Alternative Functional Forms Research Articles

Alternative functional forms for technology choice: Application to cocoa production technologies

The role of technology - its economics and factors that influence technological choice decisions have been a concern in development policy. Logit and probit functional forms have been largely used in modelling technology choice (adoption). We employed two other functional forms; loglog and cloglog, applied to adoption of Fairtrade and organic cocoa producers in the Eastern Region of Ghana. Using fractional regression modelling, we demonstrate the need to explore alternative functional forms other than logit and probit, in binary choice related problems. Interestingly, the battery of tests employed rejected the logit and probit functional forms. Alternative assessment criteria such as size, statistical significance of parameters and differences in parameter estimates produced more interesting results.

Does institutional quality resolve the Lucas Paradox?

ABSTRACTThe Lucas Paradox observes that capital flows predominantly to relatively rich countries, contradicting the neoclassical prediction that it should flow to poorer capital-scarce countries. In an influential study, Alfaro, Kalemli-Ozcan, and Volosovych (AKV) argue that cross-country variation in institutional quality can fully explain the Paradox, contending that if institutional quality is included in regression models explaining international capital inflows, a country’s level of economic development is no longer statistically significant. We replicate AKV’s results using their cross-sectional IFS capital flow data. Motivated by the importance of conducting inference in statistically adequate models, we focus on misspecification testing of alternative functional forms of their empirical model of capital flows. We show that their resolution of the Paradox relies on inference in a misspecified model. In models that do not fail basic misspecification tests, even though institutional quality is a significant determinant of capital inflows, a country’s level of economic development also remains a significant predictor. The same conclusions are reached using an extended dataset covering more recent IFS international capital flow data, first-differenced capital stock data and additional controls.

Alternative predictors in chaotic time series

In the scheme of reconstruction, non-polynomial predictors improve the forecast from chaotic time series. The algebraic manipulation in the Maple environment is the basis for obtaining of accurate predictors. Beyond the different times of prediction, the optional arguments of the computational routines optimize the running and the analysis of global mappings.

Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models

ABSTRACTHeteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.

Constitutive and numerical framework for modeling joints and faults in rock

SummaryA three‐dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre‐existing gaps or the formation of gaps. Representative stress–strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters. Copyright © 2015 John Wiley & Sons, Ltd.

CEO Pay Disparity: Efficient Contracting or CEO Entrenchment?

This paper investigates whether CEO pay disparity reflects efficient contracting or CEO entrenchment by exploiting an exogenous event which mandated option expensing, namely, the introduction of FAS 123R. Using a difference-in-difference approach, we find supportive evidence for the entrenchment hypothesis. Firms characterised by high pay disparity exhibit a significantly larger decline in options pre-versus post-FAS 123R than those characterised by low pay disparity. At the same time, firms with high pay disparity switch to salary more so than firms characterised by low pay disparity, consistent with entrenched CEOs preferring non-performance-based pay. Our findings suggest CEOs in high pay disparity firms exploited the free accounting cost advantage of options to inflate their pay rather than for their convexity property. These results are robust to alternative functional forms and measures of CEO pay disparity.

COSTS OF GREENHOUSE GAS EMISSIONS ABATEMENT UNDER THE CLEAN DEVELOPMENT MECHANISM

This paper examines the costs of emissions abatement through various types of projects financed under the Clean Development Mechanism (CDM) of the Kyoto Protocol. Using project data, cost functions are estimated applying alternative functional forms. Results show that the average cost of abatement decreases with the volume of abatement, showing economies of scale and suggesting that reducing emissions through small projects is relatively expensive. Results also show significant variation in the costs of abatement by project type and location. Nevertheless, the observed distribution of project investments does not closely match the relative cost structure, either by location or project type. Renewable energy projects accounted for 62% of the projects even though they had the second highest cost. Most of the CDM projects are located in emerging economies, principally China, India, and Brazil, even though the fixed costs of establishing CDM projects in these countries are higher than in many other developing countries. Significantly, while much of the conceptual and applied numerical literature concerning greenhouse gas abatement policies relies on presumptions about the structure of abatement cost curves, these findings suggest that comparative advantage is only one of several factors driving CDM investments and that investors hold additional preferences about project location and project type. Finally, results indicate a general, though noncontinuous, downward trend in the costs of abatement for new CDM projects.

