Example of information structure in a one-player Bayes Correlated Equilibrium Model

Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world.

The state of the world has support $\mathcal{V}$.

When DM chooses action $y\in \mathcal{Y}$ and the state of the world is $v\in \mathcal{V}$, she receives the payoff $u(y,v)$.

Let $P_V\in \Delta(\mathcal{V})$ be the DM's prior.

The DM also processes some signal $T$ with support $\mathcal{T}$ distribution $P_{T|V}$  to refine his prior and get a posterior on $V$, denoted by $P_{V|T}$, via the Bayes rule.

Let $S\equiv \{\mathcal{T}, P_{T|V}\}$ be called "information structure".

A strategy for the DM is $P_{Y|T}$. Such a strategy is optimal if it maximises his expected payoff, where the expectation is computed using the posterior, $P_{V|T}$.

Question

Suppose that the DM discovers that the state of the world, $v$, is a number in $[a,b]\subset \mathcal{V}$. Can this be written as an information structure (i.e., a distribution of a signal)?

The signal structure must specify what the DM learns in all possible states of the world, so I think your question should read:

"Suppose that the DM discovers whether the state of the world $v\in V$ is in $[a,b]\subset V$ or not. Can this be written as an information structure?"

or should read:

"Suppose that the DM discovers the state of the world $v\in V$ whenever it is in $[a,b]\subset V$ and learns the minimum otherwise. Can this be written as an information structure?".

From the comments of the question, I think you are more interested in the first one. Regardless, a couple of comments are important:

You want the  DM to assign positive probability to an interval, and there are many ways to do so. There are some restrictions that are coming from your prior, but they are relatively mild.
The most important one is that $P_V(v)>0$ for all $v\in [a,b]$. That is, the prior must assign positive probability to all numbers in the interval.
Even when you decide how much probability you want to assign to each point (assuming it is feasible given the restrictions mentioned above), there are many signal structures that can achieve this (Thus, I will be providing just a couple of examples).

Example 1:

Suppose $V=\mathbb{R}$ (the real line), and $P_V$ is the normal standard distribution over the reals, suppose that you are interested in finding a signal such that the posterior $P_{V|T}$ is the normal standard distribution truncated to $[a,b]$. Then the signal structure can simply be as follows:

Let $\mathcal{T}=\{blue,red\}$
$$P_{T|V}(blue|v)=\left\{\begin{array}{c c}
1 & ; v\in[a,b]\\
0 & ; v\notin [a,b]
\end{array}\right. \ \ \ \forall v\in V
$$

Of course $P_{T|V}(red|v)=1-P_{T|V}(blue|v)$.

Notice that if the DM gets a signal "blue", they infer that the state is in $[a,b]$,  and because the signal "blue" is equally likely to be received for any state in $[a,b]$, then the posterior has the same shape as the prior (i.e. it will be the truncated normal). Contrast this  with the following signal: (for simplicity, let's assume that $[a,b]=[1,2]$:

$$P_{T|V}(blue|v)=\left\{\begin{array}{c c}
\frac{1+v}{3} & ; v\in[a,b]\\
0 & ; v\notin [a,b]
\end{array}\right. \ \ \ \forall v\in V
$$

and $P_{T|V}(red|v)=1-P_{T|V}(blue|v)$

Now, receiving the signal "blue" also makes the DM  infer that the state is in $[a,b]$, but the  signal structure sends message "blue" more often when the state is closer to $b$, so the posterior will assign a higher probability to states closer to $b$ than what the truncated normal would do, and less probability to the states closer to $a$.

Example 2:

If instead, what you wanted from your signal was the second interpretation. Namely,  "Suppose that the DM discovers the state of the world, $v\in V$, whenever it is in $[a,b]\subset V$ and learns the minimum otherwise. Can this be written as an information structure?"

You  can simply let $T=\mathbb{R}$ and define the signal structure as follows: (for simplicity, assume again that $[a,b]=[1,2]$)

$$P_{T|V}(t|v)=\left\{\begin{array}{c l}
1 & ; \ t=v \ \& \ v\in[a,b]\\
1 & ; \ t=0 \ \& \ v\notin[a,b]\\
0 & ; \ otherwise.
\end{array}\right. \ \ \ \forall v\in V
$$
(Here the message "0" can be any other random number that is not in $[a,b]$.)

Therefore the DM receives signal "0" whenever the state is outside the interval [a,b] (so they learn the minimum possible) or they learn the state of the world (by getting message "v") when the state is in the interval.


Why are Massachusetts electricity costs so high? Massachusetts has the third highest electricity cost in the US (after Hawaii and Connecticut). Why is this?

To answer this I have to make some guesses because this is not an area of research for me, but having a spouse from there and having spent time there, I think I could make a somewhat educated guess.  Especially because it uses a market system rather than a rate setting system for generation.

First, Massachusettes has the third highest population density of any state and it is concentrated mostly around Boston.  Like rail, short distances are comparatively costly.  Higher loads in small locations require greater infrastructure costs.  Further, the variability will be harder to control because things that impact east Boston also impact west Boston, while things that impact eastern Montana do not at all impact western Montana.  There is less independence for unplanned events in a small space.  The covariance is high.  A noreaster can be far more damaging, if it is damaging, in a small space.  Repairs are costly.

Boston also has an old system.  While I could be wrong, I wouldn't be surprised if it was aging and depending on the regulation on carrying power, it might not be worth the investment without a regulatory structure that guarantees cost recovery.  Further, Massachusetts is growing and this means plugging costly new infrastructure onto old infrastructure.  As I am guessing, I don't know this, but it wouldn't surprise me that the influx is straining the infrastructure and I wouldn't be surprised if the infrastructure is past its planned life.  Boston was running electric cable cars in the 1880s.

The correct place to place this question would be with civil and electrical engineers.  You will probably find there is a really long history of how the current state of affairs came to be in Massachusettes in general and Boston in particular.  I would be surprised if Boston was not driving your costs.  I have no knowledge about Connecticut's system and if I had to guess for Hawaii it is due to the intrinsic fragility of being on an island with lots of people and no grid to support local emergencies.


Is over-valuation of a start up genuinely detrimental to the start up's future? I recently watched S02E01 of Silicon Valley.

In it, having demonstrated a breakthrough algorithm, the guys are pursued by investors with increasing funding offers.

However, the founder is warned with a higher valuation, there are higher expectations of performance, and that this may make it harder for to get funding in the future when the company is more mature.

See this Mashable article for a summary of the episode.

  Her offer? \$20 million at a \$100 million valuation.

  Naturally, Richard jumps at the opportunity, but Monica warns him
  against taking it to avoid a runaway valuation and potential for a
  future down round. After some initial resistance, Richard comes
  around, and decides to make Laurie a counteroffer she can't refuse:
  \$10 million at a \$50 million valuation.

The question is, is this a genuine dilemma for start ups, or is the rational decision always to 'take as much money as you can'?

I believe this answer is relevant:

Why a new startup should ask a big investment company to value them as low as possible?

In brief, if founders accepted the investor offering at the highest valuation, this investor would be their last one.

But if a startup is looking for money alone, it is a bad startup.

The access to reputable investors (who valuate realistically) gives more opportunities. It includes experienced members of the board, better brand to attract candidate employees, and the track record of closing investment rounds with famous investors.


Weakly monotone preferences with singleton indifference curves: do any of them admit a utility representation? Inspired by this question. The original question was answered by Amit with some nice examples. I would like to know the generalized answer:

Suppose we have a preference ordering $\succeq$, which is weakly monotone, thus for any basket of goods $x$, $y \in \mathbb{R}^n$
$$
x >> y \Rightarrow x \succ y,
$$
and which only has singleton indifference curves, thus
$$
x \sim y \Rightarrow x = y.
$$
Is there any such preference ordering which can be represented by a utility function?

A remark: without monotonicity one can simply take any bijection from $\mathbb{R}^n \to \mathbb{R}$ and claim that as a utility function. This would have singleton indifference curves.

What you're asking for is equivalent to finding an injective function $f:\mathbb R^n\to\mathbb R$ that is monotone in the sense that if $x$ is coordinate-wise at most as big as $y$, then $f(x)\le f(y)$.
As a first step, notice that this is equivalent to finding such a function from $(0,1)^n\to\mathbb (0,1)$.
And this is easy by interleaving the digits of the coordinates of $x$, i.e., if $x=(x^1,x^2,\ldots,x^n)=(0.x^1_1x^1_2\ldots,0.x^2_1x^2_2\ldots,\ldots,0.x^n_1x^n_2\ldots)$, then let $f(x)=0.x^1_1x^2_1\ldots x^n_1x^1_2x^2_2\ldots x^n_2x^1_3x^2_3\ldots x^n_3\ldots$.
This is clearly injective and we prove monotonicity as follows.
If $f(x)>f(y)$, then they differ first at some $x_i^h>y_i^h$ for which $x_j^h=y_j^h$ for all $j<i$.
But then $x^h>y^h$, so $x$ cannot be coordinate-wise at most as big as $y$.

ps. Note that $f$ is almost surjective and almost continuous; the only issue is with numbers that have a finite decimal expansion. To see that an injective $f$ cannot be continuous, consider $f^{-1}(\mathbb R_-)$, $f^{-1}(0)$ and $f^{-1}(\mathbb R_+)$ where wlog. $0$ is an inner point of the image of $f$.
By continuity, these are two open sets and a point, so they cannot form a partition of $\mathbb R^n$ for $n\ge 2$. (Here we didn't even use monotonicity.)

It is, however, possible to make $f$ into a monotone bijection.
This can be achieved as follows.
First we show the statement for $f:[0,1)^n\to [0,1)$.
Write every number in its finite decimal form, if it has one, i.e., it shouldn't end with $999\ldots$.
The number $f(x)$ will start with the first few decimal digits of $x^1$.
If $x^1_1\ne 9$, then $f(x)$ will start with $x^1_1$, and then we take the first few digits of $x^2$.
If $x^1_1=9$ but $x^1_2\ne 9$, then $f(x)$ will start with $x^1_1x^1_2$, and then we go to $x^2$.
And so on, we always go until the first non-$9$ digit of $x^1$ before we start taking digits from $x^2$.
Then we repeat this for $x^2$, then for $x^3$, etc. (in a circular order).
This finishes the construction for $f:[0,1)^n\to [0,1)$.
To make it into a function $\mathbb R^n\to\mathbb R$, just apply a monotone bijection $g:\mathbb Z^n\to\mathbb Z$ to the integer part of the numbers.
(Such a $g$ is easy to construct by induction and by taking larger and larger cubes around the origin, $0^n$.)
Such a $g$ gives a partition of $\mathbb R^n$ into cubes that are isomorphic to $[0,1)^n$.
We can combine $f$ and $g$ to obtain a final function that will map $x$ to $g(\lfloor x\rfloor)+f(x-\lfloor x\rfloor)$.


