Package {agriEquity}

agriEquity: Equity and Sustainability Assessment of Agricultural Subsidies

Description

An integrated framework for distributional analysis of agricultural support, budget-neutral subsidy allocation and productivity-equity-sustainability trade-offs.

Details

* [benefit_incidence()] - who receives the subsidy, by group or quantile. * [progressivity_index()] - concentration, Kakwani and Reynolds-Smolensky measures. * [subsidy_equity()] - multi-dimensional equity scorecard with Theil decomposition. * [distributional_effects()] - inequality and poverty with and without the subsidy, for one or more scenarios. * [budget_reallocation()] - budget-neutral allocation rules, including a welfare-optimal allocation. * [tradeoff_frontier()] - productivity-equity-sustainability frontier.

The example data set [farm_subsidy] is simulated.

Author(s)

Maintainer: Anbukkani Perumal anbueconomic@gmail.com [copyright holder]

Benefit incidence analysis of agricultural support

Description

Shows how a subsidy or support payment is distributed across groups of farm households: landholding classes, gender of the farmer, regions, or quantiles of income or landholding. For each group the function reports its (weighted) share of farm households, its share of total benefits, the parity ratio (benefit share divided by population share; values below 1 mean the group receives less than its population share), the coverage rate (share of households receiving any benefit), the mean benefit per household and per beneficiary, and, if supplied, the mean benefit per hectare and benefits as a share of group income.

Usage

benefit_incidence(
  data,
  benefit,
  group = NULL,
  rank_var = NULL,
  n_quantiles = 5,
  weights = NULL,
  area = NULL,
  income = NULL
)

Arguments

Value

A data frame of class 'benefit_incidence', one row per group, with columns 'group', 'households', 'population_share', 'benefit_share', 'parity_ratio', 'coverage', 'mean_benefit_per_household', 'mean_benefit_per_beneficiary' and, when available, 'benefit_per_hectare' and 'benefit_income_ratio'.

Examples

benefit_incidence(farm_subsidy, "fertiliser_subsidy",
                  group = "size_class", weights = "weight",
                  area = "land_ha", income = "farm_income")
benefit_incidence(farm_subsidy, "income_transfer",
                  rank_var = "farm_income", weights = "weight")

Budget-neutral reallocation of agricultural support

Description

Redistributes a fixed support budget among farm households under alternative allocation rules and evaluates every allocation on the same productivity, equity and sustainability metrics, so that reforms can be compared at equal fiscal cost.

Usage

budget_reallocation(
  income,
  current,
  weights = NULL,
  budget = NULL,
  area = NULL,
  priority = NULL,
  target = NULL,
  return_rate = 0,
  saturation = NULL,
  env_cost = 0,
  inequality_aversion = 1,
  env_weight = 1,
  area_cap = 2,
  max_per_farm = Inf,
  poverty_line = NULL,
  income_floor = NULL,
  rules = c("current", "per_farm", "per_hectare", "per_hectare_capped", "targeted",
    "optimal")
)

Arguments

Details

**Rules.** '"current"' (the existing distribution, rescaled to the budget), '"per_farm"' (equal amount per household), '"per_hectare"' (proportional to operated area), '"per_hectare_capped"' (proportional to area up to 'area_cap' hectares), '"targeted"' (proportional to a household priority score, for example higher for marginal farmers, women and resource-poor regions) and '"optimal"'.

**Household model.** A household receiving support s_i gains the transfer itself plus an additional productivity response with diminishing returns,

q_i(s_i) = r_i k_i \ln(1 + s_i / k_i),

where r_i is the marginal output value of the first unit of support (for example from better input use) and k_i a saturation scale. Support also causes an environmental cost e_i s_i (for example the damage value of nutrient surplus or groundwater depletion induced by input or power subsidies).

**Optimal rule.** Shares s_i \ge 0 with \sum_i w_i s_i = B maximise

\sum_i w_i U(y_i + s_i + q_i(s_i)) - \lambda \sum_i w_i e_i s_i,

where U has constant inequality aversion \varepsilon (Atkinson, 1970) normalised so that the marginal welfare weight at mean income is 1. \varepsilon = 0 values all income equally (pure efficiency); larger \varepsilon gives more weight to poorer households. \lambda is the weight on environmental cost. The solution equalises marginal social value across households and is found by nested bisection on the budget multiplier.

