Why does supply equal demand? My question is simple: in theory, why should we expect the total quantity that firms want to sell to be (at least approximately) equal to the total quantity that consumers want to buy?

As I understand it, the standard explanation is something like this. If supply were greater than demand (for instance), then there must be some 'frustrated' sellers who cannot sell all of the units that they want to sell. Instead of paying the market price, buyers could therefore pay a lower price to these sellers while still buying all the units that they want to purchase. This pushes the price downwards, a process that continues until supply equals demand.

I find this kind of explanation unsatisfying for two reasons:

In the standard framework of competitive equilibrium, agents choose quantities (and view prices as fixed). And yet, the disequilibrium adjustment story here relies on price setting.
The explanation is highly informal. As a result, it is unclear what assumptions are necessary for it to hold and when we should expect supply to equal demand.

I would be very grateful if anyone could improve on this explanation.

Edit: what I am looking for is a rigorous story explaining why:

If the number of units that producers want to sell exceeds the number that consumers want to buy, the price will fall.
If the number of units that consumers want to buy exceeds the number that producers want to sell, the price will increase.

This is a very fundamental assumption in economics so I think deserves a good answer on economics SE (apparently, not everyone agrees, judging by the recent downvotes!)

The puzzle (for me) is how this can happen in an environment when everyone views the price as given (i.e. the standard model of perfect competition).

You can easily change the informal explanation to a "quantity-based" approach, using a dynamic approach. Assume that firms in the market produce this period $S_1$ but the consumers that show up buy only $D_1<S_1$. What would you do if you were a producer, for period $2$, given the information you have about where demand stands?

Assume the good is perishable. Then the unsold quantity from period $1$ is destroyed. In period $2$ are you going to produce the same amount, or something less? I would say less, to reduce somehow the quantity that will go to waste and your loss from that fact.

Assume the good is not perishable, so you have inventories left over from the first period. Now, the tendency is to produce even less than when the good is perishable, because you can sell during period $2$ the inventories from period $1$.

So we see, that starting from a quantity supplied above quantity demanded, it is reasonable to expect lower quantity supplied next period.
One can easily make the analogous argument starting with quantity demanded higher than quantity supplied. This is a gradual adjustment towards "market equilibrium", where quantity supplied will equal quantity demanded, or approximately so.

...and I didn't mention prices anywhere. You can think that this is a local market where the producers are forced to sell at a specific price, "imposed" on them by other similar markets and the expectations of consumers. In other words, what I described above can roll out while the price remains fixed from period to period.

The above was just an informal description. The benchmark approach to the dynamic adjustment towards market equilibrium is the Cobweb Theorem, see Ezekiel 1938.


Are there big waves of entrepreneurship over time? In some models there are times when there are many entrepreneurs, and others when there are not. Is this a stylized fact of some kind? Are there any statistics about how entrepreneurial a particular generation is?

I think there are waves indeed. When you look at historical evidence you see a swinging between 'more free market' and 'more central planning (thus less free market)'. The more free a market is (less regulation, less taxes), the more entrepreneurship you will see.
In the Soviet-Union for example entrepreneurship was dead because everything was centrally planned by government. It made no sense taking risk or sticking your neck out for something.

For statistics, if I were you I would try to look for historical data about 'number of people self employed', 'number of starting businesses', ... Maybe you can start by looking over here: http://www.oecd.org/std/business-stats/ or here http://ec.europa.eu/eurostat/web/structural-business-statistics/entrepreneurship/indicators

hope this helps a little


Shopping example in Kőszegi / Rabin (2006) In "Section IV Shopping" of Kőszegi / Rabin (A model of reference-dependent preferences, QJE 2006), the example of consumer buying a pair of shoes is given.

They claim that "her disutility from spending on the shoes is between $(1+\eta)p$ and $(1+ \eta \lambda)p$" (p. 1146).

How do they get this result?

I can see where the second term comes from, namely buying at $p$ when expectations were to buy at 0, which generates money-related utility of

$$ -p - \eta \lambda p = - (1+\eta \lambda) p$$

But the first term is beyond me: If she buys at $p$, but expected to buy at some $p' > p$, I would obtain

$$ - p + \eta(p' - p) = -(1+\eta)p + \eta p' $$

which is not the same as the $(1+\eta)p$ stated in the paper.

What am I missing here? Thank you.

I think it is just a matter of definition. The disutility from spending on the shoes is not the utility obtained by purchasing the shoes: it is the difference between the utility obtained when she does not buy the shoes and the utility she gets when she buys them.

Suppose for instance that she expects to buy the shoes at price $p$. Her "money" utility of buying the shoes equals
\begin{equation*}
U(\text{Buying}) = -p
\end{equation*}
since there is no gain-loss utility in that case, and $-p$ is her final wealth (normalizing initial wealth to zero).

However, if she finally decides not to buy the shoes, her money utility equals
\begin{equation*}
U(\text{Not Buying}) = \eta p
\end{equation*}
since her final wealth equals $0$, and in addition she experiences a gain-utility of $p$ with respect to the reference point (spending $p$).

Therefore the disutility from buying is
\begin{equation*}
U(\text{Not Buying}) - U(\text{Buying}) = (1+\eta) p
\end{equation*}

I hope it helps.


What happens if money supply grows more slowly than inflation? I'm thinking the case of Argentina. In 2016, prices raised about 40% but according to the central bank of Argentina, money supply grew only 30%. Is this going to have an effect in 2017?
What could we expect to happen in general when money supply grows slower than inflation for a given period?

Thank you in advance.

There are three big reasons for this:

1) It takes time for businesses to price inflation in. As a business owner I am unlikely to raise my prices from $1.0 in year 1 to $1.04 in year 2 to account for 4% increase in the money supply. Instead I am likely to wait until I can justifiably raise the price to $1.25 or some other price that makes more sense for marketing. As a result there will be a lag between inflation and the money supply. In the long run I will choose to price money supply into my prices thus driving inflation but on a yearly basis in the short run businesses will not perfectly price in the money supply.

2) Money supply primarily drives inflation in the long term however short term price shocks can significantly affect inflation. For example if the price of oil suddenly drops due to discovery of new shale reserves in the United States that will be reflected in a drop in price levels across the entire country. For any business the cost of production, transportation, etc. has dropped which will be reflected in a drop in the price level (which dictates inflation) despite no change in the money supply.

3) Economic growth drives deflation even if the monetary base stays the same size. If there is economic growth through an increase in efficiency (i.e new technology) then the value of money will go up. If there is $100 in an economy and the only product within the country is 100 widgets which are produced every year with the past year's 100 widgets being consumed then the price of a widget would be $1. If suddenly a new type of tech allows us to build widgets for half the cost we could now produce 200 widgets in this economy using the same resources and capital stock. With the same $100 you can now buy 200 widgets or $.5 per widget. Effectively this means that the price level has gone down and that the value of a dollar has gone up. This happens in the real world through increases in technology and is the driving reason for a long run increase in the monetary base for almost all economies.


How were unit labor costs estimated by Gali and Gertler (1999)? I am trying to estimate a NKPC like the one
Gali & Gerter, 1999 and Gali &Gerter, 2001 estimated. I am having trouble with understangind how they calculated the marginal cost, i.e., which time series they actually used. I tried consulting '''Sbordone, 2002, who estimates the same model using the same (or at the very least a similar) proxy for the marginal costs. As far as I could understand MC = C/Y where MC is the marginal cost, Y is GDP and C are the total compensations given to workers, i.e., the sum of all real wages paid to workers. I would like to know if that is correct and, if it isnt, how Gali & Gertler calculated the marginal costs. In the specific interpretation I have described I dont know if one must use real or nominal GDP. If I use real GDP, it seems to me, that when dividing real salaries by the real GDP the deflators dividing both nominal salaries and nominal GDP will "cancel" each other and I would only get the ratio between nominal salaries and nominal GDP, which does not seem useful given the fact that in the price formation model firms are considered not to suffer money ilussion. I apologize in advance in case my words have not been precise enough and thank you all for your answers. Any help and references to articles or textbooks is greatly appreciated.

In Galı́ & Gertler (1999) the authors state that marginal costs is given by:
$$MC_t = \frac{S_t}{\alpha}$$ where $\alpha$ is the labor elasticity (from the Cobb-Douglas prod. function), and $S_t$ is the labor share of income (i.e. what portion of output GDP goes to labor). Next they actually get around estimating $\alpha$ by expressing everything in percentage changes so they actually use:
$$mc_t = \frac{MC_t - MC_{t-1}}{MC_{t-1}}= \frac{\frac{S_t}{\alpha} - \frac{S_{t-1}}{\alpha}}{\frac{S_{t-1}}{\alpha}}$$
where alpha cancels out so you are left with just  change in the labor share of income $\Delta S_t = s_t$.
They even state in the paper:

The data we use is quarterly for US over the period 1960:1}1997:4. We use the
(log) labor income share in the non-farm business sector for $s_t$

So in this case they just seem to have directly taken the labor share of income, which is plausible data for labor shares of income exist without any 'assembly' required (e.g. see this Fred dataset as an example).


Interpreting Disequilibrium: Inelastic Supply and Demand at different quantities How does one go about interpreting a case of  inelastic supply and demand that are based at different quantities? There is no equilibrium in such a case and therefore nothing supplied or demanded.

Two Questions
1.How would one go about looking at the the type of good we have here?2. Is this case even possible?

I am not sure what you mean by looking, but there is no equilibrium in this market, so any equilibrium analysis is impossible.
Situations like this are possible. Consider the Titanic. Supply of lifeboat spaces are limited and do not change depending on the price. People are willing to pay any price.

There are limitations on what an individual can pay by money though. One might argue that there were a lot of people who were willing to do anything to get a space (push in line, etc.). As long as the number of these people is larger than the supply and the price is measured in effort your graph would describe the market for places.


Finding optimal Inflation - Walsh I am solving questions from Walsh and then verifying with a solutions manual. However, I keep solving a question and arriving at a slightly different answer than that suggested by the solution manual.

