Is it common to see hedge funds go bankrupt? Have any hedge funds gone bankrupt as a consequence of the "GameStop scandal"?
And more generally is it common to see hedge funds go bankrupt?

Have any hedge funds gone bankrupt as a consequence of the "GameStop scandal"?

This is very difficult, almost virtually impossible to say as events unfold. In order to understand why consider the Greylock Capital Associates that filed for bankruptcy on 31 Jan. this year.
It would be tempting to say that this bankruptcy occurred due to GME stock shorting, but if you actually read the news around the bankruptcy you will discover that the company was already suffering heavy losses for about 3 years.
This example shows you that hedge funds and generally most companies can operate even when in red for multiple years before they need to file for bankruptcy. As such, most of the time, it is really difficult to tie one single event to firm bankruptcy.  Generally speaking, from economic theory we know that in the short-run even operating at loss might be more optimal than firm exit.
Even if some hedge fund representative would openly say that they went bankrupt because of GME shorts during this GME bubble fueled by reddit speculators, you can't take that statement at face value. The manager might simply say that as an excuse for years of poor management and underperformance.
What you need to answer this sort of question is some research that can show that there is a relationship between shorting the GME bubble and probability of bankruptcy, which would show that probability of hedge fund going bankrupt was significantly affected by this event. Otherwise all you have are just anecdotes.
Since this case was so prominent I expect that eventually someone will try research it but I doubt you will find any empirical peer-reviewed research on this in next 2-3 years even more. This is not just because research takes time but also because you need to gather more data than possibly can be avaiable in real time.

And more generally is it common to see hedge funds make bankrupt.

Depends on how broadly you define bankrupt (e.g. are you only interested in bankruptcy in legal sense or more broadly in English language sense when people often call any firm closing bankruptcy?). For example, according to Liang & Park (2010) between 1995-2004 hedge funds had attrition rate of about 8% on yearly basis. Although, not all of that is bankruptcy as some firms might leave before filing for bankruptcy. There is reason to believe this rate accelerated over time. For example, in 2019 more hedge funds closed than new opened.
Hedge funds have relatively high rate of attrition because:

They have very few limits on how to operate so hedge funds industry is very dynamic. In a dynamic industry you will often see old firms 'dying' while new innovative firms coming in (e.g. see the NBER working paper of  Getmansky et al (2015)  on this topic). This is explanation why hedge funds close quite often in general but probably cannot explain why they close so fast in recent few years.
It is widely believed that hedge funds perform poorly relative to their high fees. This is often quoted reason for why many hedge funds loose customers and are forced to close or go bankrupt recently. See the Investopedia article on 'the great exodus out of hedge funds'.  This is topic on which research is not settled. On one hand raw data clearly show hedge funds underperform. On the other hand this might be due to biases since hedge funds are not obliged to disclose their data to anyone but their customers and regulators. This can create biases in the data as the best firms might not disclose publicly their data to protect their trading strategies that are not patentable (e.g. see Fung et al (2000) or above cited Getmansky et al (2015) again). Depending on how particular research tries to correct for these biases results can change and some are more favorable to hedge funds but there is a lot of uncertainty about the results here. This being said customers would not be leaving the hedge funds if they were not believing that they are having better opportunities elsewhere.


Can banks maintain Euro accounts if the country they're in leaves the eurozone? If a country forcibly leaves the Eurozone, is it possible for banks within this country to maintain existing euro deposits?  Or does leaving the eurozone mean those deposits are automatically converted?

Arguably the problem all along with the Eurozone (and any other currency union) is the operational mechanics of the underlying banking system.

From a systems perspective, banking systems statistically multiplex liability bank deposits against asset cash and electronic equivalents. (It is mostly electronic these days.) Broadly speaking, the main function of the asset money is to provide an interchange mechanism between banks, and the deposit money is what is actually used to perform economic transactions.

There is no way of enforcing what physical currency gets used as the interchange mechanism. It doesn't really even need to be a recognised currency, and several precious metals have been used in the past. However, if a banking system uses a physical currency whose quantity is outside of its control - i.e. the money is printed by somebody else, then the banking system will collapse over time, unless there is net flow of the currency into the system.

Now, if we look at the greek money supply figures, and we know that that there are essentially three ways for liability deposits to decrease as shown - loan repayment, loan write-off and cash withdrawals, we can deduce pretty easily that Greece is experiencing a massive outflow of cash. We can assume that some of it is cash withdrawals particularly recently, but some of it also debt repayment to debt owners outside of the Greek banking system. As a very rough rule of thumb, on a 25 year loan, about twice as much money will have to flow back to the lender, as was originally borrowed, and this is what's causing the underlying systemic problems.

According to the Wall Street Journal, this is a summary of the debt picture:

Greek Debt

Mechanically speaking then, the only way a country can unilaterally stay in the Eurozone is if they are experiencing a net inflow of asset cash/money, in which case it's unlikely that they'd be under pressure to leave it. What this counter-situation does to the economy depends very much on how the banking system is regulated, and since most countries no longer depend on asset cash/aka reserve regulation as a control, the answer as also seen in the US with TARP is not necessarily very much.

A water analogy may be slightly helpful. As long as there is enough water, and any excess can be stored, then it doesn't matter if over time more water comes in than can be used. However, it's disastrous to not have enough water - and that's essentially the problem that the banking system is currently causing for Greece. The various attempts to "solve" the problem by issuing more debt, simply act to make it worse over time.


Are supply and demand always (with arbitrary dimensions but still) linear? I have economics knowledge of high school level (and basic economics from my engineering degree), and I always noticed that supply and demand functions are linear (in 4+ dimensions).

It is -in practice, in real life- always the case? If not: What counterexamples (with theoretical models) do exist?

Absolutely not, linear curves are a simplification made for (many) basic economics courses. When considering the basic mechanisms of Supply and Demand (supply rises when the price rises, demand drops when the price rises, etc.) there is no need to use more complicated curves, but as soon as you introduce elements like optimization, it is in many cases necessary to use non-linear functions.

In real life we don't generally observe curves as such, but rather different quantities sold with different prices. We can estimate curves based on this kind of data, but to me that's more of an econometric exercise.


Capital Recovery Factor for Hyperbolic Discounting I'm looking for a closed-form capital recovery factor when hyperbolic discounting is used. The Wikipedia article on hyperbolic discounting has this formula for the "present value of a series of equal annual cash flows in arrears discounted hyperbolically":
$$
V = P \frac{\ln(1 + kd)}{k}\ ,
$$
but does not include any references.

If I attempt to sum the series $\sum_{t=1}^n 1/(1 + rt)$ however, WolframAlpha gives me a more complicated formula involving the digamma function.

I would appreciate a reference for this CRF, if one exists. A derivation would be a bonus. Thanks!

I'll just expand upon what I've said in the comments as an answer. The sum $$\sum_{t=0}^n \frac{1}{1+rt}$$ will not have a nice closed form. However what wikipedia has done is approximate this sum as an integral. The integral will just be $$\int_{t=0}^n \frac{dt}{1+rt}=\frac1r\ln(1+rt)|_0^n=\frac1r \ln(1+nr)$$ Which is basically what you've got without multiplying by the principle value, and relabelling some variables. Now something to watch out for is that this will be off by a small constant. If you look at the diagram below, there is some error area that the integral fails to pick up, so it will actually be slightly smaller.

In this case however you know the error area is below 1 (because if you imagine sliding each error area into the first square (purely horizontally it will not fill it all up)

 and above one half, (draw a line between the corners of each error area to make a triangle and each triangle is half the area of the corresponding rectangle, so the sum of all the triangles is half the area of the unit square)

So since the error is between 1 and a half, for large n it should be pretty insignificant, and this is a pretty good approximation.


Will BRICS countries be the leading innovation countries 20 years from now? I wonder about the question given in the title.

What could be arguments against this statement?

Considering China and Russia: Both countries have an authoritarian political system. I claim - and please correct me if you think otherwise - that an authoritarian system hinders innovation. I would assume that universities are not free in their choice of topics to perform research on. Why is this bad for innovation? Not sure here, just a feeling. I would also say that innovation requires creative thinking and that an authoritarian system often comes with fear of stating one's own opinion and that this somehow doesn't yield the mindset necessary for innovation. Well, you can tell I am not very certain with this argument. Can you help me with it?
Considering India and Brazil and South Africa: Wealth is very unequally distributed in these countries. And I feel like this is also hindering innovation. A large portion of their population will not have free access to education, already reducing the number of people that technological innovation can come from.

I know that this is a question which doesn't have the  one ultimate answer. So should I be in the wrong forum for it, I apologize for it. Otherwise, I am excited and happy to hear your comments!

What makes you assume that there is a link between the BRIC(S) countries annd innovation, more than any other country in the world, to make them leaders?

The growth reason in each BRICS country is different. The similarity is partially because of the ratio between labor and capital, economies that invest in industrialization, capital, and get higher growth until they reach their new industrialized potential

There are large differences: Russia's economy is based on energy - oil and gas. China has been subsidizing its industry with a low exchanges rate, a subsidy that is ending now, Brazil has also plenty of energy resources, but alot of unattended poverty and corruption, India faces a lot of structural government issues etc.

An authoritarian doesn't have to lead to lower innovation, Japan in the 19th century became western country in a generation, with Japanese sent to study in Europe.
It is less probable for an authoritarian regime to support innovation, for the simplest reason - it depends on a single authority to understand it, rather than a public agenda oriented regime

What you you should look for as an indicator for innovation is R&D expenditure out of the GDP, patent protection and any "doing business" score you find reliable


Proof that utility is nonincreasing in prices The following is a proof that the indirect utility function is nonincreasing in prices, but I can't understand the last step. How do they conclude that $v(p_1, y) \ge$ from the previous reasoning?

