## wpiea2025004-print-pdf - 0.3 percent after 3 quarters

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---

### Empirical results and main findings
- An adverse weather shock (one standard deviation rise in the Soil Moisture Deficit Index, SMDI) generates a contraction in Uruguay’s economy.
- A rise in soil moisture deficits implies a contemporaneous 0.1 percent decrease in the agricultural sector (primary activities: agricultural, fishing and mining).
- Peak decline in GDP is 0.3 percent after 3 quarters.
- The weather variable vanishes after one year, but its impact on the economy is persistent:
  - Impacts primary activity output for 2 years in the SVAR.
  - In the DSGE model the impact can persist up to 5 years (model statement: “up to 5 years in the DSGE model”).
- Impulse responses are shown at the quarterly frequency for 20 periods (5 years).
- Confidence intervals are obtained from 10,000 Monte-Carlo simulations and reported as 95% error bands.
- Analysis of a recent severe drought episode (2022-2023) shows the SMDI reaches above 3 during that episode.
- Rare, but intense, droughts have an estimated impact of around one percent of GDP loss (statement from drought episode analysis).
- The weather shock in the empirical model manifests through the labor market: a fall on impact of employment followed by a rebound, which mimics the behavior of a Total Factor Productivity (TFP) shock.

### Soil Moisture Deficit Index (SMDI) construction
- Source data: spatial soil water available (PAD - Porcentaje de Agua Disponible) from INIA-GRAS, published every 10 days for nation-wide grids (~30km x 30km).
- PAD factors in precipitation, surface runoff, infiltration, evaporation, water plant uptake and soil properties.
- Index construction follows the principles of Narasimhan and Srinivasan (2005) with goals:
  - Reflect short-term dry conditions.
  - Remove seasonality.
  - Be spatially comparable.
- Aggregation:
  - Monthly soil water deficit SDy,m computed by comparing each grid’s soil water SWy,m to its historical median MSWm:
    - SDy,m = (SWy,m − MSWm) / (MSWm − minSWm) × 100, if SWy,m ≤ MSWm.
    - SDy,m = (SWy,m − MSWm) / (maxSWm − MSWm) × 100, if SWy,m > MSWm.
  - Quarterly SMDI accumulated as:
    - SMDIy,m = 0.5 × SMDIy,m−1 + SDy,m / 50.
  - The SMDI ranges from -4 to +4 representing wet to dry conditions.
- Spatial coverage: aggregation of grids covers around 80 percent of national soybean production (using U.S. Department of Agriculture crop production maps to select relevant grids).
- An alternative SMDI with countrywide coverage is available in Section A.1 and results are robust to that alternative index.

### Data and sample
- Quarterly frequency sample period: 2005Q2 until 2023Q2 (data transformed to per-capita; series seasonally adjusted where needed using X-13 in R).
- 2023Q3 and 2023Q4 are excluded because agricultural output in these quarters are estimations of future yields from crops planted (primary activity in these quarters are estimates).
- Variables used (seasonally adjusted unless stated):
  - Gross Domestic Product: Real per capita output, expenditure approach. Source: Banco Central del Uruguay.
  - Rest of the World GDP: Weighted average of GDP of main trading partners, seasonally adjusted. Sources: Haver and IMF staff calculations.
  - Agricultural Output (Primary Activity): Primary sector per capita output (agriculture, fishing and mining). Source: Banco Central del Uruguay.
  - Consumption: Household final consumption expenditure. Source: Banco Central del Uruguay.
  - Investment: Gross fixed capital formation. Source: Banco Central del Uruguay.
  - Employment: Labor force status for people aged 15 to 64 years; Employment Rate. Source: Instituto Nacional de Estadística de Uruguay.
  - Real Effective Exchange Rate: Global real effective exchange rate for Uruguay. Source: Banco Central del Uruguay.
  - Weather: Soil moisture deficit index for Uruguay. Source: INIA-GRAS and IMF staff calculations.
- Rest of the World GDP weights are updated each quarter according to Uruguay’s exports and imports; results are robust to fixed average weights.

### Identification strategy (SVAR)
- Two-stage procedure:
  1. Estimate a restricted VAR reflecting a small open economy: foreign variables (rest of the world GDP) are assumed exogenous; weather variable is assumed exogenous (domestic variables do not impact the weather).
  2. Impose similar restrictions in an SVAR to identify orthogonal structural disturbances using an A0 matrix with contemporaneous restrictions (Equation 4).
- Lag length chosen by Hannan-Quinn and Schwarz criteria: lag of one for the restricted VAR and SVAR.
- Variable ordering in the SVAR (hatted variables denote logged and detrended, except rer in log differences and SMDI not transformed):
  - 1st: weather variable ˆωt (exogenous to domestic variables).
  - 2nd: foreign real output ˆy⋆t.
  - 3rd: domestic real GDP ˆyt (most exogenous domestic variable).
  - Followed by: agricultural output ˆyA t, employment rate ˆht, consumption ˆct, investment ˆit, and real exchange rate ˆrer t (ordered last as most endogenous).
- Domestic variables are allowed to respond contemporaneously to weather and foreign output according to the restriction structure in Equation (4).
- Impulse responses to a one-standard-deviation SMDI shock are reported with 95% confidence intervals from 10,000 Monte-Carlo simulations.

