The purpose of this study is to investigate methods for assessing the value people place on preserving our natural environments and resources. It focuses on the contingent valuation method, which is a method for directly asking people about their preferences. In particular, the study focuses on the use of discrete response data in contingent valuation experiments.The first part of the study explores the economic theory of the total value of a natural resource, where the principal components of total value are analyzed; use values and non-use values. Our application is a study of the value Swedes' attach to the preservation of eleven forest areas that contain high recreational values and contain unique environmental qualities. Six forests were selected on the basis of an official investigation which includes virgin forests and other areas with unique environmental qualities. In addition, five virgin forests were selected.Two types of valuation questions are analyzed, the continuous and the discrete. The first type of question asks directly about willingness to pay, while the second type suggests a price that the respondent may reject or accept. The results of the continuous question suggest an average willingness to pay of about 1,000 SEK per household for preservation of the areas. Further analysis of the data suggests that this value depends on severi characteristics of the respondent: such as the respondent's income and whether or not the respondent is an altruist.Two econometric approaches are used to analyze the discrete responses; a flexible parametric approach and a non-parametric approach. In addition, a Bayesian approach is described. It is shown that the results of a contingent valuation experiment may depend to some extent on the choice of the probability model. A re-sampling approach and a Monte-Carlo approach is used to shed light on the design of a contingent valuation experiment with discrete responses. The econometric analysis ends with an analysis of the often observed disparity between discrete and continuous valuation questions.A cost-benefit analysis is performed in the final chapter. The purpose of this analysis is to illustrate how the contingent valuation approach may be combined with opportunity cost data to improve the decision-basis in the environmental policy domain. This analysis does not give strong support for a cutting alternative. Finally, the results of this investigation are compared with evidence from other studies.The main conclusion of this study is that assessment of peoples' sentiments towards changes of our natural environments and resources can be a useful supplement to decisions about the proper husbandry of our natural environments and resources. It also highlights the importance of careful statistical analysis of data gained from contingent valuation experiments. / digitalisering@umu

Maximum likelihood is an ubiquitous method used in the estimation of generalized linear mixed model (GLMM). However, the method entails computational difficulties and relies on the normality assumption for random effects. We propose a second-order least squares (SLS) estimator based on the first two marginal moments of the response variables. The proposed estimator is computationally feasible and requires less distributional assumptions than the maximum likelihood estimator. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is proposed. We show that the SLS estimators are consistent and asymptotically normally distributed under fairly general conditions in the framework of GLMM. Missing data is almost inevitable in longitudinal studies. Problems arise if the missing data mechanism is related to the response process. This thesis develops the proposed estimators to deal with response data missing at random by either adapting the inverse probability weight method or applying the multiple imputation approach. In practice, some of the covariates are not directly observed but are measured with error. It is well-known that simply substituting a proxy variable for the unobserved covariate in the model will generally lead to biased and inconsistent estimates. We propose the instrumental variable method for the consistent estimation of GLMM with covariate measurement error. The proposed approach does not need any parametric assumption on the distribution of the unknown covariates. This makes the method less restrictive than other methods that rely on either a parametric distribution of the covariates, or to estimate the distribution using some extra information. In the presence of data outliers, it is a concern that the SLS estimators may be vulnerable due to the second-order moments. We investigated the robustness property of the SLS estimators using their influence functions. We showed that the proposed estimators have a bounded influence function and a redescending property so they are robust to outliers. The finite sample performance and property of the SLS estimators are studied and compared with other popular estimators in the literature through simulation studies and real world data examples.

Maximum likelihood is an ubiquitous method used in the estimation of generalized linear mixed model (GLMM). However, the method entails computational difficulties and relies on the normality assumption for random effects. We propose a second-order least squares (SLS) estimator based on the first two marginal moments of the response variables. The proposed estimator is computationally feasible and requires less distributional assumptions than the maximum likelihood estimator. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is proposed. We show that the SLS estimators are consistent and asymptotically normally distributed under fairly general conditions in the framework of GLMM. Missing data is almost inevitable in longitudinal studies. Problems arise if the missing data mechanism is related to the response process. This thesis develops the proposed estimators to deal with response data missing at random by either adapting the inverse probability weight method or applying the multiple imputation approach. In practice, some of the covariates are not directly observed but are measured with error. It is well-known that simply substituting a proxy variable for the unobserved covariate in the model will generally lead to biased and inconsistent estimates. We propose the instrumental variable method for the consistent estimation of GLMM with covariate measurement error. The proposed approach does not need any parametric assumption on the distribution of the unknown covariates. This makes the method less restrictive than other methods that rely on either a parametric distribution of the covariates, or to estimate the distribution using some extra information. In the presence of data outliers, it is a concern that the SLS estimators may be vulnerable due to the second-order moments. We investigated the robustness property of the SLS estimators using their influence functions. We showed that the proposed estimators have a bounded influence function and a redescending property so they are robust to outliers. The finite sample performance and property of the SLS estimators are studied and compared with other popular estimators in the literature through simulation studies and real world data examples.