Anchoring Bias in Consensus Forecasts

8/17/2019 Anchoring Bias in Consensus Forecasts

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J O U R N A L O F F I NA NC I A L A N D OU ANTITATIVE ANALY SIS Vo l , 4 4 , No , 2 , Ap r , 2009 , p p , 3 6 9 - 3 9 0

COPYRIGHT 2009, MICHAEL G, FOSTER SCHOOL OF BUSINESS, UNIVERSITY

OF

W ASHINGTON, SEATTLE, WA 98195

do i : 10 ,1017 /S0022109009090127

Anchoring Bias in C onsensus Forecasts and

Its Effect on Market Prices

Sean

D

Campbell and Steven

A

Sharpe

Abstract

Previous empirical studies

on the

rationality

of

economic

and

financial forecasts gener-

ally test

for

generic properties such as bias or autocorrelated errors but provide only limited

insight into

the

behav ior behind inefficient forecasts. This paper tests

for a

specific form

of forecast bias.

In

particular, we examine whether expert consensus forecasts

of

monthly

econom ic releases are systematically biased toward the value

of

previous m onth s' releases.

Such

a

bias would

be

consistent with

the

anchoring

and

adjustment heuristic described

by Tversky and Kahneman (1974) or could arise from professional forec asters ' strategic

incentives,'We find broad-based and significant evidence for this form of bias, which in

some cases results in sizable predictable forecast errors. To investigate whether market

participants' expectations

are

influenced

by

this bias,

we

examine interest rate reactions

to economic news.

We

find that bond yields react only

to the

residual,

or

unpredictable,

component

of the

forecast error

and not to the

component induced

by

anchoring,

sug-

gesting that expectations

of

market participants anticipate this bias embedded

in

expert

forecasts,

•

I Jntroduction

Professiotial forecasts of macroeconomic releases play an importatit role

in markets, informing the decisions of both policymakers and private economic

decision makers. In light of this, and the substantial effects of data surprises on

asset prices, we might expect professional forecasters to avoid making systematic

prediction errors. Previous research has approached this topic by testing time se-

ries of forecasts for rationality, an approach with a fairly long and not entirely

satisfying history. Generally, such studies focus on testing for a few generic prop-


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37 Journal of Financial and Quantitative Analysis

limited insight into the nature of apparent bias. In addition, such studies provoke

but do not answer, the question: W hat are the implications of nonrational forecasts

for market prices? In particular, where persistent forecast biases exist, do the users

of these forecasts take predictions at face value when making investment dec isions

or dispensing advice? Or do they see through the biases, which would make such

anomalies irrelevant for market prices?

As noted by Tversky and Kahneman (1974), psychological studies of fore-

cast behavior find that predictions by individuals are prone to systematic biases,

which induce large and predictable forecast errors. One widely documented form

of systematic bias that influences predictions by nonprofessionals is anch oring ,

or choosing forecasts that are too close (anchored) to some easily observable prior

or arbitrary point of departure. Such behavior results in forecasts that underw eight

new information and can thus give rise to predictable forecast erro rs.

We investigate whether anchoring influences expert consensus forecasts col-

lected in surveys by Money Market Services (MMS), a widely used source of

forecasts in financial markets, between 1991 and 2006. In particular, we focus

on monthly macroeconomic data releases that are highly value-relevant, that is,

for example, Balduzzi, Elton, and

(2005)). Others, such as Aggarwal

those previously found to have substantial effects on market interest rates (see.

Green (2001), Gurkaynak, Sack, and Swanson

, Mohanty, and Song (1995) and Schirm (2003),

have subjected MMS consensus forecasts to tests of forecast efficiency and found

some evidence of systematic bias) We test the more specific hypothesis, borne of

years spent monitoring data releases and market reactions, that recent past values

of the da ta release act as an anchor on expert forecasts. For instance, in the case

of retail sales, we investigate whether the forecast of January sales growth tends

to be too close to the previously released estimate of December sales growth.

In short, we find broad-based and significant evidence that professional con-

sensus forecasts are indeed anchored toward the recent past values of the series

being forecasted. The degree and pattern of anchoring we measure is remarkably

consistent across the various data releases. Moreover, the influence of the anchor

in som e cases is quite substantial. We find that the typical forecast is weighted too

heavily toward its recent past. These results thus indicate that anchoring on the

recent past is a pervasive feature of expert consensus forecasts of economic data

releases known to move market interest rates.

These findings imply that the forecast errors or surprise s are at least partly

predictable in a fashion consistent with anchoring. Of course, interpreting this

as evidence of the behavioral bias spelled out in Tversky and Kahneman (1974)

requires the joint hypothesis that

these are meant to be unbiased forecasts. It is


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Cam pbell and Sharpe 371

Our second major contribution thus involves assessing whether anchoring

bias in economic forecasts affects market interest rates. Specifically, do interest

rates respond to the predictable, as well as the unpredictable, component of the

surprise? To answer this question, we decompose the surprise in each data release

into a predictable component induced by anchoring, plus a residual that can be

interpreted as the true surprise to the econometrician. We then test whether market

participants anticipate the bias by regressing the change in the two-year (or 10-

year) U.S. Treasury yield in the minutes surrounding the release onto these two

components of the forecast error.

We find that the bond market reacts strongly and in the expected direction

to the residual, or unpredictable, component of the surprises. On the other hand,

interest rates do not appear to respond to the predicted piece of the surprise in-

duced by anchoring. The results are similar for almost every release we consider.

We thus conclude that, by and large, the market looks through the anchoring bias

embedded in expert forecasts, so that this bias does not induce interest rate pre-

dictability or excess volatility.

The remainder of this paper is organized as follows. Section II lays out the

conceptual and empirical framework for the analysis. Section III describes basic

properties of the data releases and MM S consensus forecasts. Section IV estimates

the proposed model of anchoring b ias. Section V tests whether the anchoring bias

affects the response of market interest rates to data releases. Section VI concludes.

I I.

