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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669 views

OLS estimator derivation: second-order condition to prove global minimum?

In deriving our ordinary least squares estimates, we can partially differentiate the sum of squared errors $\sum_{i=1}^{n} {e_i^2} = \sum_{i=1}^{n} {(Y_i- \hat{\alpha}-\hat{\beta}X_i )^2}$ with ...
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223 views

Confidence Intervals for Elasticity in Simple Linear Regression

I'm pretty sure this is a very simple question that I am missing something obvious. I have a simple linear regression with multiple independent variables. I want to calculate the elasticity (no ...
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1answer
27 views

How to get the effect of one dummy variable against many others?

I have the following regression: wage = constant + (beta1)*michigan+ (beta2)*california+...+(beta49)florida+(beta50)education + u where michigan is equal to one if the person is from michigan and ...
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245 views

How do I choose the correct model for a regression?

So the central question of my project is to what extent does a country's level of export contibution towards GDP (i.e. exports as a % of total GDP) affect its GDP growth. I'm comparing this ...
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1answer
56 views

Does anyone recognize the shape of this residuals vs. fitted plot?

Hello Stack Exchange community, I'm running a regression on a survey dataset which consists of 45,381 individuals in 36 countries using Stata. My model is specified as: ...
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1answer
59 views

Principal component analysis interpretation

Suppose a wealth index is computed using information on a set of 14 assets that a household possesses. The index is generated using principal components, as the 14 individual asset variables are ...
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2answers
86 views

Specification bias - estimated variance is biased estimator of true variance of error term

Consider the two models $ (a) y = X\beta + u $ where $X$ is $n \times K$ and (b) $y = Z\gamma + \omega $ where $Z$ is $n \times r$. Under classical assumptions (and $Z$ and $X$ are non-stochastic) if ...
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1answer
58 views

Should the control variables in an econometric regression be correlated with both the dependent and the primary independent variables?

If, for instance, my dependent variable is some happiness index, and my independent variable is a dummy for whether they experienced some randomly occurred natural disaster. I am trying to analyze the ...
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1answer
2k views

In panel data application, when using Fama and MacBeth regression is preferable over the fixed or random effect model? thought

When discussing panel data, many econometric books, usually, focus just on fixed or random effect model as means of estimating regression for panel data. Despite this tendency, I have seen many papers ...
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442 views

Testing for Endogeneity

I apologize if this question is very basic. I have the following plain vanilla Instrumental Variable model. $Y=\alpha+X\beta+\varepsilon$ $X=\delta+Z\gamma+\eta$ $\varepsilon\perp\eta,\quad Z\perp\...
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1answer
549 views

Principal Components Analysis in Economic analysis

I have a data set of annual prices of various energy carriers over several decades. I want to estimate a model of output using these price series - I guess, I will do a co-integration analysis. There ...
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1answer
66 views

Can I treat pooled cross-section as panel data and do regression analysis?

I work with a large survey data that is pooled cross-section, i.e, people interviewed are randomly chosen in each time period. This is not panel data. But, I aggregate the individual cells according ...
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1answer
326 views

Are unit root tests necessary or useful on small samples of time series data?

I have a 16 year time series (annual frequency with 16 observations). I will conduct an OLS regression. In this setting do I need a unit root test? Do you have additional suggestions for things that ...
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62 views

Conditional independence and no correlation

I have a question regarding basic econometrics. Consider the model $$y_i=\alpha +\beta x_i +u_i$$ I understand that assumption 4 of the linear regression model states $$[1] \quad E(u|x)=0$$ ...
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15 views

Compute the inverse of a conditional quantile regression output

Short Clarification : This question was asked at the Cross Validated SE (Question at CV) but one highlighted in the comments, that this might be more applicable to this SE due to its economic topic. ...
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Measuring time discount in scheduled services: is there a literature in empirical economics?

