According to Blundell and Powell (2003), the development of strategies to identify and estimate certain parameters or even entire functions of regression models under endogeneity has arguably been one of the main contributions of microeconometrics to the statistical literature. The term endogeneity, in this context, refers to a correlation between observable regressor(s) and model unobservable(s), which can arise for multiple reasons such as, among others, omitted variables, measurement error, unobserved heterogeneity, or simultaneous causality. Whereas linear identification and estimation techniques to address endogeneity date back as far as 1928 (Stock and Trebbi, 2003), advances in the field of nonlinear models are much more recent: nonlinear parametric models under endogeneity only came under investigation during the 1970s and 1980s (e.g. Ameniya, 1974; Hansen, 1982), and it was not until the mid 1990s that models of (partially) unknown functional form were considered.

This thesis is comprised of three pieces of research on moral hazard, reputation and market structure. In particular, following an opening discussion of previous literature, I explore the dynamic interaction between moral hazard and market structure in two distinct game theoretic settings and empirically test a fundamental assumption of these models concerning consumer rationality. In the first Chapter, I survey the studies which shed light on some dimension of the relationship between asymmetric information and market structure and identify the gap in the literature that my research aims to fill. The mechanism of reputation has been primarily investigated in the setting of perfect competition; however, this setting is ill suited for uncovering the rich set of relations between asymmetric information and market structure. Only a handful of articles departed from the perfect competition framework and only few of those introduced strategic interaction among firms, a fundamental ingredient of my research interest. The models which do include strategic interaction have, however, ignored some important dynamics in the interaction of asymmetric information and market structure. Therefore in Chapter II, I develop a model in which market structure affects moral hazard while, in turn, moral hazard fuels market structure dynamics. The model is very general allowing for all kinds of strategic interaction among firms usually considered in the literature. I identify and analyse an important driving force -a survival contest - which has so far been overlooked. The main conclusion is that market concentration in and of itself reduces moral hazard and moral hazard drives the market towards concentration through the survival contest. The model is suitable to explain the puzzling market transformation of important industries such as banking, audit and health care. In Chapter III, I extend the model of Chapter 11 by introducing stochastic entry. First, I demonstrate that my results in the previous Chapter are robust to the entry process. Second, stochastic entry allows me to derive a non-degenerate steady state distribution which exhibits a very intuitive dynamics. Finally, although the complex nature of the dynamics prevents a detailed comparative static analysis of this distribution, it displays two well known empirical regularities. In particular, my model shows that the presence of moral hazard in and of itself produces shake-outs in the market from time to time and also correlated exit and entry rates. The reputation mechanisms in general and in the models of Chapter II and III in particular crucially depend on consumers' ability and willingness to develop an understanding of imperfect information on quality. In order to make reputation an effective disciplinary force, consumers must be strongly rational so that they read and understand imperfect quality indicators. In Chapter IV, this basic assumption on consumer rationality is tested empirically in discrete choice settings in the audit market. I find robust empirical evidence that if consumers are firms rather than individuals, they are strongly rational.

The theoretical models in this thesis address questions relating to the interaction between information and decisions. The main issues are as follows: i) decisions are based on uncertain parameters, ii) parameter estimates are used for specific policy decisions, iii) policy decisions take the form of sequential reforms whose magnitude and frequency must be determined, iv) there are dynamic interactions between the properties of estimators and the performance of decision rules. The method of investigation is by formulation of algebraic models whose properties are examined by analytic and numerical techniques. The contribution to the knowledge of the subject is as follows: i) a well-known linear control model is extended to incorporate sequential reforms, ii) the properties of a limited class of optimal active learning strategies are described, iii) in Monte Carlo simulations, least squares estimates are not found to have desirable tatist al properties when used in conjunction with active earning decision rules, iv) a number of well-known optimal tax models are extended to incorporate parameter uncertainty.

We discuss the implications of nonlinearity in competitive models of optimal endogenous growth. Departing from a simple representative agent setup with convex risk premium and investment adjustment costs, we define an open economy dynamic optimization problem and show that the optimal control solution is given by an autonomous nonlinear vector field in <3 with multiple equilibria and no optimal stable solutions. We give a thorough analytical and numerical analysis of this system qualitative dynamics and show the existence of local singularities, such as fold (saddle-node), Hopf and Fold-Hopf bifurcations of equilibria. Finally, we discuss the policy implications of global nonlinear phenomena. We focus on dynamic scenarios arising in the vicinity of Fold-Hopf bifurcations and demonstrate the existence of global dynamic phenomena arising from the complex organization of the invariant manifolds of this system. We then consider this setup in a non-cooperative differential game environment, where asymmetric players choose open loop no feedback strategies and dynamics are coupled by an aggregate risk premium mechanism. When only convex risk premium is considered, we show that these games have a specific state-separability property, where players have optimal, but naive, beliefs about the evolution of the state of the game. We argue that the existence of optimal beliefs in this fashion, provides a unique framework to study the implications of the self-confirming equilibrium (SCE) hypothesis in a dynamic game setup. We propose to answer the following question. Are players able to concur on a SCE, where their expectations are self-fulfilling? To evaluate this hypothesis we consider a simple conjecture. If beliefs bound the state-space of the game asymptotically and strategies are Lipschitz continuous, then it is possible to describe SCE solutions and evaluate the qualitative properties of equilibrium. If strategies are not smooth, which is likely in environments where belief-based solutions require players to learn a SCE, then asymptotic dynamics can be evaluated numerically as a Hidden Markov Model (HMM). We discuss this topic for a class of games where players lack the relevant information to pursue their optimal strategies and have to base their decisions on subjective beliefs. We set up one of the games proposed as a multi-objective optimization problem under uncertainty and evaluate its asymptotic solution as a multi-criteria HMM.We show that under a simple linear learning regime there is convergence to a SCE and portray strong emergence phenomena as a result of persistent uncertainty.

