## 2.1    A Simple Keynesian Model:  The Setup

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### Theoretical framework and key mechanism
- Simple Keynesian model where revisions in expected long-term output affect short-term consumption, investment, output, and unemployment via money hoarding and the marginal propensity to spend (MPS).
- Mechanism:
  - Higher (lower) expected long-term output growth → higher (lower) short-term consumption, investment, and output; unemployment falls (rises).
  - Money hoarding (hoarded money excluded from circulation) reduces money in circulation, lowering P1 and real wages (with sticky nominal wages W1 = W > 0), potentially causing unemployment.
  - Changes in consumption and investment today can reinforce expected long-term output changes, allowing for self-fulfilling dynamics.
- Expectations formation:
  - Forecasters form consensus about probability of a bad state πS in period 0 using an incomplete-information herding game à la Banerjee (1992).
  - Forecast revisions may reflect changes in fundamentals or herding/“animal spirits.”

### Model environment, preferences, and constraints
- Closed economy, agents: forecasters, many workers (W), entrepreneurs (F); three periods (0: forecasts; 1: short-term; 2: long-term).
- Preferences: representative utility ln(cj1) + β E ln(cj2), j = W,F, with 0 < β ≤ 1.
- Workers’ budget constraints:
  - P1 cW1 = W1 Ld1 − MW,h1
  - P2 cW,i2 = Wi2 L2 + MW,h1
  - cW1 ≥ 0, MW,h1 ≥ 0
- Entrepreneurs’ budget constraints:
  - P1 cF1 = Π1 − MF,h1 − P1 K2
  - P2 cF,i2 = Ri2 K2 + MF,h1
  - cF1 ≥ 0, K2 ≥ 0, MF,h1 ≥ 0
- Short-term profits and production:
  - Π1 ≡ P1 σ y1 − W1 Ld1, with 0 < σ ≤ 1 as the short-term MPS.
  - y1 ≤ A1 K1^α L1^(1−α); Π1 ≥ 0.
- Quantity equation linking circulation and output:
  - (M1 − Mh1) = P1 y1
- Long-term price level under credible monetary policy:
  - P2 = P1 (1 + φ)

### First-order conditions and equilibrium implications
- Workers’ FOC:
  - 1 / cW1 = β [ π 1 / cW,L2 (1 + φ) + (1 − π) 1 / cW,H2 (1 + φ) ]
- Entrepreneurs’ consumption FOC:
  - 1 / cF1 = β [ π (RL2 / cF,L2 P L2) + (1 − π) (RH2 / cF,H2 P H2) ]
- Entrepreneurs’ intertemporal/state allocation FOC:
  - π 1 / cF,L2 (P1 / PL2 − RL2 / PL2) + (1 − π) 1 / cF,H2 (P1 / PH2 − RH2 / PH2) = 0
- Profit-maximization FOC (period 1) yields short-term output:
  - y1 = A1 K1^α [ P1 / W1 (1 − α) (c1 + K2) ]^(1−α)
- Labor demand (short term):
  - Ld1 = [ y1 / (A1 K1^α) ]^(1 / (1−α))
- Conclusion: Consensus forecast revisions about the probability of the bad state affect money hoarding, σ (MPS), consumption, investment, output, and unemployment even if structural πS is unchanged.

### Numerical simulation scenarios (selected Table 1 entries)
- Expectation about long-term output E(y2): 0.06, 0.04, 0.01, -0.01, -0.04, -0.06
- Corresponding selected endogenous variables:
  - y1: 3.15, 3.13, 3.10, 3.08, 3.05, 3.03
  - μ (unemployment rate): 0.21, 0.22, 0.23, 0.24, 0.25, 0.26
  - M1: 1.67, 1.82, 1.96, 2.10, 2.24, 2.38
  - σ (short-term MPS): 0.91, 0.90, 0.89, 0.88, 0.88, 0.87
  - C1 (short-term consumption): 2.31, 2.27, 2.23, 2.19, 2.16, 2.13
  - I1 (aggregate investment): 0.56, 0.55, 0.54, 0.53, 0.51, 0.50
- Parameters:
  - β: 0.99
  - α: 0.30
- Exogenous/predetermined variables:
  - M1: 20.00
  - φ: 0.02
  - W1: 3.30
  - A1: 1.30
  - AL2: 0.40
  - AH2: 2.10
  - K1: 1.00
  - LS: 4.50
- Interpretation:
  - Deterioration in expected long-term growth → increased money hoarding, lower σ, lower C1 and I1, lower y1, higher μ.
  - Improvements in expected prospects produce the reverse effects.
  - Changes in expectations alone can drive current output, consumption, investment, and unemployment; lower expected future productivity reduces investment and can reinforce long-term declines.

