Anthropocentric Realism about Values

31 The choice of human goals cannot be completely subjective, because 32 there are some (even ones that motivate many humans) that are simply 33 unintelligible as ultimate goals. For example, wealth is rational as an 34 intermediate goal, a means to achieving some further end, but it is simply 35 unintelligible to suggest that wealth is an ultimate goal in itself. Second, 36 we have seen that some things are reasonable to pursue as aspects of 37 our ultimate goals (like prestige and pleasure), but they are conceptu- 38 ally dependent on some other goal to give them concrete form. In this 39 essay, I argue in favor of six candidates for ultimate goal

The dynamical U(n) quantum group

We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical R-matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these corepresentations. These elements are studied in more detail, especially the action of the comultiplication and Laplace expansions. Using the Laplace expansions we can prove that the dynamical quantum determinant is almost central, and adjoining an inverse the antipode can be defined. This results in the dynamical GL(n) quantum group associated to the dynamical R-matrix. We study a *-structure leading to the dynamical U(n) quantum group, and we obtain results for the canonical pairing arising from the R-matrix.Comment: 24 page

Calibration and Resolution Diagnostics for Bank of England Density Forecasts

This paper applies new diagnostics to the Bank of England’s pioneering density forecasts (fan charts). We compute their implicit probability forecast for annual rates of inflation and output growth that exceed a given threshold (in this case, the target inflation rate and 2.5% respectively.) Unlike earlier work on these forecasts, we measure both their calibration and their resolution, providing both formal tests and graphical interpretations of the results. These results both reinforce earlier evidence on some of the limitations of these forecasts and provide new evidence on their information content. Cet étude développe et applique des nouvelles techniques pour diagnostiquer les prévisions de densité de la Banque d’Angleterre (leur “fan charts”). Nous calculons leurs probabilités implicites pour des taux d’inflation et de croissance du PIB qui dépassent des seuils critiques (soit le taux d’inflation ciblé, soit 2.5%.) En contraste avec des travaux antérieurs sur ces prévisions, nous gaugeons leur calibration aussi bien que leur résolution, en donnant des tests formels et des interprétations graphiques. Les résultats renforcent des conclusions déjà existant sur les limites de ces prévisions et ils donnent de nouvelles évidences sur leurs valeurs ajoutées.calibration, density forecast, probability forecast, resolu, calibration, prévisions de densité, probabilités implicites, résolution.

THE CALIBRATION OF PROBABILISTIC ECONOMIC FORECASTS

A probabilistic forecast is the estimated probability with which a future event will satisfy a particular criterion. One interesting feature of such forecasts is their calibration, or the match between predicted probabilities and actual outcome probabilities. Calibration has been evaluated in the past by gropuing probability forecasts into discrete categories. Here we show that we can do so without discrete groupings; the kernel estimators that we use produce efficiency gains and smooth estimated curves relating predicted and actual probabilities. We use such estimates to evaluate the empirical evidence on calibration error in a number of economic applications including recession and inflation prediction, using both forecasts made and stored in real time and pseudo-forecasts made using the data vintage available at the forecast date. We evaluate outcomes using both first-release outcome measures as well as later, thoroughly revised data. We find strong evidence of incorrect calibration in professional forecasts of recessions and inflation. We also present evidence of asymmetries in the performace of inflation forecasts based on real-time output gaps.

The Calibration of Probabilistic Economic Forecasts

A probabilistic forecast is the estimated probability with which a future event will satisfy a specified criterion. One interesting feature of such forecasts is their calibration, or the match between predicted probabilities and actual outcome probabilities. Calibration has been evaluated in the past by grouping probability forecasts into discrete categories. Here we show that we can do so without discrete groupings; the kernel estimators that we use produce efficiency gains and smooth estimated curves relating predicted and actual probabilities. We use such estimates to evaluate the empirical evidence on calibration error in a number of economic applications including recession and inflation prediction, using both forecasts made and stored in real time and pseudoforecasts made using the data vintage available at the forecast date. We evaluate outcomes using both first-release outcome measures as well as later, thoroughly-revised data. We find strong evidence of incorrect calibration in professional forecasts of recessions and inflation. We also present evidence of asymmetries in the performance of inflation forecasts based on real-time output gaps. Une prévision probabiliste représente la probabilité qu’un événement futur satisfasse une condition donnée. Un des aspects intéressants de ces prévisions est leur calibration, c’est-à-dire l’appariement entre les probabilités prédites et les probabilités réalisées. Dans le passé, la calibration a été évaluée en regroupant des probabilités de prévisions en catégories distinctes. Nous proposons d’utiliser des estimateurs à noyaux, qui sont plus efficaces et qui estiment une relation lisse entre les probabilités prédites et réalisées. Nous nous servons de ces estimations pour évaluer l’importance empirique des erreurs de calibration dans plusieurs pratiques économiques, telles que la prévision de récessions et de l’inflation. Pour ce faire, nous utilisons des prévisions historiques, ainsi que des pseudoprévisions effectuées à l’aide de données telles qu’elles étaient au moment de la prévision. Nous analysons les résultats en utilisant autant des estimations préliminaires que des estimations tardives, ces dernières incorporant parfois des révisions importantes. Nous trouvons une forte évidence empirique d’une calibration erronée des prévisions professionnelles de récession et d’inflation. Nous présentons aussi une évidence d’asymétries dans la performance des prévisions d’inflation basées sur des estimations des écarts de la production en temps réel.calibration, probability forecast, real-time data, inflation, recession, calibration, probabilités de prévisions, données « en temps réel », inflation, récession

