Econometrics using Stata
Econometrics is a branch of economics that involves applying mathematical and statistical models to create theories that quantify an economic phenomenon. Since drawing inferences from economic data deals with complex statistical techniques and formulas, econometrists use various data analysis tools to guarantee the best results. Stata is one of the statistical programs used for analyzing economic data. With this program, econometrists can analyze and manage big data and produce graphical visualization of it for easier and effective decision-making.
GMM is short for the Generalized Method of Moments, a framework for creating estimators. A GMM estimator uses assumptions about a moment of a variable to create an objective function. It combines a given set of economic data with the data contained in a population moment condition to create estimates of unknown parameters of an economic model. GMM estimates make the conditions of a sample moment as true as possible, a technique implemented by reducing the objective function.
Also known as the design of experiments, experimental design is simply how researches or experiments are planned to provide objective and valid results. Ideally, it should:
- Describe how the participants will be allocated to various experimental groups
- Eliminate or reduce confounding variables that can produce alternative results for the research being carried out
- Allow the researcher to understand and make inferences about the correlation between dependent and independent variables
- Minimize variability so that researchers find it easier to identify differences between various experiment outcomes.
An experimental design comprises five parts; questions, observations, methods, hypotheses, and results.
Ordinary Least Squares, or simply OLS, is a technique of approximating unknown parameters or values in linear regression models. You can only be sure that you are getting the best estimates from your regression model if the model itself satisfies all the OLS assumptions for regression models. Linear regression is a powerful statistical analysis technique that allows researchers to analyze multiple variables simultaneously. If your regression model does not meet the ordinary least squares assumptions, then its results cannot be trusted.
Maximum likelihood estimation
Maximum likelihood estimation is a statistical technique for determining the parameter values of a model. These values are identified such that they increase the probability (likelihood) that the process the model simulates describes the information or data that was actually observed. This simply means that for maximum likelihood estimation to be implemented, one must assume a model and derive the likelihood function for the model data. Once one has derived the likelihood function, estimating the maximum likelihood becomes a very simple optimization process.
Random effects are statical models in which the parameters (effects) that describe systematic components in the model demonstrate some kind of a random variation. Ideally, statistical models exhibit variation in variables in terms of unsystematic and systematic components. Some models contain fixed effects and these are known as fixed-effects models. Models that contain both random and fixed effects may be referred to as mixed models or mixed-effects models. Randomness in models is usually caused by sampling units randomly while collecting data.