Macroeconomic Uncertainty Indices Based on Nowcast and Forecast Error Distributions By BARBARA ROSSI AND TATEVIK SEKHPOSYAN*

* Rossi: ICREA-University of Pompeu Fabra, Barcelona GSE and

distribution of forecast errors, a forecast error

CREI, c/Ramon Trias Fargas 25/27, Barcelona 08005, Spain (e-mail: [email protected]). Sekhposyan: Texas A&M University, 4228 TAMU, College Station, TX 77843, United States (email:

of 2% is in the 99-th percentile and the realized forecast error is indeed 2%, then we conclude

[email protected]). Acknowledgments. We thank C. Scotti for sharing the uncertainty index proposed in her paper, S. Vahey and participants of seminars at CREI, the University of Warwick, ASSA,

that there is substantial uncertainty. The

measure

we

propose

is

a

CEF, CFE, Advances in Applied Macro-Finance and Forecasting conferences for comments. This research is supported by the Spanish Ministry of Economy and Competitiveness (Grant ECO2012-33247).

The Great Recession of 2007:IV-2009:II sparked

great

interest

in

understanding

complementary and possibly more general measure of uncertainty based on assessing the likelihood of a realization. The attractive feature of our approach is that it summarizes

the

the information in the ex-ante probabilistic

macroeconomy. This paper introduces a new

forecast as well as in the ex-post realization. In

approach to measure uncertainty. We start from

addition, as it is a distribution-based measure

the same premise as in Jurado et al. (2014), that

of uncertainty, it distinguishes between periods

is: “What matters for economic decision

of high and low uncertainty measured by

making is whether the economy has become

probabilities as opposed to arbitrary thresholds.

more or less predictable; that is, less or more

Finally, our measure also has the advantage of

uncertain.” However, as opposed to Jurado et

providing

al. (2014), the uncertainty index we propose

uncertainty is upside or downside.

uncertainty

and

its

effects

on

information

on

whether

the

relies on the unconditional likelihood of the

Our measure of uncertainty relies on the

observed outcome. More specifically, our

model used to forecast the economy. We focus

proposed index is the percentile in the

on the Survey of Professional Forecasters’

historical

errors

(SPF) forecasts since they are regarded to be

associated with the realized forecast error. For

well performing benchmarks (Faust and

example, if, according to the unconditional

Wright, 2013).1

1

distribution

of

forecast

Online Appendix shows that our results are robust to using modelbased, namely equal weighted combination forecasts.

Clearly, the choice of the representative

the same. In addition, measuring uncertainty by

macroeconomic variable used in our proposed

the variance of the forecast errors implies that

index is very important. In particular, since our

positive and negative outcomes are symmetric

goal is to propose an index that measures

and of the same importance; our measure,

uncertainty of the state of the economy, we

instead, allows for asymmetry. Finally, our

focus on macroeconomic variables that are

measure is based on the realized forecast error

representative of the business cycle, such as

distribution, thus it provides a measure that

Gross Domestic Product (GDP).2

summarizes uncertainty in the data as well as

Our contribution differs from those in the literature for several reasons. First, some of the

uncertainty

associated

with

parameter

estimation (for model-based forecasts).

existing measures (e.g. Bloom, 2009) identify

Our work is also related to other recent

uncertainty as the unconditional volatility of

contributions. Baker et al. (2013) propose to

certain series (e.g. the stock market returns). As

measure economic policy uncertainty using a

discussed in Jurado et al. (2014), this approach

news-based policy uncertainty index and other

cannot distinguish between expected and

“fundamental” measures of policy uncertainty

unexpected movements; we focus, instead, on

and dispersion. Scotti (2013) uses surprises

the uncertainty relative to the predicted

from

outcome. Second, other existing measures (e.g.

measures of economic uncertainty. We,

Jurado et al., 2014) focus on the variance of the

instead, measure how likely we were to observe

forecast

the actual forecast error relative to the ex-ante

errors;

our

measure

is

a

Bloomberg

forecasts

unconditional

describe uncertainty. In fact, we measure the

Furthermore, we distinguish between upside

unconditional probability of observing the

and downside uncertainty, which might affect

realized value. The two measures are different,

the macroeconomy in different ways. Segal et

for example, in situations where the ex-ante

al. (2014) also propose to distinguish between

predictive uncertainty, measured by certain

positive and negative uncertainty, but focus on

deciles of forecast error distribution, changes,

realized volatility in high frequency data

yet the variance of the forecast error remains

environment.

