Questions tagged [regression]
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors').
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Engineering student doing an eco/fin project on ESG. Need additional resources
I am trying to get a fin/eco project and my prof has asked me to read a paper on ESG titled, "ESG performance and business risk—Empirical evidence from China's listed companies." I am ...
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OLS estimator after standardization of the regressor
Consider a population in which two random variables, $y$ and $x$, satisfy the following relationship,
$$
y=\beta_0+\beta_1 x+u,
$$
where $E[u \mid x]=0$. You wish to estimate the unknown coefficients $...
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A question on the optimisation problem and FWL theorem
Let's say we have the following model:
$$(\beta^{\star},f^{\star}) := \arg\min_{\beta,f \in \mathcal{F}} \mathbb{E}[\left(Z_i - f(X_i, E_i) - \beta^\top \boldsymbol{\tau}_{i,E_i}\right)^2|S_i^{tr} = ...
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Addressing Irregular Time Intervals of observations in Event Study/Staggered Difference-in-Difference Method
I am conducting a study using an event study/staggered difference-in-difference (DiD) method. My dataset consists of observations with irregular time intervals: some individuals have daily ...
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Why taking ln() of change in invested wealth? Methodology of a published paper
I am going through the paper referenced below, and I am struggling to understand the reasoning behind the equation to calculate their dependent variable. Please could you help me with that?
Paper of ...
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Log-Log Regression versus Delta-Delta Regression
I am trying to estimate the self- and cross-price elasticities of demand for Alaska (AS) and Southwest (WN) on a given route. I have price in quantity data that varies over time.
Which of the ...
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Difference between country-fixed and region-fixed effects
I am writing a paper about the effect of childcare on maternal employment and I use an OLS regression with time and country/region fixed effects. The regions here are not within countries, but North/ ...
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Finding the distribution in OLS
I have the following linear regression model:
$$
Y_i = \beta_0 + \beta_1 x_i + \epsilon_i
$$
where $\epsilon_i$ are independent $N(0, \sigma^2)$ random variables. Let $\hat{\beta}_i$ denote the ...
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Estimate a simple regression (homework question)
The Director of UNAM’s Student Affairs would like to investigate the relationship between the number of hours (X) students spends campaigning and the percentage of votes (Y) they end up receiving in ...
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Kernel Density Estimation and Nadaraya Watson Estimator reference
I am looking for a reference that is on kernel density estimators with the following results:
Let $(X_1,Y_1),\ldots,(X_n,Y_n) \in \mathbb{R}^{p} \times \mathbb{R}$ are i.i.d. and $\mathbb{E}(Y|X=x)=m(...
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What's a classic (paper) example in which OLS gives unreasonable result, but IV estimate gives reasonable result?
I'm wondering are there are any classic papers, especially in the field of labor economics or development economics, that include regression tables showing OLS gives unreasonable result(like ...
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In a regression of Yon X, the value of X is fixed at 5. Find the regression equation
I wanted to know how this equation will look like and how we will be able to calculate the slope coefficient.
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Regression coefficients interpretation
Can anyone help me with finding out the computations for reaching this conclusion?
"In terms of magnitude, the point estimate implies that going from the average of 8% blacks in the same-gender ...
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Regression with one independent variable bounded for some observations
I am investigating the effect of a policy on land price.
The land is transferred by English auctions. My regression looks like this:
$$
\ln(y)=\beta_0+\beta_1 x_1+\beta_2 x_2+u,
$$
where $x_1$ is the ...
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IV combined with matching
I have seen a couple of papers combining DiD with matching. Is there also something similar for IV? Especially given the problems with linear inclusion of covariates in 2SLS, see Blandhol et al. (2022)...
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Interpretation of OLS regression coefficient of -1.19 when depent variable ranges from 0-100
In an experiment, the participants were asked to allocate 100% of their budget to three categories in different scenarios.
Now, I am analyzing the allocation to one particular category via OLS ...
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RDD regression discontinuity
I have a tiny dataset for several countries: Year (2010-2022) , GDP per capita, Subsidy amount - in the second column (fossilf), and a few other variables. The subsidy amount is 0 for several years. ...
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Significance of simultaneity BIAS in local retail shop belonging to a big retail chain
This question follows from the previous question on multiplicative BIAS in cross-price elasticity, but I think it deserves its own space.
I have scanner data from a small store branch belonging to a ...
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Can you compare experimental data from students, investors, and professionals? Different N, different clusters
I have experimental data on students, retail investors, and professionals. The setup (experimental procedure is exactly identical). Each experiment consists of 5 rounds of decision-making.
However, my ...
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Multiplicative (Self-reinforcing) BIAS in Cross-Price Elasticity
I have been trying to estimate cross-price elasticity of demand on market optimum data by simple regression such as:
$$ln(x_i) = \beta_0 + \beta_i ln(P_i) + \sum_j^J \beta_j \cdot ln(P_j) + \epsilon$$
...
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Can you trust a regression model that has an insignificant F-test and insignificant coefficients?
I have a regression with an insignificant F-stat. In an even stricter regression (with fewer observations), the F-stat becomes inestimable (denoted by Stata with dots in F and Prob > F).
My ...
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Can a single dummy variable be made to meet multiple criteria?
Let say I have criteria 1, 2, 3, and 4. I would like the Dummy variable to be 1 only if a certain minimum amount of criteria are met. For example, if 3 of the 4 are true, then Dummy =1. If 4 of the 4 ...
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Can I multiply two dummy variables together?
Are there any rules about multiplying dummy variables in a regression?
For example can I say:
y = D1D2x1 + x2 + x3
Would I be able to state D1*D2 as I want both criteria to be met before x1 is ...
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Linear Regression Model and estimators
Consider the following linear model: $Y = X\beta + u$
.
