Inflation forecasting with many predictors (Lasso / Elastic Net)

This illustrates the regularization family: with many macro predictors (money supply, exchange rate, oil price, interest rate, lags…), OLS easily overfits and suffers multicollinearity. Lasso/Elastic Net select variables automatically and shrink coefficients. Figures are illustrative.

Summary: use Lasso/Elastic Net to select the best set of predictors for out-of-sample inflation forecasting.

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Step 1 — Ideation

• Question: which macro variables are actually useful for forecasting inflation, and how does the out-of-sample model perform?

Step 2 — Literature Review

Inflation forecasting, data-rich (many-predictor) forecasting, regularization.

Step 3 — Data Collection

Monthly/quarterly series: cpi (inflation) and 20–50 candidate variables (m2, er, oil, rate, output, expectations, lags…) from EcoData/World Bank/FRED.

Step 4 — Modeling

Choose the Regularized regression family → Lasso (or Elastic Net for correlated groups); standardize variables; select $\lambda$ by cross-validation.

$$\min_{\beta} \sum_{t} (cpi_t - X_t\beta)^2 + \lambda \sum_j |\beta_j|$$

Illustrative results (format — not real results):

	OLS (all variables)	Lasso
Non-zero variables	45	8
Out-of-sample RMSE	1.00 (normalized)	0.78
Retained variables	—	m2_lag, oil, er, rate…

Sample interpretation: Lasso keeps 8/45 variables and lowers out-of-sample RMSE vs full OLS ⇒ a sparse model with better forecasts and easier interpretation.

Stata

* ---- Inflation forecasting with Lasso ----
use "inflation_data.dta", clear

* Lasso with cross-validation
lasso linear inflation x1-x15, selection(cv)

* Display selected coefficients
lassocoef, display(coef, standardized)

R

# ---- Inflation forecasting with Lasso ----
library(glmnet)

# Load data and split train/test (illustrative)
df <- read.csv("inflation_data.csv")
train <- df[1:100, ]
test  <- df[101:120, ]

X_train <- as.matrix(train[, paste0("x", 1:15)])
y_train <- train$inflation
X_test  <- as.matrix(test[, paste0("x", 1:15)])

# Lasso with CV
fit <- cv.glmnet(X_train, y_train, alpha = 1)
best_lambda <- fit$lambda.min

# Predict out-of-sample
y_pred <- predict(fit, X_test, s = best_lambda)
rmse <- sqrt(mean((test$inflation - y_pred)^2))
cat("Out-of-sample RMSE:", rmse, "\n")
coef(fit, s = best_lambda)

Python

# ---- Inflation forecasting with Lasso ----
from sklearn.linear_model import LassoCV
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error
import pandas as pd
import numpy as np

# Load data and split (illustrative)
df = pd.read_csv("inflation_data.csv")
X = df[[f"x{i}" for i in range(1, 16)]]
y = df["inflation"]

X_train, X_test = X.iloc[:100], X.iloc[100:]
y_train, y_test = y.iloc[:100], y.iloc[100:]

scaler = StandardScaler()
X_train_s = scaler.fit_transform(X_train)
X_test_s  = scaler.transform(X_test)

# LassoCV with 10-fold CV
model = LassoCV(cv=10).fit(X_train_s, y_train)
y_pred = model.predict(X_test_s)
rmse = np.sqrt(mean_squared_error(y_test, y_pred))

print(f"Best alpha: {model.alpha_}")
print(f"Non-zero: {sum(model.coef_ != 0)}")
print(f"Out-of-sample RMSE: {rmse:.4f}")

Step 5 — Reporting

Export a report + the shrinkage path over $\lambda$ + replication code.

Note

Regularization is prediction-oriented, not causal inference; coefficients are shrunk. For inference, combine with theory or Adaptive Lasso.

Video tutorial

Video Tutorial: Inflation forecasting with Lasso in EcoLab

See also

• Lasso · Elastic Net · Ridge · Catalog