Comparison of Crop Yield and Pollution Production Response to Nitrogen Fertilization Models, Accounting for Crop Rotation Effect

Alternative mathematical functional forms commonly applied in modelling crop and pollution production response to nitrogen (N) fertilizer use were investigated. Data were generated using soil and water assessment tool modeling, and explicitly accounted for rotation effects on regression parameters. The Mitscherlich–Baule model best represented potato, carrot, and alfalfa yield response, while the quadratic model best described corn, winter wheat, and barley yield response to N fertilization. The quadratic functional form also best represented nitrate-N leaching response to N fertilization for most crops. Maximum economic rates of N fertilization for crops were sensitive to residual N effects of previous crops.

Analytical steady‐state solutions for water‐limited cropping systems using saline irrigation water

AbstractDue to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady‐state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed‐form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop‐water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical‐mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient‐state numerical models.

Costs of certified emission reductions under the Clean Development Mechanism of the Kyoto Protocol

This paper examines the cost structure of certified emission reductions (CERs) through various types of projects under the Clean Development Mechanism (CDM) of the Kyoto Protocol. Using the CDM project data, the costs of CERs and their variation across technology and over time and space are estimated by applying alternative functional forms and specifications. Results show that the average cost of CERs decreases with the project scale and duration, scale and duration effects significantly vary across project types, and there is an upward trend in costs. The results also show that the distribution of the projects in the CDM portfolio or a given location does not strictly follow the relative cost structure, nor does the distribution of the CDM projects in different host countries follow the principle of comparative advantage. More than 84% of the CDM portfolio consists of various energy projects with substantially higher costs of CERs than afforestation and reforestation, industrial and landfill gas reduction, and methane avoidance projects, which are only 12% of all projects. While per unit cost of abatement plays an important role in the bottom-up and top-down models to evaluate emission reduction potential and analyze policy alternatives, the findings contradict the presumption of such models that project investors seek out low-cost opportunities. At the aggregate level, the cost of CER by the projects in Asia and Europe is similar but higher than those hosted in Africa, Americas, and Oceania. Yet more than 83% of the projects in the CDM portfolio are located in Asia; more than 69% of the projects are in China and India alone. China appears to have a comparative advantage (i.e., lowest opportunity cost) in energy efficiency projects, while India has a comparative advantage in hydro power projects and Brazil has a comparative advantage in wind power projects. In contrast, energy efficiency category accounts for only 8% of the CDM projects in China, hydro power accounts for 12% of the projects in India, and wind power accounts for 18% of the projects in Brazil. The results provide a basis for evaluating the incentives that the mechanism offers as a cost effective policy instrument that balances greenhouse gas mitigation across sectors and regions, while fulfilling the objective of the convention.

Sensitivity analysis of graphical functions

AbstractDespite high degrees of uncertainty associated with graphical functions, sensitivity analysis of these functions has received less attention than parametric sensitivity analysis. Recently, a promising method was proposed in the literature to generate alternative functional forms, reducing the problem to that of parametric sensitivity. Yet the usability of the method for graphical functions in system dynamics has not been investigated. We apply this function distortion method to a sample model and identify a number of shortcomings, such as a limited variety of alternative forms. We then propose extensions to the method to address the shortcomings, and subsequently test the extensions. We find the (extended) method of function distortion to be readily applicable and efficient in testing the sensitivity of model outputs to variations in the form of graphical functions. The proposed extensions increase the variety of possible distortions, but further research can be conducted on the control of the distortions. Copyright © 2014 System Dynamics Society

Bilateral congenital nasolacrimal duct cysts mimicking bilateral choanal atresia

The choice of how to model selectivity differs among approaches to fisheries stock assessment. VPA tends to make only weak assumptions regarding (age-specific) selectivity (asymptotic selectivity and temporal stability of selectivity for the most recent years). In contrast, selectivity is more parametric in “integrated” methods, and can be age-, length-, and age- and length-based. The use of parametric selectivity functions tends to reduce estimation variation because fewer parameters have to be estimated, but incorrect choices for the functional form for selectivity can lead to bias. This paper illustrates effects of poor choices for selectivity on the outcomes of stock assessments, outlines methods for evaluating whether a particular choice for selectivity is appropriate using residual diagnostics, and summarizes current ways to select among alternative functional forms for selectivity. This paper also provides a synthesis of the results of past simulation studies which have explored the ability to correctly parameterize selectivity.

Model selection for selectivity in fisheries stock assessments

The choice of how to model selectivity differs among approaches to fisheries stock assessment. VPA tends to make only weak assumptions regarding (age-specific) selectivity (asymptotic selectivity and temporal stability of selectivity for the most recent years). In contrast, selectivity is more parametric in “integrated” methods, and can be age-, length-, and age- and length-based. The use of parametric selectivity functions tends to reduce estimation variation because fewer parameters have to be estimated, but incorrect choices for the functional form for selectivity can lead to bias. This paper illustrates effects of poor choices for selectivity on the outcomes of stock assessments, outlines methods for evaluating whether a particular choice for selectivity is appropriate using residual diagnostics, and summarizes current ways to select among alternative functional forms for selectivity. This paper also provides a synthesis of the results of past simulation studies which have explored the ability to correctly parameterize selectivity.

