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### Overview
- Purpose: Estimate fiscal multipliers by policy instrument for Bolivia, a lower middle income commodity exporter with a de facto pegged exchange rate regime, using empirical (Blanchard-Perotti framework) and DSGE modeling approaches.
- Time period for empirical analysis: 1990-2022.
- Approach: Eclectic—standard open economy macroeconomic theory, empirical time series (structural VAR), and a full neo‑Keynesian DSGE model calibrated to lower middle‑income country and Bolivian averages where possible.

### Key theoretical insights (Basic Model)
- Under standard Mundell‑Fleming assumptions with normally high capital mobility:
  - Fiscal multipliers are higher under a peg than with a float.
  - Mechanism: Under a float, fiscal expansion leads to currency appreciation and expenditure switching toward foreign goods; under a peg, monetary expansion accommodates fiscal expansion and raises output more.
- With very low capital mobility:
  - Ordering can reverse: fiscal multipliers may be higher with a float than with a peg.
  - Mechanism: Under low capital mobility a fiscal expansion requires very large domestic interest rate increases to attract capital; maintaining a peg may force a monetary tightening that weakens the fiscal expansion’s effect on growth.
- Technical notation used: BOP(e0, R, R*, Y)=0 and IS/LM shifts (IS → IS’, LM → LM’).

### Empirical findings (Blanchard‑Perotti, 1990–2022)
- Main empirical results for spending multipliers in Bolivia:
  - Public investment multipliers: more than 0.5 on a cumulative basis.
  - Public consumption multipliers: about 0.3 on a cumulative basis.
- Empirical IRF multipliers (8 quarters):
  - Current spending cumulative multiplier: 0.15 after 8 quarters; peak ~0.2.
  - Capital spending cumulative multiplier: 0.75 after 8 quarters; peak ~0.6.
- Caveats:
  - Empirical analysis focuses on spending multipliers; tax multiplier estimation is subject to wide confidence intervals because tax revenues are highly dependent on commodity revenues.
  - Data limitations and structural breaks and quarterly data reliability may limit precision.
  - Small subsamples (e.g., those used to estimate multipliers under a floating exchange rate) may limit reliability.
- Historical tax episodes cited:
  - Tax reform presented November 1994 expected revenue yield of 1.2 percent of GDP in 1995 (0.9 percent of GDP considering offsetting expenditure increases).
  - 2004 tax hikes: 2 percent of GDP.
  - 2005 tax hikes: 4.1 percent of GDP.

### DSGE model structure and calibration highlights
- Model: Neo‑Keynesian DSGE with nominal frictions (upward‑sloping Phillips curve, Rotemberg adjustment costs), wage bargaining, two household types (non‑Ricardian and Ricardian), government with public consumption and investment, and central bank regimes (peg and inflation targeting).
- Selected steady state and parameter values preserved exactly as presented:
  - Share of non-Ricardian households (hand-to-mouth consumers): 0.2
  - Steady state debt-to-GDP ratio: 0.4
  - Potential growth rate: 3.7 percent
  - Trade surplus: 0.1 percent
  - Frisch elasticity: 1.0
  - Trade elasticity of substitution: 0.25
  - Capital share: 0.38
  - Public capital share: 0.05
  - Government spending to GDP: 0.25
  - Public investment to Government spending: 0.4
  - Private investment to GDP: 0.08
  - Private consumption to GDP: 0.669
  - Net exports to GDP: 0.001
  - Depreciation rate of private capital: 0.05
  - Depreciation rate of public capital: 0.05
  - Import composition of investment: 0.35
  - Import composition of consumption: 0.35
  - Government debt to GDP: 0.4
  - Persistence of fiscal shocks: 0.15
  - Long-term Inflation: 2%
  - Foreign inflation: 2%
  - Potential growth: 3.7%
- Caveat: Calibration does not account for larger reserve adequacy needed under fixed vs flexible regimes; Bolivian macro indicators at end-2022 differ from steady state levels used as initial conditions.

### DSGE quantitative results and scenario responses
- Shock design: Shocks standardized to 1 percent of GDP, persistence 0.15; responses expressed as percentages of GDP (interest rate and nominal exchange rate as percent variations).
- 1 percent of GDP increase in government consumption:
  - Under a pegged exchange rate:
    - GDP rises by 0.65 percent in the initial period.
    - Government debt rises by the amount of the government spending increase.
    - Private consumption and investment fall slightly as domestic prices rise.
    - Central bank initially accumulates reserves, then sells reserves in period 2 as shock subsides.
    - Current account slips into deficit on impact.
  - Under inflation targeting:
    - Multipliers slightly lower due to exchange rate appreciation; domestic interest rate increases; exchange rate appreciates on impact then depreciates.
- 1 percent of GDP increase in the consumption tax:
  - Reduces GDP on impact as private consumption declines, under both peg and IT.
  - Impact is less than that of a spending reduction.
  - Under the peg, reserves accumulate then more rapidly as central bank sells domestic currency to counter drop in demand.
  - Under IT, interest rate drops as central bank expands balance sheet; nominal exchange rate appreciates after initial slight depreciation.
- 1 percent of GDP increase in transfers to non‑Ricardian households:
  - GDP declines slightly under either regime despite positive demand effect because transfers shift household preferences toward leisure, reducing hours worked and output.
  - Consumption rises substantially for non‑Ricardian households, implying reductions in transfers would have significant negative welfare effects.

### Multipliers from the DSGE model (preserving exact figures)
- On impact (high capital mobility):
  - Spending multipliers for both government consumption and public investment: 0.65 under the peg and 0.60 under inflation targeting.
  - Tax multiplier (consumption tax increase): about half of a spending reduction.
  - GDP multiplier of an increase in transfers to non‑Ricardian households: close to zero.
- Cumulative (8‑quarter horizon):
  - Cumulative spending multipliers somewhat lower than on impact; multipliers under the peg slightly higher than under IT.
  - Public investment multipliers diverge positively from government consumption over the longer run due to public capital accumulation.
- Under low capital mobility:
  - Ordering can reverse: on impact, public investment multiplier is 0.51 under the peg and 0.58 under inflation targeting.
- Fiscal consolidation tradeoff metric (ratio of change in GDP to change in government debt over 8 quarters) tracks cumulative multipliers closely but is slightly higher for both government consumption and public investment.

### Cross‑study comparison and literature context
- Literature ranges cited:
  - Spending multipliers for emerging market economies average around 1/3 – 2/3.
  - Spending multipliers for advanced economies average around 1/2 - 1.
  - Tax multipliers are typically lower, at about half of spending multipliers.
- Regional/sample averages reported:
  - Average All LAC: 0.5
  - Average Restrepo: 0.8
- Selected point estimates from the literature preserved exactly as listed (examples):
  - Valdivia (2016), Bolivia: 0.3
  - Restrepo (2020), Brazil: 0.8
  - Restrepo (2020), Chile: 1.2
  - Restrepo (2020), Colombia: 1.9
  - Mineshima et al. (2014), Survey 41 studies: 0.75
  - Colombo et al (2022), high informality 141 countries: 0
  - Geli and Moura (2023), 177 countries: 0.7
  - Kinda et al. (2022), 91 countries: 0.4

### Empirical methodology and data construction (Bolivia)
- VAR specification: follows Blanchard and Perotti (2002):
  - Y_t = A(L,q) Y_{t−1} + U_t, with Y_t ≡ [T_t, G_t, X_t]' in real per‑capita logs; A(L,q) is a four‑quarter distributed lag polynomial with quarter‑dependent coefficients.
- Identification: structural shocks e_t^t, e_t^g, e_t^x mutually uncorrelated with system:
  - t_t = a_1 x_t + a_2 e_t^g + e_t^t
  - g_t = b_1 x_t + b_2 e_t^t + e_t^g
  - x_t = c_1 t_t + c_2 g_t + e_t^x
- Data:
  - Logarithms of quarterly taxes, spending (current vs capital), and GDP, real and per capita, 1990-2022.
  - Fiscal data source: national accounts (“Cuadro N°59”).
  - Fiscal data smoothed using the X12 technique.
  - Population, deflator, and GDP data: National Statistical Institute (www.ine.gob.bo). Population extrapolated linearly from annual to quarterly frequency.
- Narrative‑style controls: dummies for years 1995, 2004, and 2005.

