKMM. Then I extended the
baseline specification with inspiration drew from RD approach, although the
empirical result do not alter HKMM’s findings.

A large number of prior works focus only on the partial effects of
unemployment benefit extensions on labor supply. The UI benefit extensions
were found to have a statistically significant negative effect on weeks of
employment [Solon, 1979]. The unemployed were more likely to review their
eligibility intensively to ensure that they meet the eligibility requirements
instead of being ready to work. The effect of UI system on the unemployment
spells was investigated by [Moffitt, 1985]. Results suggested that the
extension of UI benefit duration lead to longer spells. In the paper of
[Meyer, 1988] and [Katz and Meyer, 1990], the probability of leaving
unemployment was studied. Higher benefits were found to lower the probability
of leaving unemployment, but this probability rises rapidly when reaching the
exhaustion of benefits. [Rothstein, 2011] addressed the negative effects that
UI extensions lower the probability of exit unemployment are much smaller than
previous analyses and these effects are concentrated among long-term
unemployment. More than a half of the effect is attributed to reduced labor
force exit among unemployed rather than to the changes in reemployment.
Besides responses on supply side, extending UI benefits could meanwhile have
many onther effects. [Feldstein, 1978] was probably the pioneer to call for
the analysis of impact of policies on equilibrium market level. Using data
from the large job board CareerBuilder.com, [Marinescu, 2017] confirmed that
job seekers face reduced competition for jobs and no robust effect on vacancy
creation when increasing benefit duration. Positive effects of UI extension on
unemployment were ruled out by [Coglianese, 2015] due to the point estimates
of the impact of UI extension raises employment growth. A limited influence
that increase in benefit durations cause state-level unemployment rates rise
slightly was found by [Chodorow-Reich and Karabarbounis, 2016]. [Boone et al.,
2016] found no statistically significant impact of increasing UI generosity on
employment unless comparing adjacent counties located in neighbouring states.
By developing the quasi-differenced specification, [Hagedorn et al., 2013] and
[Hagedorn et al., 2016] suggested that benefit extensions cause increment in
equilibrium wages, which followed by a sharp contraction in vacancy creation
and a rise in unemployment. [Lalive et al., 2015] provided evidence that UI
generosity creates market externalities. Non-eligible workers in Austria have
higher job finding rate, shorter unemployment spells and lower risk of long-
term unemployment. In contrast to studies labor market responses to benefit
extensions, [Johnston and Mas, 2018] applied a regression discontinuity design
to approximate the change in unemployment rate following benefit cut. [Krause
and Uhlig, 2012] revealed a large reduction in unemployment and its duration
after the push of Hartz IV Reform in Germany. The economy in Germany rebounded
to the pre-crisis level quickly without obvious fluctuation of unemployment
rate and even emerged reports of shortage of skilled labor. The equilibrium
search framework composed by [Mortensen and Pissarides, 1994] with structural
models emphasizes that the response of unemployment to changes in benefits is
mainly depended on employers’ decisions of whether an how many jobs to create,
and not on job search and acceptance decisions.

The remainder of this paper is structured as follows. Section 2 introduces the
main UI benefits programs in the U.S. briefly. Lists 2 potential problems,
namely endogeneity and serial correlation, when we investigate the impacts of
benefit extension on unemployment. discusses border county pair
identification, quasi-difference and interactive fixed effects used in HKMM’s
methodology. Section 3 lists a set of data and their sources and describes the
calculation of county-level population weighted mean distance. Section 4
analyses the empirical results corresponding to different methods, namely
Pooled OLS, Fixed Effects and HKMM’s baseline specification, controlling for
different variables. Explains the endogeneity porblem caused by discontinuous
economic conditions and shows the ideal of endogeneity test. Tells the
inspiration draw from RD approach, then Includes distance as regressor to
construct extended specification. Section 5 presents the conclusion.

##  2 Background and Empirical Methodology

###  2.1 Development of UI Benefit Extensions

In the absence of any extensions, UI benefits in most states in the U.S. were
available for at most 26 weeks. The 2007-2009 recession brought a series of UI
benefit extensions that were unprecedented in the postwar era and exerted a
profound influence on the labor market. The federal government in the U.S. has
stepped in to provide support for unemployed workers in every recession since
1957. Unemployment benefits have been extended in states experiencing high
unemployment via Extended Benefit (EB) program since 1970. EB program is a
joint federal-state program with Federal government paying one-half of the
cost when state unemployment rates hit specific thresholds. In 2009, the
federal government provided full funding that encouraged many states to
participate the EB program. The US Congress created the Emergency Unemployment
Compensation (EUC) program to aid the unemployed to cope with the harder time
during the downturn in June 2008. Icipiently, EUC provided an additional 13
weeks of federally financed compensation to eligible individuals who exhausted
their UI benefits in all of the states. As the condition became worser,
Congress extended the program in February 2009. EUC program offered maximum 4
tiers as long as individuals remain jobless and continuing searching jobs. The
first two tiers provided a combined 34 weeks of coverage were available in all
states. The rest two tiers, adding up to 19 weeks, are available based on
state unemployment rates. Consequently, EB and EUC programs led to an
extension of UI benefit duration from 26 to at most 99 weeks. In 2012, EB
program began to phase out and EUC program was terminated at the end of 2013
since Congress refused to reauthorize.

