Bernoulli Regression Models: Re-examining Statistical Models with Binary Dependent Variables

The classical approach for specifying statistical models with binary dependent variables in econometrics using latent variables or threshold models can leave the model misspecified, resulting in biased and inconsistent estimates as well as erroneous inferences. Furthermore, methods for trying to alleviate such problems, such as univariate generalized linear models, have not provided an adequate alternative for ensuring the statistical adequacy of such models. The purpose of this paper is to re-examine the underlying probabilistic foundations of statistical models with binary dependent variables using the probabilistic reduction approach to provide an alternative approach for model specification. This re-examination leads to the development of the Bernoulli Regression Model. Simulated and empirical examples provide evidence that the Bernoulli Regression Model can provide a superior approach for specifying statistically adequate models for dichotomous choice processes.Bernoulli Regression Model, logistic regression, generalized linear models, discrete choice, probabilistic reduction approach, model specification, Research Methods/ Statistical Methods,

Introducing Asymmetric Separability in the FAST Multistage Demand System

This paper determines the set of parametric restrictions required to maintain flexibility under asymmetric weak separability for the flexible and separable translog (FAST) multistage demand system. Because there is not a unique set of parametric restrictions that ensures separability and the values of the unconditional price and expenditure elasticities depend on the parametric restrictions imposed, the appropriateness of a chosen set of parametric restrictions should be tested empirically. An empirical example that illustrates how the choice of parametric restrictions affects the estimation results and the functional form of the price and expenditure elasticities is provided.Research Methods/ Statistical Methods,

Farmers’ Willingness to Grow Switchgrass as a Cellulosic Bioenergy Crop: A Stated Choice Approach

Farmers’ Willingness to Grow Switchgrass as a Cellulosic Bioenergy Crop: A Stated Choice Approach Agriculture’s role as a source of feedstocks in a potential lignocellulosic-based biofuel industry is a critical economic issue. Several studies have assessed the technical feasibility of producing bioenergy crops on agricultural lands. However, few of these studies have assessed farmers’ willingness to produce or supply bioenergy crops or crop residues. Biomass markets for bioenergy crops do not exist, and developing these markets may take several years. Therefore, an important, yet unaddressed question is under what contractual or pricing arrangements farmers will grow biomass for bioenergy in these nascent markets. The purpose of this paper is to examine farmers’ willingness to produce switchgrass under alternative contractual, pricing, and harvesting arrangements. Contracts are likely to be the preferred method to bring together producers and processors of biomass for bioenergy. Contract design may vary across farmers and crop type, and may include attributes specific to annual crops, contract length, quantity or acreage requirements, quality specifications, payment dates, and other important features. A stated choice survey was administered in three, six-county areas of Kansas by Kansas State University and the USDA, National Agricultural Statistics Service from November 2010 to January 2011 to assess farmers’ willingness to produce cellulosic biomass under different contractual arrangements. This paper focuses on the switchgrass stated choice experiment from the survey. The stated choice experiment asked farmers to rank their preferred contractual arrangement from two contract options and one “do not adopt” option. Contractual attributes included percentage net returns above the next best alternative (e.g. CRP or hay production), contract length, a custom harvest option, insurance availability, and a seed-cost share option. Respondents then ranked their preferred contract option. The survey also collected data on farm characteristics, bioenergy crop preferences, socio-economic demographics, risk preferences, and marketing behavior. The survey used a stratified sample of farmers who farm more than 260 acres and grow corn. A total of 460 surveys were administered with a 65 percent completion rate. The underlying theoretical model uses the random utility model (RUM) approach to assess farmers’ willingness to grow switchgrass for bioenergy and determine the contractual attributes most likely to increase the likelihood of adoption. This framework allows us to define the “price,” or farmers’ mean willingness to accept, for harvested biomass sold to an intermediate processor. The estimated choice models follow the approach of Boxall and Adamowicz (2002) to capture heterogeneity across farmers and geographic regions due to management differences, conservation practices, and risk preferences. Using the percentage net return above CRP or hay production allows prices to float to levels that will entice farmers to adopt switchgrass. This will help determine a market price for bioenergy crops based on current market and production conditions without specifying an exact monetary value for the biomass. In addition, the survey results will facilitate contract designs between biorefineries and farmers while informing policymakers and the biofuel industry about farmers’ willingness to supply biomass for bioenergy production. Reference: Boxall, P.C. and W.L. Adamowicz, “Understanding Heterogeneous Preferences in Random Utility Models: A Latent Class Approach,” Environmental and Resource Economics 23(2002): 421 – 446.Biofuels, Cellulosic, Biomass, Switchgrass, Farmers, Willingness to Pay, Crop Production/Industries, Production Economics, Resource /Energy Economics and Policy,

Examining the Reliability of Logistic Regression Estimation Software

Research Methods/ Statistical Methods,

The probabilistic reduction approach to specifying multinomial logistic regression models in health outcomes research

