## 1. Inflation in Uruguay

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### Introduction and context
- The relationship between wage setting and CPI inflation is key for monetary policy in an inflation targeting regime; wage demands after inflationary shocks can create "second round effects" that increase inflation persistence.
- Recent global inflation episode (2021–2022): CPI inflation rose from below 2 percent in early 2021 to 9 percent in mid-2022; employment cost indices picked up with a lag.
- Uruguay: small open economy, highly centralized wage setting, prevalent indexation practices, and historically low central bank credibility with inflation expectations generally remaining outside the target range.

### Reduced-form empirical findings on wages
- Nominal wage growth relates to:
  - its own lag,
  - a price inflation indexing variable,
  - the level of the unemployment rate.
- Productivity growth can replace unemployment in specifications and acts as a driving force for nominal wage growth.
- Wage indexation and partial nominal wage adjustment are important features of wage formation in Uruguay.
- Selected empirical estimates and statistics (preserving reported values):
  - Sample: 1999Q1 to 2022Q4, quarterly.
  - Lagged nominal wage growth (rho): about 0.4–0.45 (examples: 0.41***, 0.44***, 0.45***, 0.35***, 0.38***, 0.45***).
  - Unemployment level coefficient (Gamma): approximately -0.18 to -0.2.
  - Indexation (Beta) examples from Table 1: 0.29**, 0.23**, 0.3, 0.48**, 0.24***, 0.36*.
  - Alpha intercept examples: 3.4***, 3.48***, 3.47***, 3.2***, 3.48***, 3.45***.
  - Adjusted R2 examples: 0.45, 0.46, 0.44, 0.43, 0.4, 0.44. SE regression examples: 0.73, 0.73, 0.74, 0.75, 0.77, 0.74.
  - When productivity (average of last 5 years) included, high negative correlation with unemployment: -0.84.
  - Table 2 highlights (with productivity): Gamma (productivity coefficient) examples: 0.17***; Rho examples: 0.43***, 0.46***, 0.46***, 0.43***, 0.49***, 0.49***. Alpha examples: 1.5***, 1.59***, 1.66***, 1.27***, 1.79***, 1.64***. Beta examples: 0.21, 0.17, 0.14, 0.38*, 0.16*, 0.2. Adjusted R2 examples: 0.45, 0.45, 0.44, 0.43, 0.44, 0.43. SE regression examples: 0.73, 0.73, 0.74, 0.74, 0.74, 0.75.
- Main reduced-form conclusions:
  - Wages react to labor market indicators—either unemployment level or medium-term productivity growth.
  - Strongest evidence for partial indexation to lagged annual CPI inflation; weak evidence for indexation to expected inflation.
  - Compared to an EM panel (WEO Oct 2022 Chapter 3), the change in unemployment is significant for the EM group but not for Uruguay.

### DSGE model, estimation, and quantitative results
- Model features:
  - Medium-scale open economy New Keynesian DSGE based on Adrian et al. (2021), modified to include wage rigidities and indexation; estimated with Bayesian methods.
  - Includes staggered price and wage setting (Calvo-style) with indexation rules.
  - Incomplete international financial markets and domestic credit/FX frictions (Gabaix and Maggiori (2015) agency friction "Γ").
  - Local currency pricing (LCP) for export prices, sticky import prices, discounting and habit formation, and endogenous borrowing spreads.
- Wage indexation and timing (model estimation outcomes):
  - Wages reset optimally once every six quarters.
  - Wages indexed more to lagged annual CPI inflation with coefficient 0.67 than to lagged nominal wage growth with coefficient 0.33.
  - Prices reset optimally about once a year with substantial indexation in the domestic inflation Phillips Curve.
- Financial and calibration details (preserving calibrated values):
  - Agency friction Γ estimated posterior mean about 0.015 (also reported about 0.02 elsewhere).
  - Baseline estimation sample: 2005:Q1–2023:Q1.
  - Selected calibrated parameters:
    - Reserves relative to quarterly GDP 0.84
    - Household subjective discount factor 0.9999
    - Steady-state inflation (APR) 6
    - Steady-state real rate (APR) 2
    - Share of government expenditure in GDP 0.258
    - Share of imports in exports 0.118
    - Share of exports and imports in GDP 0.297
    - Share of import goods in consumption 0.353
    - Term premium (APR) 1.5
    - Real growth rate (quarterly, in gross terms) 1.005
    - Capital elasticity in production function 0.3
    - Frisch elasticity of substitution 2
    - Import price elasticity 0.8
    - Export price elasticity 0.8
    - Marginal rate of consumption/leisure substitution 2.857143
    - Coefficient of relative risk aversion 1
    - Wage mark-up (net) 0.333333
    - Ownership share of financial intermediaries/investors 0.8
    - NFA relative to quarterly GDP -1.012
    - Price mark-up (net) 0.5
    - Kimball curvature 12
- Estimated posterior highlights (preserving values/text):
  - Calvo parameter for domestic prices ~ 0.66 (prices reset about once a year).
  - Calvo parameter for wages ~ 0.75 (wages reset about once every six quarters).
  - Domestic price indexation coefficient ~ 0.7.
  - Wage indexation posterior mean ~ 0.5 in prior block; model-specific posterior interpreted as 0.67 to CPI and 0.33 to lagged wage growth.
  - FX market friction Γ posterior ~ 0.015 (or about 0.02 noted).
  - Interest rate response to CPI inflation about 0.7.
  - Degree of interest rate inertia (smoothing) about 0.7.
  - FX intervention rule: response to change in exchange rate about 0.2; persistence of FXI about 0.45.