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In chapter 3, quantile regression is used to estimate probabilistic frontiers, i.e. frontiers based on the probability of being dominated. The results from the empirical application using an Italian hotel dataset show rejections of a parametric functional form and a location shift effect, large uncertainty of the estimates of the frontier and wide confidence intervals for the estimates of efficiency. Quantile regression is further developed to estimate thick probabilistic frontiers, i.e. frontiers based on a group of efficient firms. The empirical results show that the differences between the inefficient and efficient firms at lower quantiles of the conditional distribution function are from the coefficient (85 percent of the total effect) and the residual effects (25 percent) and at higher quantiles from the coefficient (68 percent) and the regressor effects (22 percent). The results from the Monte Carlo simulations in chapter 4 show that under the correctly assumed stochastic frontier models, the probabilistic frontiers can have the lowest bias and mean squared error of the efficiency estimates. When outliers or location-scale shift effects are included, more preference is towards the probabilistic frontiers. The nonparametric probabilistic frontiers are nearly always preferable to Data Envelopment Analysis and Free Disposable Hull. In chapter 5, a fixed effects quantile regression estimator is used to estimate a cost frontier and efficiency levels for a panel dataset of English NHS Trusts. Waiting times elasticities are estimated from -0.14 to 0.17 in the cross-sectional models and -0.008 to 0.03 in the panel models. Cost minimisation ranged from 33 to 60 days in the cross-sectional model and from 37 to 54 days in the panel model. The results show that the effects of the inputs and control variables vary depending on the efficiency of the Trusts. The efficiency estimates reveal very different conclusions depending on the model choice.

This thesis develops three new classes of Bayesian graphical models to forecast multivariate time series. Although these models were originally motivated by the need for flexible and tractable forecasting models appropriate for modelling competitive business markets, they are of theoretical interest in their own right. Multiregression dynamic models are defined to preserve certain conditional independence structures over time. Although these models are typically very non-Gaussian, it is proved that they are simple to update, amenable to practical implementation and promise more efficient identification of causal structures in a time series than has been possible in the past. Dynamic graphical models are defined for multivariate time series for which there is believed to be symmetry between certain subsets of variables and a causal driving mechanism between these subsets. They are a specific type of graphical chain model (Wermuth & Lauritzen, 1990) which are once again typically non- Gaussian. Dynamic graphical models are a combination of multiregression dynamic models and multivariate regression models (Quintana, 1985,87, Quintana & West, 1987,88) and as such, they inherit the simplicity of both these models. Partial segmentation models extend the work of Dickey et al. (1987) to the study of models with latent conditional independence structures. Conjugate Bayesian anaylses are developed for processes whose probability parameters are hypothesised to be dependent, using the fact that a certain likelihood separates given a matrix of likelihood ratios. It is shown how these processes can be represented by undirected graphs and how these help in its reparameterisation into conjugate form.

This thesis undertakes a Monte Carlo study to investigate the finite sample properties of several panel unit root and cointegration tests. To this end, we consider a number of different experiments which potentially affect the properties of the tests. We first consider panel unit root tests in heterogenous panels. Application of the panel tests of Im, Pesaran and Shin (2003) (IPS), and Maddala and Wu (1999) (MW) increases their power over the standard ADF test. However, the power of the tests is significantly diminished when the panel is dominated by the non-stationary series. Neglecting the presence of cross-sectional dependence results in serious size distortions. In view of this, a variety of methods are applied to correct the size distortions. However, the power of all tests is diminished as the cross-correlations reduce the amount of independent information in the panel. The simulation results from the panel cointegration tests extend the findings of the unit root tests to multivariate cases. The likelihood-based panel rank test of Larsson, Lyhagen and Lothgren (2001) is found to be more powerful than the residual-based panel tests of IPS and MW, but slightly oversized in moderate sample sizes (Z). The effects of a mixed panel and of cross-correlations in the errors are similar to those of panel unit root tests. Therefore, we again, use the bootstrap method and the Cross-sectionally augmented IPS test (CIPS) ofPesaran (2003) to correct the size distortions. The presence of structural breaks affects the size and power properties of any panel unit root tests which fail to cope with it. When the break dates are known, the exogenous break panel LM test is applied, to control the effect of structural shifts. In addition, the endogenous break selection procedures are used to estimate the break points. The endogenous break panel LM test also performs considerably well in terms of the size, power and accuracy with which the true break points are estimated. Finally, application of the panel unit root and cointegration tests provide some evidence in support of the existence of long-run PPP and the monetary model in Asia Pacific countries. In addition, the presence of structural breaks as the impact of the currency crisis is also detected. However, evidence is found to be sensitive to the choice of deterministic terms (intercepts, trends), the methods used to estimate the panel test statistic (e.g. SUR and CIPS) and the break-point selection criteria.

