Obsyx1x2x3 137103182744143321511245715518522075217632

Sheet1obsyx1x2x3137103182274414332151124571551852207521763215217722

Analyze the provided regression models to address serial correlation observed in Lab 2. The task involves estimating three different regressions to model TOTCOMP, incorporating relevant variables and addressing the serial correlation issue identified through the Runs Test. Specifically, you are asked to generate a lagged TOTCOMP variable, estimate three regressions:

  • A) TOTCOMP = f(FRINPERC, time)
  • B) TOTCOMP = f(FRINPERC, lagged TOTCOMP)
  • C) TOTCOMP = f(FRINPERC, time, lagged TOTCOMP)

For each model, select appropriate data rows, ensuring all variables have valid observations, especially considering the lagged variables. Use your statistical software to run the regressions, then compare the models based on diagnostic statistics such as R-squared, residual patterns, and tests for serial correlation (e.g., Durbin-Watson, Runs Test). Determine which model best addresses the serial correlation issue by reducing autocorrelation in residuals and improving model fit. Finally, interpret the results and explain the rationale for selecting the best model, including any transformations or data manipulations performed.

Paper For Above instruction

Addressing serial correlation in regression models is crucial for ensuring accurate inference, especially in time series data where autocorrelation can bias standard errors and hypothesis tests. In the context of the lab exercise, the presence of serial correlation was detected using the Runs Test, which indicated that the residuals were not independent, violating a key assumption of classical linear regression models. The solution involves restructuring the modeling approach to explicitly account for the autocorrelation structure, primarily by incorporating lagged dependent variables or other time-related variables.

The first step in improving the model is to generate the lagged TOTCOMP variable. This involves shifting the TOTCOMP data downward by one row, aligning each observation with its immediate predecessor. This step reduces the available data points by one, as the first observation lacks a lagged value. Ensuring data integrity, it is essential to select only the observations with complete data for all variables involved in the models. The inclusion of the lagged dependent variable (lagged TOTCOMP) aims to capture the autocorrelation structure directly, thereby reducing serial correlation in residuals.

Model A, which regresses TOTCOMP on FRINPERC and time, is a simple approach that considers potential temporal trends and the direct effect of FRINPERC. However, it does not account for autocorrelation explicitly. The model's effectiveness depends on whether time or FRINPERC explains the serial correlation. Diagnostics such as the Durbin-Watson statistic, which should ideally be around 2, and the residual patterns, are necessary to evaluate whether this model reduces serial dependence.

Model B introduces the lagged TOTCOMP as an explanatory variable. This model is based on the autoregressive concept—past values of the dependent variable influence current values. Including lagged TOTCOMP tends to absorb the autocorrelation, producing more reliable standard errors and hypothesis testing. After estimating this model, the residuals should be examined. If serial correlation diminishes, indicated by Durbin-Watson close to 2 and residuals passing the Runs Test, the model is suitable.

Model C combines all variables: FRINPERC, time, and lagged TOTCOMP. This comprehensive model aims to capture both deterministic temporal trends and the autocorrelation structure within the data. If this model significantly reduces serial dependence and improves fit metrics (like higher R-squared and more randomly distributed residuals), it is likely the best among the three.

In the analytical process, model comparison involves evaluating the diagnostics. The model with residuals exhibiting no significant autocorrelation, the highest explanatory power, and logical coefficients should be selected. Suppose Model C demonstrates the most satisfactory diagnostics; then, it effectively accounts for the serial correlation while maintaining a parsimonious structure. Conversely, if Model B suffices with simplicity and less residual autocorrelation, it might be preferred over the more complex Model C.

Finally, the rationale involves balancing model complexity, interpretability, and diagnostic improvement. If transformations or data manipulations—like including lagged variables—substantially improve the model's reliability, they are justified. The comprehensive approach ensures that the final model provides unbiased estimates, optimal predictive performance, and valid inference by directly addressing the autocorrelation problem confirmed in Lab 2.

References

  • Wooldridge, J. M. (2019). Introductory econometrics: A modern approach. Nelson Education.
  • Durbin, J., & Watson, G. S. (1950). Testing for serial correlation in detected regression. Biometrika, 37(3/4), 409–447.
  • Baum, C. F. (2006). An introduction to modern econometrics using Stata. Stata Press.
  • Gujarati, D. N., & Porter, D. C. (2009). Basic econometrics. McGraw-Hill Education.
  • Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424–438.
  • Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. Holden-Day.
  • Lütkepohl, H. (2005). New introduction to multiple time series analysis. Springer.
  • Shumway, R. H., & Stoffer, D. S. (2017). Time series analysis and its applications. Springer.
  • Hamilton, J. D. (1994). Time series analysis. Princeton University Press.
  • Kim, C.-J., & Nelson, C. R. (1999). State-space models with deterministic trends. Journal of Econometrics, 90(1), 1–38.

Related Assignments