---

### Empirical identification strategy and data construction
- Identification: use revisions to potential output growth forecasts as proxy for expectation shocks; rationale is potential output is structural and less driven by cyclical fluctuations.
- Data source: IMF World Economic Outlook (WEO) fall vintages from 1990 to 2016; forecast horizon N = 5 (forecasts for next five years from 1990 onward).
- Forecast revision measure:
  - R^{N−1}_{j,t} = E_{j,t}(y_{j,t+(N−1)}) − E_{j,t−1}(y_{j,t+(N−1)}), with N = 5, so R^{4}.
- Dependent variables:
  - Dc_{j,t} = c_{j,t} − E_{j,t−1}(c_{j,t})
  - Di_{j,t} = i_{j,t} − E_{j,t−1}(i_{j,t})
- Forecast vintages: Fall WEO of year t−1 used for forecasts; observed values for c and i at time t taken from Fall WEO of t+1 to avoid estimated values.
- Robustness: alternative potential output forecasts from OECD Economic Outlook used in robustness checks.

### Reduced-form and identification of learning parameter α
- Behavioral reduced-form:
  - D_{c,i}_{j,t} = γ + β[(1−α) R^{N−1}_{j,t} + α R^{N−1}_{j,t+1}] + μ_{j} + τ_{t} + ε_{j,t}
- Rearranged:
  - D_{c,i}_{j,t} = γ + αβ (R^{N−1}_{j,t+1} − R^{N−1}_{j,t}) + β R^{N−1}_{t} + μ_{j} + τ_{t} + ε_{j,t}
- Dynamics estimated via local projections (Jordà (2005)) and robustness checked with S-GMM (two-step with Windmeijer (2005) correction) and alternative estimators.

---

### Stylized facts on forecast revisions
- Distributional features of R^{4}:
  - Frequency distribution resembles normal but leptokurtic with slight negative skew.
  - Clustering around mean with frequent small revisions; slight negative skew suggests pessimistic revisions dominated over the sample.
- Time variation around the Global Financial Crisis (GFC):
  - Average revision hovered around zero but became negative in 2008 and 2009.
  - From 2008 expectations became more dispersed with more extreme values.
- Summary statistics (Table 2, Obs. 960, percent):
  - Full sample:
    - Mean: -0.11
    - Median: -0.04
    - Std. dev.: 0.54
    - Skewness: -0.63
    - Kurtosis: 8.44
  - AE (Obs. 718):
    - Mean: -0.08; Median: -0.02; Std. dev.: 0.45; Skewness: -0.27; Kurtosis: 8.37
  - EMDE (Obs. 242):
    - Mean: -0.17; Median: -0.08; Std. dev.: 0.75; Skewness: -0.61; Kurtosis: 5.78
  - Before GFC (Obs. 412):
    - Mean: -0.02; Median: 0.00; Std. dev.: 0.42; Skewness: 0.64; Kurtosis: 8.90
  - After GFC (Obs. 548):
    - Mean: -0.17; Median: -0.09; Std. dev.: 0.61; Skewness: -0.77; Kurtosis: 7.20
  - Directional subsamples:
    - Pessimistic (Obs. 591): Mean -0.37; Median -0.25; Std. dev. 0.45; Skewness -2.45; Kurtosis 11.68
    - Optimistic (Obs. 369): Mean 0.33; Median 0.21; Std. dev. 0.37; Skewness 2.46; Kurtosis 11.61
- Note: calculations exclude two outliers corresponding to Portugal in 1991 and 1994.

---

### Main empirical results and quantitative magnitudes
- Estimation: OLS with country and time fixed effects (baseline); results robust to alternative estimators and controls.
- Identification of α and β:
  - Full sample implied α and β estimates:
    - Private consumption (PC): α 0.467, β 1.872
    - Private investment (PI): α 0.439, β 5.212
  - AE:
    - PC: α 0.351, β 2.493
    - PI: α 0.353, β 7.234
  - EMDE:
    - PC: α 0.669, β 1.391
    - PI: α 0.563, β 3.871
- Key coefficients (selected from Table 3, with standard errors in parentheses):
  - R^{4}_{t+1} − R^{4}_{t}:
    - Full sample PC: 0.874*** (0.239)
    - Full sample PI: 2.288*** (0.687)
    - AE PC: 0.875*** (0.253)
    - AE PI: 2.550*** (0.860)
    - EMDE PC: 0.930** (0.452)
    - EMDE PI: 2.178* (1.182)
  - R^{4}_{t}:
    - Full sample PC: 1.872*** (0.365)
    - Full sample PI: 5.212*** (1.674)
    - AE PC: 2.493*** (0.440)
    - AE PI: 7.234*** (1.781)
    - EMDE PC: 1.391** (0.626)
    - EMDE PI: 3.871 (2.858)
- Implied elasticities and GDP impact (baseline and robustness ranges preserved):
  - A 0.1 percentage point upward revision to potential output growth forecast is associated with:
    - 0.19 to 0.25 percent increase in private consumption growth.
    - 0.39 to 0.72 percent increase in private investment growth.
    - For an average country with private consumption (investment) shares of GDP of 65 (16) percent, this implies an acceleration in GDP growth by 0.09 to 0.16 (0.06 to 0.11) percent.
  - A 0.1 percentage point downward revision is associated with:
    - 0.17 to 0.22 percent reduction in private consumption growth.
    - 0.51 to 0.71 percent reduction in private investment growth.
    - For the average country (consumption share 65 percent; investment share 16 percent), this implies a reduction in GDP growth by 0.11 to 0.14 (0.08 to 0.11) percent.
- Dynamics (local projections):
  - Adjustment in consumption and investment occurs primarily over two years following an expectation shock.
  - For real private consumption growth: positive effects of improved expectations phase out after two years for full sample and AE, and after one year for EMDE.
  - For private investment growth: similar pattern; effects for EMDE less often significant.

