texts:
I am new to dynare. I am trying to replicate the calibration of the paper 'Structural transformation and aggregate productivity' by Margarida Duarte and Diego Restuccia. (Picture attached)

In this calibration technique, some parameters are known while others (b and $\rho$) are estimated such that the squared difference between data and model moments reduces.

My problem is - in all the calibration exercises that I saw regarding macroeconomics models in Dynare, all the parameter values are assumed and model is calibrated by computing future period values using these initial period values of variables and parameters. [Picture attached]

My question is how can we do calibration by generalized methods of moments in Dynare? Is it possible? Can someone provide me the document or any kind of information will be helpful.


texts: Is there a correlation between pharmaceutical prices and drug dealers?

texts:
Question: Is there a quantitative or some kind of correlation between the number of drug dealers in a certain region and the price of pharmaceutical drugs?

This is for a case I'm working on, but I can't seem to find a direct correlation between the price of prescription drugs and drug dealers.
Right off the bat, it seems simple right? Lower prices force drug dealers out as consumers turn towards the brand name drugs which effectively lowers the amount of drug dealers in an area. However, I can't seem to find, anywhere, that says something along those lines.


texts: Any serious macro models for Greece's possible default or eurozone exit?

texts:
Since each news outlet says something about Greece these days, I wonder what serious economic research backs decisions made over the last seven years?

The IMF papers on austerity, both early ones and revisions (such those by Blanchard), are relevant here, but Greece now faces a more specific choice: a hypothetical default and introduction of a new currency. (Economics aside: Yes, maybe Greece isn't considering this choice right now and just negotiates with creditors.)

The default is relatively boring: The country stops paying off the debt, belonging mostly to the EU sovereigns, and then restructures it on different conditions. No idea how much of the debt will be written off in the end.

The impact of the new currency is more interesting because the Greek government will no longer depend on the ECB. It can now reduce real wages with devaluation. So, employment increases and the economy gradually returns to its potential GDP level.

But I didn't locate the research that would carefully model these counterfactuals under plausible assumptions. Did you?


texts: Proof that stochastic discount factor is positive in complete markets

texts:
I am looking for a reference (with a proof possibly) to understand why the completeness of markets implies that the stochastic discount factor is strictly positive in the context of intertemporal consumption, i.e. when a agent FOC implies
$$
p_t = \mathbb{E}\left[\beta \frac{u'(c_{t+1})}{u'(c_t)} x_{t+1}\right]
$$
where $p_t$ is the price of an asset giving $x_{t+1}$ in the following period.


texts: Textbook on the mathematics of RBC/DSGE models?

texts:
I'm reading David Romer's Macroeconomics. However, what I don't like is that he doesn't go at all into detail about the mathematical underpinnings of RBC/DSGE models. When it comes to the central mathematical parts of these models, such as how to derive and solve an expectational recurrence equation in a mathematically rigorous way, Romer instead treats it very hand-wavy and skips over steps.

Perhaps that is fine for some people, but I would like more mathematical rigour.

However, the problem is that every textbook I've found so far that is about mathematical economics only treats deterministic dynamic models.

So my question is: Is there a good textbook that treats stochastic dynamic models in a mathematically rigorous way? Note I am NOT talking about the econometric estimation of these models, but merely the purely theoretical treatment of dynamic stochastic models.


texts: Quality of French wine in the US vs French wine in France

texts: I remember reading a study/paper saying that the AVERAGE bottle of french wine drunk in the US is better than the average bottle of french wine drunk in France, due to the fact that nobody bothers to ship the crappy stuff. Anyone got a link?


texts: How do I calculate the amount of money I get from an investor and the percentage I give him in return?

texts:
Let's say I owe a company.

At the final state I want to be left with 1M cash for myself and 50 percent of the company.

The investor is not willing to buy shares and give me the money but only invest in the company.

I thought about selling my shares to a third person for one million cash after the first investment so I'll be left with 50% at the end and 1M.

How much percentage should I give the investor and for how much money, and how much should I sell to the third person and for how much money in order to be left with 1M and 50% of the company?


texts:
I figured this would be more appropriate on this forum. I came across the following slides after a Google search of cluster-robust uncertainty estimators. On slide 10 the author attempts to demonstrate how the errors of students nested within the same classroom are correlated. That is, $\textrm{E}\left[u_{ig} u_{jg'}\right] = \sigma_{(ij)g}$ if $g \neq g'$.

Shouldn't this be: if $g = g'$? I assume $g \neq g'$ represents two students ($i$ and $j$) in different classrooms (groups). If so, wouldn't this be demonstrative of dependence across clusters?

Sorry if this question is a bit in the weeds. Can anyone provide further clarity?


texts: Sequential Game Rollback Equilibria Question

texts:
For this question, I believe Albus has 3 strategies: N, E, and S, and Minerva has 8: aaa, aab, aba, abb, baa, bab, bba, and bbb.
I've also found the rollback equilibrium to be the case in which Albus chooses N and Minerva chooses b. However, I'm not sure how to represent this equilibrium (equilibria?).

Do we say that the unique equilibrium is simply (N, b), since those are the choices made by the players, or do we say there are 4 equilibria: (N, baa), (N, bab), (N, bba), (N, bbb) since Minerva's choices are in reality a set of strategies, all of which result in her choosing b in response to Albus playing N?


texts: What is the example of inaccurate impact due to endogeneity?

texts:
When learning about endogenous variable, I found an answer in a topic on StackExchange very direct:

An Exogenous Variable is defined as a variable which is unaffected by
other variables within an model.
take a multivariable regression model as an example:
$y=\beta_0+\beta_1x_1+\beta_2x_2+u$
$x_1$ is called an exogenous variable when its determination is
unaffected by $x_2$ and error term $u$.
An Endogenous Variable is defined when $x_1$ is influneced by $x_2$ or
$u$.
This is important because when we run a regression we are producing a
function which assumes a dependent and independent variable. If we
find endogeneity we wont get accurate estimates for the effect of
$x_1$ on $y$.

Why in endogeneity case, we wont get accurate estimates for the effect of $x_1$ on $y$ . Is there any sample for that statement? In reality, I faced this problem that when I add some regressors to a regression equation, one of variable coefficient changed the magnitude or even flip the sign. But I want to know the reason behind.
One theoretical explanation is: $x_1$ is correlated with $u$ or $x_2$, producing a bias in $beta_1$ that depends on the direction and magnitude of the correlation


texts: "Normal" vs "actual" variables in empirical work

texts:
In an early OECD study by Deppler and Ripley (1978), the authors distinguish between output per man hour, $OMH$, and what they call "Normal" output per man-hour, $NOMH$.

(table 2, p152)

At no point in the paper do they explain this distinction, which also occurs for the labour cost variables.

In the text (p154) they explain that:

  The cyclical component of labor costs is represented by the ratio of
  actual to "normal" output per man-hour.

This all seems very mysterious to me. Are they talking about a particular reference year value? Or is it a trend component?


texts: What is the relationship between economic growth and equality?

texts: Does economic growth create more or less equality?


texts: Find a Perfect Bayesian Equilibrium with a game that includes Nature

texts:
I want to determine all pure-strategy Perfect Bayesian Equilibria for this task, but I cannot get very far. Side note: First number is payoff for A, second number payoff for player B.
For the last stage, I know that upper A will always choose to exit, and the bottom A will always choose to pass.
But I don't know how to proceed from there? I have ascribed beliefs for player B being in the upper and bottom node (beta and 1-beta, respectively), but am not sure what to do with it.
I tried assuming that Nature goes 'up' and in that case beta=1. Then B would choose pass because it has a greater payoff than exiting. That's where I get confused.


texts: Linearity in Pricing and Duality, UMP EMP

texts:
I have read the statement below and don't quite understand what it means. This is probably because I don't have full understanding of duality with support function in math, but just to foster understanding... The statement is:

  "The utility maximization problem(UMP) has a non-linear utility objective and a linear price constraint. The expenditure minimization problem is exactly the other way around: a linear price objective and a non-linear utility constraint. This is at the heart of the idea of the meaning of dual - to recast the problem with the objective as a constraint and the constraint as the objective. An important observation to make is linearity in pricing in them. This linearity, either in objective or constraint, is the cornerstone in enabling us to use the duality theorem."


texts: Useful software for notes and graphs in economics?

texts:
I'm looking for a software which may help me to both take notes and draw graphs during university lectures. It must have the ability to switch between texts and graphs, add other formats such as Office related format and pdf. Also, the the graphs should be easily tunable (preferably on the fly) and of course, shareable. Being able to draw matrices and operate with them would be great too.

I can't seem to find an application/software for laptop which makes all of those easy in an economics related setting. Any idea?

Thanks a lot


texts:
This is a term often encountered in documents published by the Big Four (Deloitte, Ernst & Young, Price Waterhouse Coopers, KPMG), for instance in the E&Y 2018 Worldwide R&D Incentives Reference Guide.

However, I've been unable to find a definition, formal or other, anywhere on the web for this term. I would associate it with superannuations (sometimes called super), but this doesn't seem to make a lot of sense here. Another possibility would be that it is some sort of tax deduction, reducing your taxable income, and this seems more likely, but I still don't understand the super part then.

Would anyone be so kind as to explain the meaning of this term in the context in which it is used by the Big Four?


texts: The right term for a market that tends towards consumers switching suppliers freely

texts:
Say there's a bunch of competing businesses, car repair shops for example, in a certain market. Business is good and there's a substantial average turnaround time for all of them. Someone decides they're going to add a bunch of capacity - hire more mechanics and expand their space.

Say that shop finds as soon as they add the capacity, customers figure it out, get in the shortest line available to them, and very quickly the capacity is all in use, and the turnaround time is only lower, slightly, as a result of the total supply in the entire market being greater. The shop's business volume has quickly increased in close proportion to the expansion, but that's about all that changed. What is the best term for what this observation says about the market? Low perceived switching costs? High market fluidity?

