This thesis consists of three chapters on economic and econometric applications of Bayesian parameter estimation and model comparison. The first two chapters study the incidental parameter problem mainly under a linear autoregressive (AR) panel data model with fixed effect. The first chapter investigates the problem from a model comparison perspective. The major finding in the first chapter is that consistency in parameter estimation and model selection are interrelated. The reparameterization of the fixed effect parameter proposed by Lancaster (2002) may not provide a valid solution to the incidental parameter problem if the wrong set of exogenous regressors are included. To estimate the model consistently and to measure its goodness of fit, the Bayes factor is found to be more preferable for model comparson than the Bayesian information criterion based on the biased maximum likelihood estimates. When the model uncertainty is substantial, Bayesian model averaging is recommended. The method is applied to study the relationship between financial development and economic growth. The second chapter proposes a correction function approach to solve the incidental parameter problem. It is discovered that the correction function exists for the linear AR panel model of order p when the model is stationary with strictly exogenous regressors. MCMC algorithms are developed for parameter estimation and to calculate the Bayes factor for model comparison. The last chapter studies how stock return's predictability and model uncertainty affect a rational buy-and-hold investor's decision to allocate her wealth for different lengths of investment horizons in the UK market. The FTSE All-Share Index is treated as the risky asset, and the UK Treasury bill as the riskless asset in forming the investor's portfolio. Bayesian methods are employed to identify the most powerful predictors by accounting for model uncertainty. It is found that though stock return predictability is weak, it can still affect the investor's optimal portfolio decisions over different investment horizons.

The literature investigating the relationship between stock market returns and inflation is long and has produced diverse findings. This thesis examines the nature of stock–inflation relations in Sub-Saharan countries whose stock markets were established before 1992. Evidence in this thesis shows that in the short term there is a positive relationship between stocks and inflation. Using the Johansen (1988) evidence, a long-run stock–inflation relationship is confirmed only in Nigeria and South Africa, where it is found to be negative. However, accounting for structural breaks provides evidence for a long-run relationship in Botswana, Ghana and Kenya. The evidence of the effects of regimes in the relationship is further supported by a nonparametric cointegration analysis which finds a long-run relation in countries where the Johansen (1988) method had failed. Unexpected inflation is also found to be related to stock returns in Botswana, Ghana, Kenya, Nigeria and Mauritius, which raises concerns about the use of month-end stock data in analysing this relationship. The thesis confirms the existence of hidden inflation in Kenya, Mauritius, Nigeria and Zimbabwe. Imported inflation, interest rates and the exchange rate are found to have useful information about inflation movements in Sub-Saharan Africa.