The output gap and expected security returns

• DOI: http://doi.org/10.1016/j.rfe.2014.04.001
• Published date: 01 September 2014
• Author: Anindya Biswas
• Date: 01 September 2014

The output gap and expected security returns

Anindya Biswas ⁎

Divisionof Business, Spring HillCollege, Mobile, AL 36608,United States

abstractarticle info

Articlehistory:

Received16 January 2014

Receivedin revised form 24 April 2014

Accepted28 April 2014

Availableonline 5 May 2014

JEL classification:

E44

G17

Keywords:

Marketreturns predictability

Outputgap

Real-timedata

MIDASregression

Beta-weightingscheme

This paperanalyzes the impact of the output gapon market excess returns. The outputgap is usually defined as

the deviationof output from potentialoutput that is indicatedby the trend output. However,this study departs

from the common approach of calculatingthe output gap based on a simple trend line. It uses a flexible data-

driven weightingscheme, and it uses onlythe available information thatcorresponds to each forecastingorigin

to derive the outputgap. Overall, the proposed outputgap is a strong predictor of U.S. marketexcess returns.

© 2014 ElsevierInc. All rights reserved.

1. Introduction

The goal of this paper is to analyze th e impact of the output gap,

that is, fluctuationsin the aggregate output level of an economy, on fu-

ture market excess returns. Follow ing the well-known Taylor's rule

(Taylor, 1993), this gap is believed to be one of the important determi-

nantsfor the federal funds rate.

1

Such a rateis generally manipulatedin

order to regulate macroeconomic variables like inflation, unempl oy-

ment,and gross domestic product(GDP), but its impacton the financial

sector can hardlybe over-emphasized. Thereis a long-standing debate

regarding the appropriate measurementof the output gap. The debate

revolves around the questionof how potential output should be mea-

sured, as there can be no directly availabledata for a potential output.

The common practice is to measure the output gap by fitting a single

trend linefor actual output with equalweights to each period'soutput.

The outputgap is the deviation of the actual outputfrom the trend out-

put. We cannot, however,forget that underlying economic conditions

change withtime.

In general, a period'soutput is more closely related to the adjacent

periods'output than the distantperiods' output, and thecommon mea-

sure of the output gap usesfuture information because it is basedon a

trendline that is fitted to the full sampleof the data and hence, it suffers

fromlook-ahead bias, towhich the recent literaturepays closeattention

(Welch & Goyal, 2008). These twoobservations make a casefor consid-

ering distanceweighting in calculatingthe output gap. Becauseof look-

ahead bias, the use of a common measure of the output gap as an ex-

ante predictor in a real-time fore casting framework is questionable.

Since the output gap is widely used in determining many macroeco-

nomic policies, such as Taylor'srule (1993),Okun's law (1962),etc.,it

is important to investigate its derivation in an ex-ante set-up that can

alsoeffectively accountfor the changing natureof the economy. The ob-

jectiveof this study is to providea flexible data-drivenex-ante measure

of the output gap and then to test its predictability for market excess

returns.

This study proposes a new measureof the ex-ante output gap, the

weighted average output gap (WAga p). The WAgap at any point tis

equal to the (log of) output at tminus the distance-weightedaverage

of the (logof) output data until the periodt−1. The weighting scheme

on theprior output data is basedon a single parameterbeta distribution

where the weighting parameteris estimated within a Quasi-Maximum

Likelihood Estimation (QMLE) fram ework that will be explained in

detail in the next section. Throughout this analysis, the output gap is

Reviewof Financial Economics 23 (2014)131–140

⁎Tel.: +1 251 380 4386; fax:+ 1 251 470 2178.

E-mailaddress: abiswas@shc.edu.

1

Taylor'srule determinesthe targeted federalfunds rate based on the outputand infla-

tiongaps. It follows from the rule thata tightmonetary policy or a high federalfunds rate

shouldbe adopted in timesof positive gaps.Given some simplifyingassumptions,the rule

can be statedas

it¼πtþr

tþaππt−π

t



þayyt−ytÞð

wherei

t

is the federalfunds rate, π

t

is the actualinflation rate, π

t

∗

is the desiredrate of in-

flation, y

t

is the logof real output, ytis the log of potentialoutput, r

t

∗

is the assumedequi-

libriumreal interestrate, a

π

isthe coefficient of the inflationgap, and a

y

isthe coefficient of

the outputgap (a

π

and a

y

shouldbe positive according tothe rule).

http://dx.doi.org/10.1016/j.rfe.2014.04.001

1058-3300/©2014 Elsevier Inc. All rightsreserved.

Contents listsavailable at ScienceDirect

Review of Financial Economics

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