Abstract
Data often comes from observations made at multiple points in time. Obtaining repeated observations on the same units allows the researcher to access a richer information set about observed units than would be possible with single observations and to map the evolution of the phenomenon over multiple periods for both individual units and overall as a trend. (For example, relationships between two variables may strengthen, weaken, or even disappear over time.) Longitudinal data can be gathered via survey instruments or archival databases that offer repeated measures on the same variables at different times.
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Notes
- 1.
The household, income and labour dynamics in Australia (Hilda) survey is maintained by the Melbourne institute and all editions and addenda are available at https://www.melbourneinstitute.com/hilda/
- 2.
Two examples of where the N is small compared to the data points are studies about changes in exchange rates (one currency over multiple quarters) and high-frequency data on stock prices (where observations come down to minutes or seconds).
- 3.
The STATA routine to estimate OLS with White-robust standard errors is regress y x, robust.
- 4.
The command to perform Fama-MacBeth [8] estimation is similar for both the FMB-cs and FMB-ts types of regressions. Mitchell Petersen of Northwestern University posts the codes for a series of popular software with which the FMB estimation can be performed at http://www.kellogg.northwestern.edu/faculty/petersen/htm/papers/se/se_programming.htm
- 5.
We refer readers to Petersen’s webpage (please check footnote 7 in Petersen’s webpage), which provides codes for the Newey-West routine.
- 6.
The routine in STATA to perform one-way clustering is simple: either (1) regress y x, cluster (id) if time-series correlation is a concern, or (2) regress y x, cluster (time) if cross-sectional correlation is the main problem.
- 7.
Petersen’s website offers a great deal of help in the estimation of OLS with two-way clustering. The routine is simple: cluster2 y x, fcluster(id) tcluster(time).
- 8.
To be consistent with a large body of literature in accounting and finance [3,4], we use the expression “pooled-OLS regression” but refer to all types of regression approaches (e.g., logit or probit, which are commonly used) wherein the regression model specified does not take into account the fact that the data have a longitudinal structure.
- 9.
FE models control for all of the time-invariant factors that affect the relationship of interest, whereas OLS takes into account only the covariates that are available. In this example, there are unobservable variables that affect X and Y that FE estimation takes into account but OLS ignores. Since FE estimation is always less biased than OLS, it is preferable.
- 10.
The key objective of the Breusch-Pagan test is understanding whether one cand discard the clustering that is due to the same individuals being included multiple times.
- 11.
For the sake of consistency, will refer to the STATA estimation routines.
- 12.
A note of caution when employing Hausman test: Results of the test are limited to the specific models fitted with FE and RE. They are not intended as a definitive response to whether we should employ FE or RE to answer the research question of interest. Changing the specification of FE or RE models by adding different covariates will lead to different results. It is good practice to re-estimate different models and compare them before making any statement or decisions.
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Mertens, W., Pugliese, A., Recker, J. (2017). Analyzing Longitudinal and Panel Data. In: Quantitative Data Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-42700-3_6
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