Our methodology could also be applied to construct indices based on forecasts of the unobserved state of the economy, although we do

error

construct

complementary and more general way to

2

forecast

to

distribution.

not investigate this in our empirical analysis. In addition, we can also construct variable-specific uncertainty indices as discussed in the online Appendix.

I. Macroeconomic Uncertainty Index

uncertainty) or the density of forecast errors up to a certain point in time (which results in a

The macroeconomic uncertainty index we propose is based on comparing the realized forecast error of a macroeconomic variable of interest with the historical forecast error distribution of that variable. If the realization is in the tails of the distribution, we conclude that the realization was very difficult to predict from all the available (past and present) information

and

the

macroeconomic

We focus on a variable of interest that is informative on the state of the business cycle. In particular, we focus on real GDP following Stock and Watson (1999, p. 15), who note that: “although the business cycle technically is defined by co-movements across many sectors and series, (…) the cyclical component of real GDP is a useful proxy for the overall business cycle.” We extract the cyclical component by differencing.

Thus,

errors can be obtained using forecasts from parametric models or surveys. Our proposed index is based on the cumulative density of forecast errors evaluated at the actual realized forecast error, 𝑒𝑡+ℎ : 𝑒

𝑡+ℎ 𝑈𝑡+ℎ = ∫−∞ 𝑝(𝑒)𝑑𝑒. By construction, 𝑈𝑡+ℎ is

between zero and one. A large value of the index (close to one, say) indicates that the

environment is very uncertain.

first

real-time measure of uncertainty). Forecast

our

main

macroeconomic uncertainty index uses real GDP growth - although one can construct other variable-specific indices.

realized value was very different from the expected value. In particular, a realized value much higher than the expected value measures a positive “shock.” Conversely, a very small value of the index (close to zero, say) indicates that the realized value was much smaller than its expected value, i.e. a negative, unexpected “shock.” Note that uncertainty is measured by the forecast error realization relative to its exante probability. To convey information about the asymmetry in uncertainty, we propose to construct both “positive” and “negative” uncertainty

indices 1

over 1

Let the ℎ-step-ahead forecast error for the

+ (1) 𝑈𝑡+ℎ = 2 + max {𝑈𝑡+ℎ − 2 , 0}

scalar variable 𝑦𝑡+ℎ be denoted by 𝑒𝑡+ℎ =

− (2) 𝑈𝑡+ℎ = 2 + max {2 − 𝑈𝑡+ℎ , 0}

𝑦𝑡+ℎ − 𝐸𝑡 (𝑦𝑡+ℎ ), for 𝑡 = 𝑅, … , 𝑇. Let 𝑝(𝑒) denote the forecast error distribution; this could be either the unconditional density of forecast errors (which results in an ex-post measure of

1

time:

1

+ Thus, 𝑈𝑡+ℎ measures uncertainty arising

from news or outcomes that are unexpectedly positive (e.g. higher GDP than expected) and − 𝑈𝑡+ℎ measures uncertainty associated with

news or outcomes that are unexpectedly negative (e.g. lower GDP than expected). We + refer to 𝑈𝑡+ℎ as a measure of upside − uncertainty, and to 𝑈𝑡+ℎ as a measure of

downside

uncertainty.

By

construction,

+ − 𝑈𝑡+ℎ and 𝑈𝑡+ℎ are between one-half and one.

We define an overall uncertainty index as: 1

1

∗ (3) 𝑈𝑡+ℎ = 2 + |𝑈𝑡+ℎ − 2|.

To understand our index, consider Figure 1. The upper panel plots the unconditional probability distribution function (pdf) of the forecast errors (dotted line with circles) in real output growth forecasts from 1968:IV-2014:I. In addition, we plot the forecast errors associated with two recent episodes of interest. The darker (blue) vertical bar on the left

FIGURE 1. UNCERTAINTY EXAMPLE

identifies the forecast error associated with

Note: The figures depict the empirical pdf and cdf distributions of SPF forecast errors of real GDP growth as well as the realized forecast errors in the quarter of Lehman bankruptcy (2008:III) and in the first quarter after the Great Recession (2009:III).

current quarter real GDP growth forecast in 2008:III, the quarter of Lehman's bankruptcy.