Replacing Value-added Tax with more Income Tax What would be the effect on the economy if all VAT / sales tax was removed, but income tax was increased to compensate so that the government has no change in income?

In the long run there would be no difference as income will always eventually equal consumption so in the long run, flat 30% VAT tax would be equal to flat 30% Income tax. This is so because income can be only consumed or saved but saving is just deferred consumption. Assuming away some dynamic changes in taxation in future it does not make any difference from pure economics perspective.

However, in practice it is much better to have multiple sources of taxation instead of one. Having two sources of taxation helps combat tax avoidance (some people might easily avoid income tax like for example baby sitters or tutors but they can’t just as easily evade VAT). Also, in cases you care about redistribution it’s worth noting that it is very difficult to redistribute income with VAT if you apply it to individual products and not to total spending (which is virtually impossible in real life). So in cases where you want to have progressive non-linear tax to redistribute income, income tax is far superior instrument to VAT.

There is also some recent empirical evidence that shows that they might not be equivalent and which suggest labor taxes have higher welfare loss (you can see one example of such evidence here)). However, I would take the paper with a grain of salt. As the paper itself states it’s considered well known result in public economics that the two taxes are equivalent and laboratory experiments can have they own problems, and it’s hard to say what would be a convincing reason why they should not be equivalent. Still it’s worth knowing that the result is being challenged.


Recovering from large government debt without currency devaluation Current, Greece has a debt of roughly 175% of GDP.  The new government has announced it wishes to negotiate a write-off, something Eurozone leaders have so far refused.  From prior knowledge and this post, I understand that governments may want to stimulate consumption when the economy is doing poorly, and have budget surpluses / pay off debt when the economy is doing well.  Since the beginning of austerity, the Greek economy has shrunk by 25%, and unemployment is now 27%.  I have mainly read economical opinions arguing that austerity is harmful and needs to stop, but I the sources I read are probably not representative.

Is there any historical precedent of a country that recovered from a 175% debt, without either having substantial debt write-off, or a currency devaluation?  By recovering I mean: returning to substantial economic growth, increasing standards of living compared to crisis conditions, and a public debt shrinking to become substantially less than 100%.  If so, how did they do it?

By one estimate (here is another) , as a result of WWII, the United Kingdom saw a debt of more than 200 percent of GDP. They never defaulted on their debt after reaching that level. I believe they never did anything radical, just systematically growing government spending more slowly than national income, thus gradually eroding the debt as a fraction of GDP.

The paper Sustainability of High Public Debt: What the Historical Record Shows may also be of interest.

  The paper looks into the debt histories of three European countries,
  Britain, France, and Germany, to study three questions. First, are
  there historical parallels to the accumulation of high debt in
  peacetime that has taken place in the past decades? The answer to this
  is mostly in the negative. National debt was high during long periods
  but usually related to wars or their financial aftermath. Second, how
  were large debts reduced, and that were the factors determining
  decision-making? Recent research has emphasized the role of social
  conflict in this context. We find that although this may play a role,
  the dominant effect may have come from international financial
  relations. Third, what are the macroeconomic effects of budget
  stabilization, and does it pay off for a country to repudiate or
  inflate away its debt? The short-run evidence is mixed, as the success
  of debt default has varied considerably. In the long run, however,
  stabilizing the budget pays off, as there seem to be no lasting
  adverse effects of fiscal austerity on a nation's growth performance.


When a central bank buys government securities, is this exactly equivalent to printing money? When a country's central bank buys that same country's government securities, is this exactly equivalent to printing money?
There seems to be no agreement on this.
Federal Reserve FAQ:

Is the Federal Reserve printing money in order to buy Treasury securities?
No.

Carlo Cottarelli (2017, Ch. 7 "Printing money"):

central banks, by printing money, can help governments spend more than they collect in taxes. The difference (the deficit) can be bridged by borrowing not from private savers but from the central bank, primarily through the central bank’s purchase of government securities. Public debt increases, but if the securities are held by the central bank, any interest paid to it goes back to the government, which receives its profits even in countries where the government formally does not own the central bank. In other words, the portion of public debt held by the central bank is not to be regarded as real debt, at least not in the immediate future. This is essentially what has happened to varying degrees in many advanced countries, which have continued to run sizable deficits since 2008.

Who is correct? (Or, why the seeming disagreement?)
Concrete example: Say John is hired to mow the White House lawn for \$100. What then is the difference between the following two scenarios?

The US Treasury prints a \$100 note, then uses it to pay John.
The US Treasury issues a \$100 bond that the Fed buys, then uses the \$100 deposited in its account to pay John.

I don't know if you are aware that you are using the word "print" abusively but:

  The U.S. Treasury controls the printing of money in the United States. However, the Federal Reserve Bank has control of the money supply through its power to create credit with interest rates and reserve requirements.

Source : https://www.investopedia.com/ask/answers/082515/who-decides-when-print-money-us.asp

Thus both are correct. Clearly a CB does not increase the money supply by creating credits in order to buy governments securities.

It does so with other goals in mind, such as forging economic cycles, maintaining financial stability, reconfiguring the debt market and/or stimulating money multipliers in the national economy.

A CB (theoretically)(and indirectly) buys government securities in an inflation-neutral manner $\iff$ no money printed $\iff$ it uses the existing "stock of (scriptural) cash".

The difference between your two scenarios is the notion of debt. Strongly putting aside the fact that your ex-nihilo first scenario literally makes no sense without a credit underlier.


Location game between 3 firms I could solve Question 25 (simultaneous location game between 2 firms), but I'm confused between options b) and d) for Question 26 (sequential game involving a third firm). I have attached both questions since Question 25 provides context to Question 26.
Basically, I got my answer as d) for Question 26, using the method of backward induction since it's a sequential game. While the answer key for this question says b) is the correct option.
My method: Assuming that firm 3 locates at 1/2, firm 1 and 2's location described in option d) gives them both the maximum share than in any other option. Equilibrium should be such that firms 1 & 2 are at an advantage since they are first movers in the game.

Could anyone please confirm as to which should be the correct option for Question 26? Any solution and views are welcome.

$(d)$ cannot be an answer because of the following.  If 1 and 2 are located as in $(d)$, then 3 wants to be located (i) either at $\frac{1}{3}-\varepsilon$ or (ii) at $\frac{2}{3}+\varepsilon$ because doing so yields almost $\frac{1}{3}$ while choosing $\frac{1}{2}$ yields $\frac{1}{2}\times\frac{1}{3}$.  So, 1 receives $\frac{1}{2}\times\frac{1}{3}$ if 3 chooses (i), or 2 receives $\frac{1}{2}\times\frac{1}{3}$ if 3 chooses (ii).  Then, 1 and 2 does not want to act according to $(d)$.

$(b)$ is the right answer. The reasoning is: if 1 and 2 are located as in the answer, 3 is indifferent of choosing anything in $\left[\frac{1}{4}, \frac{3}{4}\right]$ all of which yield $\frac{1}{4}$ and any other location yields a lower payoff.  In other words, each of 1 and 2 can guarantee himself at least $\frac{1}{4}$.

Now, the question is: Does any of 1 and 2 want to deviate from $(b$)?  Suppose when both 1 and 2 played according to $(b)$, 3 chooses $\frac{1}{2}$ so that each of 1 and 2 obtains $\frac{3}{8}$.  Now, suppose that 1 deviates to a location $\frac{1}{4}-x$, where $x \in (0,1/4)$.  Then, he obtains $\frac{1}{4}-x + \frac{\frac{1}{2}-\left(\frac{1}{4}-x\right)}{2} =\frac{3}{8}-\frac{x}{2}$ which is clearly lower than $\frac{3}{8}$ as $x>0$.  Thus, 1 does not want to deviate.  By a similar argument, 3 does not want to deviate too.  Hence, $(b)$ is an equilibrium


Mathematical open problems that (when answered) might unlock MAJOR mathematical (micro)economics/finance/econometrics discoveries Are there any (specific) math open problems that mathematical (micro)economics / finance / econometrics researchers wish mathematicians could solve for their discoveries to flourish? If positive, which math open problems are related to which applied topics and how they are related?

When I ask that, it really comes to my mind the case of stochastic analysis and option asset pricing problems in mathematical finance.

People have argued that if $P \neq NP$ then efficient markets are impossible and certain equalibria may not exist. However, they may hold approximately, so I'm not sure if this qualifies. Additionally, if it turns out that $P=NP$ then certain economic optimization problems (e.g. in logistics) become easily solvable. On the other hand, if $P \neq NP$ then it might imply that encryption is very safe and therefore certain forms of economic arrangements will still be possible in the face of technological advance.


Is the money market model based on assumption of no interest rate targeting on the part of the central bank? This is quote from Gregory Mankiw's macroeconomics text about mechanism of formation of the interest rate in the money market model:

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

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

I remember making myself the same question when studying those models in Mankiw's book. The answer I arrived is that from the point of view of the model, the Central Bank's policy is reflected in the money supply variable, and the interest rate variable is an abstraction that represents the main interests rates in an economy that are given by the equilibrium.
Think about this, in the model when there's an increase in money supply, what happens with the equilibrium interest rate ceteris paribus? It goes down. And the opposite is also true. But, who controls the money supply variable? The Central Bank.
So if you look at what happens in reality is somehow like that, the Central Bank cuts rates so the money supply decreases. Obviously the mechanism by which this happens in reality is different compared to the model, even they're like the 'opposite', but remember that models simplify reality in order for it to be more understandable, and in this case the CB intervention is modeled this way.


Annual price of precious metals I need a list (or separate lists) with average prices of precious metals (gold, silver, platinum, palladium, etc.), by year. I prefer the annual average price or at least the price at the end/beginning of the year and I do not need graphs with prices fluctuations from one day/week/month to another.

Also price ratios (like gold/silver, gold/platinum - e.g. "in year 1900, with 33.33 ounces of silver you could buy one ounce of gold") are very useful for me.

International prices are desired of course, but the national prices are also very welcomed (like historical price of gold in the UK/US/France/Germany or any other country where someone actually bothered to record such facts).