### Model structure (DSGE) and key model features
- Two-sector, two-good small open economy with flexible exchange rate; calibrated and estimated for Uruguay.
- Sectors: agricultural (primary activity in data: agriculture, fishing, mining) and non-agricultural.
- Weather shocks affect the agricultural sector through a cost function that reduces land productivity in a land-capital-labor Cobb-Douglas production function.
- Agricultural production (firm i) specification:
  - yAit = [Ω(εW t) ℓit−1]ω (h εZ t [kAit−1]α [κA hAit]1−α) i1−ω  (Equation 5 as presented).
  - Weather cost function: Ω(εW t) = (εW t)−θ; when θ = 0 the impact of weather on the business cycle is shut down.
  - Weather shock process: log(εW t) = ρW log(εW t−1) + σW ηW t, ηW t ∼ N(0,1) (Equation 6), with ρW ∈ [0,1) and σW ≥ 0.
- Land law of motion:
  - ℓit = [(1 − δℓ) + v(xit)] ℓit−1 Ω(εW t) (Equation 7).
  - Land expenditures xit (e.g., fertilizers, water) can offset soil dryness; ν(·) has ν′(·) > 0, ν′′(·) ≥ 0.
- Physical capital accumulation for agriculture:
  - iAit = kAit − (1 − δK) kA i,t−1 (Equation 8).
- Profit function for agricultural firm includes price of agricultural goods, cost of labor, cost of land expenditure, and convex investment adjustment cost.
- Firms maximize expected discounted real profits subject to capital, land, and other constraints (Equations 9–10).

### Households, consumption, labor and budget
- Households maximize utility with habit persistence b ∈ [0,1) and discount β:
  - Et Σβτ [ (1/(1 − σ)) (Cjt+τ − b Ct−1+τ)1−σ − χ εH t+τ (1/(1 + σH)) h1+σH jt+τ ] (Equation 11).
- Labor aggregation: CES labor disutility with substitutability parameter ι ≥ 0 (Equation 12); if ι = 0, sectoral labor are perfect substitutes.
- Budget constraint includes wages, returns on domestic and foreign bonds, lump-sum taxes Tt, and a risk premium cost Φ(b∗jt) on foreign bonds (Equation 13).
- Consumption is a CES bundle of agricultural and non-agricultural goods with weight φ ∈ [0,1] and substitution elasticity μ ≥ 0 (Equation 14).
- Composite subindices permit domestic–foreign home bias with parameters 1 − αs ≥ 0.5 and μs > 0 (Equations 15–17).

### Non-Agricultural sector, government and foreign economy (model summaries)
- Non-agricultural production (firm i):
  - y^N_it = ε^Z_t (k^N_it−1)^α (h^N_it)^(1−α).
- Capital accumulation: i^N_it = k^N_it − (1 − δ_K) k^N_it−1, with δ_K ∈ [0,1].
- Firms face investment adjustment cost S(·) and maximize discounted profits subject to production and capital constraints.
- Government consumes non-agricultural output G_t, issues real debt b_t at real interest rate r_t, and charges lump-sum taxes T_t:
  - G_t = Y^N_t g ε^G_t, with g ∈ [0,1) and ε^G_t AR(1).
  - Budget: G_t + r_{t−1} b_{t−1} = b_t + T_t.
- Foreign economy modeled as an endowment with exogenous foreign consumption following AR(1) processes and a time-preference shock log(ε^E_t) = ρ_E log(ε^E_{t−1}) + σ_E η^E_t.

### Equilibrium, aggregation and trade
- Market clearing for non-agricultural goods and agricultural goods market equilibrium provided with nested price-relative terms and substitution elasticities.
- Aggregate real production:
  - Y_t = (1 − n_t) p^N_t Y^N_t + n_t p^A_t Y^A_t.
- GDP definition:
  - gdp_t = Y_t − p^N_t n_t X_t.
- Law of motion for real foreign debt and trade balance equations included in model specification.

### Calibration and estimation
- Calibration uses Uruguay-specific averages and literature standards. Selected calibrated parameter values:
  - β Discount factor = 0.9883
  - δ_K Capital depreciation rate = 0.025
  - α Share of capital in output = 0.33
  - g Share of spending in GDP = 0.216
  - φ Share of agricultural goods in consumption basket = 0.17
  - H̄_N = H̄_A Hours worked = 1/3
  - ℓ̄ Land per capita = 1.30
  - α_N Openness of non-agricultural market = 0.10
  - α_A Openness of agricultural market = 0.50
  - χ_B International portfolio cost = 0.0007
- Estimation via Bayesian methods using dataset spanning 2005Q2 to 2023Q2 with non-stationary observables processed (per-capita division, logging, quadratic detrending).
- Observable vector:
  - Y_obs_t = 100 × [ ŷ_t, ĉ_t, î_t, ĥ_t, ŷ^A_t, ŷ^*_t, Δcrer_t, ˆω_t ]'
- Posterior computation: total generated 1,000,000 draws (two parallel chains of 500,000), discarding first 25 percent; estimation and simulation in Dynare.
- Marginal log-likelihood = −1014.94

