Package 'debtkit' reference manual

Title:	Debt Sustainability Analysis and Fiscal Risk Assessment
Description:	Analyses government debt sustainability using the standard debt dynamics framework from Blanchard (1990) <doi:10.1787/budget-v2-art12-en> and the IMF Debt Sustainability Analysis methodology (IMF, 2013) and the Sovereign Risk and Debt Sustainability Framework (IMF, 2022). Projects debt-to-GDP paths, decomposes historical debt changes into interest, growth, and primary balance contributions, and estimates fiscal reaction functions following Bohn (1998) <doi:10.1162/003355398555793>. Produces stochastic fan charts via Monte Carlo simulation, standardised stress tests, and IMF- style heat map risk assessments. Computes S1/S2 sustainability gap indicators used by the European Commission. All methods are pure computation with no external dependencies beyond base R; works with fiscal data from any source.
Authors:	Charles Coverdale [aut, cre]
Maintainer:	Charles Coverdale <[email protected]>
License:	MIT + file LICENSE
Version:	0.1.3
Built:	2026-05-30 15:06:56 UTC
Source:	https://github.com/charlescoverdale/debtkit

Bohn's Fiscal Reaction Function Test

Description

Estimates the fiscal reaction function following Bohn (1998): pb(t) = rho * d(t-1) + alpha * Z(t) + epsilon(t), where pb is the primary balance-to-GDP ratio, d is lagged debt-to-GDP, and Z is a matrix of control variables.

Usage

dk_bohn_test(
  primary_balance,
  debt,
  controls = NULL,
  method = c("ols", "rolling", "quadratic"),
  window = NULL,
  robust_se = FALSE
)
dk_bohn_test(
  primary_balance,
  debt,
  controls = NULL,
  method = c("ols", "rolling", "quadratic"),
  window = NULL,
  robust_se = FALSE
)

Arguments

primary_balance

Numeric vector of primary balance-to-GDP ratios.

debt

Numeric vector of lagged debt-to-GDP ratios (same length as primary_balance).

controls

Optional data.frame of control variables (same number of rows as primary_balance). Each column enters the regression as a separate regressor.

method

Character; "ols" (default) for a single OLS regression over the full sample, "rolling" for rolling-window regressions, or "quadratic" for a non-linear specification that includes a squared debt term to detect fiscal fatigue (Ghosh et al. 2013).

window

Integer; rolling window size. Required when method = "rolling", ignored otherwise.

robust_se

Logical; if TRUE, compute Newey-West HAC standard errors using a Bartlett kernel with automatic bandwidth floor(4*(n/100)^(2/9)). This corrects for serial correlation in fiscal data. Default FALSE.

Details

A positive and statistically significant rho indicates that the government systematically raises the primary surplus in response to rising debt, satisfying a sufficient condition for debt sustainability.

Value

An S3 object of class dk_bohn with components:

rho: Estimated fiscal response coefficient (full sample or last rolling window).
rho_se: Standard error of rho.
rho_pvalue: p-value for the test H0: rho = 0.
sustainable: Logical; TRUE if rho > 0 and rho_pvalue < 0.05.
model: The lm object from the full-sample (OLS/quadratic) or last-window (rolling) regression.
method: The method used ("ols", "rolling", or "quadratic").
rho_ts: A data.frame with columns index, rho, rho_lower, rho_upper if method = "rolling"; NULL otherwise.
robust_se: Logical; whether HAC standard errors were used.
rho2: Coefficient on debt squared (only for method = "quadratic").
rho2_se: Standard error of rho2 (quadratic only).
rho2_pvalue: p-value for rho2 (quadratic only).
turning_point: Debt level where fiscal response peaks, -rho/(2*rho2) (quadratic only).

References

Bohn, H. (1998). "The Behavior of U.S. Public Debt and Deficits." Quarterly Journal of Economics, 113(3), 949–963. doi:10.1162/003355398555793

Ghosh, A.R., Kim, J.I., Mendoza, E.G., Ostry, J.D. and Qureshi, M.S. (2013). "Fiscal Fatigue, Fiscal Space and Debt Sustainability in Advanced Economies." The Economic Journal, 123(566), F4–F30.

