texts: Existence of utility representation of a rational but discontinuous preference

texts:
This is related to Do discontinuous preferences imply no continuous utility function?

I think the title of the above-linked question is phrased in such a way that obscures a subtly different but more interesting question which the OP also hinted at in the body. I'd like to ask that explicitly here.

  Does there exist a rational but discontinuous preference relation that is representable by a (potentially discontinuous) utility function?

In other words, if $\succsim$ satisfies completeness and transitivity but violates continuity, can we still find a utility function to represent it?

From known results, the answer does not seem obvious.

We know that continuous utility representation exists if and only if preference is complete, transitive, and continuous. But this doesn't tell us what happens when preference is not continuous.
We know that utility representation does not exist for some discontinuous preference (e.g. the lexicographic preference). But can this conclusion be generalized?

Finally, I want to note that the requirement for $\succsim$ to violate continuity means we're ruling out finite (and countable?) domains.


texts: Impact of auction systems that allow 'sniping'

texts:
I'm a bit perplexed that eBay has auctions that have a fixed time ending, and so winners are often determined by who can 'snipe' the auction, by putting in the winning bid at the last possible microsecond.

Often specialised software is used to achieve this.

An alternative system, like New Zealand's Trade Me auction site uses, is that the auction is auto-extended by two minutes, if a bid is put within the last two minutes of the auction.

What this means in practise (from what I've seen in auctions I've particpated in) is that an auction might be extended by 10-30 minutes due to 'last minute' bids between two or more bidders.

Now, it should be noted that the auto-extending dynamic doesn't completely negate the sniping dynamic. For example if Bob sees that Alice has put a bid on a item for \$1000, which is due to close in two days, and Bob is willing to spend \$2000 on that item, it still makes sense for Bob to hold off bidding on the auction until closing time. Alice may not be paying attention\be at her computer (though trade me allows auto-bids) at closing time, and by bidding at the last minute, he reduces the window in which she can outbid him.

This auto-extending system seems like it evaluates the market value more genuinely than the sniping system.

Ebay is surely aware of this dynamic, and it must be a conscious decision to keep the sniping-allowed system.

My hypothesis is that systems that allow sniping encourage higher selling prices, as bidders pre-emptively increase their bids as to stay out of the sniper's willing-to-bid range.


texts:
Think of the following balls as individuals of populations.

Say I have $U$ urns, and some balls. Both numbers are really large. So large, that authors like Blanchard and Diamond have approximated the binomial operations that follow with Poisson probabilities.

The balls are either red ($R$) or green ($G$). At the beginning of the period, every ball is (randomly, iid) tossed into an urn. There is no miss chance (i.e. every ball is in some urn). Some urns will have more than one ball, some might have none.

There are two exercises I want to do in this setup, and I'm not sure to what extent they're overlapping (i.e. helping me understand one would help me understand the other one as well), so I will post both.

My issue is kind of that I have a binomial thinking going on, and you can see that from the structure that I have imposed onto solving the following probabilities. Should I switch to Poisson probabilities instead? What is the neatest way to solve the following setups?

Red Ball Solo

I would like to compute the ex-ante probability of a red ball (from the perspective of a red ball) of being tossed into an urn where there is no other red ball.

So far, I was thinking about doing

$$
Prob(\text{sole red ball}) = \sum_{x = 1}^{R + G} Prob(\text{Urn has $x$ balls}) \cdot \sum_{y=0}^{x-1}Prob(\text{No other red ball }  | x \text{ balls})
$$

Red Ball Super Ball

Out of each urn, one red ball becomes a super ball. This probability is uniform. I would like to compute the probability of a red ball becoming a super ball.

My abstract idea was again similar:

$$
Prob(\text{red ball becomes super ball}) = \sum_{x = 1}^{R + G} Prob(\text{Urn has $x$ balls}) \cdot \sum_{y=0}^{x-1}Prob(\text{$y$ other red balls | $x$ total balls }) \frac{1}{1+y}
$$


texts:
If we have the following regression based on the Solow model:
log(yi) = β0 + β1 * log(si) + β2 * log(ni + gi + δi ) + ei
And we know that based on:
y* = 〖(s/(n + δ + g))〗^(α/(1-α))
log(y*) = α/(1-α) * log(s) – α/(1-α) * log(n + δ + g) )
So we can assume that beta 1 and beta 2 are equal to: α/(1-α)
Of course beta 1 should be positive and beta 2 should be negative, but what if they have different values, for example beta 1 equals 1.5 and beta 2 equals -2.5?
What does this mean economically? I am a little bit confused about how beta 1 and beta 2 can be different.
Thank you very much for every answer!
Best regards


texts:
I've been reading about final goods and commodities and some links

https://en.wikipedia.org/wiki/Final_good

https://marketbusinessnews.com/financial-glossary/final-good/

mention that final goods are commodities. However, that is contradictory with commodities' property of substantial fungibility, which is "the market treats instances of the good as equivalent or nearly so with no regard to who produced them". What am I missing here?


texts: How is it not arbitrage that EURIBOR (EUR) is around -0.5% and LIBOR (USD) is around 0.5%?

texts:
Why can I not borrow $1B of EUR at EURIBOR (pays me 50bps per year), convert it to USD (also pays me 50bps per year), lend it out at LIBOR, and collect a 1% spread? Am I missing somethign obvious?
EURIBOR
and LIBOR


texts: How do takeover deals create arbitrage opportunities that involve necessarily selling short the acquirer’s stock?

texts:
Yes, you can get a juicy yield from a pot ETF. But here’s the catch - The Globe and Mail

  Takeover deals create arbitrage opportunities that involve selling short the acquirer’s stock [I emboldened.] and going long on the target company , and the ensuing demand for borrowed shares drives up the rates Horizons can charge, Mr. Noble says.

Why sell short the acquirer's stock? Why assume that the acquirer's stock will fall? Can't it increase like the target company's?


texts:
As part of self study towards an entrance exam, I am solving the following question.

There are two consumers in the economy and two goods, one private and one public. The utilities of the consumers is given by:

$$u_1(x_1,y) = x_1+6\sqrt y$$

$$u_2(x_2,y = x_2 + 10\sqrt y$$

where $x_i$ is the quantity of the private good and $y$ is the quantity of the public good consumed. Initial endowments of the private goods:

$$\omega_1 = 40, \omega_2 = 60$$.

A unit of private good can be converted one-for-one to a public good.

My attempt:

The Pareto Efficient level of public good is determined by the equation:

$$|MRS_1| + |MRS_2| = MC(G) \quad (1)$$

where $MRS_1 = \frac{MU_G}{MU_{x_1}}$, $MRS_2 = \frac{MU_G}{MU_{x_2}}$ and $MC(G)$ is the marginal cost of providing the public good.

Solving $(1)$ with the given utility functions I get:

$$\frac{3}{\sqrt y} + \frac{5}{\sqrt y} = 1$$
$$\implies y = 64$$

Therefore, the Pareto efficient level of public good is $y=64$.

The question asks to select the Pareto Inefficient bundle $(x_1,x_2,y)$ amongst the following:

A. $(50,0,50)$

B. $(90,0,10)$

C. $(0,80,20)$

D. $(16,20,64)$

I think all of A, B and C are Pareto Inefficient.

The given answer is C.

Thanks for reading my question.


texts: Is increasing the money supply possible with a gold standard? How about controlling interest rates?

texts: I understand that under a fiat currency, the government can buy securities on the open market to increase the money supply, and decrease interest rates. This monetary policy is possible to help recover from recessions. could this be done with a gold standard? Could the government increase the supply / lower interest rates?


texts: Is it possible to transfer information through strategic games?

texts:
Let's say that there are 2 players Player A and Player B, engaged in a set of repeated strategic games. Is it then possible to transfer information from one player, say Player A, to the other player, Player B, simply by having Player B observe the strategies that Player A uses over a given period of time, in response to Player B's strategies?

For example, Player B could form a simple hypothesis about player A's beliefs  and/or preferences, and test it out by using different strategies. The hypothesis can then turn out to be true or false (over a period of time, with some probability) if Player A's strategies in response to Player B's take on a certain character.

I would like to learn more about these kinds of games, if they've been studied.


texts: How can a country ensure its national currency is used by its citizens?

texts:
I am wondering how countries are able to force everyone to use its own currency, instead of some external currency (like the U.S. dollar or Bitcoin or cookies or something else not under government control). If businesses and citizens decide that they do not like the national currency (perhaps it is too turbulent or some other reason), and instead decide that they would like to "barter" a third-party currency for goods and services rather than "buying" those goods and services with the national currency, then the country would lose control of its own currency. This does happen at a small scale, where small businesses may accept a cryptocurrency instead of the local currency.

What different methods can a country employ to ensure that it does not lose control of its currency because its citizens switch to an unofficial alternate currency not controlled by the government?

If this situation does occur, how can a government still collect taxes on the exchange of this alternate money for goods and services? If I wanted to pay someone to mow my lawn in cookies instead of currency, the government could not tax this. If every business and citizen began treating cookies as the main form of payment, the government would lose all tax revenue. How can it stop this from happening?

If the answer involves creating a law that says "10% of all cookies (or bitcoins or something else) must be given to the government", then what prevents that currency from swiftly changing its name? Perhaps cookies become brownies, which do not fall under the law. Or bitcoins become a different cryptocurrency, or just change their name. This would become a game of cat-and-mouse between the laws and the currency. It seems like accepting alternate, nontaxable unofficial currencies, would become economically beneficial for both companies and individuals. Yet established governments in the world do not have this problem. How?


texts:
I have read that the Independence of Irrelevant Alternatives axiom in expected utility theory implies the fact that compound lotteries are equally preferred to their reduced form simple lotteries. However, I am unable to prove this. I'm sure that the proof should be easy, but I just can't see it.
I read it here: http://www.econport.org/content/handbook/decisions-uncertainty/basic/von.html


texts: Econometrics: Omitting a significant variable

texts:
Im currently doing a project to construct a demand function for Meat & Fish. My data indicates that Price of Fruit & Veg is individually statistically significant.
However, after a omitting this variable (as well as 3 other insignificant variables) the F-test result highlighted the failure to reject the Null (these four variables are jointly insignificant).

Should I therefore omit Fruit & Veg variable, despite it being individually significant and also making intuitive sense for inclusion into my demand function.


texts: Cobb-Douglas production function with expenditures rather than units

texts:
I want to estimate a standard Cobb-Douglas production function of the form

$ Y=AK^{\alpha}L^{\beta}$. However, I only have data on labour expenditures, not units of labour. I don't have data on the price of labour $w$ either, so I can't back out the units of labour from expenditures. Is it okay to estimate the production function (in a GMM regression framework) using labour expenditures instead of units of labour?


texts: By what steps and contracts does new money enter the economic system?

texts:
Like many noneconomists who read about economic history and finance, I always remain somewhat baffled by the opaque generation of currency under the federal reserve system. My understanding is that the banks "loan" money to the government, which prints a federal reserve note or IOU signed by Treasury. But then what?

