texts: Effect of exogenous parameter on three player SPNE profits

texts:
Consider three agents $A_i$.

$A_1$ moves first and selects $0\leq q_1\in \mathbb{R}$. $A_2$ moves second and selects $0\leq q_2\in \mathbb{R}$. $A_3$ moves third and selects $0\leq p_1\in \mathbb{R}$ and $0\leq p_2\in \mathbb{R}$.  $0\leq x\in \mathbb{R}$ is a parameter.
$A_1$ tries to maximize $u_1(q_1,p_1, q_2,p_2, x)$, with $\frac{\partial u_1(q_1,p_1, q_2,p_2, x)}{\partial q_1}\geq 0$ and $\frac{\partial u_1(q_1,p_1, q_2,p_2, x)}{\partial p_1}\geq 0$, and independent of $q_2,p_2,x$. $u_1(q_1,p_1, q_2,p_2, x)$ is continuous in all its inputs.
$A_2$ tries to maximize $u_2(q_1,p_1, q_2,p_2, x)$, with $\frac{\partial u_2(q_1,p_1, q_2,p_2, x)}{\partial q_2}\geq 0$ and $\frac{\partial u_2(q_1,p_1, q_2,p_2, x)}{\partial p_2}\geq 0$, and independent of $q_1,p_1,x$. $u_2(q_1,p_1, q_2,p_2, x)$ is continuous in all its inputs.
$A_3$ tries to maximize $u_3(q_1,p_1, q_2,p_2, x)$, with $u_3(q_1,p_1, q_2,p_2, x)$ increasing for all $p_1<\bar{p}$ and decreasing for all $p_1\geq \bar{p}$; $u_3(q_1,p_1, q_2,p_2, x)$ decreases in $x$ and $q_1$; and $u_3(q_1,p_1, q_2,p_2\rightarrow \infty, x)=-\infty$; $u_3(q_1,p_1, q_2\rightarrow \infty,p_2, x)=-\infty$. $u_3(q_1,p_1, q_2,p_2, x)$ is continuous in all its inputs, but we do not know more about its properties for $p_2,q_2$.
We assume that in case that an agent is indifferent between two or more strategies that there exists a decision rule that selects exactly one of these strategies. These rules are known by all agents.

The existence of a unique SPNE is quite clear. However, there could be multiple other equilibria that would lead to the same profit profile (specifically equilibria in which each agent gains the same profits.)
Question: Does $A_3$'s profit decrease in $x$? If yes, why? If not, is there an easy assumption that we need for $u_3(q_1,p_1, q_2,p_2, x)$ behavior with regard to $q_2,p_2$? (I think I miss the forest for the trees) Does the sum of all agents' profit decrease in $x$?
My immediate intuition is yes, because otherwise $A_3$ would be able to pass on all its "losses" to the other agents.


texts: In practice, are retaliatory tariffs the first step (or among the first steps) in the WTO dispute resolution process?

texts:
In theory, retaliatory tariffs probably aren't first step in the WTO dispute resolution process.

Instead, the dispute is supposed to go through consultations, which take some 6.6-months on average, followed by a panel decision if necessary, which can take an additional 15.1 months etc. (Approximately two thirds of WTO-registered disputes were actually solved in the consultations stage.) Following an arbitration,

  If defendant stays idle, or if a compliance panel (and/or the AB [Appellate Body], as the case may
  be) pronounce on the inadequacy of adopted measures, then defendant might be
  facing retaliation. The framers of the DSU did not manage to agree on a clear
  method to calculate the amount of retaliation. They used the term ‘substantially
  equivalent concessions’ that would serve as the legal benchmark for calculating
  retaliation. Disputing parties might disagree on the amount of retaliation, and
  disputes on this score will be submitted to an Arbitrator (the original panel,
  whenever possible), which will decide on the appropriate amounts (Article 22.6 of
  DSU). Awards by the Arbitrator on this score are not subject to appeal.
  Retaliation can lawfully take place only following authorization to suspend (tariff)
  concessions (that is, raise the level of customs duties on imports from the
  recalcitrant WTO member). The defendant is still under the obligation to
  eventually bring its measures into compliance, and has to observe specific reporting
  requirements to this effect (Articles 21.6 and 22.8 of DSU). Suspension of
  concessions is ‘temporary’ as per the explicit wording of the DSU (Article 22.8 of
  DSU), but no statutory deadline for its expiry is provided. Consequently, whereas
  de jure the DSU (Article 22.1) calls for ‘property rules’, that is, for the obligation to perform the contract, de facto it tolerates ‘liability rules’, that is, the possibility
  for authors of an illegality to ‘buy their way out of the contract’.

So, it looks like (in theory) retaliation in the WTO framework can only legally happen after arbitration. On the other hand, there's was no shortage of retaliatory tariffs worldwide, recently. Was this always the case for trade disputes ever since WTO or GATT came about, i.e. in practice, does retaliation often work in parallel with the WTO dispute resolution? (Some statistics on this would be more interesting to me than mere opinions.)


texts: Why in some models the Friedman rule is not optimal?

texts: I want to know why in some models the Friedman rule stops being optimal. For example, in some models like MIU or CIA, where usually you don't have leisure, the Friedman rule is optimal. But in other models with bonds (for example) the Friedman rule stops being optimal because it breaks some non arbitrage conditions.


texts:
So I´m a bit stuck on this one. There are two firms in the country that sell cars. Both sell Toyotas and they buy their cars directly from the manufacturer, which is Toyota. We can assume that quantity is the strategic variable, and that the two car dealers have no other marginal costs than the wholesale price "r".

The inverse total demand:
P = 1500 - 5(q1 + q2)

MC = 30

And I got:

q1 + q2 = Q

Q = 2(1500-r)/(2+1)5 = (3000-2r)/15

Which wholesale price, r, will the Toyota set? What is the equilibrium retail price, p, and the number of units sold?

When I solve for "r" I get:

r = 1500 - 7.5Q

But after this I am stuck and I can´t figure out what to do next. Anyone with any suggestions on how I should proceed or point me in the right direction?


texts:
I was listening to a Bloomberg market update, and the journalist mentioned that the Japanese currency was down as Gold rose.

I've heard that investors park their money in Yen. Is the reason the Yen is down because investors are moving their money out of Yen and re-investing in gold?


texts: What are some great economic reforms from the Middle Ages / the Ancient History?

texts: Is there any great economic structural reforms, which date back to the Middle Ages or to the Ancient times?


texts: Does anyone know of any resources that discuss the differences between Hicksian and Marshallian remanding in depth and in an organized way?

texts:
I don't understand why the Marshallian and Hicksian demand have such different properties.
Both are functions from $$\Bbb{R}^n_+ \times \Bbb{R}_+ \rightarrow \Bbb{R}_+^n$$both are solved using the method of Lagrangian multipliers. Yet the properties of the two are very different.

Does anyone know of any resources that discuss these differences in depth and in an organized way? My professor has us using his lecture notes. These are a good introduction but just don't rigorously discuss the differences.


texts: Why does $\varepsilon_{x,p_x}^H =-s_y \sigma $?

texts:
Suppose I have two goods $x$ and $y$ and their associated prices $p_x$ and $p_y$. Income $m$. $x^H$ is Hicksian demand and $x^M$ is Marshallian demand.

Slutsky Equation:

$$\frac{\partial x^M}{\partial p_x} = \frac{\partial x^H}{\partial p_x}  -\frac{\partial x^M}{\partial m} x^M $$

Elasticity Version:

$$\varepsilon_{x,p_x}^M = \varepsilon_{x,p_x}^H - \eta_x s_x$$

$$s_x = \frac{p_x x}{m}$$

My professor claims $$\varepsilon_{x,p_x}^H =-s_y \sigma $$, but didn't give a proof even when asked. Nor could my TA provide one.

$\sigma$ is the elasticity of substitution

My Question:

Can someone show why $\varepsilon_{x,p_x}^H =-s_y \sigma $?


texts: Historical GDP of world economies back to 1945: What are the most complete and reliable data sets?

texts: I need the historical GDP of all modern countries (or at least the vast majority) from 1945 to now. It seems the world bank data only starts in 1960 or later. I found Angus Maddison's data, but I don't know how reliable it is. Can anyone tell me if it is reliable? Are there other good data sets for my needs?


texts: How can government mitigate the long-term effects of current shut downs?

texts:
I’m not well versed in economics by any stretch of the imagination. But I am confused with certain measures taken thus far by the government.

There is currently a temporary shutdown of vast sectors of the economy now and workers affected are not receiving any income.

To me, logic would dictate that here should also be a temporary cessation of payments for rental properties (for small businesses as well as individuals) and, to be fair, a temporary cessation of payments for loans for owners of those properties. In turn, banks would be given temporary cessation payments for interest to its customers since the banks would not receive any payments on loans including payments on mortgages from homeowners.
That would essentially close the loop on money flow which again would be temporary and the impact to the greater economy would be limited.

If undue burden is placed on any one of these points in the cycle, and right now, workers and small businesses are taking that brunt, then there could be long-standing damage to the economy from bankruptcies, foreclosures, etc.

The Fed is already addressing the banking side of things by keeping rates close to 0.

Why can’t the government step in to make sure the whole loop is closed off?
I don’t get it.


texts:
Monthly savings plans in stocks or funds are typical investments for many people. On aggregate, these plans generate a large demand on the underlying assets, often around the end/beginning of a month.

How do banks or fund managers handle these investments?

I assume two strategies, wich both seems to have problems:

As monthly savings plans are often due at the end of the month, a financial institution buys the underlying assets within the first days of a month. This demand would drive stock prices at the beginning of a month, but this effect is not observable in empirical research.
Financial institutions spread the buying of underlying assets. Therefore, they bear market-risk, as the claim of monthly savers on these assets is not covered by the bank/fund by actually holding these assets. I know, that this risk can be managed, but on aggregate, not all institutions can hedge their offered investment plans without holding any underlying asset.


texts: Are the average payoffs in the convex hull?

texts:
This is an exercise in the Steve Tadelis An Introduction to Game Theory book:

(10.12) Folk Theorem Revisited: Consider the infinitely repeated trust game described in Figure 10.1

(a) Draw the convex hull of average payoffs.

So, this is pretty easy:

The vector of payoffs is $V=\{(0,0),(0,0),(-1,2),(1,1)\}$

So, here is my sketch in paint:

(b) Are the average payoffs $(\overline{v_1}, \overline{v_2}) = (−0.4, 1.1)$ in the convex hull of
average payoffs? Can they be supported by a pair of strategies that form
a subgame-perfect equilibrium for a large enough discount factor $δ$?

  I don't have an idea how to do (b). If someone could explain that would be great.


texts: Recommendation on economics books for a statistician

texts:
I have mainly an statistics/informatics background and i have basically not knowledge in economics.

What some good books to star given my background?

Edit:

My principal interest is stock market analysis, investing and risk modeling.

