This thesis studies the Second-order Least Squares (SLS) estimation method in regression models with and without measurement error. Applications of the methodology in general quasi-likelihood and variance function models, censored models, and linear and generalized linear models are examined and strong consistency and asymptotic normality are established. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is used and its asymptotic properties are studied. Finite sample performances of the estimators in all of the studied models are investigated through simulation studies. / February 2009

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.

This thesis studies the Second-order Least Squares (SLS) estimation method in regression models with and without measurement error. Applications of the methodology in general quasi-likelihood and variance function models, censored models, and linear and generalized linear models are examined and strong consistency and asymptotic normality are established. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is used and its asymptotic properties are studied. Finite sample performances of the estimators in all of the studied models are investigated through simulation studies.

This thesis studies the Second-order Least Squares (SLS) estimation method in regression models with and without measurement error. Applications of the methodology in general quasi-likelihood and variance function models, censored models, and linear and generalized linear models are examined and strong consistency and asymptotic normality are established. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is used and its asymptotic properties are studied. Finite sample performances of the estimators in all of the studied models are investigated through simulation studies.

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.

This paper conducts an analysis of county level data to determine the effect of fast food restaurants on type 2 diabetes rates. Due to endogeneity concerns with respect to the location of fast food restaurants, this paper follows the work of Dunn (2010) and uses the number of interstate exits in a given county to serve as an instrument for fast food restaurants. The strength of the instrument, which is theoretically and empirically tested in this paper, imposes some restraints on the interpretation of the findings. Using the Two-Stage Least Squares estimation method, I find that the presence of fast food restaurants has a positive and statistically significant effect on type 2 diabetes rates at the county level.

Essay I: This essay provides an overview of the history of the Swedish pension system. Starting with the implementation of the public pension system in 1913, it outlines the key components of each major pension reform up until today along with a discussion of the main trade-offs and concerns that policy makers have faced. It also describes the historical background of the four largest occupational pension plans in Sweden and the mutual influence between these plans and the public pension system.        Essay II: Despite the fact that the increasing involvement of the private sector in pension provision has brought more flexibility to the pay-out phase of retirement, little is known about the characteristics of those who choose to annuitize their pension wealth and those who do not. I combine unique micro-data from a large Swedish occupational pension plan with rich national administrative data to study the choice between life annuities and fixed-term payouts with a minimum payout length of 5 years for 183,000 retiring white-collar workers. I find that low accumulation of assets is strongly associated with the choice of the 5-year payout. Consistent with individuals selecting payout length based on private information about their mortality prospects, individuals who choose the 5-year payout are in worse health, exhibit higher ex-post mortality rates and have shorter-lived parents than annuitants. Individuals also seem to respond to large, tax-induced changes in annuity prices.            Essay III: This essay estimates the causal effect of postponing retirement on a wide range of health outcomes using Swedish administrative data on cause-specific mortality, hospitalizations and drug prescriptions. Exogenous variation in retirement timing comes from a reform which raised the age at which broad categories of Swedish local government workers were entitled to retire with full pension benefits from 63 to 65. The reform caused a remarkable shift in the retirement distribution of the affected workers, increasing the actual retirement age by more than 4.5 months. Instrumental variable estimation results show no effect of postponing retirement on the overall consumption of health care, nor on the risk of dying early. There is evidence, however, of a reduction in diabetes-related hospitalizations and in the consumption of drugs that treat anxiety. Essay IV (with Per Engström): The consumption based method to estimate underreporting among self-employed, introduced by Pissarides and Weber (1989), is one of the workhorses in the empirical literature on tax evasion/avoidance. We show that failure to account for transitory income fluctuations in current income may overestimate the degree of underreporting by around 40 percent. Previous studies typically use instrumental variable methods to address the issue. In contrast, our access to registry based longitudinal income measures allows a direct approach based on more permanent income measures. This also allows us to evaluate the performance of a list of instruments widely used in the previous literature. Our analysis shows that capital income is the most suitable instrument in our application, while education and housing related measures do not seem to satisfy the exclusion restrictions.

Diploma thesis deals with designing of algorithmus for automatic controller tunning for DC motors. Automatic tuning function consist of system identification and controller parametrization. Cascade control loop was chosen for its robustness and proper DC motor control. For electric system identification of DC motor was used recursive method of instrumental variables, because of noisy signal from current transducer. In the case of identification mechanical system, there were used least sqares method. According to identified parameters, current controller was parametrized by optimum module and revolution controller according symetrcal optimum.

This paper aims to quantify the municipal tax revenue effects of built-up area increases. The assumed existence of these effects is one of the key reasons for ongoing land consumption on the side of the municipalities. Some previous case studies however suggested that these effects might be not large enough especially in rural municipalities and would thus make land development not profitable. We estimate the effect of built-up industrial and commercial (BIC) area change on the business tax revenues in cross-sectional instrumental variable (IV) estimations. Based on detailed data for Bavaria, we find a significant and positive tax revenue effect of an increase in municipal BIC area. There exist strong differences in the size of this effect between urban and rural municipalities. The largest effects are generated by the BIC area in the large cities and become substantially smaller when these are dropped from the sample. Based on these findings, we reflect on the tradable planning permits (TPP) scheme recently discussed in the land use literature in the context of policies aiming to limit land consumption. Furthermore, we relate our estimates to the average municipal costs for land development and execute a number of robustness checks.

Ce mémoire vise à estimer la densité neutre au risque (Risk neutral density (RND) en anglais) par une approche non paramétrique tout en tenant compte de l’endogénéité. Les prix transversaux des options européennes sont utilisés pour l’estimation. Le modèle principal considéré est la régression linéaire fonctionnelle. Nous montrons comment utiliser des variables instrumentales dans ce modèle pour corriger l’endogénéité. En outre, nous avons intégré des variables instrumentales dans le modèle approximant le RND par l’utilisation des fonctions d’Hermite à des fins de comparaison des résultats. Pour garantir un estimateur stable, nous utilisons la technique de régularisation de Tikhonov. Ensuite, nous effectuons des simulations de Monte-Carlo pour étudier l’impact des différents types de distribution RND sur les résultats obtenus. Plus précisément, nous analysons une distribution de mélange lognormale et une distribution de smile de Black-Scholes. Les résultats des simulations démontrent que l’estimateur utilisant des variables instrumentales pour corriger l’endogénéité est plus performant que l’alternative qui ne les utilise pas. En outre, les résultats de la distribution de smile de Black-Scholes sont plus performants que ceux de la distribution de mélange log-normale. Enfin, S&P 500 options sont utilisées pour une application de l’estimateur. / This thesis aims to estimate the risk-neutral density (RND) through a non-parametric approach while accounting for endogeneity. The cross-sectional prices of European options are used for the estimation. The primary model under consideration is functional linear regression. We have demonstrated the use of instrumental variables in this model to address endogeneity. Additionally, we have integrated instrumental variables into the model approximating RND through the use of Hermite functions for the purpose of result comparison. To ensure a stable estimator, we employ the Tikhonov regularization technique. Following this, we conduct Monte- Carlo simulations to investigate the impact of different RND distribution types on the obtained results. Specifically, we analyze a lognormal mixture distribution and a Black-Scholes smile distribution. The simulation results demonstrate that the estimator utilizing instrumental variables to adjust for endogeneity outperforms the non-adjusted alternative. Additionally, outcomes from the Black-Scholes smile distribution exhibit superior performance compared to those from the log-normal mixture distribution. Finally, S&P 500 options are used for an application of the estimator.