<p>The <strong>Linear algebra</strong> part should not worry you, it is just basic linear algebra plus familiarizing yourself a bit with <a href="http://en.wikipedia.org/wiki/Matrix_calculus">differentiation of vectors and matrices</a> (and for some chapters, visualizing the <a href="http://en.wikipedia.org/wiki/Kronecker_product">Kronecker product</a>).  Hayashi goes some length into writing out explicitly large matrices, which is virtually with no-precedent (see eg. pages 267, or 288), something that eventually facilitates understanding -as long as you don't back out from a matrix half a page large, but you really <em>look</em> at it.</p>

<p>What you should really go slow over upon is Hayashi's <strong>notation</strong>, which is non-standard in many places. So <em>don't expect to understand through familiar notation</em>. Be prepared for that and "read" carefully every symbol and its role. Many people's discomfort with this book is due to the notation, but they don't realize it.  </p>

<p>As for the <strong>Statistics part</strong>: In Econometrics, since we deal almost always with non-experimental, observational data, a large part of Statistics (originating usually in Biostatistics) do not really enter (our) picture. For example, apart from proving that under certain conditions the OLS estimator is best linear unbiased, you won't see much regarding the issues of minimum variance estimation or sufficient statistics. We don't even discuss the Exponential Family of distributions and the concept of Generalized Linear Models. Also, in statistical Hypothesis testing the Fisherian spirit prevails (oozing through the Neyman-Pearson apparatus), meaning, among other things, that issues like the "power of the test" are not so often considered.</p>

<p>Moreover "frequentist Econometrics", which is what Hayashi presents, are considerably lighter than Bayesian Econometrics in terms of the Algebra of Random Variables and probability theory.</p>

<p>What really matters is a good familiarity with <em>basic</em> Asymptotic Theory and Stochastic Processes (for the Time Series part). Although Hayashi in most cases just states results, providing references for the proofs, nevertheless it would be good to feel comfortable with asymptotic results and properties, because in most cases, <em>it will be all your estimators will possess</em>. For this part, I will once more advocate A. Spanos' book, <a href="http://www.cambridge.org/lt/academic/subjects/economics/econometrics-statistics-and-mathematical-economics/probability-theory-and-statistical-inference-econometric-modeling-observational-data">Probability Theory and Statistical Inference - Econometric Modeling with Observational Data</a>. It is a valuable book, Hayashi or not Hayashi. It is Statistics with the Econometrics graduate student in mind.  </p>

<p>In case you want some more specific Time Series material, Hamilton's <a href="http://press.princeton.edu/titles/5386.html">Time Series Analysis</a> remains a standard reference.</p>

<p>Finally, regarding <strong>Unit-root Econometrics and Co-Integration</strong>, the subject is inherently advanced, and I think Hayashi has done a good job in collecting and presenting the very basics.</p>

CC BY-SA 3.0
2014-12-20T19:58:19.603Z
The Spanos books looks like a great intro to that material.
dimitriy
CC BY-SA 3.0
2014-12-20T20:04:08.070Z
@DimitriyV.Masterov I am glad to hear it.
Alecos Papadopoulos
CC BY-SA 3.0
2014-12-19T21:05:39.197Z
2014-12-19T21:05:39.197Z
Alecos Papadopoulos
<p>What statistics and linear algebra book do I need before reading <a href="http://fhayashi.fc2web.com/hayashi_econometrics.htm" rel="noreferrer">Hayashi's Econometrics?</a></p>

<p>Basics linear algebra book seems too simple for the linear algebra part, and 
Casealla's statistical inference is missing out detail/too basic for the statistical part</p>

CC BY-SA 3.0
2014-12-19T19:58:13.610Z
Are you diving into the whole book, or there are specific chapters you will fight it out with?
Alecos Papadopoulos
CC BY-SA 3.0
2014-12-19T20:12:17.413Z
@AlecosPapadopoulos - The whole book...
Victor
CC BY-SA 3.0
2014-12-19T20:20:35.040Z
Ok. Now, do you mean that you have no statistical/econometrics background _at all_? And if you do, please include it in the answer, siting books you have dealt with in the past, courses you have taken...
Alecos Papadopoulos
CC BY-SA 3.0
2014-12-19T20:21:44.403Z
@AlecosPapadopoulos - Undergrad statistics and linear algebra.
Victor
CC BY-SA 3.0
2014-12-19T22:24:26.610Z
If you have no econometrics...I recommend Greene as a "sort of" reference while reading Hayashi. Although Hayashi's linear algebra/stats is self-contained, it just light on explanation (and Greene is a dictionary). Casealla's inference is not really "too basic", it is just not appropriate for the (very specific - typically multivariate) statistical techniques of econometrics.
Rusan Kax
CC BY-SA 3.0
2014-12-21T07:29:49.777Z
I worked my way through this book prior to a ph.d in econ.  It helped with the basics and got me understanding how linear algebra is applied in economics.  However, if economics is not your field I don't know how valuable it would be.  http://www.springer.com/economics/game+theory/book/978-3-642-20569-9   I would also recommend Wooldridge Introductory Economics when reading through Hayashi.  It will be a good reference to have for the basics.
Amstell
<econometrics><reference-request>
What statistics and linear algebra book do i need before reading Hayashi's econometrics
Victor
# What statistics and linear algebra book do i need before reading Hayashi's econometrics