Say the opposite turns out to be true. The shop adds the same extra capacity, but the total number of people walking in the door doesn't change, or is sluggish to change. Turnaround time goes down, business volume stays the same, profits go down due to the unused capacity, and the competitors are humming along as though nothing happened. The managers are left thinking, "Either we have a reputation or marketing problem, or the market we're in is just ____." What's the term for a market that behaves this way?


texts:
I don't understand. Ok, we have $\beta_1-\hat{\beta }_1=\frac{\frac{1}{n}\sum_{i=1}^{n}v_i}{(\frac{n-1}{n}){s_{X}}^{2}}$. So, for the first OLS assumption results that $E(v_i)=E((X_i-\bar{X})u_i\overset{p}{\rightarrow}E((X_i-\mu_X)u_i)=E(X_i-\mu_X)E(u_i)=0$ (since $E(u_i|X=x_i)=0$). Then Stock and Watson says that for the second OLS assumption $v_i$ is i.i.d. and $Var(v_i)<\infty$. Surely this is for the casual sampling of variables but i can't prove it clearly.
After this, we have $E(v_i)=0$ and $Var(v_i)={{\sigma _{v}}^{2}}<\infty$ so we can apply CLT and saying that for $n\rightarrow \infty$ $v_i\sim N(0,{{\sigma _{v}}^{2}}/n)$ since $\frac{1}{n}\sum_{i=1}^{n}v_i=\bar{v}$.


texts: Is Buy Nothing Day a classist protest of Black Friday?

texts:
I hope this isn't off topic, it seems specifically economic to me even though it probably intersects with other fields of study.

Black Friday is seen as an iconic hallmark of consumerism, and Buy Nothing Day is a reaction to it that's been around since the 90s. It's a protest against both Black Friday as well as consumerism in general, and a temporary boycott to draw attention to the issues. I get that the consumerist mindset being protested during this time is buying a bunch of unnecessary stuff just because it's on sale versus getting that one thing you couldn't afford but now you can. And on a wider scale, I get BND is protesting buying a bunch of unnecessary stuff period (consumerism).

But on a functional economic level, in relation to things people would be buying anyway, doesn't boycotting Black Friday just amount to paying full price (or finding other sales) at some other time of the year versus taking advantage of these sales? And thus wouldn't that be something that people of lower economic status would be excluded from participating in, as they wouldn't necessarily have the luxury of choosing to pay more just to make a statement?


texts:
There have been a number of papers in the literature (pioneered by Sanjeev Goyal, Jackson, Kranton, amongst others) emphasising the role and importance of network structure in economics, the equilibrium arising therein and the relationship between the topology and other graph properties and the equilibrium.

Such networks arise in a number of cases, for example, research collaboration, social networks, crime networks, etc. My question is what published empirical studies have tested the hypothesis presented by the theory? Do such studies also find that the graph properties are critical, as predicted by the theory? Or is network effects in economics a theory-only area?


texts: How does the imposition of import duties affect the nominal and real exchange rates in the long term?

texts:
Let's assume that a country imposes an import duty on goods imported from abroad.
How will this change the long-term real exchange rate between domestic and foreign currencies? How will it affect the long-term nominal exchange rate?


texts: Economic Impact of A Student Loan Bubble Popping?

texts:
A few pundits have been stating that we have a student loan bubble, and this bubble will pop, similar to housing.

I'm struggling to imagine the economic impact of what this would look like if these pundits are right, outside the obvious bailout or student loan forgiveness.  Hypothetically, let's say a scenario where 15% of students are unable to pay back their loans occurs, and the government bails them out (or forgives their loans), how would that be a negative economic event?  Would it create inflation?  Would it cost in terms of productivity, in that students would spend more time borrowing money and staying in school than working and producing?


texts: When the Fed increases the money supply, does any of the additional supply go directly to the government?

texts:
When a central bank increases the money supply, how much of it goes directly into the government purse? Say for example:

The money supply is $150
The populace has $100
The government has $50.

If the Fed decided to increase the money supply to \$200, does any of the extra $50 go into directly into the government purse? Does it vary?


texts: Why does the price and wealth derivatives, weighted by the price and wealth, sum to 0?

texts:
From Mas-Colell, Whinston and Green (Microeconomic Theory), we have this proposition on page 27. If homogeneity holds,

$$ \Sigma_{k=1}^{L} \frac{\partial x_l (p,w)}{\partial p_k} p_k + \frac{\partial x_l (p,w)}{\partial w} w = 0 $$

That is, the price and wealth derivatives, when weighted by the price, $ p_k$ and wealth $w$, equate to 0. What is the economic logic behind this? Homogeneity implies this -- but for this to hold, we don't require that prices and wealth increase proportionally (am I right?)

From this, we can also derive that the sum of price elasticities (own and cross price elasticities) equate to 0. I understand we can derive this mathematically-- but again, why'd these elasticities equate to 0, economically?

(Also, if these results are held only when prices and wealth increase proportionally, I completely understand -- but the book doesn't make that distinction).


texts: Definiton of information sets in rational expecations models

texts:
I am struggling with the notion of 'information sets' in the context of rational expectation models in economics. I found interesting notes on the web (http://www2.econ.iastate.edu/tesfatsi/reintro.pdf) but I am not sure whether I am understanding the concept well. Let me explain my concerns along with the first example in the notes given in the link.
Consider a small model given in the following three equations:
$$ y_t =y_t^*+ap_{t-1}+b\mathbb{E}_{t-1}p_t\\
p_t =m_t+\varepsilon_t\\
\mathbb{E}_{t}p_{t+1}=\mathbb{E}(p_{t+1}\vert I_t)$$
where
$y_t^*$ notes the log of potential real GDP in period $t$
$y_t$ denotes the log of actual real GDP in period $t$
$\mathbb{E}_{t}p_{t+1}$ denotes the subjective forward-looking expectation of a representative agent in period $t$ regarding the price level in period $t+1$
$m_t$ denotes the log of the nominal money supply in period $t$
$\varepsilon_t$ is a stochastic shock at time $t$
$I_t$ denotes a period-t information set that is available to the representative agent at the end of the period $t$.
So my possibly stupid question is: What is $I_t$ or how is it defined?
To be more precise, let me outline what I think $I_t$ is.
First of all, because most economists apply the law of iterated expectations and other propositions that can be applied to conditional expectations, I suggest $I_t$ has to be a $\sigma$-Field because otherwise, one wouldn't be able to apply these propositions.
But how is this $\sigma$-Field defined?
Following the notes, Leigh Tesfatsion writes that the equations plus classification of variables and admissibility conditions together with the true variable values a,b and the deterministic exogenous process $(m_t)_{t \in \mathbb{N}}$ have to be part of the information set, as well as the properties of the probability distribution and properties of the stochastic shocks $(\varepsilon_t)_{t\in \mathbb{N}}$ and the values of past realizations of all variables.
Typically it is assumed that $\varepsilon=(\varepsilon_t)_{t\in \mathbb{N}}$ is a stochastic process defined on the probability space $(\Omega,\mathcal{F},\mathbb{P})$.
Thus I would say $I_{t}$ has to be a $\sigma$-Field over $\Omega$ and thus it has to be a system of subsets of $\Omega$, thus it cannot include specific equations, specific variable values nor variable classifications, or am I wrong?
Let $\mathbb{F}=(\mathcal{F}_t)_{t\in \mathbb{N}}$ be a filtration on $(\Omega,\mathcal{F},\mathbb{P})$, given as $\mathcal{F}_t=\sigma(\{\varepsilon_s:s\leq t\})$.
I thought $I_{t}$ to be the history of the stochastic process, i.e. $I_{t}=\mathcal{F}_{t}$, is this correct?
If not, could you provide me a (mathematical rigorous) definition of the information set $I_{t}$ or could you provide me some literature related to this issue?
Thanks in advance
Frank


texts: Profit for business owners vs. incomes of the self employed

texts:
I am learning the way to calculate GDP with incomes. So there is labor income and capital income. One element of the labor income is incomes of the self-employed. And for  Capital income, an element is profit for business.

I not too clear on the definition of the self employed. Don't people who are self-employed also own their


texts: IS-LM-BP Model: How will income and interest rate change if government expenditure is increased?

texts:
I'm currently learning the Mundell Fleming model, and so from my textbook and other sources I've figured out the effect of increase in money supply and government expenditure increase for the following conditions:

Fixed & floating exchange rates (perfect capital mobility / BP horizontal)
Fixed & floating exchange rates (imperfect capital mobility, BP flatter than LM curve)
Fixed exchange rate (imperfect capital mobility, BP steeper than LM curve)

I'm stuck at figuring out the effect of a fiscal expansion in the case of floating exchange rate with the BP curve steeper than the LM curve. My textbook has not mentioned it but I'd like to how it'd turn out.

Here's my guess:

The economy is initially at the point A. There is fiscal expansion:

IS moves to the right (1 to 2)
At B, there is a deficit in BOP, which causes the domestic currency to depreciate.
This increases exports and decreases imports, which causes net exports to increase, which then causes Y to increase, which shifts IS further up (IS 3).
At B, because of increase in net exports, BOP improve and so BP also shifts to the right.
The economy settles at the new equilibrium C.

Am I correct?


texts: Minimum sample size for cross-sectional RDD

texts:
I haven't done a regression discontinuity design (RDD) before. I know it requires a large sample size for identification, thus I fear that my sample size is not large enough.

The study is cross-sectional, not longitudinal.
Entire sample size is around 1000, and the sample size around the cutoff point is around 100.

Is it enough for a cross-sectional fuzzy RDD?

What is the "minimum" sample size and "good-enough" sample size for cross-sectional fuzzy (sharp) RDD?


texts: Total costs as function of labor and quantity

texts:
If I have wage $w = 200$ and rental rate $r = 3050$ on short run, I can assume that $K=1$ and then get the total costs $TC = rK+wL = 3050 + 200L$.

Isn't it correct?

But what if I also have a cost of $400$ on each sold unit. Then my costs will be function of both labor $L$ and quantity $Q$.


texts:
Why is the oil price and correspondingly the down and midstream company stock prices are increasing in May 2016, when

The economic data across the world in weak
China's economy is
sluggish. They had another round of devaluation in early May 2016.
The
OPEC meeting in Doha in late April did not yield any meaningful
resolution in stemming the production of oil output.


texts: Are there any datasets for protectionism?

texts: Are there any data sources or variables that measure how protectionist a country is? If so, what are they?


texts:
In an Edgeworth economy with two agents and two goods, Player A has endowment $\left(a,\,0\right)$ and utility $u_{A}\left(x_{1},\,x_{2}\right)=\min\left(\gamma x_{1},\,x_{2}\right)$ in which $\gamma>1$, and Player B has endowment $\left(0,\,b\right)$ and utility $u_{B}\left(x_{1},\,x_{2}\right)=\min\left(x_{1},\,\gamma x_{2}\right)$. When $a=b$, the competitive equilibrium is $$\left(x_{1}^{A},\,x_{2}^{A},\,x_{1}^{B},\,x_{2}^{B}\right)=\left(\frac{a}{1+\gamma},\,\frac{\gamma a}{1+\gamma},\,\frac{\gamma a}{1+\gamma},\,\frac{a}{1+\gamma}\right),\;\frac{p_{2}}{p_{1}}=1,$$ and A's utility at the equilibrium is $\frac{\gamma a}{1+\gamma}=\frac{\gamma b}{1+\gamma}$. However, when $a>b$, the competitive equilibrium becomes $$\left(x_{1}^{A},\,x_{2}^{A},\,x_{1}^{B},\,x_{2}^{B}\right)=\left(\frac{\gamma b-a}{\gamma^{2}-1},\,\frac{\gamma^{2}b-\gamma a}{\gamma^{2}-1},\,\frac{\gamma^{2}a-\gamma b}{\gamma^{2}-1},\,\frac{\gamma a-b}{\gamma^{2}-1}\right)$$ $$\frac{p_{2}}{p_{1}}=\frac{\gamma^{2}a-\gamma b}{\gamma^{2}b-\gamma a},$$ and A's utility at the equilibrium reduces to $\frac{\gamma^{2}b-\gamma a}{\gamma^{2}-1}<\frac{\gamma b}{1+\gamma}$. Is there any intuitive explanation for this reduction? (I'm not asking for solving the equilibrium because I already solved it.)

