3.1 Identification Strategy

The identification strategy is a two stage procedure. In the first stage, a restricted VAR model is estimated to reflect the small open economy assumption that we use for Uruguay. This small open economy assumption reflects the idea that Uruguay’s macroeconomic variables may react to foreign shocks, but domestic shocks do not significantly impact the rest of the world. Therefore, the foreign variables (rest of the world GDP) is assumed to be exogenous. A similar assumption is made for our weather variable, such that changes in the weather may impact the Uruguayan economy but movements in domestic variables do not impact the weather.⁹ Following the Hannan-Quinn and Schwarz criteria a lag of one is chosen for the restricted VAR and SVAR estimation.

In the second stage, once the restricted VAR is estimated, similar restrictions are imposed in the SVAR model outlined in Equation 3, where the restrictions placed on the A_o matrix can be seen in Equation 4. The SVAR of order p, is written below such that X_t is the n x 1 vector of variables at time t, where n is 8, and is formed of a domestic weather block, a foreign economy block and a domestic economy block. The vector of variables, X_t, is assumed to be a linear function of its past values X_t-i with / being the number of lags l = 1, ...,p. A_t is the n x n matrix of lagged parameters and C is the n vector of constants. The nx1 disturbances η_t are assumed to be normally distributed as η_t ~ N(0, Σ_η).

The restrictions placed on A_o outlined in Equation 4 help us identify the orthogonal structural disturbances contained in vector η_t. Variables are written with a hat to denote that the data is logged and detrended – except the real effective exchange rate, which is in log differences and the SMDI which is not transformed. The weather variable $\begin{array}{c}{\begin{array}{c}\hat{\omega }\end{array}}_t\end{array}$ is ordered first, followed by foreign real output $\begin{array}{c}{\hat{y}}_t^{*}\end{array}$ such that these variables are contemporaneously affected by themselves only, following the exogeneity assumptions previously outlined. Domestic real GDP $\begin{array}{c}{\hat{y}}_t\end{array}$ is assumed to be the most exogenous domestic variable and is therefore ordered third. The domestic variables $(\begin{array}{c}{\hat{y}}_t\end{array},\begin{array}{c}{\hat{y}}_t^A\end{array},\begin{array}{c}{\hat{h}}_t\end{array},\begin{array}{c}{\hat{c}}_t\end{array},\begin{array}{c}{\begin{array}{c}\hat{i}\end{array}}_t\end{array},\begin{array}{c}{\begin{array}{c}r\hat{e}r\end{array}}_t\end{array})$ are able to respond contemporaneously to changes in the weather and foreign output. Agricultural output (primary activity) $\begin{array}{c}{\hat{y}}_t^A\end{array}$ is assumed to contemporaneously respond to the weather, foreign output and domestic GDP. The employment rate $\begin{array}{c}{\hat{h}}_t\end{array}$ is assumed to respond to the weather, foreign output, domestic GDP and agricultural output (primary activity). Consumption $\begin{array}{c}{\hat{c}}_t\end{array}$ and investment $\begin{array}{c}{\begin{array}{c}\hat{i}\end{array}}_t\end{array}$ respond to weather, foreign output, GDP, agricultural output (primary activity), employment and for investment it is also able to respond to consumption. The most endogenous variable in our model is the real exchange rate $\begin{array}{c}{\begin{array}{c}r\hat{e}r\end{array}}_t\end{array}$, which is ordered last.

The coefficients of the restricted VAR in Equation 4 are depicted in Section A.1.

3.2 Empirical Results

Following the estimation of the SVAR we now present the empirical results obtained from an adverse weather shock of one standard deviation of the SMDI variable. This simulates the impact of a drought on the Uruguayan economy.

