Long‐run confidence: Estimating uncertainty when using long‐run multipliers

Abstract Researchers are often interested in the long‐run relationship (LRR) between variables where the dependent variable has dynamic properties. Though determining the long‐run multiplier (LRM) for an independent variable is straightforward, correctly estimating the significance of the LRM is often difficult, especially when time series are short and tests for series’ stationarity are uncertain. We propose a Bayesian framework for estimating the LRM by using a bounded prior on the lagged dependent variable to constrain estimates for dynamic processes to the plausible range of values arising from either stationary or integrated series, and then taking draws of the posterior distribution to summarize the credible region. Doing so provides direct estimates of the LRM and its uncertainty, even for short time series. We highlight the advantages of this approach via Monte Carlo experiments and replicate several studies to show that our method clarifies LRRs that were inconclusive using existing techniques.