Confidence intervals provide a range of values where the true coefficient is likely to lie from "summary" of Introduction to Econometrics by Christopher Dougherty
Confidence intervals are a fundamental tool in econometrics that allows us to establish a range within which the true coefficient is likely to fall. This range provides a measure of uncertainty around the estimated coefficient, taking into account the variability inherent in sample data. The width of the confidence interval depends on the level of confidence chosen, with higher confidence levels resulting in wider intervals.
When estimating coefficients in econometric models, it is crucial to recognize that the estimated coefficient is just an approximation of the true coefficient. By constructing confidence intervals, we acknowledge this uncertainty and provide a more nuanced interpretation of our results. In other words, we are not claiming that the estimated coefficient is the exact value of the true coefficient, but rather that it is likely to fall within a certain range.
The process of constructing confidence intervals involves using statistical techniques to calculate the upper and lower bounds of the interval. These bounds are determined based on the standard error of the coefficient estimate, the sample size, and the chosen level of confidence. By specifying a confidence level, such as 95%, we can say that we are 95% confident that the true coefficient lies within the calculated interval.
Interpreting confidence intervals requires a clear understanding of probability and statistics. It is important to remember that the true coefficient is fixed and unknown, while the confidence interval is a range of values that captures the uncertainty surrounding our estimate. Therefore, when communicating our results, we should emphasize that the confidence interval provides a more informative and realistic assessment of the true coefficient than the point estimate alone.
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