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The Federal Reserve’s Forecast Asymmetries Over the Business

Cycle

Julieta CaunedoDepartment of Economics

Washington University at St. Louis

Riccardo DiCecioResearch Division

Federal Reserve Bank of St. Louis

Ivana KomunjerDepartment of Economics

University of California, San Diego

Michael T. OwyangResearch Division

Federal Reserve Bank of St. Louis

Keywords: forecast rationality, loss function, Taylor rule, Greenbook forecastsPreliminary and Incomplete: Please Do Not Cite or Distribute

October 30, 2011

Abstract

We jointly test the rationality of the Federal Reserve’s Greenbook forecasts of in‡ation, un-

employment, and output using the multivariate nonseparable asymmetric loss function describedin Komunjer and Owyang (2007). We …nd that the forecasts are rationalizable but exhibit di-rectional asymmetry which depends on the phase of the business cycle. In particular, we …ndthat the Greenbook’ output forecasts tend to be conservative (i.e., positive in recessions andnegative in expansions). These results have potetnially important implications for thistoricalanalysis of monetary policy. [JEL codes: C32; E32]

Kate Vermann provided research assistance. The authors bene…tted from comments from and conversationswith Costats Azariadis, Mike McCracken, and Chris Otrok. Views expressed here are the authors’ alone and do notre‡ect the opinions of the Federal Reserve Bank of St. Louis or the Federal Reserve System.



1 Introduction

The Federal Reserve produces a set of forecasts used to conduct monetary policy. Made publicly

available at a 5-year lag, these so-called Greenbook forecasts have been used to study various aspects

of Fed behavior such as whether the Fed’s forecasts are rationalizable or whether the Fed has an

informational advantage over the private sector. For example, others have previously found that

Fed’s forecast errors are, on average, biased and/or correlated with the information available at

the time the forecasts are made. Standard tests – e.g., those employing Theil—Mincer—Zarnowitz

regressions – subsequently reject that the Fed forecasts are rationalizable.

More recent studies, however, have augmented these rationality tests by allowing for direc-

tionally asymmetric preferences (see Elliott, Komunjer, and Timmermann, 2005 and 2008). For

example, private sector output forecasts might be used to predict demand for a product. Under-

predicting output could lead to excess demand; overprediction could result in excess supply. Once

could imagine circumstances in which the forecaster – in this case, the …rm producing the output

– might not experience equal loss for the two cases. After allowing asymmetric loss, Elliott, Ko-

munjer, and Timmermann (2008, EKT) show that the majority of forecasters produce forecasts

which are rationalizable. The interest then becomes the nature of the forecaster’s preferences – i.e.,

does she prefer missing high versus missing low? Komunjer and Owyang (2007) extend EKT by

proposing a family of nonseparable asymmetric loss functions. In their paper, the loss depends on

the joint outcome rather than simply the sum of the individual losses.

We reconsider the rationalizability of the Greenbook forecasts allowing for the asymmetric non-

separable preferences described in Komunjer and Owyang. We evaluate forecasts of output growth,

unemployment, and in‡ation. We allow the forecaster’s – in this case, the Fed’s – preferences to be

state dependent, varying over the business cycle. We …nd that the Fed’s directional preferences ap-

pear to change over the cycle: The Fed prefers overprediction during recessions and underprediction

during expansions.

We are not the …rst to study Greenbook forecasts. Using the univariate losses proposed by EKT,

Capistrán (2008) found the Greenbook forecasts to be rationalizable. He also argued that Paul

Volcker’s appointment as Chairman was associated with changes in the Federal Reserve’s forecast

behavior (see also Orphanides, 1998; Orphanides, 2000; Clarida, Galí, and Gertler, 1999). Studying

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the Fed’s in‡ation forecasts, Capistrán …nds that the Fed was essentially directionally symmetric

prior to Volcker but preferred overprediction of in‡ation post-Volcker. Our results slightly con-

trast Capistrán’s: We …nd that the Fed is directionally symmetric over in‡ation outcomes during

expansions both pre- and post-Volcker but overpredicts in‡ation during recessions.