  Consider $p_0\ge p_1$ and let $x_0$ solve the utility maximisation problem when $p = p_0$. Because $x_0\ge 0$, $(p_0 − p_1) · x_0 ≥ 0$. Hence, $p_1·x_0 ≤ p_0·x_0 ≤ y$, so that $x_0$ is feasible for the utility maximisation problem when $p = p_1$. We conclude that $v(p_1, y) ≥ u(x_0) = v(p_0, y)$.

That follows $v(p_1,y)$ being the highest utility one can get from a bundle affordable given prices $p_1$ and income $y$. Let $x_1$ be such a utility maximizing bundle. Then $p_1\cdot x_1\le y$ and $u(x_1)\ge u(x)$ for all $x$ such that $p_1\cdot x\le y$. In particular, $u(x_1)\ge u(x_0)$ since $p_1\cdot x_0\le y$ (this is what the argument you have shows.) Therefore,
$$v(p_1,y)=u(x_1)\geq u(x_0)=v(p_0,y).$$
Intuitively, if prices are lower, one can buy from a richer set of options, and with more options one can always get at least as high utility.


Field experiments on labour market discrimination: do sizes of randomly assigned groups matter? In traditional field experiments on racial discrimination, two identical resumes differing only by name or ID photo are sent to randomly selected firms. A statistical test is then run on the number of interview offers received by each resume to determine if any difference in the number of interview offers received between the resumes holds true in the population.
I am curious whether, if in the event that each resume is sent to a different number of companies (e.g. one is sent to 300 firms and the other 310), results that show a statistically significant difference in the number of interview offers received on one resume compared to the other will be invalidated. My intuition is that there may be a tendency for bias to be introduced as the resume that is assigned to a greater number of firms has a higher chance of being selected. Would appreciate comments on whether this is accurate.

No, this should not be a major issue. We will very carefully take into account the different sample sizes. Allow me to continue your example:
Assume "Resume A" is the the treatment resume and "Resume B" is the control resume, where the treatment has a less advantaged ethnic name (Jamal, Beyonce) and the control resume contains a anglicized name (James, Sophia). One should be careful about gender here as well.
We then compare the mean acceptance rate between the two resumes.
Suppose $N_a = 300$ and $N_b = 310$.
The accepted resumes are: $Accepted_a = 30$ and $Accepted_b = 62$.
For shortcuts, the mean rates of acceptance are $r_a = 30/300 = 0.1$ and $r_b = 62/310 = 0.2$. Notice the mean rate of acceptance normalizes each group, so size is partially accounted for here.
The variances are then:
$\sigma_a^2 = (1-r_a)*r_a = 0.090$
$\sigma_b^2 = (1-r_b)*r_b = 0.160$
And more importantly, the variance of the means of each distribution are then $\sigma_a^2/N_a$ and $\sigma_b^2/N_b$, respectively.  We are comparing the means of the two distributions with a simple mean comparison test. Notice this step explicitly uses the sample size to account for expected variation between the two distributions.
So we now compare the two to see if there is a difference, under the null hypotheses there is no difference. (In statistics, you nearly always always assume no difference/no relevance/no effect as the baseline.)
$t=\frac{r_a-r_b}{\sqrt{\sigma_a^2/N_a+\sigma_b^2/N_b}} = 3.572$
The reasoning can be very explicitly laid out as follows:

The difference between the two samples is 3.572 standard deviations
away from 0.
Under the assumptions we have made above, it seems very
unlikely that this would occur by chance if we repeated the process
(looking this up on the t-table as a one-tailed test has a p-value of less than 0.001). Bayesians will point out there are some other silent assumptions one may have made, so language is particularly important at this step, but this generally passes the intuition.
Therefore, I reject the idea that these two samples came from the same distribution. It seems implausible.
So, I am left to conclude that there is a difference between the two samples. It seems that indeed people are more accepting of the Anglicized names rather than the ethnic names.


Search terms to find a menu of currency exchange mechanisms? I'm look to find a good source for comparing mechanism designs for simple currency exchanges.
Is there a name for a category of game (e.g. Stackelberg game) that encapsulates the operation of an exchange?
What search terms should I use (the above terms don't seem to work) to find mechanism designs for simple currency exchanges?
Is there a good source text book that would cover this?

The area of research you are looking for is market microstructure, the study of how markets work and the process of price formation. Naturally, this means studying liquidity, information diffusion, uncertainty, and dynamic games. There is not a lot of mechanism design in market microstructure -- though work along those lines would certainly be welcomed.
For an introduction to the area, a good first read might be Foucault, Pagano, and Röell's book. (Sadly, the review articles which come to mind are old.) The Journal of Financial Markets is chock full of microstructure research and you would do well to start following it.
FX markets have been changing recently with more retail flow and trading on ECNs while the inter-dealer network has become less segregated and more affected by trading on those ECNs. Thus the old Olsen & Associates work like the book by Gençay, Dacorogna, Muller, Pictet, and Olsen (2001) might help explain the interbank market but won't be up-to-date.
More relevant (and shorter) would be to check into Evans and Rime (2019).


Is there some kind of consensus on the determinant factors of education achievement? There is quite a bit of literature on the economics of education. One of the most debated aspects of it arises when estimating the achievement of the student (usually in the form of standardized test scores). Which are the most relevant inputs? Which are not?

A few usual suspects are:

Parent's education
Teacher "quality", which is by itself an issue. Sometimes it is represented by years of experience, majors acquired, certification, test scores, etc.
School inputs
Peer effects
Teacher absenteeism
The list goes on...

There is no solid consensus on the inputs that go into educational achievement or attainment. The list of variables is vast and varied.

One of the most common applications of this is attempting to calculate the returns to education - i.e. the average increase in income that results from one additional year of schooling.

I myself have performed research on this topic in grad school, and a good reference is:

Bronars, Stephen G., and Gerald S. Oettinger. “Estimates of the return to schooling and ability: Evidence from sibling data.” Labour Economics 13.1 (2006) : 19-34. http://www.sciencedirect.com/science/article/pii/S0927537104000983

In my research there were many variables that were statistically significant:

age
gender
race
marital status
union membership
year at time of measurement
number of siblings
religious beliefs
opinion on sex ed in schools
opinion on national educational spending
opinion on education as catalyst for racial/class divides

Most researchers in this area agree that parental involvement is one of the main determining factors for a child's educational outcome. The difficulty is in quantifying this and other subjective data such as teacher quality and peer effects. This is one of the main issues in the field now - figuring out how to statistically measure non-numerical variables. The opinion variables I mentioned above are from national social surveys and are an attempt to quantify these subjective things. Specifically, my data came from the General Social Survey (GSS) available here: http://www3.norc.org/GSS+Website/


Measuring demand for banking services - (Maximum) Market Size I am in need of a variable measuring "demand for banking services" in general, on a country level. Specifically the (maximum) size of the market for banking services for a given country. This will be used as a control variable.

Does anyone know any standard proxies or measures used in the literature to measure something like "total demand for banks"? I need something general, not a specific banking service. Something that summarizes the different sources of demand for banking services, such as some kind of constructed index or so. Something that summarizes everything/most services through which banks make profits. If that is not possible, are there maybe two standard measures that each cover demand for deposits and demand for loans?

What variables are generally used? If nobody knows what is standard, does anyone have any plausible suggestions of proxies/measures for "demand for banking services"? Further, any suggestions on data sources I could use to get country level data (preferably a panel starting around the '80s or '90s) for such a variable?

The proxy/measure need not be perfect. The only important thing is that it captures "the size of the market for banking services (in general)" in some way. Especially a measure of demand that would determine the (maximum) number of banks in a given country.

There is no quantifiable answer as the concept is illusory.  Banks operate by mismatching short term debt with long term assets.  This has no benefit to the economy as a whole and in fact creates inflation, risk and volitionality.  Banks operate maturity mismatching because they can and it serves their own interest.  There is no natural demand for banks which is why they are in need of constant artificial support from central banks (much of which happens on a daily basis).  Without central bank support, banks would be accountable for mismatching short term debt with long term assets and they would quickly and rightly so burn up in a liquidity fire.

Perhaps a better premise to start before mathematically quantifying the demand for banks is to ask conceptually the role banks play in an economy first.  Without conceptual and contextual understanding, math is meaningless number juggling designed to impress and confuse those that don't know better.

Now...it can be said it said there is a demand for money of which banks create.  Imagine if we were to switch to the gold standard all of sudden.  Only gold could be exchanged for services.  Because gold is limited, the price for it (to acquire as a means of exchange) would shoot up astronomically.  This profiting (from gold sellers to gold buyers) represents economic loss for the buyers.  If they could acquire another means of exchange (say gold deposits that were not tied 100% to gold) they would not have to pay as much for the gold.  So in a way banks can create competition for money.  But in doing so they create either their own inflation or profiteering.  Then there is of course the matter of fiat currencies competing which never ends well...

Personally, that is why I'm in favor of a national depository that would negate the need for deposit banking.


What properties does a stable economy possess? Given the large amount of commentary on the state of the economy, I've found that most of the time the theme of the articles are always that there is something wrong/ abnormal with regards to the economy.There seems to be call for change of policy all the time.

With all this noise its often difficult to know when a "business as usual" policy should be implemented (i.e nothing should be changed or advanced). When is it possible that we should change nothing in an macroeconomy (i.e no changes in interest rates, domestic taxes or trade taxes)?

What properties would a country with a stable economy posess?

I’ll cover two of the possible policies that can be stable: interest rates and fiscal policy.