Forecast Bias Anchoring and Research Design

A. Rationality Tests and Anchoring

Many psychological and behavioral studies find that, in a variety of situa-

tions,

predictions by individuals systematically deviate too little from seemingly

arbitrary reference points, or anchors, which serve as starting points for those

predictions. As a result, those predictions underweight the forecasters' own infor-

mation.' Tversky and Kahneman (1974) define anchoring to occur when people

make estimates by starting from an initial value that is adjusted to yield the final

answer ... adjustments are typically insufficient... [and] different starting points

yield different estima tes, which are biased towards the initial values (p. 1128).

In this section, we characterize the relation between traditional tests of forecast

rationality and our proposed model of anchoring.

Testing whether macroeconomic forecasts have the properties of rational ex-

pectations has a fairly long tradition. A variety of early studies (for example,


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37 Journal of Financial and Quan titative Analysis

While the more recent studies brought some new methodological consider-

ations to the table, they have largely followed the basic formulation of this line

of research. In particular, the typical analysis involves running regressions with

the actual (realized) value of the data release,

A,,

as the dependent variable on the

most recent forecast, F,, as the independent variable; that is,

(1)

A\

= ß,F, e,.

The hypothesis of rationality holds that ß \ is not significantly different from unity

and the errors are not autocorrelated,^ Broadly speaking, the results from such

regressions tend to be mixed, with rationality being rejected in a substantial frac-

tion of the tests. Both Aggarwal et al, (1995) and Schirm (2003) find that, when

rationality is rejected, it is almost always due to a slope coefficient

ßi

greater than

unity. As an example of a strong rejection. Schirm (2003) estimates a slope coef

ficient of 1,62 in equation (1) for Durable Goods Orders, which suggests that the

MMS consensus predictions are too cautious; that is, errors would be reduced if

forecasted deviations (from average growth) were magnified 62%,

If forecasts could be improved by system atically magnifying them, the impli-

cation would be that forecasters are too slow or cautious when incorporating new

information. Indeed, in a different setting, Nordhaus (1987) provides direct evi-

dence of forecast inertia—that forecasters hold on to their prior view too long,

That inference is drawn from an analysis of fixed-event forecasts of GDP growth,

which shows that forecast revisions tend to be highly serially correlated,^ That set-

ting differs from the more conventional time series with rolling-event forecasts,

including the MMS forecasts that iw analyze.

If forecasters in the standard rolling-event setting put too little weight on new

information, this raises the question: What is the prior, or anchor, on which fore-

casters place too much weight? One plausible scenario is that forecasters treat the

value of the previous month's data as the most salient single piece of information

that has come to the fore in the time between their previous-month and current-

month forecasts. If so, then the previous month's realization might be treated as

a starting point, or anchor, for the current forecast, * More generally, forecasters

might place some weight on a few lags of the release, particularly when the fore-

casted series tends to bounce around from month to month (i,e,, exhibits negative

autocorrelation). At the extreme, forecasters might conceivably anchor their fore-

cast on a long-run average value for the series.

To develop this set of ideas more formally, consider the following transfor-

mation of equation (1), whereby the forecast is subtracted from both sides. This

yields an alternative version of the basic rationality test, where the forecast error


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Now, the canonical test of rationality examines whether the slope coefficient is

significantly different from zero. Under our alternative hypothesis, we look for

evidence in favor of the following model of forecast anchoring:

(3) F, = XE[A,]

{\-X Ä,„

where E[A,] represents the forecaster's unbiased prediction of next month's re-

lease and

Äh

represents the average value of the forecasted series over the pre-

vious

h

months. If A < 1, then we would conclude that consensus forecasts

are anchored to the recent past. Using the implication from equation (2) that

E[A,] = E[S ]

F,

and substituting for E[A ] in (3) yields an expression for ex-

pected surprise: E[5,] = 7(F, — Â;,), where 7 = (1 - A)/A. This suggests the

following regression test for anchoring bias:

(4) S, = 7 ( F , - Â / , ) + £ , .

A positive coefficient estimate would imply that consensus forecasts are system-

atically biased toward lagged values of the release (and A


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the surprise, or forecast error, arising from anchoritig bias in the same way they

react to the residual component of the surprise? Or do market participants antici-

pate the bias and thus respond only to the residual component of the surprise?

We study this question by estimating secotid-stage event-study regressions

in which the change in the two- ori 10-year Treasury yield around the time of the

release is regressed on the two components of equation (4):

5)

Ai =

where

S , =

E(S,) refers to the forecasted component of the surprise identified

from ordinary least square (OLS) estimates of equation (4). If financial mar-

kets respond to the forecasted component of the surprise induced by anchoring

in the same way they respond to the residual, or unforecasted component, then

we should find 6\ = 02- Alternatively, if financial markets see through the bias

in forecasts induced by anchoring] then we would expect that

5\ =

0. These two

alternative hypotheses are explored in Section V.

I. Data and Sam ple Characteristics

A. Macroecononnic Re leas es Forecasts and Surprises

Our analysis covers eight macroeconomic data releases: Consumer Confi-

dence, Consumer Price Index (CPI), Durable Goods Orders, Industrial Produc-

tion, Institute for Supply Management (ISM) Manufacturing Index, New Homes

Sales, and Retail Sales.^ In two cases, we also examine the consensus forecasts of

a key subcomponent of the top-line figure in the release (CPI ex-Food and Energy

(Core CPI) and Retail Sales ex-Auto). In both cases, these data are released si-

multaneously with the top-line release and are considered by market participants

to contain more value-relevant news than the top line.

Table

lists each release, thebeginning of our sample period, the timing of

the release, and the reporting convention, that is whether the release is reported as

a level, a change, or a percent change. While our last observation is March 2006

in each case, the starting date vaiiies between September 1992 and June 1996,

determined by the availability of the forecast data. For each release, we define the

consensus forecast,

F

as the mean forecast from the MMS survey.* The surprise

is measured as the difference between the release and the associated MMS mean

forecast.

We focus on these eight key releases because of their previously identi-


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TABLE 1

Économie Release Summary and Schedule

In Table 1, we report each data release, the month and year in whioh our sample period begins, the period in the foliowing

month when it is released, the time of the release, and whether the release is reported as a level, change, or percent

change.

