## 1. US: responses to a spending shock: deterministic trends

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### Context and motivation
- Fiscal deficits and public debt have risen significantly in many economies in Latin America and the Caribbean (LAC).
- Drivers:
  - Fiscal stimulus implemented in 2008-09 that was not reversed.
  - A fall in revenues led by a decline in commodity prices and economic activity since 2013.
- Many LAC countries are implementing fiscal consolidation measures and will continue to do so in the coming years (Regional Economic Outlook Western Hemisphere, October 2018).
- Knowing the size of fiscal multipliers is important to design better fiscal plans.

### Identification strategy and methodology
- Strategy: Blanchard and Perotti (2002) (BP) to identify fiscal shocks and estimate fiscal multipliers for eight LAC economies.
- Key features:
  - BP uses time-series to identify movements in government spending and tax revenues exogenous to the economic cycle.
  - Econometric approach follows Sims (1980), imposing as few restrictions as possible.
- Models estimated:
  - SVARs in first differences.
  - In some cases, SVECs.
- Practical implementation notes:
  - BP include seasonal dummies and a quadratic time polynomial in the reduced-form; impulse responses computed from a VAR without quarter dependence to obtain average dynamic responses.
  - Structural shock variances can be freely estimated; estimated B matrix should be normalized by each structural shock standard deviation.
  - BP’s timing assumption requires quarterly fiscal and output data, restricting the LAC sample to eight countries.
- External parameter used uniformly:
  - BP estimate a combined elasticity of tax base to GDP and collection equal to 2; this constant is used for all countries in the paper.

### Definitions of multipliers used
- BP (peak/trough) multiplier:
  - Multiplier = ratio of the peak (trough) response of GDP to the initial government spending (tax) unit shock, converted from elasticity to dollar-for-dollar by multiplying by the average ratio of GDP to government spending.
- Integral (two-year cumulative) multiplier (Ramey and Zubairy, 2018):
  - m = (∑_{t=1}^{8} response_Y_t) / (∑_{t=1}^{8} response_S_t) for spending; analogous with T for taxes.
- Key implication:
  - The definition and horizon used to compute multipliers matter; peak (BP) multipliers can differ substantially from two-year cumulative (integral) multipliers.

### Blanchard and Perotti’s SVAR identification (United States) — practical points
- Model setup:
  - Reduced-form VAR: 푿_t = E( L, q ) 푿_{t-1} + e_t, with 푿_t = (S_t, T_t, Y_t)' where S = log quarterly real per capita spending, T = log tax revenue (minus transfers and interest payments), Y = log GDP.
  - e_t = A^{-1} B u_t ≡ F u_t; identification relies on timing and institutional restrictions (e.g., government does not change spending in response to GDP within the quarter so b_1 = 0).
- Estimation of c_1 and c_2:
  - Obtained by BP outside the system via IV (cyclically adjusted reduced-form tax residual as instrument) or alternatively via MLE inside the SVAR; estimates can differ because the SVAR used for impulse responses does not include quarter dummies.
- Timing and data frequency:
  - BP’s timing assumption requires quarterly fiscal and output data.

### United States: replicated results (BP specifications)
- Spending shocks (spending decisions first; b_2 = 0 and a_2 estimated):
  - Deterministic-trend VAR:
    - Peak multiplier: 1.29, reached in 15 quarters.
    - Cumulative (integral) multiplier: 0.52 after two years.
    - Cumulative (integral) multiplier: 0.89 after four years.
  - First-differences VAR (stochastic trends; no cointegration):
    - Peak multiplier: 0.9, reached at impact.
    - Cumulative (integral) multiplier: 0.68 after two years.
    - Cumulative (integral) multiplier: 0.55 after four years.
- Tax shocks (tax decisions first; a_2 = 0 and b_2 estimated):
  - Deterministic-trend VAR:
    - Trough multiplier: -0.78, reached after 5 quarters.
    - Cumulative tax multiplier: -1.9 after 5 quarters.
    - Cumulative tax multiplier: -4.0 after two years.
  - First-differences VAR:
    - Trough multiplier: -1.33, reached after 7 quarters.
    - Cumulative tax multiplier: -2.54 after eight quarters.
- Summary for the United States:
  - BP’s reported and replicated estimates imply a much larger cumulative tax multiplier (e.g., -2.54) than the cumulative spending multiplier (e.g., 0.68), illustrating sensitivity to multiplier definition and VAR specification.

