We study estimation uncertainty when the object of interest contains one or more ratios of parameters. The ratio of parameters is a discontinuous parameter transformation; it has been shown that traditional confidence intervals often fail to cover a true ratio with reliable probability. Constructing confidence sets for ratios using Fieller's method is a viable solution as the method can avoid the discontinuity problem. This paper proposes an extension of the multivariate Fieller method beyond standard contexts, focusing on asymptotically mixed normal estimators that commonly arise in dynamic regressions with persistent covariates. We show that the asymptotic distribution of the pivotal statistic used for constructing a Fieller's confidence set remains a standard Chi-squared; and in many instances, the Wald-type test statistic 'self-normalizes' and thus the rates of convergence need not be known. An extensive simulation study illustrates the finite sample properties of the proposed method using both the Pooled Mean Group (PMG) estimator and Arellano and Bond's (1991) (AnB) estimator in a dynamic polynomial panel regression. Our method is demonstrated to work well in small samples, even in some persistent contexts.

Delta Method, Dynamic Polynomial Panels, Fieller's Theorem, Ratios of Parameters, The Arellano and BondMmethod, The Pooled Mean Group (PMG) Estimator, Wald-Type Tests
Annals of Economics and Statistics
Department of Economics

Bernard, J.-T. (Jean-Thomas), Chu, B. (Ba), Khalaf, L, & Voia, M.-C. (2019). Non-standard confidence sets for ratios and tipping points with applications to dynamic panel data. Annals of Economics and Statistics, (134), 79–108. doi:10.15609/annaeconstat2009.134.0079