In this thesis we examine the derivation of asymptotic expansion approximations to the cumulative distribution functions of asymptotically chi-square test statistics under the null hypothesis being tested and the use of such approximations in the investigation of the properties of testing procedures. We are particularly concerned with how the structure of various test statistics may simplify the derivation of asymptotic expansion approximations to their cumulative distribution functions and also how these approximations can be used in conjunction with other small sample techniques to investigate the properties of testing procedures. In Chapter 1 we briefly review the construction of test statistics based on the Wald testing principle and in Chapter 2 we review the various approaches to finite sample theory which have been adopted in econometrics including asymptotic expansion methods. In Chapter 3 we derive asymptotic expansion approximations to the joint cumulative distribution functions of asymptotically chi-square test statistics making explicit use of certain aspects of the structure of such test statistics. In Chapters 4, 5 and 6 we apply these asymptotic expansion approximations under the null hypothesis, in conjunction with other small sample techniques, to a number of specific testing problems. The test statistics considered in Chapters 4 and 6 are Wald test statistics and those considered in Chapter 5 are predictive failure test statistics. The asymptotic expansion approximations to the cumulative distribution functions of the test statistics under the null hypothesis are evaluated numerically; the Implementation of the algorithm for obtaining asymptotic expansion approximations to the cumulative distribution functions of test statistics is discussed in an Appendix on Computing. Finally, in Chapter 7 we draw overall conclusions from the earlier chapters of the thesis and discuss briefly directions for possible future research.

In this thesis, optimum experimental designs for a statistical model possessing a skewed error distribution are considered, with particular interest in investigating possible parameter dependence of the optimum designs. The skewness in the distribution of the error arises from its assumed structure. The error consists of two components (i) random error, say V, which is symmetrically distributed with zero expectation, and (ii) some type of systematic error, say U, which is asymmetrically distributed with nonzero expectation. Error of this type is sometimes called 'composed' error. A stochastic frontier model is an example of a model that possesses such an error structure. The systematic error, U, in a stochastic frontier model represents the economic efficiency of an organisation. Three methods for approximating information matrices are presented. An approximation is required since the information matrix contains complicated expressions, which are difficult to evaluate. However, only one method, 'Method 1', is recommended because it guarantees nonnegative definiteness of the information matrix. It is suggested that the optimum design is likely to be sensitive to the approximation. For models that are linearly dependent on the model parameters, the information matrix is independent of the model parameters but depends on the variance parameters of the random and systematic error components. Consequently, the optimum design is independent of the model parameters but may depend on the variance parameters. Thus, designs for linear models with skewed error may be parameter dependent. For nonlinear models, the optimum design may be parameter dependent in respect of both the variance and model parameters. The information matrix is rank deficient. As a result, only subsets or linear combinations of the parameters are estimable. The rank of the partitioned information matrix is such that designs are only admissible for optimal estimation of the model parameters, excluding any intercept term, plus one linear combination of the variance parameters and the intercept. The linear model is shown to be equivalent to the usual linear regression model, but with a shifted intercept. This suggests that the admissible designs should be optimal for estimation of the slope parameters plus the shifted intercept. The shifted intercept can be viewed as a transformation of the intercept in the usual linear regression model. Since D_A-optimum designs are invariant to linear transformations of the parameters, the D_A-optimum design for the asymmetrically distributed linear model is just the linear, parameter independent, D_A-optimum design for the usual linear regression model with nonzero intercept. C-optimum designs are not invariant to linear transformations. However, if interest is in optimally estimating the slope parameters, the linear transformation of the intercept to the shifted intercept is no longer a consideration and the C-optimum design is just the linear, parameter independent, C-optimum design for the usual linear regression model with nonzero intercept. If interest is in estimating the slope parameters, and the shifted intercept, the C-optimum design will depend on (i) the design region; (ii) the distributional assumption on U; (iii) the matrix used to define admissible linear combinations of parameters; (iv) the variance parameters of U and V; (v) the method used to approximate the information matrix. Some numerical examples of designs for a cross-sectional log-linear Cobb-Douglas stochastic production frontier model are presented to demonstrate the nonlinearity of designs for models with a skewed error distribution. Torsney's (1977) multiplicative algorithm was implemented in finding the optimum designs.