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Multiple econometrics cheat sheets with a complete and summarize review going from the basics of an econometric model to the solution of the most popular problems.
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Go to file💡 I am currently pursuing a PhD in macroeconomics and econometrics at Universidad Rey Juan Carlos (Madrid, Spain). Also, I am a researcher and professor at the same institution. Collaboration proposals and academic stays offers in other universities (national and international) are welcome and can help me a lot in my career! 🚀
❗ My LinkedIn. Please, send me a message when connecting or I will ignore the request.
Econometrics Cheat Sheet. Current version: CS-24.5.2
| PDF file | TeX file | |
|---|---|---|
| English 🇬🇧 | en.pdf | en.tex |
| Spanish 🇪🇸 | es.pdf | es.tex |
Time Series Cheat Sheet. Current version: TS-24.8
| PDF file | TeX file | |
|---|---|---|
| English 🇬🇧 | en.pdf | en.tex |
| Spanish 🇪🇸 | es.pdf | es.tex |
Additional Cheat Sheet. Current version: ADD-24.5.3
| PDF file | TeX file | |
|---|---|---|
| English 🇬🇧 | en.pdf | en.tex |
| Spanish 🇪🇸 | es.pdf | es.tex |
Those are the residuals from a OLS regression between $x_j$ and all the other $x$ 's.
There is some debate about the correct way to name the coefficients, their sub-index and the sub-index of the variables of a model. The naming could have an impact on how some statistics like the adjusted R-squared or some tests like the F test are written.
For example, while some econometricians write the multiple regression model with a constant term like this:
$$y_i = \beta_0 + \beta_1 x_ + . + \beta_k x_ + u_i \quad (1)$$
There are others that refer to that same econometric model as:
$$y_i = \beta_1 + \beta_2 x_ + . + \beta_k x_ + u_i \quad (2)$$
And others refer as:
$$y_i = \alpha + \beta_1 x_ + . + \beta_k x_ + u_i \quad (3)$$
All the above are equally valid representations of the multiple regression model. In the specification $(1)$ , $\beta_0$ represents the constant term, while in specifications $(2)$ and $(3)$ , it is represented by $\beta_1$ and $\alpha$ , respectively.
In this project, the main specification used is the first $(1)$ , so we can say that there are $k$ independent variables and $k + 1$ coefficients (including the constant term). The same could be said for the specification $(3)$ , that it is used punctually in the project. There are no differences in the statistics and tests formula definition between specifications $(1)$ and $(3)$ .
The specification $(2)$ , is different from the rest, since $K \neq k$ . In this specification, it could be said that there are $K - 1$ independent variables and $K$ coefficients (including the constant term).
For specification $(2)$ users, not everything is lost. There is a relation between these three specifications: $K = k + 1$ , so $k = K - 1$ . This way, a "translation" between formulas for different representations is possible (by the user). For example, the adjusted R-squared:
$$(1, 3) \quad \overline^2 = 1 - \frac \cdot (1 - R^2)$$
$$(2) \quad \overline^2 = 1 - \frac \cdot (1 - R^2) =$$
For space reasons, the version included in the cheatsheet is the matricial one. It is perfectly valid and equal to the non matrix version.
The non matrix version:
In addition to the notes taken from the Degree in Economics and Master in Modern Economic Analysis by Universidad Rey Juan Carlos, and the Master in Applied Statistics by Máxima Formación and Universidad Nebrija, the books used:
[1] Baltagi, B. H. (2011). Econometrics. New York: springer.
[2] Gujarati, D. N., Porter, D. C., & Gunasekar, S. (2012). Basic econometrics. Tata McGraw-Hill Education.
[3] James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning. New York: springer.
[4] Lütkepohl, H., & Krätzig, M. (Eds.). (2004). Applied Time Series Econometrics. Cambridge: Cambridge University Press.
[5] Ruiz-Maya, L., & Pliego, F. J. M. (2004). Fundamentos de inferencia estadística. AC.
[6] Stock, J. H., & Watson, M. W. (2012). Introduction to econometrics. New York: Pearson.
[7] Wooldridge, J. M. (2015). Introductory econometrics: A modern approach. Cengage learning.
The first way to help the project is to directly support the authors of the manuals that are included in the resources section (for example, by buying their works). Each and every one of the authors of the manuals are wonderful minds who have contributed a lot to econometrics and statistics.
Another great way to support the project is by sharing it and ⭐ it!
Multiple econometrics cheat sheets with a complete and summarize review going from the basics of an econometric model to the solution of the most popular problems.