**Metrics.** Budget, productivity gain (total q_i), productivity per unit of budget, environmental cost, net social value (productivity gain minus environmental cost), Gini of post-support income, concentration index of support by income, Atkinson equally distributed equivalent income and its gain, share of support reaching 'target' households, and optionally poverty headcount and gap.

Value

A list of class 'budget_reallocation' with 'metrics' (one row per rule), 'allocations' (data frame of support per household under each rule) and 'params'.

References

Atkinson, A. B. (1970). On the measurement of inequality. *Journal of Economic Theory*, 2(3), 244-263. doi:10.1016/0022-0531(70)90039-6

Examples

fs <- farm_subsidy
prio <- with(fs, 1 + (size_class %in% c("marginal", "small")) +
               0.5 * (gender == "female") +
               0.5 * (region %in% c("Rainfed-East", "Hill-Tribal")))
br <- budget_reallocation(fs$farm_income, fs$fertiliser_subsidy,
                          weights = fs$weight, area = fs$land_ha,
                          priority = prio,
                          target = fs$size_class %in% c("marginal", "small"),
                          return_rate = fs$marginal_return,
                          env_cost = fs$env_cost_per_rupee,
                          inequality_aversion = 1, env_weight = 1,
                          poverty_line = 60000)
br

Distributional effects of subsidies on income, inequality and poverty

Description

Compares farm household income without support with income including the benefits under one or more subsidy scenarios. For each scenario it reports mean income, the Gini coefficient, the redistributive effect, the Foster-Greer-Thorbecke poverty measures FGT_0 (headcount), FGT_1 (poverty gap) and FGT_2 (severity) at the given poverty line, the share of households lifted out of poverty, and the cost per household lifted. A quantile table shows mean benefit and the percentage income gain in each quantile of pre-subsidy income.

Usage

distributional_effects(
  income,
  benefits,
  weights = NULL,
  poverty_line,
  n_quantiles = 5
)

Arguments

Value

A list of class 'distributional_effects' with 'summary' (one row per scenario plus the no-support baseline) and 'by_quantile' (mean benefit and percentage income gain by pre-subsidy income quantile and scenario).

References

Foster, J., Greer, J. and Thorbecke, E. (1984). A class of decomposable poverty measures. *Econometrica*, 52(3), 761-766. doi:10.2307/1913475

Examples

de <- with(farm_subsidy, distributional_effects(
  farm_income,
  list(fertiliser = fertiliser_subsidy, transfer = income_transfer,
       power = power_subsidy),
  weights = weight, poverty_line = 60000))
de

Simulated farm-household data on agricultural support

Description

A synthetic cross-section of 1,500 farm households generated by 'data-raw/make_data.R' to illustrate the package. Support, income, productivity-return and environmental-cost values are simulated and are not estimates for any country, scheme or survey.

Usage

farm_subsidy

Format

A data frame with 1,500 rows and 12 columns:

household

Household identifier.

region

'"Irrigated-North"', '"Irrigated-South"', '"Rainfed-East"' or '"Hill-Tribal"'; the last two represent resource-poor regions.

gender

Gender of the principal farmer ('"female"', '"male"').

land_ha

Operated area, hectares.

size_class

Landholding class: marginal (< 1 ha), small (1-2), semi-medium (2-4), medium (4-10) or large (>= 10).

farm_income

Annual household farm income before support (currency units).

fertiliser_subsidy

Input (fertiliser) subsidy received.

income_transfer

Flat direct income transfer received.

power_subsidy

Irrigation power subsidy received.

marginal_return

Marginal output value per unit of additional support (simulated).

env_cost_per_rupee

Environmental damage cost per unit of input support (simulated).

weight

Survey weight.

Source

Simulated.

Plot a productivity-equity-sustainability frontier

Description

Plot a productivity-equity-sustainability frontier

Usage

## S3 method for class 'tradeoff_frontier'
plot(x, ...)

Arguments

Value

'x', invisibly.

Examples

fs <- farm_subsidy[1:300, ]
plot(tradeoff_frontier(fs$farm_income, fs$fertiliser_subsidy,
                       weights = fs$weight, return_rate = 0.3,
                       aversion = c(0, 2), env_weights = 0))

Progressivity of agricultural support

Description

Measures whether a benefit is distributed progressively with respect to a welfare ranking variable such as household income or landholding.