You have a few options for data. With questions of this nature, Quandl is your friend.

See here for historical gold prices, 1833 until present. I've not read about the methodology here though.
This resource has the gold/silver price ratio. Annual data. It seems pretty easy to transform this into price of silver.
For platinum
It also looks like the Perth Mint keeps a decent amount of historical data. I noticed in that list paladium as well.
The Reserve Bank of Scotland has a set which can give you prices of commodities, monthly and daily going back 15 years. I am not sure if there are any precious metals in that list.


Marginal Utility with Supply and Demand Curves Can someone explain how the equilibrium points in the image below (source: The Foundations of Econometric Analysis) represent marginal utilities.  I have read about the relationship between the marginal rate of substitution and the ratio of marginal utilities in terms of the theory of consumer behavior but have not seen marginal utility in this context.  I imagine this use is similar but my logic is failing me.

The figure represents a demand curve progressively shifting to the right with a lagging supply.

Suppose there is only one good and I fix a price, $p$. The demand curve implies a corresponding quantity $q$.

Now, reduce the price by a tiny amount to the new level $p'$. The demand curve tells us that this reduction in price will cause an increase in quantity to $q'$.

Now, let's think about what happens here. Our consumer was willing to buy the some extra units at the price of $p'$, but not willing to buy those units at the price of $p$. We can infer that the consumer's willingness to pay for these units satisfies $p'<\text{WTP}<p$.

Remember that I said the change in $p$ was tiny? If this change is almost zero then the number of extra units demanded will also be small and we can get an exact value for the consumer's willingness to pay for these units: $p\approx \text{WTP}\approx p'$.

So the willingness to pay for the marginal unit is just the price. But the price is also the height of the demand curve!$^†$ Note that if I had started with a different price and performed the same exercise then I could have calculated the willingness to pay for a different unit of the good. So the height of the demand curve at a given point measures the consumer's willingness to pay for the unit of the good below that point.

Lastly, how much should the consumer be willing to pay for a unit? The answer is that he should be willing to pay as much utility as that unit gives him (a.k.a. the marginal utility). Thus, the demand curve's height measures willingness to pay, which is just another way of saying it measures marginal utility.

$^†$ Note that the distance $PQ$ in your figure is just the height of the demand curve too.

Appendix

To see how this works in maths and with an arbitrary number of goods: note that the optimal solution to the consumer choice problem occurs where the marginal rate of substitution between each pair of demanded goods is equal to their relative price
$$\frac{\text{MU}_x}{\text{MU}_y}=\frac{p_x}{p_y}.$$
Rearranging:
$$\frac{\text{MU}_x}{p_x}=\frac{\text{MU}_y}{p_y}=\text{some number}.$$
Rearranging
$$\frac{1}{\text{some number}}\text{MU}_x=p_x$$
so the price is just some constant multiplied by the marginal utility. By appropriate normalisation of either the units in which money is measured or the utility function (which is invariant to monotone transformations) we can make $\text{some number}=1$ so that $\text{MU}_x=p_x$.


Comparative Methods of Econometric Analysis While RIMS II, IMPLAN, and other methods regularly deviate substantially from each other in the answers they yield to analytical questions, is there a "band" within results should be considered "more accurate".

For example, if RIMS and IMPLAN give a quantitative result on the order of x, and a third method gives a result 2,3, or more orders of magnitude higher, should the third method be disregarded?

I ask this because I've submitted analysis based off industry-specific methods and had it roundly rejected not because there was a flaw in my analysis, but because it didn't agree with general case tools, or differed to markedly.

Is there a best practice within econometrics that says "throw out all results farther than Y from some accepted average"?

In econometrics and statistics, you sometimes will truncate outliers. Otherwise, maybe it's worth mentioning that in the business of predicting, analysts are punished for either being wrong, but their punished even more if they were boldly wrong. This is a form of herding behavior. Deviating from the consensus can be disproportionately risky.

Here's a paper that talks about it: "Security analysts’ career concerns and
herding of earnings forecasts" in the RAND Journal of Economics.


How to convert an historic value denoted in foreign currency to a modern value in local currency? I want to convert GBP in 1968 to USD in 2018, in order to "translate" an amount paid by an individual in Britain fifty years ago. My intention is that an American reader today will be able to better understand the value of the money if it is given in inflation-adjusted USD.

In 1968, £1 exchanged to \$2.38. \$1 in 1968 adjusts to \$7.22 in 2018. £1 in 1968 adjusts to £17.02 in 2018. Finally, £1 exchanges to \$1.34 in 2018.[1]

If we do the exchange first, then £1 (1968) is equivalent to \$17.18 (2018). If we adjust for inflation first, then £1 (1968) is equivalent to \$22.81 (2018). Which is the correct way to do this? Why?

Addendum:

An answer to a similar question suggests that the exchange rate, in some form, should be commutative with inflation adjustment:

  Also, it does not matter which transformation you do first, as its purely multiplicative.

I am not sure whether the author is referring to calculations using the formula that he defines as the "real exchange rate" as "purely multiplicative", or whether he/she meant that the exchange rate and inflation are ideally always going to be commutative (and therefore this case deviates from the ideal by a degree). The answer does not go into very much detail and it is beyond my understanding of economics to determine what the "respective price level" between Britain and the US is in 1968 or 2018.

[1]
I am getting my inflation data from officialdata.org. While I have found on other websites slightly different conversion factors for inflation since 1968 in both currencies, they are only a few cents different from the figures I used here. The nominal exchange rate is, by contrast, an historical fact.

For what purpose?

Money over time acts as inflation rate, wage bundle, production good bundle, %gdp, %gdp/capita. Each represents a different “meaning” of money over time.

The US and UK economies have different consumption bundles, wage structures, skill structures, industrial structures, government policy, market agents and social meanings. 1968UK and 2018UK also vary and 1968UK and 2018UK vary in these domains.

Your question is unanswerable without the commodity or expense, the volume or market (wholesale, retail, government) and the purpose.

See measuringworth.com for essays.


VAR Models - Identifying Block Exogenous Variables Through Granger Tests I have run a VAR model, and done granger causality tests (results pasted below) and am trying to answer a textbook question which asks:

Is there any variable that appears to be close to being block exogenous with respect to the other variables?  In any case, what does this mean?

To me it seems like DLRGDP is the closest. Exogenous means that one variable is not affected by changes in the other variables The p-values on the DLRGDP seem to indicate that we cannot reject the null hypothesis that DLRM2 does not granger cause DLRGDP. But the p-value that DRS granger causes DLRM2 is fairly low, at 0.0025.

What do you think, are any of these variables close to being block exogenous?

Checking the p-values, I would suggest that in the first and second tests, the variables DRLM2 and DlRGDP have granger causality issues (since we reject for a 5% sig. level).

In the third case, DRLM2 is not rejected for a sig. level of 5%, yet, it seems to be very close (4,8%).
I don't think there's any particular meaning to having a near non-rejection area. Remember that if you draw the chi-square distribution and use the 1% sig. level for the test, you will not reject the granger causality.


A survey on the economics of loyalty programs Is there a good survey that covers the theory and empirics of loyalty programs? I am thinking of programs like Amazon Prime, Starbucks, and airlines miles/points. What are the mechanisms? Are they effective in a causal sense?

A relevant literature is that on the economics of switching costs. There are many papers in this literature and a number of surveys, but I would recommend this paper by Klemperer for a concise combination of survey and theory. A more comprehensive survey can be found in this handbook chapter by Farrell and Klemperer.

The basic idea is that loyalty programmes (among other things) create a cost for consumers who contemplate switching to another supplier. This literature studies how such costs influence strategic behaviour and competition between firms.


Utility function used to indicate bliss point How does one create a utility function to indicate existence of a bliss point? what do the goods marshillian demands look like in such a situation?

An answer that meets all the current demands of the question:

Let $(x_b,y_b)$ be the blisspoint. Let
$$
U(x,y) = \left\{
\begin{array}{cc}
1 & \mbox{ if } (x,y) = (x_b,y_b) \\
0 & \mbox{ if } (x,y) \neq (x_b,y_b).
\end{array}\right.
$$
The demand function for $x$ in this case is
$$
D_x(I,p_x,p_y) = \left\{
\begin{array}{cc}
x_b & \mbox{ if } p_x \cdot x_b + p_y \cdot y_b \leq I \\
\left[0,\frac{I}{p_x}\right] & \mbox{ if } p_x \cdot x_b + p_y \cdot y_b > I.
\end{array}\right.
$$


Calculation of term structure I am supposed to calculate term structure of interest rate. I got the table including several bonds with price of the bond, face value and number of years till maturity.

I calculated yield of each bond, picture attached below.

My question is.. how am I supposed to calculate the term structure of interest rate from this data? In other words I need the spot rates.
Comma is meant as decimal seperator.
Thanks for any help.

The wording of the question is vague, but I will assume that the objective is to get a zero/discount curve via bootstrapping.
The premise of a bootstrapping is straightforward: fit a zero curve so that the shortest maturity bond is priced perfectly. Since we don’t have any other information, assume the curve is flat up to the first maturity; the curve matches the bond yield (modulo quote conventions). In other words, we have the zero curve defined to the maturity of bond #1.
(Pricing the bond perfectly means that if we discount the cash flows of the bond by our zero curve, the sum of the discounted values equals the market price.)
We then target the next maturity. We extend the zero curve so that it is priced perfectly. We will note that the initial coupons are discounted by the already fitted curve, the later coupons and principal by the new curve. Find the discount curve extension that results in bond #2 being priced correctly. That is, the zero curve is now defined to maturity #2.
Repeat for bond #3, ... N.
Issues arise.

There are any number of ways that the curve can be interpolated, including how to define the curve. (Interpolate between knot points, functional definition, etc. Do we interpolate forward rates or zero rates? Etc.)
Bonds can be mis-priced, and the curve ends up severely distorted.

Finally, the code/mathematical formulae are complex. Even an ugly approximations take a lot of code.


