Two-way clustering in Stata I have a panel dataset and I would like to estimate a linear equation in a fixed effects framework. My question is: how should I implement a two-way clustering? Stata syntax and/or .ado file necessary would be greatly appreciated.

Have you seen http://faculty.econ.ucdavis.edu/faculty/dlmiller/statafiles/ ?

I see some entries there such as Multi-way clustering with OLS and Code for “Robust inference with Multi-way Clustering”.

EDIT: At least we can calculate the two-way clustered covariance matrix (note the nonest option), I think, though I can't verify it for now. See the following.

set more off
clear all
local n 50
local T 50

set obs `=`n'*`T''

gen id = floor((_n-1)/`T')+1
by id, sort: gen year = 1970+_n
xtset id year

set seed 1

gen x = rnormal()
gen y = 1+0.5*x+rnormal()

xtreg y x, re vce(cl id)
mat b = e(b)
mat V1 = e(V)
xtreg y x, re vce(cl year) nonest
mat V2 = e(V)
xtreg y x, re vce(cl id year) nonest
mat V12 = e(V)
mat V = V1+V2-V12
mat l V
ereturn post b V
ereturn display

set more on

This code has yet to be verified manually.

EDIT 2: Sorry for keeping editing. Just found that Stata's reg (for pooled OLS) does not allow for clustering by multiple variables such as vce(cluster id year). We should use vce(r) or just r. However, it seems that xtreg does (usually requiring nonest), though I counldn't find documentation.


Does constant money supply hinder economy? Consider an hypothetical isolated economy (an island) where:

the only form of money is Coins
the amount of Coins is constant
the Coins are never lost or destroyed

In that scenario:

can the economy grow smoothly (e.g. produce more goods, produce at lower prices, develop new goods, etc.)?
or does the Government of the island need to increase/decrease the amount of Coins from time to time, to ease the economic growth?

I suspect the second is true but the mechanisms are not clear to me. Help!

The second is true. The reason why the second is true are macroeconomic friction and the fact that constant money supply in presence of growth would lead to monetary instability.

The mechanism works as follows; If you fix money supply and your economy grows you will get deflation as you can see from the standard monetary equation $MV=PY$ where $M$ is money supply, $V$ velocity of money, $P$ aggregate prices and $Y$ output. Since the M is fixed by assumption and V does not usually change much, any economic growth (increase in Y) must be accompanied by deflation (decrease in P).

Now depending on how high the deflation is this would be bad in itself. Even if there would be no macroeconomic frictions deflation similarly to inflation is form of price instability and even frictionless economy would be able to handle only little bit of it. In presence of deflation people will unnecessary hoard money instead of actually using it in the economy, it redistributes wealth from debtors to creditors and so on. Hence, even in completely frictionless world it could be proven that the optimal monetary policy should be such that change in aggregate prices is exactly 0.

However, unfortunately we are not living in frictionless economy. In real life there are sources of frictions which make deflation dangerous. There are several of them but to keep this concise I will focus only one of the biggest one sticky wages.

Sticky wages mean that companies cannot change their wage costs in short run. This is because usually contracts have fixed wage and to change them you need to renegotiate them. If wages are sticky in presence of deflation firms that can’t decrease their wages quickly enough (and workers usually oppose pay decreases - even nominal ones very hard) will see their labor costs significantly increasing forcing them to unnecessary lay off workers thereby creating  unemployment that is higher then socially optimal. Unnecessarily high unemployment has its toll on economic growth especially when it leads to some people being permanently unemployed. Due to sticky wages and other frictions economists are usually quite vary of deflation and hence predominant mainstream view is that countries should run inflation of about 2% on average, by growing their money supply in ways that achieves that target.

An example that shows that deflation can really have serious bite is the Great Depression. As famously proven by none other than Milton Friedman and Anna Schwartz in their monetary history of US, Great Depression at the beginning seemed like a relatively mild recession, however the recession lead to contraction in money supply due to bank failures and consequently to high deflation. Instead of doing anything about it Fed was completely passive, and what according to Friedman and Schwartz could be short recession became the worst US recession in recorded history (excluding maybe the current covid recession which might beat it) and this was mainly due to extreme deflationary pressure that lead to excessive unemployment and exacerbated the negative demand shock.


Why is the rouble collapsing? What are the reasons why the rouble (RUB) is collapsing? Which one is the main one?

The primary source of the recent ruble collapse has almost certainly been the falling international oil price, aggravated by some other features of Russian politics and its economy.

Petroleum products account for over half of Russia's export revenue, and most remaining export revenue comes from other commodities, whose output it cannot easily adjust. When oil prices fall, this lost export revenue must be replaced by some combination of

(1) more (presumably non-oil) exports

(2) fewer imports

(3) a larger net capital inflow.

For the most part, these adjustments will be made in response to an equilbrating decline in Russia's exchange rate. Since Russia's export mix is so commodity-heavy, the short run response of (1) to the exchange rate is very weak; since consumers tend to be sluggish in responding to price changes, (2) is weak in the short run as well. For a modern economy with good access to international capital markets, (3) is the main short-term buffer for shocks like these, but Russia is currently suffering from Western sanctions and was not particularly well-integrated into international capital markets in the first place.

For all these reasons, a very large decline in the exchange rate is needed to induce enough of (1), (2), and (3) to offset the decline in oil export revenue. Meanwhile, skittishness about the political situation in Russia (and its dubious historical record on monetary stability) don't help.

By the way, the dependence of commodity exporters' exchange rates on commodity prices is a staple of international finance; it has even been used to forecast commodity prices.


M2-M1: what's left in the delta? If you subtract M2SL - M1SL, the chart looks as follows:

The change is due to re-classification:
M1 before:

(3) other checkable deposits (OCDs), consisting of negotiable order of withdrawal, or NOW, and automatic transfer service, or ATS, accounts at depository institutions, share draft accounts at credit unions, and demand deposits at thrift institutions.

M1 after:

(3) other liquid deposits, consisting of OCDs and savings deposits (including money market deposit accounts).

M2 before:

(1) savings deposits (including money market deposit accounts);

M2 after:

(1) removed

Essentially savings deposits were moved from M2 to M1. Does it mean that M2 in the US now excludes all deposits regardless of term (e.g. a 10 year deposit or CD)? Is this because low interest rates reduced if not eliminated losses incurred from closing long-term deposits?

No, term deposits aren’t affected, it’s a change reflecting how often transfers can be made from savings accounts, which changed last April.
Per their announcements page:

As announced on December 17, 2020, the Board's Statistical Release H.6, "Money Stock Measures," will recognize savings deposits as a type of transaction account, starting with the publication today. This recognition reflects the Board's action on April 24, 2020, to remove the regulatory distinction between transaction accounts and savings deposits by deleting the six-per-month transfer limit on savings deposits in Regulation D. This change means that savings deposits have had a similar regulatory definition and the same liquidity characteristics as the transaction accounts reported as "Other checkable deposits" on the H.6 statistical release since the change to Regulation D. Consequently, today's H.6 statistical release combines release items "Savings deposits" and "Other checkable deposits" retroactively back to May 2020 and includes the resulting sum, reported as "Other liquid deposits," in the M1 monetary aggregate. This action increases the M1 monetary aggregate significantly while leaving the M2 monetary aggregate unchanged.


What does DOD stand for in this indicator? I was looking at the indicator External debt stocks, total (DOD, current US$) on the worldbank website and I don't understand what DOD stands for.

It stands for "disbursed and outstanding debt", which is explained here, for example.


Is it easier to profit from selling, than buying, options? Reasons 1-3 and 4-6 below look correct. Is the author's conclusion correct though?

To make a profit on the buying side:

You have to be directionally correct. The price must go up for calls, down for puts.
AND the share price move must be bigger than the premium you paid.
AND the share price move must happen before the option expiration.

You will notice that it is pretty unforgiving. Sure, when you are right, you can make a 100% to 1000% profit in a few months, weeks, or even days. But there is a big chance that you will suffer death by thousands of cuts with your long call or put contracts losing value every day and become worthless.
We were discussing earlier how volatile stocks can have a high extrinsic value. What happens to your option price if the share is changing a lot and suddenly calms down? The extrinsic portion of the option price will crater quickly because volatility dropped, and time is still passing every day.
The same way you can buy options, you can also sell call and put options. Instead of buying the right to exercise your ITM calls and puts, you sell that right to a 3rd party (usually market makers).
To make a profit on the selling side:

You have to be directionally correct.
OR the share price does not move as much as the premium.
OR the share price does not move before the option expiration.

Buying calls and puts mean that you need to have strong convictions on the share’s direction. I know that I am not good at predicting the future. However, I do believe in reversion to the mean (especially in this market :)), and I like to be paid as time is passing. In case you didn't guess yet, yes, I mostly sell options, I don’t buy them. This is a different risk, instead of death by a thousand cuts, a single trade can have a big loss, so proper contract sizing is really important.
It is worth noting that because you sold the right of exercise to a 3rd party, they can exercise at any time the option is ITM. When one party exercises, the broker randomly picks one of the option sellers and exercises the contract there. When you are on the receiving end of the exercise, it is called an assignment. As indicated earlier, for most parts, you will not be getting assigned on your short options as long as there is some extrinsic value left (because it is more profitable to sell the option than exercising it). Deep ITM options are more at risk, due to the sometimes inexistent extrinsic value. Also, the options just before the ex-dividend date when the dividend is as bigger than the extrinsic value are at risk, as it is a good way to get the dividend for a smaller cash outlay with little risk.

The logic given in the question is inadequate, since it misses the point that upside potential in long option positions is much higher than the upside potential for a short option position.
If one were buying/selling options at fair value on instruments that followed the random process used to price the options, a long or short position should not have an advantage over the other. The higher chance of a short position being profitable at maturity is offset by lower profits.
However, in the real world, options can be mis-priced, such as under-valuing extreme events. Furthermore, implied volatility is quite often higher than realised, which is equivalent to there being a risk premium. Those real world pricing discrepancies need to be looked at to discuss the relative merits.