The solution given by the manual:

However, when I take the optimal $\pi^e$ and substitute into (121) I get

$$\pi^* = \frac{\pi^T[-1-\lambda]}{[-1-\lambda]} + \frac{\lambda k [ -1-\lambda]}{[-1-\lambda]} + \frac{\theta k [1+ \lambda]}{[-1-\lambda]} +e\frac{\lambda - \theta}{[-1-\lambda]}$$

and this simplifies to:

$$\pi^*= \pi^T + k(\lambda - \theta) - e\frac{\lambda + \theta}{[1 + \lambda]}$$

And so my issue is that I don't see how there is no $\lambda$ in the numerator of the fraction multiplying e at the end of the simplification.

Can anyone see my error? I must be missing something simple.

Edit: Roel Beetsma replied! He says he got the same derivation we basically got. So the solutions seem to be mistaken and we win! Also I'm removing the strikeout below.

Note that
$$+ e\frac{\lambda - \theta}{[-1-\lambda]}$$

actually simplifies to

$$ - e\frac{\lambda - \theta}{[1 + \lambda]} $$

rather than with $\lambda + \theta$ in the numerator like you had.

So the solutions has

$$- e \frac{1 + \theta}{1 + \lambda}$$

instead of what we have above. The difference between the two is:

$$-e\frac{-1 - \lambda}{1 + \lambda} = e$$


What is the likely result of rent control in Berlin? What predictions does economics make about the likely result of this policy in Berlin of capping rent prices.

  Berlin is freezing the rents of 1.5 million apartments for the next five years starting this Sunday in a controversial move to control the exploding costs that have forced many to move outside Germany's capital city.

Rent control will over time decrease the supply of housing while increasing demand causing a housing shortage. Moreover, there are also studies that show that under rent control there are not just shortages of houses but also misallocation, that is the houses are no longer allocated to people who have highest utility/consumer surplus from having them (Glaeser and Luttmer, 2003).

A recent literature review on rent control concluded (Jerkins, 2009):

  I find that the preponderance of the literature points toward the conclusion that rent control introduces inefficiencies in housing markets. Moreover, the literature on the whole does not sustain any plausible redemption in terms of redistribution.

Furthermore, the IGM forum, a platform that surveys the top policy economists, shows that virtually all of them think that rent control (at least as applied in US) had a negative effect on availability and quality of housing (see here).

However, note an important caveat is that as any policy also rent control is not always homogeneously applied. I saw some studies showing net positive redistributional effects of rent control but it’s only small minority of all studies and usually the positive results come from rent controls that were applied only to special subsection of housing market for example government owned social housing. Those studies to my best knowledge do not really apply to the Berlin case, which is going more or less the similar route as San Francisco or New York where the effects are shown to be significantly negative.


What's the term for an economic policy that has negligible effect for most, but a significant effect for a few? I remember this came up around tariffs in the US on aluminum. They have a negligible effect on the price of an aluminum can, but aggregated across all the aluminum cans sold, it can have a significant impact for a handful of US aluminum producers.

Utility Trade-offs: Pareto Efficiency vs Equality

While I tend to agree with the notion of Tragedy of the Commons as per the comments, I will provide an additional economic framework to answer your question. Perhaps this is something you already know, but is nonetheless useful for answering your question as per the welfare-economics tag. As to the exact name of the policy, I'm not sure there is a name for the policy, but the underlying economic concept can be characterized as a utility trade-off and that's likely how a policy maker would approach this.

Consider the following social indifference curve, I just made it myself, don't scrutinize it too much:

Assuming the First Theorem of Welfare Economics held before the tariff, then that point would have been on the pareto efficient curve which is the gray line in my graph. This curve is also known as the utility possibilities curve, which shows the highest utility one party can have without reducing another party's utility.

In your case, since the aluminum producers were worse off, then this is a utility trade-off. And we recall that society may be willing to trade off one group's utility for another's utility, sometimes on the grounds of equality, but for other reasons too.


Do capitalists in the Marxism world view create value? As I understand it, capital is created through the surplus value, that is the difference between the value of a worker's work (i.e. the wage that he is paid) and the new value that is created through his work. A simplified example would be this:

Worker A makes 100 ice cream cones per hour and is paid 10$ per hour
Raw material for making a single ice cream cone costs 0.2$
Worker B makes 100 scoops of vanilla ice cream per hour and is paid 20$ per hour
Raw material for making a single scoop of vanilla ice cream costs 0.5$

That would make the cost for a single cone with a scoop of vanilla ice cream exactly 1.00\$.

Cone with ice cream is sold for 2$

That would leave a profit of 1\$ per sold cone with ice cream for the owner of the ice cream shop (assuming that the building itself does not require any regular payment).

Worker A and B are paid 0.3\$ for creating a value of 1.3\$. According to Marx they are paid 1\$ too little for their work.

Is the capitalist attributed any part in the creation of this value? I don't want to talk about the fact that he owns the means of production, but rather about this: Does the capitalist create a bigger value by aggregating the work of the two workers? This is obviously trivial for ice cream cones, but I could imagine something meaningful for example in the production of cars, where the organization itself requires work. Is this work done by the capitalist considered at all in Marxism? Or is any creation of value attributed to the individual workers who in turn are therefore exploited?

I'm not a Marx expert, but I've read The Capital some years ago and as far as I can remember Marx said that only the workers produce value. All others' wages (and the workers' wages too!) and other costs are covered by the produced values of the workers, so the others decrease the "profit", which could remain at the workers otherwise. Therefore Marx suggested the workers to make collectives without any capitalists.


Historical sovereign bond yield and CDS rate data download Does anyone know where I can download from:

1) historical data for sovereign bond yields (or prices) and
2) historical data for soveregin CDS (credit default swaps) rates?

preferebly free?

There was a similar question in the Quant. Finance section (see here: https://quant.stackexchange.com/questions/22819/where-to-get-price-data-on-credit-default-swaps)

People suggested the following options: https://www.datagrapple.com/ (free for subscription), http://www.markit.com/Product/Pricing-Data-CDS (not free)

I also guess that Bloomberg and Thomson Reuters databases should also contain historical CDS rates. Practicioners use the data source extensively. Though they are very expensive for a personal use, some universities buy a license to get access to it and it is worth asking people from the finance/banking/econ department if they have access to the database.


Keynesian Cross and Balanced Budget Multiplier Hi! I am trying to understand the problem above, and was wondering if someone could help me with the last question. I think I am fine with all other questions.

Here is my attempt:

(i)
The fiscal multiplier is $\frac{1}{1-c} \Delta G$, as it is the infinite sum $ \Delta G + c\Delta G + c^2\Delta G + ... $.

Depends on c because the increase in government spending first leads to an increase in Y, which leads to an increase in C, which then leads to another increase in Y, but this time the increase in only $cY$, as part of the income is saved.

(ii) Balanced budget multiplier is 1, as $\Delta Y = \frac{1}{1-c} \Delta G + \frac{-c}{1-c} \Delta T$ with $ \Delta T = \Delta G$

This means that an increase in government spending that is matched by an identical increase in lump sum taxed increases output by the same amount as the increase in G (and T).

(iii) $$\Delta Y = \frac{\Delta X}{0.01} = 100$$

This means that giving me an additional unit of currency will increase total income by 100, as it feeds back into income and consumption infinitely.

(iv) This is the question where I would like some guidance. Here is my work so far:

We have:
$$ C= a + c(Y-T) - d\alpha Y$$

The multiplier associated with an increase in G should now be:
$$\frac{1}{1-c} + \frac{1}{1-d\alpha}$$
The first part is the "old multiplier, the second is the effect of the new part of the consumption function? I am not sure that this is correct, happy to receive comments!

This would mean that $c=d\alpha$.

And then, the multiplier associated with an increase in T:

1st round: Y increases by $c\Delta T$
2nd round: C increases by $c^2\Delta T + d\alpha \Delta T = 2 c^2\Delta T$
Then Y increases by $2 c^2\Delta T$
3rd round: C increases by $4 c^3\Delta T$

Does this mean that the multiplier is this sum: $$2^0C^1\Delta T + 2^1C^2\Delta T + 2^2C^2\Delta T + ... $$

And then the balanced budget multiplier would be this last result + 1 (the other multiplier, from the increase in G)?

I'd be super grateful to anyone who could help me with question (iv)!

The fiscal multiplier in (iv) would arise from

$$ Y = C+I+G$$

$$ Y = a + c(Y-T)-d\alpha Y +G+I.$$

This can be rearranged as

$$Y(1-c+d\alpha)=a-cT+G+I,$$

and, therefore, the fiscal multiplier would be

$$\frac{1}{1-c+d\alpha}.$$

In order for this to equal $1$, you just need $d\alpha=c.$

Note that setting $d\alpha=c$ in your "multiplier" does not yield 1:

$$\frac{1}{1-c}+\frac{1}{1-d\alpha}=\frac{1}{1-c}+\frac{1}{1-c}=\frac{2}{1-c}.$$


Examples of firms using attachment bias Are there any nice examples of firms using attachment bias to increase profits? Examples from the academic literature or well-motivated anecdotes are both acceptable. For instance, pet stores seem to let you play with the animals and GM used to have 24 hour test drives for some of their cars. However, both of these examples are also consistent with a match quality that takes some time to learn, rather than mere attachment bias.

The field of performance marketing makes ample use of attachment bias.

For example, skiers often purchase race-level ski boots and skis which are too stiff relative to their ability, so the product is actually detrimental to performance.
In this case, self-attachment bias causes buyers to overestimate their own ability.
The ski manufacturers know this and market and price the stiffness of this equipment at a premium even though it is not objectively helpful for the vast majority of consumers.

In pharmaceuticals, attachment bias to familiar medications like Tylenol cause consumers to pay premiums for this medicine even while knowing that the generics next to it on the shelves contain exactly the same active ingredients and are often made by the same manufacturers.  Here, attachment bias to a familiar product causes allows manufacturers to pay a premium, and the manufacturers tune marketing messages to amplify the attachment bias ("Tylenol, what matters most", "Advil, the original round tablet).


Pricing of a call option in a one period binomial model You are given a 5% call option worth \$2.66. The strike price, k is $41.00. S(0)=40, Sd= 35 (i.e the lower price of the stock at t=1) find Su (i.e the high price of the stock at t=1).

How would this be done? I know Cu= Su-\$41. C(0)=\$2.66 and I have something written in my notes that c(0)= B/(1+r) +ΔS(0), but I'm not sure what B is here. I assume to Find Su I need to first find Cu, but I'm not sure how to do this from the given information. Any help is appreciated.

