Carbon Lorenz curves

The purpose of this paper is twofold. First, it exhibits that standard tools in the measurement of income inequality, such as the Lorenz curve and the Gini-index, can successfully be applied to the issues of inequality measurement of carbon emissions and the equity of abatement policies across countries. These tools allow policy-makers and the general public to grasp at a single glance the impact of conventional distribution rules such as equal caps or grandfathering, or more sophisticated ones, on the distribution of greenhouse gas emissions. Second, using the Samuelson rule for the optimal provision of a public good, the Pareto-optimal distribution of carbon emissions is compared with the distribution that follows if countries follow Nash–Cournot abatement strategies. It is shown that the Pareto-optimal distribution under the Samuelson rule can be approximated by the equal cap division, represented by the diagonal in the Lorenz curve diagram.     

Technological change in energy systems: Learning curves, logistic curves and input-output coefficients

Learning curves have recently been widely adopted in climate-economy models to incorporate endogenous change of energy technologies, replacing the conventional assumption of an autonomous energy efficiency improvement. However, there has been little consideration of the credibility of the learning curve. The current trend that many important energy and climate change policy analyses rely on the learning curve means that it is of great importance to critically examine the basis for learning curves. Here, we analyse the use of learning curves in energy technology, usually implemented as a simple power function. We find that the learning curve cannot separate the effects of price and technological change, cannot reflect continuous and qualitative change of both conventional and emerging energy technologies, cannot help to determine the time paths of technological investment, and misses the central role of R&D activity in driving technological change. We argue that a logistic curve of improving performance modified to include R&D activity as a driving variable can better describe the cost reductions in energy technologies. Furthermore, we demonstrate that the top-down Leontief technology can incorporate the bottom-up technologies that improve along either the learning curve or the logistic curve, through changing input-output coefficients. An application to UK wind power illustrates that the logistic curve fits the observed data better and implies greater potential for cost reduction than the learning curve does.     

Recent approaches to estimating Engel curves

Classical approaches of estimating cross-section Engel curves are based on parametric models. However, misspecification of a parametric model implies that information of structural nature might be masked. An alternative avoiding problems related to predetermined functional relations is the nonparametric approach. This paper surveys recent advances of nonparametric statistics in their relevance to estimating cross-section Engel curves.     

Decomposition of s‐concentration curves

Abstract. For any given order of inverse stochastic dominance, standard concentration curves are decomposed into three components, called contribution curves. Those components correspond to within‐group inequalities, between‐group inequalities, and transvariational inequalities. We prove, for all orders, that contribution curve dominance implies systematically welfare‐improving tax reforms and conversely. Accordingly, as welfare expansions may be costly in terms of particular inequalities, we propose targeted fiscal reforms.     

A new approach to modelling sigmoidal curves

Growth and diffusion phenomena have become of great interest to investigators in many disciplines, such as Biology, Demography, Economy, Agriculture, etc. These processes are generally analyzed by means of growth curves. As, in nature, it is not possible for any variable to continue growing indefinitely, we can consider any growth process to have an upper limit or saturation level. Thus, should a model represent a growth phenomenon, it will be described by a sigmoidal or S-shaped curve. There are a wide variety of growth models in general and specific literature. Of these, the logistic model is without doubt one of the most studied in practice, as well as some modifications of it, including recent investigations directed to the decomposition of a growth curve into various logistic components [Technol. Forecast. Soc. Change 47 (1994) 89; Technol. Forecast. Soc. Change 61 (1999) 247.]. In all the cases above, the adopted approach includes fitting the trend curve to the data by means of a well-known estimation procedure, such as least squares. We suggest a somewhat different approach, which consists of expressing the model through its differential equation and searching for a functional specification for the variable representing growth rate. Two series have been chosen from the recent literature in order to illustrate the methodology presented.     

Functional form of engel curves for foodstuffs

Employing individual household expenditure data for six foodstuffs we test five three-parameter and four two-parameter Engel curves against a more general form. All two-parameter functions must be rejected, including Working's function; it appears that a transformation of the budget share is in order to capture the observed curvature.     

Demographic versus expenditure flexibility in Engel curves

We consider the effects of demographic and expenditure variables on consumer demand in a system of Engel curves using a smooth coefficient semiparametric model where the expenditure effects on the budget shares vary nonparametrically with demographic variables such as the age of head and number of children in the household. Our findings, based on UK micro data, suggest that with a smooth coefficient semiparametric model there is no need for nonlinear logarithmic expenditure effects in the budget shares. Furthermore, we find evidence of a trade-off between demographic and expenditure effects in Engel curves and that a rank-2 system of Engel curves where the logarithmic expenditure effects are allowed to vary with demographic characteristics either nonparametrically or as a third degree polynomial function cannot be rejected against a rank-3 (quadratic logarithmic) model. The implications on household behavior and welfare are also examined. We would like to thank an anonymous referee and Baldev Raj, the editor, for useful comments and suggestions. We would also like to thank the University of Cyprus for financial support, Theofanis Mamuneas for stimulating discussions and the Office of National Statistics for making available the UK Family Expenditure Survey data through the ESRC Data Archive. The last author would also like to acknowledge the financial support from SSHRC of Canada.     