Prices might be different, for the same service at some date, if you try to acquire the service two weeks in advance and again at a closer date (e.g. two days prior to the scheduled date), such as ...
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34 views

Regression analysis with interaction and decomposed main effect

I'm trying to figure out if I need to include the main effect in a regression analysis with an interaction if I am already including a decomposed version of the main effect. For example, let: ...
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35 views

Demand equation with demographics

I am trying to reconcile the derivation of a demand equation with what I actually run in an OLS model. After solving $$max_{x_1,x_2}U(x_1,x_2)= \alpha ln(x_1) + \beta ln(x_2)$$ subject to $$p_1x_1+...
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1answer
263 views

Appropriate estimator for FDI “gravity” model

I am trying to model Foreign Direct Investment (FDI) flows and am facing several issues; There is the well-known condition that under heteroskedasticity log-linearized OLS models are biased and ...
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23 views

Relationship between parameters estimates of continuous variables and dummy variables

I had asked this question on cross validated before, and have deleted it. Suppose we have a standard wage equation: $$w_{i}=β+β_{1}educ_{i}+x_{i}'\gamma+ϵ_{i}$$ where educ corresponds to education ...
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73 views

Professors Salary vs Alumni Earning: is the relation causal?

Elyase İskender posted in his blog an interesting plot correlating Professors Salary and Alumni Earnings Relation in US Universities. Is there a good way to establish causality here? Did the highest ...
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3answers
82 views

Why would regression coefficients be different on a subsample?

If I'm running a linear regression for example, and I take out some points, wouldn't the same line/plane still fit the data? If not, wouldn't that show that the data doesn't have a linear relationship?...
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1answer
88 views

Calculating natural rate of unemployment

I have sample data on unemployment rate in a market and am looking to calculate the natural unemployment rate. The natural unemployment rate I obtained is constant over a time period, which is not a ...
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1answer
19 views

Linear Regressions: When to expect the residuals to NOT have conditional mean 0?

Suppose that $Y, X,$ and $U$ are random variables such that the regression $$Y=\beta_0+\beta_1X+U$$ is the best linear predictor of $Y$ given $X$. My question is, when can we expect $E(U|X)=0$? I ...
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What is the interpration of results if adding or subtracting a control variable effects the significance of explanotary variables?

I am conducting some regressions on economic growth determinants and I am disillusioned. Essentially by choosing what groups of variable to regress I can get the desired significance. What does this ...
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1answer
47 views

How do I fill gaps in my data?

In my study, I have 5 independent variables which contains 21 observation each. However one of my independent variables have 3 gaps. What should I do? e,g I would need to know the effect of ...
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1answer
371 views

Independent identically distributed

When we are talking about the least squares assumptions, one of the assumpions is that (X,Y) are i.i.d. What bothers me is that if we take an example population and research distributions of age and ...
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1answer
242 views

Problem of generated regressors [closed]

I use data (adv. labor and wage) through a nonlinear model to recover the unobserved data (use fsolve in Matlab to solve this system of equations) and run a regression of labor (or wage) on these ...
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2answers
51 views

Conditional Mean and Linearity

The conditional mean of $Y$ given $X$ is:$$E[Y|X]=\int yf(y|x)dy$$ What is the relation to the linear model? I have read somewhere that when X and $Y$ are normal (their marginal ...
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1answer
56 views

Log log regression with fixed effects and cross elasticity of demand

I have a time series of units sold, and price. I'd like to calculate elasticity of demand wrt to price and a few other variables, some of them are fixed effects. ...
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1answer
34 views

Forecasting quarterly EUR/USD exchange rate

My aim is to forecast the one-quarter ahead EUR/USD exchange rate. I have constructed a regression model with the following as explanatory variables: exchange rate in the previous quarter, EUR/USD ...
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2answers
28 views

Can you take the moving average of quarterly data of an explanatory variable in a regression to smoothen noise and get more accurate coefficients?

I'm trying to use acceleration of quarterly data on household debt (the difference in the difference in debt) in a regression on unemployment (only concerned with correlation) but quarterly data is ...
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1answer
37 views

Detecting Multicolinearity

Are high R square and low t-stats a signal for multicollinearity? What is the nature of this problem and correction? Also, how do you generally decide if the problem is high enough to be corrected?
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1answer
46 views

Justification for my Random Effects estimation

I need to defend my use of the Random Effects (RE) estimator in my economics project. I've been told in cross validated that the proper place for the question is here. The causal effect of the ...
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1answer
107 views

Why does instrument exogeneity imply conditional mean zero?

