Question:
How are stock prices determined in the following cases?

I looked at this question already. I know there is an order book with bid and ask and that the price is updated when a match occurs. But I have two questions:

What happens when the bid is higher than the ask? For example someone is ready to pay $101 per share for 100 shares and someone wants to sell 100 shares at $100. What will be the new price?

What if there are multiple matches at an instance? Let's say we have someone wanting to buy 100 shares at $100 and someone wanting to sell 100 shares at $100. We also have someone wanting to buy 500 shares at $110 and someone wanting to sell 500 shares $110. What is the new price?

Explanation: The stock price is about matching the prices of exchange pairs.

$\begingroup$

As in the answer [ here
](https://economics.stackexchange.com/questions/24729/how-are-final-stock-
prices-arrived-at) (which you referred to yourself), the price of a stock is
the price the stock was last traded at (until that price is updated because a
new trade happens). A trade occurs if a bid and ask are matched.

The matching relies on a double ordering. The principle to remember here is
"buy low, sell high". Also, remember that the ask is the _minimum_ price a
would-be seller is happy to sell, while the bid is the _maximum_ price a
would-be buyer is happy to buy. The buy and sell offers are ordered in the
following way:

  * **Asks** : lowest first, highest last, then in the order they were submitted.
  * **Bids** : highest first, lowest last, then in the order in which they were submitted.

This is called **price-time-priority matching** (see [ here
](https://www.investopedia.com/terms/m/matchingorders.asp#:%7E:text=Under%20a%20basic%20FIFO%20algorithm,order%20at%20a%20lower%20price.)
). Many exchanges use a variant of that procedure with potentially some
extensions. An important exception is the NYSE, which has a pro-rate system on
top (see [ here ](https://www.nyse.com/article/parity-priority-explainer) ),
but this is not relevant for your cases.

> What happens when the bid is higher than the ask? For example, someone is
> ready to pay \$101 per share for 100 shares, and someone wants to sell 100
> shares at \$100. What will be the new price?

The matching in this case depends on the order in which instructions were
submitted and on the _best price rule_ , which says that whoever submits last
gets the best available price. One motivation for that rule is that agents
shouldn't be punished for submitting limit orders. After all, if that
principle were not in place, agents who act last could instead put in market
orders (without a limit), where a buyer immidiately buys at the lowest ask,
and a seller sells at the highest bid, which may result in a better deal for
the agent last to act. If not in place, you wouldn't get many limit orders, if
any at all. So this rule favors market liquidity.

Applying these rules, if the sell offer at \$100 was there first, the buyer,
even though she is happy to pay \$101, will only pay 100. Conversely, if the
buyer places the order first, the seller will sell for 101. So, depending on
the order of submission, the resulting price will be either 100 or 101.

> What if there are multiple matches at an instance? Let's say we have someone
> wanting to buy 100 shares at \$100 and someone wanting to sell 100 shares at
> $100. We also have someone wanting to buy 500 shares at \$110 and someone
> wanting to sell 500 shares \$110. What is the new price?

Again, the matching depends on the double ordering mentioned above and the
best price principle. I won't go through all possible cases, but provide a few
**illustrations** :

  * Bid = 500@\$110. The seller comes in with 100@\$100. The trade is executed at the best price (for the seller) at \$110. (if they submit in the reverse order, the trade will happen at a price of \$100)

  * Bid = 100@\$100, Ask = 500@\$110. There is no match. Ask = 100@\$100 comes in, "jumps the queue," and 100 shares are traded at \$100.

  * Bid = 100@\$100, Ask = 500@\$110. There is no match. A new bid comes in with 500@\$110. It jumps the bid queue and is matched with the ask, and the trade happens at a price of \$100.

Note that time-stamping these days is very accurate, to within one millisecond
(see for example [ here
](https://www.npl.co.uk/getattachment/5b94a9f8-bd79-478e-ba25-8fc56f51be33/NPLTime_Complete_Guide.pdf.aspx?lang=en-
GB&ext=.pdf) ). For any confusion to occur, orders would have the share the
same time-stamp and precisely the same price.


Question:
What's wrong with this argument that the fed's OMOs don't change the money supply

Is there anything facially stupid about the following argument that fed open market operations don't affect the money supply? And if not, are there any professional economists who have made this argument?

When the fed buys or sells treasury bonds they are not changing the broader stock of highly liquid assets that include treasury bonds (is that m3?), since they are just exchanging one of the components (cash) for another (govt bonds). Since there are no reserve requirements for commercial banks -- only capital requirements -- this doesn't actually affect the rate of credit creation since a bank that exchanges a dollar of central bank reserves for a dollar of us treasury debt is just as well capitalized as it was before.

Explanation: We need more information about model/framework of liquidity coverage ratio, and how it affects money policy.

$\begingroup$

M3 isn't even published anymore in the US (it did not include bonds though).

As Alex noted, the LCR is entirely unaffected if the FED purchases government
bonds because both are level 1. See for example this [ BIS paper
](https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.bis.org/publ/qtrpdf/r_qt1212g.pdf&ved=2ahUKEwjXiYCB7Lf5AhXAYPEDHX1lAkgQFnoECA8QAQ&usg=AOvVaw2c0uqFq3624W07Ups0mj1A)
on P.58 for a simple example demonstrating this.

Moreover, the Fed cannot control the federal funds

> rate through routine changes in the quantity of reserves, also known as open
> market operations (OMO)

as copy pasted from [ this FED note about the ample reserves regime
](https://www.federalreserve.gov/econres/notes/feds-notes/implementing-
monetary-policy-in-an-ample-reserves-regime-the-basics-
note-1-of-3-20200701.htm) . This is a direct effect of the ample reserves
regime, where the [ reserve requirement ratio is zero
](https://www.federalreserve.gov/monetarypolicy/reservereq.htm#:%7E:text=As%20announced%20on%20March%2015,requirements%20for%20all%20depository%20institutions)
.

Generally, OMO can mean a lot of things (purchase of all sorts of securities)
but (ignoring the title), I think the main argument is about the purchase of
government bonds? For short, this does neither affect the interest rate (in an
ample reserves regime), nor the liquidity ratio (LCR) / capital requirement of
a bank. The latter statement requires that the central bank is purchasing a
highly liquid (level 1) asset though (which US government bonds are).

Insofar, as written in your post, a purchase of government bonds by the FED
has

> no direct impact on credit creation,

at least not via the LCR or interest rate channel. I am inclined to believe
that this was the argument made by whoever you heard this from. I am less
convinced they mentioned money supply because traditionally the monetary base
is defined as currency in circulation plus reserve balances and while there
are more liquid types, none include bonds in the US in any case (there used to
be M4 and L which included T-bills but these were stopped long ago).

Lastly, the implementation of monetary policy has evolved considerably and
repeatedly since the financial crisis. The FED also does not (anymore) target
monetary aggregates when conducting monetary policy. I believe reading [ this
answer ](https://economics.stackexchange.com/a/49858/40033) might be
interesting, although many others have different opinions about this subject.

**Edit**

Commercial bank credit is NOT part of M1. When a bank provides a loan, the
borrower receives a deposit. From the perspective of commercial banks balance
sheets, this increases credits on the assets side and customer deposits on the
liabilities side. Most of the times (with mortgages it is frequently directly
sent to seller of the house / or mortgage notary's account) this deposit is
withdrawn quickly and usually sent to another bank (unless the seller's bank
account is at the same bank as the buyer's). Therefore, an individual
commercial bank cannot generate lasting increases in its deposits by granting
loans.

However, the banking system as a whole does see an increase in deposits (thus
money supply) despite constant amounts of central bank money. Leaving
potential reserve requirements aside, the bank will still have risk/return
considerations to take into account when providing loans. From an asset
liability management perspective, loans are long-term claims on the assets
side, while sight deposits are typically liquid and short-term liabilities. In
essence, that is one of the main reasons justifying commercial banking - it's
an intermediary that brings together investors and savers despite their
diverging requirements. Banks can offer this service because they can
diversify the credit and liquidity risks better than individuals.

For risk management, banks need to consider factors such as current and future
interest rate on loans and deposits, the likelihood of deposit withdrawals and
credit defaults and the like. On top of this, banks are tightly regulated.
Banks need to follow the standards of Basel III, which consist of 3 Pillars

  * Pillar 1: Capital requirements ( [ Capital Ratio ](https://en.wikipedia.org/wiki/Capital_adequacy_ratio) , [ Leverage Ratio ](https://en.wikipedia.org/wiki/Basel_III#Leverage_ratio) ,..), Credit risk, Market risk, [ Operational Risk ](https://en.wikipedia.org/wiki/Operational_risk) as well as [ LCR & NSFR ](https://www.ecb.europa.eu/pub/financial-stability/macroprudential-bulletin/html/ecb.mpbu201910_2%7E3237802727.en.html) .
  * Pillar 2: mainly supervision like the Supervisory Review Evaluation Process ( [ SREP ](https://www.bankingsupervision.europa.eu/banking/srep/html/index.en.html#:%7E:text=This%20activity%20is%20called%20the,supervisory%20measures%20to%20be%20taken.) , [ ICAAP & ILAAP ](https://www.eba.europa.eu/guidelines-on-icaap-and-ilaap-information) ,...
  * Pillar 3: ...