### Policy implications and recommendations (preserving source emphasis)
- Spending composition:
  - Fiscal consolidation should emphasize reductions in current spending more heavily than cuts to public investment, subject to legal commitments and productivity considerations of specific investments.
  - Include both public consumption and public investment in fiscal strategy; public investment may yield somewhat higher returns over longer horizons but differences are not large.
- Revenue measures:
  - Revenue enhancements have a role in fiscal consolidation given low tax multipliers.
  - Tax reforms recommended as part of an efficient consolidation mix, together with reductions in current spending and addressing inefficient public investment.
- Transfers:
  - Reducing transfers is efficient for GDP but likely to have significant negative welfare and distributive equity effects because transfers materially increase consumption of non‑Ricardian households.
- Exchange rate policy coordination:
  - Multipliers are generally higher with a peg than with a float given normal capital mobility; a transition to a floating exchange rate can reduce short‑term output costs of consolidation when capital is mobile.
  - Under some conditions (low capital mobility), ordering reverses and a float can increase multipliers.
  - Transition decisions should weigh these multiplier effects against benefits of floating exchange rates (resilience to external shocks, preservation of reserves, real exchange rate realignment).
  - Emphasizes need for coordination between fiscal and monetary policy in any transition to a sustainable equilibrium.
- Implementation caveats:
  - Outcomes depend on initial conditions, policy mix (revenue vs expenditure), graduality of adjustment, political environment, and external conditions.
- Contextual quantitative target cited from prior work:
  - Bolivia requires consolidation of its primary deficit from the present level of about 6 percent of GDP to 1-1½ percent of GDP, depending on the exchange rate regime.

### Key quantitative facts and diagnostics (exact figures preserved)
- Empirical IRF (8 quarters):
  - Current spending cumulative multiplier: 0.15 after 8 quarters; peak ~0.2.
  - Capital spending cumulative multiplier: 0.75 after 8 quarters; peak ~0.6.
- DSGE on‑impact spending multipliers (high capital mobility):
  - Government consumption: 0.65 under peg, 0.60 under IT.
  - Public investment: 0.65 under peg, 0.60 under IT.
- Structural/calibration shares:
  - Current spending: 25-30 percent of GDP.
  - Public investment: >40 percent of total investment.
  - Incremental capital‑output ratio (ICOR) noted as >5 in some studies.

*IMF Working Paper — Estimating Fiscal Multipliers Under Alternative Exchange Rate Regimes: The Case of Bolivia*

### Executive Summary ......................................................................................................

### Executive Summary

### Overview
- Purpose: Estimate fiscal multipliers by policy instrument for Bolivia, a lower middle income commodity exporter with a de facto pegged exchange rate regime, using empirical (Blanchard-Perotti framework) and DSGE modeling approaches.
- Motivation: Developing countries often require clear, well-planned, fiscal consolidation to restore economic stability and wish to minimize the growth cost of adjustment, which may vary by fiscal instrument and monetary/exchange rate policy.
- Approach: Eclectic—standard open economy macroeconomic theory, empirical time series (structural VAR), and a full neo-Keynesian DSGE model calibrated to lower middle-income country and Bolivian averages where possible.

### Key theoretical insights (Basic Model)
- Under standard Mundell-Fleming assumptions with normally high capital mobility:
  - Fiscal multipliers are higher under a peg than with a float.
  - Mechanism: Under a float, fiscal expansion leads to currency appreciation and expenditure switching toward foreign goods; under a peg, monetary expansion accommodates fiscal expansion and raises output more.
- With very low capital mobility:
  - Ordering can reverse: fiscal multipliers may be higher with a float than with a peg.
  - Mechanism: Under low capital mobility a fiscal expansion requires very large domestic interest rate increases to attract capital; maintaining a peg may force a monetary tightening that weakens the fiscal expansion’s effect on growth.
- Technical notation appearing in the analysis: BOP(e0, R, R*, Y)=0 and references to shifts in IS and LM lines (IS → IS’, LM → LM’).

### Empirical findings (Blanchard-Perotti, 1990–2022)
- Time period used: 1990-2022.
- Main empirical results for spending multipliers in Bolivia:
  - Public investment multipliers: more than 0.5 on a cumulative basis.
  - Public consumption multipliers: about 0.3 on a cumulative basis.
- Caveats:
  - Empirical analysis focuses on spending multipliers; tax multiplier estimation is subject to wide confidence intervals because tax revenues are highly dependent on commodity revenues for commodity exporters such as Bolivia.
  - Data limitations and structural breaks (multiple major political and economic changes in Bolivia) and quarterly data reliability may limit precision.
  - Small subsamples (e.g., those used to estimate multipliers under a floating exchange rate) may limit reliability.

### DSGE model results
- Model: Full neo-Keynesian DSGE calibrated to lower middle-income country averages and Bolivian averages where possible.
- Main quantitative outcomes:
  - Multipliers for public investment and current spending:
    - Similar on impact: about 0.65.
    - Public investment multipliers somewhat higher in the longer run as output reflects accumulated public capital stock from investment.
  - Tax multipliers: about half of spending multipliers.
- Exchange rate regime effects in the DSGE model:
  - Multipliers are higher under a peg than a float, given normally high capital mobility.
  - Ordering reverses under very low capital mobility (consistent with the basic Mundell-Fleming intuition).

### Cross-study comparison and literature context
- Literature ranges and comparisons:
  - Spending multipliers for emerging market economies average around 1/3 – 2/3.
  - Spending multipliers for advanced economies average around 1/2 - 1.
  - Tax multipliers are typically lower, at about half of spending multipliers.
- Bolivia’s estimated multipliers are in line with these literature ranges.

### Policy implications for developing countries (and Bolivia)
- Revenue measures:
  - Revenue enhancements have a role in fiscal consolidation given low tax multipliers.
- Spending composition:
  - Fiscal consolidation should emphasize reductions in current spending more heavily than cuts to public investment, subject to legal commitments and productivity considerations of specific investments.
- Exchange rate policy coordination:
  - Because multipliers are generally lower with a float than a peg (given normal capital mobility), there may be benefits to matching spending cuts or tax increases with a transition towards a floating exchange rate regime to minimize output costs of adjustment.
  - A more flexible exchange rate would soften the burden of consolidation on activity and employment by allowing the exchange rate to absorb some negative growth impact.
- Implementation caveats:
  - Outcomes depend on initial conditions, the policy mix between revenue and expenditure measures, the graduality of adjustment, the political environment, and external conditions.

### Context from prior work
- Previous work cited indicates Bolivia requires a consolidation of its primary deficit from the present level of about 6 percent of GDP to 1-1½ percent of GDP, depending on the exchange rate regime.
- Suggested efficient consolidation mix: tax reform, reductions in current spending where possible, and addressing inefficient areas of public investment.

*IMF Working Paper — Executive Summary*

### 3.  Recent Literature

### 3.  Recent Literature

### The Main Approaches
- Three main classes of empirical approaches (Ramey, 2019):
  - (1) aggregate country-level time series;
  - (2) cross-sectional or panel estimates;
  - (3) New Keynesian dynamic stochastic general equilibrium (DSGE) models.

- Aggregate Estimates (narrative and sVAR strategies):
  - Narrative approach: uses official documents to create data series of exogenous policy changes (e.g., budget documents, tax legislation, special budget items, multi-year fiscal consolidation plans).
  - sVAR approach: relies on high frequency (usually quarterly) data; two-step approach where fiscal variables (taxes and expenditures) and output are regressed on multiple quarterly lags to obtain a fiscal shock under the assumption that controlling for lags eliminates endogenous variations. Alternative identification uses sign restrictions on impulse response functions (Mountford and Uhlig, 2009).
  - Note: Chahrour, Schmitt-Grohe and Uribe (2012) investigate why narrative tax multipliers (3 percent) exceed sVAR estimates (1 percent), attributing differences to failure to identify the same tax shock or small-sample uncertainty.

- Panel Estimates:
  - Bartik instruments (Goldsmith-Pinkham, Sorkin, and Swift, 2020) exploit geographical variation to identify exogenous fiscal shifts, removing measurement biases at sub-national level.
  - Nakamura and Steinsson (2014) find large regional multipliers; Chodorow-Reich (2019) aggregates sub-national estimates to national ones and argues regional estimates provide a lower bound due to spillovers.
  - Cross-sectional estimates tacitly assume a closed economy with no monetary policy response and deficit-financed expansion; violations may bias estimates upward.
  - Panel approaches allow use of annual data and inclusion of countries with scarce high-frequency fiscal data. Auerbach and Gorodnichenko (2013) and others use IMF World Economic Outlook forecast errors as proxies for fiscal shocks.

