inflationkit: Inflation Decomposition, Core Measures, and Trend Estimation

Description

Tools for analysing inflation dynamics. Computes weighted contributions of price index components, core inflation measures (trimmed mean, weighted median, exclusion-based) following Bryan and Cecchetti (1994) doi:10.1016/0304-3932(94)90030-2, inflation persistence via sum-of-AR-coefficients, diffusion indices, Phillips curve estimation, breakeven inflation, and trend inflation using the Beveridge-Nelson decomposition and Hodrick-Prescott filter. All functions are pure computation and work with price data from any source.

Author(s)

Maintainer: Charles Coverdale charlesfcoverdale@gmail.com

See Also

Useful links:

• https://github.com/charlescoverdale/inflationkit

• Report bugs at https://github.com/charlescoverdale/inflationkit/issues

Compute breakeven inflation rates

Description

Calculates breakeven inflation as the spread between nominal and real (inflation-linked) bond yields. This provides a market-based measure of inflation expectations.

Usage

ik_breakeven(nominal_yield, real_yield, maturity = NULL)

Arguments

Details

Note: breakeven inflation is a simplified measure that does not account for inflation risk premium or liquidity premium. It should be interpreted as a rough proxy for inflation expectations, not a precise measure.

Value

An S3 object of class "ik_breakeven" with elements:

breakeven

If maturity is provided, a data.frame with columns: maturity, nominal, real, breakeven. Otherwise, a numeric vector of breakeven rates.

maturity

The maturity vector (or NULL).

Examples

# Breakeven term structure
be <- ik_breakeven(
  nominal_yield = c(4.2, 4.5, 4.8, 5.0),
  real_yield = c(1.8, 2.0, 2.3, 2.5),
  maturity = c(2, 5, 10, 30)
)
print(be)
plot(be)

# Simple breakeven (no maturity)
be2 <- ik_breakeven(nominal_yield = 4.5, real_yield = 2.0)
print(be2)

Compare multiple core inflation measures

Description

Takes multiple ik_core objects and facilitates side-by-side comparison. Produces summary statistics and a multi-line chart of all measures.

Usage

ik_compare(..., labels = NULL)

Arguments

Value

An S3 object of class "ik_comparison" with elements:

measures

List of ik_core objects.

labels

Character vector of labels.

Examples

data <- ik_sample_data("components")
core_tm <- ik_core(data, method = "trimmed_mean")
core_wm <- ik_core(data, method = "weighted_median")
core_ex <- ik_core(data, method = "exclusion", exclude = c("Food", "Transport"))

comp <- ik_compare(core_tm, core_wm, core_ex)
print(comp)
plot(comp)

Compute core inflation measures

Description

Estimates core (underlying) inflation using one of three standard methods: trimmed mean, weighted median, or exclusion-based. These measures aim to strip out transitory price movements and reveal the persistent trend.

Usage

ik_core(
  data,
  method = c("trimmed_mean", "weighted_median", "exclusion", "asymmetric_trim"),
  trim = 0.08,
  trim_lower = 0.24,
  trim_upper = 0.31,
  exclude = NULL,
  date_col = "date",
  item_col = "item",
  change_col = "price_change",
  weight_col = "weight"
)

Arguments

Value

An S3 object of class "ik_core" with elements:

core

data.frame with columns: date, core_inflation.

method

Character. The method used.

trim

Numeric. The trim fraction (if applicable).

exclude

Character vector. Excluded items (if applicable).

headline

data.frame with columns: date, headline.

References

Bryan, M. F. and Cecchetti, S. G. (1993). "The Consumer Price Index as a Measure of Inflation." NBER Working Paper No. 4505.

Bryan, M. F. and Cecchetti, S. G. (1994). "Measuring Core Inflation." In Monetary Policy, University of Chicago Press.

Examples

data <- ik_sample_data("components")

# Trimmed mean (default)
core_tm <- ik_core(data, method = "trimmed_mean")
print(core_tm)

# Weighted median
core_wm <- ik_core(data, method = "weighted_median")
print(core_wm)

# Exclusion-based
core_ex <- ik_core(data, method = "exclusion", exclude = c("Food", "Transport"))
print(core_ex)

Decompose inflation into weighted component contributions

Description

Computes the weighted contribution of each CPI component to headline inflation. The contribution of item i is weight_i * price_change_i, and headline inflation is the sum of all contributions for each period.

