## 1. Income Shocks and Fiscal Balances (No Spending, as a Share of GDP)

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### Introduction: question and main claim
- Literature often uses the spending-to-GDP ratio (“spending ratio”) as a proxy for the magnitude of automatic stabilizers.
- Central claim of the unit: the correct measure of the size of automatic stabilizers for analyses of GDP growth volatility is the revenue-to-GDP ratio (“revenue ratio”), not the spending ratio, under the simplifying assumption of unit revenue elasticity (ε_R = 1) and zero spending elasticity (ε_G = 0).
- Rationale: the effect of fiscal policy on the GDP growth rate depends on the change in the deficit with respect to GDP in the previous year (not the change in the deficit-to-GDP ratio), implying revenue ratios matter for growth volatility analysis.
- Practical implication: revenue-to-GDP data are as readily available as spending-to-GDP data; future econometric studies should use the revenue ratio.

### Why the literature focuses on the spending ratio
- Automatic stabilizers depend on elasticities of revenues and spending to the output gap and on their sizes relative to GDP.
- Many studies measure government size using spending and/or revenue ratios; results often indicate larger governments experience milder fluctuations.
- The analytic justification for focusing on the spending ratio stems from the common assumption ε_G = 0 and ε_R = 1, under which “the public expenditure ratio is the semi-elasticity of the budget balance (in percent of GDP) to the output gap.”

### Counterintuitive logic illustrated with simple examples
- Intuition: with zero spending elasticity, taxes determine how shocks to gross income affect disposable income (e.g., flat tax at 20 percent mutes a one dollar gross income shock to an 80 cent decline in disposable income).
- Example A (no domestic spending):
  - Period 1 nominal GDP = 100; Period 2 nominal GDP = 90 (Change -10).
  - Table 1 (percent of GDP):
    - Revenue: Period 1 = 30; Period 2 = 27; Change = -3.0
    - Expenditure: Period 1 = 0; Period 2 = 0; Change = 0.0
    - Balance: Period 1 = 30; Period 2 = 27; Change = -3.0
    - Memorandum: Private sector disposable income 70 → 63 (Change -7.0)
  - Despite spending ratio = 0, taxation provides automatic stabilization (private disposable income declines by 7 units against a 10 unit GDP shock).
- Example B (nonzero spending fixed at 30):
  - Table 2 (percent of GDP):
    - Revenue: Period 1 = 30; Period 2 = 27; Change = -3.0
    - Expenditure: Period 1 = 30; Period 2 = 30; Change = 0.0
    - Balance: Period 1 = 0; Period 2 = -3; Change = -3.0
    - Memorandum: Private sector disposable income 70 → 63 (Change -7.0)
  - Nominal decline in revenue mitigates impact on disposable income despite spending ratio stability.

### Scaling by potential GDP clarifies the role of revenue
- Measuring fiscal variables relative to potential GDP (or previous period GDP) shows the revenue ratio drives cyclical changes:
  - Table 3 (No spending, as a share of potential GDP; percent of potential GDP):
    - Revenue: Period 1 = 30; Period 2 = 27; Change -3.0
    - Expenditure: 0 → 0; Change 0.0
    - Balance: 30 → 27; Change -3.0
    - Nominal GDP 100 → 90 (Change -10); Potential GDP 100 → 100 (Change 0); Private sector disposable income 70 → 63 (Change -7.0)
  - Table 4 (Nonzero spending, as a share of potential GDP; percent of potential GDP):
    - Revenue: 30 → 27; Change -3.0
    - Expenditure: 30 → 30; Change 0.0
    - Balance: 0 → -3; Change -3.0
    - Nominal GDP 100 → 90 (Change -10); Potential GDP 100 → 100 (Change 0); Private sector disposable income 70 → 63 (Change -7.0)
- General result under ε_R = 1 and ε_G = 0:
  - Changes in the budget balance-to-GDP ratio depend on the spending ratio.
  - Changes in the budget balance-to-potential (or previous period) GDP depend on the revenue ratio.