### Multipliers in eight LAC countries (SVAR in first differences; SVEC where cointegration warranted)
- Data and estimation notes:
  - Variables: real per capita spending (SS), tax revenues (TT), GDP (YY).
  - Exogenous controls: terms-of-trade index and trade-weighted foreign partners’ GDP.
  - Augmented Dickey-Fuller tests: in most cases unable to reject unit root; cointegration evidence for Chile, Colombia, Paraguay (SVECs used there).
  - Multipliers reported: peak (or trough) BP multipliers and eight-quarter cumulative multipliers (two-year integral), with SVARs in first differences and SVECs where applicable.
- Country-specific multipliers (peak/trough and two-year cumulative):
  - BRA:
    - SPENDING: Peak 0.59 (SVAR; quarter 4); Cumulative 0.81 (two years).
    - TAX: Peak/Trough -0.31 (SVAR; on impact); Cumulative -0.44 (two years).
  - CHL:
    - SPENDING: Peak 1.71 (SVAR; quarter 4) and 1.12 (SVEC); Cumulative 1.19 (SVAR) and 0.42 (SVEC) after two years.
    - TAX: Peak/Trough -0.24 (SVAR; on impact) and -0.48 (SVEC; on impact); Cumulative -0.25 (SVAR) and -0.49 (SVEC) after two years.
  - COL:
    - SPENDING: Peak 1.01 (SVAR; quarter 4) and 0.99 (SVEC); Cumulative 1.89 (SVAR) and 1.56 (SVEC) after two years.
    - TAX: Peak/Trough -0.75 (SVAR) and -0.68 (SVEC); Cumulative -3.03 (SVAR) and -1.34 (SVEC) after two years.
  - DOM:
    - SPENDING: Peak 0.40 (SVAR; quarter 2); Cumulative 0.47 (two years).
    - TAX: Trough -0.48 (SVAR; on impact); Cumulative -0.38 (two years).
  - MEX:
    - SPENDING: Peak 0.40 (SVAR; quarter 4); Cumulative 0.72 (two years).
    - TAX: Trough -0.29 (SVAR; quarter 5); Cumulative -0.36 (two years).
  - PER:
    - SPENDING: Peak 0.75 (SVAR; quarter 5); Cumulative 1.14 (two years).
    - TAX: Trough -0.74 (SVAR; quarter 6); Cumulative -1.46 (two years).
  - PAR:
    - SPENDING: Peak 0.95 (SVAR; quarter 3) and 0.98 (SVEC); Cumulative 1.15 (SVAR) and 0.63 (SVEC) after two years.
    - TAX: Trough -1.51 (SVAR; quarter 4) and -1.37 (SVEC; on impact); Cumulative -3.80 (SVAR) and -3.14 (SVEC) after two years.
  - URU:
    - SPENDING: Peak 0.41 (SVAR; quarter 2); Cumulative 0.53 (two years).
    - TAX: Trough -0.71 (SVAR; quarter 5); Cumulative -2.88 (two years).
  - USA (replication noted for comparison):
    - SPENDING: Peak 1.10 (SVAR; quarter 4); Cumulative 0.68 (two years).
    - TAX: Trough -1.34 (SVAR; quarter 1); Cumulative -2.54 (two years).
- Cross-country patterns and salient observations:
  - Spending peak multipliers (SVAR estimates) range from 0.40 to 1.71 across the sample.
  - Two-year cumulative spending multipliers are often larger than peak ones, except where SVECs are used (SVEC estimates can produce smaller cumulative spending multipliers due to spending persistence in the denominator).
  - Cumulative tax multipliers are in most cases larger in absolute value than trough multipliers; tax cumulative multipliers can be very negative (e.g., -3.80 for Paraguay, -2.54 for USA under one measure).
  - In several cases (Paraguay, Uruguay, Colombia, USA), the absolute value of cumulative tax multipliers exceeds that of spending, implying potentially negative balanced-budget multipliers under the BP identification.

