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DESPERATE TIMES CALL FOR DESPERATE MEASURES: GOVERNMENT

SPENDING MULTIPLIERS IN HARD TIMES

SOKBAE LEE, YUAN LIAO, MYUNG HWAN SEO and YOUNGKI SHIN∗

We investigate state-dependent effects of scal multipliers and allow for endogenous

sample splitting to determine whether the U.S. economy is in a slack state. When the

endogenized slack state is estimated as the period of the unemployment rate higher than

about 12%, the estimated cumulative multipliers are signicantly larger during slack

periods than nonslack periods and are above unity. We also examine the possibility

of time-varying regimes of slackness and nd that our empirical results are robust

under a more exible framework. Our estimation results point out the importance of

the heterogenous effects of scal policy and shed light on the prospect of scal policy

in response to economic shocks from the current COVID-19 pandemic. (JEL C32, E62,

H20, H62)

I. INTRODUCTION

The debate over the role of scal policy

during a recession has recently taken center

stage again in macroeconomics. One particular

topic that has received substantial attention is

whether the multiplier effect of government

spending is state-dependent. On the one hand,

in a series of papers, Auerbach and Gorod-

nichenko (2012, 2013a, 2013b) used data from

the United States as well as from the organiza-

tion for economic cooperation and development

countries and provided empirical evidence sup-

porting that the scal multiplier might be larger

during recessions than expansions. On the other

hand, Ramey and Zubairy (2018) constructed

new quarterly historical U.S. data and reported

that their estimates of the scal multipliers

∗We would like to thank the Seoul National University

Research Grant in 2020, the Social Sciences and Humanities

Research Council of Canada (SSHRC-435-2018-0275), the

European Research Council for nancial support (ERC-

2014-CoG-646917-ROMIA), and the UK Economic and

Social Research Council for research grant (ES/P008909/1)

to the CeMMAP.

Lee: Professor, Department of Economics, Columbia Uni-

versity, New York, NY 10027, Research Staff, Insti-

tute for Fiscal Studies, London, WC1E 7AE, E-mail

sl3841@columbia.edu

Liao: Associate Professor, Department of Economics,

Rutgers University, New Brunswick, NJ 08901, E-mail

yuan.liao@rutgers.edu

Seo: Associate Professor, Department of Economics, Seoul

National University, Seoul, 08826, Republic of Korea.

E-mail myunghseo@snu.ac.kr

Shin: Associate Professor, Department of Economics,

McMaster University, Hamilton, ON L8S 4L8, Canada.

E-mail shiny11@mcmaster.ca

were below unity irrespective of the state of

the economy.

In this paper, we contribute to this debate

by estimating a threshold regression model that

determines the states of the economy endoge-

nously. Auerbach and Gorodnichenko (2012)

estimated smooth regime-switching models

using a 7 quarter moving average of the output

growth rate as the threshold variable. Their

primary results relied on a xed level of intensity

of regime switching. Instead of estimating the

level of intensity jointly with other parameters in

their model, they calibrated the level of intensity

so that the U.S. economy spends about 20%

of time in a recessionary regime. In Ramey

and Zubairy (2018), the baseline results assume

that the U.S. economy is in a slack state if the

unemployment rate is above 6.5%. To check

the baseline results, Ramey and Zubairy (2018)

conducted various robustness checks using

different thresholds.

To be consistent with the empirical litera-

ture, we build on Ramey and Zubairy (2018):

we use their dataset and follow their methodol-

ogy closely. Our main departure from the recent

empirical literature is that we split the sample in a

data-dependent way so that the choice of thresh-

old level is determined endogenously. It turns out

that the endogenized threshold level of the unem-

ployment rate is estimated at 11.97%, which is

ABBREVIATIONS

GDP: gross domestic product

MIO: mixed integer optimization

1

Economic Inquiry

(ISSN 0095-2583) doi:10.1111/ecin.12919

© 2020 The Authors. Economic Inquiry published by Wiley Periodicals LLC. on behalf of Western Economic Association International.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in

any medium, provided the original work is properly cited.