Long story short, banks cannot simply give away loans without end. Also,
credit creation by banks relies on a lot more details than the traditional
reserve requirement (money multiplier) argument suggests. Specifically, it is
not just the consideration of outflows (of deposits) and inflows being spread
over time and normally only being a fraction of total deposits (which is where
the name _fractional reserve banking_ originated, as only a fraction of
customer deposits have to be covered all the time). Since deposits created by
the banking system belong to the banks’ customers, the main driving force
behind credit creation are customers, not banks themselves.

In fact, the FED does not even aim to affect the broad money supply. St.Louis
FED research claims it's best to forget what we learnt about money aggregates
in [ undergrad Econ
](https://research.stlouisfed.org/publications/page1-econ/2021/09/17/teaching-
the-linkage-between-banks-and-the-fed-r-i-p-money-multiplier) . The so called
_dual-mandate_ aims to (somewhat interestingly) promote three (not two) goals:
maximum employment, stable prices, and moderate long-term interest rates

Neither of these goals mentions money supply. Also, [ New York FED - Money
Supply ](https://www.newyorkfed.org/aboutthefed/fedpoint/fed49.html) states
that

> In 2000, when the Humphrey-Hawkins legislation requiring the Fed to set
> target ranges for money supply growth expired, the Fed announced that it was
> no longer setting such targets, because money supply growth does not provide
> a useful benchmark for the conduct of monetary policy.

and [ FED - what is money supply
](https://www.federalreserve.gov/faqs/money_12845.htm) claims that

> Over recent decades, however, the relationships between various measures of
> the money supply and variables such as GDP growth and inflation in the
> United States have been quite unstable. As a result, the importance of the
> money supply as a guide for the conduct of monetary policy in the United
> States has diminished over time

[ This answer ](https://economics.stackexchange.com/a/49858/40033) has a few
charts illustrating that total money supply is not really directly impacted by
monetary policy. For example, normalizing each series to Dec 2005 = 100
(monetary base - [ BOGMBASE ](https://fred.stlouisfed.org/series/BOGMBASE) , [
M1 ](https://fred.stlouisfed.org/series/WM1NS) \- be careful, the definition
changed in May 2020 if you look at the data on FRED, [ M2
](https://fred.stlouisfed.org/series/WM2NS) ), the data looks like this (the
code to replicate this is in the link: QE stands for quantitative easing)

[ ![enter image description here](https://i.sstatic.net/muKZf.png)
](https://i.sstatic.net/muKZf.png)

The dual-mandate got its name from employment and the price level, because
under [ full employment ](https://en.wikipedia.org/wiki/Full_employment) (not
no unemployment), and stable prices, interest rates settle at moderate levels.
For details, you can read [ Frederic S. Mishkin (2007) speech at Bridgewater
College
](https://www.federalreserve.gov/newsevents/speech/mishkin20070410a.htm) .

To summarize, the main goals of the FED are to keep prices stable and to
promote full employment (closely related to a healthy economy / GDP). However,
as just seen, there is only a weak relationship between measures of the money
supply and GDP growth and inflation. Therefore, the central bank focuses on
interest rates, not only the FED Funds market, but also longer term interest
rates. Changing interest rates has a direct impact on demand for credit (by
customers) and the risk metrics of banks (current and future interest rate on
loans and deposits, the likelihood of deposit withdrawals and credit defaults,
Basel III calculations, ...).

As written above, monetary policy has evolved considerably. For example, in
the EUR area, so called Targeted longer-term refinancing operations (TLTROs)
aim to offer commercial banks attractive long-term funding conditions. To
stimulate lending to the real economy, the interest rate is negative and in a
nutshell, the more loans participating banks issue to non-financial
corporations and households (except loans to households for house purchases),
the more attractive (the more negative) the interest rate. While ultimately
there needs to be demand from customers, these favourable funding conditions
make it easier (cheaper) to offer loans.


Question:
How can the exchange rate be virtually constant with major inflation rate difference and a widening trade deficit?

I have recently had a discussion with a colleague about what seems to be a rather strange macroeconomic aspect in Romania (which has RON currency):

EUR-RON exchange rate has been virtually a flat line in the past year
Romania's Balance of Trade widened to an almost record value
EUR annual inflation rate is about 9% now
RON annual inflation rate is almost double now
All these factors seem to put pressure on RON to lose value when compared to EUR and yet it is rather constant for quite a while.

The only factor I know is very different between EUR and RON is the base interest rate and I guess is acting in the opposite direction:

EURIBOR is barely positive
ROBOR 3M is more than 8%
What could maintain such a robust exchange rate for the EUR-RON pair? Namely, how can RON not lose value in this context for a rather long time (many months)? I am interested in a mostly qualitative answer.

Explanation: The inflation rate differences and bank overnight rate differences seem consistent with uncovered interest rate parity, which would not incentivize movement in the FX markets. We can check the equations and approximations of Uncovered interest rate parity.

$\begingroup$

You are right, all your points suggest that there is downward pressure on RON
(it should depreciate). Also, (un)covered interest rate parity would suggest
that RON should depreciate!

The [ UIP equation
](https://en.wikipedia.org/wiki/Interest_rate_parity#Uncovered_interest_rate_parity)
looks like this:

$$(1+i_{\\\\\$})={\frac {E_{t}(S_{{t+k}})}{S_{t}}}(1+i_{c})$$

or rearranged:

$${{S_{t}}}\frac {(1+i_{\\\\\$})}{(1+i_{c})} = E_{t}(S_{{t+k}})$$

**EDIT**

UIP is traditionally about expected (future) exchange rates. You can
technically solve to imply spot, but that would require you to know the future
expected FX rate. Since one observes (or say at the beginning of the year
observed) spot, and has interest rate data, one typically uses this
relationship to compute the expected FX rate. Either way, you can turn the
equation around as much as you want, the higher interest rate country's
currency is expected to depreciate over time.

I did not use the OP data because I copy pasted this example (and swapped USD
for RON). Also, the data provided in the question is insufficient. You can
find current spot, that EURIBOR is  $\approx 0 \%$  and ROBOR 3m is  $>8 \%$
. In real applications (say Bloomberg's [ ` FXFA `
](https://quant.stackexchange.com/q/41799/54838) ), one would use the
associated interest rates for a tenor (maturity / date in the future) from
bootstrapped Swap curves and cross currency basis curves as opposed to simply
spot rates. Ultimately, for the purpose of the question, all that matters is
what happens to the higher interest rate currency relative to the other. To
make it a bit closer to the OP data, I will use the approximate values.

For EURRON (how many RON per EUR, say 4.8931 at the time of writing according
to the [ Source ](https://www.investing.com/currencies/eur-ron-chart) provided
in the question, if the RON interest rate is 8% and the EUR rate is 0% you get
the value of (assuming for a full year, to avoid having to compute year
fractions for the interest rate),

$${4.8931}*\frac {(1+0.08)}{(1+0.0)} \approx 5.284548$$

In other words, you need more RON per EUR - the RON depreciated, EUR
appreciated.

The image below is from a [ Quant SE answer
](https://quant.stackexchange.com/a/67940/54838) and shows the Turkish
inflation rate as well as the USDTRY exchange rate.

[ ![enter image description here](https://i.sstatic.net/utNqb.png)
](https://i.sstatic.net/utNqb.png)

As you can see, the currency of the country with the higher inflation (Turkey)
tends to depreciate against the currency of the country (US) with lower
inflation rates (also Turkey has higher interest rates compared to the US).

**Why RON does not depreciate?**

In the case of RON, there are a few aspects, like forex inflows generated by
diaspora (especially during the summer season where lots of people return
home). Also, interest rates [ did increase
](https://tradingeconomics.com/romania/interest-rate) relative to the EUR zone
in the last few months, which will results in immediate upward pressure
(potentially counterbalancing the general downward pressure), just like the
USD appreciated against the EUR in the last months (the US also increased
rates).

  * on May 10th 2022: central bank of Romania raised its key monetary policy rate by 75bps to 3.75%
  * on July 6th, 2022: raised by 100bps to 4.75%
  * on August 5th, 2022: raised by 75bps to 5.5%

However, the biggest factor is likely (direct) intervention by Romania's
central bank (NBR). NBR's governor Mugur Isarescu [ explained
](https://www.economica.net/isarescu-euro-va-ramane-sub-5-lei-atat-cat-
trebuie-nu-dai-drumul-la-un-instrument-de-control-cand-ai-razboiul-la-usa-
incercam-sa-trecem-de-inflatie-fara-
recesiune_604421.html?mc_cid=65b2f26dba&mc_eid=607bd7d763) that the monetary
authority would remain active and not leave the national currency to weaken
below RON 5 to EUR. The statement alone may help the RON exchange rate (even
if there were no actual interaction by the NBR) as long as the central bank is
credible because market participants may not try to bet against the RON if it
is seen as an uphill fight against a central bank. A good example for a strong
central bank being able to fight speculative attack is the Hong Kong Monetary
Authorities history of being able to [ maintain the peg
](https://www.reuters.com/article/uk-hongkong-protests-currency-explainer-
idUKKCN1VJ0WH) .

