Questions tagged [econometrics]

Econometrics is a field of statistics dealing with applications to economics.

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Regressions with different time periods

I'm trying to run a pooled OLS and fixed effects regression model using panel data but my problem is that my independent variables are measured monthly while my dependent variable is measured annually....
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Likelihood of polynomial time series

I want to model a time series process as follows: There are a total of T periods. I want to model audience dinamics. There is an initial audience of $N_0$ that evolves over minutes indexed by $t$. ...
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heteroskedasticity

I am struggling to understand if it is normal that, when using robust HAC estimators in estimating the parameters of the market model (with a single index and a single dependent variable), the ...
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Two-Step GMM and Instrumental Variable

I am trying to run a regression in r using country-level panel data with female labour force participation rate as the independent variable and lnGDP, lnGDP^2, Trade (as % of GDP), Fertility, School ...
nomes's user avatar
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Do I need to include confounding variables in my regression model when I use instrument variables?

Suppose I believe 'Age', 'Gender', 'Ability', and 'Motivation' are confounding variables influencing both the dependent variable and endogenous variables. I use the 'Education Level' for the treatment ...
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FD estimator: manual first differencing versus plm

I am working on a first-difference (FD) estimator for panel data (only two time periods). I calculated manually the first difference of each variable (dependent and two regressors) and then run an OLS ...
Katharina K's user avatar
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Within transformation vs. first differencing in the over-identified case

I have the following fixed effects model: $S_{it}=D_{it}'\gamma + \alpha_i + \epsilon_{it}$ My textbook says i can use first-differencing and derive a moment function that overidentifies $\gamma$ for ...
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panel causality relationship in long run and short run

What econometrics should I use when I want to estimate the causality relationship between variables in long-run and short-run for panel data? Whether models such as panel VAR, panel VECM or panel ADRL ...
Huy Lê Thanh's user avatar
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How to derive the GMM estimator for the Covariate Balancing Propensity Score?

The covariate balancing propensity score (CBPS) described by Imai and Ratkovic (2014) involves fitting a logistic regression for the propensity score $\pi_\beta(\mathbf{X}) = P(T = 1\vert\mathbf{X})$ ...
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Instrumental Variable with Conditional Randomization?

I am doing a study with an IV design. In my setting, the IV is only conditionally random within a year and within a cohort. In this case, do I simply include year and cohort as controls in the IV ...
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Modeling quesion, linear regression or survival analysis

I am analyzing a dataset where the outcome variable is "teenagers' recreational drug use in weeks." This is continuous and highly skewed outcome variable. While the range spans from 2 weeks ...
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Why is GDP a random variable? [migrated]

I have seen in time series models that GDP is considered a random variable. At first, I found this troubling because I could not see any random process underlying the measurement. However, the ...
Santiago Valdivieso's user avatar
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Bootstrapping t-statistics order of approximation error

Consider bootstrapping the $t$-statistics: $T_n = T(X_1,...,X_n) = \sqrt{n-1}\frac{\bar{X} - \mu}{\hat{\sigma}}$ for iid observations $(X_1,...X_n)$, where $\bar{X} = \frac{1}{n}\sum_{i=1}^{n}X_i$ and ...
fairlife4life's user avatar
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Understanding Fixed Regressors and Conditional Expectation on Fixed Regressors $E(Y|X_i)$

I'm having trouble with the statistical idea of a fixed regressor, it seems that our $X_i's$ are not treated as random variables, but we are still able to meaningfully condition $Y$ on them in a way ...
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log log model to estimate elasticities for 0 demand/dependent variable

Many of you will be familiar with the use of the log log linear regression model to estimate elasticity. I am in this situation where I can get zero demand, the dependent variable, which obviously ...
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Analytical approach when level of self-selected treatment variable is naturally reduced during course of longitudinal study

I realized that some data I have collected may be able to make use of what I originally considered to be a nuisance issue that arose during data collection. I'm looking for input about whether I may ...
commscho's user avatar
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Should I include a dummy variable for groups with few observations?

I am doing some analysis of US Senate races and in my regression I'm wondering if I should include a (party X state) indicator variable that essentially measures the average vote for the two major ...
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Choosing Regression Discontinuity or Difference in Difference?