### Selected posterior means (posterior means and 5%:95% intervals as reported)
- Shock process posterior means (×100):
  - σ_Z = 2.41 [2.00 : 2.81]
  - σ_H = 3.86 [2.50 : 5.16]
  - σ_G = 6.38 [5.21 : 7.58]
  - σ_I = 8.17 [6.07 : 10.18]
  - σ_N = 18.77 [13.16 : 24.21]
  - σ_W = 1.21 [1.02 : 1.41]
  - σ_E = 4.14 [3.20 : 5.05]
  - σ_C = 1.20 [1.00 : 1.40]
- AR(1) posterior means:
  - ρ_Z = 0.84 [0.75 : 0.94]
  - ρ_H = 0.78 [0.65 : 0.92]
  - ρ_G = 0.67 [0.49 : 0.86]
  - ρ_I = 0.26 [0.07 : 0.43]
  - ρ_N = 0.28 [0.10 : 0.45]
  - ρ_W = 0.44 [0.26 : 0.63]
  - ρ_E = 0.21 [0.07 : 0.35]
  - ρ_C = 0.69 [0.56 : 0.83]
- Selected structural parameter posterior means [5% : 95%]:
  - σ_C (risk consumption) = 0.28 [0.10 : 0.45]
  - σ_H (labor disutility) = 1.90 [1.11 : 2.68]
  - φ (land expenditure cost) = 1.7 [1.25 : 2.20]
  - ω (share of land in agricultural output) = 0.08 [0.02 : 0.19]
  - b (consumption habits) = 0.66 [0.50 : 0.82]
  - ι (labor sectoral cost) = 2.48 [1.65 : 3.27]
  - μ_G (substitutability by type of goods) = 3.35 [2.06 : 4.57]
  - μ_A (substitutability home/foreign for agriculture) = 1.97 [1.27 : 2.62]
  - μ_N (substitutability home/foreign for non-agriculture) = 1.0? [0.75 : 2.17]
  - δ_ℓ (land efficiency decay rate) = 0.07 [0.03 : 0.11]
  - κ (investment cost) posterior mean 2.43 [0.44 : 4.72]
  - θ (land-weather elasticity) posterior mean = 5.25 [−2.97 : 14.22]
- Posterior discussion:
  - Posterior mean of θ = 5.25 is below prior mean and includes negative values within the 90% posterior density interval; may reflect flood-related damage (excess water) to agricultural output in Uruguay and model limitations in capturing weather damage to capital or non-agricultural sectors.
  - Despite lower weather cost parameter, overall output impacts similar to Gallic and Vermandel (2020) though with lesser impact on agricultural sector, implying a more indirect transmission mechanism of droughts for Uruguay.

### Results: comparison, persistence and transmission
- Model comparison: SVAR versus DSGE
  - Both models simulate a one standard deviation weather shock to analyze drought impacts.
  - The weather shock acts as a negative supply shock via rising employment and falling output, with land productivity negatively affected and agricultural output weighed down.
  - Real exchange rate depreciates and acts as a shock absorber, helping restore farmers’ competitiveness.
  - Compared with the SVAR:
    - Impact on consumption and agricultural output (primary activity) is greater in the DSGE.
    - The model captures well the magnitude and dynamics of the impact on investment.
  - SVAR impulse responses use 10,000 Monte-Carlo simulations to construct 95% confidence intervals.
- DSGE persistence and transmission mechanisms
  - The DSGE model displays notable persistence: the impact of the weather shock lasts up to 5 years, which is 3 years longer than the SVAR results.
  - Persistence is partly explained by a persistent reduction in land efficiency governed by the estimated parameter δℓ.
  - The drought causes a negative and persistent impact on land efficiency (see Annex A.2).
  - Farmers increase use of non-agricultural inputs and labor; the increase in labor on impact is likely driven by the choice of utility function (negative wealth effect induces higher labor supply).
  - Additional DSGE results:
    - The weather shock lowers land productivity by close to 10 percent in the model.
    - Non-agricultural output rises initially as the relative price of non-agricultural goods falls, dampening the overall output impact.
    - Falling non-agricultural prices boost foreign demand for non-agricultural goods and increase non-agricultural domestic production.
    - To compensate for land productivity loss, agricultural firms increase use of non-agricultural goods (captured by a rise in xt).

### Cross-country comparison and role of weather shocks
- Cross-country comparison (Uruguay versus New Zealand)
  - GDP impact in the DSGE model is similar between Uruguay and New Zealand, but transmission differs:
    - Agricultural output falls by 1.5 percent following a one standard deviation drought in New Zealand.
    - Agricultural output decrease is more muted for Uruguay: 0.6 percent.
    - Uruguay’s consumption falls by more and employment rise is more muted relative to New Zealand.
  - Part of the difference may arise from data definitions: Uruguay uses primary sector data (agricultural, fishing and mining), while Gallic and Vermandel (2020) use agriculture, fishing and forestry.
- Role of weather shocks for the business cycle
  - Simulations feeding only weather shocks versus all shocks show cyclical impacts:
    - Agricultural output (primary activity) growth oscillates between +3 percent and - 3 percent due to weather shocks.
    - Consumption growth moves +/- 2 percent.
    - Output growth moves +/- one percent.
    - Employment impact is limited, likely due to the low share of labor force in primary activity.
  - Weather-driven losses in agricultural output and consumption co-move and help explain weather-driven business cycle impacts (notably aligning with 2008-2009, 2011, 2015 and 2022-2023 drought-related loss periods).

