Understanding the Sources of Macroeconomic Uncertainty

Transcription

1 Understanding the Sources of Macroeconomic Uncertainty Barbara Rossi, Tatevik Sekhposyan, Matthieu Soupre ICREA - UPF Texas A&M University UPF European Central Bank June 4, 6

2 Objective of the Paper Recent economic events (great recession, unconventional monetary policy, fiscal cliff, etc.) sparked great interest in understanding uncertainty and its macroeconomic impact. Stock and Watson () suggests the liquidity-risk and uncertainty shocks to be the most important contributor to the decline in the U.S. GDP during the Great Recession / of the recession s decline in GDP and employment There has been increased emphasis in trying to characterize uncertainty, which is inherently unobserved. There are many measures of uncertainty ex-ante, ex-post, disagreement, mean-squared forecast errors, forecast error distributions, etc. Our paper proposes to reconcile the various measures.

3 The Measure of Uncertainty Matters

4 The Measure of Uncertainty Matters

5 Summary of Various Measures Based on some observables realized volatility, implied volatility (VIX, VXO, Bloom, 9), Baker, Bloom & Davis (5) index Measures of ex-ante uncertainty or perceived uncertainty typically based on surveys disagreement as a special case Clements (5), Leduc & Liu (5), D Amico & Orphanides (4), Patton & Timmermann (), etc. Ex-post measures of uncertainty based on forecast errors Has the notion that What matters for economic decision making is whether the economy has become more or less predictable; that is, less or more uncertain. Jurado, Ludvigson & Ng (5), Rossi & Sekhposyan (5), Scotti (), etc.

6 Our Contribution We propose a predictive distribution-based uncertainty measure. We can further decompose this measure to measures of aggregate uncertainty and disagreement measures of bias (Knightian) and realized variance (risk) measures of ex-ante and ex-post uncertainty We provide evidence of differential macroeconomic impact. Provide simulation experiments documenting the evolution of the channels of the various measures of uncertainty.

7 Risk versus Knightian Uncertainty Risk - uncertainty stemming from the fact that a realization of the state of nature is not known in advance even if all possible states of nature and their likelihoods could be reasonably contemplated. various measures of volatility Knightian Uncertainty - uncertainty stemming from the fact that it is not possible to assign correct probabilities to future outcomes or agree on the probabilities. depends on the realization or the disagreement among forecasted probabilities

8 Uncertainty Index based on Density Forecasts At a particular point in time you have [.] the density forecast [.] realization Density Forecast Realization

9 Uncertainty Index based on Density Forecasts Work with a binary variable and cdf instead. Let x t+h (r) = {y t+h < r} p s,t+h t (r) = P(x t+h (r) = Ω s,t ) } (x t+h(r) p s,t+h, t (r)).4.. Density Forecast Ideal Density. 4 4 For a given threshold r, s-th forecaster s uncertainty is: [ (xt+h u s,t+h t (r) = E (r) p s,t+h t (r) ) ] I t t R. Has the sprit of a forecast error for a particular quantile.

10 The Uncertainty Index The measure of uncertainty is defined as the average of the individual uncertainty measure across forecasters: u t+h t (r) = N u s,t+h t (r) N = N s= N E s= [ (xt+h (r) p s,t+h t (r) ) ] I t t R Similar to Lahiri & Sheng (), Zarnowitz & Lambros (987) for a particular point in a distribution Uncertainty U t+h t = + u t+h t (r) dr

11 Decomposition I: Aggregate Uncertainty & Disagreement u t+h t (r) = N N [ (xt+h E t (r) p t+h t +p t+h t p s,t+h t (r) ) ] s= ( = E t xt+h (r) p t+h t (r) ) + N [ (pt+h t E t (r) p s,t+h t (r) ) ] N s= = u A t+h t (r) + d t+h t (r), U t+h t = }{{} Uncertainty u A t+h t (r) dr + d t+h t (r) dr = Ut+h t A }{{} + D t+h t }{{} Aggregate Uncertainty Disagreement

12 Decomposition II: Aggregate Uncertainty as Risk and Knightian Uncertainty u A t+h (r) = ( [E ( ( )] ) pt+h t (r) It R) t E xt+h (r) I t t R + V ( x t+h (r) It R) t + V (pt+h t (r) I t t R) Cov(x t+h (r), p t+h t (r) I t t R), Ut+h t A B t+h t + V t+h t + Vol t+h t }{{}}{{}}{{} Mean-Bias Dispersion (Realized) Risk Putting things together U t+h t Vol t+h t }{{} (Realized) Risk + B t+h t + D t+h t }{{} Knightian Uncertainty

