# 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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### Deriving a "Clean"/Exogeneous Measure from an Independent Variable

Say I have a variable $y$ and a independent variable $x$, I would like to come up with a new variable say $z = f(x)$ to perform a regression: $$y = \alpha + \beta z$$ Seeing that $x$ is good at ...
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### Exogenous but non-random event for DiD

I have a quick question regarding whether the following event might pose any issues for my study. I am interested in exploring perceptions of climate change. In the early 1970s, former dictator Park ...
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### Testing Exogeneity of regressors

Good evening, I have a problem with solving this exercise: I could calculate the F-Statistics with the weak instrument test on my own. But I don't know how to test for exogeneity with two endogenous ...
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### Exogenous variable having opposite effect on forecasted values in SARIMAX model

I'm modeling how many plays are made on arcade machines at a store, using the number of active machines as an exogenous variable. I'm forecasting the number of plays into the future while keeping the ...
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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 "$x$...
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### A question about exogeneity assumption in linear regression

The exogeneity assumption is stated this way: $E(e_i | x_{j1}, x_{j2}... x_{jK}) = 0$ for all i and j. The first question is: is that "0" as scalar value or a vector? The second question is: ...
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### Exogenous variables in state-space models (entering states versus entering observations)

From Shumway & Stoffer, Chapter 6 "State-Space Models" page 290: "...exogenous variables, or fixed inputs, may enter into states or into observations". Can somebody help me ...
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### Is there any relationship between "strict exogeneity" and "no anticipation effect" in DiD

Regarding "strict exogeneity" assumption, I found a discussion here:it means that conditional on observing the data, the expectation of the error term is zero, which is something relating to ...
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### Appropriateness of propensity score matching when treatment is determinsitic and exogenous (e.g., COVID restrictions)?

I recently came across this paper by Sibley et al. in which propensity score matching (PSM) was applied to examine the effects of COVID-19 lockdowns on well-being and government attitudes in New ...
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### I am modelling a time series, the results are coming fine without exogenous variables but predictions are getting wrong on including exog varaibles

I am modelling a time series, the results are coming fine without exogenous variables but predictions are getting wrong on including exog varaibles, the forecasting series is starting from a lower ...
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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 ...
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### Random Sampling: Weak and Strong Exogenity

$Y \ = \ X' \beta \ + \ e$ Where $Y = (y_1, ..., y_n)$ and $\beta = (\beta_0,..., \beta_k)$. Why would Weak Exogenity under random sampling produce Strong Exogenity? I know that weak exogenity is ...
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### Can I use an exogenous variable from my model as an instrumental variable?

Can I use an exogenous variable specified in my model as an instrument for an endogenous one? It can be reasoned that there is a relationship between the two. My conjecture is this: Given that the ...
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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 ...
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### How are standard exogeneity assumptions and indepent of potential outcomes concepts linked?

If we had a model: $y=x\beta +\eta$ and assumed exogeneity, so $E[\eta|x]$=0, is the fact that x or treatment intensity is now uncorrelated with $\eta$ equivalent to saying that x is 'independent of ...
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### Question about intuition of exogeneity with individual notation

In econometrics, we typicall assume exogeneity as, starting with $y = x\beta + \epsilon$: $E[\epsilon|x]=0$. I always intuitively thought about this in an abstract sense, away from the individual ...
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### Confused about the meaning of zero conditional mean with regressions analysis /exogeneity)

Usually the exogeneity assumption is states, given the vector E[$\epsilon$|x]=0. what this implies then is E[$\epsilon_i$|x$_i$]=0 for all i. The individual notation part is what is confusing me. ...
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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 ...
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### Confusion about method of moments for linear regression

It is known that linear regression estimator can also be viewed as a method of moment estimator derived using the moment condition $E[X\epsilon]=0$. This moment condition follows from exogeneity ...
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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 ...
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### What is the difference between the strict exogeneity assumption in OLS and the strict exogeneity assumption in DiD?

I don't really understand the difference between the strict exogeneity assumption in OLS and the strict exogeneity assumption in DiD (difference-in-differences). If they are the same, then what is the ...
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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 ...
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### Implications of strict exogeneity for OLS in time series

Zero Conditional Mean (ZCM), or Strict Exogeneity, is given by: $E[u|X]=0$ Equivalently, $E[u_t|X]=0, t=1,...,T$ Is it true that this implies: Zero Unconditional Mean: $E[u_t]=0, \forall t$ ...
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### Why don’t we need strict exogeneity for OLS consistency? [closed]

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 ...
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### Why is the assumption $E(\epsilon|X)$ called the "exogeneity assumption"?
In regression analysis, my book says that the condition $E(\epsilon_i|X_i)$ is called the "exogeneity assumption" and that the condition $E(\epsilon_i|X_1, ..., X_n)$ is called the "strict exogeneity ...