Questions tagged [instrumental-variables]
Instrumental variables (IV) are used for causal inference with observational data in the presence of endogeneity when standard regression methods yield biased and inconsistent estimates.
592
questions
56
votes
5
answers
120k
views
What do "endogeneity" and "exogeneity" mean substantively?
I understand that the basic definition of endogeneity is that
$$
X'\epsilon=0
$$
is not satisfied, but what does this mean in a real world sense? I read the Wikipedia article, with the supply and ...
- 561
47
votes
4
answers
15k
views
What is an instrumental variable?
Instrumental variables are becoming increasingly common in applied economics and statistics. For the uninitiated, can we have some non-technical answers to the following questions:
What is an ...
- 8,061
26
votes
7
answers
3k
views
Explain in layperson's terms why predictive models aren't causally interpretable
Imagine that you are asked to infer some causal effect -- a change in an outcome $y$ in response to some variable $x$. But, the person asking for this directs you to use a predictive model to do so. ...
- 13.3k
22
votes
3
answers
66k
views
Two stage models: Difference between Heckman models (to deal with sample selection) and Instrumental variables (to deal with endogenity)
I am trying to get my head around the difference between sample selection and endogeneity and in turn how Heckman models (to deal with sample selection) differ from instrumental variable regressions (...
- 715
20
votes
2
answers
4k
views
Can an instrumental variable equation be written as a directed acyclic graph (DAG)?
Directed acyclic graphs (DAGs) are efficient visual representations of qualitative causal assumptions in statistical models, but can they be used to present a regular instrumental variable equation (...
- 659
19
votes
3
answers
31k
views
Probit two-stage least squares (2SLS)
I was told that it's possible to run a two-stage IV regression where the first stage is a probit and the second stage is an OLS. Is it possible to use 2SLS if the first stage is a probit but the ...
- 305
19
votes
1
answer
5k
views
2SLS but second stage Probit
I am trying to use instrumental variables analysis to infer causality with observational data.
I have come across a two-stage least squares (2SLS) regression which is likely to address the ...
- 193
17
votes
3
answers
3k
views
Literature on IV quantile regression
In the last months I have read intensively about quantile regression in preparation for my master thesis this summer. Specifically I have read most of Roger Koenker's 2005 book on the topic. Now I ...
- 976
16
votes
3
answers
33k
views
Why doesn't measurement error in the dependent variable bias the results?
When there is measurement error in the independent variable I have understood that the results will be biased against 0. When the dependent variable is measured with error they say it just affects the ...
- 163
15
votes
1
answer
34k
views
Interpretation of ivreg() diagnostics in R
I'm trying to wrap my head around interpreting the diagnostics of the ivreg() command in R, from the {AER} package. Running the example code provided in the help ...
- 153
15
votes
6
answers
84k
views
What is the difference between effectiveness and efficacy in determining the benefit of therapy 'A' on condition 'B'?
The context of this question is within a health framework i.e. looking at one or more therapies in the treatment of a condition.
It appears that even well respected researchers confuse the terms ...
- 211
15
votes
1
answer
27k
views
How to do an instrumental variables regression with an instrumented interaction term in Stata?
I'm having a bit of a problem with Stata syntax. I need to do the following regression:
$$y = ax + bz + c(xz) + e$$
where both $x$ and $z$ are instrumented and also the interaction term $xz$ uses ...
- 151
15
votes
1
answer
2k
views
Is Just-Identified 2SLS Median-Unbiased?
In Mostly Harmless Econometrics: An Empiricist's Companion (Angrist and Pischke, 2009: page 209) I read the following:
(...) In fact, just-identified 2SLS (say, the simple Wald estimator) is ...
- 1,089
14
votes
3
answers
2k
views
Why not use instrumental variable directly as a covariate in the regression?
I know this is a silly question, as I know the theory of instrumental variables and two stage regression. Still, I never saw a clear answer to the following:
assume you have endogeneity due to ...
- 385
14
votes
2
answers
13k
views
Regress residuals in second regression
I am wondering if anyone can point me to a paper/lecture notes on the rationale behind first running an OLS on a set of variables, and then in a second regression using the residuals of that ...
- 223
13
votes
2
answers
31k
views
Standard errors of a two stage least squares regression, Stata
I use Stata. I am trying to replicate the ivreg output of a regression performing manually the first stage, predicting the instrument after the first stage and running the second stage regression with ...
- 491
13
votes
1
answer
5k
views
How do instrumental variables address selection bias?
I'm wondering how an instrumental variable addresses selection bias in regression.
Here's the example I'm chewing on: In Mostly Harmless Econometrics, the authors discuss an IV regression relating ...
