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Questions tagged [econometrics]

Econometrics is the application of statistical methods to economic data for various purposes such as of testing hypotheses, infering causal relationships and forecasting future trends.

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How do we calculate Beta in a OLS regression of the mean of y on the mean of lag of y?

In a simple OLS regression we calculate the estimator Beta by dividing the covariance of x and y by the variance of x. How do we calculate the estimator Beta if we regress the mean of a variable (at ...
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Can I draw a smaller sample from one treatment group?

in an RCT, I have 3 different treatment groups and one control group. The size of the control group is around 1000 while the size of other groups are just above 300. To test balance I used ANOVA and ...
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1answer
29 views

If two variables are not cointegrated, can one still cause the other?

For part of a project, I wanted to see if electricity consumption causes GDP in Colorado. I initially intended to follow the approach of Mozumder and Marathe (2007), who use a VECM approach, but that ...
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1answer
25 views

What R-squared is a low R-squared?

I keep hearing that R-squared does not really matter in economics research and that due to the unpredictable human nature, economics research regressions tend to have low R-squared. But how much is ...
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10 views

covariance of autocorrelated time series

When we calculate the variance of a time series with autocorrelation, we need to do some shrinkage to get the correct value. What about say we have two time series, X, Y. both have autocorrelations. ...
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1answer
19 views

Sum of residuals in multiple regression equals 0

I understand that in multiple regression $$\sum_{}^{} X_{i,j}\hat{u}_{i} = 0 $$ but I do not understand how my textbook says that if we include the intercept in the regression ($X_{i,0} = 1$)then we ...
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1answer
101 views

Convergence in probability and convergence in distribution

Im a little confused about the difference of these two concepts, especially the convergence of probability. I understand that $X_{n} \overset{p}{\to} Z $ if $Pr(|X_{n} - Z|>\epsilon)=0$ for any ...
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1answer
27 views

Independently and Identically distributed random variables

What does it mean for two random variables to be "identically distributed"? Does it mean that they come from the same probability distribution?
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1answer
31 views

Existing metric for personal productivity hours needed per life hour?

With about 50 hours of productivity a week, including work, cooking, etc. I can complete the tasks and pay the expenses necessary to live about a week. Subtract maybe 5 hours of labor that goes into ...
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37 views

Combining Difference-in-Differences with Matching Methods When Parallel Trends Are Met in Unmatched Data

I'm running a difference-in-differences (DID) regression on panel data as follows: $$ Y_{it} = \beta_{0} + \beta_{1}Treat_{i}\times Post_{t} + \mathbf{\Pi}\mathbf{X}_{it} + \tau_{i} + \gamma_{t} +\...
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18 views

Disaggregated price index

im trying to make my own consumer price index using the laspeyres index methology. However im having problems finding the individual prices. However i have the disaggregated cpi components. For ...
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8 views

Multiple regulatory changes at the cutoff

Consider a running variable $a$, and a cutoff $a_0$. There are two regulatory variables, $x$ and $z$. Both variables jump around $a_0$, in the sense of fuzzy regression discontinuity design (RDD) ...
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1answer
13 views

How does one deflate weekly price data?

It seems the highest-frequency consumer price index (CPI) data available is monthly. How does one convert weekly or daily price data into real prices?
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39 views

How to do test statistic on difference in two independent variables?

If i have time series regression $R_{i,t} = \alpha + \beta x_1 + \gamma x_2 + \delta x_3 + \varepsilon_i$ In this case, how can I conduct test statistic of $\beta - \gamma$? Is it to use unpaired two ...
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1answer
90 views

Simple Econometric question

From LLN, we have $\text{plim} Y_n=\mu$. Now you have $W_n=Y^3_n$, what is the probability limit of $W_n$? Please help me answer this and thank you!
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1answer
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how to find the elasticity of log(y) =β0+β1log(x) [closed]

I'm struggling with this question. Please help out with the correct formula. how to find the elasticity of log(y) =β0+β1log(x).
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How to control for population in Difference-in-Difference?