My proposed explanation is:

  Because the supply of the first good increases from b to a, its price
  decreases, and the price of the second good increases. Therefore
  Player A must sell more $x_{1}$ to Player B, and Player B can sell
  less $x_{2}$ to Player A. Since both players have preferences with
  perfect complementation, the lesser amount of the two goods decides
  the utility, and Player A having less $x_{2}$ must have less utility.

Is this explanation appropriate?


texts:
I have a very basic question on the somewhat cryptic Open Market Operations. So, from what I understand, say the Fed wants to reduce interest rates (increase monetary base). It will firs buy a bond by writing a cheque to the security holder, the cheque is deposited in a commerical bank, which then deposits this in the central bank. The reserve account of the central bank is credited, and the commercial bank is then able to use these "excess reserves" to create fresh loans- injecting money in the economy.
I guess my question is: when the issuer of the bond (say the government) has to pay back to the security holder (central bank), wont it decrease money supply then?

Thanks!


texts: Real-life applications of repeated games theory

texts:
What are some scenarios in which the theory of repeated games have been applied?

I am looking, for example, for scenarios in which a government, a firm or a person accepted a decision which relied upon a result such as the Folk theorem.


texts: Calculating Real Budget Deficit, given Nominal Deficit and Inflation

texts:
I am doing this course on Coursera. In the context of explaining what Budget Deficits are, the professor puts up the following formula:

  Real Deficit = Nominal Deficit - (Inflation*Total Debt)

My confusion is, where is the Total Debt coming from? Shouldn't Real Deficit be just a function of Nominal Deficit and Inflation? i.e.,

  Real Deficit = Nominal Deficit - (Inflation*Real Deficit)

My understanding is that Total Debt is just the accumulated debt over the years (including the current year's budget deficit incurred so far). Is that understanding wrong?

The professor goes on to give a numerical example to explain the concept of inflating the debt. That's when the effective burden of debt falls due to inflation.

If Nominal Deficit = \$100 billion, inflation =10% and Total Debt = $5 trillion, then

Real Deficit = 100 - (0.10*5000) = -$800 billion.

I don't get it.

Edit: This is the direct link to the 6 minute lecture where he talks about it.


texts:
I'm learning economics and I want to read/hear the world through the lenses of any economist.

What are the best periodical economics news feeds?
It could

Magazines such as theeconomist.com
Podcast etc.

Thank you,
Karsnen


texts: What is the purpose of advertising for companies like Pepsi who advertise the same product and every person in the modern world knows about it? Why waste money?


texts: Non-unique utilities in a competitive equilibrium

texts:
In continuation to this question: Uniqueness of utilities in competitive equilibrium I think I found a simple example in which the utilities in equilibrium are not unique, and wanted to check if it is true.

This is an exchange economy with two goods and two agents with utilities:

$$u_1(x,y)=2x+y$$
$$u_2(x,y)=3x+y$$

Initially, each agent has 1 unit of $x$ and 5 units of $y$.

Suppose $p_y=1$. Then, whenever $p_x\in[2,3]$, the economy is in equilibrium, since agent 1 wants to sell all his $x$ endowment and agent 2 wants to buy all $x$. So the equilibrium utilities will be:

$$u_1 = 5+p_x$$
$$u_2 = 11-p_x$$

This shows that utilities are not unique.

A. Are my calculations correct?

B. If they are correct, what is going to happen in a real competitive economy? Since the equilibria are essentially different, which of them will prevail?

EDIT: After the price theory book again, I am not sure about my calculations. The book defines a competitive equilibirum as a situation in which the sum of demands exactly equals the sum of endowments. The demand of an agent is defined as the optimal bundle he can afford using his initial endowment. Now:

Whenever $p_x<3$, the demand of agent 2 is $(1+5/p_x,0)$ - he wants to buy $x$ with all his endowment of $y$. Since the total amount of $x$ is 2, this implies $p_x\geq 5$ - a contradiction.
Whenever $p_x>3$, the demand of both agents is $(0,5+p_x)$ - both want to buy only $y$, which is obviously not an equilibrium.
Hence we must have $p_x=3$. Now agent 2 is indifferent between buying or selling $x$, while agent 1 wants to buy only $y$. Hence, the demand of agent 1 is $(0,5+p_x)=(0,8)$.
So, in this case there is a unique eqilibrium in which $p_x=3$, agent 1 gets $(0,8)$ and agent 2 gets $(2,2)$; the utilities are 8 and 8.

Now I am confused: is the utility vector unique or not?


texts: Is there a free lunch or something beneficial but with zero price? Is air in an unpolluted area free lunch? If so, the sentence "there is always a tradeoff between benefit and cost" is not in general true. Is this correct?


texts: What does this condition for a profit of a firm exist mean?

texts:
What is the intuition behind this?

Let $Y=zF(K,N)$ be a production function.
For a profit to exist Indana conditions must hold and :

$$\frac{∂^2zF(K,N^d)}{\partial K \partial N} > 0$$

I understand all the conditions intuitionally, but I can understand this one mathematically but can't understand even what is meant by $\frac{∂^2zF(K,N^d)}{\partial K \partial N} > 0$. What does this being greater than zero imply?


texts: I've been hearing a lot about the fed "pumping the stock market" with trillions of dollars to maintain prices. I know the fed isn't allowed to actually buy stocks so how is this money being spent, if not on stocks, to "pump the market"? Who is receiving this money? How do those entities receive the money and it effect their stock?


texts: When is the upward economic convergence in the EU estimated to happen?

texts:
Although the regional cohesion, i. e. the socio-economical convergence of the East and the West has been one of the EU's main goals, some economists seem to dispute there's any evidence for them being successful while others claim it's well on its way.
However, I wasn't able to find any sources that would try to estimate when the point of economic convergence should happen. Have there been any similar analyses?


texts: What's the significance of the triangular region for calculating the deadweight loss?

texts:
I am familiar with the concept of deadweight loss but I can't deduce the significance of the triangular region we consider deadweight loss as.

I mean what's the issue with taking the deadweight loss as the area under ABCD instead of CDE or for that matter CDF (F being the mid point of DE) or does that particular area represents some quantity from economic perspective that I might be missing out on?


texts: Lecture notes competitive labor market with minimum wage

texts: Can somebody recommend lecture notes that derive competitive labour market model equilibrium with minimum wages? This has been surprisingly hard to find, because most lecture notes use minimum wages to introduce the monopsony model, as for instance does the Labor Economics textbook by Cahuc et al (2014).


texts: Have countries with a monopoly on a resource in an area ever established 1-company monopolies in that area to drive up price?

texts: Say its the 18th century and South America wants tea. Britain, for example could have a monopoly on the tea trade in the area. However if multiple British companies sell in the area they will drive eachothers prices down. So the British government could only allow 1 company to trade there, or force a merger between the companies, so they can trade as a monopoly and make more money which will be payed as tax to the British government. Has this ever happened, or is there a flaw in my logic?


texts:
Would appreciate some thoughts on proving the existence of a solution (a maximum) in an applied context.
Suppose the objective function is one of maximising utility:
$$\max\Sigma\beta U(C_t)$$
Subject to some constraints on resources, say:
$$\\C_t+K_{t+1} = F_F(K_F,E_F,S_t)$$
Where the constraint is the economy's resource constraint, inclusive of current consumption $C_t$ and investment possibilities $K_{t+1}$, set equal to the production function $F_F$, which includes arguments on capital $K_t$, energy, $E_t$ and the emissions stock $S_t$ (i.e. emissions affect production costs).
The extreme value theorem states 'that a continuous function throughout a non-empty compact set will have a max (min. respectively)'.
In this respect, my questions is: what are the requirements for the feasible set of solutions to be on a compact set?

non-negativity of variables?
terminal conditions on the variables (i.e. they are all exhausted in the future)?

Would appreciated some thoughts, for sure.


texts:
I am aware that secondhand goods are not counted in GDP due to double counting issues, but I want to ask about a specific case of transaction of second-hand goods.

For instance, what if a student buys a book for 20$,

uses the book  for a bit, and then sells it to a college bookstore for

40$? And what if the college bookstore sells that used book to another

student for 50$?

I know that for the second case, the 10 $ (50 $ - 40 $) will be counted in

GDP because this represents the bookstore's services created for providing

books.

But what about the first scenario, where a student sold the book to the

bookstore for 40 $?

Would the 20 $ (40 $ - 20 $) be counted in GDP? Or would

this just count as the increase in the student's wealth?


texts: Can the Fed control the shape of the entire yield curve?

texts: Is it often taught that the Fed can only affect the short end of the (Treasury) yield curve, while the long end is governed by investors' inflation expectations. Could the Fed in principle control the long end as well, e.g. by buying long dated Treasuries. Could the Fed in theory set the whole yield curve to zero?


texts: What is the interest rate that on the vertical axis of money markets?

texts: The money market diagram showing liquidity preference and money supply intersect at an equilibrium level of interest rate, but what interest rate is it? Is it the base rate (I presume this is the rate at which commercial banks lend out loans to borrowers) or FED Funds Rate/LIBOR? Or does it simply refer to interest rates in general?


texts: What is the difference between the discount window and Fed repos?

texts:
I'm wondering how the Fed's discount window differs from it's involvement in the repo market.