### Counterfactual and policy experiment results
- Counterfactual scenarios considered:
  - Wages indexed only to steady-state inflation (central bank target) instead of lagged annual CPI inflation and lagged wage growth.
  - Reduce backward-looking behavior in domestic price Phillips Curve by setting 휄휄푝 = 0.48 (EM average) instead of Uruguay estimated 0.76.
  - FX intervention switched off for experiments (훾훾Δs = 0), so central bank uses interest rates only.
- Marginal Likelihood model comparison (preserving entries):
  - Yes / Lagged Annual: Marginal Likelihood -2985.6 (ranked highest among variants shown).
  - Yes / Lagged Quarterly: -2992.2
  - Yes / Steady State: -2992.8
  - No / Lagged Annual: -2992.8
  - No / Lagged Quarterly: -2990.9
  - No / Steady State: -2992.0
- Impulse response and shock experiment highlights (preserving reported magnitudes and qualitative outcomes):
  - Global risk (capital outflow) shock:
    - Estimated model: real depreciation ≈ 5 percent; CPI increases peak after 4 quarters at about 0.5 percent above target; nominal wage growth peaks about 8 quarters after the shock.
    - Counterfactual (wages indexed to target): muted wage inflation response → faster return of CPI to target; smaller monetary tightening; more favorable output gap dynamics.
    - Reducing backward-looking price Phillips Curve yields smaller improvement than removing wage backward-looking indexation.
  - Domestic demand shock (consumption preference shock):
    - Estimated model: higher output gap and inflation, gradual pick up of wage growth leading to persistent CPI inflation; central bank tightens; exchange rate initially appreciates then depreciates.
    - Counterfactuals without wage backward-looking indexation: muted wage growth response; inflation returns faster to target; less tightening and larger output gap effect. Improved price Phillips Curve forward-lookingness improves inflation between three and ten quarters but overall small macro change.
  - Wage mark-up shock:
    - Estimated model: higher labor costs raise CPI inflation; central bank tightens; output gap declines via lower domestic demand and appreciation; CPI response hump-shaped and highly persistent due to wage indexation feedback.
    - Counterfactuals: CPI peak is lower (about two thirds of estimated economy peak) and returns faster to steady-state; central bank tightens less; smaller output gap contraction.
  - Price mark-up shock:
    - Estimated model: domestic inflation increase triggers delayed nominal wage growth feeding back into CPI and policy tightening, lowering output gap.
    - Counterfactuals (removing wage indexation and/or improving price Phillips Curve forward-lookingness): both lower inflation persistence, reduce required policy tightening, and lessen output gap costs.
- Aggregate takeaway:
  - Indexation and partial nominal wage adjustment produce persistent CPI inflation responses because wages react with lags and feed back through labor costs and real marginal costs.
  - Indexing wages to the inflation target (steady-state) would reduce CPI inflation persistence by muting wage-price feedback; in some cases the initial inflation response would also be lower.
  - Wage indexation to past inflation acts as insurance to monetary shocks but increases inflation persistence and worsens stabilization trade-offs.
  - Improving central bank credibility and reducing backward-looking indexation lowers inflation persistence and output costs of returning inflation to target; however, reducing backward-looking price Phillips Curve has quantitatively smaller effects than changing wage indexation.

