Methodology

6. A dynamic quantitative open economy spatial multi-sector macroeconomic model² is used to analyze the economic effects of climate shocks and food insecurity in Niger. The model features both rural and urban locations. Food is produced in rural areas on household farms using labor, imported fertilizer, and capital. Urban areas specialize in non-farm activities, especially services and industry. Economic agents can trade and migrate across regions (with relative wages declining in the region where people are migrating to) subject to frictions and can import from abroad. Three features, prevalent in low-income countries, are included in the model: (i) subsistence consumption of food (which implies that households spend relatively more on food when incomes fall); (ii) limited access to finance (which introduces a trade-off between consumption today and production later); and (iii) high transportation costs and import tariffs (which results in limited internal mobility of labor and goods. Incorporating these frictions in a dynamic setting with important sources of spatial and income heterogeneity allow the model to consider the macroeconomic implications of food insecurity.

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Niger: Spatial Multi-Sector Macroeconomic Model

Citation: IMF Staff Country Reports 2023, 029; 10.5089/9798400229473.002.A006

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7. Climate shocks are modeled as a one-period temporary 25 percent decline in agricultural productivity—equivalent to two standard deviations of agricultural output.³ In order to simulate the effects of climate change on food insecurity, the model’s output is directly linked to households’ food consumption and the corresponding total number of calories. Furthermore, the model allows us to quantify the effect of climate shocks on (i) rural households’ capital level, (ii) migration, (iii) urban/rural inequality, and (iv) food prices (domestic and imported). When hit by a negative agricultural shock, households may sell productive capital to meet a minimum food consumption requirement. If the shock is small and isolated, the economy adjusts relatively quickly. Rural households only temporarily migrate to urban areas; and these adjustments are easier when trade and migration frictions are small. However, If the shock is large, the household will give up substantial productive capital to meet the subsistence food requirement. In this case, the effects could be more persistent as the household will need several periods to rebuild the capital needed to operate a productive farm again and would be more likely to migrate to work in non-farm sector to make up for farm income shortages. A household facing lower farm production causes an aggregate “food price” pecuniary externality, as nationwide food shortages and rising prices increase the likelihood that other households will also be food insecure. The result is a permanent decline in agricultural production, higher food prices, lower food consumption, migration to urban areas, increased regional inequality, lower economic growth and productivity.

8. The model enables an assessment of the comparative effectiveness of various policy responses in mitigating the effects of the shock on households. These policies include:

• Cash transfers: under this policy, the government taxes all households (urban and rural) up to 15 percent of their income and redistribute the revenue through cash transfers to rural households who are considered more vulnerable. The cash transfers scheme is considered well-defined by specifying beneficiaries/vulnerable groups to reduce leakages and increase the effectiveness of the transfers.

• Fertilizer subsidies consist of subsidizing rural households purchases of fertilizer inputs for agricultural production. This policy is financed in the same way as cash transfers.

• Trade liberalization involves eliminating import tariffs on staple food with aiming to support domestic food supply.

• Reduction in internal mobility costs implies the removal of mobility barriers between rural and urban areas. Households, goods, and services can therefore easily move from one locality to another at a lower cost. This policy not only reduces the vulnerability of localities to food shortages, but also facilitates the temporary migration of households to other localities to gain additional income in bad times.

Simulations

9. Rural households would be the hardest hit by a drop in agricultural production caused by a climate shock (Figure 3). Their food consumption would decline following the shock by 18 percent against 14 for urban households, as the share of domestically produced food staples in their consumption basket is much higher. Also, the increase in food prices would be higher in rural areas (27 percent) compared to urban areas (24 percent) mainly because of relatively higher consumption of imported foodstuff by urban households. As a result, calorie consumption would fall for both groups, but to a larger extent for rural households, which would approach the 2100 kcal/day threshold.⁴ This would lead to rising inequality in real consumption between rural and urban localities. In addition, the shock would entail an erosion of rural households’ disposable capital (by 15 percent)—only partially rebuilt 5 years later. Indeed, to smooth consumption, rural households would sell part of their capital. Urban households, similarly, to their rural counterparts, tend to increase their consumption of imported food in response to the shock.