(Asked by: username_0 on 2014-12-19)

What statistics and linear algebra book do I need before reading [Hayashi's Econometrics?](http://fhayashi.fc2web.com/hayashi_econometrics.htm)

Basics linear algebra book seems too simple for the linear algebra part, and
Casealla's statistical inference is missing out detail/too basic for the statistical part

**Tags:** econometrics, reference-request

> **Comments:**
> **username_1**: Are you diving into the whole book, or there are specific chapters you will fight it out with?  
> **username_0**: @username_1 - The whole book...  
> **username_1**: Ok. Now, do you mean that you have no statistical/econometrics background _at all_? And if you do, please include it in the answer, siting books you have dealt with in the past, courses you have taken...  
> **username_0**: @username_1 - Undergrad statistics and linear algebra.  
> **username_2**: If you have no econometrics...I recommend Greene as a "sort of" reference while reading Hayashi. Although Hayashi's linear algebra/stats is self-contained, it just light on explanation (and Greene is a dictionary). Casealla's inference is not really "too basic", it is just not appropriate for the (very specific - typically multivariate) statistical techniques of econometrics.  
> **username_3**: I worked my way through this book prior to a ph.d in econ.  It helped with the basics and got me understanding how linear algebra is applied in economics.  However, if economics is not your field I don't know how valuable it would be.  http://www.springer.com/economics/game+theory/book/978-3-642-20569-9   I would also recommend Wooldridge Introductory Economics when reading through Hayashi.  It will be a good reference to have for the basics.  

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## 1 answers

### Answer by username_1 on 2014-12-19. Score: 9 | Accepted answer

The **Linear algebra** part should not worry you, it is just basic linear algebra plus familiarizing yourself a bit with [differentiation of vectors and matrices](http://en.wikipedia.org/wiki/Matrix_calculus) (and for some chapters, visualizing the [Kronecker product](http://en.wikipedia.org/wiki/Kronecker_product)). Hayashi goes some length into writing out explicitly large matrices, which is virtually with no-precedent (see eg. pages 267, or 288), something that eventually facilitates understanding -as long as you don't back out from a matrix half a page large, but you really *look* at it.

What you should really go slow over upon is Hayashi's **notation**, which is non-standard in many places. So *don't expect to understand through familiar notation*. Be prepared for that and "read" carefully every symbol and its role. Many people's discomfort with this book is due to the notation, but they don't realize it.

As for the **Statistics part**: In Econometrics, since we deal almost always with non-experimental, observational data, a large part of Statistics (originating usually in Biostatistics) do not really enter (our) picture. For example, apart from proving that under certain conditions the OLS estimator is best linear unbiased, you won't see much regarding the issues of minimum variance estimation or sufficient statistics. We don't even discuss the Exponential Family of distributions and the concept of Generalized Linear Models. Also, in statistical Hypothesis testing the Fisherian spirit prevails (oozing through the Neyman-Pearson apparatus), meaning, among other things, that issues like the "power of the test" are not so often considered.

Moreover "frequentist Econometrics", which is what Hayashi presents, are considerably lighter than Bayesian Econometrics in terms of the Algebra of Random Variables and probability theory.

What really matters is a good familiarity with *basic* Asymptotic Theory and Stochastic Processes (for the Time Series part). Although Hayashi in most cases just states results, providing references for the proofs, nevertheless it would be good to feel comfortable with asymptotic results and properties, because in most cases, *it will be all your estimators will possess*. For this part, I will once more advocate A. Spanos' book, [Probability Theory and Statistical Inference - Econometric Modeling with Observational Data](http://www.cambridge.org/lt/academic/subjects/economics/econometrics-statistics-and-mathematical-economics/probability-theory-and-statistical-inference-econometric-modeling-observational-data). It is a valuable book, Hayashi or not Hayashi. It is Statistics with the Econometrics graduate student in mind.

In case you want some more specific Time Series material, Hamilton's [Time Series Analysis](http://press.princeton.edu/titles/5386.html) remains a standard reference.

Finally, regarding **Unit-root Econometrics and Co-Integration**, the subject is inherently advanced, and I think Hayashi has done a good job in collecting and presenting the very basics.

> **Comments:**
> **username_4**: The Spanos books looks like a great intro to that material.  
> **username_1**: @DimitriyV.Masterov I am glad to hear it.  

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