11
votes
Accepted
"Derivative" of an indicator function
As a matter of mathematical trivia, the derivative of an indicator function is zero, except at the threshold where it does not exist.
But
\begin{align}
\mathbb E[\text{I}(i)] &= \mathbb E\big[\...
- 33.9k
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 ...
- 1,366
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
...
- 4,765
8
votes
Accepted
How to prove that Adjusted R^2 is less than R^2
$$
SSRes=\sum_{i=1}^n\left(
y_i-\hat y_i
\right)^2\\
SSTotal=\sum_{i=1}^n\left(
y_i-\bar y
\right)^2
$$
$$
R^2=1-\dfrac{
SSRes/(n-1)
}{
SSTotal/(n-1)
}
$$
$$
\bar R^2=1-\dfrac{
SSRes/(n-k)
}{
SSTotal/(...
- 410
7
votes
Calculating Gini Coeffecient
All of these answers are true but don't provide an easy solution which doesn't use excel/code. Gini can be fairly easily computed by hand too.
The Gini coefficient fundamentally shows the shaded ...
- 954
7
votes
Python vs R (vs Stata): the old battle revisited
I use all three programs.
Python can do everything that R can do and R can do everything that Python does, but I must say R is superior to Python when it comes to the packages. For that reason for ...
- 57.7k
7
votes
Accepted
How is Regression different from Econometrics?
To put it simply regression modeling is a technique, a tool, used by econometricians. Regression deals with dependence amongst variables within a model. But it cannot always imply causation.
As ...
- 6,990
7
votes
Accepted
Is there any restriction for numerator of variance calculation for population?
The "deviation restriction" is not really a restriction. It's just a natural result coming from the definition of $\bar{x}$:
$$\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.
- 57.7k
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.
...
- 8,574
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
...
- 151
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 ...
- 1,182
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-$t$...
- 5,291
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 ...
- 1,924
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 $K$ ...
- 3,788
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 ...
- 3,768
5
votes
Accepted
Deriving an equation in Banerjee "A Simple Model of Herd Behavior" (1992)
To get the required probability, we just need to sum the probability of all the events with the initial history of the following type. The reason being that after any initial history of this type, it ...
- 9,411
4
votes
Partial R2 and contribution of Regressors
I'm a little baffled by your question. I've made a simple simulation, data attached:
...
- 3,477
4
votes
What is the average economic value of a human life?
As a graduate in health economics, I'd use the QALY threshold to answer this question. A QALY is a quality adjusted life year i.e., a year in perfect health-related quality of life, two years with 50% ...
- 43
4
votes
Accepted
What are some helpful online tools (databases, etc..) for economic analysts?
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 ...
- 2,911
4
votes
Accepted
How prevalent is the use of machine learning among economists?
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 ...
- 8,611
4
votes
Accepted
Do people really care about higher moments?
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 ...
- 976
4
votes
Accepted
Independently and Identically distributed random variables
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
$$F_X(z)=F_Y(z),$...
- 595
4
votes
Understanding this particular criticism of RCTs by Deaton and Cartwright
Without having read the full piece I'd say you are mostly spot on, but for a subtle difference. The objection runs a bit deeper than your rephrasing of it, where you refer to single estimate. The ...
- 2,373
4
votes
Do circular invoices count in GDP?
A firm's contribution to GDP isn't revenues. A firm's contribution to GDP is roughly the sum of the wage bill and the money earned by capital (debt (interest) and equity (economic and not accounting ...
- 16.3k
4
votes
How to average CDFs of one variable across years
The answer by @Baysiean proposed to compute a weighted average of the per-period empirical distribution functions $EDF_t(w)$ (where $w$ is the value in the support of a random variable $W$), a value ...
- 33.9k
4
votes
Is there any restriction for numerator of variance calculation for population?
It may be helpful here to distinguish three different statistics. The population standard deviation $\sigma$ is given by:
$$\sigma=\sqrt\frac{\sum_{i=1}^n(x_i-\mu)^2}{n}\qquad(1)$$
To calculate that ...
- 8,574
Only top scored, non community-wiki answers of a minimum length are eligible