## _wp1301

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### I. INTRODUCTION — Question and approach
- Central question: whether forecasters have underestimated fiscal multipliers (the short-term effects of government spending cuts or tax hikes on economic activity).
- Empirical strategy:
  - Regress the forecast error for real GDP growth on forecasts of fiscal consolidation.
  - Under rational expectations and a correct forecasting model, the coefficient on the fiscal consolidation forecast should be zero; underestimation of multipliers implies a negative coefficient.
- Motivation: October 2012 WEO box focused on early-2010 forecasts for European economies where multiyear consolidation plans and conditions conducive to larger multipliers were present.

### II. Estimation approach and data
- Regression specification:
  - Equation (1): Forecast Error of ΔY_i,t:t+1 = α + β Forecast of ΔF_i,t:t+1|t + ε_i,t:t+1.
  - ΔY_i,t:t+1 denotes cumulative (year-over-year) growth of real GDP: (Y_i,t+1/Y_i,t–1 – 1).
  - Forecast error = ΔY_i,t:t+1 – f{ΔY_i,t:t+1 | Ω_t}.
  - ΔF_i,t:t+1 denotes change in the general government structural fiscal balance in percent of potential GDP; positive values indicate fiscal consolidation.
  - Null: β = 0 under correct multipliers/forecast efficiency.
- Data:
  - Forecasts and variables from the April 2010 IMF World Economic Outlook (IMF, 2010c) WEO database.
  - Baseline sample: 26 economies (EU’s 27 members plus Iceland, Norway, Switzerland; WEO forecasts unavailable for Estonia, Latvia, Lithuania, Luxembourg): Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Germany, Denmark, Finland, France, Greece, Hungary, Ireland, Iceland, Italy, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, and the United Kingdom.
  - Growth forecast errors: actual cumulative real GDP (year-over-year) growth during 2010–11 minus the April 2010 WEO forecast.
  - Structural fiscal balance expressed as percent of potential GDP (results similar if expressed as percent of nominal GDP).

### Baseline results
- Main finding:
  - Baseline estimate of β = –1.095 (t-statistic = –4.294).
  - Interpretation: For every additional percentage point of GDP of fiscal consolidation, GDP was about 1 percent lower than forecast during 2010–11.
  - R^2 = 0.496.
  - Constant term estimate = 0.775 (t-statistic = 2.023).
- Two-stage-least-squares (addressing actual vs. planned consolidation):
  - First-stage δ = 1.057*** (0.185), R2 = 0.578, Obs = 262 (slope coefficient = 1.057, t-statistic = 5.714 reported in text).
  - Second-stage β = –1.036*** (0.228), R2 = 0.350 (1.036 percentage point output forecast error, t-statistic = –4.518).

### Robustness — three dimensions and selected numeric checks
- 1) Sensitivity to outliers and choice of economies:
  - Replacing four missing WEO forecasts with EC forecasts: little difference.
  - Excluding Germany and Greece: β = –0.776 (t-statistic = –2.249).
  - Excluding five economies with IMF programs (Greece, Iceland, Ireland, Portugal, Romania): β = –0.812 (t-statistic = –2.890).
  - Excluding four emerging economies (Bulgaria, Hungary, Poland, Romania): β = –0.992 (t-statistic = –3.568).
  - Robust regression (down-weights large residuals): β = –1.279 (t-statistic = –6.989).
  - Quantile regression (median-based): β = –1.088 (t-statistic = –4.533).
  - Cook’s distance exclusion (> 4/N): β = –0.921 (t-statistic = –4.244).
  - Broader sample (adds 10 advanced economies): OLS β = –0.538 (t-statistic = –1.322), not significant; robust regression β = –0.955 (t-statistic = –4.751); quantile β = –0.999 (t-statistic = –7.866); Cook’s exclusion β = –0.746 (t-statistic = –2.674).
  - Liquidity-trap subset (policy rate ≤ 1 percent during 2010–11): β = –0.986 (t-statistic = –3.652).
  - Emerging market sample (14 non-European emerging economies): β = 0.007 (t-statistic = 0.016).
- 2) Adding control variables (plausibly in forecasters’ information set):
  - Controls tested: initial (end-2009) government-debt-to-GDP ratio; initial fiscal-balance-to-GDP ratio; initial structural fiscal-balance-to-GDP ratio; sovereign CDS spread (average five-year CDS spread in 2010:Q1); bank CDS spread (average five-year bank CDS spread in 2010:Q1, with predicted values for missing banks from regression slope 1.093, t-statistic = 11.52); zero-one banking crisis dummy; trade-weighted fiscal consolidation of partners (coefficient on partner consolidation = –0.548, standard error = 1.343); precrisis (2007) current-account-deficit-to-GDP ratio; precrisis (2007) net foreign liabilities percent of GDP; precrisis (2007) household debt-to-disposable-income ratio.
  - Controlling for these variables does not materially change estimate of β.
- 3) Time intervals and “normal times”:
  - Within crisis:
    - Earlier intervals (2009–10 and 2010–11): coefficients typically between 0.7 and 1.0 (evidence of more underestimation).
    - Later intervals (2011–12 and 2012–13): coefficients typically between 0.3 and 0.5 and less statistically significant.
  - Precrisis decade (1997–2008): β = –0.077 (t-statistic = –0.470), no evidence of systematic forecast errors related to planned fiscal policy.

