## I. INTRODUCTION and Empirical Findings (wpiea2021272-print-pdf)

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### Research question and motivation
- Is fiscal policy more effective when macroeconomic uncertainty is high?
- Policymakers’ concern: uncertainty during episodes such as the COVID-19 pandemic or the Global Financial Crisis could hold economic activity down, exacerbate economic scars, or delay recovery.
- Theoretical background and empirical gap:
  - Wait-and-see behavior and option value of waiting can slow activity (Bernanke (1983); Bloom (2009); Bachmann et al. (2013); Dixit and Pindyck (1994)).
  - Evidence on monetary policy suggests policy ineffectiveness amid elevated uncertainty (Aastveit et al. (2017); Castelnuovo and Pellegrino (2017); Eickmeier et al. (2018); Pellegrino (2018, 2020)).
  - The effect of uncertainty on fiscal policy transmission is under-studied and empirical findings are inconclusive (Arčabić and Cover (2016); Berg (2019); Alloza (2018)).

### Focus and mechanism
- Scope: extent to which uncertainty magnifies the macroeconomic impact of discretionary public investment increases.
- Rationale for public investment:
  - Powerful instrument for fiscal stimulus; promotes short-term growth, resilience, and long-term transformation.
  - Can be temporary, deliverable in a timely fashion, and prioritize sectors with positive externalities (health, education, environment, digitalization, innovation).
  - Can mitigate excess savings and foster productivity growth, especially if it crowds-in private investment.
- Mechanism studied: private-sector confidence and expectations as a transmission channel—public investment may raise expectations of future productivity growth and thereby strengthen private response (Bachmann and Sims (2012); accelerator model references).

### Empirical strategy and data
- Sample: 72 countries over the period 1996–2019.
- Outcomes: output, private investment, employment, private-sector confidence.
- Measure of macroeconomic uncertainty: standard deviation of GDP forecasts across professional forecasters (Consensus Economics), using the spring (April) vintage for each year.
- Identification: exogenous public investment shocks defined as forecast errors of public investment spending in percent of GDP; focus on positive investment shocks (implementation uses mainly October IMF WEO forecasts, with Fall OECD forecasts for AEs during 2004–08).

*Source content from the provided unit.*

### Main empirical findings (exact figures preserved)
- Linear (baseline) public investment multipliers (local projections, k = 0,1,2):
  - Output — whole sample, public investment shock coefficients:
    - k=0: 0.2335*** (standard error 0.0807)
    - k=1: 0.5822*** (standard error 0.1007)
    - k=2: 0.5247*** (standard error 0.1877)
  - Interpretation: an unanticipated 1 percentage point of GDP increase in public investment contemporaneously increases the level of output by about 0.23 percent; peaks at 0.58 percent two years after the shock.
- Private investment (linear estimates, whole sample):
  - Public investment shock:
    - k=0: 1.1611 (1.0091)
    - k=1: 3.2018*** (0.7399)
    - k=2: 3.6812*** (0.7911)
  - A public investment shock of 1 percentage point of GDP crowds-in private investment by more than 3 percent over two years.
- Employment (linear estimates, whole sample):
  - Public investment shock:
    - k=0: -0.0248 (0.3533)
    - k=1: 0.0587 (0.4175)
    - k=2: 0.5528 (0.4610)
  - Discretionary public investment push has no statistically significant effect on employment on average.

### Role of macroeconomic uncertainty (state-dependent results; exact figures preserved)
- Transition function uses curvature 훿 set to 1; z normalized to zero mean and unit variance.
- Multiplier comparison (high uncertainty versus baseline):
  - The multiplier peaks at 2.7 over two years during periods of high uncertainty versus 0.6 for the baseline estimate.
  - Multiplier remains statistically significant at the 99 percent threshold in the third year during high uncertainty.
  - In periods of low uncertainty the null hypothesis of no effects on output cannot be rejected.
- Interaction estimates (High uncertainty * Investment shock — Whole sample):
  - Output:
    - k=0: 0.6501 (0.5327)
    - k=1: 2.7184*** (0.8446)
    - k=2: 2.4194*** (0.7114)
  - Private Investment:
    - k=0: 6.7531*** (1.6337)
    - k=1: 10.0691*** (2.3095)
    - k=2: 7.8311** (3.2494)
  - Employment:
    - k=0: 0.5088 (0.4030)
    - k=1: 1.1909*** (0.2337)
    - k=2: 1.9721*** (0.3291)
- Low uncertainty interaction (Whole sample) — effects not statistically significant; reported coefficients:
  - Output:
    - k=0: 0.6688 (0.7122)
    - k=1: -0.3493 (0.8879)
    - k=2: 0.0107 (1.0875)
  - Private Investment:
    - k=0: -1.1808 (2.7556)
    - k=1: -0.2179 (4.3849)
    - k=2: -0.1470 (5.6891)
  - Employment:
    - k=0: 0.1610 (0.7536)
    - k=1: 0.3435 (1.0436)
    - k=2: 0.6719 (1.2971)
- Observations for uncertainty interaction regressions: 147; R-squared range: 0.7334–0.8520.