The Reliability of Inflation Forecasts Based on Output Gap Estimates in Real Time

A stable predictive relationship between inflation and the output gap, often referred to as a Phillips curve, provides the basis for empirical formulations of countercyclical monetary policy in many models. In this paper, we provide an empirical evaluation of the usefulness of alternative univariate and multivariate estimates of the output gap for predicting inflation. In-sample analysis based on ex post output gap measures suggests that many of the alternative estimates we examine appear to be quite useful for predicting inflation. However, examination of out-of-sample forecasts using real-time estimates of the same measures suggests that this predictive ability is mostly illusory. We find that the usefulness of output gaps as predictors of inflation has been severely overstated and that real-time forecasts using the output gap are often less accurate than forecasts that abstract from the output gap concept altogether. Dans ce papier, on jauge l'utilité de plusieurs estimations (univariées autant que multivariées) de l'écart de production pour prévoir le taux d'inflation. Une analyse ex post suggère que plusieurs de ces estimations aident à prédire l'inflation. Néanmoins, les erreurs de prédictions hors de l'enchantillon qui se sont construites avec les écarts de production estimés en temps réel indiquent que cette amélioration de prédiction est illusoire. On trouve que l'utilité des écarts de production pour prédire l'inflation a été exagérée et que les prédictions faites avec l'écart de production sont souvent moins précises que celles qui ignorent le concept d'un écart de production.Phillips curve, output gap, inflation forecasts, real-time data, La courbe de Phillips, l'écart de production, des prévisions d'inflation, des données en temps réel

The Unreliability of Output Gap Estimates in Real Time

We examine the reliability of alternative output detrending methods, with special attention to the accuracy of real-time estimates of the output gap. We show that ex post revisions of the estimated gap are of the same order of magnitude as the estimated gap itself and that these revisions are highly persistent. Although important, the revision of published data is not the primary source of revisions in measured output gaps; the bulk of the problem is due to the pervasive unreliability of end-of-sample estimates of the trend in output. Multivariate methods that incorporate information from inflation to estimate the output gap are not more reliable than their univariate counterparts. Nous examinons la fiabilité de plusieurs méthodes qui sont utilisés pour rendre des séries chronologiques stationnaires, en portant une attention particulière à la précision des estimations en temps réel de l'écart de la production. Nous montrons que de la taille des révisions ex post de nos estimations de l'écart et celle des estimations faites en temps réels sont du même ordre de grandeur et que ces révisions sont fortement persistantes. Même si elle est importante, la révision des données n'est pas la source principale des révisions des estimations. La majorité de ce problème est due à la forte imprécision des estimations des tendances actuelles de la production. Des techniques multivariés, qui exploitent aussi le taux d'inflation pour estimer l'écart de la production, ne sont pas plus précises que leurs équivalents univariés.Real-time data, output gap, business cycle measurement, données en temps réels, l'écart de la production, l'estimation du cycle d'affaire

Elliptic U(2) quantum group and elliptic hypergeometric series

We investigate an elliptic quantum group introduced by Felder and Varchenko, which is constructed from the $R$-matrix of the Andrews-Baxter-Forrester model, containing both spectral and dynamical parameter. We explicitly compute the matrix elements of certain corepresentations and obtain orthogonality relations for these elements. Using dynamical representations these orthogonality relations give discrete bi-orthogonality relations for terminating very-well-poised balanced elliptic hypergeometric series, previously obtained by Frenkel and Turaev and by Spiridonov and Zhedanov in different contexts.Comment: 20 page