The paper provides a novel application of the probabilistic reduction (PR) approach to the analysis of multi-categorical outcomes. The PR approach, which systematically takes account of heterogeneity and functional form concerns, can improve the specification of binary regression models. However, its utility for systematically enriching the specification of and inference from models of multi-categorical outcomes has not been examined, while multinomial logistic regression models are commonly used for inference and, increasingly, prediction. Following a theoretical derivation of the PR-based multinomial logistic model (MLM), we compare functional specification and marginal effects from a traditional specification and a PR-based specification in a model of post-stroke hospital discharge disposition and find that the traditional MLM is misspecified. Results suggest that the impact on the reliability of substantive inferences from a misspecified model may be significant, even when model fit statistics do not suggest a strong lack of fit compared with a properly specified model using the PR approach. We identify situations under which a PR-based MLM specification can be advantageous to the applied researcher

Revisiting the statistical specification of near-multicollinearity in the logistic regression model

This paper revisits the statistical specification of near-multicollinearity in the logistic regression model. We argue that the ceteris paribus clause, which assumes that the maximum likelihood estimator of β remains constant as the correlation ( ρ ) between the regressors increases, invoked under the traditional account of near-multicollinearity is rather misleading. We derive the parameters of the logistic regression model and show that they are functions of ρ , indicating that the ceteris paribus clause is unattainable. Monte Carlo simulations confirm these findings and further show that: coefficient estimates and related statistics fluctuate in a non-symmetric, non-monotonic way as | ρ |→1; that the impact of near-multicollinearity is centered on the estimates of β ; and that the impact on substantive inferences does not necessarily follow what the traditional account implies

Sample Size and Robustness of Inferences from Logistic Regression in the Presence of Nonlinearity and Multicollinearity

The logistic regression models has been widely used in the social and natural sciences and results from studies using this model can have significant impact. Thus, confidence in the reliability of inferences drawn from these models is essential. The robustness of such inferences is dependent on sample size. The purpose of this study is to examine the impact of sample size on the mean estimated bias and efficiency of parameter estimation and inference for the logistic regression model. A number of simulations are conducted examining the impact of sample size, nonlinear predictors, and multicollinearity on substantive inferences (e.g. odds ratios, marginal effects) and goodness of fit (e.g. pseudo-R2, predictability) of logistic regression models. Findings suggest that sample size can affect parameter estimates and inferences in the presence of multicollinearity and nonlinear predictor functions, but marginal effects estimates are relatively robust to sample size.Logistic Regression Model, Multicollinearity, Nonlinearity, Robustness, Small Sample Bias, Research Methods/ Statistical Methods,

Farmers’ Willingness to Produce Alternative Cellulosic Biofuel Feedstocks Under Contract in Kansas Using Stated Choice Experiments

Many studies have assessed the technical feasibility of producing bioenergy crops on agricultural lands. However, while it is possible to produce large quantities of agricultural biomass for bioenergy from lignocellulosic feedstocks, very few of these studies have assessed farmers’ willingness to produce these crops under different contracting arrangements. The purpose of this paper is to examine farmers’ willingness to produce alternative cellulosic biofuel feedstocks under different contractual, market, and harvesting arrangements. This is accomplished by using enumerated field surveys in Kansas with stated choice experiments eliciting farmers’ willingness to produce corn stover, sweet sorghum, and switchgrass under different contractual conditions. Using a random utility framework to model the farmers’ decisions, the paper examines the contractual attributes that will most likely increase the likelihood of feedstock enterprise adoption. Results indicate that net returns above the next best alternative use of the land, contract length, cost share, financial incentives, insurance, and custom harvest options are all important contract attributes. Farmers’ willingness to adopt and their willingness-to-pay for alternative contract attributes vary by region and choice of feedstock

Examining Inferences from Neural Network Estimators of Binary Choice Processes: Marginal Effects, and Willingness-to-Pay

To satisfy the utility maximization hypothesis in binary choice modeling, logit and probit models must make a priori assumptions regarding the underlying functional form of a representative utility function. Such theoretical restrictions may leave the postulated estimable model statistically misspecified. This may lead to significant bias in substantive inferences, such as willingness-to-pay (or accept) measures, in environmental, natural resource and applied economic studies. Feed-forward back-propagation artificial neural networks (FFBANN) provide a potentially powerful semi-nonparametric method to avoid potential misspecifications and provide more valid inference. This paper shows that a single-hidden layer FFBANN can be interpreted as a logistic regression with a flexible index function and can be subsequently used for statistical inference purposes, such as estimation of marginal effects and willingness-to-pay measures. To the authors’ knowledge, the derivation and estimation of marginal effects and other substantive measures using neural networks are not available in the economics literature and is thus a novel contribution. An empirical application is conducted using FFBANNs to demonstrate estimation of marginal effects and willingness-to-pay in a contingent valuation and stated choice experimental framework. We find that FFBANNs can replicate results from binary choice models commonly used in the applied economics literature and can improve on substantive inferences derived from these models