Nonlinear Employment Effects of Tax Policy

• Published date: 01 August 2023
• Author: DOMENICO FERRARO,GIUSEPPE FIORI
• Date: 01 August 2023
• DOI: http://doi.org/10.1111/jmcb.12984

DOI: 10.1111/jmcb.12984

DOMENICO FERRARO

GIUSEPPE FIORI

Nonlinear Employment Effects of Tax Policy

We study the nonlinear propagation mechanism of tax policy in a

heterogeneous-agent equilibrium business cycle model with search frictions

in the labor market and an extensivemargin of employment adjustment. The

model exhibits endogenous job destruction and endogenous hiring standards

in the form of occasionally-binding zero-surplus constraints. After param-

eterizing the model using U.S. data, we nd that the dynamic response of

employment to a temporary change in the labor income tax is highly non-

linear, displaying sizable asymmetries and state dependence. Notably, the

response to a tax rate cut is at least twice as large in a recession as in an ex-

pansion.

JEL codes: E12, E24, E32, E62

Keywords: search frictions, job destruction, heterogeneity, aggregation,

tax policy

T     propagation mecha-

nism of discretionary tax policy in the context of a heterogeneous-agent equilibrium

business cycle model featuring search frictions in the labor market, and an extensive

margin of employment adjustment, that operates through endogenous job destruction

and hiring. We ask three questions related to the effects of shocks to at-rate labor

taxes on the aggregate employment rate:

(i) Is the effect of a tax rate hike larger than the effect of a tax rate cut?

(ii) Does the marginal effect of a tax rate change depend on the size of the tax rate

increase or decrease?

(iii) Is the effect of a tax rate cut larger in a recession than in an expansion?

The rst version of this paper was presented on November3, 2017, at the Junior Macroeconomics Con-

ference hosted by CASEE at Arizona State University,with the title “The Countercyclical Tax Multiplier.”

We thank Bart Hobijn, Nir Jaimovich, Valerie Ramey, Richard Rogerson, and Ay¸segül ¸Sahin as well as

conference and seminar participants at the Junior Macroeconomics Conference at Arizona State University

and North Carolina State University,for valuable comments and suggestions. All errors are our own.

D F is at Department of Economics, W. P. Carey School of Business, Arizona State

University (E-mail: domenico.ferraro@asu.edu). G F is at Board of Governors of the Federal

Reserve System, Division of International Finance (E-mail: giuseppe.ori@frb.gov).

Received January 5, 2021; and accepted in revised form October 20, 2021.

Journal of Money, Credit and Banking, Vol. 55, No. 5 (August 2023)

© 2022 The Ohio State University.

1002 :MONEY,CREDIT AND BANKING

Using a quantitative versionof our model, we nd that the answer to these questions

is “yes.” Overall, the interaction of search frictions and worker heterogeneity in skills

produces signicant nonlinearities in the propagation mechanism of tax policy to the

aggregate employment rate. Three main results stand out. First, we nd that a cut in

tax rates increases the employment rate by less than a tax rate hike reduces it, and

that the larger the size of the shock, the larger the sign asymmetry between negative

and positive tax shocks. Second, the marginal effect of a tax shock is decreasing in

the size of the shock. Third, the effects of tax changes are state-dependent. Notably,

the effect of a tax rate cut is at least twice as large in a recession as in an expansion.

Our results have important implications for a number of scal policy issues, includ-

ing, but not limited to, countercyclical tax policy: to the extent that the marginaleffect

of a tax rate cut is decreasing in its size, tax policy is less effectiveas a countercyclical

policy instrument than the estimates based on linear structural vector autoregressions

(SVARs) would imply.

Our theoretical analysis builds on two premises. First, a typical U.S. recession is

“L-shaped,” as opposed to “V-shaped,” featuring a sharp drop in the aggregate em-

ployment rate, followed by a recovery phase in which the employment rate slowly

reverts back to its prerecession level. These patterns clearly point to the presence

of signicant nonlinearities in aggregate dynamics (Neftçi 1984, Sichel 1993, Mc-

Queen and Thorley 1993, McKay and Reis 2008, Morley and Piger 2012). The Great

Recession of 2008–09 and the contraction led by the spread of the new coronavirus

(COVID-19) in early 2020 are the two most recent episodes of this phenomenon. We

view endogenous job destruction as a key feature of the propagation mechanism of

macro-economic shocks, including tax shocks.