Examples

# Simulate data with positive fiscal response
set.seed(42)
n <- 50
debt <- cumsum(rnorm(n, 0.01, 0.02)) + 0.6
pb <- 0.04 * debt + rnorm(n, 0, 0.005)
result <- dk_bohn_test(pb, debt)
print(result)

# Simulate data with positive fiscal response
set.seed(42)
n <- 50
debt <- cumsum(rnorm(n, 0.01, 0.02)) + 0.6
pb <- 0.04 * debt + rnorm(n, 0, 0.005)
result <- dk_bohn_test(pb, debt)
print(result)

Compare Debt Projections

Description

Produces a side-by-side comparison of multiple debt-to-GDP projections, aligning them by year and computing terminal values.

Usage

dk_compare(..., metric = "debt")
dk_compare(..., metric = "debt")

Arguments

...

Named dk_projection objects to compare. Names are used as scenario labels.

metric

Character. The metric to compare. Currently only "debt" is supported. Default "debt".

Value

An S3 object of class dk_comparison containing:

paths: A data.frame with a year column and one column per scenario, giving the debt-to-GDP path.
terminal: Named numeric vector of terminal debt-to-GDP ratios.

Examples

d <- dk_sample_data()
base <- dk_project(tail(d$debt, 1), 0.03, 0.04, 0.01, horizon = 5)
austerity <- dk_project(tail(d$debt, 1), 0.03, 0.04, 0.03, horizon = 5)
stimulus <- dk_project(tail(d$debt, 1), 0.03, 0.05, -0.01, horizon = 5)

comp <- dk_compare(
  Baseline = base,
  Austerity = austerity,
  Stimulus = stimulus
)
comp
plot(comp)
d <- dk_sample_data()
base <- dk_project(tail(d$debt, 1), 0.03, 0.04, 0.01, horizon = 5)
austerity <- dk_project(tail(d$debt, 1), 0.03, 0.04, 0.03, horizon = 5)
stimulus <- dk_project(tail(d$debt, 1), 0.03, 0.05, -0.01, horizon = 5)

comp <- dk_compare(
  Baseline = base,
  Austerity = austerity,
  Stimulus = stimulus
)
comp
plot(comp)

Decompose Historical Debt Changes

Description

Breaks down observed year-on-year changes in the debt-to-GDP ratio into four components:

Usage

dk_decompose(debt, interest_rate, gdp_growth, primary_balance, years = NULL)
dk_decompose(debt, interest_rate, gdp_growth, primary_balance, years = NULL)

Arguments

debt

Numeric vector of historical debt-to-GDP ratios.

interest_rate

Numeric vector of effective interest rates on government debt. Must be the same length as debt.

gdp_growth

Numeric vector of nominal GDP growth rates. Must be the same length as debt.

primary_balance

Numeric vector of primary balance-to-GDP ratios (positive = surplus). Must be the same length as debt.

years

Optional integer vector of year labels. Must be the same length as debt. If NULL (default), years are numbered sequentially.

Details

Interest effect: $r_t / (1 + g_t) \cdot d_{t-1}$
Growth effect: $-g_t / (1 + g_t) \cdot d_{t-1}$
Primary balance effect: $-pb_t$
Stock-flow adjustment (residual): actual change minus the sum of the three identified components.

This is the standard decomposition used by the IMF (2013) and European Commission. The SFA residual captures privatisation receipts, exchange-rate valuation changes, below-the-line operations, and any measurement error.

Value

An S3 object of class dk_decomposition containing:

data: A data.frame with columns year, debt, change, interest_effect, growth_effect, snowball_effect, primary_balance_effect, and sfa.
years: The year labels used.

References

Blanchard, O.J. (1990). Suggestions for a New Set of Fiscal Indicators. OECD Economics Department Working Papers, No. 79. doi:10.1787/budget-v2-art12-en

International Monetary Fund (2013). Staff Guidance Note for Public Debt Sustainability Analysis in Market-Access Countries. IMF Policy Paper.