---

### Extensions, non-linearities, robustness, and policy implications
- Non-linearities and asymmetry:
  - Tests for post-GFC dummy, pessimism dummy, and squared terms largely support linearity of effects.
  - No differential impact found between pessimistic and optimistic expectations on private consumption or private investment.
  - Large changes in expectations induce proportional changes in demand (no detected non-proportionality).
- Controls and S-GMM results:
  - Results robust to inclusion of controls: terms of trade, real public consumption/investment, real short-term interest rate, inflation, demographics.
  - Inflation forecast error: negative and significant for private consumption regressions.
  - Terms of trade forecast error: improvements associated with higher private investment.
  - Fiscal policy and credit-condition proxies generally insignificant.
  - S-GMM estimates: α when significant ≈ 0.3 (ranges between 0.4 and 0.5 in some specifications); β significant and ranges between 1.7 and 2.2 for private consumption and between 5.1 and 7.1 for private investment.
  - OECD subsample (32–34 countries): β-coefficients remain significant and comparable; α significant for investment but not for consumption.
- Robustness across estimators:
  - Pooled OLS, FGLS with time fixed effects, PCSE, 2SLS, and S-GMM all show positive impact of revisions in potential output growth forecast; sizes of α and β similar across estimators.
  - Portion of variation explained by expectations higher in OECD sample (between 28 and 45 percent).
- Policy implications:
  - If expectation revisions causally affect aggregate demand, policy may aim to curb fluctuations when they lead to inferior equilibria or undesired instability.
  - Credible institutional commitments and policy interventions that stabilize expectations can deter movements toward inferior equilibria.
  - Further analysis of policy commitment mechanisms and expectation formation is proposed for future research.

*Source: wp1801 - 2.1 A Simple Keynesian Model: The Setup; 3.1 Data; 3.2 Empirical model; 4 Stylized facts; 5 Results; 5.2 Extensions (excerpt) from https://www.imf.org/-/media/files/publications/wp/2018/wp1801.pdf*

### 2.1    A Simple Keynesian Model:  The Setup .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### 2.1    A Simple Keynesian Model:  The Setup

### Theoretical framework
- Proposes a simple Keynesian model showing that changes in expected long-term income have short-term effects in the direction of the change in expectations.
- Mechanism:
  - If agents expect long-term output growth to be high (low), short-term consumption, investment, and output increase (fall).
  - Unemployment falls when expectations are upward and increases when expectations are downward.
  - Increases (decreases) in consumption and investment today can reinforce the expected decrease (increase) in long-term output, giving rise to a self-fulfilling mechanism.
- Expectations formation:
  - Expectations are assumed to be formed à la Banerjee (1992), so that changes in forecasts may reflect either:
    - a change in fundamentals, or
    - herding in the formation of expectations (loosely assimilated to “animal spirits”).

### Motivation and links to literature
- Builds on literature on:
  - “Animal spirits” and belief-driven cycles (Cass and Shell, 1983; Akerlof and Shiller, 2010; De Grauwe and Ji, 2016).
  - Self-fulfilling changes in fundamentals via strategic complementarities (Acharya et al., 2017; Benhabib et al., 2016; Weil, 1989; Cooper and John, 1988).
  - “News-driven business cycles” where imperfect/noisy information about future fundamentals drives current activity (Cochrane, 1994; Beaudry and Portier, 2004, 2006; Lorenzoni, 2009; Jaimovich and Rebelo, 2009; Beaudry et al., 2011; Schmitt-Grohè and Uribe, 2012; Blanchard et al., 2013).
- Notes that revisions in long-term growth forecasts can reflect either correct signals about fundamentals (leading to persistent effects) or overly optimistic/pessimistic beliefs (potentially causing booms or busts).

### Empirical identification strategy (motivated by the model)
- Uses revisions to potential output growth forecasts as a proxy for changes in expectations about long-term output.
- Rationale:
  - Potential output is a structural measure and unlikely to be driven by current cyclical fluctuations, making revisions far into the future plausible instruments for expectation shocks.
  - Recognizes challenges: analysts may revise potential output forecasts based on short-term cyclical information; therefore, alternative potential output forecasts from other sources are used in empirical analysis.

### Main empirical implications tested
- Private agents expecting higher (lower) future potential output growth will consume and invest more (less) today.
- Dynamic response: adjustments in consumption and investment occur over the two years following an expectation shock.
- Non-linearities and selected dynamics of expectation shocks are studied, including frequency, skewness, and volatility before and after the Global Financial Crisis (GFC).

### Key quantitative findings (from the model-informed empirical analysis)
- For the average country with a share of private consumption (investment) to GDP of 65 (16) percent:
  - A 0.1 percentage point (pp) upward revision to potential output growth forecast would bring about an acceleration in GDP growth in the range of 0.09 to 0.16 (0.06 to 0.11) percent.
- Additional empirical observations:
  - Changes in expectations became more frequent, negatively skewed, and volatile in the aftermath of the GFC, but the estimated effects on consumption and investment are not different relative to the period preceding the GFC.
  - Pessimistic and optimistic expectations do not present a differential impact on private consumption nor private investment.
  - Large changes in expectations induce proportional changes in demand.

