Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [exogeneity]

The property of a variable being unexplained by the model or being fixed in repeated sampling. Common in economics and econometrics and an assumption of the classical linear regression model.

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What does strict exogeneity condition of OLS really mean?

In Hayashi's Econometrics, it is stated that one of the assumption of classical OLS is: $$\mathbb{E}(\epsilon_i\lvert\mathbf{x_1}, \mathbf{x_2}, \ldots, \mathbf{x_n}) = 0 \text{, for } i=1, \ldots, n. \tag{1}$$ And I know that the implications are…
hans-t
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Regression where predictors are correlated with past values of y

Setup We are interested in estimating a model for the following setup: $Y_t=\beta_0 + \beta_1^{'}X^{'}_t + \epsilon_t$ $COV(X^{'}_t,Y_{t-1,t-2,...,1} | X_{t-1,t-2,...,1}) = 0$ Where $\epsilon_t$ is iid normal. In other words: what would the effect…
jwdink
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An intuitive explanation of the instrumental variable

This is something that I had dealt with in my MSc Economics many years ago, passed the exams with flying colours, yet when I thought about it in more depth today, I was somewhat puzzled. This could perhaps be because it's been a couple of years…
Carl
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Strict Exogeneity and Seasonal Dummy Variables

Wooldridge (Intro Econometric book) he states that seasonal dummy variables (say a dummy for the calendar month) satisfy the strict exogeneity assumption because "they follow a deterministic pattern. For example, the months do not change based upon…
B_Miner
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Why don’t we need strict exogeneity for OLS consistency?

I know how to show that OLS only requires orthogonality between regressor and error for consistency, so the title is maybe a misnomer (couldn’t think of a better one) But consider the following regression: $$y_i=\alpha + x_i\beta + u_i$$ Where…
user56834
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Exogenous variables in VECM

I found the following posts interesting and I was wondering if any of you guys know of good academic papers that describe methods/relationships of exogenous variables in VECM models. If so could you kindly point them out to me as I am very…
algotr8der
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Strict exogeneity and lagged variables

I am confused why strict exogeneity must be violated when we have lagged time series variables. My understanding of strict exogeneity is that a variable must be uncorrelated with error terms in all periods. But isn't exogeneity always a necessary…
mangofruit
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Is there a relationship between a regression's conditional mean of 0 and its 0 correlation with the error term?

In regression analysis, when we impose the exogeneity assumption, we express the assumption using the zero conditional mean condition. That is, $\mathbb{E}(u|x)=0$ is equivalent the statement "$x$ is an exogenous regressor". However, we also often…
QWEQWE
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Exogenity: What does E(eX) really mean and why is it used?

What does it mean to talk about the expectation of the product of the error term and an independent variable? Like, why do we even need to mention $E(e_i X_{ik})$? What is it actually describing or what is the intuition behind it? So for a linear…
T. G.
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What is the difference between strict / strong and weak exogeneity

Let be two variables $y$ and $x$, the latter being expected to be a cause of the latter. If we suppose linearity, we can set up a model: $$y=\beta_0+\beta_1x+u$$ Where $\beta_0$ and $\beta_1$ are coefficients to be determined, and $u$ is a random…
Arthur
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Formal test for exogeneity of instruments

Is there a way for me to formally test the exogeneity of my instruments? For instance, I have an endogenous variable, FDI, which I am instrumenting with "ease of doing business ratings," as a better score on ease of doing business improves the FDI…
qayoom khachoo
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Exogeneity assumption applied to functions of the design matrix

The context of this question is ordinary least squares. $X$ denotes the design matrix. I would like a proof of the claim – or a corrected version thereof – made in this other question that the exogeneity assumption $E[\epsilon|X] = 0$ implies that…
dwolfeu
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How to check exogeneity of residuals in linear regression model?

Can you please give me some advice in testing exogeneity of residuals ? I check the internet and it says a lot of test or other ways to prove or disapprove other assumptions, but I couldn't find any for exogeneity. By exogenity I mean that…
John
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OLS - difference between exogeneity and homoscedasticity

I was wondering what the difference between the concepts of 'homoscedasticity/heteroscedasticity' and 'exogenity/endogenity' is when it comes to Ordinary Least Squares estimation. In my view, they are both defined by the existance of correlation…
dubvice
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Testing strict exogeneity in time series

One of the important OLS assumptions is a strict exogeneity assumption, i.e. $E(\epsilon_i | X) = 0, \forall i$. I'm interested in testing empirically this hypothesis, notably in the context of time series. It is known that exogeneity is rarely true…
johnny
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