Macroeconomic Regime and Regression Analysis

Overview

This article walks through a complete macroeconomic research workflow using opennaijR — from raw data retrieval to econometric modelling. We will answer one central policy question:

Is food inflation the primary driver of headline inflation in Nigeria, and can we quantify that relationship?

Along the way you will see how apply_projection(), derive_measure(), and base R modelling functions fit together into a reproducible pipeline.

The Pipeline at a Glance

1. Retrieve       cbn()
2. Clean schema   apply_projection()
3. Engineer       derive_measure()
4. Describe       table(), prop.table(), summary()
5. Test           chisq.test(), cor.test()
6. Model          lm(), glm()
7. Reproduce      attr(..., "derive_manifest")

Each step feeds into the next. The manifest system ensures you can retrace every decision.

Step 1 — Retrieve Data

library(opennaijR)

infl     <- cbn("inflation")
exchange <- cbn("exchange_rates")

cbn() returns an opennaijR_tbl — a data frame with extra attributes. You can use it anywhere a normal data frame is accepted.

Step 2 — Clean the Schema

Select only the columns needed for this analysis and give them readable names.

infl_clean <- apply_projection(
  infl,
  cols   = c("date", "headline_yoy", "food_yoy", "core_ex_farm_yoy"),
  rename = c(
    Date     = "date",
    Headline = "headline_yoy",
    Food     = "food_yoy",
    Core     = "core_ex_farm_yoy"
  ),
  reason = "Select and rename for macro regime analysis"
)

exchange_clean <- apply_projection(
  exchange,
  cols   = c("date", "buying_rate"),
  rename = c(Date = "date", Rate = "buying_rate"),
  reason = "Minimal exchange rate schema"
)

head(infl_clean)

Why do this first? Working with short, descriptive names (Headline, Food, Core) makes every subsequent step easier to read and less prone to typos.

Step 3 — Construct Inflation Regimes

We classify each observation into a policy-relevant inflation category. The thresholds below are representative; adjust them to match the CBN’s own communication framework if preferred.

Label	Condition
Deflation	`Headline < 0`
Low	`0 ≤ Headline ≤ 5`
Moderate	`5 < Headline ≤ 15`
High	`Headline > 15`

infl_regimes <- derive_measure(
  infl_clean,
  Headline_Regime = ifelse(
    Headline < 0,  "Deflation",
    ifelse(
      Headline <= 5,  "Low",
      ifelse(
        Headline <= 15, "Moderate",
        "High"
      )
    )
  ),
  Food_Regime = ifelse(
    Food < 0,  "Deflation",
    ifelse(
      Food <= 5,  "Low",
      ifelse(
        Food <= 15, "Moderate",
        "High"
      )
    )
  ),
  reason = "Construct headline and food inflation regimes"
)

Two new columns appear: Headline_Regime and Food_Regime. Every original column is preserved.

Step 4 — Descriptive Regime Analysis

4.1 Frequency counts

How often has Nigeria been in each headline inflation regime?

table(infl_regimes$Headline_Regime)

This single line tells a macro story. If most observations fall in “High”, inflation is structurally elevated, not episodic.

Do the same for food:

table(infl_regimes$Food_Regime)

Compare the two distributions side by side to see which component is more volatile.

4.2 Cross-tabulation

The key question is whether the two regimes move together.

regime_table <- table(
  Headline = infl_regimes$Headline_Regime,
  Food     = infl_regimes$Food_Regime
)

regime_table

Each cell shows how many periods had that combination of regimes. Look at the diagonal — a heavy diagonal indicates the two indicators move in lockstep.

4.3 Row proportions

Raw counts depend on the sample size. Proportions are easier to interpret.

prop.table(regime_table, margin = 1)

margin = 1 gives row percentages: given headline is High, what fraction of those months also had Food as High?

If that fraction is above 0.75, you can make a strong qualitative claim:

In more than three-quarters of high-headline-inflation episodes, food inflation was simultaneously elevated, suggesting food price dynamics are a primary transmission mechanism.

Step 5 — Statistical Association Test

Move from observation to inference with a Chi-square test.

chisq.test(regime_table)

How to read the output:

X-squared — the test statistic; a larger value indicates stronger association.
df — degrees of freedom; depends on the number of categories.
p-value — if below 0.05, the association between regimes is statistically significant (not due to chance at the 5% level).

A significant result allows you to write:

There is a statistically significant association between food and headline inflation regimes (χ²(df) = X, p < 0.05), rejecting independence.

Step 6 — Continuous Regression Models

Regime analysis tells you when indicators move together. Regression tells you how much.

Model 1 — Food alone

model1 <- lm(Headline ~ Food, data = infl_regimes)
summary(model1)

Key output to interpret:

Coefficient on Food — a one percentage-point rise in food inflation is associated with a β percentage-point rise in headline inflation. If β ≈ 0.7, food is a strong but partial driver.
R² — the share of headline inflation’s variance explained by food inflation alone. An R² of 0.80 means food explains 80% of headline variation.

Model 2 — Food and Core together

model2 <- lm(Headline ~ Food + Core, data = infl_regimes)
summary(model2)

Compare to Model 1:

Does Food remain significant after controlling for Core? If yes, food has an independent effect.
Does Core add explanatory power? Check the change in Adjusted R².
Do the two coefficients suggest which component is more influential?