Release

Consumer Ccni idence

Consumer Price index (CPi)

Core CPI

Durable Goods Orders

Industrial Production

ISM Index

Ncnfarm Payroll Employment

New Home Sales (in thousands)

Retail Sales

Retail Sales ex-Auto

Beginning of

Sample

09/1992

01/1993

01/1993

12/1992

12/1992

10/1992

10/1992

06/1996

01/1993

01/1993

Release Day

(next month)

Finai Tuesda y^

Third Wednesday

Third Wednesday

Fourth Thursday

Third week

First business d ay

First Friday

Fourth Wednesday

Second week

Seoond week

Release

Time (AM)

10:00

08:30

08:30

08:30

09:15

08:30

08:30

10:00 •

08:30

08:30

Reporting

• Convention

Levei

% change

% change

% change

% change

Levei

Change

Level

% change

% change

^Released in current month.

In Tahle 2, we present some summary statistics for each release A), its as-

sociated MMS forecast (F), and forecast surprise (5). For each variable we report

the sample mean (ju), standard deviation a), and the sum of the autoregressive

coefficients from a fifth-order autoregression ( ^ pj), a measure of persistence.^

Releases expressed in levels appear at the top of Table 2, followed by the remain-

ing releases. The mean surprise, reported in Table 2, is typically close to zero,

suggesting that the forecasts are unconditionally unbiased. Also, the standard de-

viations of the forecasts are in every case smaller than that of the releases. As one

would hope, the standard deviation of the surprises is typically smaller than that

for the underlying release, with Core CPI being the only exception. Not surpris-

ingly, for data releases that are expressed in levels, which have a high degree of

persistence, surprises are a lot less variable than the underlying release.

TABLE 2

Summary Statistics: iVIacroeconomic Releases, Forecasts, and Surprises

In Table 2, we report the sample m ean (/x), standard deviation (a ), and sum of the autoregressive coeffic ients from an

AR(5) {J2 Pi) 'Of the underiying reiease

.A),

its forecast (F), and the surprise (S = A - F). In the case of the sum of the

autoregressive coefficients J2 Pi), '. . and * denote signif icance at the 10%, 5%, and 1% levels, respectiveiy.

Release (A ) Forecast (F) Surprise (S )

Consumer Confidence

ISM ind ex

M

104.73

52.92

er

22.40

5.07

Pi

0 . 9 6 *

0.88—

ß

104.24

53.02

er

21.87

4.64

Pi

0.96***

0.89***

M

0,50

- 0 . 1 0

(T

4.97

2.06

Pi

- 0 . 1 4

0.18


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76 Journal of Financial and Quantitative Analysis

The persistence properties of the variables listed in Table 2 are informative

about the conditional properties of the MMS forecasts. In the case of the level

variables, both the release and the

releases and forecasts show small

forecast are highly persistent. The remaining

to moderate degrees of persistence, with the

exception of Durable Goods Orders and Retail Sales. These releases exhibit a

substantial and statistically significant degree of negative serial correlation; for

Durable Goods Orders, J^Pj =

- 2 . 0 8 ,

while for Retail Sales, ^pj = - 1 . 4 1 . ^ ' '

However, neither of the associated forecasts exhibits a significant amount of neg-

ative serial correlation, and thus the negative serial correlation of the data shows

up in the surprises. Interestingly, these are not the only releases where the surprise

exhibits significant negative serial correlation. The surprise is negatively serially

correlated in every case except for the ISM release. It is also statistically sig-

nificant in the case of the CPI, New Home Sales, Retail Sales, and Retail Sales

ex-A uto, suggesting that the MM S forecasts are conditionally b iased.

The finding that the serial correlation in surprises tends to be negative rather

than positive suggests that serial correlation in surprises could be due to the an-

choring of forecasts on the most recent lagged value of the release. This can be

illustrated by a simple example in which the release is serially uncorrelated. Sup-

pose forecasts were strongly anchored toward the recent past; in particulaif, that

the current forecast is set equal to the lagged actual value F, = A,_i). In this

simplified setting it is easy to see that

(6)

E [(/I, -

F

= E

[{A,

- A,_ , ) ( / ,_

I

- A,_2)]

that is, successive surprises will be negatively correlated.

Finally, before moving on to the main results, we note the unusual empirical

properties of the Core CPI and its associated forecasts. As shown in Table 2, the

Core CPI is by far the least variable of all releases; that is, both the release and the

associated surprise are significantly less volatile than any other release or surprise.

Over our sample period, the MMS

to 0.2% (monthly inflation rate) in

forecast of Core CPI is nearly constant, equal

117 out of 176 months. Thus , in the case of the

Core CPI, this sample period seems poorly suited to conducting our tests. Still,

we include the Core CPI release in our analysis because C ore CPI surprises have

substantial interest rate effects, which might otherwise be spuriously attributed to

top-line CPI surprises.

B Interest Rate Reactions to \/lacroeconomic New s Re lease s


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Bloomberg, For each release and maturity, we extract the quoted yield from a

trade occurring both five minutes prior and 10 minutes after the release. The in-

terest rate reaction is defined as the difference between the post- and pre-release

quote. If no quote exists five minutes before (10 minutes after) the release, we use

the last quote available between five and 30 minutes before the release (the first

quote available between 10 and 30 minutes after the release),'

In Table 3, we display the mean, standard deviation, and sum of au toregres-

sive coefficients of the interest rate reactions. The average interest rate response

is always close to zero, which is consistent with the near-zero mean of the as-

sociated surprises. The standard deviations of the interest rate reactions provide

some information about how much releases affect interest rates. Consistent with

the findings of Gurkaynak et al, (2005), the standard deviations of the two- and

10-year yield change are roughly similar. Also, consistent with the findings of

Balduzzi et al, (2001), the Nonfarm Payroll Employment release produces the

largest interest rate reactions.