###  2.2 Problems of Endogeneity and Serial Correlation

A number of related literature study the total effect of UI benefit extensions
by regressing state labor market variables directly on different UI
regimes.This method seems to be straightforward, but in fact problematic, due
to the endogeneity derived from it.The UI benefit extensions are triggered by
state unemployment rate resulting from nagative economic shocks,
simultaneously, these extensions are correlated with adverse labor market
conditions of the same shocks. If we attribute state-level deteriorated labor
market conditions to benefit extensions instead of those shocks, endogeneity
problem will arise and thus the estimated magnitude of UI effects will be
biased.

The classic equilibrium search framework reveals that in response of changes
in benefit, the determination of unemployment is employers’ job creation
decision. The logic behind the framework is simply: extending unemployment
benefits arouses an upward pressure on the equilibrium wage, so that lowers
the profit employers received, thus lead to a cut in vacancy creation and
finally results in an increase in unemployment. Once the state unemployment
rate exceeds certain threshold, a more generous UI program will be triggered
and thus results in a higher unemployment rate. Therefore both benefit
duration and unemployment rate will suffer from serial correlation, namely,
benefit policy and unemployment in period $t+1$ would correlate with benefit
policy and unemployment in period $t$ respectively.

###  2.3 HKMM’s Methodology: Difference between Quasi-Difference of
Each County in a Pair

HKMM provided a solution to fix the problems caused by endogeneity and serial
correlation through synthetical utilization of the Border Couty Pair
identification, Quasi-Difference approach and Interactive Fixed Effects.

The deducing process of HKMM’s specification begins with the value of a filled
job that the firms concern much about. The value of a filled job is:

(1) $J_{t}=\pi_{t}+\beta(1-s_{t})E_{t}J_{t+1},$

where $\pi_{t}$ is the profits from job in period t, $\beta$ is the discount
factor, $s_{t}$ is the probability that the job ends, also known as separation
rate and $E_{t}$ is the expectation operator using information available at
time t. The equation reads in logs as:

(2)
$\log(J_{t})=\frac{\pi}{J}\log(\pi_{t})+\beta(1-s_{t})E_{t}\log(J_{t+1})+\tilde{\eta}_{t},$

where $\pi$ and $J$ are steady-state values, with
$\pi=J(1-\beta(1-s))$.Employers consider to create job vacancies when the
value of a filled job is no less than the expected cost of posting a vacancy,
which implies the free entry condition as:

(3) $q(\theta_{t})J_{t}=c,$

$\theta_{t}$ is labor market tightness at time t, a typical measure of
$\theta$ is the ratio $v/u$, where $v$ is the number of vacancies posted in
the labor market and $u$ is the number of unemployed. $q(\theta_{t})$ is the
probability to fill a job and $c$ is the cost of maintaining a vacancy.
Equation (3) can also be approximated as:

(4) $\log(\theta_{t})=\tilde{\kappa}\log(J_{t}).$

Plugging equation (2) into (3), yields:

(5)
$\log(\theta_{t})=\tilde{\kappa}\frac{\pi}{J}\log(\pi_{t})+\tilde{\kappa}\beta(1-s_{t})\log(J_{t+1})+\log(\eta_{t}).$

Rearranging equation (5) with $\pi/J=(1-\beta(1-s))$ and
$\log(\theta_{t+1})=\tilde{\kappa}\log(J_{t+1})$, we can get:

(6)
$\log(\theta_{t})=\tilde{\kappa}(1-\beta(1-s))\log(\pi_{t})+\beta(1-s_{t})\log(\theta_{t+1})+\log(\eta_{t}).$

As shown in [Hall, 2005] and [Shimer, 2012], quarterly unemployment can be
well approximated by a linear function of $\log(\theta)$. HKMM also verified
this approximation and found it performs well in a calibrated equilibrium
search model with UI extensions. The linear approximation is written as:

(7) $\log(u_{t})=\lambda_{u}\log(\theta_{t}).$

HKMM defined the quasi-difference as:

(8)
$\begin{split}\tilde{u}_{t}&\coloneqq\log(u_{t})-\beta(1-s_{t})\log(u_{t+1})\\\
&\>=\tilde{\kappa}\lambda_{u}(1-\beta(1-s))\log(\pi_{t})+\lambda_{u}\log(\eta_{t}).\end{split}$

In the model of [Pissarides, 2000], firms’ profits from employing a worker is
given by the difference between worker’s marginal product and the wage. As
previous discussion, the wage is affected by the generosity of UI benefits.
Therefore, the log-linear approximation can be expressed as:

(9) $\log(\pi_{t})=\gamma_{z}\log(z_{t})-\gamma_{b}\log(b_{t}),$

where $z_{t}$ is workers’ productivity, $b_{t}$ are unemployment benefits.
Substituteing equation (9) into (8) and differencing between border counties
within pair denoted by $p$, then gets:

