Doctor of Philosophy / Department of Economics / Lance J. Bachmeier / This dissertation consists of three essays in nonlinear macroeconomic modeling and econometrics. In the first essay, we decompose oil price movements into oil demand (stock market) shocks and oil supply (oil-market) shocks, and examine the response of the stock market to these shocks. We find that when oil prices are “net-increasing”, a stock market shock that causes the S&P 500 to rise by one percentage point will cause the price of oil to rise approximately 0.2 percentage points, with a statistically significant positive effect one day after the stock market shock. On the other hand, the response of the stock market to an oil market shock is a decline of 6.8 percent when the price of oil doubles. For other days, the initial response of the oil market to a stock market shock is the same as in the net oil price increase case (by construction). We then analyze the response of monetary policy to the identified stock market and oil market shocks and find that short-term interest rates respond to the stock market shocks but not the oil market shocks. Finally, we evaluate the predictive power of the decomposed stock market and oil shocks relative to the change in the price of oil. We find statistically significant gains in both the in-sample fit and out-of-sample forecast accuracy when using the identified stock market and oil market shocks rather than the change in the price of oil. The second essay revisits the statistical specification of near-multicollinearity in the logistic regression model using the Probabilistic Reduction approach. We argue that the ceteris paribus clause invoked with near-multicollinearity is rather misleading. This assumption states that one can assess the impact of near-multicollinearity by holding the parameters of the logistic regression model constant, while examining the impact on their standard errors and t-ratios as the correlation (\rho) between the regressors increases. Using the Probabilistic Reduction approach, we derive the parameters (and related statisitics) of the logistic regression model and show that they are functions of \rho , indicating the ceteris paribus clause in the traditional account of near multicollinearity is unattainable. Monte carlo simulations in the paper confirm these findings. We also show that traditional near-multicollinearity diagnostics, such as the variance inflation factor and condition number can fail to detect near-multicollinearity. Overall, the paper finds that near-multicollinearity in the logistic model is highly variable and may not lead to the problems indicated by the traditional account. Therefore, unexpected, unreliable or unstable estimates and inferences should not be blamed on near-multicollinearity. Rather the modeler should return to economic theory or statistical respecification of their model to address these problems. The third essay examines the correlations between income inequality and economic growth using a panel of income distribution data for 3,109 counties of the U.S. We examine the non-spatial dynamic correlations between county inequality and growth using a System GMM approach, and find significant negative relationships between changes in inequality in one period and growth in the subsequent period. We show that this finding is robust across different sample sizes. We further argue that because the space-specific time-invariant variables that affect economic growth and inequality can differ significantly across counties, failure to incorporate spatial effects into a model of growth and inequality may lead to biased results.We assume that dependence among counties only arises from the disturbance process, hence the estimation of a spatial error model. Our results indicate that the bias in the parameter for inequality amounts to about 2.66 percent, while that for initial income amounts to about 21.51 percent.