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Niger: Impacts of a 25 Percent Decrease in Agriculture Production¹

Citation: IMF Staff Country Reports 2023, 029; 10.5089/9798400229473.002.A006

Source: IMF staff calculation1/ Food price, food consumption, capital and welfare series are normalized, i.e., all values are expressed relative to baseline value in period 0.

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10. Cash transfers appear more effective than fertilizer subsidies at safeguarding households’ welfare. Simulations depicted in Figure 4 show that, overall, cash transfers raise consumption and utility for rural households as some of the extra cash is used to buy goods (food and non-food) and accumulate additional capital, which raises farm productivity and lowers food prices and migration as the urban-rural wage gap becomes smaller. In turn, fertilizer subsidies decrease the price of domestically produced food and the share of imported food, due to lower domestic food production cost. However, this policy appears costly on net terms as evidenced by the resulting reduction in welfare for both rural and urban households and the lower level of agriculture capital even relative to the baseline “no policy response” scenario as a result of farmers substituting capital for fertilizers-which have become relatively cheaper. In other words, the marginal cost of reducing household cash-in-hand is higher than the marginal benefit from increased fertilizer usage. In contrast, households have various options to use the cash transfer, which include not only purchasing fertilizer but also smoothing their consumption, and accumulating capital.

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Niger: Cash Transfer vs Fertilizers Subsidies¹

Citation: IMF Staff Country Reports 2023, 029; 10.5089/9798400229473.002.A006

Source: IMF staff calculation1/ Food price, food consumption, capital and welfare series are normalized, i.e., all values are expressed relative to baseline value in period 0. For simplification purpose, results are shown only for rural households.

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11. Reducing mobility costs appears more effective than lowering import tariffs to mitigate the effects of climate-related food insecurity shocks on households. Figure 5 shows that the distance between total calories consumed, and the critical requirement threshold is larger in the low internal mobility cost scenario than in the trade liberalization scenario. Although the reduction in import tariffs is expected to supplement the domestic food supply by increasing food imports, its gains are not evenly distributed between urban and rural areas. Urban households benefit slightly more from this policy, as their consumption basket include a larger share of imported food. This leads to increased inequality between urban and rural areas, while in the low internal mobility cost scenario, inequality is relatively lower because farmers have access to urban areas and additional opportunities to increase their income, consumption, capital, and welfare.

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Niger: Trade Liberalization vs Low Internal Mobility Cost¹

Citation: IMF Staff Country Reports 2023, 029; 10.5089/9798400229473.002.A006

Source: IMF staff calculation1/ Food price, food consumption, capital and welfare series are normalized, i.e., all values are expressed relative to baseline value in period 0. For simplification purpose, results are shown only for rural households.

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Overview

The economy is made up of two locations, rural (R) and urban (U), and is populated by LU urban households and a continuum? of rural households of mass Lr. Both types of households consume an agricultural (F) and a non-agricultural good (M).⁷ All domestic agricultural production is carried out by rural households who may then either sell their agricultural output to urban households, export it or use it for self-consumption. Households in the urban area only produce non-agricultural goods. Rural households allocate a fixed share of their labor endowment to agricultural production and use the remaining share to supply wage labor to a perfectly competitive firm in the non-farm sector. Rural households can decide to supply wage labor in the rural or urban area. Urban households, on the other hand, only supply labor to the non-farm sector firm in the urban area and are not allowed to move outside the urban area. Both agricultural and non-agricultural goods can be imported from and exported to a foreign economy denoted by the rest of the World (ROW).

Consumption and Saving

Households residing in location i = 1, …, N have preferences over a final good C_t and net period savings B_it represented by the utility function

U_t = log(C_it – $\overline{C}$) + β logB_it+1.        (1)

Households maximize the utility function above by choosing optimal consumption and savings subject to the per-period constraint P_itC_it + B_it + 1 = Y_it + (1 – δ)B_it, where Y_it is current household income, P_it is the price of the final consumption good, and (1 - δ)B_it is the net of depreciation stock of savings carried over from the previous period, with 0 < δ = 1. Y_it is defined as household net income which consists of gross income minus income tax paid plus cash transfers received, i.e. Y_it = Y^gross(1 – tax_t) + cash_it.