The article about Isarescu is in Romanian but Google translate works well
usually. The main quote of interest is at the very beginning:

> The EURO will remain below 5 LEI as long as necessary. You don't let go of a
> control tool when you have war at your door.

[ NBRs inflation report
](https://www.bnro.ro/DocumentInformation.aspx?idInfoClass=6896&idDocument=40072&directLink=1)
(PDF download) states on P.31 that

> the stability of the EUR/RON exchange rate was an essential concern
> throughout this period.

[ ING FEB 2022 ](https://think.ing.com/snaps/ce4-fx-how-tolerant-are-cbs-to-
fx-weakness) mentions that

> the increased turnover around 4.95 suggests official offers have been
> protecting the leu.
>
> in the base case the NBR will most likely try to keep the FX rate stable
> through a combination of FX interventions and spiking carry rates if needed.

[ Erste Group Research
](https://www.erstegroup.com/de/research/report/en/SR263009) also states that

> the NBR is trying to curb the slide of the national currency

but mentions that depreciation pressures should persist.

**A bit of context**

A common misconception is that higher interest rates will lead to an
appreciation in the future, but in fact, UIP claims the opposite: any higher
interest in one country will be offset by a depreciation in that countries
currency so that an investor will be equally well off. In other words it
doesn't matter where you invest.

Forwards follow covered interest rate parity. Uncovered interest rate parity
is the same arbitrage condition but unhedged with FX forwards (hence
uncovered). If you have access to Bloomberg, you can look at ` FRD ` for the
former, and ` FXFA ` for the latter.

FRD:

[ ![enter image description here](https://i.sstatic.net/yUuzC.png)
](https://i.sstatic.net/yUuzC.png) [ ![!\[enter image description
here](https://i.sstatic.net/I0yVt.png) ](https://i.sstatic.net/I0yVt.png)

$\color{blue}{SP}$  stands for Spot, Pts (Points, the most common way of
quoting FX forwards)) represent what is added to Spot, Fwds are the forwards
computed from quoted Spot and Pts. The darker values at the bottom indicate
that these are implied (computed) from interest rates via no arbitrage. This
is done when there aren't enogh liquid market quotes. You can see that a
substantial depreciation of RON relative to EUR is quoted / implied at the
time of writing. FXFA is the tool to compute this systematically.

FXFA: Interest rates are deliberately chosen to follow your EURIBOR / ROBOR
example. [ ![enter image description here](https://i.sstatic.net/RPXpI.png)
](https://i.sstatic.net/RPXpI.png) Note, that you see the warning ` Mismatched
yield curves ` because it would not be the curves conventionally used but
market standards do not matter for the purpose of this question and the next
screenshot from the results section shows that the implied forward is not even
that different from the actual market quoted forward. The column 7) FX Swap
corresponds to the market quote, which combined with yield curves (column 8)
EUR Yield and 9) RON Yield) can be used to compute FX Swap implied (the
highlighted column). The column with red and green values shows the difference
bewteen the market quoted forwards and implied forwards. [ ![enter image
description here](https://i.sstatic.net/BRjLm.png)
](https://i.sstatic.net/BRjLm.png)

Bottom line, these BBG screens should just help to showcase that (un)covered
interest rate parity also suggests that RON should depreciate.

` Shouldn't higher interest rates lead to an appreciation in that currency
because it is more favourable? ` Usually higher interest rates (if
unanticipated) will result in the higher rates currency appreciating very
quickly (if it was fully anticipated, that effect happened already before the
hike). This is the basis of the so called [ overshooting models
](https://en.wikipedia.org/wiki/Overshooting_model) that were developed to
explain the excess volatility puzzle (typically, FX volatility exceeds that of
the underlying economic fundamentals substantially). Since FX reacts asap but
goods prices are delayed, the spot rate must overshoot its value in the short
run, followed by a depreciation (UIP) afterwards.

Overshooting models are also called [ sticky price monetary models
](https://www.minneapolisfed.org/research/sr/sr277.pdf) . They combine capital
markets, goods markets and money markets. [ Dornbusch
](https://www.mit.edu/%7E14.54/handouts/dornbusch76.pdf) (1976) was the first
to develop this theory.


Question:
Why did the Federal reserve balance sheet capital drop by 32% in Dec 2015?

Here's a graph of the capital on the Federal reserve balance sheet from 2003 until present:

https://fred.stlouisfed.org/series/WCTCL

Capital dropped by 32% in December 2015.

Is there anywhere I can read about why the capital dropped so dramatically at that point?

And perhaps why has it not changed much since then?

Explanation: This may be related to the enforcement of some act. We can check factors affecting reserve balance.

$\begingroup$

The Fixing America's Surface Transportation Act (FAST), which was enacted on
December 4, 2015, requires that aggregate Federal Reserve Bank surplus not
exceed \$10 billion.

The amounts of the line items "Other liabilities and capital" on table 1, and
"Surplus" on tables 5 and 6 reflect the payment of approximately \$19.3
billion to Treasury on December 28, 2015, which was necessary to reduce
aggregate Reserve Bank surplus to the \$10 billion limitation in the FAST Act.

[ Source: Factors Affecting Reserve Balances - H.4.1
](https://www.federalreserve.gov/releases/h41/20151231/)


Question:
How to pass long lag of unobserved into Kalman filter

I am trying to replicate multivariate filter for potential output from paper.

I have already understood which variables in the model are observed and which are unobserved. This model should be rewrited in the state space model setup in order to be stimated. However, in the formula for long run GPD there is NAIRU that is lagged for 20 quarters (see picture below).

formula for long-run GDP

Both NAIRU in period t and NAIRU in period t-20 are unobserved, which mean that they should enter vector of unobserved variables.

In this case I do not understand how we are able to formulate transition matrix since we have NAIRU(t) and NAIRU(t-19) on LHS of transition equation and NAIRU(t-1) and NAIRU(t-20) on RHS.

What coefficients should I put into row of transition matrix for NAIRU(t-19).

I want to estimate this model by bayesian sampling. This mean that I am able to sample coefficients for transition matrix and pass them to Kalman filter.

Explanation: We may need to preserve the identities of the lags in the transition matrix. To fit the specific case, it is ideal that state space representation can be modified to include an arbitrary number of quarterly variables.

$\begingroup$

The "trick" is to preserve the identities of the lags in the transition
matrix. In period  $t$  , you have (for some state variable  $x$  )  $$ x_t =a
x_{t-1} \\\ x_{t-1} = x_{t-1}\\\ x_{t-2} = x_{t-2}\\\ \cdots $$  So, the
corresponding block of the transition matrix becomes:  $$ \begin{bmatrix} x_t
\\\ x_{t-1}\\\ x_{t-2}\\\ \vdots\\\ x_{t-20}\\\ \end{bmatrix} =
\begin{pmatrix} a & 0 & \cdots && 0\\\ 1 & 0 & \cdots && 0\\\ 0 & 1 & 0 \cdots
&& 0\\\ \vdots & & \ddots && \vdots\\\ 0 & \dots & 0 & 1 & 0 \end{pmatrix}
\begin{bmatrix} x_{t-1} \\\ x_{t-2}\\\ x_{t-3}\\\ \vdots\\\ x_{t-21}\\\
\end{bmatrix} $$  The  $a$  coefficient captures the one-period transition for
$x$  from  $t-1$  to  $t$  . This coefficient may or may not be estimated.
Note that lag 21, which you don't want, has a zero coefficient and is not
carried along.

See, for example, appendix B in [ Banbura, Marta and Giannone, Domenico and
Reichlin, Lucrezia, Nowcasting (November 30, 2010). ECB Working Paper No. 1275
](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1717887)


Question:
Why do E85 prices track gasoline prices?

It's easy to understand why, as the Ukraine war disrupts global oil markets, gasoline prices are rising. What puzzles me is that E85, which is at most 49% gasoline, rises the same amount. It seems that it would me affected at most half as much as gasoline. Do we import a lot of ethanol from Russia?

I'm curious to know if there's a valid economic basis for this that doesn't involve price gouging.

Explanation: The similar rise may be related to the energy return in making ethanol.

$\begingroup$

In the U.S., most ethanol is corn ethanol. [ Research indicates
](https://doi.org/10.1021/es052024h) that corn ethanol has an [ energy return
on investment ](https://en.wikipedia.org/wiki/Energy_return_on_investment)
ratio of between 0.84 and 1.65. This means, basically, that it takes almost as
much energy to make a gallon of ethanol, as that gallon contains -- you're
either losing 16% in the process, or gaining 65%. Compare this to conventional
oil with a ratio above 18.

So the question isn't really about why ethanol prices track gasoline, but why
do energy prices track gasoline -- which of course is easier to answer.


Question:
How to view GDP as a network graph?

I was looking at the GDP by industry data at https://apps.bea.gov/iTable/iTable.cfm?reqid=150&step=2&isuri=1&categories=gdpxind

I'm curious how to view all these industries in a network.

For example, someone who owns a rental property may use their rental income to buy a car. So this would contribute to an arrow from the "real estate" industry to the "motor vehicle and parts" industry.

