Implicit Copulas from Bayesian Regularized Regression Smoothers

We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors --- a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection --- and both univariate and multivariate function bases. The implicit copulas are high-dimensional, have flexible dependence structures that are far from that of a Gaussian copula, and are unavailable in closed form. However, we show how they can be evaluated by first constructing a Gaussian copula conditional on the regularization parameters, and then integrating over these. Combined with non-parametric margins the regularized smoothers can be used to model the distribution of non-Gaussian univariate responses conditional on the covariates. Efficient Markov chain Monte Carlo schemes for evaluating the copula are given for this case. Using both simulated and real data, we show how such copula smoothing models can improve the quality of resulting function estimates and predictive distributions

The Form Factors of the Gauge-Invariant Three-Gluon Vertex

The gauge-invariant three-gluon vertex obtained from the pinch technique is characterized by thirteen nonzero form factors, which are given in complete generality for unbroken gauge theory at one loop. The results are given in $d$ dimensions using both dimensional regularization and dimensional reduction, including the effects of massless gluons and arbitrary representations of massive gauge bosons, fermions, and scalars. We find interesting relations between the functional forms of the contributions from gauge bosons, fermions, and scalars. These relations hold only for the gauge-invariant pinch technique vertex and are d-dimensional incarnations of supersymmetric nonrenormalization theorems which include finite terms. The form factors are shown to simplify for $N=1,2$, and 4 supersymmetry in various dimensions. In four-dimensional non-supersymmetric theories, eight of the form factors have the same functional form for massless gluons, quarks, and scalars, when written in a physically motivated tensor basis. For QCD, these include the tree-level tensor structure which has prefactor $\beta_0=(11N_c-2N_f)/3$, another tensor with prefactor $4N_c-N_f$, and six tensors with $N_c-N_f$. In perturbative calculations our results lead naturally to an effective coupling for the three-gluon vertex which depends on three momenta and gives rise to an effective scale which governs the behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The results of this paper are an important part of a gauge-invariant dressed skeleton expansion and a related multi-scale analytic renormalization scheme. In this approach the scale ambiguity problem is resolved since physical kinematic invariants determine the arguments of the couplings.Comment: 53 pages, 10 figures. v2: added reference

The Inflationary Process in Israel: Shocks and Accommodation

The rate of inflation in Israel increased from 8 percent in 1965 to 300-400 percent in the first half of 1984. The inflationary process until 1977 was not qualitatively different from that in the OECD countries, but after the financial liberalization of 1977 the economy appeared to move into a new era in which the inflation rate seemed capable only of rising. Our explanation of the inflationary process is that because of institutional adaptations, and as a result of accommodating monetary and fiscal policies, the stabilizing forces in the economy are so weak that the inflation rate is in a meta-stable equilibrium. We ascribe the apparent asymmetry of the inflation to the expansionary underlying thrust of monetary and fiscal policy. We develop an analytical framework that assigns roles to indexation, to the financial structure, and to the exchange rate system in determining the dynamics of the economy. We place very little blame for the inflation on wage indexation, which has been incomplete, but we regard the extensive indexation of the returns on financial assets, and the steady shift out of nominal assets, as major contributing factors, for the economy is now left with virtually no nominal anchor. The paper concludes with a brief discussion of alternative stabilization plans, arguing that a successful stabilization program will have to be comprehensive and rapid.

Seigniorage, Operating Rules and the High Inflation Trap

A given amount of seigniorage revenue can be collected at either a high or a low rate of inflation. Thus there ray be two equilibria when a government finances its deficit by printing money--implying that an economy may be stuck in a high inflation equilibrium when, with the same fiscal policy, it could be at a lower inflation rate. We show that under rational expectations the high inflation equilibrium is stable and the low inflation equilibrium unstable; under adaptive expectations or lagged adjustment of money balances with rational expectations, it may be the low inflation equilibrium that is stable. Extending the model to allow for bond as well as money financing of deficits, we show that one of the equilibria disappears if the government sets a nominal anchor for the economy, for instance by fixing the growth rate of money. The dual equilibria and their stability.

Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series

We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension $rT$, where $T$ is the number of observations and $r$ is the number of series, and are difficult to estimate using previous methods. The vine pair-copulas are carefully selected to allow for heteroskedasticity, which is a feature of most ordinal time series data. When combined with flexible margins, the resulting time series models also allow for other common features of ordinal data, such as zero inflation, multiple modes and under- or over-dispersion. Using six example series, we illustrate both the flexibility of the time series copula models, and the efficacy of the variational Bayes estimator for copulas of up to 792 dimensions and 60 parameters. This far exceeds the size and complexity of copula models for discrete data that can be estimated using previous methods

Updown categories: Generating functions and universal covers

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for distinct objects c,c'. If we keep in place the latter axiom but allow for more than one morphism between objects, we have a sort of generalized poset in which there are multiplicities attached to covering relations, and possibly nontrivial automorphism groups. We call such a category an "updown category". In this paper we give a precise definition of such categories and develop a theory for them. We also give a detailed account of ten examples, including updown categories of integer partitions, integer compositions, planar rooted trees, and rooted trees.Comment: arXiv admin note: substantial text overlap with arXiv:math/040245

THE REAL RATE OF PROTECTION: THE STABILIZING EFFECT OF PRICE POLICIES AND DIRECT PAYMENTS

Traditional indicators of protection refer to the level effect of price policies on income and ignore the stabilizing effect. We derive a measure of the real rate of protection which incorporates these dual dimensions. The income stabilizing effects of price policy protection lead to a greater level of real protection than would be measured conventionally. Computed real protection rates for the European Union wheat market over the pre- and post-MacSharry reform periods were found to be some 3-5 percent greater than traditional indicators. Moreover, the compensatory payments to farmers following the 1992 reforms had a major risk reducing impact.International Relations/Trade,