The valuation of the EQ-5D in Portugal

The EQ-5D is a preference-based measure widely used in cost-utility analysis (CUA). Several countries have conducted surveys to derive value sets, but this was not the case for Portugal. The purpose of this study was to estimate a value set for the EQ-5D for Portugal using the time trade-off (TTO). A representative sample of the Portuguese general population (n = 450) stratified by age and gender valued 24 health states. Face-to-face interviews were conducted by trained interviewers. Each respondent ranked and valued seven health states using the TTO. Several models were estimated at both the individual and aggregated levels to predict health state valuations. Alternative functional forms were considered to account for the skewed distribution of these valuations. The models were analyzed in terms of their coefficients, overall fit and the ability for predicting the TTO values. Random effects models were estimated using generalized least squares and were robust across model specification. The results are generally consistent with other value sets. This research provides the Portuguese EQ-5D value set based on the preferences of the Portuguese general population as measured by the TTO. This value set is recommended for use in CUA conducted in Portugal.

A Cautionary Tale: Council Amalgamation in Tasmania and the Deloitte Access Economics Report

Contemporary Australian public policy has come to rely increasingly on technical reports produced by commercial consultants in contrast to the traditional approach, which employed disinterested public servants to generate the specialist information required to inform decision makers. This approach is fraught with problems, not least the fact that ‘hired guns’ have strong incentives to create the ‘answers’ sought by their employers. By way of a ‘cautionary tale’, this paper examines the empirical evidence adduced in favour of radical amalgamation of Tasmanian local authorities in Local Government Structural Reform in Tasmania, produced by Deloitte Access Economics (DAE) (2011), and commissioned by the Property Council of Tasmania. In particular, the paper provides a critical analysis of the econometric modelling undertaken in the DAE (2011) Report. We find that if the DAE model is re‐estimated – employing alternative functional forms – then the empirical evidence in support of Tasmania council merges evaporates.

Technical Progress as a Solution for Romania and Greece to Face the Global Crisis’ Problems and the Bad Forecasts

1. Introduction Greece and Romania have a common historic, cultural and economic destiny. This is why both countries have to face to a complicated challenge nowadays. The global crisis forced both countries to adopt severe austerity measures in order to obtain the economic survive. Greece and Romania asked for the international financial institutes' support and started to implement painful economic reforms which attract the hostility of the civil society. On short and medium term will be not much financial possibilities to support a big recovery of the jobs, industries and welfare. This is why an alternative possibility would be the efficient use of the technical progress. We talk about human capital and technical support of it, because both countries have enough average and high skill labour, which is able to support the economic recovery. The technical progress in economy represents a dynamic complex process which introduces the latest techniques and scientific research's results on capital and labour, in order to increase productivity, output and economic efficiency. An important element of the economic development is the optimal dimension and the efficient use of the demo-economic resources. As a result of the obsolete and relative labour decrease in economy related to the demographic trend, the training and the human capital become essential to a modern economy. In order to analyse the economic development in Romania and Greece under the technical progress impact, a production function will be used. This production function is based on two control parameters and one behaviour parameter. Cobb and Douglas used the production functions for the first time in 1928. During the 50s-70s, there were a lot of theoretical debates on this kind of function. The greatest problems were focused on aggregate production functions, even that the microeconomic production functions were put under scrutiny, as well. The debate in this field started criticizing the way the factor input, capital, was measured and how the notion of factor proportions had distracted economists. (2) Other specialists succeeded to make the production function more realistic by adding in natural resources. (3) Other specialist criticised Solow and Stieglitz's approach which was considered a trick against the laws of thermodynamics. (4) Neither Solow nor Stiglitz addressed his criticism, despite an invitation to do so in the September 1997 issue of the journal Ecological Economics? (5) An interesting retrospective of the production function approach evolution was made in 2003. (6) The same historical approach was made by in 2007, as well. (7) In the same period, the analysis concerned production functions and was robust with respect to increases in the number of independent variables and to alternative functional forms. (8) On the other hand, the meta-production function was presented as best-practice production function. (9) The paper takes a supplementary step under production function approach, in order to use this type of function to quantify the technical progress on economic development and to realise a pertinent comparative analysis between Greece and Romania. 2. Methods This proposal is a model based on a production function. In order to apply this theoretical approach to the macroeconomic evolution, a Cobb-Douglas function is used as follows: Y = A[L.sup.a][K.sup.b], in which: A: technical parameter, A L: labour; K: fixed capital; a: parameter proportional to relative labour productivity; b: parameter proportional to fixed capital efficiency. Both labour productivity and fixed capital efficiency are under the impact of the technical progress. This technical progress in the economy is quantified by the growth of the labour knowledge ([alpha]) and the growth of fixed capital use degree ([beta]). …