- DSGE Models:
  - Models with no or limited nominal frictions: fiscal multipliers tend to be smaller (e.g., Baxter and King (1993); Burnside, Eichenbaum and Fisher (2004)).
  - New-Keynesian DSGE models with nominal frictions: multipliers are larger and especially large in liquidity traps or at the zero lower bound (e.g., Christiano, Eichenbaum and Rebelo (2011); Leeper, Traum, and Walker (2017)).
  - Farhi and Werning (2017): within a currency union or fixed exchange regime, multipliers tend to be larger when spending is externally financed rather than self-financed.
  - Heterogeneous-agent models highlight the role of income and wealth inequality in enlarging multipliers (e.g., Kopiec (2022); Brinca et al. (2016)).
  - Timing and anticipation matter (Ramey (2011)); timing of composition of public spending or revenues affects short-run vs. medium/long-run outcomes (Kass-Hanna, Kpodar and Tessema (2020)).
  - DSGE modeling generally finds lower tax multipliers than spending multipliers; modeling of timing and news aspects of taxes is key (e.g., Leeper, Walker and Yang (2013); Chahrour, Schmitt-Grohe, and Uribe (2012)).

### Conditions Affecting Multiplier Estimates
- Exchange rate regime and monetary policy:
  - Flexible exchange rate regimes tend to have smaller multipliers because exchange rate movements can offset discretionary fiscal policy effects (Corsetti and others, 2012; Born and others, 2013; Ilzetzki and others, 2013).
  - Multipliers can be larger when monetary policy transmission is impaired (e.g., at the zero interest lower bound) (Erceg and Lindé, 2014; Woodford, 2011).

- Business cycle and downturns:
  - Multipliers are larger during downturns and when there is slack (Auerbach and Gorodnichenko, 2012; Baum, Ribeiro, and Weber, 2012).
  - Mineshima, Poplawski-Ribeiro, and Weber (2014) and Canzoneri et al. (2016): higher proportion of credit-constrained households and firms during downturns increases multipliers.
  - Kinda, Lengyel, and Chahande (2022): during health crises, social distancing and uncertainty may lower multipliers initially; multipliers increase as economies re-open and pent-up demand is unleashed.

- Development level and structural factors:
  - Theoretical expectation: higher multipliers in developing economies due to constraints and lower public capital stocks (Baxter and King, 1993) — empirical evidence is mixed.
  - Factors that may reduce multipliers in low-income countries: larger precautionary savings, low efficiency of public expenditure, difficulty unwinding expenditure, low revenue levels, lower fiscal policy credibility (Miyamoto et al., 2020; Ilzetzki, Mendoza, and Végh, 2013).
  - Less consumption smoothing when: (i) liquidity constraints in less developed financial markets; (ii) agents are less forward looking under instability.
  - Automatic stabilizers are less important in developing countries.

- Informality, imports, and corruption:
  - Significant leakage through imports and a large informal economy can lower multipliers (Colombo et al., 2022; Dime, Ginting and Zhuang, 2021).
  - Colombo et al. (2022), using local projections and a two-sector DSGE model across 141 countries, find higher informality is associated with weaker fiscal multipliers.
  - Corruption can enable tax evasion and undermine tax collection, potentially leading to larger-than-necessary policy changes required for consolidation (IMF, 2019).

- Commodity exporters and openness:
  - Commodity exporters are typically studied from the spending angle because fiscal revenues depend on international prices and vary exogenously; tax multipliers often not estimated.
  - Spending multipliers in commodity exporters are found to be similar in magnitude to non-commodity exporters.
  - Countries with a lower propensity to import (large countries or partially open economies) tend to have higher multipliers (Barrell and others, 2012; Ilzetzki and others, 2013; IMF, 2008).

- Labor market rigidity and debt:
  - More rigid labor markets (stronger unions, stronger regulation) imply larger fiscal multipliers if rigidity reduces wage flexibility (Cole and Ohanian, 2004; Gorodnichenko and others, 2012).
  - Larger automatic stabilizers reduce multipliers (Dolls and others, 2012).
  - High-debt countries generally have lower multipliers because consolidation can improve credibility and private demand and lower sovereign risk premia (Ilzetzki and others, 2013; Kirchner and others, 2010).

### Different Types of Fiscal Multipliers
- Definitions:
  - Impact multiplier: contemporaneous effect of a fiscal shock or effect at a future horizon (Spilimbergo, Symansky, and Schindler, 2009).
  - Peak multiplier: largest response over any horizon.
  - Cumulative multiplier: cumulative change in output over cumulative change in fiscal policy over a period.
  - Present value (PV) multiplier (for expenditure): discounted cumulative output response divided by discounted cumulative fiscal shock (Mountford and Uhlig, 2009).

- Persistence and shape:
  - Output effect of an exogenous fiscal shock typically vanishes within five years even if measures are permanent; effect usually follows an inverted U shape with maximum impact in the second year (Batini and others, 2014; Baum and others, 2012; Coenen and others, 2012).
  - Mineshima and others (2014): the second-year multiplier is, on average, 10–30 percent higher than in the first year.
  - Duration depends on: (i) persistence of the fiscal shock; (ii) type of fiscal instrument; (iii) conjunctural factors (cyclical position, monetary policy response).

- Instrument-specific persistence:
  - Permanent discretionary changes in indirect taxes, government consumption, and transfers: short-term output effects, typically vanishing within five years (Anderson and others, 2013; Coenen and others, 2012; European Commission, 2010).
  - Permanent discretionary changes in public investment or corporate taxes: longer-lasting effects that may be permanent; multipliers may increase after the first year toward long-term values (Coenen and others, 2012). Rationale: corporate income taxes distort investment and reduce long-run capital stock; cuts in government investment can reduce productive capacity.

### Summary of Estimates
- Consensus:
  - Spending multipliers are positive and typically in the range of 0.5-1 at peak and 0.3-0.5 during the first year (Guajardo, Leigh, and Pescatori, 2014; Ilzetzki, Mendoza, and Végh, 2013; IMF, 2010; Blanchard and Perotti, 2002).
  - Public investment multipliers are generally higher than consumption multipliers (Izquierdo et al., 2019; Ilzetzki, Mendoza, and Végh, 2013).

- Focus for this study:
  - Emphasis on spending multipliers given Bolivia is a commodity exporter and focus on LAC.

- Regional and sample averages reported in the literature (as compiled in Table 1):
  - Average All LAC: 0.5
  - Average Restrepo: 0.8

- Selected estimates from Table 1 (authors, sample, spending multiplier):
  - Anós-Casero et al (2010), Argentina: 0.0
  - Valdivia (2016), Bolivia: 0.3
  - Restrepo (2020), Brazil: 0.8
  - Matheson and Pereira (2016), Brazil: 0.5
  - Restrepo (2020), Chile: 1.2
  - Fornero, Guerra‐Salas, Perez (2017), Chile: 0.6
  - Restrepo (2020), Colombia: 1.9
  - Estevão and Samake (2013), Costa Rica: 0.2
  - Estevão and Samake (2013), Dominican Rep.: 0.1
  - Restrepo (2020), Dominican Rep.: 0.5
  - Restrepo (2020), Mexico: 0.7
  - Valencia (2016), Mexico: 0.7
  - Restrepo (2020), Paraguay: 1.1
  - David (2017), Paraguay: 0.8
  - Restrepo (2020), Peru: 1.1
  - Vtyurina and Leal (2016), Peru: 0.3
  - Restrepo (2020), Uruguay: 0.5
  - Mineshima et al. (2014), Survey 41 studies: 0.75
  - Colombo et al (2022), high informality 141 countries: 0
  - Geli and Moura (2023), 177 countries: 0.7
  - Kinda et al. (2022), 91 countries: 0.4
  - IMF (2013), US/EU: 0.7
  - Geli and Moura (2023), EME: 1
  - Ilzetzki and others (2013), EMEs: 0
  - Ilzetzki, Mendoza, and Végh (2013), EMEs: -0.03
  - Ilzetzki and Vegh (2008), EMEs: 0.4
  - IMF (2008), EMEs: 0.2
  - Ilzetzki (2011), EMEs: 0.2
  - Honda, Miyamoto, and Taniguchi (2020), EMEs: 0.1
  - Espinoza and Senhadji (2011), GCC: 0.7
  - Cerisola (2015), MENAP: 0.7
  - Geli and Moura (2023), LIC: 0

### Empirical Analysis (methodology and data used for Bolivia)
- VAR specification follows Blanchard and Perotti (2002) as in Restrepo (2020):
  - Y_t = A(L,q) Y_{t−1} + U_t
  - Y_t ≡ [T_t, G_t, X_t]' is a three-dimensional vector in logarithms of the quarterly taxes, spending (differentiating by current vs. capital spending), and GDP. All variables are in real and per capita terms.
  - U_t ≡ [u_t^t, u_t^g, u_t^x]' is the corresponding vector of reduced-form residuals.
  - A(L,q) is a four-quarter distributed lag polynomial with quarter-dependent coefficients to capture seasonality.