### 2022-2023 drought simulation and robustness checks
- 2022-2023 drought simulation
  - The SMDI increase observed between 2022Q4 and 2023Q2 is mimicked: SMDI around 2 in 2022Q4, peaking above 3 in 2023Q1, then decreasing in 2023Q2; after 2023Q2 SMDI reverts to steady state per estimated autoregressive component.
  - The simulated increase in the SMDI is estimated to provide around a one percent fall in GDP for 2023, driven by losses in agricultural output (primary activity) and investment.
  - According to the SVAR, the drought impact should subside in 2024; the DSGE model shows a longer-lasting effect.
  - In reality, normalization of rainfall in the second half of 2023 (fall in SMDI) is expected to bolster primary sector recovery.
- SVAR robustness and alternative SMDI specifications
  - Lag selection: Hannan–Quinn and Schwarz criteria indicate an SVAR lag length one is preferred; robustness checks with higher order lags produce similar results.
  - SMDI-Countrywide versus agricultural-weighted SMDI:
    - Both indices show droughts negatively impact primary activity, consumption and investment.
    - SMDI-Countrywide shows a small uptick in primary output in the second quarter following the shock and a delayed response of consumption.
    - Preferred measure is agricultural-weighted SMDI; SMDI-Countrywide is robust and requires less granular data.
  - Truncated SMDI (positive values only):
    - Truncating negative SMDI values to 0 isolates drought impacts.
    - A one standard deviation drought shock with the truncated index lowers agricultural output by 0.7 percent at the peak compared to 0.3 percent with the baseline index.

### Variance decomposition, omitted channels and contextual notes
- Variance decomposition and relative importance of shocks
  - Forecast error variance decomposition at posterior mean for horizons (one, ten, fifty and unconditional) shows:
    - Supply shocks (technology shock, labour supply shock and sector reallocation shock) explain the majority of movements in GDP, agricultural output, consumption and employment.
    - Weather shocks play a role for GDP and agriculture but play a significantly diminished role in Uruguay compared to Gallic and Vermandel (2020) for New Zealand.
    - Part of the diminished role may be due to the sample period including Covid-19 and a relatively small sample size (quarterly data from 2005Q2-2023Q2 may impact FEVD accuracy).
- Additional contextual and transmission channels noted
  - Agricultural sector in Uruguay combines cultivation of crops and rearing of livestock; cultivation is more susceptible to droughts than livestock, but the model does not split the sector.
  - Severe droughts may have additional economy-wide consequences omitted from the analysis:
    - Heightened water scarcity;
    - Reduced hydroelectric electricity generation;
    - Increased chance of wildfires;
    - Financial transmission channel (e.g., unusually hot days increase delinquency rates in agricultural sector) is omitted, though expected to be muted given credit-to-GDP is relatively low at close to 30 percent of GDP (IMF, 2024).

### Key quantitative findings (exact reported values)
- DSGE persistence: impact lasts up to 5 years (3 years longer than SVAR).
- New Zealand agricultural output fall after one standard deviation drought: 1.5 percent.
- Uruguay agricultural output fall after one standard deviation drought: 0.6 percent.
- Simulated GDP fall for 2023 from 2022-2023 drought episode: around a one percent fall in GDP for 2023.
- Land productivity reduction in DSGE: close to 10 percent.
- Truncated SMDI peak agricultural output fall: 0.7 percent (versus 0.3 percent baseline).
- Business-cycle oscillations from weather shocks:
  - Agricultural output growth: +3 percent to - 3 percent.
  - Consumption growth: +/- 2 percent.
  - Output growth: +/- one percent.
- SVAR Monte-Carlo simulations used: 10,000 runs.
- Sample period noted for FEVD concerns: quarterly data from 2005Q2-2023Q2.
- Credit-to-GDP in Uruguay cited as: close to 30 percent of GDP.

*Source: wpiea2025004-print-pdf.*

### 0.3 percent after 3 quarters.

### wpiea2025004-print-pdf - 0.3 percent after 3 quarters.

### Empirical results and main findings
- An adverse weather shock (one standard deviation rise in the Soil Moisture Deficit Index, SMDI) generates a contraction in Uruguay’s economy.
- A rise in soil moisture deficits implies a contemporaneous 0.1 percent decrease in the agricultural sector (primary activities: agricultural, fishing and mining).
- Peak decline in GDP is 0.3 percent after 3 quarters.
- The weather variable vanishes after one year, but its impact on the economy is persistent:
  - Impacts primary activity output for 2 years in the SVAR.
  - In the DSGE model the impact can persist up to 5 years (model statement: “up to 5 years in the DSGE model”).
- Impulse responses are shown at the quarterly frequency for 20 periods (5 years).
- Confidence intervals are obtained from 10,000 Monte-Carlo simulations and reported as 95% error bands.
- Analysis of a recent severe drought episode (2022-2023) shows the SMDI reaches above 3 during that episode.
- Rare, but intense, droughts have an estimated impact of around one percent of GDP loss (statement from drought episode analysis).
- The weather shock in the empirical model manifests through the labor market: a fall on impact of employment followed by a rebound, which mimics the behavior of a Total Factor Productivity (TFP) shock.

### Soil Moisture Deficit Index (SMDI) construction
- Source data: spatial soil water available (PAD - Porcentaje de Agua Disponible) from INIA-GRAS, published every 10 days for nation-wide grids (~30km x 30km).
- PAD factors in precipitation, surface runoff, infiltration, evaporation, water plant uptake and soil properties.
- Index construction follows the principles of Narasimhan and Srinivasan (2005) with goals:
  - Reflect short-term dry conditions.
  - Remove seasonality.
  - Be spatially comparable.
- Aggregation:
  - Monthly soil water deficit SDy,m is computed by comparing each grid’s soil water SWy,m to its historical median MSWm for that month using Equation (1):
    - SDy,m = (SWy,m − MSWm) / (MSWm − minSWm) × 100, if SWy,m ≤ MSWm.
    - SDy,m = (SWy,m − MSWm) / (maxSWm − MSWm) × 100, if SWy,m > MSWm.
  - Quarterly SMDI is accumulated using Equation (2):
    - SMDIy,m = 0.5 × SMDIy,m−1 + SDy,m / 50.
  - The SMDI ranges from -4 to +4 representing wet to dry conditions.
- Spatial coverage: aggregation of grids covers around 80 percent of national soybean production (using U.S. Department of Agriculture crop production maps to select relevant grids).
- An alternative SMDI with countrywide coverage is available in Section A.1 and results are robust to that alternative index.