To the best of my knowledge, both are tools used to conduct monetary policy and both are also short-term, collateralised loans for commercial banks that are facing liquidity problems. So what is the difference between the two? The only one I can think of is that the discount window has different tiers of loans whereas Fed repurchase agreements do not but this seems like too small a difference to be the only one between the two.


texts: Interest rate rule in monetary DSGE model

texts:
I am studying DSGE models and try to solve exercise 2.2 from Gali's (2008) book. In short, consider the simple classical economy where the following approximate equilibrium conditions must be satisfied:
$$y_t = E_t\{y_{t+1}\} - \frac{1}{\sigma}(i_t - E_t\{\pi_{t+1}\} - \rho)$$
and
$$r_t = i_t - E_t\{\pi_{t+1}\}$$
and $y_t$ and $r_t$ determined independently of monetary policy.

Derive an interest rate rule that guarantees full stabilization of inflation (i.e. $\pi_t = \pi^* \;\; \forall t$).

I thought of the simple rule like $i_t = \phi\pi_t$. It is possible to show (using forward iteration) that in this case
$$\pi_t = \sum_{i=0}^{\infty}\frac{1}{\phi^{i+1}}E_t\{r_{t+i}\}$$
and letting $\phi \to \infty$ inflation goes to zero. However, I think that this not what was meant by the author. Any help appreciated.


texts:
I am an economist interested in looking at panel data on mothers, their husbands and their grandparents to determine the effect of the economic shock of the recession on their self-reported health outcomes.

Initially I had planned to fit fixed-effect models in order to control for fixed individual differences.

However, thinking on this further, as my analysis will consider the effects of economic shocks on health outcomes of all adults in this dataset at baseline and then ten years later, I wonder if family should be included as a random factor in order to account for potential correlations between related individuals.

Thus, should the analyses be undertaken using a linear mixed model? Any insights you could provide on this would be great!


texts:
Satava (2007) estimates that the costs of Columbus's 1492 voyage was 1,765,734 maravedís.
In today's money, what was the value of a 1492 Spanish maravedí?


texts: Why's Bernie Sanders wrong to allege that JP Morgan received more than $390 billion in financial assistance from the Fed?

texts:
This r/badeconomics post avouches:

    [JP Morgan] received more than $390 billion in financial assistance from the Fed.

  Sanders has repeated this lie for several years. He gets the \$390bn number from Table 8 of this report [p. 131 on the printed page, or 144/266 of the PDF] but forgets to adjust for the length of the loans. Table 9 [p. 132 on the printed page, or 145/266 of the PDF] adjusts for the term of the loan and finds that JP Morgan received about $31 billion in assistance, one-tenth of Sanders' amount. So he's established that he can't read a GAO report.

Why ought Sanders use the term-adjusted borrowing? What's wrong with using the not term-adjusted total transaction amount?


texts: Classical Dichotomy and Money Neutrality

texts:
I have some questions on the concepts of the classical dichotomy and money neutrality:

What is the difference, if any, between the concepts of classical dichotomy and money neutrality? As I understand it, the classical dichotomy is the assumption that changes in nominal variables do not affect real variables. But my textbooks and lectures do not seem to distinguish between this concept, and that of money neutrality.
If the classical dichotomy suggests that changes in nominal variables do not affect real variables, does it have anything to say in the reverse direction? Do changes in real variables affect nominal variables, in a world/model in which the classical dichotomy holds?
I know that the classical dichotomy does not hold in the short run. But what evidence is there that the classical dichotomy may or may not hold in the long run? Is there a well-known academic piece on this issue, or a consensus in the literature?


texts:
There's a lot of literature describing the relationship between growth and trade, but I'm not sure what conclusions I can draw from GDP per capita (specifically) and trade in one particular year for multiple countries. The graph is a regression I ran, so the red line demonstrates a positive relationship between the two variables in that year. But I'm also confused because the R squared value is very low, indicating a weak relationship. Is this because I have included too many countries in the test or because of the many other factors playing a part? Apologies as this question is probably quite stupid, but I'm very confused.

The task: "The United Kingdom government has asked you to write a report on the relationship between gross domestic product (GDP) per capita and trade openness. In particular, they would like to know whether the sum of exports and imports as a percentage of GDP had a positive effect on GDP per capita in 2015. To allow you to do this, they make available data on GDP per capita, exports of goods and services and imports of goods and services. GDP per capita is measured in constant 2010 United States dollars and exports and imports are expressed as a percentage of GDP."


texts: Coefficient of Determination with Weighted Coefficients

texts:
I want to compare coefficients of determination (i.e., $R^2$) of the following two models. $fe_{t+h}$ is a forecast error in $t+h$ and $\mathbf{\varepsilon}_t$ is a shock of interest occurring between $t$ and $t+h$. The idea is to interpret the coefficient of determination as the share of forecast error variance (FEVD) which can be explained by my shock of interest.
Model 1
\begin{align*}
fe_{t+h} = \beta_0 \mathbf{\varepsilon}_{t} + ... + \beta_h\mathbf{\varepsilon}_{t+h} + u_t
\end{align*}
Model 2
\begin{align*}
fe_{t+h} = F(z_t) \left(\beta_0^I \mathbf{\varepsilon}_{t} + ... + \beta_h^I \mathbf{\varepsilon}_{t+h}\right) + \left( 1-F(z_t)\right) \left(\beta_0^{II}\mathbf{\varepsilon}_{t} + ... + \beta_h^{II} \mathbf{\varepsilon}_{t+h}\right) + u_t
\end{align*}
where $F(z_t)$ is a smooth logistic function with $F(z_t)\in [0,1]$ which weights the coefficients $\beta_0, ..., \beta_h$ between regimes 1 and 2.
In my model at hand, $h$ is equal to 15.
Is it ok to use the non-adjusted $R^2$? I am aware that typically, $R^2$ will rise with the number of additional explanatory variables. However, in my case I have no additional variables but only weighted coefficients.


texts: How can all the bitcoin in the world be worth more than McDonald's Corporation?

texts:
What makes bitcoin so valuable?  It has already surpassed the value of almost all publicly traded companies.  I understand it can be used to buy things like digital money but why does the price go up?  Can't people buy things with a more steady price of bitcoin?  It seems like a steady price would be better for using it to buy things.

Have people missed this rally or does the current price grossly undervalue bitcoin?


texts: Why the ageing population creates problems for a country to fund old-age social protection program and what solution do we have?

texts:
Senior citizens are considered as one of the vulnerable groups and therefore, they need some social protection during their old age. However, we also face the worldwide trend of an ageing population.

If a country just starts planning for their old-age protection during this time, how could the program be financed since there will be an issue to fund the program?
Can re-employment after retirement minimize the vulnerability faced by senior citizens or will it just create other problems?
Are there any other options that can be used to address the issue of funding old-age protection?


texts:
Wiki's article provides with 3 sources for GDP data: IMF, World Bank and CIA.

I wonder which of them is better (i.e. more accurate)? Also, what about reliability of so called Penn tables?

If anyone is aware of the source which is better than the above mentioned, please, share it.


texts: Why GDP series always has an unit root problem?

texts:
In one of the lecture slides of class that I am currently taking our professor mentioned that when it comes to the GDP is it safe to always assume it has unit root and testing for it is just superfluous. However, why is this the case? Is that just an empirical regularity or is there some reason why GDP will always have unit root?

I suppose this could be due to the economic growth, but we did also learn about trend stationary series. I also understand that the reason why any series has unit root is that the shocks to the series never die out, but why wouldn't that hold for GDP? In our macroeconomics class we were always taught that business cycle shocks are transitory and ultimately GDP grows around its balanced growth path.


texts: Modeling market growth, without compound interest or regression

texts:
I am working on predicting the growth of a certain market. Traditionally, this is done through a simple compound interest model:

$$ ThisYear'sMarket * (1 + g)^n $$

What would be a better way to mimic progressive growth in real life? Perhaps through a natural log function or some form of $ y = e^x $? (There isn't enough past data so I'm not comfortable using regression).


texts: Minimum Sample Size For Clustered Data Randomized Experiment

texts:
I need help determining the minimum sample size for a randomized controlled experiment.  The treatment (1 Factor, 3 Levels) will be administered to different households clustered within 5 routes. There are at least two dependent variables: the proportion of households with citations (citation is a binary 0/1 measure) and number of citations per household. I am having trouble identifying a formula that can compare the three means/proportions and provide a breakdown of the number of observations needed per treatment and control groups. My goal is to be able to identify which treatment is most effective. Any help is much appreciated!
Model Details
Violations(i,t) = Treatment1 + Treatment2 + Treatment3 + Controls
The number of violations for household i, period t is a function of which treatment the household received plus other fixed effects/controls such as median income, population density, etc.


texts: Good books to learn social choice theory

texts:
I wanted to learn Social Choice Theory and have fine mathematical background. I have read about it as a part of advanced microeconomics (Jehle and Rene)- Arrow's Impossibility Theorem etc. and got intrigued by it.

What are some good books to read to know more about Social Choice Theory and in particular, the mathematics of voting systems?


texts: Who first formulated the Political Business Cycle Theory?

texts:
The first time I saw it, was in Stephen Harper's Master's Thesis

http://dspace.ucalgary.ca/bitstream/1880/24345/1/1991_Harper.pdf

It comes across as being very similar to the Austrian Business Cycle Theory, but I have not come across it in their writings as of yet.

Who was the one to first coin and formulate the theory?


texts: Rothschild-Stiglitz (RS) Separating Equilibrium

texts:
In RS model, where there are only two risk types (high and low risks), there is no pooling equilibrium but a separating one (when there are sufficiently large number of high risks.)

Additionally, they state that if there are continuum of risk types, there can never be an equilibrium.

I have 2 questions:

I am trying to understand the analytical proof of the continuum case. I have the technical report of their paper and will provide that section here. However, I think the proof is not well-organised and I appreciate a clear explanation to the proof.**
In the proof, there is a section (highlighted) stating "necessary condition for existence is that.." and giving an inequality afterwards. To my understanding, this inequality gives how large the high risk population should be in order to guarantee the separating equilibrium. (Please let me know if I am wrong at this point). However, they take the derivative of the incentive compatibility constraint to derive this inequality, i.e. they take the derivative of an inequality to reach another inequality. Don't you think this approach is wrong as taking the derivative of an inequality does not have to yield another inequality?