2 ECONOMIC INQUIRY

much higher than 6.5% adopted in Ramey and

Zubairy (2018). Using this new threshold level

combined with the same data and specications

as in Ramey and Zubairy (2018), we nd that the

estimated scal multipliers are signicantly dif-

ferent between the two states and above unity

for the high unemployment state. Specically,

if the threshold level is 6.5%, the estimates of

2-year integral multipliers are around 0.6 regard-

less of the state of the economy. However, if the

threshold level is 11.97%, the estimates are 1.58

for the high employment state and 0.55 for the

low employment state, respectively. If we look

at observations used in estimation, there is no

period after World War II with the unemployment

rate higher than 11.97%. In fact, there is only

one timespan of severe slack periods in 1930s.

In other words, the period of the Great Depres-

sion is isolated from other periods, as an outcome

of our estimation procedure. Therefore, our esti-

mation results suggest that (1) the scal multi-

plier can be larger than unity if the slackness of

the economy is very severe and that (2) the post-

World War II period does not include the severe

slack state and thus, our estimates for the high

unemployment state are not applicable to mod-

erate recessions in the post-WWII period. How-

ever, after the outbreak of the COVID-19 pan-

demic, the U.S. unemployment rate rose to 14.7%

in April 2020.1Therefore, the estimation results

in this paper shed light on the prospect of the s-

cal policy in response to the current economic

shocks. We also examine the possibility of time-

varying regimes of slackness by including a time

dummy for the post-WWII period and nd that

our empirical results are robust under this more

exible framework. All the computer codes and

data les for replication are available at https://

github.com/yshin12/llss-rz.

The remainder of the paper is organized as

follows. In Section II, we describe the econo-

metric model and present empirical results. In

Section III, we give concluding remarks.

II. MODEL AND EMPIRICAL RESULTS

In this section, we give a brief description

of the methodology developed by Ramey and

Zubairy (2018, RZ hereafter). They consider

the state-dependent local projection method of

Jordà (2005). Their baseline regression model

1. Source: U.S. Bureau of Labor Statistics, https://

www.bls.gov/news.release/empsit.nr0.htm, accessed on May

25, 2020.

for each horizon hhas the following form (see

equation (2) in RZ):

xt+h=It−1(𝛼A,h+𝜓A,h(L)zt−1+𝛽A,hshockt)

(2.1)

+(1−It−1)(𝛼B,h+𝜓B,h(L)zt−1+𝛽B,hshockt)

+𝜖t+h,

where It(·) is a dummy variable denoting the state

of the economy, xtis the variable of interest, zt

is a vector of control variables including GDP,

government spending, and lags of the defense

news variable, 𝜓(L) is a polynomial of order 4

in the lag operator, and shocktis the defense

news variable.

Recall that RZ assume that the economy is in

the slack state when the unemployment rate is

above 6.5%. We instead adopt a threshold regres-

sion model and parameterize It=1{unempt>𝜏},

where 1{·} is an indicator function and unemp

denotes the unemployment rate. In other words,

we estimate the model that endogenously deter-

mines the slack states that t the data best. Specif-

ically, we estimate the following model using the

least squares (see, e.g., Hansen 2000; Hidalgo,

Lee, and Seo 2019):

GDPt=1{unempt−1>𝜏}(2.2)

×(𝛼A+𝜓A(L)zt−1+𝛽Ashockt)

+1{unempt−1≤𝜏}

×(𝛼B+𝜓B(L)zt−1+𝛽Bshockt)+𝜖t.

To estimate the threshold regression model in

(2.2), dene the objective function

QT(𝜏,𝜃)∶=

T

∑

t=1

[GDPt−1{unempt−1>𝜏}

×(𝛼A+𝜓A(L)zt−1+𝛽Ashockt)

−1{unempt−1≤𝜏}(𝛼B+𝜓B(L)zt−1

+𝛽Bshockt)]2,

where 𝜃:=(𝛼A,𝜓A(L), 𝛽A,𝛼B,𝜓B(L), 𝛽B). Note

that the model (2.2) is linear in 𝜃conditional

on 𝜏. Thus, we obtain the (restricted) ordinary

least squares estimator ̂

𝜃(𝛾)easily for any given 𝛾.