I assume 5% is the interest rate. If we knew stock price in each state, formula for call option price in binomial model should be
$$
C_0 = \left(S_0 - \frac{S_d}{1+r}\right) \frac{S_u-K}{S_u-S_d}
$$
Now just invert the formula to get $S_u$, given values of $C_0, S_0, S_d, K, r$.

Where did we get that formula for call option price in the first place? That's pretty important, so I'd recommend you to look into your notes more closely. In short, you want to form a portfolio of stocks and bonds that replicates the option payoff in the next period, i.e. find $a, b$ such that
$$
\begin{split}
a S_u + (1+r)b &= S_u - K \\
a S_d + (1+r)b &= 0
\end{split}
$$
(here, $a$ stands for how many stocks you buy, $b$ for how much you save into bonds)

If you solve this system, then the price of the option in current period must be just the value of this portfolio, $C_0 = a S_0 + b$ (otherwise one could make easy profits from the mispricing), and doing the algebra should yield the formula at the beginning.


Do outputs of a country produced outside its borders contribute to its citizens' well-being? For example, a Japanese automobile company of which manufacturing factory located in China. Do the outputs produce from the factory located in China contribute to the well being of the Chinese people or the Japanese people?

Why do outputs of a Japanese company manufactured in China counted in China's GDP instead of being counted as exports from Japan to China?

GDP stands for Gross Domestic Product: this is the amount of activity that happens within the borders of the country itself, irrespective of source.

What you are thinking of is GNP: Gross National Product- which ideally would be the amount of economic activity worldwide attributable to citizens or corporations or the government of a particular country.

Historically, countries liked the idea of GNP and it used to be the 'favoured' way of reporting economic activity. However from a practical perspective as the world has become more and more globalized, it turns out that GDP is easier to estimate and is somewhat more realistic when trying to assess the level of economic activity happening in a geographic area.

Ultimately who cares who owns the factory, the fact that it exists where it is and not somewhere else is a huge boost to the local economy. Many industries have profit margins of 5% or less, guess where much of the expenses are being spent?


How does price fixing work if it requires an almost universal agreement? From what I gather, price fixing works by getting all the relevant actors in a certain economic sector to agree to fix the price of the goods they sell at a certain, higher-than-normal price, so that the consumer is forced to buy overpriced goods.

My question is: how does this even work in real life? If the goods are overpriced, what stops a new seller from offering his/her goods at the real (lower) price, rendering the price fixers unable to profit from their scheme?

In the real world, "price fixing" is very difficult to accomplish.  In most industries, it would be very easy for a new seller to enter the market and offer their goods at the lower price, stealing the customers from the "price fixing" sellers.  For these sectors of the economy, "price fixing" is not an option unless the "price fixing" sellers can convince/coerce any entering sellers to commit to the existing fixed price.

Ordinarily, "price fixing" occurs in industries with either a monopoly or an oligopoly.
In a monopoly, there is only one seller.  So, they alone are able to dictate the price of the good or service.
In an oligopoly, there are only a few sellers.  These few sellers can easily conspire with each other to elevate the price.  However, even then, there is always the danger that one of the sellers will eventually drop their prices and try to steal the consumers from the other sellers.


How many US Dollars are lost or destroyed annually? Are there any estimates on how many US Dollars are lost or destroyed annually? By "lost or destroyed", I mean permanently removed from circulation because the currency is no longer usable

For instance, if I had a briefcase full of $100 bills that I either misplace (any nobody ever finds it) or toss into a fire, that money is no longer usable and cannot circulate within the economy. How much money is lost or destroyed in ways like these annually?

I'm primarily interested in estimates for physical currency, but would be interested in other means of money loss (can this happen electronically?) as supplementary information.

Are there any estimates on how many US Dollars are lost or destroyed
annually? By "lost or destroyed", I mean permanently removed from
circulation because the currency is no longer usable.

The link I offered as a comment covers this question nicely.

When Currency Is Physically Destroyed
Obviously, not all money is electronic. Just look at your wallet.
Bills and coins are destroyed every day. There are three destroyers of
money, and they're the same ones who create and regulate it.
(1) The Bureau of Engraving and Printing and (2) The U.S. Mint
The U.S. Bureau of Engraving and Printing creates all of the nation's
bills, while the U.S. mint creates its coins. But they also destroy
money.
Banks and individuals will hand over "mutilated" bills and coins to
these agencies. They then validate its authenticity and issue a
Treasury check in return. The Bureau of Engraving and Printing
receives around 25,000 mutilated currency redemption claims annually.
Each bill is shredded and sent to waste energy facilities for
disposal.

Here is a great video I found on the subject.

For instance, if I had a briefcase full of $100 bills that I either
misplace (any nobody ever finds it) or toss into a fire, that money is
no longer usable and cannot circulate within the economy. How much
money is lost or destroyed in ways like these annually?
I'm primarily interested in estimates for physical currency, but would
be interested in other means of money loss (can this happen
electronically?) as supplementary information.

By your situation previously, it is neigh-impossible to track such bills in circulation. As these bills don't transmit a signal as to their location, or who the buyer/seller is in a private party transaction. i.e. I meet up with you to buy your phone and pay in cash.
But at the same time, all US bills are serialized, meaning each are unique. A 1 dollar bill might have the same value as another $1, but each has its own unique identifier (serial number). When the US Treasury (through the Mint for coins and Bureau of Engraving and Printing for paper bills) issues new currency, the flow and supply chain of the money is tracked from its raw materials (ink, cotton, etc.) to distribution (banks, credit unions, foreign countries). Whenever a bill 're-enters' the system (i.e. deposited at a bank) the serial can be tracked from its origin point to its reentry point. However I am unaware of a system that can actively track its location in between.
At the same time, counterfeits are also taken into account the total supply of US dollars in circulation.
As for electronic loss, the current ACH System acts like a central authority that syncs all of the electronic activity that takes place. This is why when you pay, items on your bill are 'pending' until a couple of days later when they are 'posted'. At the same time, banks have several layers of backup systems and redundant systems to ensure 100% up-time and preventing data-loss.
Some reading to get started, but by no means definitive.


Why does neoclassical economics assume preferences are fixed and exogenous in nature? Why does neoclassical economics assume preferences are fixed and exogenous in nature? Is this because it's just a convenient assumption to make?

Does this link with the idea of "De Gustibus Non est Disputandum" (tastes are not a matter of dispute), if so, how?

Surely it isn't accurate to say that preferences are fixed when societal influences can easily change the preferences of individuals (e.g. through herd mentality etc.)?

As you suggested in your answer it is precisely this:

  Does this link with the idea of "De Gustibus Non est Disputandum" (tastes are not a matter of dispute), if so, how?

Also in psychology and sociology there is great debate between “nurture and nature”, that is whether really people’s behavior is fully exogenous determined by genes and so forth or endogenous determined by upbringing and society and the debate is still ongoing although both views seem have some merit in.

Second, even though it’s likely that society can affect preferences of the individual it is less clear if economy/economic system or many economic issues studied by economics can so.


Why can't countries print another country's currency? Counterfeiting money is clearly a difficult thing for individuals, but surely a country should have no problems counterfeiting another country's currency. Why don't countries do it? For example, for the US to exert pressure on North Korea (or vice versa), it could conceivably print lots of North Korean Won and use that to cause hyperinflation in North Korea. Similarly for Greece to dig itself out of its debt crisis it could just print USD or any other major currency, and convert that into Euros.

My best guess is that this isn't done because it's an act of war, but countries are apparently willing to sling cyberweapons at each other, in which case I don't understand why they don't also do this, at least on a small scale.

Why assuming that it isn't done in the first place? Turns out, it was actually done by Nazis in WWII

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

Also, suppose that somebody actually made dollars that are indistinguishable from genuine, Fed-printed dollars. How would you find out in the first place? How sure are you that nobody is doing it? :)


cournot competition with strategic consumers I am not familiar with economics but does anybody know any reference about cournot competition with strategic consumers?

In other words, is there any known competition where both producer and consumer can behave strategically and set the prices?

Studying a situation where consumers and producers interact to set price is precisely the study of bargaining. Any game theory text you pick up will almost certainly cover bargaining. The text I learned from, which I enjoyed thoroughly was Osborne's an introduction to Game Theory.

A first example of a bargaining game would be Rubinstein's game of alternating offers

I don't think adding consumer strategic behaviour to Cournot directly would be particularly more enlightening than studying bargaining separately, since Cournot already abstracts from the price setting mechanism.


When can I say that a utility function has constant marginal utility? Does this utility function have increasing/decreasing or constant marginal utility?

$ U(x,y) = x^2 y^2 $

Now, $ f_x = 2xy^2 $, $ f_{xx} = 2y^2 $, $ f_y = 2yx^2 $, $f_{yy} = 2x^2 $

$ f_{xx} $ has no $ x $ term in it -- so is the marginal utillity of $ x$ constant or increasing? It increases as $ y $ increases, of course, but it stays constant if we increase $ x $. My textbook says that this is a case of increasing marginal utility, but I don't understand why. Similar problem for $ f_{yy} $ , which has no $ y $ term.

Marginal utility (of $x$) in your case is $U_x(x,y)=2xy^2$. You use the sign of the derivative of MU, namely $U_{xx}$, to tell whether MU is increasing, constant, or decreasing.

Specifically, you have

increasing MU if $U_{xx}>0$,
constant MU if $U_{xx}=0$, and
decreasing MU if $U_{xx}<0$.

In your case, assuming that $y>0$, you'd have $U_{xx}>0$, hence increasing MU.


Does Pareto-efficency take into account growth? I'll try to state my question clearly:

For a given a "wealth" allocation Wt = (w1, w2, w3, ... ) for individuals I = (i1, i2, i3, ... ).

And a distribution of D= (w1/|W|, w2/|W|, w3/|W|, ... ), that is, as a percentage of the total.

Where Wt is Pareto Efficient at a given time frame  t , and W(t+1) is Pareto Efficient at  t+1 .

When there is growth such that     |W(t+1)| > |Wt|

Is Dt=D(t+1)?

If so, why? If not, how do you allocate say, capital, whose value is intrinsically linked to growth?

I understand many of my assumptions may be plain wrong or badly stated, I am still an undergrad. Sorry about that. And thanks in advance.

Further clarifications:

For each element  w  of Wt = (w1, w2, w3, ... ),

w= P * B

Where P is the price vector of a commodity bundle B.