How much can we trust macroeconometric analysis? I am a student of economics in my masters and I have learned quite a lot about microeconometrics (I mean mainly quasi-experimental methods / causality determination). Here my current understanding is that obviously you can't ever fully trust any analysis, but basically you can get to a point where results are relatively convincing, i.e. when one can make a strong argument for the identification assumption to hold (so parallel trends in a Dif-in-Dif, exclusion restriction in an IV approach, etc.). Alternatively, you get identification through a well designed RCT. So basically you can find ways to solve problems of reverse causality and omitted variables.
I have now recently started to learn more about macroeconometrics (i.e. time series methods) and it kind of appears to me that reverse causality and omitted variable bias kind of get ignored here (I am thinking of 3-4 variable VARs that obvisouly don't capture all the variables that might explain e.g. output or inflation). Is there some mathematical argument that makes these problems disappear magically? Or is macroeconometrics in general less convincing?
I have heard of the credibility revolution in empirical micro and that nothing similar happened in macro, but how much can we trust results from something like an IRF estimation or how convincing are arguments based on IRF results?
PS. I know that in forecasting you can be kind of agnostic to any causality issues, so in this question  I am not asking about forecasts. Also I am not putting microeconomics vs macroeconomics in this question. I am only talking about two different econometric approaches.

I do not think that macroeconomic analysis would be 'less trust worthy'. In the same ways as you can solve the issue of omitted variables and reverse causality in microeconomics you can do it macroeconomics as well. Macroeconomics, is not just vector autoregressions (VAR - which by the way corrects for endogeneity). Simultaneous equation techniques, even difference-in-difference (DiD) and regression discontinuity (RD) etc are used even in macro literature even if they are less common (see this recent paper on identification in macroeconomics Nakamura & Steinsson, 2018).
In addition I think you are actually exaggerating quality of quasi-experimental methods such as IV or DiD. For example, this recent paper shows that large portion of IV papers uses weak instruments as the rule of thumb that $F$-stat. should be above 10 is invalid and  true threshold is around $F>105$ (see here Lee McCrary Moreira & Porter 2020). In addintion DiD are notorious for $p$-hacking and other issues,  Duflo & Mullainathan (2004) literally have paper titled: "How much should we trust differences-in-differences estimates?" Spoiler alert their answer is not as much as people usually do.
I think it would be fair to say that a reasonable person could defend saying that typical VAR has probably on average less issues that let's say DiD (but to be clear I am not claiming that as  even this lacks nuance as the model selection and specification is always case dependent there is no one model uber ales - even RCTs have a problem when it comes to generalization of results).
When it comes to just empirics in general I could not find any paper that would show that empirical research in macroeconomics is less replicable than in microeconomics. I would also take an issue with claim that macroeconomic models cannot control for all relevant variables. There are macro models (e.g. dynamic stochastic general equilibrium  (DSGE)) that include scores of different equations and even more variables. Next, even despite of this when it comes to omitted variable bias you might have a valid point although a lot of attention is being paid to the issue it might sometimes be hard to solve, but with the reverse causality your accusation that macroeconomics does not pay enough attention is unfounded. Most published research in macroeconomics pays very large attention to reverse causality (especially in present day, maybe 50-60 years ago that would be valid point as well). In fact that is why models and estimation techniques like VAR, DSGE, IV, GMM and many other simultaneous equations approaches are so popular and dominate macroeconomics, so this second charge is simply unfounded.
However, when it comes to forecasts I would agree that macroeconomic forecasting is for sure less accurate then microeconomic forecasting (e.g. forecasting aggregate output vs firm forecasting demand for its onw products). However, there the fault would not be in the models themselves necessary but rather with the fact that macroeconomic aggregates contain more noise, are harder to measure, and are reported on lower frequency and of course with less data it is harder to build good forecasting model.
Lastly, it is not really easy to qualify how much you should trust a model in any field. You should approach any model and set of results with healthy doze of skepticism, be they from VAR or RTC or any other approach. Different situations will require different identification strategies. Furthermore, you should not put all faith into single paper but wait for replications/put the paper into larger context of pre-existing literature. I also tried to find some work that would compare replicability of microeconomics vs macroeconomics, but unfortunately there does not seem to be such paper but I would not expect macroeconomics having much worse replicability rates then microeconomics per se.


Are the primary dealers obliged to buy treasuries no matter what? It is said that treasuries are the highest quality debt because the government can always "print money" to pay the debt.
But, isn't so that the ones printing the money to loan to the government are the primary dealers.

If so is the reason it is said that the government can always pay their debt because the primary dealers are obliged to always loan to the government?

Is there a case in which the primary dealers could refuse to buy treasuries?

In general, are the primary dealers incentivized or compelled under the law to always bid for the treasuries?

I assume this refers to the U.S.
(Also, see this question/answer: link to question.)

If so is the reason it is said that the government can always pay their debt because the primary dealers are obliged to always loan to the government?

That’s one reason, but most people are unaware of this angle. I would argue that the usual reason given is that the central bank can buy government bonds in “unlimited” size.
There are limitations on this, and government debt issuance, but they can be bypassed at any time by issuing a new law. Another thing to keep in mind that jurisprudence around Treasury default is not settled, there are arguments that a Treasury default is a “more illegal” option than the Treasury not paying for spending that was authorised by Congress.
From the perspective of underlying economics, the reality that there is an open-ended buying capacity at the central bank is why people refer to currency sovereign debt as default risk free.

Is there a case in which the primary dealers could refuse to buy treasuries?

They submitted to an agreement to bid, so not really. At most, the bids might not cover the auction.

In general, are the primary dealers incentivized or compelled under the law to always bid for the treasuries?

Incentivised - certainly. They get first chance to bid on Treasuries, and their job is to have a sales force that is capable of finding bidders who will pay a higher price in the secondary market. This is why firms become primary dealers in the first place.
“Compelled under law” is a strong phrase; they have a binding contract to bid. Since primary dealers are financial entities whose overall activities are regulated by the Federal government, they would put themselves in a very awkward situation if they tried to break a legal agreement with the government.


Strict preference relations and utility representations Suppose I have a rational preference relation $\succsim$ on some consumption set $X$.

Suppose also that there is a utility function $u:X \to \mathbb{R}$ representing $\succsim$.

Definition: A function $u: X \to \mathbb{R}$ is a utility function representing preference relation $\succsim$ if, for all $x, y  \in X$, $$x \succsim y \iff u(x) \geq u(y)$$

Is it possible to prove that $x \succ y \iff u(x) > u(y)$ without a continuity condition on $\succsim$?

My intuition says no, but am having difficult finding a suitable counter example. Any help is appreciated.

Yes it is:
If direction
$$
x \succ y \Rightarrow x \not \precsim y \Rightarrow u(x) > u(y).
$$
Only if direction:
For all $x, y  \in X$,
$$
x \succsim y \iff u(x) \geq u(y)
$$
implies
$$
x \sim y \iff u(x) = u(y).
$$
Also
$$
u(x) > u(y) \Rightarrow u(x) \geq u(y) \Rightarrow  x \succsim y ,
$$
$$
u(x) > u(y) \Rightarrow u(x) \not = u(y) \Rightarrow  x \not\sim y.
$$
and
$$
x \succsim y \mbox{ AND } x \not\sim y \Rightarrow x \succ y.
$$


Does good geographical location count as land in economics? For example, the North pole is in the northern part of the earth and is very cold, making it suitable to build a site to study polar bears. Is the cold and northern location of north pole counted as land? But since the site is already built so the place should be counted as capital?

Sorry I know this example sounds a bit stupid but I'm very confused and couldn't think of a better one.

In Economics "Land" as a form of capital is those parts of the natural environment that had become a subject of economic transactions (market or otherwise).

Consider a piece of land that is public property, say, a mountain. No economic activity is taking place related to that mountain. Then, it is not consider part of the Fixed Capital base of the national economy. Certainly the mountain may have minerals. The mountain contributes to the local climate which in turns affects the weather and so the local economy. But to the degree that it is not used productively through purposeful economic behavior, it is not considered part of the Capital base (that estimations of natural resources are calculated for various economic plans has to do with future actions, not with the capital base at present).

Assume now that the Government actually sells part of this mountain to a company that wants to build a winter resort. This part of the mountain becomes now a real-estate asset of that company, and so part of its Fixed Capital and so part of the Fixed Capital base of this economy.

The features and characteristics of this piece of the mountain (that it has, say, good slopes for skiing, low temperature that is good for snow, etc) through the transaction are priced, i.e. they are (somehow) evaluated and acquire a specific monetary value, usually as a whole, and not as distinct entities from the piece of land itself.

Assume now that the company, after buying the piece of the mountain, seriously delays building the resort, say, for some years. Should we count this asset as part of the capital base of the economy for these idle years? Sure: it is now "idle capital" not "potential future capital".

At the micro-level, the performance of the company must be judged against the total investment that it has made. If it has made an investment (i.e.it has spent company resources) that it doesn't exploit economically, this worsens the company's performance overall. This in turn affects the private sector of the economy on aggregate: there is an amount of Fixed Capital that "sits idle" while it shouldn't (and it shouldn't, because by buying it the company revealed a decision to use it productively, and has sacrificed resources for this decision).


If all Banks in the world are emptied..? What would happen if every person in the world pulled their money out of their bank accounts?

The thing with these economics questions that never happened empirically is always the same: nobody really knows.
Befor Creditanstalt 1931 nobody thought that a bank can go bancrupt, during BrettonWoods/Goldstandard freely floating exchange rates were sought of being detrimental and dumb....

But in theory everything should collapse due to our fractional reserve system that requires banks to have a certain amount of money stored in their books for every granted loan.
But thats not going to happen because centralbanks would intervene and convince people that they are going to do anything to keep the banking system working. If the CB is able to make a trustworthy commitment that should work. Because a rational individual should have no incentive to have so much cash... The costs of carrying so much money are simply too high...

Once there was this Eric Canton attempt....


The period of the business cycle in which the real GDP is increasing is called the? The period of the business cycle in which the real GDP is increasing is called the?

And no, this is not an homework question. I'm a college student and we starting our exams soon. I'm just going through a lot of questions. Both online and previous year's questions from my school. This is quite confusing. I think it is expansion. Then I saw an article on trough on wikipedia that says it is trough. https://en.wikipedia.org/wiki/Trough_(economics)
 Please explain

The trough is not a period, it is simply the lowest point. The opposite of this is a peak, i.e. the highest point. The answer you are looking for is "Expansion" or "Boom". The period in which GDP is falling is called "Recession" or "Contraction".

Also note that the business cycle is typically not defined using real GDP, but rather nominal GDP.


