Package 'agriTradeRisk'

Constant market share decomposition of export growth

Description

Decomposes the change in a country's exports between two periods into four effects (Leamer and Stern, 1970; Ahmadi-Esfahani, 2006):

$\Delta X = rX^0 + \sum_k (r_k - r)X_k^0 + \sum_k\sum_j (r_{kj} - r_k)X_{kj}^0 + \sum_k\sum_j (X_{kj}^1 - X_{kj}^0 - r_{kj}X_{kj}^0)$

world growth

exports would have grown at the rate $r$ of world imports covered by the data;

commodity composition

gain from specialising in products whose world demand grew faster than average;

market distribution

gain from exporting each product to markets where its demand grew faster;

competitiveness

the residual, the change in market shares.

$r_{kj}$, $r_k$ and $r$ are growth rates of world imports of product $k$ in market $j$, of product $k$ in all markets, and of all products in all markets in the data.

Usage

cms_decomposition(data, product, market, export0, export1, world0, world1)

Arguments

data	A data frame with one row per product-market pair.
product, market	Names of product and market columns.
export0, export1	Columns with the country's exports in the base and end periods.
world0, world1	Columns with world imports of the product by the market in the base and end periods (must be positive).

Value

A list of class 'cms_decomposition' with 'effects' (data frame of the four effects, their total and their shares of the export change), 'by_product' (effects by product) and 'growth' (world growth rates).

References

Leamer, E. E. and Stern, R. M. (1970). *Quantitative International Economics*. Allyn and Bacon, Boston.

Ahmadi-Esfahani, F. Z. (2006). Constant market shares analysis: uses, limitations and prospects. *Australian Journal of Agricultural and Resource Economics*, 50(4), 510-526.

Examples

d0 <- subset(hort_exports, year == 2015)
d1 <- subset(hort_exports, year == 2023)
cms <- merge(d0, d1, by = c("product", "destination"),
             suffixes = c("0", "1"))
cms_decomposition(cms, "product", "destination", "export_value0",
                  "export_value1", "world_import0", "world_import1")

---

Revealed comparative advantage and export competitiveness

Description

Computes standard competitiveness indicators for a country's exports of product $k$:

• Balassa revealed comparative advantage $RCA = (x_k / X) / (w_k / W)$, where $x_k$ and $X$ are the country's exports of the product and of all goods, and $w_k$ and $W$ the corresponding world exports. Values above 1 indicate a revealed comparative advantage.

• Revealed symmetric comparative advantage $RSCA = (RCA - 1)/(RCA + 1)$, bounded between -1 and 1.

• World market share $x_k / w_k$.

• If quantities are supplied, the export unit value, the world unit value and their ratio, a price-based competitiveness (or quality) indicator.

Usage

competitiveness_index(
  data,
  export,
  total_export,
  world_export,
  world_total,
  quantity = NULL,
  world_quantity = NULL
)

Arguments

data	A data frame, one row per product (and year).
export	Column with the country's exports of the product.
total_export	Column with the country's total exports.
world_export	Column with world exports of the product.
world_total	Column with world total exports.
quantity, world_quantity	Optional columns with the country's and the world's export quantities of the product.

Value

'data' with added columns 'rca', 'rsca', 'world_share' and, when quantities are given, 'unit_value', 'world_unit_value' and 'unit_value_ratio'. The result has class 'competitiveness_index'.

References

Balassa, B. (1965). Trade liberalisation and "revealed" comparative advantage. *The Manchester School*, 33(2), 99-123. doi:10.1111/j.1467-9957.1965.tb00050.x

Examples

prod_year <- aggregate(cbind(export_value, world_import) ~ product + year,
                       data = hort_exports, FUN = sum)
dat <- merge(prod_year, trade_totals, by = "year")
ci <- competitiveness_index(dat, "export_value", "india_total_exports",
                            "world_import", "world_total_exports")
head(ci[, c("product", "year", "rca", "rsca", "world_share")])

---

Exchange-rate exposure of a multi-currency export portfolio

Description

Treats export earnings invoiced in several currencies as a currency portfolio. Using log changes of exchange rates (home currency per unit of foreign currency) and the share of export value earned in each currency, it computes:

• annualised volatility of each currency and their correlations;

• a trade-weighted (geometric) effective exchange-rate index;

• portfolio volatility $\sigma_p = \sqrt{s'\Sigma s}$ and the undiversified volatility $\sum_i s_i \sigma_i$; their ratio is the diversification ratio (values above 1 indicate risk reduction from currency diversification);

• each currency's percentage contribution to portfolio variance, $s_i(\Sigma s)_i / \sigma_p^2$;

• parametric and historical value at risk of export earnings in home currency over 'horizon' periods at confidence level 'conf'.

