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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 ...

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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.

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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 ...

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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 $\mathbb E[xy] = \mathbb ... 4 I'm a little baffled by your question. I've made a simple simulation, data attached: sum x1 x2 x3 x1_proportion x2_proportion x3_proportion ones 1.44975 .884738 .331214 .233797 .6102698 .2284629 .1612673 1 1.75989 .793748 .655205 .310937 .4510212 .3722992 .1766796 1 1.35571 .462276 .882351 .011085 .3409837 .6508396 .0081768 ... 3 They are virtually the same thing but you should not use them completely interchangeably. Disturbance Term Disturbance term is a synonym for an error term. For example, as explained in Verbeek's A Guide to Modern Econometrics pp 14:$ε_i$is unobserved and referred to as an error term or disturbance term So these two words can be interchanged. Innovations ... 3 The output from the model you mention would be not accurate at all for several reasons, including amongst other reasosns: Your post you mention you want to use labor costs as predictable variable - there is no such thing as predictable variable in econometrics. If you by that mean predicted variable (i.e. dependent variable) it would be wrong to have labor ... 3 The$E(u_i|X_i) = 0$can hold even without having simple random sample or random assignment. However, random assignment guarantees this will hold (in expectations). A violation of$E(u_i|X_i) \neq 0$is typically consequence of omitted variable bias. For example, in regression of education on wages reason why$E(u_i|X_i) \neq 0$can be that experience also ... 2 How can anyone possibly predict how the price of anything (stocks, Bitcoin, fiat, etc.) will change without “insider knowledge”? You can do that by forecasting based on data. Exact forecasting model will depend on exactly what you want to forecast but most economic variables can be forecasted with a degree of accuracy that is generally higher than just 50/... 2 Asymptotics are done as N goes to infinity and not T. If T is larger than N, this assumption is odd. True for most of what is commonly called panel data estimators. 2 Yes it is important indeed to use precise language to clarify methods and issues, especially in econometrics, a discipline in which fundamental but confusing nuances between different types of variables: some are endogenous, other exogenous, observed, unobserved, random, conditionally random, etc. I did not often encounter such subtleties in mathematics (or ... 2 I'm not a statistician... and this is the economics forum, so forgive me for the possible mistakes. I got most of this information from these slides. Consider a statistic of interest$\theta$with a consistent but biased estimate$\hat \theta$. The Jacknife estimates$\hat \theta_{(i)}$with is the same statistic, based on the sample that is obtained from ... 2 what you describe is not criterion, but model specification. Criteria are used to determine lag order (e.g. you have Akaike criterion etc). You should choose the specification that best matches your data. If you choose wrong specification your model will be misspecified and that typically leads to bias in the coefficient values. On the other hand if you ... 2 They are most likely standard errors of the estimates, it is a convention in some subfields of economics to report standard errors in brackets under the mean estimates in brackets. 1 If I understood correctly the gap is in the middle of the data. In such cases you should not use forecasts that extrapolate the data, but some interpolation method. If there is relatively large amount of variation in the data you would have best results using something like Catmull–Rom spline. Catmull–Rom spline has some nice properties (see here). The main ... 1 I guess$m < 1$. Otherwise$x^{1/(m-1)} \to \infty$as$x \to 0$. There's a possibility that I made a mistake, so let me know if you spot one. Let's first compute the cumulative distribution function of$X_2$: $$F_{X_2}(a) = \Pr(X_2 \le a) = \Pr(X_1 \le a \text{ and } X_2 \le a) = \Pr(X_1 \le a)\Pr(X_2 \le a) = a^2.$$ This assumes that the two uniformly ... 1 You presumably should be using all 3 years for the data. Given that you had the appropriate conditions for diff-in-diff (parallel trends), and you're looking at a standard case of the treatment only being relevant in treated periods (no lagged effects), then the additional data should not hurt your estimates. Additional years of untreated data will help you ... 1 Fixed effects model is estimated as: $$y_{i t} − \bar{y_i} = ( X_{i t} − \bar{X_i} ) \beta + ( \alpha_i − \bar{\alpha_i} ) + ( u_{it} − \bar{u_i} )$$ So the country fixed effect is always relative to the average fixed effect. If a country has negative fixed effect that means it is less productive than average country in your sample. If you choose ... 1 Prices are stochastic and cannot be predicted with perfect accuracy. So when you talk about "predicting" prices or price movements, you have to specify what exactly you mean. Imagine a truly random price that in each month goes UP by \$1 with 90% probability and DOWN by \\$9 with 10% probability. (Like a typical stock price that slowly climbs and ...

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First, there are substantial reasons to believe the data is not log-normal so it would be improper to assume log-normality. So, no you should not do that. You can research the literature on youth wages, it may have information on distributions. However, that is probably more than is necessary. There are two primary ways to estimate the standard deviation ...

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