The balance of the paper is outlined as follows: Section 2 reviews the multivariate nonseparable

asymmetric loss function and its properties. We also provide an illustrative example of nonseparable

versus separable loss. Section 3 describes the Greenbook forecast data, the realization data, and

the instruments. This section also describes the estimation of the loss function parameters and the

J-test used to evaluate forecast rationality. Section 4 describes the results of the forecast rationality

test and the estimates of the asymmetry parameters in the forecast loss function. Section 5 discusses

the implications of the precious section’s …ndings for modeling monetary policy. Section 6 concludes.

2 Multivariate Forecast Rationality and Asymmetric Loss

Past studies have sought to test the rational expectations hypothesis by evaluating private sector

forecasts. Using the earliest methods (e.g., the Theil—Mincer—Zarnowitz regressions), a forecast

was deemed rational if the forecast errors were mean zero and uncorrelated with information avail-

able at the time that the forecast is made (Theil, 1958; Mincer and Zarnowitz, 1969; Figlewski and

Wachtel, 1981; Mishkin, 1981; Zarnowitz, 1985; Keane and Runkle, 1990). Many – if not most – of

these studies found evidence against rationality. These methods, however, implicitly assume that

the forecaster’s loss function is symmetric (and, in most cases, quadratic).

More recently, Elliott, Komunjer, and Timmermann (2005, EKT) introduced a family of uni-

variate asymmetric loss functions and showed that private sector forecasts can be rationalizable

under this new loss. Unlike quadratic or linear loss, asymmetric loss assigns di¤erent penalties

depending on whether the realization was above or below the forecast. As an example, EKT

found that private sector forecasts could be rationalizable if forecasters were attaching more loss

to overpredicting output growth than underpredicting.

Komunjer and Owyang (2011, KO) generalized the asymmetric loss introduced by EKT to allow

for joint outcomes. Using individual Blue Chip forecasts, they estimated asymmetric nonseparable

loss function parameters for in‡ation, output, and a short term interest rate. They found that

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forecasters loss was increased with unexpectedly worse joint economic outcomes, i.e., lower-than-

expected output growth, looser-than-expected monetary policy, and higher-than-expected in‡ation.

2.1 Nonseparable Asymmetric Loss

In this section, we describe the framework with which we can test the rationalizability of the

Greenbook forecasts and characterize the directional asymmetry – if any – in the Fed’s forecast

loss function. We adopt the multivariate nonseparable asymmetric loss framework of KO. The

forecaster attempts to predict future values of an (N 1) vector of macroeconomic variables yt.

De…ne f t+s;t as the forecast of the speriod-ahead yt+s computed using information available at

time t. The forecaster’s information set F t may include lagged values of yt in addition to other

covariates used to predictyt+s. De…ne

et+1 as the forecast errors for

yt, where

et+1 =

yt+1

f t+1;t.

The forecaster’s problem is to construct a prediction which, conditional on information known at

time t, minimizes the expected loss:

L p ( ;e)

kek p + 0e

kek p1 p ; (1)

where kuk p is the l p-norm of the vector u = (u1; : : : ; un)0 2 Rn.1;2

The asymmetric nonseparable loss function (1) has N + 1 parameters: p, 1 6 p < 1, and an

(N 1) vector , 1 6 n 6 1. The parameter p determines the shape of the loss function. When

p = 1, the loss function collapses to a univariate tick loss sometimes used in quantile estimation.

The vector governs the degree of asymmetry associated with each of the forecasted variables.

For = 0, there is no asymmetry – L p ( ; e) is additively separable and places equal weight on

forecast errors in either direction. If any element n is nonzero, n determines both the direction and

magnitude of the asymmetry. For example, values of n greater than zero indicate greater loss for

positive forecast error (underprediction). Greater loss means that, conditional on the information

at time t, the distribution of forecast errors will have nonzero mean. The larger is j nj, the greater

the loss and the more the distribution of forecast error will be biased away from zero.