Examples

d <- dk_sample_data()
dec <- dk_decompose(
  debt = d$debt,
  interest_rate = d$interest_rate,
  gdp_growth = d$gdp_growth,
  primary_balance = d$primary_balance,
  years = d$years
)
dec
plot(dec)
d <- dk_sample_data()
dec <- dk_decompose(
  debt = d$debt,
  interest_rate = d$interest_rate,
  gdp_growth = d$gdp_growth,
  primary_balance = d$primary_balance,
  years = d$years
)
dec
plot(dec)

Estimate Joint Distribution of Macro Shocks

Description

Estimates the joint distribution of GDP growth, interest rate, and primary balance shocks for use in stochastic debt sustainability analysis. Three estimation methods are supported: a VAR(1) model (default), residual bootstrap, and a simple multivariate normal fit.

Usage

dk_estimate_shocks(
  gdp_growth,
  interest_rate,
  primary_balance,
  method = c("var", "bootstrap", "normal"),
  years = NULL
)
dk_estimate_shocks(
  gdp_growth,
  interest_rate,
  primary_balance,
  method = c("var", "bootstrap", "normal"),
  years = NULL
)

Arguments

gdp_growth

Numeric vector of historical real GDP growth rates.

interest_rate

Numeric vector of historical nominal (or real) interest rates.

primary_balance

Numeric vector of historical primary balance-to-GDP ratios.

method

Character; one of "var" (default), "bootstrap", or "normal".

years

Optional numeric vector of year labels (same length as data).

Details

For method = "var", a VAR(1) is estimated equation-by-equation via OLS on the lagged system. The residual variance-covariance matrix captures the joint shock distribution. For method = "bootstrap", the same VAR(1) is estimated and residuals are stored for block resampling. For method = "normal", the sample means and covariance of the raw series are used directly.

Value

An S3 object of class dk_shocks with components:

vcov: 3x3 variance-covariance matrix with rows/columns named growth, interest_rate, primary_balance.
means: Named numeric vector of variable means.
method: The estimation method used.
residuals: Matrix of residuals (for "var" and "bootstrap") or NULL (for "normal").
var_coefficients: VAR(1) coefficient matrix (for "var") or NULL.
n_obs: Number of observations used.

Examples

set.seed(1)
n <- 30
g <- rnorm(n, 0.02, 0.015)
r <- rnorm(n, 0.03, 0.01)
pb <- rnorm(n, -0.02, 0.01)
shocks <- dk_estimate_shocks(g, r, pb)
print(shocks)

set.seed(1)
n <- 30
g <- rnorm(n, 0.02, 0.015)
r <- rnorm(n, 0.03, 0.01)
pb <- rnorm(n, -0.02, 0.01)
shocks <- dk_estimate_shocks(g, r, pb)
print(shocks)

Stochastic Debt Fan Chart

Description

Projects debt-to-GDP paths via Monte Carlo simulation using the standard debt dynamics equation. At each step, correlated shocks to growth, the interest rate, and the primary balance are drawn from a multivariate normal distribution and added to the baseline paths. The result is a fan chart showing the distribution of projected debt paths.

Usage

dk_fan_chart(
  debt,
  interest_rate,
  gdp_growth,
  primary_balance,
  shocks = NULL,
  shock_vcov = NULL,
  n_sim = 1000L,
  horizon = 5L,
  confidence = c(0.1, 0.25, 0.5, 0.75, 0.9),
  seed = NULL
)
dk_fan_chart(
  debt,
  interest_rate,
  gdp_growth,
  primary_balance,
  shocks = NULL,
  shock_vcov = NULL,
  n_sim = 1000L,
  horizon = 5L,
  confidence = c(0.1, 0.25, 0.5, 0.75, 0.9),
  seed = NULL
)

Arguments

debt

Numeric scalar; initial debt-to-GDP ratio.

interest_rate

Numeric scalar or vector of length horizon; baseline interest rate path.

gdp_growth

Numeric scalar or vector of length horizon; baseline GDP growth path.

primary_balance

Numeric scalar or vector of length horizon; baseline primary balance-to-GDP path.

shocks

A dk_shocks object (from dk_estimate_shocks()) providing the shock distribution, or NULL.

shock_vcov

Optional 3x3 variance-covariance matrix (alternative to shocks). Rows/columns ordered: growth, interest_rate, primary_balance. Ignored if shocks is provided.

n_sim

Integer; number of Monte Carlo simulations (default 1000).

horizon

Integer; projection horizon in years (default 5).

confidence

Numeric vector of quantile levels for fan bands (default c(0.10, 0.25, 0.50, 0.75, 0.90)).

seed

Optional integer seed for reproducibility.