TABLE 3

Summary Sfatisfics: Inferesf Rate Reactions to Macroeconomic Releases

In Table 3, we report the sample mean ((j), standard deviation

(CT),

and sum of the autoregressive coefficients

from an AR(5) Y, Pi) for the chang e in the tvïo-year U.S, Treasury yieid {AÍ2) an d the 10-year U.S. Treasury

in the moments surrounding each reiease. In the case of the sum of the autoregressive coefficients

and • '* den ote significance at the 10%, 5%, and 1 % ievels, respectively.

Consumer Confidence

ISM Index

New Heme Sales

Consumer Price index (CPI)

Core CPI


Industriai Production

Retaii Sales

Retaii Saies ex-Auto

Nonfarm Payroil Employment

0.0Ó

0.00

0.00

0.00

0.00

0.00

0.00

- 0 . 0 1

- 0 . 0 1

0.00

Tvïo-Year R esponse

ÍAÍ

0,02

0.03

0.02

0,03

0.03

0,03

0.02

0,04

0.04

0.09

. EP ,

0 . 2 7

0,37—

0,38

- 0 . 0 5

- 0 . 0 5

- 0 , 6 9 —

0.27- '

0.17

0.17

- 0 . 1 8

0.00

0.00

0.00

0.00

0.00

0.00

0.00

- 0 . 0 1

- 0 . 0 1

0.00

10-Year Response

î to

7

0.03

0.03

0.02

0.03

0.03

0.02

0.02

0.03

0.03

0.07

^P i

0,37—

0,28--

- 0 . 2 7

- 0 . 0 5

- 0 . 0 5

- 0 . 3 3

0 . 2 9

0.12

0,12

- 0 , 2 8

Looking at the persistence properties of the interest rate reactions indicates

that the degree of serial correlation in the interest rate responses is typically sm all,

ranging from -0,3 to 0,3 in most cases. In the case of Consumer Confidence,

ISM , Durable Goods O rders, and Industrial Production, however, the serial corre-

lation is statistically significant, which suggests that interest rate reactions might


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IV Estimates of Anchoring Bias

As discussed in Secfion II, our test for anchoring bias in MMS consensus

forecasts is based on the regression

(7) S, j{F,-Á, +e,,

where the dependent variable is the realized forecast error (or surp rise ) and the

independent, or prediction, variable equals the difference between the forecast

and the hypothesized an cho r. Implemen tation requires specifying the history of

release values h) used in our estimate of the anchor Ah). We focus on two cases;

in the first,

Äh

is simply the lagged value of the release '(/i=

),

while in the second

it equals the average value of the release over the lagging three months {h

3).'^

A positive value of the coefficient 7 would constitute evidence that forecast e rrors

are biased in a predictable fashion

Before proceeding, it should

that is consistent with anchoring.

be noted that this regression has some fairly

close an tecedents in the literature on rationality tests. In particular, equation (7) in

Aggarwal et al. (1995) would look very similar if the forecast were subtracted

from both sides

of

their equation.

In

add ition, their regression differs

in

two

respects: i) they effectively include only one lagged value of the release, mul-

tiplied by a constant (the autoregressive parameter of the forecasted series); and

ii) their estimation places no testable constraint on the coefficient estimates. In

sense, our main innovation relative to that regression is to employ a somew hat dif-

ferent set of testable constraints, which are suggested by our somewhat different

analytical orientation,'-'

We present the two alternative estimates of equation (4) for each of the

macroeconomic releases listed in

Table 1, The results for the three releases re-

ported (and predicted) in the form of levels are shown in the top three rows of

Table 4, The resu lts for the remaining re leases follow. The first two colum ns show

the coefficient on the forecast-anchor gap , the 7, and the R ^ for the case where the

anchor is assumed to be the prior

month's release

It =

1). The t;hird and fourth

columns show the analogous statisfics when the anchor is set to the average value

of the release over the prior three m onths

h=3).

For each macroeconomic release,

the results from the model with the highest R ^ are shown in bold.

Broadly speaking, the results indicate a fairly consisten t pattern of bias in

macroeconomic forecasts. The estimated coefficient

on

the gap between

the

consensus forecast and the previous month's release (one-month anchoring)

i

positive for every release, and, in six of 10 cases, it is significant at the 1%


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TABLE 4

Anchoring in Macroeconomic Forecasts

In Table 4, we report estimated slope coefficient, 7 , and f l^ from the modei, S( = 70 + 7(^ 1 — A_ f, ) + £|, The results that

equa te the previous m onth's value of the release vnith Âh fi = 1, are contained in the first tv O columns. The results that

equate the average of the three previous mon th's release with Ä/ i, h = 3, are contained in the final two columns, New ey

and West (1987) I-statistics are reported in parentheses. Results from the modei with the highest

R^

appear in bold.

Consumer Confidence

ISM Index

New Home Sales


^


Nonfarm Payroii Empioyment

Retaii Sales


Consumer Price Index (CPI)

Core CPI

7

0,71

6,10

0,22

1,26

0,53

2,75

0,16

(4,51)

0.14

3.24

0,06

(0,75)

0,25

4,74

0,29

4,04

0,06

(1,52)

0,04

0,67

One-Month

Anchoring

ñ 2 ( )

11.52

1.34

4,85

6,61

7,30

0,48

25,09

15,36

1,49

0.18

Three-Month

Anchoring

7

, 0,11

(1,60)

0,09

(0,88)

- 0 , 1 1

(0,57)

0.49

5.74

0,19

- (2,92)

0,25

1,91

0,34

(2,82)

0,37

• (3,12)

0,26

4,89

- 0 , 0 6

(0,41)

R 2 ( )

1,38

0,75

0,36

13.28

6,81

3,36

17,79

,7,50

15,36

0,10

level, Consideritig these results together with those frotn the three-motith atichor-

itig model, we find that the dotnitiatit model (in bold) has a significantly positive

coefficient for eight of 10 releases. Aside from the Core CPI, which earlier was

shown to be a poor candidate for this analysis, the coefficient in the dominant

(bold) model fails to be significant onlyjn the case of the ISM Manufacturing In-

dex. The ̂of the dominant models (again excluding the Core CPI) ranges from

1.3 to 25 , with an average value of around 11 .