*Source: wp1801 - 2.1    A Simple Keynesian Model:  The Setup (excerpt) from https://www.imf.org/-/media/files/publications/wp/2018/wp1801.pdf*

### 2.1  A Simple Keynesian Model: The Setup

### 2.1  A Simple Keynesian Model: The Setup

### Model purpose and key mechanism
- Revises a simple Keynesian model showing that revisions in expected future income affect short-term equilibria via money hoarding.
- Money hoarding subtracts from aggregate demand, decreasing the marginal propensity to spend (MPS).
- Money hoarding is modeled explicitly (hoarded money excluded from circulation); money in circulation is used for transactions.
- Keynesian insight emphasized: when prospects about future income deteriorate, people hoard money, reducing effective demand and MPS.

### Agents, timing, and market structure
- Closed economy with a few economic forecasters, many workers (W) and entrepreneurs (F).
- Three periods: period 0 (forecasts), period 1 (short-term), period 2 (long-term). All transactions occur in periods 1 and 2.
- Perfect competition in goods and factor markets; nominal rigidities limited to fixed short-term nominal wages (W1 = W > 0).
- Short-term prices are flexible except for nominal wages; if effective demand is low, unemployment may result (Ld1 ≤ L > 0).

### Preferences, constraints, and objectives
- Representative consumer utility: ln(cj1) + βE ln(cj2), where j = W,F and 0 < β ≤ 1.
- Workers’ budget constraints:
  - P1 cW1 = W1 Ld1 − MW,h1
  - P2 cW,i2 = Wi2 L2 + MW,h1
  - cW1 ≥ 0, MW,h1 ≥ 0
- Entrepreneurs’ budget constraints (consumption/investment/hoarding):
  - P1 cF1 = Π1 − MF,h1 − P1 K2
  - P2 cF,i2 = Ri2 K2 + MF,h1
  - cF1 ≥ 0, K2 ≥ 0, MF,h1 ≥ 0
- Short-term monetary profits:
  - Π1 ≡ P1 σ y1 − W1 Ld1, with 0 < σ ≤ 1 as the MPS.
- Short-term production constraints:
  - y1 ≤ A1 K1^α L1^(1−α)
  - Π1 ≥ 0
- Short-term MPS defined as:
  - σ(·) ≡ (P1 y1 − Mh1) / (P1 y1) = 1 − Mh1 / (P1 y1)

### Prices, money supply, and monetary policy
- Short-term money supply set by monetary authority: M1 = M > 0.
- Quantity equation linking circulation and output:
  - (M1 − Mh1) = P1 y1
- Long-term price level determined by credible monetary policy and inflation target φ:
  - P2 = P1 (1 + φ)
- Conclusion: higher aggregate money hoarding → lower money in circulation → lower P1 → lower real wages (given sticky nominal wages) → possible unemployment.

### Expectations and information aggregation
- Consensus forecast about probability of bad state πS is formed in period 0 by N forecasters using an incomplete-information herding game (Banerjee (1992) structure).
- True πS unknown but 0 < π ≤ πS ≤ π < 1.
- Forecasters receive signals with accuracy ψ (0 < ψ < 1); correct guess yields compensation ξ > 0; aggregate forecaster compensation Γ ∈ [0, ξN] and is assumed negligible relative to economy size.
- Sequential forecasting with observed history can generate multiple equilibria via herding: optimistic equilibria (consensus π < πS) and pessimistic equilibria (consensus π > πS).

### First-order conditions and equilibrium determination
- Workers’ FOC (equalizing marginal utilities):
  - 1 / cW1 = β [ π 1 / cW,L2 (1 + φ) + (1 − π) 1 / cW,H2 (1 + φ) ]
- Entrepreneurs’ consumer FOC:
  - 1 / cF1 = β [ π (RL2 / cF,L2 P L2) + (1 − π) (RH2 / cF,H2 P H2) ]
- Entrepreneurs’ intertemporal/state allocation FOC:
  - π 1 / cF,L2 (P1 / PL2 − RL2 / PL2) + (1 − π) 1 / cF,H2 (P1 / PH2 − RH2 / PH2) = 0
- Entrepreneurs’ profit-maximization FOC (period 1) gives short-term output:
  - y1 = A1 K1^α [ P1 / W1 (1 − α) (c1 + K2) ]^(1−α)
- Labor demand (short term):
  - Ld1 = [ y1 / (A1 K1^α) ]^(1 / (1−α))
- Long-term factor demands (period 2):
  - Pi2 (1 − α) Ai2 Ki,d^α2 Li,d^(−α2) = Wi2
  - Pi2 α Ai2 Ki,d^(α−1)2 Li,d^(1−α2) = Ri2

### Keynesian channel emphasized
- Short-term output depends on effective demand through the MPS; money hoarding raises unsold production (inventories) and lowers effective demand.
- Changes in consensus forecasts about the bad state of the world directly affect short-term money hoarding, MPS, consumption, investment, output, and unemployment—even if the structural probability πS is unchanged.

