Continuous-time modelling in econometrics and engineering - juli 2002

This paper discusses a widely used discrete-time analog of dynamic continuous-time models. This analog can not be used for the estimation of models with fast adaption to shocks. This has been overlooked in the econometric literature. In the engineering literature this same analogon is defined, using other names and other notation. Here warnings can be found against the estimation of fast models. The engineering literature is ignored in the econometric literature.

The derivatives of complex characteristic roots in the econometric modelling textbook of Kuh et al.

Characteristic roots, or eigenvalues, are a useful tool in the study of linear dynamic economic models. The relation between the roots and the model coefficients are expressed in the derivatives of the former with respect to the latter. In general, the roots are complex numbers. This note discusses the derivatives of both the modulus and the cycle time of the complex roots. An important reference on this subject is Kuh et al. (1985) [hereafter: KNH]. Below it is shown that KNH discusses these derivatives unsatisfactory. In the next two sections the model and the derivatives of the roots are given. Section 4 presents the formulas for the derivatives of the modulus and the cycle time of complex roots. The substance of the paper is section 5, with a critical comment on the discussion of these derivatives in KNH. The last section gives a short conclusion. �

The Impact of Provincial Maternity and Parental Leave Policies on Employment Rates of Women with Young Children in Canada

Maternity and parental leave policies are on the forefront of the current political agenda in Canada. This paper answers the question: does maternity and parental leave (M/PL) policy raise or lower the probability of employment for a woman? One unique feature of M/PL policy in Canada is the variation in mandated unpaid job-protected leave allowances across provinces. This variation is used in this study to identify the effect of provincial M/PL policies on employment rates of women with young children. Using the Canadian Labour Force Survey (LFS) data from 1976 to 2000, I find evidence that M/PL policy reduces the gap between the employment probabilities of women with young children versus women with older children. Moreover, a difference-in-differences model predicts a 3 to 4 percent increase in the probability of employment for women with young children (aged 0 to 2) relative to women with older children as a result of M/PL policy.

Modelling the reporting discrepancies in bilateral data

This paper is about the discrepancies in reported bilateral statistical data ("mirror data"). For example the trade from country A to country B is not reported the same in the two countries. The discrepancies are used to estimate the accuracy of the reporters. The estimated accuracies are to be used to compute optimal combinations of mirror data. Two models of the discrepancies are presented: (a) unbiased reporting with inaccurate reporters having a large variance, and (b) biased reporting with inaccurate reporters having a large bias (either positive or negative). Estimation methods are least squares regression and maximum likelihood. A numerical illustration is given, using data of the international trade in services. It is shown how to judge the two models empirically. For an updated�version, see CPB Discussion Paper 216 .�

Arithmetic and geometric mean rates of return in discrete time

This memorandum presents some basic equalities and inequalities about rates of return in discrete time, without auto-correlation. The arithmetic and geometric means are discussed. Estimation of the expected payout and the median payout is discussed, including maximum likelihood estimation.

Hourglass models of world-wide problems such as climate change

A simple model of “hourglass†problems is presented. For such problems, the benefit of a national policy measure is propagated to all countries through one single world-wide variable. The prime example is the effect of the reduction of CO 2 emission on the world climate. Five optimal solutions are given, for various situations and points of view, followed by a comparison with the outcome of permit trading.

Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees

We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations of the monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixed-point logic (FO(LFP1)) theories of this class of structures. These logics can express important properties such as reachability. Using model-theoretic techniques, we show by a uniform argument that these axiomatizations are complete, i.e., each formula that is valid on all finite trees is provable using our axioms. As a backdrop to our positive results, on arbitrary structures, the logics that we study are known to be non-recursively axiomatizable

The Elmar model: output and capacity in imperfectly competitive electricity markets

With the ongoing liberalization and integration of European energy markets and the increasing worries about security of supply, the need for thorough economic analysis of electricity markets is growing. Elmar is a model for the European electricity market, taking into account imperfect competition through conjectural variations, as well as imperfect international competition due to import capacity restrictions. The model distinguishes between competition on the output market and competition in capacity investments. We find that the least competitive of these determines wholesale prices.