Value

An S3 object of class dk_fan with components:

simulations: Matrix of dimension n_sim x (horizon + 1) containing all simulated debt paths.
quantiles: Matrix of quantiles at each time step, with rows corresponding to the confidence levels.
baseline: Numeric vector of length horizon + 1; the deterministic baseline debt path.
confidence: The quantile levels used.
horizon: The projection horizon.
prob_above: Named list with the probability of debt exceeding 60 percent, 90 percent, and 120 percent of GDP at the terminal year.

Examples

set.seed(1)
n <- 30
g <- rnorm(n, 0.02, 0.015)
r <- rnorm(n, 0.03, 0.01)
pb <- rnorm(n, -0.02, 0.01)
shocks <- dk_estimate_shocks(g, r, pb)

fan <- dk_fan_chart(
  debt = 0.90,
  interest_rate = 0.03,
  gdp_growth = 0.02,
  primary_balance = -0.02,
  shocks = shocks,
  n_sim = 500,
  horizon = 10,
  seed = 42
)
print(fan)

set.seed(1)
n <- 30
g <- rnorm(n, 0.02, 0.015)
r <- rnorm(n, 0.03, 0.01)
pb <- rnorm(n, -0.02, 0.01)
shocks <- dk_estimate_shocks(g, r, pb)

fan <- dk_fan_chart(
  debt = 0.90,
  interest_rate = 0.03,
  gdp_growth = 0.02,
  primary_balance = -0.02,
  shocks = shocks,
  n_sim = 500,
  horizon = 10,
  seed = 42
)
print(fan)

Gross Financing Needs

Description

Computes gross financing needs (GFN) as a share of GDP over a projection horizon. GFN represents the total amount of new borrowing a government requires each year to cover its primary deficit, interest payments, and maturing debt:

Usage

dk_gfn(debt, interest_rate, maturity_profile, primary_balance, horizon = 5)
dk_gfn(debt, interest_rate, maturity_profile, primary_balance, horizon = 5)

Arguments

debt

Numeric scalar. Initial debt-to-GDP ratio.

interest_rate

Numeric scalar or vector of length horizon. Effective nominal interest rate on government debt.

maturity_profile

Numeric vector or scalar. If a vector, gives the share of GDP maturing in each year of the horizon. If a scalar, interpreted as the average maturity in years; debt is assumed to mature uniformly at debt / maturity_profile per year.

primary_balance

Numeric scalar or vector of length horizon. Primary balance as a share of GDP (positive = surplus).

horizon

Integer scalar. Projection horizon in years. Default 5.

Details

$GFN_t = -pb_t + r_t \cdot d_t + m_t$

where $pb$ is the primary balance (positive = surplus), $r$ is the effective interest rate, $d$ is debt-to-GDP, and $m$ is maturing debt as a share of GDP.

Value

A data.frame with columns:

year: Year index (1 to horizon).
primary_deficit: Primary deficit (negative of primary balance).
interest_payments: Interest payments as a share of GDP.
maturing_debt: Maturing debt as a share of GDP.
gfn: Total gross financing needs as a share of GDP.

References

International Monetary Fund (2013). Staff Guidance Note for Public Debt Sustainability Analysis in Market-Access Countries. IMF Policy Paper.

Examples

# Scalar average maturity of 7 years
dk_gfn(debt = 0.90, interest_rate = 0.03,
       maturity_profile = 7, primary_balance = -0.02)

# Explicit maturity profile
dk_gfn(debt = 0.90, interest_rate = 0.03,
       maturity_profile = c(0.15, 0.12, 0.10, 0.08, 0.05),
       primary_balance = -0.02)
# Scalar average maturity of 7 years
dk_gfn(debt = 0.90, interest_rate = 0.03,
       maturity_profile = 7, primary_balance = -0.02)

# Explicit maturity profile
dk_gfn(debt = 0.90, interest_rate = 0.03,
       maturity_profile = c(0.15, 0.12, 0.10, 0.08, 0.05),
       primary_balance = -0.02)

IMF-Style Risk Heat Map

Description

Classifies sovereign debt risk as low, medium, or high based on IMF (2013) thresholds for debt-to-GDP, gross financing needs, and optional debt-profile indicators. Advanced economies and emerging markets use different thresholds.