### Effects on economic confidence (mean and dispersion of GDP forecasts; exact figures preserved)
- Confidence proxied by change in mean and change in dispersion (standard deviation) of growth forecasts among professional forecasters.
- Linear specification (selected coefficients):
  - Public investment shock on Mean Forecast of GDP:
    - k=1: 0.5417* (0.2929)
    - k=2: 0.1756 (0.3389)
    - k=3: 0.6620 (0.4670)
  - Effects on Standard Deviation of GDP Forecast: insignificant at all horizons in linear specification.
- Nonlinear specification by uncertainty (High vs Low uncertainty interactions; selected exact coefficients):
  - High uncertainty * Investment shock — Mean Forecast of GDP:
    - k=1: 3.1377*** (0.3969)
    - k=2: 2.4207*** (0.3652)
    - k=3: 2.1909*** (0.5280)
  - High uncertainty * Investment shock — Standard Deviation of GDP Forecast:
    - k=1: -0.8800*** (0.0738)
    - k=2: -1.0797*** (0.1143)
    - k=3: -0.8850*** (0.0756)
  - Low uncertainty * Investment shock — Mean Forecast of GDP:
    - k=1: -1.9205*** (0.5451)
    - k=2: -1.9936*** (0.5308)
    - k=3: -1.2212* (0.6588)
  - Low uncertainty * Investment shock — Standard Deviation of GDP Forecast:
    - k=1: 0.7755*** (0.0702)
    - k=2: 0.7634*** (0.1119)
    - k=3: 0.7687*** (0.1322)
- Observations: Mean Forecast regressions 145,135,131; SD regressions 144,134,130; R-squared up to 0.9203.

### Interaction with the state of the economy (growth and unemployment regimes; exact figures preserved)
- Distinction between uncertainty-dependent and cycle-dependent effects: uncertainty tends to be countercyclical but not always; a state-dependent model (recessions/expansions) is not equivalent to an uncertainty-dependent model.
- Growth regime interaction (Low vs High growth dummy; selected coefficients):
  - Low growth dummy (difference vs high) — Output:
    - k=0: -0.0178*** (0.0062)
    - k=1: -0.0308*** (0.0078)
    - k=2: -0.0349*** (0.0098)
  - High uncertainty # Low growth — Output:
    - k=0: 0.2486 (0.6965)
    - k=1: 2.1650*** (0.6000)
    - k=2: 1.7493*** (0.5984)
  - High uncertainty # High growth — Output:
    - k=0: 3.3101** (1.4446)
    - k=1: 4.5245* (2.6008)
    - k=2: 4.3036 (6.1230)
- Unemployment regime interaction (High vs Low unemployment; selected coefficients):
  - High unemployment dummy (difference vs Low) — Output:
    - k=0: -0.0224*** (0.0062)
    - k=1: -0.0322*** (0.0090)
    - k=2: -0.0392*** (0.0113)
  - High uncertainty # Low unemployment rate — Output:
    - k=0: 2.5580** (0.9456)
    - k=1: 7.3697*** (1.7891)
    - k=2: 9.2249*** (3.1788)
  - High uncertainty # High unemployment — Output:
    - k=0: 0.4417 (0.5594)
    - k=1: 2.2590*** (0.3215)
    - k=2: 1.7549*** (0.5601)
- Conclusion: Larger multipliers during high uncertainty are not driven by the state of the economy; when uncertainty is heightened, public investment shocks have positive and statistically significant effects on output irrespective of business cycle state.