1 KO show that (i) Lp ( ; ) is continuous and non-negative on Rn; (ii) Lp ( ;e) = 0 if and only if e = 0 and

limkekp!1Lp ( ;e) = 1; (iii) Lp( ; ) is convex on R

n. Detailed proofs of these assertions can be found in theappendix of KO.

2 In the univariate case, this ‡exible loss family includes: (i) squared loss function L2(0; e) = e2, (ii) absolutedeviation loss function L1(0; e) = jej, as well as their asymmetric counterparts obtained when 6= 0 (or 6= 1=2)which are called (iii) quad-quad loss L2(; e), and (iv) lin-lin loss L1(; e).

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In the separable case, each n measures magnitude of the directional asymmetry for a single

variable. In the nonseparable case, can be thought to measure both the asymmetry for directional

forecast errors and the asymmetry across variables. Thus, determines the relative importance of

the directional errors for each forecasted variable.

The forecaster’s problem outlined above does not depend on the model used to generate the

forecasts. We can think of the loss function as a¤ecting the forecaster’s estimates of the coe¢cients

of whatever model she uses. This means that the model that the forecaster uses does not a¤ect the

econometrician’s estimates of her loss function parameters. Also, these estimates do not depend on

the scheme – rolling or recursive – that the forecaster uses to construct the time series of forecasts.

2.2 An Illustrative Example

The consequences of nonseparable asymmetric loss can be made more apparent by describing the

bivariate case. For simplicity of exposition, also assume p = 2. In this case, the loss function (1)

can be rewritten as

L2 ( ; e) = e21 + e22 + ( 1e1 + 2e2)

e21 + e221=2

: (2)

The shapes of iso-loss curves – representing combinations of forecast errors corresponding to con-

stant loss – are determined by the parameters 1 and 2. Figure 1 shows the iso-loss curves for a

few di¤erent parameterizations. When 1 = 2 = 0, the loss L2 ( ; e) symmetric and the iso-loss

curves are perfectly circular. If either 1 6= 0 or 2 6= 0, the iso-loss curves are warped in the

direction of the asymmetry. The closer the iso-loss curve is to the origin, the larger is the loss for

those directional forecast errors for that variable. Note that, even if loss is directionally symmetric

in one variable (i.e., 1 = 0), asymmetry in any other variable (i.e., 2 6= 0) can produce bias in

the forecasts of y1 though the nonseparability. This e¤ect is revealed in the third term of (2) when

1 = 0. The loss induced by e1 is e21 + ( 2e2)

e21 + e221=2

, which depends on both the magnitude

and direction of e2. Note, however, that if 1 = 0, the direction of e1 does not enter the loss.

We can also examine the forecasts which would be produced from various parameterizations of

the loss function. Suppose that yt is generated from a VAR(1):

yt = c + Ayt1 + "t; (3)

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where "t is iid multivariate normal with zero mean and covariance matrix .3 Based on the loss

function, the one-period-ahead forecast is f t+1;t = c + Ayt, where

(c; A) arg min(c;A)

P 1P

Xt=1

L2( ;yt+1 c Ayt); (4)

which minimizes the expected value of the loss conditional on the data and a correctly speci…ed

VAR(1), (3). We then construct p = 250 periods of bivariate forecasts for given sets of asymmetry

parameters using the same generated data.

The joint distribution of the resulting bivariate time series of forecasts are shown in Figure

2. The directional asymmetry in the loss function is evident in the bias of the forecast errors.

Moreover, as the second panel shows, the distribution of the forecast errors for a variable whose

loss is symmetric can still be biased if there exists any directional asymmetry in the joint loss

function.