** In the continuum case, I understand their reasoning that it is enough to show the inexistence of an equilibrium by only showing the inexistence for 2 close risk types, and they start from the maximisation problem of low risks. However, rest is foggy.


texts: Why doesn't stock market help to boost the economic growth directly?

texts:
For example, during the recession, the central bank often goes to buy financial instruments that are riskier than government bonds (such as corporate bonds)- which is called "quantitative easing" that increases the price and lower the interest yield of these riskier assets.
So, by the action, the central bank indirectly encourages people to invest in the real sector (and not in the stock as returns/interest yields are low) directly which will help boost the economy. This could be an investment in buying a house, land, factory, etc. Even pure consumption could put pressure to produce more commodities.
Therefore, I'm wondering why stocks trading couldn't help to boost economic growth. For example, if the interest yields are high, people will invest in these stocks and earn higher returns thus having extra income that they are willing to spend more on goods and products. Or what is the role of the stock market in economic growth?


texts: Why do indebted governments fear deflation?

texts:
It's widely accepted among people who follow finance that various governments around the world, including the US government, are doing (or their central banks are doing) everything possible to keep their economy out of a deflationary state. (cf. Ben Bernanke's "drop dollars from helicopters" comment.)  The rationale given is that deflation makes your debt more expensive and harder to service.

This rationale doesn't make sense, at least not on the surface.  With inflation, prices in general go up as the value of the currency goes down; with deflation, prices in general go down as the value of the currency goes up.  Therefore, in a deflationary environment, debt service would become more expensive but all the other things on your budget become cheaper, and therefore, as long as debt service comprises less than 50% of the budget, doesn't the country come out ahead?


texts: The potential dilution of cryptocurrencies

texts:
What is to stop the value of cryptocurrencies being diluted by the emergence of other cryptocurrencies?  For example, according to Wikipedia, Bitcoin was 80% of the crypto market cap in 2016, but this had been reduced to 40% by 2017 due to the emergence of Ethereum and others.   Although during this period the price of Bitcoin kept going up, what's to stop them all eventually cannibalizing each other?

The definition of dilution and cannibalization for these purposes means a significant reduction in market cap of an individual cryptocurrency.


texts: Converse in supermodularity and single-crossing

texts:
Suppose I denote $$f(x,t)=g(x,t)+h(x)$$ where $X\in \mathbb{R}$, $t\in [0,1]$ and $h(x)$ is any function.

I want to prove that if the single-crossing property holds in $f(x,t)$, then $g(x,t)$ must be supermodular over $X\times T$.

I know in general supermodular means single-crossing but the converse is not true, but my guess adding a random function $h(x)$ should guarantee single-crossing property will show supermodularity.


texts: Why can per share earnings growth only keep up with GDP growth, if no new shares are issued?

texts:
I transcribe Ben Felix's speech (BSc Mechanical Engineering (Northeastern University), MBA Finance (Carleton University), CFA, CFP, CIM) starting from 8:33. I just screen shot his animation, rather than taking the time to create a GIF out of it.

But growth in aggregate corporate earnings does not directly benefit investors. It is increase in earnings per share that benefits investors. The problem here is that per share earnings growth can only keep up with GDP growth, if no new shares are issued.
Let me explain. If you own shares in a company in a rapidly growing economy, and a new company listed shares on the stock exchange, you don't benefit from the new company's economic impact. You'd need to re-allocate some of your capital to the new company, to participate in its earnings. But doing so does not increase the value of your portfolio. The economy is grown, but your portfolio has not. Over time, the effect of this slippage has been meaningful.

China might again be a good example. Much of the growth in the market value of Chinese equities has come from an increase in the number of listed companies, as opposed to price appreciation from existing listed companies.

Please see the titled question.

I don't fathom the boldened phrase. What if company B's share price rockets faster than company A's? Wouldn't company B's faster rate of share price increase increase my portfolio's value?


texts: Organ sale is legal in Iran. I was wondering: are organ markets Pareto efficient? Or could an argument be made for them being Pareto efficient? I have been thinking that both the buyer and the seller benefit from the transaction, thus no parties are made worse off. However, coercion/kidnap could occur. There has also been the emergence of black markets (which some scholars attribute to the lack of a legitimate market in almost every country in the world).


texts: Is 'full employment' synonymous with 'the natural rate of unemployment'?

texts:
Is the phrase 'full employment' synonymous with the phrase 'the natural rate of unemployment'? Parkin, et al. (2010) seem to use these two terms interchangably in chapter 20, but looking up these two terms in the Oxford dictionary of economics (Black, Hashimzade & Myles 2009) shows two different meanings: Black, Hashimzade and Myles state that 'full employment' relates to the equilibrium point in the labour market, whereas 'the natural rate of unemployment' is a Keynesian concept which looks at the level of unemployment given constant inflation.
My interpretation of this is that 'full employment' is a classical concept, whereas 'the natural rate of unemployment' is not, because it seems as if the latter varies according to the rate of inflation (a nominal variable).
EDIT: The answers I have gotten so far are incorrect in that they say that 'full employment' means '100% employment'. This is incorrect because full employment actually takes into account frictional unemployment. I quote two dictionaries on the definition of full employment:

A situation where the labour market has reached a state of equilibrium, so that those in the active labour force who are willing and able to work at going wage rates are able to find work, and the only remaining unemployment is frictional unemployment.
(Black, Hashimzade & Myles 2009)

The following definition comes from The Economist

Jobs for all that want them. This does not mean zero unemployment because at any point in time some people do not want to work. Also, because some people are always between jobs, there will usually be some frictional unemployment. Full employment means that everyone who wants work and is willing to work at the market wage is in work. Most governments aim to achieve full employment, although nowadays they rarely try to lower unemployment below the nairu: the lowest jobless rate consistent with stable, low inflation.

The Economist goes on to define frictional unemployment as

That part of the jobless total caused by people simply changing jobs and taking their time about it, because they are spending time on job search or are taking a break before starting with a new employer. There is likely to be some frictional unemployment even when there is technically full employment, because most people change jobs from time to time.

In South Africa, unemployment is defined as those people who are actively seeking work, but who have not found work. Frictional unemployment seems to be a looser concept: the citizen wants work, but is happy to give up their previous job. It may be entirely possible for them to get work, just that it's taking them a while to secure their next contract. For this reason, one cannot say that an economy with a surplus of jobs is not at full employment.
References
Black, J, Hashimzade, N & Myles, G. 2009. Oxford dictionary of economics.  3rd edition. New York: Oxford University Press.
Parkin, M, Kohler, M, Lakay, L, Rhodes, B, Saayman, A, Schöer, V, Scholtz, F & Thompson, K. 2010. Economics: global and Southern African perspectives. Cape Town: Pearson.


texts: Difference in interpretation of log-lin coefficients with binary variable

texts:
Consider the model:
$$y_i=\beta_0+\beta_1D_1+\beta_2D_2+u_i$$
Where $D_1=\{0,1\}$ and $D_2=\{0,1\}$ are binary (dummy) variables, and $y_i$ is a continuos variable in levels.
In this model, for example $\beta_1$ is interpreted as the gap between the category when $D_1=1$ and $D_1=0$. Besides, this gap is in absolute terms, say in terms of the units of the $y_i$ variable.
Now, consider the similar model but dependent variable is in logs:
$$\ln (y_i)=\beta_0+\beta_1D_1+\beta_2D_2+u_i$$
I would thought that, for example, $\beta_1$ is the gap between the mentioned categories but in relative terms, say a proportion or percentage. Say in average category $D_1=1$ receives $\beta_1*100$ percent more (or less) of $y_1$ than $D_1=0$ in average.
But I found another approximation in my class for this gap, and it takes the gap starting with the fact that the relative gap:
$$Rel. gap\; between\; [D_1=1]\; and\; [D_1=0]=\frac{y_1-y_0}{y_0}*100\% = \left(\frac{y_1}{y_0}-1\right)*100\%$$
Where $y_1=y(D_1=1)$ and $y_0=y(D_1=0)$
Taking this into account we can get:
$$\ln (y_1)-\ln(y_0)=\beta_1 \implies \frac{y_1}{y_0}=e^{\beta_1}$$
Replacing this into the relative gap equation specified earlier we get:
$$Rel. gap\; between\; [D_1=1]\; and\; [D_1=0]=\left ( e^{\beta_1} -1 \right)*100\%$$
My question is: What is specifically the difference between those two approximations? And even if one of those perhaps is wrong, because the resulting gaps that you can obtain are way different. Moreover, which one should one use with academic purposes.
Thanks!


texts: Under what conditions does market failure occur?

texts: Edit: Is it possible to broadly categorize the ways in which market failures occur into relatively few categories? If so, what are they?


texts:
Say I would like to investigate whether a particular product feature affects its sales. We would like to match products based on feature vs non-feature. But the sales also depends on the retailers who sell the products, like marketing expense, ect.

In this case, I would like to match at both product level and retailer level. Is there any matching method addressing the issue? Or just combine all the features, both products and retailers, together and do the matching as usual?


texts: Connection between low demand for US Treasuries and expectation of inflation

texts:
The expectations for inflation and fear of accelerated rate hikes on the part of the Fed seem to be driving the stock market correction in the US this February, 2018, and as a result of the jobs report on Friday, February 2.

As a measure of inflation, the 10 year Treasury notes yields are inching higher, close now to 2.9 percent.

  I want to ask what is the connection between inflation expectations and the "tepid demand" for Treasuries in the most recent auctions (10 year notes).

Presumably yields at the auctions are perfectly fine-tuned to meet supply and demand. Therefore, if the issue was simply an expectation of higher yields in the near future, this would have been factored in at the time of the auctions.

At this point the fiscal hole of $1 trillion created by the recently enacted tax cuts is already known. Presumably, economists still see US Treasuries as risk free. And there is the "flight-to-safety" effect, which would anticipate investors fleeing the stock market to seek refuge in US Treasuries, and is seemingly absent here...

  So what is behind the "tepid demand"? Is it in some way connected to the main issue of inflation concerns at a technical level, or is it a parallel topic (e.g. institutional trust)?

I am not asking for an opinion-based answer, but a beginner's account of the technical connections between these concepts to the extent that this is possible.


texts: Necessary indifference conditions in mixed equilibrium

texts:
Suppose we are playing a game where the Action set for Player 1 is $(a,b)$, for Player 2 is $(c,d)$, and for Player 3 is $(L,M,R)$. Assume that for Player 3, the action $M$ is weakly dominated by some mix between $L$ and $R$. I am attempting to find all of the possible mixed equilibria.

Let $p$ be the probability that Player 1 chooses $a$, let $q$ be the probability that Player 2 chooses $c$, and let $r_1, r_2, r_3$ be the probabilities that Player 3 choose $L, M, R$ respectively.

I have two questions:

First, because action $M$ is weakly dominated for Player 3, does everyone assume that $r_2=0$?

Second, the probabilities $p$ and $q$ are subject to the constraint that Player 3 be indifferent between his/her own actions. Does Player 3 need to be indifferent between $L$, $M$, and $R$, or just between $L$ and $R$, since $M$ is weakly dominated?


texts: Interpretation of the Impulse Response Function

texts:
I have an IRF that shows the GDP shock to GDP.