The pattern of results is also sensible in light of the time series properties

of the releases. The top three data releases, each of which is expressed in levels,

were shown in Table 3 to display a high degree of persistence. In all three of

these cases, we find that the model with the one-month lag as the anchor clearly

dominates the model based on the three-month anchor. Although anchoring itself

may or may not be rational, the forecasters seem sophisticated enough to treat


12/23


value, (1 - A) = 7 /( 1 + 7 ) = 0.7|l/1.71 « 0.40. The

R ^

statistics of 11.5% for

Consum er Confidence and 4.9% for New Hom e Sales are also notable. Given the

importance of these releases for bond markets and the relatively large variance of

surprises, an

R ^

of even 5% represents a substantial amount of predictability with

potentially noticeable implications for interest rate responses to these releases.

The remaining releases in Table 4 are expressed in terms of changes or

percent chan ges . Am ong these, the evidence for anchoring is pretty strong for both

the one-month and the three-month anchoring models. In three of the six cases

(again leaving aside the Core CRI), the one-month anchoring model yields the

best fit. And in four cases (Durable Goods Orders, Industrial Production, Retail

Sales, and Retail Sales ex-Auto), the null hypothesis of no anchoring is rejected

at all conventional significance levjels regardless of whether a one- or three-m onth

anchor is employed. For CPI and Nonfarm Payroll Employment, anchoring is

significant in the case of the three- month anchor but not the one-month anchor.

The magnitude of anchoring in the MMS forecasts of the change variables

is generally somewhat less than that of the level variables, though it appears to

be economically meaningful in most cases. The magnitude for Retail Sales falls

close to the middle of the pack; the coefficient of 0.25 in the one-lag model for

Retail Sales implies forecasters place roughly 20% (0.25/1.25 = 0.20) of the

weight on that anchor. In addition, the forecast errors for Retail Sales appear to be

unusually predictable: the

R ^

suggests that the forecast-anchor gap explains 25%

of the variance in surprises. Among the other change variables, the R ^ covers a

range comparable to that ofth e level variables.

An implicit assumption of the OLS framework is that the professional fore-

casters' goal is to minimize the squared forecast errors. But they might face in-

centives under which this goal is not optimal, making our evidence potentially

misleading. As an alternative, Basu and Markov (2004) suggest the use of a lin-

ear loss function, which is implemented vis-à-vis median regression, based on the

notion that a 3% forecast error may only be three times m ore costly than a 1% er-

ror, rather than nine times as costly. Indeed, in a study of earnings forecasts, they

find that evidence of bias is significantly weakened when the median regression

approach is adopted.

We examine the robustness of our results by estimating equation (7) using

the median regression approach and find remarkably consistent results to those

in Table 4.''* Specifically, we find significant evidence of anchoring (i-statistic

in excess of 2.0) in all but one ease where the OLS produced significant evi-

dence of anchoring, the exception being New Home Sales (the three-month c ase).

Moreover, median regression estimates also resulted in statistically significant an-


13/23


The results in Table 4 indicate that the gap between the current forecast and

the anchor predicts future surprises in almost every release we consider. In those

tests,

the alternative hypothesis is that forecast errors are unpredictable, that is,

orthogonal to all known information. A more dem anding test of our model would

involve testing it against a more general model, for instance, a model where the

forecast error m ight be related to the current forecast for some unspecified reason.

To implement this, we test whether the coefficient on the hypothesized anchor is

opposite in sign and equal in magnitude to the coefficient on the current forecast.

In Table 5, we show estimates of the un restricted anchoring model,

8) , S =

For these regressions, we choose the anchor from the best-fitting model in Table 4.

The first column in Table 5 denotes the choice of anchor. The next two columns

display the point estimates of 7/ and 7^. The final two colum ns display the Wald

test that 7f = - 7 ^ and the model R^.

TABLE 5

Anchoring in Macroeconomic Forecasts:

Predicting Surprises with Forecasts and Lagged Reieases

In Table 5, we report estimates from the model, Si = 7f F, .̂ -TAA- I , + £(. The number' of months (h) used in construct-

ing the anchor {Ah , is seiected from the best-fitting model in Table 4 and is reported in the first column. The second

and third column report yp an d - I A . The fourth column reports the asymptotic p-vaiue of the Wald test of the re-

striction 7f = —fA . and the fifth coium n reports the R^. Newey and West (1987) f-statistics appear in parentheses.

h 7 , - A Wa ld fl2 ( )

Consumer Confidence

ISM Index

New Home Sales

Durabie Goods Orders

industriai Produotion


Retaii Saies

Retaii Sales ex-Auto

Consumer Price index (CPi)

1

1

1

3

1

3

1

1

3

0.76

(5.92)

0.25

(1.29)

0.46

(2.14)

0.55

(3.35)

• 0.23

(3.11)

0.36

(2.18)

0.31

(2.59)

0.36

(2.11)

0.35

- 0 . 7 4

(6.03)

- 0 . 2 4

(1.31)

- 0 . 5 0

(2.50)

- 0 . 4 2

(2.00)

- 0 . 1 1

(2.47)

- 0 . 2 3

(1.77)

- 0 . 2 3

(5.80)

- 0 . 2 7

(3.48)

- 0 . 1 5

0.27

0.72

0.38

0.68

0.06

0.08

0.43

0.61

0.07

12.00

1.43

5.40

13.38

9.42

4.92

25.43

15.53

17.22


14/23


the difference in the coefficients' magnitude is often remarkab ly sm all (e,g,, for

Consumer Confidence, 7/ = 0,76 and 7^ = —0,74),

The Wald tests reported in the fourth column of Table 5 show that only in

the aberrant case of Core CPIis the null hypothesis that 7/ = —7̂ rejected at

all conventional significance levels. Elsewhere, the Wald statistic provides scant

evidence against the null hypothesis. The possible exceptions are Industrial Pro-

duction and Nonfarm Payroll Employment, where the null hypothesis can be re-

jected at the 10 , but not the 5 , level. Even there, the discrepancies betw een

7/

and 7^ are relatively small. Finally, comparing the fit of the unrestricted and

restricted (Table 4, bold) models reveals only a small deterioration in fit when we

impose the 7/ = -74 restriction (in the original specification); the decline in

^

i

typically on the order of a percentage point.