Usage

dk_heat_map(
  debt,
  gross_financing_needs,
  debt_profile = NULL,
  country_type = c("ae", "em")
)
dk_heat_map(
  debt,
  gross_financing_needs,
  debt_profile = NULL,
  country_type = c("ae", "em")
)

Arguments

debt

Numeric scalar. Debt-to-GDP ratio.

gross_financing_needs

Numeric scalar. Gross financing needs as a share of GDP.

debt_profile

Optional named list of debt-profile indicators (all as ratios):

share_st_debt: Share of short-term debt in total debt.
fx_share: Share of foreign-currency-denominated debt.
nonresident_share: Share of debt held by non-residents.
bank_share: Share of debt held by domestic banks.
change_st_debt: Year-on-year change in the share of short-term debt (in percentage points of GDP).

country_type

Character. Either "ae" (advanced economy, default) or "em" (emerging market).

Value

An S3 object of class dk_heatmap containing:

ratings: Named list of risk ratings ("low", "medium", or "high") for each indicator.
overall: Character. Overall risk level: "high" if any indicator is high, "medium" if any is medium, otherwise "low".
values: Named list of input values.
thresholds: The thresholds used for classification.
country_type: The country type used.

References

International Monetary Fund (2013). Staff Guidance Note for Public Debt Sustainability Analysis in Market-Access Countries. IMF Policy Paper.

International Monetary Fund (2022). Staff Guidance Note on the Sovereign Risk and Debt Sustainability Framework for Market Access Countries. IMF Policy Paper.

Examples

hm <- dk_heat_map(
  debt = 0.90,
  gross_financing_needs = 0.18,
  debt_profile = list(fx_share = 0.30, share_st_debt = 0.15),
  country_type = "ae"
)
hm
hm <- dk_heat_map(
  debt = 0.90,
  gross_financing_needs = 0.18,
  debt_profile = list(fx_share = 0.30, share_st_debt = 0.15),
  country_type = "ae"
)
hm

Project Debt-to-GDP Path

Description

Projects a debt-to-GDP ratio forward using the standard debt dynamics equation:

Usage

dk_project(
  debt,
  interest_rate,
  gdp_growth,
  primary_balance,
  sfa = 0,
  horizon = 10,
  date = NULL
)
dk_project(
  debt,
  interest_rate,
  gdp_growth,
  primary_balance,
  sfa = 0,
  horizon = 10,
  date = NULL
)

Arguments

debt

Numeric scalar. Initial debt-to-GDP ratio (e.g., 0.90 for 90 per cent of GDP).

interest_rate

Numeric scalar or vector of length horizon. Nominal effective interest rate on government debt.

gdp_growth

Numeric scalar or vector of length horizon. Nominal GDP growth rate.

primary_balance

Numeric scalar or vector of length horizon. Primary balance as a share of GDP. Positive values denote a surplus; negative values a deficit.

sfa

Numeric scalar or vector of length horizon. Stock-flow adjustment as a share of GDP. Default 0.

horizon

Integer scalar. Number of years to project forward. Default 10.

date

Optional Date. If supplied, the projection is anchored to this date (stored in the output for labelling purposes).

Details

$d_{t+1} = \frac{1 + r_t}{1 + g_t} d_t - pb_t + sfa_t$

where $d$ is the debt-to-GDP ratio, $r$ is the effective nominal interest rate on government debt, $g$ is nominal GDP growth, $pb$ is the primary balance as a share of GDP (positive = surplus), and $sfa$ captures stock-flow adjustments (e.g. privatisation receipts, exchange-rate valuation changes, below-the-line operations).

Value

An S3 object of class dk_projection containing:

debt_path: Numeric vector of length horizon + 1, giving the debt-to-GDP ratio from the initial period through the terminal period.
decomposition: A data.frame with columns year, debt, interest_effect, growth_effect, snowball_effect, primary_balance_effect, sfa_effect, and change.
horizon: The projection horizon.
inputs: A list storing all input parameters.