Did capitalism exist before the 18th century? Were there capitalistic economies before the 18th century?

According to some yes. In this (historically oriented) view, whatever succeeded feudalism is called capitalism.

Capitalism, broadly accepted as a phase of history, is dominating the last half-a-millennium. It has also become conventional that capitalism itself had various phases and stages. Its antecedents go back to ancient history. Barter and exchange of one thing for another, as Adam Smith, the main advocate and ideologue of market capitalism argued, are a part of human nature. The pockets of private-market economy and its institutions, especially in urban settlements, flourished in medieval Europe. Moneylenders and urban merchants were its main representatives.
Its continuous development, however, began mostly from the sixteenth century. Historiography produced a vast literature on the transition from feudalism to capitalism. These writings maintain that declining productivity, a demographic crisis, and the scarcity of peasant labor generated the lowering of rents, a decrease of labor services, and an increase in peasant mobility and freedom in Western Europe. In most of these countries, consequently, serfdom was gradually loosened and disappeared by the sixteenth century. Commercialization of agriculture played a central role in the development of capitalism. The flourishing textile industry in Britain with an excess production over consumption led to the enlargement of productive capacities in an unheard scale and made England the ‘workshop of the world.’
This stage between the sixteenth and eighteenth centuries is often called ‘commercial capitalism’ in history. The system was based on private ownership of warehouses and ships and buying and selling goods all over the world. The merchants also lent out money at interest and established connections with production. They bought and distributed raw materials for peasants who worked at home in the traditional way (putting-out system), and gradually subordinated the rural cottage industry. It led to a proto-industrialization, the development of a decentralized putting-out system coordinated by merchants, and later the establishment of (nonmechanized) factories, which introduced division of labor in the production procedure.

Quoted from I.T. Berend, "Capitalism" in International Encyclopedia of the Social & Behavioral Sciences, 2001
Alternatively, what he calls "commercial capitalism" is called "merchant capitalism" by others. And as the Wikipedia article linked shows, others (Ellen Meiksins Wood in particular) disagree on whether that was really capitalism.

She argues that commerce is not equivalent to capitalism and does not produce it because 'the dominant principle of trade everywhere was not surplus value derived from production but "profit on alienation", "buying cheap and selling dear" ': that is, although trade involves the seeking of profits, it does not in itself affect how goods are produced. Wood argues that polities which flourished from trade such as medieval Florence and the early-modern Dutch Republic that did not become capitalist are not examples of a 'failed transition', but rather examples of how trade and urbanisation has flourished widely in human history without capitalism developing. She likewise argues that various past societies, such as early modern France, had peasantries with ample opportunity to enter into commercial production, which, however, did not take this opportunity. Thus Wood concludes that capitalism must have arisen from changing imperatives in fundamental relations of production.

Both Berend and Woods have serious Marxist leanings, so even in this relatively narrow camp there's disagreement on when capitalism bagan...
In yet other terms, this is the divergence of views between the "commercialization" vs the "agrarian" model of the emergence of capitalism. It seems to me that the latter is mainly favored by Marxists, while the former has a broader appeal (so Berend is a bit of a heretic among Marxists in this respect.)


What is meant by the abbreviation 'MSV solution', used in the context of DSGE modeling? What is meant by the abbreviation MSV solution, used in the context of adaptive learning in DSGE modeling? E.g. see Bullard and Mitra (2002)

minimum state variable (MSV) solutions it is in full, but what does that mean?

Minimum state variable (MSV) solution is a special technique used to find an unique equilibrium with desirable properties in DSGE models. Often DSGE models can have multiple paths that will satisfy the conditions given by the system you are modelling.

Hence to provide some meaningful results you have to somehow choose between the all possible paths/solutions possible. There are multiple ways how to do that. MSV solution is a solution that helps to avoid sunspot equilibria and bubbles (see McCallum (1999)). In addition huge advantage of this approach as pointed out by McCallum is that  "the MSV criterion is designed to yield a single bubble-free solution by construction." It can be also shown that this kind of method is quite efficient and guaranteed to yield unique solution for wide ranges of models (albeit not all).

As you can see in Bullard and Mitra (2002), they talk about MSV solution when they want to show that there is unique solution that can determine their model coefficients $a,b,c$, so when they talk about MVS solution they are just saying that they applied this approach to select an unique solution this way as opposed to some other one.


Form of security with a potentially infinite amount of equity for a continous payout for game? I'm trying to create a game that's a bit like monopoly. The objective of the game is to earn money by investing money. The game has a limited amount of players and an increasing amount of money each game. That is done through regular stocks with a fixed supply but also through a system that involves buying shares of a revenue stream whose intensity changes through the course of the game.
For the game, its very important that users can buy into that stream at any given time with any given amount of money. It should not be possible to limit access to that revenue stream by simply buying up all shares and then refusing to sell them at any price.
I don't want to get into to much detail about how the game would work, its just important that this revenue stream remains open to all players at any given time for any lump sum.
But that does not mean its always a good idea to invest in it, but it should still be profitable for the players to correctly predict incoming revenue.
The "shares" can be bought directly from the "bank" and traded amongst players (but it would not be a problem if buying directly from the bank would be a better option in every case).
A share in the revenue stream would grant the player a portion of it. The revenue stream should always be divided amongst players as the money comes in (it should never flow to the bank). Also shares cannot be sold back to the bank.
Now since the "bank" would be an autmated system and not an active player in the game, it needs a system to automatically determine the price of the shares. And this is where I am stuck. How can I incentivize players to buy into a portion of something that is reduced over time? One idea that I had was to set the price of shares equal to the amount of shares. That way the shares should always arrive at the ideal equilibrium and people getting in early are rewarded. The problem with this is, that if the revenue stream is expected to go down, almost nobody will buy new shares, essentially cutting them off from buying it.
So can somebody help me create a system like this? A system that

rewards getting early
is always open to new investors
reduces equity as more people buy in

One "natural" approach would be to base the price on the expected discounted revenue stream. Writing $R_t$ as the (random) revenue in period $t$ of one share, this then would be:
$$
p_t = \mathbb{E}\left(\sum_{t = 0}^T \frac{R_t}{(1+r)^t}\right) = \sum_{t = 0}^T \frac{\mathbb{E}(R_t)}{(1+r)^t}.
$$
In addition, you might want to lower this price a bit, especially if the income stream is very volatile and if you would expect that individuals are risk averse.
One thing determine then is the rate $r$. Ideally, this should be set equal to the rate of return of a risk-free asset (if you have this in your game). If the game does not last very long, I guess setting $r = 0$ also makes sense.


Has the assumption that individuals' tastes do not change over time been rigorously challenged? In their seminal paper De Gustibus non est Disputandum, Stigler and Becker (1977) surveyed four classes of phenomena widely believed to be inconsistent with the stability of tastes: addiction, habitual behavior, advertising, and fashions, and in each case offered an alternative explanation.

All these explanations are based on the assumption that individual tastes are stable over time. They compare tastes to the Rocky Mountains: "both are there, will be there next year, too, and are the same to all men.”

Question: I am wondering if the assumption that individual's tastes do not change over time has been rigorously challenged. And how?

Note: I added rigorously because their argument is subtle and very persuasive. For example, the role of experience and addiction can be explained with stable preferences. As a consumer gains experience with a good, it becomes easier to use. Thus the cost of using it goes down as use goes up, resulting in higher marginal profit. As the marginal utility diminishes with usage, equilibrium is reached when the diminishing marginal utility gains match the reduction in cost obtained by increases usage.

Update: I found a nice related survey on Endogenous Preferences by Samuel Bowles.

Stigler and Becker's argument is methodological, not philosophical. They do not try to convince us that preferences are indeed identical across individuals and invariant across time as a matter of reality (the "Rocky Mountains" metaphor is an "as if " approach).

Their point is that any outcome can be rationalized by assuming that "it was preferences that made it so", since "De Gustibus Non Est Disputandum", and also they are unobservable.  But then, we could "explain everything" in this way, and so explain nothing.

Their goal is to defend in terms of useful modelling the other extreme: assume immovable preferences and try to find explanations for the observed outcomes based on observable, quantifiable concepts, like prices. I believe the following passage from the first page of the paper summarizes the approach

  "On the traditional view, an explanation of economic phenomena that reaches a difference in tastes between people or times is the terminus
  of the argument: the problem is abandoned at this point to whoever
  studies and explains tastes (psychologists? anthropologists?
  phrenologists'? sociobiologists?). On our preferred interpretation,
  one never reaches this impasse: the economist continues to search for
  differences in prices or incomes to explain any differences or changes
  in behavior. The choice between these two views of the role of tastes
  in economic theory must ultimately be made on the basis of their
  comparative analytical productivities."

Bold my emphasis.

So the question of the OP appears to be mistargeted: people's tastes may very well change over time, and I don't think that Stigler and Becker would deny that.
The question is, can we arrive at more useful economic models by assuming changing tastes, compared to the models where tastes are fixed (while avoiding the "explain everything and so explain nothing" trap)? But this would be a whole research program, not some rigorous argument in a paper.


When the convexity assumptions fail We constantly assume convexity in economics. Convexity of production sets, convexity of preferences etc.

Is there literature that addresses when convexities fail? For example, is there any literature that addresses the existence of equilibria when agents have non-convex preferences? What are the problems associated with non-convex production sets?

It just seems like GE theorem relies heavily on convexity assumptions and I have yet to hear anyone reasonably addresses how to approach situations in which these assumptions fail.

I would appreciate any good references or any general discussion of non-convexity from both a consumer and a producer perspective.

If you are only looking for references, try google scholar: https://scholar.google.be/scholar?start=0&q=economics+%22without+convexity%22&hl=nl&as_sdt=0,43.

