Bohn's Fiscal Reaction Function Test — dk_bohn

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
)

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.

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).

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.

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)
#> 
#> ── Bohn Fiscal Reaction Function ───────────────────────────────────────────────
#> • Method: ols
#> • Observations: 50
#> • rho = 0.0365 (SE = 0.0058, p = 8.47e-08)
#> ✔ Sustainable: rho > 0 and significant at 5% level.