+ − Thus, our indices 𝑈𝑡+ℎ and 𝑈𝑡+ℎ assign a higher

The lighter vertical bar on the right (in green)

uncertainty to 2008:III as shown in the bottom

depicts the forecast error in 2009:III, the first

panel. We can quantify the difference in the

quarter after the trough of the Great Recession.

uncertainty levels with probabilities: the

The middle panel plots the cumulative

realization in 2008:III had 24% less chance of

distribution function (cdf) corresponding to the

occurring than that in 2009:III. Thus, we

pdf in the upper panel, that is 𝑈𝑡+ℎ . The figure

associate 2008:III with downside uncertainty

suggests that the ex-ante probability of

and 2009:III with upside uncertainty.

observing the forecast error realized in 2008:III

Figure 2 plots our estimated uncertainty

was 0.07, while it was 0.69 for the forecast

index, together with its 90th percentile value.

error realized in 2009:III. The deviation of

The index is based on GDP forecasts from the

these probabilities from the average occurrence

SPF by the Philadelphia Fed and the

(0.50) is larger in 2008:III than in 2009:III.

“Advance” release of the GDP. We focus on

the quarterly growth rate of the four-quartermoving average real GNP/GDP for the current quarter, ℎ = 0, as well as four quarters ahead, ℎ = 4. We assume the forecasters know the past realized values from the Real-time dataset (Croushore and Stark, 2001), a fair assumption according to the SPF documentation.3 The two upper panels in Figure 2 plot our + − downside (𝑈𝑡+ℎ ) and upside uncertainty (𝑈𝑡+ℎ )

indices together with NBER recessions dates (shaded areas). It is clear that our measure of downside uncertainty coincides with, and in many occasions leads, the NBER recession dates. The uncertainty measure based on fourquarter-ahead forecasts is less noisy and contains more precise information about the recessions relative to the ones based on the nowcasts. Interestingly, our measure also picks up several episodes of upside uncertainty, notably in the late 1990s, a period associated with under-estimation of productivity growth. The two bottom panels in Figure 2 plot our uncertainty measure in real-time. The real-time measure updates the forecast error distribution

FIGURE 2. UNCERTAINTY INDICES Note: The figures depict the uncertainty measures obtained from SPF output growth nowcast and four-quarter-ahead forecast error densities.

II. A Comparison with Existing Measures

each quarter from 1985:I onwards. As shown, the real-time measure of uncertainty is less volatile

the

upside

and

compare

our

SPF-based

downside

macroeconomic uncertainty index associated

uncertainty episodes are more sharply defined.

with four-quarter-ahead GDP growth forecasts

3

and

We

The SPF respondents also provide probabilistic density forecasts of current and following year output growth. Unreported robustness exercises show that uncertainty measures from these densities are

similar, yet less noisy and more clearly leading the cycle. These measures, however, have the drawback of mixing multi-horizon forecasts.

with several indices proposed in the literature,

of GDP, the (log) of employment, the Federal

including: VXO as in Bloom (2009); Baker et

Funds rate, the (log) of stock prices and the

al.'s (2013) policy uncertainty index, “BBD”;

uncertainty index (we consider several indices,

Jurado

macroeconomic

one-at-a-time), in addition to a deterministic

uncertainty index, “JLN”; and Scotti's (2013)

trend and a constant.4 We report mean impulse

macroeconomic surprise based uncertainty

responses to one standard deviation increase in

index, “Scotti.” We make the measures

uncertainty as well as the 90% bootstrapped

comparable by picking index values for the

coverage areas based on 2000 simulations.

et

al.'s

(2014)

dates (months) closest to the SPF survey’s deadline dates. We further standardize the indices to express them in the same units. In the common sample period our overall ∗ uncertainty index, 𝑈𝑡+ℎ , is more closely

correlated with VXO than the other measures (corr = 0.29). When we split the measure to account for upside and downside uncertainty, we find that the downside measure is more correlated with “JLN” (corr = 0.37), while the upside measure is more correlated with “VXO” (corr = 0.19) and closely linked, yet negatively

FIGURE 3. IMPACT OF UNCERTAINTY ON GDP Note: The figures depict impulse responses of GDP to various uncertainty shocks measured by various indices.

correlated, with “JLN” (corr = -0.23).

Figure 3 shows the impact of various

III. Uncertainty and the Macroeconomy

uncertainty measures on output. Our overall

In order to assess the macroeconomic

∗ uncertainty measure, 𝑈𝑡+ℎ , only marginally

a

affects output, yet its effects are persistent.