Let's say I have a 5-year forecast of GDP. If there is an immediate 1% decrease in GDP today, can I adjust the original 5-year forecast by using the IRF?

e.g., GDP forecast in year 3 is 500 USD. The IRF says a 1% decrease in GDP will cause a 0.1 % decrease in year 3. Can I simply adjust the forecast downwards by 0.1% to to 499.5 USD?

Thank You


texts: Questions about Paul Krugman's 1998 Japan Analysis

texts:
I'm reading some of Paul Krugman's writing on Japan and the liquidity trap; specifically this article: Japan's Trap. However, I'm not an economist (just an enthusiast) so I have some basic questions.

First, PK uses the notation $y_t$ to refer to an endowment that's received at the start of each period. It's my understanding that this can be thought of as output, I.e. What individuals have to sell at the start of each period. Is it correct, then, to interpret the model as follows?

For $t=1$:

The endowment is $Y_1$
The nominal value of the endowment is $p_1Y_1$
A portion of this is used to purchase one-period bonds and the remainder is used to purchase consumption, $c_1$. Cash is required for consumption but not for the purchase of bonds. Thus, $M_1 = p_1c_1$ is the money demand for period 1, where $M_1 < p_1Y_1$ if any bonds are purchased.

For $t=2$:

An endowment of $Y_2$ is received
The nominal value of the endowment is $p_2Y_2$
Additionally, people will be paid from their bond purchases in the previous period, receiving $(p_1Y_1 - M_1)(1+i_1)$.
Thus, total income available in period 2 is the nominal value of period 2 output plus the principal and interest on period 1 investment: $p_2Y_2 + (p_1Y_1 - M_1)(1+i_1)$
This total income is then allocated to second-period bond purchases and consumption, $c_2$.

Essentially, my interpretation is that total income available in period 2 and beyond may be larger than the endowment received each period, $Y_t$, and this is due to investment. Thus, for any period t, if the amount of income that is used for bond purchases is $I_t$, then $C_t + I_t = RGDP_t > Y_t$ if bond purchases $I_t$ are above 0, the economy is closed, and the government contributes nothing beyond open-market operations and lump-sum transfers.

If the above is correct, then I don't understand PK's reasoning in section 1, where he makes some assumptions about periods 2 and beyond, saying that "from the second period onwards output (and therefore also consumption) will remain constant at a level y*." I don't understand this statement. I'm fine with the assumption that $y_t = y*$ for all $t > 1$, as PK says at the beginning of the paper that $Y_t$ is exogenous. What I don't get is why it follows that $c_t = y_t$.


texts:
In the following picture two preference relations are defined -

Ist preference relation defines lexicographic relation. Though we know that lexicographic preferences doesn't have utility function. They are defined at a point so we cannot define a utility function - is discontinuous. But how can we show it in terms of upper and lower contour set being closed?

Why second one is continuous?

Note - some terminologies -

A binary relation >~ on the metric space X is continuous if, for all x in X, the upper and lower contour sets, { y in X : y > ~ x} and {y in X : x >~ y}, respectively, are closed.

The upper contour set of x is >~ (x) = {y in X : y >~ x}

The lower contour set of x is >~ (x) = {y in X : x>~ y}


texts: Why income elasticity of demand of luxury good in greater than 1?

texts:
According to textbook and wikipedia, "if income elasticity of demand of a commodity is less than 1, it is a necessity good. If the elasticity of demand is greater than 1, it is a luxury good or a superior good."

Why was 1 chosen as the threshold?

I think that luxury good is consumed in larger proportion by relatively rich people. How does
income elasticity of demand is greater than 1 reflect this?


texts: Are Cobb Douglas goods complements or substitutes?

texts:
Given
$$U(x,y)= x^\alpha y^{1-\alpha}$$
$\alpha \in (0,1)$,
are Cobb Douglas goods (here $x$ and $y$) complements, substitutes, or neither? Why?

An explanation with mixed partial derivatives would be great. My calculus is better than my economics skills.


texts:
What levers are typically available to a Government to exit an economic downturn?

I can think of currency devaluation, efficiency improvements and infrastructure spending (possibly using funds raised by borrowing).


texts: When and why did governments impose restrictions on money creation

texts:
In many countries governments have made laws that bar themselves from creating money directly. Instead they have to go via a circuitous route involving the creation of bonds. This means that the government has to go into debt in order to create more money. The reason for this self imposed restriction seems obvious to me - it is a kind of advertising to prospective purchasers of government bonds. It says "don't worry about us devaluing your bonds through excessive money creation because we have written it in stone that we're never going to do that". If it wasn't for this assurance then government bonds would be harder to sell.

Whatever the reasoning - after many years being interested in this question I have never come across any official explanation. Surely somewhere there must be a record of how these restrictions came into existence. Where are these records?


texts: Is the global Automobile Industry changing from an oligopoly to monopolistic competition?

texts:
The current situation is the automobile industry is an oligopoly as there are few big firms and massive barriers to entry due to cost.

However, The industry seems like it is changing to a monopolist competition structure as new firms join the industry (Apple, Google). This is as a result of bigger differentiation’s in cars product (due to software)


texts: If a dummy variable is insignificant can I remove it from the regression?

texts: I have completed an F-test on the variable which gives p = 0.6, should I remove it from the model?


texts: Friedman rule vs Friedman's k-percent rule

texts:
Friedman has stated in his "k-precent rule" that the money supply should increase by a fixed percentage each year.

On the other hand, the "Friedman rule" states that the nominal interest rate should be 0, (which would cause deflaction).

Am I correct in thinking that Friedman is contradicting himself here?

Something else that seems to contradict the Friedman rule: he at a different point has stated that he would be in favor of a gold standard, which would effectively mean that the money supply would grow by an amount that depends on whatever gold production is, which is generally a small percentage.


texts: Have any economists ever argued that the notion of opportunity cost should be done away with?

texts:
I hold the opinion that the notion of opportunity cost "muddies the intellectual waters" so to speak, and I'd like to know if any professional economists have expressed this sentiment, or similar.

  Question. Have any economists ever argued that the notion of opportunity cost is problematic, or that it should be done away with?

Let me illustrate with an example. Define a function $f : \mathbb{R} \rightarrow \mathbb{R}$ as follows: $$f(x) = 3-x^2$$

Pretend we get to choose $x,$ and that the resulting payoff is $f(x)$. Then obviously, the optimal choice of $x$ is $x=0$, and this gives a payoff (or "benefit", or "utility") of $3$. Seems simple enough.

Okay, but now look what happens once we admit opportunity cost into the issue. It could be argued that by choosing $x=0$ and getting a payoff of $3$, we forgo the benefit associated with choosing $x=1$ at getting a payoff of $2$. So the true payoff of choosing $x=0$, once opportunity costs have been factored in, is at most $3-1$, which is $2$. Proceeding in this way, we can show that the true payoff, after subtracting all the relevant opportunity costs, is at most $3-(3-\varepsilon^2)$, for any choice of $\varepsilon$, no matter how small. Hence the true payoff is at most $\varepsilon^2$ for each choice of $\varepsilon$. So under the viewpoint of opportunity cost, the true payoff of choosing $x=0$ is not $3$, its $0$.

The is a general principle; if we take the concept of opportunity cost seriously, then every continuous decision problem (involving continuous functions) has a maximum payoff of at most $0$, and most choices actually yield a negative payoff. Obviously, this is pretty artificial. With discrete problems, its even worse; the maximum payoff of any decision is vastly reduced, but its only $0$ at the second-best choice(s); the best choice(s) yield a positive payoff.

Anyway, I'd like to know whether any professional economists have ever argued against using this concept.


texts: The marginal cost function is meaningful only when the produced quantity is normalized

texts:
The cost function depends on the number of produced items.

Let the value of the cost function C be in hundreds of thousands $ and the quantity is in 1,000,000 items, thus q = 1 indicates 1,000,000 items and q = 0.000001 indicates 1 item.

The marginal cost at a certain number of items (say 1560 items corresponding to q = 0.00156) is in one hand interpreted as the cost of an additional produced item (so it is the cost of the 1561th item), and from another hand it is the derivative of the cost function

$\frac{\partial \text{C(q)}}{\partial q}$ and then applying q to be 0.00156.

I see a good approximation for $\frac{\partial \text{C(q)}}{\partial q}$ to be $\frac{\partial \text{C(q)}}{1additionalitem}$ since 1 additional item is (0.001561 - 0.001560) which is an infinitly small quantity suitable to be considered as ${\partial q}$.

But what if in some other case, q actually represented just item units and not normalized item numbers e.g.:

q = 1 indicates 1 item, q = 1560 indicates 1560 produced items, and so on, so in this case $\frac{\partial \text{C(q)}}{\partial q}$ can't be $\frac{\partial \text{C(q)}}{1additionalitem}$ since 1 additional item is (1561 - 1560) which is 1 and not an infinitly small quantity.

would it be possible then to use the derivative of the cost function?

What I'm saying is that considering the marginal cost to be the derivative of the cost function is conditioned by having q a normalized value of a very big number of produced items. Do you agree?


texts: Why does a reduction in regional differences in unemployment shift the Phillips curve?

texts:
According to this question below, apparently a reduction in the regional differences in the level of unemployment would shift the short run Phillips curve SRPC leftwards. The answer to the question is A).