13 Decomposition III: Aggregate Uncertainty as Ex-Ante and Ex-Post Uncertainty Let ŷ t+h t N(µ t+h t, σ t+h t ). This is the density forecast. Ut+h t A = E Y y t+h.5e Y Y = [ ( ) yt+h µ t+h t σ t+h t φ + ( ) ( ( yt+h µ t+h t y t+h µ t+h t Φ } σ t+h / π }{{} Ex-Ante σ t+h t {{ Ex-Post σ t+h t )

14 Recap We propose to look at total uncertainty as an average squared distributional forecast error still has the notion that the unpredictable elements constitute to uncertainty We can distinguish between aggregate uncertainty and disagreement realized risk and Knightian uncertainty ex-ante and ex-post uncertainty

15 Empirical Implementation Density forecasts from the Survey of Professional Forecasters provided by the Philadelphia Fed assign a probability value over pre-defined intervals for a variety of variables forecasts are for the current year and next year year-over-year growth rates Use Dovern et al. () re-weighting scheme to get 4-step-ahead forecasts: f t+4 t FH = k FE f t+k t + 4 k f FE 4 4 t+k+4 t. 4-quarter-ahead growth of Advance release in real time Empirical counterparts with 4-quarter-moving averages

16 Data Predictive quantiles of SPF SPF Mean Probability Density Forecast Current Year % 9% 5% Mean Prediction

17 Data Predictive quantiles of SPF SPF Mean Probability Density Forecast Next Year % 9% 5% Mean Prediction

18 Data Predictive quantiles of SPF versus the realizations SPF Mean Probability Density Forecast Four quarter ahead Fixed % 9% 5% Mean Prediction Realization

19 Results: Decomposition I Uncertainty, Aggregate Uncertainty and Disagreement. Uncertainty U A t+h t Disagreement The role of disagreement is very small Disagreement lags the aggregate measure

20 Results: Decompositions II and III 4.5 Knightian vs. Realized Risk Knightian Uncertainty/Realized Risk 4.5 Ex-Ante vs Ex-Post Ex Ante vs. Ex Post Decomposition 4 4 U A t+h t.5 U A t+h t B t+h t V t+h t Vol t+h t.5 Ex Post Ex Ante.5 Cov t+h t Ex-ante volatility larger than the realized volatility Ex-ante volatility is smoother than the realized one Knightian uncertainty and ex-post are more important for the aggregate uncertainty

21 Resolution of Uncertainty over Uncertainty Aggregate Uncertainty Forecast horizon Forecast horizon.5 Disagreement Forecast horizon

22 Resolution of Uncertainty over U A t+h t B t+h t Forecast horizon Forecast horizon V t+h t Vol t+h t Forecast horizon Forecast horizon Cov t+h t Forecast horizon

23 Results: Decomposition I for Inflation Uncertainty, Aggregate Uncertainty and Disagreement Uncertainty U A t+h t Disagreement

24 Results: Decompositions II and III for Inflation Knightian vs. Risk Knightian Uncertainty/Realized Risk Ex-Ante vs Ex-Post Ex Ante vs. Ex Post Decomposition.5 U A t+h t B t+h t V t+h t.5 U A t+h t Ex Post Ex Ante Vol t+h t.5 Cov t+h t Ex-ante volatility larger than the realized volatility Ex-ante volatility is smoother than the realized one Bias and ex post are more important for the aggregate uncertainty, though the latter more for dynamics

25 Comparison with some Existing Measures 6 4 JLN BBD ExAnte ExPost Jurado et al. (5) similar to ex-post Baker et al. (5) similar to ex-ante Roughly similar patterns

26 Macroeconomic Impact Based on (the log of) real GDP, (the log of) employment, the Federal Funds rate, (the log of) stock prices and uncertainty indices + const Uncertainty indices are standardized Identification according to recursive ordering Lag length is selected via BIC Robust to an variable specification

27 Decomposition I rgdp emp rgdp.5 emp 5 5 rovnght Aggregate Uncertainty stock rovnght Disagreement stock Insignificant response to disagreement

28 Decomposition II.5 rgdp.5 emp rgdp.5 emp rovnght Mean Bias stock rovnght (Realized) Risk stock Insignificant response to realized risk