Someone who receives a social security payment may go out to eat at a resturaunt, the restaurant uses that money to pay a loan, etc.

So all these sectors would have arrows to and from each other.

Has anyone done research to look at this or produce some graph or visualization? I am curious what the sources and drains are in this graph or what kind of loops there are.

Explanation: This is related to input-output models, which represent the interdependencies between different sectors. The question is to find related information, e.g., derivation, examples, etc.

$\begingroup$

Seems like you are looking for [ Input-output models
](https://en.wikipedia.org/wiki/Input%E2%80%93output_model) .

> In economics, an input–output model is a quantitative economic model that
> represents the interdependencies between different sectors of a national
> economy or different regional economies.

The representation of is numerical, not graphical, but other than this, it
seems to be what you want.


Question:
How is Elon Musk's free Tesla charge a sustainable business model?

I came across this video, where Elon says charging a Tesla car at Tesla supercharge station is free and will be free always

How is this a sustainable business model? Where will the money for electricity come from?

Explanation: When companies give away a product or service at a loss, they usually do it to promote the sale of complementary goods. We can check more details about complementary goods.

$\begingroup$

**It's hard to know how to answer this question as stated, without a lot more
information about basic parameters** (as of 2022-04-28, 10:45 AM CDT).

  * When companies give away a product or service at a loss, they _usually_ do it to promote the sale of [ complementary goods ](https://en.wikipedia.org/wiki/Complementary_good) . The classic example of this would be [ Gillette's longstanding business practice of giving away safety-razor handles in order to sell their replaceable safety-razor blades ](https://www.bbc.com/news/business-39132802) . (Caveat: [ Randal Picker argues that this actually has a more complicated business history than is commonly understood ](https://hbr.org/2010/09/gillettes-strange-history-with) ; but Gillette certainly has given away a lot of free safety-razor handles, and even started mailing them out unsolicited using marketing lists. I got one in the mail myself when I turned 18, back in the 1990s.)

When this is sustainable, the money to do it typically comes from the sale
price of the complementary good(s), when and if this is enough to cover losses
from the giveaway. The profit in it comes from the shift in demand, if this
increases the quantity of the complement that can be sold or the price at
which it can be sold.

  * In economics jargon, the strategy is a particular form of a [ two-part tariff ](https://en.wikipedia.org/wiki/Two-part_tariff) : there is a lump-sum entry fee for using the composite product (the fixed cost of the razor handle, or the printer, or the Tesla car), and a variable cost for usage (the cost of replaceable blades, or ink cartridges, or electrical charging stations). The basic strategy here is to try to take a loss on the revenue from one of the two parts of the composite product, and subsidize it by increasing revenue from the other.

In some sense, Tesla's strategy here works in the opposite direction from
Gillette's. Gillette lowers the fixed cost of the razor-blade handle to 0, and
then covers the cost from the increased revenue that they make from the
variable usage cost (selling new replaceable blades). As you've described it,
Tesla's strategy seems to be to lower to 0 the _variable_ cost of discharging
your Tesla car (by driving it around) and then recharging at a Tesla charging
station; they presumably hope to cover the cost from the increased revenue
that they make from the _fixed_ lump-sum sale price when people buy new
Teslas. (There are lots of reasons they might think this will be useful for
increasing sales; besides any direct financial effects of the subsidy or
psychological effects toward brand loyalty, the availability of free charging
stations is also almost certainly intended to help reduce [ range anxiety
](https://www.jdpower.com/cars/shopping-guides/what-is-range-anxiety-with-
electric-vehicles) in prospective customers when they consider buying a new
Tesla.)

Will that turn out to be sustainable over the long term? Well, that depends on
a lot of details, as well as quite a bit of unpredictable luck. In no
particular order:

    * How many stations will Tesla build?
    * How much of the recharging do they expect Tesla drivers to do at company charging stations (as opposed to charging up at home, or charging at a 3rd party charging station)? (I.e., what share of the variable costs of driving a Tesla are they actually expecting to be subsidizing?)
    * How much does it cost them on the margin to provide the electrical charge?
    * How much or how little does this boost sales of Tesla cars? (I.e., how much do they expect to increase their revenue from the lump-sum fee?)
    * How long do people who buy a new Tesla car keep driving it? (I.e., does the lump-sum payment generally have to cover 6 months' worth of driving on average, or 2 years', or 5, or 10, or...? This will make a big difference to how affordable it is likely to be.)
    * How much does this influence people's likelihood to replace their old Tesla car with a new Tesla car?

There are a lot of other questions that you might want to ask. If you have
some possible ballpark estimates or reasonable minimum-maximum ranges for any
of these figures -- either in terms of what Tesla might expect the figures to
be, or what they might realistically turn out to be in fact, or whatever
scenario you want to run -- then those could provide some guidance for a more
concrete answer to your question. In the absence of that, the best answer
you're likely to be able to find is to get some kind of model that will lay
out the blanks you'd need to be able to fill in to get a concrete answer.


Question:
What is the economic nature of water?

How should one classify water in economic terms?

Is it a commodity, a natural resource, can it be both? Does it depend on how it is being used (e.g., as input/raw material in some process)? I was curious about all the ways water could be characterized economically (e.g., as a rival good, a commodity etc.) and would be grateful for some pointers.

Explanation: To check whether water is commidity or natural resource, we can check their definitions.

$\begingroup$

Most of the terms you mention are not mutually exclusive.

Commodity is not a specialized term and it just denotes some (mostly) fungible
economic good (see [ here ](https://www.merriam-
webster.com/dictionary/commodity) or [ here ](https://www.economist.com/the-
economist-explains/2017/01/03/what-makes-something-a-commodity) ). So water is
a commodity.

Natural resources can be defined as ( [ OECD 2005
](https://stats.oecd.org/glossary/detail.asp?ID=1740#:%7E:text=Definition%3A,for%20economic%20production%20or%20consumption.)
):

> Natural resources are natural assets (raw materials) occurring in nature
> that can be used for economic production or consumption.

So water is also a natural resource.

In terms of economic classification water (tap or bottled) is _private good_
because it is both rival and excludable (see Mankiw Principles of Economics pp
226). However, here it also depends which water we are talking about. I assume
you mean tap or bottled drinking water. An argument could be that water in
rivers, lakes and seas is non-excludable (in the case of lakes it would also
depend on size of the lake). If we would be talking about water in a sea it
would _common resource_ because of non-excludability.


Question:
Does low nominal interest rate encourage lending?

In expansionary monetary policy, it's written:

The Fed purchases more government bonds to drive down interest rates and increase the money supply.

Now, low interest rate can infer two things:

People find it easier to take loans and invest. So, investment goes up.

But, at the same time, low interest rate may mean that lenders may not be very keen on giving out loans. For example, people would find no use in keeping cash into bank accounts which provide low interest rates. This may drive down lending, and hence investment.

Is point (2) correct? If so, why is low n.i.r. considered good for economic growth?

Thanks

Explanation: We can check the influence of low nominal interest rate from more perspectives, e.g., the difference between leading and other companies.

$\begingroup$

> But, at the same time, low interest rate may mean that lenders may not be
> very keen on giving out loans. For example, people would find no use in
> keeping cash into bank accounts which provide low interest rates. This may
> drive down lending, and hence investment.

This is not entirely true. Bank profitability and willingness to lend depend
on intermediation margin. Difference between the deposit or Fed funds interest
rate and interest on loans they make.

For example a bank would be much happier to lend at 3% interest rate when
federal funds rate or deposit rate is 0% than it would be happy to lend when
interest rate is 20% but federal funds rate or deposit rate is 19.5% as they
earn more profit at the lower rate with higher intermediation margin.

What low interest does is to discourage supply of saving, although even here
the decision depends more on real interest rate than nominal one. Nonetheless,
banks could always just get their funds from Fed, so unless Fed decides not to
provide ample reserves they could in principle go on lending as much as they
want.

> If so, why is low n.i.r. considered good for economic growth?

It can actually be considered bad for the growth, but it is because of their
effect on market concentration and firm productivity not because of any limits
on loans. For example, [ Liu et al 2022
](https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA17408?casa_token=5FHV2nV9xc4AAAAA:LKhvLjACcREu3imovDbGTyrLDncbAR-
dhn8epTo-t15rpBf1B66iV0BAhnzmlxq401RaIHVUxbLjIsg) show that:

> a decline in the long-term interest rate can trigger a stronger investment
> response by market leaders relative to market followers, thereby leading to
> more concentrated markets, higher profits, and lower aggregate productivity
> growth. This strategic effect of lower interest rates on market
> concentration implies that aggregate productivity growth declines as the
> interest rate approaches zero.

Moreover, [ Bikker & Vervliet (2017)
](https://onlinelibrary.wiley.com/doi/full/10.1002/ijfe.1595) argue low
interest rates promote excessive risk taking which is clearly bad for
macroeconomic stability.

Low interest rates can stimulate economic activity in short run, but long run
economic growth depends on how fast productivity of different factors is
growing.


Question:
What are the reasons for Russian Ruble to strengthen in the past few days?

