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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57 views

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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34 views

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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Feedback and lagged variables in panel data

In the static linear panel data model we have that: $$y_{it} = \alpha + X_{it}'\beta +n_i + U_{it}$$ where we assume $n_i$ are unobserved individual specific effects. My main question is why strict ...
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Exclusion restriction and exogeneity

Can an instrument variable satisfy exogeneity but not exclusion restriction, or the other way round? Are the two things equivalent or do they have subtle differences?
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Would the exogeneity assumption be violated with year as a variable?

Let's suppose that I have a model. I have made this model up for simplicity purposes. Death Rate= b0 + b1(gdp_per_capita) + b2(year) + error I know that the exogeneity assumption for a linear ...
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1answer
44 views

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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1answer
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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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1answer
150 views

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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371 views

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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441 views

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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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 ...
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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. ...
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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 ...
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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 ...
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646 views

weak exogeneity in VAR analysis

I have a problem interpreting the notion of "weak exogeneity in a VAR process". Assuming we have the following structural form: $y_t = b_{12}z_t + \gamma_{11}y_{t-1} + \gamma_{12}z_{t-1} + \epsilon_{...
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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. ...
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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 ...