### Summary and policy-relevant conclusions
- Methodological conclusions:
  - BP’s SVAR identification can be replicated for the United States and applied to LAC countries, but results depend on timing assumptions, external parameter choices (e.g., tax elasticity = 2), treatment of deterministic vs stochastic trends, inclusion of quarter dummies, and whether SVAR or SVEC is estimated when cointegration is present.
- Key empirical findings:
  - United States (BP replication): peak spending multipliers can exceed 1 (e.g., 1.29 peak), but two-year cumulative spending multipliers are smaller (e.g., 0.52–0.68); cumulative tax multipliers are substantially negative and large in absolute value (e.g., -2.54 under some specifications).
  - LAC sample: multipliers vary markedly across countries; spending peak multipliers as large as 1.71 (Chile, SVAR) and as small as 0.40 (Dominican Republic, Mexico); tax cumulative multipliers can be very negative (e.g., -3.80 Paraguay SVAR).
- Policy implication:
  - The definition and horizon used to compute fiscal multipliers matter for assessing the output effects of fiscal consolidation and for designing fiscal plans (speed and composition of consolidation across taxes vs spending). Country-specific multiplier estimates (peak vs cumulative; SVAR vs SVEC) can inform likely short- and medium-run output costs of fiscal adjustment.

*Source: Section II–IV of wpiea2020017-print-pdf (Replication and application of Blanchard and Perotti’s approach for the United States and eight LAC economies).*

### 1. US: responses to a spending shock: deterministic trends ___________________________8

### 1. US: responses to a spending shock: deterministic trends ___________________________8

### Context and motivation
- Fiscal deficits and public debt have risen significantly in many economies in Latin America and the Caribbean (LAC) in recent years.
- Drivers cited:
  - Fiscal stimulus implemented in 2008-09 that was not reversed.
  - A fall in revenues led by a decline in commodity prices and economic activity since 2013.
- Many LAC countries are implementing fiscal consolidation measures and will continue to do so in the coming years (Regional Economic Outlook Western Hemisphere, October 2018).
- Knowing the size of fiscal multipliers is important to design better fiscal plans.

### Identification strategy and methodology
- The paper uses the strategy of Blanchard and Perotti (2002) (BP) to identify fiscal shocks and estimate fiscal multipliers for eight LAC economies.
- BP’s strategy uses time-series to econometrically identify movements in government spending and tax revenues that are exogenous to the economic cycle.
- The econometric approach follows Sims (1980), imposing as few restrictions as possible on relations among the endogenous variables to let the data "speak for itself".
- Models estimated:
  - SVARs in first differences.
  - In some cases, SVECs.

### Definitions of multipliers used
- Two definitions of multipliers are used:
  1. The peak spending or trough tax multipliers of Blanchard and Perotti.
  2. The two-year cumulative multiplier (two -year cumulated response of GDP to the two-year cumulated response of government spending or tax revenues) as in Ramey and Zubairy (2018).

### Scope, potential determinants, and limitations
- The size of multipliers could depend on many factors such as:
  - Income,
  - Degree of openness,
  - Government size,
  - Debt level,
  - Composition of spending and taxes,
  - Business cycle.
- Explaining cross-country differences in multipliers is beyond the scope of this paper, given the small number of countries in the sample ("eight LAC economies" and "small number of countries in the sample").

*Source: wpiea2020017-print-pdf - 1. US: responses to a spending shock: deterministic trends*

### Section II discusses BP’s approach in detail and shows some interesting results that come out

### wpiea2020017-print-pdf - Section II discusses BP’s approach in detail and shows some interesting results that come out

