Questions tagged [econometrics]

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

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1answer
22 views

Frisch-Waugh-Lovell Theorem: Partialing out a set of regressors [duplicate]

I am trying to understand the result of the Frisch-Waugh-Lovell Theorem that we can partial out a set out regressors. The model I am looking at is $y=X_1\beta_1 + X_2\beta_2 +u$ So the first step ...
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0answers
12 views

Stationarity with ANNs

I have a background in Econometrics, and am essentially always checking stationarity when I am conducting time-series analysis. Recently, I have started to look into other Machine Learning methods ...
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1answer
32 views

Can someone explain me how I compute $Cov[X_t, X_{t+1}]$ in this case?

I have some problems computing the autocovariance in the above exercise. Especially when given different lags, I do not understand why the number of lags is in the exponent of $\phi$.
2
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1answer
29 views

truncated model estimation, on an interval of unobserved variable Y*

$Pr[L<Y^*<U]=Pr[Y^*<U]-Pr[Y^*<L]$ $=F^*(U)-F^*(L)$ $lnL_n(\theta)=\sum_{i=1}^nd_iln[F^*(U|x_i,\theta)-F^*(L|x_i,\theta)]$ ^is the above likelihood function appropriate for ...
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1answer
19 views

What is the expectation of the product of 2 random variables (Gauss-Markov assumptions)?

In the two variable (intercept and slope) model: among other, one of the Gauss-Markov assumptions is (in the BLUE framework of OLS) My coarse slides state this implies that there is no correlation ...
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0answers
12 views

Are country fixed effect necessary?

I have a model where I'm trying to estimate the effect of FDIs on a technological variables across countries. Y= X1, X2, ...., u Y is my technological variable X1 FDI X2 exp .. other control ...
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1answer
23 views

Difference-in-difference analysis and the common trend assumption

I have a question concerning covariates in a difference-in-difference analysis: To check graphically whether there are parallel trends for the treatment and control group before the intervention, I ...
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0answers
6 views

Panel cointegration test

I have a panel data in which one variable is stationary at I(0) and two variables are at I(1). I want two test the coingeration. Which method would you suggest is the best one in that case and why?
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0answers
28 views

About the use of GDP and GDP squared in econometric analysis

I have found many econometric studies on the Environmental Kuznets Curve (EKC)* include time-series of 1) GDP, 2) GDP squared, and 3) environmental quality proxy (e.g. CO$_2$ emissions). ...
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0answers
15 views

Can lsqlincon (or a similar function) in R replicate results of lsqlin in MATLAB for data matrices that are not full column rank?

I am trying to replicate code written originally in MATLAB / Octave, in the R programming language. This is a constrained optimization problem using the lsqlin function available in MATLAB and Octave. ...
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0answers
15 views

Fitting a single time series forecasting model for multiple series

I am trying to build a macroeconomic time series forecasting model for some developing countries. In the end, I want to estimate capital flows for each country using a selection of macroeconomic ...
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0answers
12 views

Model Confidence Set by Hansen [closed]

Is anyone familiar with the MCS of Hansen for comparing relative performance of forecasting models (most usually volatility ones)? I have trouble understanding which statistic should one use, since ...
2
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1answer
63 views
+100

Two step regression using group effects and DAG

Consider the following model $$y_i = \sigma_{c(i)} + \mathbf x_i^\top\beta + u^y_i $$ $$\sigma_{c} = z_c\lambda + \eta_c$$ where for all $i$ $$\mathbb E[u^y_i \lvert x_i] = 0$$ Data is given for a ...
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0answers
16 views

The point of VAR conditional forecasts

I wonder what's the point of making conditional forecasts in VARs as in Waggoner, Zha (1998) in favor of forecasting via VARX. What makes it especially dubious is the fact that VAR is estimated step ...
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0answers
18 views

Compute initial value in Kalman Smoother

Suppose we observe data $y_t$ and $X_t$ from $t=1,...,T$ and want to estimate a dynamic linear model of the form $y_t = X_t\beta_t + \epsilon_t$ $\beta_t = \beta_{t-1} + \omega_t$ where $\epsilon_t$...
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0answers
26 views

OLS regression in stata. Dummy dependent variable vs if== at the end of the coding [closed]

I have the following regression. Y(tcs)= X1(tcs), X2(tcs), X3(tcs), u t= time, I have eleven years c= countries, I have 34 countries s= sector, I have two sectors, let's name them a and b. I ...
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0answers
18 views

How to rewrite population model

Suppose you had the following model: log(FatalAcc) = B0 + B1 HrsTrain + B2 log(medianInc) +b3 log(Pop) + u how can you show that the population model can be ...
2
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1answer
30 views

Why does SUR improve efficiency of parameter estimation over OLS?