(10) $\Delta\tilde{u}_{p,t}=\alpha\Delta b_{p,t}+\Delta\epsilon_{p,t},$

here $\Delta$ is the difference operator,
$\Delta\tilde{u}_{p,t}=\tilde{u}_{p,i,t}-\tilde{u}_{p,j,t}$, $\Delta
b_{p,t}=\log(b_{p,i,t})-\log(b_{p,j,t})$ and the coefficient of interest
$\alpha=-\gamma_{b}\lambda_{u}\tilde{\kappa}(1-\beta(1-s))$.
The effect of extending benefit duration from $w_{1}$ to $w_{2}$ weeks for $n$
time periods is:

(11)
$\hat{\alpha}\times\frac{1-(\beta(1-s))^{n}}{1-\beta(1-s)}\times(\log(w_{2})-\log(w_{1})).$

The Border County Pair identification is proposed to overcome the endogeneity
problem. This identification strategy is widely used and the works of [Holmes,
1998], [Dube et al., 2010]and [Dube et al., 2016] are typically influential
among others. In our case, the identification concentrates on contiguous
county $i$ and county $j$ that located in adjacent state borders. After
differencing the quasi-differenced log unemployment, the contemporaneous
shocks, affecting both counties in a pair and causing endogeneity problem, are
eliminated.

It is still difficult for labor market entities to fully respond to future
changes in benefit policy, let alone having perfect foresight of expected
policy changes before the occurrence of actual policy changes. Therefore, only
under the circumstance that expectation are known or controlled for, the
relationship between contanporaneous changes in benefit duration and
unemployment is informative of the true impact of UI policies. Suppose that
raising benefit level leads to a rise in unemployment and increasing benefits
today is more likely to cause further benefit extensions in the future. It is
of great concern that the coefficient $\alpha$ is biased if we just simply
regress $u_{p,t}$ on $b_{p,t}$ instead of applying quasi-difference method,
because the serial correlation still remains. The expectation controlling
mechanism of HKMM’s estimation strategy is realized through quasi-difference.
The market tightness $\theta_{t}$ depends on $J_{t}$ and thus on the whole
sequence of future benefit levels in $t$, $t+1$, $t+2$,… Similarly,
$\theta_{t+1}$ depends on $J_{t+1}$ and thus on future benefit levels in
$t+1$, $t+2$, $t+3$… In equation (6), market tightness $\theta_{t}$ depends
also on current profits $\pi_{t}$ and $\theta_{t+1}$, linearly related to
$E_{t}J_{t+1}$ and depends on the sequence of benefits. Hence, a change in
current benefit $b_{t}$ affects current profits, current vacancy creation and
thus market tightness. Unlike changes in current variables, changes in future
benefits, say $b_{t+k}$, affects market tightness $\theta_{t}$,
$\theta_{t+1}$, …, $\theta_{t+k}$, for $k\geq 1$. For simplicity, setting
$k=1$, the effect of change in $b_{t+1}$ drops in the quasi-difference
identification. Due to the effect of $b_{t+1}$ on $\theta_{t}$ is discounted
by $\beta(1-s_{t})$ and the construction of quasi difference need to multiply
$\beta(1-s_{t})$ to the effect of $b_{t+1}$ on $\theta_{t+1}$. The effect of a
change in $b_{t+2}$, $b_{t+3}$, … are eliminated in the same way. After
controlling for expected future benefit policies, the serial correlation
problem can be solved. Therefore, the quasi-difference approach yields an
unbiased estimation of $\alpha$.

The term $\Delta\epsilon_{p,t}$ contains expectation error and permanent
difference in $\tilde{u}$ across border counties. Rather than additive fixed
effects, HKMM make use of interactive fixed effects model proposed by [Bai,
2009], so as to improve the accuracy of the estimation. The reason to apply
interactive effects is clear, as the impacts of shocks and policy changes
affecting aggregate economy are likely heterogenous across county pairs and
the key to a consistent estimation is to treat the unobserved factors and
factor loadings as parameter to be estimated. Hence this approach provides a
natural way to control for not only the observed and unobserved spatial
heterogeneity, as well as allowing for a much flexible model of county-level
trends in variables.

Bai’s model is shown to be consistent even when the effects are allowed to be
correlated with the regressor.

The error term is decomposed as:

(12) $\Delta\epsilon_{p,t}=\lambda^{\prime}_{p}F_{t}+\upsilon_{p,t},$

where $\lambda_{p}$ is a vector of pair-specific factor loadings, $F_{t}$ is a
time specific common factor. Equation (10) can then be also written as:

(13) $\Delta\tilde{u}_{p,t}=\alpha\Delta
b_{p,t}+\lambda^{\prime}_{p}F_{t}+\upsilon_{p,t}.$

Since equation (13) treat the unobserved factors and factor loadings as
parameters to be estimated, the estimation of $\alpha$ is theoretically
unbiased and consistent.

