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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Changes in F-value of instrument

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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59 views

Is the key assumption for instrumental variables not testable?

The key assumption: the IV is independent of the response varible Y, cannot be tested empirically and can be argued only theoretically. Is this true? Why? And why is this a problem when we use ...
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Characterizing weak instruments bias with more than one endogenous variable

With a single endogenous variable, it is well known that a weak instrumental variable (or set of weak instrumental variables*) will bias 2SLS estimates toward OLS estimates. But how can one ...
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32 views

Endogeneity problem

I am doing a panel random effects model for estimating the relationship between remittances and poverty. My results are significant. But literature suggests there may be a problem of endogeneity or ...
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Large standard errors in IV regression [duplicate]

I am encountering very large standard errors of the endogenous regressor (bigger than the size of the coefficient) in the second step of my treatment-effects model (...
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6 views

Is it wrong to instrument panel data with an instrument without time series variation?

I have a balanced panel of individuals with an endogenous independent variable $x$. Fortunately I have an instrument $z$ that meets the exclusion restriction, but unfortunately this $z$ has no ...
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44 views

OLS versus IV regression results

I am doing an IV regression after OLS. From OLS I get significant results but I want to control for endogeneity and check reverse causality. So when I do IV, the sign of my main explanatory variable ...
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37 views

An example of Instrumental Variables use

In the following example of Greene's Econometric Analysis, he writes at a certain moment: «If the number of weeks worked, and the accepted wage offer are determined jointly, then $ln Wage_{it}$ and ...
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32 views

positive price coefficient after instrumentation in demand estimation

I need to complete an assignment for Industrial Organization course where one of the tasks is to estimate a discrete choice demand model. This means I basically need to estimate a linear model: ...
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36 views

Endogenous interactions in nonparametric instrumental variables

I'm interested in estimating a model along the lines of $$ pr(y==1) = g^{-1}\left(f(x_1,x_2)+X'\beta\right)+\epsilon $$ where $g$ is logit and $f$ is some smooth function. I'm using GAM's in ...
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62 views

High Collinearity between Instrument and Endogenous Variable in IV Estimation: Weak Instrument Problem?

I am estimating an IV Tobit model with one endogenous variable X and one instrument Z. $$Y=X\beta+ covariates +\epsilon$$ where $cov(X,\epsilon) \ne 0$ due to endogeneity of $X$. I am using IV ...
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42 views

Estimation of individual demand for gasoline

Quantity and price of gasoline are clearly endogenous because the quantity and price are determined by the supply and demand. However, the estimation of individual demand for gasoline is often done ...
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64 views

Choice of an instrument

In order to estimate the demand for electricity, I decided to instrument for monthly electricity consumption in a geographic area with the number of heating and cooling days. My thinking is that ...
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33 views

How to deal with weak instrument with GMM estimator?

I use the two-step system GMM estimator (panel data) and I get the following results: ...
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20 views

A proper use of the Cragg-Donald F-Statistic with more than one endogenous variable

I've read that the Cragg-Donald F-Statistic is similar to an F-test on the first-stage OLS regression when you have one endogenous variable. But with more than two endogenous variables, you should use ...
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22 views

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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80 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 ...
2
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1answer
112 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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85 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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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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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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118 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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42 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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30 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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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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42 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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51 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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21 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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94 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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39 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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80 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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55 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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76 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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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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80 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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103 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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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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297 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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75 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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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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175 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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82 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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288 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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108 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
1k 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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290 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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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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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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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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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 ...