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Leobardo Diosdado David Galaz
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“Longitudinal data analysis represents a marriage of regression and time series analysis.” Source: Edward Frees (http://tinyurl.com/hw76x5a)
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We live in a world with dynamic relationships. Panel data allows us to model the uniqueness of subjects. With long data we can see the effect of an intervention on an observational unit. Drawback: attrition. Source: Edward Frees (http://tinyurl.com/hw76x5a)
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OLS is no longer BLUE. It’s not efficient. Standard errors are no longer appropriate. Why does this happen?
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What does the i and t subscript represent? What happens if we use OLS?
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Panel data is also known as longitudinal data Observations for multiple individuals that were observed at two or more time periods i = individuals t = time The data comes from the National Longitudinal Survey of Youth 1997 Balanced panel that includes observations for each individual and each time period
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idtFinancial AssetsDebt Steve200015009000 Steve2005500010000 Steve20101500030000 Douglas20001200300 Douglas2005350022500 Douglas2010700014000
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The pooled OLS estimator ignores the panel structure of the data This approach can be used when the group to be pooled are relatively similar. Ordinary Least Squares can be used on the concatenated groups. Large standard errors (small T-Stats), could be a warning that the groups are not homogenous Advanced Models like Random Effects Model may be more suitable.
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Measure differences in the intercepts for each group “Least Squares Dummy Variables” and is essentially an OLS model with dummy variables to control for group differences Constant slopes (coefficients ) for independent variable Constant variance across groups The individual-specific effect is a random variable that is allowed to be correlated with the independent variables Related effects explicitly states that the absence of the unrelated assumption that the individual specific effect is a random variable that is not correlated with any of the independent variables of past, current and future observation for the same individual Effect variance explicitly the absence of that constant variance of the individual specific effect Identifiability assumes the time-varying independent variable are not perfectly collinear and cannot include a constant or any time invariant variables
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Leverages the differences in the variance of error term to group models together, assuming constant intercept and slopes Radom models are more complex to estimate compared to Fixed Effects Models The individual- specific effect is random variable that is uncorrelated with the independent variables Unrelated effects assumes that the individual specific effect is a random variable that is not correlated with any of the independent variables of past, current and future observation for the same individual Effect variance is assumes that constant variance of the individual specific effect Identifiability assumes that the regressors have a non-zero variance and not too many extreme values
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Data collection issues that occur can include non-response in micro panels and cross-country dependency in marco panels. Attrition refers to the gradual erosion of responses from participants over time created an unbalanced panel Selection bia could when a rule other than simple random sampling is used to select observational units The limitations include problems in the design, data collection, and management of the data panel surveys Measurement errors that may arise due to unclear question, memory error, misrecordings and interviewer effects
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Katchova, A. (2013). Panel Data Models. Retrieved from Econometrics Academy: https://docs.google.com/file/d/0BwogTI8d6EEiX2ZGeTRObjktOVk/edit?pref=2&p li=1 McManus, P. A. (2011, October). Indiana.edu. Retrieved from Indiana.edu: http://www.indiana.edu/~wim/docs/10_7_2011_slides.pdf Stock, J. H., & Watson, M. W. (2007). Introduction to Econometrics. Boston: Pearson. Torres-Reyna, O. (2010, Fall). Princeton.edu. Retrieved from Princeton.edu: http://www.princeton.edu/~otorres/Panel101R.pdf Smart. F., (2013). EconBS, Econometrics By Simulation: Simulations and Analysis github.com/EconometricsBySimulation. http://www.econometricsbysimulation.com/2013/12/unobserved-effects-with- panel-data.html
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