I hope that my representation of growth as an increase in the magnitude of the W vector is correct. This is what has been bugging me the most. It's safe to assume that growth causes an increase in |W|, right?

It seems to me that as long as every person likes wealth any allocation $W_t$ will be Pareto-optimal.

Even if this was not the case, so supposing that $w_1, w_2,...$ are not real numbers representing wealth but vectors representing bundles of goods the distribution from one time to another can change drastically if you do not specify how growth occurs. At $t=1$ someone might have everything, then at $t=2$ someone else might have everything. Both of these states are Pareto-optimal, but the distributions are quite different.

So no, it does not follow from your conditions that $D_t$ necessarily equals $D_{t+1}$.


Why two goods are of different types of Cross Elasticity if we swap them in formula? I am using this formula for calculating Cross elasticity of demand:

$ E_{XY}^D = \Large\frac{(Q_2^X - Q_1^X)(P_2^Y + P_1^Y)}{(Q_2^X + Q_1^X)(P_2^Y - P_1^Y)}
$

If $E_{XY}^D$ > 0 Then goods X and Y are substitutes.
If $E_{XY}^D$ < 0  Then goods X and Y are complementary.
If $E_{XY}^D$ = 0 Then goods X and Y are independent.

I have this data:

P1 and P2 are prices; Q1 and Q2 are quantities.

Using above formula I have calculated cross elasticity $E_{XY}$ and $E_{YX}$ in Excel:

I calculated Cross Elasticity for X and Y and the goods turned out to be Complementary goods, but when I swapped X and Y and calculated using the same formula the goods X and Y become Substitutes.

Why two goods belong to one type of cross elasticity, but if we swap X and Y and plug values into formula the goods turn out to be another type of Cross Elasticity. Can two goods be considered substitutes and complementary at the same time? Isn't it illogical?

Excel file with data and calculations available here: Dropbox

The cross elasticity of demand $E_{XY}^D$ is defined as the percent change in quantity demanded for X divided by the percent change in price of Y, holding the price of X fixed.

The problem with your calculation is that you did not use the quantity change when the price is fixed. Therefore, you need additional data to calculate the cross elasticities.

Another part of your question is whether cross price elasticities are symmetric. The answer depends on what type of demand you are working with. For Hicksian demand (where we hold the utility constant), the cross elasticities are symmetric. For Marshallian demand (where we hold the income constant), cross price elasticities are generally different, even the signs could be different. The reason that the Marshallian demand has different cross price elasticities is that when price of a good changes, it has both price effect (self and cross) and income effect (self and cross). The "pure" cross price effect should be symmetric, which is what we see in Hicksian demand. But the "gross" cross price effect, the combined effect of price and income, is not symmetric, because the income effects caused by different goods can be very different. For more details about Hicksian and Marshallian demand, price and income effects, consult any decent intermediate micro textbook. Or probably Google will show you plenty lecture notes on these topics.


A question regarding definition of Pareto efficiency It says on Wikipedia: "All the points on this locus are Pareto efficient allocations, meaning that from any one of these points there is no reallocation that could make one of the people more satisfied with his or her allocation without making the other person less satisfied." But aren't different points on the contract curve different "reallocations"? Some of the points have better utility for both players than others. Isn't that a contradiction or did I miss something?

the process of moving from one point to another i.e. reallocation makes one person better off while making another person worse off. for instance, moving from the lower part of the contract curve to a higher part makes Octavio better off as Octavio's indifference curve goes further away from the origin. However, the process makes Abby worse off as Abby's indifference curve moves closer to the origin.

There exist multiple points of pareto efficient outcomes which are stable, i.e. no more trading occurs.


How do I calculate the amount of money I get from an investor and the percentage I give him in return? Let's say I owe a company.

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

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

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

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

Well basically it pretty easy to calculate:

A + B + C = X

A:  0.25X : 25% of the company for investors

B:  0.5X : 50% you want to be left with

C:  1M : The price for selling to third party

X:  The value of the company that we would like to find

So in your case it's:

0.25X + 0.5X + 1M = X ->
0.25X = 1M ->
X = 4


Structural shocks in economic models are unobservable and country-specific? Let's consider an exogenous oil price shock ($e_t$) as an example in the following equation $oil_t = \rho \; oil_{t-1} + e_t$, where $oil_t$ is one variable in a VAR system. We normally want to recover $e_t$ based on some structural model we have for some given economy. So I guess that makes $e_t$ also country-specific, right?
So, for example, we cannot just look visually at oil-price time series data and say that oil price shocks are more volatile or less volatile. Like it depends on the economy of interest?
So although oil prices may be more or less volatile in general for a given period, it does not say anything about oil price shocks for a given economy, I guess. We need a structural model to recover the oil-price shocks to see how it behaves, right?

If $oil_t$ is the worldwide price of oil, neither $\rho$ nor $e_t$ are determined in a country specific model (unless the country's economy is so large that it affects global oil demand, which is not the case here).
Because there is no feedback from domestic variables to the worldwide oil price $e_t$ is the structural shock if AR(1) is an appropriate model of the oil price.The residual of the regression of $oil_t$ on $oil_{t-1}$  $\widehat{e_{AR(1),t}}$ is already an estimate for the structural shock $e_t$. So you can assess the volatility of the structural oil price shock $e_t$ based on $\widehat{e_{AR(1),t}}$. For an AR(1)-process it is possible to do this by looking at a plot of the original series.


Does US gold reserves includes other counties' gold reserves? http://www.tradingeconomics.com/country-list/gold-reserves

For example, some of German's gold reserves are stored in US central bank as explained in https://en.wikipedia.org/wiki/Gold_repatriation:

  The gold in the U.S. was earned by West Germany through trade surpluses in the 1950s and 1960s and never moved it out of the United States due to fear of invasion by the Soviet Union.

In the case, does the 8133 tonnes gold reserves in US include the gold liability to other countries?

No.

The $8,133.5$ tonnes of gold, i.e. $261,498,926.230$ fine troy ounces, of the U.S. Government owned gold reserve is detailed in a monthly status report produced by the US Department of the Treasury, with the latest figure being for August 31, 2016.

The weight and notional value of $\$11$ billion (based on a statutory rate of $\$42.2222$ per Fine Troy Ounce) have change by very small amounts in recent years, I would guess related to selling gold coins and buying stock to make them.  For example the total in January 2012 was $261,498,899.316$ fine troy ounces, a difference of about $27$ troy ounces from the current figure.

Gold belonging to other countries are stored in the US, particularly in New York as being convenient for the market and for transport. But this is not counted in the US Treasury report.


Price when both supply and demand have market power I have an intermediate sector that operates using labor only. There is 1-1 pairs between firms and workers, with profits

$$\pi = (Ap - w)\cdot 1$$

$p$ is the price, $A$ productivity, $w$ wage. Entrance to this market comes through a Mortensen Pissarides matching market, where vacancies and unemployed meet. Free entry and search cost $c$ implies

$$ \frac{c}{q(\theta)} = \pi $$

where $q(\theta)$ is the matching rate given market tightness.

There is matching on the final goods market happening as well, which is why there is a free-entry given search cost $k$ to becoming a final goods producer. The details are not important here, but the final goods producer operate without using labor. Let $e$ denote the measure of intermediate firms (since it's also the employment rate), and $s$ the measure of final firms.

I'm wondering how prices are determined here. Wages are given by Nash bargaining, such that

$$ w = \arg\max_{\tilde w} \beta \log (\tilde w - U) + (1 - \beta) \log(\pi(\tilde w))$$

for some outside-option value $U$. However, I wonder how the price of the intermediate good $p$ is determined, given that firms of both sides ($e$, $s$) have some market power. I'm happy to do additional assumptions if necessary, as long as the approach is in line with what has been done in the literature.

To be frank, I don't care about details on this margin at all, I just need closure.

I suppose one way to solve this - but I'm still looking for a proper way without - is to fall back to matching.

If there is matching between the intermediate and the final stage, at zero search cost and symmetric arrival rates, the surplus will be split given the Nashbargaining weights - which then determines the price.


Log-linearization of real exchange rate I have a doubt on how to log linearize an expression for the real exchange rate. I have read in several papers that they express it using substitutions. I haven't been able to find out what substitutions they use, so that is why I come here to ask for help.

For example, suppose that the law of one price holds such that:

\begin{gather}
P_{H,t}=S_tP^*_{H,t} \quad \quad \text{and} \quad \quad P^*_{F,t}=\frac{P_{F,t}}{S_t}
\end{gather}

Let $Q_t=\frac{S_tP^*_t}{P_t}$ be the real exchange rate and $T_t=\frac{S_tP^*_{F,t}}{P_{H,t}}$. Moreover, let the CPI be

\begin{gather}
P_t=[aP^{1-\theta}_{H,t}+(1-a)P^{1-\theta}P_{F,t}]^{\frac{1}{1-\theta}}
\end{gather}

I know that the log-linear version of $Q_t$ is given by

$$\hat{Q_t}=(2a-1)\hat{T}_t$$

Can someone please tell me how to obtain this latter expression?

Thank you very much.

Let $P$ be the CPI of the Home country, $P^*$ the CPI of the Foreign country, $P_H$ and $P_F$ the price of Home and Foreign intermediate goods expressed in domestic currency, and $P^*_H$ and $P^*_F$ be the price of Home and Foreign intermediate goods expressed in foreign currency.

