Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography

We rigorously define the Liouville action functional for finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that the classical action - the critical point of the Liouville action functional, considered as a function on the quasi-Fuchsian deformation space, is an antiderivative of a 1-form given by the difference of Fuchsian and quasi-Fuchsian projective connections. This result can be considered as global quasi-Fuchsian reciprocity which implies McMullen's quasi-Fuchsian reciprocity. We prove that the classical action is a Kahler potential of the Weil-Petersson metric. We also prove that Liouville action functional satisfies holography principle, i.e., it is a regularized limit of the hyperbolic volume of a 3-manifold associated with a quasi-Fuchsian group. We generalize these results to a large class of Kleinian groups including finitely generated, purely loxodromic Schottky and quasi-Fuchsian groups and their free combinations.Comment: 60 pages, proof of the Lemma 5.1 corrected, references and section 5.3 adde

Equity Style Returns and Institutional Investor Flows

This paper explores institutional investor trades in stocks grouped by style and the relationship of these trades with equity market returns. It aggregates transactions drawn from a large universe of approximately $6 trillion of institutional funds. To analyze style behavior, we assign equities to deciles in each of five style dimensions: size, value/growth, cyclical/defensive, sector, and country. We find, first, strong evidence that investors organize and trade stocks across style-driven lines. This appears true for groupings both strongly and weakly related to fundamentals (e.g., industry or country groupings versus size or value/growth deciles). Second, the positive linkage between flows and returns emerges at daily frequencies, yet becomes even more important at lower frequencies. We show that quarterly decile flows and returns are even more strongly positively correlated than are daily flows and returns. However, as the horizon increases beyond a year, we find that the flow/return correlation declines. Third, style flows and returns are important components of individual stock expected returns. We find that nearby style inflows and returns positively forecast future returns while distant style inflows and returns forecast negatively. Fourth, we find strong correlations between style flows and temporary components of return. This suggests that behavioral theories may play a role in explaining the popularity and price impact of flow-related trading.

Inventories and Optimal Monetary Policy

We introduce inventories into a standard New Keynesian Dynamic Stochastic General Equilibrium (DSGE) model to study the effect on the design of optimal monetary policy. The possibility of inventory investment changes the transmission mechanism in the model by decoupling production from final consumption. This allows for a higher degree of consumption smoothing since firms can add excess production to their inventory holdings. We consider both Ramsey optimal monetary policy and a monetary policy that maximizes consumer welfare over a set of simple interest rate feedback rules. We find that in contrast to a model without inventories, Ramsey-optimal monetary policy in a model with inventories deviates from complete inflation stabilization. In the standard model, nominal price rigidity is a deadweight loss on the economy, which an optimizing policymaker attempts to remove. With inventories, a planner can reduce consumption volatility and raise welfare by accumulating inventories and letting prices change as an equilibrating mechanism. We find also find that the application of simple rules comes very close to replicating Ramsey optimal outcomes.Ramsey policy, New Keynesian model

Deep Habits in the New Keynesian Phillips Curve

We derive and estimate a New Keynesian Phillips curve (NKPC) in a model where consumers are assumed to have deep habits. Habits are deep in the sense that they apply to individual consumption goods instead of aggregate consumption. This alters the NKPC in a fundamental manner as it introduces expected and contemporaneous consumption growth as well as the expected marginal value of future demand as additional driving forces for inflation dynamics. We construct the driving process in the deep habits NKPC by using the model’s optimality conditions to impute time series for unobservable variables. The resulting series is considerably more volatile than unit labor cost. General Methods of Moments (GMM) estimation of the NKPC shows an improved fit and a much lower degree of indexation than in the standard NKPC. Our analysis also reveals that the crucial parameters for the performance of the deep habit NKPC are the habit parameter and the substitution elasticity between differentiated products. The results are broadly robust to alternative specifications.

Inventories, Inflation Dynamics and the New Keynesian Phillips Curve

We introduce inventories into an otherwise standard New Keynesian model and study the implications for in.ation dynamics. Inventory holdings are motivated as a means to generate sales for demand-constrained .rms. We derive various representa- tions of the New Keynesian Phillips curve with inventories and show that one of these speci.cations is observationally equivalent to the standard model with respect to the behavior of in.ation when the model.s cross-equation restrictions are imposed. How- ever, the driving variable in the New Keynesian Phillips curve - real marginal cost - is unobservable and has to be proxied by, for instance, unit labor costs. An alternative approach is to impute marginal cost by using the model.s optimality conditions. We show that the stock-sales ratio is linked to marginal cost. We also estimate these various speci.cations of the New Keynesian Phillips curve using GMM. We .nd that predictive power of the inventory-speci.cation at best approaches that of the standard model, but does not improve upon it. We conclude that inventories do not play a role in explaining in.ation dynamics within our New Keynesian Phillips curve framework.

Deep Habits in the New Keynesian Phillips Curve

We derive and estimate a New Keynesian Phillips curve (NKPC) in a model where consumers are assumed to have deep habits. Habits are deep in the sense that they apply to individual consumption goods instead of aggregate consumption. This alters the NKPC in a fundamental manner as it introduces expected and contemporaneous consumption growth as well as the expected marginal value of future demand as additional driving forces for inflation dynamics. We construct the driving process in the deep habits NKPC by using the model's optimality conditions to impute time series for unobservable variables. The resulting series is considerably more volatile than unit labor cost. GMM estimation of the NKPC shows an improved fit and a much lower degree of indexation than in the standard NKPC. Our analysis also reveals that the crucial parameters for the performance of the deep habit NKPC are the habit parameter and the substitution elasticity between differentiated products. The results are broadly robust to alternative specfications.Phillips curve; GMM; marginal costs; deep habits.

Casimir effect of electromagnetic field in Randall-Sundrum spacetime

We study the finite temperature Casimir effect on a pair of parallel perfectly conducting plates in Randall-Sundrum model without using scalar field analogy. Two different ways of interpreting perfectly conducting conditions are discussed. The conventional way that uses perfectly conducting condition induced from 5D leads to three discrete mode corrections. This is very different from the result obtained from imposing 4D perfectly conducting conditions on the 4D massless and massive vector fields obtained by decomposing the 5D electromagnetic field. The latter only contains two discrete mode corrections, but it has a continuum mode correction that depends on the thicknesses of the plates. It is shown that under both boundary conditions, the corrections to the Casimir force make the Casimir force more attractive. The correction under 4D perfectly conducting condition is always smaller than the correction under the 5D induced perfectly conducting condition. These statements are true at any temperature.Comment: 20 pages, 4 figure