I will assume that a “stable” interest rate policy is to keep the policy rate (e.g. Fed Funds in the United States) unchanged. This is is a case discussed in “mainstream” economics, and the argument is that such a policy leads to inflation drifting at random. (As in Section 2.4.1 of “Monetary Policy, Inflation, and the Business Cycle” by Jordi Galí.) In other words, if you lose monetary policy, you lose control of inflation.

Of course, the policy rate has been at the same level for years in many countries, and not much happened. The reason why the policy rate was stable was usually that the economy was growing slowly, and no inflation risk was seen. That is, the economy was in a sense (temporarily) “stable”, and policy rate reflectd that.

Even if the central bank says it will not change short rates, bond yields would likely still move around on the basis that the policy will not be sustained. So things like mortgage rates would still move.

Some critics of “mainstream” economics think that the models that lead to this inflation instability are incorrect. In particular, some proponents of Modern Monetary Theory argue in favour of locking the policy rate at 0% forever. That is very much a minority position.

If we turn to fiscal, I am unaware of any formal theory. In basic “mainstream” models, fiscal policy is often left unchanged. However, this was not viewed as having much if an effect, since monetary policy is believed to be the main policy variable.

We have seen unchanged tax rates for years in many countries, and I do not believe anything unusual was associated with that. However, taxe rates are only part of fiscal policy. Spending changes from year-to-year, and in the real world, that is unlikely to change. For example, the Canadian Federal Government is helping pay for a bridge near where I live. That spending will hopefully cease when that construction is complete.

To top it off, the dollar amounts of deficits vary based on the business cycle. If people lose jobs, they pay less taxes and end up receiving more governmental assistance. So if someone defines fiscal policy “stability” as an unchanged fiscal deficit, that is almost guaranteed to never happen. However, these changes to the deficit are believed by some economists to help dampen the business cycle (the “automatic stabilisers”). (I see little discussion of automatic stabilisers in modern “mainstream” theory, but it was discussed more by the old Keynesians.)

In summary, “stable” policy settings imply that the government cannot lean against fluctuations like recessions, or control inflation. Economists of the Keynesian persuasion would likely argue that this will result in deep depressions, such as in the 1800s. Many non-Keynesians would dispute that.


Equation of exchange and inflation target The inflation target is $2$% and the equation of exchange states $MV=PQ$. Is the idea that we want to have greater money supply growth then real growth in general?

It is rather other way around. We want to target about $2\%$ inflation and to do so money supply should expand faster than real growth. Also, the $2%$ target is not commonly interpreted as a target that has to be kept all the time.
For example, as explained in this Brookings blog many central bankers advocate targeting the $2\%$ over business cycle. During recessions it might be prudent to have more 'loose' monetary policy and during expansions more 'tight' one.
Furthermore, relationship given by the quantity theory of money (i.e. the equation of exchange) in more complex models depends not just on the actual realization of the variables but also on their expectations (see Krugman et al 1998). An expansion of money supply that is not expected to last might as well never happen.
Lastly, if an economy happens to be at zero lower bound (ZLB) increasing money supply is no longer helpful in targeting inflation (at least not increasing money supply by usual interest rate targeting). This is because at ZLB peoples preference to hold cash becomes so strong that any increase in money supply will be just offset by drop in velocity as people will just hold on the money (see again Krugman et al 1998).
Thus to sum up, while in order to target $2\%$ inflation often central banks try to expand money supply faster than the real growth, it is not always possible to do so nor it is always desirable to expand money supply so fast across business cycle.


How to interpret the difference between natural level and steady state in Macroeconomic theory I am reading Monetary policy, inflation, and the business cycle: an introduction to the new Keynesian framework and its applications by Gali.

In this question I am going to use the output $Y_t$ as an example. I am going to use the notation from Gali.

$y$ is notation for the steady state.
$y_t^n$ is notation for the the natural level of output.
$\tilde{y}_t = y_t-y_t^n$ is the output gap: deviation from the natural level.
$\hat{y}_t = y_t-y$ is the deviation from steady state.

My question is: Intuitively speaking, what is the difference between steady state level and natural level?

Note: $y_t = \log Y_t$

Natural level of output is equivalent to full employment output. This does not mean full employment of all resources, there is always a natural level of unemployment even in full employment output level.

Neoclassical economics: Steady state output is achieved when capital-labour ratio is stable or constant. In steady state, economy is not growing and also not in recession, all variales grow at the same rate i.e. birth rates equal death rates, capital accumulation rates equal depreciation rates, etc.


Spatial Durbin model in Stata - How it is estimated? Can someone explain to me how the estimation of the spatial Durbin model is made in Stata ? The documentation of XSMLE command (for spatial panels) says that for dynamic cases the estimator are based upon the article of Yu et. al. (2008). But I have not found references in the article to the estimation process of the Spatial Durbin model.

I'm assuming you know how to do spatial weights matrices and such, so I will just skip that and throw out a disclaimer that I use R as my primary statistical programming language, not STATA, so let's first observe a generic spatial model:

spatreg $ylist $xlist, weights(W) eigenvalues(E) model(lag)

The lag in that function can be replaced with an error option if you want the SEM. To do a spatial durbin model (SDM) in R I find that using mixed or a durbin option does the job. Try and see if that works in place of lag in model(), for future reference. Sometimes the option is there but not many people use it because they don't usually care about estimating the model.

Next, try out the spmlreg function which appears to have the spatial durbin option:

spmlreg $ylist $xlist, weights(W) wfrom(Stata) eigenvar(E) model(durbin)

For a better understanding of the function, check out P. Wilner Jeanty's documentation of spmlreg.

Maybe both of them work fine, and that'd be cool. The more options the better.


Recent estimates of CPI bias? The Dec 1996 Boskin report (May 1997 AER summary)

  concluded that the change in the Consumer Price Index (CPI) overstates the change in the cost of living by about 1.1 percentage points per year (the range of plausible values is 0.8-1.6 percentage points) (1997, p. 78).

Breakdown (1997, p. 80):

My question: What, if any, are some more recent and similarly-"authoritative" estimates of CPI bias?

Redding and Weinstein in their paper "A Unified Approach to Estimating Demand and Welfare" develop a unified price index that nests all existing major price indexes. Existing price indexes can be thought of as arising from the imposition of parameter restrictions on their unified index.

Their examination with barcode data suggests that standard methods of measuring welfare overstate cost of living increases by ignoring new products and demand shifts. However, contrary to the Boskin report, they do not put an overall number on the bias.


Derive utility function with both substitutes and complements I know that in the 2-good world it is easy to derive the demand functions from a utility function for imperfect substitutes or complements, but what if I have N goods that include many combinations of substitutes and complements?

For example if you have hot dogs $D$, hamburgers $H$ (substitutes of each other), and mustard $M$, mayo $Y$ (substitutes of each other, complements with hot dogs and hamburgers), I can try something like this:

$$
U(D, H, M, Y) = (D^{0.5} + H^{0.5})(M^{0.5} + Y^{0.5})
$$

Unfortunately the math gets pretty hairy for this one pretty quickly. Before I dive in much further with solving these equations, is there a well-known function that is used in the literature for this type of analysis?

Note: I am interested in the more general N-good case, not just the 4-good one.

The general way to do this would be using a nested CES Function.  CES Wikipedia

For your example you could define the utility of sandwiches (S) and condiments (C) to be

$$ U(D,H,M,Y) = (a_1 S^{\frac{s-1}{s}} + a_2 C^{\frac{s-1}{s}})^{\frac{s}{s-1}} $$
then you can define $S$ and $C$ "nests" as
$$ S = (b_1 D^{\frac{\rho-1}{\rho}} + b_2 H^{\frac{\rho-1}{\rho}})^{\frac{\rho}{\rho-1}} $$
$$ C = (c_1 M^{\frac{\eta-1}{\eta}} + c_2 Y^{\frac{\eta-1}{\eta}})^{\frac{\eta}{\eta-1}} $$

$s$ determines whether S and C are complements ($s \rightarrow 0$) or substitutes ($s \rightarrow \infty$), or neither ($s=1$).

The same holds for $\rho$ and $\eta$ in the "nests".  $a$, $b$, and $c$ establish the relative importance of each item within a nest.

Extending this to $N$ you can have an arbitrary number of nests and an arbitrary number of elements within each nest.  This way may look complicated, but it has a lot of flexibility and gives you nice derivatives when solving maximization problems.


Why is an inverted yield curve NOT a good predictor for recessions except in the US? I am trying to better understand the mechanism (if there is one) behind an inverted yield curve predicting - or causing, as some would argue - a recession. In order to do that, I'm trying to understand why an inverted yield curve has historically NOT been a good predictor in countries other than the US.

See e.g. this article by AQR, which discusses the track record of yield curve inversions in Australia, Japan and Germany. The authors qualitatively argue why that track record hasn't been great but don't provide much of a general framework to think about it. I suspect that they are on to something in the case of Japan: "It is possible to argue that the banking system in Japan is so broken that it doesn’t matter how steep the yield curve is, banks won’t lend anyway. But, more likely, the relationship has broken down because interest rates have been stuck at or near zero for so long. The yield curve can no longer tell you whether the Bank of Japan has raised rates too much or not, because it hasn’t raised rates at all." I agree that the banking system looks pretty zombified, which would explain why banks (and the economy in general) don't really react to cues from interest rates. In addition, the Bank of Japan has such an outsize weight in the market for government bonds these days that the true information content of interest rates is probably quite low. However, I don't think either of these characterizations would apply to Australia, so clearly a broader line of thinking is necessary.

Academic references and/or plain English welcome. Thanks.

