## Notes on Time Series and Panel Time-Series Econometrics for Junior Researchers Using Stata

**NOTES ON TIME SERIES AND PANEL TIME-SERIES ECONOMETRICS **

**FOR JUNIOR RESEARCHERS USING STATA**

Author: **Phùng Thanh Bình**

(ptbinh@ueh.edu.vn)

In 2009, I had a chance to give a series of lectures on time series econometrics for Vietnam – The Netherlands Programme (VNP) for M.S. in Applied Economics. Those days, time series econometrics had rarely been recognized as a separate course in economics curriculum of the Vietnamese universities. It took me many months to read textbooks, reference manual and research articles, then prepared the first draft of the notes. Master theses and published articles using time series models have gradually increased since then. In early 2018, I received an email of a professor of macroeconomics and time series econometrics from Lucerne, Switzerland, and his detailed comments motivated me to revise the initial draft. It was then used as a supplementary reading for undergraduates of economics programmes at School of Economics, UEH1. In 2019, EfD (www.efd.vn) and VNP (www.vnp.edu.vn) offered me an opportunity to complete this first edition of Notes on Time Series and Panel Time-Series Econometrics for Junior Researchers Using Stata.

The main purpose of the notes is to explain the basic concepts and models in a simplest language for students and junior researchers in economics. I hope the notes is also a useful reference for other courses such as econometrics for finance, economic forecasting and data analysis for undergraduates, and applied econometrics for graduates. Whenever a term is clearly defined in a proper textbook, the notes will not rewrite. Instead, an exact reference is suggested for further reading the original source. Various examples, including datasets are borrowed from the econometrics textbooks, Stata time series/panel data reference manuals and research articles, but the hands-on instructions make the notes become completely different. Similar to other econometrics texts, the usage of mathematics and statistics is unavoidable, but I try to use the verbal approach and backward substitution method in order to help undergraduates in economics who do not have a strong mathematical background able to understand the statistical tests and models. In addition, the notes present all the statistical tests in a step-by-step manner, and tries to explain how each test can be carried out using Stata do-files. I think that this approach will make the study of time series and panel time-series econometrics more fascinating and more enjoyable.

I hope this series of notes is a useful complementary reading of very famous textbooks in time series and panel time-series econometrics at UEH & VNP. I also hope it can play a role as technical guidebook for junior researchers in economics, especially environmental economics within the EfD networks and Economy & Environment Partnership for Southeast Asia (EEPSEA).

Thank you very much for reading the notes. If you find any errors or typos, please let me know by e-mailing me at the below address.

Phùng Thanh Bình

ptbinh@ueh.edu.vn

1. Introduction | 1 |

2. The structure of economic data | 3 |

3. Data management in Stata | 6 |

4. The nature of time series | 18 |

5. Stationary stochastic process | 20 |

6. Nonstationary stochastic process | 42 |

7. The spurious regressions | 53 |

8. Testing for non-stationarity | 58 |

9. Short-run and long-run relationships | 98 |

10. Cointegration and error correction model | 103 |

11. Vector autoregressive models | 163 |

12. Vector error correction models | 182 |

13. Causality analysis | 231 |

14. Panel time-series models | 258 |

15. Panel vector autoregression | 314 |

Concluding remarks | 320 |

References: | 324 |

Appendix A: Partial regression coefficients | iv |

Appendix B: ARIMA models | vii |

Appendix C: ARDL and EC models | xxi |

Appendix D: An explanation of ADF test equations | xvi |

Appendix E: Impulse response function | xl |

I write this series of notes on time series and panel time-series econometrics for my students in Applied Economics at the University of Economics Ho Chi Minh City (UEH). Since most economics students in Vietnam are likely to have problems with English as a second language, mathematics background, and especially access to updated resources for self-study, this series hopefully has some helpful contributions. The aim is to help my students understand key concepts of time series and panel time-series econometrics through hands-on examples in Stata. To its end, they are able to read time-series and panel time-series data articles. Moreover, I also expect that they will have a sufficient interest, and write a thesis in this field. As the time this series of lecture notes is preparing, I believe that the Vietnam time series data is long enough to conduct such a study. In addition, large-N-large-T panel data2 may be also good sources for doing empirical researches in macroeconomics.

