Nominal GDP Targeting with Heterogeneous Labor Supply

• Published date: 01 February 2020
• Author: JAMES BULLARD,AARTI SINGH
• Date: 01 February 2020
• DOI: http://doi.org/10.1111/jmcb.12615

DOI: 10.1111/jmcb.12615

JAMES BULLARD

AARTI SINGH

Nominal GDP Targeting with Heterogeneous

Labor Supply

Westudy nominal gross domestic product (GDP) targeting as optimal mone-

tary policy in a model with a credit market friction followingAzariadis et al.

(2018), henceforth ABSS. Weextend the ABSS framework to allow for het-

erogeneous labor supply. We show that nominal GDP targeting continues

to characterize optimal monetary policy in this setting. We also analyze the

incomplete markets equilibrium that exists when the monetary policymaker

pursues a suboptimal policy, and show how an extension to more general

preferences can limit the ability of the policymaker to provide full insurance

to households in this setting.

JEL codes: E4, E5

Keywords: Non-state contingent nominal contracting, optimal monetary

policy, nominal GDP targeting, life cycle economies, heterogeneous

households, credit market participation, labor supply.

INTRODUCTION.RECENT PAPERS BY SHEEDY (2014), Koenig

(2013), and Azariadis et al. (2018), hereafter ABSS, provide analyses of optimal

monetary policy in economies where the key friction is in the credit market in the

form of nonstate contingent nominal contracting (NSCNC). They all show that op-

timal policy can be characterized as a version of nominal gross domestic product

(NGDP) targeting in that environment. The monetary policy provides a form of

insurance to private sector credit-using households.

We thank two anonymousreferees, David Andolfatto, Been-Lon Chen, Yunjong Eo, Thomas Sargent,

Chung-Shu Wu, and seminar participants at Narodowy Bank Polski, Bank of Korea’s Policy Conference,

Academia Sinica, Society for Computational Economics and Finance, and London School of Economics

for their constructive input. We are grateful for the financial support from the Facultyof Arts and Social

Sciences, University of Sydney FRSS grant(Singh). The usual disclaimers apply.

Any views expressed are those of the authors and do not necessarily reflect the views of others on the

Federal Open Market Committee.

JAMES BULLARD is the President of the Federal Reserve Bank of St. Louis (E-mail:

james.b.bullard@stls.frb.org). AARTI SINGH is a senior lecturer in the School of Economics, University of

Sydney (E-mail: aarti.singh@sydney.edu.au).

Received February 13, 2017; and accepted in revised form November 27, 2018.

Journal of Money, Credit and Banking, Vol. 52, No. 1 (February 2020)

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2019 The Ohio State University

38 :MONEY,CREDIT AND BANKING

The ABSS model is based on credit-using households with inelastic labor supply.

An open question is whether the optimal monetary policy they isolate could continue

to be characterized as NGDP targeting if credit-using households were allowed

to adjust labor supply in response to shocks. In principle, these (heterogeneous)

households may be able to partially self-insure in this circumstance, thus altering the

nature of the NGDP targeting policy or even rendering it unnecessary. Our goal is to

study this issue in this paper.

We construct an extension of the life cycle framework of ABSS to a case of

endogenous (and heterogeneous) labor supply.1In particular,credit-using households

now have homothetic preferences defined overboth consumption and leisure choices.

We think that this is a step toward realism in models of this type, but we do not

consider this version of the model to be sophisticated enough to compare to data in a

comprehensive way.2

Our main finding is that NGDP targeting continues to characterize the optimal

monetary policy in the situation with endogenous and heterogeneous labor supply.

The policy completely repairs the distortion caused by the NSCNC friction and

allows all credit-using households to consume equal amounts at each date. This is

the hallmark of the NGDP targeting policy in this model—under this policy, credit

markets are characterized by “equity share” contracting, which is optimal when

preferences are homothetic. In this respect, the findings here are consistent with the

findings of Koenig (2013) and Sheedy (2014).

Our main result is a version of the “divine coincidence” result familiar from the

New Keynesian monetary policy literature.3In our model, there is a single friction,

which is NSCNC in the credit sector. Monetary policy can alter the price level to

eliminate the distortion arising from this friction and restore the first-best allocation

of resources. Our main result shows that, in this situation, households are able to

choose their optimal level of labor supply as well, and, in fact, these heterogeneous

labor supply choices are independent of the aggregate shock in the model. The divine

coincidence is that, by completely mitigating the credit market friction, the monetary

policy also allows for optimal labor supply choices.

Additional Motivation. Aside from the issue of the circumstances under which the

NGDP targeting policy remains optimal in the face of endogenous labor supply

in this setting, we additionally motivate the paper with a contemporary issue in

monetary policy. Since the 2007–09 financial crisis, the labor force participation rate

in the U.S. has been low and falling.4A key question for monetary policymakers

has been whether the falling labor force participation rate is driven by business

1. Sheedy (2014) and Koenig (2013) also consider labor supply in their models. In our model, we

have more than two types of agents and so it is not clear how endogenous labor supply would impinge on

the NGDP targeting result in that case.

2. We hope to take up the challenge of matching data in future versionsof the model.

3. See Blanchard and Gali (2010) and Woodford (2003).

4. The literature documenting the fall in the labor force participation rate is growing. See, for example,

Aaronson et al. (2014), Van Zandweghe(2012), Daly et al. (2012), and Hotchkiss and Rios-Avila (2013)

among others.

JAMES BULLARD AND AARTISINGH :39

FIG. 1. The first figure, left panel, from Erceg and Levin(2014). After the financialcrisis and recession of 2007–09, labor

force participation in the United States fell more than its forecast by leading government agencies.

cycle factors, in which case monetary policymakers may want to attempt to increase

the participation rate through monetary policy choices. But an alternative, and we

think more traditional, view is that the labor force participation rate is driven by

demographic factors, in which case policymakers will be unable to meaningfully

change the participation rate via monetary policy. The results in this paper provide

some support for the traditional view.

Figure 1 is the first figure from Erceg and Levin (2014). They suggest, based

on this evidence from 2004 to 2013, that labor force participation fell much more

than expected by some government agencies in the aftermath of the financial cri-

sis and recession of 2007–09 in the U.S. They construct a New Keynesian model

of monetary policy in which the labor force participation rate would not be an

important cyclical variable in normal times, but which may remain significantly

depressed following a particularly large macroeconomic shock. They find that mon-

etary policy may be able to help mitigate an inefficiently low level of labor force

participation.

Figure 2 offers a different take on the same data. This figure again shows the

U.S. labor force participation rate, the solid line, this time from 1991 to 2015. The

figure also shows a forecast labor force participation rate due to Aaronson et al.

(2006), represented by the dotted line in the figure. The Aaronson et al. (2006)

model is based importantly on demographic effects. Their 2006 model successfully

predicted the decline in labor force participation as of the 2013–15 time frame, about

7–9 years in the future.5We think of the Aaronson et al. (2006) findings as consistent

5. Hall and Petrosky-Nadeau (2016) and Daly et al. (2012) among others also attribute declining labor

force participation rates to ongoing secular change in trend. In a recent paper, Krueger (2016) plots a