### Blanchard and Perotti’s (BP’s) SVAR identification strategy (United States)
- Model setup:
  - Reduced-form VAR: 푿_t = E( L, q ) 푿_{t-1} + e_t, with 푿_t = (S_t, T_t, Y_t)' where S = log quarterly real per capita spending (government consumption and investment), T = log tax revenue (minus transfers and interest payments), Y = log GDP.
  - Relationship between reduced-form residuals e_t and structural shocks u_t imposed linearly via matrices A and B, yielding e_t = A^{-1} B u_t ≡ F u_t.
  - Identification relies on timing and institutional restrictions to recover A, B, and F; e.g., government does not change spending in response to GDP within the quarter so b_1 = 0.
- External estimates used by BP:
  - BP estimate a combined elasticity of tax base to GDP and collection equal to 2; this constant is used for all countries in the paper.
  - c_1 and c_2 (coefficients relating surprise movements) obtained by BP outside the system via IV (cyclically adjusted reduced-form tax residual as instrument) or alternatively via MLE inside the SVAR; estimates can differ because the SVAR used for impulse responses does not include quarter dummies.
- Practical issues and implementation:
  - BP include seasonal dummies and a quadratic time polynomial in the reduced-form to capture quarter dependence and deterministic trends; impulse responses are ultimately computed from a VAR without quarter dependence to obtain average dynamic responses.
  - Structural shock variances can be freely estimated, but the estimated B matrix should then be normalized by each structural shock standard deviation (divide each column by its diagonal element).
  - BP’s timing assumption requires quarterly fiscal and output data, restricting the LAC sample to eight countries.

### Definition of multipliers and implications
- BP multiplier definition (peak/trough):
  - Multiplier = ratio of the peak (trough) response of GDP to the initial government spending (tax) unit shock, converted from elasticity to dollar-for-dollar by multiplying by the average ratio of GDP to government spending.
- Integral (cumulative) multiplier (Ramey and Zubairy, 2018):
  - m = (∑_{t=1}^{8} response_Y_t) / (∑_{t=1}^{8} response_S_t) for spending, or analogous with T for taxes (two-year cumulative response).
- Key implication:
  - The definition of multiplier matters; peak (BP) multipliers can differ substantially from two-year cumulative multipliers (integral multipliers). Using BP’s estimated impulse responses for the United States, the cumulative tax multiplier is much larger (in absolute value) than the cumulative spending multiplier.

### United States: replicated results (BP specifications)
- Spending shocks (spending decisions first; b_2 = 0 and a_2 estimated):
  - Deterministic-trend VAR:
    - Peak multiplier: 1.29, reached in 15 quarters.
    - Cumulative (integral) multiplier: 0.52 after two years.
    - Cumulative (integral) multiplier: 0.89 after four years.
  - First-differences VAR (stochastic trends; no cointegration):
    - Peak multiplier: 0.9, reached at impact.
    - Cumulative (integral) multiplier: 0.68 after two years.
    - Cumulative (integral) multiplier: 0.55 after four years.
- Tax shocks (tax decisions first; a_2 = 0 and b_2 estimated):
  - Deterministic-trend VAR:
    - Trough multiplier: -0.78, reached after 5 quarters.
    - Cumulative tax multiplier: -1.9 after 5 quarters.
    - Cumulative tax multiplier: -4.0 after two years.
  - First-differences VAR:
    - Trough multiplier: -1.33, reached after 7 quarters.
    - Cumulative tax multiplier: -2.54 after eight quarters.
- Summary for the United States:
  - BP’s reported and replicated estimates imply a much larger cumulative tax multiplier (e.g., -2.54) than the cumulative spending multiplier (e.g., 0.68), illustrating that multiplier estimates depend materially on definition and VAR specification.

