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We provide a general class of tests for correlation in time series, spatial, spatio-temporal and cross-sectional data. We motivate our focus by reviewing how computational and theoretical difficulties of point estimation mount, as one moves from regularly-spaced time series data, through forms of irregular spacing, and to spatial data of various kinds. A broad class of computationally simple tests is justified. These specialize to Lagrange multiplier tests against parametric departures of various kinds. Their forms are illustrated in case of several models for describing correlation in various kinds of data. The initial focus assumes homoscedasticity, but we also robustify the tests to nonparametric heteroscedasticity.

This paper examines the distributional properties of stock returns in the Nigerian stock market. Because emerging stock markets present several institutional, political and economic barriers, we hypothesize that the structural adjustment program begun in 1986 resulted in a sustained increase in the variability of stock returns. Conventional variance homogeneity tests could not reject the hypothesis of changing volatility in the security returns process. However, the Lagrange multiplier test reveals the presence of autoregressive conditional heteroscedasticity (ARCH) effect in the stock returns.

A Lagrange multiplier was introduced by Chow in 1997 to give a set of necessary conditions for optimal control with respect to a general continuous stochastic differential system. Many applications to the continuous financial markets were derived. Inspired by Chow's idea, this paper introduces a Lagrange multiplier to derive rigorously some necessary conditions for optimal control with respect to stochastic differential systems with jumps. The results reduce to Chow's case for continuous systems. An application to optimal consumption for the financial market with jumps is provided.

Dynamic panel data models are widely used by econometricians to study over time the economics of, for example, people, firms, regions, or countries, by pooling information over the cross-section. Though much of the panel research concerns inference in stationary models, macroeconomic data such as GDP, prices, and interest rates are typically trending over time and require in one way or another a nonstationary analysis. In time series analysis it is well-established how autoregressive unit roots give rise to stochastic trends, implying that random shocks to a dynamic process are persistent rather than transitory. Because the implications of, say, government policy actions are fundamentally different if shocks to the economy are lasting than if they are temporary, there are now a vast number of univariate time series unit root tests available. Similarly, panel unit root tests have been designed to test for the presence of stochastic trends within a panel data set and to what degree they are shared by the panel individuals. Today, growing data certainly offer new possibilities for panel data analysis, but also pose new problems concerning double-indexed limit theory, unobserved heterogeneity, and cross-sectional dependencies. For example, economic shocks, such as technological innovations, are many times global and make national aggregates cross-country dependent and related in international business cycles. Imposing a strong cross-sectional dependence, panel unit root tests often assume that the unobserved panel errors follow a dynamic factor model. The errors will then contain one part which is shared by the panel individuals, a common component, and one part which is individual-specific, an idiosyncratic component. This is appealing from the perspective of economic theory, because unobserved heterogeneity may be driven by global common shocks, which are well captured by dynamic factor models. Yet, only a handful of tests have been derived to test for unit roots in the common and in the idiosyncratic components separately. More importantly, likelihood-based methods, which are commonly used in classical factor analysis, have been ruled out for large dynamic factor models due to the considerable number of parameters. This thesis consists of four papers where we consider the exact factor model, in which the idiosyncratic components are mutually independent, and so any cross-sectional dependence is through the common factors only. Within this framework we derive some likelihood-based tests for common and idiosyncratic unit roots. In doing so we address an important issue for dynamic factor models, because likelihood-based tests, such as the Wald test, the likelihood ratio test, and the Lagrange multiplier test, are well-known to be asymptotically most powerful against local alternatives. Our approach is specific-to-general, meaning that we start with restrictions on the parameter space that allow us to use explicit maximum likelihood estimators. We then proceed with relaxing some of the assumptions, and consider a more general framework requiring numerical maximum likelihood estimation. By simulation we compare size and power of our tests with some established panel unit root tests. The simulations suggest that the likelihood-based tests are locally powerful and in some cases more robust in terms of size. ; Solving Macroeconomic Problems Using Non-Stationary Panel Data

In this paper, we study the impact of government's budget constraint on the optimal industrial policy in industries with increasing returns to scale. We show that privatization is preferred to regulation for intermediate values of the shadow cost of public funds (i.e., the Lagrange multiplier of the government's budget constraint). However, the advantage of privatization is likely to disappear once the product market allows the entry of more than one firm.In this paper, we study the impact of government's budget constraint on the optimal industrial policy in industries with increasing returns to scale. We show that privatization is preferred to regulation for intermediate values of the shadow cost of public funds (i.e., the Lagrange multiplier of the government's budget constraint). However, the advantage of privatization is likely to disappear once the product market allows the entry of more than one firm.