### Extensions of baseline results (selected findings)
- A. Government spending and revenue:
  - Separate equation for change in structural spending ΔS and change in structural revenue ΔT.
  - Coefficient on forecast of government spending = 1.244 (t-statistic = 4.989).
  - Coefficient on forecast of revenue = –0.865 (t-statistic = –3.822).
  - p-value for δ + γ = 0: 0.102 in (1); 0.095 in (2).
  - Results similar using overall government spending or primary government spending (excluding interest payments).
  - Conclusion: underestimation of multipliers on average for both government spending and revenue; slightly larger underestimation for government spending.
- B. Components of aggregate spending and unemployment:
  - Planned fiscal consolidation associated with significantly lower-than-expected consumption and investment growth.
  - Coefficient for investment growth = –2.681 (standard error = 0.910).
  - Coefficient for private consumption growth = –0.816 (standard error = 0.138).
  - Exports and imports: not statistically significant in main GDP regressions (exports β = –1.109 (0.925), imports β = –0.639 (1.006)), though alternative specifications show large coefficients on export/import regressions (e.g., exports coefficient 8.866*** (1.442) in another regression).
  - GDP deflator: β = –0.185 (0.253), not significant.
  - Unemployment rate: β = 0.608*** (0.193), statistically and economically significant.
- C. Alternative forecasters:
  - Using IMF, EC, OECD, EIU forecast errors: negative relation holds across forecasters.
  - Coefficient range across forecasters: –1.095 to –0.371 in reported examples.
  - IMF forecasts: β = –1.095*** (0.255), Obs = 260, R2 = 0.496.
  - European Commission forecasts: β = –0.837** (0.358), Obs = 270, R2 = 0.291.
  - OECD forecasts: β = –0.371*** (0.125), Obs = 210, R2 = 0.274.
  - Economist Intelligence Unit forecasts: β = –0.696** (0.318), Obs = 220, R2 = 0.220.
  - Equalized sample IMF: β = –1.129*** (0.304), Obs = 170, R2 = 0.539.

### Interpretation, conclusions, and policy-relevant caveats
- Main interpretation:
  - Multipliers were substantially above 1 in the early years of the crisis (evidence strongest for 2009–10 and 2010–11).
  - Smaller coefficients in 2011 and 2012 may reflect forecaster learning and/or smaller actual multipliers.
- Suggested ranges and context:
  - Precrisis studies and WEO chapters report average multipliers around 0.5.
  - March 2009 IMF staff note: assumptions of multipliers of 0.3–0.5 for revenue and 0.3–1.8 for government spending.
  - Using reported coefficients suggests actual multipliers were substantially above 1 early in the crisis.
- Caveats and policy implications:
  - Forecasters do not typically use explicit multipliers; models imply multipliers depend on type of fiscal adjustment and economic conditions.
  - Results provide average multipliers for groups of countries; individual-country multipliers may differ materially.
  - Larger-than-expected short-term fiscal multipliers are only one factor in determining appropriate pace of fiscal consolidation.
  - As economies recover and exit liquidity traps, multipliers likely return to precrisis levels.
  - Prudence: assume higher multipliers than before the crisis when thinking about fiscal consolidation, but do not infer a specific fiscal stance solely from these short-term multiplier assessments.

### Appendix highlights and robustness to ex-post controls
- Purpose and caveat: regressions controlling for variables not known at forecast time are reported for completeness; coefficients on such post-forecast controls lack a clean causal interpretation.
- Selected additional controls and point estimates:
  - Change in sovereign CDS (2010:Q1 to 2011:Q4): β = –0.839 (t-statistic = –2.797); γ = –0.054 (t-statistic = –2.3? reported as –0.054** (0.023) in table).
  - Change in bank CDS (2010:Q1 to 2011:Q4): β = –1.002 (t-statistic = –4.158).
  - Revision to initial (end-2009) government debt-to-GDP ratio: β = –1.090 (t-statistic = –4.395).
  - Unexpected fiscal consolidation (forecast error): β = –1.077 (t-statistic = –5.033); coefficient on forecast error of fiscal consolidation = –0.309 (t-statistic = –1.626).
- Panel 2009–12 (Europe):
  - Panel baseline (2009-10 to 2012-13): β = –0.667*** (0.161), Obs = 1050, R2 = 0.413.
  - By forecast year (Europe):
    - 2009-10: β = –0.699*** (0.185), Obs = 260, R2 = 0.208.
    - 2010-11: β = –1.095*** (0.255), Obs = 260, R2 = 0.496.
    - 2011-12: β = –0.467 (0.450), Obs = 250, R2 = 0.091.
    - 2012-13: β = –0.358** (0.147), Obs = 280, R2 = 0.194.
- Robustness summary:
  - Negative β estimates on fiscal consolidation forecasts are robust across OLS, robust regression, two-stage least squares, panel regressions, sample definitions, and when controlling for IMF Early Warning Exercise vulnerability ratings.
  - Magnitude and significance of β tend to be larger for forecasts made in 2009–10 and 2010–11 than for 2011–12 and 2012–13.