References

Blanchard, O.J. (1990). Suggestions for a New Set of Fiscal Indicators. OECD Economics Department Working Papers, No. 79. doi:10.1787/budget-v2-art12-en

International Monetary Fund (2013). Staff Guidance Note for Public Debt Sustainability Analysis in Market-Access Countries. IMF Policy Paper.

Examples

d <- dk_sample_data()
proj <- dk_project(
  debt = tail(d$debt, 1),
  interest_rate = 0.03,
  gdp_growth = 0.04,
  primary_balance = 0.01
)
proj
plot(proj)
d <- dk_sample_data()
proj <- dk_project(
  debt = tail(d$debt, 1),
  interest_rate = 0.03,
  gdp_growth = 0.04,
  primary_balance = 0.01
)
proj
plot(proj)

Interest Rate-Growth Differential and Debt-Stabilising Primary Balance

Description

Computes the interest rate-growth differential ( $r - g$ ), a key indicator of debt sustainability. When $r > g$ , debt grows faster than the economy (the "snowball effect" is adverse) and a primary surplus is needed to stabilise the debt ratio. When $r < g$ , the government can run a primary deficit and still see the debt ratio fall.

Usage

dk_rg(interest_rate, gdp_growth, inflation = NULL, debt = NULL)
dk_rg(interest_rate, gdp_growth, inflation = NULL, debt = NULL)

Arguments

interest_rate

Numeric. Effective nominal interest rate on government debt. Scalar or vector.

gdp_growth

Numeric. Nominal GDP growth rate. Scalar or vector (same length as interest_rate).

inflation

Numeric or NULL. If supplied, the inflation rate used to compute the real $r - g$ . Scalar or same length as interest_rate. Default NULL.

debt

Numeric or NULL. If supplied, the debt-to-GDP ratio used to compute the debt-stabilising primary balance. Scalar or same length as interest_rate. Default NULL.

Details

If debt is supplied, the function also computes the debt-stabilising primary balance: the primary surplus (as a share of GDP) required to hold the debt-to-GDP ratio constant at its current level. This is given by:

$pb^* = \frac{r - g}{1 + g} \cdot d$

If inflation is supplied, the function computes the real $r - g$ differential by deflating both the interest rate and GDP growth: $r_{real} = (1 + r)/(1 + \pi) - 1$ and $g_{real} = (1 + g)/(1 + \pi) - 1$ .

Value

A named list with:

rg_differential: Numeric vector. The nominal $r - g$ differential.
real_rg: Numeric vector. The real $r - g$ differential. Only present if inflation was supplied.
debt_stabilising_pb: Numeric vector. The debt-stabilising primary balance as a share of GDP. Only present if debt was supplied.

References

Blanchard, O.J. (1990). Suggestions for a New Set of Fiscal Indicators. OECD Economics Department Working Papers, No. 79. doi:10.1787/budget-v2-art12-en

Barrett, P. (2018). Interest-Growth Differentials and Debt Limits in Advanced Economies. IMF Working Paper, WP/18/82.

Examples

# Simple scalar case
dk_rg(interest_rate = 0.04, gdp_growth = 0.03)

# With debt: compute stabilising primary balance
dk_rg(interest_rate = 0.04, gdp_growth = 0.03, debt = 0.90)

# With inflation: compute real r-g
dk_rg(interest_rate = 0.04, gdp_growth = 0.05, inflation = 0.02)

# Vector case using sample data
d <- dk_sample_data()
dk_rg(
  interest_rate = d$interest_rate,
  gdp_growth = d$gdp_growth,
  debt = d$debt
)
# Simple scalar case
dk_rg(interest_rate = 0.04, gdp_growth = 0.03)

# With debt: compute stabilising primary balance
dk_rg(interest_rate = 0.04, gdp_growth = 0.03, debt = 0.90)

# With inflation: compute real r-g
dk_rg(interest_rate = 0.04, gdp_growth = 0.05, inflation = 0.02)

# Vector case using sample data
d <- dk_sample_data()
dk_rg(
  interest_rate = d$interest_rate,
  gdp_growth = d$gdp_growth,
  debt = d$debt
)

Sample Fiscal Data

Description

Provides built-in sample datasets for running examples and tests without requiring external data.

