Residuals are the differences between observed values and the values predicted by a model, serving as a diagnostic tool to assess the model's accuracy. Analyzing residuals helps identify patterns or biases in the model, indicating areas where the model may be improved or where assumptions may be violated.
Variance is a statistical measure that quantifies the dispersion of a set of data points around their mean, providing insight into the degree of spread in the dataset. A higher variance indicates that the data points are more spread out from the mean, while a lower variance suggests they are closer to the mean.
Hansen's J-test is a statistical test used to assess the validity of instrumental variables in econometric models, specifically testing the overidentifying restrictions. It evaluates whether the instruments are uncorrelated with the error term, ensuring that they are valid and exogenous for reliable parameter estimation.
Overidentifying restrictions occur in econometric models when there are more instruments than endogenous variables to be estimated, allowing for a test of the model's validity. This situation enables the use of statistical tests, such as the Sargan or Hansen test, to evaluate whether the instruments used are appropriate and uncorrelated with the error term, thereby ensuring the model's reliability.
The Hansen Test, also known as the J-test, is a statistical method used to assess the validity of instruments in econometric models, particularly in the context of instrumental variable regression. It helps determine whether the instruments are uncorrelated with the error term, ensuring that the model is correctly specified and the instruments are valid.
The Spatial Error Model is used in spatial econometrics to account for spatial autocorrelation in the error terms of a regression model, which can lead to inefficient and biased estimates if ignored. It extends traditional regression models by incorporating a spatially lagged error term, allowing for more accurate inferences in the presence of spatial dependence.