I have a degree in statistics and other informatic engineering(something like CS), i don't have problems with math-heavy books if it helps me to build a solid understanding.


texts:
Throughout microeconomic literature i see the following restiriction placed on the nature of elasticities in demand system estimation.

This being for some arbitarary good $x$ we require price elasticities and income elasticities to be:

$$\varepsilon(x,p_x)+\varepsilon(x,p_y)+\varepsilon(x,I)=0$$

What is the proof for this? (I cant seem to find it).


texts: Short, Medium and Long-Run Profit Maximization

texts:
Suppose that, in a perfectly competitive industry, the firms' technology have the following cost function: $C(x) = 100 + 3x + 0.04x^2$. Assume the fixed costs are sunken.
a) If the demand for the product is given by $D(p) = 200(10-p)$, what is the long-run equilibrium for this industry? (price, quantity demanded and consumed, number of firms).
In the long-run equilibrium, the price should equal the minimum average cost. That happens when $MC = AC$, which means:
$$
3 + 0.08x = \frac{100}{x} + 3 + 0.04x \implies x = 50, x > 0
$$
For this value of $x$, we have, equating $p = CMg$:
$$
p = 3 + 0.08 \cdot 50 = 7
$$
and, therefore,
$$
D(7) = Q^D = 600
$$
which means that the number of firms is $n = 600/50 = 12$.
b) Under a negative and permanent demand shock, it dislocates to $D(p) = 200(8-p)$. In the very-short run, the firms cannot change their production plans. What is the new equilibrium price? In the medium-run, however, the firms can adjust their production plans. Find the medium-run equilibrium (price, quantity produced and consumed, number of firms).
If in the very-short run the productions plans cannot be changed, let's assume the total market output is still 600. Using the new demand function:
$$
600 = 200(8-p) \implies p = 5
$$
In the medium-run, the firms can adjust their production plans and therefore we should find the value of $q$ that satisfies $MC = AVC$:
$$
3 + 0.08x = 3 + 0.04x \implies x = 0
$$
And so:
$$
p = 3 + 0.08 \cdot 0 \implies p = 3
$$
and therefore
$$
D(3) = Q^D = 1000
$$
However, since the best option for the firms is to not produce, we can (can we?) suppose that all of them leave the market, resulting in $n = 0$.
c) Find the new long-run equilibrium (price, quantity produced and consumed, number of firms). Compare your results with the medium-run equilibrium and interpret.
In the new long-run, we will again have $MC = AC$, resulting in a price of $p = 7$ and $x = 50$ again. However, given the change in the demand function, the quantity demanded now will be
$$
D(7) = 200(8-7) = 200
$$
which means that the new number of firms is $n = 200/50 = 4$, an increase for the medium-run, due to the absence of fixed-costs in the long-run.
Are my answers correct? I had never encountered a question asking about medium-run before. Also, is the profit maximization level of production different from the equilibrium level of production?
Thanks!


texts: What's the opposite of a Pareto improvement called?

texts:
Wikipedia defines a Pareto Improvement, "given a certain initial allocation of goods among a set of individuals" as:

  a change to a different allocation that makes at least one individual or preference criterion better off without making any other individual or preference criterion worse off

Given this definition, then, the opposite of a Pareto Improvement should be:

  a change to a different allocation that makes at least one individual or preference criterion worse off without making any other individual or preference criterion better off.

What's the correct way to refer to this? Does it have a name?


texts: Why is there so little automation at McDonald's?

texts:
I'm currently at a McDonald's in Norway (so, not a country where labour is dirt cheap, even for relatively unqualified jobs), and I'm struck by how manual every process is, from cooking the meat to assembling burgers to serving.
The fries-making process is particularly baffling. It goes like this:

An employee pours frozen fries in a basket and dunks it in oil
After a while, an alarm rings and an employee has to come to manually raise the basket from the oil
An employee put the fries in a bin and salt them with a handheld salt shaker
The employee shovels the fries into little bags that are brought to the trays

It seems like it would be trivial to automate away the second step here (for example by having the basket rise by itself after a set time), and not that hard to have the rest done by a machine either.

Other industries employing unqualified labour, like groceries stores, have spent considerably more money and effort into automating their checkout lines, for example. Why hasn't the fast food industry followed suit?


texts: Is there a complete picture of Inflation?

texts:
Is there a book, or a broad study, that explains inflation thoroughly?

I've read so many articles, and there are multiple school of thoughts that approach inflation from different point of views. All of them has truth in it, but is there a good book, that summarize and compare them?


texts: Economic interpretation: IS curve contra GDP in equilibrium

texts: I have in a problem shown that for the IS curve (Y) contra the GDP in equilibrium ($Y^*$) it applies that: $\frac{\partial Y}{\partial G}>\frac{\partial Y^*}{\partial G}$. Where G is public consumption. I think my calculations make sense. But what will the economic interpretation of this result be? Can anyone help me?


texts: What are the currently accepted methods to estimate a firm's productivity?

texts:
While there are a lot of methods one can think of, like computing the ratio of profits to assets or profits to sales, apparently it is a difficult problem.

It would be useful to know how effectively are firms using their inputs in a marginal or an average sense, say by looking at the cost of labor, capital inputs, electricity, etc, and comparing that with the output of a plant or a firm.

Some methods assume a Cobb'Douglas function and also assume which factors are fixed and which are variable over which periods, etc. Is there a typically accepted method yet?


texts:
Introduction

There are different ways of estimating the parameters of a production function. For example, single-equation and system equation techniques are both possible. Another difference among methods is that estimable forms may either involve direct or indirect estimation of the parameters. For instance, rather than estimate the production function as is, one may instead estimate the derived demand functions or, say, use other relations such as factor shares. Also to be considered are the underlying economic assumptions; such possibilities being perfect competition, constant returns to scale, profit maximization, etc.

Question

Bearing the above in mind, my question is what is the standard (accepted?) method of estimating normalized CES (constant elasticity of substitution) production functions?

For information, a normalized CES  production function can be written as

$$
Y = Y_{0} \lbrace \pi_{0} K_{0}^{\frac{1-\sigma}{\sigma}}(K_{t}\cdot e^{\gamma_{K}(t-t_{0})})^{\frac{\sigma-1}{\sigma}} + (1-\pi_{0})N_{0}^{\frac{1-\sigma}{\sigma}}(N_{t}\cdot e^{\gamma_{N}(t-t_{0})})^{\frac{\sigma-1}{\sigma}}\rbrace
$$

following the notation found in Klump, McAdam, and Willman (2011, p.22).

Importantly, what data is required to estimate the parameters of this particular production function? And, what is the exact procedure involved? Demonstrations and references are most welcome!

Reference:

Rainer Klump, Peter McAdam, and Alpo Willman, The normalized nested
CES production function, theory and empirics, ECB Working Paper Series,
No. 1294. (Feb., 2011), 2011.


texts: Is this weighted least squares or just weighting the dependent variable

texts:
I am a little confused as to what the following line means. Do the authors mean they run a weighted least squares using the sample size as weights, or just weight the dependent variable using the sample size?

Here's the link to the original paper. The part I'm talking about is in page 19:
https://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/783.pdf


texts: If Y=K+C, why the value of a marginal unit of capital is the same of the value of a marginal unit of output?

texts:
In a simple model of welfare dynamic optimisation with non-renewable natural resource where:

$$
\dot S_t = -R_t
$$
$$
\dot K_t = Q(K_t,R_t)-C_t
$$

one of the first order condition is that $P_t=\omega_t Q_{R}$, where $P_t$ is the shadow price of the natural resource stock $S$, $Q_{R}$ is the marginal product of the natural resource and $\omega_t$ is the shadow price of the human-capital stock $K$.

In the Perman et al. (2011) "Natural resource and environmental economics" this equation is explained as "the marginal value (or shadow price) of the natural resource stock must be equal to the value of the marginal product of the natural resource".
In particular $\omega_t$ is redefined as the value of one unit of output, with the justification that units of outputs and units of capital are in effect identical in this economy among the optimal path, as any output that is not consumed is added to capital.

It is this redefinition that I do not understand.


texts: Does unit elasticity has to be at exactly the middle of the demand curve?

texts: Can unit elasticity be anywhere else on the demand curve other than the midpoint?


texts: Are Cobb-Douglas preferences monotone according to the marginal utility condition?

texts:
I understand that Cobb-Douglas preferences represented by $U(x,y)=x^ay^b$ are strictly monotonic, because increasing at least one of the goods in the bundle increases utility.
However, another definition of strict monotonicity says that marginal utility of each good should be strictly positive. This is not the case with the above function at $(0,0)$. Is there a way to resolve this?


texts:
A while back, someone decided to auction off something unique and valuable, as a silent auction: everyone would submit one bid only, and whoever bid the highest would win.

I submitted a bid that I thought would be higher than most people would pay, but I didn't win.  He posted the final result, though, and the winning bid wasn't much higher than mine.  If I had known it would go that high, I would have bid higher, and other people probably would have as well, which means he ended up leaving money on the table.

That makes me wonder: what is the point of running a silent auction if it can so easily be shown that it brings in less money than an auction in which people can openly bid against each other?


texts: When can we expect China to become a developed country?

texts: China has the 2nd largest GDP in the world and also has a high GDP growth rate. According to Richard Lynn's IQ and Global Inequality, the Chinese have a mean IQ of 105, which is one of the highest in the world. So, it just seems to be a matter of time before China becomes a developed country. The only question is when: Will it be 10 years from now? 20 years? 50 years?


texts: What does the term Market Power mean in microeconomic theory


texts: Exam question implies that a perfect labour market can have wage differentials?

texts:
My understanding is that wage differentials should not exist in a perfect labour market for occupations, but the following exam question seems to imply that this can be the case. A brief marking scheme also implies this.

and its marking scheme explanation:

I have always thought that if occupations belonged to a perfect labour market, it would mean that due to the assumptions of perfect mobility and homogeneity of labour, wages will always adjust so that wages are always equal across industries. The marking scheme seems to imply that this does not have to be the case.
One possible caveat I suspect would make the question's situation possible would be if the firms do not operate in perfectly competitive product markets, though I am not sure about this, and neither did the marking scheme mention this.


texts: How can China shield its public from the effects of a trade war?

texts:
I found an interesting read in the NYTimes today. It read:

  The Chinese government also has much greater control over the economy, allowing it to shield the public from job cuts or factory closings by ordering banks to support industries suffering from American tariffs. It can spread the pain of a trade war while tolerating years of losses from state-run companies that dominate major sectors of the economy.

