The Time‐Varying Response of Hours Worked to a Productivity Shock

• Published date: 01 October 2023
• Author: HUACHEN LI
• Date: 01 October 2023
• DOI: http://doi.org/10.1111/jmcb.12976

DOI: 10.1111/jmcb.12976

HUACH EN LI

The Time-Varying Response of Hours Worked to a

Productivity Shock

This paper revisits the dynamic response of hours worked to a total factor

productivity (TFP) shock. I estimate a structural vector autoregression that

includes time-varying parameters and stochastic volatility. The estimation

produces structural parameters that are consistent with the long-run identi-

cation. The impulse response functions of hours worked to a TFP shock

are negative on impact and at the business cycle horizons. This is evidence

that Galí (1999) would interpret as supporting new Keynesian theory. My

results also show that TFP shocks are the dominant source of variation in

average labor productivity.Structural changes in the U.S. economy play an

important role in the TFP–hours worked relationship.

JEL codes: E32, E24, J22

Keywords: hours worked, structural vector autoregression,stochastic

volatility, total factor productivity, time-varying parameters

T     factor productivity (TFP) shock on

hours worked has been debated by macroeconomists since at least Lucas and Rapping

(1969). One reason for the controversy is the disparate predictions made by neoclassi-

cal and new Keynesian models. Canonical one-sector stochastic growth models with

Cobb–Douglas technology, a random walk TFP shock, and history-independent pref-

erences call for a positive response of hours worked to a TFP shock. Traditional and

new Keynesian models are often associated with a promise that hours worked fall in

reaction to a TFP shock.

The lack of consensus among macroeconomists is given empirical content by

studying the dynamic relationship between average labor productivity (ALP) and

hours worked. Galí (1999) stands out as important for changing the debate about TFP

This paper is based on the rst chapter of my Ph.D. dissertation. I thank my dissertation advisor Jim

Nason. I am grateful to the editor,Pok-sang Lam, and two referees for their valuable comments and sugges-

tions that improved the paper. Thanks also go to Giuseppe Fiori, Eric Leeper,Douglas Pearce, Xiaoyong

Zheng, and participants at the N.C. State University Monday lunch macroeconomics workshop and the

macroeconomics seminar series for their thoughtful comments. Remaining errors are my own.

H L is an Assistant Professor of Economics, Department of Economics, KenyonCollege (E-

mail: Li8@kenyon.edu).

Received November 26, 2018; and accepted in revised form December 17, 2021.

Journal of Money, Credit and Banking, Vol. 55, No. 7 (October 2023)

© 2022 The Ohio State University.

1908 :MONEY,CREDIT AND BANKING

and hours worked. Motivated by the results of Dickey–Fuller tests, he assumes that

ALP and hours worked are integrated of order 1, which means that both variables are

rst-differenced (in logs) to achieve stationarity. Galí uses a long-run restriction to

identify the orthogonalized structural shocks. The restriction imposes long-run neu-

trality on ALP.This restricts ALP to respond only to TFP shocks in the long run.1He

nds evidence that a positive TFP shock leads to a decline in hours worked, which he

interprets as a rejection of real business cycle (RBC) theory.This is evidence for Galí

to argue that output uctuations are dominated by nontechnology shocks. Hence, the

result favors new Keynesian models with imperfect competition and sticky prices,

according to Galí.

I investigate the TFP-hours worked relationship following Gambetti (2005) and

Galí and Gambetti (2009) to include time-varying parameters (TVPs) in a structural

vector autoregression (SVAR) that also has stochastic volatility (SV) in the errors.

Advances in econometric methods allow me to estimate the TVP-SV-SVAR that is

consistent with the nonlinear identication induced by Galí’s identifying restriction.

The TVP-SV-SVARs are estimated to ask: Can robust implications about the effect

of hours worked to a TFP shock be drawn by allowing for structural change in the

post-war U.S. data?

Keeping Galí (1999)’s long-run identication intact, this paper presents evidence

about the response of hours worked to a TFP shock that is robust to structural changes

in the U.S. economy since 1948. Similar to Galí and Gambetti (2009), I account for

structural change in the data with TVPs and SVs. Including TVPs and SVs gives the

SVAR the exibility to capture any changes in the conditional mean, volatility, and/or

persistence in the data. Allowing for changes in the macroeconomic environment is

an important step in deriving reliable VAR estimates (Stock and Watson 2002, Galí,

Lopez-Salido, and Valles 2003).

I estimate TVP-SV-SVARs on ALP and hours worked from 1948Q1 to 2017Q2.

The estimates rely on a Metropolis-within-Gibbs algorithm developed by Canovaand

Perez-Forero (2015). The Canova and Perez-Forero (CPF) TVP-SV-SVAR estimator

is useful for at least three reasons. First, the CPF estimator is exible enough to consis-

tently estimate the Blanchard and Quah decomposition within a TVP-SV-SVAR. The

intercepts and slope parameters in this paper are consistent with the long-run identi-

cation. The algorithm is a Bayesian Markov chain Monte Carlo (MCMC) posterior

simulator that estimates a nonlinear state space model. Since long-run identication

is nonlinear in the reduced-form TVP parameter space, the CPF algorithm imposes

restrictions during the Gibbs sampling steps to estimate long-run identied SVARs,

instead of at postestimation after a block by block routine such as Primiceri (2005).

Second, the structural intercepts and slope parameters are adjusted and checked

for stationarity at each draw and each date following Koop and Potter (2011). Ac-

cording to Koop and Potter, failure to ensure stationarity of the intercepts and slope

parameters at each date leads to erroneous estimates of the posterior of the Bayesian

SVAR. Third, the sampler in this paper draws from the correct posterior distribution

1. In this paper, I refer to a technology shock and a TFP shock interchangeably.