3 Data and Estimation

3.1 Data

Our dataset contains three components: (1) the forecast data; (2) the realizations; and (3) the

instruments used to test rationality with a total sample period of 1966:09 to 2005:12. The forecast

data are the one- and two-period-ahead forecasts of output growth, in‡ation, and unemployment

taken from the Greenbook. The Greenbook forecasts are publicly available at a 5-year lag and vary

in frequency over the sample period. At the beginning of the sample, the Greenbook forecasts were

available monthly; subsequent to 1979, the Greenbook was constructed only for FOMC meetings.

Thus, prior to 1979, we have 12 monthly vectors of observations per year; after 1979, we have eight

or nine irregular observations per year.

The realization data are a matter of some controversy, the answer to which depends on one’s

beliefs about the veracity for data revisions. One could believe, for example, that the intent of the

forecaster is to predict the value of that was released in real time. That is, the forecaster tries to

3 To generate the data, we simulate T = R + P 1 periods of data from the VAR(1) after discarding the …rst1000 periods to remove any initial values e¤ects. The forecaster uses a rolling window of size R = 100 to constructP = 250 one-period-ahead forecasts.

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predict the value of, say, 1979:I output growth which is released in April 1979. On the other hand,

one could argue that the initial release of the data are poor estimates and that the revisions which

occur over time make the data closer re‡ections of the truth. If the forecaster’s intent is to predict

these values, one should use the most recent vintage of the data. Similar arguments can be made

for any intermediate vintage under the assumption that signi…cant amounts of data revisions are

unpredictable and outside the scope of most agents’ forecasting problems. Two common approaches

are taken in the literature. The …rst is to use as realizations the one year revision of the data. The

second approach is to use the latest vintage. As a …rst pass, we report results using the latest

available vintage (June 2011) as the realization.

In addition to changes in frequency, the Greenbook changes the forecasted output growth vari-

able in 1992 from GNP growth to GDP growth. In order to remain consistent, when the Greenbook

changes the forecasted variable, we change the realization – that is, we match GNP with forecasted

GNP, etc.

Finally, we use as instruments one lag of the forecasted series available before the time that the

forecast is released.4 Unfortunately, we cannot judge when exactly the forecast is created; we know

only the time at which the Greenbook was released. We, therefore, assume that any data released

in the previous month was available to the forecaster and would be suitable as an instrument.

Because forecaster’s wold not have revisions available at the time they made the forecasts, we use

the previous month’s vintage of the forecasted variables in our instrument set.

3.2 Estimation and Rationality Testing

KO show that the asymmetry parameters in the loss function can be estimated from the forecast

errors using GMM. KO also argue using Monte Carlo evidence that the shape parameter requires

a very long time series for inference – much longer than we have for the Greenbook forecasts.

They suggest calibrating p; in sections to follow, we report results for p = 2. The estimationattempts to choose the value of the asymmetry parameter which maximizes the GMM objective

function derived from the …rst order condition for the nonseparable asymmetric loss. In doing so,

we ascertain estimates of consistent with the data and the most favorable to rationality.

4 In principle, one could use many lags. KO, however, noted that this could lead to the common many instrumentproblem and result in size distortions of the rationality test.

6



The resulting value of the GMM objective function is used to construct the J-statistic for use in

the rationality test. The test employs the standard test for overidenti…cation to determine whether

the forecasts are rationalizable , conditional on the chosen instrument set.

4 Empirical Results

In this section, we assess the directional asymmetry in the Fed’s forecast loss function estimated

using the Greenbook forecasts. In evaluating the results, it is important to keep in mind that values

of n greater than zero indicate greater loss for positive forecast error (underprediction).

4.1 Full Sample Results

To illustrate the e¤ect of adding nonseparability to the forecaster’s loss function, we …rst estimate

the as asymmetry parameters for the full sample. As a baseline for comparison, we obtain the

separable loss function parameters by estimating univariate versions of the loss function, (1). These

results are compared in Table 1. For the full sample, the Greenbook forecasts display statistically

signi…cant asymmetry for output growth and the unemployment. In‡ation, however, displays no

statistically signi…cant asymmetry. Consistent with results from KO, the nonseparable loss function

exhibits considerably less directional asymmetry for two of the three variables. For unemployment,

the separable and nonseparable loss functions yield similar asymmetry parameters.