Among the papers on the first pages of results :

Conley, John P., and Simon Wilkie. "The bargaining problem without convexity: extending the egalitarian and Kalai-Smorodinsky solutions." Economics Letters 36.4 (1991): 365-369.
Yamazaki, Akira. "An equilibrium existence theorem without convexity assumptions." Econometrica: Journal of the Econometric Society (1978): 541-555.
Hurwicz, Leonid, and Stanley Reiter. "On the boundedness of the feasible set without convexity assumptions." International Economic Review (1973): 580-586.
Hamano, Tadashi. "On the existence of equilibria without convexity or free disposal on production technologies." Journal of Mathematical Economics 23.6 (1994): 565-583.
Shapley, Lloyd S., and Martin Shubik. The core of an economy with nonconvex preferences. No. RM-3518-PR. RAND CORP SANTA MONICA CA, 1963.

Then look at the papers who cite the above papers. That usually allows you to uncover other relevant references.


What is a good proxy for government quality? Is it ok to use corruption as a proxy for government quality?

Using corruption is part of it but a bit restrictive way to measure government "quality". You may use aggregate indicators as the one developed by the Worldwide Governance Indicators (WGI) project from the World Bank. They reports aggregate and individual governance indicators for over 200 countries and territories over the period 1996–, for six dimensions of governance:

Voice and Accountability
Political Stability and Absence of Violence
Government Effectiveness
Regulatory Quality
Rule of Law
Control of Corruption

What is Governance ?

According to the WGI project Governance consists of the traditions and institutions by which authority in a country is exercised.  This includes the process by which governments are selected, monitored and replaced; the capacity of the government to effectively formulate and implement sound policies; and the respect of citizens and the state for the institutions that govern economic and social interactions among them.


How does interest rate impact exchange rate? When I’m using the forward exchange rate formula based on non-arbitrage theory, it tells me that a positive interest rate spread (i_domestic > i_foreign)would cause the forward exchange rate(units of foreign currency that I get for each 1 unit of domestic currency I pay) to be lower than the spot exchange rate, indicating that a positive domestic-to-foreign interest rate spread would lead to depreciation of the domestic currency.

However, people keep saying that if the domestic Central Bank decides to raise the domestic interest rate, it would make the domestic currency to appreciate as international investors would be more willing to pour their money into the domestic market(selling foreign currency for domestic currency) due to a higher yield. This is saying domestic interest has a positive relationship with the exchange rate(units of foreign currency that I get for each 1 unit of domestic currency I pay).

So I’m confused about how these two different approaches give contradictory results. Can someone please explain this to me?

Your first paragraph, except the last part of the sentence, is the statement of covered interest rate parity (CIP), which holds perfectly if not absolutely, except after the 2008 financial crisis (See this paper). However, in the last part of the sentence, if you use forward exchange rate to represent expected future exchange rate, this is where the uncovered interest rate parity comes in, which does not hold according to many papers.

About your second paragraph, the confusion arises from the benchmark that you want to compare. According to CIP, if the domestic interest rate is higher than foreign interest rate, then the spot exchange rate is less than the forward exchange rate (in domestic currency per foreign currency). In other words, if you use forward rate to represent expected future exchange rate, you expect that the domestic currency will depreciate and the foreign currency will appreciate. In this case, you are comparing spot rate and forward rate at the same point in time.

If, suddenly and unexpectedly, the domestic central bank raises interest rate, immediately you will observe a sharp drop in the spot rate (in domestic currency per foreign currency). So if you compare the spot rates before and after raising the interest rate, you find that the domestic currency appreciate. However, whether you stand at the time before or after raising the interest rate, you always observe that the spot rate is less than the forward rate (in domestic currency per foreign currency) as long as the domestic interest rate is greater than the foreign interest rate.


When a country adopts the Euro, what happens to its debt? When a country, say Greece, adopted the Euro as its currency, what happened to the debt that was based on the Drachma? Was it converted into Euros?

Yes, upon the introduction of the euro on January 1, 1999, all debt (indeed, all nominal contracts) in participating countries was converted from national currency to euros at a legally defined conversion rate. See this press release from December 31, 1998, which states:

  In accordance with Article 109l (4) of the Treaty establishing the
  European Community, the irrevocable conversion rates for the euro were
  today adopted by the EU Council, upon a proposal from the Commission
  of the European Communities and after consultation of the European
  Central Bank (ECB) for effect at 0.00 on 1 January 1999 (local time).
  In compliance with the legal framework for the use of the euro, the
  irrevocable conversion rate for the euro for each participating
  currency is the only rate to be used for conversion either way between
  the euro and the national currency unit and also for conversions
  between national currency units.

  The euro conversion rates are the following...

For the particular case of Greece, which joined the euro on January 1, 2001 instead, the conversion rate with the drachma was apparently set at 1 euro = 340.750 drachma by this regulation in June 2000.


Calculating the elasticity of substitution between factors of production Following the work of Lu (1967) (Full text available here!) I got stuck trying to derive the elasticity of substitution between factors. He use the formula developed by Allen, that when the production function is linear and homogeneous is the following:

$$\sigma =\frac{\frac{\partial V}{\partial K}\frac{\partial V}{\partial L}}{V\frac{\partial^2 V}{\partial K\partial L}}$$

The partial derivatives of L and K and the cross second-order partial derivative are the following:

$$(1)\frac{\partial V}{\partial K}=\frac{dY}{dX}=\frac{1}{X}\left ( Y-\alpha X^{-\frac{c}{b}}Y^{\frac{1}{b}} \right )=\frac{1}{K}\left ( V-\frac{\partial V}{\partial L}\cdot L \right )$$
$$(2)\frac{\partial V}{\partial L}=Y-X\frac{dY}{dX}=\alpha X^{-\frac{c}{b}}Y^{\frac{1}{b}}$$
$$(3)\frac{\partial^2 V}{\partial K \partial L}=\frac{\alpha}{bL} X^{-\frac{c}{b}-1}Y^{\frac{1}{b}-1}\left ( X\frac{dY}{dX}-cY \right )$$

And the expected result (the one the author gets) is:

$$\sigma =\frac{b}{1-\frac{cf}{cf'}}$$

Is there anyone who can help me with this? Thanks.

First of all, I think that 'linear and homogeneous' is a typo of 'linearly homogeneous.' Indeed, it can be shown that if the production function $V$ is linearly homogeneous, Allen Elasticity of Substitution between $K$ and $L$ can be expressed as
$$
\sigma = \frac{V_K V_L}{V \cdot V_{KL}}
$$
by using the fact that $V_K$ and $V_L$ are homogeneous of degree 0, resulting in
$$
V_{LL}L + V_{LK}K=0
\\
V_{KL}L + V_{KK}K=0
$$
.

Moreover, by the definitions in the paper (Lu, 1967), note that
$$
X \equiv \frac{K}{L}
\\
Y \equiv \frac{V}{L} = F(\frac{K}{L}, 1) \equiv f(X)
\\
$$

Now, by substituting the results given by the author, we have
$$
\sigma = \frac{\bigg[\frac{1}{K}(V-V_LL)\bigg]  \bigg[\alpha X^{-\frac{c}{b}}Y^{\frac{1}{b}}\bigg]} {V \cdot \frac{\alpha}{bL} X^{-\frac{c}{b}-1}Y^{\frac{1}{b}-1}\left ( X\frac{dY}{dX}-cY \right )}
$$
, or
$$
\sigma = \frac{b}{V} \cdot \frac{L}{K} \cdot \frac{(V-V_LL)XY}{X\frac{dY}{dX}-cY}
\\
= \frac{b}{V} \cdot \frac{(V-V_LL)Y}{X\frac{dY}{dX}-cY}
\\
= \frac{b}{V} \cdot \frac{V-V_LL}{\frac{X}{Y} \frac{dY}{dX}-c}
$$

Note that, since $V$ is linearly homogeneous,
$$
V-V_LL = V_KK = \frac{dY}{dX}K
$$
where the second equality holds for (3.18) in the paper.

Therefore,
$$
\sigma = \frac{b}{V} \cdot \frac{\frac{dY}{dX}K}{\frac{X}{Y} \frac{dY}{dX}-c}
\\
= b \cdot \frac{\frac{X}{Y} \frac{dY}{dX}}{\frac{X}{Y} \frac{dY}{dX}-c}
\\
= \frac{b}{1-c(\frac{X}{Y} \frac{dY}{dX})^{-1}}
$$

Finally, note that
$$
\frac{X}{Y} \frac{dY}{dX} = \frac{X}{f(X)} \frac{dY}{dX} = \frac{X}{f(X)}f'(X)
$$
, and thus we have
$$
\sigma = \frac{b}{1-\frac{cf}{Xf'}}
$$

(You have a typo on this expression)


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

In the Varian textbook Intermediate Microeconomics (I am guessing in most micro textbooks), the chapter on Equilibrium discusses price controls in the presence of a demand and supply function. You can apply that discussion directly to the (competitve) labor market, were the price of labor is of course the wage.


Where to find series of capital-output ratio for the US? While the capital-output ratio is widely used in Macroeconomics as a target in calibration, it is usually just set to be equal to 3, without specifying the data source nor the methodology used to compute it. After doing online research, I couldn't find any available data with the series of capital-output ratio.

Capital to output ratio can be calculated using the BLS productivity measures data.
Capital to output ratio is simply K/Y.  Capital (K) is usually called either capital input or capital services and output which would be called real value added output.

Which can be found here:  https://www.bls.gov/mfp/mprdload.htm   under 1987–2019 Major Sector Multifactor Productivity.

https://www.bls.gov/mfp/special_requests/mfptable.xlsx

Or the World Bank group- Capital-Output ratio (NKY)
https://datacatalog.worldbank.org/dataset/capital-fundamentalism-economic-development-and-economic-growth/resource/babcd99a-16a3-4bef


If the economy is not always on the Price setting curve, can the Central Bank target unemployment? In the usual textbook model, in which there's imperfect competition, the economy is always on the Price-Setting(PS) curve, and to have a target unemployment level, above equilibrium unemployment, will cause an inflation bias.

First, is it possible for the economy to be on the wage-setting curve every time, but only in the PS curve in the medium-run? In this setting, would there be some leeway for a central bank to target also an unemployment level different from the equilibrium one, instead of just inflation, without causing inflation bias?

