# Tagged Questions

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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### Endogenous ordered probit (Stata, R)

main equation $y_1 = y_2 \beta + x_1 \gamma + u_i$ Instrumental equation $y_2=x_1 \pi_1 + x_2 \pi_2$ I have a binary endogenous variable $y_2$ in my main estimation equation. My instrument $x_2$...
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### 2SLS - 2 OLS for 2 endogenous variables in 1st stage and logit/probit in the 2nd stage?

I came across this question (here) saying that I can manually run an OLS in the 1st stage with the endogenous variable as dependent variable (i.e. the instrument) get the fitted values for the ...
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### Probit with more than one instrument

I am estimating a probit model with instruments in R (using ivprobit). My simplified model looks like this: ...
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### Multilevel Binary Logistic Instrumental Variables Regression

Context I have hierarchical data where individuals ($i$) are nested in groups ($j$) and am interested in examining the degree to which a continuous group-level variable ($X_j$) moderates the effect ...
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### How can I compute the standard error of the Wald estimator?

According to Cameron and Trivedi Microeconometrics 2006, page 98-99, the Wald estimator can be written : $$\widehat{\beta}_{Wald} = \frac{(\bar{y_1} - \bar{y_0})}{(\bar{x_1} - \bar{x_0})}$$ with :...
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### How to estimate a fixed effects regression WITH robust standard errors AND instrument variables

I have been trying to estimated the stated problem, but I only succeed in parts of it. The following artificial setup is supposed to illustrate my problem in detail: Setup the data: ...
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### 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.
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### IV - 2SLS with only an instrumental variable (operative problem)

I have some problems with IV estimation. I read in several works of experiments that using the 2SLS with just one instrumental variable but more than one $X$ variables. When I try to run a 2SLS ...
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### Time series and instrumental variables

I have a time series model that suffers from endogeneity. In other contexts it would be reasonable to use instrumental variables. However, I have not seen this done before with time series. Can I ask ...
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### Control variables in instrumental variable regression

I have seen published papers include "exogenous controls" in their instrumental variables regression. Can someone explain: What is meant by "exogenous" in this case? The purpose of these "controls" ...
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### Generalized Instrumental Variable Estimator (GIVE)

In some literature it is possible to find the Generalized Instrumental Variable Estimator (GIVE), but this is not always well-specified. Is this estimator equivalent to an estimator found using the ...
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### 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 ...
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### Double lasso variable selection

Currently I am learning about variable selection and lasso. I found the paper by Urminsky et al. "Using Double-Lasso Regression for Principled Variable Selection" (2016) which proposes a double lasso ...
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### 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-...
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### Why instrumental variables? Or: why not nonparametric regression?

Usually instrumental variables are introduced as a means to solve the problem $E(u|X)\neq 0$ in the model $Y = X'\beta + u$. This may happen if we omit important variables from the covariate vector $X$...
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### Past values of Y correlated with future values of X1 in fixed effects model: use instrumental variable?

I am using panel data, running a fixed effects regression using xtreg Y X1 X2 X3, fe. I suspect, however, that past values of Y ...
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### 2SLS Regression, 1 Instrument effecting more than one explanatory variable?

So in my situation I have my dependent variable Log Income my Instrument Diabetes and my supposedly endogenous explanatory variable Reads Nutri. Where things start to get confusing for me is that ...
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### How to interpret hausman test results?

I'm trying to do 2 stage least squares regression in python using the statsmodels library. ...
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### Why I can not perform a Haussman test with pweight data?

I am studying the effect of mobile phone over household development (development as a dependent variable and mobile as a independent). I have a datas et of micro data that are weighed and i am working ...
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### Sign of the correlation between endogenous/instrument variable and error term

I am doing my thesis using 2SLS, the IVs that I include to the model are not weak (F-stat>20), however, to prove that they are exogenous is a problem. I am going to use imperfect instrument approach ...
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### Instrumental variable approach when having a binary variable in first and second stage [duplicate]

I am trying to estimate an IV model where my dependent variable is on the 0-1 scale, which is why I want a Logit estimator. Further, my independent variable, which is endogenous, as well as my ...
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### 2 stage least squares

I am looking into the effect of immigration on crime (using random effects panel data). there are 2 problems which 2 stage least squares should help with, firstly the endogeneity of immigration (as ...
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### How to interpret instrumental variables estimate if the identifying assumption is not satisfied?

Following the notation here, consider a model $$Y_{i} = \alpha + \beta X_{i} + \eta_{i}$$ where $X_{i}$ is the endogenous variable such that $Cov(X_{i},\eta_{i})\ne 0$. Suppose we have a binary ...
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### Instrumental variable identification for price elasticity

I am working on a price elasticity problem and i am using Log-Log linear model. Below are the set of variables Dependent variable: logarithm of my quantity sold (LogQ) Independent variable: ...
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### Do I have a problem of endogeneity?

I'm currently writing a dissertation on the impact of microfinance activity in a country on the poverty headcount ratio. It's a panel data model where i = country and t = year. I would like to ...
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### Instrumental variables regression Vs Linear Regression for price elasticity

Based on comment here that What do "endogeneity" and "exogeneity" mean substantively? should we use linear regression or instrumental regression for price elasticity? As price and ...
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### Instrument caused by dependent variable

Suppose that my instrument z is sufficiently correlated with the endogenous independent variable x in consideration (z->x). Now, I know that my dependent variable y is also a predictor of z (y->z) but ...
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### Using an interaction term as the instrument variable

I recently came across Barro and Redlick QJE (2011) paper, "Macroeconomic Effects from Government Purchases and Taxes", in which the authors instrument for US defense spending with an interaction term ...
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### Simultaneous equations with instrumental variables

I am trying to estimate the simultaneous equations model with instruments in STATA. I have two equations such as: ...
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### What can go wrong using lagged terms as instrumental variables?

Can anybody give one example of when the set of all lagged $X$ can (or can't) be a good choice of IV's for $X_{t}$?
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### Endogeneity in censored data

I estimate Instrumental Tobit using Newey’s (1987) minimum chi-squared estimator. My question is whether I can use lagged values of the endogeneous regressors as internal instruments for the ...
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### Same instruments with different impact on multiple endogenous regressors

I have a regression containing 2 binary endogenous (X1 and X2) regressors. I have 2 instruments (Z1 and Z2), where both Z1 and Z2 have a significant positive effect on X1 and a significant negative ...
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### Multiple exogenous IV 2sls in Stata [closed]

In my model I have two exogenous variables which I want to use as instruments. Can you please help me with Stata code for it? I assume it should be something like this: ...
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### How do weak instruments violate full rank condition?

So I know that if the instruments $(Z_i)$ in 2SLS regression are weak i.e. $X_i$ and $Z_i$ are uncorrelated, then full rank condition for matrix $\Sigma_{ZX}=E[Z_iX_i]$ will fail to hold, but how can ...
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### how to explain instrumental variables to a layman

I am giving a talk to a group that contains both quantitative and qualitative researchers, but most of the quants' understanding stops at crosstabs and regression. Does anyone have any ideas which ...
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### Questions on IV (2sls) model with cross section data

I want to test cross sectional data with a household survey with 60k plus of respondents (however missing data result in overall data loss). The survey asks questions that answer either 0 or 1 or are ...
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### Instrumental variable changes significance of other regressors

I have a linear regression:I am regressing price index and price volatility on some number of conflict events (dependent variable). Looking for a causal relationship between price index and number of ...
I have the following problem regarding fitting of a model where some variables can be biased so that their values are based on knowledge or at good guestimate of $Y$ in the past. In other words: some (...