### Monetary policy transmission and FX interventions
- Interest rate shock transmission (reported magnitudes):
  - Domestic interest rate increase of about 130bps (estimated annualized standard deviation) leads to:
    - Output gap decline ≈ 0.3 percent.
    - Exchange rate appreciates ≈ 1 percent.
    - CPI inflation reaction muted, peaking at about 0.1 percent.
  - Removing wage indexation to lagged inflation reduces inflation persistence; reducing backward-looking behavior in domestic price Phillips Curve has smaller quantitative effect.
- FX intervention effects:
  - Historical FX rule: a global risk shock depreciation induced selling of FX reserves ≈ 0.7 percent of GDP to offset depreciation.
  - Quantitative macro effects of FXI on exchange rate, inflation, output, and interest rates are very small and similar to no-FXI responses, reflecting small estimated Γ (about 0.02 or 0.015).
  - Caveat: Γ may be state-dependent and larger in crises; Uruguay has not experienced large financial stress episodes over the last two decades, complicating identification.

### Wage bargaining in Uruguay — institutional features and evolution
- Historical and institutional highlights:
  - Collective bargaining introduced in 1943 (Law 10.449); resumed and expanded with Law 18.566 in 2009 extending wage setting to all workers.
  - Highly centralized, tripartite bargaining (labor unions, employers, government) coordinated by the Tripartite Superior Council (TSC): 9 government members, 6 representing workers, 6 representing employers, plus substitutes.
  - Currently 24 sectors (with subdivisions); ten rounds of negotiations since 2005.
- Government role and contract features:
  - Executive Power convenes the TSC and issues guidelines ("pautas") on suggested wage increases; government ratifies and issues decrees for agreements and may submit alternative proposals to vote if no agreement.
  - Typical contract adjustment components:
    1. expected inflation,
    2. “correctivo” to compensate when past actual inflation exceeded expected inflation,
    3. “recuperación” (recovery or real growth, partially reflecting aggregate productivity improvements).
  - Agreement duration has increased to about two years for most agreements; wage adjustment frequency predominantly semi-annual.
  - Measures of expected inflation used evolved from past inflation/private analysts to central bank measures and, most recently, the government's expected inflation published in "Rendición de Cuentas".
- Legal and institutional changes:
  - Law 20.145 (approved May 2023) addressed ILO recommendations points 1–5; remaining point addressed in 2012.
  - Key legal changes: expired contracts cease to apply unless a new agreement is signed; employers’ and workers’ associations required to have recognized legal status; implication that companies cannot withhold employee union contributions unless workers’ association formalizes registration.
  - Tenth bargaining round covers July 2023–June 2025; government guidelines (June 2023) aimed at recovering real wages to pre-pandemic levels where not recovered.
  - After announcement, inflation declined faster than expected in the second half of 2023; government adjusted downwards public sector wage increases in January 2024 to reflect the decline in inflation expectations.
  - Noted asymmetry in adjustments: positive corrections when inflation exceeds expectations, but no symmetric reduction when inflation is below expectations.

### Institutional criticisms and legal recommendations (ILO)
- 2010 ILO review recommended aligning legislation with International Labor Conventions; recommendations included (as reported):
  1. Employers’ and workers’ organizations should have recognized legal status for confidential information exchange and organizational responsibility for non-compliance.
  2. Level of negotiation should be determined by workers and employers, not subject to a tripartite vote.
  3. Agreements should not need government ratification ("homologacion"); government role should be circumscribed to communication.
  4. Eliminate "ultraactividad" (agreements remaining valid after expiry).
  5. If no union at company level, workers could designate a representative to negotiate instead of defaulting to sector union.
  6. Minimum wages can be set tripartitely but other labor relation conditions should be bipartite.

### Conclusions
- The paper documents a highly centralized wage bargaining system and widespread wage indexation in Uruguay, linked to historically low central bank credibility.
- Reduced-form and DSGE evidence:
  - Nominal wage growth shows partial adjustment and indexation to lagged annual CPI; reacts to unemployment level or productivity growth.
  - DSGE estimates confirm partial nominal wage adjustment, lagged indexation to annual CPI inflation, and a domestic price inflation Phillips Curve with significant backward-looking behavior.
  - These features imply high inflation persistence in response to shocks.
- Policy implications:
  - Indexing wages to the inflation target (steady-state) rather than past inflation would mute price-wage feedbacks, reduce CPI inflation persistence, and yield a more favorable trade-off for monetary policy.
  - Improving central bank credibility and reducing backward indexation are complementary: reducing backward-looking price Phillips Curve yields smaller quantitative gains than changing wage indexation, and changes in indexation practices are more likely when inflation is stable around the target.
  - FX interventions, given estimated parameters, show quantitatively small benefits on average; state-dependent estimation of FX frictions is a suggested extension.

*Source: IMF WORKING PAPERS — Examining Price-Wage Dynamics in a Small Open Economy: The Case of Uruguay*

### 1. Inflation in Uruguay ................................................................................................