29 Decomposition II rgdp.5 emp rovnght Dispersion stock Effects of dispersion are expansionary

30 Decomposition III 4 rgdp emp rgdp emp rovnght 5 5 Ex Ante stock rovnght Ex Post stock 5 5 Effects of ex-ante uncertainty are insignificant

31 Glancing through a lens of a model Model and parameter values inspired by Ilut and Schneider (4) Data is generated by Z t+ = ρ z Z t + µ t + u t+ µ t ambiguous component, µ t iidn(, σ z σ u ) lack confidence to assign probabilities to all relevant events u t+ random component (capturing risk),u t iidn(, σ u ) can assign probabilities to all relevant events Agents get noisy signals about µ t conflicting news reports, disagreement among experts, poor information, etc.

32 Glancing through a lens of a model Data is generated by Z t+ = ρ z Z t + µ t + u t+ Agents get noisy signals about µ t Their beliefs set is µ t [ a t, a t + a t ] They choose µ t scenario = min[ a t, a t + a t ], worst case While the agents get signals according to a t+ ā = ρ a (a t ā) + σ a ɛ a t+. ā = nσ z and σ a = σ n σ z for n (, )

33 Glancing through a lens of a model General notions about the model: Ambiguity is about the mean. It yields a perceived law of motion that is misspecified in the mean. The shocks to risk (σ u ) not only affect the second moment dynamics, but can propagate through the mean. It affects the width of the confidence set. Different than the news shocks since the signal does not need to be validated by a realization.

34 Glancing through a lens of a model Baseline Parameter Values ρ z.65 estimated ρ a.887 IS mode n.995 IS mode σ u.78 estimate σ µ.5 arbitrary σ n.4 IS mode Simulate for 54 periods, with a burn in of. Scenarios. changing level of ambiguity - change in the quality of the mean signal. changing level of risk - implies change in the ambiguity mean and variance. changing risk in a model with no ambiguity

35 Simulation Results. Changing the Level of Ambiguity n =. n =.8.5 Uncertainty, Aggregate Uncertainty and Disagreement.5 Uncertainty, Aggregate Uncertainty and Disagreement Knightian Uncertainty/Realized Risk Uncertainty U A t+h t Disagreement Knightian Uncertainty/Realized Risk U A t+h t B t+h t.5 Ex Ante vs. Ex Post Decomposition V t+h t Vol t+h t Cov t+h t Ex Ante vs. Ex Post Decomposition U A t+h t Ex Post Ex Ante 5 5 5

36 Simulation Results. Changing the Level of Risk σ u =. σ u = 4.5 Uncertainty, Aggregate Uncertainty and Disagreement 4.5 Uncertainty, Aggregate Uncertainty and Disagreement Knightian Uncertainty/Realized Risk.5 Uncertainty U A t+h t Disagreement Knightian Uncertainty/Realized Risk 4 4 U A t+h t B t+h t V t+h t Ex Ante vs. Ex Post Decomposition Vol t+h t Cov t+h t Ex Ante vs. Ex Post Decomposition 4 4 U A t+h t Ex Post Ex Ante

37 Simulation Results. Changing the Level of Risk, no Ambiguity σ u =. σ u = Uncertainty, Aggregate Uncertainty and Disagreement Uncertainty, Aggregate Uncertainty and Disagreement Knightian Uncertainty/Realized Risk Uncertainty U A t+h t Disagreement Knightian Uncertainty/Realized Risk U A t+h t B t+h t.5 Ex Ante vs. Ex Post Decomposition V t+h t Vol t+h t Cov t+h t Ex Ante vs. Ex Post Decomposition U A t+h t Ex Post Ex Ante 5 5 5

38 Scenario 4: Increasing Cross-Sectional Dispersion in Ambiguity σ n,i =.5 σ n,i = Uncertainty, Aggregate Uncertainty and Disagreement Uncertainty, Aggregate Uncertainty and Disagreement Knightian Uncertainty/Realized Risk Uncertainty U A t+h t Disagreement Knightian Uncertainty/Realized Risk U A t+h t.5 B t+h t V t+h t Ex Ante vs. Ex Post Decomposition Vol t+h t Cov t+h t Ex Ante vs. Ex Post Decomposition U A t+h t Ex Post Ex Ante 5 5 5

39 Conclusions Propose a way to reconcile various measures of uncertainty. They differ with their business cycle dynamics, as well as macroeconomic impact. One can reconcile the dynamics of the various measures of uncertainty with a model with ambiguity.