If residuals for the same observation from two 'seemingly unrelated' equations are correlated, then it is often stated that there are efficiency gains from estimating the parameters of the two ...
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32 views

How can i correct a variable that is significant for the same model in one year and not in the other year?

I need some help with my master's dissertation. I am using a simple regression, often used in literature that establishes a relationship between ...
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2answers
36 views

With Ordinary Least Squares, how do we know that when the partial derivative of RSS is 0, that is a minima?

To minimise the residual sum of squares, we take its derivative with respect to the beta parameters and set this to 0. But when a derivative is set to 0, this means it can be one of the minima or one ...
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0answers
22 views

Staggered DDD (DDD with Multiple Time Periods)

I have a question about DDD (triple difference) with multiple time periods. There are several useful answers regarding DD with multiple time periods and this question (3 related questions about DDD (...
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0answers
13 views

Fixed effect model

I performed the F test to test the presence of fixed effects in the model. Since p-value = 1, there are no fixed effects. With this in mind, does it make sense to interpret the model's coefficients? ...
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0answers
23 views

Correlation between regression coefficients

Consider an i.i.d sample and assume the linear conditional expectation model yi = xi$\beta$ + $\epsilon$i ${\mathbb{E}}$[$\epsilon$i | xi] = 0 In general, if I estimate $\beta$ many times, will it ...
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0answers
24 views

Simultaneous equation model

I have a question about the resolution of a simultaneous equation model. We consider two continuous variables $V1$ and $V2$ that are jointly determined at the same time and a multiple times. It means ...
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0answers
12 views

Covariance matrix estimation under heteroskedasticity hc3

I have a question on HC3 covariance matrix: When constructing a covariance matrix, the ideal variance matrix would require the true squared error $e^2$, which is unobservable. Therefore, researchers ...
2
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0answers
114 views

Do specification differences make a difference in difference-in-differences?

My question relates to the following post: How do I interpret a "difference-in-differences" model with continuous treatment? I am reproducing an equation from Acemoglu, Autor and Lyle (...
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1answer
48 views

How do I solve this system of equations?

I am doing something that is commmon practice in economics to uniquely identify matrices. After deriving 3 unrotated factors from PCA, I then want to rotate them to be able to interpret them in ...
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0answers
18 views

Interpretation of Hausman test - IV models

I ran two IV models: 1) ivreg 2sls y x1 (x2=z1) 2) ivreg 2sls y x1 (x2=z1 z2) than I did a Hausman test, and it was not significant, so I could not reject the null. What does that mean? Is z2 a valid ...
2
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1answer
64 views

time series model with additional, time-independent regressors?

How does one introduce time-independent regressors into a time-series model? Let's say that you want to model house prices based on mortgage valuations from the past 5 years AND based on additional ...
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0answers
24 views

Regression Elasticities in multiple regression with continuous and dummy variables

So let's say I have a multiple regression as such: Y = constant + a1X1 + a2X2 + a3X3 Here ac is the coeffcient corresponding to the Xc Y is a normal variable constant is a non-zero constant X1 is ...
1
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1answer
21 views

Using Principal Components to create my y variable when many different y variables are available

I have a set of LHS variables ($y_{1i},y_{2i},...y_{ki})$ where $i=1..N$ represents observations, and $j=1...k$ represent different possible $y$ variables. These variables are highly correlated- think ...
5
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1answer
64 views

R-square and Intrumental Regression

Given that a linear regression model has been estimated using instruments can R-square then be interpreted in the usual fashion (as in linear regression without instruments)?
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0answers
34 views

Should I drop variable highly correlated with independent variable? (Causal inference)

I estimate OLS: Y = c + b1*x1 + ....+ bn*xn +err corr (Y, x1) = 0.8, Corr(x1,err)>0 Should I drop variable x1? What kind of biases would I have in both cases: with and without x1.
2
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1answer
85 views