Second, congestion effects due to random search in the labor market, exacerbated

by a disproportionate inow of workers in the unemployment pool at the onset of

recessions, can induce convexity in hiring costs and thereby a high degree of curva-

ture in the cost of producing output. This curvature leads to interesting nonlinearities,

implying that the responsiveness of the economy to discretionary tax policy may con-

siderably vary over the business cycle, and its efcacy depends on the magnitude of

the tax rate change itself.

Prominent features of our model are (i) search frictions, which give rise to equilib-

rium unemployment, as in the Diamond–Mortensen–Pissarides (DMP) framework

(Diamond 1982, Mortensen 1982, Pissarides 1985), and (ii) worker heterogeneity

in productivity or skills, which delivers an extensive margin of employment adjust-

ment.1Taxrates impinge on equilibrium allocations via two channels. First, they alter

the relative return of market to nonmarket activity, as in the standard model of labor

supply with home production. The second channel operates through the effective bar-

gaining power of the worker.That is, the higher the tax rate on labor income, the lower

the share of the surplus generated by a match accruing to the worker.

1. Recent empirical work points to the importance of worker heterogeneity for aggregatelabor-market

dynamics (Barnichon and Figura 2015, Ahn and Hamilton 2019).

DOMENICO FERRARO AND GIUSEPPE FIORI :1003

The model features endogenous separation and hiring in the form of occasionally

binding zero-surplus constraints: given a value for the tax rate and a level of aggre-

gate productivity, a zero-surplus constraint denes a cutoff on worker productivity

such that existing matches with workers whose productivity is below the cutoff are

endogenously destroyed. Analogously, meetings between employers posting vacan-

cies and workers whose productivity is below the cutoff are not converted into jobs.

In this sense, the model exhibits endogenous hiring standards in that who gets hired

depends on tax rates as well as aggregate productivity.

Given these features, the model embeds two mechanisms whose interaction can

yield highly nonlinear effects of tax policy. First, absent search frictions, the model

collapses to a frictionless setting with indivisible labor and heterogeneous workers.

A reservation wage rule determines the extent to which available labor services are

fully used or left idle. More specically, if the prevailing wage is above the reser-

vation wage, the individual is employed and producing output—otherwise, he or

she is unemployed. This mechanism generates V-shaped responses to tax rate hikes:

sharp contractions followed by quick recoveries. Second, search frictions, the extent

of which varies over the business cycle, impede the instantaneous creation of jobs,

leading to gradual recoveries. This mechanism induces L-shaped-type responses to

tax rate changes.

The dynamic response of the aggregate employment rate to changes in tax rates is

driven by two forces. First, the extent of search frictions, as measured by the market

tightness ratio, varies in response to tax shocks. Specically, the tightness ratio, and

therefore the probability that an unemployed worker bumps into a job vacancy, falls

in response to a tax rate hike. Furthermore, because the job-meeting probability is

concave in the tightness ratio, it drops more in response to a tax rate hike than it rises

in response to an equally sized tax rate cut. Note also that the stimulative, positive

effect of a tax rate cut on employment is damped by the presence of search frictions.

In the absence of frictions, the employment rate jumps to its new steady-state level

insofar as the tax rate cut is large enough to make workers willing to supply labor.

Second, a tax rate hike makes the zero-surplus constraint bind, implying an imme-

diate adjustment in employment through endogenous job destruction. Furthermore,

the larger the tax rate increase, the larger the fraction of workers hitting the zero-

surplus constraint and the more important is the active margin of job destruction.

This mechanism is a key driver of state dependence in tax policy. Specically, during

recessions, a larger fraction of low-productivity workers is at the margin, so even a

small tax rate cut can induce large responses in the aggregate employment rate.

To quantify these mechanisms, we parameterize the model using U.S. data, in-

cluding impulse response functions (IRFs) from proxy SVARs. Along with other

data moments, the model reproduces the “peak” response of the U.S. employment

rate (one minus the unemployment rate) to a narratively identied shock to the aver-

age marginal tax rate (AMTR). In the model, consistently with the IRF from proxy-