Usage

dk_sample_data(country = c("sample", "high_debt"))
dk_sample_data(country = c("sample", "high_debt"))

Arguments

country

Character. Which sample dataset to return. Options: "sample" (default) provides a synthetic 20-year history for a mid-income country; "high_debt" provides a high-debt scenario.

Value

A list with components:

years: Integer vector of years.
debt: Numeric vector of debt-to-GDP ratios.
interest_rate: Numeric vector of effective interest rates on government debt.
gdp_growth: Numeric vector of nominal GDP growth rates.
primary_balance: Numeric vector of primary balance-to-GDP ratios (positive = surplus).

Examples

d <- dk_sample_data()
d$debt
d$years
d <- dk_sample_data()
d$debt
d$years

IMF Standardised Stress Tests

Description

Applies six standardised IMF stress-test scenarios to a baseline debt projection using the debt dynamics equation:

Usage

dk_stress_test(
  debt,
  interest_rate,
  gdp_growth,
  primary_balance,
  horizon = 5,
  growth_shock = -0.01,
  interest_shock = 0.02,
  exchange_shock = 0.15,
  fx_share = 0,
  pb_shock = -0.01,
  contingent_shock = 0.1,
  calibrate = NULL
)
dk_stress_test(
  debt,
  interest_rate,
  gdp_growth,
  primary_balance,
  horizon = 5,
  growth_shock = -0.01,
  interest_shock = 0.02,
  exchange_shock = 0.15,
  fx_share = 0,
  pb_shock = -0.01,
  contingent_shock = 0.1,
  calibrate = NULL
)

Arguments

debt

Numeric scalar. Initial debt-to-GDP ratio.

interest_rate

Numeric scalar or vector of length horizon. Baseline nominal effective interest rate.

gdp_growth

Numeric scalar or vector of length horizon. Baseline nominal GDP growth rate.

primary_balance

Numeric scalar or vector of length horizon. Baseline primary balance as a share of GDP (positive = surplus).

horizon

Integer scalar. Projection horizon in years. Default 5.

growth_shock

Numeric scalar. Percentage-point reduction in GDP growth applied in the first two years. Default -0.01 (1 pp lower growth).

interest_shock

Numeric scalar. Percentage-point increase in the interest rate. Default 0.02 (200 basis points).

exchange_shock

Numeric scalar. Depreciation fraction applied to foreign-currency debt. Default 0.15 (15 per cent depreciation).

fx_share

Numeric scalar. Share of debt denominated in foreign currency. Default 0.

pb_shock

Numeric scalar. Percentage-point deterioration in primary balance in the first two years. Default -0.01.

contingent_shock

Numeric scalar. One-off increase in debt-to-GDP from contingent liabilities materialising. Default 0.10.

calibrate

Optional named list for data-driven shock calibration. Should contain numeric vectors gdp_growth_hist, interest_rate_hist, and primary_balance_hist. When provided, shock sizes are computed as one standard deviation of each historical series, replacing the fixed defaults. When NULL (default), the fixed defaults are used.

Details

$d_{t+1} = \frac{1 + r_t}{1 + g_t} d_t - pb_t + sfa_t$

The six scenarios are:

Growth shock: GDP growth reduced by growth_shock for the first two years.
Interest rate shock: interest rate increased by interest_shock for the full horizon.
Exchange rate shock: debt increases by debt * fx_share * exchange_shock in year 1 (one-off stock-flow adjustment from currency depreciation).
Primary balance shock: primary balance reduced by pb_shock for the first two years.
Combined shock: simultaneous growth shock of growth_shock / 2 and interest rate shock of interest_shock / 2.
Contingent liabilities: one-off debt increase of contingent_shock in year 1.

Value

An S3 object of class dk_stress containing:

scenarios: A data.frame with columns year, baseline, growth, interest_rate, exchange_rate, primary_balance, combined, and contingent.
terminal: Named numeric vector of terminal debt-to-GDP under each scenario.
inputs: A list storing all input parameters.

References

International Monetary Fund (2013). Staff Guidance Note for Public Debt Sustainability Analysis in Market-Access Countries. IMF Policy Paper.

International Monetary Fund (2022). Staff Guidance Note on the Sovereign Risk and Debt Sustainability Framework for Market Access Countries. IMF Policy Paper.