I’m currently researching this topic, and I have not found any single reference that answers this (... besides my work). I will summarise what I have seen.

I would point out that from a research perspective, having the yield curve work is interesting, while a failure to predict recessions is not interesting. Very few journals publish articles on failed indicators, since the number of those is very large.

If we ignore term premia, an inverted curve normally indicates that the bond market is pricing a cut in interest rates. The way central banks react is that they normally cut rates when recessions hit. As such, we would typically expect inversions ahead of recessions. However, the logic can break down.

Bond market participants are wrong about the forecast.
The central bank cuts rates, but no recession. (U.S., 1998).
Proximity to 0% makes inversion difficult (Japan, euro area).
Central bank does not cut rates in response to recession (possible for euro periphery).
“Technical factors” in bond market lead to flat/inverted curves (U.K., Australia.) For the U.K., pensions were forced to match the liability of duration, and there was not enough supply of long-dated bonds. For Australia, the government had surpluses, and I believe that duration supply was extremely low. (Would need access to paid bond index data to validate that claim.)

The issue is therefore not U.S. versus non-U.S., it’s just that the U.S. managed to avoid most of these factors (except in 1998 in the recent history).


Areas of Europe with more women than men have higher GDP and lower unemployment. Why might this be? Using Eurostat data I've found that regions of Europe with more women than men (i.e. female biased sex ratio) have higher GDP and lower unemployment than areas with male biased sex ratios. any idea why this might be?
Cheers

I believe this is generally true in the US, and I'll offer at a few reasons that are sometimes suggested here.

Women are more likely to go to college than men, and colleges tend to be located in higher productivity areas.
Women are more likely to live and work in cities (a majority in 81 of the 100 largest cities but a majority in only 58 percent of small metropolitan areas ), and wages are higher in cities.
Depending on the sample period, for much of the time since 2007 female unemployment rates have been lower than the male rate, so you might expect places with more women to have have lower unemployment rates.


What are the known / alleged problems against using energy as currency? What are the known (and alleged) problems of using Joules (i.e. a measure of energy/work) as a currency? I tried to find such idea in Google (searched terms like "technocracy", since someone told me that technocracy had such idea), but I'm not clear about where to search in.

(Edit : asked in contrast to fiduciary/trust/faith-based currencies)

(Edit 2 : found this link, but i'm not quite an expert in eco to judge the possible problems, not exposed in the article)

(Edit 3 : This one is my fault since I asked a not-so-clear question, becuase my lack of knowledge. I have to clarify that this proposal is not mine, and I want to just study the concept. In this way, many principles I should enumerate are:

Energy taken into account is the "seizable" energy, like solar or fossil.
Fossil energy can be stored. Fossil industry would be credited for that.
Solar energy can be captured, transformed, and injected into the power network to be credited for that [as currently is, in many countries, right now], and have such energy redeemed later; the only difference with the current situation is that [the modern proposals support that] the economy could be based in such energy, instead the vice-versa case.
The exchange act would not involve energy directly, since a wallet of that type could be quite dangerous to carry in the ... ¿pocket?.

In this sense, I think useful answers have already been provided to cover the expressed points, althought I don't want to consider the answer as just-closed, but narrow the extent of the issues I want to understand about).

tl;dr: Energy is one of the worst ideas for a currency that anyone's had.
It's not fungible, it's not a store of value, and has absolutely no scarcity. Let's look at the details.
Commodity currencies are problematic
jmbjera has listed core problems with the gold standard, and with commodity currencies generally: its supply is managed not by a democratically-elected government, but by one industry, so you remove a hugely useful tool from the policy-makers' toolbox; and you expose yourself to very high short-term volatility.
But even amongst commodities, energy has unique issues that make it worse than useless as a currency.
Energy is ubiquitous and bountiful
There's absolutely enormous quantities of it lying around everywhere. One kilogramme of anything contains mind-boggling amounts of energy - $E=mc^2$, right? c, the speed of light, is huge. Squaring it makes it a lot bigger (when we're in SI units). $3\times10^8m/s$ squared becomes $9\times10^{16}$ - that's how many joules of energy in 1kg of matter. Any matter. Soil, platinum, flesh and blood, it doesn't matter, it's all the same amount of energy: 90 Petajoules; aka 25 Terawatt-hours. That's a few weeks worth of electricity supply in Britain. So an energy currency means one kilogramme of sand is equivalent value to sufficient electricity to power that G7 country for a few weeks.
Additional energy arrives on Earth every second of the day
So not only is there immense quantities of energy lying around for free, but vast amounts arrive every second from our friendly neighbourhood fusion reactor, the sun. Irradiation on the earth is about 130 Petawatts. That's about four orders of magnitude more than human energy consumption. Or, to put it another way, sunlight on one ten-thousandth of the Earth's surface brings energy in at about the same average rate as global energy demand.
Energy's value varies hugely in time and space
But it gets worse, as far as currencies are concerned. See, energy's value differs constantly in time, in space and in form. You must have noticed that wind and sunlight are free - no one's charging you for them - and they're energy. Whereas you have to pay for natural gas. You probably pay even more, joule for joule, for diesel or petrol (gasoline). And you will pay a lot more for electricity. On top of that, one unit of electricity has a very different price depending on where and when you buy it, and the quantity you're buying it in.
Energy's form drives its economic value. 1 Joule is rarely worth 1 Joule
Electricity is a really high quality vector of energy: it can do huge amounts of work. But you can only use it in the instant it's generated (ok, you can store it briefly in a capacitor, but that will cost you, too). Heat is a really low quality vector of energy: and the closer the temperature is to ambient temperature, the less work it can do. i.e. the less economic value it has. Now, we've got enough problems with variable marginal values of money as it is, without this scale of problem. The other thing is, if you're storing your currency of energy as heat, it's losing its value every second as it cools off. Yet, at the same time, cooling has economic value, in aircon and in refrigeration. So that's a lack of energy that has economic value.
Many energy transformations add economic value but consume energy
Refining crude oil costs you energy and other resources. And the end product is more valuable, which is why people do it, and make a profit at it. But that would be absurd if energy were the currency.
On sophistry
I've seen the argument for an energy currency before. Usually, when you dig deeper, they're not really talking about an energy currency. They're actually trying to sell something. Typically, but not always, fossil gas. So their proposed energy currency turns out to be something very like gas futures contracts (which have the usual commodity-currency problems: control of supply lies with one industry, not democratically-elected governments; and the whole economy is exposed to high short-term volatility). Now, as we know, we've got far more gas than we can possibly burn (see my colleagues' paper in Nature on this), and the gas industry is starting to get nervous. And so it should. This desparate bid for a "gas currency" is just one more bit of special pleading and rent-seeking from what must become a dying industry.


Does net exports has to do with borrowing and lending? In my course notes, it says that "when net exports is negative it means that the country is borrowing from other countries" but I do not get it if net exports is negative that only means that exports < imports so net exports is negative, how does that relate to borrowing from other countries? or does it does assume that we traded our exports for imports instead of paying in cash?
Thanks in advance.
Edit : and I apologize if my question sounds stupid
Edit : the answer by @BB King on A country borrowing from the rest of the world did not help me , what i do not get exactly is how net exports component works and how it is calculated, ik that net exports = exports - imports and that we subtract imports for the fact that GDP is concerned only with domestically produced products so we subtract imports from consumption component (C-M) but we "rearrange" the formula of GDP and call (X-M) net exports (tho it's still the same formula), if i as citizen made some purchases online from other countries, that would be subtracted from GDP only cuz it's not domestically produced and if for some reason citizens of my country imported more than what they exported , XN becomes negative simply cuz of rearrangement of the formula so why does that mean my country owes other countries anything (citizens paid for everything out of their own pocket)?, what i am saying is that net exports component only exists cuz of the rearrangement of the formula so if NX is negative, it means M>X , except if X,M are calculated with something like X = imports + amount of money borrowed from other countries, M = Exports + amount of money lent to other countries (of course I made those up , to explain my point of view)

Maybe this will help: imagine that trade is done in the currency of the foreign country.
Suppose you are American, you are standing on the border of Mexico, and you sell a hot dog to a Mexican for 20 pesos. Now you want to buy tacos from him, but you want 30 pesos of tacos. So he lends you 10 pesos, then you buy the tacos.
So X=20, M=30, and net exports= -10 and you borrowed 10.
Side note: some poor, risky countries (e.g. North Korea) can't have negative net exports, because no one will lend to them.


Impact of Natural Disaster on Production Function Say a natural disaster strikes. People were killed but the losses were small relative to the size of the work force. However, many buildings and infrastructures have been severely damaged. I'm thinking how would such an event impact the shape of the production function. Assume the production function is of Cobb-Douglas form.

On one hand, I'm compelled to say that the production function shifted down. The labor force is still there but there are now perhaps too many people to work the reduced amount of capital, so productivity of labor decreases, shifting the function downwards.

However, I also feel like it's just a movement. The technological level remains the same. We would just move further down the function as capital decreases.

Those are my thoughts. I'm having trouble thinking this through.

Suppose the Cobb-Douglas production function is $Y = AK^{\alpha}L^{\beta}$, and the effect of the disaster is to reduce $K$ from $K_0$ to $K_1$. If any change in $A$ and $L$ is insignificant, then you can look at this in two ways:

Focusing on a partial production function in terms of $L$ only (that is, treating $A$ and $K_i$ as fixed parameters in the short term), there has been a change from $Y=AK_0^{\alpha}L^{\beta}$ to $Y=AK_1^{\alpha}L^{\beta}$. With $K_1<K_0$, that implies a shift downwards, with labour productivity having decreased.
However, the full production function in terms of $K$ and $L$ is unchanged, and there has been a movement on the surface defined by the function. If the function were plotted in three dimensions, with $K$ and $L$ on horizontal axes and $Y$ vertical, then this would be a movement downward (and along the $K$ dimension).