Table 1 also shows the values of the J-statistic used to test rationality. As has been found in

previous studies, the J-test shows that, when accounting for potential directional asymmetry, the

Greenbook forecasts are rationalizable. This results is consistent across any sample split.

In the full sample, the directional asymmetry is similar for both unemployment and output

growth – i.e., greater loss obtains when the forecaster underpredicts real variables. The opposite

occurs when forecasting in‡ation – overpredicting in‡ation produces larger losses. These directional

asymmetries are consistent with those estimated by Capistrán for a shorter Greenbook forecast

sample. However, they appear to be opposite of those estimated for private sector forecasts (see,

for example, EKT for univariate loss and KO for multivariate loss). They also could be construed

as counterintuitive in that the Fed appears to incur higher loss for better economic outcomes –

higher than predicted growth makes the Fed worse o¤.

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4.2 Directional Asymmetry and the Business Cycle

Previous studies have argued that the Fed’s objective has changed over time. For example, Capistrán,

examining the Greenbook in‡ation forecasts, split the samples in 1979 when Paul Volcker became

the chairman of the FOMC. Changes in the Fed’s policy preferences – exhibited by shifts in the

in‡ation and output responses in an empirical Taylor rule – might also manifest in changes in the

forecasting preferences of the Fed. Indeed, Capistrán …nds that the direction of the in‡ation asym-

metry ‡ips from the pre- to the post-Volcker regimes. In this section, we investigate whether there

may have been changes in the joint directional asymmetry associated with in‡ation, unemployment,

and output.

As a motivating example, consider Figure 3, which plots the Greenbook forecast errors for

output, in‡ation, and the unemployment rate, along with the NBER recession dates. The commonly

used Volcker split is shown by a vertical line. From the top panel (output), it is evident that

the asymmetry appears associated with the NBER recession periods, not necessarily the Volcker

split. During recessions, the forecast errors are generally positive; the reverse is true for expansion

periods. In light of this, we split the sample into three regimes: recessions, pre-Volcker expansions,

and post-Volcker expansions.5

Table 2 presents the results with the three subsamples. To obtain these results, we took the

recession and expansion dates as determined by the NBER Business Cycle Dating Committee as

given. In addition, we split the expansion periods when Volcker takes o¢ce in October, 1979.

When we consider in‡ation in isolation, we …nd results consistent with those found by Capistrán

(2008). In particular, the direction of the forecast asymmetry changes after Volcker enters o¢ce.

During expansions, prior to October 1979, overprediction is more costly; after 1979, the directional

asymmetry reverses. Contrary to Capistrán, we …nd that the directional asymmetry for in‡ation

is statistically insigni…cant once we account for variation over phases of the business cycle. During

recessions, however, the Greenbook in‡ation forecasts do exhibit astatically signi…cant directional

asymmetry: underprediction is more four times more costly than overprediction. This suggests

that the true directional asymmetry is being driven by recessions, two of which were considerably

5 The split of recessions into the pre- and post-Volcker periods is not particularly revealing because of the limitedtotal number of cycle periods.

As an alternative, we also considered the expansion split at the Great Moderation. Results were qualitativelysimilar and are available upon request.

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shallower than average in the post-Volcker period.

For the real variables, unemployment and output growth, we …nd directional asymmetry across

the business cycle phases. During recessions, the estimated asymmetry parameter for output growth

is negative and statistically signi…cant: The Fed has larger loss when worse output outcomes obtain

during recession. This result is contrary to the full sample result which suggested that the Fed

always prefers underprediction.