How do the banks actually receive federal currency and/or credit... and determine the amounts they receive? My understanding is that banks can effectively receive as much money as they can "justify" by credit contracts, ratings, and a given ratio of leverage or fractional reserve. Apart from market forces and assumed prudence, are these the only factors that legally limit the amounts of money banks can receive? Can banks essentially get as much money as they say they can securely loan?


texts:
When trying maximize the utility having a cobb-douglas utility function $u=x_1^ax_2^b$, with $a+b = 1$, I found the following formulas (Wikipedia: Marshallian Demand):

$x_1 = \frac{am}{p_1}\\
x_2 = \frac{bm}{p_2}$

In one of my books I also find these formulas for the same purpose:

$x_1 = \frac{a}{a+b}\frac{m}{p_1} \\
x_2= \frac{b}{a+b}\frac{m}{p_2}$

With $p_i$: prices of the goods; $m$: budget

I tested all of them and they produced the same results.
So are there any differences?


texts: First Order Condition for Profit Maximization in Gambling Industry

texts:
I am working on a model of optimal payout percentages in the gambling industry.

Because the nominal price of a \$1 ticket is always \$1, we use an effective price strategy where Q = \$1 in won prizes. If a game pays out 50%, the effective price is \$2, since that is what would need to be spent to win an expected \$1 in prizes. Pretty simple, right?

Well, I ran into this footnote in some research, and can't figure out how they got to the First Order Condition for Profit Maximization from the first equation:

"Let $C(Q)$ represent operating costs as a function of quantity units, where one quantity unit is defined as one dollar in expected value of prizes.

The lottery agency's net profits are given by

$$N = PQ - Q - C(Q)$$

where $P$ is the price charged for a quantity unit.

The first-order condition for profit maximization can be written

$$-E_{PQ} = P(1 - C')/[P(1 -C')- 1] $$

If marginal operating costs are $6$ percent of sales and the payout rate is $50$ percent, we have $P = 2$ and $C' = .12$, implying that the price elasticity of demand at maximum profit is $-2.3$.

For an increase in the payout rate to increase profits, $E_{PQ}$ must exceed $2.3$ in absolute value."

-[Citation] Clotfelter, Charles T, and Philip J Cook. "On the Economics of State Lotteries." Journal of Economic Perspectives: 105-19.

In the FOC equation, $-E_{PQ}$ is the effective price elasticity of demand. That normally would be found by taking the derivative of $P$ with respect to $Q$ in the first equation.

How did they end up where they did? There has to be something I'm missing.

I am having trouble understanding how that particular First Order Condition was reached- whether it was a result of some some derivative process on the Net Revenue equation, or if it is simply an external condition being applied.

Thanks!


texts: Departure point for research in economics

texts:
I hope this is the place to ask this question. I am in the first year of PhD in economics. As most of PhD students in economics, I try to show some economic mechanisms by theoretical modelling in environmental economics.

Most of time, I have a tendency to base largely on other models in the literature. I try to incorporate my idea in existing models but it does not work really well. For those who are in economics, how do you start to model your idea ? Do you start from a really basic model and complexify after ?


texts: Quasilinear Utility: Pareto Optimality Implies Total Utility Maximization?

texts:
I read that if we have quasilinear utility for all consumers, then any pareto optimal allocation maximizes the sum of utility levels of all consumers. That is:

$\textbf{What we know:}$
$$1)\quad u^i(m^i,x^i)=m^i+\phi^i(x^i)\; \quad \forall i=1,...,I$$
$$2)\quad\phi^i(\;)\;\text{is continous and strictly increasing (but not necessarily differentiable)}$$
$$3)\quad \text{An allocation,}\,x\, \text{satisfies}\;\neg\,\exists\,\hat{x}\; s.t. \;\hat{m}^i+\phi^i(\hat{x}^i)\geq m^i+\phi(x^i)\;\forall i$$
$$\text{and} \quad \hat{m}^i+\phi^i(\hat{x}^i)> m^i+\phi(x^i)\,\text{for some}\,i$$

$\textbf{What to show:}$
$$x\;\text{solves}\;max\sum_{i=1}^Im^i+\phi^i(x^i)$$

Can anyone provide a proof of this? Any help would be greatly appreciated!

$\textbf{Edit:}\,$I don't know if this is the right path, but by the strict increasing property of $\phi(\,)$, preferences satisfy local non-satiation, which implies they satisfy the first welfare theorem. Now, If I could figure out whether all pareto optimal allocations are competitive equilibria with quasilinear utility, I may be on to something!


texts:
My Lagrangian is:

$L=\sum\limits_{t=0}^T \beta^tU(f(k_t)-k_{t+1})+\sum\limits_{t=0}^T\lambda_t(f(k_t)-k_{t+1}).$

My FOC for $[k_{t+1}]$ is:

$\beta^tU'(f(k_t)-k_{t_1}^*)(-1)-\lambda_t^*+\beta^{t+1}U'(f(k_{t+1}^*-k_{t+2})+\lambda^*_{t+1}f'(k_{t+1})^*=0$.

$\textbf{My Question:}$
I try to recover from their FOC and backtrack, but how did they get (5) as the Euler Equation on page 11?

Their EE is:

$\beta f'(k_t)U'[f(k_t-k_{t+1})]=U'[f(k_{t-1})-k_t]$ for $t=1,...,T$.

Reference:

Stokey, N., R. Lucas, and E. Prescott, Recursive Methods in Economic Dynamics, Harvard Univ. Press, 1989


texts: What are the pros and cons of Vienna's publicly owned social housing market?

texts:
This article and this article report on Vienna's social housing market. Rent controlled since 1917 and now publicly owned.

What are the relative pros and cons from an economic standpoint of such a policy? How's it working there?

Why is it apparently unique in the world? What are the barriers to copying its successes elsewhere? What, if any, are its failures?


texts: Is Foreign investment positive or negative for a country?

texts:
When a state company is sold to foreigners in a country, people who live in that country generally do not like it. Because the company is sold to foreigners. People are acting with a sense of nationalism.

On the other side if there is an economic crisis or economic recession in that country, foreign investment is needed and the money is very important for the development of the country.

How foreign investment can be interpreted for a country? Is Foreign investment good or bad for a country?


texts:
In an article of a respected German newspaper (Die Zeit) I found the following statement (translation by me):

  90 % of all foreign exchange trades are dealt in USD. Since every electronic transaction of USD legally takes place on American territory, the US authorities can almost always take legal action against the involved individuals and companies, even if they are not located in the US.

I´ve tried a Google search, but did not find an explanation, so I thought I´d ask here (also, I´m quite new to economics).

Are really 90 % of all foreign exchange trades dealt in USD?
Why does every electronic transaction of USD legally take place on American territory? What laws/processes are responsible? What about non-electronic transactions in USD?

I´d be interested in an explanation or suggestions for further research!


texts: Does deflation mean drop in asset prices?

texts:
Usually when inflation rises the stock market rises with it. The second point i want bring your attention to before i ask my question is when there are stimulus measure enacted by the government, thereby increasing the government deficit and there being a corollary between government spending and asset prices.

If there is a scenario where the economy enters a period of deflation, does this necessarily mean that asset prices will depress? Or could this be avoided where asset prices stay the same or keep rising ?


texts: Was there a drop in liquidity in the corporate bond market during the Global Financial Crisis?

texts: It is often said that the increase in the perceived default risk led to a fall in the demand for the corporate bonds. This led to the fall in their prices and hence, their interest rates rose significantly. In fact, the risk and liquidity premium rose 360 basis points from 1.85% before the crisis to 5.45% afterwards. However, can we also attribute this fall in the demand for corporate bonds to a decrease in liquidity of these assets. It seems to make sense to say that as a result of there being less buyers, the market for these corporate bonds is thus less liquid. This decreased liquidity further diminishes the attractiveness of these assets, causing the demand for them to fall even more. I am asking if such a vicious cycle exists: Increased perceived default risk, leading to decrease in number of buyers, leading to decreased liquidity, leading to further decreases in the number of buyers, and so on?


texts:
This question is from MWG
if walrasian demand function is generated by a rational preference relation then it must satisfy weak axiom.
I cannot prove this statement. How can I do?Thanks alot.


texts: Is it possible for disposable income to be lower than consumption expenditure?

texts:
I have an issue dealing with dataset provided for my coursework.

Because of the fact that I've been failing to find time-series of the same or similar values anywhere from world bank to Office for National Statistics, I strongly doubt it.

The data series provided is shown below in a form of line chart. The brief provided says it's in constant prices, it unfortunately does not indicate the reference year. What it is supposed to describe is consumption and disposable income for the United Kingdom over the period of 03Q2 to 15Q4. I don't believe there would be negative savings for the whole period.

I have been looking around to find some hint that would prove this true, unfortunately the graph below shows the opposite. I can explain the jump in disposable income by change in reference year, however the consumption data does not make sense to me. At all.


texts: Big Mac Index based on other products or services?

texts:
The Big Mac Index compares the cost of a McDonalds Big Mac in different currencies around the world. In doing so, it provides:

an informal way of measuring the purchasing power parity (PPP) between two currencies and provides a test of the extent to which market exchange rates result in goods costing the same in different countries

Have any academics, organisations, or think tanks made similarly useful indices based on other product/s or service/s?


texts: Why were there numerous banks run right after the stock market crash of 1929? Why would a bank fail because the stock market crashes?


texts: What are the general charateristics of matching markets that make then different from regular markets?

texts: I would like to know what exactly makes matching markets different from regular markets. If you could illustrate with examples to help me understand better, that would be nice. Thanks in advance.


texts: Selection bias - Will multiple regressions solve the problem?

texts:
Now I have a data from an African country concerning (i) levels of corruption across public sectors and (ii) perceptions of service quality from households (bad, medium and high). The data consist two types of household: those who have used the public services and those who have NOT.

I have read several papers from some respected journals (World Development, Journal of Development Economics) that address the problem of selectivity bias: those who have not engaged in public services might do so because they knew they would have to bribe (corruption) or they had bad experience from the past, and they would end up feeling bad.

Authors from the papers, however, do not use Heckit models, that I have learned from my degree. Instead, they argue that by running two regressions: (i) using data on those who actually used the services and (ii) all households in the sample, regardless of the service usage. I feel this approach is not correct.

I wish to understand further how selection bias, particularly in this example, should be handled. Some problems with the data are that the data might be subjective, quite small (around 500 households), and prone to measurement errors. Do you have any suggestions on dealing with the problems?

Many thanks.


texts: Hybrid Phillips curve under two-state Markov process

texts:
I am studying a New Keynesian model with a hybrid Phillips curve which reads
\begin{align*}
\pi_t=\beta E_t \pi_{t+1} + \varpi \pi_{t-1}+ \kappa x_t.
\end{align*}
The demand shock in the IS curve follows a two-state Markov process, i.e. I assume that there are two states, states $n$ and $z$. The transition probabilities are given as follows
\begin{align*}
P(s_{t+1}=n| s_t=n)&=p\\
P(s_{t+1}=z| s_t=n)&=1-p\\
P(s_{t+1}=z| s_t=z)&=q\\
P(s_{t+1}=n| s_t=z)&=1-q\\
\end{align*}
For $\varpi=0$, it follows that the Phillips curve in state $n$ reads
\begin{align*}
\pi_n = \beta\left[ p\pi_n + (1-p)\pi_{z}\right]+ \kappa x_n.
\end{align*}
However, I am interested in the Phillips curve in state $n$ for the case where $\varpi\neq 0$. My idea is that, given the economy is in state $n$ today, this can be only because

The economy was in state $n$ in $t-1$ and remained in state $n$ with probability $p$, or
The economy was in state $z$ in $t-1$ and switched to state $n$ with probability $1-q$.