Then, the threshold parameter 𝛾can be estimated

by minimizing the proled objective function:

̂𝜏 ∶= argmin

𝜏∈

Q∗

T(𝛾),

where Q∗

T(𝛾)∶=QT(𝛾,̂

𝜃(𝛾)).Toestimatethis

model, it is necessary to specify the parameter

LEE ET AL.: DESPERATE TIMES CALL FOR DESPERATE MEASURES 3

space for 𝜏. We set it to be the interval between

the 5 and 95 percentiles of the unemployment

rates in the dataset and estimate ̂𝜏 by the grid

search method.

In our view, the threshold regression model

above provides a natural way to endogenize the

level of slackness since there is a change point

at 𝜏for GDP in the model. Note that the level of

the slackness is determined endogenously by t-

ting the regression model for GDP in (2.2) and

then it is imposed in the specication of It−1in

(2.1). Considering that both RZ and Auerbach

and Gorodnichenko (2012, 2013a, 2013b) deter-

mine the criterion for the economic slackness

based on the researchers’ discretion, it is novel

to determine the threshold point endogenously.

Furthermore, as we will see in the next section,

the endogenous threshold estimate is beyond the

range of the values that RZ considered for a

robustness check.

In general, estimating the change point 𝜏tends

to be robust to model misspecication. Speci-

cally, in our context, the local projection argu-

ment may imply that the model (2.2) is poten-

tially misspecied; however, it is worthwhile to

emphasize that the change-point estimation tends

to be robust against mild misspecication in the

regression function employed in each regime, as

shown by for example Bai et al. (2008).

Before looking at the estimation results, we

briey describe the dataset adopted in our empir-

ical analysis. RZ constructed new quarterly U.S.

data from 1889 to 2015 for their analysis. The

main variables include real GDP, real govern-

ment spending, the unemployment rate, and the

defense news series. The real GDP data come

from Historical Statistics of the United States for

1889–1928 and from the National Income and

Product Accounts from 1929 to 2015. Real gov-

ernment spending is calculated by dividing all

federal, state, and local purchases by the GDP

deator. The unemployment rates before 1948

were calculated by interpolating Weir’s (1992)

series and the NBER Macrohistory database.

Finally, the defense news series is constructed

by the narrative method of Ramey (2011), which

measures changes in the expected present dis-

counted value of government spending. For addi-

tional details of the dataset, we refer to Ramey

and Zubairy (2018).

A. Endogenous Sample Splitting

Using the same dataset constructed by RZ, we

obtain ̂𝜏 =11.97%for the threshold parameter.

This estimate is even higher than 8%, which RZ

used for their robustness check. To appreciate

our estimation result, we plot the proled least

squares objective function (1 −R2) as a function

of 𝜏in the left-panel of Figure 1.

It can be seen that the minimizer is well sepa-

rated at 11.97%, which gives the graphical veri-

cation of ̂𝜏. On the contrary, there is even no local

minimum around RZ’s threshold value at 6.5%.

To check the possibility of the second threshold

level below 11.97%, we re-estimated the model

with the subsample for which the unemployment

rate is lower than 11.97%. The right-hand panel

indicates that there could be a second threshold

around 4%, but not around 6.5%.

We test for the existence of the threshold for

the whole sample and for the subsample with

unemp <11.97 by adopting the sup-Wald test in

Hansen (1996). Figure 2 gives a graphical sum-

mary of the testing results. We set the number of

bootstraps to 2,000 and the trimming ratio to 5%.

We use the heteroskedasticity-robust test statis-

tic. The bootstrap p-value for the whole sample

is 0.053 and we can reject the null hypothesis

of no threshold effect at the 10% signicance

level. For the subsample with the unemployment

rate below 11.97, the bootstrap p-value for the

same test is 20.3%. Thus, we conclude that there

is mild evidence for the single threshold in the

data. Finally, the 95% condence interval for the

threshold variable is (11.97, 13.56).

The periods with high unemployment rates are

relatively rare. The U.S. economy spent less than

10% of time in the new slack regime dened

by 11.97%. The shaded areas in Figure 3 show

slack periods over GDP and unemployment rates.