Any help would be appreciated.

The role of the central bank is solely to enact monetary policy, not government (fiscal) policy. Monetary policy of the central bank is independent (in the legal and political sense) from government.


List of EU banks that received state aid Is there a list of EU banks that got state aid / bailed out since 2008 crisis? I know EU state aid commission approves the fundings to banks, but does anyone keep track of which banks are tapping into these aids?

Pro Publica keeps an ongoing list of bailout recipients in the United States.

Here is a report on the UK bailouts during the crisis:
The Comptroller and Auditor General’s Report on Accounts to the House of Commons: The financial stability interventions

The SoFFin Wikipedia page has a list of participating German institutions.

FACTBOX - Bank bailouts around the world covers a few additional countries's bailouts between September 2008 and February 2009. A further update came in April of 2009 but it doesn't seem exhaustive.

Page 28 of Stability Programme of the Netherlands April 2011 Update contains information on their biggest bailouts but I am unsure if it is exhaustive.

The Spanish Fund for Orderly Bank Restructuring appears to be the key Spanish bailout program. The FROB FAQ lists entities receiving FROB support but again, this may not be exhaustive.


What does speculative bid mean? I tried to look for this term on the Internet, to no avail, as what I found does not fit into the context I found this word in.

My context is:
The incentive-compatible instrument of Vickrey Auction is that there is no incentive for bidders to submit speculative bids.

What does "speculative bid" mean here?

Thanks in advance.

A speculative bid in a Vickrey auction means that it is not what the bidder really thinks that the product is worth. Hence, a speculative bid is anything different from the true valuation of this product by the bidder (either a smaller or a larger price than the true one).

In a Vickrey auction, the bidder has incentive to reveal his/her true valuation. If he/she does not do so, he/she risks losing (either by winning the bid and paying more than what the product is worth for them - if price was higher than true valuation -, or by losing the bid - if price was lower than true valuation).


Independently and Identically distributed random variables What does it mean for two random variables to be "identically distributed"? Does it mean that they come from the same probability distribution?

Suppose $X$ and $Y$ are iid random variables. The 'identically distributed' part means both random variables have the same distribution function (cdf). Formally this can be stated as
$$F_X(z)=F_Y(z),$$
where $F_X(\cdot)$ and $F_Y(\cdot)$ are the marginal cdfs of $X$ and $Y$, respectively. The 'independently distributed' part means the joint cdf of $X$ and $Y$, denoted $F_{XY}(x,y)$ is simply the product of the marginal cdfs $F_X(x)$ and $F_Y(y)$, i.e.
$$F_{XY}(x,y)=F_X(x)F_Y(y).$$


what is the marginal cost divided by the average cost Marginal cost and average cost are both a u-curve. They cross in the competitive equilibrium. If we divide one by the other, is the ratio the degree of competition?   Ratio is 1 in perfect competition. What is the name of this quantity, MC/AC?

$MC/AC$ is not a quantity, it is a function. More precisely it would be written as $MC(y)/AC(y)$.

It is true that in a competitive setting in the long-run equilibrium $MC(y^*) = AC(y^*)$.

However, this can also be true in a monopoly setting. For example in the special case when $C(y) = c y$ where $c \in \mathbb{R}_+$, you have
$$
\forall y: \ MC(y) = c = AC(y).
$$
Also the monopolist's profit-maximizing $y^*$ is independent of any fixed costs $F$, but $AC(y^*)$ is not. For example if the inverse demand function is $p(y) = 1 - y$ and the cost function is $C(y) = y^2 + F$ then
\begin{align*}
y^* & = \arg\max_y (1 - y)y - y^2 - F = 1/4 \\
MC(y^*) & = 2y^* = 1/2 \\
AC(y^*) & = y^* + F/y^* = 1/4 + 4F.
\end{align*}
In this case
$$
\begin{array}{lcl}
MC(y^*)/AC(y^*) < 1 & \mbox{ if } & F > 1/8 \\
MC(y^*)/AC(y^*) = 1 & \mbox{ if } & F = 1/8 \\
MC(y^*)/AC(y^*) > 1 & \mbox{ if } & F < 1/8.
\end{array}
$$
Yet there is exactly one firm in the market, so there is no competition in the classical sense. Nor is it the case that the firm is a natural monopoly at $F = 1/8$. This could mean that this is the 'efficient level of competition', but it is not the case, because when  $F = 1/8$ we have
\begin{align*}
y^* & = 1/4 \\
p(y^*) & = 3/4 \\
AC(y^*) & = 1/2 \\
\text{Profits} & = 1/16 > 0.
\end{align*}


Why will Australia increase its interest rate only after the US increases its interest rate? According to this article, Australia will increase its interest rate only when the US increases its interest rate.

The Aussie dollar (AUD) keeps going down, which is not very good for importing businesses. Why doesn't the Reserve Bank of Australia increase the interest rate right now rather than just wait for the US to increase first? What is the point?

Australia's cash rate is already quite low. There's no need at the moment for the RBA to drop the interest rate any more, and as you can see from past decisions it's been unchanged for a while. Some economists think the RBA will move up soon, but that's uncertain - I wouldn't say it too confidently anyway - the bank is meeting its inflation targets and appears to be maintaining stability. Some are predicting later in 2015 anyway.

With low rates already, the article is stating that the RBA is watching the Fed to see what it does. The Aussie dollar is going down, you're correct. And while this isn't good for  importing businesses, businesses using overseas intermediatary goods or my eBay Christmas shopping, it will increase competitiveness for our exporting / manufacturing businesses and, in Glenn Steven's words, allows for 'more balanced growth' across the economy. Also mentioned is that the Australian dollar is higher than its fundamental value and the RBA wants it to go down even more.

If the Fed cuts their rates more then the RBA may need to act because there will be higher demand for Australian investment as a result of higher returns, resulting in currency appreciation, which the RBA doesn't want any more of.


How is signaling theory different from cue utilization theory? I think they are quite similar. I am a bit confused. Can anyone explain this to me?

I got the name and the information about the cue utilitarian theory from a journal article that related to organic food consumption. According to the authors, when people buy products like organic food, they could hardly evaluate the quality by merely observing it, since organic food could be kind of credence product. It is difficult to evaluate whether it is really free from chemicals and pesticides. So, people tend to rely on some cues to make the quality evaluation indirectly. This is how the Cue Utilitarian Theory works.

Let me narrow it down to a consumer behavior context. It seems to me that both theories can be used to explain that when there is an information asymmetric between retailers and consumers, some product attributes will be used as cues to evaluate product quality. I just wonder if they are basically the same in concept, then how and which one should I use them respectively.

I think you do mean cue utilization theory. According to the link provided in @NickJ's comment, and as far as economic theory goes, I'd say that cue utilization is basically a signaling story.

Putting "cues" on organic food products (e.g. the "organic" label, information on nutrition and natural content) amounts to a signaling act committed by the seller. Since the organic cues is less costly for the real organic food producers to produce (for instance, labeling non-organic foods as organic would face legal disputes, and hence a negative expected cost), these cues (or signals) are reliable.

Thus in principle, organic food sellers sending cues to consumers is no different from the classical signaling model where job seekers uses university degrees to signal their ability.


Simple arbitrage model of a single commodity Maybe, my question is a little chaotic. I want a mathematical model to describe the  arbitrage of a single commodity.

As I know , if I have much money, I can buy out or buy most of some commodity, such as apple. Then, the price of apple will go up.  Next, I sell my apple at high price. Seemly, I can make profit by this method. But, in fact, there are some question. When I bulk sell my apple, the price will decline quickly, so, I make profit a little or loss.  But if I slowly sell my apple, the new apple will be produced, the price decline too, although decline slow, but I need more time to sell my apple, as time go on, the price will return to normal, so I still make profit little.

Obviously, this process has not a clear expression by language. So, I guess there must be  a mathematical model to describe this process. What is the relation of supply, demand, price, and what is the best method of arbitrage ?  What paper or book I should read ?

As I noted in the comment, buying a major position in a commodity does not qualify as an arbitrage, rather it would be informally referred to as “cornering the market.”

I am unsure whether there is any theoretical work on such strategies. However, from a practical perspective, we can see that it is hard to characterise what would happen.

I will assume that we are talking about a physical commodity; things might be different for a financial asset.

Firstly, going into a market and trying to buy up the supply is difficult. There will be both physical commodities to buy, as well as derivatives (such as futures). How exactly can you get the physical inventories away from other commodities traders and consumers, when they see someone buying up all the other sources? You need to find a way to buy up the commodity ahead of time quietly, and then you need some event (such as a bad harvest) wiping out the holdings of the other commodity traders. Cornering a market has been done, but you need particular circumstances to make it work.

(I would recommend looking up the history of the Hunt Brothers and silver.)

The next problem is your ability to take advantage of your high inventory position. The producers of the commodity will ramp up production (and demand may be destroyed) if you try to only sell at a high price. You could get stuck with a large inventory of a commodity that has fallen in price. If you borrowed to finance your position, you might be forced into distressed selling - and everyone will know about it.

In other words, there are a lot of possibilities, and there is no easy way to characterise what will happen to the price.

Things are different if you control the production of the commodity. That ends up just being te situation of a monopoly (or oligopoly). There is a large literature on monopolies in economics; I am not familiar with it.


Interpreting the Reference Outcome in Thaler (1985) On page 18 of  Thaler 1985 on Value-functions $V(\cdot)$, he makes an example about an individual expecting some outcome $X$, who instead obtains $(X + \Delta X)$ which he then defines as the reference outcome $(X + \Delta X:X)$.
How is the ':' interpreted in this case?
In this post the ':' implies $(X + \frac{\Delta X}{X})$. However, I don't how that fits into the overall problem stated in the paper.

