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Uncertain and Asymmetric Forecasts

Eric Vansteenberghe

TL;DR

This paper develops two distribution-based measures to unlock policy-relevant information from subjective probability distributions: Normalized Uncertainty (NU), a variance-stabilized indicator that removes mechanical level effects, and Asymmetry Coherence (AC), which combines central tendency and skewness to capture directional tail risks. Using ECB-SPF data for the euro area, NU behaves as a state variable that shapes monetary policy transmission and growth expectations, while AC provides incremental information about macro risks and growth vulnerabilities, largely independent of NU. In a suite of applications, NU explains how policy shocks de-anchor inflation expectations and how transmission to credit markets and growth forecasts evolves over state space, and AC reveals when forecast tails align with directional risks that influence policy stance, especially in tightening vs. easing episodes. A joint VAR and Growth-at-Risk analysis shows that uncertainty and asymmetry inform different channels of macro dynamics, suggesting that regulators and forecasters should treat belief-based uncertainty and directional tail risk as distinct yet complementary sources of information for assessing vulnerability and crafting policy.

Abstract

This paper develops distribution-based measures that extract policy-relevant information from subjective probability distributions beyond point forecasts. We introduce two complementary indicators that operationalize the second and third moments of beliefs. First, a Normalized Uncertainty measure applies a variance-stabilizing transformation that removes mechanical level effects around policy-relevant anchors. Empirically, uncertainty behaves as a state variable: it amplifies perceived de-anchoring following monetary-policy shocks and weakens and delays pass-through to credit conditions, particularly across loan maturities. Second, an Asymmetry Coherence indicator combines the median and skewness of subjective distributions to identify coherent directional tail risks. Directional asymmetry is largely orthogonal to uncertainty and is primarily reflected in monetary-policy responses rather than real activity. Overall, the results show that properly measured uncertainty governs state-dependent transmission, while distributional asymmetries convey distinct information about macroeconomic risks.

Uncertain and Asymmetric Forecasts

TL;DR

This paper develops two distribution-based measures to unlock policy-relevant information from subjective probability distributions: Normalized Uncertainty (NU), a variance-stabilized indicator that removes mechanical level effects, and Asymmetry Coherence (AC), which combines central tendency and skewness to capture directional tail risks. Using ECB-SPF data for the euro area, NU behaves as a state variable that shapes monetary policy transmission and growth expectations, while AC provides incremental information about macro risks and growth vulnerabilities, largely independent of NU. In a suite of applications, NU explains how policy shocks de-anchor inflation expectations and how transmission to credit markets and growth forecasts evolves over state space, and AC reveals when forecast tails align with directional risks that influence policy stance, especially in tightening vs. easing episodes. A joint VAR and Growth-at-Risk analysis shows that uncertainty and asymmetry inform different channels of macro dynamics, suggesting that regulators and forecasters should treat belief-based uncertainty and directional tail risk as distinct yet complementary sources of information for assessing vulnerability and crafting policy.

Abstract

This paper develops distribution-based measures that extract policy-relevant information from subjective probability distributions beyond point forecasts. We introduce two complementary indicators that operationalize the second and third moments of beliefs. First, a Normalized Uncertainty measure applies a variance-stabilizing transformation that removes mechanical level effects around policy-relevant anchors. Empirically, uncertainty behaves as a state variable: it amplifies perceived de-anchoring following monetary-policy shocks and weakens and delays pass-through to credit conditions, particularly across loan maturities. Second, an Asymmetry Coherence indicator combines the median and skewness of subjective distributions to identify coherent directional tail risks. Directional asymmetry is largely orthogonal to uncertainty and is primarily reflected in monetary-policy responses rather than real activity. Overall, the results show that properly measured uncertainty governs state-dependent transmission, while distributional asymmetries convey distinct information about macroeconomic risks.

Paper Structure

This paper contains 48 sections, 3 theorems, 54 equations, 34 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Related literature
  3. Uncertainty
  4. Inflation uncertainty and its impact on economic growth
  5. Asymmetry
  6. Inflation Asymmetry and its impact on economic growth
  7. Normalized Uncertainty
  8. Variance-stabilizing transformation for survey-based uncertainty
  9. Interpretation.
  10. Learning and a linear variance--distance relationship
  11. Link to standard macro evidence on time-varying volatility.
  12. Connection to Inflation-at-Risk via regime-dependent volatility.
  13. An application to measuring the impact of uncertainty on the perception of monetary policy
  14. Linear relationship between forecast variance and distance from the inflation target
  15. Average SPDs.
  16. ...and 33 more sections

Key Result

Lemma 1

Let $X\sim\mathrm{Exp}(\lambda)$ with cdf $F_X(x)=1-e^{-\lambda x}$ for $x\ge 0$. Then $Q_p(X)=F_X^{-1}(p)=-\lambda^{-1}\ln(1-p)$ and which is independent of $\lambda$. Proof.$Q_1=\lambda^{-1}\ln(4/3)$, $Q_2=\lambda^{-1}\ln 2$, $Q_3=\lambda^{-1}\ln 4$. Hence $Q_3+Q_1-2Q_2=\lambda^{-1}\ln(4/3)$ and $Q_3-Q_1=\lambda^{-1}\ln 3$. ∎

Figures (34)

  • Figure 1: The left panel is based on averaged SPDs, the right on the cross-section of individual forecasters. In both cases, the solid line shows an OLS fit of forecast variance on $|\mu_t-\pi^*|$, with regression coefficients reported in the legends. For individual SPDs, observations below the 30th percentile of mean were excluded to mitigate zero-lower-bound effects, and means above 5% were trimmed in line with the ECB-SPF bin design.
  • Figure 2: EPU is taken form baker2016measuring on Euro-Area countries against our Normalized Inflation Uncertainty from the ECB-SPF one-year ahead inflation SPD.
  • Figure 3: France: NFC overnight overdraft--deposit spread, inflation, and the monetary policy stance
  • Figure 4: Local projections: monetary policy transmission to the NFC overnight overdraft--deposit spread across uncertainty states
  • Figure 5: Local projections: monetary policy transmission to the NFC overnight overdraft--deposit spread across asymmetry coherence states
  • ...and 29 more figures

Theorems & Definitions (3)

  • Lemma 1: Exponential baseline
  • Lemma 2: Sign reversal under reflection
  • Proposition 1: Bowley of a sum can have a different sign than the average Bowley