There is only one timespan of severe slack peri-

ods from 1930Q3 to 1940Q3, namely the Great

Depression. We call this new slack periods as

severe slack states (“hard times”) compared to

moderate slack states in RZ. There is no period

after WWII that belongs to the hard times in this

dataset. However, the current recession belongs

to the hard times, as the unemployment rose to

14.7% in April 2020.

B. State-Dependent Cumulative Multipliers

We now report the estimation results of the

cumulative multipliers under endogenous sam-

ple splitting. It turns out that the new regime

classication produces quite different implica-

tions. Following RZ, we adopt the local projec-

tion method in Jordà (2005) and use the military

news as an instrument. Figure 4 reports the cumu-

lative multiplier over 5years (20 quarters) in each

4 ECONOMIC INQUIRY

FIGURE 1

Least Squares Objective Function

Note: In the left-hand panel, the long-dashed vertical lines are the 5 and 95 percentiles of the empirical distribution of the

unemployment rate. The dashed vertical lines are the 10 and 90 percentiles and the dotted lines are the 15 and 85 percentiles,

respectively.

regime. To make the comparison straightforward,

we also show the estimation results of Ramey and

Zubairy (2018) next to our results.

When the 6.5% threshold is used in classica-

tion of slack state (i.e., the moderate slack state),

the multipliers in the high-unemployment state

are negative up to 3 quarters and are indistin-

guishable to those in the low-unemployment state

after 6 quarters. It is counterintuitive to observe

that the multipliers are higher for the low unem-

ployment state. On the other hand, if the 11.97%

threshold is adopted (i.e., the severe slack state),

the multipliers in the high-unemployment state

are mostly positive and largely above those in

the low-unemployment state and are around unity

after 10 quarters. In other words, the multipliers

are all less than unity in the case of the mod-

erate slack state; however, they are substantially

higher in the case of the severe slack state. These

results are robust to the choice of the instrumental

variable. As additional empirical results, Figure 5

depicts the impulse response functions in non-

slack and slack periods, respectively. Both gov-

ernment spending and GDP responses are much

higher in slack periods.

In Table 1, we report the 2-year and 4-year

cumulative multipliers when we use the military

news, Blanchard and Perotti (2002) shock, and

the combined variable of these two as an instru-

ment, respectively. The basic implication does

not change. The estimates of the 2-year multiplier

vary from 1.58 to 2.21 and the 4-year multipli-

ers are around 1. The main implication from our

empirical results is that scal multipliers can be

signicantly larger during severe recessions than

in normal periods.

We illustrate the difference between our

results and those in RZ by comparing the

effects of the COVID-19 stimulus package.

The COVID-19 pandemic and the following

economic lockdown increased the U.S. unem-

ployment rate up to 14.7% in April 2020. This is

the highest unemployment rate since World War

II. To mitigate the economic hardship, the U.S.

congress has passed the COVID-19 stimulus

package (the CARES act) whose total amount is

2 trillion dollars. In Table 2, we report the differ-

ence of the estimated multiyear integral effects

of the stimulus package when we use the multi-

pliers in this paper and those in RZ. We assume

that 25% of the total amount (500 billion dollars)

will be spent in the immediate quarter and use

the cumulative multiplier estimates based on the

military news shock. Two approaches provide

LEE ET AL.: DESPERATE TIMES CALL FOR DESPERATE MEASURES 5

FIGURE 2

Inference for Multiple Regimes

Note: The red dashed line denotes the 95% critical value for the existence of the threshold point. In the left panel, we

conrm that the Wald test statistic at 𝜏=11.97 is very close to the 95% critical value. In the right panel, we use the subsample

and test if there exists an additional threshold point. The result conrms that there is no additional threshold point in the

subsample.

FIGURE 3

Periods of Slack States over GDP and Unemployment

Note:GDP denotes real per capita GDP divided by trend GDP. The red dashed line in the right panel is the change-point

estimate, ̂𝜏 =11.97. The blue shaded area denotes the slack states estimated from the data.