The two notations you refer to have nothing to do with each other.
In Thaler's paper an outcome $(y:x)$ means that outcome $y$ realized while the agent expected to get outcome $x$. It refers to the idea that a reference point ($x$) matters when an actual outcome ($y$) is evaluated.
The other post refers to a mathematical notational convention used in some parts of the world. Here, $:$ is a mathematical operation, division. The historical reason for this is that $\frac{x}{y}=x/y$ was sometimes written as $x \div y$ for longer expressions $x$ and $y$ "back in the day" when calculations were done by hand on paper. Then, I guess, people became lazy and $x \div y$ became $x : y$.


theoretical macroeconomic topic for bachelor project? A lot of my peers are writing empirically oriented bachelor projects, where they take some topic ("tax evasion", "pollution", "ricardian equivalence", "liquidity trap", "fiscal multiplier") and look at the data, and seek to explain the mechanics behind the data by use of models. So it's mostly empirical and investigative, with a bit of theory to support the arguments made.

My question is, what would be a good idea for a purely theoretical bachelor project in macroeconomics? Is there something like that which would be a good idea for a bachelor project, as opposed to an empirical study?

The reason is that I have a very strong background in mathemathics, so I would like to use that to my benefit and write a technical project, but I am not sure what kind it would be.

I would be careful about confusing topics and tools. Theoretical mathematics and data analysis are ways that you can approach a specific topic. No matter what topic you choose, you can apply your mathematical tools. I would recommend looking for something that interests you at a conceptual level and then seeing how you can apply your given set of tools to answer it.


People pathologically hoard so much cash that they impoverish the entire nation "If a man has an apartment stacked to the ceiling with newspapers we
  call him crazy. If a woman has a trailer house full of cats we call
  her nuts. But when people pathologically hoard so much cash that they
  impoverish the entire nation, we put them on the cover of Fortune
  magazine and pretend that they are role models." - B. Lester

My aunt posted this to her facebook page. She believes that people are poor because some other people are rich. I know that is totally fallacious, but I don't know how to explain it to her. Can any one help me to explain it to her?

But when people pathologically hoard so much cash that they impoverish
  the entire nation

This sentence seems to imply that we should fault the rich not because they are rich, but because they do not spend their riches.

Ok, let's scrutinize this assertion, and not go into philosophical and sociopolitical arguments about inequality, justice, etc, which is a totally different discussion and off-topic on this site (although I suspect that your aunt may in the end has something like this in mind...)

Who said rich people don't spend their riches?

1) Last time I heard, we are all too ready to criticize them for "lavish life-styles". But lavish life-styles cost a lot of money, so it appears they do spend a lot...so part of their riches becomes income for the rest.

But they are still rich!

2) Yes, because most of their wealth is invested in productive economic activities (directly or indirectly through mutual funds etc).

It follows that wealth is NOT "hoarded" - because hoarding means "stash away wealth, don't spend it, don't invest it, just stash it away from any interaction with other humans and economic activities". A "Scrooge McDuck" kind of situation.

This is not what is happening in today's world, and so the specific sentence from this excerpt is simply factually wrong.

Now, the fact that even without hoarding, rich people may stay rich or become richer, the fact that there are people dying of hunger while others live lavish life-styles, in other words the issue of wealth and income inequality could be certainly an on-topic subject here if, indicatively,

a) It was examined as regards its effects on economic efficiency (there is growing evidence that efficiency and distribution are linked and that inequality affects negatively efficiency and economic growth, see for example this recent IMF report)

or

b) It was placed and studied in the context of normative economics (and "normative" is not a synonym for "value judgements" or "opinions"). I would suggest to check this meta-thread on the matter.


Clarifying the meaning of market capitalization I'm new to this kind of topic and I'm trying to get a deeper understand.
I read that "the shares' price times the number of shares outstanding is the value of a company (=market capitalization)".

However, I'd say that it's just the value of that part of the company that is in the stock market.
In other words, when a company issues an IPO, it might not issue ALL of its shares, but just some of them.
So, let's say that the total amount of shares of a company (A) is 1000. The outstanding shares are 300 at the price of 10\$. The market cap is 300x10=3000\$. This number is the cumulative value of all the issued stocks.

Let's take this a bit further by taking another company (B). The second company has a total amount of share of 10000 (ten times that of A). So, if B issues 100 shares at the price of 10\$ its market cap will be 1000\$.

By comparing the market cap of A and B I'd say that the value of A is three times greater than B, however, that's not correct. Or I should say that it is indeed correct for what regards the market cap, but that's not the case if we consider the shares that have not been issued yet.

So the question is, how can the market capitalization give a hint about the value of a company? Also, how can the market cap be used to compare companies without taking into account the ratio between outstanding shares and the total amount of shares? (like the example above)

The "shares outstanding" variable used in the calculation of market capitalisation is defined as all shares that exist (and not was issued in public offerings). The market capitalisation is the share price times the outstanding. Therefore, the numbers in question do not apply.

There is no need for shares to be transferred in a public offering; an initial investor in a firm before it was listed could sell to another investor privately. This means that there is no good way of tracking how many shares are held by "the public," and that number is not used in calculations.


GDP Growth QoQ vs YoY: Why do the figures not match? According to statista.com, US Q4 GDP growth rate was 2.6% over the economy in Q3. However, why is the annualized growth rate for the US therefore not be a sum of all 4 quarters if their definition of QoQ growth is basically how much the economy grew over the previous quarter? i.e. why is according to statista, the GDP growth of the US in 2018-19 only 2.9%, and not 2.6 + 3.4 + 4.2 + 2.2?

Because those data are Seasonally adjusted annual rate: https://en.wikipedia.org/wiki/Seasonally_adjusted_annual_rate


Container-shipping industry Why is the container-shipping industry in a downturn?

  Investments in container-shipping, oil production and drilling—sectors suffering severe, concurrent downturns—are no longer the safe bets they once seemed.

The Economist Espresso: Diversifying: American conglomerates

This seems to be driven, in large part, by the recent economic downturn in China, which is both a major source and a major destination for trade in goods.

A Bloomberg report has this to say:

  Shipbuilders, container lines, and port operators feasted on China’s rise and the global resources boom. Now they’re among the biggest victims of the country’s slowdown and the worldwide decline in demand for oil rigs and other gear amid the oil price plunge. China’s exports fell 1.8 percent in 2015, while its imports tumbled 13.2 percent.

Moreover, there seems to be an overcapcity in the shipping industry thanks to the fact that shipbuilders ordered many new fuel-efficient ships in a bet that oil prices would remain high. From the same article:

  Just a few years ago, as the global economy improved and oil prices rose, many companies ordered more fuel-efficient ships. There were more than 1,200 orders for bulk carriers that transport iron ore, coal, and grain in 2013, compared with just 250 last year, according to Clarksons. Many of the ships ordered are now in operation, says Tim Huxley, chief executive officer of Wah Kwong Maritime Transport Holdings, a Hong Kong-based owner of bulk carriers and tankers. “You have a massive oversupply,” he says.

Any standard economic model is going to predict that an oversupply of ships implies a reduction in the price of shipping, which hits the profits of shipping companies.


Is there existing research on predicting the number of house listings based on exogenous data? I've been looking for prior research by economists that predict the number of house listings in a particular city (or even, say, the probability that an individual in the city will list his house that year).

So, for example, the former would be something like:

$NumListings=1.5*GDP+ 2*income+3*interestRate+unemployment+.3*population$

and the second could be a logit regression like

$ProbListing=\frac{(GDP+1.1*income)}{population}$

Is there any existing literature on this? The only things I have been able to find is literature on people using the number of listings to predict house prices-- I want to know if anyone has used exogeneous data like unemployment, income, consumption, gdp, interest rate, unsold listings, etc.. to predict the number of listings in the future.

It looks like what you're really after is determinants of housing mobility or migration. You get that, you can then just apply it to a specific city and aggregate to predict. One of the earliest and most seminal works in this field was Rossi's Why Families Move, originally published in '56 and redone in '80. The book is here and a review is here.

Another giant paper in the literature is Massey "Social Structure, Household Strategies, and the Cumulative Causation of Migration". It is also a little older (1990), but brings together a lot of the previous literature (great paper for lit review) and formalizes the decision making process of migration.

Newer papers in the literature look more at specific issues related to relocation, like eviction, fertility and housing decisions, and connection with life-course events.


Crypto-tokens: how do they function in a latter stage of company? I am newbie to cryptocurrencies and just read an article about ICO (Initial Coin Offerings). However, I didn’t quite get the functioning and role of tokens. Lets say there is a company that plans to build a marketplace that operates on blockchain, where you can buy and sell many different things. To use the marketplace the user however needs to buy company’s tokens.

To raise money to build the marketplace, the company one day decides to participate in an ICO, where it will issue its tokens for a low price. The ICO is very successful and the company manages to build the platform and attract a reasonably sized customer base.

Let’s say that in a few years the value of the company goes up, which means that the value of the token will also increase. Then come new users who are attracted to the platform and want to participate in it. This is the part which I don’t understand. Because they need to buy the tokens to participate in the market, wouldn’t the high price of tokens (compared to their original price at ICO) significantly deter new users from coming to the platform? The new users would have to pay high costs (buying the tokens) just to enter the platform. How do blockchain companies (like Status.im) solve this problem?

Thanks a lot for clarifying the problem.