### Data and sample
- Quarterly frequency sample period: 2005Q2 until 2023Q2 (data transformed to per-capita; series seasonally adjusted where needed using X-13 in R).
- 2023Q3 and 2023Q4 are excluded because agricultural output in these quarters are estimations of future yields from crops planted (primary activity in these quarters are estimates).
- Variables used (seasonally adjusted unless stated):
  - Gross Domestic Product: Real per capita output, expenditure approach. Source: Banco Central del Uruguay.
  - Rest of the World GDP: Weighted average of GDP of main trading partners, seasonally adjusted. Sources: Haver and IMF staff calculations.
  - Agricultural Output (Primary Activity): Primary sector per capita output (agriculture, fishing and mining). Source: Banco Central del Uruguay.
  - Consumption: Household final consumption expenditure. Source: Banco Central del Uruguay.
  - Investment: Gross fixed capital formation. Source: Banco Central del Uruguay.
  - Employment: Labor force status for people aged 15 to 64 years; Employment Rate. Source: Instituto Nacional de Estadística de Uruguay.
  - Real Effective Exchange Rate: Global real effective exchange rate for Uruguay. Source: Banco Central del Uruguay.
  - Weather: Soil moisture deficit index for Uruguay. Source: INIA-GRAS and IMF staff calculations.
- Rest of the World GDP weights are updated each quarter according to Uruguay’s exports and imports; results are robust to fixed average weights.

### Identification strategy (SVAR)
- Two-stage procedure:
  1. Estimate a restricted VAR reflecting a small open economy: foreign variables (rest of the world GDP) are assumed exogenous; weather variable is assumed exogenous (domestic variables do not impact the weather).
  2. Impose similar restrictions in an SVAR to identify orthogonal structural disturbances using an A0 matrix with contemporaneous restrictions (Equation 4).
- Lag length chosen by Hannan-Quinn and Schwarz criteria: lag of one for the restricted VAR and SVAR.
- Variable ordering in the SVAR (hatted variables denote logged and detrended, except rer in log differences and SMDI not transformed):
  - 1st: weather variable ˆωt (exogenous to domestic variables).
  - 2nd: foreign real output ˆy⋆t.
  - 3rd: domestic real GDP ˆyt (most exogenous domestic variable).
  - Followed by: agricultural output ˆyA t, employment rate ˆht, consumption ˆct, investment ˆit, and real exchange rate ˆrer t (ordered last as most endogenous).
- Domestic variables are allowed to respond contemporaneously to weather and foreign output according to the restriction structure in Equation (4).
- Impulse responses to a one-standard-deviation SMDI shock are reported with 95% confidence intervals from 10,000 Monte-Carlo simulations.

### Model structure (DSGE) and key model features
- Model is a two-sector, two-good small open economy with flexible exchange rate; follows Gallic and Vermandel (2020) but calibrated and estimated for Uruguay.
- Sectors: agricultural (primary activity in data: agriculture, fishing, mining) and non-agricultural.
- Weather shocks affect the agricultural sector through a cost function that reduces land productivity in a land-capital-labor Cobb-Douglas production function.
- Agricultural production (firm i):
  - yAit = [Ω(εW t) ℓit−1]ω (h εZ t [kAit−1]α [κA hAit]1−α) i1−ω  (Equation 5 as presented).
  - Weather cost function: Ω(εW t) = (εW t)−θ; when θ = 0 the impact of weather on the business cycle is shut down.
  - Weather shock process: log(εW t) = ρW log(εW t−1) + σW ηW t, ηW t ∼ N(0,1) (Equation 6), with ρW ∈ [0,1) and σW ≥ 0.
- Land is endogenous with law of motion:
  - ℓit = [(1 − δℓ) + v(xit)] ℓit−1 Ω(εW t) (Equation 7).
  - Land expenditures xit (e.g., fertilizers, water) can offset soil dryness; ν(·) has ν′(·) > 0, ν′′(·) ≥ 0.
- Physical capital accumulation for agriculture:
  - iAit = kAit − (1 − δK) kA i,t−1 (Equation 8).
- Profit function for agricultural firm includes price of agricultural goods, cost of labor, cost of land expenditure, and convex investment adjustment cost (Christiano et al. 2005).
- Firms maximize expected discounted real profits subject to capital, land, and other constraints (Equations 9–10).

### Households and consumption
- Continuum of identical households maximize utility with habit persistence b ∈ [0,1) and discount β.
- Utility:
  - Et Σβτ [ (1/(1 − σ)) (Cjt+τ − b Ct−1+τ)1−σ − χ εH t+τ (1/(1 + σH)) h1+σH jt+τ ] (Equation 11).
- Labor:
  - CES labor disutility aggregates non-agricultural and agricultural hours with substitutability parameter ι ≥ 0 (Equation 12). If ι = 0, sectoral labor are perfect substitutes.
- Budget constraint (real terms) includes wages, returns on domestic and foreign bonds, lump-sum taxes Tt, and a risk premium cost Φ(b∗jt) on foreign bonds (Equation 13).
- Consumption is a CES bundle of agricultural and non-agricultural goods with weight φ ∈ [0,1] and substitution elasticity μ ≥ 0 (Equation 14).
- Composite subindices permit domestic–foreign home bias with parameters 1 − αs ≥ 0.5 and μs > 0 (Equations 15–17).

