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.

learn more… | top users | synonyms (1)

1
vote
1answer
22 views

Why report r-squared in Instrumental Variables Estimation?

I mean the the R-squared calculated such as in $R^2=1-\frac{RSS}{TSS}$ when you use the $RSS$ from the original structural model and not recalculation that you should do in order to do an F test. With ...
0
votes
1answer
36 views

Is LIML consistent under heteroskedastic errors?

Please let the answer be yes. Suppose we have a model \begin{eqnarray} y= X \beta + \epsilon \\ X = Z \Pi + V \end{eqnarray} and we compute the LIML estimator \begin{eqnarray} \hat{\beta}_{LIML} = ...
0
votes
1answer
20 views

Deriving the common LIML estimator from first principles

David Hendry (1976) comments that deriving the LIML estimator is hard. I tend to agree. Guido Imbens has a nice expression here which reads \begin{eqnarray} \hat{\beta}_{LIML} = (X'(I - \lambda M_Z) ...
1
vote
0answers
22 views

Who to credit for “control functions” in econometrics?

The idea is pretty simple, and I think it came out sort of by-the-way in a paper about something else, so I'm having a hard time figuring out who to cite. Basically you've got a GLM (like a probit or ...
3
votes
1answer
32 views

Instrumental variables and noisy measurement

I am interested in the effect of the unemployment rate at the time of labor market entry ($u^{LME}$) on wages later in life (this is an old question, but I have a new data set). I'd like to run ...
0
votes
1answer
32 views

Combining propensity score matching with 2SLS

Inspired by the probit 2SLS estimation (see e.g. Wooldridge p.623, procedure 18.1 or check here probit two stage least squares), I am wondering if instead of running a Probit in the very first step, I ...
0
votes
1answer
15 views

IV or latent factor to process multiple measures?

I have several measures on different memory tests. I consider these measures may actually measure different aspects of memory functioning and every measure contains a measurement error. I am thinking ...
3
votes
3answers
56 views

Clustering in Instrumental Variables Regression?

I am wondering whether clustering in IV estimation would mean I have a fixed effect for both error terms or just for the structural error. For example, in the model \begin{eqnarray} y = X \beta + ...
0
votes
1answer
30 views

Typos in Hayashi Econometrics? How to understand this 2SLS as an IV estimator

Below are a few passages of Hayashi's Econometrics. According to the notation there, $X$ the matrix of instruments, $Z$ the matrix of original regressors, and $Y$ vector of dependent variable. A few ...
0
votes
2answers
68 views

2 stage least Squares as an Instrumental variable estimator

$\mathbf{X}_{n \times K}= \begin{bmatrix} \mathbf{x}'_1 \\ \cdots \\ \mathbf{x}'_n \end{bmatrix}$ $\mathbf{Z}_{n \times L}= \begin{bmatrix} \mathbf{z}'_1 \\ ...
1
vote
0answers
46 views

Can I interact my randomly-assigned variable with another variable in TSLS?

I'm working on an IV setup that uses random courtroom assignment as an instrument for whether a defendant goes to jail or not. (Similar to here and others). I have about five years of courtroom data, ...
3
votes
1answer
69 views

Identifying $\beta_1$ with one instrumental variable and one exogenous variable

$\textbf{Question:}$ Suppose we have ${(Y_i, X_i,Z_i,W_i)^{n}_{i=1}}$ which is a random sample from the joint distribution of $(Y,X,Z,W)$ that satisfies the following relation: ...
5
votes
0answers
24 views

Rule of thumb for excluded variable in Heckman selection model?

I'm working on a project that involves the use of a Heckman selection model (more specifically a Roy or move-stay model, which is essentially a two-sided Heckman) of the following form: $$ Y_{i1} = ...
3
votes
1answer
78 views

Show that $\widehat{Cov(\hat{\mu},Z_i)}$ is always zero even $Cov(\mu,Z_i)$ is not always $0$

I will state the question first then my work. Q: We have a regression model, $Y_i=\beta_0+\beta_1X_i+\mu_i$ where $Cov(\mu_i,X_i)=0$ is not guaranteed. Suppose that $Z_i$ is an instrumental ...
2
votes
1answer
66 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 ...
1
vote
1answer
49 views

Fixed Effects and Dynamic Panel Data

I have a theoretical model that suggests I should estimate the following regression using longitudinal data: $s_{it} = \eta_{i} + \beta_0 x_{it} + \beta_1 x_{it}^2 + \epsilon_{it}$ where $x_{it} ...
1
vote
1answer
53 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 {AER} package. Running the example code provided in the help page: ...
2
votes
1answer
56 views

Endogeneity test instrumental variables

I'm reading a paper in which is used the following endogeneity test: First of all, we have the initial linear model: $$y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + e$$ $x_3$ is the ...
1
vote
0answers
17 views

Can dependent variables appear in interaction terms in a system of simultaneous equations?

Given a system of 2 equations with y1 and y2 the dependent variables: \begin{align} y1 &= a0 + a1x1 + a2(x2y2) + ... + e1 \tag 1 \\ y2 &= b0 + b1x1 + b2(x2y1) + ... + e2, \tag 2 \end{align} ...
2
votes
1answer
59 views

Joint significance test in 2SLS (instrumental variables) regression

I'm trying to implement a joint test of the two coefficients comprising a quadratic term in a 2-stage least squares regression. The quadratic term is endogenous. I'm using ...
3
votes
0answers
68 views

Deriving the log-likelihood with heteroskedastic errors in linear IV model (with interesting applications once done)

I am trying to derive the concentrated log-likelihood within a limited information maximum likelihood context. The linear model is a compacted instrumental variable regression model and I am ...
4
votes
1answer
161 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 ...
4
votes
1answer
92 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 ...
2
votes
2answers
326 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 ...
5
votes
1answer
99 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 endogeneity ...
5
votes
1answer
304 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 ...
0
votes
0answers
33 views

quadratic endogenous variables in R

As part of ongoing research I'm to test a certain model on some data. One of the questions asked (c.f. one of the hypotheses) involves estimating the quadratic term of an independent variable (in R). ...
0
votes
0answers
27 views

PANEL model (MCMC): Equivalent of system GMM in MCMC

I want to fit a PANEL model via MCMC. I am concerned, that I got some covariates that are endogenous. I use MCMC for various reasons, particularly cause I got some spatial dependencies in my model. I ...
2
votes
1answer
62 views

Can the endogenous variable be insignificant while the instrument is significant?

