Over-Fitting in The TVP Model: A Comparison of Shrinkage Priors in Inflation Forecasting

Abstract

The study is empirically motivated to analyze the performance of new class of Bayesian shrinkage priors that are powerful in reducing time-varying parameters to static ones to avoid over-fitting problem in time-varying parameter models. We utilized newly improved shrinkage priors in a non-centered parameterization form following Bitto and Fruhwirth-Schnatter (2019) who introduced variance selection using normal-gamma prior which nests the Bayesian LASSO prior of Belmonte et al. (2014) and spike and slab prior as in Schnatter and Wagner (2010). Therefore, the priors are able to discriminate time-varying coefficients from the static ones and the coefficients that can be shrunk to zero. In the empirical exercise, we estimated the generalized Phillip curve for three inflation-targeting countries and produced evidence of significant time-variation in most of the predictors. We compare the performance of the priors in density forecast of inflation allowing for constant and stochastic volatility in the model estimation. Evidence from the estimates of the log predictive density score shows that the hierarchical Normal Gamma shrinkage prior produces the best results for Canada and South Africa whilst the Normal Bayesian LASSO produces the best results for New Zealand, and that adding stochastic volatility improves the performance of models in density forecast.