The log-linear version of the real exchange rate is given by

\begin{gather}
\hat{Q}_t = \hat{S}_t + \hat{P}^*_t - \hat{P}_t
\end{gather}

We know that the CPI of home and foreign country (log-linear versions) are given by

\begin{gather}
\hat{P}_t = a\hat{P}_{H,t} + (1-a)\hat{P}_{F,t} \quad \quad \hat{P}^*_t = a\hat{P}^*_{F,t} + (1-a)\hat{P}^*_{H,t}
\end{gather}

We only need to substitute this in the log-linear version of the real exchange rate:

\begin{gather}
\hat{Q}_t = \hat{S}_t + \hat{P}^*_t - \hat{P}_t \\
= \hat{S}_t + a\hat{P}^*_{F,t} + (1-a)\hat{P}^*_{H,t} - a\hat{P}_{H,t} - (1-a)\hat{P}_{F,t} \\
= \hat{S}_t - a(\hat{P}^*_{H,t} - \hat{P}^*_{F,t}) + \hat{P}^*_{H,t} + a(\hat{P}_{F,t}-\hat{P}_{H,t}) - \hat{P}_{F,t} \\
= \hat{S}_t - a\hat{T}^*_t + \hat{P}^*_{H,t} + a\hat{T}_t - \hat{P}_{F,t} \\
= \hat{S}_t + \hat{P}^*_{H,t} - \hat{P}_{F,t} + a(\hat{T}_t - \hat{T}^*_t)\\
= \hat{P}_{H,t} - \hat{P}_{F,t} + a(\hat{T}_t - \hat{T}^*_t) \quad \text{given that the law of one price holds}\\
= -\hat{T}_t + a(\hat{T}_t - \hat{T}^*_t)\\
= -\hat{T}_t + 2a\hat{T}_t \quad \text{given that the law of one price holds, $\hat{T}^*_t = -\hat{T}_t$}\\
\hat{Q}_t = (2a-1)\hat{T}_t
\end{gather}


If a company buys a robot, it's part of investment. If a person buys a car, it's part of consumption. Why? As I understand it, a company buying a robot -- something that depreciates over time and will eventually break -- is included in investment because it provides a long term benefit (increase in GDP). But then why is a car considered consumption? It also depreciates over time (though not in a year) and provides long term benefits to GDP.

Because there is a definition of what is production and what is consumption, and households are generally outside the production boundary. From the 2008 System of National Accounts (at 6.24):

  Economic production may be defined as an activity carried
  out under the control and responsibility of an institutional
  unit that uses inputs of labour, capital, and goods and
  services to produce outputs of goods or services. There
  must be an institutional unit that assumes responsibility for
  the process of production and owns any resulting goods or
  knowledge-capturing products or is entitled to be paid, or
  otherwise compensated, for the change-effecting or margin
  services provided.

The distinction therefore has nothing to do with cars versus robots, and everything to do with who purchases the car or robot. A car purchased by a consumer is considered consumption, but a car purchased by a firm is considered investment. This is intuitively reasonable; the stream of transport services that a household receives from owning an automobile is generally consumption, and likewise for a business it is generally an input into production. While it's true that a car owned by an individual may be used both for production and consumption, the point raised by denesp is precisely why no distinction is made: we simply do not know how people are using their personal cars at any moment in time, and it's probably not worthwhile to spend the resources to know, so we use the ownership of the automobile as a proxy for how it is used.

However, one might reasonably argue that even though the purchases are made by consumers, one should count the stream of transport services received by the household as consumption, and capitalize the purchase of the automobile. This is how we treat housing, as described in part in the answer here. Indeed, this point has been raised even by researchers at the US Bureau of Economic Analysis:

  The treatment of consumer durable goods other than owner-occupied housing as
  final consumption expenditure rather than as fixed capital formation is also a long-standing
  criticism made by many users of the national accounts. Consumer durables are similar in
  many ways to owner-occupied dwellings, but the treatment in the accounts is quite
  different. The owner of a dwelling is treated as an owner of an unincorporated enterprise
  that produces housing services, but consumer durables are not assumed to provide services
  within the SNA production boundary (SNA 6.89, 9.40). Many durables, such as cars, trucks,
  and furniture, can be used either by consumers or by business enterprises—the SNA
  definitions count their purchase by households immediately as final consumption
  expenditure whereas they are to be capitalized by enterprises. “Extended” national
  accounts developed by researchers such as Eisner, Jorgenson and associates, Kendrick, and
  Ruggles and Ruggles include the services of consumer durables (for a review, see Eisner
  1988). Fraumeni and Okubo (2001) illustrate the possible options of capitalizing motor
  vehicles or all consumer durables.

Why this is not done is a fair question, but I would speculate that (in the US at least) the answer is probably simply that given the limited resources available to the BEA, this potential improvement to the national accounts simply isn't as high a priority as other projects.


CAAR t-test for event-study I have a set of data that I have gathered for an event-study. I computed the CARs, CAARs (cumulated average abnormal returns) and now I have to do a t-test to test if CAARs are significantly different from zero. I work with excel and I am not sure how to do that.

You will need a One sample bilateral t-test.

Let say your cum abnormal returns are:

-0,15   -0,2    -0,02   -0,19   0,17    0,06    0,05    -0,1    0,03    0,12
-0,14    0,02   -0,2     0     -0,33   -0,1    -0,14    -0,28   -0,19   -0,29
 0,09   -0,33   -0,03   -0,4    -0,24  -0,26    0,12    0,22    -0,33   -0,02
-0,15   -0,03   -0,06   -0,1    0,14    -0,14   -0,43   -0,18   0,09    0,08

Then you have:

Mean              -0,096
Standard error     0,02620139
Standard deviation 0,165712138
Sum               -3,84
Count              40

In your case the null hypothesis will be $\mu=0$.

The main statistic to be computed is the observed $t$:

$t_{obs}= \frac{\bar{x}-\mu}{s/\sqrt{n}}=\frac{-0,096-0}{0,02620139}=-3,6639278$.

In Excel you can compute the theoretical $t$ with $\alpha=5\%$. You can use the following function $t_{crit}=T.INV(0,025;40-1)=-2,02269092$. *1.

Or you can compute the p-value with the following function $pval=2*T.DIST(-3,6639278;40-1;1)=0,000737103$. *1.

In any case you reject the Null (H0)($|t_{obs}|>|t_{crit}|$, or $pval<\alpha$).

*1. It is considered the half of $\alpha$ in $T.INV$ or double the $T.DIST$ result because of the bilateral test.


Mathematical analysis of Marginal Cost Marginal cost is the cost associated with producing one more unit of output.         Mathematically speaking, marginal cost is equal to the change in total cost divided by the change in quantity.

$\ MC(q_{1},q_{2})=\frac{TC(q_{2})-TC(q_{1})}{q_{2}-q_{1}}$

Marginal cost can either be thought of as the cost of producing the last unit of output or the cost of producing the next unit of output. Because of this, it's sometimes helpful to think of marginal cost as the cost associated with going from one quantity of output to another, as shown by q1 and q2 in the equation below.

To get a true reading on marginal cost, q2 should be just one unit larger than q1.

That said, as we consider smaller and smaller changes in quantity, marginal cost converges to the derivative of total cost with respect to quantity.

$\ MC(q_{1},q_{2})=\frac{dTC}{dQ}$

What if we need to calculate marginal cost as we go from one output point to a much bigger one?

For example, if the TC of producing 3 units of output is \$15 and the TC of producing 9 units of output is \$21, the marginal cost, simply put, is \$1.

Once we are considering a change in TC values due to a variation of quantity produced higher than 1 unity, are we applying the concept of average rate of change to measure the MC value?

I think you're getting things backwards. Marginal cost (at a certain quantity $q_0$) really only makes sense as the derivative of the total cost function with respect to quantity at point $q_0$:
$$
MC(q_0)=\frac{dTC(q_0)}{dq}.
$$
The interpretation of marginal cost as "the cost of producing the last unit of output or the cost of producing the next unit of output" is based on the (linear) approximation
$$
\widehat{MC}^+(q_0)\approx\frac{TC(q_0+1)-TC(q_0)}{(q_0+1)-q_0}\quad\text{or}\quad
\widehat{MC}^-(q_0)\approx\frac{TC(q_0)-TC(q_0-1)}{q_0-(q_0-1)}
$$
This interpretation is usually introduced in undergraduate textbooks because of its intuitive appeal, not for its mathematical rigor. Imagine trying to explain the concept of marginal cost as the cost associated with an infinitesimal amount of change in quantity to a freshman who probably has no idea what "infinitesimal" means, let alone the concept of derivative.

A first problem related to interpreting marginal cost as the cost associated with the previous or the next unit of output is that producing the two units (the previous and the next) may imply different costs. This is illustrated by the formulas $\widehat{MC}^+$ and $\widehat{MC}^-$. Suppose total cost is quadratic, i.e. $TC(q)=q^2$. Then it can be easily verified that $\widehat{MC}^+(q_0)\ne \widehat{MC}^-(q_0)$, for any admissible $q_0$. This is problematic because we want the marginal cost (at a particular $q_0$) to be unique.

Second, and this relates to your question at the end, the concept of "unit" is somewhat arbitrary. And this arbitrariness makes measures such as $\widehat{MC}^+$ and $\widehat{MC}^-$ unstable as well. To illustrate, continue with the quadratic total cost example. When the unit of quantity is kg, the "marginal cost" at $1$kg--as you would refer to the cost associated with producing one extra unit--is $$\widehat{MC}^+(1)=2^2-1^2=3.$$
But what if we suddenly want to change the unit of quantity to gram (g)? Then the "marginal cost" at $1$kg, or $1000$g, would change as well:
$$
\widehat{MC}^+(1)=(1.001)^2-1^2=0.002001.
$$
To avoid such instability caused by changes in units of measurement, marginal cost is defined as a derivative, not as a difference.

If you want to measure the change in total cost due to change in some arbitrary quantity, simply apply the first formula in your question. But keep in mind that this cost is not marginal cost as an economist would understand it.


Convert DSGE paper to structural econometrics, anything to be noted？ I'm intent to bring some insights of a DSGE paper to a structural econometric model. The paper is Liu, Wang and Zha's 2013 Econometrica paper on land collateral channel. Now I have some good datasets containing firm's land holding information, so I want to "estimate" than "assume and simulate". However, my coauthors and I are largely macro guy and know only a little about structural estimation.

(1). We are focusing on firm's investment decision (purchasing land or real estate asset) and borrow behavior. In Liu et al, they also modeled the household sector. So for our purpose , we can safely ignore the household sector, and treat (land) price exogenous ,right?

(2). The macro paper normally contains dozen of shocks, some of which we are interested (like the "collateral shocks"), some we are not (habit persistence). Then we just treat those we are interested in as parameters to be estimated , and others as unobservable impact?

Personally, I don't quite believe the DSGE model which specifies dozens of shocks .  I want to "bring some insights" and replicate from the LWZ paper. Most DSGE studies struggle to meet the general equilibrium condition, which , in my opinion, is one of their weakness. The price are too complicated and hard to fully capture, so if you are concerning something else, why just keep it exogenous and put other more realistic stuff.