### Robustness checks and alternative definitions (selected exact findings)
- Simpler high-uncertainty indicator (uncertainty index above sample median) confirms larger multipliers during high uncertainty (Annex Table 9).
- Alternative state indicators (unemployment-based) confirm that larger multipliers in high uncertainty are not driven by the state of the economy (Annex Table 10). During high uncertainty, multipliers are relatively lower when unemployment rate is high.
- Alternative investment-shock definition (difference between realized investment and spring forecast vintage) yields similar conclusions—multipliers larger and statistically significant during high uncertainty (Table 11, Panel A).
- Subsample and control robustness:
  - Restricting to advanced economies or to period 2007–2019 yields similar conclusions.
  - Controlling for output gap: public investment shocks have larger effects on output, investment, and employment during high uncertainty even when controlling for output gap.
  - Different curvature 훿 values: results robust to 훿=1.5; 훿=0.75 results similar (available upon request).
- Statistical significance indicators preserved: *p < .10; **p < .05; ***p < .01.

### Interpretation and transmission channel (policy-relevant implications)
- Discretionary increases in public investment have larger effects on output, employment, and private investment when implemented during periods of high uncertainty.
- Mechanism supported by the evidence:
  - Direct effect: investment spending raises aggregate demand.
  - Indirect effect: public investment boosts private-sector confidence (mean expectations rise and forecast dispersion falls under high uncertainty), which spurs private demand and crowding-in of private investment.
- When implemented in low uncertainty periods, unanticipated public investment shocks may weaken confidence and raise disagreement among forecasters.
- Policy implication: timing public investment pushes during periods of heightened macroeconomic uncertainty can yield substantially larger multipliers and stronger private-sector responses, according to the empirical evidence in this sample.

*Source: I. INTRODUCTION, III. EMPIRICAL STRATEGY, IV. ECONOMETRIC RESULTS, V. CONCLUSION and annex tables from wpiea2021272-print-pdf (IMF staff calculations and tables).*

### REFERENCES  ___________________________________________________________ 22

### I. INTRODUCTION

### Research question and motivation
- Is fiscal policy more effective when macroeconomic uncertainty is high?  
- Context: policymakers worry that uncertainty during episodes such as the COVID-19 pandemic or the Global Financial Crisis could hold economic activity down, exacerbate economic scars, or delay recovery.  
- Theoretical background:
  - Higher uncertainty can slow economic activity via wait-and-see behavior (Bernanke (1983); Bloom (2009); Bachmann et al. (2013)).
  - Option value of waiting to invest (Dixit and Pindyck (1994)).
  - Higher uncertainty may reduce policy effectiveness by making firms and households more cautious (Bloom et al. (2018)).
  - Empirical studies find policy ineffectiveness amid elevated uncertainty for monetary policy (Aastveit et al. (2017); Castelnuovo and Pellegrino (2017); Eickmeier et al. (2018); Pellegrino (2018, 2020)).
- Gap: The effect of uncertainty on the transmission of fiscal policy shocks has been rarely studied and existing empirical findings are inconclusive (some find larger multipliers when uncertainty is high: Arčabić and Cover (2016), Berg (2019); others find lower multipliers: Alloza (2018)).

### Focus: public investment multipliers and channels
- Scope: Assess the extent to which uncertainty magnifies the macroeconomic impact of discretionary public investment increases.  
- Rationale for focusing on public investment:
  - Powerful instrument for fiscal stimulus.
  - Potential to promote short-term growth, strengthen resilience, and support long-term transformation.
  - Temporary in nature, deliverable in a timely fashion, and capable of prioritizing sectors with large positive externalities (health, education, environment, digitalization, innovation).
  - Can mitigate excess savings and foster longer-term productivity growth, especially if it crowds-in private investment.
- Secondary objective: Explore the mechanism through which uncertainty affects the fiscal multiplier, with emphasis on private-sector confidence and expectations.
  - Empirical literature: positive shocks to economic confidence generate positive and persistent output effects (Guimaraes et al. (2016); Barsky and Sims (2012); Carroll et al. (1994)).
  - Theory: changes in expectations are an important driver of economic fluctuations (Beaudry and Portier (2006); Benhabib and Farmer (1999)).
  - Open question: How do public investment shocks affect economic confidence, especially during turmoil? (Empirical evidence is scarce; see Bachmann and Sims (2012), Alesina et al. (2015), Berg (2019) as rare exceptions.)

### Empirical strategy and key metrics
- Sample: 72 countries over the period 1996–2019.  
- Outcomes analyzed: output, private investment, employment, and private-sector confidence.  
- Measure of macroeconomic uncertainty: the standard deviation of GDP forecasts across professional forecasters (Altig et al. (2020)).  
- Identification: analysis focuses on short-to-medium run effects of public investment shocks; emphasis on discretionary increases of public investment.