### Numerical simulation (selected results from Table 1)
- Expectation about long-term output E(y2): 0.06, 0.04, 0.01, -0.01, -0.04, -0.06

- Selected endogenous variables by scenario (corresponding to E(y2) entries above)
  - y1: 3.15, 3.13, 3.10, 3.08, 3.05, 3.03
  - μ (unemployment rate): 0.21, 0.22, 0.23, 0.24, 0.25, 0.26
  - M1 (money supply in period 1 circulating? — table reports): 1.67, 1.82, 1.96, 2.10, 2.24, 2.38
  - σ (short-term MPS): 0.91, 0.90, 0.89, 0.88, 0.88, 0.87
  - C1 (short-term consumption): 2.31, 2.27, 2.23, 2.19, 2.16, 2.13
  - I1 (aggregate investment): 0.56, 0.55, 0.54, 0.53, 0.51, 0.50

- Parameters (constant across scenarios)
  - β: 0.99
  - α: 0.30

- Exogenous/predetermined variables (constant)
  - M1: 20.00
  - φ: 0.02
  - W1: 3.30
  - A1: 1.30
  - AL2: 0.40
  - AH2: 2.10
  - K1: 1.00
  - LS: 4.50

### Simulation interpretation (qualitative findings)
- Deterioration in expected long-term growth (higher perceived probability of bad state) leads to:
  - Increased money hoarding
  - Lower MPS (σ)
  - Lower effective demand (C1 and I1)
  - Lower short-term output (y1)
  - Higher unemployment (μ)
- Improved expected future prospects have the reverse effects.
- A change in expectations alone is sufficient to affect current output, consumption, investment, and unemployment; lower expected future productivity also reduces investment, reinforcing long-term output declines.

*Source: Authors’ calculations.*

### 3.1  Data

### 3.1  Data

### Data sources and vintages
- Data source: International Monetary Fund’s (IMF) World Economic Outlook (WEO), released twice a year (spring and fall).
- WEO database: actual macroeconomic data and forecasts submitted by country teams and vetted by the IMF’s Research Department for internal and multilateral consistency.
- Spring WEO release timing: May up through 2001 and in April thereafter; fall version typically in October, occasionally in September.
- Forecast horizon: Starting in 1990, every vintage contains forecasts for the next five years (N = 5).
- Forecast production timing: Spring forecasts performed during February or March; Spring WEO data for the previous year may be an estimate or forecast for some countries. Fall WEO is based on final information.
- Sample vintages used: Fall WEO vintages from 1990 to 2016.

### Construction of key variables
- Dependent variables: deviations of observed real consumption growth (c) or real investment growth (i) from previous year growth forecast:
  - Dc_{j,t} = c_{j,t} − E_{j,t−1}(c_{j,t})
  - Di_{j,t} = i_{j,t} − E_{j,t−1}(i_{j,t})
- Forecasts for consumption and investment used: Fall WEO of year t−1 (to ensure IMF revised potential real GDP growth information is not yet available).
- Expectation measure about economy j: use Fall WEO of year t forecast of potential real GDP growth y* for year t+(N−1) (with N = 5); denote E_{j,t}(y_{j,t+(N−1)}).
- Forecast revision measure:
  - R^{N−1}_{j,t} = E_{j,t}(y_{j,t+(N−1)}) − E_{j,t−1}(y_{j,t+(N−1)})
  - The second-to-last year of the forecast horizon (t+(N−1)) is used because it is available in the Fall WEO at both t and t−1.
- Favorite measure: the farthest computable revision (to isolate structural changes far into the future from cyclical movements).
- Observed values for c and i at time t are taken from the Fall WEO of t+1 to avoid using still-estimated values.

---

### 3.2  Empirical model

### Behavioral assumption and reduced-form specification
- Agents adjust consumption and investment based on two information sources:
  - Proportion α: learn about future potential output growth at Fall WEO publication of year t (adjust overt).
  - Proportion (1−α): learn from same information used by IMF to produce forecasts (adjust int−1).
- Reduced-form equation for private consumption and private investment:
  - D_{c,i}_{j,t} = γ + β[(1−α) R^{N−1}_{j,t} + α R^{N−1}_{j,t+1}] + μ_{j} + τ_{t} + ε_{j,t}
- Rearranged to identify α:
  - D_{c,i}_{j,t} = γ + αβ (R^{N−1}_{j,t+1} − R^{N−1}_{j,t}) + β R^{N−1}_{t} + μ_{j} + τ_{t} + ε_{j,t}
  - α = (αβ) / β
- Identification argument: unexpected cyclical movements in private consumption and investment are unlikely to affect forecasts of potential output growth far into the future; robustness check uses OECD Economic Outlook estimates of potential output.