During expansions, the Fed experiences relatively larger loss if unemployment or output growth

are higher than predicted. While the direction of the forecast asymmetries for unemployment and

output are consistent for expansions before and after Volcker, the magnitudes of the asymmetries

do. After the break, the relative weight on output underpredictions declines and the relative weight

on unemployment underpredictions rises.6

4.3 Di¤erentiating Between Directional Preferences and Bad Forecasting

Previous studies have found that identifying turning points is di¢cult. If the conditional means of

the variables of interest change across the turning points (e.g., in a model such as Hamilton, 1989),

could we mistake regime dependent forecast errors for directional preferences? In this subsection,

we make the case that it is unlikely that the directionality of the forecast errors are the result of

poor forecasting versus asymmetric preferences.Suppose that the Fed’s forecasting model cannot predict turning points in real time. Expansions

are, by and large, the dominant business cycle phase. Thus, one would imagine that the forecast

during expansion should be more accurate than during recessions. Moreover, the forecast errors

should increase around turning points as the Fed learns only ex post that the state of the economy

has changed.

Reconsider the forecast errors from Figure 3. During the expansions occurring in …rst part

of the sample, the forecast error is consistently negative. This suggests either a conscious intentto underpredict output growth or a model in which output growth is forecast as an average over

business cycle periods. For three of the …rst four recessions, however, the forecast errors are

relatively small after the turning point and increase in magnitude over the recessions. Moreover,

6 This may re‡ect a change in emphasis in policy associated with the volatility reduction in output and increasedunemployment in expansions due to the jobless recoveries.

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the direction of the forecast error is positive: the realized value is greater than the forecast. This

suggests that, during recessions, as the Fed becomes aware of the state of the economy, the forecast

is pushed lower and the magnitude of the recession is overestimated . The Fed’s forecasts over the

recessions belies a simple average model of the output growth rate.

Finally, if one believes that the change in directional asymmetry across business cycle phases

occurs because of some characteristic of the Fed’s model rather than a true change in preferences,

there are still implications to the analysis above. In the following section, we detail some of these

implications which will not depend on the business cycle dependence of preferences – it is enough

that forecasts have a systematic bias in expansions.

5 Economic Implications of Asymmetric Rationality

The results in the preceding section suggest that the Greenbook forecasts can be rationalized only

with asymmetric directional preferences and that the direction of the asymmetry changes over the

business cycle. But what does it mean that the Fed has asymmetric preferences? Many standard

models of rationality (e.g., Quad-Quad loss) imply that the distribution of forecast error is mean

zero – that is, f t+h = yt+h + et+h, where et+h is mean zero and uncorrelated with F t. Thus, our

results may have implications for models which rely on (mean zero) rationality.

As an example, Clarida, Galí, and Gertler (2000) suggest that the parameters in a forward-

looking Taylor rule can be estimated using GMM under the assumption of rational expectations.7

Consider a standard forward-looking Taylor rule:

rt = rt1 + (1 ) [ (E tt+h ) + E txt+h] + "t;

where E tt+h is the forecasted in‡ation rate at a horizon h; is a target in‡ation rate; E txt+h is

a forecast of the output gap at horizon h; and rt is the nominal interest rate (usually the fed fundsrate). Clarida, Galí, and Gertler rewrite this as:

rt = rt1 + (1 ) [r + (1 + ) t+h + xt+h] + "t;

7 Judd and Rudebusch (1998), Woodford (2003), and Stock and Watson (2002), typically deal with backwardlooking rules. In contrast, Clarida, Gali and Gertler (2000), Orphanides (2002), and, more recently, Boivin (2006)make inferences for a forward looking rule.

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where r is a “steady-state” interest rate and the error term

"t = (1 ) [ (t;k E tt+h) + (xt+h E txt+h)]

is a function of the di¤erence between the unobserved expectations and their future realizations.