We introduce a consumption requirement $\overline{C}$ to capture the notion that households must consume a minimum amount of goods (a mix of agricultural and non-agricultural goods) to satisfy their basic needs. Importantly, the consumption requirement generates a consumption smoothing motive so that if income falls temporarily in the current period the household reacts by decreasing their savings rate, i.e. by allocating a larger share of wealth W_it = Y_it + (1 - δ)B_it towards current consumption. The opposite happens under a temporary income windfall. Note, however, that under a permanent income increase the household reacts by increasing the savings rate. Intuitively, the higher income allows the household to move away from the consumption constraint and save at a rate closer to the “ideal” savings rate β / (1 + β).

The household will optimally select to spend a nominal amount Xit on goods consumption given by

where P_it is the price of purchasing the minimum consumption bundle. The remaining amount of household wealth will be saved, i.e.

The savings rate savit is therefore given by savit = [β/(1 + β)](1 - P_itC/W_it) and is increasing in wealth.

The final goods consumption bundle Cit is made up of agricultural and non-agricultural goods. Here, again, we introduce a subsistence requirement but this time for food consumption $\overline{C^F}$ to capture non-homothetic preferences in the final goods bundle. Note the important distinction between $\overline{C}$ and $\overline{C}$. The first is an upper-tier consumption requirement that introduces non-homotheticity in final goods consumption vs savings preferences, while the second is a lower-tier consumption requirement that introduces non-homotheticity for agricultural vs non-agricultural goods preferences. Thus, preferences for the final good are described by the Stone-Geary utility function

where we omit the time subscripts for simplicity. Households take the price of the agriculture good $P_i^F$ and non-agriculture good $P_i^S$ as given and maximise function (2) subject to $P_i^F{C}_i^F+P_i^S{C}_i^S=P_i{C}_i,$ where P_iC_i is total household spending on goods. This problem yields optimal food (or agricultural) consumption.

Calorie consumption kcalit has a constant elasticity of substitution relation with food consumption so that kcalit = a(C_it^F)^ζ, where 0 < ζ < 1 and a is a constant.

We assume households always spend enough to satisfy the food subsistence requirement, i.e. $P_i{C}_i\ge P_i^F{\overline{C}}^F,$ for all households. For non-agriculture, optimal consumption is

Optimal consumption implies the final goods consumption price index

where ζ ≡ α^–α(1–α)^–(1-α) is a constant. We assume households derive utility from consuming different local varieties of goods and define the Armington aggregator with elasticity of substitution σ , with σ > 1

where c^F_in denotes food goods imported into i = {U,R} from location n = {U,R,ROW}. The urban area produces only non-agricultural goods and so $c_{iU}^F=0$ for all i = {U,R}. The Armington aggregator implies the CES price index:

where p^j_in is the price of sourcing goods from location n into i. Shipping goods from one location to another incurs an iceberg trade cost τ_in for any pair n,i with τ_in = 1 and τ_ii = 1 for all i, n. The price of importing goods from abroad, p^j_ROW, is exogenously determined. The net price of goods imported into i from n will equal factory gate prices in n plus a transportation cost τ_in, so that

One can show that the wholesaler will optimally choose to source goods according to the import share equation:

where π_in^j is the share of expenditures X_i^jF spent on purchasing goods from origin n and τ_i,ROW is the cost of importing goods from abroad into i. The share of expenditures from location n falls with farm-gate price p^j_n and shipping cost τ (or τ_i,ROW from imports) and rises with the CES price index P_i^j. In other words, more is purchased from origin n whenever sourcing goods from there becomes relatively cheaper than the cost of final food goods bundle C_i^jF.

Agricultural Production

Each rural household has access to a plot of land of size h which they use to produce an agricultural good according to the production function

where z_t is farm productivity, k_t is installed farm capital and ft is fertilizer input. Capital should be interpreted in a broad sense so as to include a wide range of productive inputs like, seeds, tools, machinery, irrigation and livestock. All rural households supply the same fixed amount of labor to their total farm production, which we set equal to 0 < ρ < 1. Households allocate their savings across the two productive factors so that their marginal productivity is equalized, i.e.

where p^f and p^k are the prices of fertilizer and capital, respectively. Households are unable to borrow and so installed capital k_t and fertilizer f_t are financed exclusively through the accumulation of household savings. Rural households employ all their savings B_it in the form of farm capital and fertilizer and may then decide to either carry over the net-of-depreciation capital stock to the next period or sell it off to finance current consumption. Contrarily to capital, fertilizer depreciates fully in each period. All capital goods and fertilizer are imported from the foreign economy.⁸