I am interested in investigating the impact of a policy implemented in 2020 aimed at fostering sustained engagement in music-related activities. This policy involves providing a Conditional Cash ...
Retir's user avatar
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3 votes
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Why are regression models utilizing time anachronistic while autoregressive models are preferred?

I was reading the accepted answer to this question that asked what was the difference between autoregressive models and models that directly utilize time, it states that: Models using time or time-...
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How to address endogeneity concerns using a recursive bivariate probit model?

I read a paper that addresses endogeneity concerns related to a binary moderator using recursive bivariate probit models. Their approach is: Analyze data using a recursive bivariate probit model. Get ...
Puneet Sachdeva's user avatar
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Regression when multiple observations per individual but final result is the same

I'm very new to data analysis. I'm trying to find the causal effect of seating row and laptop use on grades at a specific university. I have data from 15 introductory economics lecture sessions ...
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Inconsistency of GLS Estimator in the Presence of Predetermined Regressors and Serial Correlation

Let be the linear model: $$y_i = x_i'\beta + \varepsilon_i$$ Using its matrix form, consider strictly exogenous assumption and spherical assumption, respectivelly: $$E[\varepsilon | X]=0, \quad E[\...
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Advantages of GLS Estimator for OLS in the Presence of Violated Spherical Assumption

Let be the linear model given by: $$y_i = x_i'\beta + \varepsilon_i$$ Using its matrix form, consider strictly exogenous assumption and spherical assumption, respectivelly: $$E[\varepsilon | X]=0, \...
user346624's user avatar
3 votes
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Multicollinearity and control variables dilemma

I had some superficial understanding of multicollinearity, that two highly correlated variables in the regression model are not what we want, as the estimated coefficient would be biased. Control ...
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What is the difference between pointwise confidence interval and uniform confidence interval in econometrics?

I'm reading Callaway, Bacon, Sant'Anna (2021) paper on continuous treatment. In section 6 they show their result of applying their proposed method to Acemoglu and Finkelstein (2008) medicare example. ...
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Log transformation uses

I am trying to understand how the migration of a male member affects the number of hours spent by left-behind women in various agricultural and non-agricultural activities. I used a simple OLS model ...
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1 vote
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Interpretation of coefficients in panel data

A colleague asked me a question about the interpretation of coefficients in a panel data regression. I'm not familiar with this field but I want to help. The question is this: In our project, we ...
Flounderer's user avatar
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Difference-in-differences when treatment status is revoked

I am trying to analyze the effect of receiving "elite" status on a university's number of international first-year students. I have a perfectly balanced panel of 17 universities over an 18-...
Stephanie's user avatar
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General Expression for the $t$-th difference of conditional means

In econometrics, it is common to work with the difference-in-differences of conditional means. For example, let $Y$ denote a variable of interest and $X_{1}$ and $X_{2}$ denote binary regressors. The ...
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Independence of Shocks in ARCH(1): A Doubt from Hayashi’s Book

I am reading Hayashi's Econometrics book, and on pages 104 and 105 he defines the ARCH(1) model for a time series $g_i$ as: \begin{aligned} g_i &= \sqrt{h_i} \varepsilon_i, \\ h_i &= \zeta + \...
user346624's user avatar
2 votes
2 answers
45 views

Why can the method of moments be expressed as a minimization problem?

Generalized method of moments (GMM) estimation seems to be called generalized method of moments because the standard method of moments (MoM) is a special case, following the following logic. MoM is ...
Dave's user avatar
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1 vote
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Undergraduate econometrics - linear model

I have the following model which I am trying to understand: $y_i=\beta_0+\beta_1 x_{1i} + \beta_2 x_{2i}+ u_i \sqrt{x_{2i}}_i$ where: $u_i\sim i.i.d.N(0,\sigma^2)$, $x_{1i}=x_{2i}+\epsilon_i$, $\...
Katharina K's user avatar
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Test serial correlation for panel data

I have a set of panel data (including variables X1, X2, X3. and N=193; T=22) these variables are used as independent variables in the model. I want to check the autocorrelation of each of these ...
Huy Lê Thanh's user avatar
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Linear regression with pglm: factor effect and country

For my thesis I try to run a linear regression on a gravity trade model. The goal is to analyze the influence of investments on exports between several country pairs over time. For this purpose I have ...
k_c's user avatar
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1 vote
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Width of Confidence Intervals for Variance Estimates in Contrast to Point Estimates

We are conducting a variance decomposition using a hierarchical linear random effects Bayesian model to investigate the variance in a DV that is affected by three nested layers. We estimate credible (...
james_westfield's user avatar
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Detrending and data transformation to logarithm can be done together?