I do not see how this could be the case, because "a reduction in the regional differences in the level of unemployment" could mean the regions could either all experience more unemployment, or could all experience less unemployment. I don't see how either scenario would affect the expectation for inflation (in this question it would seem to be a deflationary expectation) to result in a leftwards shift in the SRPC.


texts: Interpretation of sub-unity money velocity

texts:
I've read through questions like: Implications of declining money velocity and noticed this trend has intensified since, with velocity printing the lowest readings in history in the past few months. Currently, velocity stands at 1.13.
https://fred.stlouisfed.org/series/M2V
From what I gather, the mainstream interpretation is that the low velocity levels are a result of monetary stimulus making its way into M2. The expanded balance sheet of the Fed was mainly aimed at stabilizing financial markets rather than the real economy. With interest rates near/at zero, cash replaces short-dated bonds as the preferred risk-free liquid asset. In this sense, velocity reflects growing demand to hold cash versus use it for transactions in the real economy.
I haven't found any literature on sub-unity velocity, so I'm left wondering if there is some sort of singularity that cannot be crossed without violating a sacred economic theorem. However, given that:
$$ V = GDP/M2 $$
It would seem that there is nothing in the laws of physics (indeed, nor economics) that would serve as a fool -proof guarantee that GDP must exceed money supply. Surely with Weimar Germany and other hyperinflationary episodes, the ratio slipped into sub-unity territory. I concede it may be an extreme scenario for much of the developed world, but in the face of supply chain disruption and quarantine measures, it merits a thought experiment.
Question
Hypothetically, if the US was to fall into sub-unity velocity, would there be a clear interpretation and how much significance would the act of crossing below one have? Optionally, what if V was negative?
(I realize not everything can be taken to the extreme in econ. As an example, take negative prices. Instead of customers paying firms for goods, they would pay firms not to produce. Or whatever the case, the interpretation of negative prices isn't clear.)


texts: Solved applied econmics question. Problem is the value of TVC, TC, AVC, ATC, & AFC are all negative. Should I ignore negative value?

texts:
Disclaimer: This is not a "Do my homework" type of question. Instead, this is, "I'm confused whether what I did is right or wrong?" type of question.
If I ignore negative signs in TVC value, everything other values come in positive form. But is it okay to do so? If not, then the solution I have written here should be correct.


texts: AS-AD model and labor force increase and natural rate of unemployment

texts:
I am trying to analyze the effects on the unemployment rate $u$ as the labor force $L$ increases, by use of the AS-AD model.

I have however some issues I can't wrap my head around:

If we increase the labor force L, how does it affect the natural rate of output? I am looking at the equation:

$$ P = (1+m)P_eF(1 - \frac{Y}{L},z)$$

where $P$ is the price level, $P_e$ is the expected price level, $m$ is the markup, and $F$ is a function of unemployment $u = 1 - \dfrac{Y}{L}$ and a catch-all variable $z$.

If we are initially at equilibrium with $ P = P_e$, that is equilibrium $Y$ is $Y_n$, the natural level, then what happens in the medium-run once we increase the labor force? Here I use the AS-AD model, and figure that an increase in $L$ causes a downwards shift in the $AS$-curve so equilibrium output initially increases, but then reverts back to $Y_n$ due to people changing their expectations of the price level.... but what happens to the unemployment rate in the medium run?


texts: Is there some background/explanation why the Fed discontinued publishing their M3 indicator, circa 2006?

texts: As Wikipedia says and as it can be easily verified, since 2006, the Fed no longer publishes an M3 indicator (unlike the ECB which still hangs on to that notion). So is there some background or explanation to this 2006 Fed decision to abandon their M3?


texts: Why doesn't land value go to 0 when tax rate goes to 100%?

texts:
I'm looking at this equation here:

$$y = \frac{ra}{r+x}$$

Where:

$y$ = market value of land
$r$ = real interest rate, set at 0.01
$a$ = land value, set at 1
$x$ = tax rate

I don't really understand this equation conceptually.


texts: Solving differential equation in The Economics of Superstar (by Rosen)

texts:
I am currently reading "The Economics of Superstar" written by Rosen (1981). I don't understand one differential equation he used in the paper. The equation is as follows:
$$\frac{dp}{dz} = (p+s)/z.$$

He says if we integrate this, we get $p(z) = vz-s$ for $v = (p+s)/z$. I think that it is a simple differential equation, but I am having trouble solving this. Could you give some help?


texts: Is 'price hike' synonymous with 'price rise'?

texts:
Since my childhood I have a belief that in economics price rise and price hike synonymous with each other.
Moreover, the Collin dictionary strengthens by belief:
Hike
But what you experts have to say--- are they absolutely same?


texts: Time Series Analysis - What lag level is appropriate?

texts:
In my undergraduate econometrics class we were taught the basics of time series analysis. We were basically told to use a model with a one period time lag (lag = 1). However, I wonder that there must be cases where more lags might be appropriate. What would those instances look like? Is there a way to find what might be the optimal number of lags to look at for a particular time series. Could you guide me to appropriate resources that deal with the intuitive Math for this and possibly an implementation of how to find optimal lags in R if possible.
Thanks for your help!


texts: Can a horizontal merger in a highly concentrated market be beneficial to consumers if the cost synergy of the 2 merging firms is large enough?

texts: There are three firms in a market and they compete in quantities ( a la Cournot).Two of the three firms merge (horizontal merger). The two merging firms will be able to reduce marginal costs substantially once the merger is complete due to proprietary technology,so the merger from three firms to two firms is profitable (merger paradox does not apply).The merged firms will also be able to license this new technology to the other firm so that their marginal costs will be substantially reduced as well. Because there are only 3 firms in the market, the market is already highly concentrated and the merger would result in a substantial increase in HHI for the market. Using the cournot model to solve for equilibrium price and quantities, I find that the consumer surplus in the market increases after the merger. Is the increase in consumer surplus enough to justify the merger even though the market has become significantly more concentrated?


texts: Are there certifications or professional designations that are specifically geared for economists? i.e much like the CPA and CA exists for accountants.


texts: Development economics papers that used Difference-in-Differences

texts:
I need to write an assignment paper in development economics that explains the concept of differences-in-differences estimation, and I feel like it can certainly be helpful to look at some examples that actually used this method.
So I wish to look for some sample papers which dealt with issues in development economics that used
the difference-in-differences method as a reference for the paper.
I spent some time searching for examples but it's been surprisingly difficult to find actual example papers displaying this method (I was only able to find hypothetical examples or examples used in the United States). Maybe there is a problem with my searching method.
Is there a website where I can specifically find examples or sample papers on development economics (so the estimation has to be used in developing countries) that used Differences-in-Differences? I think there are friends here who are used to searching for or writing papers like this, and I would appreciate advice on places to refer to or how to find these kinds of papers that match my needs.


texts: Solow model and economic interpretation of $\dot{K}=sY(t)$

texts: I am reading Robert Solow's 1956 paper, entitled 'A Contribution to the Theory of Economic Growth'. I am trying to understand the economic interpretation of the differential equation $$\dot{K}=sY(t),$$ which is located on page 67 (Solow denotes this equation by $(3)$). I have understood each term as: $s$ is the proportion of saved output, $Y(t)$ is the production function at time $t$, and $\dot{K}$ is the rate of increase of capital stock with respect to time $t$. Although, I am having trouble understanding what this equation actually means (I am a novice at economics).


texts: Using the CPI to inflate real estate prices

texts:
I got my hands on an interesting dataset of property transfers covering four decades and I'm unsure of how to properly inflate prior-year sale prices.

I typically use the 'bushel basket' metro CPI-U to adjust dollar amounts, but I'm wondering if I should specifically use the 'housing' index instead of the full bushel basket? What would be the benefits/drawbacks of using the more targeted price index?

Additionally, what sort of price index should I use to adjust commercial property transfers if I were to include those into the analysis?


texts: Can we "prove" that slow growth is due to deficient demand?

texts:
We hear more and more these days about growth, particularly in the Eurozone and Britain, being beneath its long-term trend due to deficient demand. I can think of a few things which support that idea - such as a drying up of the credit which fuelled pre-crash consumer growth, low inflation and perhaps even deflation, long-term stagnant wages, and all this despite ultra low interest rates and QE. In short, the deficient demand story is one which has an intuitive appeal.

What I don't get is simply this: can we prove that deficient demand is the cause of the problem, and if so how?


texts: Can a complex interaction term mean more than what it's composed of?

texts:
I'm cross-posting this question on both Economics and Cross Validated to get answers from a different perspective on each field. It is generally accepted to cross-post if the question is tailored to fit better in each community. See: https://meta.stackexchange.com/a/64069/510233

Cross-posted in Cross Validated: https://stats.stackexchange.com/q/403213/243829

I'll try to be as detailed as possible to best deliver what I want to know in this question.

In economic data, there are some variables that are composed of many other variables. Mostly indices or multiples. I can think of some examples like CPI, Consumer Sentiment Index, or even EV/EBITDA, PER.

Better and more general example would be something like Wind chill Temperature Index which is

where:

WCI = wind chill index, kcal/m2/h
v = wind velocity, m/s
Ta = air temperature, °C

What I want to know is whether a variable like WCI can have more meanings(effects) than v and Ta seperately combined.

Based on what I learned in regression analysis from Ecnonometrics class, a simple interaction term like  would be interpreted as the difference in marginal effect between a control group (D=0) and a treatment group (D=1), when expressed like:

Also, more general interaction term like VariableA * VariableB would be interpreted as an impact of VariableA on the coefficient of VariableB, in some examples like

PollutionLevel = B0 + B1*Population + B2*NumberOfCars + B3*Population*NumberOfCars
= B0 + B1*Population + (B2 + B3*Population)*NumberOfCars

(originally from a question posted on Cross Validated)

But I think these interpretations are too simple to capture the whole meaning(effect) of a new variable derived from other variables, which leads to other questions like:

What would be the interpretation of a super complex interaction term like WCI in regression perspective? (and other data science methods like Random Forest or Deep Neural Network, etc if possible.)
Would it still be valid and preferable to include an explanatory variable like WCI in the model when I already have v and Ta? Would it make the model more accurate?
Intuitively, I feel like people would care more about important indices but not necessarily the variables it is composed of. Can a complex interaction term derived from other variables have more effect than a simple combination of the other variables?

The third one is related to my original question of whether one variable that is composed of other variables in a dataset can have more effect on the dependent variable.

One example I can think of is the steepness of the yield curve that is considered very important in the bond market, which is a mere slope of the interest rates of bonds with different YTM.

People seem to care about the slope of the yield curve more than individual rates of each bond so I think it is a legit explanatory variable but it is unclear whether it is justified to introduce this new variable from existing variables or how it should be interpreted.


texts: Does combination of the paradox of thrift and the acceleration principle reduce economy to c=a level of consumption during recession?

texts:
By "c=a level" I mean situation when all consumption by households equals to autonomous spending, more or less. I assume no counter-cyclical policies(including automatic stabilizers). I also assume that no suprise positive shocks (like new resources, new technology) will happen midway.

Suppose there is a recession. And as it's typical for a recession, it starts as a slump in planned investment spending. As a consequence, aggregate disposable income of households decreases. Households decrease their aggregate consumption in response. It increases unplanned inventories investments by firms, consequently making firms to decrease their planned investment spendings (because they produce less).

Rinse, repeat. Economy gets caught in a feedback loop. And if I understand the acceleration principle correctly (I understand it as "If consumption decreases, then planned investment spending decreases even more. If consumption increases, then planned investment spending increases even more"), this is not a negative feedback loop, but a positive feedback loop. In other words, each cycle becomes only stronger (Households consume less, it causes firms to invest even less, it causes households to restrict their consumption even stronger than before, etc.) Without counter-cyclical government intervention (I count as counter-cyclical intervention automatic stabilizers aswell), or positive shocks in the midway, the whole thing will stop only when it will hit the wall, and the wall is autonomous spending. Households will stop tightening their belts when consumption spending will equal autonomous spending.

