Relations between Abs-Normal NLPs and MPCCs. Part 1: Strong Constraint Qualifications

This work is part of an ongoing effort of comparing non-smooth optimization problems in abs-normal form to MPCCs. We study the general abs-normal NLP with equality and inequality constraints in relation to an equivalent MPCC reformulation. We show that kink qualifications and MPCC constraint qualifications of linear independence type and Mangasarian-Fromovitz type are equivalent. Then we consider strong stationarity concepts with first and second order optimality conditions, which again turn out to be equivalent for the two problem classes. Throughout we also consider specific slack reformulations suggested in [9], which preserve constraint qualifications of linear independence type but not of Mangasarian-Fromovitz type.

The Tail Behavior due to the Presence of the Risk Premium in AR-GARCH-in-Mean, GARCH-AR, and Double-Autoregressive-in-Mean Models*

We extend the results in Borkovec (2000), Basrak, David, and Mikosch (2002a), Lange (2011), and Francq and Zakoïan (2015) by describing the tail behavior when a risk premium component is added in the mean equation of different conditional heteroskedastic processes. We study three types of parametric models: the traditional generalized autoregressive conditional heteroskedastic (GARCH)-M model, the double autoregressive (AR) model with risk premium, and the GARCH-AR model. We find that if an AR process is introduced in the mean equation of a traditional GARCH-M process, the tail behavior is the same as if it is not introduced. However, if we add a risk premium component to the double AR model, then the tail behavior changes with respect to the GARCH-M. The GARCH-AR model also has a different tail index than the traditional AR-GARCH model. In a simulation study, we show that larger tail indexes are associated with the traditional GARCH-M model. When the size of the risk premium component increases, the tail index tends to fall. The only exception to this rule occurs in the double AR model when the risk premium depends on log-volatility. Parameter configurations where the strong stationarity condition of the risk premium models fails are also illustrated and discussed.

Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints

The main aim of this paper is to develop necessary Optimality conditions using Convexifactors for mathematical programs with equilibrium constraints (MPEC). For this purpose a nonsmooth version of the standard Guignard constraint qualification (GCQ) and strong stationarity are introduced in terms of convexifactors for MPEC. It is shown that Strong stationarity is the first order necessary optimality condition under nonsmooth version of the standard GCQ. Finally, notions of asymptotic pseudoconvexity and asymptotic quasiconvexity are used to establish the sufficient optimality conditions for MPEC.

Medical Net Discount Rates: Updated and Re-examined

Abstract1 Schap, Guest and Kraynak (2013) examines time series properties of medical net discount rates (MNDRs) based on three different, short-term Treasury securities. The article finds attributes of stationarity in each of the series examined and notes greater support for total offset of interest rates and medical cost growth rates than does previously published research. The present study makes four adjustments to Schap, Guest and Kraynak (2013). First, the data set is updated by two years and four months. Second, the t-test applied in the original study and also used in earlier studies of total offset fails to account for autocorrelated error terms, so a substitute test is applied to both the original data set and the newly extended data set, with results reported. Third, Phillips-Perron testing is conducted in addition to Augmented Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin testing of stationarity of the various series analyzed, with results reported. Finally, Zivot-Andrews testing is applied diagnostically, to identify stationary sub-series of MNDRs, similar to an approach used successfully to identify stationary sub-series of wage net discount rates (Schap, Baumann and Guest, 2014). The data analysis suggests two options available to practicing forensic economists who endorse the use of Treasury securities of short duration in formulating MNDRs. One option is to use total offset (i.e., a zero MNDR), based on modestly favorable empirical support in the period 1981:01 to 2014:10. The alternative option would be to rely on a body of evidence amassed over a shorter time frame, from 2001:01 to 2014:10, but which has remarkably strong stationarity properties and yields MNDRs between minus 1.5 and minus 2.0% (i.e., an implicit forecast of medical cost growth exceeding the discount factor).