Recursive Rules with Aggregation: A Simple Unified Semantics

Complex reasoning problems are most clearly and easily specified using logical rules, especially recursive rules with aggregation such as counts and sums for practical applications. Unfortunately, the meaning of such rules has been a significant challenge, leading to many different conflicting semantics. This paper describes a unified semantics for recursive rules with aggregation, extending the unified founded semantics and constraint semantics for recursive rules with negation. The key idea is to support simple expression of the different assumptions underlying different semantics, and orthogonally interpret aggregation operations straightforwardly using their simple usual meaning

Real estate investment dynamics

This thesis is motivated by the steadily increasing interest in the dynamic relationship between the macro-economy and the real estate sector. One of the main issues in this respect is to study the investment dynamics. Since the bursting of the U.S. housing bubble in 2006 is identified as the point of origin of the so called subprime crises, which led to the collapse of the U.S. financial system, the dynamics of real estate investments is of particular interest. In the first part of my thesis I investigate the dynamics of residential investment and its relationship to the overall economy by the means of a dynamic stochastic general equilibrium (DSGE) model in which a consumption good sector and a housing sector are incorporated. Residential investment is characterized in this model by a time-to-build restriction. The model is brought to U.S. quarterly data - in the period 1970 - 2007 - in order to evaluate whether it can account for stylized facts of the U.S. housing economy as well as the U.S. Macro - economy. Another much talked real estate topic with respect to the subprime crisis is the relationship between bank lending, property prices and economic activity. To that end, the second part of my thesis examines the potential effects of macro-policy and bank lending shocks on the German real estate sector. In particular, the importance of macroeconomic factors like credit to real estate construction, residential investment, and gross domestic product for the dynamics of German commercial real estate prices are analyzed by the means of a structural Vector-Autoregression (SVAR). The SVAR estimation is conduct for both, aggregate Germany and the largest regional states of Bavaria and Nordrhein-Westfalen for the period 1975 to 2004

The new keynesian approach to dynamic general equilibrium modeling: models, methods, and macroeconomic policy evaluation

This chapter aims to provide a hands-on approach to New Keynesian models and their uses for macroeconomic policy analysis. It starts by reviewing the origins of the New Keynesian approach, the key model ingredients and representative models. Building blocks of current-generation dynamic stochastic general equilibrium (DSGE) models are discussed in detail. These models address the famous Lucas critique by deriving behavioral equations systematically from the optimizing and forward-looking decision-making of households and firms subject to well-defined constraints. State-of-the-art methods for solving and estimating such models are reviewed and presented in examples. The chapter goes beyond the mere presentation of the most popular benchmark model by providing a framework for model comparison along with a database that includes a wide variety of macroeconomic models. Thus, it offers a convenient approach for comparing new models to available benchmarks and for investigating whether particular policy recommendations are robust to model uncertainty. Such robustness analysis is illustrated by evaluating the performance of simple monetary policy rules across a range of recently-estimated models including some with financial market imperfections and by reviewing recent comparative findings regarding the magnitude of government spending multipliers. The chapter concludes with a discussion of important objectives for on-going and future research using the New Keynesian framework

Optimal growth for linear processes with affine control

We analyse an optimal control with the following features: the dynamical system is linear, and the dependence upon the control parameter is affine. More precisely we consider $\dot x_\alpha(t) = (G + \alpha(t) F)x_\alpha(t)$, where $G$ and $F$ are $3\times 3$ matrices with some prescribed structure. In the case of constant control $\alpha(t)\equiv \alpha$, we show the existence of an optimal Perron eigenvalue with respect to varying $\alpha$ under some assumptions. Next we investigate the Floquet eigenvalue problem associated to time-periodic controls $\alpha(t)$. Finally we prove the existence of an eigenvalue (in the generalized sense) for the optimal control problem. The proof is based on the results by [Arisawa 1998, Ann. Institut Henri Poincar\'e] concerning the ergodic problem for Hamilton-Jacobi equations. We discuss the relations between the three eigenvalues. Surprisingly enough, the three eigenvalues appear to be numerically the same

Incremental Query Evaluation in a Ring of Databases

This article approaches the incremental view maintenance problem from an algebraic perspective. The algebraic structure of a ring of databases is constructed and extended to form a powerful aggregate query calculus. The query calculus inherits the key properties of rings, such as distributivity and the existence of an additive inverse. As a consequence, the calculus has a normal form of polynomials and is closed under a universal difference operator. This difference operator allows to express the so-called delta queries of the incremental view maintenance literature, but also deltas to the deltas (second deltas), deltas to second deltas (third deltas), and so on. The k-th delta of a query of polynomial degree k is purely a function of the update, not of the database. This gives rise to a multi-layered incremental view maintenance scheme in which a view is maintained using a hierarchy of auxiliary materialized views of k-th deltas. What is gained by this hierarchy is that the work required to keep all views fresh given an update is extremely simple. The method allows to eliminate expensive query operators such as joins and aggregate sums entirely from programs that perform incremental view maintenance. The main result is that, for non-nested queries, each individual aggregate value can be incrementally maintained using a constant amount of work. This is not possible for nonincremental evaluation and provides a complexity separation between the incremental and nonincremental query evaluation problems. As a byproduct, we obtain a query language that is significant in its own right. It is an algebraic language in which queries, like in relational calculus, are built up from base objects (generalized relations) using an extremely small set of connectives -- addition, multiplication, and aggregation. It is based on a family of algebraic structures developed in this article -- called avalanche (semi)rings -- which algebraizes range-restriction. Thus these structures guarantee finite query results in the presence of inequalities, without making use of an explicit selection operation. The entire language behaves like a polynomial ring of relations and thus makes algebraic manipulation very easy. As a simple algebraic language of interesting expressive power -- relational algebra with SQL-style aggregation and unlimited nesting -- it is a natural internal representation language for query processors and compilers