### 1. Inflation in Uruguay

### Introduction and context
- The relationship between wage setting and CPI inflation is key for monetary policy in an inflation targeting regime; wage demands after inflationary shocks can create "second round effects" that increase inflation persistence.
- Recent global inflation episode (2021–2022): CPI inflation rose from below 2 percent in early 2021 to 9 percent in mid-2022; employment cost indices picked up with a lag, raising concerns about price-wage spirals.
- Uruguay is a small open economy exposed to multiple domestic and external shocks, with a highly centralized wage setting process and prevalent indexation practices.
- The central bank of Uruguay historically had low credibility, with inflation expectations generally remaining outside the target range.

### Reduced-form empirical findings on wages
- Nominal wage growth relates to:
  - its own lag,
  - a price inflation indexing variable,
  - the level of the unemployment rate.
- Specifications where labor productivity growth replaces the unemployment rate indicate productivity growth is also a driving force for nominal wage growth.
- Wage indexation and partial nominal wage adjustment are important features of wage formation in Uruguay.

### DSGE model, estimation, and quantitative results
- A medium-scale open economy New Keynesian DSGE model (based on Adrian et al. (2021)) is modified to include wage rigidities and indexation and estimated with Bayesian methods on Uruguayan data.
- Estimated model parameters confirm:
  - partial nominal wage adjustment,
  - lagged indexation to annual CPI inflation in the wage formation process,
  - a domestic price inflation Phillips Curve with a significant degree of backward-looking behavior (indicative of low central bank credibility).
- These features imply high inflation persistence in response to shocks.

### Counterfactual and policy experiment results
- Counterfactual: wages are sticky but indexed to the central bank inflation target.
  - Result: muted price-wage feedback effects, CPI inflation exhibits less persistence.
  - The central bank faces a more favorable trade-off between stabilizing inflation and the output gap.
- Lowering inertia in the price inflation Phillips Curve to the Emerging Markets (EM) average further decreases inflation persistence, though this channel is quantitatively less important than wage indexation.
- Overall: improving central bank credibility and reducing backward indexation would lower inflation persistence and the output costs of returning inflation to target.
- Foreign exchange interventions (FXI):
  - Model includes financial frictions (as in Gabaix and Maggiori (2015)) that break uncovered interest rate parity and allow the central bank to influence the exchange rate via reserves.
  - Given estimated parameters, there are no significant benefits from using FXI as an additional policy tool in Uruguay.

### Wage bargaining in Uruguay — institutional features and evolution
- Key historical and structural points:
  - Collective bargaining introduced in 1943 (Law 10.449); bargaining paused at times and resumed in 2005; since 2009 governed by Law 18.566 extending wage setting to all workers.
  - Uruguay’s wage bargaining is highly centralized (illustrated by the "Flexible Wage Determination" index where a lower value denotes more centralized bargaining).
  - Bargaining is tripartite: labor unions, employers, and the government; agreements negotiated at sectoral level.
  - The Tripartite Superior Council (TSC) coordinates labor relations: 9 government members, 6 representing workers, 6 representing employers, plus substitutes.
  - Currently 24 sectors (with subdivisions); since 2005 there have been ten rounds of negotiations.
- Government role in bargaining:
  - Executive Power convenes the TSC to start negotiations; government issues guidelines ("pautas") on suggested wage increases.
  - Government ratifies and issues decrees for agreements; if no agreement, government submits an alternative proposal to vote.
- Contract features and changes over time:
  - Contracts typically include three components for adjustment:
    1. expected inflation,
    2. “correctivo” to compensate when past actual inflation exceeded expected inflation,
    3. “recuperación” (recovery or real growth, partially reflecting aggregate productivity improvements).
  - Duration of agreements has increased and is currently about two years for most agreements.
  - Frequency of wage adjustment is predominantly semi-annual.
  - Earlier rounds experimented with productivity-based adjustments; most recent rounds have not included productivity components.
  - Recent rounds have split sectors by pandemic impact and differentiated adjustments by company size and sectoral employment recovery (noted for June 2023).
- Measures of expected inflation used in negotiations have evolved:
  - Initially allowed selection among past inflation, private analysts’ expectations, etc.
  - Over time moved to using central bank’s measure of inflation expectation.
  - In most recent rounds, the government’s expected inflation as published in its fiscal reports to Congress ("Rendición de Cuentas") has been used.