If an export series is supplied, the exposure elasticity is estimated by regressing its log change on the log change of the effective exchange rate.

Usage

exchange_rate_exposure(
  rates,
  shares,
  export_value = 1,
  freq = 12,
  horizon = 1,
  conf = 0.95,
  exports = NULL
)

Arguments

rates	A data frame or matrix of exchange rates, one column per currency (home currency per unit of foreign currency), one row per period, in time order.
shares	Named numeric vector of export shares by currency; names must match columns of 'rates'. Normalised to sum to 1.
export_value	Export value (home currency) exposed over the horizon, used for value at risk.
freq	Periods per year (12 for monthly data) for annualisation.
horizon	Value-at-risk horizon in periods.
conf	Confidence level for value at risk.
exports	Optional numeric series of export values or prices (same length as 'rates') for estimating the exposure elasticity.

Value

A list of class 'exchange_rate_exposure' with 'currencies' (share, annualised volatility and risk contribution per currency), 'correlation', 'portfolio' (annualised portfolio and undiversified volatility, diversification ratio, parametric and historical value at risk), 'effective_index' (trade-weighted index, first period = 100) and, if 'exports' is supplied, 'elasticity' (estimate, standard error, p-value).

Examples

sh <- c(USD = 0.35, EUR = 0.20, GBP = 0.15, AED = 0.20, BDT = 0.10)
ex <- exchange_rate_exposure(fx_rates[, names(sh)], sh,
                             export_value = 1e9, freq = 12)
ex

---

Export concentration indices

Description

Measures how concentrated exports are across destinations (or across products, by passing the product column as 'partner'). For partner shares $s_j$ the function reports the Herfindahl-Hirschman index $HHI = \sum_j s_j^2$, its normalised form $(HHI - 1/n)/(1 - 1/n)$, the equivalent number of equally sized partners $1/HHI$, the combined share of the 'top' largest partners, and Theil's entropy $-\sum_j s_j \ln s_j$ with its normalised form (divided by $\ln n$). Higher HHI and lower entropy indicate greater concentration and therefore greater exposure to shocks in individual markets.

Usage

export_concentration(data, value, partner, by = NULL, top = 3)

Arguments

data	A data frame with one row per partner (and group).
value	Name of the column holding export values (non-negative).
partner	Name of the column identifying destinations (or products).
by	Optional names of grouping columns, for example product and year.
top	Number of leading partners for the top-share measure.

Value

A data frame of class 'export_concentration' with one row per group and columns 'total', 'n_partners', 'hhi', 'hhi_normalised', 'equivalent_partners', 'top_share', 'entropy', 'entropy_normalised', 'leading_partner' and 'leading_share'.

Examples

ec <- export_concentration(hort_exports, value = "export_value",
                           partner = "destination",
                           by = c("product", "year"))
head(ec)

---

Simulated monthly exchange rates of the Indian rupee

Description

Synthetic monthly exchange rates (Indian rupees per unit of foreign currency), January 2014 to December 2023. AED and SAR follow their US dollar pegs. Not official statistics.

Usage

fx_rates

Format

A data frame with 120 rows and 8 columns: 'date', 'USD', 'EUR', 'GBP', 'AED', 'SAR', 'BDT' and 'RUB'.

Source

Simulated.

---

Simulated monthly grape export and domestic prices

Description

Synthetic monthly export unit values and domestic wholesale prices of grapes (INR per kg), January 2012 to December 2023, generated as a cointegrated pair with faster adjustment when domestic prices are above their long-run relationship. Not official statistics.

Usage

grape_prices

Format

A data frame with 144 rows and 3 columns: 'date', 'export_unit_value' and 'domestic_price'.

Source

Simulated.

---

Simulated Indian horticultural exports by product and destination

Description

Simulated annual exports of four Indian horticultural product groups to eight destination markets, with world imports of each product by each destination. The data are **synthetic**, generated by 'data-raw/make_data.R' for illustration; they are not official trade statistics.