Random example, but let's say I'm examining the effect of a health program on influenza cases in India. They just randomly start the program in 7 of the 29 states. I have data on the number of flu ...
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1answer
37 views

Endogeneity problem with a dummy variable

I have a panel data model as following, $$Y_{it}=intercept +B_1X_{it}+B_2Q_{it}+error_{it}$$ where $i$ is for firm and $t$= time. $Y$= trade credit demand, $X$= inventory cycle, as inventory ...
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1answer
42 views

What are general equilibrium effects?

Im reading alot on public finance and have been seeing alot of mention of measuring "general equilibrium effects". I know what general equilibrium is, but i dont know what general equilibrium ...
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1answer
37 views

Imbens and Angrist (1994): the $D_i(z)$ variables

I'm referring to the Econometrica (1994) paper by Imbens and Angrist. In particular, I don't really understand the random variables $D_i(z)$ (defined on page 468). Could you please provide me with ...
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1answer
56 views

features of Generalised Method of Moments estimation

[ What does it mean that GMM is robust to distributional assumptions?
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0answers
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Decomposition of interest rate risk

Hi I needed some clarification on something. I have three variables: $V_1$ which is an indicator of an interest rate risk premia $V_2$ which is an indicator of a credit risk premia $V_3$ which is ...
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14 views

Are there phi2 phi3 statistics for the DF-GLS unit root test?

It's known that there are phi 2 and phi 3 statistics when performing ADF unit root tests. These statistics tell us the correct specification of the model (Trend, constant, or none). When running ADF ...
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2answers
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Randomisation and balance in experiments

Suppose we are interested in the effect of some 'treatment' on some outcome of interest. A common practice is to select a group of people and then randomly choose some fraction (often half) to receive ...
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40 views

Estimation of a Non-linear production function with Non-linear least squares

Suppose that you have to estimate a Non-linear production function (for instance a Cobb-Douglas or a CES) by using Non-linear LS (and hence without log-linearization). You have just aggregate time ...
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Error Correction Model with two independent (control) variables [duplicate]

Is it possible to build an Error Correction Model with two independent ( control) variables? I mean with one dependent variable, and two independent variables. If yes, what are the assumptions/...
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20 views

Error Correction Model with more than one independent variables

I was wondering if it is possible to set up an Error Correction Model with two independent variables (one dep var, and two indep vars)? If yes, what are assumptions/conditions to be met? In the ...
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2answers
53 views

Unbiased but inconsistent estimator [closed]

Assume a random sample X1, ..., Xn with a normal distribution with mean μ and variance σ2. How do we know the following estimator is unbiased, but inconsistent?
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12 views

Resources on the Rotterdam demand system

I've been doing some self study on the Almost Ideal Demand System, and have been hearing a lot about the Rotterdam demand system developed by Henri Theil. I've been looking for resources on google ...
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Does the European Central Bank still conduct monetary policy under the assumption of NAIRU?

My question is about NAIRU (Non-Accelerating Inflation Rate of Unemployment) and its relevance with respect to the European Central Bank's monetary policy. I have read somewhere that Philips Curve ...
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1answer
47 views

Smaller variance of estimators in matrix sense

When comparing asymptotic variances, you usually conclude that a covariance matrix A is more efficient whenever the difference B - A ≥ 0 (where ≥ 0 means that the difference is a positive semidefinite ...
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0answers
14 views

Calculating volatility forecast errors - how to obtain “actual volatility” for comparison?

I have to replicate Liu & Morley (2009) on Polish data. They compare different methods of forecasting volatility in terms of Mean Absolute Error and other metrics. They use Hang Seng Index. What ...
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2answers
64 views

Using the sample mean to test hypotheses

Suppose that we have some data-points $x_1, ..., x_n$ and want to test a model that specifies a stochastic process which supposedly generated the data points. For example, we might want to test the ...
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matching methods from multiple entities

Say I would like to investigate whether a particular product feature affects its sales. We would like to match products based on feature vs non-feature. But the sales also depends on the retailers who ...
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1answer
45 views

Can central bank interest rate hikes lead to a price gain in equities?