6 ECONOMIC INQUIRY

FIGURE 4

Cumulative Multipliers

Note: The blue solid line denotes cumulative multipliers for slack states (high unemployment) and the red dashed line for

nonslack states (low unemployment). The 95% pointwise condence bands are also presented along with cumulative multipliers.

We also draw a dot-dashed horizontal line at multiplier =1.

LEE ET AL.: DESPERATE TIMES CALL FOR DESPERATE MEASURES 7

FIGURE 5

Government Spending and GDP Responses to News Shock

Note: A news shock is equal to 1% of GDP. The red line with circles denotes the impulse response function in nonslack

periods and the blue solid line denotes the same function in slack periods. The related 95% pointwise condence bands are also

provided. The threshold point dividing slack/nonslack periods is ̂𝜏 =11.97 estimated from the data.

quite different results of the policy effect. Over

2 years, the difference between the two estimates

is 490 billion dollars. The gap decreases over

time but it is still 70 billion dollars after 5 years.

Therefore, we conclude that the endogenous

threshold estimate gives quite different results

of the scal policy effect, especially when the

slackness of the economy is severe.

C. Possibly Time-Varying Regimes

In this subsection, we explore the possibility

of time-varying regimes of slackness. One might

be worried that the U.S. economy changed after

WWII such that the level of slackness changed

from the pre-WWII period to the post-WWII

period. To deal with this issue, we extend the

endogenous sample splitting to the following

specication:

It−1=1{unempt−1+𝜏1dt−1−𝜏0>0},

where dt=1iftis greater than or equal to

1945Q4. The resulting regression model has the

following form:

GDPt=1{unempt−1+𝜏1dt−1−𝜏0>0}

×(𝛼A+𝜓A(L)zt−1+𝛽Ashockt)

+1{unempt−1+𝜏1dt−1−𝜏0≤0}

×(𝛼B+𝜓B(L)zt−1+𝛽Bshockt)+𝜖t.

To estimate this model, we need to optimize

the least squares objective function with respect

to unknown parameters jointly. The parame-

ters could be estimated through the proling

method as explained in Section II. Specically,

one may rst estimate the slope parameters

𝜃:=(𝜃A,𝜃B)=(𝛼A,𝜓A,𝛽A,𝛼B,𝜓B,𝛽B)given

𝜏:=(𝜏0,𝜏1) and then optimize the proled

objective function over 𝜏by the two-dimensional

grid search.

We adopt more efcient computational

algorithms developed in our previous work

(Lee et al. 2018) with the aid of mixed inte-

ger optimization (MIO). To explain the

algorithm, we rst dene some notation:

yt:=DGPt,ft:=(unempt−1,dt−1,−1), and

xt:=(1, zt−1,shockt). Then, the least squares

estimator can be written as

(̂𝜏, ̂

𝜃B,̂

𝛿)∶=argmin

𝜏,𝜃B,𝛿

T

∑

t=1

[yt−x′

t𝜃B−x′

t𝛿1(2.3)

×{f′

t𝜏>0}]2,

where 𝛿=𝜃A−𝜃B. Instead of multidimensional

grid search over 𝜏, Lee et al. (2018) propose

an equivalent optimization problem by introduc-

ing a set of binary parameters dt∶= 1{f′

t𝛾>0}

and 𝓁j,t=𝛿jdtfor j=1, …,dx, where dxis the

dimension of xt. The new objective function can

be written as

T

∑

t=1[yt−xt𝜃B−

dx

∑

j=1

xj,t𝓁j,t]2

.(2.4)

8 ECONOMIC INQUIRY

TABLE 1

Estimates of Cumulative Multipliers

High

Unemploy-

ment

Low

Unemploy-

ment

p-value

for

difference

in multipliers

Panel A: Threshold at 11.97%

Military news shock

2 year integral 1.58 0.55 0.000

(0.099) (0.064)

4 year integral 0.94 0.61 0.000

(0.017) (0.050)

Blanchard– Perotti shock

2 year integral 1.65 0.34 0.005

(0.425) (0.105)

4 year integral 1.23 0.40 0.000

(0.130) (0.104)