*Source: _wp1301 - References; Section II–V; Appendix summaries as provided in the supplied content.*

### References .............................................................................................................

### _wp1301 - References .............................................................................................................

### I. INTRODUCTION — Question and approach
- Central question: whether forecasters have underestimated fiscal multipliers (the short-term effects of government spending cuts or tax hikes on economic activity).
- Empirical strategy referenced: regress the forecast error for real GDP growth on forecasts of fiscal consolidation.
  - Under rational expectations and a correct forecasting model, the coefficient on the fiscal consolidation forecast should be zero.
  - If forecasters underestimated fiscal multipliers, a negative relation is expected between fiscal consolidation forecasts and subsequent growth forecast errors (i.e., larger growth disappointments where planned fiscal cutbacks were greater).
- The October 2012 World Economic Outlook (WEO; IMF, 2012b) box focused on forecasts made for European economies in early 2010 because many large multiyear fiscal consolidation plans were announced then and conditions for larger-than-normal multipliers were present.

### Why fiscal multipliers may be larger than normal (mechanisms and supporting findings)
- Binding zero lower bound (liquidity trap) on nominal interest rates:
  - Central banks could not cut interest rates to offset negative short-term effects of fiscal consolidation.
  - Christiano, Eichenbaum, and Rebelo (2011) using a DSGE model find that under such conditions fiscal multipliers can exceed 3.
  - Historical evidence: Almunia and others (2010) using data for 27 economies during the 1930s (a period when interest rates were at or near the zero lower bound) conclude fiscal multipliers were about 1.6.
  - Caveat noted: even at the zero lower bound, central banks have used quantitative and qualitative easing measures, which can lower interest rates at longer maturities.
- Greater reliance of consumption and investment on current income/profits when output is low and the financial system is poorly functioning:
  - Eggertsson and Krugman (2012) point to these channels as amplifying multipliers.
- Larger multipliers when there is a great deal of slack in the economy:
  - Auerbach and Gorodnichenko (2012b) using U.S. data find fiscal multipliers associated with government spending can fluctuate from being near zero in normal times to about 2.5 during recessions.
- Implication: If forecast models implicitly assumed multipliers consistent with normal times while actual multipliers were larger, growth forecast errors should be systematically correlated with fiscal consolidation forecasts.

### Prior findings and motivation for the paper
- The October 2012 WEO box found a negative relation between fiscal consolidation forecasts and subsequent growth forecast errors for primarily European economies in early 2010.
- This paper restates the original methodology, revisits results, examines robustness, and considers a number of extensions in response to comments, criticisms, and suggestions received after the October box.

*Source: _wp1301 - References .............................................................................................................*

### Section II presents our estimation approach and reports our baseline results. Our forecast data

### _wp1301 - Section II presents our estimation approach and reports our baseline results. Our forecast data

### Estimation approach and data
- Regression specification:
  - Equation (1): Forecast Error of ΔY_i,t:t+1 = α + β Forecast of ΔF_i,t:t+1|t + ε_i,t:t+1.
  - ΔY_i,t:t+1 denotes cumulative (year-over-year) growth of real GDP: (Y_i,t+1/Y_i,t–1 – 1).
  - Forecast error defined as ΔY_i,t:t+1 – f{ΔY_i,t:t+1 | Ω_t}, where f denotes the forecast conditional on Ω_t.
  - ΔF_i,t:t+1 denotes the change in the general government structural fiscal balance in percent of potential GDP; positive values indicate fiscal consolidation.
  - Under the null of correct multipliers/forecast efficiency, β should equal zero.
- Data:
  - Forecasts and variables come from the April 2010 IMF World Economic Outlook (IMF, 2010c) WEO database.
  - Baseline sample: 26 economies (EU’s 27 members plus Iceland, Norway, Switzerland; WEO forecasts unavailable for Estonia, Latvia, Lithuania, Luxembourg), specifically: Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Germany, Denmark, Finland, France, Greece, Hungary, Ireland, Iceland, Italy, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, and the United Kingdom.
  - Growth forecast errors measure actual cumulative real GDP (year-over-year) growth during 2010–11 minus the April 2010 WEO forecast.
  - Structural fiscal balance expressed as percent of potential GDP (results similar if expressed as percent of nominal GDP).