HKMM extended the quasi-difference methodology to further explore the effects
of future benefit duration on current unemployment. Through iterating equation
(8) for quasi-difference $\tilde{u}_{t}$ forward via substitution, the
$k$-period ahead quasi-difference yields:

(14)
$\tilde{u}_{t}^{k}\coloneqq\log(u_{t})-(\prod_{m=1}^{k}\beta(1-s_{t+m-1}))\log(u_{t+k}).$

The $k$-period-ahead quasi-difference depends on sequence of benefits $b_{t}$,
$b_{t+1}$, …, $b_{t+k-1}$. The effects of current and future benefit policies
can be directly estimated with equation below:

(15) $\Delta\tilde{u}_{p,t}^{k}=\displaystyle\sum_{m=1}^{k}\alpha_{m}\Delta
b_{p,t+m-1}+\lambda_{p}^{k{\prime}}F_{t}^{k}+\upsilon_{p,t}^{k},$

where $\upsilon_{p,t}^{k}$ comprises expectation errors of future benefit
levels from period $t+1$ to period $t+m-1$, due to the assumption that firms
have rational expectation of future benefit policies rather than perfect
policy foresight.

With the help of equation (15), in which includes the future benefits, we are
able to explore the expectational channel of policy. This specification can be
extended to estimate for any arbitrary $k$, and thus allows to assess the
impact of benefits at an arbitrary future date on current unemployment. The
effect of increasing benefit duration from $w_{1}$ to $w_{2}$ weeks for $n=k$
periods in the extended quasi-difference can be calculated with:

(16) $\displaystyle\sum_{m=1}^{k}\alpha_{m}\times(\log(w_{2})-\log(w_{1})).$

Similar to equation (11), the permanent effect in the change of benefit
duration from $w_{1}$ to $w_{2}$ weeks is measured as:

(17)
$\frac{\sum_{m=1}^{k}\alpha_{m}}{1-(\beta(1-s))^{k}}\times(\log(w_{2})-\log(w_{1})).$

HKMM performed a experiment with various value of $k$ to compute the permanent
effect and the implied unemployment rate with benefit duration rising from 26
to 99 weeks and a $5\%$ equilibrium unemployment when 26 weeks of benefits are
available. They found the estimated effects of benefit durations are quite
stable across specification with different $k$. This finding indicates the
one-period-ahead specification, namely, $k=1$ is sufficient to balance both
simplicity and precision. Hence, I opt for equation (13) as baseline
specification in my experiments.

##  3 Data

###  3.1 Quarterly unemployment rate

The data for unemployment rate come from the Local Area Unemployment
Statistics (LAUS)111County-level unemployment rate can be collected from BLS
Data Finder by keywords on website:
https://beta.bls.gov/dataQuery/find?fq=survey:%5Bla%5D&s=popularity:D .. It is
a federal/state cooperative program that provides monthly labor force
statistics produced by Labor Market Information Center. Each of the states
follows the same methodology to produce employment and unemployment estimates.
Econometric models for estimation are developed by economists and
statisticians at the Bureau of Labor Statistics (BLS), a division of the U.S.
Department of Labor. In this paper, I use counties and county equivalents
seasonally adjusted unemployment rate from LAUS program and aggregate it to
quarterly data to match the dataset of prior works.

###  3.2 County average weekly wages within a quarter

County-level employment data from the Quarterly Census of Employment and Wages
(QCEW)222https://www.bls.gov/cew/downloadable-data-files.htm . Provided by the
BLS is also considered in the paper. In particular the average weekly wages in
a given quarter is controlled for as an important factor in the model.

###  3.3 Quarterly otal separation rate in the U.S.

The monthly seasonally adjusted separation rate in the U.S. is obtain from the
BLS’s Job Opening and Labor Turnover Survey (JOLTS). It is converted to
quarterly data333It is more handy to obtain the data from FRED by editing
’modify frequency’ as ’quarterly’ and ’aggregation method’ as ’sum’ on
https://fred.stlouisfed.org/series/JTSTSR . in the estimation.

###  3.4 List of border county pairs

To analyse the impact of the difference in UI policies on the difference in
unemployment between border counties in neighboring states, I mainly based on
the county pair data444Harvard Dataverse:
https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/15969 of
[Dube et al., 2010]. Since there were several modifications in the county FIPS
codes, I dropped some counties that no longer exist and made some county FIPS
code adjustments in order to map the border county pair specification. After
data cleaning, there are 1132 border county pairs in total. The set of border
counties is visualized as area marked in blue in Figure B1.

###  3.5 Quarterly maximum benefit duration

Data on UI benefit duration in each state can be obtained from trigger notice
555https://oui.doleta.gov/unemploy/claims_arch.asp released by the U.S.
Department of Labor. These weekly notices contain detailed information such as
available weeks corresponding to different tiers, begin and end date of the
program and indicator thresholds triggering the program in each state. the
benefit duration consists of two programs over the primary sample period:
Extended Benefit (EB) program and Emergency Unemployment Compensation (EUC08).
Program details has mentioned in Section 2.1. I employ the potential maximum
benefit duration to investigate to what extent do benefit duration affects
unemployment rate. The available weeks of two programs are summed up and the
maximum sum of EB and EUC08 weekly notices within a given quarter is then
picked up as the quarterly benefit duration in the model. Maximum benefit
duration of each state increased dramatically since 2008Q4 and stayed at a
relative high level until the end of 2011, see Figure B3.