13
votes
2
answers
588
views
Does direction of causality between instrument and variable matter?
The standard scheme of instrumental variable in terms of causality (->) is:
Z -> X -> Y
Where Z is an instrument, X ...
- 1,844
13
votes
1
answer
14k
views
How to interpret second-stage coefficient in instrumental variables regression with a binary instrument and a binary endogenous variable?
(fairly long post, sorry. It includes lots of background info, so feel free to skip to the question at the bottom.)
Intro: I am working on a project where we are trying to identify the effect of a ...
- 353
12
votes
3
answers
19k
views
Why use a lagged DV as an instrumental variable?
I have inherited some data analysis code that, not being an econometrician, I am struggling to understand. One model runs an instrumental variables regression with the following Stata command
...
- 1,139
12
votes
0
answers
2k
views
Instrumental variables with interactions between endogenous variables
I have two endogenous variables $x_1$ and $x_2$ and am trying to estimate the following model:
$$y = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + \theta_{12} x_{12}$$
where $x_{12} = x_1\times x_2$. I'm ...
- 171
11
votes
3
answers
16k
views
Definition of validity of an instrumental variable
What does "validity of an instrument" mean exactly?
In my econometrics course we have just defined instrument validity as $E[Z|u]=0$, where $Z$ is the instrumental variable and $u$ is the error term ...
- 3,069
11
votes
1
answer
15k
views
Consistency of 2SLS with Binary endogenous variable
I have read that 2SLS estimator is still consistent even with binary endogenous variable (http://www.stata.com/statalist/archive/2004-07/msg00699.html). In the first stage, a probit treatment model ...
- 421
11
votes
3
answers
2k
views
Random assignment: why bother?
Random assignment is valuable because it ensures independence of treatment from potential outcomes. That is how it leads to unbiased estimates of the average treatment effect. But other assignment ...
- 648
10
votes
2
answers
445
views
What can we say about models on observational data in the absence of instruments?
I've had in the past a number of questions asked of me relating to published papers in a number of areas where regressions (and related models, such as panel models or GLMs) are used on observational ...
- 283k
10
votes
1
answer
455
views
DAGs: instrumental and adjusted variables
While drawing DAGs, we can define variables as exposure, outcome and unobserved etc. Could you please explain, what are instrumental and adjusted variables?
- 2,197
10
votes
3
answers
12k
views
Why is the variance of 2SLS bigger than that of OLS?
... Another potential problem with applying 2SLS and other IV procedures
is that the 2SLS standard errors have a tendency to be ‘‘large.’’ What
is typically meant by this statement is either that ...
- 1,159
10
votes
0
answers
2k
views
Dynamic Panel/GMM in R with group:time fixed effects? [closed]
Is there a solution coded in R to estimate models of the form
$$
y_{igt} = \alpha_i + P_{gt} + \beta_1y_{igt-1}+ \beta_2y_{igt-2} + X_{igt}'\gamma + \epsilon_{igt}
$$
?
...
- 13.3k
9
votes
2
answers
31k
views
Proxy variables versus instrumental variables
Very short question. What exactly is the difference between an instrumental variable and a proxy variable when building a regression model?
- 5,955
9
votes
2
answers
2k
views
Proving the LATE Theorem of Angrist and Imbens 1994
Assume we have a binary instrument $Z_i$ which can be used to estimate the effect of the endogenous variable $D_i$ on the outcome $Y_i$. Suppose the instrument has a significant first stage, it is ...
- 167
9
votes
2
answers
1k
views
Instrumental variables equivalent representation
Let us work with the following structural model: $$y=\mathbf{x_{1i}β}+x_{2i}β_2+\varepsilon_i$$
where $x_{2i}$ is our single endogenous regressor. It turns out that given my instruments and my first ...
- 491
9
votes
1
answer
3k
views
Control Function Approach and Bootstrap
Let's start assuming that I have cross-sectional data on $y$, $x_1$, $x_2$ (see below for $y$, $x_1$, $x_2$).
I want to estimate the effect of variables $x_1$ and $x_2$ and their interaction ($x_3= ...
9
votes
1
answer
3k
views
Instrumental variables and mixed/multilevel models
I want to estimate a growth model to model the growth trajectories of individuals $j$ over multiple time points $t$ by applying a standard mixed/mutilevel model (also known as random coefficient ...
- 1,032
8
votes
1
answer
5k
views
Can I ignore the negative R-squared value when I am using instrumental variable regression?
I am running an instrumental variable regression using 'ivreg' command in R program.