There's no correct method to do this.  DSGE guys will estimate the model by doing something like this: plugging in priors for their parameters and then running an optimization that minimizes the distance between model and data moments while maximizing the log likelihood from the priors.  The data moments for them will be well known values of variances and covariance of the deviations of c, y, i, p from trend.

Structural estimation guys will do any number of things: a)  take a model predicted relationship,  like a investment to q relationship,  $i=b\cdot f(q)$ where b is a parameter,  estimated the relationship and infer the value of b; b)  general method of moments or simulated method of moments or indirect inference: use a characterization of the data into moments or auxiliary statistics,  and then find parameter values such that the model (analytically or with simulations)  replicates the values of these moments or auxiliary statistics.

Which moments / statistics to use?  Who knows!  Follow tradition!

Which macro variances or covariances?  Who knows!  Follow tradition! (plus the values of these maybe change dramatically depending on how and when you calculate them....)


How to assign a set of parameters to a macroeconomic model in Matlab? I am trying to assign a vector of values (v= [1/3 0.01 0.5]) to a vector of parameters (w = [alpha beta gamma]) in order to make Matlab save the entries of the value vector as the parameter values. So for instance the third entry of v should be assigned to the third value in w. Matlab should then save gamma = 0.5 in the workspace. I was not able to figure out how to do it. My solution always just overwrites the other vector but does not save the entries in the workspace. I hope, someone can help me out.

Here is my approach to assign a set of parameters to a macroeconcomic model:
function para=assign_parameters(v)

if length(v)==3
   para.alpha=v(1);
   para.beta=v(2);
   para.gamma=v(3);
else
   error('parameter input has not correct format of length 3!');
end

The advantage is that the parameter set can be changed on the fly. That is, one can assign to the same underlying macroeconomic model a different set of numerical parameters without observing any conflict among the analyzed models. This would allow a quick comparison of model outcomes and ensure a clear as well as consistent model environment.
For instance, the example from the post can be assigned by
pm=assign_parameters(v)

and if one wants to study a second model like
v2=[2/3 1/100 1/2]

one should assign this set of parameters to a different structure name like
pm2=assign_parameters(v2)

Then both sets remain separated and the first parameter set will not be overwritten by the second.


Python vs R (vs Stata): the old battle revisited I am an avid Python user. I know Stata but I'm not a pro. I don't know R. I do econometrics (mostly time series, but also cross-section and panel), and statistics, and Python seems quite sufficient in meeting my needs.

I know that economists (at least old schoolers) are mainly using Stata and statisticians mostly R.

I read here and there that 1) R's libraries are superior to Python's, and 2) when it comes to visualization nothing can beat R's ggplot.

My questions are:

a) What are examples of econometric/statistical analyses that can be easily done in R but not (as easily or at all) in Python?

b) Is visualization in R really superior to Python? In what sense: less coding, ease of coding, more intuitive, or the quality of the final output?

c) Where will you put Stata in this comparison?

I use all three programs.

Python can do everything that R can do and R can do everything that Python does, but I must say R is superior to Python when it comes to the packages. For that reason for most econometric analysis I usually default to R. I find also producing nice standard statistics graphics with R easier (but for maps I prefer Python).

However, Python is far superior for web-scraping, numerical analysis and sentiment text analysis (although R has some good packages for that as well). Also, I prefer to use Python when I need to set up my own program as programming in Python is more natural (if that makes any sense) than in R, unless the program can be build easily from ready made functions from various packages.

I always recommend to people around me to learn both Python and R - the difference between them is not that big and with R you don’t really need to invest heavily into programming skills but just basics and then use packages.

Also, Jupyter Notebooks that can accommodate both R and Python make using both of them easier.

When it comes to Stata I use it only for a educational purposes (I teach econometric tutorials at university). To be honest I don’t like stata for several reasons:

Stata is not a freeware and i don’t think that the price tag is justified given that it’s inferior product compared to free ware programs like R and Python. If you can get it for free from uni then you probably don’t care about that but still it’s something to keep in mind.
Stata is a program not a language so if you want to create a new complex function you need to separately get and learn Mata (statas programming language).
Stata has some serious limitations on matrix sixes even in the most expensive edition the max mat size is 11000 which is serious limit when you work with panel data and have to run some iterative model with large number of variables. You will be routinely forced to run for example panel LR heteroskedasticity test on random subsamples even with the most expensive edition.
Creating beautiful graphics in Stata is nearly impossible - now don’t get me wrong you can make some decent graphics in Stata but it pales in contrast to what you can do with Python or R.
Stata is clunky with time series analysis. If you look for easy to use program for time series analysis it would be EViews. For example Stata can’t handle if you have quarters that are expressed in date format it will think you have gaps in your time series and won’t let you run basic time series commands until you create new time series variable. Also the offer of time series models is quite low and programming your own is painful.
While technically possible webscraping or numerical analysis in Stata is hell - if you need that for your work don’t use it.

However, Stata has also few advantages:

It’s more user friendly than R or Python, and can be even used without coding through interface (that’s why we use it for tutorials for students as a first program they see so they don’t get overwhelmed).
Doing some adjustments to datasets creating dummy variables etc is easier compared to Python or R but that’s mostly because in both Python and R you can have various types of data, lists, data frames etc.
With purchase to Stata you get access to Stata forums - it’s something like stack exchange but they actually pay professionals to give you answers there and often beside support you can get there very good advice even on econometrics, and you will usually get advice really quick.

I personally would not use Stata for my own scientific work. Python and R are superior to every aspect of Stata - but it’s very good starting program for students.


Multiple Equilibria and Index Theorem Consider the following 2x2 game:

\begin{array}{|c|c|c|}
\hline
&C&R\\\hline
M&0,0&3,5\\\hline
D&4,4&0,3\\\hline
\end{array}

This game has two distinct pure-strategy Nash equilibria.

I recall that in cases like this there is almost always a third mixed NE, and this had to do with the index theorem and having an odd number of equilibria.

Can someone provide the idea behind the index theorem and why having two distinct pure strategy NE in 2x2, 2 person game, static, complete information results into a third mixed NE with probability 1?

What about
\begin{array}{|c|c|c|}
\hline
&C&R\\\hline
M&0,0&0,0\\\hline
D&0,0&1,1\\\hline
\end{array}
?

This game has two pure equilibria, $(M,C)$ and $(D,R)$ but no mixed equilibra.

You are probably referring to Wilson's Oddness Theorem, which guarantess your claim for generic games. See
Oddness of equilibrium points.


Elasticity and its types Does 'infinitely elastic' and 'inelastic' pertain to same meaning? What is the difference between them? Please explain in brief.

No. In fact, they mean quite the opposite.
Infinitely elastic, means the elasticity is infinity.
Perfectly Inelastic means not elastic, i.e. the elasticity is 0.
Ineslastic means the elasticity is very low, so between 0 and 1. This means there is "underreaction" (less than proportional).

So if something is infinitely elastic there will be an extremely large reaction.
If something is perfectly inelastic there will be no reaction.
If something is inelastic,  there will be very little reaction.

Let's take the example of price elasticity for an ordinary good where price increases cause demand to fall.

A good with a very close substitute would have a large price elasticity. If it's infinite: At a given price there will be a given demand. As soon as we increase the price even marginally the demand will fall to 0.

A good with no substitute and especially addictive goods usually have a price elasticity of (close to) 0 typically. There is the same demand at all prices. Assume an individual who always must smoke a pack of cigarettes a day. If we increase the price of cigarettes and if his elasticity is 0, then he will continue to purchase one pack a day. Even if we double the price or more, there will be no reaction (in this case reduction).


markov-switching model and stationarity To test the structural breaks and to perform markov-switching model  in time series data,  should i have stationary data.
Thank you in advance.

In this lecture it is stated at chapter 2.3 that "The Markov switching model and its variants discussed in the preceding sections are
only suitable for stationary data". Perhaps you'd like to read into that more thoroughly.
Possible solution:
Since differentiation is allowed, you should also be able to produce an Error-Correcting Model -and its variants- through cointegration if stationarity is not achieved.


Government debt and Fiscal Theory of Price Level I am trying to understand the Fiscal Theory of Price Level (FTPL) and how it explains inflation. I've been reading several papers by Eric Leeper and I am slightly confused about some of his claims. For example in this paper he argues:

  Suppose that higher deficits do not create higher expected surpluses and that central
  banks either peg short-term nominal interest rates or raise them only weakly with inflation.
  Because a tax cut today does not portend future tax hikes, individuals initially perceive the
  increase in nominal debt to be an increase in their real wealth. They try to convert higher
  wealth into consumption goods, raising aggregate demand. Rising demand brings with it
  rising prices, which continue to rise until real wealth falls back to its pre-tax-cut level and
  individuals are content with their original consumption plans.

I understand that he is explaining 'non-Ricardian' policies. However, if the government increases its deficit by issuing bonds, would that not decrease AD in the period the bonds are sold? Say that the government increases its deficit in period $t$ by selling bonds. Private agents buy these bonds and thus give up consumption goods. So in period $t$, should AD not decrease? And when the bond matures and the agents receive their payoff, they will spend it as long as the government is credible enough in not raising taxes. I might be overcomplicating things about this is just a thought I have had.

And lastly;

  By preventing nominal interest
  rates from rising sharply with inflation, monetary policy prevents debt service from growing
  too rapidly, which stabilizes the value of government bonds.

I understand the reasoning that keeping interest rates stable will stabilize the debt servicing. However, suppose that interest rates rose. If the interest  rate is higher than the growth rate of the economy, the government will have to monetise its debt in order to pay the interest component, this will obviously be inflationary. Or, they can issue more debt. If they choose the roll over on the debt (i.e paying the interest by issuing even more debt), will this be inflationary or deflationary? Using the same reasoning as above, I would think this is deflationary because by selling bonds to private agents, they have to give up consumption goods, thus reducing AD.

I'm trying to understand the intuition behind fiscal and monetary authority interaction. So if my questions can be answered by academic literature, I would gladly give it a read.

Thanks in advance!

Question:

  I understand that he is explaining 'non-Ricardian' policies. However,
  if the government increases its deficit by issuing bonds, would that
  not decrease AD in the period the bonds are sold? Say that the
  government increases its deficit in period t by selling bonds.
  Private agents buy these bonds and thus give up consumption goods. So
  in period t, should AD not decrease?