- Identification strategy (structural shocks e_t^t, e_t^g, e_t^x mutually uncorrelated):
  - t_t = a_1 x_t + a_2 e_t^g + e_t^t
  - g_t = b_1 x_t + b_2 e_t^t + e_t^g
  - x_t = c_1 t_t + c_2 g_t + e_t^x
  - Interpretations:
    - Movements in taxes within a quarter (t_t) can result from response to unexpected GDP movements (a_1 x_t), response to structural spending shocks (a_2 e_t^g), or tax-specific structural shocks (e_t^t). Analogous interpretations apply to spending and output equations.

- Data construction:
  - Logarithms of quarterly taxes, spending, and GDP, in real and per capita terms, over 1990-2022.
  - Fiscal data source: national accounts provided by the Ministry of Economy and Finance (“Cuadro N°59”).
  - Fiscal data are smoothed using the X12 technique due to monthly frequency and high seasonality.
  - Population, deflator, and GDP data: National Statistical Institute (www.ine.gob.bo). Population is extrapolated linearly from annual to quarterly frequency.

- Narrative-style controls:
  - Dummies added for the years 1995, 2004, and 2005 following David and Leigh (2018) in line with the narrative approach of Blanchard and Perotti (2002).

*IMF Working Paper — Estimating Fiscal Multipliers Under Alternative Exchange Rate Regimes: The Case of Bolivia (chapter 3: Recent Literature).*

### 0.9 percent of GDP, with a tax increase of 1.2 percent of GDP, offset by a spending increase of 0.3 percent of

### wpiea2023240-print-pdf - 0.9 percent of GDP, with a tax increase of 1.2 percent of GDP, offset by a spending increase of 0.3 percent of

### Background and context
- Tax policy episodes referenced:
  - Tax reform presented to Congress in November 1994 with an expected revenue yield of 1.2 percent of GDP in 1995 (0.9 percent of GDP considering offsetting expenditure increases).
  - In 2004, tax hikes amounted to 2 percent of GDP.
  - In 2005, tax hikes amounted to 4.1 percent of GDP.
- Motivation for tax hikes included covering costs of structural reforms, reducing the fiscal deficit, and long-run considerations (greater role of the state in hydrocarbons).

### Empirical impulse-response results (VAR/IRF)
- Current spending:
  - A 1 percentage increase in current spending leads to a cumulative multiplier of 0.15 after 8 quarters.
  - Peak multiplier is in the order of 0.2.
- Capital spending:
  - A 1 percentage increase in capital spending leads to a cumulative multiplier of 0.75 after 8 quarters.
  - Peak multiplier is in the order of 0.6.
- Comparative points:
  - Restrepo (2020) shows peak spending multipliers of 0.8 on average for Latin American countries; Bolivia’s capital expenditure multiplier estimated at 0.6.
  - Bolivia’s multipliers show similarities with Dominican Republic, Mexico, and Uruguay: relatively low and stable multipliers.
- Additional context:
  - Current spending in Bolivia is at 25-30 percent of GDP.
  - Public investment typically accounts for more than 40 percent of total investment in Bolivia.
  - Incremental capital-output ratio (ICOR) noted as more than 5 in some studies.

### DSGE model overview and parameterization
- Model type:
  - Neo-Keynesian DSGE calibrated to Bolivian values over the past 30 years; some parameters based on developing country averages; trade elasticities set for coherence (e.g., Marshall-Lerner condition).
  - Includes upward-sloping Phillips curve, Rotemberg adjustment costs, wage bargaining by labor unions.
  - Two household types: non-Ricardian (“hand-to-mouth”) and Ricardian households.
  - Government: public consumption, public investment, transfers, interest payments; revenues from consumption, capital, and labor taxes, royalties, and seignorage.
  - Central bank regimes: currency peg (baseline) and inflation targeting (alternative).
- Steady state and calibration highlights:
  - Share of non-Ricardian households (hand-to-mouth consumers): 0.2
  - Steady state debt-to-GDP ratio: 0.4
  - Potential growth rate: 3.7 percent
  - Trade surplus: 0.1 percent
- Selected parameter values (as presented):
  - Frisch elasticity: 1.0
  - Trade elasticity of substitution: 0.25
  - Share of hand-to-mouth consumers: 0.2
  - Capital share: 0.38
  - Public capital share: 0.05
  - Government spending to GDP: 0.25
  - Public investment to Government spending: 0.4
  - Private investment to GDP: 0.08
  - Private consumption to GDP: 0.669
  - Net exports to GDP: 0.001
  - Depreciation rate of private capital: 0.05
  - Depreciation rate of public capital: 0.05
  - Import composition of investment: 0.35
  - Import composition of consumption: 0.35
  - Government debt to GDP: 0.4
  - Persistence of fiscal shocks: 0.15
  - Long-term Inflation: 2%
  - Foreign inflation: 2%
  - Potential growth: 3.7%
- Caveats:
  - Calibration does not account for larger reserve adequacy needed under fixed vs flexible regimes, limiting divergence of scenario results.
  - Bolivian macroeconomic indicators at end-2022 differ from steady state levels used as initial conditions; results indicate channels and magnitudes rather than a transition path to a sustainable equilibrium.

### Responses to standardized fiscal shocks (DSGE experiments)
- Shock design:
  - Shocks standardized to 1 percent of GDP, persistence 0.15.
  - Responses shown as percentages of GDP (interest rate and nominal exchange rate shown as percentage variations from baseline).
- 1 percent of GDP increase in government consumption:
  - Under a pegged exchange rate:
    - GDP rises by 0.65 percent in the initial period.
    - Government debt rises by the amount of the government spending increase.
    - Private consumption and investment fall slightly as domestic prices rise.
    - Central bank initially accumulates reserves, then sells reserves in period 2 as shock subsides.
    - Current account slips into deficit on impact.
  - Under inflation targeting:
    - Reserves maintained at steady state by assumption.
    - Domestic interest rate increases as central bank sells bonds to reduce demand and limit inflation.
    - Exchange rate appreciates on impact then depreciates as shock subsides.
    - GDP, private demand, and fiscal deficit responses similar to peg but multipliers slightly lower due to exchange rate appreciation.
- 1 percent of GDP increase in the consumption tax:
  - Reduces GDP on impact as private consumption declines, under both peg and IT.
  - Impact is less than that of a spending reduction.
  - Under the peg, reserves accumulate then more rapidly as central bank sells domestic currency to counter drop in demand.
  - Under IT, interest rate drops as central bank expands balance sheet to compensate for decline in consumption demand; nominal exchange rate appreciates after initial slight depreciation.
- 1 percent of GDP increase in transfers to non-Ricardian households:
  - GDP declines slightly under either regime despite positive demand effect.
  - Mechanism: transfers shift household preferences toward leisure, reducing hours worked and output.
  - Consumption rises substantially, implying reductions in transfers would have significant negative welfare effects.

### Multipliers estimated from the DSGE model
- On impact (high capital mobility):
  - Spending multipliers for both government consumption and public investment: 0.65 under the peg and 0.60 under inflation targeting.
  - Implied short-term effect: a reduction of 1 percent of GDP in government consumption or public investment results in a 2/3 of 1 percent drop in GDP in the short term.
  - Multiplier for consumption tax increase: about half that of a spending reduction.
  - GDP multiplier of an increase in transfers to non-Ricardian households: close to zero.
- Cumulative (8-quarter horizon):
  - Cumulative spending multipliers somewhat lower than on impact; multipliers under the peg slightly higher than under IT.
  - Public investment multipliers diverge from government consumption multipliers over the longer term due to public capital accumulation raising productivity.
- Under low capital mobility:
  - Ordering of spending multipliers can reverse.
  - On impact, public investment multiplier is 0.51 under the peg and 0.58 under inflation targeting.
  - Exchange rate depreciation under IT helps maintain private sector demand in this scenario.
- Consumption multipliers:
  - Ratio of change in consumption to each fiscal measure used to gauge welfare impact.
  - Transfers have little impact on GDP but substantial and opposite effects on consumption, particularly for non-Ricardian households.
- Fiscal consolidation tradeoff metric:
  - Ratio of the change in GDP to the change in government debt computed over an 8-quarter horizon; results track cumulative multipliers closely but are slightly higher for both government consumption and public investment.

