The first aim of this thesis is to expand a range of econometric models available to investigate the behaviours and the drivers of economic output (e.g. real Gross Domestic Product (GDP)), labour productivity growth (real GDP per capita)). The second aim is to develop algorithms to estimate the proposed models. The third aim is to develop an inferential framework for each proposed model.Chapter 2 generalises some of the existing methods to account for statistical noise in the estimation of a frontier, and to gain new insights on the drivers of labour productivity growth. We apply the model specification to the data set used in Kumar and Russell (The American Economic Review, 2002). We confirm that capital deepening is the main source of labour productivity growth, and also is the factor driving the transformation of the distribution of labour productivity from one single mode density to a density of two modes. When accounting for statistical noise in the estimation of the frontier, we find that capital deepening does not contribute to growth convergence, but instead efficiency change is a driver of growth convergence. The results indicate that improving technical efficiencies might reduce the gap between the poor and the rich.Chapter 3 proposes a non-linear state space stochastic frontier model which provides a researcher a tool to jointly model the dynamic effects of environmental variables on both a production function and an inefficiency term. A test for time-variation in technical inefficiencies is also provided. We apply the proposed model to the economic study of 21 OECD countries. We wish to investigate under what channels foreign direct investment (FDI) affects a production process: through a production function, an inefficiency term, or both. The results show that FDI plays more important role in influencing the shift of the production frontier rather than the distribution of technical inefficiencies. This is to suggest that an output growth of an economy might further increase by investing FDI in innovation to improve technological change (shift of the frontier). We find statistical evidence in favour of time-variation in technical inefficiencies, and the temporal effect therefore should not be ignored in measuring technical inefficiencies.Chapter 4 considers an econometric model where interdependent relationships between GDP and other key macroeconomic variables are allowed. We achieve impulse response functions of some key macroeconomic variables from a large VAR model with 119 variables. The precision of estimating a such large VAR model is obtained by using a dimension reduction approach, namely a reduced rank regression which has a specification independent to the order of the variables. The impulse responses of a selection of macroeconomic variables to a contractionary monetary policy have expected sign. For instance, a contractionary monetary policy is followed.i by a decrease in GDP, price level and an increase in unemployment rate. The results support the conventional channel of the e...