The act of issuing bonds does not directly affect AD, it only results in a rebalancing of portfolios: the household sector gives up money balances in exchange for government bonds. (If your model implies that spending depends upon money balances, there might be an indirect effect on the economy. In many models, money balances are zero, and so there is no effect. See below.) In any event, the end-of-period money holdings of the household sector depend upon the reaction function of the central bank within the model, and so that reaction function will effectively determine the final household portfolio allocation between money/bonds. (The reaction function is usually specified as a rule for the interest rate, which determines money holdings within the household's money demand function.)

The lack of relationship between money balances in macro models and transaction volume is not entirely obvious. The reason is that money balances are meant to represent end-of-period holdings, and transactions clear simultaneously. This means that a household with \$100 income can spemd \$100, and leave a \$0 cash balance at the end of the period. Since it is better to hold bonds/bills if interest rates are positive, the end-of-period money holdings woukd normally end up at zero. It can do this in every period, and so it is continuously transacting, yet measured money balances never appear. This is obviously unrealistic, and so other classes of models introduce reasons for end-of-period money holding. Two typical cases are a cash-in-advance requirement, or money in the utility function. The cash-in-advance requirement is that money holdings have to be at least some percentage of consumption spending (which simulates the reality that most wages are paid at a lower frequency than spending). Money in the utility function creates a demand for money within the optimisation problems, which usually depends upon the rate of interest. The end result is that the model assumptions imply a relationship between money holdings and the economy; change the assumptions, and the relationship changes.

Leeper is discussing a tax cut, which can trivially give rise to unchanged consumption (multiplier of 0). The government consumes the same amount as before, and thus runs a higher deficit (which is matched by greater bond issuance). If the household sector consumes the same amount, its savings rises by the amount of the tax cut, which it invests in bonds.

If the "multiplier" on the tax cut is positive, it implies that the household consumes more as a result of the tax cut, and so we have greater output. The exact effect depends upon the model you are using.

The question asks:

  However, suppose that interest rates rose. If the interest rate is
  higher than the growth rate of the economy, the government will have
  to monetise its debt in order to pay the interest component, this will
  obviously be inflationary.

The quote from Leeper is a discussion of "Regime F." Within the analysis of the paper, monetising of debt has nothing to do with determination of the price level. The paper, the price level in regime F is given in equation (14), which is described:

  At time t, the numerator of this expression is predetermined,
  representing the nominal value of household wealth carried into period
  t. The denominator is the expected present value of primary fiscal
  surpluses from date t on, which is exogenous.

That is, the expectation is that future primary surpluses will be used to stabilise the debt level.


Does each stock exchange only trade in one currency? And if not, how are currency exchange rates accounted for?

An exchange can handle more than one currency, but this would be uncommon for equities.  An example is the ICE futures exchange in Europe.

Multiple currencies doesn't cause any particular problems - transactions are carried out in currency and it is up to you to convert to whatever currency you prefer.  Usually done by fx sweeps by your custodian bank.

For margin purposes combined exposure (e.g risk netting) can be calculated at prevailing fx rates.

Each security only trades in one currency, and each security trades basically like a mini exchange so there isn't really any problem.  Think of it like two exchanges run by the same company.


Why teach Arrow's impossibility theorem? As part of a Macro class on social welfare, I am about to teach a very brief introduction to Arrow's impossibility theorem.

The classic demonstration of this involves three voters choosing between three alternatives, whose preferences are as follows:

  A B C
1 x y z
2 y z x
3 z x y

We are then shown the supposedly interesting result that, given these obviously incompatible preferences, no possible voting system can pick a favoured option in a non-arbitrary way.

More generally, any voting system risks ending up in this kind of three-way tie situation.

But this seems impossibly theoretical a concern. Clearly if voters' preferences split n alternatives precisely n ways, as in this example, there's no outcome that satisfies a majority. But in an electorate, the probability of this is vanishingly small. Also, if each alternative is joint first in preference, we surely don't care which one is selected.

Why do we teach this mysterious theorem at all? Is it just because it's got a cool name? Has it ever been usefully applied to a real-world problem?

What you describe has not much to do with Arrow's impossibility theorem. This is called the Condorcet paradox. The preference profile you gave is used to demonstrate that even if all individual preferences are transitive group judgement may not be. Using majority voting y beats z, z beats x and x beats y.

Arrow's impossibility theorem is a more nuanced theorem. If you have not studied it do read up on it, it is fascinating! (You probably have to get a book on Social Choice to get familiar with the concepts the theorem uses.)

Judgement aggregation is covered in basic micro courses to show that it is not clear which of the efficient allocations a social planer should use, because society may not agree.


Who really benefits from economic growth? In recent social protests, I have heard the claim that the economic growth benefits only the rich: they become richer while most people become poorer.

To check whether this claim is realistic, I looked for data relating economic growth (measured by the increase GDP) and real wages. I found this blog post, which shows that in the UK in 2008-2014, there has been positive economic growth while the real wages were declining.

The writer offers several explanations to this phenomenon, but they may be specific to the UK. So, my question is: what are some other examples of economic growth that comes together with decreasing real wages?

In general, what are examples of economic growth periods, in which few people benefit while most people become poorer?

I suppose that it depends on the time scale you are considering. Over the very long run the poor seem to have benefited far more than the rich from growth. See for example Robert J. Samuelson in the Washington Post:

  By 1915, the United States was the world’s richest nation — and yet,
  most Americans were dirt poor by today’s standards. Adjusted for
  inflation, men’s average wages were about a third of what full-time
  workers now earn. The average workweek in manufacturing hovered around
  50 hours, and many employees worked a half day on Saturday. Less than
  a third of homes had electric lights. Less than a fifth of the adult
  population were high school graduates.

A hundred years ago leisure and electric lighting were luxuries. Now they are near ubiquitous in the west. Higher education used to be rare, now it is common. Heath-care was once dangerous and of limited efficacy for poor and rich alike, and now we use lasers, chemicals, and radiation to great curative effect.

Billionaires All (Or Practically So) by Don Boudreaux

  In 1916 even Rockefeller had little access to air conditioning; the
  range of cuisines from which he could choose his meals was drearily
  narrow; he was attached by wire to a wall or a floor whenever he spoke
  on the telephone; he could entertain and inform himself neither with
  radio nor television; forget about computers or tablets.  Every movie
  he watched was silent and in black and white.  Unlike us today, in
  1916 it took Rockefeller days, rather than hours, to get from New York
  to Europe – or even to California.  Although he was chauffeured in his
  (un-air-conditioned) limousine, the ride he experienced was bumpier
  and more perilous than is any ride enjoyed today by an ordinary
  American.  Rockefeller’s fine Swiss watch was far less accurate than
  is today’s cheapest Timex.  Were he to need the services of a fire and
  rescue team, it would have taken that team longer to reach
  Rockefeller, and the effectiveness of their efforts to save his life
  or his property were much less than is the effectiveness of such
  teams’ efforts today.

  If in 1916 Rockefeller or any of his children or grandchildren caught
  pneumonia or cut a finger on a rusty nail, the risk of death was much
  higher than it is today because antibiotics were unavailable.  Of
  course, Rockefeller also had no access to statins, hip- or
  knee-replacement surgeries, Lasik procedures, contact lenses,
  antihistamines, or even sunglasses that protected his eyes from
  ultraviolet rays.  Yet he was then one of the world’s richest men –
  deprived as he nevertheless was of many of the miraculous goods and
  services that we ordinary Americans today take for granted.


Kelly criterion wealth allocation alternatives Thanks for your patience with answering my question.

I am interested in building an optimal wealth allocation strategy across multiple betting opportunities, correlated or uncorrelated and with different types of constraints.

I've been looking for relevant papers and literature.

What I've found so far is all Markowitz theory, Kelly criterion related. My question is if there are other alternatives to such strategies that may have very different idea behind them.

Also if there are some papers that you yourself found very relevant to Markowitz and Kelly. Papers about informed betting strategies, investments across multiple opportunities, wealth allocation etc.

Yes.  I just published a paper deriving the distributions of returns for all asset and liability classes.  It isn't one distribution or one family of distributions.  Stocks are a mixture of multiple distributions.  Some of these distributions have covariance structures, and some do not.  You may have to do a bunch of your own math though.  I have been contemplating writing a Kelly bet paper, but have not had the time.  I am about to present a distribution-free replacement for Ito calculus that does not assume the existence of first or higher moments at the Southwestern Finance Association Conference.  As such, I have been busy.  It is nearly independent of the economic model in use.  I say that because it would cover a model built around panda bears if that were the true model in nature but nobody knew it, but it may not hold if certain implicit biological assumptions became untrue in the future about humans.

What you will want to do is account for bankruptcy risk, cash merger risk, stock-for-stock merger risk and liquidity risk in addition to return risk.  There are distributions for each in the paper.  Because a Kelly bet is equivalent to having logarithmic utility, my recommendation is to solve it as a log problem.

The difficulty you will find in the paper is that for stocks, there is no equivalent to a covariance matrix.  As you add dimensions, you do not add terms for the scale parameter.  If you ignore liquidity, the limitation on liability, bankruptcy and mergers then the returns for one asset are: $$\frac{1}{\pi}\frac{\sigma}{\sigma^2+(r-\mu)^2},$$ but for two assets it becomes $$\frac{1}{2\pi}\frac{\gamma}{(\gamma^2+\sum_{i=1}^2(r_i-\mu_i)^2)^{3/2}}$$ and for three assets it becomes $$\frac{1}{\pi^2}\frac{\delta^2}{\sqrt{\delta^3}\left(\delta+\sum_{i=1}^3(r_i-\mu_i)^2\right)^2}.$$

Notice that the scale parameter changes as assets are added which I denote by simply changing the variable name $(\sigma,\gamma,\delta)$.  This is really challenging to work with because of the poor form.  Also, I didn't work out the correct constant of integration since I didn't want to sit around working out the integrals under the limitation of liability.  It is late, and I teach in the morning.  These assume up to infinitely negative returns.

There is a practical alternative as well here, and you should assume no correlation as well.  Graham and Dodd investing provide the clue.  If you assume an all-or-none utility function, that you receive a utility of one if your return exceeds a threshold and a zero otherwise, then you get a simple answer.

First calculate the Kelly bet on a binomial, which is trivial, for your threshold rate of return.  That becomes your allocation level.  Second, as price falls, the probability of meeting the level increases and so your variance falls.  So pay as little as possible for a bet.  As you are reducing your price, you are also exposing less money to each bet, so you are reducing your risk in three ways, both through the probability of loss is reduced, the variance is reduced and the exposure size being reduced per unit of risk.