Following this idea, for $\varpi\neq 0$, I would write down the Phillips curve in state $n$ as
\begin{align*}
\pi_n = \beta\left[ p\pi_n + (1-p)\pi_{z}\right]+ \varpi\left[p \pi_n + (1-q)\pi_z\right]+ \kappa \pi_n.
\end{align*}
Is this approach correct? If not, how do I add $\pi_{t-1}$ given the economy is in state $n$ in period $t$?


texts:
The certainty equivalent is a guaranteed return that someone would accept now, rather than taking a chance on a higher, but uncertain, return in the future. Otherwise, some definitions say that the certainty equivalentis the mean income of a gamble. If we see the vast literature of microeconomic and game theory papers, then we shall see that they assume CARA Gaussian normal preferences (or negative expnential utility, i.e. $\mathbb{U}(\widetilde{W})=-e^{\rho\widetilde{W}}$). Specifically the certainty equivalent in such case is $$CE(\widetilde{W})=\mathbb{E}(\widetilde{W})-\frac{\rho}{2}\mathbb{V}ar(\widetilde{W})$$
How can someone claim that this return is guaranteed, since we need to use $\mathbb{V}ar(\widetilde{W})$ to measure the utility gain of an individual?


texts: Auction mechanism with no trusted third-party

texts:
I have been using a double-auction mechanism to solve a two-sided market where multiple agents are competing to supply/use slices of a shared resource. The owner of the resource is a trustable third-party who is not biased towards any of the traders and is not using the resource (*simplified description of the problem in the footnote). The setup and the auction algorithm works just fine.

Now, considering a new scenario, where the auctioneer (the primary supplier) joins the market as a trader, thus cannot be trusted to hold the auction, what other alternatives to auction are there to assure trust?

*A bakery bakes 1000 baguettes per day and distributes them equally among the 10 restaurants in the town every morning. However, depending on the day some of the restaurants might be short on Baguettes or have an excess supply. We have designed a sealed-bid double-auction mechanism that allows the restaurants to share their excess Baguettes with the restaurants short on baguettes and get monetary compensation for it. As we assume that the bakery is not biased towards any of the restaurants, we trust him to be the auctioneer.

The bakery buys one of the restaurants, and it cannot be trusted anymore to run the auction as it is biased. Is it possible to hold the auction without having a central trusted auctioneer and distribute the decision making to solve the trust issue? If so, how we can minimize the communication between the traders?


texts: What is the relevance of economic growth?

texts:
Economic policies often mention high economic growth as a desirable path. For example,

"We started to lay a new foundation for stronger, more durable economic growth."
-- President Obama, Speech in 2013

But also

"Jeb Bush pledged Monday to give the U.S. an economic growth rate of 4 percent a year"
-- Politico

and many others in the USA and abroad (Hollande, Merkel, etc.)
Politicians from different sides seem to agree that economic growth is desired. For example, some of them say that growth helps against misery. Some of them say that higher growth helps a government with paying back their debt.
How does economic growth help the economy and the society? Through which mechanism does that work?
See also How do economies grow?


texts: What are the identification problems in measuring peer effects?

texts:
I am currently writing my bachelor thesis on peer effects. However, the more I read about the identification problems (I read e.g. Manski, Moffitt, Angrist, Goldsmith et al.), the less I understand. I particularly have a problem with understanding how endogenous selection affects my estimates (omitted variables? Selection bias?) and understanding the correlated unobservables/ related errors in variables and the endogenous membership problem and how or whether they relate to each other.

I know this is a lot but any help is appreciated!!! Thanks a lot!!!


texts: How to deal with potential output in the Sims (2002) framework?

texts:
In Sims(2002), the author explains how one solves a linear rational expectations model.

$$\Gamma_0S_t=\Gamma_1S_{t-1}+C+\Psi z_t + \Pi \mu_t$$

The only thing exogenously defined in the $z_t$ variable. Everything else is endogenous.

In the Smets and Wouters (2007) paper, we have the monetary policy rule dependent on the potential output, i.e. the output at flexible prices and wages.

How do we deal with the potential output? Is it assumed to be endogenous, and then included in the $S$ terms? If so, will I have to create $S=(S^f,S^s)'$, where $S^f$ are the state variables for the flexible economy, and $S^s$ are the state variables for the sticky economy?


texts:
I was reading a document released by our Central Bank and I came across this line:

  Finally, inflation in the items of daily use was much lower as
  compared to other items. The contribution of essential items of daily
  use was only 1.1 percentage points in the overall inflation of 4.5 %
  in FY15.

What does this mean in very simple terms? How do I explain this to school going children, for example?


texts: Is $\frac{ \Delta \ \text{endogenous variable}_1 }{\Delta \ \text{endogenous variable}_2}$ well-defined ... and what is it?

texts:
When solving economic models, wec get expressions of endogenous variables (say, production $P$, or consumption $C$) in terms of parameters or exogenous variales, and we can then ask what the change in, say, production is given a change in, say, public spending.

But can we also ask what the change in production is given a change in another endogenous variable, like for example $C$? That is, what is $$\frac{\Delta P}{\Delta C},$$ for example in the simple goods market model where the equations are $$\text{Demand} = C + \text{investments} + \text{public spending}, \\ C = c_0 + c_1(P - \text{taxes}), \\ P = \text{Demand},$$ where $P, \text{Demand}$ and $C$ are endogenous?

I have searched online and found that the answer is infinity, but no explanation is given. Why is it infinity?


texts: Estimating Demand for Goods with n Choices

texts:
I have a data set containing n observations (rows) of mobile applications. The dependent variable is the number of installations -- the variable is categorical (with more than 2 categories). Therefore the econometric approach is an ordinal probit/logit model. Besides my dependent variable I have plenty variables which describe the apps characteristics (pricing, rating, reviews, description length, the category etc.).

I would like to find a theory which explains the customer demand for apps. I have limited prior knowledge, but I found that one could use either the theory of product space or product characteristics. To apply the former, I would need to find groups in which the apps "compete" in. This cannot be done sufficiently in my case.

The second approach (product characteristics) utilizes a discrete choice approach. One customer maximizes its utility by comparing the characteristics of all products and chooses the one which suits him/her best. However, all customers can choose only one product, this is not the case here. One customer could choose n applications to download and therefore maximize his/her utility.

Is there any theory which supports my observed data?

EDIT: An app can fall in one of 12 categories. They have a natural ordering, but different sizes (Google reports them this way). They look like this:

1-5 Downloads = Category 1
6-10 Downloads = Category 2
11-50 Downloads = C 3
51-100 Downloads = C 4
and so on.


texts: Good book/article that goes into depth about transversality conditions?

texts:
I know how to derive the transversality condition in simple models like the Ramsey model.

However, I am looking to develop a deeper understanding of transversality conditions in more complex models. However most macroeconomics books I've seen only have about 1 page about the transversality condition, namely its simplest form.

Is there a good book that shows how to deal with more complex trannversality conditions than the one in the ramsey model? e.g. if the utility function contains a term for assets?


texts:
I am told that the following equality follows from integration by parts:
$$\int_{R-k}^{1}(\theta-R)dG(\theta)-G(R-k)k=\int_{R-k}^{1}(1-G(\theta))d\theta-k$$ Where $R>k>0$ and $G$ is the CDF of $\theta$ which is distributed on $[0,1]$. Can someone explain how integration by parts has been used here? Thank you.


texts: The government is issuing massive debt for coronavirus relief - why aren't interest rates rising?

texts:
As I understand it, the US Treasury Department issues bonds to pay for the government's coronavirus rescue spending. I might have thought that such a large input to the fixed income market on the demand side would increase prices, i.e., that interest rates would rise.

This hasn't happened though, in fact, the opposite seems to have happened. For example, the yields on 10 year treasuries have gone down since the beginning of 2020 (ref).

Why is this happening?


texts: Endogenous Growth: Balanced Growth Path with CRRA Utility

texts:
I've got a model of endogenous growth due to spillovers.

$\textbf{Model:}$
$$K_t=\frac{1}{n}\sum_{t=1}^nk_t$$
In this model, $k_t$ is chosen by agents, and $K_t=\bar{k}_t$ (the average of all $k_t$).

Now, agents want to dynamically maximize utility (under certain constraints) and they have CRRA (constant relative risk aversion) utility, so the maximization looks like:
$$\sum_{t=0}^\infty\beta^t\bigg(\frac{c_t^{1-\gamma}}{1-\gamma}\bigg)$$
$$s.t.\;Y_t=k_t^\alpha(E_tL)^{1-\alpha}$$
$$c_t+i_t=Y_t$$
$$k_{t+1}=(1-\delta)k_t+i_t$$
$$c_t,i_t\geq0$$

$E_tL$ is effective labor and the rest of the variables are typical  (I can give their definitions if requested).

One last addition to the model is that there are two equilibrium constraints:
$$E_t=\frac{K_t}{L}$$
$$k_t=K_t$$
$\textbf{Solution:}$

Using an Euler equation approach, two terms in the objective:
$$...\frac{\beta^t[k_t^\alpha K_t^{1-\alpha}+(1-\delta)k_t-k_{t+1}]^{1-\gamma}}{1-\gamma}+\frac{\beta^{t+1}[k_{t+1}^\alpha K_{t+1}^{1-\alpha}+(1-\delta)k_{t+1}-k_{t+2}]^{1-\gamma}}{1-\gamma}...$$
FOC:

w.r.t  $k_{t+1}$ and substituting in consumption:

$$\beta^tc_t^{-\gamma}=\beta^{t+1}c_{t+1}^{-\gamma}[\alpha k_{t+1}^{\alpha-1}K_{t+1}^{1-\alpha}+1-\delta]$$
Substituting in the equilibrium constraints:
$$c_t^{-\gamma}=\beta c_{t+1}^{-\gamma}[\alpha+1-\delta]$$
$$\implies \frac{c_{t+1}}{c_t}=[\beta(\alpha+1-\delta)]^{\frac{1}{\gamma}}$$
This implies that consumption grows at a constant rate which depends on preference parameters.