Do I understand everything correctly (the end results and the whole mechanism how we get where)? Or did I misunderstand something?


texts: Can we stabilise the price of a cryptocurrency?

texts: Currently, the volatile price of cryptocurrencies such as Bitcoin means that they are currently poor stores of value and therefore are unlikely to achieve mass adoption. What can be done to stabilise the price of a cryptocurrency, apart from pegging the cryptocurrency to a fiat currency?


texts: When estimating VAR(1) by OLS, I get transpose of AR matrix. Why?

texts:
Model: $y_t = \Phi y_{t-1} + (\mathbb{I_n}-\Phi)\mu + \Sigma \varepsilon_t$
s.t. $y_t$ is a $(n \times 1)$ vector, and $\varepsilon_t \sim N(\vec{0},\mathbb{I}_n)$. $\mathbb{I}$ is the identity matrix. $\Phi$ and $\Sigma$ are $(n \times n)$ matrices.

Consider the following MATLAB code.

Sigma = eye(2); %sqrtm(Covariance matrix)
Phi{1} = [0.9,0.12;0,0.9]; %Autoregressive matrix
mu = [0;0]; %Constant vector
nTs = 1000; %Length of simulation

%Specify Model
mdl = varm(2,1);
mdl.AR = Phi;
mdl.Constant = mu;
mdl.Covariance = Sigma^2;

%Simulate Model
simTs = simulate(mdl,nTs); %Simulate VAR(1) (nTs x 2)

%Estimate Model
X = simTs(1:end-1,:);
Y = simTs(2:end,:);
hatPhi = (X'*X)\(X'*Y)

>> hatPhi =
       0.8939  -0.0057
       0.1721   0.8732

Notice the output is the transpose of the AR matrix supplied. Why is this? I feel dumb, lol.


texts: The relation between the Black-Scholes model and quantum mechanics

texts:
As an active participant on the Physics Stack Exchange I have, on several separate occasions, run into some vague remarks about the 'intimate relation' between the famous Black-Scholes model in economics and the Schrödinger equation that appears in quantum mechanics. In particular, people mention that path integrals (a certain technique that is very useful in quantum mechanical calculations) find many applications in economic settings.

I'd love if someone could make this connection clearer by

Explicitly (i.e. in equations) showing how the Schrödinger equation and the Black-Scholes equation are related
Discussing the use of path integrals in economics


texts: Uniqueness of Competitive Equilibrium Conditions

texts:
I know that if a consumer has strictly convex preferences it may not guarantee uniqueness of CE.
I believe that we need monotonicity of preferences as well but would like to hear any thoughts of this claim or whether any other conditions may be needed.

Thanks


texts: Would insurance plan be necessary if we had instant access to credit?

texts:
Assuming one could instantly have access to an loan to cover his recent loss/accident at an affordable interest, would it make sense to pay premium for an insurance plan?

I was thinking that it would make more sense to save the premium money and use it to pay part of a loan to cover the losses if it happens. That way one would save the trouble of paying insurance and never using it and make better use of that money.

But I believe in economics. It wouldn't be such a big thing if it didn't make sense. So, how can one evaluate when it makes sense to pay for insurance or just count on a loan?


texts: Right definition of natural rate of unemployment?

texts:
Earlier I studied macroeconomics from Blanchard. But now while reading Mankiw's Macroeconomics I found different definition for natural rate of unemployment. According to Blanchard,

"the rate of unemployment (and by implication the level of output) that prevails if the price level and the expected price level are equal." (pg. 135, sixth edition) and

"The natural rate of unemployment is the rate of unemployment required to keep the inflation rate constant." (pg. 170, sixth edition)

But according to Mankiw,

"The natural rate is the rate of unemployment toward which the economy gravitates in the long run, given all the labor-market imperfections that impede workers from instantly finding jobs."(pg. 177. eighth edition),i.e., where unemployment rate reaches steady-state, it neither increases or decreases, where rate of job finding is equal to rate of job separation.

What is the common ground between all these definitions? Are they different or essentially the same? If so, then how?


texts: Black-Scholes Formula Satisfies Black-Scholes Equation

texts:
My professor told me that each term of the Black-Scholes formula satisfy the Black-Scholes PDE. I have been trying to work this out for the last week and have been unsuccessful. I correctly showed the first term satisfied it, but I have had difficulty with the second term. My work is below:

We need to show that:
$$Q=-ke^{-r(T-t)}N\bigg(\frac{log\big(\frac{S}{k}\big)+(r-\delta+\frac{1}{2}\sigma^2)(T-t)}{\sigma\sqrt{T-t}}-\sigma\sqrt{T-t}\bigg)$$

(where $N(w)$ is a standard normal distribution evaluated at $w$) satisfies the following:
$$(r-\delta)Q_sS+Q_t+\frac{1}{2}Q_{ss}\sigma^2S^2-rQ=0$$

Where $Q_s,\;Q_{ss}\;and\,Q_t$ are the derivative of Q w.r.t S, the second derivative of Q w.r.t S, and the derivative of Q w.r.t t respectively.

Let $d_2=\frac{log\big(\frac{S}{k}\big)+(r-\delta+\frac{1}{2}\sigma^2)(T-t)}{\sigma\sqrt{T-t}}-\sigma\sqrt{T-t}$

$$Q_s=\frac{-ke^{-r(T-t)}N'(d_2)}{s\sigma\sqrt{T-t}}$$
$$Q_{ss}=\frac{-ke^{-r(T-t)}N''(d_2)\big(\frac{1}{s\sigma\sqrt{T-t}}\big)-\sigma\sqrt{T-t}}{S^2\sigma^2(T-t)}$$
$$Q_t=-kre^{-r(T-t)}N(d_2)+N'(d2)\bigg(\frac{log\big(\frac{S}{k}\big)}{2\sigma(T-t)^{\frac{3}{2}}}-\frac{r-\delta+\frac{1}{2}\sigma^2+\sigma}{2\sqrt{T-t}}\bigg)$$

When I plug these derivatives into the Black-Scholes PDE, I cannot get the equality to hold. Can anyone please help?


texts:
In social choice theory, Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem stating that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting a specified set of criteria: unrestricted domain, non-dictatorship, Pareto efficiency and independence of irrelevant alternatives (IIA)

So, I'm looking for an example where the preferences satisfy unrestricted domain, non dictatorship, IIA and is an ordering, but not meet the Pareto criteria.


texts: How does the stock market correlate with the economy?

texts:
What's the Correlation Coefficient between the Canadian and US stock  and economy?  Don't hesitate to discuss other stock exchanges.

On Apr 30 2020, Paul Krugman wrote Opinion | Crashing Economy, Rising Stocks: What’s Going On?

  Yet stock prices, which fell in the first few weeks of the Covid-19 crisis, have made up much of those losses. They’re currently more or less back to where they were last fall, when all the talk was about how well the economy was doing. What’s going on?

  Well, whenever you consider the economic implications of stock prices, you want to remember three rules. First, the stock market is not the economy. Second, the stock market is not the economy. Third, the stock market is not the economy.

  That is, the relationship between stock performance — largely driven by the oscillation between greed and fear — and real economic growth has always been somewhere between loose and nonexistent. Back in the 1960s the great economist Paul Samuelson famously quipped that the market had predicted nine of the past five recessions.

I know it's $< +1$, because

The stock market only consists of publicly traded companies, which is a subset of the economy (generally large businesses). Economic activity can also come from private companies (most small businesses are private), government activity, and not-for-profit organizations. A US stock index can also track companies that have a lot of foreign production, so the value of a company can increase from production that's not measured in US GDP.
The current economy can mismatch what investors expect the economy to be in the future. Stock prices don't only reflect current wealth but also future payoffs. After all, people invest to transfer wealth from one time period to another. That is one of the tasks (if not the most important task) of financial markets.


texts: Unbalanced panel data in prodest package in R

texts:
I have a question regarding the usage of unbalanced panel data for TFP estimation by using the prodest package.
The dataset could be found here: https://drive.google.com/file/d/1W5pva05hRiruo1AMNc62ln0GNtcVr5p6/view?usp=sharing
As you can see from the dataset, there are a lot of firms that have not reported some values in specific years, ending up with unbalanced panel data.
The code is the following. BUT in case I do not filter the data with >0 values, I receive error messages coming from the estimation of TFP, saying that there are NaNs.
remove(list=ls())

library(plm)
library(dplyr)
library(ggplot2)
library(prodest)

pckg<-c("plm","readxl","dplyr","ggplot2","prodest")
#install.packages(c("plm","readxl","dplyr","ggplot2","prodest"))
lapply(pckg, require, character.only = TRUE)

# Set the working directory
setwd("C:/Users/vadya/Desktop/LT original currency")

# Downloading the survey data
Data <- read.csv("LToc.csv", header=TRUE, sep=",")
str(Data)

Data$ID<-as.numeric(as.factor(Data$ID))

summary(Data)

# Creating a panel data frame

DataA <- Data %>%
  #filter(NACE == 'A') %>%
  #filter(TURN > 0, TFA > 0, FA > 0, VA > 0, L > 0, M > 0) %>%
  mutate(ID = ID,
         Year = Year,
         turn = log(TURN),
         tfa = log(TFA),
         fa = log(FA),
         va = log(VA),
         cogs = log(COGS))
         #l = log(L),
         #m = log(M))
################################################################################################

mod2ACF <-  prodest::prodestACF(DataA$va, fX = DataA$cogs, sX = DataA$tfa, pX = DataA$cogs, idvar = DataA$ID, timevar = DataA$Year,
                                R = 100, cX = NULL, opt = 'optim', theta0 = NULL, cluster = NULL)

mod2ACF
omegaACF <- prodest::omega(mod2ACF)
summary(mod2ACF)
summary(omegaACF)

mod2W <-  prodest::prodestWRDG(DataA$turn, fX = DataA$cogs, sX = DataA$tfa, pX = DataA$cogs, idvar = DataA$ID, timevar = DataA$Year,
                               cX = NULL)
mod2W
omegaW <- prodest::omega(mod2W)
summary(mod2W)
summary(omegaW)

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If I do not filter the dataframe, in the TFP estimation part (e.g., ACF method) I get the following error message.

Am I doing something wrong, and is there a way to make the prodest functions to work with unbalanced panel data?
Thanks in advance for the ideas! Would really much appreciate your concern!