Three essays in econometrics

This dissertation comprises three essays on econometric methodologies. The first essay investigates the asymptotic properties of the fixed effects (FE) estimator of the autoregressive conditional heteroskedastic (ARCH) model with individual-specific effects using panel data. I establish the consistency and asymptotic normality of the FE-ARCH estimator in a large-N-and- T asymptotic framework and show that its asymptotic bias is Op(1/T). I also propose a procedure to examine whether or not the ARCH effects exist. The test statistic has a chi2 (1) limiting distribution, and simulations show that it has an accurate finite sample size and satisfactory power. The proposed test and estimator are used to detect and estimate the ARCH effects in individual earnings using the PSID data. The ARCH(1) effect is statistically significant in earnings dynamics.;The second essay considers how to improve the accuracy of the kernel estimator of long run covariance matrices in time series analysis. Despite its asymptotic efficiency, the truncated flat (TF) kernel estimator of long-run covariance matrices is seldom used because the TF estimate is not always positive semidefinite. We propose estimators that are always positive semidefinite, yet inherit the asymptotic efficiency of the TF estimator and allow for a non-integer bandwidth. We also propose a bandwidth selection method for the proposed estimators, which keeps them asymptotically efficient relative to other familiar kernel estimators. Simulations show that the proposed estimators outperform existing kernel estimators in terms of the MSE.;The third essay proposes a robust method to examine if the parameters of a panel data model are constant across individuals in the population. I utilize the L-moment to measure the dispersion of the estimates to propose a test, which is robust against outlying observations. The test statistic asymptotically has the standard normal distribution under the null hypothesis, as long as some mild conditions are met. My simulations show that this test delivers a more accurate size than existing tests in panel data models. The proposed test is also applied to examine whether or not the rates of convergence of economic growth are the same across countries.