# Questions tagged [linear-algebra]

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### How can I write a conditional expectation of finite state markov process in matrix notation

NOTE: This question is related to the econometric method explored in the following two questions: Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/...
208 views

### Has this differential calculus inequality approach to optimizing the production possibility curve exist?

I just started micro-economics at my community college and my teacher mentioned the derivative of the PPF for two output resources. I thought about it a while and came up with this approach. Some of ...
75 views

### Regression Optimization problem under constraints

To estimate a simple linear regression: $$y = \beta_0 + \beta_1 x + \epsilon$$ I have the assumptions that a researcher $A$ can only sample individuals with a value $y < y^A$. Similarly, a ...
123 views

### Negative Definite vs Semi-definite Hessian - Sufficient vs Necessary conditions?

When a Hessian matrix is negative definite at a critical point then that critical point is a local maximum (Sufficient Condition). As per the calculus wiki: Link, when the Hessian is negative semi-...
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### How to utilize the projection matrix in econometrics?

When consider the following DGP : $y=X\beta^{*}+\epsilon$ where $\beta^{*}$ is a $\tilde k\times1\$ vector. Define the projection matrices: $P_{X}=X(X^{T}X)^{-1}X^{T}$ and $M_{X}=I-X(X^{T}X)^{-1}$. ...
57 views

### What are the concepts in Linear Algebra that model the idea of Identification Strategy in Econometrics?

I just would like to know what concepts one should know before talking about identification strategies in econometrics. I see people studying such concepts but I'm not sure they realize (or even know) ...
53 views

### $x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$, then the preference is linear?

$x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (or disprove by counterexample) that: Suppose $x\sim y$ ...