According to the Structural VAR model, an adverse weather shock, a one-standard deviation rise in the drought variable (Figure 5), generates a contraction in Uruguay’s economy. The dashed red lines are responses to the shock, while the gray areas show the 95% error bands obtained from 10,000 Monte-Carlo simulations. Impulse responses are shown at the quarterly frequency for 20 periods (5 years). A rise in soil moisture deficits implies a contemporaneous 0.1 percent decrease in the agricultural sector (primary activities: agricultural, fishing and mining) and a peak decline in GDP of 0.3 percent after 3 quarters. The weather variable vanishes after one year, however its impact on the economy is persistent – impacting primary activity for 2 years in the SVAR. The weather shock manifests itself through the labor market by a fall on impact of employment followed by a rebound, which mimics the behavior of a TFP shock, where a fall in productivity of the worker leads the firm to hire more workers to sustain output.

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SVAR Impulse Response from a drought shock in Uruguay

Citation: IMF Working Papers 2025, 004; 10.5089/9798400298059.001.A001

Sources: IMF staff calculations.Notes: Impact on the Uruguayan economy from a one standard deviation shock to the Soil Moisture Deficit Index (weather shock). Time series is quarterly. The red dashed line is the Impulse Response Function, the gray band represents the 95% confidence intervals obtained from 10,000 Monte-Carlo simulations. The time horizon is plotted on the x-axis while the percent deviation from the steady state is plotted on the y-axis.

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4.1 Agricultural Sector (Primary Activity)

The economy is populated by a unit mass of i ∈ [0,1] firms where a fraction of the firms i ∈ [0, n_t] belong to the agricultural sector and the remaining fraction 1 – n_t belong to the non-agricultural sector.¹⁰

Production from the agricultural sector follows a Cobb-Douglas production function with land, which is further augmented to include a cost function for weather that impacts land productivity. Agricultural output by firm i is given by $\begin{array}{c}{y}_{it}^A\end{array}$, which is a combination of the land used that firm l_i,t-1, the physical capital $\begin{array}{c}{k}_{i,t-1}^A\end{array}$ and labor demanded $\begin{array}{c}{h}_{it}^A\end{array}$. The parameter ω ∈ [0,1] is the elasticity of output to land and α ∈ [0,1] governs the share of physical capital in the production process. Technology parameter K_A > 0 is also included to help endogenously determine the steady state of the model. Motivated by the SVAR we assume that agricultural production is impacted by the weather shock, such that an increase in the weather shock (drought) causes a fall in agricultural output through a temporary drop in land productivity. The impact of weather enters the model through a cost function defined by $\Omega \left({\in }_t^W\right)$ and described in more detail below. Capital and labor are subject to an economy-wide technology shock ${\in }_t^Z$, which follows a standard AR(1) process impacting both the agricultural and non-agricultural sectors.

Damage of the weather shock to land productivity depends on the estimated parameter θ that forms part of the weather cost function: $\Omega \left({\in }_t^W\right)={\left({\in }_t^W\right)}^{-\theta }$. When θ = 0 the impact of weather on the business cycle is shut down. The weather shock is assumed to follow an AR(1) process:

with persistence p_w ∈ [0,1) and standard deviation σ_w > 0. Although the weather shock may not be persistent it can have persistent impact on agricultural output and throughout the economy.

We assume that land is not fixed and can vary over time. This is an important assumption in the model to better capture the impact of the drought on critical cultivation periods that appear throughout the year. Therefore, land follows a law of motion defined by:

where δ_ℓ ∈ (0,1) is the rate of decay of land productivity. As in Gallic and Vermandel (2020) it is assumed that the marginal product of land is increasing in the accumulation of land productivity, which is captured by assuming that land expenditures x_it yield a gross output of new productive land ν(x_itℓ_it-1 with ν’(·) > 0, ν”(-) ≥ 0. Land expenditure x_it can be thought of as spending on fertilizers and water used to maintain farmland that can be increased to offset the soil dryness caused by a drought.