I could not understand what that meant. Could anybody explain it?


texts: Monotonicity and continuity implies that all bundles are weakly preferred to 0

texts:
Suppose a consumer has a preference ordering $\succsim$ on $X$ that is complete. Show that if preferences are continuous and monotone, then $x\succsim0$ for any $x\in\mathbb{R}_{+}^{N}$, where $0$ is the $0$ vector in $R_{+}^{N}.$
My approach so far is the following.
Case 1. $x$ has more of all commodities, in which case the result follows from monotonicity.
Case 2. $x$ has more of only one commodity, in which case monotonicity is not sufficient. We want to show that $x$ is in the upper contour set of $0$, i.e. that $x\in\{\phi\in X:\phi\succsim0\}$. If we can show that there exists some sequence of bundles in this set with bundle $x$ as its limit, then the result would follow from continuity. But I am not sure how to do this.
Case 3. $x:=0$. Trivial.


texts:
I have a question based on reading some speeches and research papers, mainly by Ben Bernanke, on the portfolio balance effect. Here is Bernanke in a recent paper he authored where he describes the portfolio-balance effect as one of the two principal channels of large-scale asset purchases:

  "The portfolio balance channel depends on the premise that securities are  imperfect substitutes in investors’ portfolios, reflecting differences in liquidity, transactions costs, information, regulatory restrictions, and the like. Imperfect substitutability implies that changes in the net supply of a security affect asset prices and yields, as investors must be induced to rebalance their portfolios (Bonis et al., 2017). In principle, the two channels of QE can be distinguished by the fact that the signaling channel operates by affecting expectations of future policy rates while the portfolio balance channel works by changing term and risk premiums."- Bernanke (2017), in a paper that can be located here: https://www.brookings.edu/wp-content/uploads/2017/10/bernanke_rethinking_macro_final.pdf

I'm having some trouble here understanding the finance of this. In particular, how does this channel necessitate imperfect substitutability? I understand that the argument hinges on 'habitat preferences' -- certain investors prefer, say, a specific type of security -- but I haven't been able to put the pieces together.

As a potential example: let's say that we have an investor who will only deal with 5-year Treasury bonds due to either preference, risk appetitive, liquidity requirements, and so forth. The Federal Reserve then purchases 5-year Treasury bonds. Bernanke seems to suggest that the reason that reductions in the supply of these securities will increase their prices and reduce their yields is that investors don't view other securities as perfect substitutes. Is the argument perhaps that, if our investor considered 7-year bonds a perfect substitute, the increase in the price of the 5-year bond would cause him to sell off his supply of 5-years for a significant capital gain and purchase some other security? Or, for that matter, his portfolio would consist of such a wide array of different maturities that buying 5-year bonds wouldn't impact his behavior at all, as he would just replace it with any other bond.

I know this has something to do with elasticity of demand, but I just haven't been able to piece together the logistics of imperfect substitutability, hopefully, leading to a rebalancing of investor portfolios and a decline in interest rates across asset classes in a broad-based way.

I'd appreciate any insights people might have on this.


texts: Terminal and annual surplus distribution in participating life insurance

texts:
I consider a participating life insurance contract which is fair if $P_0 = e^{-rT} \mathbb{E}^{\mathbb{Q}}\left[ L(T) \right)$ ($\mathbb{Q}$ denotes the risk-neutral measure), where $P_0$ is the premium and $L(T)$ the claims paid by the insurance company. $L(T)$ is given by:
$$ L(T) = P(T) + \delta B(T) - D(T), $$ with
$$P(t) = P(t-1) (1+g) + \max \left( \alpha \gamma (A(t) - A(t-1))-g P(t-1),0\right),$$
$$B(T) = \max\left(\frac{P_0}{A_0} A(T) - P(T),0\right),$$
$$ D(T) = \max\left( P(T) - A(T),0\right).$$
$g$ is the guaranteed minimum interest rate, $\delta$ the terminal surplus participation rate, $\alpha$ the annual surplus rate, and $\gamma \in (0,1)$. The asset $A$ follows a geometric brownian motion:
$$A(T) = A(0) \exp\left( (r-\sigma^2/2)T + \sigma W_T^{\mathbb{Q}}\right).$$
Does it make sense to consider a terminal or an annual surplus rate larger than 100%? An annual rate larger than 100% leads to a decrease in reserves for the insurance company, in my opinion this is not a realistic distribution rule, right? But what about the terminal surplus rate?


texts: Deriving formulas from Gali's book on the New Keynesian model

texts:
I've found this link with all the derivations from Gali's book on New Keynesian model.
In page 13, eq. $(3.7)$, the author derives the optimal price-setting rule  $P_t^*$ by a representative firm that solves an intertemporal profit maximization problem. Equation $(3.7)$ contains two infinite series. The author then does a log-linearization on both and proceeds to the solution. Log-linearization is a local approximation, right? Then how can we be sure that the two series, with these approximations will converge?


texts: How can Finance influence economic activity?

texts:
I'm not sure how to put it. I'm currently reading Blanchard's Macroeconomics. In a chapter, he explains how for example an unexpected shift in monetary policy, or in consumption or in fiscal policy, can affect the stock values, and the yield curves of bonds, but not how for example a financial bubble (stock/bond overpricing) can affect the economic activity of consumption, investment, etc. The perspective presented in the book seems a bit too one-way. I'm interested also in the other direction, from finance to economic activity.

Is there any bibliography that presents, in a academic way, this other perspective of finance affecting the economy?


texts: Why do cities with rich areas still contain poor areas?

texts:
A cynic would attribute the disparity (and the failures to gentrify) to indifference or inattention, (or worse) disdaining neglect or ignoring, by the politicians and rich of the poor in the poor areas.

I exemplify with cities whose disparities I have witnessed, followed by links to the maps overlaying location with income, but I exclude downtown areas which always appear rich:

New York: (Lower) Manhattan vs. The Bronx and Brooklyn (e.g. Bedford-Stuyvesant, Bushwick)
<Google search: 1, 2>

London (Boroughs): Hammersmith & Fulham, Kensington & Chelsea, Westminster
vs. Hackney, Tower Hamlets, and the southern boroughs like Lewisham, Croydon.
<Google search: 3, 4, 5>

Toronto: Midtown (along Yonge St. subway line, like Lawrence Park) vs. Jane & Finch, Rexdale
<Google search: 6>

Vancouver: West & North Vancouver, West Side, South Vancouver vs. Downtown East Side, Surrey
<Google search: the Vancouver Sun has many maps.>


texts: How do you utilize event studies in policy research?

texts:
I apologize if this isn't exactly the right forum to pose this question. I am trying to use an event study to evaluate the adoption of a specific policy in several different states that happen at different times. I had a professor suggest using an event study but I am struggling to find resources on the use of event studies in policy research. I understand the mechanics of how to formulate the equation and structure the data and come up with a graph. However, I feel like I'm lacking knowledge that would allow me to fully interpret results. I feel like I don't know all the requirements of an event study or what it means to have a significant divergence from 0 following the treatment period.
Does anyone know of any resource that explains event studies in the policy context? I'm aware it's used more often in finance literature but those works don't follow the work I'm doing. This paper is an example of policy event studies but I'm looking for a more in-depth breakdown of when and how to use this technique.
A good example of a confusing result for me would be the following:
The treatment, in this case, is the implementation of a law that requires those under domestic violence restraining orders turn in their firearms and the outcome is the number of intimate partner homicides per 100,000 people. There are an additional set of policy and sociodemographic controls. I spoke to my advisor and he said to shift the graph down and center the year before treatment at 0 (but to do so transparently). I get the following when I do so: .
The problem is that I don't know how to fully interpret this or why it would be okay to make this transformation. If anyone could shed any light on why someone might do this, that would be very helpful. However, more broadly, I'd appreciate any resources that would help me help myself a bit more with this topic.


texts:
I came across this term in the following paragraph and I could not comprehend what it meant.

  The new WPI series does not include any indirect taxes, which brings it conceptually closer to the producer prices and also removes fiscal impulse impact


texts: Amazon's 1-Click Check Out : any feedback?

texts:
Does anyone have feedbacks or analysis on Amazon's 1-Click Check Out ?

Any numbers about the conversion rates (before/after using the 1-click checkout button) , etc. ?

This page is about a $300 Million per year magic button, but doesn't mention which site is using it.

Thanks.

Zaky


texts: There are several methods measuring integration capital market. What best to measure for integration capital market?


texts: Can a Discount Rate be Inferred within a Solow-Swan Growth Model?

texts:
I'm trying to understand the implications of a Solow-Swan growth model with, to keep things simple, constant population, and constant Cobb-Douglas technology written in per capita form as $y=k^{\alpha} (0<\alpha<1)$. Given an initial capital stock, depreciation rate $\delta$ and assumptions on the saving ratio s, I understand how to obtain time paths for y, k and per capita consumption c, properties of steady states and of the golden rule steady state.

Question: Is it possible within this model, perhaps with plausible additional assumptions, to infer the path of discount rates $\rho$, and consequently of interest rates r, corresponding to a given feasible time path of y, k and c?


texts: Why should marginal cost be equal to the price an item is sold at?

texts:
My interpretation of the condition $P=MC$ is that a firm's cost of producing one additional good should be equal to the firm's price. This means that the next item a the firm produces won't yield any profit to the firm.
What's the point of producing this additional unit? Do you have a hands-on explanation?


texts: List of production functions that satisfy the Inada conditions

texts: It is known that in the class of CES production functions, only the Cobb-Douglas production function satisfies the Inada conditions. Which other functions satisfy the Inada conditions?


texts:
In an economy with several agents who have different utility functions, it is common to define a welfare function, defined as an aggregate of the utility functions of the different agents. Then we can ask if and how this welfare function can be maximized.

AFAIK, the most common welfare function is the sum of utilities, also called utilitarian welfare. A more general function is a weighted-sum, in which each agent has a different weight. Such functions are well-studied. For example, it can be proved (e.g. Varian, 1976) that an allocation is Pareto-efficient, if and only if it maximizes a weighted-sum welfare function, for some choice of weights.

I am looking for references in which social welfare is measured using the median, or a similar statistic (e.g. a certain percentile), instead of a weighted sum. Particularly, I am looking for references about existence of an allocation which maximizes the medial social welfare in various settings.


texts: What is time inconsistency in monetary policy?

texts:
I am reading through a bit of policy literature and see authors referring often to the problem of time inconsistency when setting monetary policy.

Can anyone explain what is time inconsistency?

An example from Daniels and Vanhoose (1998):

  Rogoff’s paper makes one of the most fundamental points about policy coordination: In the presence of time inconsistencies, monetary policy coordination is not necessarily welfare improving.


texts: Would this alternative to fractional reserve banking work?

texts:
While reading the answer to Implications of abolishing Fractional Reserve Banking on mortgages and interest rates, I started to wonder if there wasn't a simple solution to the problems that would arise with the introduction of a constant money supply.

Right now, banks create the illusion of more money existing by accepting deposits and holding onto only a fraction of them while lending out the rest.  Alternatively, could they not just package up loans into investments and essentially sell shares in the investments to average people.  This would essentially have the same effect, your cash would be tied up in the bank and you would receive some amount of interest on it.  The investments could even be structured and insured in a similar way to the current system in order to maintain some amount of liquidity.  The only big change is that people would be very much aware of where there money is when they put it in the bank, which to me would only increase the robustness of the system and reduce the possibility of bank runs, as there would be a general understanding that some of your money is loaned out at any given time.

