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.

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Graph showing the first stage effect

I am using a 2SLS approach in order to estiamte the effect from increased education. I want to show the effects of the first stage graphically, ie I want to show that the instrument affects schooling ...
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37 views

2SLS probit vs LPM

I am using 2SLS to estimate the effect of education on the probability that one works. In the first stage I regress education on my instrument and the other exogenous control variables. The same ...
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1answer
56 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 ...
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49 views

Mixing instruments in ivreg2 estimation in Stata

When using a 2sls estimation with ivreg2 with more than one endogenous variable, Stata necessarily -- as it seems to be -- instruments both endogenous variables ...
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14 views

Dynamic nonlinear IV question — how do you think about the exclusion restriction when you have multiple periods?

The setup is an experiment with a binomial outcome, repeated over two (or more) periods. In the first period, $X$ is randomly allocated. Of interest is its effect in predicting the probability of ...
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19 views

Is the application of the Frisch-Waugh-Lovell Theorem really necessary?

Suppose I have a model \begin{eqnarray} y = X_1 \beta + X_2 \gamma + \epsilon \\ X = Z \Pi + V \end{eqnarray} where $X_1$ is endogenous, Z are instruments, $X_2$ are exogenous. If I however include ...
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77 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 ...
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39 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} = ...
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25 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) ...
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25 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 ...
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36 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 ...
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40 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 ...
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17 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 ...
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68 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 + ...
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34 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 ...
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72 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 \\ ...
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48 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, ...
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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: ...
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28 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} = ...
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1answer
79 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 ...
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75 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 ...
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55 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} ...
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94 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: ...
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65 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 ...
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21 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} ...
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82 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 ...
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76 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 ...
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230 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 ...
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1answer
98 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 ...
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2answers
547 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 ...
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175 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 ...
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532 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 ...
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36 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). ...
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30 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 ...
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1answer
74 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 ...
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71 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 ...
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68 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 ...
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2answers
128 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 - ...
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58 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 ...
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1answer
81 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, ...
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1answer
134 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 ...
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1answer
67 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 ...
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1answer
188 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 ...
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2answers
247 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 ...
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250 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 ...
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37 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 ...
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114 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 ...
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225 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 ...
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1answer
157 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 ...
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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 ...