### Institutional criticisms and legal recommendations (ILO)
- A 2010 ILO review following complaints recommended aligning Uruguayan legislation with International Labor Conventions; most recommendations have been addressed. Recommendations included:
  1. Employers’ and workers’ organizations should have recognized legal status to ensure appropriate exchange of confidential information and organizational responsibility for non-compliance.
  2. The level of negotiation should be determined by workers and employers and not be subject to a tripartite vote.
  3. Agreements should not need to be ratified ("homologacion") by the government; the government’s role should be circumscribed to communication.
  4. The possibility that agreements remain valid after expiry ("ultraactividad") should be eliminated.
  5. If there is no union at the company level, workers could designate a representative to negotiate with the company instead of defaulting to the sector union.
  6. Minimum wages can be set in a tripartite setting but other labor relation conditions should be set in a bipartite negotiation.

*Source: IMF WORKING PAPERS — Examining Price-Wage Dynamics in a Small Open Economy: The Case of Uruguay*

### 7. Equal representation in the TSC.

### 7. Equal representation in the TSC.

### Legal and institutional changes to bargaining
- Law 20.145 (approved May 2023) addressed points 1–5 noted previously; the remaining point had been addressed in 2012.
- Key legal changes:
  - Once a contract expires, its terms cease to apply unless a new agreement has been signed.
  - Employers’ and workers’ associations are required to have recognized legal status.
  - Implication: unless the workers’ association formalizes their registration, companies cannot withhold the employee contribution to the union.
- Recent bargaining round:
  - The tenth round covers July 2023–June 2025.
  - Government guidelines (June 2023) aimed at recovering real wages to pre-pandemic levels in sectors where these had not been recovered.
  - Following the announcement, inflation declined faster than expected in the second half of 2023; as a result the government adjusted downwards the increase in public sector wages in January 2024 to reflect the decline in inflation expectations.
  - The wage adjustment measure is described as unusual given Uruguay’s inflation dynamics and the de facto asymmetry in adjustments by which if inflation is above expected inflation there is a positive adjustment, but the opposite does not hold.

### Aggregate wage dynamics — reduced-form evidence
- Structural wage equation estimated (sample 1999Q1 to 2022Q4, quarterly), based on Galí (2011) and augmented with lagged nominal wage growth (partial adjustment) and different indexation specifications:
  - Dependent variable: quarterly wage inflation (휋휋푡푤).
  - Explanatory variables include: unemployment level (푢푢푡), change in unemployment (∆푢푢푡), and a reference price inflation variable (indexing variable).
  - Indexing variables considered: (a) lagged annual (year-on-year) CPI inflation, (b) lagged quarterly (quarter-on-quarter) CPI inflation, (c) CPI inflation expectations from Consensus Forecasts.
  - Estimation methods: OLS and GMM (instruments: two lags of nominal wage growth, CPI inflation, and unemployment rate).
- Empirical findings (summary):
  - The (negative) relationship between the level of unemployment and wage growth is always significant across specifications (Gamma ≈ -0.18 to -0.2 in Table 1).
  - The change in the unemployment rate (Delta) is not statistically significant in the reported specifications, although it has the expected sign in some alternative estimations.
  - Lagged nominal wage growth (rho) indicates inertia: estimated effect of lagged dependent variable about 0.4–0.45 across specifications (examples from Table 1: Rho 0.41***, 0.44***, 0.45***, 0.35***, 0.38***, 0.45***).
  - Indexation variable importance:
    - Highest coefficients obtained with lagged annual CPI inflation, especially under GMM (example point estimate in text: 0.48).
    - Table 1 Beta coefficients examples (preserving entries): Beta 0.29**, 0.23**, 0.3, 0.48**, 0.24***, 0.36* (standard errors shown in table).
  - Table 1 Alpha intercept examples: Alpha 3.4***, 3.48***, 3.47***, 3.2***, 3.48***, 3.45*** (with reported standard errors).
  - Adjusted R2 examples from Table 1: 0.45, 0.46, 0.44, 0.43, 0.4, 0.44. SE regression examples: 0.73, 0.73, 0.74, 0.75, 0.77, 0.74.
  - When productivity growth (average of last 5 years) is included with unemployment, neither is significant—likely due to high negative correlation between labor productivity growth and unemployment in Uruguay (-0.84).
  - When estimated with productivity growth only (excluding unemployment terms), productivity growth is significant for wage dynamics.
- Table 2 (wage inflation with productivity) highlighted results:
  - Alpha examples: 1.5***, 1.59***, 1.66***, 1.27***, 1.79***, 1.64*** (standard errors reported).
  - Beta examples: 0.21, 0.17, 0.14, 0.38*, 0.16*, 0.2 (with reported standard errors).
  - Gamma (productivity coefficient) examples: 0.17*** consistently in Table 2.
  - Rho (lagged wage growth) examples: 0.43***, 0.46***, 0.46***, 0.43***, 0.49***, 0.49***.
  - Adjusted R2 examples from Table 2: 0.45, 0.45, 0.44, 0.43, 0.44, 0.43. SE regression examples: 0.73, 0.73, 0.74, 0.74, 0.74, 0.75.
- Main reduced-form conclusion:
  - Aggregately, wages in Uruguay react to labor market indicators—either the level of unemployment or medium-term productivity growth.
  - Wages exhibit partial indexation to lagged inflation (with strongest evidence for lagged annual CPI inflation) and partial nominal wage adjustment (inertia).
  - Evidence of partial indexation to lagged annual CPI inflation is strongest; weak evidence of indexation to expected inflation.
  - Compared to a panel of emerging markets (WEO Oct 2022 Chapter 3), the main difference is that the change in unemployment is significant for the EM group but not significant for Uruguay.