Combined

2 year integral 2.21 0.35 0.000

(0.406) (0.092)

4 year integral 1.11 0.46 0.000

(0.108) (0.086)

Panel B. Threshold at 6.5%

Military news shock

2 year integral 0.60 0.59 0.954

(0.095) (0.091)

4 year integral 0.68 0.67 0.924

(0.052) (0.121)

Blanchard– Perotti shock

2 year integral 0.68 0.30 0.005

(0.102) (0.111)

4 year integral 0.77 0.35 0.001

(0.075) (0.107)

Combined

2 year integral 0.62 0.33 0.099

(0.098) (0.110)

4 year integral 0.68 0.39 0.021

(0.052) (0.110)

Note:Thep-values for difference in multipliers are calcu-

lated by the HAC-robust p-values in Newey and West (1987).

Panel A is based on our threshold estimate (11.97%). Panel B

comes from Ramey and Zubairy (2018) where the threshold

point (6.5%) is chosen by the authors.

The equivalent optimization problem becomes a

mixed integer programming problem with some

additional constraints. The new optimization

problem can be solved efciently by the modern

MIO solvers such CPLEX and GUROBI. One

can solve the optimization jointly or by iterating

between (𝜃B,𝛿) and the remaining parameters.

The advantage of the new algorithm is that one

can construct and estimate the model, where the

regimes are determined in a more sophisticated

way by a multidimensional factor ft. We refer to

Lee et al. (2018) for additional details.

By applying the joint and iterative algorithms

proposed in that paper, we obtain the following

results:

Joint algorithm ∶(̂𝜏1,̂𝜏0)=(−1.82,11.97),

obj =0.0002636456,

TABLE 2

GDP Increases Caused by the COVID-19

Stimulus Package (in $ bn)

LLSS

(Threshold

at 11.97%)

RZ

(Threshold

at 6.5%) Difference

2 year integral 790 300 490

3 year integral 510 355 155

4 year integral 470 340 130

5 year integral 465 395 70

Note: The estimates denote the increased cumulate GDP

when the U.S. government spends 500 billion dollars in the

period of high unemployment (14.7%). Military news shocks

are used as an instrument.

Iterative algorithm ∶(̂𝜏1,̂𝜏0)=(0.56,11.97),

obj =0.0002636456.

That is, two algorithms yield different estimates

but the same objective function values. It turns

out that the regimes determined by two estimates

are identical; that is, ̂𝜏1has no role in determining

slack periods.

In addition, we apply the model selection

algorithm proposed in our previous work (Lee

et al. 2018). Specically, we specify the penal-

ized least squares objective function with the

penalty term consisting of a tuning parameter

𝜆>0 times the number of nonzero coefcients.

The resulting specication of the endogenous

sample splitting rule is as follows:

T

∑

t=1[yt−xt𝜃B−

dx

∑

j=1

xj,t𝓁j,t]2

+λ|𝜏|0,

where |·|0is an 𝓁0norm of a vector. We implement

it using MIO with λ=̂σ2log(T)/T, where Tis

the sample size and ̂σ2=0.00027 is estimated

from the baseline model with a single threshold at

11.97%. When we apply the penalized estimation

algorithm, we nd that the 𝜏1estimate becomes

zero and is dropped from the model. Therefore,

there is no empirical evidence that supports time-

varying regimes of slackness.

III. CONCLUSIONS

We have investigated state-dependent effects

of scal multipliers and have found that it is

crucial how to determine whether the U.S. econ-

omy is in a slack state. When the slack state is

dened as the period of the unemployment rate

higher than about 12%, the estimated cumulative

multipliers are signicantly larger during slack

LEE ET AL.: DESPERATE TIMES CALL FOR DESPERATE MEASURES 9

periods than nonslack periods and are above

unity. Our estimation results emphasize the

importance of endogenous sample splitting.

Furthermore, the effect of the scal policy may

be heterogenous with respect to the level of

slackness in the economy, thereby calling for

more research in understanding the heteroge-

nous effects of scal policy. Finally, our paper

sheds light on the prospect of scal policy in

response to economic shocks from the current

COVID-19 pandemic.

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