### Main empirical findings (exact figures preserved)
- Public investment shocks have positive and long-lasting effects on output, private investment, and employment.  
- During periods of heightened uncertainty, a 1 percentage point of GDP increase in public investment leads over a two-year period to:
  - Output increase of 2.7 percent.
  - Private investment increase of 10.1 percent.
  - Employment increase of 1.2 percent.
- Comparison benchmarks:
  - Linear model estimate: 0.6 percent increase in output in response to the same shock.
  - In periods of low uncertainty the null hypothesis of no effects cannot be rejected.
- Interpretation: Under high uncertainty, private spending starts from a lower level; public investment more strongly boosts activity that would otherwise be postponed, yielding larger multipliers.

### Effects on economic confidence
- Discretionary increases in public investment improve economic confidence, proxied by the change in the mean (and the dispersion) of growth forecasts.  
- Under high uncertainty, increases in public investment significantly buttress private-sector confidence.  
- Proposed mechanism: public investment raises expectations of future productivity growth (Bachmann and Sims (2012)), which strengthens private response to fiscal stimulus (accelerator model: Jorgenson (1963); Jorgenson and Siebert (1968); Hall (1977)).
- Contrasting result: public investment shocks weaken confidence when implemented in periods of low uncertainty, possibly by reinforcing some investors’ pessimistic near-term expectations.

### Robustness and business-cycle interaction
- The analysis allows the effect of uncertainty on public investment multipliers to vary with the state of the economy (to distinguish from high multipliers measured during recessions).  
- Findings:
  - During periods of high uncertainty, public investment shocks have a positive and statistically significant effect on output irrespective of whether the economy is in a high or low growth state.
  - When uncertainty is low, the null hypothesis of no effect cannot be rejected regardless of the state of the economy.
- Conclusion: The degree of uncertainty matters for the size of public investment multipliers even after controlling for the business cycle.

### Contribution of the paper
- Extends the literature on state-dependency of fiscal multipliers to account for the degree of macroeconomic uncertainty.
- Focuses on positive investment shocks, helping disentangle stimulative government investment increases from spending cuts in recessions and addressing potential asymmetry in responses to spending increases versus decreases.
- Presents the first large-sample empirical study of how macroeconomic uncertainty impacts the effects of public investment on economic confidence (previous attempts limited, e.g., Berg (2019) for Germany).

*Source: I. INTRODUCTION (text from wpiea2021272-print-pdf - REFERENCES  ___________________________________________________________ 22)*

### Section III lays out the empirical strategy which results are discussed in section IV. Section V is

### III. EMPIRICAL STRATEGY

### Measuring Macroeconomic Uncertainty
- Macroeconomic uncertainty is measured by the standard deviation of GDP growth forecasts across professional forecasters as published by Consensus Economics, using the spring (April) vintage for each year.
- Rationale for this choice:
  - High levels of disagreement between professional forecasters about GDP growth are treated as proxies for economic uncertainty.
  - Changes in professional forecasts predict subsequent changes in expectations in the broader population (Carroll (2003)).
  - Focusing on GDP forecasts captures uncertainty surrounding the broader macroeconomic outlook rather than stock-market-based measures.
  - The Consensus Forecast dataset allows for broad country coverage.

### Identifying Public Investment Shocks
- Endogeneity challenge: countries with high growth are more likely to engage in large infrastructure projects, while public investment can itself foster growth.
- Identification approach: Exogenous investment shocks are defined as forecast errors of public investment spending in percent of GDP. This approach follows Auerbach and Gorodnichenko (2012) and related literature.
- Implementation details:
  - Investment shock for country i and year t: ∆I_{i,t} = I_{i,t} − I^a_{i,t}, and ∆I^a_{i,t} = ∆I_{i,t} if ∆I_{i,t} > 0, where I_{i,t} is realized public investment spending as a share of GDP and I^a_{i,t} is the forecasted public investment spending.
  - Forecasts are taken mainly from the October publications of the IMF World Economic Outlook for the same year. (For advanced economies during 2004–08, Fall OECD Economic Outlook forecasts are used due to WEO data limitations.)
  - The paper focuses on positive investment shocks to explore the effects of a public investment push and to disentangle stimulative increases from cuts in recession periods.
  - The same-year October forecasts are used to control for potentially endogenous responses of public investment to within-year information.