### Dynamics and estimation approach
- Impulse responses via local projection method (Jordà (2005)):
  - D_{c,i}_{j,t+h} = γ_{h} + α_{h} β_{h} (R^{N−1}_{j,t+1} − R^{N−1}_{j,t}) + β_{h} R^{N−1}_{j,t} + μ^{h}_{j} + τ^{h}_{t} + ε^{h}_{j,t}, h = 0,1,2,...,s
- Robustness to additional covariates:
  - D_{c,i}_{j,t} = γ + αβ (R^{N−1}_{j,t+1} − R^{N−1}_{j,t}) + β R^{N−1}_{t} + δ D_{x}_{j,t} + ψ S_{j,t} + μ_{j} + τ_{t} + ε_{j,t}
  - D_{x}_{j,t} are controls expressed as deviations with respect to forecasts; S_{j,t} are controls where observed values must be used due to data availability.
- Endogeneity concerns and estimator:
  - Use System Generalized Method of Moments (S-GMM): system of two simultaneous equations (levels and first differences) with lagged differences and lagged levels as instruments.
  - Estimator variant: two-step S-GMM with Windmeijer (2005) finite-sample correction to the two-step covariance matrix.

---

### 4  Stylized facts

### Distributional properties of revisions to potential output growth forecasts
- General distribution:
  - Frequency distribution resembles a normal distribution but with leptokurtic features and slight negative skew.
  - Clustering around the mean reflects frequent small revisions.
  - Slight negative skew suggests pessimistic expectations dominated optimistic ones over the sample period.
- Time variation (around the Global Financial Crisis, GFC):
  - Average revision hovered around zero for entire period but became negative in 2008 and 2009.
  - Starting in 2008 expectations became more dispersed with more extreme values.
- Pre- vs. post-GFC (1991-2007 vs. 2008-16):
  - Negative revisions became more frequent after the GFC.
  - Extreme values were both positive and negative in the post-GFC period, possibly reflecting policy reactions and structural falls in output.
- Figures: Figure 2 and Figure 3 display these distributions (notes: panels exclude two outliers corresponding to Portugal in 1991 and 1994).

### Summary statistics (Table 2: Revisions to Potential Output Growth Forecasts, Percent)
- Full sample (Obs. 960):
  - Mean: -0.11
  - Median: -0.04
  - Std. dev.: 0.54
  - Skewness: -0.63
  - Kurtosis: 8.44
- Income groups:
  - AE (Obs. 718):
    - Mean: -0.08
    - Median: -0.02
    - Std. dev.: 0.45
    - Skewness: -0.27
    - Kurtosis: 8.37
  - EMDE (Obs. 242):
    - Mean: -0.17
    - Median: -0.08
    - Std. dev.: 0.75
    - Skewness: -0.61
    - Kurtosis: 5.78
- Periods:
  - Before GFC (Obs. 412):
    - Mean: -0.02
    - Median: 0.00
    - Std. dev.: 0.42
    - Skewness: 0.64
    - Kurtosis: 8.90
  - After GFC (Obs. 548):
    - Mean: -0.17
    - Median: -0.09
    - Std. dev.: 0.61
    - Skewness: -0.77
    - Kurtosis: 7.20
- Direction:
  - Pessimistic (Obs. 591):
    - Mean: -0.37
    - Median: -0.25
    - Std. dev.: 0.45
    - Skewness: -2.45
    - Kurtosis: 11.68
  - Optimistic (Obs. 369):
    - Mean: 0.33
    - Median: 0.21
    - Std. dev.: 0.37
    - Skewness: 2.46
    - Kurtosis: 11.61
- Note: calculations exclude two outliers corresponding to Portugal in 1991 and 1994.