These are both valid ways of describing the situation: which is more useful would depend on what you are trying to do.

One caveat. Although production functions often suggest otherwise, labour is not homogeneous. Even if only a few people are killed, the effect on production could be significant if those people happen to have key skills that are in short supply, or knowledge the loss of which would affect the technological level.


How can a citizen contribute to get his country out of the poverty trap? I am from Madagascar. We are in what is called a "povery trap".
Building a business is very difficult because the population is agglomerating in the capital and the competition is very high. Moreover, there is a lack of public infrastructure that freezes the economy.

What do you suggest me to do as a citizen without any governmental control to have a good impact in the economy?

I think the best way for an individual citizen to improve their country's economic development is to raise their productivity, while also following ethical standards. "Raising productivity" is a very traditional economic viewpoint, and it basically requires one to move away from rural or subsistence living and towards activities that contribute to society, as measured by the income that you generate. But, I think there also needs to be a focus on long-term developmental outcomes, which may not necessarily be tied to economic profit because of negative externalities.

I haven't done a lot of research into the lives of poor people, but after reading some chapters from Banerjee and Duflo's Poor Economics, I would say that the economy loses out when people are not persistent, motivated, or when they make economically irrational decisions. For example, poor people in India do not use the most cost-effective treatment for diarrhea (rehydration liquid with salt and sugar) because they do not trust and are not accustomed to Western medicine. Another example is that poor people in Morocco who can't afford food buy televisions, but I understand the reason for this. The reason is that poor people cannot be expected to cut out all luxuries in their lives, because they also need things that make their life bearable and pleasurable. If poor people didn't buy expensive food and other luxury items, the generations below them might rise out of poverty sooner, but such a process takes a long time. Income-earners would not want to forego a better life for themselves just so that their children's children will not live in poverty.

All in all, I advise you to become a change agent in your community. Strive to motivate others to do work. Technology will help, so you will need to try to find out what the most technologically advanced way of doing your work is. That knowledge comes with education, which may be difficult to access in your situation, but nevertheless try to find it. Lastly, public participation in governance is important for economic development, so try to actively participate in your country's governance.


Deriving aggregate output from labor demand and supply I was reading the following paper:
http://eml.berkeley.edu//~moretti/growth.pdf
I got stuck at equation (7)
The firm's production function is $Y_{i}=A_{i}L_{i}^{\alpha}K_{i}^{\eta}T_{i}^{1-\alpha-\eta}$
Labor supply is $W_{i}=V\frac{P_{i}^{\beta}}{Z_{i}}=V\frac{\bar{P_{i}}^{\beta}L_{i}^{\beta \gamma_{i}}}{Z_{i}}$
Labor demand is $L_{i}=(\frac{\alpha^{1-\eta}\eta^{\eta}}{R^{\eta}}\frac{A_{i}}{W_{i}^{1-\eta}})^{\frac{1}{1-\alpha-\eta}}T_{i}$
The paper says that if we impose aggregate labor demand is equal to aggregate labor supply (normalized to one), then the aggregate output $Y=\sum_{i}Y_{i}$ is
$Y=(\frac{\eta}{R})^{\frac{\eta}{1-\eta}}[\sum_{i}(A_{i}[\frac{\bar{Q}}{Q_{i}}]^{1-\eta})^{\frac{1}{1-\alpha-\eta}}T_{i}]^{\frac{1-\alpha-\eta}{1-\eta}}$
This step looks drastic to me. How can the aggregate output be derived from the above conditions?

Use $W_{i}=V \cdot \frac{P_{i}^{\beta}}{Z_{i}}=VQ_i$, then $$L_{i}=\left(\frac{\alpha^{1-\eta} \eta^{\eta}}{R^{\eta}} \cdot \frac{A_{i}}{(V_{i} Q_{i})^{1-\eta}}\right)^{\frac{1}{1-\alpha-\eta}} \cdot T_{i}$$ and $$\sum L_i = {\left({\frac{\alpha}{V}}\right)}^{\frac{1-\eta}{1-\alpha-\eta}} {\left({\frac{\eta}{R}}\right)}^{\frac{\eta}{1-\alpha-\eta}} \sum\left(\frac{A_i}{Q_i^{1-\eta}}\right)^{\frac{1}{1-\alpha-\eta}}T_i = 1$$ $$\frac{V}{\alpha} = {\left({\frac{\eta}{R}}\right)}^{\frac{\eta}{1-\eta}} \left(\sum\left(\frac{A_i}{Q_i^{1-\eta}}\right)^{\frac{1}{1-\alpha-\eta}}T_i\right)^{\frac{1-\alpha-\eta}{1-\eta}}  $$.
Use the FOC on labor, $W_i=\alpha \frac{Y_i}{L_i}$, then $$\sum Y_i = \frac{V}{\alpha}\sum L_iQ_i = \frac{V}{\alpha} \bar{Q}$$, and replace $\frac{V}{\alpha}$ with above equation then you get equation (7).


real exchange rate appreciation i find the topic of real exchange rate appreciation / depreciation often not very well explained.

even the excerpt below from the following accepted answer on this website is not correct in my opinion.

  The home currency appreciates in real terms against a foreign currency either if the home currency appreciates in nominal terms or if the home country's inflation rate is lower than that in the foreign currency.

specifically, the part in bold i believe is wrong. if the home country's inflation rate is lower than that of the foreign country, then all else equal, the home currency should depreciate in real terms as the domestic consumption basket becomes cheaper relative to the foreign consumption basket

some of the confusion abounds because of the different quoting conventions (X vs 1/X, foreign vs domestic, etc)

You need a clear understanding of what is exchange rate and how it is determined.

Consider two countries with free flow of goods and services that is there is no transaction, transportation, tariff costs etc. [I am assuming an ideal world here].

say,

India (Currency: Indian Rupee abbreviated as INR) and USA (Currency: Dollar abbreviated as $ ).

Exchange rate:

$ 1 = INR 50

Consider a commodity let us say pencils:

Assume that in year 2018 - one pencil costs $ 1 in USA and INR 50 in India.

Now let us suppose that India faces an inflation of 10% per annum and there is no inflation in USA.

Hence new prices of pencil in year 2019:

India - INR 55

USA - $ 1

Since, there are no transportation and transaction costs Indians will start purchasing pencil from USA since 1 US $ still equals INR 50 and Indians get pencils relatively cheaper in USA after converting their currency into dollars. This will push up Indian imports and hence Indian currency will depreciate and US dollar will appreciate because US exports have gone up.

This process will continue till 1$ = INR 55.

Now coming back to your question say home country is USA and due to relatively lower inflation rate in USA, the US dollar appreciates (NOT depreciate).


How does Infrastructure impact on Aggregate Supply? I was just wondering how Infrastructure can impact on Aggregate Supply. More specifically, how does the improvement of infrastructure improve Aggregate Supply?

Aggregate supply is typically modelled as

$$ Y = F(A, K, L) $$

where

$Y$ = total production

$L$ = labour input

$K$ = capital input

$A$ = total factor productivity

Investment in infrastructure can increase both capital input $K$ and total factor productivity $A$. In a standard $AS - AD$ model, the aggregate supply curve would shift to the right, as a result, and the equilibrium output of the economy would increase.

Investment in infrastructure can increase capital input, because if there are more roads in the country, the economy can produce more goods and services (think about a truck company, for example, which can do more jobs per day if its trucks travel on more direct roads or faster highways).

It can also increase total factor productivity, because the proportional increase in output is potentially higher than the proportional increase in capital input. If with a short road I link a town to a national highway network, the benefits can be disproportionally high, as a short road link now provides access to a huge existing highway network. Or think about the 50 mile Panama Canal. It provides ships an 8,000 mile shortcut.


How to theoretically explain an exponential income distribution? I have been working on income distributions for a while, and I've been asked to do a theoretical justification for the idea that income distribution follows an exponential function for low incomes. There's a lot of literature about Pareto distributions in the upper tail of the distribution, but I haven't been able to find literature for the lower tail and the exponential.

There's empirical work on this topic, mainly done by physicists: https://arxiv.org/pdf/cond-mat/0008305.pdf

One of those physicists asked me to find economic theories that support the exponential hypothesis, but, as I've said, I haven't found any.

Could you point some pieces of economic literature to get me on the right way? Thank you.

...find economic theories that support the exponential hypothesis, but, as I've said, I haven't found any.

I don't think you will. For purposes of economic argument, the characteristic of the Exponential distribution that stands out and must be defended, is that it has its maximum at zero.

Then, arguing that an Income distribution follows the Exponential, means that we accept that the most probable situation to be observed is zero income. Is it? I don't think so.

As regards the study you link to, the main piece of evidence for the fit of the Exponential to the data is Fig 1 page 2. The authors write that they consider it a very good fit. I most certainly don't: the histogram in Fig 1. has clearly a mode at strictly positive values and not at zero. Βut this is the most critical piece of evidence as to whether the data follows an Exponential or not.

At page 4, the authors try to deal with this critical deviation of the data from the Exponential graph, by mentioning that there may be under-reporting at low values, but that's a very vague argument, unsupported and unsubstantiated.

a) From a theoretical perspective, it is not realistic to argue that the most probable income observed is zero
b) The data support this by providing a strictly positive mode for the frequency.

Therefore I don't see a case for the Exponential.