Our model of anchoring bias

assumes that forecasters always tilt their fore-

cast toward the value of the previous m onth 's (or few m onth s') release by a simila

proportion. On the other hand, it is plausible that the extent to which forecasters

treat a lagged release as a reasonable starting point for current-month forecasts

could depend on whether that lagged release is viewed as representative or nor-

mal. For instance , when lagged realizations are far out of line with recent trends or

broader historical experience, they may have,less influence on current forecasts.

Of course, the opposite might be true; that is, it might be that most of the anchor-

ing occurs on the heels of outliers or trend-breaking obse rvations, while very little

anchoring occurs in normal times.

In principle, such considerations would suggest that a more complex spec-

ification than our simple anchoring model might be informative, but there is no

clear a priori case for any particular alternative. Thus, rather than postulate a m ore

complicated anchoring model, we simply re-estimate equation (4) on a subsam-

ple of observations that excludes outliers. Specifically, we exclude observations

in which the change in the release from month f

—

2 to f

—

1 is larger than

standard deviations of the historical monthly change in the release. The results are

contained in Table 6,

As with the model restrictioi tests in Table 5, we report results only for the

best-fitting model (one- or three-month anchoring) based on the Table 4 regres-

sions. The second and third columns report the estimates of 7 and the ̂ statistic

from the full sample, while the final two columns report the same for the sample

that excludes outliers. Broadly speaking, the outlier exclusion does not substan-

tially alter the picture. The estimates of 7 are all still positive; in most cases, the

estimated degree of anchoring appears to increase somewhat. The most notable

change is in the case of the ISM Manufacturing Index release, where the coeffi-


15/23


TABLE 6

Anchoring in Macroeconomic Forecasts: Excluding Outliers

In Table 6. we report estimates from the mo del, S| = 7 ( F | — / \ _ (, ) £(. using the fuli samp le and a subsa mp ie that excludes

observations in which the change in the previous month's release over the prior month is large (see text for detaiis). The

first column reports the number of months (fi) used in constructing the anchor (Äh). The second and third columns report

the parameter estimate. 7. and

^

from the fuil sampie. The fourth and fifth columns report the parameter estimate.

7. and

^

from the subsampie. Newey and West (1987) t-statistics appear in parentheses.

Consumer Confidence

iSM index

New Home Saies


Core CPI


ihdustriai Production

Nonfarm Payroii Employment

Retaii Sales



Core CPI

Lags

h

1

1

1

3

1

3

1

3

1

1

3

,1

Ail

Observations

7

0.71

• (6.10)

0.22

(1.26)

0.53

(2.75)

0.26

(4.89)

0.04 •

(0.67)

0.49

(5.74)

0.14

(3.24)

0.25

(1.91)

0.25

(4.74)

0.29

• (4.04)

0.26

(4.89)

0.04

(0.67)

R 2 ( )

11.52

1.34

4.85

15.36

0.18

13.28

7.30

3.36

25.09

15.36

15.36

0.18

7

0.79

(5.48)

0.44

(2.17)

0.54

(2.01)

0.21

(1.41)

0.03

(2.24)

0.61

(3.67)

0.17

(2.19)

0.17

(1.83)

0.23

(3.78)

0.41

(3.33)

0.21

(1.41)

0.03

(2.24)

Outiiers

Excluded

R2

( )

13.16

4.89

3.41

10.54

0.03

17.98

4.89

1.68

15.59

15.86

10.54

0.03

variance in future surprises. The pattern in the results is remarkably uniform. Ac-

cordingly, anchoring appears to be an important and robust feature of the MMS

forecast data. These findings thus raise the question that we examine in the sec-

ond part of our analys is: How does anchoring bias in these forecasts affect market

reactions to the measured surprises?

V. Testing Market Reactions

A, The Framework


16/23


(9)

Ai, =

6S

y

where Ai represents the change in the asset price in a small window surrounding

the release and the coefficient

ô

measures the sensitivity of the asset price to the

surprise, S = A

—

F .

The results above imply that these surprises—or forecast errors, to be

precise—are partly predictable due to anchoring bias in the MMS forecasts. If

markets are informationally efficient and market participants understand the na-

ture of this bias, then market prices should anticipate this component of the fore-

cast error. In particular, market interest rates should not respond to the p redictable

component of the forecast error. We investigate this hypothesis using the model

laid out in equation (5) of Section II, Ai =

Ô\S^ Ô2{S —

5f) +v,. Again, Ai r

resents the change in either the two- or 10-year U.S. Treasury bond yield in the

moments surrounding the release and 5f = 7(F, — Â;,) represents the predicted

component of the surprise induced by anchoring. We thus refer to the second

regressor as the residual component of the surprise—the true surprise, from the

econometrician s point of view.

We focus on two hypotheses concerning how market participants react to the

predicted and residual components of the surprise. If market participants take the

forecasts at face value and are unaware of the predictability in surprises, then we

would expect to find no difference in the response to the predicted and residual

components of the surprise, or ¿i =62. Finding ¿ =62 would indicate that the bond

markets are not informationally efficient in the sense that data known at the time

of the forecast can help predict movements in bond p rices. Alternatively, if market

forecasts are informationally efficient—market participants are aware of the pre-

dictability induced by anchoring in the MMS forecasts—then we would expect to

find no response of interest rates to variation in the predictable component of the

surprise, or ô\ = 0,

Our investigation of the response of interest rates to the predicted and resid-

ual components of surprises in macroeconomic releases is related to the previous

work of Mishkin (1981). Mishkin examines whether the surprise implied by the

reaction of interest rates to inflation news is consistent with the unpredictable

component of inflation identified from an autoregressive specification. Specifi-

cally, Mishkin estimates the following system.