I ran an empirical analysis on recent interest rate changes of European central banks on Swiss equity prices and found statistically significant results. A 1 percentage point increase in interest ...
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1answer
99 views

Confusion over homoskedacity assumption

In my introductory econometrics course, we have been discussing the GM-assumptions and homoskedasticity. Unfortunately, I have some confusions and interlinked questions, so I am wondering if somebody ...
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1answer
31 views

Fixed Effects Estimation and Inconsistency

Consider estimation of the following population regression function: $G{Y_{it}} = {\beta _0} + {\beta _1}IN{F_{it}} + {\beta _2}DE{M_i} + {\beta _3}POI{L_t} + {\varepsilon _{it}}$ Where: $GY_{it}$ = ...
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2answers
143 views

Deriving the translog production function

Ive been having difficulty deriving the translog production function defined as: $$\ln y=\alpha_0+\sum_{i=1}^n\alpha_i \ln x_i+\frac{1}{2}\sum_{i=1}^n\sum_{j=1}^n\ \beta_{ij}\ln x_i\ln x_j $$ I know ...
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3answers
79 views

what is the interpretation of $\beta_{ij}$ in the translog production function?

The translog production function is defined as the following. $$\ln y=\alpha_0+\sum_{i=1}^n\alpha_i \ln x_i+\frac{1}{2}\sum_{i=1}^n\sum_{j=1}^n\ \beta_{ij}\ln x_i\ln x_j $$ I know it is a ...
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26 views

Bias in an Autoregressive Model

In Stock and Watson 3E.Updated, they posit in chapter 14 that if we estimate an Autoregressive equation using an AR(1) $$ y_t = \beta_0 + \beta_1 y_{t-1} + \varepsilon_t $$ where in fact the true ...
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1answer
50 views

Advance Microeconomics [closed]

Show that u=a+bM-yM^2 represents a risk averter's utility function who is interested only in the mean and the variance of the state distribution of Income M. Can anybody send me the full solution. ...
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1answer
33 views

Validity condition for Instrumental Variables

My professor states the validity condition in the following way: $W$ (the matrix of instrumental variables) must be such that $ \text{plim} \, \frac{W'u}{N}=0$, where $u$ is the error term. ...
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1answer
59 views

Statistical Learning and Econometrics

The principal goal of Econometrics is to find causal effects between economic variables. But the growing technology level seems to show us that Big Data and Statistical Learning result in a tradeoff ...
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47 views

Profit maximization problem using linear regression (pooled OLS)

I'm currently on a university assignment where I'm stuck more or less in the middle. I have to answer the following problem: Suppose you are interested in estimating the production function for ...
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1answer
41 views

Plim of ols estimator

Suppose you are given 2 models. Model of 1 has $y$ as the dependent variable and $x$ as the independent. Model 2 has $w$ as the dependent variable and $x$ as the independent variable. Both models have ...
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1answer
62 views

Whats the rationale for using taylor series in economics?

I've been reading about the translog production function and know its really just a log-log production function approximated using a first order maclauren series. Why not just leave the function as ...
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1answer
29 views

Analyzing vast economic/financial data

I have data science projects coming up in a university course in the upcoming quarters, and I was interested in using financial/economic data since there is so much of it. Also, I do have a hobby for ...
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Expectation conditional on a sum of random variables

The setting is a simple OLS regression where the true model has regressor $x$ and error term $u$, but we can only measure $\bar{x}=x+v$ where $v$ is iid with mean 0. According to the textbook: $\...
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2answers
64 views

Does omitted variable bias 'contaminate' coefficients for regressors not correlated with the omitted variable?

Suppose we have a model that is: $$ y = X_1\beta_1 + X_2\beta_2 + X_3\beta_3 + \varepsilon $$ where $X_1$ is independent of $X_2$ and $X_3$ but $X_2$ and $X_3$ are correlated with each other. ...
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How do I measure effects over years in panel data with individuals?

I'm working with a longitudinal panel dataset that surveys the same few thousand individuals biennially and I have six years of this data. My dependent variable would be how much individuals spend on ...