The Econometrics Cheat Sheet Project

Econometrics cheat sheets created using $\LaTeX$:

• Econometrics Cheat Sheet: Basic concepts, OLS assumptions, properties, interpretation, error measuremets, hypothesis testing, confidence intervals, dummy variables, structural change, popular OLS problems and more!
• Time Series Cheat Sheet: Time series components, seasonality, auto-correlation, stationarity, cointegration and heterocedasticity on time series.
• Additional Cheat Sheet: OLS matrix notation, variable omission, proxy and instrumental variables, TSLS, information criterias, hypothesis testing (+), functional form test, logistic regression, statistical definitions, VAR, SVAR, VECM.

💡 I am currently pursuing a PhD 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 national/international universities are welcome! 🚀

🚩 LinkedIn. Please, send me a message when connecting or I will ignore the request.

🌐 Do you want to translate any of these cheat sheets to your language? Open an issue and I will provide instructions.

🖨️ If you want to print them two-sided, select the Flip on Short Edge option on your printer.

Download links

Econometrics	PDF	TeX
English 🇬🇧	CS-24.11	CS-24.11
Spanish 🇪🇸	CS-24.11	CS-24.11

Time Series	PDF	TeX
English 🇬🇧	TS-24.11	TS-24.11
Spanish 🇪🇸	TS-24.11	TS-24.11

Additional	PDF	TeX
English 🇬🇧	ADD-24.11	ADD-24.11
Spanish 🇪🇸	ADD-24.11	ADD-24.11

Complete set (PDF and TeX, all languages): ZIP

Frequently Asked Questions (FAQ)

What does $\mathrm{resid}$ $x_j$ mean?

Those are the residuals from a OLS regression between $x_j$ and all the other $x$ 's.

Why is $\beta_0$ the constant term? My reference manual / professor's definition of the econometric model is different.

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:

$$y_i = \beta_0 + \beta_1 x_{1i} + ... + \beta_k x_{ki} + u_i \quad (1)$$

There are others that refer to that same econometric model as:

$$y_i = \beta_1 + \beta_2 x_{2i} + ... + \beta_k x_{Ki} + u_i \quad (2)$$

And others refer as:

$$y_i = \alpha + \beta_1 x_{1i} + ... + \beta_k x_{ki} + u_i \quad (3)$$

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:

$$(1, 3) \quad \overline{R}^2 = 1 - \frac{n - 1}{n - k - 1} \cdot (1 - R^2)$$

$$(2) \quad \overline{R}^2 = 1 - \frac{n - 1}{n - (K - 1) - 1} \cdot (1 - R^2) =$$

$$= 1 - \frac{n - 1}{n - K} \cdot (1 - R^2)$$

Where is the non matrix version of the standard error of the $\hat{\beta}$ 's?

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:

$$\mathrm{se}(\hat{\beta}_j)=\sqrt{\frac{\hat{\sigma}^2_u}{\mathrm{SST}_j \cdot (1-R^2_j)}} \quad , \quad j=1,...,k$$

Why don't they have 2 or 4 pages each?

Each of them are 3 pages long, and there are no plans on changing that for the time being.

I understand that if you print them two-sided, the second page ends up with an empty side. Consider this as an space to take your own notes 😄.

Currently, I am very comfortable with the content and font size used. Also, all cheat cheets are made in a way that you can combine any page of one with any page of another or skip them.

Resources

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] Pfaff, B. (2011). Analysis of integrated and cointegrated time series with R. New York: Springer.

[6] Ruiz-Maya, L., & Pliego, F. J. M. (2004). Fundamentos de inferencia estadística. AC.

[7] Stock, J. H., & Watson, M. W. (2012). Introduction to econometrics. New York: Pearson.

[8] Wooldridge, J. M. (2015). Introductory econometrics: A modern approach. Cengage learning.

Contributions

• Reddit user _bheg_ - Pointed out about the importance of including strong and weak exogeneity and their consequences on bias and consistency properties of OLS.

Support the project

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!