Usage

ik_decompose(
  data,
  date_col = "date",
  item_col = "item",
  change_col = "price_change",
  weight_col = "weight"
)

Arguments

Value

An S3 object of class "ik_decomposition" with elements:

contributions

data.frame with columns: date, item, weight, price_change, contribution.

headline

data.frame with columns: date, headline_inflation.

Examples

data <- ik_sample_data("components")
decomp <- ik_decompose(data)
print(decomp)
plot(decomp)

Compute an inflation diffusion index

Description

Measures the breadth of price increases across CPI components. For each period, computes the (weighted or unweighted) fraction of items with price changes exceeding a threshold. A diffusion index above 0.5 indicates that more than half of items are experiencing above-threshold price increases.

Usage

ik_diffusion(
  data,
  threshold = c("zero", "mean", "target"),
  target = 0.02,
  weighted = TRUE,
  date_col = "date",
  item_col = "item",
  change_col = "price_change",
  weight_col = "weight"
)

Arguments

Value

An S3 object of class "ik_diffusion" with elements:

diffusion

data.frame with columns: date, diffusion_index.

threshold

Character. The threshold type used.

weighted

Logical. Whether weights were used.

Examples

data <- ik_sample_data("components")

# Fraction of items with rising prices
d <- ik_diffusion(data, threshold = "zero")
print(d)
plot(d)

Evaluate inflation forecasts

Description

Runs standard forecast evaluation tests. The bias test (Mincer-Zarnowitz) checks whether forecasts are unbiased. The efficiency test (Nordhaus) checks whether forecast errors are autocorrelated. The Diebold-Mariano test compares predictive accuracy of two competing forecasts.

Usage

ik_forecast_eval(
  actual,
  forecast,
  test = c("bias", "efficiency", "dm"),
  forecast2 = NULL,
  horizon = 1L,
  alternative = c("two.sided", "less", "greater")
)

Arguments

Value

An S3 object of class "ik_forecast_eval" with elements:

test

Character. The test performed.

statistic

Numeric. The test statistic.

p_value

Numeric. The p-value.

coefficients

Named numeric vector (for bias and efficiency tests).

conclusion

Character. A plain-language summary of the result.

References

Diebold, F. X. and Mariano, R. S. (1995). "Comparing Predictive Accuracy." Journal of Business and Economic Statistics, 13(3), 253-263.

Examples

set.seed(42)
data <- ik_sample_data("headline")
actual <- data$inflation[5:80]
forecast1 <- data$inflation[4:79] + rnorm(76, 0, 0.2)
forecast2 <- data$inflation[4:79] + rnorm(76, 0, 0.4)

# Mincer-Zarnowitz bias test
bias <- ik_forecast_eval(actual, forecast1, test = "bias")
print(bias)

# Diebold-Mariano test
dm <- ik_forecast_eval(actual, forecast1, test = "dm", forecast2 = forecast2)
print(dm)

Measure inflation persistence

Description

Estimates the degree of persistence in an inflation series using one of three methods: sum of AR coefficients, half-life, or largest autoregressive root.

Usage

ik_persistence(
  x,
  method = c("sum_ar", "half_life", "largest_root"),
  ar_order = NULL,
  max_order = 12L,
  ic = c("bic", "aic")
)

Arguments

Value

An S3 object of class "ik_persistence" with elements:

value

Numeric. The persistence measure.

method

Character. The method used.

ar_order

Integer. The AR order fitted.

ar_coefficients

Numeric vector. The estimated AR coefficients.

interpretation

Character. A plain-language interpretation ("High persistence", "Moderate persistence", or "Low persistence").

References

Andrews, D. W. K. and Chen, H.-Y. (1994). "Approximately Median-Unbiased Estimation of Autoregressive Models." Journal of Business and Economic Statistics, 12(2), 187-204.

Marques, C. R. (2004). "Inflation Persistence: Facts or Artefacts?" ECB Working Paper No. 371.

