19 votes

Prove the sample variance is an unbiased estimator

For a shorter proof, here are a few things we need to know before we start: $X_1, X_2 , ..., X_n$ are independent observations from a population with mean $\mu$ and variance $\sigma^{2}$ $\mathbb E(...
  • 581
11 votes

P-value hacking

Under the assumption of i.i.d. Normal characteristics, the situation described is taken care by separate Welch's t-tests that account for possibly different sample sizes and different variances. ...
9 votes
Accepted

Prove the sample variance is an unbiased estimator

I know that during my university time I had similar problems to find a complete proof, which shows exactly step by step why the estimator of the sample variance is unbiased. The proof I used can be ...
9 votes
Accepted

What is the average economic value of a human life?

It depends on the context, of course, but most often in policy analysis "the value of a life" has nothing (directly) to do with output, etc, but instead means the maximum amount that people would want ...
8 votes

Lack of skilled IT workforce, but they do not raise wages

The factual observations you've listed fit neatly with the law of supply. You've seen that wages (price) have fallen, and during the same period, supply has gone down. The fact that companies ...
  • 1,346
8 votes
Accepted

What R-squared is a low R-squared?

Disclaimer: this answer comes from a microeconomic research perspective. Time series / macroeconomic specialists will likely have other perspectives. There is no general rule for what's too low ...
  • 458
8 votes
Accepted

Type - I Error & Type - II Error: Pregnancy test analogy - is it legit?

Presumably here the null hypothesis is $H_0:$ You are not pregnant the alternative hypothesis is $H_1:$ You are pregnant so being pregnant would be the positive result. You take a pregnancy test ...
  • 4,714
7 votes

Calculating Gini Coeffecient

All of these answers are true but don't provide an easy solution which doesn't use excel/code. Gini can be fairly easily computed by hand too. The Gini coefficient fundamentally shows the shaded ...
7 votes

Python vs R (vs Stata): the old battle revisited

I use all three programs. Python can do everything that R can do and R can do everything that Python does, but I must say R is superior to Python when it comes to the packages. For that reason for ...
  • 47.6k
7 votes
Accepted

How is Regression different from Econometrics?

To put it simply regression modeling is a technique, a tool, used by econometricians. Regression deals with dependence amongst variables within a model. But it cannot always imply causation. As ...
  • 6,702
7 votes
Accepted

Is there any restriction for numerator of variance calculation for population?

The "deviation restriction" is not really a restriction. It's just a natural result coming from the definition of $\bar{x}$: $$\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)=\sum_{i=1}^{n}x_{i}-n\...
  • 366
7 votes

Where can I find lorenz curve of countries?

Knoema has visualizations of Lorenz curve for a large number of countries, however note if you are doing some research it is expected you will make your own visualizations based on the data.
  • 47.6k
6 votes

P-value hacking

I agree with @AlecosPapadopoulos we want something like: $$ \Pr(p_{(1)} \leq p^*) = 1- \big [1-p^*\big]^K$$ But I don't see how $n$ and $M$ couldn't enter into the proper test statistic. For example, ...
  • 16.1k
6 votes
Accepted

Martingale, random walk and rational expectations

All concepts are used in Economics. Definitions (not stated in a fully rigorous manner): Martingale : A stochastic process $\{X_t\}$ is called "martingale" if and only if it holds that $$E(X_{t+1} \...
6 votes

Lack of skilled IT workforce, but they do not raise wages

Developing a point made in Dan's answer, it is important to distinguish between a movement along a supply curve and a shift of the whole curve, in this case the supply curve for skilled IT personnel. ...
  • 7,554
6 votes
Accepted

How to prove that Adjusted R^2 is less than R^2

$$ SSRes=\sum_{i=1}^n\left( y_i-\hat y_i \right)^2\\ SSTotal=\sum_{i=1}^n\left( y_i-\bar y \right)^2 $$ $$ R^2=1-\dfrac{ SSRes/(n-1) }{ SSTotal/(n-1) } $$ $$ \bar R^2=1-\dfrac{ SSRes/(n-k) }{ SSTotal/(...
  • 325
5 votes

Robust Standard Errors in Fixed Effects Model (using Stata)

Use -areg- in Stata, and the standard errors will come out as in the textbook. Specifically, the command ...
5 votes
Accepted

Interpreting the ratio of two variances in a Bayesian decision problem

Excuse the word-play, but the interpretation of $n'$ is a... posterior one. Meaning, the important thing is not how $n'$ is defined (ratio of variances, although this will prove consistent with the ...
5 votes

Did previous researchers fail to detect the hot hand simply because of a statistical fallacy?

Neither of the two papers are clear enough as regards their applications of Statistics, so in this answer I will attempt a clarification. Gilovich, Mallone, and Tversky (1985) in their Abstract ...
5 votes
Accepted

Have social accounting matrices and input output models fallen out of fashion? if so, why?

National Statistical Institutes do still compile IO tables (see http://ec.europa.eu/eurostat/web/esa-supply-use-input-tables for EU versions, although these are 5-yearly as well). They're generally ...
  • 251
5 votes

Lack of skilled IT workforce, but they do not raise wages

There is a possible hazard to raising wages. It does two things: Draw more workers to your company. Increase the cost of your existing workers. The first should be obvious. If you increase ...
  • 1,162
5 votes
Accepted

Convergence in probability and convergence in distribution

I will attempt to explain the distinction using the simplest example: the sample mean. Suppose we have an iid sample of random variables $\{X_i\}_{i=1}^n$. Then define the sample mean as $\bar{X}_n$. ...
  • 595
5 votes

How to average CDFs of one variable across years

Why don't you just take a weighted average? Suppose you have ten years $t \in \{1,...,10\}$ and year $t$ has $N_t$ observations such that in total you have $\sum_t N_t=N$ observations. Let the year-$t$...
  • 5,100
5 votes

How to find $\phi$, that denotes the correlation of signals among informed traders?

A degenerate joint normal is distribution is one in which you cannot find a PDF for the distribution. They assume you can. (The covariance matrix is invertible). Let $f(s_1,s_2\dots,s_n,v)$ be the ...
5 votes

Why do we need at least as many instrumental variables as endogenous regressors to identify parameters in 2SLS?

In standard linear regression model $$y = x^\top \beta + \epsilon$$ with exogeneity $\mathbb E[x\epsilon] = \mathbf 0$ you have $K$ parameters because $\beta$ is $K \times 1$ and you have $K$ ...
  • 3,206
5 votes
Accepted

Variance of a random variable / Econometrics

$$E[(X-E[X])^2]$$ We FOIL the quadratic, $$E[X^2 -2XE[X]+(E[X])^2]$$ We apply the expectation to each term, $$E[X^2] -2E[XE[X]]+(E[X])^2$$ In the middle piece, $E[X]$ is a constant number that can be ...
4 votes

How can I get total home values on Zillow?

To answer your question of whether you can get a number for 'total home value,' the answer is no–at least not easily. Zillow (somewhat) recently made available a data set similar to what you are ...
4 votes

Prove the sample variance is an unbiased estimator

Let's improve the "answers per question" metric of the site, by providing a variant of @FiveSigma 's answer that uses visibly the i.i.d. assumption (showing also its necessity). We want to prove the ...

Only top scored, non community-wiki answers of a minimum length are eligible