### Baseline results
- Main finding:
  - Baseline estimate of β = –1.095 (t-statistic = –4.294).
  - Interpretation: For every additional percentage point of GDP of fiscal consolidation, GDP was about 1 percent lower than forecast during 2010–11.
  - R^2 = 0.496.
  - Constant term estimate = 0.775 (t-statistic = 2.023).
- Figure 1: scatter plot illustrating the negative relation between fiscal consolidation forecasts and growth forecast errors (as described).

### Robustness — three dimensions
- 1) Sensitivity to outliers and choice of economies
  - Replacing four missing WEO forecasts with EC forecasts makes little difference.
  - Excluding two largest policy changes (Germany and Greece): β = –0.776 (t-statistic = –2.249), significant at the 5 percent level.
  - Excluding five economies with IMF programs in 2010 or 2011 (Greece, Iceland, Ireland, Portugal, Romania): β = –0.812 (t-statistic = –2.890), significant at the 1 percent level.
  - Excluding four economies classified as “emerging” (Bulgaria, Hungary, Poland, Romania): β = –0.992 (t-statistic = –3.568).
  - Robust regression (down-weights large residuals): β = –1.279 (t-statistic = –6.989), significant at the 1 percent level.
  - Quantile regression (median-based): β = –1.088 (t-statistic = –4.533), significant at the 1 percent level.
  - Cook’s distance outlier exclusion (discard Cook’s distance > 4/N): β = –0.921 (t-statistic = –4.244), significant at the 1 percent level.
  - Broader sample: all advanced economies (adds 10 economies: Australia, Canada, Korea, Hong Kong SAR, Israel, Japan, New Zealand, Singapore, Taiwan Province of China, United States):
    - OLS estimate declines to β = –0.538 (t-statistic = –1.322), not statistically significant.
    - Robust regression for broader sample: β = –0.955 (t-statistic = –4.751), significant at the 1 percent level.
    - Quantile regression for broader sample: β = –0.999 (t-statistic = –7.866).
    - Cook’s distance exclusion for broader sample: β = –0.746 (t-statistic = –2.674).
    - For subset defined as in a liquidity trap (central bank policy rate ≤ 1 percent during 2010–11): β = –0.986 (t-statistic = –3.652).
  - Emerging market sample (14 non-European emerging economies): β = 0.007 (t-statistic = 0.016), no evidence of underestimated multipliers for this group; robust/quantile/Cook’s checks yield same conclusion.
- 2) Adding control variables
  - Results robust to controls plausibly in forecasters’ information set:
    - Initial (end-2009) government-debt-to-GDP ratio; initial fiscal-balance-to-GDP ratio; initial structural fiscal-balance-to-GDP ratio.
    - Sovereign CDS spread (average five-year CDS spread in 2010:Q1).
    - Bank CDS spread (average five-year bank CDS spread in 2010:Q1); for missing banks, predicted values from regression of bank CDS on sovereign CDS during 2009–10 (slope 1.093, t-statistic = 11.52).
    - Zero-one banking crisis dummy (Laeven and Valencia, 2012).
    - Trade-weighted fiscal consolidation of partners (scaled by share of exports in GDP): coefficient estimate on partner consolidation = –0.548 (standard error = 1.343), not statistically significant but economically nontrivial when combined with domestic β in that specification.
    - Precrisis (2007) current-account-deficit-to-GDP ratio; precrisis (2007) net foreign liabilities percent of GDP (Lane and Milesi-Ferretti dataset).
    - Precrisis (2007) household debt-to-disposable-income ratio.
  - Controlling for these variables does not materially change the estimate of β.
  - Note: Controlling for ex-post developments (unknown at forecasting time) is not valid for the question posed; results controlling for such ex-post variables are reported in appendix and do not materially influence β.
- 3) Time intervals and “normal times”
  - Within crisis:
    - Earlier intervals (2009–10 and 2010–11): evidence of more underestimation; coefficients typically between 0.7 and 1.0.
    - Later intervals (2011–12 and 2012–13): coefficients typically between 0.3 and 0.5 and less statistically significant.
  - Precrisis decade (1997–2008): no evidence of systematic forecast errors related to planned fiscal policy.

### Extensions of baseline results (Section IV)
- Split by fiscal instrument:
  - Underestimation of multipliers on average for both government spending and revenue changes, with slightly larger underestimation associated with changes in government spending.
- Other macro variables and GDP components:
  - Forecasters significantly underestimated the increase in unemployment and the decline in private consumption and investment associated with fiscal consolidation.
- Comparison across forecasters:
  - Using forecast errors from IMF, EC, OECD, EIU: results hold for all forecasters considered, with coefficient range from –1.1 to –0.4.
  - Results strongest economically and statistically for IMF forecasts and, slightly less so, for EC forecasts.