Model 3 — Augmented with Exchange Rate

Exchange rate depreciation can feed into import prices, amplifying food and headline inflation. Merge the datasets and test this hypothesis.

macro <- merge(infl_regimes, exchange_clean, by = "Date")

model3 <- lm(Headline ~ Food + Core + Rate, data = macro)
summary(model3)

A positive, significant coefficient on Rate would mean that periods of naira depreciation are associated with higher headline inflation — a pass-through effect. This is policy-relevant because the CBN uses exchange rate policy partly as an inflation tool.

Step 7 — Logistic Regression: Predicting the High-Inflation Regime

Sometimes the policy question is binary: are we in a high-inflation episode or not? Logistic regression estimates the probability of being in that state.

# Create the binary outcome
infl_binary <- derive_measure(
  infl_regimes,
  High_Inflation = Headline > 15,
  reason         = "Binary indicator for high-inflation regime"
)

# Estimate the model
logit_model <- glm(
  High_Inflation ~ Food,
  data   = infl_binary,
  family = binomial()
)

summary(logit_model)

Interpreting logistic coefficients:

Logistic regression does not produce a direct percentage-point effect. Instead, exponentiate the coefficient to get an odds ratio:

exp(coef(logit_model))

An odds ratio of 1.15 on Food means: for every one percentage-point increase in food inflation, the odds of being in a high-inflation regime increase by 15%.

Adding the exchange rate to the logit model

macro_binary <- merge(infl_binary, exchange_clean, by = "Date")

logit_model2 <- glm(
  High_Inflation ~ Food + Rate,
  data   = macro_binary,
  family = binomial()
)

summary(logit_model2)
exp(coef(logit_model2))

Step 8 — Advanced: Interaction Terms

Does the impact of food inflation on headline inflation depend on how high core inflation already is? An interaction term tests this.

model_interaction <- lm(
  Headline ~ Food * Core,
  data = infl_regimes
)

summary(model_interaction)

The term Food:Core is the interaction. A significant, positive interaction coefficient means food inflation has a larger marginal effect on headline inflation when core inflation is also elevated — the two pressures compound each other.

This is the kind of finding that motivates coordinated monetary and supply-side policy responses.

Step 9 — Inspect the Manifest

Every derive_measure() call left a record. Retrieve it to document your research trail.

manifest <- attr(infl_binary, "derive_manifest")

# How many derivation steps were recorded?
length(manifest)

# Inspect the most recent step
tail(manifest, 1)[[1]]$timestamp
tail(manifest, 1)[[1]]$expressions
tail(manifest, 1)[[1]]$reason

For a published paper or policy report, include the manifest output in an appendix. It demonstrates exactly which transformations were applied to the raw CBN data.

Step 10 — Interpreting Results for Policy

Once you have run the models, translate the numbers into plain language. Here is a template:

Descriptive: High headline inflation coincided with high food inflation in prop.table() of observed months, suggesting food price dynamics are the dominant transmission channel.

Statistical: A Chi-square test confirms this association is statistically significant (p < 0.05), rejecting the hypothesis that headline and food regimes are independent.

Regression: A one percentage-point increase in food inflation is associated with a β₁ percentage-point increase in headline inflation (p < 0.001), controlling for core inflation. Food inflation explains R²% of variation in headline inflation.

Policy implication: Interventions targeting food supply chains — storage infrastructure, agricultural inputs, border trade logistics — are likely to have a measurable dampening effect on headline inflation.

Summary of the Full Pipeline

# ── 1. Data ────────────────────────────────────────────────────────────────────
infl     <- cbn("inflation")
exchange <- cbn("exchange_rates")

# ── 2. Schema ──────────────────────────────────────────────────────────────────
infl_clean <- apply_projection(
  infl,
  cols   = c("date", "headline_yoy", "food_yoy", "core_ex_farm_yoy"),
  rename = c(Date = "date", Headline = "headline_yoy",
             Food = "food_yoy", Core = "core_ex_farm_yoy"),
  reason = "Select and rename for macro regime analysis"
)

exchange_clean <- apply_projection(
  exchange,
  cols   = c("date", "buying_rate"),
  rename = c(Date = "date", Rate = "buying_rate")
)

# ── 3. Features ────────────────────────────────────────────────────────────────
infl_regimes <- derive_measure(
  infl_clean,
  Headline_Regime = ifelse(Headline < 0, "Deflation",
                    ifelse(Headline <= 5, "Low",
                    ifelse(Headline <= 15, "Moderate", "High"))),
  Food_Regime     = ifelse(Food < 0, "Deflation",
                    ifelse(Food <= 5, "Low",
                    ifelse(Food <= 15, "Moderate", "High"))),
  High_Inflation  = Headline > 15,
  reason          = "Regime construction and binary flag"
)

# ── 4. Association ─────────────────────────────────────────────────────────────
regime_table <- table(infl_regimes$Headline_Regime, infl_regimes$Food_Regime)
prop.table(regime_table, margin = 1)
chisq.test(regime_table)

# ── 5. Regression ──────────────────────────────────────────────────────────────
model1 <- lm(Headline ~ Food,        data = infl_regimes)
model2 <- lm(Headline ~ Food + Core, data = infl_regimes)

macro   <- merge(infl_regimes, exchange_clean, by = "Date")
model3  <- lm(Headline ~ Food + Core + Rate, data = macro)

logit1  <- glm(High_Inflation ~ Food + Rate, data = macro, family = binomial())

# ── 6. Manifest ────────────────────────────────────────────────────────────────
attr(infl_regimes, "derive_manifest")

This is a reproducible, publishable macroeconomic analysis — written entirely in R, documented entirely by the opennaijR manifest system.

Lawrence Garba