Questions tagged [simultaneous-equation]
31 questions
8
votes
1 answer
How Many Moments Uniquely Define a Distribution with Finite Support?
Simple question, but one to which I could not find the exact answer elsewhere. How many moments of a discrete probability distribution with finite support are required to uniquely identify the exact probability mass function? Suppose we know that…
housed_off_space
- 83
- 4
8
votes
1 answer
How to express cells of a 2x2 table in terms of phi coefficient and marginal probabilities
Consider a typical 2x2 table of frequencies (shown in this image):
Notation: The row variable is denoted R and takes on values 0 or 1; the column variable is denoted C and takes on values 0 or 1. The cells of the table indicate the frequency of…
John K. Kruschke
- 2,153
- 12
- 16
4
votes
1 answer
About Identification in a 3 equation SEM
I got this example and I was wondering about a certain statement:
$$
\begin{aligned}
(I) \ y_1 &= \alpha_{12}y_2 + \alpha_{13}y_3 + \beta_{11}z_1 + u_1 \\
(II) \ y_2 &= \alpha_{21}y_1 + \beta_{21}z_1 + \beta_{22}z_2 + \beta_{23}z_3 u_2 \\
(III) \…
Druss2k
- 783
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- 22
4
votes
1 answer
How to derive 2x2 cell counts from contingency table margins and the odds ratio
I'm certain there's a unique solution to this, and I think I've worked it out before but now it has me pulling my hair out:
Given the margins of a 2x2 contingency table such as the prevalences of a binary exposure and a binary outcome, as well as…
JayDee
- 43
- 4
3
votes
0 answers
Estimating a linear system of simultaneous equations at once
Consider the following simultaneous system
$$
y_{1} =\beta _{1}y_{2}+\alpha _{1}z+u_{1} \\
y_{2} =\beta _{2}y_{1}+\alpha _{2}z+u_{2}
$$
where $y_{1}$, $y_{2}$ and $z$ are vectors of random variables each of length $n$. $u_{1}$
and $u_{2}$ are…
Bert Breitenfelder
- 165
- 8
3
votes
1 answer
Structural equation models in econometrics vs psychology, political science, etc
Can anyone tell me if the sort of the sort of simultaneous equation/structural equation modeling of economic relationships that that was championed and to some extent developed out of the Cowles Commission (later Foundation) is technically the same…
andrewH
- 2,587
- 14
- 27
3
votes
1 answer
SUR and interaction terms
Suppose I want to determine if a simultaneous model (A) was identified:
$y_1 = \beta_{10} + \beta_{11} x_1 + \beta_{12} y_2 + \epsilon_1$
$y_2 = \beta_{20} + \beta_{21} y_1 + \beta_{22} x_2 + \epsilon_2$
Where the y's are endogenous and the x's are…
RegressForward
- 1,254
- 7
- 13
3
votes
2 answers
Is this model identified?
Is this model identified? The paper is in plosone, but it seems to be that the combination of regression paths from PCS ~ MCS and MCS ~ PCS, plus the error covariance, means that this shouldn't be identified. Any pointers much appreciated. I'm…
bjw
- 395
- 3
- 14
2
votes
0 answers
VAR with different distributions: Does this model exists?
I would like to know if models like the one below exist/make sense and, if so, how they are called.
\begin{equation}
X_t \sim \mathcal{Pois} ( \lambda_t ) \\
\lambda_t = \mu_1 + \alpha_1 X_{t-1} + \beta_1 \lambda_{t-1} + \gamma_1 Y_{t} + \delta_1\…
pietrosan
- 53
- 3
2
votes
0 answers
Testing simultaneous equality of contrasts
I have a one-way ANOVA model with 3 treatments. I have contrasts $\hat{\theta}_1=\hat{\mu}_1+\hat{\mu}_2$ and $\hat{\theta}_2=\hat{\mu}_3-\frac{1}{2}(\hat{\mu}_1+\hat{\mu}_2)$.
I want to do a simultaneous test $H_0:\theta_1=\theta_2=0$.
The two…
Mark
- 41
- 1
2
votes
1 answer
help with some symbolic computation/EM algorithm
I have to maximize $Q(\theta;\theta')$ with respect to $\theta$ at every iteration of my EM algorithm. It boils down to solving these two equations for $\eta$ and $\gamma$ (all the $s_i$s are sufficient statistics):
$$
0 = -\frac{1}{2}(1 + e^{\eta}…
Taylor
- 18,278
- 2
- 31
- 66
1
vote
0 answers
SURE vs SEM: which one to use?
in my understanding, SEM should be applied in a case such as:
\begin{equation}
Y= \alpha_1 + \beta_1 X + \epsilon
\end{equation}
\begin{equation}
X= \alpha_2 + \beta_2 Y + \epsilon
\end{equation}
as $X$ and $Y$ are jointly determined, while SURE in…
Andrea
- 297
- 2
- 16
1
vote
0 answers
detect incalculable variables
I have a bunch of equations in the form as follows.
a+b+c+d=10
c+d+e+f=12
d+e+c=13
Where I am tying to calculate the values of each variable (many more equations in the actual list ofc).
However, I cannot separate the values of a and b (I can only…
lwl59438cuoly
- 11
- 5
1
vote
0 answers
Simultaneous GMM estimation: standard errors of common coefficients
So I am estimating a production function based on Wooldridge (2009) GMM adaptation of preexisting semi-parametric, 2-stage techniques. One of the upsides of GMM is simultaneous instead of sequential estimation, which alleviates correlation problems…
Magean
- 33
- 5
1
vote
0 answers
Econometrics of demand for substitute goods
I've got a problem that seems to be exposing a fairly fundamental hole in my econometrics training. I'm looking for a canonical reference for how to deal with the following sort of problem:
For example, say that firms have demand for security, and…
generic_user
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