###  3.6 Quarterly state GDP per worker

Data of state real GDP and employment level at a quarterly frequency are
collected from the Regional Economic Accounts at the Bureau of Economic
Analysis 666https://apps.bea.gov/iTable/iTable.cfm?reqid=70&step=1&isuri=1.
The value of real GDP divided by employment level is defined as State GDP per
worker, applying to approximate state productivity.

###  3.7 Distance from county population center to shared boundary of border
counties in a pair

To investigate the potential endogeneity associated with discontinuous
economic conditions at the state border, I refer to the RD approach applied by
[Dieterle et al., 2020], utilize the distance between county population center
and shared boundary of border counties to account for both county-level
specific labor market condition in the absence of a difference in UI policy
and economic shocks, that triggered UI benefit extensions, affecting either
side of the border dissimilarly. I acquire geographic population distribution
and distance data by calculation. For the sake of granular data, I use smaller
geographic scope: census blocks, to compute the distance. Data of blocks’
population 777https://data.census.gov/cedsci/advanced within each state is
provided be the U.S. Census Bureau through Decennial Census Survey. Precise
geographic location data is extracted from the 2010 Census TIGER/Line
Shapefiles 888https://www.census.gov/cgi-
bin/geo/shapefiles/index.php?year=2010&layergroup=Blocks released by Census
Bureau.

There are 3 key steps to construct the distance data. First of all, calculate
the county population weighted center. Download Census Block Shapefiles and
Decennial Population data by state, join shapefiles dataframe and populatioin
dataframe of all states respectively to get a large block-shapefiles dataframe
and a large block-population dataframe. Extract the geography identity of
block-population properly to make an one-to-one mapping to both dataframe.
This one-to-one mapping is used as a key to merge these 2 large dataframes
together and generate the combined-dataframe. Since the key contains
information of county id and the combined-dataframe contains blocks’
population, we can get information of county population through group by
county id and sum up block’s population under the same county id. The weight
is defined as the ration of (population in individual block) / (population of
the county that block belongs to). Multiplying the block’s geographic center
(longtitude, longtitude) with wight (weighted longtitude, weighted latitude )
and sum weighted longtitudes and weighted latitudes up by county, yields
county population weighted center, namely population center. Second, obtain
county shapefiles and read it into geodataframe, extract the geometry
information of each county. Open the modified list of county pairs as
dataframe and split pair id to 2 border county ids. Merge geometry information
to 2 border counties respectively, therefore we generate a dataframe that
contains geometry information of border counties in a pair in the same row,
then, we are able to calculate the intersection of border county boundaries
row by row. At last, we can acquire distance data given population center and
intersection of boundaries.

Figure B2 displays an example of border counties’ population centers computing
with census block population and census block shapefiles. County in gray is
Baldwin County in Alabama, that in blue is Escambia County in Florida.
Population centers are marked with green dots, the geography location of
population center might be far away from county geometric center marked with
red triangle.

##  4 UI Benefit Durations and Unemployment

###  4.1 Empirical Results

Table A1 shows the estimated effect of UI benefit durations on unemployment
rates with different specifications. All the experiments are implemented under
the framework of border county pair identification. The result of Baseline
specification strictly following HKMM’s methodology is in column (3). Changes
in benefit duration have a statistically significant positive effect on
unemployment, consistent with the results of HKMM. In the short run, a $1\%$
rise in benefit duration for a quarter leads to 0.052 log points increase in
unemployment rate.

Column (4) and (5) shows results of including additional regressors into
baseline model. Regardless of the number of extra regressors and the
statistical implications behind them, the coefficient magnitude of benefit
duration does not fluctuate dramatically, besides, in comparison to results in
column (1) and (2), the coefficients in column (3), (4) and (5) are
significantly smaller.

Column (2) corresponds to Fixed Effects regression. I set the difference of
log unemployment between 2 border counties rather than diffenence in quasi-
differenced log unemployment as dependent variable, which means the
expectation of future benefit policy has not been controlled for. The effects
of future benefits on current unemployment is accumulated in the coefficient
of current benefits. Column (1) corresponds to Pooled OLS regression, sharing
the same dependent variable with Fixed Effects regression. a $1\%$ rise in
benefit duration for a quarter leads to $0.477\%$ increase in unemployment
rate. If benefit duration extend from 26 weeks to 99 weeks, the unemployment
rate would increase from $5\%$ to $11.68\%$. However, the estimation is
biased, the standard OLS assumption: no correlation between a specific unit’s
observations in different periods is violated, due to the serial correlation
in both sequences of unemployment and benefit extension.