The next thing I want to prove that we have a balanced growth path. By this I mean that all variables grow at the same constant rate. $$\frac{k_{t+1}}{k_t}=\frac{c_{t+1}}{c_t}?$$
I have started to answer the question, but I have gotten stuck. Here is what I have so far:
$$k_{t+1}=k_t^\alpha K_t^{1-\alpha}+(1-\delta)k_t-c_t$$
In equilibrium $K_t=k_t$:
$$k_{t+1}=k_t+(1-\delta)k_t-c_t$$
$$\implies \frac{k_{t+1}}{k_t}=1+(1-\delta)-\frac{c_t}{k_t}$$
If we have a constant rate of capital growth, suppose:
$$\frac{k_{t+1}}{k_t}<\frac{c_{t+1}}{c_t}$$
If this is true:
$$\underset{t\rightarrow \infty}{lim}\;\frac{k_{t+1}}{k_t}=\underset{t\rightarrow \infty}{lim}\;1+(1-\delta)-\frac{c_t}{k_t}=-\infty$$
This means that the growth rate will continue decreasing. Now there are two ways this can happen. The first way is if $\underset{t\rightarrow \infty}{lim}\;k_t=-\infty$, which would clearly show that it couldn't be the case because capital cannot be negative. The second way which this could happen is if $\underset{t\rightarrow \infty}{lim}\;k_t=D$ where $D$ is some positive horizontal asymptote. If it did approach some asymptote, there is no reason why it could not be the case that consumption grows at a faster rate than capital. This is where I am stuck. How can I show that it cannot converge to some asymptote, and that $\underset{t\rightarrow \infty}{lim}\;k_t=-\infty$? Also, if there is an easier way to show that this model exhibits balanced growth paths, what is it? Any help would be greatly appreciated!


texts: Credible Threat in the Perfect Bayesian Equilibrium

texts:
Consider a simple game between P1 and P2 shown in Figure 1.

We consider a Perfect Bayesian Equilibrium. P1 uses a cutoff strategy based on his $c_1$ that has the Cumulative Distribution Function of $F$. If his $c_1$ is lower than a threshold $c_1^*$, which depends on P2's strategy, P1 takes the strategy $x$.

Similarly, P2 uses a cutoff strategy based on his $c_2$ that has the Cumulative Distribution Function of $G$. If his $c_2$ is lower than a threshold $c_2^*$, which depends on P1's strategy, P2 takes the strategy $a$.

We denote the optimal cutoff strategies as $F(c_1^*)$ and $G(c_2^*)$.

Suppose the game has slightly changed as shown in Figure 2.

Now P1 has one more turn. Suppose that, given the initial $F(c_1^*)$ and $G(c_2^*)$, we set P1's gain from the strategy j as always being equal to the strategy k. We assume that P1 takes the strategy j if P1 is indifferent between j and k.

In this case, does P2 still continue to use the same cutoff strategy $G(c_2^*)$? For P2, the node from the path $k$ is never reached while P2 cannot verify it. As long as P2 uses the same cutoff strategy $G(c_2^*)$, P1 will take the strategy $j$. I am wondering if P2's threat is credible.

In the new game, P2's gain remains unchanged. However, P2 may try to increase his gain by deviating from the optimal cutoff strategy $G(c_2^*)$ if P1 never use the strategy k. But, P1 will be aware of it and may use the strategy k again. If so, P2 will again use the same optimal cutoff strategy $G(c_2^*)$. I got stuck here.

I appreciate any help.


texts: How can an increase in the interest rate make bonds more attractive and reduce their price?


texts:
I have two questions about statements made in this video: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/bank-bailout/v/bailout-2-book-value

At 6:25, the video shows a Collateralized Debt Obligation divided into an AAA-rated tranche, an AA-rated tranche, and an equity tranche, in order of increasing risk but also increasing return, and the claim is made that no one wants to buy the equity tranche. In my mind, the return on the equity tranche should self-adjust to make the market indifferent between the riskier and less risky tranches. Why would it have been so difficult to sell equity tranches that banks had to give up on the idea and hold them instead?

At 10:30, the video claims that a stock price goes to \$0 when a company has \$0 equity. Does this actually happen in the real world?  The video seems to state that this doesn't imply you can pick up the stock for free, but that's what a \$0 stock price sounds like to me. Since the value of a stock is indeed its equity divided by the number of existing shares, how does this case play out in companies that have \$0 or negative equity?


texts: How to interpret "scale efficiency" in DEA?

texts:
I am reading the book Benchmarking with DEA, SFA, and R by Bogetoft and Otto. In Section 4.8 they discuss the concept of scale efficiency, and I am having trouble interpreting this concept.

The usual output of Data Envelopment Analysis (DEA) is a collection of efficiency scores. If we consider the input efficiency scores, then these scores represent the fraction of a firm's current costs which should, in principle, be able to be used to produce a firm's current output. Thus when a firm is judged as inefficient, a reasonable reaction might be to reduce costs and focus on making internal practices more efficient.

When investigating scale efficiency, one compares two different DEA outputs: one using the assumption of constant returns to scale, and the other using varying returns to scale. This expresses whether a firm is operating at it's "optimal size." If it is not, then using further comparisons of DEA outputs (using increasing or decreasing returns to scale) it is possible to see whether the firm is "too large" or "too small."

While the concept of scale efficiency makes sense to me intuitively, I don't see how the practical response to a scale efficiency analysis is any different from the response to the usual DEA efficiency analysis. For example, suppose we do a DEA input efficiency analysis and find that a firm is inefficient. Then the practical response is to reduce the budget and focus on making internal practices efficient. Suppose now instead that a firm is found to be scale inefficient. The practical response again seems to be to reduce costs and focus on making internal practices more efficient... but what exactly are the proposed gains? With the original DEA analysis we had some estimate of how much we could reduce costs and keep the same level of production. But with a scale efficiency analysis, how much production should expect to keep up given the reduction in the size? Should we expect a proportional reduction in production as well? If so, what is the advantage of downsizing?

Finally, there is the somewhat more confusing case (whose interpretation may help me to make sense of all this) where a firm is judged to be maximally input efficient (i.e. is assigned a score of 1 by the DEA) but is not scale efficient. What is the practical response to this case?

Cross posted at Cross Validated: https://stats.stackexchange.com/questions/144554/how-to-interpret-scale-efficiency-in-dea


texts: "The citizens know their own utility functions better than the politicians"

texts:
In informal discussions about public policy, I often hear the claim that the government should not intervene in a certain way, because the citizens know what is good for them better than the politicians. As an example, a discussion about a public housing program can proceed like this:

  Supporter: The government should help the poor by giving them apartments for a low rent.

  Opposer: It is better to help the poor by just giving them cash. For a fixed government expense, giving cash is better than giving apartments, since the poor can use the cash  either for renting apartments or for buying other things that are more important for them.

  Supporter: But if you give them cash, they might waste all the money on alcohol or gambling and will remain homeless.

  Opposer: A citizen knows what's best for him/her better than the politicians. If a citizen decides that the best way to use the money is buying alcohol or gambling, then this provides the highest increase in utility, and thus it is the best way to help him/her.

There are many things to say about this claim, but here I do not ask whether this claim is correct or not - my question is: does such claim appear also in main-stream economic publications? For example, is such claim mentioned in a paper published in a respectable economics journal (in the context of public economics)? If not, is it mentioned in a blog-post by a respectable economist?


texts: Are urban land (location) markets considered competitive even though the market price does not equal marginal cost (zero)?

texts:
Urban land (location) supply is fixed and the marginal cost of bringing an urban plot into production is zero. Even when land owners do not collude to limit the supply, the fixed supply arguably results in the same market power (monopoly rent).
If urban land (locations) could indeed be replicated, wouldn't that imply that demand would move to rent-free land on the edge of civilisation thereby driving the urban land (location) market price to zero? In the absence of the latter doesn’t the presence of rent in the urban land (location) market imply that it is not competitive?


texts: Which foreign workers in USA who send remittances to family are getting the best bang for their buck?

texts:
There are probably a lot of ways to measure that, but I want to measure it like this: Foreign national workers grouped by country of origin, which group sends the most money per capita in remittances?

That way it's kind of like saying they have the most income per capita after living expenses.

Maybe that means the skills they brought to USA are getting the best return compared to other groups.

It doesn't say anything about how far that remitted money goes in the origin country. So bang for buck is referring to getting paid in the US, not spending it abroad.

I'm not sure where to start searching for this information. I googled around but just found ads for remittance companies.


texts: Is the implicit function theorem needed to relate the EMP to UMP?

texts:
My professor says the expenditure function and the indirect utility function are inverses of each other. But how is this possible? Consider each.

$$v:(p_x,p_y,m) \rightarrow \Bbb{R}$$

$$e:(p_x,p_y,\bar{U}) \rightarrow \Bbb{R}$$

These are both mappings from $\Bbb{R^3}\rightarrow \Bbb{R}$. How can one be the inverse of the other?

Only if one was a scalar field and the other a vector field would this work.

My Question:

What is the relationship between the expenditure minimization function and the indirect utility function?


texts:
I am doing an undergraduate course in econometrics where we are using the text Introduction to Econometrics by Dougherty. While going through time series, it was mentioned that one of the necessary assumption to justify OLS, is weakly dependence, which then states that this concept will be covered in more detail in next chapter, which after completing is primarily about stationarity and no mention about weak dependence. I am now wondering if weak dependence and stationarity are similar or related?
In a particular textbook, Introduction to Econometrics by Wooldridge, he states that weak dependence and stationarity are different concepts. While he states that weak dependence is a necessary assumption for OLS, stationarity is not but however needed for the Central Limit Theory to hold. And Wooldridge also defines an integrated process as highly dependent process that can be transformed into weakly dependent. Whereas Dougherty (and Gujarati) links integrated process with stationarity.
Could someone clarify the concepts of stationarity vs weak dependence and how they fit into OLS and also the definition of integrated process.


texts: Show that strict preference ordering is not reflexive

texts: How do i show that the strict preference (>) ordering is not reflexive. I've tried to prove this by asymmetry but I am not sure this is the way to do it. Any help? Thank You.


texts: Questions about the gold standard and exchange rates

texts:
So I'm a total economics noob and I'm trying to understand some of the consequences of using vs. not using a gold standard listed on Brad DeLong's blog here: https://www.bradford-delong.com/why-not-the-gold-standard-talking-points-on-the-likely-consequences-of-re-establishment-of-a-gold-st.html. The first point DeLong mentions is that with a gold standard an economy somewhat loses it's ability to stimulate growth by increasing the money supply. He gives the following example:

  ...in the spring of 1995 the dollar weakened against the yen. Under a gold standard, such a decline in the dollar would not have been allowed: instead the Federal Reserve would have raised interest rates considerably in order to keep the value of the dollar fixed at its gold parity, and a recession would probably have followed.

It's been a while since I've taken Econ 101 so bear with me. I'm trying to work through this example with some simple test numbers to understand whats going on. Say that the U.S. is on the gold standard, and a \$1 bank note can be exchanged at any time for 1 unit of gold. In DeLong's example the dollar weakened against the yen, so let's say the exchange rate between dollar and yen was previously \$1/¥5, and now it's \$1/¥3.

