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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 $\sigma^{2}$ $\mathbb E(X_i) = \mu$ , $\mathbb{Var}(X_i)= \sigma^{2}$ $\mathbb E(X^2) = \sigma^{2} + \mu^{2}$ $\mathbb{Var}(X)=\mathbb E(X^2)-\mathbb [E(X)]^2$ $\mathbb E(\bar{X}^2) ... 11 Under the assumption of i.i.d. Normal characteristics, the situation described is taken care by separate Welch's t-tests that account for possibly different sample sizes and different variances. Denote the statistics of these tests$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 ... 9 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 ... 9 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 The "deviation restriction" is not really a restriction. It's just a natural result coming from the definition of$\bar{x}$: $$\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)=\sum_{i=1}^{n}x_{i}-n\bar{x}\equiv0.$$ It's not something we intentionally pose on the sample variance, it's a by-product or side effect arises when we replace sample mean$\mu$by ... 8 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 ... 8 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 ... 7 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 ... 7 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 if the pregnancy test gives a positive result when you are not pregnant then this is a false positive, a Type I error when the null hypothesis$H_0$is in fact ... 7 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 economists, we are biased towards establishing causal relationships. So, this explains our focus on endogeneity issues and strategies of identification to establish ... 7 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. 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 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 ... 6 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 most econometric analysis I usually default to R. I find also producing nice standard statistics graphics with R easier (but for maps I prefer Python). However, ... 6 It may be helpful here to distinguish three different statistics. The population standard deviation$\sigma$is given by: $$\sigma=\sqrt\frac{\sum_{i=1}^n(x_i-\mu)^2}{n}\qquad(1)$$ To calculate that we need to know the values of$x_i$for the whole population. The standard deviation of a sample can be calculated using exactly the same formula, albeit with ... 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 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 ... 5 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 define the "Hot-Hand effect" as follows: "Basketball players and fans alike tend to believe that a player’s chance of hitting a shot are greater following a ... 5 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, if the underlying data is normally distributed i.i.d. data then$N$and$M$do matter. Consider that noise mean$\mu$and variance$\sigma$, which, by ... 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 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 ... 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 ... 5 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-$t$CDF be$F_t$with support$[\underline w_t,\overline w_t]$. You can then define a weighted average CDF as $$\overline F (w) = \sum_t \frac{N_t}{N} F_t(w).$$ ... 5 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 distribution. If I was to exchange$s_1$for$s_2$,$f(s_2,s_1,\dots,s_n,v) = f(s_1,s_2\dots,s_n,v)$, the distribution does not change. And you can exchange as ... 5 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$K$equations $$\mathbb E[x\epsilon] = \mathbb E[x(y - x^\top \beta)] = \mathbf 0 \Leftrightarrow \mathbb E[xy] = \mathbb E[xx^\top]\beta,$$ where$\mathbb E[xy] = \mathbb ...

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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 ...

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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 ...

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(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})...

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