Back to the baseline specification, according to equation (11), we can assess
the effects under various scenarios of interest with the assumption that
employers have perfect foresight of future UI policy. For example, a state
implemented the most generous 99 weeks of benefit duration in 2009Q4, with
unemployment rate around average level ($9.9\%$). Then adjusted the UI policy
to standard duration (26 weeks), the unemployment rate in 2010Q4 and 2011Q4
would haven been $7.8\%$ and $6.7\%$. As the realistic benefit cut was less
aggressive, the true unemployment rate in 2010Q4 and 2011Q4 was $9.5\%$ and
$8.6\%$. Although the benefits in 2010 and 2011 maintained in similar level,
the implied effect on unemployment in 2011 was relatively larger than that in
2010, due to the expectation that benefit duration will continue to decline in
2011. As a result, expected wage bill was lowered and the cost of vacancy
creation was made easier to cover, and thus encouraging firms’ job creating
decision in the following years. Whereas, if firms considered the high benefit
duration would last longer following 2010, they would shrink additional
positions and even cut jobs in spite of the economic downturn was reversed.
Another scenario of interest involves a permanent unanticipated increase in
benefit duration that cause the strongest negative impact on labor demand. Let
say discount rate $\beta=0.99$, JOLTS average quarterly separation rate of
$10\%$, benefit duration rise from $w_{1}=26$ to $w_{2}=99$ and unemployment
rate in base period is $5\%$, the permanent effect ($n=\infty$) can be
calculated with equation (11) and we can get the value of the long run average
unemployment rate equals to $9.6\%$.

###  4.2 Testing for Endogeneity

In this section, I will point out in which case arises the endogeneity problem
and implement an experiment to check the existence of endogeneity. I begin
with a case that imposes stronger condition than that required for
identification to outline the origin of endogeneity intuitively. In order to
make the description convenience, I use the following setting.

A border county pair consists county $a$ and county $b$. County $a$ locates in
state $A$ and the area in state $A$ excludes county $a$ is denoted by
$\mathcal{A}$. County $b$ belongs to state $B$.

Continuous economic conditions at state border.

Imagine a large shock affecting the economy of $\mathcal{A}$. Suppose the
economic impacts of this shock transmit geographically to reach county $a$
without any particular reason to terminate reaching the state border, that is
to say, these economic impacts would continue spreading and affecting county
$b$ similarly to county $a$. If the supposition were true, there would be no
endogeneity problem in the baseline empirical specification in equation (13),
because the difference in in unemployment between border counties depends only
on the difference in benefit policies. Moreover, under the assumption of
continuous economic fundamental, shocks spreading directly to county $a$ and
county $b$ do not cause endogeneity even if either one or both counties are
large enough to trigger state level policy changes.

Discontinuous economic conditions at state border.

The endogeneity problem emerges when the shocks to e.g., productivity, stop at
the state broder. For example, a shock to $\mathcal{A}$ may affect
productivity in county $a$ and thus triggers a change in UI benefit policy in
state $A$. However, this shock terminate when reaching state border, so that
county $b$’s productivity and state $B$’s benefit policy will not be affected.
Therefore, the difference in unemployment between county $a$ and county $b$ is
caused by both the difference in productivity and difference in benefit
policy. According to the standard Pissarides model, workers’ productivity
affects firms’ profits, which determines employers’ willing to create job
vacancies, and consequently cause change in unemployment triggering change in
benefit policy. Therefore, the estimate of the effect of benefits on
unemployment would be biased, if the difference in state productivity is not
controlled for.

To analyse the endogeneity in a general way, we need a more formal exposition.
The assumption of the empirical identification is that the error term
$\upsilon_{p,t}$ is uncorrelated with $\Delta b_{p,t}$. The unobserved county-
specific factors such as productivity or demand are part of $\upsilon_{p,t}$.
In other words, the difference in productivity, demand, etc. across border
counties are not correlated with the difference in benefits between border
counties. Since benefits are a function of state level variables, which means
the assumption can also be interpret as the difference in county level
productivity, demand, etc. has to be uncorrelated with the corresponding
difference in state level,

(18) $Corr(\upsilon_{p,t},\Delta z_{p})=0,$

where $\Delta z_{p}$ is the difference of state level variables such as
productivity, demand, etc. across states. Hence the identifying assumption
does not require border counties to be identical conditional on differences
explained by the factor model, so that $\upsilon_{p,t}$ is pure measurement
error. In this case, endogeneity problem would not arise if discontinuous
idiosyncratic shocks to county $a$ or county $b$ do not affect the state level
conditions triggering changes in benefit policy.