### Interpretation, conclusions, and caveats (Section V)
- Main interpretation:
  - Multipliers were substantially above 1 in the early years of the crisis.
  - Lower coefficients in recent years may reflect a combination of forecaster learning and smaller actual multipliers.
- Caveats:
  - Forecasters do not typically use explicit multipliers; models used imply actual multipliers depend on type of fiscal adjustment and other economic conditions. The assumed multipliers cannot be directly observed.
  - Results provide average multipliers for groups of countries; individual-country multipliers may differ materially from the average.
  - Larger-than-expected short-term fiscal multipliers do not imply a mechanical policy prescription; the short-term output effects are only one factor in determining the appropriate pace of fiscal consolidation for any single economy.
- Actual versus planned consolidation concern:
  - Two-stage-least-squares exercise:
    - First-stage regression of actual fiscal consolidation on forecast of fiscal consolidation: slope coefficient = 1.057 (t-statistic = 5.714), indicating on average actual consolidation was neither smaller nor larger than expected.
    - Second-stage (briefly introduced): indicates a 1 percent of GDP fiscal consolidation is associated with a – [text truncated in source at that point].

*Summary based solely on the supplied content unit.*

### 1.036 percentage point output forecast error (t-statistic = –4.518), which is, again, close to

### _wp1301 - 1.036 percentage point output forecast error (t-statistic = –4.518), which is, again, close to

### Robustness of baseline results
- The 1.036 percentage point output forecast error (t-statistic = –4.518) is close to the baseline.
- Robustness checks indicate results for the baseline sample are robust to inclusion of additional variables that could bias results toward finding actual multipliers larger than assumed multipliers.
- Controlling for variables that measure other weaknesses of the economy associated with fiscal consolidation does not materially affect the coefficient on the forecast of fiscal consolidation.
- The constant term is 0.907 (t-statistic = 2.834); the slope coefficient of 1.057 indicates the forecast error of fiscal consolidation is not correlated with the initial fiscal consolidation forecast (regressing the forecast error on the initial forecast yields a coefficient of 0.057 with a t-statistic of 0.190).

### Different forecast vintages (2009–12 panel and precrisis decade)
- Panel specification (including time-fixed effects λt) for two-year intervals t = 2009, 2010, 2011, 2012; European sample size is 105 observations.
- Newey-West standard errors used to correct for MA(1) serial correlation.
- 2009–12 panel estimate of β = –0.667 (t-statistic = –4.143).
- Individual-year estimates:
  - Early 2009: β statistically significant.
  - Early 2010: β statistically significant.
  - Early 2011: β = –0.467 (t-statistic = –1.038), not statistically significant.
  - Early 2012: β = –0.357 (t-statistic = 2.429), statistically significant at the 5 percent level.
- Broader samples for 2009–12:
  - All advanced economies: β = –0.410 (t-statistic = –2.060), significant at the 5 percent level.
  - Advanced economies in a liquidity trap: β = –0.648 (t-statistic = –3.042), significant at the 1 percent level.
  - Emerging market economies: β = –0.108 (t-statistic = –0.394), not significant.
- Precrisis decade (1997–2008) two-year intervals:
  - β = –0.077 (t-statistic = –0.470), indicating no evidence of underestimated multipliers in more normal times.

### Extensions — A. Government spending and revenue
- Equation separating change in structural spending ΔS and change in structural revenue ΔT estimated (ΔT = ΔF + ΔS).
- Baseline results hold for both government spending and revenue.
- Coefficient on forecast of government spending = 1.244 (t-statistic = 4.989).
- Coefficient on forecast of revenue = –0.865 (t-statistic = –3.822).
- Difference between spending and revenue coefficients has p-value = 0.102 (just short of statistical significance).
- Results similar using overall government spending or primary government spending (excluding interest payments).
- Conclusion: fiscal multipliers were, on average, underestimated for both sides of the fiscal balance, slightly more so for government spending.

### Extensions — B. Components of aggregate spending and unemployment
- Modified baseline for private consumption forecast errors: Forecast Error of ΔC = α + β Forecast of ΔF + ε.
- Planned fiscal consolidation associated with significantly lower-than-expected consumption and investment growth.
- Coefficient for investment growth = –2.681.
- Coefficient for private consumption growth = –0.816.
- Export and import growth results: not statistically significant.
- GDP deflator forecast error: negative but statistically insignificant relation.
- Unemployment rate forecast error: coefficient = 0.608, statistically and economically significant.
- Conclusion: forecasters significantly underestimated the increase in unemployment and the decline in domestic demand associated with fiscal consolidation.

### Extensions — C. Alternative forecasters
- Alternative forecast sources: EC (spring 2010 European Economic Forecast), OECD (May 2010 Economic Outlook), EIU (April 2010 Country Forecast).
- For EIU regressions, fiscal consolidation forecasts taken from April 2010 WEO due to EIU not publishing structural fiscal balance forecasts.
- Baseline negative relation between growth forecast errors and planned fiscal consolidation holds across forecasters considered.
- Relation strongest in economic and statistical significance for IMF forecasts, and slightly smaller for EC forecasts.