Rational expectations and the short-run Phillips curves

The purpose of the present paper is to study certain derivable implications of the rational expectations hypothesis (REH) in the context of a simultaneous wage-price model of the U.S. economy and to subject the REH to statistical tests. The empirical evidence indicates that implementation of the REH in the context of these models does wipe out the conventional short-run Phillips curves, and the assumption that public expectations of future rates of inflation are true conditional mathematical expectations based on all available information is indeed borne out quite well against its alternatives.     

Constrained nonparametric regression analysis of load curves

In this paper, we analyze household load curves through the use of Constrained Smoothing Splines. These estimators are natural smoothing splines that allow to incorporate periodic shape constraints. Since the time pattern of electricity demand combines strong periodical regularities with abrupt changes along time, a nonparametric regression estimator that is able to incorporate regularity constrains appears to be very well suited to approach load curves. In the paper we also propose a method to compute the penalty parameters that appear in the constrained smoothing spline estimator, we show some statistical properties and finally we construct confidence intervals. First version received: February 1998/final version accepted: July 1999     

Engel curves and systems of demand functions

The functional forms of the Engel curves implied by several popular complete systems of demand functions are discussed. Among the systems are those generated by generalized quadratic indirect utility (the translog system, the generalized Leontief system, etc.), the linear and quadratic expenditure systems, and Deaton and Muellbauer's PIGL and AIDS. A new system, which can produce the Engel curves of all these systems as special cases, is suggested. The different Engel curves are tested against data from a Norwegian survey of consumer expenditure. This is done both in a complete system of Engel curves for eight commodities and commodity by commodity.     

Robust estimation of models of Engel curves

Both standard and robust methods are used here to estimate models of Engel curves for three household commodities, namely, food, transport, and tobacco and alcohol in Canada. The income elasticities of demand computed from the various methods differ significantly for the transport and tobacco-alcohol consumption where there are obvious outliers and zero expenditures problem. Robust estimators point to lower income elasticities and have better performance than the standard LS and Tobit estimator. These results are analyzed in the light of the information on finite-sample performance obtained in a previous Monte Carlo study. First version received: July 2000/Final version received: July 2001 RID="*" ID="*"  I wish to thank Victoria Zinde-Walsh, John Galbraith, Clint Coakley, two anonymous referees and an associate editor for helpful comments. I would also like to thank Anastassia Khouri for kindly providing the 1992 Family Expenditure Survey of Canada data.     

Shapes of Engel curves and demand curves: Implications of the expenditure allocation model,applied to Dutch data

Section 1 reviews properties of the expenditure allocation model, particularly concerning income and price elasticities.     

Statistical considerations in the fitting of growth curves

In long range trend projection, one of the most frequently used models is the “S”-shaped growth curve originally suggested by Pearl and Reed. Because of the nonlinear form of this model, problems exist in the statistical evaluation of model fit and in estimating the precision of forecasts developed from the model. Based on an approach first suggested by Yule, a procedure for fitting and evaluating the Pearl–Reed curve is developed. Confidence intervals for parameters and forecast prediction intervals are presented.     

The secular inflation term in open-economy Phillips curves

Robert Flood has compared three alternative specifications for the secular inflation term in an open-economy Phillips curve, attributed, respectively, to Buiter-Miller, and Frankel and Mussa. We point out (1) an arithmetic error, (2) the equivalence of the Frankel and Mussa versions, and (3) some arguments against the Buiter-Miller version.     

Estimating inflation compensation for Turkey using yield curves

Inflation compensation derived from nominal and real bond yields contains market based, real time information regarding the inflation expectations and the pricing of inflation risks. In this study, we calculate inflation compensation for Turkey by using nominal and real yield curves. The findings of event study analysis on inflation compensation indicate that changes in the term structure of inflation compensation contain information regarding the credibility of monetary authority. Moreover, we find that, at daily frequency, liquidity conditions have no significant effect on inflation compensation and hence the effects of events such as monetary policy decisions and inflation surprises on inflation compensation can be attributed mainly to changes in inflation expectations and pricing of inflation uncertainty.     

Technological growth curves : A competition of forecasting models

In order to determine procedures for appropriate model selection of technological growth curves, numerous time series that were representative of growth behavior were collected and categorized according to data characteristics. Nine different growth curve models were each fitted onto the various data sets in an attempt to determine which growth curve models achieved the best forecasts for differing types of growth data. The analysis of the results gives rise to a new approach for selecting appropriate growth curve models for a given set of data, prior to fitting the models, based on the characteristics of the data sets.     

Introducing errors in progress ratios determined from experience curves

Progress ratios (PRs) derived from historical data in experience curves are used for forecasting development of many technologies as a means to model endogenous technical change in for instance climate–economy models. These forecasts are highly sensitive to uncertainties in the progress ratio. As a progress ratio is determined from fitting data, a coefficient of determination R² is frequently used to show the quality of the fit and accuracy of PR. Although this is instructive, we recommend using the error σ_PR in PR, which can be directly determined from fitting the data. In this paper we illustrate this approach for three renewable energy technologies, i.e., wind energy, bio-ethanol, and photovoltaics.