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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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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Which economic model and variables should I use to investigate the impact of sentimental shocks in central bank statements on investment?
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I am currently working on a research project that aims to investigate the impact of sentimental shocks in central bank statements on investment in the economy. I am looking for guidance on selecting ...
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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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How to use Census Tract data?
I am trying to control for neighborhood characteristics using census tract data. I've never done this before. I have home addresses and census shapefiles. How do I do this? Do I need to geocode the ...
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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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What are different ways to determine how an explanatory variable affect a target variable?
I'm trying to determine a quantitative value by which a target variable change (inflation) by changing an indicator variable (interest rate).
The industry basically uses linear models such as VAR. Are ...
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Should you deflate prices by index when doing multiple regression?
I have data ranging from 2008 - 2016. I have been studying effects on the %satisfaction of creditors in debt relief (Czech Republic). I have used modified "One vs. All" method, where I forgo ...
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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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Event study with individual fixed effects
Suppose we have a treatment that varies at the group level before and after some t, where g is rather small with a couple of categories. Would we estimate an event study with group or individual fixed ...
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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 do I instruct R that there are no duplicates in my data? [duplicate]
I am trying to construct a panel dataframe in R.
...
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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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Why don't Time Series books talk about exogeneity like in classical linear regression models?
Consider the following linear regression:
$$y_t = \beta_0 + \beta_1 x_{t} + u_t$$
Typically, we need to assume (assuming a random sample):
\begin{equation}\label{I}\tag{I}
E[u_t]=0, \quad cov(u_t ,x_t)...
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When should I NOT control for unit-fixed effects?
I see most of the applied econometrics papers using the two-way fixed effects model, controlling for time and units fixed effects, so:
$$y_{it}=\alpha_{i}+ \gamma_{t} +\beta x_{it} +\epsilon_{it}$$
I ...
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The definition of control variables
My professor provided the following when introducing control variables
Suppose we have the causal model
Y = Beta_0 + Beta_1*D + U
Suppose E[UD] not 0
then, if we have extra observable characteristics ...
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Do Aggregated consumers make sense?
Aggregated consumers as a biased concept (in case of cross-price elasticity)?
I try to approach aggregated consumption data as if it was a new consumer (similarly to approaching average data as if it ...
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Find Lerner Index from Cobb Douglas regression
I'm currently following a Master's in Finance, and we have to calculate the Lerner Index.
To do that, we are given the following Cobb- Douglas regression, where the alphas have to sum up to 1:
$$\ln(...
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Elasticity of substitution by regression: Biased results (simulation)
I have the following simulation problem:
Consumers, whose utility I know, go shopping for two goods. However, prices differ each time they visit a shop. Therefore, these consumers always purchase ...
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Diff-in-diff with two control groups: compare parallel trends
Suppose in a diff-in-diff problem, I have two control groups, but just one can be used as comparison, so I want to check which of them provides a better comparison. My idea is to compare the parallel ...
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Can I use negative binomial regression to estimate amount of money type data?
I know that the negative binomial regression is for count variables - can the amount of money be considered as count data? There is a paper on which I have to extend upon, where the authors are ...
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What is the common way to separate panel sample by firms' profitability?
I have panel data on firms in 3 countries (e.g., 100 firms in 3 countries in 5 years, and event happen at the 3rd year in all countries at the same time). For an example, for each firms I have 4 ...
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Interpreting the regression results
This might be a basic question.
The article given below checks the relationship between crime and income inequality.
https://www.sciencedirect.com/science/article/pii/S0165176508001110. Both crime and ...
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Difference in Differences with panel data/repeated cross section with dummy
I have to do a public policy evaluation (on R) based on an article where the authors use a quarterly survey to study the effect of a parental leave reform in 2015(reducing the length of leave) on the ...
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unobserved heterogeneity and time fixed effects
I understand that if there are correlated effects i.e. (one of) our explanatory variables are correlated with unobserved heterogeneity $\alpha_{i}$ then there will be omitted variable bias. Because ...
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Industry-specific control variables
I am writing about bank-lending to a specific industry and how that could be affected by the level of carbon intensity of a given industry within the EU. I have some thoughts on this:
Trying to think ...
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Comparison of two AR(1) regression models (lead in dependent vs lag in dependent variable)
What is the difference between these time series AR(1) regression models (lead in the dependent vs lag in the dependent variable)?
$$\begin{align}y_t = constant + \alpha y_{t-1} + error \tag{1}\label{...
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In Panel Data models, could we apply the existing Unit Root Tests (i.e. IPS) to the residuals in order to test for Cointegration?
The Engle Granger approach suggests that we check the regression residuals stationarity with ADF test and if the residuals are stationary, even if not all other model variables are, we can say there ...
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how to use projection matrices in econometrics
We have the below expression:
$$
P_{M_{1}.X_{2}} \cdot y
$$
I guess its interpretation is that they are the fitted values obtained from the regression of $y$ on residuals that are obtained from the ...
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How to show SSR of the residual vector from regression of y on X1 and X2 is equal to SSR of y on X1 and X2
What I mean in the title is that when we regress $y$ on $X_1$ and by using projection matrix $M_{X1}$
how can I proceed with that:
the model is
$$
y = X_1 \cdot \beta_1 + X_2 \cdot \beta_2 + u
$$
or ...
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Omitted Variable Bias with interaction terms
Suppose we have the long regression
$$ y = \alpha + \beta D + \gamma X + \varepsilon $$
but instead use the short regression
$$ y = \alpha + \beta D + \varepsilon $$
then one can show that the OLS ...
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Construction of F-Test
While constructing the F-test with matrix notation,
For the Unrestricted model, we have:
$$ y=X_{1}\cdot b_{1}+X_{2}\cdot b_{2}+e $$
For the Restricted model;
$$ y=\widehat{X}_{1}.b_{1}+e_{R} $$
...
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How to prove that Adjusted R^2 is less than R^2
The adjusted R^2 formula is :
$$ \overline{R}^{2}=1-\left( \left( 1-R^{2}\right) \cdot
> \dfrac{n-1}{n-k}\right) $$
In case of k > 1 , I continue like that;
$$ \overline{R}^{2}=1-\left(
\...
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Understanding how to estimate the model of Fung and Hsieh (2001) for the hedge funds risk factors
There is an old paper about the risk of hedge fund strategies that it gathers its focus in the trend followers. This is the Fung and Hsieh (2001) paper.
$\textbf{Definition of Trend Followers (TFs):}$ ...
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