Measuring effects of degree of (buyer) competition on price: references I would like to examine the effect of degree of competition (market power?) among buyers on price of a product. I have data on product price, number of buyers with nonzero purchases and a couple more variables in multiple (around 400) different locations over multiple (around 70) consecutive times periods. I am not familiar with the literature on the topic and might be ignorant of some relevant keywords. I have found very few seemingly relevant papers, e.g. Digal & Ahmadi–Esfahani (2002), and I wonder if there are newer or more important ones that I have missed.
(Update: I do not think this paper offers any method that could be used given the type of data I have.)
Could you recommend a paper or a textbook chapter to bring me up to date with the relevant methodology?
References

Digal, L. N., & Ahmadi–Esfahani, F. Z. (2002). Market power analysis in the retail food industry: a survey of methods. Australian Journal of Agricultural and Resource Economics, 46(4), 559-584.

You might be looking for the term monopsony power or perhaps oligopsony power.
A superficial look at the literature indicates that the Herfindahl-Hirschman index (HHI), so commonly used in assessing seller market power, is also used to measure buyer market power. Recall that the HHI is the sum of the squared market shares measured in percent (so a duopoly with two sellers of 10% and 90% market shares has an HHI of $90^2 + 10^2 = 8,200$.
If you have buyer level figures (not clear to me from your question) then your data allows you to construct local and aggregate buyer market shares. You'll have to  convince yourself which is the right market share for understanding the relevant market. For example, if they were dry cleaners, they tend to draw resources from a small area, and each store is probably a distinct market. If they are car dealers, they draw customers from all over, and so perhaps the entire set of sales is the relevant market.
In the follow up comments and question, Hardy asks, "I want to see how the market power is exercised in terms of its effect on price." In general, you can't do this with price and quantity data alone because prices are simultaneously determined by supply and demand. Unless you know whether supply or demand or shifting, you can't know why prices are changing.
If you really knew that "an additional buyer comes into the market at a given location", and you knew something about what their demand schedule looked like, and you knew that their arrival was exogenous to changes in supply, then I think you could trace out the supply curve and learn about the supply elasticity (for example). But I think you generally need exogenous variation in supply to trace out the demand curve (and vice versa).
However, I'm concerned that the arrival of a purchasing customer is an equilibrium outcome (they only buy when they like the price) while the arrival of a potential customer is what actually is in the demand curve and influences the degree of monoposony. To see this starkly, recall that there are a number of competitive settings where even potential entrants can fully discipline a monopolist to provide the competitive price and ensure they earn zero profits. For example, Tirole Chapter 8. The monopsonist version probably works the same way: in the presence of free entry, if the monopsonist earns any rents then other buyers will enter until those rents are competed away. Therefore we cannot generally learn much just from observing the market quantities (what we really want is unobserved). This makes me skeptical that your data can identify what you are hoping to identify.
However, if you can argue, using your knowledge of the institutional setting, that the appearance of positive quantity purchasers are independent of pricing (they are movements of the demand curve and not movements along a demand curve), then I think you trace out the supply curve with your data. Then, you can look for something similar to the Monopsony and the Minimum Wage outcome. In that setting, the minimum wage raises price and quantity demanded. In yours, entry would lead to higher prices and higher quantities. Could you do that in your data? After deciding whatever is the exogenous shift in demand, can you look (perhaps in a regression difference in difference setting (diff 1: markets with and without such entry with the same change in quantity, diff 2: before and after entry) to see if prices go up along with quantities after entry?


Is there any fundamental reason that output elasticity of capital $<1$ in general? In Solow growth model, if one perturb the saving, there is convergence of old equilibrium capital to new equilibrium capital as investment breaking point capital is attractor.

However, in derivation of convergence, one needs to invoke $a_K$ elasticity of output to capital. Assuming growth in knowledge, growth of population and decay of capital. Then I need $a_K<1$ to guarantee convergence of old equilibrium to new equilibrium. I am assuming Inada condition on output per effective labor and knowledge is only labor augmenting in the model.

Is $a_K<1$ predetermined by Solow growth model or some condition on the model? This discussion does not assume any particular form of production function, in particular, Cobb-Douglas function.

Ref. Romer, Advanced Macroeconomics, Chpt 1, Sec 5 on speed of convergence.

The elasticity of output with respect to capital will be less than 1 due to the diminishing marginal returns of capital - this is both realistic on macroeconomic scale and also one of the central assumptions of the model.

According to Romer’s advanced macroeconomics, pp 12 section 1.2 assumptions:

  “The intensive-form production function, $f(k)$, is assumed to satisfy $f(0)=0$, $f’(k)>0, f’’(k)<0$ ... Thus the assumptions that $f’(k)$ is positive and $f’’(k)$ negative imply that the marginal product of capital is positive, but that it declines as capital (per unit of effective labor) rises.”

This is one of the standard assumptions of Solow-Swan models so $a_K$ (or in Romers book $\alpha_K$) will be less than 1 just by assumptions of the model.

Side note: this is actually also implied by the Inada conditions themselves (which as Romer points out are stronger than needed for the model's central result) since $\lim_{k\rightarrow 0 } f’(k)=\infty$ and $\lim_{k\rightarrow \infty } f’(k)=0$ together with other assumptions of the model imply that $a_k<1$ - and hence the model should always converge.


How did the massive flight to long-term bonds create a liquidity crisis? A few weeks ago I noticed that several blogs and such were adamantly proposing that the Fed lower rates immediately by 50 bps. They said that the flight to safety -- to long-term government bonds -- had created a liquidity crisis.

I understand what a liquidity crisis is on a personal level and in a business, but I don't understand it in this case.

How did the massive flight to long-term bonds create a liquidity crisis?

This is because in order for many business to stay liquid they often have to issue short term debt. Many financial firms need liquidity so much that they literally make loans that are for duration of only one day.

However, the more people invest their savings in bonds which are usually long term debt (most bonds have maturity over 5-10y), the less money is there available to borrow short term. That means that even profitable business that has healthy profit ratios could get itself into bankruptcy just because of not being able to get short term loan to cover some important immediate financial obligation.


Who took utimatum game and dictator game as the evidence against Homo Economicus assumption of individual utility maximization? Wikipedia and this McGill University page states that the two games "have been taken as both evidence for and against the Homo economicus assumptions of rational, utility-maximizing, individual decisions"

This argument makes some senses; however I am having trouble finding one famous economist, mathematician, or scientist who explicitly states that the assumption of individual utility maximization is "wrong" because of the findings in these games.

Utility maximization is a proposition that can neither be confirmed nor refuted. For one thing, "utility" does not even exist as an entity; it's a mere conceptual construct. For another, "maximization" as a motivation is inherently unobservable. Even behavioral economists, who are adept at finding so-called empirical "anomalies" --- behaviors that apparently contradict economic predictions --- talk of "rationalizing" those anomalous behaviors by coming up with models in which the anomalies are outcomes of some maximization process. See, for example, Thaler's review of the literature on ultimatum/dictator games which he pioneered.

What the experimental results from ultimatum/dictator (and trust) games tells us is merely that people are not income maximizers. It is nevertheless invalid to conclude that people do not seek to maximize some other criterion or objective, which may or may not be part of what economists call "utility".

As economists, we understand that the specific measures we use for utility, like income, satisfaction, or selfishness, are adopted because of analytical convenience for the problem at hand, not because we seriously believe that those measures reflect human nature in any deep philosophical sense.

In a way, it's unsurprising that no economist, famous or otherwise, would declare utility maximization "wrong", since doing so would first require a precise definition of what "utility" is. Such a definition, despite nearly two hundred years of intellectual endeavor, remains frustratingly elusive.


Negative interest rates - Monetary Policy (This is 1st part of series of questions under "Negative interest rates")

I've happen to stumble on two articles, with some weeks, that the central bank(CB) of switzerland, due to Russia ruble crisis, and being a stability haven, has decided to use a negative nominal interest rate for reserve deposits of banks at the CB, to facilitate the exchange rate peg. Bank of Japan(BoJ) also seems have implemented a nominal negative interest rate, even if for different reasons(not sure about the reasons).

In all textbooks, the topic of negative interest rates is easily dismissed, or simply taught of as impossible, and so the authors work with non-negative lower bound(ex:deflation trap). Almost every part of the economic theory is going to be influenced by this.

Hence I'm dividing my question into several.

This part is for monetary policy. With negative interest rates, what changes for monetary policy(scope, effects, etc.) can we expect?

Any help would be appreciated.

Edit: Here is an article by Nouriel Rubini on negative nominal interest rates. He writes on why these negative rates exist, their rationale, and one possible way(fiscal policy) to bring the economy out of this situation.

Real interest rates can be negative without a negative benchmark rate set by the central bank (inflation is higher than nominal interest rates) so in that sense we won't see any new effects.

Regarding the interest rate set by the Central Bank, it does decrease the real interest rate as the banks won't deposit money and have more incentive to give out loans but effectively it is not different from a zero rate (you can't force the bank not to sit on the cash) though I guess the bank has to pay the interest on the mandatory deposits.


Is this lottery like stock market? Consider the following imaginary lottery (motivated by
Massachusetts' Cash WinFall):

  Ticket money obtained in the previous draw are given to the participants of the next draw proportionally to the ticket price they pay.

For example, suppose that in the first draw people bought tickets costing 5 million dollars, and in the second draw - costing 1 millions; if I bought a 1 dollar ticket in the second draw, then I win 5 dollars; and that's for sure, no minuscule probabilities, cool! People will like it and buy more tickets in the third draw, say 10 millions, and win 10 cents for a dollar spent, that is lose 90 cents overall; in the fourth draw almost nobody will like to take part, people buy tickets costing only 0.5 million, and win 20 dollars for one dollar spent, cool again! And so on...

Of course, the organizer will have to take a share, say 10% of ticket price, but it seems that it does not really change the mechanism, that is ticket money fluctuating up and down.

Such a strange lottery looks like something from a stock market - so can one really model it there?