Rationality implies that this di¤erence is orthogonal to information know at time t. Thus, we can

estimate the Taylor rule coe¢cients using a GMM orthogonality condition of the form:

E frt rt1 + (1 ) [r + (1 + ) t+h + xt+h] ztg = 0;

where zt F t is a vector of instruments known at time t.8

Implicit in the Clarida, Galí, and Gertler estimation is the assumption that E tt+h = t+h and

E txt+h = xt+h – i.e., the expectations (forecasts) errors are mean zero rational. If one believes that

the Greenbook forecasts are produced for policymaking, an instrumental variables approach that

does not take into account the bias in the forecast errors will produce biased TR coe¢cients. If

the forecasts are systematically upwardly (downwardly) biased, the Taylor rule coe¢cients will be

downward (upward) biased.

6 Conclusions

In this paper, we applied the methods of Komunjer and Owyang (2007) to the Federal Reserve’s

Greenbook forecasts. Similar to other papers, we …nd that, once accounting for directional asym-

metry, the Greenbook forecasts are rationalizable. Unlike other papers before us, we …nd that, once

accounting for di¤erences across the business cycle, the Fed’s directional preference over in‡ation

during expansion disappears.

Our results have implications for the estimation of forward-looking monetary policy rules. If

one believes that the Fed uses the Greenbook forecasts in making policy, the zero mean forecast

error assumption underlying standard GMM estimation of Taylor rules is violated. This results in

8 Orphanides (2002) estimated the Taylor rule with real time data using Greenbook forecasts as instruments.He showed that, using these data, the orthogonality condition fails. Boivin (2006) estimates a dynamic version of Orphanides (2002) which allows the Taylor rule parameters to change over time. He makes explicit the fact that acritical assumption is that the Greenbook forecasts are contemporaneously uncorrelated with the policy shock (i.e.,the error term in the Taylor equation). However, if the policy rule changes with the business cycle, the Greenbookforecast will typically not be orthogonal to the policy shock.

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biased Taylor rule coe¢cients and a misinterpretation of the intentions of policy. This point was

initially made by Orphanides (2004) but, here, has a behavioral interpretation.

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Nonseparble Separable

Unemp Output In‡ation Unemp Output In‡ation

0.196 0.367 -0.017 0.177 0.770 -0.125

J-Stat 3.89 3.80

Table 1: Full Sample Results. Notes: The table contains the asymmetry parameters for the separable and

nonseparable losses for the full sample, 1966 to 2005. The J-Stat is constructed from the GMM ob jective function.

Derivation of the J-Stat is described in detail in Komunjer and Owyang (2007).

Unemp Output In‡ation Sample

Full 0.196 0.367 -0.017 9/66 - 12/05

Recession -0.281 -0.114 -0.054 n/a

Pre-GM Exp. 0.295 0.577 -0.012 9/66 - 12/83

Post-GM Exp. 0.424 0.359 0.001 1/85 - 12/05

Table 2: Split Sample Results. Notes: The table contains the estimated asymmetry parameters for the non-

separable loss for the split sample. The recession dates are taken from the NBER Business Cycle Dating Committee.

Figure 1: Notes: The …gure depicts the Iso-loss contours for given asymmetry parameters for thenonseparable (left) and separable (right) loss functions.

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Figure 2: Notes: The …gure depicts the Iso-loss contours for given asymmetry parameters for thenonseparable (left) and separable (right) loss functions.

Figure 3: The …gure depicts the forecast error distributions using 10000 simulated data pointsconstructed from a VAR(1) with the given asymmetry parameters.

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Figure 6: The …gure shows the forecast errors for the unemployment rate constructed from theGreenbook. NBER recessions are shaded in gray. The forecast errors are constructed assumingthat the realizations of unemployment are the current (2011) vintage.

Figure 7: The …gure shows the forecast errors for the output growth rate constructed from theGreenbook. Output in this …gure is de…ned as GNP prior 1992 and GDP thereafter. NBERrecessions are shaded in gray. The forecast errors are constructed assuming that the realizations of output growth are the current (2011) vintage.

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Figure 8: The …gure shows the forecast errors for the in‡ation rate constructed from the Green-book. NBER recessions are shaded in gray. The forecast errors are constructed assuming that therealizations of in‡ation rate are the current (2011) vintage.

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greenbook forecasts 10-30-2011

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