### Key quantitative summaries and ranges
- Empirical IRF multipliers (8 quarters):
  - Current spending cumulative multiplier: 0.15 after 8 quarters; peak ~0.2.
  - Capital spending cumulative multiplier: 0.75 after 8 quarters; peak ~0.6.
- DSGE on-impact spending multipliers (high capital mobility):
  - Government consumption: 0.65 under peg, 0.60 under IT.
  - Public investment: 0.65 under peg, 0.60 under IT.
- DSGE cumulative behavior:
  - Public investment shows higher longer-term multipliers than consumption due to public capital accumulation.
- Broad ranges and comparisons:
  - Spending multipliers generally range from one-third to two-thirds.
  - Tax multipliers are around half of spending multipliers.
  - Multipliers associated with transfers are lower still and difficult to distinguish from zero.
- Structural and calibration numbers:
  - Current spending: 25-30 percent of GDP (Bolivia).
  - Public investment: >40 percent of total investment.
  - ICOR noted as >5 in some studies.

### Policy implications and recommendations
- Include both public consumption and public investment in fiscal strategy; public investment may yield somewhat higher returns over longer horizons but differences are not large.
- Low tax multipliers imply tax reforms should play a role in fiscal consolidation, though structural and political impediments may limit short- and medium-term revenue increases.
- Reducing transfers:
  - Efficient for GDP but likely to have significant negative welfare and distributive equity effects because transfers materially increase consumption of non-Ricardian households.
- Monetary regime considerations:
  - Multipliers under a peg are normally higher than under inflation targeting when capital is mobile.
  - Under some conditions (low capital mobility), the ordering can reverse; a shift to a float can reduce fiscal multipliers if capital is mobile, potentially easing the short-term output cost of fiscal adjustment.
  - Transition decisions should weigh this effect against clearer benefits of floating exchange rates (resilience to external shocks, preservation of reserves, real exchange rate realignment).
  - Highlights need for coordination between fiscal and monetary policy in a transition to long-run sustainability.

*IMF WORKING PAPERS  Estimating Fiscal Multipliers Under Alternative Exchange Rate Regimes  The Case of Bolivia*

### Annex I. Model Structure

### Annex I. Model Structure

### Households
- Continuum of households indexed by i ∈ [0,1]. Households in interval [0,ω) cannot access financial markets and have no initial capital endowment; they consume disposable income each period. Households in (ω,1] have access to financial markets and own physical capital.
- Utility function (common across agents):
  - u_t(C_t, N_t) = z_{u,t} ln(C_t − hab C_{t−1}) − γ_N N_t^{1+σ_L} / (1+σ_L) + γ_m + 1/(1−σ_M) (M_t / P_t)^{1−σ_M}
  - Parameters: inverse Frisch elasticity σ_L, elasticity of money demand σ_M, scale parameters γ_N and γ_m, habit parameter hab, preference shock z_{u,t} (follows an ARMA process).
- Non-competitive labor market: wedge between marginal rate of substitution and real wage following Schmitt‑Grohé and Uribe (2005) formulation.

### Non-Ricardian Households
- Budget constraint:
  - (1+τ_{c,t}) P_{c,t} C_{r,t} + M_{r,t} = (1−τ_{w,t}) ∫ W_{j,t} N_{r,t}^j dj + M_{r,t−1} + P_{c,t} T_{r,t}
  - Notation: ∫ W_{j,t} N_{r,t}^j dj = labor income; C_{r,t} = per-capita non‑Ricardian consumption; P_{c,t} = consumer price index; τ_{c,t}, τ_{w,t} = marginal tax rates; T_{r,t} = government transfers.
- First‑order conditions (consumption and money demand):
  - (1+τ_{c,t}) Λ_{r,t} P_{c,t} = z_{u,t} / (C_{r,t} − hab C_{r,t−1}) − β hab E_t( z_{u,t+1} / (C_{r,t+1} − hab C_{r,t}) )
  - γ_m (M_{r,t})^{σ_M} + β E_t(Λ_{r,t+1}) − Λ_{r,t} = 0
  - Λ_{r,t} is the Lagrange multiplier.

### Ricardian Households
- Resource constraint:
  - (1+τ_{c,t}) P_{c,t} C̄_{o,t} + P_{x,t} X̄_{o,t} + M̄_{o,t} + B̄_{o,t} + S_t B̄_{o,t}^* = R_{t−1} B̄_{o,t−1} + S_t R_{t−1}^* B̄_{o,t−1}^* + (1−τ_{w,t}) ∫ W_{j,t} N̄_{o,t}^j dj + [ (1−τ_{t}^k) R_{t}^k + τ_{t}^k δ Q_{t−1} ] K̄_{o,t−1} + γ_{com} (1−ω) S_t C̄_{o} P_{c,o,t}^* + T̄_{o,t} + ξ̄_{o,t} + M̄_{o,t−1}
  - Notation: C̄_{o,t} per‑capita Ricardian consumption; X̄_{o,t} investment; P_{x,t} price of investment good; B̄_{o,t} nominal government bond; S_t nominal exchange rate (domestic per foreign); B̄_{o,t}^* foreign‑currency bond. Negative numbers imply debt (footnote).
- After‑tax capital income:
  - [ (1−τ_{k,t}) R_{t}^k + τ_{k,t} δ Q_{t−1} ]
  - R_{t}^k = nominal rate of return on capital; Q_t = nominal price of installed capital; τ_{k,t} = marginal tax rate on capital income.
- Commodity revenue to Ricardian household:
  - γ_{com} (1−ω) S_t C̄_{o} P_{c,o,t}^* where P_{c,o,t}^* = external nominal commodity price; C̄_{o} = constant commodity export flow.
- Investment adjustment cost:
  - f(X̄_{o,t} / X̄_{o,t−1}) = a/2 ( X̄_{o,t} / X̄_{o,t−1} − 1 )^2 ; parameter a controls investment adjustment speed.
- Capital accumulation:
  - K̄_{o,t} = (1−δ) K̄_{o,t−1} + z_{x,t} X̄_{o,t} (1 − f(X̄_{o,t} / X̄_{o,t−1}))
  - z_{x,t} = investment‑specific exogenous shock (ARMA).
- First‑order conditions (consumption, domestic bonds, foreign bonds, investment, capital, money):
  - (1+τ_{c,t}) Λ̄_{o,t} P_{c,t} = z_{u,t} / (C̄_{o,t} − hab C̄_{o,t−1}) − β hab E_t( z_{u,t+1} / (C̄_{o,t+1} − hab C̄_{o,t}) )
  - −Λ̄_{o,t} + β E_t( Λ̄_{o,t+1} R_t ) = 0
  - −Λ̄_{o,t} S_t + β E_t( Λ̄_{o,t+1} S_{t+1} R_t^* ) = 0
  - −Λ̄_{o,t} P_{x,t} + μ_t z_{x,t} (1 − f( X̄_{o,t} / X̄_{o,t−1} ) − f′( X̄_{o,t} / X̄_{o,t−1} ) X̄_{o,t} ) + β E_t( μ_{t+1} z_{x,t+1} f′( X̄_{o,t+1} / X̄_{o,t} ) X̄_{o,t+1}^2 ) = 0
  - −μ_t + β μ_{t+1} (1−δ) + β E_t( Λ̄_{o,t+1} [ (1−τ_{k,t+1}) R_{t+1}^k + τ_{k,t+1} δ Q_t ] ) = 0
  - γ_m (M̄_{o,t})^{σ_M} + β E_t( Λ̄_{o,t+1} ) − Λ̄_{o,t} = 0
  - f′(X̄_{o,t} / X̄_{o,t−1}) = a ( X̄_{o,t} / X̄_{o,t−1} − 1 ) (1 / X̄_{o,t−1}), f′(X̄_{o,t+1} / X̄_{o,t}) = a ( X̄_{o,t+1} / X̄_{o,t} − 1 ) (1 / X̄_{o,t}^2).