In the following slide ECON4150 - Introductory Econometrics Lecture 16: Instrumental variables, Monique de Haan it says that "instrument exogeneity implies $E[u_i \mid Z_i]=0$" where instrument ...
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1answer
60 views

Dummy variable regressor OLS coefficient formula

Consider the standard linear regression model: $y_i = \alpha + \beta D_i + e_i$ where the coefficients are defined by linear projections and $D_i$ is a dummy variable. In the population, the ...
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1answer
108 views

Regression with Dummy Variables

When I analyzed a data set with two categories, I used a dummy variable $z=1$ for category 1, and 0 otherwise, and added the extra term $\beta z$ to the regression model. Suppose the least squares ...
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1answer
133 views

RDD with multiple cutoffs

I am trying to study the effects of a policy on educational attainment of individuals (years of schooling, primary/secondary school completion, literacy). Since the policy starts in a specific year I ...
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1answer
84 views

RDD, wages, and day of birth

What I am doing: I use the regression discontinuity design (henceforth RDD) to study differences in wages received by people born at the end of the year and by those people born at the beginning of ...
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1answer
42 views

Alternative normalisation to triangular restriction on cointegrating vectors

Johansen recommends that cointegrating vectors must be normalised for inference making purposes. All software packages use triangular normalisation of the cointegrating vectors i.e. the top $r$ by $r$ ...
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1answer
81 views

How do I obtain a correlation between two variables?

Can I differentiate a quadratic regression model formula with the form $$Y_i=\beta_0+\beta_1 X_{1i} +\beta_2 X_{1i}^2+\epsilon_i$$ (added to this formula would be other control variables e.g dummy ...
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1answer
49 views

How to interpret this regression coefficient?

I am performing a simple single variate regression on the variables crime rate (denoted by crrate) and the probability of getting arrested (denoted by prarrest). To be precise, the variables are ...
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2answers
53 views

Difference between a multiple regression and several linear regressions?

Context: I'm an undergrad who took Intermediate Econometrics more than a year ago and I'm trying to brush up on some of the skills. As I was reviewing multiple regression, I realized I didn't quite ...
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1answer
51 views

Hedonic regression and attribute-shares in house prices

Given a house with price $P$ and attributes $h_1,\dots,h_n$, I want to estimate how much each attribute costs as a percentage of house price $P$. In other words, if we express house price as the sum ...
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2answers
37 views

Meaning of regression coefficients

I am having some trouble understanding exactly what is meant by the "true" Regression coefficients. Let's say it is stated that "the true regression coefficients are given as $y=a+bx+e$ where the ...
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1answer
41 views

Is conditional mean independence, $E(e_i | x_i)=0$, a different assumption from $E(x e) = 0$? (from Hansen)

This question comes out of Hansen's Econometrics ((https://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf)) In section 2.18, we only impose the assumptions of finite variance and $Q_{xx}$ ...
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1answer
40 views

Is this a valid derivation of FWL?

$Y = X\hat{\beta} + Z\hat{\gamma} + e\\ (X'X)^{-1}X'Y = (X'X)^{-1}X'X\hat{\beta} + (X'X)^{-1}X'Z\hat{\gamma} + (X'X)^{-1}X'e\\ \hat{\beta}_{short} = \hat{\beta} + \hat{\delta}\hat{\gamma} $ where $\...
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2answers
57 views

regression method for data that contain a number of observation for several years

I have a data set about 125 companies. For each company I have the salary and some other variables about the top 5 managers in each company. One observation contains the top 5 managers in each one of ...
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1answer
39 views

Correct Equation for Pooled OLS Regression (with Time Dummies and Interaction Terms)

I have a question regarding a pooled OLS regression. Basically, I’m not sure I’m writing out the equation properly. The data is on feature films released between 2006 and 2016 (11 years); box office ...
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1answer
84 views

Linear Regression Assumptions of Homoskedasticity

When I studied linear regression analysis, one of the assumptions taught was that of homoskedatiscity. I understood that homoskedasticity was required for significance testing on the coefficients. ...