### More formal treatment (cyclical adjustment and elasticities)
- Definitions provided:
  - Cyclically-adjusted revenue (CA_R): CA_R = R × (Y_p / Y)^{ε_R}
  - Cyclically-adjusted expenditure (CA_G): CA_G = G × (Y_p / Y)^{ε_G}
  - Cyclically-adjusted balance scaled by potential GDP (cab*): cab* = r × (1 / (Y / Y_p))^{ε_R} ― g × (1 / (Y / Y_p))^{ε_G}
  - r and g are revenue and spending ratios to nominal GDP; a star denotes ratio to potential GDP.
- Under ε_R = 1 and ε_G = 0, cab* simplifies to:
  - cab* = r ― g × (1 / (Y / Y_p))
- Implication: with the common elasticity assumptions, cyclical balance scaled by potential GDP reduces to a function of the revenue-to-GDP ratio.

### Fiscal impact on GDP growth: multiplier perspective
- Keynesian setup and relationships:
  - Y = C + G
  - C = a + c(Y - T)
  - B = T - G
  - Multiplier result: Y = (a + (1-c)T - B) / (1 - c)
- Lagging one period, growth rate of GDP (g_y) depends on changes in T and B relative to previous period nominal GDP:
  - g_y = [1 / (1 - c)] × [ (T_t - T_{t-1}) / Y_{t-1} - (1 - c)(B_t - B_{t-1}) / Y_{t-1} ]
- Conclusion: the impact of the budget position on the growth rate is measured with respect to previous year nominal GDP; thus, measuring fiscal policy effects on GDP growth calls for scaling by prior-period GDP, which, under ε_R = 1 and ε_G = 0, implies the revenue-to-GDP ratio is the relevant metric.

### Does it matter in practice? Measurement error analysis
- Using an inappropriate regressor (spending ratio instead of revenue ratio) introduces bias in estimated coefficients (errors-in-variables framework).
- Under large-sample assumptions and measurement error uncorrelated with the correct regressor, bias in a single-regressor case is downward and increases with Var(measurement error) / Var(correct regressor).
- Authors' computed values for the top 50 economies, 2000–10 (WEO data), reported in Table 5:
  - V ar(revenue ratio) (v1) by year:
    - 2000 130.9; 2001 122.4; 2002 115.6; 2003 110.5; 2004 111.9; 2005 117.0; 2006 117.6; 2007 106.8; 2008 120.7; 2009 104.5; 2010 106.9
  - V ar(deficit ratio) (v2) by year:
    - 2000 19.0; 2001 25.5; 2002 27.0; 2003 29.2; 2004 34.6; 2005 27.9; 2006 30.7; 2007 22.9; 2008 44.6; 2009 16.9; 2010 17.2
  - Estimate bias (in percent of correct coefficient), computed as 1/(1+v1/v2), by year:
    - 2000 12.7; 2001 17.2; 2002 19.0; 2003 20.9; 2004 23.6; 2005 19.2; 2006 20.7; 2007 17.7; 2008 27.0; 2009 13.9; 2010 13.8
- Interpretation:
  - Bias ranges across years from a minimum of 13 percent to a maximum of 27 percent of the correct coefficient in a simple single-regressor equation.
  - Even if bias is relatively small, using the spending ratio when the revenue ratio is available is unjustified.

### Conclusions and recommendation
- Key points:
  - Under the simplifying assumptions ε_R = 1 and ε_G = 0, the appropriate metric for government size as a proxy for automatic stabilizers (for analyses of output growth volatility) is the revenue-to-GDP ratio.
  - The revenue ratio should be the preferred regressor in econometric exercises on the relationship between government size and volatility of output.
- Practical recommendation:
  - Abandon routine use of spending ratios in future studies when revenue ratios are readily available and analytically more appropriate in the contexts discussed.