Auctions and finding nash equilibrium of a dynamic game Suppose we have a sequential version of an Auction game:
• Player 1 places a bid.
• Player 2 observes player 1’s bid, then places a bid.
• The player with the highest bid wins the item at auction.
• In case of a tie, the winner is determined randomly (with equal probability among
those tied).
• The winning player pays his bid.
Two players bid for a rare bottle of Scotch. This is an auction in which they
can bid any amount in $\Bbb R_+$. Suppose the two players both value the item at £500.
Find all pure-strategy Nash equilibria of this game.
The answer provided didn't seem too intuitive:

Player 1’s strategy is to bid 500.
At the information set following 1 bidding 500, Player 2’s bid is in [0, 500].
At all information sets where 1 bids any x1 below 500, Player 2 bid is in (x1, $\infty$).
At all information sets where 1 bids above 500, Player 2 bids anything in $\Bbb R_+$.

I somehow get that we do NOT need to consider sequential rationality, but how does point 4 follow i.e P2 bids anything in $\Bbb R_+$?
Any help will be greatly appreciated.

You are only required to get Nash equilibria and not sequentially rational/subgame perfect equilibria. Hence Player 2's actions at information sets that do not occur (that do not reflect Player 1's actual strategy) do not need to be best responses. All you have to make sure is that no one is better off by deviating.
In case 4., regardless of what Player 2 does, Player 1 cannot get a positive surplus; she wins with a higher than 500 bid or loses. This is not better for her than bidding 500 and losing.


Asymmetric vs incomplete information I am having difficulties in distinguish them. I kind of understand what is the difference intuitively, but I still fail to put some games in the correct category.

Can you give me two examples of games and show me the difference from a mathematical (notation) point of view?

Consider

where $\epsilon_1,\epsilon_2$ are iid random variables with distribution $F$. $a,b,\dots,h$ are constant parameters.

Game of incomplete but symmetric information
would be something like: $F$ is common knowledge among the two players.

Game of asymmetric and incomplete information
would be something like: before making their respective decision, Player 1 observes the realization of $\epsilon_1$ but not $\epsilon_2$ and Player 2 observes $\epsilon_2$ but not $\epsilon_1$.


What does the value of bitcoins depend on? I've been looking up stuff about bitcoins for some time now and i have two question stuck in my mind:

How is the value of bitcoins so unstable?

And can there be bitcoin inflation?

The price is unstable because there's a fairly small free float (the quantity available for buying and selling with true currencies) compared to the level of transactions.

It's a Ponzi scheme, so demand is driven by Bitcoin marketing: it is in immediate financial interest of the holders of Bitcoin to drive up the price by "ramping" it: talking up the market price. The amount of attention that the media gives Bitcoin goes up and down - this affects demand, and that drives the price, as supply is fairly stable.

The originators of Bitcoin, and the original hoarders, have most to gain: it was easiest for them to create Bitcoins. It would be rational for them to slowly release their hoard into the market as price goes up.

It's also attracted a lot of gullible but evangelical supporters: for them, continuing to hold Bitcoin is a means of validating their beliefs, and even validating the identity they've built for themselves around it. That's why the free float tends to stay low.


How is GDP counted between different countries? Sorry if this question is dumb, but I did not manage to find the answer on the web. The questions is as follows:

As far as I understand, GDP is the total value of a country's production. It includes all the output, and thus it represents the cost of all the wages and primary ressources used to produce this output. But how is this cost passed from one country on other countries, considering a globalized economy?

For example, let's say that country A as a 3 000 $ GDP. And country B as a 2 000 GDP.
But country A's economy consists only in producing computers, which are built with processors built by country B: For one computer, cost = 3, two processors (each cost = 1) are needed.
So in the end, when country A sells 1 000 computers which gives 3 000 GDP, 2 000 of this GDP is buying the GDP of country 's B (2 00 processors = 2 000 of GDP).

In the end, A's GDP is higher than B's GDP but A's income is lower than B's income. And somehow, A's GDP is (B's GDP + A's working value) with A's working value being only 1 000, while B's GDP is (B's working value) with B's working value being higher (2 000) than A's.

Is all this analysis true in the real world?
And example in the real world: China has a big GDP but it consists mainly of B2B sellings to other countries: are those sellings, sold again in other countries (let's say USA), counted as GDP for USA?

So, from the link posted by @Brian Romanchuk, I got this paper and got the answer:

GDP = Consumption + Investment + Government spending + eXports – iMports

So in the example, country A GDP would end up to be:
GDPA_A = 3 000 - 2 000 = 1 000 and being correctly a smaller quantity than country B's GDP.

Thanks to contributors


Isn't the liquidity trap about real interest rates? Here is a so-called thought experiment. Suppose the inflation rate is negative, the nominal interest rate slightly negative, and the real interest rate positive (call it $r$). I think people would rationally make the same savings decisions as if they were in an economy with a real interest rate of $r$, but positive inflation.

But, the liquidity trap is about the nominal interest rate. It says that the nominal interest rate can't drop below zero. I'm trying to understand why, and I think the question can be framed in terms of what banks will decide to do with bonds they own. When the real interest rate is positive, banks will continue to create money and buy bonds, no matter what the long run nominal interest rate is. If the real interest rate were negative, banks would not buy any more bonds, would get less money when selling their current bonds, and they would start to run out of liquidity (no matter what the nominal interest rate is).

The situation you describe, one with negative nominal rates, only can happen with the use of force or where the instrument acts as an insurance policy.  In the case where the instrument serves as an insurance policy, the implicit premium is that negative rate.

To consider why this is the case, consider two investments.  The first investment provides an $\alpha$ percent rate of return where $-100\%<\alpha<0$.  Now consider holding a bank note that pays a zero percent rate of return.  Bank notes have, at times, paid positive rates of return.  Let us assume that we have perfect foreknowledge of future deflation and we know that both will provide a positive real rate of return.

The bank note would always dominate the negative rate of return.  No one would invest in the security that provided negative nominal returns unless they believed the banknote itself was suspect.  There are two ways this dominates.  First, the note provides a higher real rate of return.  Second, however, the banknote will do a better job at preserving its value even under an assumption of future inflation because it pays a higher nominal rate, which is zero percent.  The banknote is both more valuable and simultaneously less risky.

As to the second part of your thinking, that banks would run out of liquidity, you are in error.  The reverse would happen.  As banks buy fewer bonds, they become less leveraged and intrinsically are more flexible and liquid.  Banks become fragile so that their customers can be flexible.  If there are no offers to borrow from the bank at advantageous rates to the bank, then the bank builds reserves instead.

So the banks should be more liquid.  Of course, this does imply that commerce will become less liquid.  It would imply that access to liquidity would be more costly than normal as banks want nominal returns to at least cover costs plus an economic profit on those costs.

What is an issue is whether or not deflation triggers an exchange between debt and equity investing.  The least risky projects can no longer be financed with debt or equity.  It could be asked, "does deflation make the entire system increasingly risky with the passage of time?"  Are there situations that are unwise for the system, though individually rational for each separate actor?  There is also a question of sectoral transfers.  Does commerce transfer profit from itself to banks to preserve treasury operations and basic liquidity functions?


Textbook claims that price level accompanied by decrease in interest rates? I read from this textbook the following, quoted as:

  In addition, a decline in the price level is usually accompanied by a
  fall in the rate of interest...

I interpret this as meaning: "A fall in price causes interest rates to fall".
This quote, in context, was meant to explain the interest rate effect - a reason why the aggregate demand curve slopes downwards.
Can someone verify and explain why this is the case? Additionally, is my interpretation correct?

Presumably the context is deriving the AD curve from the IS-LM model. Start from money market equilibrium $$M/P=L(i,Y).$$
If $P$ falls then the supply of real money balances rises. With $M$ and $Y$ fixed the nominal interest rate $i$ must fall in order to induce people to hold the greater supply of real money balances. This is because the alternative to holding money is holding it in bonds which pay interest. To get people to hold more money (which pays no interest) we need the opportunity cost of holding money to be lower, so yes your interpretation is correct.

With sticky inflation expectations (recall the Fisher equation $i=r+\pi^e$) the change in the nominal interest rate will map one to one to changes in the real interest rate. This means that the LM curve shifts down at any given level of $Y$ in $(r,Y)$ space. This produces a new equilibrium in the IS-LM model with a lower real interest rate and a higher income (since the lower real interest rate has stimulated investment). Thus a negative relationship between $P$ and $Y$: the AD curve.


What does n stand for in the taylor rule? I was asked what the relationship of $\bar m$ and $\bar n$ are with the taylor rule.

Using $\bar m$'s definition which is the sensitivity of real interest rate to inflation in a market's monetary policy rule. I said $\bar n$ is the sensitivity of the interest rate to changes in short run output in a monetary policy rule.

To answer the question, i said the parameters  $\bar m$ and $\bar n$ indicate the sensitivity of the taylor rule towards changes inflation and short-run output.

The taylor rule being
$$R_t-\bar r  = \bar m (\pi_t -\bar \pi)+ \bar{n}\bar{Y}   \quad \bar m>0, \, \bar n>0$$

And the resulting new AD curve being
 $$Y^t_t = \bar a - \bar{b} \bar m (\pi_t -\bar \pi)-\bar{b} \bar{n}\bar{Y}$$

$$ Y^t_t = \frac{\bar a}{(1+\bar{b}\bar{n})} - \frac{\bar{b}\bar m}{(1+\bar{b}\bar{n})} (\pi_t -\bar \pi) $$

As in the addition $\bar{n}\bar{Y}$

As you mentioned before, $\bar{n}$ is the sensitivity parameter of the interest rate to changes in short run output in a monetary policy rule. What is the relationship of $\bar{m}$ and $\bar{n}$ within the Taylor rule? It heavily depends on the given economic climate.