### Multipliers in eight LAC countries (SVAR in first differences; SVEC where cointegration warranted)
- Data / estimation notes:
  - Variables: real per capita spending (SS), tax revenues (TT), GDP (YY).
  - Exogenous controls: terms-of-trade index and trade-weighted foreign partners’ GDP.
  - Augmented Dickey-Fuller tests: in most cases unable to reject unit root; cointegration evidence for Chile, Colombia, Paraguay (SVECs used there).
  - Multipliers reported: peak (or trough) BP multipliers and eight-quarter cumulative multipliers (two-year integral), with SVARs in first differences and SVECs where applicable.
- Table 3 summary (peak/trough and two-year cumulative multipliers; notes on SVEC when reported):
  - BRA:
    - SPENDING: Peak 0.59 (SVAR; quarter 4); Cumulative 0.81 (two years).
    - TAX: Peak/Trough -0.31 (SVAR; on impact); Cumulative -0.44 (two years).
  - CHL:
    - SPENDING: Peak 1.71 (SVAR; quarter 4) and 1.12 (SVEC); Cumulative 1.19 (SVAR) and 0.42 (SVEC) after two years.
    - TAX: Peak/Trough -0.24 (SVAR; on impact) and -0.48 (SVEC; on impact); Cumulative -0.25 (SVAR) and -0.49 (SVEC) after two years.
  - COL:
    - SPENDING: Peak 1.01 (SVAR; quarter 4) and 0.99 (SVEC); Cumulative 1.89 (SVAR) and 1.56 (SVEC) after two years.
    - TAX: Peak/Trough -0.75 (SVAR) and -0.68 (SVEC); Cumulative -3.03 (SVAR) and -1.34 (SVEC) after two years.
  - DOM (Dominican Republic):
    - SPENDING: Peak 0.40 (SVAR; quarter 2); Cumulative 0.47 (two years).
    - TAX: Trough -0.48 (SVAR; on impact); Cumulative -0.38 (two years).
  - MEX:
    - SPENDING: Peak 0.40 (SVAR; quarter 4); Cumulative 0.72 (two years).
    - TAX: Trough -0.29 (SVAR; quarter 5); Cumulative -0.36 (two years).
  - PER:
    - SPENDING: Peak 0.75 (SVAR; quarter 5); Cumulative 1.14 (two years).
    - TAX: Trough -0.74 (SVAR; quarter 6); Cumulative -1.46 (two years).
  - PAR:
    - SPENDING: Peak 0.95 (SVAR; quarter 3) and 0.98 (SVEC); Cumulative 1.15 (SVAR) and 0.63 (SVEC) after two years.
    - TAX: Trough -1.51 (SVAR; quarter 4) and -1.37 (SVEC; on impact); Cumulative -3.80 (SVAR) and -3.14 (SVEC) after two years.
  - URU:
    - SPENDING: Peak 0.41 (SVAR; quarter 2); Cumulative 0.53 (two years).
    - TAX: Trough -0.71 (SVAR; quarter 5); Cumulative -2.88 (two years).
  - USA (replication noted in Table 3 for comparison):
    - SPENDING: Peak 1.10 (SVAR; quarter 4); Cumulative 0.68 (two years).
    - TAX: Trough -1.34 (SVAR; quarter 1); Cumulative -2.54 (two years).
- Cross-country patterns and salient observations:
  - The cumulative tax multipliers are in most cases larger in absolute value than the trough multipliers.
  - Two-year cumulative spending multipliers are often larger than peak ones, except where SVECs are used (SVEC estimates can produce smaller cumulative spending multipliers due to spending persistence in the denominator).
  - Substantial heterogeneity across countries: spending peak multipliers range from 0.40 to 1.71 (SVAR estimates) across the sample; tax cumulative multipliers can be large and negative (e.g., -3.80 for Paraguay, -4.0 for USA under one measure).
  - In several cases (Paraguay, Uruguay, Colombia, USA), the absolute value of cumulative tax multipliers exceeds that of spending, implying potentially negative balanced-budget multipliers under the BP identification.

### Summary and policy-relevant conclusions
- Methodological:
  - BP’s SVAR identification can be replicated for the United States and applied to LAC countries, but results depend on timing assumptions, external parameter choices (e.g., tax elasticity = 2), treatment of deterministic vs stochastic trends, inclusion of quarter dummies, and whether SVAR or SVEC is estimated when cointegration is present.
- Key empirical findings:
  - For the United States (BP replication): peak spending multipliers can exceed 1 (e.g., 1.29 peak), but two-year cumulative spending multipliers are smaller (e.g., 0.52–0.68); cumulative tax multipliers are substantially negative and large in absolute value (e.g., -2.54 under some specifications).
  - In the LAC sample, multipliers vary markedly across countries; spending peak multipliers are as large as 1.71 (Chile, SVAR) and as small as 0.40 (Dominican Republic, Mexico); tax cumulative multipliers can be very negative (e.g., -3.80 Paraguay SVAR).
- Policy implication:
  - The definition and horizon used to compute fiscal multipliers matter for assessing the output effects of fiscal consolidation and for designing fiscal plans (speed and composition of consolidation across taxes vs spending). Knowing country-specific multiplier estimates (peak vs cumulative; SVAR vs SVEC) can inform the likely short- and medium-run output costs of fiscal adjustment.