I have a few, potentially silly questions. First, why does the change in exchange rate change the "gold parity" of the dollar? If a \$1 bank note still gets you one unit of gold (since the gold standard ensures it), won't you still be able to get one unit of gold, assuming you only have U.S. dollars? Maybe this assumption is where my confusion lies? My other thought was maybe that if the dollar weakens against the yen, people with yen will be able to get more gold, which may be problematic for the U.S's gold reserves, but how does increasing interest rates address this problem? As I recall, raising interest rates reduces the amount of money circulating in the economy. But again, \$1=1 unit of gold always, so how does this change things? Sorry if this is somewhat incoherent -- any help explaining DeLong's reasoning (ideally in very, very simple terms with not a lot of jargon) would be greatly appreciated. Thanks!


texts:
All the rankings available on the internet are "R&D expenditure by % of GDP".

Is there any ranking of countries based on per-capita expenditure in R&D?


texts: How does an increase in the price of "non-wage-goods" increase employment?

texts:
Keynes (1936, Chapter 2) says that based on the classical theory, "there are only four possible means of increasing employment", the fourth of which is:

  an increase in the price of non-wage-goods compared with, the price of
  wage-goods, associated with a shift in the expenditure of
  non-wage-earners from wage-goods to non-wage-goods.

What does the above quote mean? What are wage-goods and non-wage-goods? And why would an increase in the price of non-wage-goods increase employment?

P.S. Keynes's discussion here is with reference to AC Pigou's Theory of Unemployment (1933), which I can't find online. It seems that Pigou makes a distinction between "wage-goods" and "non-wage-goods". Keynes mentions very briefly that "non-wage-goods" is "Professor Pigou's convenient term for goods upon the price of which the utility of the money-wage depends", but I'm not sure I understand this.


texts: Unique Nash-equilibria in multi-unit auctions with uncertain participation

texts:
Setup
Consider a one shot sealed bid multi-unit auction where $N$ bidders compete for $K$ identical objects and each bidder $i$ has demand $d_i\in \{1,\dots,K\}$. Bidders receive private i.i.d. signals on the value of the objects $v_i^1, \ldots, v_i^{d_i}$. The pricing rule can be either pay-as-bid or uniform price with the clearing price equal the bid of the last accepted bidder.

Assume further that participation is uncertain: Any given player is inactive with positive (but small) probability. Inactivity is independent across bidders and of the signals.

Question(s)
Is there a unique (Bayes-)Nash-equilibrium?
If so, under what conditions (pricing rule, distributions for private values, ...)?

I am looking for literature which either provides an argument for unique equilibria or for an example with multiple equilibria.

I conjecture (based on Ausubel et. al 2014) that one cannot prove uniqueness of equilibria independent of the pricing rule.


texts: Substitute a continuos variable with a categorical one in Linear regression

texts:
I am pretty new to econometrics, and I am thinking about substituting a continuous variable (say assets for a company) with a categorical one containing a number based on which quintile the continuos value was (so 1-5). Obviously doing so I will lose some information however I was hoping that doing so would semplify the interepretation of an interaction variable made of the original continuos variable and of another continuos variable. Especially as I am going to plot a marginsplot (in STATA). I wanted to ear the opinion of someone more experienced and if this is a good/ feasible idea or it will backfire in some way.
Thanks in advance


texts: Improve my solution: Question on solow model

texts:
There is a question about Solow growth and Ramsey model,

  compared to solow model, the Ramsey model is better to explain growth patterns across countries because it predicts a slower convergence rate.

Can we evaluate this statement?

Firstly consider the production function as

$$f(k)=k^{\alpha}$$

For Ramsey model utility function is as:

where rho is discount rate. And it’s lagrangian function can be set up as;

After some calculations, speed of convergence is calculated as

where g is technological growth and n is labor growth.

And for solow model speed of convergence is $$μ_2= (1-\alpha)(\delta + n+ g$$

delta is depreciation rate.
Again I obtain this formula after some calculations,  it I don’t want to show in detail here.

Now assume that we set α=1/3 ρ=4%, n=2% g=1% θ=1 β=2%

Then we get

$μ_1=5.4 $ and $ μ_2=2%$  for delta is zero.

Thus adjustment is quite rapid in this caseof Ramsey model; for comparison, the Solow model with the same values of α, n, and g (and as here, no depreciation) implies an adjustment speed of 2 percent per year. The reason for the difference is that in this example, the saving rate is greater than $ s∗$ when k is less than $k∗$ and less than s∗ when k is greater than $k∗$. In the Solow model, in contrast, s is constant by assumption.

For the evaluation of this statement, I consider such and explanation. But I wonder what you add this explanation? How can I explain more perfectly? Please share your ideas with me. Thanks.


texts: Does control system engineering have a place in economics?

texts:
Do central banks use some form of engineering-style PID control systems/feedback loops to implement monetary policy?

I'm an electrical engineering student taking microeconomics/macroeconomics and a lot of it, at least in terms of government policy to control inflation and interest rates, seems applicable to control systems engineering. However, I can't find a great deal of hard literature about it.

Just as a for instance, one could use PID control to set an output, say inflation rate, to follow a specific course or remain steady given certain inputs, say GDP or interest rates or productivity, and given external disturbances, say Brexit. And even if the controller can't prevent catastrophes altogether, it can dampen the response so that sudden and jerky crashes are smoothed out.

Why or why not does economic policy use established control theory? If it does, what applications can this be seen?

Thanks in advance!


texts: Recursive Models of dynamic linear economics (Hansen / Sargent, 2014) - optimal linear regulator problem / solution of bellman equation p. 34 ff

texts:
The optimal linear regulator problem according to Hansen/Sargent, 2014, Recursive models of dynamic linear economies, on page 34 ff. is stated as follows:
$-E\sum_{t=0}^{\infty}\beta^t[x_t' R x_t+u_t'Qu_t+2u_t'Wx_t],\; 0<\beta<1$
subject to
$x_{t+1}=Ax_t+Bu_t+Cw_{t+1},t\geq 0$
$\{x_t\}_{t\geq 0}$ are state variables,
$\{u_t\}_{t\geq 0}$ are control variables, and
$\{w_t\}_{t\geq 0}$ are stochastic innovations into the system.
The Bellman equation is
$V(x_t)=\text{max}_{u_t}\{-(x_t' R x_t+u_t'Qu_t+2u_t'Wx_t)+\beta E_tV(x_{t+1})\}$
In the text on page 35 we have as a solution
$V(x_t)=-x_t'Px_t-\rho$
with the following expressions after using an iteration model
$P=R+\beta A'PA-(\beta A'PB+W)(Q+\beta B'PB)^{-1}(\beta B'PA+W')$
and
$\rho=\frac{\beta}{1-\beta}\text{trace}\{PCC'\}$
I am looking for an explanation how to derive $V,P,\rho$. Also the decision rule for the control variable
$u_t=-(Q+\beta B'PB)^{-1}(\beta B'PA+W')x_t$
is of interest and requires clarification.


texts: Volume of trade covered by regional trade agreements

texts: Is anyone aware of statistics about the total volume of trade that happens under regional trade agreements (RTAs)? It's easy to find figures for the number of agreements, but not so easy for their cumulative impact.


texts: I am wondering if any one has attempted to describe household expenses as a function of income. I have an idea that the curve should look something like a natural log over a root function. It creates a curve with a hump at the left side and a dip in the middle on to an ever growing tail. Does anyone know of a model that describes such behavior?


texts: Can technical change have a negative growth rate?

texts:
Using the following nested CES function

I have backed out augmentation indices $A_L$ and $A_E$. Where $A_L$ is a labour-augmenting technical change index and $A_E$ is an energy-augmenting technical change index. $Y$ is GDP, $K$, $L$ and $E$ are factors of production.

Implied technical change indices are shown below:

What puzzles me is that the energy-augmenting technical change index $A_E$ is downward sloping (or has a negative growth rate). Usually, one would expect technical change to have a positive trend or at least no trend (no growth). I am now trying to make sense of this result.

One possible explanation I can think of is the presence of energy efficiency rebound effect. As energy-specific technologies are introduced, greater quantities of energy is consumed since the technical progress reduces the price of effective energy. Cheap energy induces greater consumption offsetting the efficiency gains.

I would appreciate your comments and suggestions.


texts: Present value of perpetual rise in income

texts:
If a student successfully completes an MBA program in 2 years, he will earn $50,000 more than what he could earn without the degree for his lifetime. Calculate the present value of this perpetual rise in his income associated with the degree. The rate of interest in the market is 10%.

My attempt:

He will earn \$50,000 more at the end of his 1st year at the job. Let the present value of this increase be $PV_1$.

$\displaystyle 50,000=PV_1\left(1+\frac{10}{100}\right)^3$

The exponent is 3 because he will spend the next 2 years attending the MBA program and be paid at the end of the 3rd year.

$\implies 50,000=PV_1\times(1.1)^3$

$\displaystyle PV_1=\frac{50,0000}{(1.1)^3}$

$\displaystyle PV_2=\frac{50,000}{(1.1)^4}$

and so on.

$\begin{aligned}[t]
PV&=PV_1+PV_2+\ldots \\
&=\frac{50,000}{(1.1)^3}+\frac{50,000}{(1.1)^4}+\ldots \\
&=\frac{50,000}{(1.1)^3}\times\frac{1}{1-\frac{1}{1.1}} \\
&=\frac{50,000}{(1.1)^3}\times\frac{1.1}{0.1} \\
&=\frac{500,000}{(1.1)^2} \\
\end{aligned}$

The answer given by the professor is "PV of lifetime increase in salary is $500,000." Where have I gone wrong?


texts: Syndicated Loans Terminology - Borrower & Sponsor

texts:
I am trying to understand what is the difference between the Borrower and the Sponsor entities in a syndicate loan agreement.

Namely, it looks like quite often, the Borrower entity will be a Company that is getting acquired by the Sponsor entity - what I don't understand is if the Sponsor is acquiring the Company, why isn't the Sponsor borrowing the money?


texts: Is the ECB a lender of last resort for european governments?

texts:
One of the usual functions of a Central Bank is to be the last resort of commercial banks, and governments.

Does the ECB behave in this usual way toward European Governments? What about toward banks? Is the banking union related to this?

Any help would be appreciated.


texts: Does a more even distribution of wealth result in lower taxation?

texts:
A proportion of government spending is associated with welfare. There are also many factors related to poverty that may result in higher government spending (e.g. poor health, crime, etc.).
Does it follow that a society with a more even distribution of wealth would likely require less government spending and hence lower taxation?


texts: Effects of shocking budget or indifference curves on optimum point?

texts: I am supposed to determine if shocking either the income or preferences would certainly change the optimum solution in case of a corner solution?


texts: Index Theorem for Regular Infinite-Agent Economies

texts:
A formulation of the Index theorem states that for a regular economy:
$\sum_{p | z(p) = 0, p_L = 1} index p = +1$
Does this hold for models with uncountably many agents?


texts: How does explanatory variables in variance affect unconditional variance of GARCH(1,1)

texts:
I have a question about the unconditional variance of a GARCH process, where exogenous explanatory variables are included in the variance.
The usual GARCH models the variance using: $$\sigma^2_t=\omega+\alpha\cdot\epsilon_{t-1}^2+\beta\cdot\sigma_{t-1}^2$$
The usual GARCH unconditional variance, without additional explanatory variables, is given by:
$$\sigma^2_=\frac{\omega}{1-\alpha-\beta}$$
My question is, if we include an explanatory variable $x_t$ in the variance equation, how does this change the unconditional variance?
If the model is:
$$\sigma^2=\omega+\alpha\cdot\epsilon_{t-1}^2+\beta\cdot\sigma_{t-1}^2+\phi\cdot x_{t-1}$$
My guess would be that on some day $t$, the unconditional variance would change with the previous days value of $x_t$, so something like:
$$\sigma^2_t=\frac{\omega+\phi\cdot E[x_{t-1}|I_{t-1}]}{1-\alpha-\beta}$$
Hope it makes sence!


texts: which policy (fiscal or monetary) is better to stabilize the cycle?

texts:
I am currently studying for a test and the following sentence "In an open economy with high capital mobility, monetary policy is preferable to fiscal policy to stabilize the cycle", the "answer" is true, but I don´t understand why it is true.