I suspect that this is entirely possible since the endogenous variable coefficient can biased in many possible way, thus leading to a near 0 estimate despite having a real causal relationship. More ...
4
votes
1answer
61 views

Using predicted probabilities as regressors

I am working on a project where I investigate growth in wages due to migration. I correct for the endogeneity in the decision to migrate (only those that are most likely to gain from migration will ...
0
votes
0answers
57 views

R ivreg command vs. manual 2-stage method

What is the difference between the ivreg command in R and doing the IV regression by hand in two stages? The estimate is the same, but the standard error is not the ...
2
votes
2answers
127 views

Instrumental Variable Interpretation

I have an explanatory variable, 'social class' which I am trying assess the effect on a child's test score. Social class is a 6 fold categorical that breaks down based upon the parent's occupation - ...
1
vote
1answer
54 views

How to estimate model where instrument is correlated with dependent variable

I have the following problem: I would like to estimate the effect of price variation caused by uncertainty on an outcome variable. P is my price, X is the variable measuring uncertainty and Y is the ...
3
votes
1answer
79 views

Variance of Beta IV

I'm trying to calculate the variance of the Instrumental Variables (IV) estimator $${\hat \beta _{IV}} = {\left( {{Z^T}X} \right)^{ - 1}}{Z^T}y = \beta + {\left( {{Z^T}X} \right)^{ - 1}}{Z^T}u$$ (or, ...
2
votes
1answer
120 views

Assessing strength of instrument

I want to use a risk score (RS) as an instrument for an exposure on a clinical outcome. However, I wont have access to data on the outcome for some time, and wish to examine whether this risk score ...
2
votes
1answer
63 views

Rewrite instrumental variables estimator into formula with covariances?

In the book Microeconometrics of Cameron and Trivedi, they write the IV estimator as $\widehat{\beta}_{IV} = \frac{Cov[z,y]}{Cov[z,x]}$, formula (4.49) on p. 99. They say that they derived this from ...
3
votes
1answer
144 views

2-stage panel model - am I doing it right?

I ran a 2-stage fixed-effects panel model in R. The goal is to find the effect of strategic alliance participation on firm performance. Alliance participation is not random - firms self-select (and ...
6
votes
2answers
222 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 ...
1
vote
1answer
194 views

OLS vs IV estimates - Sign and Significance

Assume I have an equation with 1 endogenous variable, and many other exogenous variables. Also assume I have 2 valid instruments for the endogenous variable for IV estimation. If I were to estimate ...
0
votes
0answers
36 views

$J$ statistics to $p$-value of $J$ statistics an vice versa

I am not entirely sure if I should ask this question here, but does EViews has a function of converting J statistics to p-value of Jstats, or other way around. I am running several GMM estimations ...
0
votes
1answer
99 views

J stat problem, GMM

I have recently performed a GMM estimations, my problem is that all the J-stats are 0.0000. It means that the IV are overrefined right or the model is not well specified. I used one-period lags of the ...
3
votes
3answers
204 views

Endogeneity & IV = model misspecification?

I'd like to raise a controversial point: if you need instrumental variables, your model is wrong. Basic endogeneity problem and the IV solution Let us suppose the basic framework of endogeneity and ...
2
votes
1answer
140 views

Practical issues with dynamic panel data modeling

Unfortunately for me, I've got a situation where I need to control for the lag of a dependent variable as a robustness check against an alternative interpretation of my main regression. The baseline ...
3
votes
1answer
1k 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 ...
2
votes
1answer
224 views

IV-RE xtoverid testing both IV validity and RE vs FE?

I am running an xtivreg, re and an xtoverid afterwards. My understanding of the help file and what I found online is that ...
1
vote
1answer
84 views

IV and Exogeneity Tests

Read something about the Hausman test that didn't sound right in some grad course handout online. It stated that the Hausman null of OLS and IV not being statistically different, if not rejected, ...
3
votes
1answer
218 views

Basic Instrumental Variables Dummy Variable question

I have been reading Mostly Harmless Econometrics and have been won over by the virtues of splitting my instrument into groups. In particular, I have a continuous variable as an instrument representing ...
3
votes
0answers
101 views

Dynamic Panel/GMM in R with group:time fixed effects?

Is there a solution coded in R to estimate models of the form $$ y_{igt} = \alpha_i + P_{gt} + \beta_1y_{igt-1}+ \beta_2y_{igt-2} + X_{igt}'\gamma + \epsilon_{igt} $$ ?? ...
2
votes
0answers
32 views

More than one function of a single instrumented endogenous variable — is the model still underidentified?

The typical instrumental variable setup seeks a consistent estimate of $\beta$ from $$ y = \alpha + \beta x + \epsilon $$ where $cor(x,\epsilon) \neq 0$, in the univariate case, without loss of ...
2
votes
1answer
537 views

Basic 2SLS IV Questions in Stata

(1) If I believe my instrument is exogenous conditional upon a few exogenous variables, do I include them only in the first stage? I.e. would the command be: ...