### Baseline Specification and Estimation Method
- Baseline regression (local projections framework):
  - The paper estimates responses of log macroeconomic variables (real GDP, employment, private investment) using local projections (Jordà (2005)) for horizons k = 0, 1, 2.
  - General specification (notation as in source): y_{i,t+k} − y_{i,t−1} = α_i + γ_t + β_k ∆I^a_{i,t} + θ_k M_{i,t} + ε_{i,t}^k, for k = 0,1,2.
  - α_i = country fixed effect; γ_t = time fixed effect; ∆I^a = identified public investment shock; M = set of control variables including lagged GDP growth.
  - Lagged investment shocks are included to control for potential serial correlation in the shock variable (following Ramey and Zubairy (2018)).
- Advantages of local projections:
  - Do not impose the dynamic restrictions embedded in VAR specifications.
  - Appropriate for estimating nonlinearities in dynamic responses and robust to misspecification.
- Inference:
  - Confidence intervals for impulse response functions obtained from estimated (clustered robust) standard errors of β_k to control for potential serial correlation from successive leadings of the dependent variable.

### IV. ECONOMETRIC RESULTS — Linear Public Investment Multipliers
- Sample and data sources:
  - Unbalanced panel of 72 countries over the period 1996-2019.
  - Primary data sources: IMF World Economic Outlook, OECD, and Consensus Economics.
- Key empirical findings:
  - Output responses:
    - An unanticipated 1 percentage point of GDP increase in public investment contemporaneously increases the level of output by about 0.23 percent.
    - The output response remains statistically significant until the third year, and peaks at 0.58 percent two years after the shock.
    - Interpretation: reflects both Keynesian demand effects during construction and expansion of productive capacity as public investment augments physical infrastructure stock.
    - These estimates fall within the range reported by previous research (around zero to as high as 2).
  - Private investment:
    - Public investment shocks crowd-in private investment in the short-to-medium term.
    - A public investment shock of 1 percentage point of GDP crowds-in private investment by more than 3 percent over two years.
    - The positive private investment response is not statistically significant in the first year but becomes significant over two years.
  - Employment:
    - A discretionary push to public investment is found to have no statistically significant effect on employment.
    - Effects on employment increase over time but remain statistically insignificant—possible explanation: on average, employment is not far from full capacity.
  - Heterogeneity:
    - Separate estimations for advanced economies and emerging and developing countries indicate that multipliers and the elasticity of employment are larger in advanced economies, where investment efficiency is likely to be higher.

_Italic line: Source content from the provided unit._

### Annex Table 1 presents the countries covered by the analysis, the time coverage, and the exercise where they appear.

### Annex Table 1 presents the countries covered by the analysis, the time coverage, and the exercise where they appear.

### Effects of Uncertainty on Public Investment Multipliers
- Specification: state-dependent specification using transition function G(z) with curvature 훿 set to 1 (equation (2)); z normalized to zero mean and unit variance.
- Key findings:
  - The multiplier peaks at 2.7 over two years during periods of high uncertainty versus 0.6 for the baseline estimate.
  - The multiplier remains statistically significant at the 99 percent threshold in the third year during high uncertainty (see Annex Table 5).
  - In periods of low uncertainty, the null hypothesis of no effects on output cannot be rejected.
  - Private investment response:
    - During high uncertainty, private investment increases by more than 10 percent over a period of 2 years after a 1 percentage point of GDP push to public investment.
    - This private investment response is more than twice larger compared to the private investment response in the linear model.
    - During low uncertainty, the null hypothesis of no public investment impact on private investment cannot be rejected.
  - Employment response:
    - Public investment shocks have statistically significant and long-lasting positive effects on employment when economic uncertainty is high; employment response increases over time.
    - During low uncertainty, the null hypothesis of no impact on employment cannot be rejected.
- Interpretation:
  - Discretionary increases in public investment have larger effects on output, employment, and investment when implemented during periods of high uncertainty.
  - Mechanism: private investment starts from a low level during high uncertainty, so public investment lifts private investment more compared to normal times, producing larger multipliers.
  - Public investment shocks during high uncertainty may signal government commitment to aggregate stability and promote growth, improving expectations about future economic developments.