You can find the paper at

  Harris, D.E. (2017) The Distribution of Returns. Journal
  of Mathematical Finance, 7, 769-804.

The paper is built around the observation that questions such as $\text{var}\left(\frac{S_{t+1}}{S_t}\right)$ are built around two observable stock prices.  This implies that stock prices and stock volumes are data, but returns are a function of data and therefore a statistic and not data itself.

Since the return is future value divided by present value minus one, it follows that returns are a ratio distribution of future prices divided by current prices.  Under mild assumptions about how stocks are traded and the number of investors involved, stock prices should be normally distributed at any static moment.  More precisely, the limit order book should be.  These distributions are just the ratios of two normal distributions for each stock.  It also nicely fits the data if you make adjustments for things like bankruptcy and so forth.

By converting your problem to a binomial you tame it and put yourself in Warren Buffett's shoes with a mathematical explanation as to why that is the case.  The downside is you now have all the terrible reading to do of annual reports as you have to restate them from their official values to their economic values for this to work.  So a ten year deferred tax liability for $100 million needs reduced to present value since this is an interest-free loan from the Treasury and the difference added to equity.  Still, once you do the analysis, you can make a good return.

Also note that these distributions lack both a mean and a sufficient statistic. In the real world they are truncated at -100% and so no non-Bayesian solution exists for any of these that is unbiased and admissible.  Don't plug in your R function. It won't work.  You have to build this from scratch if you are going to make predictions.  Nicely, Bayesian predictions are of the form:

$$\Pr(\tilde{x}|\mathbf{X})=\int_{\theta\in\Theta}\Pr(\tilde{x}|\theta)\Pr(\theta|\mathbf{X})\mathrm{d}\theta,$$ so you can form predictions that do not depend upon the value of the parameters.  Use the CDF of $\tilde{x}$ to form your binomial density.

Technically, this is not quite correct because the multi-asset form is not independent.  No two returns can ever be independent, even if there is no correlation.  Still, it is a reasonable heuristic.


White versus Newey-West standard errors could you please help me to understand when I should use either white or newey-west standard erros?

I do work with time-series data. I look at both contemporaneous and intertemporal realtionships.

My understanding is that NW s.e. are appropriate when I look at an intertemporal realtionship and one variable is constracted using overalapping observations.

example I have y(t) and x(t) for t=1,...,T.

I construct y3(t) as y(t) + y(t+1) + y(t+2) for t=2:T-2, and then I regress y3(t+1) on x(t).

For this kind of regressions, it is common to use NW s.e., in particular if x is highly persistent.

Can you please help me to understand more in general how to choose between White and NW s.e. (or other s.e. appropriate for time-series analysis)?

Thanks a lot!

White standard errors correct for heteroscedasticity only, whereas Newey West standard errors are robust to both Heteorscedasticity and Autocorrelation (HAC) .


Whatever happened to efficiency wage theories? Older macroeconomics texts give much space to efficiency wage explanations of how unemployment could coexist with wages in equilibrium higher than the reservation wage of workers.

However, there seems to be very little current research on these theories, with most recent papers modelling unemployment using search frictions.

Is the decline in popularity of efficiency wage models due to their having failed in some sense? I would greatly appreciate any references to the literature.

I don't believe that Search Unemployment (MP) actually "won" over efficiency wages. The whole discussion of search literature would be too long for this post, so I'll just skim the most important parts.

(i) As a first, Shimer (2005) discusses that the MP model actually fails to get employment (market tightness) volatility right
(ii) In the same AER issue, Hall(2005) proposes rigid wages. He and Shimer (in his booklet) argue that there is a set of wages which satisfy Barro (1977). Moreover, an intuition for wage rigidity is that old wages are an anchor for new negotiations
(iii) Many papers show more or less convincingly that while average wages are rigid, wages of new matches actually are quite flexible.
(iv) Bewley (1999) presents survey evidence where managers respond that they don't want to reduce wages because it would lead to detrimental climate.

First, to the extent that the MP model actually needs exogenous wage rigidity to get the moments in the data right, it has not won over efficiency wages, as these could be understood as a complementary theory (as being the reason for wage ridigity, as an alternative to (ii)).

Second, (iii) kind of goes against both MP and efficiency wages at the same time - at least to the extent that they explain fluctuations in hirings. Note that this is the relevant margin for unemployment fluctuations: [I think it was Shimer who] showed that the most fluctuations in labor come from volatility in hiring, and not from firing.

Finally, a personal opinion. I was interested in the story myself, but I wouldn't know how you could find efficiency wages in the data we have. Also, there's not really more to the theoretical component than was written in the past century.

The trend in the past decade has gone to microfounded, self-consistent models that are found using empirical data. I don't believe that this is really possible at the moment with the efficiency wages story. We believe efficiency wages exist, but we can't detect them and they (arguably) don't explain the Shimer puzzle, which makes them less interesting these days.


Why are pricing charts treated as continuous series? I understand that prices are set by actors' offers to buy and sell within the market, however, when analyzing the data it seems to often be treated as though the price is continuously varying like some natural process that is independent of the actors' choices to buy/sell at certain prices... said offers being what actually creates the discrete datasets.

Is there a reasoning/rationale behind this? Does it make a difference? Am I missing something here?

Inherently discrete variables (like "count data") have special properties, and it matters when it comes to econometric estimation.

The usual criterion to treat a variable as continuous or discrete, is I believe not what we observe but what could be conceivably observable.
Example: if one counts number of people, the variable is inherently discrete. In large samples, the continuous approximation may not matter -in numerical analysis, starting the search for a solution by "pretending" that the data is continuous is done all the time. But in small samples it may matter. Also, there are variables that take only a few specific values (usually integers). Here, taking into account the discreteness is crucial.

Prices have no reason to be treated as discrete. They are continuous because in principle nothing constrains a price to not take any value on the half-real line.

As for the data sets: data is always discrete -simply because between any two real numbers there is an "infinite" number of other real numbers (with the appropriate mathematical definition of infinity). So since the sample is always of finite size, it will always be discrete. The issue is whether the Data Generating Mechanism can be conceived as being continuous or not.

Finally, for certain purposes continuity is a great analytical helper bar one-dimension: the time-dimension, especially in stochastic setups. Continuous stochastic calculus notoriously carries a mathematical baggage that many times (but not always) one feels that is not worth the trouble.


Does diminishing government spending lead to a reduction in trade deficit? NX ≡ (S-I) + (T-G)

  Read this as “the trade balance (net exports) is identical to the sum
  of net savings (savings minus investment) and the government’s budget
  surplus or deficit (taxes minus spending).”  This is not a theory of
  what causes what; it’s an identity, different ways of expressing the
  same “what”.

http://econospeak.blogspot.com/2016/12/the-identity-equals-causation-fallacy.html?m=1

Since the government spending less won't impact negatively savings, especially if savings is already low (people will save more because they will want insurance, etc.) and won't necessarily lead to companies spending a lot more to offset it, it will most of the time lead in a reduced trade deficit. It seems that although cause/effect relationship in a large system is complex and goes both ways, the government spending less will in almost all cases lead to a reduction in trade deficit. Is this true?

I will give an overview based on the analysis of Chapter 6 of “Monetary Economics: An Integrated Approach to Credit, Money Income, Production and Wealth” by Wynne Godley and Marc Lavoie. This is a Post-Keynesian textbook; neoclassical economists might debate the exact model structure, but their models probably give qualitatively similar results.

There’s a lot of issues buried in your question. One immediate problem is that we should not really look at just the government deficit: what the government is doing also matters. For example, the government could decrease spending in aggregate, yet greatly increase its imports (e.g. defense spending) and so the trade deficit could get worse. We will assume that something like that is not happening.

Arguing that government spending “will not impact savings” (as the question is now stated) is incorrect. Savings desires might well be unchanged, but changing government spending changes incomes, and so actual saving will change. Furthermore, cutting spending presumably has some multiplier effect (the precise level of the multiplier is hotly debated), and this will affect investment plans.

In the model in “Monetary Economics,” cutting government spending reduces the trade deficit. Since it is a multi-equation system that is solved simultaneously, one needs to be careful about verbal descriptions of mechanisms. However, I would describe the mechanism as follows: reduced government spending reduces national GDP, and this implies less imports (since imports are a fixed propensity to import out of all spending). As a result, the trade deficit falls, but it is not 1:1 with the reduction in spending - as your question phrasing (at the time of writing this answer) suggests.

One could debate the model structure, but I cannot think of many model structures that would suggest that the trade deficit would widen in response to government spending cuts. The implication is that the real debate is about the coefficient that relates the size of the cut in government spending to the trade deficit reduction. In almost any model, that coefficient would be parameter dependent, and so one would need to look at observed data to come up with a prediction for the real world.


Are stock exchanges market makers? Are stock exchanges like NASDAQ and NYSE market makers? In other words, are they providing liquidity by pairing individual buyers and sellers with each other in real-time? Or does it work differently?

No, they are not market makers.

A market maker is someone who (i) quotes two prices (one 'low' and one 'high'), (ii) will buy from any seller at the low quoted price (even if there is no corresponding buyer right now), (iii) will sell to any buyer at the high quoted price (even if there is no corresponding seller) right now.

This injects liquidity into the market when there is an imbalance in the number of sellers and buyers.

NASDQ and NYSE are not market makers, they are marketplaces in which market makers operate.


Macro Economics Question: How will this curve shift? I am studying for a Macroeconomics Test on the Money Market and was wondering how the Demand Curve for Money would shift when there are changes in Taxation, Income, and Price Levels? (i.e. it would move to the left / right because...)

Here is the graph and slide I am referring to:

If anyone can help explaining this I would really appreciate it!

You can look at IS-LM models in order to understand the intuituion more deeply.
In this graphic, IS curve shifts to left when there exists a demand-sided economic policy like government spendings etc. This will for sure increase the demand of people in economy, which will increase price levels.  If the price level increases, with the same quantity of money circulated in economy, the interest rate will increase. (you can see it on the graph) So, a central bank must control these kind of policies with a monetary policy in order to stabilize its inflation.

The same logic in increase of income. This will increase demand, which will increase price levels and agents will need more quantity of money in order to realize their transactions.