Has this idea been studied, and are there any known or obvious flaws that I am not seeing?


texts: Macroeconomic model or knowledge base representing connected industries in the world

texts:
I'm looking for data (model, Expert system, knowledge base) that describes how different industries and countries interact with each other. And the nature of the relationship between them.
An example of such a relationship could be the recent covid-19 crisis.
The crisis forced countries to close the borders, which affected travel, and hospitality industries in a negative way. But the lockdown and people's inability to go shopping led to profits of shipping companies.
Is there a database/API/graph or any source of data showing this kind of connection between industries and the nature of that connections? Some books research papers discussing such a model?
Some question that might be answered with this data:

What will happen if say, Belgium (or any country), would force 'iron curtain' on itself and stop all economic activity with the rest of the world. What industries, in the world, might be affected?
What industries will be affected if the USA banned oil production?
What industries rely on Maritime transport? If for some reason only 10% of all Maritime transport will be operational what industries will increase their profit and what industries register a loss?

The other question is, knowing that the world is infinitely complex, is it even possible to have such a model, even on the macro level?


texts: Calculating optimal level of negative externality

texts:
I am trying to solve the following question(s):
Let $h \geq 0$ represent a negative externality of a firm's production on one (representative) consumer. The consumer has a quasi-linear utility function and attaches a utility of $\phi(h) = -2h^2$ to the externality. The firm's profit function is $\pi(h)=120-2(h-10)^2 $.

Compute the pareto optimal level of $h$, $h^o$.

Compute the firm's optimal level of $h$, $h^f$.

Suppose the consumer rather than the firm can determine the specific externality levelh with which the firm operates. Compute the optimal level of $h$, $h^c$, from the consumer's perspective.

My approach so far:

To find $h^o$ I maximize the aggregate surplus/welfare of h. $$\max_{h \geq0} \pi(h) + \phi(h)$$
$$ W(h)=120-2(h-10)^2 - 2h^2 = 0 $$
$$ \frac{dW}{dh}= -4(h-10)-4h = -8h + 40 = 0 $$
$$ 8h=40 \rightarrow  h^o=5$$

To find $h^f$
$$FOC\ of\ \pi(h): \frac{d\pi}{dh} =-4(h-10) = -4h+40 = 0 \rightarrow h^f=10 $$

To find $h^c$
$$ FOC\ of\ \phi(h): \frac{d\phi(h)}{dh} = -4h = 0 \rightarrow h^c=0 $$

Is this correct?


texts: How can autonomous private spending change budget surplus?

texts: I was reading Keynesian economics in R.Dornbusch's book where he mentioned the defects of using budget surplus as a measure where he says it can be changed and effected by autonomous private spending which I couldn't logically get.Can someone explain?


texts: What is a good way to generate realistic utility curves?

texts:
I am aiming to program a basic simulation of a simplified economy to look at the impact of various interventions.

The economy will have N groups of homogeneous consumers and M producer / employer sectors. Each producer sector makes one type of good that the consumers can purchase, so there are M goods. To try to keep it (relatively) simple, the goods will all be independent with no close substitutes or compliments. E.g. goods will be steak and diapers, not steak and chicken, nor steak and potatoes.

Each group of consumers will need to have a demand curve for each of the M goods, as well as a "demand" for leisure.

Given the marginal utilities for each good, you can calculate a demand curve for that good. So, the approach I'm thinking is to generate utility curves for each good, then use those utility curves to derive demand curves which then drive consumer purchasing behavior and other downstream effects.

This brings me to the question, what's a good way to randomly generate a lot of plausible utility curves?

For example, if I wanted a linear utility curve I could randomly generate a slope and an intercept. That is simple and easy to do, but it misses diminishing marginal utility which is one of the most important features.

What's a form that's easy to work with, has relatively few parameters to specify, and still captures most of the key features of utility curves?


texts: Where does the extra money come from when a new country joins the Euro and converts its currency?

texts: Whenever a new country becomes a member of the Eurozone, they convert all their local currency into the Euro. What I don't understand is where does this huge new volume of Euros come from overnight? Does the European Central Bank simply print the extra money? If so, why doesn't this cause significant inflation?


texts: Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/eigenvector

texts:
I'm trying to understand the tools used/presented in Lars Hansen's Econometrica paper "Dynamic Valuation Decomposition within Stochastic Economies." In a part in the paper, Hansen introduces a long-term approximation. This approximation first requires us to solve for a principle eigenfunction of a kind of conditional expectation operator. As an exercise, I'm trying to solve the following example.
$\newcommand{\E}{\mathbb E}$
Suppose that
$$
X_{t+1} = A X_t + B W_{t+1}
$$
where A has stable eigenvalues and $\{W_{t+1} : t = 0,1,... \}$ is an iid sequence of multivariate standard normally distributed random vectors. Suppose that
$$
\log M_{t+1} - \log M_t = D \cdot X_t + F \cdot W_{t+1}.
$$
I want to show that there exists a solution to the equation
$$
\E \left [ \frac{M_{t+1}}{M_t} e(X_{t+1}) \mid X_t = x \right ] = \exp(\eta) e(x) \tag{1}
$$
for $\log e(x) = H \cdot x.$ I also want to compute that value of $\eta$.

Progress:

The beginning of the problem is straightforward. Using the properties of log-normal random variables, we can calculate from (1)
\begin{align}
\exp\{ (D' + H'A) x + \frac 12 (F' + H' B)'(F' + H'B)\} &= \exp\{\eta + H' x\} \\
(D' + H'(A - I)) x + \frac 12 (F' + H'B)'(F' + H'B) &= \eta.
\end{align}
This is probably a simple question from here. It seems clear that a solution exists, and I have solved for $\eta.$ But from what I understand, solving this problem involves making a "guess" that $e$ was linear in $x$. I don't know what $H$ is. Thus, I need to solve for $H$ and $\eta$. How would I do this?

Note: This problem is related to this problem about the "Decomposition of an additive functional into a Martingale part and other."


texts: Is there a (mostly) objective study regarding minimum wage and job growth?

texts:
I think over the course of the past couple years the topic of wealth-inequality and living wages has become increasingly commonplace, and really one of the most debated topics (among us casuals at least).

Personally, I don't believe that "unbiased" studies exist, but is there some sort of mostly objective study (or really just a good one) done that correlates job growth/loss with the rising of minimum wage, or conversely, the abolishment of a minimum wage?


texts: Why some countries are wealthier than others?

texts:
Twin-peak of economic growth is one of the concepts discussed in economics. Most of explanations for poverty traps are baseed on the lack of infrastructures and public goods.
How could be another main reasons to explain this important issue ?

Any academic reference is appreciated.


texts: Which mathematics are required for fully understanding the theories of the firm?

texts:
When I say "theories of the firm", I'm referring, in particular, to the theories exposed in the next works: 1) Transaction Cost Economics exposed in "Transaction Cost Economics" by Tadelis and Williamson (2013) (chapter 4 of "The Handbook of Organizational Economics" by Gibbons and Roberts); 2) Property Rights Theories exposed in "The Costs and Benefits of Ownership" by Grossman and Hart (1986), "Property Rights and The Nature of The Firm" by Hart and Moore (1990), and "Firms, Contracts, and Financial Structure" by Hart (1995); and 3) Incentive System Theories exposed in "The Firm as an Incentive System" by Holmstrom and Milgrom (1994), and "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design" by Holmström and Milgrom (1991).
When I say "Which mathematics", I would appreciate if a list of chapters of a highly recommended math book is given, due to I need to be prepared for analyzing those theories as soon as possible. In this regard, it should be noted that I have studied the first eight chapters of the first volume of Apostol's Calculus. In advance, thanks so much.


texts: Does omitted variable bias 'contaminate' coefficients for regressors not correlated with the omitted variable?

texts:
Suppose we have a model that is:

$$
y = X_1\beta_1 + X_2\beta_2 + X_3\beta_3 + \varepsilon
$$

where $X_1$ is independent of $X_2$ and $X_3$ but $X_2$ and $X_3$ are correlated with each other.

Suppose we don't have data on $X_3$ so we omit it and run the regression:

$$
y = X_1\gamma_1 + X_2\gamma_2 + \nu
$$

Econometric theory on OVB states that $\gamma_2$ will be biased.

My questions:

Will $\gamma_1$ be biased in this case as well? I ran a simulation with some data I created and I do get a biased result.
If it is unbiased then how do I prove it? I use FWL theorem to find $\gamma_1$ and show that its expectation equals $\beta_1$ but get stuck here:

$$
\hat{\gamma_1} = \beta_1 + (X_1'M_{X_2}X_1)^{-1}(X_1'M_{X_2}X_3\beta_3) + (X_1'M_{X_2}X_1)^{-1}(X_1'M_{X_2}\varepsilon)
$$

The third term will become 0 when we take the expectation but not sure how to make the second term 0.


texts: Explaining fluctuations in inflation rate

texts: I have been tasked to explain the changes in economic performance of a particular country as part of my class assignment. In particular, I need to explain the changes in the inflation rate of Malaysia over the past 10 years. The general trend seems to be that over time, the fluctuations in the rate of inflation has become smaller, maintaining at 2-4% in recent years. However, there is this large fluctuation in the period from 2008 to 2010. I am quite sure this has got  to do with the Great Recession of 2008. However, I am not quite sure what is the connection between a global financial crisis and large volatility in prices of goods and services.


texts: What is meant by credit-based investment?

texts:
My knowledge of economics is very small so I would be grateful if anyone could answer this question in the style of 'economics for dummies'!

What is meant by the term 'credit-based investment' or 'credit-fuelled investment'? I have come across the term a number of times describing China's fiscal policy.


texts: The social welfare of a unique general competitive equilibrium in an exchange economy

texts:
The first theorem of welfare economics states that "Every Walrasian Equilibrium (WE) is Pareto Efficient (PE)" - Microeconomic Theory Nicholson, Synder 11th ed. p477. But PE is quite a weak condition. Is WE a stronger condition or is does WE just mean any PE allocation?

I was specifically wondering; suppose we have an exchange economy with agents $N$, and there is a unique competitive equilibrium (WE) solution, $q^*$. Does this also maximize aggregate social welfare amongst possibly many PE outcomes? Where aggregate social welfare is defined as:

$$
  SW(q^*) = \sum_i^N U_i(q_i^*)
$$

To ask this question only makes sense if WE $\subset$ PE allocations, because if there is a single PE allocation then it must by definition maximize aggregate social welfare, because there is no other feasible solutions.