### Public Investment Shocks and Economic Confidence
- Confidence measurement:
  - Proxied by two indicators: change in the mean and change in the dispersion (standard deviation) of growth forecasts among professional forecasters (Consensus Economics).
- Linear specification (equation (3)) results:
  - Public investment shocks significantly increase mean expectations of forecasters in the short term; effects turn statistically insignificant in the medium term (Figure 2, Panel A.1).
  - Public investment shocks reduce uncertainty around forecasts, but effects are insignificant at all time horizons (Figure 2, Panel B.1).
- Nonlinear specification by uncertainty (equation (4)):
  - Public investment shocks have nonlinear effects on confidence depending on ex-ante economic uncertainty; effects are statistically significant (see Annex Table 7).
  - When implemented during high uncertainty:
    - Public investment shocks increase growth expectations by economic agents.
    - They reduce forecasters’ disagreement about short-and-medium-term growth paths (Figure 2, Panels A.2 and B.2).
  - When implemented during low uncertainty:
    - Unanticipated shocks lead to pessimistic expectations and higher disagreement between forecasters (Figure 2, Panels A.3 and B.3).
- Transmission channel conclusion:
  - During high uncertainty, public investment shocks boost economic confidence, leading to a stronger private demand response and larger crowding-in effects on private investment.
  - The macroeconomic effects decompose into:
    - Direct effect: investment spending is a component of aggregate demand.
    - Indirect effect: public investment improves confidence which spurs private sector response.
  - These panel findings extend previous results for the US and Germany that confidence is a potential transmission channel of fiscal policy.

### Public Investment Multipliers and the Role of the State of the Economy
- Dynamics:
  - Analysis of changes in the uncertainty index and annual growth rate for selected economies (China, Germany, UK, USA) over 1994-2019 shows uncertainty tends to be countercyclical but not always.
  - Counterexamples: periods where growth accelerates with growing uncertainty (e.g., China 2002-2004; Germany 2004 and 2006; UK 1997, 2003, 2017; US 2018).
  - Conclusion: a state-dependent model distinguishing recessions and expansions is not equivalent to an uncertainty-dependent model distinguishing high and low uncertainty regimes.
- Controlling for state of the economy (equation (5)):
  - State indicator D(i,t) identifies low/high growth state: year t is low growth (D=1) if growth rate in year t is lower than average growth rate of past three years.
  - Results (Figure 4):
    - Larger multipliers during high uncertainty are not driven by the state of the economy.
    - When uncertainty is heightened, public investment shocks have positive and statistically significant effects on output irrespective of business cycle state (low or high growth).
    - When uncertainty is low, the null hypothesis of no effects cannot be rejected regardless of state.
    - On average, multipliers are lower during periods of low growth compared to periods of high growth; the difference is statistically significant (Annex Table 8).

### Robustness Exercises
- Simpler specification (equation (7)):
  - Define D(i,t) as high uncertainty if uncertainty index higher than sample median.
  - Result: investment multipliers are larger during periods of high uncertainty (Annex Table 9).
- Alternative state indicators:
  - Using unemployment rate as indicator of state (high unemployment if unemployment in year t higher than average of past three years) confirms larger multipliers in high uncertainty are not driven by state of the economy (Annex Table 10).
  - During high uncertainty, fiscal multipliers are relatively lower when unemployment rate is high; public investment shocks have on average lower effects when implemented during periods of high unemployment.
- Additional robustness (Annex Table 11):
  - Public investment shocks defined as difference between realized investment and spring forecast vintage: conclusions similar—multipliers larger and statistically significant during high uncertainty.
  - Limiting sample to subsample of advanced economies or to period starting from the Global Financial Crisis: conclusions similar.
  - Introduction of additional control variables including output gap: public investment shocks have larger effects on output, investment, and employment during periods of high uncertainty even when controlling for output gap.
  - Different values of curvature parameter 훿: results robust to using 훿=1.5 (Auerbach and Gorodnichenko (2013a)); results for 훿=0.75 are similar (available upon request).

### Conclusion
- Main conclusions:
  - Macroeconomic uncertainty has a positive and significant effect on the public investment multiplier.
  - This effect holds after controlling for the business cycle, indicating uncertainty matters for fiscal policy effectiveness.
  - During heightened uncertainty, public investment surprises boost economic confidence in the short-to-medium-term; when shocks occur in low uncertainty periods they may weaken confidence.
  - Improved private sector confidence during high uncertainty amplifies private sector response (consumption, hiring, investment) to public investment shocks, generating larger multipliers.
  - These findings are supported by a variety of robustness checks and are consistent with the interpretation that public investment raises private investment more during high uncertainty because private investment starts from a lower level.

*Source: Annex Table 1 and associated sections of the provided IMF working paper content.*

### REFERENCES

### REFERENCES

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### Uncertainty, confidence, and investment dynamics
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- Bloom, N. 2009. The Impact of Uncertainty Shocks. Econometrica, 77(3):623–85.
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- Bernanke, B. S. 1983. "Irreversibility, Uncertainty, and Cyclical Investment." The Quarterly Journal of Economics, February 1983, Vol. 98, No. 1, pp. 85–106.
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- Carroll, C. 2003. Macroeconomic Expectations of Households and Professional Forecasters, The Quarterly Journal of Economics,118, issue 1, p. 269–98.