Assuming the basic Canonical New Keynesian DSGE Model the equations of our economy are the following:

IS (investment/saving) curve:
$$   y_t = E_t [y_{t+1}] - \theta r_t +u_t^{y} $$
AD (aggregate demand) curve:
$$ \pi_t = \beta E_t [\pi_{t+1}] +\kappa y_t + u_t^{\pi}$$
Taylor rule:
$$   r_t = m E_t [\pi_{t+1}] + n E_t [y_{t+1}] +  u_t^{r} $$

If you estimate the Taylor rule empirically with some kind of economic techniques, there should be considered 4 scenarios (shocks) .

Demand shock ($m, n > 0$)
Supply shock ($m > 0, n < 0$)
Monetary policy shock ($m, n < 0$)
Technology shock ($m > 0, n < 0$)


Isn't it pointless to care about GDP? If I pick up a stone there and sell it to you for 1 million dollars, 1 million dollars added value is created and added to GDP. If you sell it to me for the same price, virtually nothing has happened but GDP increased by 1 million dollars.

We can increase GDP by any number we want.

Why do we care about GDP?

Yes, GDP can indeed be inflated by meaningless circular transactions. Furthermore, GDP growth completely ignores underlying changes to a country's asset base. Corporate accounts are considerably less naive. Any company that only ever reported growth in turnover wouldn't be trusted: turnover is vanity, profit is sanity.

Real increases in GDP can be a useful proxy for economic growth, because it measures the total transaction value within the economy, and historically that's been closely correlated to general perceptions of economic growth. So much so, that it's now pretty much used as the definition of economic growth.


Concavity of Cobb-Douglass Utility Function on Non-Open set My textbook argues that the Cobb-Douglass utility function $u=(x1)^a(x2)^b$ with $a,b>0$ and $a+b<1$ is concave on $R2+$ by computing the Hessian and showing it to be negative semidefinite for all points in $R2+$.

However, I feel this method is flawed because $R2+$ is not an open set. A function is  concave on the set $A$ if and only if its Hessian is negative semidefinite for all $x$ in $A$, but the assumption is that $A$ is an open and convex set. This does not hold, so the above methodology seems flawed. I am getting confused about this, so I would really appreciate some help please!

For reference, the textbook I am using is this: https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/cvn/t

I assume the notation $\mathbb R^2_+$ refers to $[0,\infty)^2$.

Note that the set on which a function is defined need not be the same set on which a function is differentiable. In particular, it's typical that differentiability requirements are imposed on open sets (see e.g. the fundamental theorem of calculus). This is because defining differentiability on boundary points requires extra care that's usually unnecessary for the issue at hand (such as defining concavity of a function via the Hessian matrix).

The Cobb-Douglas function is defined on $\mathbb R^2_+=[0,\infty)^2$, (continuous also on that domain), and differentiable on $(0,\infty)^2$, which is open and convex.


Optimal Production Input in Relation to Cost Minimization Problem I was doing my homework and got really confused about how to approach the optimal levels of inputs when there are three variables. My current understanding is that the problem is to solve the optimization problem

$$\min_{H, L, K}\;{sH + wL +rK}$$
subject to
$$q = \min\{H,L\} + \min\{H,K\}$$

However, I don't know how to determine the inputs of H, L, and K. Below is the problem:

  A monopolist can hire high skill labor $H$, low skill labor $L$, and robots $K$. The per-unit price of these inputs are $s$, $w$, and $r$. High skill labor is more expensive: $s > w$. The production function is $f(H, L, K) = \min\{H, L\} + \min\{H, K\}$. The demand curve that the monopolist faces is $D(p) = A-p$, where $A > w + r + s$. Suppose that robots are cheap: $r < w + s$.

Essentially, we're asked to find the optimal levels (yields lowest costs) of input in terms of q for H,L,K

I initially thought since $r<w+s$, and $w<s$, we can deduce that $r<s+s$, and for this reason, the production function would give either $q = H+K$, $q = L+H$, or $q = L+K$ (making $H+H$ the only impossible combination). However, I'm super unsure if this is the right thought process, and I don't know how to proceed from here.

Any help is greatly appreciated.

I`d propose you to follow these steps:

Set up the minimization cost problem (i.e. for a given output quantity $y$ minimize costs):
\begin{align}
\min_{H,L,K}&  \quad sH + wL + rK \tag{1} \label{1}\\
\text{such that} &\quad  \min\{H,L\} + \min\{H, K\}\geq y \tag{2} \label{2}
\end{align}
In principle you have 3 cases, depending on price of factors $(s,w,r)$.

1) When $r>s+w$, then buying a unit of $L$ and one of $H$ is going to cost you strictly less than buying a unit ok $K$. Consequently the monopolist opts for producing only using $H$ and $L$ ($K=0$). Thus $H = L = y$

2) The second case happens for $s>r+w$ which is, anyway, ruled out by the assupmption $w>s$ (if this was not the case, then producing only using $H$ and $K$ would have been optimal, i.e $H = K = y$ and $L = 0$).

3) Finally, when none of the above occurs, you have $L = H$ and $K = H$ because of the fixed proportions production function. Then the constraint \eqref{2} becomes $H + H \geq y$ and the inequality sign become equality. The equality sign comes from the fact that producing more than $y$ (the LHS of \ref{2} being strictly larger than the RHS) is just overshooting and inflates production costs for a given $y$. $L = H$ and $K = H$ comes from the Leontief production set-up of the problem: inside the $\min\{...,...\}$ operator is never convenient to exploit more one of the two factors (because by decreaing the most used factor one still gets the same amount of output but a lower cost). Therefore, each of the two $\min\{...,...\}$ can just be seen as one of its inner arguments, namely, for convenience, $H$. So you finally get $H+H = y$ and, from there: $H = y/2$ and $L = K = y/2$

Substitute the optimal values ${\big(H^*\small{(s,w,r)},L^*\small{(s,w,r)},K^*\small{(s,w,r)}\big)}$ in \eqref{1} so to get an expression only in $(s,w,r)$. This expression is the cost function $C(s,w,r,y)$
Now solve the monopolist's pricing problem for given factor prices:
\begin{equation}
\max_p \quad p\cdot D(p) - C\big(s,w,r,D(p)\big)
\end{equation}
and find the profit maximizing price, $p^*$ for output level $y^* = D(p^*)$

I hope this helps, comment below if you need any more hint.


I need something like “how to calculate equilibrium price for complete idiots” My grandfather raises, sells and resells livestock and I want to help him by calculating when and for what price to (re)sell or buy livestock. As far as I understand(although I have a hunch that I need something more), I need to calculate the so-called "equilibrium price". I know only school level of mathematics(I know how to plot functions, find a derivative, find a primitive function).

First, the equilibrium price is, at a very basic level, just the market price for livestock. If you have a perfectly competitive market (a lot of suppliers) and all livestock is about the same, then the market price should be about the best your grandfather can do.

That being said, there are lots of reasons why perfect competition breaks down. This can come from number of sellers (just a few for a buyer to pick from), unobserved product heterogeneity (some livestock is better than others, but can't always see it just by looking), and more. Preferences over different types of products also interact with these other issues (if there's only one person selling and he knows how much a buyer is willing to pay, he can charge exactly that amount, etc.).

This is where the profit-maximizing price issue comes in to play. Your grandfather wants to charge the price that maximizes his profit

$\pi = p*q(p) - c(q)$

with $q$ the demand function (how much he can sell at price $p$) and $c$ the cost function (how much it costs, including what is being given up, to "produce" -- whatever that means in this market -- $q$ units of the good). (Quick note: I'm abusing notation a little in the profit function, but I'm doing it to make the point). The profit maximizing price is just the price level at which the first order condition of $\pi$ is equal to zero (assuming $\pi$ satisfies some regularity conditions). This will end up in the solution that he should produce/charge such that the marginal revenue is equal to marginal cost.

Taking advantage of this in practice requires having a really good measure of both $q$ and $c$. Although difficult for economists, $c$ is usually straight forward for firms themselves to get because they can actually calculate their own costs. The difficult part for everyone is estimating $q$. It takes a lot of data and a really good model of the market, taking into account all the issues previously discussed.

This answer discusses how this might be done by really big firms. Note that one of the main methods they use is experimentation. Large firms can do this easily and often. For smaller firms -- like your grandfather's, I'd expect -- some of the best data your grandfather might have is, like @denesp pointed out in a comment, his experience. If he's been at it for a while, the data that he has gathered over time selling in this market has likely given him a pretty good feel for what he can charge for what and to whom.

To give an example of this type of experience in practice, an economist friend of mine as an undergrad used his father's hardware business as the motivation behind a paper he was writing. He decided that he would use the store's data to estimate preferences and improve profits. He ended up pitting his estimates against his father's experience-based pricing and, try as he might, could not outperform his father's method.

This is not to say that you can't use models and estimation to improve profits. It does indicate, however, that this is not a simple problem and can require a lot of pretty sophisticated methods to outperform the natural market evolution that would be in many ways already internalized by your grandfather.


Completeness of Preferences Economists assume that consumers have a set of preferences that they use to guide them in choosing between goods. These preferences have to satisfy three properties: completeness, transitivity and "more is better".

By completeness I mean that when consumers face a choice between any two bundles of goods, they can always rank them. This rules out the possibility that consumers cannot decide which bundle is preferable. I am wondering how to deal with the introduction new goods? Does it mean that this property only apply to available/existing goods? And should a consumer also rank today a good that is coming tomorrow? I have the intuition that if a new good replaces an existing one, the rank of preferences may change and I dont know how deal with that. Any reference would be appreciated.

Would you like to buy a pack of sugar flavored amazonian soil for 500 dollars?