Any solution maximizing social welfare has to be PE, but not all PE solutions are SW maximizing. For example, at a given PE allocation agent $i$ could lose 1 util in exchange for agent $j$ gaining 2.


texts: Speed of convergence of output on the balanced growth path

texts:
Find how quickly $y$ converges to $y^*$ in the vicinity of the balanced growth path
  $$ y=Y/AL=f(k); \; y^*=f(k^*) $$
  They suggest the hint, write $k=g(y)$, where $g(\bullet)=f^{-1}(\bullet)$.)

  $Y$ is product output; $AL$ is effective labour; $K$ is capital; lowercase letters are divided by $AL$ (e.g. $y=Y/AL$); $k^*$ is the balanced growth path of capital.

This is problem $1.11$ in Advanced Macro by Romer.  I have tried looking at Lagrange Inversion Theorem, and applying the above get to the first order Taylor series centered around $k^*$

$$ \displaystyle g(y) = k^* + \lim_{k \to k^*} \left( \frac{y-f(k^*)}{1!} \right) \frac{d^0}{dw^0} \left( \frac{k-k^*}{f(k)-f(k^*)} \right) $$

but since $y=f(k)$ and the zeroth derivative is the function itself, we get the following cancelation:

$$ = k^* + \lim_{k \to k^*} \frac{f(k)-f(k^*)}{f(k)-f(k^*)}(k-k^*) $$

$$ = k^* + \lim_{k \to k^*}(k - k^*) = k^* $$

Which doesn't tell us anything ... Do we need to look at the second order derivative?


texts: Running ols when dependent variable is correlation coefficient

texts: I am new to this form. I am going to run an OLS regression with dependent variable as a correlation coefficient (between -1 and 1). I am aware that this dependent variable may be problematic in the OLS regression. But what can I do in order to implement the regression? Thanks!


texts: Relation of Engel-curve to income elasticity of demand; is the slope of the Engel-curve equal to the elasticity of income?

texts:
I learnt that $\frac{\Delta x}{\Delta m} \gt 0$ for normal goods, $\frac{\Delta x}{\Delta m} \lt 0$ for inferior goods, $\frac{\Delta x}{\Delta m} \gt 1$ for luxury goods and $0 \lt \frac{\Delta x}{\Delta m} \lt 1$ for necessary goods (where x is the amount of units of some good and m is the income).
Now, looking at the Engel-curve for homothetic preferences (i.e. Cobb-Douglas, perfect substitutes/perfect complements), I understand $\frac{\Delta x}{\Delta m} = 1$ for homothetic goods (btw is that a term, "homothetic goods"?).
Since the slope of the Engel-curve is $\frac{\Delta m}{\Delta x_1}$, I'm wondering if $\left(\frac{\Delta m}{\Delta x_1}\right)^{-1}$ is a way to determine the elasticity of demand, which, from my understanding, deals with the exact same values to categorise goods.
So I'm wondering if $\left(\frac{\Delta m}{\Delta x_1}\right)^{-1}$ is equal to the elasticity of income or if there's a way to determine the elasticity of income from the Engel-curve.


texts: Adam Smith: If humans are self-interested individuals, why should we reinvest our wealth?

texts: According to Adam Smith, humans are self-interested individuals. If this is true, why does he argue that people should reinvest their wealth? How does this benefit a self-interested individual? Does morality play a role here? What role does productive and unproductive labor play here precisely?


texts:
The Marginal Cost (MC) of an additional unit of output is the cost of the additional inputs needed to produce that output.
Here is one of the formulas for calculating marginal cost:

$\ MC=\Delta CF\div\Delta output$

For example, suppose it costs  €1600 to produce 100 units and €2300 to produce 200 units. MC = €7

What does it mean to have the marginal cost equal to 7?


texts: What have been some trade-offs that the U.S. has made?

texts:
In Thomas Sowell's book titled, "Basic Economics", he says the following:

"Unmet needs" are inherent in these circumstances, whether we have a capitalist, socialist, feudal, or other kind of economy. These various kinds of economies are just different institutional ways of making trade-offs that are inescapable in any economy.

He has been talking about what scarcity means and what it implies -

It means (Scarce) that what everybody wants adds up to more than there is. What this implies is that there are no easy "win-win" solutions but only serious and sometimes painful trade-offs.

In a real world context, what would be some big trade-offs that  the U.S., specifically, has made? And, what have been some consequences or maybe some pros of those decisions?

The reason I am asking this is because I can't really 'picture' what exactly a trade-off is.

Thanks for your time!


texts: Making mathematical sense of the expression for realized bond return

texts:
I came across the following statement regarding the realized 10-year maturity bond's return over a year:

  The realized bond return (H) over a year has two components: the yield income earned over time and the capital gain or loss due to yield changes:
  $$H_{10} \approx Y_{10}-\text{Duration}_{10} \times \Delta Y_{10}.$$

I am a complete economics rookie and I'm trying to understand what's going on here from the mathematical point of view, which I'm gonna present here, but my calculations don't seem to add up.

If we denote the bond's coupon with $C$, and the bond's time $t=0$ yield to maturity with $y_0$, then the bond's value at time $t=0$ equals:
$$V_0=\frac{C}{1+y_0}+\frac{C}{(1+y_0)^2}+\dots+\frac{C}{(1+y_0)^9}+\frac{F+C}{(1+y_0)^{10}}.$$

At time $t=1$, we can express the bond's value as the function of the time $t=1$ yield to maturity $y$, so we have
$$V_1(y)=\frac{C}{1+y}+\frac{C}{(1+y)^2}+\dots+\frac{C}{(1+y)^8}+\frac{F+C}{(1+y)^{9}}.$$
Derivative of $V_1$ with respect to $y$ is equal to:
$$\frac{dV_1}{dy}=-1\cdot\frac{C}{(1+y)^2}-2\cdot\frac{C}{(1+y)^3}-\dots-8 \cdot \frac{C}{(1+y)^9}-9 \cdot\frac{F+C}{(1+y)^{10}} .$$
Now, we can apply some basic calculus here and state that for $\Delta y$ small "enough", we have that
$$ V_1(y_0+\Delta y)\approx V_1(y_0)+\frac{d V_1}{dy}(y_0)\cdot \Delta y. $$
So now, if we consider the absolute return on our position (buying this bond at time $t=0$, selling it at $t=1$) from the time $t=0$ perspective, under the assumption that the time $t=1$ bond's yield to maturity is $y_1=y_0+\Delta y$, we have that:
$$\text{AbsReturn} \approx-V_0+\frac{C}{1+y_0}+\frac{V_1(y_0)+\frac{d V_1}{dy}(y_0)\cdot \Delta y}{1+y_0}.$$
That is - we buy the bond for $V_0$, at the end of the first year we are paid the coupon which discounted value is $\frac{C}{1+y_0}$, and the approximation of the time $t=1$ bond's value taking into the account the YTM change is $V_1(y_0)+\frac{d V_1}{dy}(y_0)\cdot \Delta y$ and we also discount it to time $t=0$.

Now, we can simplify the expression for AbsReturn since $-V_0+\frac{C}{1+y_0}+\frac{V_1(y_0)}{1+y_0}=0$ and we get:
$$ \text{AbsReturn}= \frac{\frac{d V_1}{dy}(y_0)\cdot \Delta y}{1+y_0} ,$$
which I guess we can also divide with our initial investment of $V_0$ to get the rate of return so we get:
$$ \text{RateOfReturn}= \frac{\frac{d V_1}{dy}(y_0)\cdot \Delta y}{V_0(1+y_0)} ,$$
aaand this is where I completely lose it. I can't seem to understand the connection between the original expression and the thing I end up with. What does the term $\text{Duration}_{10}$ in the original formula even stand for - I guess it is the derivation of bond's value with respect to yield - but bond's value at what time: $t=0$ or $t=1$? Does it even make any difference? If it is at time $t=0$, how can we be using linear approximation of that function for approximating bond's value change at time $t=1$? I'm completely puzzled over this. Am I doing something completely wrong in this derivation? I appreciate any insights on this. Thanks!


texts:
Why is in flation preferable to deflation?
I appreciate this is largely due to the fact that deflation causes a large decrease in demand as people continually wait for prices to decrease, but if anyone has finer points I would be grateful.


texts: Econometrically estimating the Leontief cost function

texts:
in general the Leontief cost function is represented as:

$$c(w,y)=y\sum_{i=1}^kw_ix_i$$

where:
 $$y=\min\left[{\frac{x_1}{\alpha_1},...,\frac{x_n}{\alpha_n}}\right]$$

How does one go about estimating this econometrically if one does not know the underlying production function a firm exhibits (i.e we know the amount of $y$ produced however we don't know if the production technology is $\min\left[{\frac{x_1}{\alpha_1},...,\frac{x_n}{\alpha_n}}\right]$)?


texts:
Well, i'm interested in model a GARCH for a serie. The original serie is $y_t$ (price index of a Stock Market), which has a unit root. So i create the returns:
$x_t = ln(y_t) - ln(y_{t-1})$.
Now, i'm confused about the fact of using $\lvert x_t\rvert$ for my GARCH. Why can i use absolute value, i'm thinking, that because i want to model volatility i'm just interested in how the series deviates from his mean in a period of time? Thank's a lot for the answers!


texts: Why is the expected value conditional on the trade taking place in an adverse selection problem?

texts:
I have been asked the following question, and I don't understand why the expected value of the firm is conditioned on the trade taking place.

"Suppose that a firm owns a business unit that it wants to sell. Potential buyers know that the seller values the unit at either $100m, $110m, $120m, . . . , $190m, each value equally likely. The seller knows the precise value, but the buyer only knows the distribution. The buyer expects to gain from synergies with its existing businesses, so that its value is equal to seller’s value plus $10m. (In other words, there are gains from trade.) Finally, the buyer must make a take-it-or-leave-it offer at some price p. How much should the buyer offer?"

The answer is the
$$ (10 + E[value|trade takes place] - (Price Paid for business)) \times Prob(trade takes place|Price paid)$$

I don't understand why $E[value|trade takes place]$ is conditioned on the trade, I would have though that it would just be $E[value]$.