*Source: IMF Working Paper content unit "1. Income Shocks and Fiscal Balances (No Spending, as a Share of GDP)".*

### 1. Income Shocks and Fiscal Balances (No Spending, as a Share of GDP) ..............................6

### 1. Income Shocks and Fiscal Balances (No Spending, as a Share of GDP)

### Introduction: question and main claim
- Literature often uses the spending-to-GDP ratio (“spending ratio”) as a proxy for the magnitude of automatic stabilizers (Galì, 1994; Fatás and Mihov, 2001; Debrun, Pisani-Ferry and Sapir, 2008; Debrun and Kapoor, 2010).
- Paper’s central claim: the correct measure of the size of automatic stabilizers for analyses of GDP growth volatility is the revenue-to-GDP ratio (“revenue ratio”), not the spending ratio, under the common simplifying assumption of unit revenue elasticity and zero spending elasticity.
- Rationale: the effect of fiscal policy on the GDP growth rate depends on the change in the deficit with respect to GDP in the previous year (not the change in the deficit-to-GDP ratio), implying revenue ratios matter for growth volatility analysis.
- Practical implication: revenue-to-GDP data are as readily available as spending-to-GDP data; therefore future econometric studies should use the revenue ratio.

### Why the literature focuses on the spending ratio
- Automatic stabilizers are nondiscretionary fiscal responses and depend on elasticities of revenues and spending to the output gap and on their sizes relative to GDP.
- Many studies have used spending and/or revenue ratios as measures of government size; often results point to larger governments experiencing milder fluctuations.
- The prevalent analytic justification for the spending ratio arises from the standard assumption: zero elasticity of spending and unit elasticity of revenues to the output gap, where “the public expenditure ratio is the semi-elasticity of the budget balance (in percent of GDP) to the output gap.”

### Counterintuitive logic illustrated with simple examples
- Intuition: with zero spending elasticity, taxes (revenue) determine how shocks to gross income affect disposable income; e.g., flat tax at 20 percent mutes a one dollar gross income shock to an 80 cent decline in disposable income.
- Example A (extreme): government collects taxes at a rate of 30 percent of pre-tax income and spends nothing domestically.
  - Period 1 nominal GDP = 100; Period 2 nominal GDP = 90 (a -10 decline).
  - Table 1 figures (in percent of GDP):
    - Revenue: Period 1 = 30; Period 2 = 27; Change = -3.0
    - Expenditure: Period 1 = 0; Period 2 = 0; Change = 0.0
    - Balance: Period 1 = 30; Period 2 = 27; Change = -3.0
    - Memorandum items: Nominal GDP 100 → 90 (Change -10); Private sector disposable income 70 → 63 (Change -7.0)
  - Despite spending ratio = 0, taxation provides automatic stabilization (private disposable income declines by 7 units against a 10 unit GDP shock).
  - Observing the surplus-to-GDP ratio (30 percent constant) would misleadingly imply no automatic stabilizers.
- Example B (nonzero spending): same as above but spending level fixed at 30.
  - Table 2 figures (in percent of GDP):
    - Revenue: Period 1 = 30; Period 2 = 27; Change = -3.0
    - Expenditure: Period 1 = 30; Period 2 = 30; Change = 0.0 (in percent of potential GDP: shows 30 → 30, Change 0.0)
    - Balance: Period 1 = 0; Period 2 = -3; Change = -3.0
    - Memorandum items: Nominal GDP 100 → 90 (Change -10); Private sector disposable income 70 → 63 (Change -7.0)
  - Again, nominal decline in revenue mitigates impact on disposable income despite spending ratio stability.

### Scaling by potential GDP clarifies the role of revenue
- Measuring fiscal variables relative to potential GDP (or previous period GDP) shows the revenue ratio drives cyclical changes:
  - Table 3 (No spending, as a share of potential GDP) — values in percent of potential GDP:
    - Revenue: Period 1 = 30; Period 2 = 27; Change -3.0
    - Expenditure: 0 → 0; Change 0.0
    - Balance: 30 → 27; Change -3.0
    - Nominal GDP 100 → 90 (Change -10); Potential GDP 100 → 100 (Change 0); Private sector disposable income 70 → 63 (Change -7.0)
  - Table 4 (Nonzero spending, as a share of potential GDP) — values in percent of potential GDP:
    - Revenue: 30 → 27; Change -3.0
    - Expenditure: 30 → 30; Change 0.0
    - Balance: 0 → -3; Change -3.0
    - Nominal GDP 100 → 90 (Change -10); Potential GDP 100 → 100 (Change 0); Private sector disposable income 70 → 63 (Change -7.0)
- General result under unit revenue elasticity and zero spending elasticity:
  - Changes in the budget balance (surplus or deficit)-to-GDP ratio depend on the spending ratio.
  - Changes in the budget balance-to-potential (or previous period) GDP depend on the revenue ratio.