I find that all my validity tests related to endogeneity are satisfied only except the R-squared value which is ...
- 506
8
votes
2
answers
178
views
Do I need to include confounding variables in my regression model when I use instrument variables?
Suppose I believe 'Age', 'Gender', 'Ability', and 'Motivation' are confounding variables influencing both the dependent variable and endogenous variables. I use the 'Education Level' for the treatment ...
- 3,465
8
votes
1
answer
4k
views
Estimating number of compliers
Be $X$ a dichotomous endogenous variable and $Z$ its dichotomous instrumental variable. Suppose that for compliers if $Z_i=0$ then $X_i=0$ and if $Z_i=1$ then $X_i=1$.
Assuming that defiers do not ...
- 2,137
8
votes
1
answer
822
views
Why are standard errors downward biased when considering weak instruments
I was wondering why standard errors are (severely) downward biased when you are using the (general) instrumental variable - estimator or the generalized method of moments (gmm) estimator.
- 117
8
votes
1
answer
3k
views
Instrumental variables: In which cases would the average treatment effect on the treated (ATT) and local average treatment effect (LATE) be similar?
It seems that if the proportion of always-takers in the control group (to whom eligibility was not assigned) is much smaller than the proportion of compliers in the treatment group (to whom ...
- 569
8
votes
1
answer
275
views
Intuitive understanding of instrumental variables for natural experiments
I am wondering if my understanding of Instrumental vairables to exploit natural experiments is correct, or if I am misunderstanding something.
Is the logic as follows: by using an instrument, you are ...
- 651
7
votes
1
answer
30k
views
Instrumental variable exclusion restriction
When verifying whether a potential instrumental variable is valid, how should I check if it meets the exclusion restriction? To reject that it meets the exclusion restriction, do I simply have to come ...
- 71
7
votes
3
answers
5k
views
Fuzzy regression discontinuity design and exclusion restriction
In a fuzzy regression discontinuity design, what does the exclusion restriction look like in terms of a conditional expectation between the instrument in the first stage and the error term in the ...
- 815
7
votes
2
answers
20k
views
Weak first stage in 2SLS
I have a simple IV model with 1D variables:
$N = \alpha_z + \beta_z Z + \epsilon_z$
$S = \alpha_s + \beta_s N + \epsilon_s$
$N$ is an integer, while $S$ is dummy.
$Z$ is by construction ...
- 1,302
7
votes
2
answers
15k
views
2SLS - logit/probit in the second stage?
I just have a quick question: what if I'm interested in estimating a logit/probit model in the second stage, can I follow this two-step procedure by running OLS in the first stage (endogenous variable ...
- 155
7
votes
3
answers
6k
views
Limited Information Maximum Likelihood (LIML) estimation in R?
Curious whether anyone knows a package, or has written an implementation themselves, for conducting instrumental variables regressions using LIML in R. All of the R packages I have seen for IV ...
- 317
7
votes
1
answer
34k
views
Interpreting significance of Cragg-Donald F-Statistic for weak instruments
I have a first-stage F value of 9 for a model with 1 instrument and 1 endogenous variables, the mechanical rule of thumb of 10 would say my instruments are weak. However, I am reading the 2005 paper ...
- 105
7
votes
1
answer
938
views
How to calculate and interpret a marginal treatment effect (local instrumental variable)? (Intuition through simple example.)
I am working on the intuition behind local instrumental variables (LIV), also known as the marginal treatment effect (MTE), developed by Heckman & Vytlacil. I have worked some time on this and ...
- 659
7
votes
1
answer
671
views
Definition of "optimal" instruments
The book I read (Davidson,MacKinnon - Econometric Theory and Methods) describes the definition of "optimal instrument variables" as the following:
Usually, and this is seen very often in ...
- 1,103
7
votes
2
answers
6k
views
What is the relationship between LATE and TOT?
My understanding of LATE was that it was the effect of a treatment on individuals who were induced to be treated by the experiment. That is, the effect on compliers. My understanding of Treatment-on-...
- 1,010
7
votes
1
answer
3k
views
Why would an instrumental variable have its strength measured by an F-statistic?
A typical "rule of thumb" for instrumental variables is that an F-statistic of ten or higher indicates a strong instrument. This is mentioned in this Cross Validated post, which contains a ...
- 62.5k
7
votes
1
answer
775
views
Instrument Variables and Exclusion Restriction from a Mediation perspective
I'm having trouble making sense of the exclusion restriction in instrumental variables.
I understand that the unbiased treatment effect is $B = \frac{Cov(Y, Z)}{Cov(S, Z)}$, where $Y$ is the outcome,...
- 121