Usage

hort_exports

Format

A data frame with 448 rows and 6 columns:

year

Year, 2010-2023.

product

'"mango"', '"grapes"', '"pomegranate"' or '"processed"' (processed fruit and vegetable products).

destination

Destination market.

export_value

Exports from India, USD million.

export_quantity

Export quantity, tonnes.

world_import

World imports of the product by the destination, USD million.

Source

Simulated.

---

Risk-efficient destination market mix

Description

Applies mean-variance portfolio analysis (Markowitz, 1952) to the allocation of exports across destination markets. Each market is an "asset" whose return is a performance measure such as the growth of export earnings or the realised export price (unit value) change. The function finds destination shares $w$ that minimise $w'\Sigma w - \tau \mu' w$ subject to $\sum w = 1$ and $l \le w \le u$, where share bounds reflect market-access or capacity limits. It reports the minimum-variance mix, the mix with the highest return per unit of risk on the efficient frontier, the current mix and the efficient frontier, so that the risk reduction available from diversification can be compared with the current market structure.

Usage

market_diversification(
  returns = NULL,
  shares = NULL,
  mean = NULL,
  cov = NULL,
  min_share = 0,
  max_share = 1,
  n_frontier = 25
)

Arguments

returns	A data frame or matrix of returns, one column per market and one row per period. Alternatively supply 'mean' and 'cov'.
shares	Optional named vector of current destination shares.
mean, cov	Optional mean vector and covariance matrix of returns, used instead of 'returns'.
min_share, max_share	Lower and upper bounds on each market's share (scalars or one per market).
n_frontier	Number of points on the efficient frontier.

Details

The problem is solved by projected gradient descent on the bounded simplex, which needs no additional packages.

Value

A list of class 'market_diversification' with 'weights' (data frame of current, minimum-variance and best return-to-risk shares by market), 'summary' (expected return, risk, return-to-risk ratio and Herfindahl index of each mix), 'frontier' (data frame of efficient portfolios) and the inputs 'mean' and 'cov'. A 'plot()' method draws the frontier.

References

Markowitz, H. (1952). Portfolio selection. *The Journal of Finance*, 7(1), 77-91. doi:10.2307/2975974

Examples

grapes <- subset(hort_exports, product == "grapes")
wide <- reshape(grapes[, c("year", "destination", "export_value")],
                idvar = "year", timevar = "destination",
                direction = "wide")
vals <- as.matrix(wide[order(wide$year), -1])
colnames(vals) <- sub("export_value.", "", colnames(vals))
growth <- diff(log(vals))
cur <- vals[nrow(vals), ] / sum(vals[nrow(vals), ])
md <- market_diversification(growth, shares = cur, max_share = 0.4)
md
plot(md)

---

Composite market-entry risk score

Description

Combines indicators of the risk of entering or expanding in destination markets, for example sanitary and phytosanitary rejection rates, tariff rates, non-tariff measure counts, price volatility, exchange-rate volatility, distance or transit time, and competitor market share, into a single score. Each indicator is rescaled to 0-1 by min-max normalisation and oriented so that 1 is the riskiest value; the score is the weighted mean of the rescaled indicators. Optionally, a market attractiveness indicator (such as import demand growth) is combined with the score into a risk-adjusted attractiveness index $A (1 - \rho \, risk)$, where $A$ is rescaled attractiveness and $\rho$ the risk aversion.

Usage

market_entry_risk(
  data,
  market,
  indicators,
  higher_is_riskier,
  weights = NULL,
  attractiveness = NULL,
  risk_aversion = 0.5
)

Arguments

data	A data frame with one row per market.
market	Name of the market column.
indicators	Names of indicator columns.
higher_is_riskier	Logical vector, one per indicator: 'TRUE' if a higher value means more risk.
weights	Optional non-negative weights, one per indicator (normalised to sum to 1). Equal weights by default.
attractiveness	Optional name of a column measuring market attractiveness (higher is better).
risk_aversion	Weight $\rho$ (0 to 1) of risk in the risk-adjusted attractiveness index.

Value

A data frame of class 'market_entry_risk' with the market, the rescaled indicators, 'risk_score', 'risk_rank' (1 = least risky) and, if 'attractiveness' is given, 'attractiveness_scaled', 'risk_adjusted_attractiveness' and 'priority_rank'.