I tried to analyze from the perspective of the Mundell-Fleming model in open economies, but I can't assume which exchange rate is present in the economy.

Thank You


texts: Per capita consumption in the steady state

texts:
Could you please help me with the following question:
Suppose the saving rate is $20$%, population increases $3$% annually, and capital depreciates $3.5$% annually. What is the steady state value of per capita consumption. $\alpha = 0.6$

I want to use this formula but we do not know $A$.

$(1-s)A (sA /n + d)^{1/1-α}$


texts: Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?

texts:
$\succsim$ is a weak order over $\mathbb R^L$.

For a closed budget set $B\subset\mathbb R^L$, define demand correspondence: $$D(B)=\{x\in B|x\succsim y\forall y\in B\}$$.

We know that $D$ is always none empty and both upper and lower hemi-continuous, can we conclude that $\succsim$ is continuous? Can we conclude that $D$ is rationalizable by a utility function?

My approach: For the first question, I guess we can first show that $D$ is rationalizable by a utility function $u$. Secondly, since $D$ is continuous, $u$ must be continuous, and $\succsim$ is continuous. But I doubt this approach will work, because the second step seems not work.

For the second part, if $\succsim$ is continuous then it is represented by a continuous utility function. Even if $\succsim$ is not continous, it must be upper-semi continuous and we can still find a upper semi-continuous utility rationalization for $D$ by Rader theorem.

We could consider a simpler version of the problem: Let the demand function be continuous, is the preference relation also continuous? (This is proved by Mas-Colell in 1978, I think)


texts: How do I change the base year of real GDP using the GDP deflator and nominal GDP?

texts:
I'll use the US as an example. I have three data series

nominal GDP $(Y)$
real GDP in 2005 USD $(\bar{Y})$
the GDP deflator $(d)$, with 2005 as the base year, so $d_{2005} = 100$

I want to change the base year to 2000. Are these calculations accurate? I use the notation $\$_{t}$ for USD in year $t$ prices to help myself keep the units straight.

My goal is $\bar{Y}_{t} \ \$_{2000}$.
\begin{align}
\frac{d_{2000}}{d_{t}} \cdot Y_{t} \ \$_t
&= \frac{Y_{2000} \ \$_{2000}}{\bar{Y}_{2000} \ \$_{2005}} \cdot \frac{\bar{Y}_{t} \ \$_{2005}}{Y_{t} \ \$_{t}} \cdot Y_{t} \ \$_t \\
&= \frac{Y_{2000} \ \$_{2000}}{\bar{Y}_{2000}} \cdot \bar{Y}_{t} \\
&= \bar{Y}_{t} \ \$_{2000} \cdot \frac{Y_{2000}}{\bar{Y}_{2000}}
\end{align}

I think those are all the correct unit cancellations, but now I'm stuck with the unitless quantity $\frac{Y_{2000}}{\bar{Y}_{2000}}$, so I don't know how to complete the conversion.

Am I doing this right?


texts: I'm looking for a book to refresh my macroeconomics and also continue studying the topics that I did not have. My math background is solid. Can anyone suggest a macro book that takes it from the beginning to advanced and covers hopefully most macroeconomics? if there is no such a book and a few books should be read, please also let me know your suggestions.


texts: Gap between BOP and macroeconomic terminologies (In my opinion)

texts:
I have not studied BOP well, but as far as i can understand, there is a mismatch between BOP and macroeconomics terminologies. In BOP we say that capital outflow (inflow) occures when finacial account is greater (smaller) than zero i.e. increase in residents abroad assets is greater (smaller) than increase in liabilities to non-residents. On the other hand, in macro (for example in IS-LM-BP) we say that we have capital outflow when bank deposits denominated in domestic currency moves abroad conducted by exchange of domestic curency in case of decrease of monetary policy rate.
Imagine now that for example that we have BOP for US made in euros and:

US exporter has sold some goods for 100 EU bank deposit in European bank;
US importer has bought some goods in exchange for dollar deposit in US bank valued as 22\$ (or 20 euro by current exchange rate);
In that case our BOP is:

Imagine now that afterwards some EU company decided to sell 22$ deposit in US bank for euros. In that case our US liabilities decrease and assets also does so since we need to exchange dollars for euro. Our BOP is now:

In terms of BOP we have no increase in capital outflow since our FA is still equal to 80. But in terms of IS-LM-BP we have capital outflow. Because Eu company withdrew its assets from our economy. Can you please tell me where is my mistake. Thanks in advance.

Edit: Thank you for your comment. I opened a Mankiw 7th edition textbook to read, what he calls a capital inflow and outflow. On page 123 Mankiw wrote:

the flow of capital can
also take the form of foreigners buying domestic assets, such as when a citizen of
Germany buys stock from an American on the New York Stock Exchange.

If i understood the idea of Mankiw correctly, he means that if German citizen firstly buy 10 dollars for euros and then exchange this 10 dollars for a stock, then there will be capital inflow. But again, in terms of BOP purchase of dollars for euro will simultaneously increase the liabilities of our country to non-residents (since we gave 10 dollars to non-resident) and increase our abroad assets (by some amount of euro which are liabilities of EU CB (if we talk about cash) and hence abroad assets of residents). This is why our Financial Account will be unchanged while there will be capital inflow in terminology of Mankiw. This is what i cannot understand pretty hard.


texts:
$u(x,y) = min(2x,y)+ y?$

I don't understand how we can plot it. I know that there's going to be minimum so I am familiar with the cusp shape of perfect complements. But this looks like a quasilinear utility function. So how can I systematically plot it?


texts: Book recommendations on empirical methods in economic research and econometrics?

texts:
This question is more so geared toward anyone with research experience within economics, though of course, anyone is welcome to respond.

I'm an undergraduate math major with a minor in economics. I'd like to know which textbooks are decent for introducing one to research methods in economics? Graduate level is fine, perhaps even preferred. If a student was to take his research to "the next level" (publishing worthy), which textbooks would provide the rigor and insight to develop said research?

Also, any introductory recommendations for econometrics?

Thank you in advance.

ANNENDUM:
From the limit experience I have in economics, I've found the following areas to fascinate me on multiple occasions (in no particular order):

Game theory
Macroeconomics (monetary policy)
Microeconomics (i.e., commodity pricing)
Pricing theory


texts: Using Propensity Score Matching to evaluate non randomized and fully implemented village fund program

texts:
So i want to make a research about the impact of this program to community empowerment and infrastructure in villages. But the problem is the program itself (at the first year) implemented to almost all villages across countries. So can i use propensity score matching to evaluate this program?

So i have the data of villages level in 2014 (before the program is implemented) and villages level data in 2018 (after the program is implemented). Can i combine the data into cross-sectional and find the matching?

Thank you everyone:)


texts: Is conditional mean independence, $E(e_i | x_i)=0$, a different assumption from $E(x e) = 0$? (from Hansen)

texts:
This question comes out of Hansen's Econometrics ((https://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf))

In section 2.18, we only impose the assumptions of finite variance and $Q_{xx}$ being positive definite, and then derive the linear projection coefficient $\beta = E(\textbf{x} \textbf{x}^\prime)^{-1} E(\textbf{x} y)$ as the minimizer of the expected squared error of the linear projection model $y = \textbf{x}^\prime {\beta} + e$. This leads to the implication (NOT the assumption) that $E(\textbf{x} e) = \textbf{0}$.

Then in section 4.4, under assumption 4.2, we have: $E(e_i | \textbf{x}_i)=0$.

My question is: is $E(e_i | \textbf{x}_i)=0$ a newly-imposed assumption in chapter 4? Or is it equivalent to the condition $E(\textbf{x} e) = \textbf{0}$ which we reached in chapter 2, not by assumption but by implication?

I know that $E(\textbf{x} e) = E(E(\textbf{x} e|\textbf{x})) = E(\textbf{x} E(e|\textbf{x}))$
 (by law of iterated expectations and conditioning theorem, respectively), so imposing the assumption that $E(e|\textbf{x}) = \textbf{0}$ yields the implication that $E(\textbf{x} e) = \textbf{0}$. But is the reverse true? Does $E(e_i | \textbf{x}_i)=0$ follow from $E(\textbf{x} e) = \textbf{0}$, or is $E(e_i | \textbf{x}_i)=0$ a new assumption that we're imposing?


texts: Is there a formal definition of opportunity costs, economic costs, and/or economic profits?