I want to get the effect of bitcoin price changes on foreign currency price. The third variable is inflation, which is an explanatory variable. Should variables be detrended before regressing? Is it ...
user405402's user avatar
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Staggered DiD: Single Treatment

Consider a study involving subjects from 30 cohorts. The key event is a law passed by the Federal Government in 2017, which banned the use of certain vaping products. Among the 30 cohorts, individuals ...
Sundown Brownbear's user avatar
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1 answer
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How to interpret a regression with years on the LHS

I would like to know how I can interpret the coefficients in a regression when the dependent variable is years. For example, suppose I am interested in the year different cities received a new Apple ...
Cola's user avatar
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Deriving the Exact Percentage Change Formula in Logarithmic Models

I have been studying the relationship between logarithmic changes and percentage changes in the context of regression analysis. I understand that when working with small changes, the change in the ...
Newbie's user avatar
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1 vote
1 answer
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Conditional expectation function and causal inference

!For the question itself skip to the last paragraph! It is my understanding that iff we have a model of the form $$Y = m(X) + e$$ and $E[e|X] = 0$ we know that $m(X)$ is the conditional expectation ...
ArOk's user avatar
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3 votes
1 answer
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OLS Forecasting Intervals

currently studying for my econometrics exam and struggling to understand the difference between these two forecasting intervals. xf are new observations added to the sample. Could someone please ...
Quack's user avatar
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dummy variable approach versus fixed effect and first difference approach

While studying Panel data analysis I came across the following reasoning. We have the following general model $$ Y_{it} = \beta_0 + \beta_1 X_{it} + v_t + \alpha_i + u_{it}$$ where $v_t$ is the fixed ...
manav's user avatar
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5 votes
1 answer
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Constants in Frisch-Waugh-Lovell / Partialling Out

If in general one wants to apply the Frisch-Waugh-Lovell "Partialling Out"-approach, should we include constants and in which of the following regressions? (1) In the first stage where we ...
Marlon Brando's user avatar
2 votes
1 answer
49 views

How do I handle outliers?

I'm calculating the beta coefficients for some stocks using a single-index linear model with the OLS method. I'm computing the betas at different return intervals to assess the interval effect on the ...
Mattia's user avatar
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Bias vs consistency in instrumental variable estimation

So in Mostly Harmless Econometrics, page 154, they analyse the bias of instrumental variables: They consider the case of one endogenous variable $x$, multiple instruments $Z$, and $\eta$ is the ...
clog14's user avatar
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How to interpret results from diff-in-diff binary treatment

I ran a dynamic diff-in-diff , of the form $$ y_{it} = \gamma_{i} + \lambda_{t} + \delta T_{it} + \epsilon_{it} $$ y : log(lead concentration) , log concentration of lead in drinking water. $\gamma_{...
Bridgeport BaaS's user avatar
1 vote
0 answers
25 views

System GMM Estimator

Consider the dynamic linear model given by: \begin{equation} y_{it} = \rho y_{i,t-1} + \alpha_i + \nu_{it} \end{equation} where $\alpha_i$ represents individual fixed effects. The GMM two-step ...
Rebecca 's user avatar
9 votes
1 answer
92 views

Adjusted R2 and bias

Consider the population $R^2$: \begin{equation} \rho^2 = 1- \frac{\sigma^{2}_u}{\sigma^{2}_y} \end{equation} This equation describes the proportion of the variation in $y$ in the population explained ...
Dimitru's user avatar
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two fixed effect question

I was reading this journal article on two way fixed effects by Michelle M. Marcus & Pedro H. C. Sant'Anna The Role of Parallel Trends in Event Study Settings: An Application to Environmental ...
Science11's user avatar
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5 votes
1 answer
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Is zero condition mean preserved after transforming the conditioned variable?

In my econometrics class regarding multiple linear regression, we learned that one of the Gauss-Markov assumptions is the zero conditional mean, expressed as $ E(y|\boldsymbol{x}) = 0$. My question is:...
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