### More formal treatment (cyclical adjustment and elasticities)
- Cyclically-adjusted revenue (CA_R) is defined as:
  - CA_R = R × (Y_p / Y)^{ε_R}  [notation from source: R, Y, Y_p, ε_R]
- Cyclically-adjusted expenditure (CA_G) is:
  - CA_G = G × (Y_p / Y)^{ε_G}
- Cyclically-adjusted balance (CAB) scaled by potential GDP (cab*):
  - cab* = r × (1 / (Y / Y_p))^{ε_R} ― g × (1 / (Y / Y_p))^{ε_G}
  - where r and g are revenue and spending ratios to nominal GDP; a star indicates ratio to potential GDP.
- Under ε_R = 1 and ε_G = 0, algebra yields:
  - cab* = r ― g × (1 / (Y / Y_p))
  - cb (cyclical balance scaled by potential GDP) reduces to a function of the revenue-to-GDP ratio.
- Using mixed scalings (nominal and potential GDP) leads to the common result that the expenditure ratio appears as the semielasticity of the budget balance (in percent of GDP) to the output gap — which explains the literature’s frequent focus on g.

### Fiscal impact on GDP growth: multiplier perspective
- Simple Keynesian setup:
  - Y = C + G
  - C = a + c(Y - T)
  - B = T - G
  - Multiplier result: Y = (a + (1-c)T - B) / (1 - c)
- Lagging by one period, the growth rate of GDP (g_y) depends on changes in T and B relative to previous period nominal GDP:
  - g_y = [1 / (1 - c)] × [ (T_t - T_{t-1}) / Y_{t-1} - (1 - c)(B_t - B_{t-1}) / Y_{t-1} ]
  - Thus, the impact of the budget position on the growth rate is measured with respect to previous year nominal GDP.
- Conclusion: to measure fiscal policy effects on GDP growth, the correct scaling variable is GDP in the previous period, which under the simplifying elasticities implies the size of automatic stabilizers should depend on the revenue-to-GDP ratio, not the spending ratio.

### Does it matter in practice? Measurement error analysis
- Using an inappropriate regressor (spending ratio instead of revenue ratio) introduces bias (errors-in-variables framework).
- Under assumptions (large samples; measurement error uncorrelated with correct regressor), bias in a single regressor case is downward and increases with the ratio Var(measurement error) / Var(correct regressor).
- Authors computed relative variances for the top 50 economies, 2000–10 (World Economic Outlook data). Table 5 reports:
  - V ar(revenue ratio) (v1) by year: 2000 130.9; 2001 122.4; 2002 115.6; 2003 110.5; 2004 111.9; 2005 117.0; 2006 117.6; 2007 106.8; 2008 120.7; 2009 104.5; 2010 106.9
  - V ar(deficit ratio) (v2) by year: 2000 19.0; 2001 25.5; 2002 27.0; 2003 29.2; 2004 34.6; 2005 27.9; 2006 30.7; 2007 22.9; 2008 44.6; 2009 16.9; 2010 17.2
  - Estimate bias (in percent of correct coefficient), computed as 1/(1+v1/v2), by year: 2000 12.7; 2001 17.2; 2002 19.0; 2003 20.9; 2004 23.6; 2005 19.2; 2006 20.7; 2007 17.7; 2008 27.0; 2009 13.9; 2010 13.8
- Interpretation: bias varies across years from a minimum of 13 percent to a maximum of 27 percent of the correct coefficient in a simple single-regressor equation.
- Bottom line: even if bias is relatively small, there is no justification to persist in using the spending ratio when revenue ratios are equally available.