### Macro methods, fiscal foresight, and structural analysis
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- Auerbach, A., and Gorodnichenko, Y. 2012. “Measuring the Output Responses to Fiscal Policy.” American Economic Journal: Economic Policy. 4(2): 1–27.
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*Source: wpiea2021272-print-pdf - REFERENCES*

### 372.  The MIT Press.

### wpiea2021272-print-pdf - 372.  The MIT Press.

### Key empirical findings on public investment shocks
- Dependent variable: Output — whole sample, public investment shock coefficients:
  - k=0: 0.2335*** (standard error 0.0807)
  - k=1: 0.5822*** (standard error 0.1007)
  - k=2: 0.5247*** (standard error 0.1877)
- Lag of Public investment shock (whole sample):
  - 0.5910* (standard error 0.3101)
- Lag of real GDP growth rate (whole sample):
  - k=0: -0.0028 (0.0024)
  - k=1: -0.0021 (0.0018)
  - k=2: -0.0017 (0.0011)
- Observations and fit (Output regressions):
  - Whole sample: Observations 389, R-squared 0.5533
  - Advanced Economies: Observations 213, R-squared 0.7325
  - Emerging and Developing Economies: Observations 176, R-squared 0.4883

### Effects on private investment (linear estimates)
- Dependent variable: Private Investment — whole sample
  - Public investment shock:
    - k=0: 1.1611 (1.0091)
    - k=1: 3.2018*** (0.7399)
    - k=2: 3.6812*** (0.7911)
  - Lag of Public investment shock (whole sample):
    - 1.9166** (0.7635), 1.5879* (0.9430), 1.0084 (1.0700)
  - Constant (whole sample): 1.8739*** (0.0665)
  - Observations: 386; R-squared: 0.6480
- Advanced Economies — private investment:
  - Public investment shock: k=1: 3.5494 (2.7993); k=2: 5.9359 (4.0480)
  - Observations: 213; R-squared: 0.4999
- Emerging and Developing Economies — private investment:
  - Public investment shock: k=1: 3.1126*** (0.7918); k=2: 3.7240*** (0.8235)
  - Observations: 173; R-squared: 0.6667

### Effects on employment (linear estimates)
- Dependent variable: Employment — whole sample
  - Public investment shock:
    - k=0: -0.0248 (0.3533)
    - k=1: 0.0587 (0.4175)
    - k=2: 0.5528 (0.4610)
  - Lag of Public investment shock (whole sample):
    - k=0: 0.3050 (0.3318)
    - k=1: 0.7170* (0.4252)
    - k=2: 0.6047 (0.4348)
  - Lag of real GDP growth rate (whole sample):
    - k=0: 0.0042*** (0.0014)
    - k=1: 0.0045*** (0.0015)
    - k=2: 0.0044*** (0.0016)
  - Observations: 311; R-squared: 0.5329

### Role of macroeconomic uncertainty (interaction effects)
- High uncertainty * Investment shock (Whole sample, Output / Private Investment / Employment):
  - Output: k=0: 0.6501 (0.5327); k=1: 2.7184*** (0.8446); k=2: 2.4194*** (0.7114)
  - Private Investment: k=0: 6.7531*** (1.6337); k=1: 10.0691*** (2.3095); k=2: 7.8311** (3.2494)
  - Employment: k=0: 0.5088 (0.4030); k=1: 1.1909*** (0.2337); k=2: 1.9721*** (0.3291)
- Low uncertainty * Investment shock (Whole sample):
  - Output: k=0: 0.6688 (0.7122); k=1: -0.3493 (0.8879); k=2: 0.0107 (1.0875)
  - Private Investment: k=0: -1.1808 (2.7556); k=1: -0.2179 (4.3849); k=2: -0.1470 (5.6891)
  - Employment: k=0: 0.1610 (0.7536); k=1: 0.3435 (1.0436); k=2: 0.6719 (1.2971)
- Lag of Public investment shock in uncertainty regressions:
  - Whole sample: 0.9027*** (0.3139), 1.2937** (0.5750), 1.4290** (0.6213)
- Observations: 147 for the uncertainty interaction regressions; R-squared range: 0.7334–0.8520 across panels and dependent variables