1 USD was about 75 Russian Rubles before the war in Ukraine began. After the sanctions, Russian Ruble quickly declined and 1 USD skyrocketed to 139 Rubles. Now it is back to around 85. What are the reasons for it? As the West is proposing more and more sanctions, shouldn't it be declining even more?

Explanation: The stronger ruble may be related to the increased rate bt Russian central bank. We can check whether there is news.

$\begingroup$

It’s likely combination of several factors.

  1. Some of it it’s because Russia has instituted capital controls (see [ Reuters ](https://www.reuters.com/world/europe/russia-says-capital-controls-were-tit-for-tat-move-after-reserves-were-frozen-2022-03-25/) ). That means that Russians are limited or in some cases even prevented from exchanging rubles for other currencies. Exchange rates are ultimately determined by supply and demand. If people are not allowed to supply rubbles to the market, ruble supply shifts to the left and that, ceteris paribus, causes exchange rate to appreciate.

  2. Russian central bank increased interest rates to 20% (see [ the economist ](https://m.economictimes.com/news/international/business/russias-central-bank-hikes-key-rate-to-20-percent/amp_articleshow/89890648.cms) ) that strengthens the ruble.

  3. Exchange rate often overshoots (see [ Dornbusch 1976 ](https://www.mit.edu/%7E14.54/handouts/dornbusch76.pdf) ). The initial depreciation in ruble likely did not just reflect fundamentals.

  4. Some of it is also because Russia recently started using Gazprombank to partially evade sanctions on Russian central bank (see my [ answer ](https://economics.stackexchange.com/a/50980/15517) here about that). Russia essentially requires other countries to pay for energy exports there and Gazprombank then converts the foreign currency to rubles, since it is not sanctioned.

  5. It’s partially also because while the sanctions for sure hurt Russia they do not hurt much Russian energy exports. EU imports 26.9% of oil, 41.1% of gas and 46.7% of coal from Russia (see [ Eurostat ](https://ec.europa.eu/eurostat/cache/infographs/energy/bloc-2c.html#carouselControls?lang=en) ). These important energy imports are not yet sanctioned and realistically there is no way how EU could manage to get some substitutes for that in near term. As long as Russia can continue its energy exports and as long as exports will be greater than imports (with which the sanctions help actually) Russia will be accumulating current account surplus which will help prop up the ruble.


Question:
Optimal stopping (reference request)

I am interested in the following optimal stopping problem:

On each day, a number 𝑎𝑖
 is drawn from a (possibly fixed) distribution.
I can either stop now, getting a payoff of 𝑎𝑖
, or wait for a later draw.
In principle, this could go on forever. However, future payoffs are discounted at a (possibly constant) rate.
I know this kind of problem has been analysed extensively. Can anyone recommend some references on how one characterises optimal strategies in this context?

Explanation: This is known as the McCall search model in economics. We need to check how the optimal strategy is determined.

$\begingroup$

This is known as the McCall search model in economics. The original paper
shows that the optimal stopping strategy rule is given by a "reservation
wage", there is a threshold such that it is optimal to accept any draw above
this threshold:

McCall, John J. " [ The economics of information and optimal stopping rules
](https://www.jstor.org/stable/2351065) ." _The Journal of Business_ 38.3
(1965): 300-317.


Question:
Loans that don't have to be paid back (only the interest)

A normal loan has to be paid back with interest. Every now and then there are interest-free loans where only the loan has to be paid back but no interest, e.g. among relatives or friends, but also as a form of state subsidy.

I am looking for the name and examples of interest-only loans from practice where only an interest has to be paid for some period of time, but the loan itself doesn't have to be paid back. I can imagine situations where such loans (or gifts) may make sense (again among relatives or friends or as a form of state subsidy). The idea might be: The borrower must continuously prove that he is serious and worth the gift.

Explanation: Classic example are the British consol bonds. British consol bonds are perpetuities so that means the principal never has to be paid back (although government could repurchase them on an open market).

$\begingroup$

Classic example are the British [ consol bonds
](https://en.wikipedia.org/wiki/Consol_\(bond\)) . British consol bonds are
perpetuities so that means the principal never has to be paid back (although
government could repurchase them on an open market).

Consols only pay coupon payments (interest equivalent for bonds) and since
they are perpetual the principal never has to be paid back.

General term for such loans where principal does not need to be repaid is
_perpetual loans_ (although most people will just use term perpetuity which is
umbrella term that can be used for any asset, not just loan, which entitles
owner to perpetual interest rate payments).


Question:
Why is Russia demanding oil payments in rubles?

In response to sanctions, Russia is demanding that oil purchases be conducted in rubles to prop up the value of the ruble. Why is this advantageous for Russia to have foreign buyers convert dollars to rubles before purchasing oil? Could they not just take payment in dollars and then buy rubles on the domestic market? Oil companies and the banks that service them are currently not under sanctions, to my knowledge.

Explanation: This is related to the sanctions in Russia, which freezes Russian central bank assets.

$\begingroup$

  1. If we talk about private companies they would not necessarily have incentive to always buy the Rubble because Rubble is not as stable as dollar. In fact the whole reason why oil and many other commodities are traded in dollar is that many companies do not need to hold the local currency and have little incentive to do so. As [ Fed ](https://www.federalreserve.gov/econres/notes/feds-notes/the-international-role-of-the-u-s-dollar-20211006.htm) explains:

> For most of the last century, the preeminent role of the U.S. dollar in the
> global economy has been supported by the size and strength of the U.S.
> economy, its stability and openness to trade and capital flows, and strong
> property rights and the rule of law. As a result, the depth and liquidity of
> U.S. financial markets is unmatched, and there is a large supply of
> extremely safe dollar-denominated assets. This note reviews the use of the
> dollar in international reserves, as a currency anchor, and in transactions.

  2. I believe this is response to US unprecedented freezing the USD holdings of Russian central bank (see this being reported by [ NY Times ](https://www.nytimes.com/2022/02/28/us/politics/us-sanctions-russia-central-bank.html) ).

Previously Russia was actually accumulating dollars from the oil & gas sales
so they have hard currency to use exactly in times of crisis like this (this
was part of the 'Fortress Russia' strategy - see The Economist [ here
](https://www.economist.com/europe/2020/03/25/russias-economy-is-isolated-
from-the-global-rout) ). Considerable share of the Russian central bank
reserves were in dollars, because prior to 2022 Russian invasion that resumed
hostilities in Russo-Ukrainian war of 2014, this was considered more or less
unthinkable.

This demonstrated that US is willing to declare USD invalid for
political/geopolitical reasons. This means that if you are an autocratic
country you have to think twice before using dollars, since at any moment they
could become worthless. Dollars are ultimately just worthless pieces of paper
if you are not allowed to use them. As a result you now see not just Russia,
but also some OPEC countries and China trying to move away from using dollars
to using different currencies such as yuan (see [ WSJ
](https://www.wsj.com/articles/saudi-arabia-considers-accepting-yuan-instead-
of-dollars-for-chinese-oil-sales-11647351541) reporting on that).


Question:
Is there a long-run tradeoff between inflation and unemployment?

In most first-year undergrad macroeconomics courses, students are taught about the Phillips curve and how whilst there may exist a tradeoff between inflation and unemployment in the short-run, there is no such thing in the long-run as a result of agents adjusting inflation expectations. Is this result valid or could it be the case that the natural rate of unemployment changes with the output gap, in which case there could exist a long-run trade-off between inflation and unemployment?

Explanation: This depends on the long-run shape of Philips curve. We need to check studies to see how Philips curve looks like in the long-run.

$\begingroup$

> could exist a long-run trade-off between inflation and unemployment?

This depends on the long-run shape of Philips curve. Well done and highly
cited empirical studies generally cannot reject the long run Philips curve is
flat implying there is no long run inflation unemployment trade-off, although
alternative explanation is that current studies are simply not powered enough
to detect (very) small slope of long run Phillips curve.

Following [ Benati 2015
](https://www.sciencedirect.com/science/article/abs/pii/S0304393215000793) :

> Both cointegration methods, and non-cointegrated structural VARs identified
> based on either long-run restrictions, or a combination of long-run and sign
> restrictions, are used in order to explore the long-run trade-off between
> inflation and the unemployment rate in the post-WWII U.S., U.K., Euro area,
> Canada, and Australia. Overall, neither approach produces clear evidence of
> a non-vertical trade-off. The extent of uncertainty surrounding the
> estimates is however substantial, thus implying that a researcher holding
> alternative priors about what a reasonable slope of the long-run trade-off
> might be will likely not see her views falsified.

....

> Overall, the evidence discussed in this paper provides essentially no
> support to the notion of a non-vertical long-run Phillips trade-off—in
> particular of a trade-off which can be actively exploited by a policymaker
> in order to permanently reduced the unemployment rate.

In addition you can also see from data that there does not seem to be any
long-run relationship (see ibid pp 258).

[ ![enter image description here](https://i.sstatic.net/yKoTC.png)
](https://i.sstatic.net/yKoTC.png)

* * *

PS: One should not confuse hysteresis effect (situation where temporary shocks
have permanent effect), with Phillips curve inflation-unemployment trade-off
where increase in inflation can decrease unemployment and vice versa.