### Labor Markets and Wage Setting
- Labor decisions are delegated to a continuum of labor unions (one per labor type j); labor types i uniformly distributed across households.
- Resource constraint for union j: N_{j,t} = ∫_{0}^{1} N_t(j,i) di. (Eq1)
- Labor demand for type j: N_{j,t} = ( W_{j,t} / W_t )^{−ε_w} N_{t}^d. (Eq2) ε_w = elasticity of substitution across labor varieties; N_{t}^d = aggregate labor demand; W_t = aggregate nominal wage index; W_{j,t} = wage fixed by union j.
- Wage rigidity: each period there is a 1−θ_w probability of setting wages optimally. When unable to adjust, unions follow indexation:
  - W_t = W_{t−1} g_z π_{t−1}^{χ_w} π̄^{(1−χ_w)} where π_t = consumer price inflation, π̄ = inflation target, g_z = long‑run productivity growth, χ_w = wage indexation parameter (χ_w = 1 ⇒ full indexation to past inflation).
- Nominal wage s periods after last re‑optimization:
  - W_{j,t+s} = W_t^* ∏_{k=1}^{s} ( g_z π̄^{(1−χ_w)} π_{t+k−1}^{χ_w} )
  - Real wage: w_{j,t+s} = w_t^* X_{t,s}^w where X_{t,s}^w = ∏_{k=1}^{s} ( g_z π̄^{(1−χ_w)} π_{t+k−1}^{χ_w} π_{t+k}^{−1} )
- Union optimality condition (weighted average utility of Ricardian and non‑Ricardian households):
  - U_N(N_{j,t}) = (1−τ_{w,t}) w_t ( ω λ_{r,t} + (1−ω) λ̄_{o,t} ) mct_{t}^w
- When able to set wages, optimal real wage w_t^* satisfies:
  - E_t ∑_{s=0}^∞ (θ_w β)^s { [ (1−ω) 1/MRS_{t+s}^{o} + ω 1/MRS_{t+s}^{r} ] X_{t,s}^w w_t^* − ε_w (ε_w − 1) } = 0
  - MRS definitions:
    - MRS_{t+s}^{o} = (1+τ_{c,t+s})(1−τ_{w,t+s}) U_{N,t+s} / U_{c,t+s}^{o}
    - MRS_{t+s}^{r} = (1+τ_{c,t+s})(1−τ_{w,t+s}) U_{N,t+s} / U_{c,t+s}^{r}
- Wage dispersion/in-efficiency:
  - N_t = ν_{w,t} N_t^d where ν_{w,t} > 1 measures inefficiency from wage dispersion.
  - Recursive law: ν_{w,t} = θ_w ( (w_{t−1} / w_t g_z π_{t−1}^{χ_w} π̄^{1−χ_w} )^{−ε_w} ν_{w,t−1} ) + (1−θ_w) ( (w_t^* / w_t)^{−ε_w} ).
  - Flexible wages ⇒ ν_{w,t} = 1.
- Aggregate real wage index:
  - w_t = [ θ_w ( (w_{t−1} / g_z π_{t−1}^{χ_w} π̄^{1−χ_w} )^{1−ε_w} ) + (1−θ_w) ( w_t^* )^{1−ε_w} ]^{1/(1−ε_w)}.

### Firms

Producers of Final Goods
- Final consumption good combines domestic C_{H,t} and foreign C_{F,t} inputs:
  - C_t = [ (1−α_c)^{1/η_c} C_{H,t}^{(η_c−1)/η_c} + (α_c)^{1/η_c} C_{F,t}^{(η_c−1)/η_c} ]^{η_c/(η_c−1)}
  - η_c = elasticity of substitution; α_c = share of foreign goods.
- First‑order demand conditions:
  - C_{H,t} = (1−α_c) (p_{H,t})^{−η_c} C_t
  - C_{F,t} = α_c (p_{F,t})^{−η_c} C_t
  - p_{H,t} = P_{H,t} / P_{c,t}; p_{F,t} = P_{F,t} / P_{c,t} = rer_t.

Investment Good
- Investment aggregator:
  - X_t = [ (1−α_x)^{1/η_x} X_{H,t}^{(η_x−1)/η_x} + (α_x)^{1/η_x} X_{F,t}^{(η_x−1)/η_x} ]^{η_x/(η_x−1)}
  - First‑order conditions:
    - X_{H,t} = (1−α_x) ( p_{H,t} / p_{x,t} )^{−η_x} X_t
    - X_{F,t} = α_x ( p_{F,t} / p_{x,t} )^{−η_x} X_t
  - p_{x,t} = P_{x,t} / P_{c,t} = relative price of investment (function of domestic and imported prices).

Producers of Domestic Good
- Domestic final good Y_{H,t} produced by continuum of varieties j:
  - Y_{H,t} = ( ∫ Y_{j,t}^{(ε_H−1)/ε_H} dj )^{ε_H/(ε_H−1)} where ε_H = elasticity of substitution across varieties.
- Demand for intermediate variety j and price index:
  - Y_{H,j,t} = ( P_{H,j,t} / P_{H,t} )^{−ε_H} Y_{H,t}^d
  - P_{H,t} = ( ∫ P_{H,j,t}^{1−ε_H} dj )^{1/(1−ε_H)}
- Demand for final domestic goods:
  - Y_{H,t}^d = C_{H,t}^* + C_{g,t} + X_{g,t} + C_{H,t} + X_{H,t}
  - C_{H,t}^* = foreign demand for domestic output (exports); X_{g,t} = public investment.

Intermediate Goods
- Continuum of monopolistic firms l use capital and labor:
  - Y_{H,l,t} = z_{y,t} K_{l,t−1}^{α} Z_t^{1−α−α_g} (N_{l,t})^{1−α} (K_{t−1}^g)^{α_g}
  - α ∈ (0,1) is capital share; Z_t = permanent productivity shock with Z_{t+1} / Z_t = g_{z,t}
    - g_{z,t} = (1−ρ_{gz}) ḡ_z + ρ_{gz} g_{z,t−1} + ε_{z,t}
  - z_{y,t} = transitory productivity shock; K_{t−1}^g = public capital (common to all firms).
- Labor composite input (following Schmitt‑Grohé and Uribe, 2017):
  - N_{l,t} = [ ∫ N_{j,t}^{(ε_w−1)/ε_w} dj ]^{ε_w/(ε_w−1)}. (Eq3)
- Firms choose labor varieties via cost minimization; optimal demand:
  - N_{l,j,t} = ( W_{j,t} / W_t )^{−ε_W} N_{l,t}^d
  - Aggregation yields N_{j,t} = ( W_{j,t} / W_t )^{−ε_W} N_t^d (labor demand used in households).
- Cost minimization optimality conditions:
  - W_t = (1−α) MC_{H,t} Y_{l,t} / N_{l,t}
  - R_t^k = α MC_{H,t} Y_{l,t} / K_{l,t−1}
  - Marginal cost:
    - MC_{H,t} = 1 / ( Z_t^{1−α−α_g} K_{g,t−1}^{α_g} ) ( R_{k,t} / α )^{α} ( W_t / (1−α) )^{1−α}
- Price setting (Calvo pricing):
  - Fraction 1−θ_H firms optimally adjust prices; θ_H follow indexation when not adjusting:
    - π_t^{rH} = π_t^{ι_H} π̄_t^{1−ι_H}; when price not adjusted: P_{H,l,t} = P_{H,l,t−1} π_{t−1}^{ι_H} π̄^{1−ι_H} where ι_H controls degree of price indexation (ι_H = 1 ⇒ full indexation to past inflation).
- Firm profit maximization (nominal):
  - max_{P_{H,l,t}} ∑_{s=0}^∞ (β θ_H)^s E_t [ λ̄_{o,t+s} P_{c,t} Z_t / ( λ̄_{o,t} P_{c,t+s} Z_{t+s} ) ( P_{H,l,t+s} Y_{H,l,t+s} − MC_{H,t+s} Y_{H,l,t+s} ) ] subject to demand Y_{l,t} = ( P_{H,l,t} / P_{H,t} )^{−ε_H} Y_{H,t}^d.
- First‑order condition (stationary variables) leads to recursive system for optimal price p_{H,t}^* and function f_t^H:
  - f_t^H = p_{H,t}^* y_{H,t} + θ_H E_t[ ... f_{t+1}^H ] and
  - f_t^H = ε_H/(ε_H−1) mc_{H,t} y_{H,t} + θ_H E_t[ ... (−ε_H) f_{t+1}^H ]
- Price dispersion and aggregation:
  - Y_{H,t} = ν_{H,t} Y_{H,t}^d where ν_{H,t} = ∫ ( P_{H,l,t} / P_{H,t} )^{−ε_H} dl captures price distortion.
  - Recursive law: ν_{H,t} = θ_H ( π_{t−1}^{rH} / π_{t}^{H} )^{−ε_H} ν_{H,t−1} + (1−θ_H) ( P_{H,t}^* )^{−ε_H }.

### Monetary Policy
- Two regimes modeled: inflation targeting with flexible exchange rates, and a peg regime.
- Inflation targeting rule (central bank controls short‑term nominal interest rate):
  - R_t / R̄ = ( R_{t−1} / R̄ )^{ρ_R} ( ( π_t / π̄ )^{φ_π} )^{1−ρ_R} exp( z_{t}^m )
  - Parameters: ρ_R = smoothing parameter; φ_π = sensitivity to inflation deviations; z_{t}^m = monetary policy shock (exogenous ARMA).
- Peg regime: nominal devaluation rate constant:
  - d_t = S_t / S_{t−1} = d̄
- Central bank balance sheet:
  - M_t = B_{cb,t} + S_t B_{cb,t}^*
  - Flow of funds:
    - M_t − M_{t−1} + R_{t−1} B_{cb,t−1} + R_{t−1}^* S_t B_{cb,t−1}^* = B_{cb,t} + S_t B_{cb,t}^* + P_{c,t} qfb_t
  - Quasi‑fiscal balance qfb_t depends on returns on external and domestic assets, domestic inflation, and real exchange rate.
- Regime adjustment of balance sheet:
  - Inflation targeting: central bank adjusts money supply so short‑term interest rate aligns with policy rate; holdings of external assets constant; net domestic assets adjust endogenously.
  - Peg: central bank adjusts external asset holdings to maintain exchange rate target and accommodates changes via money supply; changes in government assets at central bank lead to changes in foreign asset holdings.