The companies who engage in these sort of mechanisms expect the token to have a variable price which remains accessible and fair for the product in question, and also keep some tokens for themselves which can be used to influence the. In case the price rises beyond intended, some companies reserve large amounts of initial tokens to sell in the market (sell high volumes of tokens to keep the price low), or they even reserve the right to produce new tokens.
However, these companies also benefit from a high valuation of the token, which creates a speculative risk, benefiting the company but not necessarily consumers. See the long example/explanation below.
Example: Amusement park tokens
The situation can be illustrated as an amusement park who requires tokens to access and use the rides. Instead of selling the tokens themselves, the park sells lots of tokens before being built (similar to an ICO). Consider they sell it for €1 instead of the typical €2 or €3 on other amusement parks. You can then go to the park and try to sell the tokens to anyone. The logic is any visitor would still pay 2 or 3€ for the tokens, since he/she is a casual visitor. If it is a regular visitor, maybe he or she would try to save some money by buying the early tokens, but once those were used, the rides are still fairly priced at €2 or €3.
However, if the tokens are in too much demand, their price would climb to, for instance €10. When this happens, people would stop buying until the price lowers again until an acceptable value. If this doesn't happen due to whatever reason (e.g. speculation) the amusement park could sell some reserve tokens at the intended price (2€). Some amusement parks would even say they can produce new tokens at any time, to avoid this risk. However, remember that the amusement park benefits from selling reserve or new tokens for high prices at any time, and this would be a profit without delivering any value or product.
Research and further reading on ICOs
Please note that this is a very new area and very few studies have been performed yet on this field. I've recently read one paper on "Red Flags for ICOs", and another one is the economics of ICOs, if you want to learn more.


Macroeconomics differences of 2008 financial crisis and 2020 economic crisis How is 2020 financial crisis different from 2008 financial crisis? For example, why have stock market indices (e.g. S&P500, NASDAQ-100) recovered so quickly (about 3 months instead of longer than a year during 2008 financial crisis) despite the fact that unemployment rate is higher now and there were no lockdown back then?

There are a lot of differences between the two crises + how these differences manifest in the stock market.
First, on the point of the stock market- it's "kinda" an indicator of the overall economy. However, it's not a perfect metric; really, it reflects the weighted sentiment of those who participate. Furthermore, the stock market is more akin to a leading economic indicator, in that it predicts the future. In contrast, GDP is a lagging indicator and has taken a severe hit. Thus, people who participate in the markets are overall confident that the economy will rebound after COVID ends, in spite of hits to GDP.
This optimism is driven by a few factors that differ from the 2008 crisis:

Fiscal policy has been strong and immediate - PPP + other stimulus has passed rapidly and in huge volumes. The CARES act was almost \$2 trillion (compared to the 2008 fiscal support of $800 billion).
Expanding role of monetary policy - while monetary policy has greatly supported banks, the Fed has also directly supported businesses with loans and injections into specific capital markets. This is a huge expansion compared to the 2008 financial crisis
There are no obvious systemic failures in the financial system - yes, some banks are under stressed by non-performing loans, but the monetary and fiscal policy has both helped banks. Furthermore, stimulus has mostly been saved, meaning that banks have even more capital.

Even though the stock market is high, this is not necessarily a guarantee of future macroeconomic stability - there are rising concerns of exploding corporate and sovereign debt, trade tensions, collapsing supply chains... there are still many risks that will need to be addressed. Additionally, some characterize Wall Street as being "disconnected" from Main Street, again related to the fiscal/monetary policy described above.
Main takeaway: the performance of the stock market does not mean households and individuals are also doing well during the crisis.


Can number of children in rich country is small due to this simple economic factor? In rich countries, people are expensive.

Even taxi driver in Singapore earns $6k per month.

Now, the "market" tend to correct it self.

If something is expensive, and it's marginal productivity is low, then the "market" would produce less of that thing.

The market produces far more computer than abacus for obvious reason. Once the market produces more and more computer abacus become obsolete and too expensive.

The same way with humans. Humans are getting more and more expensive. So the market produce less of them.

And that's why rich countries produce less and less of them.

Now, I have many doubt about this theory. After all, the number of children you have is not up to the market fully.

It depends on how well you can attract mates to knock up. Yes. That would be market mechanism.

However, there are many government rules that sort make this not market mechanism. Polygamy tend to be illegal. Government tend to subsidize children of the poor with public schools and welfare. Minimum wage means poor people's salary are set by government. Child support laws are set proportional to man's wealth.

But still, market "distortion" may not be that "big". The market may still handle it.

And overall, things still follow market mechanism. The market, decides that we have too many humans. The market stop producing it.

Poor men, for example, can't get a girlfriend. Or poor people think that cost of raising children is too high they decided not to produce children and so on. Those seem like the way the market handles things.

Am I right? Wrong? Anyone study this?

Let me fist answer that individual decisions on whether to try to have children or not is a decision that is not driven by economics alone. There are many other factors that influence these decisions such as individual experiences and preferences and social norms.

That being said there is a relatively large literature on the economics of families and children. Some of the arguments as to why people have fewer children in developed countries include:

The costs of children are higher and the direct economic benefits are lower in developed countries. In developing countries children constitute extra labour (although they also need to be fed) and they require little education and other investments. In developed countries children typically do not contribute towards family income, and need large investments in terms of education and raising. A related argument that was put forward by Becker and Tomes is that there is a trade-off between the "quality" and the quantity of children, and in developed countries there is a larger demand for quality as opposed to quantity of children.

Another argument is that the need for a large number of children is lower in developed countries. In developing countries children are your old-age insurance policy, and infant mortality is high. In developed countries we have pension systems, good (partly) public health care and elderly homes, all of which reduce the necessity of having many children. The good health care system reduces the infant mortality so you don't need more children to be sure that you'll have a few when you get old. The pension systems, good public health care system and elderly homes mean you have to rely less on your children for income and care when you get old.

A final argument that has been made is that the opportunity costs of children are larger in developed countries. Most people are highly educated, and receive a relatively high salary. If they have to reduce their working hours to provide care to children, the opportunity costs are higher (all else being equal).


Finding the minimum # of items to be sold to meet a goal, based on likelihood Let's say that I have a project and I need to earn some target to be successful, let's say $50,000

The way I earn is by one time donations at various levels.  1, 5, 7.5 (some discounted item), 10, 15, 20, and 25.

If i say that i want the least number of pledges, then it seems obvious that I would like to maximally sell as much $25 items as possible.

But in reality, there is some sort of distribution that tells me how likely it is that I'll be able to sell each type of items.  For example, if this were a kickstarter project, typically there are fewer higher tier bids and a lot more lower tier ones.  As to how to obtain this type of information, let's say I have found a model, or I can just draw out the histogram myself based on some reasonable guess about the relative potential of a person choosing a pledge level.

My question is, how do I figure out, given some likelihood about how people tend to pledge, how to reach this particular target?  Perhaps let's say I assume that the distribution is the same no matter how many people end up bidding.  So I guess I really am trying to find the minimum number of bids necessary, given the liklihood of certain bids actually being sold.

The reason I'm asking this is because I want to try to quantify in some way the importance of exposure.  The more people see something, there's some likelihood they'll be interested, and even if they are, they're going to pick the tier item that suits them, which is typically low.  I know it might be a bit silly to think about this without regard to the quality of the project itself, but I was wondering if thinking about this might provide some insight on how important it is to do proper marketing.

I'm also interested in a reverse question.  Let's say I can only reach about 5000 people, based on the fact maybe that similar projects to mine only got an average of that maybe people to back them.  Is there a way to figure out how to shape the distribution to reach the goal in a way that sticks to the goal? Or perhaps to start with my initial distribution, and see how to morph it as little as possible to reach the target?

Thanks

Let's start with an environment in which there is only ever a single pledge level. The question at hand is: how do we choose the dollar amount of that level to maximise revenue (income)?

Observation 1: your probability distribution implies a demand curve.

We can plot the cumulative distribution of willingness to pledge and it will probably look roughly like this (with most of the mass at the bottom, as you speculate):

The $y$ value in this figure tells us the probability that a given individual's willingness to pledge (WTP) is no greater than the dollar value on the $x$ axis.

By turning this upside down, we get the probability that somone is willing to pay at least this much:

This tells us, for example, that there is a rouly 55% chance of a randomly selected individual being willing to pledge at least \$10. If we take 100 people then, on average, 55 of them will pledge. Thus, we can think of the vertical axis as being an indirect way of measuring pledge quantities, corresponding with the pledge level (or price) on the horizontal axis. If we swap the two axes, we therefore get something that looks very much like a textbook demand curve:

Given this demand curve, we can use all of the usual tools from the kind of standard monopoly optimisation problem that you can find in and introductory economics textbook. For example, if the CDF in the first figure is given by function $F$ then$$\Pr(\text{WTP}>x)=1-F(x)$$ so the revenue from setting the pledge level at $x$ when the audience consists of $n$ potential pledgers is $R(x)=[1-F(x)]xn$. Just like a standard monopolist's problem, we can compute the revenue-maximizing pledge level ("price") by setting marginal revenue equal to zero:

$$R'(x)=n[1-F(x)]-xnF'(x)=0.$$

Substituting your empirical distribution for $F$ in this equation and solving for $x$ gives your optimal pledge level.

Now, if we allow for multiple pledge levels then things become much more complicated. Firstly, we need a model of the behaviour of people and why it is that some people might pledge more than others.

If, for example, we are working in a Kickstarter-like environment then the main motive would be to get the goodies that come with the higher pledge tier. But that means we need a model not only of the pledge levels, but what you get in return. A complete treatment of this is beyond the scope of this answer, but a fairly readable summary can be found in "Versioning Information Goods" by Hal Varian. If you want a more detailed, technical treatment then the best place to look is "The Economics of Contracts: A Primer" by Salanie.


Is there fundamental economical reasoning for patriotism? Patriotism is an emotional attachment to a nation which an individual
  recognizes as their homeland.

That is description from Wikipedia and I think it is safe to say that universally all countries in the world trying to create their patriotic agendas. Sometimes it seems natural as it is with deep roots in history, culture. Sometimes it looks very like a ”project”,especially for relatively new countries.
I am wondering, is there fundamental economical reasoning for that?
For example, patriotism can lower cost of armies that in one or other history moment helps for country to survive or helps to create more stable economical system and so on.

Is there any research made in economical reasoning for patriotism? If anyone could give any links to articles or books or just give insights what is economical reasoning for patriotism (if there is one).

I think the purpose of patriotism is to create incentives for actions with positive externalities.

Your example of joining the army is a good one. The opportunity cost of joining the army is huge. You are risking your life for a relatively meager salary and are not gaining skills in the workplace which you could outside of the army. There is however a very strong positive externality of having a large army with willing participants.