### DSGE model setup (estimated Adrian et al. (2021) adaptation)
- Purpose: analyze interactions between wage-setting behavior, CPI inflation, and monetary policy in a medium-scale DSGE for a small open economy; estimated with Bayesian methods and extended to include supply (productivity) shocks, including a permanent shock with unit root drift parameter 휇휇
푍푍.
- Key model features and frictions:
  1. Staggered price and wage setting (Calvo-style) with indexation rules.
  2. Incomplete international financial markets; frictions in domestic credit and FX markets (Gabaix and Maggiori (2015) agency friction "Γ" proxied as FX market depth).
  3. Local currency pricing (LCP) for export prices (set in US dollars in this model), sticky import prices—implying gradual pass-through.
  4. Discounting and habit formation to mute potency of future policies.
  5. Micro-founded endogenous private and sovereign borrowing spreads.
- Wage indexation in model:
  - Wages, when not reoptimized, are indexed to a convex combination of lagged nominal wage growth and annual CPI inflation—consistent with reduced-form evidence.
  - Empirical estimation yields wage reset frequency and indexation weights:
    - Wages are reset optimally once every six quarters.
    - Wages are indexed more to lagged annual CPI inflation with coefficient 0.67 than to lagged nominal wage growth with coefficient 0.33 (text statement: "Wages are reset optimally once every six quarters, and they are indexed more to lagged annual CPI inflation, with a coefficient of 0.67, than to lagged nominal wage growth, that has a coefficient of 0.33.").
  - Prices are reset optimally about once a year with substantial indexation, especially in the domestic inflation Phillips Curve.
- Financial block and FX friction:
  - Agency friction Γ estimated posterior mean about 0.015 (text) and elsewhere reported about 0.02; low relative to most EMs and closer to AEs—implying limited macroeconomic power of FX interventions on average.
- Estimation details:
  - Baseline model estimated on quarterly data 2005:Q1–2023:Q1 for Uruguay.
  - Observables (domestic): real GDP growth, real imports and exports growth, real government spending growth, CPI inflation, nominal wage growth (seasonally adjusted), employment, short-term (1 month) interest rate, 10-year government bond yields, bilateral exchange rate with USD, and FX intervention as percent of GDP.
  - Foreign observables: US series (real output growth, government spending growth, CPI inflation, wage growth, employment, policy rate); model conditions on a pre-estimated US economy.
  - Calibration and priors: steady-state ratios calibrated via historical means; other structural parameters calibrated using Uruguay info or EM sample where needed.
- Selected calibrated parameters (exact values as presented):
  - Reserves relative to quarterly GDP 0.84
  - Household subjective discount factor 0.9999
  - Steady-state inflation (APR) 6
  - Steady-state real rate (APR) 2
  - Share of government expenditure in GDP 0.258
  - Share of imports in exports 0.118
  - Share of exports and imports in GDP 0.297
  - Share of import goods in consumption 0.353
  - Term premium (APR) 1.5
  - Real growth rate (quarterly, in gross terms) 1.005
  - Capital elasticity in production function 0.3
  - Frisch elasticity of substitution 2
  - Import price elasticity 0.8
  - Export price elasticity 0.8
  - Marginal rate of consumption/leisure substitution 2.857143
  - Coefficient of relative risk aversion 1
  - Wage mark-up (net) 0.333333
  - Ownership share of financial intermediaries/investors 0.8
  - NFA relative to quarterly GDP -1.012
  - Price mark-up (net) 0.5
  - Kimball curvature 12