### Conclusions and interpretation for multipliers and policy
- Results suggest actual fiscal multipliers have been larger than forecasters assumed.
- Evidence supports a reasonable case that multipliers used at the start of the crisis averaged about 0.5 (citing precrisis studies and WEO chapters reporting averages of 0.5).
- March 2009 IMF staff note reports assumed multipliers of 0.3–0.5 for revenue and 0.3–1.8 for government spending.
- Using range of coefficients reported suggests actual multipliers were substantially above 1 early in the crisis.
- Smaller coefficients for forecasts made in 2011 and 2012 could reflect smaller actual multipliers or partial learning by forecasters.
- Possible reasons for decline in multipliers despite zero lower bound: easing of credit constraints and less economic slack relative to 2009–10.
- Cautions:
  - No single multiplier applies to all times and countries; multipliers vary across time and economies.
  - Confidence effects may offset direct effects in some cases.
  - As economies recover and exit the liquidity trap, multipliers likely return to precrisis levels.
  - Policy implication: when thinking about fiscal consolidation, it seems prudent to assume higher multipliers than before the crisis, but fiscal stance decisions require more than assessments of short-term multipliers.
  - Results do not imply any specific fiscal policy stance or that fiscal consolidation is undesirable; they are one input among many for determining pace of consolidation.

### Appendix summary
- Appendix reports sensitivity of baseline results to inclusion of ex-post variables (Appendix Table 1).
- Appendix shows how broader sample results change when controlling for other variables (Appendix Table 2).
- Appendix reports how 2009–12 panel results are influenced by additional controls (Appendix Tables 3, 4, 5).
- Appendix reports robustness when controlling for a summary statistic for economic and financial vulnerabilities based on the IMF’s Early Warning Exercise (Appendix Table 6).

*Source: IMF working paper content provided in the supplied PDF section.*

### Appendix Table 1 reports the results of controlling for variables that were not known at the

### _wp1301 - Appendix Table 1 reports the results of controlling for variables that were not known at the

### Controlling for variables unknown at forecast time: purpose and caveat
- Purpose: report regressions controlling for variables not known at the time forecasts were made because commentators have run such regressions and the authors want to report results using their sample.
- Caveat: even if controlling for such variables significantly changed the estimate of β, the coefficient would no longer have an economic interpretation.

### Results for specific additional controls (point estimates and t-statistics)
- Change in sovereign CDS spreads (2010:Q1 to 2011:Q4)
  - β = –0.839 (t-statistic = –2.797)
  - Comment: not statistically distinguishable from baseline estimate of –1.095.
- Change in bank CDS spreads (2010:Q1 to 2011:Q4)
  - β = –1.002 (t-statistic = –4.158)
- Revision to initial (end-2009) government debt-to-GDP ratio (latest estimate minus spring 2010 estimate)
  - β = –1.090 (t-statistic = –4.395)
  - Comment: similar to baseline.
- Unexpected fiscal consolidation (fiscal consolidation forecast error)
  - β = –1.077 (t-statistic = –5.033)
  - Coefficient on forecast error of fiscal consolidation: –0.309 (t-statistic = –1.626)
  - Comment: the forecast error estimate suffers from two-way causality and cannot be given a structural interpretation; over two-year intervals changes in fiscal policy are unlikely to be orthogonal to economic developments.

### Handling missing data for bank CDS changes
- For 11 missing observations for change in bank CDS spreads, missing values were filled using predicted values from a regression of change in bank CDS spreads on change in sovereign CDS spreads.
  - Reported slope coefficient: 0.931 (t-statistic = 22.370).

### Robustness across broader samples and methods (Appendix Tables 2–6)
- Appendix Table 2: broader group of all advanced economies
  - OLS: estimate of β negative but statistically insignificant when adding additional control variables (influence of outliers).
  - Robust regression: estimate of β statistically significant in each case, typically above 0.9 in absolute value.
- Appendix Table 3: panel specification (equation (2)) with additional controls (one at a time and jointly)
  - β remains significant in each case; ranges from –0.447 to –0.712.
  - Baseline panel estimate without controls: –0.667.
- Appendix Table 4: β allowed to vary across forecast vintages (2009, 2010, 2011, 2012), using Newey-West correction for MA(1) serial correlation
  - Forecasts made in 2009: coefficient ≈ –0.6 and statistically significant in all specifications.
  - Forecasts made in 2010: coefficient ≈ –1 and statistically significant in all specifications.
  - Forecasts made in 2011: coefficient typically around –0.4 and statistically insignificant.
  - Forecasts made in 2012: coefficient typically around –0.3; significant in some specifications and not in others.
- Appendix Table 5: both coefficient on fiscal consolidation forecast and on each additional control allowed to vary over time
  - Estimates for coefficients on fiscal consolidation forecasts similar to earlier tables when allowing time variation.
- Appendix Table 6: controls for IMF Early Warning Exercise (EWE) vulnerability ratings (spring ratings matching forecast vintage)
  - EWE ratings used as a summary statistic of economic and financial vulnerabilities perceived at forecast time.
  - Estimation results similar to prior results: coefficients on fiscal consolidation forecasts (2009–12) are all negative, larger in absolute value and more statistically significant for forecasts made in 2009–10 than in 2011–12.
  - Note: EWE vulnerability ratings are confidential; regression results reported but underlying ratings not included in replication dataset.