P. S. English is not native to me, so please feel free to correct the question.

Theoretically, the fair value of a company is based on its earnings prospects (or its expected dividends, which is related to earnings). Since not everyone agrees on those prospects, and technical issues hit (investors need to sell for some reason), stock prices fluctuate. However, the fundamental value of a company is relatively stable from day-to-day, regardless of the volume of trading. This valuation stability is quite different from your proposed lottery system, where the value is entirely based on previous purchase volume.


utility maximization with nested Cobb–Douglas–CES preferences I'm trying to understand the following paper: Hsieh & Ossa: A global view of productivity growth in China (2016). The pdf can be found here: https://faculty.chicagobooth.edu/chang-tai.hsieh/research/hsieh_ossa_jie.pdf

I struggle to understand the utility maximization problem right at the beginning of the paper. Can someone show me how to maximize the following utility with respect to $x_{ijs}$:

$U_j=\prod_s^S\left(\sum_i^N \int_0^{M_is^e}x_{ijs}(\nu_{is})^{\frac{\sigma_s-1}{\sigma_s}}d\nu_{is} \right)^{\frac{\sigma_s}{\sigma_s-1}\mu_{js}}$

The end result is:

$x_{ijs}=\frac{p_{ijs}^{-\sigma_s}}{P_{js}^{1-\sigma_s}}\mu_{js}E_j$

where $P_{js}=\left(\sum_i^N M_{is}^ep_{ijs}^{1-\sigma_s}\right)^\frac{1}{1-\sigma_s}$

$N$: number of countries

$S$: number of industries

$M_{is}^e$: number of entrants in industry s of country i

$x_{ijs}$: quantity of an industry s variety from country i consumed in country j

$\mu_{js}$: fraction of country j income spent on industry s varieties

$\sigma_s>1$: elasticity of substitution between industry s varieties

$p_{ijs}$: price of an industry s variety from country i in country j

$P_{js}$: ideal price index in industry s of country j

$E_j$: total expenditure in country j

Take the following utility function:
$$
\prod_{s \in S} \left(\sum_{i \in N} x_{i,s}^{\frac{\sigma_s-1}{\sigma_s}} \right)^{\frac{\sigma_s}{\sigma_s-1}\mu_{s}}
$$
Which is a CES nested in a Cobb-Douglas.
Consider the sub-utility function:
$$
Q_{s} = \left(\sum_{i \in N} x_{i,s}^{\frac{\sigma_s - 1}{\sigma_s}}\right)^{\frac{\sigma_s}{\sigma_s - 1}}.
$$
Then we can re-write the utility function succinctly as:
$$
U = \prod_{s \in S} Q_s^{\mu_s}
$$
To solve the utility maximisation problem. Notice that $U$ is separable in the subgroups. As such, we can solve the problem using two stage budgeting.

In the first step, we can determine the optimal allocation within each subgroup $s$ by maximize the sub-utility functions $Q_s$ given the total expenditure $E_s$ given on each subgroup $s$.
In the second step, we determine the optimal allocation of income across each subgroup $s$.

For Step 1, we solve the following problem:
$$
\max\left(\sum_{i \in N} x_{i,s}^{\frac{\sigma_s - 1}{\sigma_s}}\right)^{\frac{\sigma_s}{\sigma_s - 1}} \text{subject to } \sum_{i \in N} p_{i,s} x_{i,s} = E_s.
$$
This is a CES utility function. The first order condition gives:
$$
Q_s \frac{x_{i,s}^{-\frac{1}{\sigma_s}}}{\sum_{w \in N} x_{w,s}^{\frac{\sigma_s - 1}{\sigma_s}}} = \lambda p_{i,s}.
$$
Then:
$$
x_{i,s} = \lambda^{-\sigma_s} p_{i,s}^{-\sigma_s} \left(\frac{\sum_w x_{w,s}^{\frac{\sigma_s - 1}{\sigma_s}}}{Q_s}\right)^{-1\sigma_s}
$$
Multiplying by $p_{i,s}$ and adding over all $i \in N$ gives:
$$
\begin{align*}
E_s = \sum_{i \in N} p_{i,s} x_{i,s} &= \lambda^{-\sigma_s} \left(\frac{\sum_w x_{w,s}^{\frac{\sigma_s - 1}{\sigma_s}}}{Q_s}\right)^{-\sigma_s} \sum_{i \in N} p_{i,s}^{1 - \sigma_s}\\
&= \lambda^{-\sigma_s} \left(\frac{\sum_w x_{w,s}^{\frac{\sigma_s - 1}{\sigma_s}}}{Q_s}\right)^{-\sigma_s} P_s^{1 - \sigma_s}
\end{align*}
$$
Where $E_{s} = \sum_{i\in N} p_{i,s} x_{i,s}$ and $P_{s}^{1- \sigma_s} = \sum_{i \in N} p_{i,s}^{1- \sigma_s}$.
Then:
$$
x_{i,s} = E_{s} \frac{p_{i,s}^{-\sigma_s}}{P_{s}^{1-\sigma_s}} \tag{1}
$$
Let's compute the value of $Q_s$:
$$
\begin{align*}
&x_{i,s}^{\frac{\sigma_s-1}{\sigma_s}} = E_{s}^{\frac{\sigma_s-1}{\sigma_s}} \left(\frac{p_{i,s}^{-\sigma_s}}{P_{s}^{1 -\sigma_s}}\right)^{\frac{\sigma_s-1}{ \sigma_s}},\\
\to &\sum_{i \in N} x_{i,s}^{\frac{\sigma_s-1}{\sigma_s}}= E_{j,s}^{\frac{\sigma_s-1}{\sigma_s}} \left(\frac{1}{P_{s}^{1- \sigma_s}}\right)^{\frac{\sigma_s-1}{\sigma_s}} \sum_{i \in N} p_{i,s}^{(1-\sigma_s)},\\
\to& \sum_{i \in N} x_{i,s}^{\frac{\sigma_s-1}{\sigma_s}} = E_{s}^{\frac{\sigma_s-1}{\sigma_s}} P_{s}^{\frac{1 - \sigma_s}{\sigma_s}}\\
\to & \left(\sum_i x_{i,s}^{\frac{\sigma_s-1}{\sigma_s}}\right)^{\frac{\sigma_s}{\sigma_s-1}} = E_{s} P_{s}^{-1}\\
\to& P_{s} Q_s = E_{s}.
\end{align*}
$$
This shows that the price index $P_s$ and the quantity index $Q_s$ are exact price and quanty indices for this subgroup (as is expected as we were maximising a CES utility function).
Let's now go to step 2. Notice that the budget constraint can be rewritten as:
$$
E = \sum_{s} E_s = \sum_s P_s Q_s.
$$
We want to determine $E_s$ to maximize:
$$
U = \prod_{j \in S} Q_{s}^{\mu_{j,s}} \text{ s.t. } \sum_s P_{s} Q_{s} = E.
$$
This is a simple Cobb-Douglas utility function. As such, we know that expenditure shares are proportional to income:
$$
P_s Q_s = E_s = \frac{\mu_s}{\sum_w \mu_w} E
$$
Finally, substitute this into the equation $(1)$:
$$
x_{i,s} = \frac{\mu_{s}}{\sum_w \mu_w} E \frac{p_{i,s}^{-\sigma_s}}{P_{s}^{1- \sigma_s}}
$$


Monopoly pricing under constant elasticity of demand While reading Ch. 24-Monopoly from Intermediate Microeconomics by Hal Varian (8 th edition), on pg. 441, he writes that a monopolist will never choose to operate where the demand curve is inelastic. I understand the argument, but, if we have constant elasticity demand curve with

$|\epsilon| < 1 $

then how this effect the monopolist's choice?

A constant elasticity demand function has the form $q=p^{-\epsilon}$. Let's check this indeed gives us a constant elasticity...
$$\frac{d q}{dp}=-\epsilon p^{-\epsilon-1}$$
so, as we'd hoped, the elasticity is constant:
$$\frac{d q}{dp}\frac{p}{q}=-\epsilon p^{-\epsilon-1}\frac{p}{p^{-\epsilon}}=-\epsilon p^{-\epsilon-1+1+\epsilon}=-\epsilon p^{0}=-\epsilon.$$

Now, suppose a monopolist has constant marginal cost $c\geqslant0$ (and no fixed cost). It's profit is
$$q(p-c)=p^{-\epsilon}(p-c).$$
The effect on the firm's profits of a small increase in its price is
$$\frac{d}{d p}p^{-\epsilon}(p-c)=p^{-\epsilon -1} [c \epsilon -p\epsilon+p].$$
Now we can answer the question: if $\epsilon<1$ then $c \epsilon -p\epsilon+p$ is definitely positive for every $p$. That means, no matter how high the price is, the firm would still like to increase the price further—the optimal price is $+\infty$!

Intuitively, constant  $\epsilon<1$ means that the firm can always more than double its price by foregoing less than half its current sales. Provided marginal cost isn't very quickly decreasing, this is always an attractive prospect for the firm.


How does borrowed money affect GDP? Suppose that a household borrows from the bank with %2 interest rate and uses the money for paying rent;

Is this a Consumption?
May households borrow money from the bank for consumption, not investment purposes? (I haven't seen such thing in a circular flow graph, that's why I'm asking)
Is factor payments are being paid to another household who lends his savings to the bank?
Is this payment of saving is counted as lender's income?
What kind of approach of GDP would borrowing money from the bank for paying the rent, and interest income earned by another househould?

Yes, this is consumption.

There are 3 ways to calculate GDP, income effect, value added effect, and value of final products.

The simplest to understand is probably the income effect where the value of all wages and profits at every stage of production are added together to find final GDP. Since the household has paid rent and paid the bank for a service both payments count towards the income of both the landlord and the bank.

If the household in your example borrowed $1000 to spend on rent at 2% interest and then paid back that $1020 next year it would be a $1020 net gain for GDP with $1000 going to the landlord's income and $20 going to the bank's income for their service of lending out money. If the household defaulted on its debt then the bank would report a loss of $1000 on their income which would cancel out the $1000 gain on the part of the landlord.


How to visually present a simultaneous game with continuous strategies I've been asked to model a game where two players have an infinite choice of strategies and move simultaneously.

The question asks to present the game in game table or extensive form, and to justify that choice. I understand that a game table wouldn't work, given the infinite strategies.

I understand the diagram below to be a game with continuous strategies and sequential moves. Is there any way to adapt it to show simultaneous moves?