Concentration index C_b

of the benefit, ranking households by 'rank_by'. Negative values mean the benefit is concentrated among the poorer (or smaller) households in absolute terms.

Gini G_x

of pre-subsidy income.

Kakwani index

K = G_x - C_b (Kakwani, 1977), positive when the benefit is distributed more equally than income, i.e. relatively progressive.

Redistributive effect

RE = G_x - G_{x+b}, decomposed into the vertical (Reynolds-Smolensky) effect G_x - C_{x+b} and re-ranking G_{x+b} - C_{x+b}.

Concentration and Gini indices are computed with survey weights using the covariance formula. Optional bootstrap confidence intervals resample households with replacement (set a seed beforehand for reproducibility).

Usage

progressivity_index(
  benefit,
  income,
  rank_by = income,
  weights = NULL,
  n_boot = 0,
  conf = 0.95
)

Arguments

Value

A list of class 'progressivity_index' with 'estimates' (named vector of the indices) and, if 'n_boot > 0', 'ci' (bootstrap percentile intervals) and an 'interpretation' string.

References

Kakwani, N. C. (1977). Measurement of tax progressivity: an international comparison. *The Economic Journal*, 87(345), 71-80. doi:10.2307/2230485

Reynolds, M. and Smolensky, E. (1977). *Public Expenditures, Taxes, and the Distribution of Income: The United States, 1950, 1961, 1970*. Academic Press, New York.

Examples

with(farm_subsidy, progressivity_index(fertiliser_subsidy, farm_income,
                                       weights = weight))
set.seed(1)
with(farm_subsidy, progressivity_index(income_transfer, farm_income,
                                       weights = weight, n_boot = 99))

Multi-dimensional equity scorecard for agricultural support

Description

Assesses a subsidy along several equity dimensions at once, for example landholding class, gender of the farmer and region. For each dimension and group it reports population and benefit shares, the parity ratio (benefit share / population share), coverage, and mean benefit per household relative to a reference group. Inequality of benefits across households is measured by the Theil index and decomposed into between-group and within-group components for each dimension, so the share of benefit inequality explained by farm size, gender or region can be compared.

Usage

subsidy_equity(
  data,
  benefit,
  dimensions,
  weights = NULL,
  reference = NULL,
  target = NULL
)

Arguments

Details

A summary row per dimension gives the minimum parity ratio (the most under-served group), the between-group Theil share and the target-group parity when 'target' groups are named.

Value

A list of class 'subsidy_equity' with 'groups' (data frame by dimension and group) and 'summary' (one row per dimension).

Examples

se <- subsidy_equity(farm_subsidy, "fertiliser_subsidy",
                     dimensions = c("size_class", "gender", "region"),
                     weights = "weight",
                     target = list(size_class = c("marginal", "small"),
                                   gender = "female",
                                   region = c("Rainfed-East",
                                              "Hill-Tribal")))
se

Productivity-equity-sustainability trade-off frontier

Description

Solves the welfare-optimal budget-neutral allocation of [budget_reallocation()] over a grid of inequality-aversion and environmental-weight values and records the resulting productivity gain, environmental cost, post-support Gini, target-group share and poverty. Plotting productivity against equity for each environmental weight shows how much output must be given up for a more equal, or a less environmentally damaging, allocation of the same budget, and where the current allocation lies relative to the frontier.

Usage

tradeoff_frontier(
  income,
  current,
  weights = NULL,
  budget = NULL,
  target = NULL,
  return_rate = 0,
  saturation = NULL,
  env_cost = 0,
  aversion = c(0, 0.5, 1, 2, 3),
  env_weights = c(0, 1, 2),
  max_per_farm = Inf,
  poverty_line = NULL,
  income_floor = NULL
)

Arguments

Value

A list of class 'tradeoff_frontier' with 'frontier' (one row per combination of 'aversion' and 'env_weights') and 'current' (metrics of the current allocation). A 'plot()' method draws productivity gain against the Gini of post-support income.

Examples

fs <- farm_subsidy[1:400, ]
tf <- tradeoff_frontier(fs$farm_income, fs$fertiliser_subsidy,
                        weights = fs$weight,
                        return_rate = fs$marginal_return,
                        env_cost = fs$env_cost_per_rupee,
                        aversion = c(0, 1, 3), env_weights = c(0, 2))
tf
plot(tf)