Examples

st <- dk_stress_test(
  debt = 0.90,
  interest_rate = 0.03,
  gdp_growth = 0.04,
  primary_balance = 0.01,
  fx_share = 0.20
)
st
plot(st)
st <- dk_stress_test(
  debt = 0.90,
  interest_rate = 0.03,
  gdp_growth = 0.04,
  primary_balance = 0.01,
  fx_share = 0.20
)
st
plot(st)

S1 and S2 Sustainability Gap Indicators

Description

Computes the S1 and S2 fiscal sustainability gap indicators used by the European Commission to assess the size of the permanent budgetary adjustment required to ensure debt sustainability.

Usage

dk_sustainability_gap(
  debt,
  structural_balance,
  gdp_growth,
  interest_rate,
  ageing_costs = 0,
  target_debt = 0.6,
  target_year = 20,
  indicator = c("both", "S1", "S2")
)
dk_sustainability_gap(
  debt,
  structural_balance,
  gdp_growth,
  interest_rate,
  ageing_costs = 0,
  target_debt = 0.6,
  target_year = 20,
  indicator = c("both", "S1", "S2")
)

Arguments

debt

Numeric scalar. Current debt-to-GDP ratio.

structural_balance

Numeric scalar. Current structural primary balance as a share of GDP (positive = surplus).

gdp_growth

Numeric scalar. Real GDP growth rate.

interest_rate

Numeric scalar. Real interest rate.

ageing_costs

Numeric scalar. Projected increase in age-related expenditure as percentage points of GDP. Default 0.

target_debt

Numeric scalar. Target debt-to-GDP ratio for S1. Default 0.60.

target_year

Integer scalar. Number of years to reach the target debt ratio. Default 20.

indicator

Character. Which indicator to compute: "S1", "S2", or "both" (default).

Details

S1 measures the permanent adjustment in the structural primary balance needed to bring the debt-to-GDP ratio to target_debt in target_year years, taking into account projected increases in age-related expenditure.

S2 measures the permanent adjustment needed to stabilise the debt-to-GDP ratio over an infinite horizon, incorporating the full net present value of future increases in age-related spending.

Value

An S3 object of class dk_sgap containing:

S1: The S1 sustainability gap (or NA if not requested).
S2: The S2 sustainability gap (or NA if not requested).
risk_S1: Risk classification for S1: "low", "medium", or "high".
risk_S2: Risk classification for S2: "low", "medium", or "high".
required_pb: The required structural primary balance implied by S1.
current_pb: The current structural primary balance.
inputs: A list storing all input parameters.

References

European Commission (2012). Fiscal Sustainability Report 2012. European Economy 8/2012, Directorate-General for Economic and Financial Affairs.

Examples

dk_sustainability_gap(
  debt = 0.90,
  structural_balance = -0.01,
  gdp_growth = 0.015,
  interest_rate = 0.025,
  ageing_costs = 0.02
)
dk_sustainability_gap(
  debt = 0.90,
  structural_balance = -0.01,
  gdp_growth = 0.015,
  interest_rate = 0.025,
  ageing_costs = 0.02
)

Package 'debtkit'

Help Index

Bohn's Fiscal Reaction Function Test

Description

Usage

Arguments

Details

Value

References

Examples

Compare Debt Projections

Description

Usage

Arguments

Value

Examples

Decompose Historical Debt Changes

Description

Usage

Arguments

Details

Value

References

Examples

Estimate Joint Distribution of Macro Shocks

Description

Usage

Arguments

Details

Value

Examples

Stochastic Debt Fan Chart

Description

Usage

Arguments

Value

Examples

Gross Financing Needs

Description

Usage

Arguments

Details

Value

References

Examples

IMF-Style Risk Heat Map

Description

Usage

Arguments

Value

References

Examples

Project Debt-to-GDP Path

Description

Usage

Arguments

Details

Value

References

Examples

Interest Rate-Growth Differential and Debt-Stabilising Primary Balance

Description

Usage

Arguments

Details

Value

References

Examples

Sample Fiscal Data

Description

Usage

Arguments

Value

Examples

IMF Standardised Stress Tests

Description

Usage

Arguments

Details

Value