Regression to the mean

I recently asked this question In regression model with random regressors $$(1) \ \ y = a + bx + e$$ can I change the equation to $$(2) \ \ x = (-a/b) + (1/b)y + (-1/b)e$$ and ...
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0answers
33 views

Regression changing of dependent variable [duplicate]

In regression model with random regressors $$y = a + bx + e$$ can I change the equation to $$x = (-a/b) + (1/b)y + (-1/b)e$$ and consistently estimate $(1/b)$ with OLS?
3
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2answers
103 views

Identification from implicit function

Suppose my observed data $y$ and $x$ is generated by the following relationship for each observation $i$: $$ y_i = h(y_i,\theta) + x_i + \varepsilon_i$$ where $x_i$ is a strictly exogenous variable ,...
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0answers
13 views

Stationarity in a time series implying that the correlation between consecutive terms must be constant?

I'm reading this definition (from Chapter 11 of an introductory econometrics textbook from Wooldrige) as the following: each consecutive pair of terms (let's let m = 2) are assumed to have the same ...
0
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1answer
62 views

Stata Help Simulation study AR(1) model [closed]

so I have a question similar to this example https://www.statalist.org/forums/forum/general-stata-discussion/general/1512656-ar-1-simulations However I don't understand how they have done the ...
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0answers
45 views

How to make optimization work normal in GARCH estimation, and question on standard errors?

I am currently trying to implement GARCH-M (garch in mean) model in Python (cannot use existing packages, and just want to understand the ground). I wanted to write not a big (but enough) piece of ...
3
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1answer
91 views

meaning of error term being correlated with regressor

I have encountered the statement that "the error term and one of the regressors are correlated" a few times and I am having trouble understanding what is meant exactly. Let's say we have a DGP $$y=\...
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0answers
41 views

How to bootstrap the time series data for assets portfolio mean - variance optimization?

As known among professionals and amateur investors, the classical Markovitz portfolio mean - variance optimization yields very unstable results that perform poorly in the real world. One of the ...
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0answers
17 views

Logistic regression: Equation for marginal effect at the mean

I am estimating the following logistic regression (binomial family) by maximum likelihood: $$ \ln\left(\frac{Y}{1-Y}\right) = \beta_{0} + \beta_{1}D + \beta_{2}X + \epsilon$$ where D is a dummy. ...
1
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1answer
58 views

Omited variable bias clarification

Let’s say we have a true model for health that goes $h=c+bw+di+u$ where w is weight and i is income. Now this means that holding weight constant a one unit change in income on average causes a d unit ...
2
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1answer
21 views

Derive explained sum of squared from beta

May I ask, how should I calculate $$SSE=\sum_{i=1}^n(\hat{y}-\bar{y})^2$$ given $$\beta=-0.094=\frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{\sum(x_i-\bar{x})^2}$$ $$intercept=1.9781$$ and $\bar{x}=4.9817$,$\...
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1answer
48 views

how does omitted-variable bias violate exogeneity

I understand that when omitted-variable bias occurs the coefficient estimated for some regressors is the sum of the direct effect and indirect effect through the omitted-variable. What I fail to see ...
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0answers
14 views

causal inference in linear regression where regressors have causal effect on each other

I am having some issues with the concept of causality. I have seen the causal effect of one variable on another "defined" as the effect that a change would cause if other variables are kept equal. ...
0
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0answers
8 views

Clinically meaningful explanation of marginal treatment effect (MTE) in instrument variable study

I am working on an instrumental variable application using clinical data. We will use a so-called preference-based instrument. We may include this as a continuous variable. With a continous instrument,...
2
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1answer
19 views

Hedonic Regression

I have some data for housing prices from sales for given areas and I also have data on several characteristics of these houses. I was wondering if there was a way to construct a simple housing price ...
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0answers
16 views

Can you recursively forecast one series with two series?

My question is probably very elementary but I haven't been able to find an explanation of recursive forecasting that I fully understand. I've read a journal article that seemed to recursively ...
3
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1answer
61 views

Counterfactuals in Econometric Modeling (Abortion-Crime Hypothesis Revisited)

Donohue and Levitt (2019) recently published a working paper revisiting the abortion-crime link. My question is specific to equation (2) in their paper (see below): $$ ln(CRIME_{st}) = \beta_{1}...

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