texts:
[Edited to remove a mistake in a definition and some typos.]
According to various econ textbooks (e.g. this one), there is a fundamental distinction between economic profit and accounting profit:
(i) While accounting profit subtracts only explicit costs (out-of-pocket costs) from revenue,
(ii) economic profit subtracts opportunity costs, also known as economic costs, which consist of explicit and implicit costs. Here,
(iii) opportunity costs are generally defined as the "value of the best foregone alternative". In the context of firms, "value" of course means profits.
(iv) Furthermore, when economists talk about "costs" and "profits", they always mean economic costs and economic profits. For example, firms are assumed to maximize economic profits.
All the definitions I found were verbal and informal as above. Is there a formal definition of these concepts? Do they make sense at all? Since I didn't find anything in the literature (by a quick search, admittedly), I tried to formalize it myself for the firm context:
Let $X$ be a set of alternatives the firm can choose from, and let $z\in X$. Let's assume that alternative $z$ yields revenue $r(z)$ and generates explicit costs $c_e(z)$ for the firm. Accounting profit $\pi_a(z)$ is defined as revenue minus explicit costs, so $\pi_a(z)=r(z)-c_e(z)$. Economic profit $\pi_e(z)$ is then defined as accounting profit minus implicit costs $c_i(z)$, thus $\pi_e(z)=\pi_a(z)-c_i(z)=r(z)-(c_e(z)+c_i(z))=r(z)-c_o(z)$.
Opportunity costs of choosing $z$ are the value of the best foregone alternative, so $c_o(z)=\max_{k\in X,\,k\ne z}\pi(k)$.
Now, what is the "profit" $\pi(k)$ here? Economic profit or accounting profit? This might not be immediately obvious. Let's have a closer look.
Finite sets of alternatives
Assume for simplicity that there are only two alternatives, $X=\{x,y\}$, with $r(x)>r(y)$.
(i) Let's try economic profits, so $\pi(k):=\pi_e(k)$:
Then $c_o(x)=\pi_e(y)$ and $c_o(y)=\pi_e(x)$.
Therefore $\pi_e(x)=r(x)-c_o(x)=r(x)-\pi_e(y)$. Now, analogously, $\pi_e(y)=r(y)-c_o(y)=r(y)-\pi_e(x)$. Substituting, $\pi_e(x)=r(x)-r(y)+\pi_e(x)$, implying $r(x)=r(y)$. This is a contradiction, so this approach makes no sense.
(ii) Let's interpret "profit" as accounting profit, i.e. $\pi(k):=\pi_a(k)$.
Then $c_o(x)=\pi_a(y)$ and $c_o(y)=\pi_a(x)$, so $\pi_e(x)=r(x)-c_o(x)=r(x)-\pi_a(y)=r(x)-r(y)+c_e(y)$. Similarily, $\pi_e(y)=r(y)-c_o(y)=r(y)-\pi_a(x)=r(y)-r(x)+c_e(x)$. This is at least not contradictory.
Infinite sets of alternatives
But there are rarely only two alternatives. Consider instead a standard quantity-setting monopolist. The set of alternatives is the set of quantity choices, so $X=\mathbb R^+$. Let's denote by $q^*$ the firm's optimal choice. Then the firm accrues accounting profits denoted by $\pi_a(q^*)=r(q^*)-c_e(q^*)$, where both $r$ and $c_e$ (and therefore $\pi_a$) are assumed to be continuous. What is the firm's economic profit $\pi_e(q^*)$ then?
Well, the firm's "(accounting) profit from it's best foregone alternative" is the accounting profit resulting from the smallest strictly positive deviation from $q^*$, which, unfortunately, doesn't exist. To the rescue, let's interpret the "(accounting) profit from the best foregone alternative" as the supremum (instead of the maximum) of the foregone accounting profits: $c_o(q^*)=\sup_{k\in X,\,k\ne q^*}\pi_a(k)$. This, however, is just $\pi_a(q^*)$. Then $\pi_e(q^*)=r(q^*)-\pi_a(q^*)=c_e(q^*)$.
Economic profit of a profit-maximizing monopolist being equal to its out-of-pocket costs? This seems not to make sense.
So do the concepts of economic profit and opportunity costs as defined in (i)-(iv) make sense at all? Or which of (i)-(iv) above is wrong? Or is the "value" of the best foregone alternative in the context of firm decisions neither economic nor accounting profit of the best foregone alternative? What else?


texts:
This is an asset pricing question. What is the difference between conditional and unconditional risk premia? Here's the context:

  The fact that carry trade strategies typically earn positive average returns
  is a manifestation of the failure of the uncovered interest parity (UIP) hypothesis, a major longstanding puzzle in international finance. A longstanding consensus in the international finance literature attributed all of carry trade average returns to conditional risk premia, finding little evidence of nonzero unconditional risk premia on individual currencies throughoutmost ofthe 20th century (e.g., Lewis (1995)) Consequently, much of the literature has focused on explaining conditional currency risk premia by ruling out asymmetries (e.g., Verdelhan (2010), Bansal and Shaliastovich (2012), Colacito and Croce (2013)). However, Lustig, Roussanov, and Verdelhan (2011) show that unconditional currency risk premia are, in fact, substantial and Hassan and Mano (2014) further argue that they drive the bulk of carry trade profits.

Some explanation, and / or a reference would be greatly helpful.


texts:
The question I'm dealing with is:

  Suppose A plays bf, Which of B's strategies would lead to an outcome that is not pareto efficient?

The answer is apparently ei as $(bf,ei)=(0,5)$, but I don't understand why. If this answer is correct, could you please explain why?

My understanding of pareto efficiency is that by moving from $(x,y)$, we cannot make any player better off without making the other worse off. If this is the case, then $(x,y)$ is pareto efficient.

$(x,y)$ would be pareto inefficient if there exists a movement away from $(x,y)$, where a player can be made better off without the other being made worse off.

From $(bf,ei)=(0,5)$, we can move to:

$(4,4), (5,0),(2,2)$

I don't see how we can move to any of these without making B worse off, I think that $(bf,ei)$ represents a pareto efficient outcome.

Any chance you could offer some advice?

Thanks.


texts: What are the acronyms for? SA, WDA, NSA. I was able to find WDA: written down allowance, but I am not sure is correct and how is applicable to GDP.


texts:
It is very likely that Banks have more loans that have been repaid compared to loans that have not been repaid. Otherwise the bank would lose money instead of money. (otherwise the bank will go bankrupt)

Are there statistics (research papers with references) about this?
(Can be of any country or individual bank etc.)


texts: A country borrowing from the rest of the world

texts:
Well I'm having a some difficulty in understanding completely what the following sentence means and I would like to be sure.

«(...) a country running a trade deficit is buying more from the rest of the world than it is selling to the rest of the world. In order to pay for the difference between what it buys and what it sells, the country must borrow from the rest of the world. It borrows by making it attractive for foreign financial investors to increase their holdings of domestic assets- in effect, to lend to the country.»

How does this borrowing(in italic) work? I'm not understanding the italic part. Does the country A sells bonds in domestic currency, receives foreign currency, when the foreign investor buys the domestic currency of A to buy the domestic bond of A?

Also why should the current account plus the capital account be equal to zero (up to a statistical discrepancy)?


texts: Difference between the minimum selling price and the actual selling price

texts:
I'm actually wondering what the correct name for the difference between the minimum selling price and the actual selling price is?

Let's say I'm having an product A. After all calculations(costs, planned profit, possible discounts,...) I can sell my product for 7€(my minimum selling price). On the market I can offer it for 10€. In this case im making an extra margin of 3€.

That means: extra Margin(3€) = actual Selling price(10€) - minimum selling price(7€)

Now I'm wondering what the correct name of this extra margin(3€) is?

I already thought it could be the contribution margin, but isn't this something different?


texts:
My knowledge of economics is quite limited, but as far as I understand, the "added value" which is taxed by value-added tax refers to the difference in the cost of production and the cost in the store. Since the product has to be processed, packaged, transported etc. the cost will rise because every person in this chain wants a bit of money for themselves. The government then taxes this added value. Correct?

If this is true, then why is there VAT on services? Most of the services are "supplied" directly to the customer. For example, if a hairdresser cuts your hair, there were no intermediate persons in this process and the cost of the hair cutting service didn't rise because of them. If you're a web designer, you make a website and provide it directly to the customer - it doesn't have to be transported etc.

Basically, why would someone have to pay value-added tax if there is no added value?

(This also goes for all goods that are sold directly to the customer - but unlike services, goods can be passed on (the customer can sell the good that he has bought) whereas services can't, so I think that most services should be exempt from VAT).


texts: Concept of return on investment but for the state instead a firm

texts:
So, following a discussion I had today, I have the following question.

If we use the return on investment (ROI) to describe the gain of an investment is there a similar concept not for a company but the state as whole.

The idea is the following: if a state 'invests' (is this the correct word in the sense of a state?!) in infrastructure, education, healthcare, there is a 'return' on the spent money. For example, return on infrastructure would be companies using faster internet or streets to be more efficient, making more money, in the last run paying more taxes, money spent for education would give educated people earning more money, paying more taxes; and finally, healthcare would lead to more people paying longer taxes. I think you get the idea.

Unfortunately I am no economist and do not really know where or how to look, whether such a concept exists.

Thank you and appreciate your answers.


texts: Pricing a negative externality under high uncertainty and severe non-linearity

texts:
Take a negative externality such as excess greenhouse gas emissions.

We know some awkward things about the economic cost of this externality:

There is fairly large uncertainty about the timing of damage associated with a unit of emissions. And about the scale of economic consequences of that damage.

Furthermore, there are significant non-linearities: if the world were to emit just one more tonne of CO2, the unit cost of damage is tiny. If we hit a trillion tonnes total emitted, then we're looking at costs that start to hit percents of global GDP. If we burn most of our remaining fossil fuel resources, then we're looking at damage potentially of the order of tens of percent of global GDP, and potentially threatening the existence of human civilisation as we know it.

Normally, a pigouvian tax or similar would have a unit price that represented the cost of damage: here, the uncertainty means that there would need to be some sort of option pricing within that. But also, it is typically a fixed unit price, which cannot be efficient if the damage costs are highly non-linear. What sort of correction to market pricing could take account both of the uncertainties, and the non-linearities?

I've tagged with pigouvian-taxes, but that's just one possible instrument, so I'll add coasian-bargaining too (though my own hunch is that Pigou, rather than Coase, holds the answer here - YMMV)


texts: Most important but untested theories in economics?

texts:
In the opinion of the economists here, what are some of the more important theories in economics that remain untested? By untested I mean theories that, though perhaps evaluated using empirical data, have not been tested in a laboratory setting.

This interests me because of experimentalists track record with fundamentally altering how the field views certain theories. The most obvious example of tested theories are expected utility theory and the convergence of double auction markets with no restrictions.

What theories do you think the field should eventually test and why?

examples:

monetary policy experiments:

https://www.macroeconomics.tu-berlin.de/fileadmin/fg124/heinemann/publications/CHsurvey-2014-08-25.pdf

macroeconomic experiments:

http://www.socsci.uci.edu/~duffy/papers/expmacro2.pdf


texts: Methodology of Economics: interpretation and explanation

texts:
I am interested in understanding the interaction between interpretation and explanation in social sciences in general and in economics particularly.

It is argued that interpretation is pervasive in all methodologies, even in physical sciences. However, as I understand, interpretation cannot escape subjectivity: the interpretation must reflect knowledge and understanding of the interpreter. For example, some interpret recessions as crucial parts of the business cycle, but other interpret it in other ways.

Yet, we tend to be interested more in what causes the phenomenon, or finding the explanation of it.

My question is:

How can we think of interpretation and explanation in economics?
What is the relation between the two?  (I have senses that they can't go without the other, but are there any sources of reading in this topic?)


texts: Why is macroeconomics studied through "Shocks"?

texts:
"Why is modern macroeconomics all about identifying this shock and that shock?"

Coming from a theoretical econometrics background, I have recently delved into empirical macro literature. I am a bit confused about the meaning and significance of the notion of shock. Why we are trying to see the macro-world through the lens of shocks? What is the nature of these shocks that gives them this much explanatory power?

The only explanation I could come up with is that this obsession with shocks is a result of trying to fit macro problems into the framework of Wold decomposition theorem. Any covariance stationary process can be decomposed into a deterministic part and an $MA(\infty)$ part. The deterministic part fits well with the idea of steady-state of the endogenous variables, while the stochastic part gives rise to the idea of seeing the macro variables fluctuation as a result of MA shocks.

What is confusing to me is that it seems macroeconomists are trying to find "real" meaning for this merely-statistical notion of shock. The impulse response function of tax shock, government expenditure shock, etc., are how they see the world.