To illustrate the testing mechanism clearly, $\upsilon_{p,t}$ can be
decomposed into part depends on the state $\Delta z_{p}$ and the other part
$\tilde{\upsilon}_{p,t}$ depends on county-specific factors,

(19) $\upsilon_{p,t}=\chi\Delta z_{p}+\tilde{\upsilon}_{p,t}.$

Plugging into equation (13), yields:

(20) $\Delta\tilde{u}_{p,t}=\alpha\Delta
b_{p,t}+\lambda^{\prime}_{p}F_{t}+\chi\Delta z_{p}+\tilde{\upsilon}_{p,t}.$

So far, what we need to think of is converted to: whether the coefficient
$\chi$ is statistically different from zero. It is clear that UI benefit
extensions are triggered by state labor market variables determined by state’s
economic conditions such as state-level productivity or demand $z$. A negative
shock to $z$ may induce an increase in unemployment of all counties in state
and simultaneously trigger an extension of benefits. Suppose state-level
shocks do not affect border counties similarly, i.e., $\chi\neq 0$, the
estimated value of $\alpha$ would be biased in the baseline specification in
equation (13). Thus the bias presents if $\chi$ is statistically different
from zero, furthermore, $\alpha$ would change in magnitude or even lose its
statistical significance under certain circumstance.

To implement the endogeneity test, I use state productivity measured as real
gross state product per worker (state real GDP / employment level) to
represent $z$. [Bai, 2009] proved Interactive Fixed Effects yields consistent
estimation even when the effects are allowed to be correlated with the
regressor. Depend solely on the result of HKMM’s method with interactive
factor loadings might not discover the endogeneity. Therefore, I adopt both
HKMM’s and Fixed Effects model to estimate $\chi$.

Results are shown in Table A2. We are not able to reject $\chi=0$ base on the
result (p-value = 0.521) in column (1). But $\chi$ in column (3) is
statistically different from zero when Fixed Effects adopted, additionally,
there is a subtle change in $\alpha$ when we compare column (2) and (3). The
findings can not help to rule out the emergence of endogeneity caused by
discontinuous economic conditions across states. It remains uncertain that
discontinuous idiosyncratic shocks to border counties affect the state level
conditions and trigger changes in benefit policy.

###  4.3 Extending Baseline Specification by Controlling for Distance between
Population Center and Shared Boundary

HKMM’s quasi-diffeneced model performs well if border counties experience
similar labor market conditions in the absence of difference in benefit
policies. It also requires that the shocks triggering UI benefit extension in
one state must evolve over space and affect either side of the border
similarly. however, the finding in section 4.2 has told the later condition is
difficult to satisfy and the discontinuous economic conditions become a source
of endogeneity. [Dieterle et al., 2020] develop a Regression Discontinuity
(RD) based approach to embrace the challenging endogeneity to estimate the
total effect of UI benefit extensions. They found a relative smaller impact of
benefits on unemployment after controlling for distance to border.

Compared to border county pair identification, RD approach treat each
individual county as an observation unit. Distance is used as continuous
variable in RD setup to capture unobservable factors. An ideal setup requires
granular data, due to lacking of reliable sub-county disaggregate data,
population distribution within county is of great importance in distance
calculation.
The expression of RD specification controlling for distance is:

(21) $\displaystyle y_{c,s,g,t}={}$ $\displaystyle\pi+\gamma
b_{s,g,t}+\delta_{g,t}$
$\displaystyle+\mathbf{D}_{g,t}\left[(1-\mathit{T}_{s,g,t})\left(\displaystyle\sum_{r=1}^{R_{0,g,t}}\theta_{g,t}^{0}\overline{x^{r}}_{c}\right)+(\mathit{T}_{s,g,t})\left(\displaystyle\sum_{r=1}^{R_{1,g,t}}\theta_{g,t}^{1}\overline{x^{r}}_{c}\right)\right]+\upsilon_{c,s,g,t},$

where
$c$ indexes the counties; $s$ indexes states; $g$ indexes state boundaries;
$t$ indexes quarters
$y_{c,s,g,t}$ is log unemployment rate: $y_{c,s,g,t}=\ln(u_{c,s,g,t})$
$b_{s,g,t}$ is the log benefit duration
$\delta_{g,t}$ are boundary-by-quarter fixed effects
$\mathbf{D}_{g,t}$ is a vector of indicators for each boundary-by-quarter
$\mathit{T}_{s,g,t}=\mathbf{1}[\,b_{s,g,t}>b_{-s,g,t}]\,$ are indicators for
being on the high-benefits side
$\overline{x^{r}}_{c}$ is the $r^{th}$ uncentered moment of the distance to
the border distribution
$R_{T,g,t}$ is the order of the polynomial in distance for group $T$

Distance plays an important role in RD approach, whereas, it dose not mean
that the coefficient magnitude of $\alpha$ in equation (13) would be affected
greatly after controlling for distance under border county pair
identification. RD approach, unlike the quasi-differenced method, dose not
control for expected future benefit policies. Also it treat individual county
rather than county pair as observation unit. To check whether $\alpha$ is
affected by including distance as exogenous variables, I change the definition
of population weighted mean distance slightly in order to fit the baseline
specification better. Since our experiment is conducted within the framework
of border county pair, I allow counties close to several state borders, have
more than one nearest distance to borders.
Including distance in the model, the baseline specification is modified as:

(22) $\Delta\tilde{u}_{p,t}=\alpha^{\prime}\Delta b_{p,t}+\psi\Delta
d_{p,t}+\lambda^{\prime}_{p}F_{t}+\upsilon_{p,t},$

where $\Delta d_{p,t}$ is the difference of log distance between border
counties. It should bo noted that $\psi$ captures information of polynomial
order $r$ and coefficients $\theta$ in equation (21).