### Fiscal Policy
- Government receipts: taxes on consumption, capital, labor; quasi‑fiscal balance from central bank; commodity sector revenues. Issues public debt to finance overall balance. Central bank holds fraction α_g of government debt; households hold the remainder.
- Real government budget constraint:
  - rer_t p_{c,o,t}^* (1−γ_{com}) C̄_o + Tax_{t}^c + Tax_{t}^l + Tax_{t}^k + b_t + qfb_t = p_{H,t} ( C_{g,t} + X_{g,t} ) + R_{t−1}/π_t b_{t−1} + Tr_t
  - Tax definitions:
    - Tax_{t}^k = τ_{t}^k [ r_{t}^k − δ q_{t−1} / π_t ] K_{t−1}
    - Tax_{t}^l = τ_{t}^l w_t N_t
    - Tax_{t}^c = τ_{t}^c C_t
  - Government consumption and investment (p_{H,t} C_{g,t}, p_{H,t} X_{g,t}) included.
  - In current setup: marginal tax rates, government consumption, government investment are constant (alternative would include fiscal rules).
- Government objective and transfers:
  - Government sets transfers optimally to maximize:
    - U_{p,t} = U(C_t, N_t, m_t) + ω_1 ( b_t^g − b̄^g )^2 + ω_2 ( Tr_t − Tr̄ )^2
    - U(C_t, N_t, m_t) is weighted average of Ricardian and non‑Ricardian utilities.
    - ω_2 (Tr_t − Tr̄)^2 captures cost of adjusting fiscal instrument; ω_1 penalizes public debt deviations from steady state to encourage time consistency.
- Public capital accumulation and investment implementation lags:
  - K_{g,t} = (1−δ) K_{g,t−1} + z_{xg,t} A_{g,t−L}
  - Implemented government investment:
    - X_{g,t} = ∑_{n=0}^{L−1} b_n A_{g,t−n} with ∑_{n=0}^{L−1} b_n = 1.
  - z_{xg,t} = productivity shock in public investment.

### External Sector and Current Account
- External interest rate: R_t^* = R̄_t^* − Ω_u ( exp( rer_t^{ nfa_t / GDP_t } − rer̄^{ nfā / GDP̄ } ) − 1 )
  - Country risk premium is negative function of NFA/GDP; Ω_u = elasticity of country risk to NFA‑to‑GDP ratio. (Eq 4)
- GDP:
  - GDP_t = p_{t}^H Y_{t}^H + rer_t C̄_o P_{c,o,t}^*
- Non‑commodity exports:
  - C_{t}^{h*} = ( p_{t}^H / rer_t )^{−ε_e} C_t^* where C_t^* proportional to external output and ε_e elasticity of exports to exchange rate.
- Balance of payments (aggregating household, government, central bank constraints):
  - rer_t ( nfa_t − nfa_{t−1} ) = [ ( p_t^H C_{t}^{H*} + C̄_o rer_t P_{c,o,t}^* ) − rer_t ( C_{t}^m + X_t^m ) ] + ( R_{t−1}^* / π_{t}^* − 1 ) rer_t nfa_{t−1}^*
  - Net foreign asset position in domestic currency: nfa_t = b_t^* + b_{cb,t}^*.
- Footnote definition: Real net foreign assets defined as nfa_t = b_{cb,t−1}^* − b̄_{o,t−1}^*.

*Annex I adapted from the annex to “Fix vs float: Evaluating the Transition to a Sustainable Equilibrium in Bolivia” (WP/22/43); provided for reference.*

### References

### References (from "Estimating Fiscal Multipliers Under Alternative Exchange Rate Regimes: The Case of Bolivia")

### Theoretical and methodological contributions
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- Chahrour, Ryan, Stephanie Schmitt-Grohé, and Martín Uribe, 2012, "A Model-Based Evaluation of the Debate on the Size of the Tax Multiplier." American Economic Journal: Economic Policy, 4 (2): 28-45.
- Christiano, Lawrence, Martin Eichenbaum, and Sergio Rebelo, 2011, “When Is the Government Spending Multiplier Large?” Journal of Political Economy, Vol. 119, No. 1, pp. 78–121.
- Galí, Jordi, J. David López-Salido, and J. Vallés, 2007, "Understanding the Effects of Government Spending on Consumption," Journal of the European Economic Association, MIT Press, Vol. 5(1): 227-270.
- Leeper, Eric M., Nora Traum, and Todd B. Walker, 2017, “Clearing Up the Fiscal Multiplier Morass,” American Economic Review,” 107(8):2409–54.
- Mountford, Andrew, and Harald Uhlig, 2009, “What are the Effects of Fiscal Policy Shocks?” Journal of Applied Econometrics, Vol. 24, No. 6, pp. 960-992.
- Ramey, Valerie A., 2011, “Can Government Purchases Stimulate the Economy?” Journal of Economic Literature, 49, 673–85.
- Ramey, Valerie A., 2019, “Ten Years After the Financial Crisis: What Have We Learned from the Renaissance in Fiscal Research?” Journal of Economic Perspectives, Vol. 33, No. 2, pp. 89-114.
- Romer, C. D., & Romer, D. H., 2010, The macroeconomic effects of tax changes: estimates based on a new measure of fiscal shocks. American Economic Review, 100(3), 763-801.
- Schmitt-Grohé, S., and M. Uribe, 2005. "Optimal Fiscal and Monetary Policy in a Medium-Scale Macroeconomic Model." NBER Macroeconomics Annual 20: 383-425.
- Schmitt-Grohé, Stephanie, and Martín Uribe, 2017, Open Economy Economics. Princeton University Press.
- Woodford, Michael, 2011, "Simple Analytics of the Government Expenditure Multiplier." American Economic Journal: Macroeconomics, 3 (1): 1-35.

### Empirical evidence on fiscal multipliers and fiscal policy effectiveness
- Auerbach, Alan J., and Yuriy Gorodnichenko, 2012, “Measuring the Output Responses to Fiscal Policy,” American Economic Journal: Economic Policy, Vol. 4, No. 2, pp. 1-27.
- Attinasi, Maria, and Alexander Klemm, 2016, “The growth impact of discretionary fiscal policy measures,” Journal of Macroeconomics, Vol. 49, pp. 265-279.
- Brinca, P., H. A. Holter, P. Krusell, and L. Malafry ,2016, “Fiscal Multipliers in the 21st Century,” Journal of Monetary Economics, 77, 53 – 69.
- Canzoneri, Matthew, Fabrice Collard, Harris Dellas, and Behzad Diba, 2016, “Fiscal Multipliers in Recession,” The Economic Journal, Vol. 126, No. 590, pp.75-108.
- Chodorow-Reich, Gabriel, 2019, “Geographic Cross-Sectional Fiscal Spending Multipliers: What Have We Learned?” American Economic Journal: Economic Policy, Vol. 11, No. 2, pp. 1-34.
- Coenen, G., C. J. Erceg, C. Freedman, D. Furceri, M. Kumhof, R. Lalonde, D. Laxton, J. Lindé, A. Mourougane, D. Muir, S. Mursula, C. de Resende, J. Roberts, W. Roeger, S. Snudden, M. Trabandt, and J. in’t Veld, 2012, “Effects of Fiscal Stimulus in Structural Models,” American Economic Journal: Macroeconomics, Vol. 4, No. 1, pp. 22–68.
- Corsetti, G., Meier, A., Müller, G. J., & Devereux, M. B, 2012, “What determines government spending multipliers?” Economic Policy, 27(72), 521–565.
- Dolls, M., C. Fuest, and A. Peichl, 2012, “Automatic Stabilizers and Economic Crisis: US vs. Europe,” Journal of Public Economics, Vol. 96, pp. 279–94.
- Galí, Jordi, J., David López-Salido, and J. Vallés, 2003, "Understanding the effects of government spending on consumption," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
- Guajardo, Jamie, Daniel Leigh, and Andrea Pescatori, 2014, “Expansionary Austerity? International Evidence,” Journal of the European Economic Association, Vol. 12, No.4, pp. 949-968.
- Ilzetzki, Ethan, Enrique G. Mendoza, and Carlos A. Végh, 2013, “How Big (Small?) are Fiscal Multipliers?” Journal of Monetary Economics, Vol. 60, No. 2, pp. 239-254.
- Miyamoto, Hiroaki, Anja Baum, Nikolay Gueorguiev, Jiro Honda, and Sébastien Walker, 2020, “Growth Impact of Public Investment and the Role of Infrastructure Governance,” in Well Spent: How Strong Infrastructure Governance Can End Waste in Public Investment, ed. by Gerd Schwartz, Manal Fouad, Torben S. Hansen, and Genevieve Verdier (Washington: International Monetary Fund).
- Nakamura, Emi, and Jon Steinsson, 2014, “Fiscal Stimulus in a Monetary Union: Evidence from US Regions,” American Economic Review, Vol.104, No. 3, pp.753-792.
- Ramey, Valerie. A., and Matthew D. Shapiro, 1998, “Costly Capital Reallocation and the Effects of Government Spending,” Carnegie-Rochester Conference Series on Public Policy, Vol. 48, pp. 145-194.
- Restrepo, Jorge, 2020, “How Big are Fiscal Multipliers in Latin America?”, IMF Working Paper 20/17 (Washington: International Monetary Fund).