Patriotism creates an additional incentive for individuals to perform these types of actions which otherwise might not be performed. Actions such as voting, community building, paying taxes, and working in certain industries for lower pay (think ACLU lawyers) are in large part undertaken due to a feeling of community that people within a country feel. This social incentive promotes positive externalities and benefits the society as a whole which is why patriotism is likely such a desirable attribute to be fostered within a country.


Is opportunity cost market prices of input goods or income from alternative investments? Reading my development economics textbook, I was informed that the opportunity cost of a private investment is the market value of the wages, goods and services used for the investment.

Here's a hypothetical situation: suppose that the firm could invest in an alternative project with the same amount of resources but a higher return. Would it not be myopic to overlook this alternative investment when asserting that the opportunity cost is the market value of inputs? It leads me to wonder why the inputs weren't valued higher. It could be because others in the market don't have access to capital, knowledge of the opportunity or the expertise required to make the investment. Still, why would the opportunity cost not be the income that could potentially be created from the alternative investment? Is a 'market value' approach just a simplification?

The market value of the inputs are determined by the most lucrative possible investment opportunity. Yes, the concept of market value is a simplification. If your firm alone can make the investment then the market is not functioning in a competitive way and hence is unable to assign prices in an informative way. If other firms cannot make the same investment but they can at least make investments with similar returns then the market value of the inputs would still be informative.


How can you know which is the "current dollar value" of a dollar value from another decade? Is there a mathematical ecuation or some method, which allows you to have the "current dollar value" of an amount dollar from other year, let's say, decades ago? For example, it's said that the Marshall Plan where United States gave 13 billions dollars to Europe is equivalent to $130 billion in current dollar value as of June 2016.

There are quite a few websites which will do a point-to-point calculation for you, if all you want is the comparison of the CPI.  For example, https://www.measuringworth.com/uscompare/

Saying how much a dollar was "worth" at a past point, however, is not a very precise question unless it's made more specific.  The price of computers, for example, have fallen even as they have become more powerful -- and even as the price level has risen.  It's simply not accurate to say that a five-hundred-sixty-three dollar computer today (of which there are many choices) would have cost only $1 in 1774!

I recommend this essay for a lot more detail on the matter.


How does printing money cause inflation? I've had this doubt for a long time and I still can't find a proper answer to it. Most answers I get just partially explain the phenomenon of a general increase in price level. I want to understand WHY and HOW monetary issue causes inflation.
I'm always told that if a country A has a total amount of output of $100 and this amount is represented by 100 coins of gold, then each coin of gold stands for one unit of output. If one day I stumble upon a gold mine and produce 100 further coins of gold, then I'll have 200 coins, so each coin now represents 0.5 units of output. It's is completely obvious that now each monetary unit has a lower purchasing power, but how do suppliers notice this? How does the economy as a whole detect this increase in money? If the answer is an increase in the demand for goods, then why do suppliers raise their prices? Why don't they just keep prices on a the same level if they know inflation is going to destroy us all?

WHY and HOW monetary issue causes inflation.

When a central bank emits money (or decrease key interest rates), commercial banks will be able to refinance themselves at a lower cost. Which means that at the end, these commercial banks will also be more, say, flexible, and thus will stimulate demands (here and there) in the national economy by lending money (here and there). If supplies stay constant, markets will reach a new equilibrium via prices rising due to these stimulated demands $\implies$ inflation.


How does an import quota affect the demand / supply of currency? An import quota in an open economy might not have the desired affect of increasing the GDP as it increases the demand of domestic currency in the open market raising exchange rate. How does it happen that import quota causes demand to shift positively ?

The goal of import quotas is to get people to buy domestic goods, which can only be bought for local currency. Therefore import quotas increase demand for local currency. But...

Setting import quotas is a very undesirable economic policy. It is basically a state intrusion into a market economy. Quotas for imports are usually implemented as a desperate measure when there is a continuously negative trade balance, local currency rapidly loses value, and every other measure (increasing taxes, customs, subsidizing exporters, etc.) failed. Distribution of quotas usually involves plenty of corruption. On top of that, World Trade Organization does not normally allow import quotas.

The more common use of import quotas is in agriculture, to support local farmers or production of a certain crop. But such limited use of import quotas should have very limited effect on the currency, unless it is a 'banana republic' where agriculture is the main economic activity.


Question on real exchange rate 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%."?

Note that I am not 100% sure. But in my understanding, we have

Year 1

Price for a product in the US :  $p_{US}=v$ \$
Exchange rate: $x$ pesos for $1$\$
Price of the product in the Philipines: $p_{Ph})=v.x$ pesos

Year 2

Price for the same product in the US : $p^\prime_{US} = (1+\alpha_v)v$ \$. The price increased due to the inflation $\alpha_v$.
Nominal exchange rate: $(1+\alpha_x)x$ pesos for $1$\$. A drop in value means you need more pesos for one USD.
Inflation in the Philipines: $p^\prime_{Ph} = \frac{P_{Ph}}{1+\alpha_p}$. Due to the inflation, the acquisitive power of the pesos is reduced.
Price of that product : $p^\prime_{Ph}=[(1+\alpha_v)v].[(1+\alpha_x)x].[\frac{1}{1+\alpha_p}] = \frac{(1+\alpha_v).(1+\alpha_x)}{1+\alpha_p}.v.x$

Variation

The effective variation compared to the previous year is thus, $\frac{(1+\alpha_v).(1+\alpha_x)}{1+\alpha_p}$, which corresponds to a rise in effective exchange rate of

$$\frac{1+\alpha_p}{(1+\alpha_v).(1+\alpha_x)}-1=2.7\%$$


What do people think are good economic policies to reduce informality? It seems that lots of informality, ie. people or firms that exist without being part of the tax, health, legal, regulatory systems, is one of the main issues to deal with in developing economies or poor parts of developed economies. Is there some sort of consensus on how to reduce informality?

Three part answer:

Causes:

Trust in the system (particularly trust in politics)
Attitudes to risk (i.e. being caught)/Enforceability of regulatory power
Education levels
Economic empowerment/unemployment/low wage level
Law of unintended consequences
Cultural considerations
Geographical considerations

Reduction:

Political corruption cleansing
Tighter regulation on informality
Greater communication and transparency
Demand and supply side policies

Evaluation:

Extent to which informality is a problem
'Trickle-down' effects
Ease in assessing magnitude of informality


Bertrand game - Nash equilibrium The quantity is limited to 300 but the monopoly quantity is equal to 400 and gives a monopoly price of 600. But if we plug the quantity of 300 into the demand function we get a price of 700.But I am confused.

Any help will be appreciated.Thank you.

Firm $i$'s profits $(\pi_i)$ as a function of its own price $(p_i)$ and the other firm's price $(p_j)$ are as follows :

\begin{eqnarray*} \pi_i(p_i, p_j) = \begin{cases} (p_i-200)\min(1000- p_i, 300) & \text{if } p_i < p_j \\ (p_i-200)\min\left(\frac{1000- p_i}{2}, 300\right) & \text{if } p_i = p_j \\ 0 & \text{if } p_i > p_j\end{cases}  \end{eqnarray*}

, $i, j \in \{1,2\}$ and $i \neq j$.

We now find the best response correspondence of firm $i$ $(\text{BR}_i(p_j))$ by solving the following problem
\begin{eqnarray*} \max_{0 \leq p_i \leq 1000} & \ \ \pi_i(p_i, p_j) \end{eqnarray*}

and we'll obtain

\begin{eqnarray*}
\text{BR}_i(p_j) = \begin{cases} \{700\} & \text{if } p_j > 700 \\ \emptyset & \text{if } 400 < p_j \leq 700 \\ \{p_j\} & \text{if } 200 < p_j \leq 400 \\ \{p : p \ge 200\} & \text{if } p_j = 200 \\ \{p : p > p_j\} & \text{if } p_j < 200\end{cases} \end{eqnarray*}

$(p_1^*, p_2^*)$ is a Nash equilibrium of this game if it satisfy $p_1^* \in \text{BR}_1(p_2^*)$ and $p_2^* \in \text{BR}_2(p_1^*)$. This yields the following set of Nash equilibria :

$\{(p_1^*, p_2^*) : 200 \leq p_1^*=  p_2^* \leq 400\}$

i.e., any action profile where both firms charge the same price, and that price lies in the interval $[200, 400]$ is a Nash equilibrium of the game.


Maximization problem FOC and Euler equation Can someone please help me with the Lagragian and the derivation of the following objective function ? Beneath I provide the objective function, the constraint and the Euler equation that results from the maximization. Your help is very much appreciated !!

Thanks !

Taking a variable as given comes from the assumptions of the model and cannot result from any optimisation problem (think simply that when a variable is taken as given it is treated as a constant in your problem so one cannot lead to the other). Here, taking the public good as given means the household is not able to choose the level of public good to maximize their discounted lifetime utility, and instead this is taken as given (i.e. for a given level of public good I can simply choose my lifetime consumption and bond holdings path to maximize my utility). As for why this is assumed it really depends on the model you are looking at (the level of public good might be fixed (although note that in your problem there is a time subscript) or any individual might be to "small" to exert any influence on the level, etc.) but unless you are looking to endogenously determine the optimal amount of the public good the taken as given assumption is pretty standard.

As for the maximization problem, what is exactly your doubt? Have you tried setting up the Lagrangian and obtaining the FOCs to get the consumption Euler equation?


How is trade in services conducted under the WTO in the absence of the Doha conclusion? The Doha round of negotiations for the WTO had a focus on services, but that round has not been concluded.

Does that mean that trade in services between trading partners without a preferential trade agreement in place, for example the EU and the USA is effectively prohibited? Or legislated for on a case-by case basis?

Or is trade in services effectively unaffected by the traditional tariff model of the WTO?

It's definitely not prohibited; the US-EU trade in services is worth some $200 billion (each way).