What am I missing?


texts: Where to find a list of U.S. policy changes for causal studies?

texts:
I'm currently trying to figure how the topic of my paper, which is supposed to be related to policy evaluation (causal inference). I thought it would be great if I could first obtain a list of recent U.S. policy changes, and then decide what exact policy I would like to dive in.
If you are familiar with this field, would you please recommend to me some sources / lists for U.S. policy changes?


texts: Cobb–Douglas utility maximized by spending a "fixed fraction of income on each good"?

texts:
Consider a Cobb–Douglas utility function having the form
$$u(x) = \prod_{j=1}^n x_j^{a_j} $$
where $x$ is an allocation vector and $a_j$ are utility parameters with $\sum a_j = 1$. My question has to do with the demand of a buyer with a Cobb–Douglas utility function and fixed prices budget. That is, $$\arg \max_x \lbrace u(x) : \pi^T x \leq w \rbrace$$
where $\pi$ is a fixed price vector and $w$ is the budget.
This is easy to solve, but I am confused by the following claim, which I read in an optimization textbook [1]:

It is not difficult to show that a trader with a Cobb–Douglas utility function spends a fixed fraction of her income on each good.

This is clearly true when $a_j = 1/n, \forall j$ and the prices are the same.
But suppose $n = 2$, $\pi = (1, 1)$, $w = 1$, and $a = 0.8, 0.2$. Then "spending a fixed fraction of the budget on each good" would mean spending $w / n = 0.5$ on each good, or buying $0.5$ units of each good, implying $x^* = (0.5, 0.5)$. This is clearly suboptimal, as the following table of values shows:
 x_1  x_2  u(x)
 0.0  1.0  0.0
 0.1  0.9  0.155185
 0.2  0.8  0.263902
 0.3  0.7  0.355399
 0.4  0.6  0.433789
 0.5  0.5  0.5
 0.6  0.4  0.553265
 0.7  0.3  0.590885
 0.8  0.2  0.606287   (*)
 0.9  0.1  0.579955
 1.0  0.0  0.0

Instead, the maximum is at $x = (0.8, 0.2)$, which I would describe verbally as

A trader with a Cobb–Douglas utility function allocates each good in proportion to its utility per unit cost.

In this example, resource 1 yields $a_1 / \pi_1 = 0.8$ utils per dollar, resource 2 yields $0.2$ utils per dollar, and the optimal allocation is a scalar times $(0.8, 0.2)$.
Is my interpretation correct? Is the textbook's interpretation quoted above correct? If both are correct, what explains the discrepancy in the example above?
Please note that I am not asking how to compute the demand of a trader with a Cobb–Douglas utility function. I am asking about the specific claim that the trader spends a "fixed fraction of her income" on each product.

[1] Nisan, Noam, Tim Roughgarden, Éva Tardos, and Vijay V. Vazirani, eds. 2007.
Algorithmic Game Theory. Cambridge University Press.


texts:
i am currently working on a paper on demand curves for stocks and have some questions.
I've read that many models (CAPM, APT, Modigliani-Miller theorem) assume demand curves for stocks to be flat. Can you tell me why?
Now research suggests that they actually slope down. Why is this relevant and what implications does this have?


texts: World bank data - GDP per capita current US\$ vs constant 2005 US\$

texts:
I'm looking at two charts from world bank on GDP per capita for Croatia and Russia - and this is what I get:

Now, from what I gathered, the first chart should represent nominal gdp and the second one real gdp (in 2005 US$).

Shouldn't the charts look similar, only with different absolute values? I thought that, for example, you could get 2014 real values simply by adjusting nominal values for total inflation between 2005 and 2014. If that inflation was 25%, then 2014 real = 2014 nominal / 1.25 (in 2005 US$).

How come that in the first chart GDP per capita is almost the same in 2014, and in the second one Croatia's GDP per capita is more than 50% larger?


texts:
If the Phillipine peso falls in value against the USD by 5% in a year, but the domestic inflation rate in the Phillipines is 10%, compared to 2% in the USA, the nominal exchange rate has fallen (by 5%), but the real exchange rate has risen by 3%.

Could anyone help me explain why "the real exchange rate has risen by 3%."?


texts: I'm trying to understand how a subsidy on a monopoly would affect the deadweight loss. I know a subsidy shifts the marginal cost curve downwards, creating a new equilibrium price (price decreases) and quantity (quantity increases), but my question is if the deadweight loss is going to be bigger than before the subsidy?


texts:
Over and over again reputable economists and pundits like Alan Greenspan tell us that the 0% interest rates are "unsustainable", yet they are sustained.

How can interest rates be so low? Throughout all of history I could only find interest rates down to 3%, never lower, yet now we have 0% or even negative interest rates. How is this possible?


texts: Income and substitution effect for perfect substitutes

texts:
I was recently asked about what the income and substitution effects are for perfect substitutes are. Given the rather peicewise nature of the demands for each good in a utility function considering perfect substitutes I'm not sure what the answer is.

That being said, what are the income and substitution effects for a utility function considering goods that are perfect substitutes?


texts: Constant to the power of t in steady state

texts:
I am wondering how to get the steady-state for the following Euler equation. I know that we can get rid of time in subscripts. However, here I have a constant (a) to the power of $t$. Does anyone know if there is a way to get rid of $t$ in power? Or can I just consider $a^t$ a new constant, say $\bar{a}$?
$$ \frac{1}{c_{t}}=a^t \beta E_t \Big[(1+r_{t+1})\dfrac{1}{c_{t+1}}\Big] $$


texts: When a support function is found to be more profitable than the primary business

texts:
Sometimes in the course of pursuing its primary business, a company discovers an unexpected source of revenue.  It is particularly interesting in cases when a humble support function is found to be more profitable than the final product or service.

For example, I was reading about a company which set up an aluminum smelter in a developing country.  Aluminum smelters require a lot of electricity, and since the power supply in this country was unreliable, they also had to build their own mini power station.

They soon realized that the power they could generate from their power station was more valuable than the aluminum they could produce, so they shut down their aluminum smelter and made money from selling power!

Are there other examples of this?  Is there a name for this, other than listening to the market and being responsive?  (I don't like the word "pivot" because that has the connotation of what entrepreneurs and startups do when their effort has failed and they're trying to put a brave face on it.)

I am looking for more examples of joyful serendipity in business.


texts:
I have studied some Marxian economics, and realise that Marx's writings were not very mathematical. I recently came to know of Analytical Marxism and Neo-Marxian economics. I read the Wikipedia page on the Feldman- Mahalanobis model and also a short article by Samuelson.

What are some good books or other resources to study mathematical models based on Marxian economics, say, that were developed in Analytical Marxism or Neo-Marxian Economics or any other field?


texts: Compound interest ($r$ in terms of $\frac{dA}{dt}$)

texts:
Suppose the amount of money in bank account that is compounded annually is given by $A(t)$. The annual rate of interest is $r$. Find a relation between $\displaystyle\frac{dA}{dt}$ and $r$.

My attempt:

$A(t)=A(0)(1+r)^t$

$\displaystyle\frac{dA}{dt}=A(0)(1+r)^t\ln (1+r)$

Dividing, we get

$\displaystyle\frac{1}{A}\frac{dA}{dt}=\ln(1+r)$

However, I think the answer should be $\displaystyle r=\frac{1}{A}\frac{dA}{dt}$.

What am I doing wrong?


texts: Swanson and Williams (2014): restricting based period response to one

texts:
I would like to replicate the results as in Swanson and Williams (AER 2014): "Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates"
https://www.aeaweb.org/articles?id=10.1257/aer.104.10.3154.
However, I don't understand their specification for equation (9) (p. 11)
$\Delta y_{t} = \gamma^{\tau_{i}}+ \delta^{\tau_{i}}\boldsymbol \beta \boldsymbol X_{t}+\varepsilon_{t}$ in the paper. "Where $\gamma^{\tau_{i}}$ and $ \delta^{\tau_{i}}$ are scalars that are allowed to take on different
values in each calendar year $i$". $t$ indexex days and $\Delta y_{t}$ is the chagne in yield, $\boldsymbol X_{t}$ is a set of macroeconomin data surprise. They wrote

"We normalize the $\delta^{\tau_{i}}$ so that they have an average value of unity from 1990–2000, ..."

What chould they mean that the coefficients have an average value of one? Could it mean simply set $\delta^{\tau_{1990}} = 1$, $\delta^{\tau_{1991}} = 1$ ... $\delta^{\tau_{2000}} = 1$?
They have also posted their MATLAB code on the (bottom of the) website. But I still don't fully understand the specification. Would be nice if someone can help me out here.


texts: What would happen if central banks were no longer able to provide loans

texts: Actually I'm asking because of two reasons.  I'm still not clear how everything works.  First money is supposedly a debt, and it is created by creating loans?  Second central banks seem to want countries to take on huge loans.  Based on these two points (assuming they are true)  If they stopped providing loans or had no one left to provide huge loans to - what would happen to certain aspects of the economy like inflation, employment, etc. What would happen to the banks?


texts: What happens if you cannot lend more than what you have?

texts:
This is hypothetical but what would happen if you cannot lend more money than you have? Say you have £100, the maximum you can lend is £100. But somehow you lend £200 to Joe, and Joe spends all of it on chocolate and eats it all, but doesn't pay you back. So have you effectively just created an extra £100 out of thin air and inserted it into the money supply? Is this what banks are doing when they lend out more money than they actually have? What if we abolished this ability, what would happen? (just a guy interested in economics so apologies for my ignorance).

Thanks!


texts: maximization program with a discount factor in monopoly with learning by doing

texts:
I would know something about the multiproduct monopoly. In the case with independent demands and costs dependents, it is in the case with only 1 physical good sold out of 2 periods. For example (learning by doing).
$$q_i = D_i(p_i); C_1(q_1); C_2(q_1,q2)$$
with $$\frac{\partial C_2}{\partial q_1} < 0$$
I want to write the maximization program assuming that there is a discount factor d.   But I have no idea how I can do it
Thanks in advance.
So I did it for the moment, but I'm not sure at all
$$p_1D_1(p_1)-C_1(D_1(p_1))+\delta[p_2D_2(p_2)-C_2(D_2(p_2),D_1(p_1))]$$


texts: Request of references regarding Friedman's Nobel Prize

texts: I've been trying to find the work for which Friedman was awarded the Nobel prize in economics. Does anybody know what was he awarded the prize for and where can you read the original paper?


texts:
China imports $14B of soybeans from the US annually.  In response to US Tariffs, China has put Tariffs on US soybeans and is switching to Brazil for their beans.

In the long term and based on history, can one expect that Brazil will retain China's business after the tariffs are sorted out between the US and China? Or is their some economic force (price?) that would shift the soybean market back from Brazil to US farmers/


texts: Why is macroeconomics about general equilibrium?

texts:
In a fairly popular paper published a couple of years ago ("On the future of macroeconomic models"), Blanchard (2018) makes the following statement, among other "widely believed propositions":

  (i) Macroeconomics is about general equilibrium.

Unfortunately, no note or reference is given for this statement.

Is this statement true? How can it be formally proven? What is the intuition behind it?