Non-agricultural Sector

In both the urban and rural areas there is a perfectly competitive firm that produces non-agricultural goods by hiring labor from households. In the rural area, only rural households are hired. Production is given by the linear production technology:

where ψ_t is the share of rural households who decide to stay in the rural area. The remaining portion (1 - ψ_t) migrates to the urban area for wage work and so production in the urban area is given by

where z^M is local non-agricultural TFP. Households earn wage rate w_it. In equilibrium, firms make zero profits or, equivalently, the marginal revenue product of labor is set equal to the wage rate

where p^S_it is the price of local non-agricultural goods. The foreign economy ROW has an exogenously set wage rate (and consumption price index) that households take as given.

To incorporate the wage work location choice by rural households, we assume they face the location choice problem

where D_i is the amenity value of location i. The assumption that D_R > Dn for any n = {U,ROW} captures moving costs which make rural households more likely to supply labor in the rural area than elsewhere, holding fixed real wages w_it/P_it|n.⁹ Term k_it(ω) captures an idiosyncratic work location preference that follows a Frechet distribution with scale parameter 1 and dispersion parameter λ, iid across households and time. The choice of work location will depend on the household’s idiosyncratic draws for the costs of temporary migration.

Households that draw a low cost of temporary migration for a given destination will be more likely to exploit spatial differentials in real wages by seeking employment in that location. For other households, the costs will be so high that they will prefer all members to remain in the residence location rather than migrate to another, higher-paying location. The dispersion parameter λ measures the degree of heterogeneity in idiosyncratic location preferences, with λ → ∞ representing the extreme case where preferences are fully homogeneous across all households. Lower values of λ correspond to more heterogeneity in personal preferences for locations.

Note that V_t depends on a migration-adjusted real wage. The price index P_it|_R combines the price indices of rural and destination location according $P_{it|R}=P_{it}^{\varphi }{P}_{RT}^{1-\varphi }$ with 0 < Φ < 1. We employ this migration-adjusted price index to account for the role of remittances.¹⁰ We assume all members of the household pool their income and use transfers to equalize real consumption with some members of the household buying goods at the destination price index P_it and the remaining at the origin price index P_nt. Parameter Φ governs the relative consumption expenditure at the two locations and we set it equal to the share of migrating household members. To ensure real consumption is equalized across members of the household, migrants send remittances back to their residence location, where the other members of the household live.

Using the properties of the Frechet distribution, one can show that the probability of sending migrants to (or remaining in) location i, ξ_it, is given by

With the existence of a continuum of rural households, the law of large numbers implies that actual migration flows will match the probability above. This implies that ξ_Ut = ψt. Seen through the expression above, parameter λ controls the size of migration responses to changes in local conditions. A lower λ implies that an increase in wages in i will generate a smaller inflow of migrants into that location. λ therefore governs the elasticity of migration flows with respect to seasonal migration-adjusted real wages. In the extreme case of λ → ∞, the elasticity of migration is infinite and indirect utility V_t(ω) must be equalized for all households. Note that real wages will not necessarily be equalized across locations due to amenity differences.

Market Clearing

In this section we close the model by providing market clearing conditions. To ensure market clearing in goods markets, we impose the condition that sales Y_i^J for j = {A, S} must equal the sum of sales across all destinations. First, assume exports to the rest of the world X_ROW,n^jF are given by a constant elasticity function of prices with elasticity 1 - σ

where k^j is a constant. The market clearing condition for goods is then given by

which pins down the vector of equilibrium farm-gate price of goods p^j_i for i = {R,U}. Since markets are perfectly competitive, sales must equal expenditures which must in turn equal total farm sales. We can then write

This expression provides us with a system of equations that pin down equilibrium prices in the market. Given trade shares π_ni (which depend on the characteristics of the trade network and the relative efficiency of each location) and exports X_ROW,_i^F , the equation provides the vector of equilibrium goods prices (p^S_U, p^F_R, p^S_R) that are consistent with market clearing. Finally, we assume the government budget is balanced so that tax revenues R_t must equal spending S_t on cash transfers and fertilizer subsidies

for in all time periods t = {1, 2, …}. Note we assume that rural households are the sole recipients of government benefits.