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11

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 $\sigma^{2}$ $\mathbb E(X_i) = \mu$ , $\mathbb{Var}(X_i)= \sigma^{2}$ $\mathbb E(X^2) = \sigma^{2} + \mu^{2}$ $\mathbb{Var}(X)=\mathbb E(X^2)-\mathbb [E(X)]^2$ $\mathbb E(\bar{X}^2) ...


10

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 the government to spend in order to save a randomly chosen life. So in a country of 300,000,000, the question is: What, to you, is the monetary equivalent ...


9

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. Denote the statistics of these tests $t_j, j=1,...,K$. The p-value associated with each is $$p_j = \Pr\big(|t_j|\geq t(\alpha)\mid H_0\big) $$ where $H_0$ is the ...


8

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 found under http://economictheoryblog.wordpress.com/2012/06/28/latexlatexs2/ The proof itself is not very complicated but rather long. That also the reason why ...


6

(This answer was completely rewritten for greater clarity and readability in July 2017.) Flip a coin 100 times in a row. Examine the flip immediately after a streak of three tails. Let $\hat{p}(H|3T)$ be the proportion of coin flips after each streak of three tails in a row that are heads. Similarly, let $\hat{p}(H|3H)$ be the proportion of coin flips ...


6

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 $$E(X_{t+1} \mid X_t,X_{t-1},...) = X_t \tag{1}$$ There are extensions like "sub-martingale", "super-martingale" but the basic definition is the above Random walk : A ...


6

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 region above the lorenz curve in order to get a relative gauge of the distance the lorenz curve is from the line of equality. Fundamentally what this shows is the ...


6

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 publicly complain that there aren't lots of cheap, highly skilled workers available is not the same as companies being willing to convert that into effective demand ...


5

Use -areg- in Stata, and the standard errors will come out as in the textbook. Specifically, the command areg lpassen lfare ldist ldistsq y98 y99 y00, absorb(id) vce(robust) will produce the desired result. -xtreg- with fixed effects and the -vce(robust)- option will automatically give standard errors clustered at the id level, whereas -areg- with -vce(...


5

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 more interested in producing the Supply and Use tables (which are then transformed into input-output tables) due to their usefulness in balancing the 3 measures ...


5

Perhaps there is some evidence toward your claim, but I would argue that in most situations, people do not use point estimates (although some "smoothing" likely occurs). In particular, there is no doubt that people care about the second movement (variance). The commonly employed, and robustly empirically documented, notion of risk aversion captures exactly ...


5

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 $\bar{X}_n$. As the sample size grows, our value of the sample mean changes, hence the subscript $n$ to emphasize that our sample mean depends on the sample size. Noting ...


4

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 searching for. I suspect, however, that they do not want the public to have access to aggregated value because it would showcase the volatility of Zillow home value ...


4

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 unbiasedness of the sample-variance estimator, $$s^2 \equiv \frac{1}{n-1}\sum\limits_{i=1}^n(x_i-\bar x)^2$$ using an i.i.d. sample of size $n$, from a ...


4

(Disclaimer: I don't know this literature.) It seems to me that Miller and Sanjurjo have a valid criticism of a particular statistical measure. I don't know if this should be considered to invalidate all prior work on the hot-hand effect, since they focus on only this particular measure. The measure is $$ M := P(\text{make shot }|\text{ made previous shot})...


4

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 interpretation), but how it functions in the posterior mean and variance. What does it do? For the posterior variance, it is easiest: firstly, it appears as an ...


4

I'm still not sure if I'm doing something wrong. However, it is useful to note that I get the same results in R. library(foreign) library(plm) library(lmtest) df <- read.dta("airfare.dta") fe.out <- plm(lpassen ~ lfare + ldist + ldistsq + y98 + y99 + y00, data=df, index = c("id", "year"), method = "within", effect = "individual") ...


4

We'd like to test if an variable $x_j$ is relevant in the respect of the model means that we want to test its "statistical significance", so the null hypothesis is $$\text{H}_0 : \beta = 0$$ (by the way, historically, that's why it is called the "null" hypothesis: a hypothesis of "null"-zero- effect). The $t$-statistic for this test is $$t=\frac{\hat{\...


4

St. Louis Fed: https://fred.stlouisfed.org/ Has very good US data. I am not aware of a database that systematically aggregates city-level data. I recommend state government sites and, for larger cities, city government sites.


4

I will attempt to answer the first (How prevalent is it?) and last question (Where can I see their work?). There was a recent post in The Economist about the emergence of machine learning into standard economic papers. They produced a nice graph, reproduced below: Albeit machine learning is confounded with big data, it shows a rise in their use since 2014. ...


4

If, as they claim, there is a lack of skilled IT workers in Portugal, They have 4 options: Raise IT salaries. Import IT workers. Export IT jobs. Tolerate existing conditions. Another thing to consider - where do the skilled IT workers in Portugal go? Are they perhaps leaving Portugal for other countries? If Portuguese companies are training entry ...


4

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 wages, you can attract workers from other companies. More workers for you. The second is less obvious. You don't necessarily have to raise the pay of your ...


4

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. When a company decides what wage (price) it will pay, it is making a judgment about its preferred position on the supply curve it faces. In other words it is ...


4

Suppose $X$ and $Y$ are iid random variables. The 'identically distributed' part means both random variables have the same distribution function (cdf). Formally this can be stated as $$F_X(z)=F_Y(z),$$ where $F_X(\cdot)$ and $F_Y(\cdot)$ are the marginal cdfs of $X$ and $Y$, respectively. The 'independently distributed' part means the joint cdf of $X$ and $...


4

Completing the notation with the indices $$ \forall j: \sum_{i=1}^{n} X_{i,j}\hat{u}_{i} = 0. $$ As you say, if $X_0$ is the constant then $$ \forall i: X_{i,0} = 1. $$ Inputing $j = 0$ into the first equation $$ \begin{align*} \sum_{i=1}^{n} X_{i,0}\hat{u}_{i} & = 0 \\ \\ \sum_{i=1}^{n} 1\hat{u}_{i} & = 0 \\ \\ \sum_{i=1}^{n} \hat{u}_{i} & = 0. \...


4

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 across the entire field of economics. Yes, microeconomic models (i.e., individual-level observations) will tend to give low R-squared values (often in single ...


3

Most agents, including firms, do not actively set-up utility functions in their heads. A firm might however might have a worker create a profit function. A course related to labor economics will usually give you an idea of what sorts of things a firm considers. A generic macroeconomic profit maximization problem that you'll commonly see is $$\max_{K, L} \ \...


3

The response to the Lucas Critique was the emergence of RBC and DSGE models. Using microeconomic foundations of macro models we can simulate how behavior changes when policy changes and only estimate "deep" structural paramateres that are not policy variant. Before microfoundations we were estimating models where the estimation included the actions of people....


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