*Source: wpiea2025004-print-pdf.*

### 4.3    Non-Agricultural Sector

### 4.3    Non-Agricultural Sector

### Production function
- Firms indexed by i ∈ [n_t, 1], where 1 − n_t denotes the relative size of the non-agricultural sector.
- Cobb-Douglas production function:
  - y^N_it = ε^Z_t (k^N_it−1)^α (h^N_it)^(1−α)
  - y^N_it is production of intermediate goods firms.
  - k^N_i,t−1 is the stock of physical capital of firm i.
  - h^N_it is labor employed in the non-agricultural sector for firm i.
  - ε^Z_t is the AR(1) technology shock.
  - Parameter α governs the elasticity of capital and labor in non-agricultural goods production.

### Capital accumulation and investment
- Physical capital accumulation:
  - i^N_it = k^N_it − (1 − δ_K) k^N_it−1
  - δ_K ∈ [0,1] is the depreciation rate of physical capital.

### Profits and firm optimization
- Real profits for firm i:
  - d^N_it = p^N_t y^N_it − p^N_t [ i^N_it + S(ε^i_t, i^N_it, i^N_it−1) i^N_it−1 ] − w^N_t h^N_it
  - (Expression presented in source with S(·) adjustment-cost term involving ε^i_t, i^N_it, i^N_it−1.)
- Firms maximize discounted sum of profits:
  - max_{h^N_it, i^N_it, k^N_it} E_t ( Σ_{τ=0}^∞ Λ_{t,t+s} d^N_it+τ )
  - Subject to the production technology and capital accumulation constraints.

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### 4.4    Government (model specification summary)
- Government consumes non-agricultural output G_t, issues real debt b_t at real interest rate r_t, and charges lump-sum taxes T_t to households.
- Government consumption specification:
  - G_t = Y^N_t g ε^G_t, where g ∈ [0,1) and ε^G_t follows an AR(1) stochastic shock.
- Government budget constraint:
  - G_t + r_{t−1} b_{t−1} = b_t + T_t

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### 4.5    Foreign Economy (model specification summary)
- Foreign economy modeled as an endowment economy with exogenous foreign consumption:
  - log(c^*_jt) = (1 − ρ_C) log( c̄^*_j ) + ρ_C log(c^*_jt−1) + σ_C η^C_t,  η^C_t ∼ N(0,1)
  - 0 ≤ ρ_C < 1 determines return to steady state of foreign consumption.
  - σ_C and ρ_C are estimated to match foreign demand.
- Foreign households optimization:
  - max_{c^*_jt, b^*_jt} E_t ( Σ_{τ=0}^∞ β^τ ε^E_{t+τ} log(c^*_{jt+τ}) )
  - Subject to r^*_t−1 b^*_{jt−1} = c^*_jt + b^*_jt
- Time-preference shock process:
  - log(ε^E_t) = ρ_E log(ε^E_{t−1}) + σ_E η^E_t

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### 4.6    Equilibrium and aggregation equations
- Market clearing for non-agricultural goods:
  - (1 − n_t) Y^N_t = (1 − φ) [ (1 − α_N) (P^N_t / P^N_{C,t})^{−μ_N} (P^N_{C,t} / P_t)^{−μ_C_t} + α_N (1 / e^*_t P^N_t / P^{N*}_{C,t})^{−μ_N} (P^{N*}_{C,t} / P^{**}_t)^{−μ_C^*_t} ] + G_t + I_t + n_t x_t + Φ(b^*_t)
  - (Equation displayed in source with nested price-relative terms and substitution elasticities.)
- Aggregate real production:
  - Y_t = (1 − n_t) p^N_t Y^N_t + n_t p^A_t Y^A_t
- Agricultural goods market equilibrium:
  - n_t Y^A_t = φ [ (1 − α_A) (P^A_t / P^A_{C,t})^{−μ_A} (P^A_{C,t} / P_t)^{−μ_C_t} + α_A (1 / e^*_t P^A_t / P^{A*}_{C,t})^{−μ_A} (P^{A*}_{C,t} / P^*_t)^{−μ_C^*_t} ]
- GDP definition:
  - gdp_t = Y_t − p^N_t n_t X_t
- Law of motion for real foreign debt:
  - b^*_t = r^*_t−1 (rer^*_t / rer^*_t−1) b^*_t−1 + tb_t
- Trade balance:
  - tb_t = p^N_t [ (1 − n_t) Y^N_t − G_t − I_t − n_t X_t − Φ(b^*_t) ] + p^A_t n_t Y^A_t − C_t