Let me illustrate the difference.

**Inflation Unemployment Trade-off**

Suppose that the Phillips curve is given by following equation (see Romer
Advanced Macroeconomics pp 259):

$$\pi = \pi^* + \beta (y_A- \bar{y}_A) + e$$

where  $\pi$  is inflation  $\pi^*$  expected inflation and  $y$  is a log of
actual output and  $\bar{y}$  log of natural level output so the expression in
brackets is output gap. Output gap in turn determines the level of employment
in the economy.

Now in short run there will be a inflation/unemployment trade-off (non-flat
Phillips curve) as long as  $\pi \neq \pi^*$  (since  $\pi \neq \pi^*$
implies inflation can affect output and thus employment which correlates with
output). However, suppose that in long run  $\pi = \pi^*$  . In that case we
will have no inflation employment trade-off.

**Hysteresis**

Now suppose we have not just one equation but 2

$$\pi = \pi^* + \beta (y_A- \bar{y}_A) + e \tag{1}$$

and

$$\pi = \pi^* + \beta (y_B- \bar{y}_B) + e \tag{2}$$

where  $(y_B- \bar{y}_B)< (y_A- \bar{y}_A)$  , with a switching rule that we
move from equation (1) to (2), whenever output gap  $(y_A- \bar{y}_A)$  passes
some threshold for triggering hysteresis  $k$  .

Clearly as long as we assume that  $\pi= \pi^*$  in long run Philips curve is
flat (no employment inflation trade-off) in spite of the hysteresis effect.


Question:
Game for negotiations

For a while I've been bouncing around an idea for a game to be used in negotiations, with a quantitative voting element. The basic idea goes like this: there is a list of things each side of the negotiation wants (e.g. in a peace negotation, this might be a list of towns). Each side gets 100 points. Then the two sides each secretly write down how many points they're willing to bid for each of those things. Then both sides reveal what they wrote down, and the highest bidder for each thing gets the thing they bid on. The idea is that some things are worth more to one side than the other, so they will hopefully bid over their opponent for the things they want more than their oppenent, and vice versa.

Is there already a game like this floating around? I'd like to read about it.

Explanation: This is related to Colonel Blotto game, where players (officers) are tasked to simultaneously distribute limited resources over several objects.

$\begingroup$

This is very much like a [ Colonel Blotto game
](https://en.wikipedia.org/wiki/Blotto_game) , except there the cities are
ordered and the players can only assign points in a decreasing sequence.

Simultaneous multi-unit auctions with a budget constraint may also be
relevant.


Question:
Why would a company sabotage its product's ability to be used for a particular purpose?

I saw in the news recently that NVIDIA has placed limits on the hash rate for mining Ethereum cryptocurrency. This is purportedly to get more GPUs into the hands of gamers instead of crypto miners.

What is the advantage to NVIDIA to doing this? Why are they not aiming to simply maximize the demand for their product?

Explanation: This is related to segments of the market, where companies can charge elastic/inelastic customers with different prices.

$\begingroup$

This topic is explained by [ market segmentation with price discrimination in
monopolies ](https://www.youtube.com/watch?v=o6d8vbWcIO4) .

This is widely used in, for example, price discounts for senior/retired
people.

By targetting different market segments with different prices you can maximize
profits because [ their price sensitivity is different
](https://www.tutor2u.net/economics/reference/monopoly-3rd-degree-price-
discrimination) (i.e. miners are likely to buy at higher prices, while regular
consumers will sharply reduce their willing to buy at those same prices).

This is true as long as the following conditions are met:

  * Consumers can't easily switch between segments (i.e. a retired man can't suddenly turn into a child)
  * Consumers can't (easily) resell their goods to the other segments
  * It's a monopoly (or oligopoly). In a perfect market situation, your competitors will offer cheaper prices for your more costly segment.

This is the same reason why consoles used to be region locked. Otherwise it
would be convenient to travel to the cheapest region, and then bring those
products back to your home country for resell.

In order to enforce these requirements, GPUs used for gaming can't be used for
mining.

Additionally there could be other reasons. For example NVIDIA wants to heavily
push Raytracing because it gives them an edge compared to the competition.

However games will not adopt Raytracing if a large portion of their users
don't have capable cards. Right now the number of titles supporting RT is low.
And those who do, it is just an optional gimmick that doesn't add much to the
experience; and the first gen RT cards (i.e. RTX 2080) aren't fast enough for
a raytracing-rich experience.


Question:
Why did Allied countries not freeze German and Japanese central bank assets in WWII?

Supposedly such an action would cause massive turmoil in their domestic markets, cause exchange rates to rise, inflation to rise, and thus prevent them from engaging in meaningful trade. Why did Allied countries not try this in WWII? Was the world simply not as connected then?

Explanation: We need to first check whether German and Japan assets were freezed. The US government may have already used the economic weapons.

$\begingroup$

You mean something like this?

> **Freezing Foreign-owned Assets**
>
> Germany invaded Denmark and Norway on April 8, 1940, and the United States
> quickly responded to the aggression. In an attempt to keep the Germans from
> taking control of Danish and Norwegian assets held in the United States,
> Executive Order 8389 "froze" all financial transactions involving Danes and
> Norwegians. The freezing order prohibited [...]
>
> The U.S. government had first considered the use of such economic weapons in
> 1937. In response to the Japanese bombing and sinking of the American
> gunboat Panay in Chinese waters, Herman Oliphant, General Counsel in the
> Treasury Department, suggested to Treasury Secretary Henry Morgenthau that
> foreign exchange controls and a system of licenses for financial
> transactions could be instituted against the Japanese. Tensions with Japan
> subsequently eased and Oliphant's proposals were shelved. [...]
>
> As Germany continued its invasions, the U.S. government successively froze
> assets, country by country, over the European continent. Thus, on May 10,
> 1940, FFC extended freezing controls to cover the Netherlands, Belgium, and
> Luxembourg. The assets of France and Monaco (June 17), Latvia, Estonia, and
> Lithuania (July 10), and Romania (October 9) were subsequently frozen that
> year.8 By the end of April 1941, the United States added Bulgaria, Hungary,
> Yugoslavia, and Greece to the list.
>
> The further extension of controls to belligerents and neutrals remained
> controversial. While Treasury favored a rapid extension of controls, the
> State Department, concerned about maintaining America's status as a neutral
> as well as U.S. diplomatic privileges, objected. Assistant Secretary of
> State for Economic Affairs Dean Acheson noted that "from top to bottom our
> [State] Department, except for our corner of it, was against Henry
> Morgenthau's campaign to apply freezing controls to Axis countries and their
> victims."
>
> Eventually, the course of the war dictated a shift in U.S. policy. On June
> 14, 1941, through Executive Order 8785, the United States extended freezing
> controls to cover all of continental Europe, including "aggressor" nations
> and annexed or invaded territories (Germany and Italy; Danzig, Austria, and
> Poland) as well as neutral nations, small principalities, and countries not
> previously included (Spain, Sweden, Portugal, and Switzerland; Andorra, San
> Marino, and Liechtenstein; Albania and Finland). Turkish assets were never
> blocked, and Soviet assets were only blocked for a relatively short time
> until Germany invaded Russia in June 1941. As the United States moved from
> being a neutral to a belligerent, the role of FFC, an administrative agency
> within the Treasury Department, expanded.

From " [ Plunder and Restitution: Chapter III
](https://govinfo.library.unt.edu/pcha/PlunderRestitution.html/html/StaffChapter3.html)
"

But you also asked why the US did not freeze Japanese assets?

> On July 26, 1941, President Franklin Roosevelt seizes all Japanese assets in
> the United States in retaliation for the Japanese occupation of French Indo-
> China.

[ https://www.history.com/.amp/this-day-in-history/united-states-freezes-
japanese-assets ](https://www.history.com/.amp/this-day-in-history/united-
states-freezes-japanese-assets)

> President Roosevelt last night issued an order freezing Japanese funds in
> this country. Thus again was emphasized the fact, if at this stage further
> emphasis be necessary, that this world of ours has become an inextricably
> bound-up entity.

[ https://www.nytimes.com/1941/07/26/archives/war-has-no-boundary.html
](https://www.nytimes.com/1941/07/26/archives/war-has-no-boundary.html)


Question:
GDP: business incorporation location vs citizenship criteria [duplicate]

This question already has answers here:
Textbooks claim that the difference between GDP and GNP (or GNI) is about geography vs citizenship--is this correct? (2 answers)
Closed 2 years ago.
Suppose a US citizen resides in Germany. He is a business-owner in Germany and the business is legally incorporated in Germany. However, he is a US citizen. The value of the good produced by this business will be part of Germany's GDP since they are produced in Germany. But do they count towards German GDP since he is a resident and the business is incorporated there, or towards US GDP since he is a US citizen?

Explanation: This is concerned about the domestic measures and national measure. We can check their definitions.

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Same as this [ question ](https://economics.stackexchange.com/q/42216/37817) .
If in doubt, look at the source, not at textbooks or wherever.

In the US, that is [ BEA ](https://www.bea.gov/resources/methodologies/nipa-
handbook/pdf/chapter-02.pdf) .