Demographics and demand: Evaluation of alternative functional forms

We evaluate the role of functional form of demographics in demand analysis by proposing the GQL ‘unstructured’ demographically transformed model which nests the Barten–Gorman demographically modified model and popular rank-3 and rank-2 demand systems. We use UK individual data and find that the equivalence of the ‘unstructured’ and Barten–Gorman forms and identification of meaningful equivalence scales depend on the degree of flexibility of the demand system in demographic, price and income effects.

Predicting invasions: alternative models of human‐mediated dispersal and interactions between dispersal network structure and Allee effects

Summary Human‐mediated dispersal has been shown to be the most important vector for the spread of invasive species, yet there has been little evaluation of alternative models of dispersal in terms of differences in their predictions of invasion patterns. Moreover, no analyses have been attempted to elucidate the potential interaction between alternative models of human‐mediated dispersal and population dynamical characteristics, such as Allee effects, which are central to the probability of an invasion. Two prominent models in the literature which have previously been employed to predict human movement patterns are explored: (i) gravity models, which use the attractiveness of and distance to a location to predict travel patterns, and (ii) random utility models, which assume that individuals decide where to travel by maximizing the benefits that they receive according to some partially observable function of individual and site characteristics. While distinction is often drawn between them in the literature, we demonstrate that these two approaches can be reduced to alternative functional forms describing the trip‐taking decisions of individuals. Each model was empirically parameterized using a survey of recreational boaters in Ontario, Canada. Within each model, both boater‐ and site‐specific characteristics were important and the functional form provided by the gravity model was significantly better at capturing the behaviour of recreational boaters Synthesis and applications. The dispersal and establishment of species into novel habitats are central components of the invasion process and of quantitative risk assessments. However, predictions are dependent on the estimated spatial structure of the dispersal network and its potential interactions with species characteristics. This study demonstrates that Allee effects can interact with dispersal network structure to significantly alter predicted spread rates and that the consequences of these interactions manifest differently at the system and site levels. This modelling framework can be used to inform management interventions aimed at modifying human‐mediated dispersal to reduce the spread of invasive species.

Embedding risk attitude and decision weights in non-linear logit to accommodate time variability in the value of expected travel time savings

In recent years we have seen important extensions of logit models in behavioural research such as incorporation of preference and scale heterogeneity, attribute processing heuristics, and estimation of willingness to pay (WTP) in WTP space. With rare exception, however, a non-linear treatment of the parameter set to allow for behavioural reality, such as embedded risk attitude and perceptual conditioning of occurrence probabilities attached to specific attributes, is absent. This is especially relevant to the recent focus in travel behaviour research on identifying the willingness to pay for reduced travel time variability, which is the source of estimates of the value of trip reliability that has been shown to take on an increasingly important role in project appraisal. This paper incorporates, in a generalised non-linear (in parameters) logit model, alternative functional forms for perceptual conditioning (known as probability weighting) and risk attitude in the utility function to account for travel time variability, and then derives an empirical estimate of the willingness to pay for trip time variability-embedded travel time savings as an alternative to separate estimates of time savings and trip time reliability. We illustrate the richness of the approach using a stated choice data set for commuter choice between unlabelled attribute packages. Statistically significant risk attitude parameters and parameters underlying decision weights are estimated for multinomial logit and mixed multinomial logit models, along with values of expected travel time savings.

Evidence For Non-Linear Causality Between Public Spending And Income In The European Union Countries

<p class="MsoSubtitle" style="text-align: justify; margin: 0in 0.5in 0pt;"><span style="font-family: Times New Roman;"><span style="color: black; font-size: 10pt; font-weight: normal; text-decoration: none; text-underline: none;">This paper deploys the non-linear Granger causality methods in order to determine the causal relationship between national income and government expenditure in the European Union countries over the post-war time period. For this purpose, six alternative functional forms of Wagner’s law have been adopted. The empirical results </span><span style="font-size: 10pt; font-weight: normal; text-decoration: none; text-underline: none;">indicate support for non-linear causality between income and government expenditure and they may prove useful theoretical and empirical research for the regulators and the policy makers. </span></span></p>