I’m currently undergraduate student studying economics and mathematics. I took econometric class and mathematical statistics class last semester. So during the vacation, I decided to study econometrics more because I’m planning to do Phd in economics in the future and I thought it will be helpful. But, come to think of it, I feel like I made a wrong choice. I don’t know what the exact reason is, but whenever I study econometrics, I find that I’m just ‘reading’ a book. And I think that’s because of my lack of statistics and other math ability. So now I’m considering to study mathematical statistics more deeply and other maths, and postpone studying econometrics. One of my professor said that it’s fine not to study econometrics now deeply because I will study during Phd course, but it’s crucial to fully study and understand maths, statistics before Phd. What do you think?
If you are looking to understand how Econometrics are and should be grounded in Statistics, read Aris Spanos "Probability Theory and Statistical Inference: Econometric Modeling with Observational Data". Be prepared for a bit of a shock.
As for Mathematical Statistics, they are a difficult subject, and there is no magical textbook that has ever succeeded in making them "accessible".
A really good textbook for introductory econometrics for me was Essentials of Econometrics by Damodar Gujarati. The problem is, it is quite old (mine was from 1992), so it does not even mention some of the more recent breakthroughs like cointegration analysis. But it really gets you into the subject.
I would say that for me at least, study of econometrics looks relatively useful and interesting precisely because I have moderate knowledge of different economic theories, so I know how and where to put those methods to good use (to test wether models based on one or other theory fits the real world data better).
Other than that, stats and math is also important to grasp the deeper aspects of econometric methods.
Econometrics in undergraduate curriculum is often presented as a black box. "Run these regressions in R and check the results". If you really want to understand what you're doing with econometrics, then yes you should approach it from the bottom up. Learn the math so you can understand the black boxes.
Econometrics at the PhD level requires a few specific skills you should really cultivate. First, extensive undergraduate training in Probability Theory and Mathematical Statistics is essential. Applied statistics courses are not going to help you because they take the underlying econometrics as given and just tell you how to push the buttons. You should take Linear Algebra and study it as hard as you can- I just did the bare minimum in LA and I really, really regretted it. You want to be able to eat,sleep, and breathe:
- Matricies and Matrix Operations, especially rank and determinant conditions, and inversion.
- Linear Projection- understand the geometry of this thoroughly, not just in the tiny little bites you'll get in most books. You should be extremely comfortable with projections and orthogonal complements.
- Summation Operators- you should feel extremely comfortable manipulating summations, breaking things into double summations, etc.
Econometrics I usually consists of a very thorough coverage of linear techniques (linear in parameters, that is). Metrics II generally goes into MLE, Logit, Probit, and other more advanced techniques. You will also have a graduate stat course prior to this, which covers much of the same material as Prob Theory at a higher level. To get a taste of this, my stats class used "Statistical Inference" by Casella and Berger, and my Econometrics class used Bruce Hansen's Econometrics text, available on his site here: https://www.ssc.wisc.edu/~bhansen/econometrics/
A word of advice- self study is only ever effective toward a specific end. You need a fire under your proverbial behind. I taught myself a lot of convex analysis- but only after I realized I needed it to prove something in my first project. Your brain is designed to forget that which is not used. If you really want to learn it, you should do each and every practice problem, and be hard on yourself about getting them wrong- a live and let live attitude of "it doesn't matter really because this isn't a class" tells your brain not to remember.