Vector

Quantitatively these results are similar to the

Autoregression (VAR) that includes the (log)

VXO, “BBD” and “Scotti” indices. However,

4 The VAR specification is the same as in Baker et al.'s (2013), although ours is at a quarterly frequency, and accordingly we use GDP instead of real industrial production. We order the variables as in the benchmark specification of Jurado et al. (2014), i.e. from slow to fast

moving. Our results are robust to using the industrial production index and alternative ordering assumptions of Baker et al. (2013). The lag order is one, selected by the Bayesian Information Criterion. For each uncertainty index the VAR is estimated over a period for which there is available data.

impact

of

recursively

uncertainty, ordered

we

estimate

six-variable

when we distinguish between downside and

aimed to quantify the overall uncertainty in the

upside uncertainty, we find that downside

labor market.

− measure, 𝑈𝑡+ℎ , has a larger effect on output

REFERENCES

than the overall index. The upside uncertainty + index, 𝑈𝑡+ℎ , also has significant effects. They

Bloom, Nicholas. 2009. “The Impact of

are similar in magnitude and opposite in sign to

Uncertainty Shocks.” Econometrica 77(3),

the downside index. The “JLN” index

623-685.

estimates much larger effects on GDP.

Baker, Scott R., Nicholas Bloom, and Stephen

Furthermore, the responses are statistically

J. Davis. 2013. “Measuring Economic Policy

different from those based on the VXO and

Uncertainty.” Unpublished.

other measures.

Faust, Jon and Jonathan Wright. 2013. “Forecasting Inflation.” In: Graham Elliott

IV. Conclusions

and Allan Timmermann (eds.), Handbook of

This paper proposes new measures of macroeconomic uncertainty. Our proposed

Economic Forecasting. 2-56. Jurado, Kyle, Sydney Ludvigson, and Serena Uncertainty.”

Ng.

in

American Economic Review, forthcoming.

predicting

relevant

macroeconomic

2014.

“Measuring

indices quantity how unexpected the mistakes

historic

Scotti, Chiara. 2013. “Surprise and Uncertainty

distributions. Moreover, they characterize

Indexes: Real-time Aggregation of Real-

uncertainty in terms of probabilities. For the

Activity Macro Surprises.” Federal Reserve

following reasons, our measures differ from

Board International Finance DP 1093.

outcomes

are

relative

to

their

those in the literature. First, they distinguish

Segal, Gill, Ivan Shaliastovich, and Amir

between upside and downside uncertainty.

Yaron. 2014. “Good and Bad Uncertainty:

Second, they uncover that the late 1990s are

Macroeconomic

characterized by upside uncertainty. Third, we

Implications.” Unpublished.

find that the upside uncertainty has significant

and

Financial

Market

Stock James H. and Mark W. Watson. 1999.

macroeconomic effects, which remains to be

“Business

explained theoretically. Our framework can be

Macroeconomic Time Series.” In: Taylor

extended to construct joint measures of

John

uncertainty for groups of variables. This could

Handbook of Macroeconomics. 3-64.

be useful if, for instance, the Federal Reserve

and

Cycle

Fluctuations

Michael

in

Woodford

U.S.

(eds.),

Macroeconomic Uncertainty Indices Based on Nowcast and Forecast ...

CREI, c/Ramon Trias Fargas 25/27, Barcelona 08005, Spain (e-mail: ... The Great Recession of 2007:IV-2009:II sparked great interest in understanding.

381KB Sizes 1 Downloads 213 Views

Recommend Documents

Impact of Load Forecast Uncertainty on LMP - IEEE Xplore
always contain certain degree of errors mainly due to the random nature of the load. At the same time, LMP step change exists at critical load level (CLL).

Maestre, Puche - 2009 - Indices based on surface indicators predict ...
Maestre, Puche - 2009 - Indices based on surface indic ... oil functioning in Mediterranean semi-arid steppes.pdf. Maestre, Puche - 2009 - Indices based on ...

Macroeconomic Uncertainty and the Impact of Oil Shocks
Following Baum and Wan (2010), the first alternative measure ..... 20 There is an extensive literature that deals with the effect of uncertainty on investment dynamics, .... [43] Regnier, E. (2007): Oil and energy price volatility, Energy Economics, 

Macroeconomic Uncertainty and the Impact of Oil Shocks
economic activity reacts more aggressively to oil shocks when macroeconomic volatility is already high. ... allowed to determine whether the economy is in a high or low uncertainty regime.2 is. 2 We discuss possible ...... price shocks - A comparativ

Satellite based land use and landscape complexity indices as ...
model. We used a simple linear least square model for all species groups with the exception of the threatened species where we used a poisson model because ..... Randomization, bootstrap and Monte-Carlo. Methods in biology. Chapman & Hall, New York.