### Conclusions and recommendation
- Two simple points:
  - The appropriate metric for government size as a proxy for automatic stabilizers (for analyses of output growth volatility, under the simplifying assumption of ε_R = 1 and ε_G = 0) is the revenue-to-GDP ratio.
  - The revenue ratio should be the preferred regressor in econometric exercises on the relationship between government size and volatility of output.
- Practical recommendation: abandon routine use of spending ratios in future studies, since revenue ratios are readily available and analytically more appropriate in the contexts discussed.

*Source: IMF Working Paper content unit "1. Income Shocks and Fiscal Balances (No Spending, as a Share of GDP)".*

### References

### _wp10155 - References

### References cited
- Andrés, Javier, Rafael Doménech, and Antonio Fatás (2008), “The Stabilizing Role of Government Size,” Journal of Economic Dynamics and Control 32: 571–93.
- Baunsgaard, Thomas and Steven Symansky (2009), “Automatic Fiscal Stabilizers,” IMF Staff Position Note No 09/23, (Washington, D.C: International Monetary Fund).
- Bouthevillain, Carine, Philippine Cour-Thimann, Pablo Hernandez Cos, Matthias Mohr, Mika Tujula, Geert Langenus, Sandro Momigliano and Gerrit Van Den Dool (2001), “Cyclically-adjusted Budget Balances: An Alternative Approach,” ECB Working Papers No. 77 (Frankfurt: European Central Bank).
- Darby, Julia and Jacques Mélitz (2008), “Social Spending and Automatic Stabilizers in the OECD,” Economic Policy 56: 715–56.
- Debrun, Xavier and Radhicka Kapoor (2010), “Fiscal Policy and Macroeconomic Stability: Automatic Stabilizers Work, Always and Everywhere” IMF Working Paper 10/111.
- Debrun, Xavier, Jean Pisani-Ferry, and André Sapir (2008), “Should We Forsake Automatic Stabilization?” European Economy—Economic papers No. 316 (Brussels: European Commission); forthcoming in Buti, Marco, Servaas Deroose and Vitor Gaspar (eds.) The Euro—the first decade, Cambridge University Press.
- Fatás, Antonio, and Mihov, Ilian (2001), “Government Size and Automatic Stabilizers: International and Intranational Evidence,” Journal of International Economics 55: 3–28.
- Fedelino, Annalisa, Anna Ivanova and Mark Horton (2009) “Cyclically-Adjusted Balances and Automatic Fiscal Stabilizers: Some Computational and Interpretation Issues” IMF Technical Guidance Note No. 5.
- Galì, Jordi (1994), “Government Size and Macroeconomic Stability,’ European Economic Review 38: 117–132.
- Girouard, Nathalie and Christophe André, (2005) “Measuring Cyclically-Adjusted Budget Balances for OECD Countries,” OECD Economics Department Working Paper No. 434 (Paris: Organization for Economic Cooperation and Development).
- Lee Young and Taeyoon Sung (2007), “Fiscal Policy, Business Cycles and Economic Stabilization: Evidence from Industrialised and Developing Countries,” Fiscal Studies 28: 437–62.
- Maddala, G. S. (1992), “Introduction to Econometrics,” Macmillan Publishing Company, New York.
- Mohanty, M. S. and Fabrizio Zampolli (2009), “Government Size and Macroeconomic Stability,” BIS Quarterly Review December: pp55–68, (Basle: Bank for International Settlements).
- Silgoner, Maria-Antoinette, Gerhard Reitschuler, and Jesus Crespo-Cuaresma (2003), “Assessing the Smoothing Impact of Automatic Stabilizers: Evidence from Europe,” in Gertrude Tumpel-Gugerell and Peter Mooslechner (eds.), Structural Challenges for Europe, Edward Elgar.
- Virén, Matti (2005), “Government Size and Output Volatility: Is There a Relationship?” Discussion Papers No. 8 (Helsinki: Bank of Finland).

*Source: _wp10155 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10155.pdf_