Testing Parameter Stability in Quantile Models: An Application to the U.S. Inflation Process

This paper considers parameter instability tests in conditional quantile models. I suggest tests for quantile parameter instability based on the asymptotically optimal tests of Lee (2008) both in parametric and semiparametric set-up. In parametric models, Komunjer (2005)'s tick-exponential family of distributions is used as the underlying distribution, in which the test has asymptotically correct sizes even when the error distribution is misspecified. I apply our test statistic to various quantile models of the U.S. inflation process such as Phillips curve, P-star model, and autoregressive models. The test result shows an evidence of parameter instability in most quantile levels of all models. The semiparametric test rejects the stability even in more recent period with moderate economic volatility. Phillips curve model and autoregressive model have asymmetric test results across quantile levels, implying the asymmetric response of inflation to economic shocks.