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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Inconsistency of GLS Estimator in the Presence of Predetermined Regressors and Serial Correlation

Let be the linear model: $$y_i = x_i'\beta + \varepsilon_i$$ Using its matrix form, consider strictly exogenous assumption and spherical assumption, respectivelly: $$E[\varepsilon | X]=0, \quad E[\...
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Exogeneity of volatility shocks in Local projection model

I want to estimate the impact of volatility shocks on cross-assets spillovers. I have series of spillovers, and I want to use a Local Projection model, and the volatility of some financial assets ...
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Partially Endogenous Regressors

If I have a linear model $$ Y = X_1 \beta_1 + X_2\beta_2 + e$$ where $X_1$ is endogenous to $e$ but $X_2$ is not, then simply performing OLS will yield an unbiased estimate for $\beta_2$ but not $\...
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Why are the variables in a VAR model considered endogenous?

Does it have to do with the interdependence of one equation on the lagged values of its own as well as the other equations? If I remember correctly, in simultaneous equations, cross-causality is also ...
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Exogeneity Check of Control Variables? Covariance

I have performed an exogeneity check on my control variables to assess their validity before incorporating them into my regression analysis. Upon conducting the analysis, I observed a significant ...
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Dataset has no candidates for prophet add_regressor

I'm a student working with https://www.kaggle.com/aksha17/superstore-sales, primarily as an exercise in resampling and using prophet and it was suggested to me to create dummy variables and use the ...
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Show that $E [u] = 0$ and $cov(u,x_j)=0$ does not imply $E[u|x]=0$

In the regression model $$y= x'\beta + u, \quad x = (1, x_2,...,x_K)$$ with $$E[u |x]=0,$$ we know that it implies: $E [u] = 0$ and $cov(u,x_j)=0$, for $j=1,...,K$. I think that the reciprocal is not ...
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Rigorous book for multivariable concepts

I am looking for a rigorous book that clearly defines and explains terms such as ‘endogenous variable’, ‘exogenous variable’, ‘multicollinearity’, ‘heteroscedasticity’ and other such terms whose names ...
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Conditional exogeneity when regressors are causally, linearly related

Let's say there is a multiple regression: $$ Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \beta_4X_4 + \beta_5X_5+U. $$ I know that conditional exogeneity implies that the error terms are mean ...
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Synthetic control, exogeneity of treatment, parallel trends assumption?

I am relatively new to methods for causal inference. So, please excuse my conceptual confusion. However, I have been looking into the synthetic control method first proposed by Abadie and Gardeazabal (...
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Check $cov(X,e)=0$ using residuals [duplicate]

I know it is wrong but I am not sure why. We run a linear regression $$ Y = a + bX + e$$ we get the residual $$ \hat{e} = Y -(\hat{a}+ \hat{b} X)$$ Why can we not check $cov(X,e)=0$ using $corr(X,\...
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Determining weakness of Instrumental Variables

The problem is about doing a regression on the impacts of money supply growth and output (GDP) growth on ...
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Does an instrument variable become exogenous if its values are random?

In order to use an instrument variable it has to be exogenous. My question: Does IV become exogenous if its values have been randomized? Ex. finding people with diabetes by pulling names from resident ...
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For a given $Y$ , what is the minimum variance of a $X$ such that $E[Y|X]=X$?

Suppose $Y$ is a given (real-valued continuous) random variable. We define any variable $X$ as exogenous to $Y$ if $\forall X: E[Y|X]=X$. The question is this: For a given $Y$ , What is the minimum ...
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Trend in exogenous variable in time series

I have a time series of a variable V1 with seasonality and a strong trend. The trend however seems to be closely related to (and caused by) the trend of another time varying variable (V2). As V2 grows ...
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Are control variables always exogenous?

My professor said that control variables are generally thought to be exogenous in an OLS context, i.e. uncorrelated with the main independent variable in my regression. However, I think that they are ...
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My instrument (z) only affects y through x, but y affects z directly. Is my instrument valid?

I'm running a regression model to test whether unionisation rates have an impact on wages. I've introduced an instrumental variable: public support for unions. As far as I can tell, this instrument ...
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Consequences of Strict Exogeneity in a i.i.d. random sample

In the context of Strict Exogeneity on the classical regression model $$y_i = \beta x_i+ \varepsilon_j$$ we have: $$E(\varepsilon_i | x_i , x_j )=0,\quad \forall i,j$$ Under the linearity assumption, ...
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A question about the strict exogeneity assumption on the linear regression model

In the context of the linear regression model: $$y_i = x_i'\beta + u_i, \quad E(u_i|x_i)=0, \quad i=1,...n.$$ one of the assumptions is strict exogeneity: $$E(u_i|x_1,...,x_n )=0,\quad \forall \, i =1,...
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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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Why is strict exogeneity an assumption of OLS when it follows as a consequence?

Strict exogeneity is generally listed as an assumption for OLS, i.e., $E[\epsilon\ |\ X]=0$. But then if I take the minimum mean squared error estimate of $Y$, i.e. $\hat Y=E[X\ |\ Y]$ $$E[\epsilon\ |\...
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How does control function approach resolve endogeneity?

Suppose I want to estimate $$Y = \beta_1 + \beta_2 X + \varepsilon$$ Now I know that $X$ and $Y$ are also reversely related $$X = \gamma_1 + \gamma_2 Y + \xi$$ such that $Cov(\varepsilon,X) \neq 0$. $...
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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 ...
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How does correlation between independent variable and error term imply dependence of the independent variable on the dependent variable?

We know that a crucial assumption of employing OLS is that the independent variable and the error terms are uncorrelated. That is the "textbook" definition. I've seen in many (1, 2) online ...
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First difference estimator inconsistent

This is a simple issue but I seem to need some illustration . If I have a first difference model as in : $$ y_{it}-y_{it-1} = (X_{it}- X_{it-1})'\beta + (U_{it}- U_{it-1}) \ \ t=2,..T$$ which I am ...
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OLS variance estimator in linear regression without strict exogeneity

(I don't remember seeing this result stressed enough.) Consider the "benchmark" linear regression model $$\mathbf{Y} = \mathbf{X} \beta + \varepsilon.$$ $$E(\varepsilon) = 0,\, E(\varepsilon ...
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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 ...
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