Can anyone shed light on why this is the case?


texts:
Suppose that I am trying to use the jack-knife to estimate the variance of some estimator $E$. If I have $n$ data points, I begin by computing $n$ estimates (call them $B_1$, ..., $B_n$), each obtained from leaving one of the $n$ data points out of my sample. If I understand it correctly, the Wikipedia page then suggests that my estimate of the variance should be
$$\hat{Var(E)} = \frac{\sum_{i = 1}^n (B_i - \bar{B_i})^2}{n-1}$$
where $\bar{B_i}$ is the average of my $n$ estimates. The standard error is then $\sqrt(\hat{Var(E)})$.
On the other hand, the notes here seem to suggest
$$\hat{Var(E)} = \sum_{i = 1}^n (B_i - \bar{B_i})^2\left(\frac{n-1}{n}\right)$$
What am I missing here? And which formula should I use? Many thanks in advance!
Extra question: if the answer is indeed the second formula, will standard errors indeed get smaller (as one would expect) as $n$ gets large? I ask because $\sum_{i = 1}^n (B_i - \bar{B_i})^2/n \approx Var(B_i)$ for large $n$; so it appears that the second estimate is roughly $Var(B_i)(n-1)$. It is not clear to me that this is decreasing in $n$ (even if $Var(B_i)$ goes to zero as $n$ gets large).


texts: How does Brouwer's fixed point theorem relate to Walrasian equilibrium?

texts:
I am trying to understand Walrasian equilibrium and its connection to fixed points, especially how we can apply Brouwer’s fixed point theorem to the notion of Walrasian equilibrium. I understand the implications of Brouwer’s fixed point theorem, and that conversion of prices to the unit simplex is an admissible transformation such that we know, by the theorem, there must be at least one fixed point. I understand Walrasian equilibrium as a price and consumption vector such that utilities of all households are maximized s.t. budget constraints and markets clear.

What I do not understand is the link between the two. I struggle with the intuition as to how fixed points map onto equilibrium prices.

Please excuse me if I am asking a stupid / obvious question. I cannot find an explanation of the intuition of the link anywhere I have looked.

Thanks in advance for your help,

R.


texts: Is an input-output model an equilibrium model?

texts:
I know the difference between CGE and input-output models.
But can an input-output model be called a equilibrium model?


texts: Equilibrium value of $b$ (market tightness) in a search model

texts:
Consider the following one-shot version of a labour market matching model. Let the labour force be normalized at 1, who, because there is only one period, all start out as unemployed. There is a very large number of firms who can enter the market and search for a worker. Firms who engage in search first have to pay a fixed cost, $k$. If a measure $v$ of firms enters the labour market, a constant returns to scale matching function $m(1,v)$ gives us the total measure of matches in the economy.

Within each match, the firm and the worker bargain for the wage, $w$, so that the workers get a constant proportion of $y$. Denote this proportion by $\beta$, which is interpreted as the bargaining power of the worker. Assume $\frac{k}{y} < 1 - \beta$ for the firm.

Define market tightness as $ b \equiv \frac{1}{v}$ and assume that the arrival rate for a firm is given by: $a_{F} = 1 - e^{-b}$.

Consider the firms can enter the labour market freely if they pay the entry cost, then what is the equilibrium value of $b$? Describe it graphically? Does it always exist? Is it unique?

My solution: The value of a vacancy: $$V = -k + a_{F}(b)(J-V),$$
and the value of a filled job: $$J = y-w.$$
If the firms enter the labour market freely then $V=0$. Then from these two equations I am left with this equation $$ 1 - e^{-b} = a_{F}(b) = \frac{k}{y (1-\beta)}.$$

Graphically, the function looks something like this:

From the graph, it looks like that $b^*$ is unique, but how do I know if it always exists or not?


texts: Quadratic utility: monotonicity and risk aversion

texts: I am taking macro class this fall. One of the problems asks whether decreasing absolute risk-aversion and ever-increasing consumption are two unattractive implications of the quadractic utility function. Could anyone please help with this?


texts: Certainty Equivalents and Risk Premiums in Expected Utility Theory for Asymmetric Distributions

texts:
I want to calculte risk-premiums in order to assess how much risk-averse customers would be willing to pay for an insurance against an uncertain loss modeled by a random variable $X$. How would a risk-premium be calculated, if $X$ does not follow a normal distribution? My reading of the literature is as follows:

1) Expected utility theory: Assumes CARA (CRRA) like utility functions with well behaved properties that are more or less agreed to model the behavior of rational risk-averse decision makers by satisfying certain axioms. The risk-aversion of decision makers can be modelled by Arrow-Pratt with $\alpha=R(X)=-\frac{u''(x)}{u'(x)}$. Using Arrow Pratt, one can calculate a risk-premium $\pi$ if $X$ is normally distributed such that $\pi(X)=\frac{\alpha}{2}\sigma^2(X)$ which derives from the formula of the certainty equivalent.

2) Downside risk measures from finance: Since losses (or returns) may not be normally distributed, finance has developed other measures to capture the concept of risk. One of these measures is the semi-variance as a special case of lower partial moments, which is very similar to the idea of mean-variance principle as outlined above: $SV=E((max[0,E(X)-X])^2)$.

Now the problem is as follows:

Aiming to calculate a risk-premium I can either follow utility theory. If $X$ is normally distributed we get a well contained formula to calculate the risk-premium $\pi(X)$. If not, then what? Would the certainty equivalent be calculated based on numerical integrat? If so, how would this look like for an arbitrary distribution of $X$?

On the other hand, I could follow a down-side risk measure approach: Given that I use semi-variance as a concept to measure risk, how could you account for the risk-aversion of customer in order to derive a risk-premium? I would just weight the semi variance with a factor $\tau^{~}SV$ (with $\tau$ being some kind of a proxy for risk-aversion) this wouldn't do the trick, would it? Essentially it would probabily not satisfy the expected utility axioms such as CARA or CRRA do correct?

How to approach this problem then? Are there any alternative strategies that I have overlooked?

**Addition after update

Now I have also found this post on the matter which would give a solution to my problem - as far as I understand - since it allows $X$ to have a non-zero expected value? This is due to the fact that the taylor approximation is - as it says - only an approximation of the risk premium with regard to various moments of the given distribution $X$. This also explains why the risk-premium can be correctly calculated for the normal distribution which is completely defined trough first and second moment.

This brings me to my last question: Considering the risk premium for non-zero expected values this would according to the post listed above also be approximated by the formula $\pi \approx \frac{1}{2}R(w)\sigma^{2}_X$? And the approxmation error for non-normal distributions is then depending on the question how well first and second moment capture the true nature of a distribution?


texts: Are there studies that empirically validate results in contract theory?

texts: I have started learning contract theory of late, and I find some of the assumptions and findings of the theory are too technical. Are there empirical studies that have validated concepts in contract theory? Or are there papers that talk about its relevance to practitioners (economists or operations managers)?


texts: What is the link between econometric theory and applied work?

texts:
I just don't understand how the theory, particularly pertaining to parameter identification is relevant when conducting applied work. Why must we present a sound identification strategy when carrying out an applied project.I hope this is clear. Thank you.

Edit: I guess I wasn't very clear in my question. I understand how identification strategies work in applied papers. I was more interested in how, say, somebody introduces a new estimation method in an academic paper. Then they propose the conditions on which the estimated parameters are identifies using this method. There is usually some talk of the dimensions of some parameters, and technical things like that. I just wanted to know why these kinds of concerns are relevant when one wants to apply said estimator empirically.


texts: Interest Rate Differential and Fisher's Interest Rate Parity

texts:
The Fisher formula for interest rate parity, as explained here shows that for a given currency pair, the currency with the higher interest rate will depreciate relative to the the currency with the lower interest rate, over a given period of time, for it not then riskless arbitrage is possible. In other words, higher interest, weaker currency.

However, there is another point of view, as given here, that if a country hikes interest rates, then its currency will appreciate, as there will be increased demand for that currency in order to enjoy higher returns, carry-trade style. In other words,higher interest, stronger currency.

The question here is - which is correct? Or are there other assumptions which have not been accounted for here?


texts: Yuan to be a reserve currency, IMF is considering

texts: If yuan becomes a reserve currency, can we expect the petrodollars to be swapped with petroyuans given china's ever increasing mammoth demand for energy resources?


texts: What are the advantage of chain-linked prices over constant prices?

texts:
Some variables in economics like GDP are computed in chain-linked prices or constant prices.

What are advantages of chain-linked prices vs constant prices?

Thank you


texts: Target2 Balances at the ECB-will it lead to the collapse of the Euro?

texts: Target 2 imbalances within the Eurosystem have continued to grow during 2020.  Currently Germany is owed Eur 1TN by the other countries, principally Italy and Spain.  If Germany at some point insists on redressing these balances, is the collapse of the Euro inevitable?


texts: What is the probability of an unemployed worker receiving no job offer during a time period?

texts: we are currently covering one sided search models and I had a question for you all. I kind of understand the raw calculus behind finding the probability of a job offer over a time interval h, but what about the reverse. Suppose we have a time interval h, what would the probability for an unemployed worker to receive no job offer during said time interval h? Would it just be 0?


texts: I'm trying to figure out how the Gross value added is calculated. The first question that I have encountered is "Does the Gross value added of an activity includes workers salary?" If not, what is the difference between GVA and an activity profit?


texts: How much would it take to end global extreme poverty?

texts:
E.g., according to this page, Jeffrey Sachs estimated that it would take $175bn/year for 20 years to do so.

What are some other estimates?


texts: Which are the different Schools of Economic Thought?

texts:
It would be great to have a brief but comprehensive list of current (e.g. Austrian) and defunct (e.g Mercantilism) schools of thought in Economics. I think an ideal answer would include:

the defining features of the school, which enable it to differentiate it with the rest.
major authors/writers behind the school.
key papers/books/textbooks presenting/defending the ideas of the school of thought.

Note: To order the discussion and avoid very lengthy answers, I suggest we have one school of thought per answer (like they do in other forums, like TeX).


texts: Higher interest rates and default probabilities for longer loan term

texts:
I am analyzing LendingClub data with two available loan terms: 36 and 60 months. In the course of my analysis I have spotted that both the interest rates associated with each loan and the default probabilities, obtained from my logistic regression, are higher for the longer term.

I am thinking about a way of explaining why both interest rates and PDs are higher for the longer term. For the former the only thing I can come up with is that considering the assets are frozen for longer time lender expects to obtain higher premium.

Is there any formal way to explain these relations?


texts: Can we use hotelling's lemma as a rule of thumb when wage rate can vary?

texts:
Disclaimer: I've been doing some simulation with excel to see how Hotelling's Lemma behaves when allowing another parameter to vary. I did this by producing 150 randomly generated profit functions (based on normal distributions) and allowed them to vary in the parameters of interest. The goal is to learn about how far I can apply use of Hotelling's lemma outside of ideal conditions (like when wage varies as well).

Recall that  what Hotelling's Lemma tells us (essentially) is that the change in profit from a change in price is proportional to the quantity produced,meaning that the profit function increases/decreases linearly when price changes holding all else fixed. This is exactly the  result I got  when simulating it.

.

I then asked If we allow wage rate to vary as well, I found some neat and messier structures of how Hotelling's Lemma changes. In this case the dermination of price and wage are sampled from a normal distribution such that $\mathcal{N}(5,2)$ and inputs and outputs are sampled from a normal distribution such that $\mathcal{N}(50,25)$. These are my results:

Though, this method is (clearly) unscientific and violates the strict definition of the lemma, can we use hotelling's lemma as a rule of thumb when variability in wage rate is small?.