Chapter 2: 2-6 Domestic measures cover activities that take place within the
geographic borders of the United States, while national measures cover
activities that are attributable to U.S. residents. Footnote 17 accompanied
with this statement defines that in detail.

“U.S. residents” includes individuals, governments, business enterprises,
trusts, associations, nonprofit institutions, and similar organizations that
have the center of their economic interest in the United States and that
reside or expect to reside in the United States for 1 year or more. (For
example, business enterprises residing in the United States include U.S.
affiliates of foreign companies.) In addition, U.S. residents include all U.S.
citizens who reside outside the United States for less than 1 year and U.S.
citizens residing abroad for 1 year or more who meet one of the following
criteria: owners or employees of U.S. business enterprises who reside abroad
to further the enterprises’ business and who intend to return within a
reasonable period; U.S. government civilian and military employees and members
of their immediate families; and students who attend foreign educational
institutions.

HTH


Question:
Difference between two different ways of adjusting for inflation daily given annual rate

This is a follow up question to this

I found two different ways to "adjust for inflation" on a daily basis given an annual rate (without doing daily compounding). Both yield the same result at the end of the timeframe however I can't determine if there is any error in the interpolated result.

𝑟:annual rate
𝑡:time in days
𝑦𝑒𝑎𝑟𝑠:total time in years, constant
𝑃𝑉:Present Value, constant
𝐹𝑉(𝑡):Future Value for a given time 𝑡 (in days)

For example, if 𝑦𝑒𝑎𝑟𝑠=2
 then 𝑡∈[0,730]

Plots below are generated using 𝑟=0.50
 and 𝑃𝑉=1000

The first approach is using Giskard's proposal (see related anwer) and let the rate fixed and let the time vary:
𝑥=1+𝑟‾‾‾‾‾√365−1
𝐹𝑉(𝑡)=𝑃𝑉(1+𝑥)𝑡

The second solution fixes the time and changes the interest rate based on time:
𝑥(𝑡)=𝑟365∗𝑡365
𝐹𝑉(𝑡)=𝑃𝑉(1+𝑥(𝑡))𝑦𝑒𝑎𝑟𝑠

I think the second approach is incorrect because when computing 2 years, the value for one year changed from 666.67
 to ≈640
 whereas in the first method the original value is kept but I cannot justify why this happens.

Explanation: The calculation is related to that compound interest. We can check the formula there.

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**Your graphs do not seem to match your explanation of the formulas.**

* * *

Let us look at the formulas  $$x(t) = \frac{r}{365} \cdot \frac{t}{365}$$
$$FV(t) = PV(1 + x(t))^{years}$$

at the end of the period, that is where  $t = 365 \cdot years$  .

$$x(365 \cdot years) = \frac{r}{365} \cdot \frac{365 \cdot years}{365} =
\frac{r}{365} \cdot years$$  $$FV(365 \cdot years) = PV(1 + x(365 \cdot
years))^{years} = PV\left(1 + \frac{r}{365}\cdot years\right)^{years}.$$

For  $years = 1$  this would mean an  $FV$  of  $PV\left(1 +
\frac{r}{365}\right)$  , much smaller than the expected  $PV\left(1 +
r\right)$  .

* * *

Perhaps you meant to write  $x(t) = \frac{r}{365} \cdot t?$

For  $years = 1$  and small  $r$  values this results a decent but imperfect
approximation of the result yielded by daily compounding formula with  $x =
\sqrt[365]{1 + r} - 1$  .

However for  $years = 10$  we have  $$FV(365 \cdot 2) = PV\left(1 + r \cdot
10\right)^{10}.$$

The compounding is going on for 10 years as expected, but the yearly interest
rate has also increased _tenfold_ , which is probably not intentional.

* * *

Instead of experimenting with your own formulas for  $FV$  , I recommend
reading up on this is a [ well-explored subject, as there are several formulas
for discounting, including one for continuous time
](https://en.wikipedia.org/wiki/Compound_interest#Calculation) , and it is
proven that the smaller time period you choose the closer you get to this.


Question:
When debt to GDP is only around 85%, how can this article quote as 300%?

I was reading an article in FT, where debt to GDP is quoted as 300% for US and Japan. However, all the official sites for US quotes the debt to GDP as 85% for US.

This article is from a reputed investment banker in Wall Street. Can someone explain? Link:

Economic Trends 2022

From the article: Twenty-five countries including the US and China have total debt above 300 per cent of GDP,

Explanation: We first need to figure out components of gross national debt, and then check the amount (percentage) of each part of debt.

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The author of the FT article is talking about total debt.

For Q3 2021, US federal government debt alone was 122% of GDP. Source: [
https://fred.stlouisfed.org/series/GFDEGDQ188S
](https://fred.stlouisfed.org/series/GFDEGDQ188S)

For Q2 2021, US household debt was 78% of GDP. Source: [
https://fred.stlouisfed.org/series/HDTGPDUSQ163N
](https://fred.stlouisfed.org/series/HDTGPDUSQ163N)

To get total debt you would also need to add the debt of corporations and
state and local governments. The total being over 300% seems very likely.


Question:
Can there be a game where there are no opponents?

I am considering a scenerio where all the players a in collaboration with each other in an attempt to maximize some profit. However, each player is not 100% sure of the strategy of other player so have to figure out the strategy of other player to play his own strategy to collectively maximize some profit.

Is this covered by game theory? i.e. there are no opposition or state of nature?

Explanation: This is related to coordination game where players earn higher payoff when they choose the same course, e.g., their interests are perfectly aligned.

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In a [ **coordination game**
](https://en.wikipedia.org/wiki/Coordination_game) , players' interests are
perfectly aligned, so there is no "opposition" in the ordinary sense of the
word. The game has simultaneous moves, which means, at the time of decision,
players don't know what the others would choose.


Question:
Simple description of how interest impacts inflation

I always was taught that inflation is impacted by interest like so:

Lower interest rate => Loaning money is cheaper => More money in the system => Higher inflation

However recently I am also hearing opposite theories as to how lower interest rate can lead to lower inflation.

I found some discussions and explanations but all of them stretch several paragraphs. Is there a short and easy to follow logic like the one I just quoted that can explain this directional impact?

I won’t prevent people from adding context or evaluation as to when each direction is relevant, but please make sure this is clearly separated from the actual impact explanation.

Explanation:
This is related to Fisher effect, which states a positive
relationship between the nominal interest
rate and inflation.

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The theory is called Neo-Fisherishm. The [ Fisher equation
](https://en.wikipedia.org/wiki/Real_interest_rate#Fisher_equation) states
$$r \approx i - \pi_e,$$

where  $r$  is the real interest rate,  $i$  the nominal, and  $\pi_e$  the
expected inflation rate.

Primary determinants of long-term equilibrium real rates are mostly non-
monetary: potential growth rates; demographics; risk preferences in
portfolios.

> Real rates  $r$  are determined by fundamentals: increasing  $i$  => Higher
> inflation

There are a lot of nuances and details for this to "hold". However, the same
is true for

> Lower interest rate => Loaning money is cheaper => More money in the system
> => Higher inflation


Question:
What would Russia gain economically speaking if it conquered Ukraine?

Russia seems to take preparations for an invasion of Ukraine. Would Russia get richer or economically more powerful if it managed to annex ukraine? If so, in what ways? On the one hand Ukraine has a lot of natural resources like iron ore, coal, manganese, natural gas, oil, salt, sulfur, graphite, titanium, magnesium, kaolin, nickel, mercury, and arable land. But on the other hand the country is poorer than russia.

Explanation: Thie is related to resource curse, where ountries with an abundance of natural resources are not necessarily rich and better.

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> Would Russia get richer or economically more powerful if it managed to annex
> ukraine?

Likely not.

  1. Countries generally do not get rich by having a lot of natural resources. In fact it is often the opposite (e.g. see [ paradox of plenty ](https://www.economist.com/special-report/2005/12/20/the-paradox-of-plenty) or also the [ Dutch disease ](https://www.investopedia.com/terms/d/dutchdisease.asp) which is one reason for paradox of plenty). Empirical studies also show that most resource rich countries are economically poor save for few exceptions (Venables 2016). Also Russia is already is resource rich country with abundance of natural gas, oil etc.

  2. How 'rich' country is in economic terms generally depends on how much output country can produce. Larger countries of course can produce more output just because they are large, so typically for any international comparison we would compare output **per person** as that is more accurate measure of how rich country is. Currently Russia's output _per person_ is about \$10000 and Ukraine's output per person is about \$3700 (according to the [ World Bank data ](https://data.worldbank.org/indicator/NY.GDP.PCAP.CD?locations=UA-RU) ).

Hence if Russia would annex Ukraine (and productivity of Ukraine would not
change), _new_ Russia (e.g. Russia with extra state of Ukraine), would become
poorer in per capita terms.

Only if under new Russian management would Ukraine somehow manage to become
significantly more productive than it currently is, Russia would become
richer.


Question:
Has Evergrande defaulted or not?

so many news headlines harbinger evergrande's default! today, dec 9 2021, bloomberg reports Evergrande Declared in Default as Huge Restructuring Looms. but scroll down!