This is just a concise summary of the body of knowledge in time series and panel time-series data econometrics according to my own limited understanding. Obviously, it has not much scientific value for citations because many parts of the text are cited from the original sources of references. Researches using bivariate models are not strongly appreciated by prestigious academic journal’s editors3 and university’s supervisors as well. Thus, multivariate time series with structural breaks and panel time-series models should be paid special attention. As a junior researcher, you must be independently and fully responsible for your own choice of the research project. My advice is that you should firstly start with the research problem of interest, not with the data availability and the statistical techniques. Therefore, you just use the model whenever you really need and crystal clearly understand it.

Some topics such as ordinary least squares regression with stationary time series, modelling volatility clustering, seemingly unrelated regression equations, nonlinear time series modelling such as switching, threshold autoregression and smooth transition autoregression, nonlinear autoregressive distributed lag and time-varying coefficient models, and traditional panel data models are beyond the scope of this notes. You can find them in advanced econometrics textbooks, journal articles, and updated Stata reference manuals. After studying this series of notes with hands-on practice in Stata (at least version 15), you should be able to basically understand the following topics in time series and panel time-series econometrics:

- The structure of economic data
- Data management in Stata
- The nature of time series
- The concepts of stationarity, non-stationarity, autoregressive (AR), moving average (MA), and random walk processes
- ARMA and ARIMA models
- The concept of spurious regression
- Tests for non-stationarity (ADF, DF-GLS, PP)
- Tests for stationarity (KPSS)
- Tests for non-stationarity with structural breaks (Zivot-Andrews, Perron-Volgelsang, Clemente-Montanes-Reyes)
- The short-run dynamics and long-run relationship
- Autoregressive distributed lag (ARDL) model
- Error-correction (EC) models
- Tests for cointegration: Residual-based approach (AEG, CRDW)
- Tests for cointegration: Bounds testing approach (ARDL bounds test)
- Test for cointegration: Gregory and Hansen approach
- Estimation of long-run parameters (fully-modified OLS – FMOLS, dynamic OLS – DOLS, canonical cointegrating regression – CCR)
- Vector autoregressive (VAR) models
- Impulse-response function and forecast-error variance decomposition
- Tests for cointegration: Johansen tests (multiple equation approach)
- Vector error correction (VEC) models
- Granger causality analysis (standard, augmented versions and Toda-Yamamoto)
- Panel time-series analysis (cross-sectional dependence tests, slope homogeneity tests, panel unit root tests, panel cointegration tests, estimation of long-run parameters (e.g., FMOLS and DOLS methods), panel ARDL models, and panel Granger causality analysis)
- Panel vector autoregression models (model selection, estimation, impulse-response function, and Granger causality analysis).

To get started, you should be familiar with basic econometrics and statistics4. Searching for research articles, I realize that time series and panel time-series data analyses have been widely applied in fields of macroeconomics, financial economics, and especially energy economics. Therefore, time series and panel time-series models in these notes just equip basic tools for you to do empirical researches, specialized knowledge from literature review is indeed a key.

Furthermore, a good way to use these notes is to replicate the do-file examples with Stata, and read the original articles that are used to illustrate the respective tests.

*Chương trình Việt Nam – Hà Lan (VNP) là chương trình đào tạo Thạc Sĩ Kinh Tế MAE, Thạc Sĩ Bằng Đôi DDP và Tiến Sĩ Liên Kết JDP hợp tác giữa Trường Đại Học Kinh Tế Tp.HCM (UEH) và Viện ISS thuộc Đại Học Erasmus Rotterdam, Hà Lan*