Display of excel code/setup available upon request.


texts: How to Find Real Disposable Income for Iran?

texts: I'm doing a project for my macro course, and I'm trying to find real disposable income for Iran over a 25 year period. In my course Disposable income, $Y_d = Y - T$, where $Y$ is output (income) and $T$ is taxes. I've been to the IMF and World Bank websites and have had no success in finding a disposable income indicator. Can someone please help me? Thank You!!


texts: Why did the US credit rating downgrade in 2011 decrease US government bond yields?

texts: I'm not sure how bond yields were decreased by the  US credit rating downgrade in 2011. Since the credit rating is down, shouldn't the yields increase since the US government wants to attract more bond buyers?


texts: Why do many papers not write the actual utility function?

texts:
Why do many papers write the intertemporal maximisation problem for the household as
\begin{equation}E_{0} \sum_{t=0}^{\infty} \beta^{t} U\left(C_{t}, N_{t}\right)\end{equation}
and then do not write the actual utility function that could be something like
\begin{equation}U\left(C_{t}, N_{t}\right)=\frac{C_{t}^{1-\sigma}}{1-\sigma}-\frac{N_{t}^{1+\varphi}}{1+\varphi}? \end{equation}
Many papers state that they are following woodford (2003) for the microfundations. However also in that book there is no explicit utility function.
How is it possible to get the Euler equation or the IS curve without the actual functon?


texts:
I'm asked to write an essay supporting the statement which says the convexity axiom has little economic content and should be eliminated from the economic models of consumer theory.

I'm supposed to find literature which supports my point with theoretical and empirical evidence but I've been searching for weeks and all I have found so far are papers which stress the importance of the convexity axiom. Perhaps you all can assist me in locating the material I'm looking for.

Regards


texts: Empirical research into sectoral comovement

texts:
I'm looking for some empirical studies into sectoral comovement. In particular, I'm interested in how manufacturing and services industries move together both in the long run and over the course of a business cycle. Most importantly, I'd like to know more about how the performance of manufacturing affects the performance of services. Are there any papers on this topic that you'd recommend?

So far I've only found a few papers which study sectoral comovement in more general terms and a few which only touched on this topic very briefly as an aside.

Many thanks!


texts: What Is the Economic Meaning of "Structural Reforms"

texts:
I see tweets like this a lot:

  Poor 2q growth shows its not just a "1q curse". Cannot ever cause eco recovery thru just #QE, low interest rates.  #StructuralReforms

They seem to be saying essentially that structure should be the focus, not interest rates.  What is an economic structural reform?


texts: Why can principal not be lost, if a bond fund is held for a period equal to its duration?

texts:
[Source:] Which leads us to the key message for investors: as long as your time horizon is at least as long as the duration of your bond fund, you won’t lose any capital.
You’ve probably heard people say they prefer individual bonds to bond funds, because as long as they hold on until maturity, they won’t lose principal. Well, the same is true if you hold a bond fund for a period equal to its duration. You can be sure that XBB will not have a negative total return over any period longer than 6.3 years: any price decline from rising interest rates will be offset by higher coupons within that time frame. In fact, history suggests the recovery is likely to be more swift than that: even a three-year period of negative bond returns is extremely rare.

1. Are the bolded clauses true absolutely? To wit, capital loss is identically (and NOT just near) 0?
2. Why are the bolded true?


texts: Factor-augmenting technologies (Acemoglu and Restrepo 2018c)

texts:
In that paper, they consider the following production function:

$Y = F(A_KK,A_LL)$.

Where:

  K denotes capital, L is labor, and $A_K$ and $A_L$ denote capital-augmenting
  and labor-augmenting technology, respectively. We assume throughout
  that F is continuously differentiable, concave, and exhibits constant
  returns to scale. Let $F_K$ and $F_L$ denote the derivatives of F with
  respect to capital and labor. We focus on competitive labor markets,
  which implies that the equilibrium wages is equal to the marginal
  product of labor:

$W = A_L F_L(A_KK,A_LL)$.

Why? Shouldn't simply be:

$W = F_L(A_KK,A_LL)$.

Without the $A_L$ multiplying the derivative?


texts: Is an unconditional basic income pleasurable idea or it cannot be achieved?

texts: I would like to know if you can tell me, what are economical theories that are in support of this kind of social system if any? Can this system be efficient?


texts: Is the money market model based on assumption of no interest rate targeting on the part of the central bank?

texts:
This is quote from Gregory Mankiw's macroeconomics text about mechanism of formation of the interest rate in the money market model:

How does the interest rate get to this equilibrium of money supply and
money demand? The adjustment occurs because whenever the money market is
not in equilibrium, people try to adjust their portfolios of assets and, in the
process, alter the interest rate. For instance, if the interest rate is above the equi-
librium level, the quantity of real money balances supplied exceeds the quantity
demanded. Individuals holding the excess supply of money try to convert some
of their non-interest-bearing money into interest-bearing bank deposits or
bonds. Banks and bond issuers, who prefer to pay lower interest rates, respond to
this excess supply of money by lowering the interest rates they offer. Conversely,
if the interest rate is below the equilibrium level, so that the quantity of money
demanded exceeds the quantity supplied, individuals try to obtain money by sell-
ing bonds or making bank withdrawals.To attract now-scarcer funds, banks and
bond issuers respond by increasing the interest rates they offer. Eventually, the interest rate reaches the equilibrium level, at which people are content with their
portfolios of monetary and nonmonetary assets.

I also noticed that the money supply curve is strictly vertical.
Both of these things make me suspect that this model assumes that the central bank doesn't target the interest rate. Am I right? Or is it somehow possible for the central bank to target the interest rate in this model without breaking the interest-rate forming mechanism outlined above?


texts: Derivation of Equilibrium Strategy in 1st-price Auction?

texts:
Hey, everyone. I desperately need help understanding some math in auction theory.  I have been writing a paper as an undergrad for auction theory, and after all of my research I just cannot understand one step the author of a book uses to derive the equilibrium strategy for first-price auctions under independent private value conditions.
The steps in the derivation process essentially follow this:
Let x = the chosen player's personal valuation, G(x) = the probability that the highest opposing bid, an order statistic, Y_1, is < x.
\begin{equation}
\beta(x) = x - \int_0^x\frac{G(y)}{G(x)} \, dy \\
\end{equation}
Then without much explanation, other than "values are uniformly distributed on [0,1]" he just converts this equation to
\begin{equation}
\beta(x) = \frac{N-1}{N},
\end{equation}
Which makes sense and is usable.

The book I am using is Vijay Krishna's Auction Theory, and I would extremely appreciate someone helping me understand this last step.


texts:
I don't know if this is the correct forum for this question, but do we have to pay taxes on checks from the government that were paid from taxes in the first place.

For example, like Social security checks and Paid Family Leave checks?
If that is the case, what is the point of paying those taxes anyway?

If we pay x% on taxes on a $y paycheck every year, and after n number of years, we need to avail some of that money due to disability or paid family leave, etc, if we are to pay z% tax on that, would that be double taxation? even though z would be lesser than x?


texts: What does it mean that a production set is closed and non-empty? And why is it important?


texts: Open access datasets for teaching IV regression

texts:
I am looking for a dataset to show (to a group of engineers) how the instrumental variables technique is used in econometric practice.

I could always make up my own data, but I think it might be more interesting to everyone using real (not to complicated) data to replicate an actual study.

ps. Forgive me if this is off-topic for this site.


texts:
I'm looking for GDP projections for the fifty American states (up till 2040, or 2050). Are these available online, or in any economics papers?

I've found GDP projections for America, and historical GDP data for the fifty states. While GDP projections are not reliable, I need this for a project that I'm working on.


texts: Difference-in-Difference (DID) Regression with Non-Stationary (but Cointegrated) Treatment and Control Groups

texts:
I would like to run a DID regression between two periods where each period spans multiple years. For example:
Period 1: 1970Q1-1990Q4
Period 2: 1991Q1-2010Q4.
My treatment and control variables are non-stationary, but they are cointegrated. Thus, the error term is stationary and normally distributed. All assumptions of OLS also hold for DID. However, in a standard setting where you have two cointegrated variables one would have to use a DOLS or FMOLS to properly estimate the standard errors. Yet, the setup of a DID regression is different than the standard assumptions of regressing Y on X (with both being I(1) and cointegrated) which is what all of the theory on cointegration (in levels) is based on.
My question is if the variables are non-stationary, but cointegrated is the DID estimation valid? If it is, then the estimates would be superconsistent as is the case with an OLS between cointegrated variables, however, I am not sure if one can correct for the standard errors in this setup.
Any help would be much appreciated!


texts:
A unit of money in Country X may buy far more goods in Country Y than in the former. But Country X prides in calling itself a larger economy and a more prosperous entity.
As money is just a social construct created as a substitute to represent the value of goods and thus is useless by itself : How can mere money, such as GDP be given more importance and atfention than its PPP counterpart ?


texts: Proof of Concavity of Cobb-Douglas Function

texts:
Given the function $F(\mathbf{x})=x^{a_1}_1x^{a_2}_2 \ldots x^{a_n}_n$ defined on the set $S=\{\mathbf{x}=(x_1, \ldots, x_n) \in \mathbb{R}^n: x_1>0, \ldots ,x_n>0\}$ with $a_1,a_2,\ldots,a_n > 0$ and $a_1+a_2+\ldots+a_n=3$, I want to:
(i) Show that $\mathbf{x} \cdot \nabla F(\mathbf{x}) = 3F(\mathbf{x})$ at every $\mathbf{x}$, where $\nabla F(\mathbf{x}) = (\frac{\delta F(\mathbf{x})}{\delta x_1},\ldots,\frac{\delta F(\mathbf{x})}{\delta x_n})$.
I was able to work out that $\mathbf{x} \cdot \nabla F(\mathbf{x}) = a_1x^{a_1}_1 + \ldots + a_nx^{a_n}_n$ but got no further. Need help with this part!
(ii) Determine whether $F(\mathbf{x})$ is concave in $\mathbf{x}$ on the set $\mathbf{x}$.
My first thought was to use a Hessian matrix but that would be too tedious for this function. Is there a better method?


texts:
In dynamic macroeconomic model(without production sector), Euler equation is $$U'(C_t)=b(1+r)U'(C_{t+1})$$

I found another equation related with Euler which is called Euler condition.
In New Keynesian model,
$$Y_t-E(Y_{t+1})=-\left(\frac{1}{\sigma}\right)(i_t-E(\pi_{t+1})-\rho)$$

which means Euler condition. In this equation, what is the Economic meaning for Euler condition?


texts: Advice on upper and lower hemicontinuity?

texts:
Consider the correspondence f: $\mathbb{R}$ -> $\mathbb{R}$ defined by:

f(a) = {x $\in$ $\mathbb{R}$:x2 + x $\leq$ a2} for all a $\in$ $\mathbb{R}$.

Find the points where the correspondence is uhc and the points where it is lhc. Justify your conclusions exhaustively.