Examples

data <- ik_sample_data("headline")
p <- ik_persistence(data$inflation, method = "sum_ar")
print(p)

p_hl <- ik_persistence(data$inflation, method = "half_life")
print(p_hl)

Estimate a Phillips curve

Description

Fits a Phillips curve relating inflation to an economic slack measure (output gap or unemployment rate). Supports traditional, expectations- augmented, and hybrid specifications.

Usage

ik_phillips(
  inflation,
  slack,
  expectations = NULL,
  type = c("traditional", "expectations_augmented", "hybrid"),
  lags = 4L,
  robust_se = FALSE
)

Arguments

Value

An S3 object of class "ik_phillips" with elements:

coefficients

Named numeric vector of estimated coefficients.

std_errors

Named numeric vector of standard errors.

p_values

Named numeric vector of p-values.

r_squared

Numeric. R-squared of the regression.

type

Character. The Phillips curve type.

slope_estimate

Numeric. The estimated slope on the slack variable.

n_obs

Integer. Number of observations used.

residuals

Numeric vector. Regression residuals.

Examples

data <- ik_sample_data("headline")
pc <- ik_phillips(data$inflation, data$unemployment, type = "traditional")
print(pc)
plot(pc)

Generate sample inflation data

Description

Creates synthetic data for testing and demonstrating inflationkit functions. Two types are available: component-level CPI data and headline macro data.

Usage

ik_sample_data(type = c("components", "headline"))

Arguments

Value

A data.frame. For "components": columns date, item, weight, price_change (120 months, 10 items, 1200 rows). For "headline": columns date, inflation, output_gap, unemployment (80 quarterly observations).

Examples

comp <- ik_sample_data("components")
head(comp)

macro <- ik_sample_data("headline")
head(macro)

Decompose inflation into sticky and flexible components

Description

Splits CPI components into sticky-price and flexible-price categories based on a user-provided classification, then computes separate weighted inflation measures for each group. This follows the Atlanta Fed methodology.

Usage

ik_sticky_flexible(
  data,
  classification,
  date_col = "date",
  item_col = "item",
  change_col = "price_change",
  weight_col = "weight"
)

Arguments

Value

An S3 object of class "ik_sticky_flex" with elements:

result

data.frame with columns: date, sticky, flexible, headline.

classification

Named logical vector mapping items to sticky/flexible.

References

Bils, M. and Klenow, P. J. (2004). "Some Evidence on the Importance of Sticky Prices." Journal of Political Economy, 112(5), 947-985.

Examples

data <- ik_sample_data("components")
# Classify items
class_vec <- c(
  Food = FALSE, Housing = TRUE, Transport = FALSE,
  Clothing = FALSE, Health = TRUE, Education = TRUE,
  Communication = TRUE, Recreation = FALSE,
  Restaurants = TRUE, Other = FALSE
)
sf <- ik_sticky_flexible(data, classification = class_vec)
print(sf)
plot(sf)

Estimate trend inflation

Description

Extracts the trend component from an inflation series using one of four methods: Hodrick-Prescott filter, Beveridge-Nelson decomposition, exponential smoothing, or centred moving average.

Usage

ik_trend(
  x,
  method = c("hp", "beveridge_nelson", "exponential_smooth", "moving_average"),
  frequency = c("quarterly", "monthly", "annual"),
  lambda = NULL,
  window = NULL
)

Arguments

Value

An S3 object of class "ik_trend" with elements:

trend

Numeric vector. The estimated trend component.

cycle

Numeric vector. The cyclical component (original minus trend).

method

Character. The method used.

lambda

Numeric. HP filter lambda (if applicable).

window

Integer. Moving average window (if applicable).

alpha

Numeric. Exponential smoothing parameter (if applicable).

original

Numeric vector. The original series.

References

Hodrick, R. J. and Prescott, E. C. (1997). "Postwar U.S. Business Cycles: An Empirical Investigation." Journal of Money, Credit and Banking, 29(1), 1-16.

Ravn, M. O. and Uhlig, H. (2002). "On Adjusting the Hodrick-Prescott Filter for the Frequency of Observations." Review of Economics and Statistics, 84(2), 371-376.

Examples

data <- ik_sample_data("headline")
tr <- ik_trend(data$inflation, method = "hp")
print(tr)
plot(tr)

tr_ma <- ik_trend(data$inflation, method = "moving_average", window = 4)
print(tr_ma)