---

### 5  Results

### 5.1 Baseline estimations — main findings (Table 3)
- Estimation method: OLS with country and time-fixed effects.
- Samples and dependent variables:
  - Dependent variables: real private consumption (PC) growth forecast error and real private investment (PI) growth forecast error.
  - Samples: Full sample, AE (Advanced Economies), EMDE (Emerging Market and Developing Economies).
- Key coefficients and interpretation:
  - Coefficients on R^{4}_{t+1} − R^{4}_{t} and R^{4}_{t} are significant across country groups and for both PC and PI, except the time difference coefficient in PI for EMDE (likely due to reduced observations).
  - For the full sample, the α coefficient is close to 0.5, suggesting agents learn about future potential output growth both at Fall WEO publication and at the time IMF produces its forecasts.
  - α differences by group:
    - AE: α substantially smaller than EMDE, indicating AE agents learn mostly at the same time as the IMF (more sophisticated information processing).
    - EMDE: higher α, indicating more learning at Fall WEO publication.
  - β coefficients:
    - Private consumption specifications: β ranges between 1.9 and 2.5.
    - Private investment specifications: β ranges between 3.9 and 7.2.
    - Interpretation: a 0.1 pp downward revision in the potential output growth forecast is associated with:
      - 0.19 to 0.25 percent reduction in private consumption growth.
      - 0.39 to 0.72 percent reduction in private investment growth.
    - For the average country with private consumption (investment) shares of GDP of 65 (16) percent, this implies a reduction in GDP growth by:
      - Consumption channel: 0.09 to 0.16 percent.
      - Investment channel: 0.06 to 0.11 percent.
- Table 3 (selected results summary):
  - Columns: Full sample (PC, PI), AE (PC, PI), EMDE (PC, PI).
  - R^{4}_{t+1} − R^{4}_{t} coefficients:
    - Full sample PC: 0.874*** (std. err. 0.239)
    - Full sample PI: 2.288*** (0.687)
    - AE PC: 0.875*** (0.253)
    - AE PI: 2.550*** (0.860)
    - EMDE PC: 0.930** (0.452)
    - EMDE PI: 2.178* (1.182)
  - R^{4}_{t} coefficients:
    - Full sample PC: 1.872*** (0.365)
    - Full sample PI: 5.212*** (1.674)
    - AE PC: 2.493*** (0.440)
    - AE PI: 7.234*** (1.781)
    - EMDE PC: 1.391** (0.626)
    - EMDE PI: 3.871 (2.858)
  - Constants:
    - Full sample PC: -0.514* (0.281)
    - Full sample PI: -4.969* (2.527)
    - AE PC: -0.245 (0.283)
    - AE PI: -5.249** (2.535)
    - EMDE PC: -0.125 (1.063)
    - EMDE PI: 5.464* (3.186)
  - Observations and fit:
    - Observations: Full sample PC 782, PI 566; AE PC 598, PI 396; EMDE PC 184, PI 170.
    - R^2: Full sample PC 0.199, PI 0.187; AE PC 0.332, PI 0.274; EMDE PC 0.082, PI 0.124.
  - Number of countries: Full sample 89; AE 33; EMDE 50.
  - Implied α and β estimates:
    - Full sample: α 0.467, β 1.872 (PC); α 0.439, β 5.212 (PI).
    - AE: α 0.351, β 2.493 (PC); α 0.353, β 7.234 (PI).
    - EMDE: α 0.669, β 1.391 (PC); α 0.563, β 3.871 (PI).
  - Significance notation: ***, **, and * indicate statistical significance at 1, 5, and 10 percent, respectively.
- Figures and dynamics:
  - Figure 4: Scatter plots of weighted average revisions [(1−α) R^{N−1}_{j,t} + α R^{N−1}_{j,t+1}] vs. forecast errors in real private consumption and investment show a positive relationship—better expectations associated with increased demand.
  - Figure 5: Impulse response functions (local projections) show:
    - For real private consumption growth: positive effect of an improvement in expectations phases out after two years for the full sample and AE, and after one year for EMDE.
    - For private investment growth: similar pattern, with the exception that the effect is not significant for EMDE.
    - Red dots (α-related) tend to approach one over time, consistent with agents becoming increasingly informed by the Fall WEO publication.

*Source: Authors’ calculations (content unit: wp1801 - 3.1 Data).*

### 5.2  Extensions

### 5.2 Extensions

### Non-linearities and interaction tests
- Tested possible non-linearities by adding interaction terms: dummy after the GFC; dummy for negative revisions to potential output growth forecasts (pessimism); and squared expectations terms to proxy large revisions.
- Main finding: effects of forecast revision of long-term potential output growth are generally linear.
- Exception: column 5 for real private consumption growth shows a small positive and significant coefficient for the time-difference term of the revision of output growth forecast, suggesting that in presence of large revisions to potential output growth forecast, private economic agents increase their consumption to a larger extent before the WEO Fall publication, as indicated by a larger α-coefficient.

### Controls included and theoretical rationale
- Controls added to Dx_t in equation (27): terms of trade, real public consumption growth (or real public investment growth), real short-term interest rate, and inflation.
  - Terms of trade: ambiguous net effect on consumption (income and composition effects).
  - Real public consumption/investment: Ricardian-equivalence predicts offsetting effects; empirical sign ambiguous (substitutes imply offset; complements could increase private consumption).
  - Real short-term interest rate: ambiguous net effect (substitution, income, and human-wealth effects differ for net creditors vs net debtors).
  - Inflation: generally lowers consumption via higher current prices and precautionary saving; ambiguous overall due to intertemporal substitution and real rate effects.
- Demographics S_t include old-age dependency ratio and share of urban population.
  - Old-age dependency ratio: LCH predicts hump-shaped saving; increase in old-age dependency ratio should bring about an increase in consumption.
  - Share of urban population: ambiguous effect on consumption.

### S-GMM estimations with controls (Table 5) — key empirical findings
- Impact of revisions to potential output growth forecast remains generally robust to inclusion of control variables.
- Persistence: lag of real private investment growth is significant.
- Inflation forecast error: negative and significant in regressions for real private consumption growth.
- Terms of trade forecast error: improvements reflected in higher private investment.
- Fiscal policy and credit-condition proxies (real public consumption/investment, short-term interest forecast error): do not turn out significant, possibly due to delays in affecting macroeconomic variables.
- Coefficient magnitudes:
  - α, when significant, is about 0.3 (ranges between 0.4 and 0.5) for real private consumption (investment) growth.
  - β is always significant, and ranges between 1.7 and 2.2 for real private consumption growth and between 5.1 and 7.1 for real private investment growth.
- Implied effects:
  - A 0.1 pp downward revision in the potential output growth forecast is associated with a 0.17 to 0.22 (0.51 to 0.71) percent reduction in private consumption (investment) growth.
  - For the average country with a share of private consumption (investment) to GDP of 65 (16) percent, this would bring about a reduction in GDP growth by 0.11 to 0.14 (0.08 to 0.11) percent.

