Questions tagged [econometrics]
Econometrics is a field of statistics dealing with applications to economics.
2,508
questions
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About difference in difference with a lot of zero in outcome variable
Hi I use a difference in difference framework to study the policy effect. My outcome variable has a lot of zero, actually 75% are zero. My question is that how to interpret the aggregate effect based ...
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Comparing two countries using time series data
I'm considering using time series data to compare Spain's and China's economic performance during various years of economic growth. However, I'm wondering if it's valid to compare them when they ...
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Does reverse causality from Z to Y violate exclusion restriction in IV?
I am estimating the effect of endogenous X on Y using 2SLS estimator with an instrument variable (Z).
X: Safety net program participation (binary), designed to increase household income
Y: Household ...
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Should I adjust for inflation in a staggereded DiD with money as outcome and if so, how?
This question is currently making my head spin, and I haven't been able to find a discussion on it so far:
Suppose I am interested in the effect of an intervention, such as a healthcare reform, on a ...
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Contrasting Results in Regression Models: Flow vs Stock Variables in Policy Impact Analysis
I am conducting a study to analyze the impact of a specific policy on the number of businesses in each region. The policy was implemented in a staggered manner across different regions, and I'm ...
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Partial effect interpretation and zero conditional mean assumption
Let's say we have the following population equation.
$$
y = \beta_{0} + \beta_{1}x_{1} + \beta_{2}x_{2} + u
$$
Then to explain the interpretation of $\beta_{1}$ or $\beta_{2}$, we can look at the ...
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90
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Expectation of the realized volatility
I was reading Zhang and Wang 2023 and I have some doubts regarding it. The realized Stochastic Volatility Model is expressed as follows:
$$\begin{matrix}
y_t = \exp \big( \frac{h_t}{2} \big) \...
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12
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Difference in differences to estimate differential impact of treatment?
I'm having some trouble thinking through the implementation of difference-in-differences / if DD is the best approach to use when I am comparing two groups who are both treated, but which I ...
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17
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Using an EM algorithm for a random parameters model with mixed data
Suppose $x_i \sim f(\theta,\nu_i)$ and $y_i \sim g(\tau,\theta,\nu_i)$ and $\nu_i \sim N(0,\sigma)$. Importantly, $f$ is smooth in $\theta$, but $g$ is not.
We have data on $x_i$, $y_i$ and the goal ...
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Condition variance of $\hat{\beta}$ different under heteroskedasticity
I am following Bruce Hansen's Econometric textbook. Under the assumptions that $\{x_i,y_i\}$ are i.i.d., $E(e_i|x_i) = 0$, and errors are heteroskedastic, we derive the variance of the OLS estimator
$...
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How to deal with a summation term in a regression model?
In the following fixed-effects model, $EI$ is a dummy variable indicating an economic integration agreement in place between $i$ and $j$. $A$ is used to index the specific agreement an $i, j$ pair ...
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Unbiasness of OLS estimates under Stochastic Regressor
I found although the Gauss-Markov Theorms are so widely used, it has so many different versions. Appreciate it if anyone could help me clarify this specific question I have.
Given the OLS estimators:
$...
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How to evaluate the effect of each group in dummy D to endogenous variable X in 2SLS regression?
I have a question in terms of evaluating the effect of a dummy $D$ to endogenous variable $X$ in two-stage least squares (2SLS) regression.
Suppose I have dependent variable $Y$, endogenous variable $...
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What should the estimand be in Coarsened Exact Matching?
I am using the MatchIt package in R for Coarsened Exact Matching. I only understand the basic idea of Coarsened Exact Matching. ...
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The correct condition for OLS estimates to be unbiased?
For the ordinary least square (OLS) estimates of regression ($\vec{y} =\mathbf{X} \cdot \vec{\beta} + \vec{\epsilon}$) to be unbiased (without considering the efficiency), which one of the three ...
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Distinguishing between $\epsilon$ and $e$ in interaction with residual maker matrix $M$
I've hit a small snag in working out some of the implications of the residual maker matrix $M$.
Through previous posts I've been able to understand the difference between the use of $e$ and $\epsilon$,...
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Constructing a meaningful regression model
I'm developing a probit model to predict the partial effect of independent variables on the expected probability of my dependent variable being one (that is the event that a strong growth in GDP ...
