Two essays in microeconomic theory and econometrics

The thesis contains two chapters which address questions important both for the economic theory and applications. In Chapter I we show that inequalities are an important tool in the theory of production functions. Various notions of internal economies of scale can be equivalently expressed in terms of upper or lower bounds on production functions. In the problem of aggregation of efficiently allocated goods, if one is concerned with two-sided bounds as opposed to exact expressions, the aggregate production function can be derived from some general assumptions about production units subject to aggregation. The approach used does not require smoothness or convexity properties. In Chapter II we introduce a new forecasting techniques essential parts of which include using average high-order polynomial estimators for in-sample fit and low-order polynomial extension for out-of-sample fit. We provide some statements following the Gauss-Markov theorem format. The empirical part shows that algebraic polynomials treated in a proper way can perform very well in one-step-ahead prediction, especially in prediction of the direction of exchange rate movements

Short-memory linear processes and econometric applications

This book serves as a comprehensive source of asymptotic results for econometric models with deterministic exogenous regressors. Such regressors include linear (more generally, piece-wise polynomial) trends, seasonally oscillating functions, and slowly varying functions including logarithmic trends, as well as some specifications of spatial matrices in the theory of spatial models. The book begins with central limit theorems (CLTs) for weighted sums of short memory linear processes. This part contains the analysis of certain operators in Lp spaces and their employment in the derivation of CLT

Asymptotic distribution of the OLS estimator for a mixed spatial model

We find the asymptotic distribution of the OLS estimator of the parameters [beta] and [rho] in the mixed spatial model with exogenous regressors Yn=Xn[beta]+[rho]WnYn+Vn. The exogenous regressors may be bounded or growing, like polynomial trends. The assumption about the spatial matrix Wn is appropriate for the situation when each economic agent is influenced by many others. The error term is a short-memory linear process. The key finding is that in general the asymptotic distribution contains both linear and quadratic forms in standard normal variables and is not normal.Lp-approximability Mixed spatial model OLS asymptotics

CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF LINEAR PROCESSES: LP -APPROXIMABILITY VERSUS BROWNIAN MOTION

Standardized slowly varying regressors are shown to be L -approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.

Asymptotic distribution of the OLS estimator for a purely autoregressive spatial model

We derive the asymptotics of the OLS estimator for a purely autoregressive spatial model. Only low-level conditions are used. As the sample size increases, the spatial matrix is assumed to approach a square-integrable function on the square (0,1)2. The asymptotic distribution is a ratio of two infinite linear combinations of [chi]2 variables. The formula involves eigenvalues of an integral operator associated with the function approached by the spatial matrices. Under the conditions imposed identification conditions for the maximum likelihood method and method of moments fail. A corrective two-step procedure using the OLS estimator is proposed.Spatial model OLS estimator Asymptotic distribution Maximum likelihood Method of moments