This thread has some game trees. In case you want put them on your documents, you can do like this (using LaTeX with istgame package):

\documentclass{standalone}

\usepackage{istgame}

\begin{document}

\begin{istgame}[font=\scriptsize]
\setistgrowdirection{east}
\cntmdistance{20mm}{20mm}
\cntmAistb{q_1=0}[at end,below]{q_1=1,000}[at end,above]
\istrootcntmA(0){1}
  \istbA[draw=none]
  \endist
\cntmAistb{q_2=0}[at end,below]{q_2=1,000}[at end,above]
\istrootcntmA(1)(0-1)<[xshift=3pt]90>{2}
  \istbA[draw=none]{}{\pi_1,\pi_2}
  \endist
\end{istgame}

\end{document}

\documentclass{standalone}

\usepackage{amsmath}
\usepackage{istgame}

\begin{document}

\NewDocumentCommand\vpay{m}
{ \begin{matrix} #1 \end{matrix} }

\begin{istgame}[scale=1.5,font=\scriptsize]
\cntmApreset{.9}
\cntmdistance{15mm}{20mm}
\istrootcntmA(0)[null node]{1}
  \istbA(.977)[->,thick]{q_1}[r]
  \istbm
  \endist
\cntmAInfosetO[thick,dashed](0)[-11](2em)
\istrootcntmA(1)(0-1)[null node]<180>{2}
  \istbm
  \istbA(.977)[->,thick]{q_2}[r]
    {\vpay{\pi_1(q_1,q_2)\\\pi_2(q_1,q_2)}}
  \endist
\end{istgame}

\end{document}

\documentclass{standalone}

\usepackage{amsmath}
\usepackage{istgame}

\begin{document}

\NewDocumentCommand\vpay{m}
{ \begin{matrix} #1 \end{matrix} }

\begin{istgame}
\xtdistance{15mm}{40mm}
\cntmdistance{15mm}{30mm}
\cntmApreset[draw=none]{1}[red!50,opacity=.2]
\istroot(0){Challenger}
  \istb{In}[al]  \istb{Out}[ar]  \endist
\cntmAistb[draw=none]
\istrootcntmA(1)(0-1)<135>{Incumbent}
  \istbA{q_I}[left]  \endist
\cntmAInfosetO(1)
\cntmAistb[draw=none]
\istrootcntmA(2)(0-2)<45>{Incumbent}
  \istbA*{q_I}[left]
    {\vpay{\pi_C(0,q_I)\\\pi_I(0,q_I)}}
  \endist
\cntmApreset[draw=none]{1}[blue!50,opacity=.2]
\cntmAistb[draw=none]
\istrootcntmA(3)(1-1)<180>{Challenger}
  \istbA*{q_C}[midway,left]
    {\vpay{\pi_C(q_C,q_I)\\ \pi_I(q_C,q_I)}}
  \endist
\end{istgame}

\end{document}


What is data trapezoid form? For one of our class project we are required to do the following:

  Download U.S. real GDP in data trapezoid form (vintages)

I tried to search online for what does the data in trapezoid form means but could not find any answer, the trapezoid form is not mentioned in the textbook either. Does anyone happens to know what that term means?

The brackets behind the term say "vintages" and I managed to find a lot of datasets with vintages of real GDP such as this one from Eurostat but I am not sure if "vintages" are the trapezoid form because in none of the datasets that mention GDP vintages there are any mentions for the "trapezoid form"

I got the answer from the professor after the assignment was graded during review. I am posting it here as it may help someone else in the future. Apparently, (vintage) data in trapezoid form for GDP are provided at Philadelphia Fed.
They have a trapezoid form because when they are plotted on a contour graph they have a trapezoid shape (the graph is from a correct review sample assignment from our professor):


3 Firm Stackelberg's Oligopoly Game Consider a market in which there are three firms, all producing the same good. Firm i's cost of producing qi units of the good is Ci(qi)=0 for qi≥0 for each i∈{1,2,3};  the price at which output is sold when the total output is Q is Pd(Q)=max{16−Q,0}, where Q=q1+q2+q3.

Each firm's strategic variable is output and the firms make their decisions sequentially: initially firm 1 chooses its output, then firm 2 does so, knowing the output chosen by the firm 1, and finally, firm 3 chooses its output, knowing the output chosen by firms 1 and 2. Find the equilibrium and outcome of Stackelberg's oligopoly game. List q1,q2,q3

The answer has been stated as (8,4,2)

I understand that we're supposed to use the Best Response functions of the other firms and then move sequentially by first solving the subgame of length 1.
I was able to find the Best Response of Firm 3 in terms of q1 and q2, but I do not understand how we're supposed to move forward with the question using the given Best Response. For a 2 Firm Stackelberg's oligopoly game, we can simply use the Best Response function of the follower firm and use it in the profit maximization function of leader's firm. However, when I repeat the procedure with a 3 firm Stackelberg's game, the results seem inconclusive. Please help me with this problem!

I assume that you found Firm 3's best response to be
\begin{equation}
q_3^*(q_1,q_2)=\frac12(16-q_1-q_2).
\end{equation}

The next step would be to solve for Firm 2's best response. Since Firm 2 observes Firm 1's output and correctly anticipates Firm 3's best response, its profit maximization problem is
\begin{equation}
\max_{q_2}\;(16-q_1-q_2-q_3^*(q_1,q_2))q_2=
\max_{q_2}\;\left(16-q_1-q_2-\frac12(16-q_1-q_2)\right)q_2.
\end{equation}
Solve this problem, you should get Firm 2's best response as a function of $q_1$ only. Denote this best response $q_2^*(q_1)$.

Then, you solve Firm 1's profit maximization, with Firm 1 correctly anticipating the responses of the subsequent two firms:
\begin{equation}
\max_{q_1}\; \bigl(16-q_1-q_2^*(q_1)-q_3^*(q_1,q_2)\bigr)q_1.
\end{equation}


How are working hours statistics computed? In a recent conversation, I was suggested that national working hours aggregates, as provided by bureaus of statistics, are based on surveys on time use.

Is that true? Can macro labor data, which is used for so many different puzzles and theories, be vulnerable to things such as time-varying biases in estimating time use? How are national working hour statistics computed?

Referring to USA, the place to go and learn a lot (if not everything) about the matter is The Bureau of Labor Staitstics

Indicatively, for one of BLS's many outputs, they report that:

  Payroll survey — methods and measurement issues

  The Current Employment Statistics (CES) program, also known as the
  payroll survey or the establishment survey, is a monthly survey of
  approximately 143,000 businesses and government agencies representing
  approximately 588,000 worksites throughout the United States. From the
  sample, CES produces and publishes employment, hours, and earnings
  estimates for the nation, states, and metropolitan areas at detailed
  industry levels.

  The CES employment series are estimates of nonfarm wage and salary
  jobs, not an estimate of employed persons; an individual with two jobs is counted twice by the payroll survey. The CES employment series
  excludes employees in agriculture, private households, and the
  self-employed.

  ...The entire sample is redrawn annually, and a supplemental sample of
  new business births is selected midway through the year. About
  one-fourth of the sample is rotated out each year and replaced with
  newly selected businesses.

  All new sample is solicited by computer-assisted telephone interview
  (CATI), and data are collected for the first 5 months via this mode.
  After the initiation period, many sample units are transferred to one
  of several less costly reporting methods that are self-initiated by
  the respondent...

  Estimation Methodology.
  CES monthly employment estimates are made using a two-part estimator.
  The sample reports are used to estimate month-to-month employment
  change from continuing businesses and a birth/death model is used to
  account for new firm births that otherwise would not be sampled in a
  timely fashion.

  Estimate review.
  CES uses automated edit and screening techniques to identify potentially erroneous sample data; respondents are
  re-contacted as needed to validate or correct their reported
  information. After the microdata edit process is complete, monthly
  estimates are calculated. Automated edits of the estimates are
  supplemented by analysts who look for errors and outliers and provide
  final validation of the series before publication.

  Seasonal Adjustment.
  The seasonal adjustment process removes from the series the effects of
  normal variation from recurring events within a year, such as holidays
  and weather changes, and helps reveal underlying economic trends. CES
  uses a concurrent seasonal adjustment methodology, meaning that it
  incorporates estimates up through and including the current month’s
  data to achieve the best possible series.

  Monthly Revisions.
   CES first preliminary estimates of employment, hours, and earnings are published each month approximately 3 weeks
  after the reference period. Estimates are then revised twice before
  being held constant until the annual benchmarking process. Second
  preliminary estimates for a given month are published the month
  following the initial release, and final sample-based estimates are
  published 2 months after the initial release.


Why'd a company issue unpaid shares, to acquire or merge companies? Under the heading Why would a company issue unpaid shares? by Johnathan Korchak

Although unpaid and partly paid shares are far less common than fully paid shares, there are a number of reasons why a company might choose to issue them:
[...]
[second-last bullet] In line with a strategy to implement an acquisition or merger of companies.

Under the heading Why would I issue unpaid shares?

Companies may choose to issue partly-paid or unpaid shares for a variety of reasons, including:
[...]
[last bullet] As part of a strategy to implement a merger or acquisition.

Why would a company issue unpaid shares?

Possible reasons are:

buyer's temporary lack of sufficient funds to perform the
acquisition, whence the issuer of shares is willing to grant credit for
the sake of "closing the sale";
fiscal planning (be it the buyer's and/or the issuer's planning) might be such
that delaying payment of shares will place him at a more convenient tax bracket
in the acquisition and/or disbursement fiscal year(s) (this is more evident in cash based accounting systems), and/or the delay of payment will allow
him to qualify for certain tax deductions;
issuer predicts the price of shares will fall (and possibly discourage prospects of merger/acquisition), so he hedges against
that risk by entering a forward contract with the buyer, with the incentive --to the buyer-- that transfer of shares will be effective immediately;
buyer is willing to commit to a higher price on unpaid shares so as
to anticipate upcoming legislation that will make it harder to
perform akin mergers/acquisitions.


Why aren't lengthier expirations offered, especially when a competitor offers it? My grandparents in Canada screenshot from their Questrade IQ Edge.

Why wouldn't the options exchange sell options with lengthier expiration dates for Vanguard's Russell 2000 ETF, when they do for iShares's? Wouldn't Vanguard complain to Vanguard about this, because Vanguard desires to indirectly benefit from option traders who desire dates after 18 Dec 2020?

In general, why aren't lengthier expiration dates offered at all for some stocks or ETFs? For instance, FXB is the only ETF for GBP, but doubtless some traders desire dates after 18 Dec 2020?

I am not sure of the exact procedure, but it is not purely an administrative decision of the exchange - they need market makers who want to support the product. Given the rise of algorithmic trading, one could imagine that any conceivable product could be created, and hope that people set up algorithms that create a two-way market. However, exchanges have rules about margin calls, and so sketchy financial products raise the concern of entirely artificial squeezes.
The revealed preference is that not many entities want to trade long-dated equity options, and so we return to the previous point. This is not a general property across all financial products; fixed income supports long-dated option trading (swaptions) as a side effect of hedging embedded call options in bonds/mortgages.