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74
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Intuition behind twoway fixed effects
Let us assume we have the following linear regression model:
$$
w_{it}=\alpha_i+v_t+\varepsilon_{it}
$$
where $w_{it}$ represents wage of an individual $i$ at time $t,$ $\alpha_i$ is an individual ...
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How to show mathematically that random effects are more efficient than fixed effects?
I have read in several places now that random effects estimators are more efficient than fixed effects estimators, in particular here
I’ve searched this site and Google and couldn’t find this result. ...
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Interpreting regressions with multiple year and month dummy variables
I have a dependent variable measuring some event, say for each person, I have them in a dataset for a certain amount of months until they die, and they exit the data set. I define my dummy variable = ...
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Is it unwise to create a predictive model based off 20 independent variables when only 10 variables will be available for future observations?
I've created a predictive model which is based off a historical dataset and has 20 independent variables as the dataset set is comprised of completed projects, so have full information and dataset of ...
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VAR on I(1) and I(3) time series
I want to analyze the effect of interest rate to exchange rate with VAR. After some unit root and stationarity tests (ADF, PP, KPSS), all of the exchange rate time series are I(1) series, whereas ...
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Question about Regression, Projection model, CEF, and Structural Model
I want to clarify different concepts that seem kind of mixed in my head, name how the relationship between the linear regression model and the conditional expectation relate to notions of causality. ...
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Bivariate State Space Model Using R Package DLM. Modelling correlation
I am trying to estimate a bivariate dynamic linear model. The data are public sector wages and private sector wages in the UK which we can assume are highly correlated. That is, a seemingly unrelated ...
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1
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70
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Using feols() vs plm() vs lm() in panel regressions in R
I am using panel data at the district level. My outcome variable is the share of employed individuals in a given district. I am regressing this variable on a binary treatment dummy called "treat&...
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53
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How to Handle a Trend-Stationary Dep. Variable and Stationary and Non-Stationary (Unit-Root) Ind. Variables?
I am trying to determine the best way to proceed when one has a mix of stationary, trend-stationary and non-stationary variables with unit roots.
My dependent variable $Y_t$ is a trend-stationary ...
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39
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When adding control variables to a regression, are we actually literally changing the comparisons being made in the data?
If I am regressing wages on years of schooling, I can think of this as I am comparing the wages of people with different years of education. But now if I were to add the age of the individual as a ...
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33
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Outlier Detection By Dummy Regression Models
The standard procedure for outlier detection in time series implemented in almost all statistical
software tools is based on regression the time series to candidate regression variables. These
...
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86
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Expression for OLS estimator in multivariate setting
Assume that we have the following DGP:
$$
y=\beta_{1}+\beta_{2}X+\epsilon
$$
where $X=\{0,1\}$ is an indicator variable. The OLS estimator in
this case is easy to compute:
$$
\hat{\beta}_{OLS}=E\left[...
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18
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Discrepancy in 2SLS Estimation Results
I've been exploring the 2SLS (Two-Stage Least Squares) estimation method to analyze a model involving endogeneity and instrumental variables. To better understand the process, I performed manual ...
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10
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Modeling non-additive seasonal variable
Let's say I have some variable $x_{1}$ and some variable $x_{2}$ and I have the result of $y$ on a specific day/week/month/year. I believe $y$ is a random variable and its result is not very useful. ...
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Estimating treatment effect using panel data and absorbing binary treatment
I have a panel dataset of a large N and T = 24. I want to estimate the effect of a treatment (in this case, taking on a certain type of credit product) on Y which is an individuals credit score. I ...
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Using residuals to estimate synthetic control weights
I would like to estimate weights using the synthetic control method (SCM), in particular using the synthdid package provided by Arkhangelsky et al. (2021) for R. Since I would like to include time-...
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Seeking Literature on Triple Difference (DDD) for Heterogeneous Effects in DD Evaluation
I'm currently exploring the use of difference-in-differences (DD) for my evaluation and have estimated my primary DD effects. I'm interested in understanding if there are differentiated effects ...
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Figuring out if my problem is about a difference-in-differences with a continuous treatment
I am interested to find the causal effects of a state level policy on some outcome of interest. The policy affects some states each year but not other states. The states that are affected can vary ...