### Selected reported table findings and key numeric results
- Baseline estimate (Europe, Table 1)
  - β = –1.095*** (0.255), Obs = 260, R2 = 0.496
- Robustness to additional controls (Table 2 examples)
  - Initial debt ratio: β = –1.146*** (0.270), R2 = 0.504
  - Initial fiscal balance: β = –1.173*** (0.299), R2 = 0.500
  - Initial sovereign CDS: β = –0.990*** (0.296), R2 = 0.504
  - Initial bank CDS: β = –1.007*** (0.281), R2 = 0.502
  - Initial potential growth forecast: β = –1.126*** (0.251), R2 = 0.524
  - Precrisis current account balance: β = –0.935*** (0.274), R2 = 0.531
  - Precrisis household debt: β = –1.086*** (0.262), Obs = 250, R2 = 0.489
- Two-stage least squares (Table 3)
  - First-stage δ = 1.057*** (0.185), R2 = 0.578, Obs = 262
  - Second-stage β = –1.036*** (0.228), R2 = 0.350
- 2009–12 panel (Table 4)
  - Panel baseline (2009-10 to 2012-13, Europe): β = –0.667*** (0.161), Obs = 1050, R2 = 0.413
  - By forecast year (Europe):
    - 2009-10: β = –0.699*** (0.185), Obs = 260, R2 = 0.208
    - 2010-11: β = –1.095*** (0.255), Obs = 260, R2 = 0.496
    - 2011-12: β = –0.467 (0.450), Obs = 250, R2 = 0.091
    - 2012-13: β = –0.358** (0.147), Obs = 280, R2 = 0.194
- Government revenue and spending (Table 5)
  - δ (forecast of ΔT): –0.865*** (0.225) in (1); –0.783*** (0.221) in (2)
  - γ (forecast of ΔS): 1.244*** (0.254) in (2)
  - γ (forecast of ΔS (primary)): 1.179*** (0.243)
  - p-value for δ + γ = 0: 0.102 in (1); 0.095 in (2)
  - Obs = 262, R2 = 0.554 in (1); R2 = 0.557 in (2)
- GDP components and unemployment (Table 6, Europe)
  - GDP: β = –1.095*** (0.255), Obs = 260, R2 = 0.496
  - Private consumption: β = –0.816*** (0.138), R2 = 0.330
  - Investment: β = –2.681*** (0.910), R2 = 0.174
  - Exports: β = –1.109 (0.925), Obs = 260, R2 = 0.070; exports coefficient on another regression 8.866*** (1.442)
  - Imports: β = –0.639 (1.006), imports coefficient on another regression 6.520*** (1.665)
  - GDP deflator: β = –0.185 (0.253), R2 = 0.016
  - Unemployment rate: β = 0.608*** (0.193), R2 = 0.270
- Alternative forecasters (Table 7, Europe)
  - IMF forecasts: β = –1.095*** (0.255), Obs = 260, R2 = 0.496
  - European Commission forecasts: β = –0.837** (0.358), Obs = 270, R2 = 0.291
  - OECD forecasts: β = –0.371*** (0.125), Obs = 210, R2 = 0.274
  - Economist Intelligence Unit forecasts: β = –0.696** (0.318), Obs = 220, R2 = 0.220
  - Equalized sample IMF: β = –1.129*** (0.304), Obs = 170, R2 = 0.539

### Overarching analytical conclusions from these appendices
- The negative β estimates on fiscal consolidation forecasts are robust across multiple additional controls, estimation methods (OLS, robust regression, two-stage least squares, panel regressions), sample definitions, and when using summary vulnerability metrics (EWE ratings).
- The magnitude and statistical significance of β tend to be larger (in absolute value) for forecasts made in 2009–10 than for forecasts made in 2011–12.
- Estimates that include controls known only after forecasts were made generally do not materially change the baseline inference that higher-than-forecast fiscal consolidation is associated with negative forecast errors for output growth; however, coefficients on such post-forecast controls lack a clean economic (causal) interpretation.

