Multivariate Quantile Autoregression-Mixed Data Sampling (MVQAR-MIDAS) Modeling of Cost of Living and Supply Chain Dynamics in Canada.

In recent years, the rising cost of living as a result of persistent inflationary pressures, disruptions in the global supply chains, and changes in the macroeconomic landscape has become a critical topic of discussion. To address this, we move beyond a mean-based framework and employ a quantile regression approach. This allows the persistence of each series and the transmis- sion of shocks between the Consumer Price Index (CPI) (the total CPI which is a percentage change over the past 12 months), the Interest Rate (IR)(the target for the overnight rate), the New Housing Price Index (NHPI), and high-frequency supply chain indicators such as the Global Supply Chain Pressure (GSCPI), the Industrial Product Price Index (IPPI), and the Energy Price Index (EPI) to differ across the lower, middle, and upper parts of their condi- tional distributions. Consequently, this study develops and implements a Multivariate Quantile Autoregression (MVQAR) framework, extended with Mixed Data Sampling (MIDAS), to in- vestigate the dynamic, quantile-specific effects of supply chain pressures on Canada’s cost of living. The model links quarterly measures of the CPI, IR, and NHPI to monthly indicators of GSCPI, IPPI, and EPI over the period January 1998 to February 2025. Indexes NHPI, and IPPI were sourced from the Statistics Canada website; GSCPI from the Federal Reserve Bank of New York website; CPI, IR and, EPI from the Bank of Canada website. We estimated the MVQAR–MIDAS model at several quantiles (τ = 0.10, 0.25, 0.50, 0.75, 0.90) under a recursive triangular structure that treats CPI as contemporaneously exogenous, IR as reacting to current CPI, and NHPI as reacting to both current CPI and IR. This setup allows the persistence of each series, the contemporaneous transmission between CPI, IR and NHPI, and the impact of high-frequency supply chain variables to vary across the lower, middle, and upper parts of the conditional distributions. Overall, the MVQAR–MIDAS framework provides a more comprehensive description of how supply chain shocks propagate through the Canadian economy, while the simulation results highlight significant estimation bias, especially for extreme quantiles, which should be kept in mind when interpreting the coefficients. The results from the real data suggest an asymmetric, quantile-dependent interest rate (IR) response to contemporaneous inflation (CPI) movements, stronger in the lower tail of interest rate changes and weaker in the upper tail. NHPI behaviour is clearly quantile-specific, with the autoregressive profile shifting across the distribution so that high-growth periods exhibit more pronounced propagation from past housing-price changes than the lower tail. This research provides a structured way to study how supply chain pressures feed into the Canadian cost of living across the entire distribution, not just on average. Thus, com- bining MVQAR with MIDAS shows that the effects of global supply chain pressure, energy prices, and industrial product prices on CPI, IR, and NHPI differ considerably across quantiles, with monetary policy and housing prices reacting more strongly in periods of unusually high or low inflation. This offers policymakers and analysts a clearer picture of how shocks propa- gate through prices, financing conditions, and the housing market under different states of the economy, while the observed difficulties in capturing extreme episodes point directly to where future modelling improvements are most needed.