2014/11/04 by Laurent Callot, Callot, Laurent, Johannes Tang Kristensen +1
Economics, Econometrics and Finance · #91G70 #Economic Policies and Impacts #FOS: Computer and information sciences #FOS: Mathematics #Italy: Economic History and Contemporary Issues #Machine Learning (stat.ML) #Monetary Policy and Economic Impact #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1411.0877
openalex publication_date 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a parsimoniously time varying parameter vector\nautoregressive model (with exogenous variables, VARX) and studies the\nproperties of the Lasso and adaptive Lasso as estimators of this model. The\nparameters of the model are assumed to follow parsimonious random walks, where\nparsimony stems from the assumption that increments to the parameters have a\nnon-zero probability of being exactly equal to zero. By varying the degree of\nparsimony our model can accommodate constant parameters, an unknown number of\nstructural breaks, or parameters with a high degree of variation.\n We characterize the finite sample properties of the Lasso by deriving upper\nbounds on the estimation and prediction errors that are valid with high\nprobability; and asymptotically we show that these bounds tend to zero with\nprobability tending to one if the number of non zero increments grows slower\nthan \√(T).\n By simulation experiments we investigate the properties of the Lasso and the\nadaptive Lasso in settings where the parameters are stable, experience\nstructural breaks, or follow a parsimonious random walk. We use our model to\ninvestigate the monetary policy response to inflation and business cycle\nfluctuations in the US by estimating a parsimoniously time varying parameter\nTaylor rule. We document substantial changes in the policy response of the Fed\nin the 1980s and since 2008.\n