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.

Filter by
Sorted by
Tagged with
1 vote
1 answer
16 views

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 ...
user avatar
2 votes
1 answer
45 views

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, ...
user avatar
  • 223
1 vote
0 answers
19 views

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,...
user avatar
  • 223
0 votes
0 answers
49 views

Strict exogeneity and AR(1) on the error term

I have a theoretical Fixed Effect GLS model (FEGLS) in which I assume that errors follow an AR(1) process. Below I describe the main model Now, notice that it is specified that the epsilon is ...
user avatar
0 votes
0 answers
13 views

Paval VAR impulse response for exogen variable

Using pvargmm function in R, I am trying to estimate impulse response for the oirf function, but the oirf does impulse response only for endogen variables, ignoring the exogen variables. I need to ...
user avatar
1 vote
0 answers
15 views

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 ...
user avatar
4 votes
1 answer
101 views

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 "$x$...
user avatar
  • 501
0 votes
0 answers
26 views

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: ...
user avatar
  • 123
1 vote
0 answers
19 views

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 ...
user avatar
0 votes
0 answers
12 views

What is the purpose of testing "additional effect" in "strict exogeneity" in Diff-in-Diff?

The strict exogeneity are different in using OLS and Difference-in-Differences (DiD) as pointed here. From a recently published paper of Miller, 2021, in the Reviewing DID Assumption part (sorry I did ...
user avatar
1 vote
0 answers
35 views

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 ...
user avatar
0 votes
0 answers
60 views

Include exogenous variable in both level and first-difference

I am wondering if I could include, in a VECM, exogenous variable in both level and first-difference, such as : $\Delta X_t = \alpha \beta^{'} X_{t-1} + \Delta X_{t-1} + Y_t + \Delta Y_t + U_t$ Is ...
user avatar
  • 13
2 votes
1 answer
70 views

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 ...
user avatar
0 votes
0 answers
13 views

Is there strict exogeneity with a lagged dependent variable and independent error?

If an error $\epsilon_t$ is completely independent, is there strict exogeneity even if there is a lagged dependent variable? I understand 'strictly exogeneity' to mean $E(\epsilon_t \vert X)=0$ for ...
user avatar
  • 63
2 votes
1 answer
73 views

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\ |\...
user avatar
2 votes
1 answer
204 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 $Cov(\varepsilon,X) \neq 0$. $...
user avatar
  • 73
6 votes
2 answers
430 views

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 ...
user avatar
  • 1,030
1 vote
1 answer
163 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 ...
user avatar
  • 715
1 vote
0 answers
32 views

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 ...
user avatar
  • 47
2 votes
1 answer
115 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 ...
user avatar
0 votes
0 answers
34 views

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 ...
user avatar
  • 1
6 votes
0 answers
133 views

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 ...
user avatar
  • 261
0 votes
1 answer
162 views

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 ...
user avatar
  • 232
1 vote
2 answers
354 views

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 ...
user avatar
  • 85
4 votes
1 answer
147 views

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 ...
user avatar
  • 232
2 votes
1 answer
87 views

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 ...
user avatar
  • 385
0 votes
1 answer
66 views

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 ...
user avatar
  • 385
1 vote
2 answers
199 views

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. ...
user avatar
  • 385
3 votes
2 answers
68 views

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 ...
user avatar
  • 476
1 vote
1 answer
317 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 ...
user avatar
3 votes
1 answer
370 views

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 ...
user avatar
  • 289
1 vote
1 answer
827 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 ...
user avatar
5 votes
0 answers
3k views

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 ...
user avatar
  • 161
0 votes
1 answer
602 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: $E[u_t]=0, \forall t$ ...
user avatar
  • 13
5 votes
1 answer
1k views

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 ...
user avatar
  • 2,177
0 votes
1 answer
598 views

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 ...
user avatar
  • 2,177
3 votes
1 answer
2k views

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 ...
user avatar
  • 389
12 votes
1 answer
20k views

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. ...
user avatar
  • 519
6 votes
3 answers
12k views

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 ...
user avatar
4 votes
2 answers
10k views

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 ...
user avatar
1 vote
0 answers
682 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_{...
user avatar
  • 665
5 votes
2 answers
5k views

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. ...
user avatar
  • 7,660
3 votes
1 answer
4k views

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 ...
user avatar
  • 638
5 votes
0 answers
2k views

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 ...
user avatar