### Estimated parameters and policy rule features (posterior highlights)
- Calvo/indexation and inertia estimates (posterior mean excerpts from Table 4 summary):
  - Calvo parameter for domestic prices ~ 0.66 (implies prices reset optimally about once a year).
  - Calvo parameter for wages ~ 0.75 (implies wages reset optimally about once every six quarters).
  - Domestic price indexation coefficient ~ 0.7 (posterior mean reported in table blocks).
  - Wage indexation posterior mean ~ 0.5 in prior/prior distribution block; model-specific posterior interpreted above as 0.67 to CPI and 0.33 to lagged wage growth.
- FX market friction Γ posterior ~ 0.015 (text) and small value about 0.02 noted later; implication: FX interventions have small macroeconomic effects on average.
- Interest rate rule posterior features:
  - Interest rate response to CPI inflation about 0.7 (text: "response to inflation is quite high (about 0.7)").
  - Degree of interest rate inertia (smoothing) estimated about 0.7 for Uruguay (text notes this is somewhat lower than >0.8 typical in other EMs/AEs).
- FX intervention rule:
  - Estimated response to change in exchange rate about 0.2 (text).
  - Persistence of FXI about 0.45 (text: "higher degree of policy inertia (0.45) than in other economies").

### Counterfactual experiments and policy implications
- Counterfactuals considered:
  - Wages indexed only to steady-state inflation (i.e., to central bank target) rather than to lagged annual CPI inflation and lagged wage growth.
  - Reduced backward-looking behavior in the domestic price Phillips Curve by setting 휄휄
푝푝 = 0.48 (EM average) instead of Uruguay estimated 0.76.
  - FX intervention switched off for experiments (훾훾
Δs = 0) so central bank uses interest rates only.
- Marginal Likelihood model comparison (preserving table entries):
  - Lagged wage growth: Yes; Indexing Variable = Lagged Annual: Marginal Likelihood -2985.6 (ranked highest among variants shown).
  - Other entries: Yes/Lagged Quarterly -2992.2; Yes/Steady State -2992.8; No/Lagged Annual -2992.8; No/Lagged Quarterly -2990.9; No/Steady State -2992.0.
  - Conclusion: baseline model with wages indexed to combination of lagged wage growth and annual CPI inflation ranked highest by Marginal Likelihood.
- Impulse response summaries (quantitative highlights preserved):
  - Global risk (capital outflow) shock:
    - Estimated model: real depreciation of the peso about 5 percent; CPI increases peaks after 4 quarters at about 0.5 percent above target; nominal wage growth peaks about 8 quarters after the shock; central bank tightens policy rate; output gap initially declines then recovers.
    - Counterfactual (wages indexed to target): CPI initially reacts same amount but wage inflation response is much more muted → faster return of CPI to target; needed monetary tightening is smaller; output gap responds more positively.
    - Reducing backward-looking price Phillips Curve (휄휄
푝푝) yields slightly more favorable dynamics but quantitatively smaller improvement than removing wage backward-looking indexation.
  - Domestic demand shock (consumption preference shock):
    - Estimated model: higher output gap, inflation, gradual pick up of wage growth leading to persistent CPI inflation; central bank tightens; exchange rate initially appreciates then depreciates.
    - Counterfactuals: without wage backward-looking indexation, wage growth response muted and inflation returns faster to target; central bank tightens less and output gap effect is larger. Improved central bank credibility (less backward-looking price Phillips Curve) improves inflation profile between three and ten quarters but overall macro dynamics nearly unchanged.
  - Wage mark-up shock:
    - Estimated model: higher labor costs raise CPI inflation, central bank tightens, output gap declines via lower domestic demand and appreciation; CPI response is hump-shaped and highly persistent due to wage indexation feedback.
    - Counterfactuals: CPI peak is lower (about two thirds of estimated economy peak) and returns faster to steady-state; central bank tightens less; output gap contraction smaller. Improvement in central bank credibility has modest quantitative effects.
  - Price mark-up shock:
    - Estimated model: increase in domestic inflation triggers delayed nominal wage growth which feeds back into CPI inflation, raising policy rate and lowering output gap.
    - Counterfactuals (removing wage indexation and/or improving price Phillips Curve forward-lookingness): both changes lower inflation persistence, reduce required policy tightening, and lessen output gap costs.
- Aggregate counterfactual takeaway:
  - Presence of indexation and partial nominal wage adjustment produces persistent CPI inflation responses because wages react with lags and feed back through labor costs and real marginal costs.
  - If wages were indexed to the inflation target (steady-state), CPI inflation persistence would decline by muting wage-price feedback; in some cases initial inflationary response would also be lower.
  - Wage indexation to past inflation acts as insurance to monetary shocks and thereby makes inflation more persistent, worsening the central bank’s stabilization trade-offs.
  - Improving central bank credibility (making price Phillips Curve more forward looking) typically yields smaller additional declines in inflation persistence than removing backward-looking wage indexation; but changing indexation practices requires improved credibility.