---

### 4.7    Calibration and estimation
- Model calibration uses standard literature parameters and Uruguay-specific averages.
- Reported calibrated parameter values (Table 1):
  - β Discount factor = 0.9883
  - δ_K Capital depreciation rate = 0.025
  - α Share of capital in output = 0.33
  - g Share of spending in GDP = 0.216
  - φ Share of agricultural goods in consumption basket = 0.17
  - H̄_N = H̄_A Hours worked = 1/3
  - ℓ̄ Land per capita = 1.30
  - α_N Openness of non-agricultural market = 0.10
  - α_A Openness of agricultural market = 0.50
  - χ_B International portfolio cost = 0.0007
- Notes on specific calibrations and sources:
  - g = 0.216 derived as average of public consumption and public investment shares of GDP between 2016-2022.
  - φ = 0.17 calculated from agricultural-related product weights in Uruguay’s CPI.
  - ℓ̄ = 1.30 derived from World Bank WDI and employment/population data; noted discrepancy with Gallic and Vermandel (2020) which use ℓ̄_NZ = 0.4 for New Zealand.
  - α_N and α_A determined by average export shares of respective sectors between 2016-2022.
- Estimation approach:
  - Remaining parameters estimated via Bayesian methods using dataset spanning 2005Q2 to 2023Q2 (same dataset as the VAR model).
  - Non-stationary observables processed: per-capita division by working-age population, logging, detrending with a quadratic trend.
  - Observable vector:
    - Y_obs_t = 100 × [ ŷ_t, ĉ_t, î_t, ĥ_t, ŷ^A_t, ŷ^*_t, Δcrer_t, ˆω_t ]'
      - ŷ_t = output gap
      - ĉ_t = consumption gap
      - î_t = investment gap
      - ĥ_t = index of employment
      - ŷ^A_t = agricultural production gap
      - ŷ^*_t = foreign production gap
      - crer_t = real exchange rate
      - ˆω_t = soil moisture deficit index
  - Measurement equations mapping model variables to observables provided in source.
  - Posterior moments computed with total generated 1,000,000 draws (two parallel chains of 500,000), discarding first 25 percent; estimation and simulation in Dynare.
- Priors and posterior findings (summary from Table 2; posterior means and 5%:95% intervals):
  - Selected shock process posterior means (×100):
    - σ_Z = 2.41 [2.00 : 2.81]
    - σ_H = 3.86 [2.50 : 5.16]
    - σ_G = 6.38 [5.21 : 7.58]
    - σ_I = 8.17 [6.07 : 10.18]
    - σ_N = 18.77 [13.16 : 24.21]
    - σ_W = 1.21 [1.02 : 1.41]
    - σ_E = 4.14 [3.20 : 5.05]
    - σ_C = 1.20 [1.00 : 1.40]
  - Selected AR(1) posterior means:
    - ρ_Z = 0.84 [0.75 : 0.94]
    - ρ_H = 0.78 [0.65 : 0.92]
    - ρ_G = 0.67 [0.49 : 0.86]
    - ρ_I = 0.26 [0.07 : 0.43]
    - ρ_N = 0.28 [0.10 : 0.45]
    - ρ_W = 0.44 [0.26 : 0.63]
    - ρ_E = 0.21 [0.07 : 0.35]
    - ρ_C = 0.69 [0.56 : 0.83]
  - Selected structural parameter posterior means [5% : 95%]:
    - σ_C (risk consumption) = 0.28 [0.10 : 0.45]
    - σ_H (labor disutility) = 1.90 [1.11 : 2.68]
    - φ (land expenditure cost) = 1.7 [1.25 : 2.20]
    - ω (share of land in agricultural output) = 0.08 [0.02 : 0.19]
    - b (consumption habits) = 0.66 [0.50 : 0.82]
    - ι (labor sectoral cost) = 2.48 [1.65 : 3.27]
    - μ_G (substitutability by type of goods) = 3.35 [2.06 : 4.57]
    - μ_A (substitutability home/foreign for agriculture) = 1.97 [1.27 : 2.62]
    - μ_N (substitutability home/foreign for non-agriculture) = 1.0? [0.75 : 2.17] (reported as "1" in Table 2's shape/mean column)
    - δ_ℓ (land efficiency decay rate) = 0.07 [0.03 : 0.11]
    - κ (investment cost) = 1.5? posterior mean 2.43 [0.44 : 4.72] (Table 2 lists "4 1.5" under prior shape/mean; posterior mean reported)
    - θ (land-weather elasticity) posterior mean = 5.25 [−2.97 : 14.22]
  - Posterior discussion:
    - Posterior mean of θ = 5.25 is below prior mean and includes negative values within the 90% posterior density interval; possible reflection of flood-related damage (excess water) to agricultural output in Uruguay and limitations of model not capturing weather damage to capital or non-agricultural sectors.
    - Despite lower weather cost parameter, overall output impacts similar to Gallic and Vermandel (2020) though with lesser impact on agricultural sector, implying a more indirect transmission mechanism of droughts for Uruguay.
  - Marginal log-likelihood = −1014.94

*Source: wpiea2025004-print-pdf (sections 4.3–4.7) — IMF staff calculations and model tables as provided in the source content.*

### 4.8    Results

### 4.8    Results

### Model comparison: SVAR versus DSGE
- Both models simulate a one standard deviation weather shock to analyze drought impacts.
- The weather shock acts as a negative supply shock via rising employment and falling output, with land productivity negatively affected and agricultural output weighed down.
- Real exchange rate depreciates and acts as a shock absorber, helping restore farmers’ competitiveness.
- Compared with the SVAR:
  - Impact on consumption and agricultural output (primary activity) is greater in the DSGE.
  - The model captures well the magnitude and dynamics of the impact on investment.
- The SVAR impulse responses use 10,000 Monte-Carlo simulations to construct 95% confidence intervals.

### DSGE persistence and transmission mechanisms
- The DSGE model displays notable persistence: the impact of the weather shock lasts up to 5 years, which is 3 years longer than the SVAR results.
- Persistence is partly explained by a persistent reduction in land efficiency governed by the estimated parameter δℓ in the land-evolution function.
- The drought causes a negative and persistent impact on land efficiency (see Annex A.2).
- Farmers increase use of non-agricultural inputs and labor:
  - The increase in labor on impact is likely driven by the choice of utility function (negative wealth effect from the shock induces higher labor supply).
- Additional DSGE results:
  - The weather shock lowers land productivity by close to 10 percent in the model.
  - Non-agricultural output rises initially as the relative price of non-agricultural goods falls, dampening the overall output impact.
  - Falling non-agricultural prices boost foreign demand for non-agricultural goods and increase non-agricultural domestic production.
  - To compensate for land productivity loss, agricultural firms increase use of non-agricultural goods (captured by a rise in xt, additional effort to combat the drought).

