The forthcoming article “Long-run confidence: Estimating uncertainty when using long-run multipliers” by Mark David Nieman and David A. M. Peterson is summarized by the author(s) below.
Our paper tackles a longstanding problem in time series analysis: how to estimate uncertainty for the long-run effect of a predictor in a regression model that includes a lagged dependent variable. This is a pervasive challenge in political science, where time series are often short and the test for ascertaining their properties underpowered. Conventional uncertainty estimates—essential for hypothesis testing—break down under such conditions.
We address this issue using a Bayesian estimator with a semi-informed prior that yields theoretically informed estimates of uncertainty even in short or noisy time series. We start by using a bounded, uniform prior for the estimated coefficient on the lagged DV. The semi-informed prior accommodates series of X and y with unclear dynamic properties by limiting the range of the coefficient on a lagged DV to its theoretical bounds for either stationary or integrated series. By giving equal density to the values between these bounds, however, the prior does not bias point estimates.
We then estimate the model via Markov chain Monte Carlos (MCMC). The use of a sampling-based method, like MCMCs, allow for direct estimation of the variance of the long-run multiplier, without requiring large sample sizes. This is made possible by exploiting a well-known property of MCMC methods, namely, that one can estimate and summarize the distribution of functions of parameters (e.g., ratios of coefficients) directly from the posterior distribution.
Our proposed method leads to more accurate and reliable estimates of uncertainty than alternatives that rely on asymptotic assumptions that may not hold. Moreover, our framework requires minimal additional assumptions over existing approaches and is easy to estimate in most existing software. We highlight the advantages of this approach via Monte Carlo experiments and replicate several studies to show that our method clarifies long-run relationships that were inconclusive using existing techniques.
About the Author(s): Mark David Nieman is an Assistant Professor in the Department of Political Science and Trinity College, as well as an affiliate of the Data Sciences Institute and David A. M. Peterson is the Lucken Professor of Political Science in the Department of Political Science at Iowa State University. Their research “Long-run confidence: Estimating uncertainty when using long-run multipliers” is now available in Early View and will appear in a forthcoming issue of the American Journal of Political Science.









