# Aenorm

## Econometrics 1: A personal reflection

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Disclaimer: The content provided below was compiled by a second-year student with a 9+ GPA. The article is a personal reflection, so the content may not be 100% accurate. However, the student has tried his best to provide the most accurate information possible with the main aim to share an overview of the course, instead of the details, with his fellow colleagues.

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Dear first year students, you may be wondering why you had to wait one and a half years, or half of the entire Econometrics program before actually studying a course of the same name: Econometrics 1. Having been a first-year student myself, I, too, have always pondered the same question. I had thought to myself, after victoriously defeating the “very simple” UvA matching, what could possibly be difficult about the OLS and the linear model. Boy, was I wrong!

Having completed this course recently, I realized there was much more to the linear model, and studying EC1 was initially quite confusing. In order to alleviate this confusion, I would like to share with you my experiences of the Econometrics 1 (EC1) course, and I hope that this will update what you should expect from this course and help you further orientate yourself to the program.

To start, the UvA matching was too simple to reflect EC1 as it only demonstrated how we can do some interpretation from the linear model. Moreover, I honestly did not remember anything from the first-year course “Introduction to Econometrics” before starting EC1, so I would say these courses are definitely not the necessary prerequisites to do well in EC1. The necessary tools that you need in EC1, however, lies in all the previous mathematics, statistics, and programming courses , but before we freak out, I can guarantee that we will mostly be applying results instead of focusing on proofs and theorems as in previous courses. In fact, EC1 is mostly geared towards application, and the course aims to provide you with a fairly complete picture of the linear model.

Even having said that, it goes without saying that UvA is still a research university, so if you want to score high in EC1, it is important that you delve into the underlying mathematics of what you learn.

Below, I have compiled a list of topics that you will encounter in EC1 and its respective prerequisites. I try to make this list as complete as possible, but I also try to organize it in a structurally comprehensive way, so that you get a good grip of the logic of this course. A nice study tip, in my opinion, is to use this list to track your knowledge as you go through the course. In addition, I personally found it to be quite handy for exam preparations.

Before I start, we keep in mind these abbreviations:

- Linear Algebra: Linalg
- Mathematics 4: M4
- Statistics: Stat

(Note that some of the material is new, so you don’t need to read every single bullet point in the list.)

- Part 1: The Classical Linear Regression Model (aka the CLRM)

Motivation: In this part, you truly go down to the very basics. By basics, I mean the base of what follows, and not that it is too easy. In my opinion, the most important step here is to remember the 7 assumptions of this model. This is crucial since most of all other topics that follow will be a relaxation of one of these assumptions, and you should be expecting to compare these variants with the classical (base) model.

Returning to the classical model, you should keep in mind the following key topics:

- Derivation of the OLS estimator: note that everything now is expressed in matrix notation ( Linalg : M2+3, multivariate differentiation: M4)
- Properties of the OLS estimator: Always ask yourself the whether the estimator satisfies the following properties:

+ Unbiasedness (Stat 1)

+ Consistency (Stat 3)

+ Efficiency* (Stat 3)

+ The derivation of the distribution of OLS estimator (keep in mind the relation with the error term)

+ Inference (Stat 2+3): significance of the effects of independent variables on the dependent variable. Watch out for the derivation of the t and F tests!

- *Guass-Markov theorem (M4): comparing which estimator has the lower variance, but here we’re comparing variance matrices so definiteness from M4 is required. Indeed, this is related to efficiency, and in fact, OLS estimator is the most efficient linear estimator.
- Frisch-Waugh theorem (Linalg): a quick way to find the formula for a subset of the estimators. In other words, rather than finding the estimator for every beta (recall the coefficients in the linear model), you are only interested in some of those estimators.
- Omitted variable bias & redundant variable problem: ask yourself what happens to the properties of the OLS estimator when we run into such problems. Note that Frisch-Waugh theorem is very useful here.

- Part 2: Problems encountered

Motivation: The CLRM sounds awesome and great due to its desirable properties. However, this is only true under all the 7 assumptions! In reality, satisfying all 7 is usually not the case. Thus, a treatment for possible violations of the assumptions is necessary. While studying one-by-one these violations, you should systematically analyze them in the following order:

+ Problem: what is the problem exactly?

+ Cause: what causes the problem? Note: rather than mechanically remembering the different situations that cause the problem, try to intuitively understand the reason why.

+ Consequences: What consequences does it have on the model? In other words, ask yourself whether the properties from part 1 above still hold for the OLS estimator.

+ Solution: Different techniques to fix the problem, so that the fixed model will have the desired properties of the classical model.

+ Detection: given your dataset, how would you detect the problem? This part is especially important since the tests that are used in detection will definitely be asked in the exam.

I won’t discuss in detail the problems since I do not want to spoil all the fun, but below is a list of which problems are discussed:

- Multicollinearity
- Non-normality
- Heteroskedasticity
- Autocorrelation
- Endogeneity (most difficult one in my opinion!)

Part 3: Additional topics

The two main additional topics are prediction and asymptotic analysis.

In prediction, the main difference is that we are now forecasting (predicting) the value of the dependent variable given new data rather than only fitting a model to our data. This is done via the fitted model we obtained from our original dataset. Since the model was not fitted using the new data, the residuals in forecasting is to be more variable compared to the residuals from those of the fitted model, and this will be mathematically apparent from an additional term in the variance of these residuals. On a side note, for inference, keep in mind how you can construct the prediction interval (and also note the difference from a confidence interval) of your predictions.

Last but not least, sometimes a really simple solution is to just increase the sample size, and through asymptotic properties (large sample properties) , we already obtain the desirable properties for our estimator. For example, if we don’t have normal distribution for the error, then with our asymptotic tools, this is certainly not a problem! In my opinion, this asymptotics part is quite difficult, but luckily for us, we are only expected to apply these results! However, to easily remember these results, it is handy to draw a parallel with what we’ve studied in Stat 3.

The above 3 parts has been a brief overview of the most important topics in EC1, and by thoroughly understanding these topics, you can be expected to do well in the course. In addition to the book recommended by the course, if you would like to go a bit deeper into the mathematics, then I would suggest the “Econometric analysis” book by William Greene. This book is also suggested to me by my tutorial teacher, and it is perhaps the book that every econometrician at the bachelor level will put underneath his or her pillow every night!

Apart from the exam, there will also be computer tests using R and Eviews. In R, you will be doing simulations to test the properties of the OLS estimator which further motivates the material you are studying. With a basic grip in programming and a solid understanding of Part 1, this should be a piece of cake! As for the Eviews test, a solid understanding of the detection tests and good interpretation skills of the model will give you an easy pass. If you are not familiar, Eviews is a statistical software that is very convenient for Econometrics. Eviews is first introduced to you in this course, so there is no need to worry about its technical usage. Following the computer classes, in my opinion, is enough to get you comfortable with the software.

To end, I hope that my experiences could help you get through this difficult course.