Dixit Stiglitz price index FOC? In the solution to the problem below provided by my professor he applies a first order condition to the lagrangian for ct, getting pt for the partial derivative of the argument "$\frac{d}{dc_t(t)} \int p_t(w)*c_t(w)dw$". This is puzzling to me since the derivative of a indefinite integral of ct should be ct not 1.

What's going on with this derivative and is it correct?

$\frac{d}{dc_t(t)} \int p_t(w)*c_t(w)dw$ = $p_t(w)$

Edit: Removed hand written notes.

A good way to think about this is to think about the cases where there are a finite number of goods, indexed by $\omega \in \Omega$. In this case, the partial derivative is
$$
p(\omega) = \frac{\partial}{\partial c(\omega)} \sum_{\omega' \in \Omega} p(\omega') c(\omega').
$$
The case in which $\Omega$ is a continuum of goods follows as a sort of limiting extension. See that even this finite sum can be expressed as an integral, given the proper measure $\mu$:
$$
\sum_{\omega \in \Omega} p(\omega) c(\omega) = \int_{\Omega} p(\omega) c(\omega) \,\mu(\mathrm d \omega).
$$

You mention,

  This is puzzling to me since the derivative of a indefinite integral
  of $c_t$ should be $c_t$, not 1.

If you provided your reasoning for this, it would be easier to see where the confusion is. In any case, hope this helps!

Also, this guide may provide further assistance: The basics of “Dixit-Stiglitz lite”


In a production function, the technology can vary across the firms and times. But the "power" must be same for the same industry? Let $F_t=A_tK_t^\alpha L_t^{1-\alpha}$ be the production function with two parameters.

In regression, we know the firm level $F_t$, $K_t$, and $L_t$. We want to estimate $A_t$ and $\alpha$.

I've heard that, for the same industry, $\alpha$ is the same for all the firms. $\alpha$ is also usually assumed to be the same across the time period.

However, the technology parameter can shift across the firms and times.

I am not sure if I am correct on this.

You can estimate it in multiple ways. If you have panel data then you could first log linearize the expression giving you:

$$ln(F_{it})=ln(A_{it}) + \alpha ln(K_{ti}) + (1-\alpha) ln(L_{it}) $$

Which could be estimated in multiple ways. You could estimate it as a pooled cross-section where the technology would be assumed constant across the time and same for all firms (lower case variables are in logs, and betas here give you the estimates of exponents from original specification):

$$f_{it}=a+\beta_1 k_{it} + \beta_2 l_{it} +e_{it}$$

You could run firm fixed effects specification where you allow every firm to have its own technology but technology is constant across the time:

$$f_{it}=a_i+\beta_1 k_{it} + \beta_2 l_{it} +e_{it}$$

You could assume that it’s the same for all firms but different across time:

$$f_{it}=a_t+\beta_1 k_{it} + \beta_2 l_{it} +e_{it}$$

Or you could also have a specification where you would assume that technology can be different across firms and also change in time (but the change in time has to be the same for all firms)

$$f_{it}=a_t+a_i+\beta_1 k_{it} + \beta_2 l_{it} +e_{it}$$

If you would also want to allow for technology to change differently across firms you could employ some multi equation estimation where you estimate the parameters for each firm separately.

So really depending on what you think is the most appropriate for your dataset you could make different assumptions on this. For example if it’s an industry that relies on basic research so there are no intellectual property rights - it might be appropriate to assume all firms have the same technology which can change in time. If it’s some industry where technological progress is unlikely - let’s say some services like barbers then the best assumption might be to have constant technology for all firms and times etc.


Are there conventions in economics for coding the distance between states? I know there are lots of gravity models in economics that take as an input distance between countries. My understanding is distance is typically coded based on the distance between capital cities, either in $L_2$ norm or great-circle distance. Most countries are small relative to the distances between them, and so maybe it doesn't matter much how they code the center of these countries for purposes of trade. But in my application I'm looking at US states, and many states are large enough that the internal placement of the location for calculating distances between states makes a difference. Additionally, state capitals are often not the economic center of the state (Carson City, NV and Albany, NY come to mind) nor the geographic center (North Folk, CA is hours away from Sacramento, CA), so I don't know of obvious choices.
Are there any standard choices I should know about here?
As a resource to others here are some sample data:

Average Latitude and Longitude for US States
US Census Centers of Population
List of geographic centers of each U.S. state

Would anyone provide a list of the economic center of each state?

I think the answer depends on who is impacted by your measure of distance and for what purpose. Kennan and Walker (2011) Econometrica measure distance between states as "the great circle distance between population centroids" in an attempt to model moving costs. They also include an indicator for whether or not the state is adjacent.


Terminal Condition for American Put Option In a recent book I read the author mentioned the terminal condition:

$$\mathop {\lim }\limits_{t \to T} V(S,t) = \max \left\{ {X - S,0} \right\}$$

This is intuitive to understand.

Then, the author defines: $$\tau  \equiv T - t$$

With this, the terminal condition above can be simplified to:

$$\mathop {\lim }\limits_{\tau  \to 0} V(S,\tau) = 0$$

This is not so intuitive. How can the value of the option be equal to zero in this case?

(note: in the space)   $${\Sigma _1} = \left\{ {(S,\tau )|B(\tau ) \le S <  + \infty ,0 \le \tau  \le T} \right\}$$

Notations:

$X$ = exercise price

$S$ = underlying stock price

$T$ = time to maturity

$t$ = time to today

$B(\tau)$ = optimal exercise boundary

I don't think this boundary condition has anything to do with the optimal exercise price and it should therefore hold for both European and American style options. It is simply a terminal condition which allows us to rewrite the PDE in closed-form.

The relationship you show above in which:

  $\mathop {\lim }\limits_{t \to T} V(S,t) = \max \left\{ {X - S,0} \right\}$

$\to$

  $\mathop {\lim }\limits_{\tau  \to 0} V(S,\tau) = 0$

simply means that the extrinsic value of the option (i.e., the value in excess of $X-S> 0, \forall S<X)$ tends towards $0$ as $t \to T$.

Dropping the "$max$" function is simply a restatement of the payoff condition in terms of the Heaviside function. The Heaviside function is essentially equivalent to the maximum function except that it enforces the following boundary at $t=T$:

${\displaystyle V(S,\,\tau)=0\quad \forall \;\;S<X}$,

Though the difference seems subtle, it is important since $V_t$ need not be finite at S = 0, or even defined for that matter, which allows us to more easily perform the substitution of variables required to express the contingent pay-off in terms of the (heat) diffusion equation which is the general solution to the Black-Scholes model.

I hope that the intuition of this boundary condition is clearer from this explanation.


What are some of the barriers to trading services? As I understand it countries negotiate free trade agreements in services using the WTO GATS.

But what are some of the barriers to the transnational exchange of services that an FTA would seek to address?

Surely something as ephemeral as a service can be sold across national borders easily because there are few or no physical components?

If you look at the four different ways that international service trade is categorised by the GATS, that will help you think about what sort of constraints are faced.  The four GATS "modes" are:

Cross border (the most simple): a firm in country A supplies a service to customers in country B.
Consumption abroad: someone from country B visits A and uses a service there.
Commercial presence: a firm in country A sets up a subsidiary in B to supply B's customers.
Presence of natural persons: a firm in country A moves staff to B to provide services there.

Some example constraints, by mode:

Some countries don't allow their citizens to hold accounts with foreign banks.
The US historically not allowing its citizens to visit Cuba.  (Mode 2 constraints are the rarest.)
Rules specifying that service companies must be 51% owned by locals have been common in various countries.
All immigration law places restrictions on this.


Why did the stock of consumer loans held by commercial banks jump in March 2010? The graph below refers to "Consumer Loans: Credit Cards and Other Revolving Plans, All Commercial Banks", from here.

What happened in March 2010? The data come from the balance sheets of commercial banks in the US. Did an entity that was previously not a commercial bank somehow change status?

Because of a change in regulation about how different accounts are to be recorded. That change was stated in the Financial Accounting Statements No. 166.

If you look into Notes on Data relating the "Assets and Liabilities of Commercial Banks in the United States - H.8", you find the following statement from April 9, 2010:

  As of the week ending March 31, 2010, domestically chartered banks and foreign-related institutions had consolidated onto their balance sheets the following assets and liabilities of off-balance-sheet vehicles, owing to the adoption of FASB's Financial Accounting Statements No. 166 (FAS 166), "Accounting for Transfers of Financial Assets," and No. 167 (FAS 167), "Amendments to FASB Interpretation No. 46(R)." Domestically chartered commercial banks consolidated \$363.4 billion in assets and liabilities. The major asset items affected were: other securities, mortgage-backed securities, -\$6.4; other securities, non-MBS, -\$23.5; commercial and industrial loans, \$19.1; real estate loans, revolving home equity loans, \$5.5; real estate loans, closed-end residential loans, \$20.9; real estate loans, commercial real estate loans, \$1.2; consumer loans, credit cards and other revolving plans, \$321.9; consumer loans, other consumer loans, \$24.6; other loans and leases, all other loans and leases, \$46.1; allowance for loan and lease losses, \$36.4; cash assets, \$4.1; trading assets, other trading assets, -\$1.7; and other asset items, -\$11.9. The major liability items affected were: borrowings, borrowings from banks in the U.S., \$2.6; borrowings, borrowings from others, \$379.8; and other liability items, -\$1.6. The residual (assets less liabilities) decreased \$17.4. The major memoranda items affected were: securitized consumer loans, securitized credit cards and other revolving plans, -\$322.7; securitized consumer loans, other securitized consumer loans, -\$24.5; and securitized real estate loans, -\$23.9. Foreign-related institutions consolidated \$20.7 billion in assets and liabilities. The major asset items affected were: other securities, non-MBS, \$1.1; commercial and industrial loans, \$0.7; and other loans and leases, \$18.9. The major liability items affected were: deposits, other deposits, \$0.5; borrowings, borrowings from others, \$21.0; net due to related foreign offices, -\$12.0; and other liabilities, \$11.2.

I highlighted the one corresponding to the graph you show. The magnitude of the jump precisely matches the amount the statement above mentions.