Examples

mk <- data.frame(market = c("UAE", "UK", "Netherlands", "USA",
                            "Bangladesh"),
                 sps_rejections = c(2, 5, 8, 6, 1),
                 tariff = c(0, 0, 0, 2, 10),
                 price_cv = c(0.15, 0.10, 0.12, 0.18, 0.25),
                 demand_growth = c(0.06, 0.03, 0.04, 0.05, 0.08))
market_entry_risk(mk, "market",
                  c("sps_rejections", "tariff", "price_cv"),
                  higher_is_riskier = c(TRUE, TRUE, TRUE),
                  attractiveness = "demand_growth")

---

Plot the efficient frontier of destination markets

Description

Plot the efficient frontier of destination markets

Usage

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

Arguments

x	A [market_diversification()] object.
...	Further arguments passed to [graphics::plot()].

Value

'x', invisibly.

Examples

set.seed(1)
r <- matrix(rnorm(60, 0.05, 0.1), 20, 3,
            dimnames = list(NULL, c("A", "B", "C")))
plot(market_diversification(r))

---

Vertical price transmission between export and domestic prices

Description

Tests whether domestic prices (for example wholesale or farm-gate prices) move with export prices (or export unit values) in the long run and how quickly deviations are corrected.

Usage

price_transmission(
  domestic,
  world,
  log = TRUE,
  ecm_lags = 1,
  max_lag = 4,
  asymmetric = FALSE
)

Arguments

domestic	Numeric vector or time series of domestic prices.
world	Numeric vector or time series of export or world prices, same length as 'domestic'.
log	Logical; take natural logarithms of prices first.
ecm_lags	Number of lagged differences $p$ in the error correction model.
max_lag	Maximum lag order considered in the residual ADF test.
asymmetric	Logical; estimate an asymmetric error correction model.

Details

**Step 1: long-run relationship.** $d_t = a + b\,w_t + u_t$, where $b$ is the long-run price transmission elasticity when prices are in logs.

**Step 2: Engle-Granger cointegration test.** An augmented Dickey-Fuller regression without deterministic terms is fitted to the residuals $u_t$, with the lag order chosen by AIC up to 'max_lag'. The t statistic is compared with the asymptotic critical values of MacKinnon (2010) for two variables with a constant: -3.896 (1 -3.044 (10

**Step 3: error correction model.**

$\Delta d_t = c + \beta_0 \Delta w_t + \sum_{i=1}^{p}(\phi_i \Delta d_{t-i} + \theta_i \Delta w_{t-i}) + \alpha u_{t-1} + e_t.$

$\beta_0$ is the short-run elasticity and $\alpha$ (expected to be negative) the speed of adjustment; the half-life of a deviation is $\ln 0.5 / \ln(1 + \alpha)$ periods. With 'asymmetric = TRUE' the error correction term is split into positive and negative parts (Granger and Lee, 1989), and an F test of equal adjustment speeds is reported.

Value

A list of class 'price_transmission' with 'long_run' (intercept, elasticity, R-squared), 'cointegration' (ADF statistic, lag, critical values and decision at 5 percent), 'ecm' (coefficient table of the error correction model), 'adjustment' (speed of adjustment and half-life; separate values for positive and negative deviations when asymmetric, with the F test), and the fitted 'lm' models.

References

Engle, R. F. and Granger, C. W. J. (1987). Co-integration and error correction: representation, estimation, and testing. *Econometrica*, 55(2), 251-276. doi:10.2307/1913236

Granger, C. W. J. and Lee, T. H. (1989). Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models. *Journal of Applied Econometrics*, 4(S1), S145-S159. doi:10.1002/jae.3950040508

MacKinnon, J. G. (2010). Critical values for cointegration tests. Queen's Economics Department Working Paper No. 1227, Queen's University, Kingston, Ontario.

Examples

pt <- price_transmission(grape_prices$domestic_price,
                         grape_prices$export_unit_value)
pt
price_transmission(grape_prices$domestic_price,
                   grape_prices$export_unit_value,
                   asymmetric = TRUE)$adjustment

---

Simulated total exports of India and the world

Description

Synthetic annual totals used with [hort_exports] to compute revealed comparative advantage. Not official statistics.

Usage

trade_totals

Format

A data frame with 14 rows and 3 columns: 'year', 'india_total_exports' and 'world_total_exports' (USD million).

Source

Simulated.

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