Even Fitch has struggled to get information from Evergrande, noting on Thursday that the developer didn’t respond to its request for confirmation on this week’s coupon payments. “We are therefore assuming they were not paid,” Fitch analysts wrote in a statement. Bloomberg reported earlier this week that bondholders hadn’t received the money.

so fitch is JUST "assuming" evergrande defaulted. but this doesn't prove evergrande defaulted!!!!

Explanation: Default is also a legal concept, and as such it is sometimes debatable whether an entity is in the state of default or not. It is helpful to see some related discussions, e.g., Greece crisis.

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_Default_ is also a legal concept, and as such it is sometimes debatable
whether an entity is in the state of default or not.

E.g., see [ Greece debt crisis: when is a default not a default?
](https://www.theguardian.com/business/2015/jun/30/greece-debt-crisis-default-
analysis-imf)


Question:
Unresolved paradoxes or puzzles in financial economics

What are some (unresolved) paradoxes or puzzles in financial economics?

I am looking for paradoxes or puzzles like for example:

The equity premium puzzle (Mehra & Prescott, 1985).
Siegel's paradox (Siegel, 1972).
Dividend puzzle (Black 1976)
I am especially looking for some that were never resolved or only partially so, and I would also be interested in some reference that describes/identifies the puzzle or paradox.

Explanation: One examples is merger paradox, where mergers between firms may not be always profitable.

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Merger paradox from industrial organization: I believe a fairly good overview
is here: Garcia, F, Paz y Miño, JM, Torrens, G. The merger paradox, collusion,
and competition policy. J Public Econ Theory. 2020; 22: 2051– 2081. [
https://doi.org/10.1111/jpet.12448 ](https://doi.org/10.1111/jpet.12448) .

You can find a fair deal about it here as well: R. Rothschild, John S.
Heywood, Kristen Monaco, Spatial price discrimination and the merger paradox,
Regional Science and Urban Economics, Volume 30, Issue 5, 2000, Pages 491-506
[ https://doi.org/10.1016/S0166-0462(00)00044-2
](https://doi.org/10.1016/S0166-0462\(00\)00044-2)

The general overview of this paradox is that it is unclear, under traditional
models, why one firm would bother to purchase another. If they do so, the only
point is to cut total overall production. But the sale price of any such firm
will (under most conditions) be prohibitively expensive. Furthermore, the
firms that are excluded from this merger benefit from reduced production - and
they didn't have to bother to buy anyone. Some solutions include assuming
extremely concave production functions, sticky/immobile customers distributed
along some preference space, and others.

Previously, IO had an unsolved mystery of how firms chose to enter
sequentially in spatially price-discriminating markets for the n-firm case in
linear markets and circular markets. I know circular markets have been solved,
and I think linear markets have also been solved recently.


Question:
In a setting with N goods how many combinatorial bits do we need to construct a preference map

I am reading this paper:

https://www.researchgate.net/publication/5208445_The_market_for_preferences

By P.E Earl and J.Potts

On page 3 the following is written:

"If we think of individual preference orderings as units, then if there are n goods and we ignore computational overheads, each preference map will require (n-1)^2 combinatorial bits to construct."

This confused me a little bit because with just trial and error you can see that in a market with 2 goods, 1 combinatorial bit is needed

I.e

Good A > Good B

However when we have 3 goods we only need 2, not as the formula suggests 4 as,

Good A > Good B

Good B > Good C

Where Good A > Good C is implied due to transitivity, but even if not this comes out to 3 bits not 4

Explanation: Preference relations are also called total preorders or weak orders in mathematics. We need to find the formula to calculate number of distinct weak orders on an n-element set.

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First, a correction. What you are counting is the number of _total orders_ .
You forgot the possibility of _indifference_ . For example,  $A \sim B \sim C$
is a perfectly fine preference relation. The correct count of preference
relations on  $3$  elements should be  $13$  .

Preference relations are also called [ total preorders or weak orders
](https://en.wikipedia.org/wiki/Weak_ordering#Total_preorders) in mathematics.
According to this [ wiki page
](https://en.wikipedia.org/wiki/Weak_ordering#Combinatorial_enumeration) , the
number of total preorders on a finite set of cardinality  $n$  is given by the
[ ordered Bell number  $a(n)$
](https://en.wikipedia.org/wiki/Ordered_Bell_number) .

The ordered Bell number  $a(n)$  satisfies the following recurrence relation:

$$ a(n) = \sum_{i=1}^n {n \choose i} a(n-i) $$

The exact formula is given by the following double sum:

$$ a(n) = \sum_{k=0}^n \sum_{j=0}^k (-1)^{k-j} {k \choose j} j^n $$

For large  $n$  , we can approximate  $a(n)$  by

$$ a(n) \approx \frac{n!}{2 (\ln 2)^{n+1}} $$

I won't go into details, but using the [ Stirling approximation
](https://en.wikipedia.org/wiki/Stirling%27s_approximation) , you can prove
that the number of required bits is on the order of

$$ \log_2 a(n) = O(n \log_2 n) $$

Thus, you are correct that **a preference relation on $n$  elements requires
much less than  $(n-1)^2$  bits to specify ** .


Question:
New Business - How do I set a price for my product?

This is my first question here, but since I am used to the Stack Exchange format I will give as much detail about my problem without giving an overload of details.

In a nutshell I work with US weather radar data and decided I could make an app for storm chasers and emergency management. I have done research and know about what my fees to customers will be, and I have an expectation of how many signups I will have. During the process of creating this, I have also created some custom data that I realized I could sell to weather data provider companies. They will not compete with my web app, so this would be great extra income.

This is where the problem is. A company has expressed interest in licensing this data from me on a monthly basis. Besides the cost of my servers ($1,000 to $2,000 a month?) I do not know how much to offer this data for. The last thing I want to ask them is "how much would you like to pay?".

To them, this would be helpful as they can re-sell the data to their own emergency management customers. I feel like it would be worth about $1,000 to $3,000 a month on top of server costs. It's not super revolutionary data, but it's going to be useful for them and they might be expecting to pay $8,000 a month (random guess). I am afraid to ask for that right off the bat because they may laugh it off. I am not a bashful person, but I don't want to come across so far left field that they just say nevermind to the whole thing.

I am looking for any sort of advice on how to approach this problem. I think the main problem with something new like this is that the actual value of the product seems either somewhat arbitrary, or the actual value could be anything within a range from $3,000 to $8,000 or more.

Explanation: First of all, we will need to built a complete business canva and answer the following questions: (a) what's the mission?, (b) what's the long-term vision?, (c) want your business to incorporate economic and/or social impact considerations? Answering those questions will help to determine if we want to make a profit. Not every business needs to make a profit. We can have a small business and plan your price to cover only interest payments, labor cost, capital cost, and depreciation. Doing the business model canva will also lead to evaluate the operating costs (what need to pay to run the business on a day to day basis). We will also need to detail all the operating cost according to the cost structure.

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to answer this question you'll need a bit more information (which you may have
or not at the moment). I'll assume that there's no competition for your app,
and that there's no explicit price on the market (prices from other firms
offering the same service).

First of all, you'll need to built a complete business canva and answer the
following questions: (a) what's your mission?, (b) what's your long-term
vision?, (c) do you want your business to incorporate economic and/or social
impact considerations? Answering those questions will help you determine if
you want to make a profit. Not every business needs to make a profit. You can
have a small business and plan your price to cover only interest payments,
labor cost, capital cost, and depreciation. Doing the business model canva
will also lead you to evaluate your operating costs (what you need to pay to
run the business on a day to day basis).

Here's a good reference to write your business model canva: [
https://corporatefinanceinstitute.com/resources/knowledge/strategy/business-
model-canvas-template/
](https://corporatefinanceinstitute.com/resources/knowledge/strategy/business-
model-canvas-template/) . You'll need to detail all your operating cost
according to those categories: [ https://www.strategyzer.com/business-model-
canvas/cost-structure ](https://www.strategyzer.com/business-model-
canvas/cost-structure)

Now that you have a better vision of your whole business, there's two main way
to estimate pricing.

_Pricing without profit_

If you don't want to generate profit and only give yourself a good salary, you
can calculate the price for your product in the following way:

\begin{equation*} P\ =\ OPEX/n \end{equation*}

In that case, the product price is equal to your total (annual) operating
expenses (OPEX) divided by the amount of client you expect to sell to (n). A
bit of market research will be needed to estimate the size of your expected
clientele.

_Pricing with profit_

If you decide to generate a profit (ex: if you want to invest in your business
for expansion, you'll need to set some money aside for advance payments), you
can calculate the price for your product in the following way:

\begin{equation*} P\ =\ \frac{OPEX\ +\ CAPEX\ +\ SEI}{n} \end{equation*}

In that case, the price of your product is the sum of operating expenses
(OPEX), capital investment expense (CAPEX), and social/environmental
investment (SEI), divided by the expected number of sales (n).

_Some advice_

If you currently live in a medium-size or large-size town, I would suggest you
to get in touch with the entrepreneurial ecosystem and support network. There
may be some public or private business incubator that could provide you with
advanced support and a office to start.