The law of motion of physical capital in both the agricultural and non-agricultural sectors are standard. For the agricultural sector, capital accumulation through investment in capital:

where δ_K ∈ [0,1] is the depreciation rate of physical capital. The firms in the agricultural sector maximize their profits, which are determined by the value of their production (price of agricultural good multiplied by the volume of agricultural goods produced) taking into account the cost of labor, the cost of land expenditure and the convex cost of investment as defined in Christiano et al. (2005) to provide the hump shaped response of investment seen in the SVAR. The real profits are summarized by:

The investment cost includes a shock process, governed by ${\in }_t^i$, which follows an AR(1) process and makes investment more expensive. The representative firm in the agricultural sector is assumed to be a price taker and their maximization problem can be summarized as follows:

where E_t is the expectation operator and Λ_t,t+τ is the household stochastic discount factor between t and t + τ.

4.2 Households

There is a continuum j ∈ [0,1] of identical households that consume, save and work in the two production sectors. Households aim to maximize their welfare expressed as the sum of their utility discounted by β. Household consumption is expressed as C_jt. Households are assumed to have habit persistence, governed by the estimated parameter b ∈ [0,1), such that they enjoy a similar level of consumption to their past. Households also work, with their labor effort defined as the aggregate of their work in the agricultural and non-agricultural sectors by h_jt. Degree of relative risk aversion and labor disutility is governed by σ > 0 and σ_H > 0, respectively. Steady state labor supply is calibrated through a shift parameter χ and ${\in }_t^H$ represents a labor supply shock term that follows an AR(1) process that makes working have a greater negative impact on welfare. The utility function is given by:

where as in Horvath (2000) there is imperfect substitutability of labor supply between the agricultural and non-agricultural sectors to explain the co-movements in labor at the sector level. The CES labor disutility index consists of employment in the non-agricultural sector $h_{jt}^N$ and agricultural sector $h_{jt}^A$. Labor reallocation between sectors is assumed to be costly and is governed by the substitutability parameter ι ≥ 0. If the estimated parameter ι is zero then work between the non-agricultural and agricultural sectors are perfect substitutes. A positive value for ι mean that there is a preference by households of work between the sectors such that employment in each sector responds less to the sector wage differential between the sectors. The CES labor disutility index is outlined below:

Households maximize their utility (Equation 11) subject to a budget constraint (Equation 13). Expressed in real terms the household budget constraint is:

Households gain a wage for their work, defined as the real wage $w_t^s$ multiplied by the hours worked $h_{jt}^s$ where s = N for the non-agricultural sector and s = A for the agricultural sector. Households gain a return from the risk-free domestic bonds that they hold b_jt and $b_{j,t-1}^s$ defined by the domestic and foreign real interest rate (r_t-1 and $r_{t-1}^{*}$, respectively), where the latter is affected by the real exchange rate $re{r}_t^{*}$. The real exchange rate is defined by the nominal exchange rate adjusted for the relative price differences in the foreign and home economies $(re{r}_t^{*}=e_t^{*}{P}_t^{*}/P_t)$. Taxes are assumed to be lump sum (T_t) so that they do not distort the household’s optimization problem. The last term in the budget constraint is the risk premium cost Φ (6*_t) of foreign bonds which are paid for in terms of domestic non-agricultural goods at the relative market price $p_t^N=P_t^N/P_t$.¹¹

Household consumption is a CES bundle of agricultural and non agricultural goods where µ ≥ 0 denotes the elasticity of substitution between the two types of consumption goods and φ ∈ [0,1] is the fraction of agricultural goods in the household’s consumption basket, which is calibrated using the weights in the consumer price index. The consumer price index, P_t, in the economy can be similarly written out as a CES bundle with φ governing the weight of non-agricultural priced goods $P_{C,t}^N$ and agricultural goods $P_{C,t}^A$. The CES consumption bundle is summarized below:

with each index $C_{jt}^{N}and{C}_{jt}^A$ being a composite consumption subindex that is composed of domestic and foreign produced goods:

We allow for home bias in origin of consumption goods that the households consume, given by 1 − α_s ≥ 0.5 and µ_s > 0 denotes the elasticity of substitution between home and foreign goods. In a similar way as the consumer price index of the CES consumption bundle, the production price index exists for each sector is given by a CES of the price of home and foreign goods in sector s, weighted by the home bias 1 — α_s and with an elasticity of substitution µ_s.