Result is shown in Table A1 column(4) and (5). The insignificance indicates
the difference of distance to county pair shared boundary does not account for
difference in unemployment after controlling for expected future benefits. In
addition, the magnitude of $\alpha^{\prime}$ (0.05207) is so close to $\alpha$
(0.05203) of baseline specification. However, I could not recklessly draw the
conclusion that my finding conflicts with that of RD approach, as distance
might partially account for the unemployment within each individual county and
might have negligible explanatory power in the partition determining the
difference between border counties. Another concern is attributed to the data
itself. Because the data from Decennial Census Survey revised every 10 years,
distance can be regarded as a time-invariant variable in the sample data. When
implementing quasi-difference in each county within a pair, we expect the
distance maintains unchanged and the terms contain distance in period $t$ and
$t+1$ would have been counteracted quite a bit. As a result, the impact of
population weighted mean distance on the difference of quasi-differenced
unemployment between border counties could be ignored in light of the
empirical results.

##  5 Conclusion

I successfully replicated the baseline specification developed by HKMM with my
own dataset. The empirical results are highly consistent with HKMM’s. An $1\%$
extension in benefit duration lead to a $0.052$ log point increase in
unemployment rate. Serial correlation and endogeneity are inevitable when
dealing with longitudinal data, it is critical to apply strategies to
alleviate these issues. Border county pair identification eliminates aggregate
shocks of both counties to alleviate endogeneity. Quasi-difference drops
serial correlation by controlling for expectation of benefit policy. However,
there still remains problems to be solved. For example, the effect of the
idiosyncratic shocks is difficult to measure. The empirical results only have
shown statistically that distance could be ignored when accounting for the
endogeneity caused by idiosyncratic shocks, and the endogeneity does not show
up after we treat unobserved factors and their loadings as parameters to be
estimated. Whereas we are not able to tell how well interactive fixed effects
model approximates idiosyncratic shocks or whether it is proper to use
distance to estimate these shocks. Furthermore, the problem might associate
with the dataset, because the shocks and policy changes facing by each state
during Great Recession would be alike, the impact of idiosyncratic shocks
could be neglected. In most instances, different strategies are constructed
with different assumptions. In order to avoid the undesirable issues, we
usually combine multiple strategies to fix problems as much as possible.
However, combination of different strategies give rise to another problem:
conflict of assumptions, which is uneasy to detect and lead to a failure in
model specification construction. Fortunately, more and more strategies and
model specifications will be discussed and inspected. As long as we stay
interested in the problem and keep reading literature, better solution will be
figured out.

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##  Appendix A Tables

Table A1: Unemployment Benefit Extensions and Unemployment

Regressor | (1) | (2) | (3) | (4) | (5)
---|---|---|---|---|---
Weeks of Benefits |  | 0.477
---
(0.000)
| 0.147
---
(0.000)
| 0.052
---
(0.000)
| 0.052
---
(0.000)
| 0.051
---
(0.000)
| Population Weighted
---
Mean Distance
|  |  |  | 0.000
---
(0.799)
| 0.000
---
(0.496)
Average Weekly Wages |  |  |  |  |  | -0.01
---
(0.000)

  * *

All empirical results in this table produced with $\beta=0.9975$,
corresponding to a $1\%$ annual discount rate.

  * *

Column (1): Pooled OLS model not controlling for expected future benefit
extensions,

  * *

Column (2): Fixed Effects not controlling for expected future benefit
extensions,

  * *

Column (3): Baseline specification in equation (13),

  * *

Column (4): Baseline model controlling for distance,

  * *

Column (5): Baseline model controlling for distance and wages.

Table A2: Testing for Endogeneity

Regressor |  (1) |  (2) |  (3)
---|---|---|---
Weeks of Benefits |  0.052 (0.000) |  0.01758 (0.000) |  0.01762 (0.000)
State GDP per worker |  0.002 (0.521) |  |  -0.048 (0.000)

  * *

All empirical results in this table produced with $\beta=0.9975$,
corresponding to a $1\%$ annual discount rate.

  * *

Column (1): Baseline specification controlling for productivity

  * *

Column (2): Additive Fixed Effects model,

  * *

Column (3): Additive Fixed Effects controlling for productivity.

##  Appendix B Figures

Figure B1: Border counties contained in the sample data.

(a) A pair of border counties and the states they belong to

(b) Zooming in border counties in (a) to show boundary and to label
geometry/population centers

Figure B2: Border counties and their population centers

Figure B3: The changes of maximum benefit duration in each state at given
periods

Statement of Authorship

I hereby confirm that the work presented has been performed and interpreted
solely by myself except for where I explicitly identified the contrary. I
assure that this work has not been presented in any other form for the
fulfillment of any other degree or qualification. Ideas taken from other works
in letter and in spirit are identified in every single case.

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