*Source: _wp1301 - Appendix Table 1 reports the results of controlling for variables that were not known at the*

### Appendix Table 1. Europe: Controlling for Ex-post Developments

### Appendix Table 1. Europe: Controlling for Ex-post Developments

### Regression specification
- Equation: Forecast Error of ΔY i,t:t+1 = α + β Forecast of ΔF i,t:t+1|t + γ X i,t+1 + ε i,t:t+1
- Note: Table reports point estimates and heteroskedasticity-robust standard errors in parentheses. ***, **, and * denotes statistical significance at the 1,5, and 10 level, respectively. Constant term included in specification but estimates not reported. The additional controls appear in the specifications one at a time.

### Baseline estimate (no additional control)
- β = -1.095***  (0.255)
- Obs = 260
- R2 = 0.496

### Additional controls (each control entered one at a time)
- Ex-post change in sovereign CDS:
  - β = -0.839**  (0.300)
  - γ = -0.054**  (0.023)
  - Obs = 260
  - R2 = 0.548
- Ex-post change in bank CDS:
  - β = -1.002***  (0.241)
  - γ = -0.100  (0.135)
  - Obs = 260
  - R2 = 0.509
- Revision to initial debt ratio:
  - β = -1.090***  (0.248)
  - γ = -0.026  (0.056)
  - Obs = 260
  - R2 = 0.499
- Unexpected fiscal consolidation:
  - β = -1.077***  (0.214)
  - γ = -0.309  (0.190)
  - Obs = 260
  - R2 = 0.528

### Cross-checks and broader robustness (selected highlights from related appendices in the content)
- All Advanced Economies (Appendix Table 2) — Robust Regression (same weights as baseline):
  - Baseline robust β = -0.955***  (0.201); Obs = 360; R2 = 0.400
  - Robust with initial debt ratio: β = -0.967***  (0.234); Obs = 350; R2 = 0.432
  - Robust with initial structural fiscal balance: β = -0.729***  (0.261); Obs = 350; R2 = 0.464
  - Robust with precrisis current account balance: β = -0.784***  (0.255); Obs = 350; R2 = 0.475
- Europe 2009–12 panel (Appendix Table 3) — Panel regressions with Newey-West SEs:
  - Column (1) baseline β = -0.667***  (0.161); Obs = 105; R2 = 0.413
  - Columns with controls show β ranging from -0.712***  (0.165) to -0.486***  (0.161) depending on specification and control inclusion
  - Selected γ estimates (with Newey-West SEs in parentheses):
    - Initial sovereign CDS γ = -0.032***  (0.006) in one specification
    - Precrisis current account balance γ = 0.074***  (0.027) in one specification
    - Precrisis net foreign liabilities γ = -0.007*  (0.004) in one specification
- Time-varying β (Appendix Tables 4–5) — β allowed to vary by year interval:
  - Coefficients on fiscal consolidation forecast by interval (selected baseline/time-varying results):
    - 2009-10: β = -0.699***  (0.185) or -0.699***  (0.185) in time-varying specifications
    - 2010-11: β = -1.095***  (0.255) (largest-magnitude negative effect)
    - 2011-12: β = -0.467  (0.450) (often not statistically significant)
    - 2012-13: β = -0.358**  (0.147)
  - Time-varying specifications with controls show consistent negative β in 2009-10 and 2010-11, with smaller or insignificant β in 2011-12 and moderate negative β in 2012-13.
- Controlling for vulnerability rating (Appendix Table 6):
  - Panel baseline β = -0.667***  (0.161); Obs = 105; R2 = 0.413
  - Including vulnerability rating (constant γ): β = -0.724***  (0.232); γ = -0.149  (0.390); Obs = 80; R2 = 0.509
  - Time-varying β with vulnerability rating shows large negative β for 2009-10 and 2010-11 in some specifications (e.g., β: 2009-10 = -0.699***  (0.185); β: 2010-11 = -1.095***  (0.255)), with vulnerability-rating γ coefficients estimated by year (large standard errors in some years)

### Key patterns and empirical conclusions (as reported in the tables)
- The forecast coefficient on fiscal consolidation (β) is consistently negative across specifications and samples, indicating that larger forecasted fiscal consolidation is associated with more negative forecast errors for real GDP growth.
- The negative association is strongest in the 2010-11 period (β = -1.095***  (0.255) in multiple specifications).
- Inclusion of ex-post measures (sovereign CDS, bank CDS, revisions to debt ratio, unexpected fiscal consolidation) alters point estimates modestly but does not overturn the core negative relationship; for example, adding ex-post sovereign CDS yields β = -0.839**  (0.300) and adds a statistically significant γ = -0.054**  (0.023).
- Robust regressions and alternative controls (initial debt ratio, fiscal balances, CDS, banking crisis indicators, precrisis external vulnerability measures) generally confirm the negative and often statistically significant β, though magnitude and significance vary with specification and sample.

*Source: _wp1301 - Appendix Table 1. Europe: Controlling for Ex-post Developments*

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