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Is there any intuition behind the variance of the multiple linear regression coefficient?
The variance of the coefficients from a multiple linear regression are:
$$ Var(\beta_k|X) = \sigma^2(X'X)^{-1} $$
The single linear regression formula seems fairly intuitive with the denominator being ...
- 521
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14
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Serial correlation and heteroskedasticity in a first-stage regression of a 2SLS
I am about to test a Campbell-Mankiw's based model like:
$$\Delta c(t) = \mu + \lambda \Delta y(t) + \theta r(t) + e(t)$$
where $ \Delta y(t) = \ln(y(t)) - \ln(y(t-1)),~ \Delta c(t) = \ln(c(t)) - \ln(...
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How to keep time-varying but entity-invariant variables in a panel regression fixed effects model?
I am working with a panel dataset that spans 2000Q1 to 2020Q3 and captures quarterly capital flows to 35 different Emerging Market Economies (EMEs). Along with the capital flows data, I have several ...
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Equivalence of Surrogacy and Causal Mediation Assumptions?
I am interested in characterizing the statistical surrogacy condition $Y \perp W | S$ as per the setup in: https://arxiv.org/abs/1603.09326.
Suppose $Y_{i} \in \mathbb{R}$ is the outcome of interest, ...
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47
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Panel data cointegration test: Package pco in R, how to interpret output from pedroni99 function?
I have a panel dataset and I want to test cointegration between 2 variables. I cleaned the missing values and set my data frame as required but I don't know and can't find how to interpret the outcome ...
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How to use Kernel weighted PSM and IPW in Triple Difference estimator (ika Difference in Difference-in-Differences)
I have learned a lot from @dimitriy answer in this post: Propensity Scores Weighted DID
I am currently utilizing the triple difference estimator for estimating treatment effects (please see the paper ...
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What econometrics method is better for the analysis?
I need some tips and tricks to figure out what would be an appropriate econometric method to find causal relationships between $x₁$ and $Y$ in my model $Y = α + β₁x₁ + β₂x₂ + \dotsm + βᵣxᵣ + ε$
where ...
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26
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The magnitude of an two-stages least squares coefficient is always larger than the ordinary least squares coefficient?
I have a hard time wrapping my head around this. I know that in case of measurement errors, the OLS estimate is biased downwards zero. Omitted variables can bias the explanatory variable of interest ...
anon
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14
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Conditional likelihood with missing values
I want to estimate a logistic regression model on a panel data (subject-time) with subject-fixed effects.
$$\log(p_{it}/(1-p_{it})) = \alpha_{i} + \beta x_{it} + \epsilon_{it}.$$
To do so, I want to ...
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1
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112
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How can the potential outcomes $(Y_0,Y_1)$ be independent of the treatment variable $T$? - Causal Inference
currently I am studying the model of potential outcomes and am still confused after reading the other answers on the other threads but also books treating this model.
How can the potential outcomes $(...
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Linear Endogenous treatment effect model
I am investigating the impact of MAC clauses on offer premium and i want to use Linear Endogenous treatment model address endogeneity. The MAC clause is a dummy variable with 1 if there is MAC and 0, ...
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1
answer
16
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Causal inference for spatio-temporal panel data with an continuous independent variable varying over time and cross-sections
For a research project, I have spatio-temporal panel data with an continuous independent variable varying over time and cross-sections, i.e. countries. I have recently read this paper by Papadogeorgou ...
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4
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2
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258
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Conditional expectation for exogeneity
I am reading about ordinary least squares regression, and I came across this assumption called "strict exogeneity", defined such that $\mathbb{E}[\epsilon | X] = 0$ for error $\epsilon$ and ...
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33
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Does it satisfy Parallel trend assumption if coef before the shock is non-zero yet constant over time?
A shock happened in early 2003. I want to estimate how the shock changed the impact of X.
However, X existed all the time even before 2003. That's a difference from typical DID setting where X happens ...
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0
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22
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Covariance between slope parameters/regression coefficients in a regression model
Let's assume a three-variable regression model.
$$
\large
Y_i = \beta_1 + \beta_2X_{2i} + \beta_3X_{3i} + u_i
$$
Can you derive the formula of covariance given below?
$$
\large
var(\hat{\beta_3}) = \...