For a correspondence f: $\mathbb{R}$ -> $\mathbb{R}$, define its graph as:

$\Gamma$f = {(x, y) $\in$ $\mathbb{R}$2: y $\in$ f(x)}.

Prove that if $\Gamma$f is an open subset of $\mathbb{R}$2, then f is lhc.

I know that for a function to be upper hemicontinuous, there must be a convergent sequence in the domain mapping to a sequence of sets in range which contain convergent sequences, and an image of the convergent sequence limit must contain the limit of the sequence in the range. Additionally, for a lower hemicontinuous, if the function has open graph Gr(f) it is lower hemicontinuous. Do I have the right criteria?

I would appreciate any tips as to how to get started on these two questions, as I am somewhat unsure as to how to start.


texts:
If it is assumed that every consumer within a particular region has the same 'valuation' for a certain product, and consumers will purchase no more than one unit of the product, is the market demand curve perfectly elastic (horizontal)?

Any insight would be appreciated.


texts: Can quantative easing be summarized as "The state prints cash to pay its debt to private sector"?

texts:
I find that most sources describe quantitative easing in an overly complicated way that obscures what it basically means.

As far as I understand a central bank is a public entity  owned by a state, so I don't see much point in distinguishing a state entity from a central bank entity.

Therefore, I tend to find that the traditional descriptions like  "the central banks buys government bonds from private banks in order to inject money in the economy" are ridiculously  convoluted and funny.

As far as I understand, if I have a government bond, it is a promise that the state will pay me back some money at some point. So when I'm hearing "the central bank buys government bonds", all I'm hearing is actually "the government is printing cash from nothing to pay me right now, and destroy its debt".

Is my interpretation correct? Why isn't my interpretation the standard official intuitive explanation of quantitative easing? Is it just for newspapers and bankers to sound "serious"?


texts: What are production limiting programmes?

texts:
Under WTO domestic support norms, blue box measures include:

  Direct payments under production limiting programmes (often referred to as “Blue Box” measures) are exempt from commitments if such payments are made on fixed areas and yield or a fixed number of livestock.

These are also referred to as production limiting subsidies? Why would governments want to limit production? And isn't subsidy usually aimed at increasing production?

Reference: https://www.wto.org/english/tratop_e/agric_e/ag_intro03_domestic_e.htm


texts: Monetary expansion leads to decrease in inflation?

texts:
This is my professors answer to the question.

Lower cash rate by the Reserve bank will lead to lower nominal interest rate.

And real interest rate = nominal interest rate minus inflation.

And because change is nominal variable does not change real variables, real interest rate remain the same, therefore inflation must decrease.

Lower nominal interest rate leads to a lower opportunity cost of borrowing, which in turn increases investment and consumption, which leads to a higher GDP.

Her answer seem to be very different from what I learn in macroeconomic course, where monetary expansion using the LM-IS AD-AS models. Which monetary expansion would lead to higher inflation in both the short run and the long run.

Is her answer correct in any economic sense?


texts: Compute yield to maturity for a bond with coupons when price is different from face value

texts:
Given the formula  $P = \sum_{t=1}^n \frac{CF_t}{(1+i)^t} $
 we can apply it to the case of a bond with constant coupons so that :

$\displaystyle P =\sum_{t=1}^n \frac{C}{(1+i)^t} + \frac{FV}{(1+i)^n}  \implies P = C(\frac{1-(1+i)^{-n}}{i})+\frac{FV}{(1+i)^n}$

with  $P$ = price , $C$ = coupon at the time $t$ , $FV$ = face value , $i$ = yield to maturity

My problem : How is it estimated $i$ when $P\neq FV$ and $P, C,FV$ are known ?

I think that it's not possible to obtain an exact result , because it doesn't seem possible to separate the $i$ from the rest . I tried to use Taylor formulas somehow to get an approximation but I haven't come to anything.

EDIT :

Is bisection method the only possible way to proceed ? Is something about polynomial approximation possible?


texts: Wold Decomposition and autocorrelations of AR

texts:
Is it possible to retrieve Autocorrelations ( value or any other info) up to a certain lag
for an AR(2) stationary model using the Wold decomposition?

Example:

$$X_t=0.32X_{t-1}+0.51X_{t-2}+ \varepsilon_t $$

Lag Poly Form

$$(1-0.32L-0.51L^2)X_t= \varepsilon_t$$

Char Eq

$$Z^2-0.32Z-0.51=0$$

Wold Decomposition form $(L^J:- \phi_1 \psi_{j-1}-\phi_2 \psi_{j-2}+ \psi_j = 0)$:

$L^0:\psi_0 = 0 $

$L^1:-0.32 \psi_{0}-\psi_1 = 0$

$L^2:-0.32 \psi_{1}-0.51 \psi_{0}+ \psi_2 = 0$

$L^3:-0.32 \psi_{2}-0.51 \psi_{1}+ \psi_3 = 0$

$L^4:-0.32\psi_{3}-0.51 \psi_{2}+ \psi_4 = 0$


texts: Is DARA utility implying CRRA most of the time?

texts:
The Wikipedia page on risk aversion states that a "Constant Relative Risk Aversion implies a Decreasing Absolute Risk Aversion, but the reverse is
not always true". Let me decompose this statement in two parts:

1/ "Constant Relative Risk Aversion implies a Decreasing Absolute Risk Aversion."

A simple example is the log utility function, $u(c) = \ln(c)$, with $c>0$ satisfies the DARA because the utility function is positively skewed $\left(u'''=\frac{2}{c^3} >0\right)$ and implies a Relative Risk Aversion equals to $1 \left(=-c\frac {u''(c)}{u'(c)}\right)$.

2/ "but the reverse is not always true".

I am wondering if this is the most frequent case? Or if most of the time DARA utility functions also exhibit CRRA?

I would be grateful if you can illustrate your answer with some utility functions.


texts: How to properly interpret logged interaction variables

texts:
I have the following regression to interpret elasticity of demand:
$$\ln(demand) = const - 0.6*\ln(fare)$$
I understand that a 1% increase in fare results in a 0.6% decrease in demand
I want to add dummy variables for days of week (excluding one of course) and want to add day-of-week $* \ln(fare)$ interactions so that I can determine the elasticity of demand by day of week (which I already know differs)
For simplicity in writing this out let’s pretend there are 3 days: mon, tue, wed and I will leave Wednesday out as my base
So now my regression is:
$$\ln(demand) = const - 0.45*\ln(fare) + 10*(mon) + 15*(tue) + 0.05*\ln(fare)*(mon) - 0.15*\ln(fare)*(tue)$$
Here, my elasticity of demand for Wednesday is interpreted as a 1% increase in fare results in a 0.45% decrease in demand
But my question is how to interpret elasticity of demand for Tuesday. I know that the interaction and even the dummies are relative to the base.
So the question is for Tuesday should The coefficients be added? Or multiplied since it’s logged?


texts: What is the difference between utility function and characteristic function

texts:
I read that normative theories such as social welfare and game theory have as tasks computing the peoples' (average) utility function in the first case, and the characteristic function in cooperative games with transferable utility. Moreover, in game theory the characteristic function constitutes "the game" itself.

I appreciate very much any gentle intuitive explanation of the difference between these two concepts.

(Edited: Thanks for the comment; the question is edited)


texts:
Should a country be more inclined or less inclined to join a currency union (common currency) under the following events:
a) Increase in the size and frequency of AD shocks to the economy.
b) Increase in the size and frequency of money demand shocks to the economy.
c) Increase in the cultural similarities between the country and the country or region it is joining.
d) Decrease in capital mobility restrictions combined with an increase in immigration restrictions.

In case a, I feel as though it depends on whether or not the AD shocks are similar between the joining regions; if they are, then they would be more inclined, but if they're not, then otherwise.
In case b, I think the country would be less inclined since they would have less control over monetary policy.
In case c, I would say more inclined because it would encourage labor movement.
Finally, in case d, I would say less inclined because, although capital would flow freely, a decrease in labor flows would be worse.
What are your thoughts on these four cases?


texts: Similarities between microeconomic and macroeconomic failure. And, how microeconomic failures affect the economy at the macro level?

texts:
I can't make a relation between microeconomic and macroeconomic failures? I know they have differences. However, I want to know the effect of these two economic breakdowns on each other.
I am meaning recessions and inflation for macroeconomy failure. And for micro economy failure, I am meaning by the free rider, externality, market power


texts: How are historic economic statistics calculated?

texts: Sources like Our World in Data can have statistics that date back hundreds of years. Specifically, the Our World in Data source has a graph of GDP Per Capita in England dating all the way back 1270. What kind of resources do these statistics draw upon? Finally, is these any metric to determine how accurate they may be?


texts: In the Cournot Duopoly Model,why is the Equilibrium achieved at 1/3 Rd of the Market Share?

texts: I've been reading it for a while,while I do get the action reaction movements,I can't understand as to how the 1/3rd value was reached. Can anyone intuitively or mathematically explain as to how it's necessarily 1/3rd and not say 1/6 or 3/5?


texts:
The world's Bitcoin mining in the aggregate uses surprisingly large amounts of electricity.  Princeton computer scientist Arvind Narayanan estimates that Bitcoin mining now uses about five gigawatts of electricity per day, or somewhat more than the state of New York.

How does the dollar value of all bitcoin compare with the total cost of the electricity required to generate it?   (Not over one day, but up to now.)


texts: Is IS-LM still used in research or we learn it just to understand basic macro?

texts: Since i had my "Introduction to advanced macroeconomics" and discovered DSGE i've been wondering if IS-LM is used in research, i know it was used in the 80's or so, but now?


texts: Are there examples of strategies where a combination of third degree pricing and two-part tariffs are used together?

texts: Of course, I am only interested in instances where the combination of the two strategies ultimately lead to higher profits than if the monopolistic firm had used only one.


texts:
Let's split each period into $n$ intervals. There's a continuum $u$ of unemployed and $v$ of vacancies. During each interval, there is a total of $X/n$ job offers. That means that each unemployed gets a job offer with probability $X/(nu)$ (assuming that $n$ is eventually so small that the chance of multiple job offers to the same person will go to zero).

Single individual Number of job offers - for a single individual - in the interval is distributed $Binomial(k, n, \frac{X}{un})$. Letting $n\to\infty$, the distribution in the continuous-time analog converges to $Poisson(k, \frac{X}{u})$.

I'm interested in the probability of $x$ individuals getting at least one job interval during a whole interval. That is $(1 - Binomial(0, n, \frac{X}{nu}))^x$:

$$ (1 - (1 - \frac{X}{un})^n)^x $$

If I'm not mistaken, the continuous-time analog is

$$ (1 - e^\frac{-X}{u})^x$$

Is that correct? The combination of exponential and power function is making me quite uncomfortable.


texts: Having a lower inflation rate is not the same as having lower overall prices?

texts:
Having a lower inflation rate is not the same as having lower overall prices.Why?

lower CPI(inflation) means price levels in country decreases?