Why don't profitable firms use previous profits to offset current loss It is being reported that EasyJet expects a heavy loss in the current year due to Covid-19 pandemic. The report states that

The airline said it expected to sink into a pre-tax loss of between
£815m and £845m in the current financial year, which is worse than
analysts' forecasts of a £794m loss. It would be the first time in
EasyJet's 25-year history it has not made an annual profit.

The report also says that EasyJet has laid off more than 4000 people and has taken a government loan.
I looked at their profit profile and it looks like they have made more than 300 Million pounds profit for last many years.
Why can't they offset the loss (caused by special case) from their earlier profits rather than resort to drastic job cuts and government bailout?

The primary goal of most companies is to make money for its shareholders. They put money in, and they expect to either get dividends, or be able to resell their shares for a higher amount. It's the shareholders who own the company, and they are the ones deciding. And they want money. Otherwise they would give their money to charity.
So when a company makes a profit, they will do a combination of one or more of these:

Set aside some as reserves (in some cases there are mandatory reserves by law)
Re-invest some of the profit to make more money in the future (buy new equipment, buy companies, hire people, send money on R&D...)
Pay dividends to shareholders, or buy back shares (two ways of giving money back to shareholders)
And the rest will remain as cash.

Investors usually don't want the company to hoard profits. A safe reserve so it can go through difficulties, but that's it. Cash in the bank makes very little money, it's not a useful use of those funds for the investor: they'd rather get the money and invest it themselves according to their own risk profile.
If the company doesn't do what the investors want, then the shareholders will usually change management to make sure it complies.
So keeping employees on the payroll in tough times is not a primary goal of most companies. Of course, it's not a good idea to fire everybody at the first sign of trouble (it has an impact on the morale and performance of the other employees, it may cost a lot in severance, and when business picks up it will take time and cost money to hire and train new people), but if things are too bad, then it's the only option the company has to fulfil its obligation to shareholders.
There may be exceptions: a company and its shareholders may decide that their social responsibility is more important than making money. Cue all the "fair", "equitable", "social", "responsible", etc. keywords. But those are really the exception rather than the norm, and there's a limit to what can be done. Even if it made profits consistently and kept those as reserves, those reserves can't last forever while the company is burning through cash.
Remember that many companies have very small profits compared to the revenue and costs.
Consider a company with usual revenue of 1 billion pounds, but with tight margins: their expenses could be 900 million pounds, so the profit is 100 million pounds. They keep the profit year after year for 5 years, so they now have 500 million pounds in the bank, and the shareholders haven't complained yet (as if).
Now Covid strikes, and the revenue dwindles to 100 million pounds. If they keep all their costs the same, they're haemorrhaging 800 million pounds a year. They won't last a year like that! So yes, they will have to reduce costs, and part of this is laying off staff.
Don't think those figures are realistic? In 2019, Easyjet has revenue of about 6.385 billion pounds, but expenses of over 6 billion pounds! With revenue slashed to a fraction of what it was, they obviously can't keep spending like they did. They would have needed to keep profits of the last 20 years just to be able to get through this year.


Year effects inconsistent between random effects and fixed effects I am running a panel data estimation, where I am including year effects. My goal is to see if there is a time trend in the data, after controlling for other factors.

Using random effects, I find the trend is upward sloping. Using fixed effects, I find the trend is downward sloping.

Is this a bad result? A Hausman test rejects the RE with p-value of 0.000. Does it mean that the trend values from the RE can be inconsistent? Or is the FE capturing something different than the RE model? Differences in differences perhaps?

This is an interesting result, not a bad result. If there are no regressors other than time dummies, then I think OLS = RE = FE. (I've done a few experiments with reg y i.year, xtreg y i.year, fe, and xtreg y i.year, re, but I have not proved.)

If $X_{it}$ have trends and are correlated with fixed effects, anything can happen. For example, run the following Stata script (copy & paste):

set more off
clear all
local n 100
local T 5
set seed 1
set obs `=`n'*`T''
gen id = floor((_n-1)/`T')+1
by id, sort: gen year = _n
xtset id year
tempvar a0
gen `a0' = rnormal() if year==1
by id: egen a = mean(`a0')
gen x = a-year+rnormal()
gen y = a+x-0.2*year+rnormal()
drop a
* So far x and y have been generated.
xtreg y x year, fe
est store fe
xtreg y x year, re
hausman fe ., sigma
set more on

You will see that FE gives a negative trend, RE gives a positive trend, and the Hausman test is very significant. (Above I included a linear trend for simplicity. The results are similar when i.year is used instead.) I think it is trends in X and the presence of fixed effects.

. set more off

. clear all

. local n 100

. local T 5

. set seed 1

. set obs `=`n'*`T''
number of observations (_N) was 0, now 500

. gen id = floor((_n-1)/`T')+1

. by id, sort: gen year = _n

. xtset id year
       panel variable:  id (strongly balanced)
        time variable:  year, 1 to 5
                delta:  1 unit

. tempvar a0

. gen `a0' = rnormal() if year==1
(400 missing values generated)

. by id: egen a = mean(`a0')

. gen x = a-year+rnormal()

. gen y = a+x-0.2*year+rnormal()

. drop a

. * So far x and y have been generated.

. xtreg y x year, fe

Fixed-effects (within) regression               Number of obs     =        500
Group variable: id                              Number of groups  =        100

R-sq:                                           Obs per group:
     within  = 0.8276                                         min =          5
     between = 0.9353                                         avg =        5.0
     overall = 0.8066                                         max =          5

                                                F(2,398)          =     955.57
corr(u_i, Xb)  = 0.4473                         Prob > F          =     0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |   .9803594   .0483021    20.30   0.000     .8854004    1.075318
        year |  -.2207004   .0568937    -3.88   0.000    -.3325502   -.1088506
       _cons |   .1019471   .1021303     1.00   0.319    -.0988351    .3027294
-------------+----------------------------------------------------------------
     sigma_u |  1.1387103
     sigma_e |  .97339535
         rho |  .57779363   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(99, 398) = 3.61                     Prob > F = 0.0000

. est store fe

. xtreg y x year, re

Random-effects GLS regression                   Number of obs     =        500
Group variable: id                              Number of groups  =        100

R-sq:                                           Obs per group:
     within  = 0.8066                                         min =          5
     between = 0.9353                                         avg =        5.0
     overall = 0.8436                                         max =          5

                                                Wald chi2(2)      =    2432.08
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |    1.40149   .0391177    35.83   0.000      1.32482    1.478159
        year |    .196468   .0523296     3.75   0.000     .0939039     .299032
       _cons |   .1267828    .123712     1.02   0.305    -.1156882    .3692539
-------------+----------------------------------------------------------------
     sigma_u |   .3602397
     sigma_e |  .97339535
         rho |  .12046423   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. hausman fe ., sigma

Note: the rank of the differenced variance matrix (1) does not equal the number
        of coefficients being tested (2); be sure this is what you expect, or
        there may be problems computing the test.  Examine the output of your
        estimators for anything unexpected and possibly consider scaling your
        variables so that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           .          Difference          S.E.
-------------+----------------------------------------------------------------
           x |    .9803594      1.40149       -.4211302        .0389278
        year |   -.2207004      .196468       -.4171684        .0385616
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                  chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =      117.03
                Prob>chi2 =      0.0000

. set more on


Why is it possible to calibrate your subjective probabilities? Humans tend to be overconfident in their predictions; when most people say that there's a 95% chance that something will happen, they're usually wrong far more than 5% of the time.  Whereas what ought to happen is that for all $x$, if a person makes a lot of predictions of the form "There is an $x\%$ chance that P will occur," then about $x\%$ of them should come true.  If a person's predictions does satisfy this property, then their subjective probabilities are said to be well-calibrated.

Now there may be no one who is perfectly well-calibrated, but some people are better than others; see the book "Superforecasting" for information on people who are extremely well-calibrated.  But calibration isn't something fixed from birth; you can train yourself to be better-calibrated by playing a game where you assign a probabilities to a bunch of things and then you're scored by how well-calibrated your subjective probabilities are (using e.g. the Brier score).  See this web site and this website.

But my question is, why is it possible to become well-calibrated using such a game?  Let $A$ be the set of possible events $f$ be a function from $A$ to $\mathbb R$ that gives a numerical assessment of how confident a person feels about a given event.  Then what playing the game is designed to do is to help you find an increasing function $g$ from $\mathbb R$ to $[0,1]$ such that $g \circ f$ is well-calibrated.

But in order for such a $g$ to exist, it needs to be the case that for all $x,y \in \mathbb R$, if $x>y$ then the percentage of outcomes in $\{P \in A: f(P) =x\}$ which are true needs to be greater than the percentage of outcomes in $\{P \in A: f(P) =y\}$ which are true.  In other words, it needs to already be true that you're right more often about statements that you're more confident in than statements you're less confident in.  But why should this be the case?  Are there any decision-theoretic assumptions or rationality axioms that imply this is the case?  Has it been empirically observed that humans are more often right about what they're more confident in?

It would certainly be a useful evolutionary skill if humans' internal confidence levels reflected external reality, but I've never heard of anyone discuss this before.

Empirically yes, it seems confidence has a positive correlation with correctness. One reference is Bordalo et al. 2018 Beliefs about gender, see Fig.1 for example. The actual probability of a correct answer is different from own or other people's estimate of the probability of a correct answer, but if the estimated probability is higher, then the actual probability is higher.

As to the axioms or theoretical assumptions - you can just assume that people's estimates of their correctness are increasing in the correctness. Or assume Bayesian updating about own correctness, in which case past correct guesses would increase the guesser's confidence in own correctness. The number of past correct guesses in turn is positively correlated with the guesser's actual correctness (by the Law of large numbers).


What does it mean when we talk about "same basket" exactly for both GDP and CPI? When we say about "the basket used for calculating the CPI is the same as the composition of GDP" What does it mean the "same basket"? Does it just mean the goods and service are the same but the weights of each good itself do not matter?(Basket of CPI and GDP are also included A and B but no matter weights) . Or it means the weights of each good in the basket are the also same? (Basket of CPI and GDP are included A and B, also the weights of A is 0.4 and B is 0.6 in both baskets)

I'm really confusing.

In additon, this is the original question though I think it would be useless for this question:

"Assume that the basket used for calculating the CPI is the same as the composition of GDP. Will CPI in a given year then equal the GDP deflator? If so why, if not why not?"

Thanks to all the people willing to help!!

Same basket means same goods and services at factor cost or market price. Weighting method could be different.