Demand schedules for each type of good can be defined as a function of their relative prices, weight in the consumption basket and home basket:

4.3 Non-Agricultural Sector

Production in the non-agricultural sector is similar to the agricultural sector, except firms do not face weather shocks and the Cobb-Douglas production function does not include land. Within the non-agricultural sector there exists a continuum of firms indexed by i ∈ [n_t,1], with 1 – n_t denoting the relative size of the non-agricultural sector. Their Cobb-Douglas production function is given by:

where $y_{it}^N$ is the production of the intermediate goods firms, $k_{i,t-1}^N$ is the stock of physical capital of firm i, $h_{it}^N$ is the labor employed in the non-agricultural sector for firm i and ${ϵ}_t^Z$ is the AR(1) technology shock. The parameter α governs the elasticity of capital and labor in the production on non agricultural goods.

Similarly to the agricultural firms, the non-agricultural firms also need to invest $i_{it}^N$ to accumulate physical capital. This is given by:

where δ_K ∈ [0,1] is the depreciation rate of physical capital. Real profits are given by:

and firms maximize the discounted sum of profits:

under technology and capital accumulation constraints.

4.4 Government

The government is kept purposely simple. The government consumes non-agricultural output G_it, issues debt b_t at a real interest rate r_t and charges lump sum taxes T_t to households. Government consumption is assumed to be exogenous, $G_t=Y_t^{N}g{\in }_t^G$ where g ∈ [0,1), and is impacted by a standard AR(1) stochastic shock process for ${\in }_t^G$.

4.5 Foreign Economy

The Foreign economy is stylized as Uruguay is a small open economy, which by assumption cannot impact the foreign block. The foreign country is needed in the model to determine Uruguay’s exports and real exchange rate dynamics. The foreign country is modeled as an endowment economy with exogenous foreign consumption:

where 0 ≤ pc < 1 determines the return to steady state of foreign consumption. The parameters σ_c and ρ_c are estimated to match foreign demand.

Each period, foreign households solve the following optimization scheme:

where variable ${\in }_t^E$ is a time-preference shock defined as follows:

4.6 Equilibrium and Aggregation Equations

The market clearing condition for non-agricultural goods is determined by equating aggregate demand and aggregate supply:

where aggregate real production is given by:

In addition, the equilibrium of the agricultural goods market is given by:

GDP is given by :

The law of motion for the total amount of real foreign debt is:

where the trade balance is:

4.7 Calibration and Estimation

The model is calibrated using standard parameters from the literature and Uruguay-specific parameters calculated using historical averages. Table 1 summarizes the calibration of the model. The discount factor β, capital depreciation rate δ_K, the share of capital in output a, hours worked ${\overline{H}}^N={\overline{H}}^A$ and international portfolio cost are all standard.¹². The share of public spending in GDP g = 0.216 is derived by taking the average of the share of public consumption and public investment of GDP between 2016–2022. The share of agricultural goods in the consumption basket φ = 0.17 is calculated by aggregating the weights of the agricultural related products in Uruguay’s consumer price index. Uruguay’s land-to-employment $\overline{l}=1.30$ parameter is derived from the World Bank’s World Development Indicators (WDI) and estimates of the population and persons employed – the final result is the average of land-to-employment between 2005 to 2021. Land-to-employment is where the largest discrepancy with respect to Gallic and Vermandel (2020) arises regarding the calibration of parameters, who calibrate their model ${\overline{l}}^{NZ}=0.4$ for New Zealand. This discrepancy arises as Uruguay has around a five times larger rate of arable land per capita than New Zealand.¹³. The openness of non-agricultural market α_N and agricultural market α_A are determined by the average value of non-agricultural exports as a share of non-agricultural GDP and share of agricultural exports as the share of agricultural GDP (primary sector GDP) between 2016 to 2022.