### Country and region-focused empirical studies and policy notes
- Anós-Casero, P., D. Cardero, and R. Trezzi, 2010, “Estimating the Fiscal Multiplier in Argentina,” World Bank Policy Research Working Paper 5220 (Washington: World Bank).
- Cerisola, Martin, Chadi Abdallah, Victor Davies, and Mark Fischer, 2015, Assessing The Impact Of Fiscal Shocks On Output In MENAP Countries, IMF Technical Notes and Manuals 15/01 (Washington: International Monetary Fund).
- David, M. A. ,2017, Fiscal Policy Effectiveness in a Small Open Economy: Estimates of Tax and Spending Multipliers in Paraguay. IMF Working paper 17/63 (Washington: International Monetary Fund).
- Dime, Roselle, Edimon Ginting, and Juzhong Zhuang, 2021, “Estimating Fiscal Multipliers in Selected Asian Economies,” Asia Development Bank, Economics Working Paper Series, No. 638 (Manila: Asian Development Bank).
- Ducanes, G., Cagas, M. A., Qin, D., Quising, P. F., & Razzaque, M. A., 2006, Macroeconomic effects of fiscal policies: empirical evidence from Bangladesh, China, Indonesia and the Philippines. Asia Development Bank, ERD Working Paper Series No. 85.
- Endegnanew, Y., and D. Tessema, 2019. Public Investment in Bolivia: Prospects and Implications. IMF Working paper 19/151 (Washington: International Monetary Fund).
- Fornero, J., Guerra-Salas, J. and Pérez, C, 2019, "Fiscal Multipliers in Chile". Journal Economía Chilena , 22 (1), 58-80.
- Izquierdo, Alejandro, Ruy E. Lama, Juan Pablo Medina, Jorge P. Puig, Daniel Riera-Crichton, Carlos A. Végh, and Guillermo Vuletin, 2019, “Is the Public Investment Multiplier Higher in Developing Countries? An Empirical Investigation,” NBER Working Paper No. 26478 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Matheson, T., and J. Pereira, 2016, Fiscal Multipliers in Brazil. IMF Working Paper 16/079.
- Narita, M., 2014, Chapter 8. Fiscal Multipliers in the Caribbean. In Caribbean Renewal. USA: International Monetary Fund (Washington: International Monetary Fund).
- Restrepo, Jorge, 2020, “How Big are Fiscal Multipliers in Latin America?”, IMF Working Paper 20/17 (Washington: International Monetary Fund).
- Valencia, F. 2016, “Fiscal Multipliers in Mexico,” in Mexico: Selected Issues, Country report 15/314 (Washington, DC: International Monetary Fund).
- Vtyurina, S., and Z., Leal, 2016, "Fiscal Multipliers and Institutions in Peru: Getting the Largest Bang for the Sol ", IMF Working Paper 14/144 (Washington: International Monetary Fund).
- Valdivia, J., 2017. Impacto del gasto de capital del SNPF sobre el crecimiento economico de Bolivia en el periodo 2016-2016. Cuadernos de Investigación Económica Boliviana - Vol. 2(1), Dic. 2017
- Valdivia, D., and M., Montenegro, 2020, "Reglas Fiscales en Bolivia en el contexto de un Modelo de Equilibrio Dinámico General Estocástico ", Banco Central de Bolivia, unpublished manuscript, available at https://www.bcb.gob.bo/webdocs/EEB/Valdivia%20%20Montenegro_Paper.pdf.
- Gonzalez, Andres, Etibar Jafarov, Diego Rodriguez Guzman, and Chris Walker, 2022, “Fix vs. Float: Evaluating the Transition to a Sustainable Equilibrium in Bolivia”, IMF Working Paper 22/043 (Washington: International Monetary Fund).
- Endegnanew, Y., and D. Tessema, 2019. Public Investment in Bolivia: Prospects and Implications. IMF Working paper 19/151 (Washington: International Monetary Fund).

### IMF staff notes, datasets, models, and broader policy literature
- Anderson, D., B. Hunt, M. Kortelainen, M. Kumhof, D. Laxton, D. Muir, S. Mursula, and S. Snudden, 2013, “Getting to Know GIMF: The Simulation Properties of the Global Integrated Monetary and Fiscal Model,” IMF Working Paper 13/55 (Washington: International Monetary Fund).
- Batini, N., L. Eyraud, and A. Weber, 2014, “A Simple Method to Compute Fiscal Multipliers,” IMF Working Paper 14/93 (Washington: International Monetary Fund).
- Baum, Anja, Marcos Poplawski Ribeiro, and Anke Weber, 2012, “Fiscal Multipliers and the State of the Economy,” IMF Working Paper No. WP/12/286 (Washington: International Monetary Fund).
- Geli, J. F., & Moura, A. S., 2023, Getting into the Nitty-Gritty of Fiscal Multipliers: Small Details, Big Impacts. IMF Working Paper No. 2023/029 (Washington: International Monetary Fund).
- Goldsmith-Pinkham, Paul, Isaac Sorkin, and Henry Swift, 2020, “Bartik Instruments: What, When, Why, and How,” American Economic Review, Vol. 110, No. 8, pp. 2586-2624.
- Honda, M. J., Miyamoto, H., & Taniguchi, M., 2020), Exploring the output effect of fiscal policy shocks in low income countries. IMF Working Paper No. 2020/012 (Washington: International Monetary Fund).
- Ilzetzki, E., 2011, “Fiscal Policy and Debt Dynamics in Developing Countries,” Policy Research Working Paper Series 5666 (Washington: The World Bank).
- IMF, 2008, “Fiscal Policy as a Countercyclical Tool,” in World Economic Outlook October 2008: Financial Stress, Downturns, and Recoveries (Washington: International Monetary Fund).
- IMF, 2019, Fiscal Monitor, Chapter 2, Curbing Corruption.
- Kass-Hanna, T., K. Kpodar, D. Tessema, 2020, “Public Investment over the Fiscal Cycle”. Well Spent, 2, 85.
- Kinda, Tidiane, Andras Lengyel, and Kaustubh Chahande, 2022, “Fiscal Multipliers During Pandemics,” IMF Working Paper No. 2022/149 (Washington: International Monetary Fund).
- Mineshima, Aiko, Marcos Poplawski-Ribeiro, and Anke Weber, 2014, “Size of Fiscal Multipliers” in Post-Crisis Fiscal Policy, ed. by Carlo Cottarelli, Philip Gerson, and Abdelhak Senhadji (Cambridge, Massachusetts: MIT Press).
- Spilimbergo, A., S. Symansky, and M. Schindler, 2009, “Fiscal Multipliers,” IMF Staff Position Note 09/11 (Washington: International Monetary Fund).
- Organisation for Economic Co-operation and Development, 2009, “The Effectiveness and Scope of Fiscal Stimulus,” OECD Economic Outlook Interim Report (Paris).
- European Commission, 2010, “Fiscal Policy, Debt Reduction, and Growth after the Crisis,” chapter III of Public Finances in EMU (Brussels).
- Farhi, Emmanuel, and Iván Werning. 2017, "Fiscal Unions." American Economic Review, 107 (12): 3788-3834.

*Estimating Fiscal Multipliers Under Alternative Exchange Rate Regimes: The Case of Bolivia — Working Paper No. WP/2023/240*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023240-print-pdf.pdf_