(10)

Ai,

= a

ô

v ,

and


17/23

Campbell

and

Sharpe

85

which presumably incorporate a wealth of information beyond the lags of the

series being forecasted. Moreover, our analysis differentiates between forecasters

and trader/investors.

B Em pirical Results

Before reviewing the empirical results, we first introduce two variations on

the basic specification

of

equation (5) that apply

to

some o fthe releases. First,

we

control for revisions to previously released data that are announced along with the

current month's data. This is done by including the value ofthe revision as an ad-

ditional regressor. Revisions

are

announced with the release

of

Industrial Produc -

tion, Nonfarm Payrolls, and Retail Sales (both the top-line and ex-Auto releases).

For Nonfarm Payrolls and Retail Sales, revisions to two previous months of data

are released

and

included

as

regressors;

but to

conserve space,

we

only report

the parameter estimate

for

the most recent m onth's revision.

In

the Nonfarm Pay-

rolls regression, we also include a control for the surprise to the unemployment

rate (based on the MM S survey), which is released simultaneously but generally

with less market impact than

the

payroll num bers. Thus,

our

general event-study

regression

can be

written

as

(11)

Ai, =

6\S ,+52{S,-S ,) + R,-\-v,.

The second variation, used for Retail Sales and the CPI, is to include the

surprise decom positions

of

tw forecasted releases, the top-line release,

5 f,

and

its

key subcomponent,

¿ Xf

(Retail Sales ex-Auto or Core CPI, ex-Food and E nergy):

(12) Ai, = 5iS ,+02{S,-S ¡)+o\SX ¡ +

Here, {5\, Ô2 are the coefficients

on

the predicted surprise and the residual

for

the

top-line release, whereas {ô[, ¿2)

are the

coefficients

on the

key subcomponents.

The model

is

estimated via generalized method

of

moments (GM M).

In

par-

ticular, note that the terms S^{SXf) that appear in equations (11) and (Í2) are not

directly observed

and

must

be

estimated from

the

first-stage anchoring model

in

equation

(4).

These generated regressors infiuence

the

sampling distribution

of

the interest rate response coefficients {Si,S2,ô[,Ô2). In particular, the sampling

variability induced

by

using generated regressors tends

to

increase

the

amount

of

sampling variability

in the

secon d-stage coefficients. We follow

the

approach

of

Newey (1984) by including the first-stage anchoring model (equation (4)), along

with

the

second-stage event-study regressions (equations

(11) and

(12)),

in the

GMM system.'^

The

resulting variance-covariance matrix fully accounts

for the


18/23

386 Journal of Financial and Qua ntitative Analysis

one standard deviation of the (total) surprise,

S .

The ¡first three columns report

the parameter estimates. The fourth column reports the Wald test of the null hy-

pothesis that bond yields react symmetrically to the predictable and unpredictable

component of th MMS surprise,

\

= ¿ 2 ' ' ' T he fifth column reports the model

R^.

TABLE 7

Interest Rate Reactions to Ma croeconomic Releases

n Tabie 7, we report GMM estimates of the model,

the Wa id test that (5i = 62, the mod el's

R^.

and th

R | , in the final three columns. *** and ** deno te st

Consumer Confidence

2-year

10-year

ISM Index

2-year

10-year

New Home Sales

2-year

10-year


2-year

10-year


2-year

10-year


2-year

10-year

Retail Saies: Auto

2-year

10-year

Retail Sales: ex-Autc

2-year

10-year

CPI: Food and Energy

2-year

10-year

Core CPI

2-year

10-year

Looking down

0.19

0.07

- 2 . 3 3

- 3 . 4 5

0.09

0.10

- 0 . 2 5

- 0 . 4 5

- 0 . 1 2

0.00

1.06

0.97

0.03

0.09

- 0 . 2 0

- 0 . 3 2

- 0 . 3 2

- 0 . 7 4

7.43

6.50

the columns

Ail =

¿1S, + Ri

.̂ V|. We also report the p -value o

R^ from a regression of the interest rate chang e on the total surprise

itistical significance at the

1%

an d 5% levels, respectiveiy.

¿2

1 69

1 60

2.31***

2.09***

0.85***

0.82***

1 39

1 16

0.76***

0.74***

6.27***

4.96***

1 44

1.31***

3.28***

2.80***

- 0 . 3 8

- 0 . 3 6

2 2 9 —

2.14***

of Table

-

-

-

-

0.55***

0.49***

1 65

1 08

1 62

1 02

1 23

1 08

-

-

7 reveals

0.00

0.00

0.23

0.21

0.21

0.23

0.00

0.00

0.07

0.09

0.08

0.07

0.17

0.12

0.02

0.01

0.96

0.71

0.68

0.69

R 2 ( % )

46.9

44.0

52.4

51.9

17.3

17.6

• 22.6

19.4

20.7

19.2

57.3

50.8

30.4

29.2

30.4

29.2

28.8

28.6

28.8

28.6

three broad findings.

fl| (•%

38.1

39.4

49.6

47.4

16.6

17.0

18.5

14.4

19.2

18.2

56.3

49.8

25.4

23.5

25.4

23.5

28.5

28.3

28.5

28.3

First

consistent with previous research, we find that the releases account for a

signif

icant fraction of bond yield movements, ranging from roughly 20% to 50%, as

measured by the iO^. Second, the estimate of

¿2,

the coefficient on the unexpect

component of the surprise on bond yields, is significant at the 1% level for ev-


19/23


Wald test of the null hypothesis that bond yields react symmetrically to the un-

expected and expected components of the surprise is rejected at the 10% level or

lower in five out of eight cases,'^ This is notable, since the Wald test fully ac-

counts for the extra variability in the measurement of

ôi

resulting from 5f being a

generated regressor.

Focusing on the results for individual releases indicates that the exceptions

to the broad pattern of results can largely be rationalized as special situations.