### Monetary policy transmission and FX interventions
- Interest rate shock transmission:
  - A domestic interest rate increase of about 130bps (estimated annualized standard deviation) leads to:
    - Output gap decline ≈ 0.3 percent.
    - Exchange rate appreciates ≈ 1 percent.
    - CPI inflation reaction muted, peaking at about 0.1 percent—attributed to large nominal rigidities.
  - Removing wage indexation to lagged inflation reduces inflation persistence; reducing backward-looking behavior in domestic price Phillips Curve has smaller quantitative effect.
- FX intervention effects (estimated model):
  - In an estimated historical FX rule capturing BCU practice until early 2020, a global risk shock depreciation induced a selling of FX reserves ≈ 0.7 percent of GDP to offset depreciation.
  - Quantitative macro effects of FXI on exchange rate, inflation, output, and interest rates are very small and not too different from responses when FXI is not used—reflecting a small estimated Γ (about 0.02 or 0.015).
  - Caveat: Γ may be state-dependent; it could be small in normal times but larger in crises when FX markets freeze—future research should study state-dependence and identification with limited crisis observations.

*Source: IMF staff estimates and analysis as presented in the supplied chapter content.*

### Conclusions

### Conclusions

### Overview
- The increase of inflation globally in recent years has led to a renewed interest in understanding the link between inflation and wages.
- The paper examines this interaction for Uruguay, which is characterized by a highly centralized wage bargaining setting and widespread wage indexation practices due to the historical lack of credibility of the monetary authorities in keeping inflation inside the target.

### Wage bargaining and reduced-form evidence
- The first part of the paper:
  - Describes how the wage bargaining process works in Uruguay.
  - Presents reduced-form estimates of a standard wage Phillips Curve using the Galí (2011) framework.
- Key empirical findings from reduced-form estimates:
  - Nominal wage growth displays partial adjustment and indexation to lagged annual CPI.
  - Nominal wage growth reacts to labor market indicators: either the unemployment rate or labor productivity, but not both in the same specification.
  - Main finding: nominal wage growth is related to its own lag, a price inflation indexing variable, and the level in the unemployment rate.
  - Specifications where labor productivity growth replaces the unemployment rate suggest labor productivity growth is also a driving force for nominal wage growth.

### DSGE model and general equilibrium analysis
- The second part of the paper:
  - Studies the interaction of price and wage inflation, and the role of monetary policy credibility in general equilibrium.
  - Presents a medium-scale open economy New Keynesian DSGE model as in Adrian et al. (2021), modified to include relevant wage rigidities and indexation and estimated using Bayesian methods on Uruguayan data.
- DSGE parameter and dynamics findings:
  - Parameter estimates confirm partial nominal wage adjustment and lagged indexation to annual CPI inflation in the wage formation process.
  - The domestic price inflation Phillips Curve exhibits a significant degree of backward-looking behavior, symptomatic of low credibility by the central bank.
  - As a result, inflation displays high persistence in response to shocks.

### Counterfactuals and credibility
- Counterfactual exercise:
  - Wages are assumed to be sticky but indexed to the central bank inflation target.
  - Outcome: by muting price-wage feedback effects, CPI inflation exhibits less persistence, and the central bank faces a more favorable trade-off with respect to stabilizing inflation and the output gap.
- Important contextual points:
  - Wage indexation practices are a response to lack of central bank credibility and/or the presence of large monetary shocks (Gray, 1976).
  - Lowering the degree of backward indexation and moving to indexing wages to the central bank target can only occur if inflation fluctuations are stable around the central bank target.
  - Suggested extension: endogenize the degree of indexation as a function of central bank credibility.

### Foreign exchange intervention (FXI)
- The paper investigates the role of foreign exchange interventions, allowed for in the Adrian et al. (2021) model.
- Estimated effects of conducting FXI are quantitatively small given the model and parameter estimates.
  - One possibility: small effects during normal/average times, consistent with Bucacos et al. (2019).
  - Important extension: estimate relevant parameters that measure frictions in a state-dependent way.
  - Caveat: Uruguay has not suffered periods of large financial stress over the last two decades, which may complicate parameter identification.

*IMF Working Papers — Examining Price-Wage Dynamics in a Small Open Economy: The Case of Uruguay — Conclusions*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024105-print-pdf.pdf_