### Cross-country comparison (Uruguay versus New Zealand)
- GDP impact in the DSGE model is similar between Uruguay and New Zealand, but transmission differs:
  - Agricultural output falls by 1.5 percent following a one standard deviation drought in New Zealand.
  - Agricultural output decrease is more muted for Uruguay: 0.6 percent.
  - Uruguay’s consumption falls by more and employment rise is more muted relative to New Zealand.
- Part of the difference may arise from data definitions: Uruguay uses primary sector data (agricultural, fishing and mining), while Gallic and Vermandel (2020) use agriculture, fishing and forestry.

### The role of weather shocks for the business cycle
- Simulations feeding only weather shocks versus all shocks show cyclical impacts:
  - Agricultural output (primary activity) growth oscillates between +3 percent and - 3 percent due to weather shocks.
  - Consumption growth moves +/- 2 percent.
  - Output growth moves +/- one percent.
  - Employment impact is limited, likely due to the low share of labor force in primary activity.
- Weather-driven losses in agricultural output and consumption co-move and help explain weather-driven business cycle impacts (notably aligning with 2008-2009, 2011, 2015 and 2022-2023 drought-related loss periods).

### 2022-2023 drought simulation
- The SMDI increase observed between 2022Q4 and 2023Q2 is mimicked: SMDI around 2 in 2022Q4, peaking above 3 in 2023Q1, then decreasing in 2023Q2; after 2023Q2 SMDI reverts to steady state per estimated autoregressive component.
- The simulated increase in the SMDI is estimated to provide around a one percent fall in GDP for 2023, driven by losses in agricultural output (primary activity) and investment.
- According to the SVAR, the drought impact should subside in 2024; the DSGE model shows a longer-lasting effect.
- In reality, normalization of rainfall in the second half of 2023 (fall in SMDI) is expected to bolster primary sector recovery.

### SVAR robustness and alternative SMDI specifications
- Lag selection: Hannan–Quinn information criterion and Schwarz Information Criterion indicate an SVAR of lag length one is preferred; robustness checks with higher order lags produce similar results.
- SMDI-Countrywide (equal weight to each grid cell) versus agricultural-weighted SMDI:
  - Both indices show droughts negatively impact primary activity, consumption and investment.
  - Using SMDI-Countrywide shows a small uptick in primary output in the second quarter following the shock and a delayed response of consumption.
  - The preferred measure is the agricultural-weighted SMDI as it more accurately captures droughts in areas of agricultural importance; SMDI-Countrywide is robust and requires less granular data.
- Truncated SMDI (positive values only) results:
  - Truncating negative SMDI values to 0 isolates drought impacts.
  - A one standard deviation drought shock with the truncated index lowers agricultural output by 0.7 percent at the peak compared to 0.3 percent with the baseline index.

### Variance decomposition and relative importance of shocks
- Forecast error variance decomposition at posterior mean for horizons (one, ten, fifty and unconditional) shows:
  - Supply shocks (technology shock, labour supply shock and sector reallocation shock) explain the majority of movements in GDP, agricultural output, consumption and employment.
  - Weather shocks play a role for GDP and agriculture but play a significantly diminished role in Uruguay compared to Gallic and Vermandel (2020) for New Zealand.
  - Part of the diminished role may be due to the sample period including Covid-19 and a relatively small sample size (quarterly data from 2005Q2-2023Q2 may impact FEVD accuracy).

### Additional contextual and transmission channels noted
- Agricultural sector in Uruguay combines cultivation of crops and rearing of livestock; cultivation is more susceptible to droughts than livestock, but the model does not split the sector due to tractability and data constraints.
- Severe droughts may have additional economy-wide consequences omitted from the analysis:
  - Heightened water scarcity;
  - Reduced hydroelectric electricity generation;
  - Increased chance of wildfires;
  - Financial transmission channel (e.g., unusually hot days increase delinquency rates in agricultural sector) is omitted, though expected to be muted given credit-to-GDP is relatively low at close to 30 percent of GDP (IMF, 2024).

### Key quantitative findings (exact reported values)
- DSGE persistence: impact lasts up to 5 years (3 years longer than SVAR).
- New Zealand agricultural output fall after one standard deviation drought: 1.5 percent.
- Uruguay agricultural output fall after one standard deviation drought: 0.6 percent.
- Simulated GDP fall for 2023 from 2022-2023 drought episode: around a one percent fall in GDP for 2023.
- Land productivity reduction in DSGE: close to 10 percent.
- Truncated SMDI peak agricultural output fall: 0.7 percent (versus 0.3 percent baseline).
- Business-cycle oscillations from weather shocks:
  - Agricultural output growth: +3 percent to - 3 percent.
  - Consumption growth: +/- 2 percent.
  - Output growth: +/- one percent.
- SVAR Monte-Carlo simulations used: 10,000 runs.
- Sample period noted for FEVD concerns: quarterly data from 2005Q2-2023Q2.
- Credit-to-GDP in Uruguay cited as: close to 30 percent of GDP.

*Source: IMF staff calculations and the content of "4.8    Results" from the supplied PDF chapter.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025004-print-pdf.pdf_