First, for the (top-line) CPI, both the expected and unexpected components of

the surprise are not significant, so vve obviously would be unable to reject the

hypothesis that the components have the same effect. But this owes to the finding

that, conditional on Core CPI, shocks to the total CPI (including Food and Energy)

have little incremental effect on bond yields,'^ The market perceives the Core

CPI as a better indicator of future inflation and Federal Reserve policy. The o ther

obvious exception is in the Core CPI results. Here, we find that the estimated

magnitude of ¿2 is large and not significantly different from ¿1, But this result

presumably owes to the poor performance of the anchoring model for the Core

CPI, which explains less than 1% of the variation in the surprise. As previously

argued, this could be attributable to the granularity of Core CPI and its resultant

lack of time-series variation in our sample period,

A few other aspects to our finding s in Table 7 are notable, even if not central

to our main hypotheses. First, we are comforted by the finding—consistent with

previous research findings and views on Wall Street—that the employment release

shows the largest interest rate effects and has the most explanatory power of all

the releases (in the event study window). It is also interesting to note that in every

case where it is available, the revision to the previous month's data (^) also has

a significant positive effect on interest rates. Surprisingly, in most of these cases,

the coefficient on the revision is almost as large as the coefficient on the current

month (residual) surprise.

Finally, for comparison purposes, column (6) shows

R^

statistics from the

standard event study regression model of data surprises (equation (9)), which

does not split up the forecast error into two pieces. Comparing these statistics

to those in column (5) provides one quantitative measure of how much better our

anchoring model explains interest rate movements compared to that benchmark.

Comparing columns (5) and (6) reveals that adjusting for the predictable com-

ponent of the surprise increases the explanatory power of the releases for interest

rate movements in every case that we consider,^° In some cases such as Consumer


20/23


Confidence, Durable Goods, and Retail Sales the increase in ̂ can be substan-

tial, on the order of

2 5 % ,

while in the case of other releases the improvement is

more modest, ranging between 1% and 10%,

Summing up, the resuhs in Table 7 suggest that market participants do react

to the unpredictable com ponent but not to the predictable component of the M MS

surprises. Moreover, focusing on the unpredictable component of the surprise uni-

formly increases the explanatory power of the releases for interest rate changes.

Accordingly, these results suggest that the informational inefficiency of MMS

forecasts identified in Tables 4, 5,

and 6 does not lead to any important source of

inefficiency in interest rate marke ts. Market participants apparently anticipate the

anchoring behavior of professional forecasters.

V I Conclusions

We find that professional economic forecasts are biased in a manner consis-

tent with a specific behavioral model of forecasting behavior: the anchoring and

adjustment hypo thesis of Tversky and Kahnem an (1974), Specifically, we find

that forecasts of any given release are anchored toward recent months' realized

values of that release, thereby giving rise to predictable surprises. In some cases,

such as Retail Sales, we find that up to 2 5 % of the surprise in the macroeconom ic

release is predictable, due to a substantial weight being placed on the anchor by

professional forecasters. Moreover, the evidence in favor of anchoring is remark-

ably consistent across each of the key releases that we study and is robust to the

exclusion of outliers.

In light of the significant evidence of systematic bias in professional fore-

casts,

we examine the implications for market prices of U.S, Treasury bonds.

Specifically, we exam ine whe ther ¡yields on two- and 10-year Treasury yields react

to thé predictable component of forecast surprises induced by anchoring behav-

ior. Across the board, we find that interest rates only respond to the unpredictable

component of the surprise. Estimates of the market reaction to the predictable

component of data surprise in every case are small and insignificant, whereas the

estimated reaction to the unpredictable component is large and significant.

We thereby conclude that market participants do not take professional fore-

casts at face value when responding to macroeconomic news. To the contrary, at

least some influential market participants are apparently able to parse the com-

ponent of these forecasts due to anchoring from the component of the forecasts

containing useful information about the expected future path of these macro-

economic variables. As a result.

the behavioral bias displayed by the forecasts


21/23


In that case, minimizing mean squared or absolute error would not necessarily be

the optimal strategy,

A related point is that our findings only provide a characterization of the bias

of a represen tative forecaster, and this ignores the likelihood that there are sub-

stantial cross-sectional differences in ability. What is more, individual forecasts

are likely to be influenced by strategic considerations, as suggested by Ehrbeck

and Waldmann (1996) or Ottaviani and Sorensen (2006), Indeed, the latter study

models circumstances in which forecasters might find it optimal to issue forecasts

that underweight their own private signals.

Finally, our findings raise the question of whether other markets are as adept

as the U.S, Treasury market at processing the information in professional fore-

casts.

In

particular, we wonder whether biases

in

professional forecasts are

a

source of inefficiency in markets that are comm only perceived to be less efficient

than the U.S, Treasury market, such as markets for individual stocks.

Appendix Specification of GM M System R eported in Table 7

Following Newey (1984), we account for the generated regressors in equations (10)

and (11) by including the specification of the anchoring model, equation (4), in the GMM

system. Specifically, we estimate the following exactly identified GMM system for each

data release (row) contained in Table 7:

A-l

=

-h,

(6 )

=

y

5,-70-71

{Pt-Ah))

F,-Â,,)

{Ai, - ¿0 - 5|5f -

Ö2

(5 , - 5 0 - 0/?,)

{Ai, -

¿0

-

àxS',

-

Si {S,

-

SI)

-

4>R,)

5f

{Ai,

-

(5o

-

(5,5f

-

¿2 (5 ,

-

5f)

-

R,) R ,

in the case of Consumer Confidence, ISM Index, New Homes Sales, Durable Goods, In-

dustrial Prod uction, and Nonfarm Payroll Employm ent, In the case of Retail Sales and CPI,

we estimate the system

(A-2)

{S ,

-

10

-

jy {F,

-

Ak))


22/23


in the case of Retail Sales and the GPI. In each case the GMM system is estimated by

minimizing, gT{0)'gT{0), over 6 andlnote the omission of a weighting matrix due to the

just identified nature of the system. Finally, the variance-covariance matrix is estimated by

(A-3)

where

(A-4)

ST =

' o , r

E

^ ^ ^

dgr {e) •

system is estimated for each release and each bond maturity

and

(A-5)

Finally, we note that a separate

(two and 10 years).

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Anchoring Bias in Consensus Forecasts

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