### Effects on confidence (mean and dispersion of GDP forecasts)
- Linear Effects on Confidence (Mean Forecast of GDP / Standard Deviation of GDP Forecast):
  - Public investment shock (k=1,k=2,k=3) — Mean Forecast of GDP: 0.5417* (0.2929), 0.1756 (0.3389), 0.6620 (0.4670)
  - Lag of Public investment shock — Mean Forecast of GDP: -0.1682 (0.2212), 0.1506 (0.2079), -0.3519* (0.1884)
  - Lag of real GDP growth rate — Mean Forecast of GDP: -0.0030*** (0.0004), -0.0018* (0.0009), -0.0037*** (0.0009)
  - Observations: Mean Forecast regressions 147,137,133; R-squared 0.9036, 0.8556, 0.8539
- Nonlinear Effects of Investment Shocks by uncertainty:
  - High uncertainty * Investment shock — Mean Forecast of GDP:
    - k=1: 3.1377*** (0.3969)
    - k=2: 2.4207*** (0.3652)
    - k=3: 2.1909*** (0.5280)
  - High uncertainty * Investment shock — Standard Deviation of GDP Forecast:
    - k=1: -0.8800*** (0.0738)
    - k=2: -1.0797*** (0.1143)
    - k=3: -0.8850*** (0.0756)
  - Low uncertainty * Investment shock — Mean Forecast of GDP:
    - k=1: -1.9205*** (0.5451)
    - k=2: -1.9936*** (0.5308)
    - k=3: -1.2212* (0.6588)
  - Low uncertainty * Investment shock — Standard Deviation of GDP Forecast:
    - k=1: 0.7755*** (0.0702)
    - k=2: 0.7634*** (0.1119)
    - k=3: 0.7687*** (0.1322)
  - Observations: 145,135,131 (Mean) and 144,134,130 (SD); R-squared up to 0.9203

### Interaction of uncertainty with the state of the economy (growth and unemployment)
- Interaction with growth regime (Low vs High growth dummy):
  - Low (diff. VS high) growth period (Dummy=1) — Output:
    - k=0: -0.0178*** (0.0062)
    - k=1: -0.0308*** (0.0078)
    - k=2: -0.0349*** (0.0098)
  - High uncertainty # Low growth — Output:
    - k=0: 0.2486 (0.6965)
    - k=1: 2.1650*** (0.6000)
    - k=2: 1.7493*** (0.5984)
  - High uncertainty # High growth — Output:
    - k=0: 3.3101** (1.4446)
    - k=1: 4.5245* (2.6008)
    - k=2: 4.3036 (6.1230)
  - Lag of Public investment shock (interaction regressions):
    - 0.6993*** (0.2169), 1.0621** (0.4547), 1.1560** (0.5515)
  - Observations: 147; R-squared up to 0.9042
- Interaction with unemployment regimes:
  - High (difference versus Low) unemployment period (Dummy=1) — Output:
    - k=0: -0.0224*** (0.0062)
    - k=1: -0.0322*** (0.0090)
    - k=2: -0.0392*** (0.0113)
  - High uncertainty # Low unemployment rate — Output:
    - k=0: 2.5580** (0.9456)
    - k=1: 7.3697*** (1.7891)
    - k=2: 9.2249*** (3.1788)
  - High uncertainty # High unemployment — Output:
    - k=0: 0.4417 (0.5594)
    - k=1: 2.2590*** (0.3215)
    - k=2: 1.7549*** (0.5601)
  - Lag of Public investment shock (unemployment interaction regressions):
    - 0.7198** (0.2900), 0.9570* (0.4949), 1.0157** (0.4796)
  - Observations: 147; R-squared up to 0.8822

### Robustness and alternative definitions of investment shocks
- Table 11 panels (A–E) report alternative specifications; selected coefficients (Output, Private Investment, Employment):
  - Panel A (Output k=0): 0.0996 (0.5948); k=1: 2.0931** (0.9029); k=2: 1.4860 (0.9096)
  - Panel A (Private Investment k=0): 6.7248*** (2.2162); k=1: 10.6270** (4.3037); k=2: 8.4824* (4.5695)
  - Panel A (Employment k=0): 0.1793 (0.4101); k=1: 0.9010** (0.3414); k=2: 1.3265* (0.7564)
  - Notes specify: Panel A uses difference between realized investment and spring forecast vintage; Panel B restricts to advanced economies; Panel C to period 2007-2019; Panel D controls for output gap; Panel E sets curvature of transition function equal to 1.5 as in Auerbach and Gorodnichenko (2013a).
- Statistical significance indicators preserved as reported: *p < .10; **p < .05; ***p < .01

_Italic: Source: IMF staff calculations and tables in wpiea2021272-print-pdf - 372. The MIT Press._

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021272-print-pdf.pdf_