Phone-based Authentication Global Market Outlook and Forecast ...
Phone-based Authentication Global Market Outlook and Forecast 2015-2019.pdf. Phone-based Authentication Global Market Outlook and Forecast 2015-2019.

Panoramic-based mandibular indices in relation to ...
predictive values (ranging from 47 to 83% and 40 to 79%, respectively). Conclusion: MCI is a simple three-graded classification of changes in the cortex but is ...

Uncertainty Aware Minority Game Based Energy ...
energy meters/sensors; and (ii) uncertain working behaviors from load side. Firstly, agents ... time control; (ii) management of renewable energy resources; and.

Panoramic-based mandibular indices in relation to ... - BIR Publications
acterized by low bone mass, microarchitectural weakening leading to ... E-mail: [email protected]. Received 13 .... No DXA software specifically designed for the mandible is ..... best specificity, sensitivity, negative and positive predictive .

macroeconomic policies focused on employment ...
In the early 1990s, the IMF supported capital account liberalization and fixed .... monetary and fiscal policies at a high level of decision-making power. ..... those papers and the interest rate earned by the central bank's international reserves.

macroeconomic policies focused on employment ...
An alternative to inflation targeting in Latin America: macroeconomic policies ... monetary policy is the macreconomic setting currently recommended in Latin ...

On the Macroeconomic and Welfare Effects of ...
qdelaying retirement interchangeablyrto refer to the law%mandated increase in the age at which ...... stipulated in the Federal Insurance Contributions Act Tax.

indices-glycemiques.pdf
Pêches (fruit frais) 35 Pepino, poire-melon 40 Porridge, bouillie de flocons d'avoine 60. Petits pois (frais), pois chiches, fafanel 35 Petits pois (boîte) 45 Potiron 75. Poireaux 15 Pruneaux 40 Poudre chocolatée (sucrée) 60. Poivrons 15 Raisin (frui

A novel approach to Monte Carlo-based uncertainty ...
Software Ltd., Kathmandu, Nepal, (3) Water Resources Section, Delft ... was validated by comparing the uncertainty descriptors in the verification data set with ... The proposed techniques could be useful in real time applications when it is not ...

Indices prompt sheet.pdf
www.inquirymaths.org. Page 1 of 1. Indices prompt sheet.pdf. Indices prompt sheet.pdf. Open. Extract. Open with. Sign In. Main menu. Displaying Indices prompt ...

Physically-based Grasp Quality Evaluation under Pose Uncertainty
intelligence in decision making often leads to a better and reliable result.5 ..... to a fully automated robot grasping planner, such a grasp set would improve not ...

Physically-based Grasp Quality Evaluation under Pose Uncertainty
uncertainty into the static grasp quality analysis by computing the probability of .... Refer to [7] to see how to incorporate soft contact into a force- closure based ...

On the Dynamic Macroeconomic Effects of ...
KEYWORDS: FDI, Heterogeneous firms, International Business Cycle, technology transfer ... large-scale privatization programs, and market conditions. ... of countries, the magnitude of within vertical fragmentation can be reasonably expected to be sma

On the Macroeconomic Consequences of Over-Optimism
The views expressed in this paper are those of the authors and should not be ..... −0.000071∗. (−1.75). Mission Chief fixed effects no yes time fixed effects yes.

Macroeconomic Interdependence and the Transmission Mechanism
Aim. Once the global equilibrium (equilibrium in the goods and asset markets) has been attained, the aim of the analysis is to study the transmission of endowment and preference shocks within and between the two economies, focusing on the effects of

Macroeconomic Experiences and Expectations: A ... - Semantic Scholar
1 How do macroeconomic experiences influence expectations? ... Individuals believe that a macroeconomic variable xt follows a perceived law of motion, e.g., a first-order autoregressive process, xt+1 = α + φxt + ηt+1. (1) ..... real estate or to p

Fiscal News and Macroeconomic Volatility
Mar 29, 2013 - business cycle volatility in an estimated New Keynesian business ... However, anticipated capital tax shocks do explain a sizable part of ... follow fiscal rules with endogenous feedback to debt and current .... We first discuss the in

Interference Mitigation and Capacity Enhancement based on ...
Interference Mitigation and Capacity Enhancement ba ... Dynamic Frequency Reuse for Femtocell Networks.pdf. Interference Mitigation and Capacity ...

Uncertainty and Unemployment
This paper previously circulated under the title “Uncertainty,. Productivity and Unemployment in the Great Recession”. †Email: [email protected]; ...