### Robustness checks (Tables 6 and 7)
- Varying lags of the revisions to potential output growth forecast (R5−R4, R3, R2, R1 constructions) produce generally robust results; α and β coefficients remain comparable in magnitude to baseline.
- Using OECD data reduces sample to 32 to 34 countries; β-coefficients remain significant and comparable; α significant for real private investment growth but insignificant for real private consumption growth in the OECD sample.
- Alternative estimators considered: pooled OLS; FGLS with time-fixed effects; Panel Corrected Standard Error (PCSE); 2SLS with country- and time-fixed effects; S-GMM with country- and time-fixed effects.
  - Positive impact of revisions in potential output growth forecast is robust across estimators.
  - Sizes of α and β coefficients are strikingly similar across estimators, supporting baseline estimation credibility.
- Additional robustness details:
  - The portion of variation in dependent variables explained by expectations is higher when using OECD data (between 28 and 45 percent), likely due to higher homogeneity in that subsample.

### Linearity, asymmetry, and post-GFC patterns
- Changes in expectations became more frequent, negatively skewed, and volatile in the aftermath of the GFC, but estimated impacts are not statistically different relative to the period preceding the GFC.
- No differential impact between pessimistic and optimistic expectations on private consumption or private investment.
- Large changes in expectations induce proportional (i.e., non-proportionality not detected) changes in demand — overall supporting linearity.

### Summary quantitative estimates (from baseline and robustness)
- Upward revisions:
  - A 0.1 pp upward revision in the potential output growth forecast is associated with a 0.19 to 0.25 percent increase in private consumption growth.
  - A 0.1 pp upward revision is associated with a 0.39 to 0.72 percent increase in private investment growth.
  - For the average country with private consumption (investment) shares of 65 (16) percent, this implies an acceleration in GDP growth by 0.09 to 0.16 (0.06 to 0.11) percent.
- Downward revisions (mirror estimates reported):
  - A 0.1 pp downward revision is associated with a 0.17 to 0.22 percent reduction in private consumption growth.
  - A 0.1 pp downward revision is associated with a 0.51 to 0.71 percent reduction in private investment growth.
  - For the average country with private consumption (investment) shares of 65 (16) percent, this implies a reduction in GDP growth by 0.11 to 0.14 (0.08 to 0.11) percent.

### Policy implications
- If changes in expectations about future economic conditions cause short-term fluctuations in aggregate demand, economic policy could aim to curb such fluctuations when they place the economy in an inferior equilibrium or generate undesired instability.
- Credible institutional commitments remain valuable: credible commitments to policy intervention to stabilize undesired fluctuations could act on expectation formation mechanisms by deterring agents from moving the economy to an inferior equilibrium.
- Further analysis on policy commitment mechanisms and expectation formation is left for future research.

*Source: Authors’ calculations, extracted from "5.2 Extensions" of the provided chapter.*

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### Appendix A. Country Groups
- Advanced Economies:Australia, Austria, Belgium, Canada, Cyprus, Czech Republic, Den- mark, Estonia, Finland, France, Germany, Greece, Hong Kong, Iceland, Ireland, Israel, Italy, Japan, Latvia, Lithuania, Luxembourg, Malta, Netherlands, New Zealand, Norway, Portugal, Singapore, Slovak Republic, Slovenia, South Korea, Spain, Sweden, Switzerland, Taiwan, United Kingdom, United States.
- Emerging Market and Developing Economies:Algeria, Antigua and Barbuda, Armenia, Ba- hamas, Barbados, Belize, Bosnia and Herzegovina, Brazil, Bulgaria, Chile, China, Colombia, Costa Rica, Croatia, Dominica, Dominican Republic, Egypt, El Salvador, Georgia, Grenada, Guatemala, Haiti, Honduras, Hungary, India, Indonesia, Jamaica, Kazakhstan, Kenya, Lebanon, Malaysia, Mauritius, Mexico, Moldova, Montserrat, Nicaragua, Pakistan, Panama, Peru, Philippines, Poland, Romania, Russia, South Africa, St.  Kitts and Nevis, St.  Lucia, St.  Vincent and the Grenadines, Swaziland, Thailand, Togo, Turkey, Ukraine, Uruguay.

### Appendix B. Data
- Table B.1 lists all variables used in the empirical analysis, along with the source and scales.
- Table B.1:  Data Sources
  - VariableSourceScale
  - Real private consumptionIMF World Economic OutlookPercent growth forecast error
  - Real private investmentIMF World Economic OutlookPercent growth forecast error
  - Revision in potentialIMF World Economic OutlookPercent growth forecastand OECD Economic Outlook
  - General government debtIMF World Economic OutlookPercent of GDP
  - Inflation forecast errorIMF World Economic OutlookPercent
  - Terms of trade forecastIMF World Economic OutlookPercent error
  - Real public consumptionIMF World Economic OutlookPercent growth forecast error
  - Real public investmentIMF World Economic OutlookPercent growth forecast error
  - Real short-term interestIMF International Financial StatisticsPercent rate forecast errorand Haver
  - Old-age dependency ratioWorld Bank World DevelopmentPercent of working-age Indicatorspopulation
  - Share of urban populationWorld Bank World Development IndicatorsPercent of population

*Source: wp1801 - References (PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1801.pdf_