*Source: Section II–IV of wpiea2020017-print-pdf (Replication and application of Blanchard and Perotti’s approach for the United States and eight LAC economies).*

### References

### References

### Fiscal multipliers and macroeconomic effects
- Blanchard O. and R. Perotti, 2002, “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output.” QJE, November 1329-68.  
- Ilzetzki E., E. Mendoza and C. Vegh, 2011, “How Big (Small?) Are Fiscal Multipliers?” International Monetary Fund WP/11/52.  
- Ramey, V. S. Zubairi, 2018, “Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data.” JPE 126, no. 2 (April 2018): 850-901.  
- Matheson, T. and Pereira, J., 2016, “Fiscal Multipliers for Brazil” IMF Working Paper WP/16/79 (Washington: International Monetary Fund).  
- Valencia, F., 2015, “Fiscal Multipliers in Mexico.” IMF Country Report No. 15/314 Selected Issues Papers.  
- Vtyurina, S. and Z. Leal, 2016, “Fiscal Multipliers and Institutions in Peru: Getting the Largest Bang for the Sol” IMF WP/16/144.  
- IMF Western Hemisphere Department Regional Economic Outlook, 2018, Chapter 4. “Fiscal Multipliers: How Will Consolidation Affect Latin America and the Caribbean?” (Washington: International Monetary Fund).  
- World Bank, 2018, “Fiscal Adjustment in Latin America and the Caribbean: Short-run pain, long-run gain?” Semiannual Report Office of the Regional Chief Economist April.

### Country- and region-specific fiscal policy and consolidation studies
- Carriere-Swalow, Y., A. David and D. Leigh, 2018, “The Macroeconomic Effects of Fiscal Consolidation in Emerging Economies: Evidence from Latin America.” IMF Working Paper WP/18/142 (Washington: International Monetary Fund).  
- David, A., 2017, “Fiscal Policy Effectiveness in a Small Open Economy: Estimates of Tax and Spending Multipliers in Paraguay.” IMF Working Paper WP/17/63 (Washington: International Monetary Fund).  
- López-Vera, A., A. Pinchao-Rosero, and N. Rodríguez-Niñoa, 2018, “Non-Linear Fiscal Multipliers for Public Expenditure and Tax Revenue in Colombia.” Ensayos de política económica vol.36 no. 85. Banco de la República de Colombia.  
- Fornero, J., J. Guerra-Salas, and C. Pérez, 2019, “Multiplicadores fiscales en Chile.” Revista de Economia Chilena, Central Bank of Chile, 22: 58-80.  
- Restrepo, J. and H. Rincón, 2006, “Identifying fiscal shocks in Chile and Colombia.” Central Bank of Chile, Working Paper 360.  
- Central Reserve Bank of Peru, 2012, “Inflation Report: Recent Trends and Macroeconomic Forecasts 2012–14” (June).  
- Ministry of Economy and Finance of Peru, 2015, “Multiannual Macroeconomic Framework,” 2016-18. Ministry of Finance of Peru, April.  
- International Monetary Fund (IMF), 2018, “Poverty, inequality and redistribution in the Dominican Republic,” in Dominican Republic 2018 Article IV Consultation—Selected Issues, IMF Country Report No. 18/294 (Washington).

### Fiscal policy dynamics, consolidation, and debt-feedback analyses
- Estevao, M. and I. Samake, 2013, “The Economic Effects of Fiscal Consolidation with Debt Feedback.” IMF Working Paper WP/13/136 (Washington: International Monetary Fund).  
- Céspedes, L.F., J. Fornero y J. Galí, 2012, “Non-Ricardian Aspects of Fiscal Policy in Chile.” En Fiscal Policy and Macroeconomic Performance, editado por L.F. Céspedes y J. Galí, serie Banca Central, Análisis y Políticas Económicas, vol. 17, Banco Central.

### Methodology, modeling, and tools
- Ouliaris, S. A. Pagan, and J. Restrepo, 2018, Quantitative Macroeconomic Modeling with Structural Vector Autoregressions – An EViews Implementation. https://www.eviews.com/StructVAR/structvar.html

*Content compiled from the References section of the source PDF.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020017-print-pdf.pdf_