If Gauss-Markov assumptions hold, I'm trying to prove that $\hat{\sigma}^2 = \frac{\hat{u}'\hat{u}}{N-K-1}$ is an unbiased estimator for the ...
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Regression discontinuity design
I have this setting:
Where V is the running variable and M=1 if V>0. It is a sharp RDD. D is a set of period dummies and $\tau$ is the calendar year. Coefficients in
vector $\beta$ capture the ...
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Controlling for Log population with Log GDP per Capita outcome in OLS
Bartlett and Partnoy (BP) (2020) show that OLS with natural log dependent variables that are ratios must include the ln(denominator) on the RHS or they must assume that the numerator and denominator ...
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Ordered Logit Model: Marginal Effects Signs Opposite
I'm deeply stuck in an issue in my research paper's methodology. I'm getting the following disparate results for my marginal effects.
In my Ordered Logit model, I have Y = Trust in banks (4-Max trust,...
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Variance of OLS Error Variance Estimator
Consider a model $Y=X\beta+e$ and define the OLS error variance estimator as $\hat{\sigma^2}=1/n\sum_{i=1}^n \hat{e}_i^2$, assuming that $ E[e_i^2]=\sigma^2 $ More precisely I want to derive the ...
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Regression and RDD give results in opposite directions but both statistically significant
I am conducting an RDD on an attitude and how it shifts over time due to a shock (sharp RD measured in days), I am using RDROBUST in STATA. I do not think I have coding errors but I need help ...
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What could a negative output elasticity of an input imply?
Output elasticity of an input means (consider the non-calculus formulation) the percent change in output for a percent change in input (it is customary to substitute “change” with “increase”).
Let’s ...
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data on US college spending
I am writing a research paper on college spending and profit optimization. I need data on US colleges' expenditures, revenues, and the total number of students. Since I am not from the US I am not ...
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Difference in Difference - how to choose the control group (difference with no clear trend, parallel series or cointegrated?)
I'd like to use difference in difference methodology to test the impact of a treatment. Being the formula of the regression:
...
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Abadie's Kappa (2003) for continuous treatments / IVs
Does somebody know if there exist results and estimators to deal with controls in IV estimation under heterogeneous treatment effects, analogous to Abadie's Kappa (2003) for the binary case?
Abadie, ...
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How does one include a "linear time trend"
I've seen this mentioned often in papers, but I never fully got what it means. Below I simulating some diff-in-diff type of data with Stata.
How would a "linear trend" be included in a two-...
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coefficient interpretation
I have a regression:
y=b_0+b_1x(treatment)+b_2x(female)+b_3x(treatmentxfemale)+e
the effect of the treatment for the female is b_1+b_3. So that, what is the interpretation for coefficient b_2?
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Difference between Quantile Regression and Endogenous Stratification
I have a question that stems from an ongoing experiment I'm conducting, focusing on treatment heterogeneity.
Initially, my approach involved considering a beyond-mean analysis utilizing quantile ...
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difference perfect and imperfect multicollinearity?
I am struggling with two examples where I wanted to identify whether it is a problem of perfect or rather imperfect multicollinearity. First, a variable "expenditure" is calculated by ...
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Deriving `\beta_1` in OLS
I'm studying for an Econometrics exam and going over an old lecture slide (see picture).
In it the lecturer is deriving \beta_1 in a basic OLS regression with one ...
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Elasticity computation
Suppose that we have the following regression:
$$ln (h) = e_{0} + e_{1} ln (w) + u$$.
Isn't elasticity $e_{1}$? in other words: $\frac{\delta ln (h)}{\delta ln (w)}$? I am a bit confused since I have ...
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Critical Value for Chow Test
What are the degrees of freedom for the F-distribution used to find critical values for the Chow Test?
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OLS-estimation and regression models
I have the following Model and would like to know how to acquire the OLS-estimates when the model is expressed like this? I have tried to look it up, but no one is explicit about how to acquire the ...
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Regression Discontinuity in Time (RDiT)
Is it correct to specify an RD model where time is the running variable but the data is not measured at the time the running variable is referencing to?
Let's say I want to estimate the impact of a ...
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Testing Kaldor's Second Law
According to Kaldor's second law, as manufacturing industry grows, the productivity in manufacturing will increase:
$$p_i=f(g_m)$$
And, from the article of Heather Wells and A.P. Thirlwall (Testing ...
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Regression Discontinuity Design equation
Dear all,
I found this equation to estimate a RDD in a paper. $(f_i-f_z)$ is the running variable, hence $\alpha$ should be the slope to the left of the cutoff and $\lambda$ the variation in the slope ...
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Greene's Econometric Analysis (8th edition), Table 6.12, p.233
I tried, but without success so far, to reproduce Greenes' empirical results using his gasoline data available at:
https://pages.stern.nyu.edu/~wgreene/Text/econometricanalysis.htm
You will find the R-...
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How to read this regression table?
The image is from Abhijit Banerjee's Legacy of Colonial Land Tenure Systems
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How to overcome the problem of duplicates in Panel data in R
I tried to convert my data to panel data but i kept experiencing an error message. The data is in the form of likert scale. The error message was
duplicate couples (id-time) in resulting pdata.frame ...
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Regression on individual vs collapsed data
Lots of analysis in the US collapse CPS or Census data and run regressions on the group means. I wonder why not run the regression on the individual data? Absent measurement error, should we expect ...
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What is the difference between fixed effect regression and (panel) fixed effect regression?
What's the difference between fixed effect regression and (panel) fixed effect regression?
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Is matching combined with Diff-in-Diff a bad idea?
I remember seeing such a comment on Twitter long time ago but I see so many prominent papers doing it that I doubt it can really bad. Does somebody know more (e.g. papers) on this?
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