You can probably answer this question even though you have never heard of this product before. Being able to answer this question, being able to place the newly available consumption alternatives within your ranking is the assumption of completeness.

The same is true if a type of good is replaced. The set of consumption alternatives is changed, but given any two you can still tell which one you prefer.


Giffen Goods & Complementary Goods Consider that good X and good Y are complements and good X is a Giffen good. If I increase the price of good X, what affect does this have on the price and quantity demanded of good Y?

My reasoning was as follows. An increase in the price of good X will increase the quantity demanded of good X (as it is a Giffen Good). Increasing the quantity demanded of good X decreases the price of good Y (as they are complements). A decrease in price of good Y will increase the quantity demanded of good Y (Law of Demand).

This is wrong. The correct answer according to my textbook is that both the price and quantity demanded of good Y will increase.

How can this be?

If $X$ and $Y$ are complements, an increase in the quantity demanded of $X$ also implies an increase in the demand for $Y.$ This is why both the price and the quantity of $Y$ will also have to increase.


Money supply control vs. interest rate control In a macroeconomics book I'm reading, the author talks about money supply control vs. interest rate control as two different approaches in monetary policy of a central bank.

With the goal of price stability being the same in both cases, money supply control alters the supply of money and thus effects the interest rates within the economy in either a expansive or restrictive manner. With interest rate control, the central bank defines a central interest rate to increase or decrease the money supply for the commercial banks, which in turn translate this into the economy.

The author claims that money supply control is only a viable option when there is certainty about the money demand. Interest rate control is preferred when there is uncertainty about money demand.

I don't quite understand the difference between these two approaches as in my opinion they are essentially the same. They are not even comparable as two different approaches, they are both part of the same approach from my understanding: Interest rate control in consequence effects the money supply. So interest rate control allows money supply control.

In most media you'll only read about how the central banks in the US and Europe alter the central interest rate to increase or decrease money supply. I never read about direct money supply control. I feel like I might be confusing terms or just misunderstand the author.

Can anybody shed light on this topic?

Thank you in advance!

I think that with money supply control the central bank actively influences The money supply by adding or withdrawing money. By setting the interestrates the central bank influences the lendingcapacity of the banks and the people, lowering the interestrate creates more lendingcapacity and thus 'adds' to the moneysupply... By setting interest rates higher it diminishes lending capacity and thus 'tightens' the money supply..


What links can be made between the marginal productivities of the factors of production and the costs of production What links can be made between the marginal productivities of the factors of production and the costs of
production

Assume the following profit function: $\pi = pY - wL -rK$ and a two factor economy $Y(L,K)$.
Optimal labour and capital inputs for the firm can be found by taking the respective derivatives and setting them to zero:
$\frac{\delta \pi}{\delta L} = p \frac{\delta Y}{\delta L} -w = 0  \iff \; \frac{\delta Y}{\delta L} = \frac{w}{p} $
$\frac{\delta \pi}{\delta K} = p \frac{\delta Y}{\delta K} -r = 0  \iff \; \frac{\delta Y}{\delta K} = \frac{r}{p} $
Now you can see that marginal productivities are equal marginal costs. The derivative with respect to the input factor tells you what the next unit of capital or labour will produce and the right hand side tells you what they will cost (real wage or real interest rate). If this condition does not hold firms could be better off by adjusting their production towards this condition. For example assume marginal product of labour is greater than the real wage $(\delta Y / \delta L > w / p)$. The firm should hire an additional worker since she will produce more than she costs. This logic holds true until the conditions are fulfilled.


How does expected utility theory treat losses? I've been reading about prospect theory lately and have read often that prospect theory predicts people will be risk averse in gains and risk seeking in losses. This statement is typically supplemented with the phrase ", contrary to the standard expected utility theory model".

However, I'm not sure how expected utility theory deals with losses. Is it that EU theory assumes people who are risk averse in gains will be risk averse in losses as well? If so, how do you model this mathematically?

If our risk-averse EU maximizer has $u(x)=\sqrt{x}$ for $x>=0$, would the equivalent function in losses be $u(x) = -x^2$ for $x<0$? If so, wouldn't that mean that they are overweighting the loss component relative to the gain component - which is not an element of expected utility theory.

Graphically, a prospect theory value function is typically drawn as
.

How would you draw the equivalent graph for an expected utility theory value function?

Gains and losses presuppose a reference point, which is not a feature in standard expected utility theory. In this theory, the only argument in the utility over wealth is $w$, the absolute level of wealth. A common form of utility function is the constant relative risk aversion (CRRA) form:
\begin{equation}
u(w)=\frac{w^{1-\rho}}{1-\rho},
\end{equation}
where $\rho$ is the coefficient of relative risk aversion. Note that this incorporates the commonly seen $\sqrt w$ and $\ln w$ forms when $\rho$ is $\frac12$ and $1$, respectively. As is obvious, there is no term that helps differentiate between gains and losses in this formulation. The graph for a standard EU function with risk aversion is the same as any strictly increasing and strictly concave function.

Prospect theory is motivated by empirical regularities found in psychology experiments. A typical utility form is
\begin{equation}
u(x,r)=
\begin{cases}
(x-r)^\alpha &\text{if }x\ge r\\
-\lambda(r-x)^\beta &\text{if }x<r
\end{cases}
\end{equation}
where $x$ is the payoff from some choice alternative (or "prospect" if the choice involves risks), $r$ is the reference point (which is $0$ in your example), $\alpha,\beta\in(0,1)$ are parameters that govern the degree of risk preference, and $\lambda$ is a parameter that separately captures loss aversion. Tversky and Kahneman (1992) estimate that $\alpha=\beta=0.88$ and $\lambda=2.25$.


Why do longer maturity treasuries normally have higher yields than shorter ones? The conventional reason I see for this everywhere is that "investors take on larger risk locking up their money for longer."
This is unsatisfactory for me because of the secondary market. The price of a 30-year bond, for example, should be increasing by YTM% (yield-to-maturity) since the NPV of all future outflows increases (less time till the outflows).
So comparing a 30-year bond and a 1 month bill, why can't an investor buy the 30-year bond, hold it for a month, then sell it?
Both bond and bill are exposed to interest rate risk the same time. Furthermore, the sum of the bond's outflows + higher price, as mentioned above, should produce YTM% of value. So now since the 30-year bond's yield is higher than the 1 month bill, the investor should make more with the 30-year bond.

Existence of secondary market only reduces liquidity risk. It does not affect the inherent risk of purchasing long term debt because situation can change. For example, long term bonds have higher interest rate risk because there is higher chance that interest rate will change in long term than in the short term (and raise in the interest rate will lead to lower bond price).
People at a secondary market will not buy bonds from you at any price you will fancy. Any prospective buyer will take into account that long term debt is more risky even if there is a secondary market. Advantage of secondary market is that it makes the bonds more liquid so it primarily reduces liquidity risk but virtually all other sources of risk remain unaffected, and generally (from a perspective of a buyer) the risk of buying debt increases with the time to maturity of the debt and so the buyer has to be compensated for that (plus there is the time value of money - money now is always better than money tomorrow). For example, the person that buys the bond from you will have to either factor in the price that either they will have to hold the bond to maturity (with all risks that carriers) or find another buyer who will then have to factor in the same problem. The bond will have to end up in someone's hands at the end of the day so all disadvantages of holding that long term debt will be priced at secondary market as if the bond would be held to maturity from the date the transaction is made (save for liquidity related issues).
Consequently, in the end regardless of whether secondary market exists it generally does not change riskiness of purchasing bond save for the liquidity risk. Since longer term debt is riskier for buyer (e.g. interest rate risk etc.) they need to be compensated more for purchasing it than in the case of short term debt that carries less risk.


Why does Ricardian Equivalence not hold when there are different borrowing and lending rates on the market? If you can propose any explanation (intuitive, graphical or algebraic), I will appreciate it

Barro helped define Ricardian equivalence, wherein one of the assumptions was that the capital market is perfect(can lend and borrow at a single rate).
so it can be easily inferred that Ricardian equivalence does not hold true when borrowing and lending rates are different.
and while it is assumed under Ricardian equivalence that consumers are able to save/ spend according to tax regimes, it is debatable, as was mentioned by Ricardo himself, that people may have a myopic approach towards tax regimes.
although it holds credibility in some specific examples, the discounting of one of its basic assumptions can be the reason for it not holding true when borrowing and lending rates are different.

it would be more helpful if you could elaborate on the type of examples/statements you want to support your answer.


How can I control for trade between UK and Australia in my difference-in-difference trade model? I am doing a report on whether environmental regulation has an impact on trade, using a difference-in-difference model and seeing whether the EU Industrial Emissions Directive had an effect on UK trade. The UK is my treatment group and Australia is my control group. However, what is the best way to control for bilateral trade between the two? Would I need bilateral trade data on UK and Australia trade or can I just use a dummy variable? If I am using a dummy variable, how can I use it? Thanks!

I can’t imagine what dummy could you use there. Here trade is your dependent variable if you would use dummy you would have to switch to some non-linear probabilistic model such as logit or probit.

Most of the time I see papers using just exports from country i to j as proxy for bilateral trade. But there are multiple ways how you could in principle measure it, and it’s not easy to provide some short review of all possible ways. For example, more sophisticated metric would be to measure it in terms of value added like here. It would really depend on exact situation, I would maybe recommend starting with the exports from UK to AU for UK and vice versa for AU and then move onto more fancy measures, it might be good idea to do extensive robustness checks using different possible metrics.


Money Metric Utility Function: Budget constraints become Utility Functions? Im currently reading up on the "money metric utility function" (also known as the minimum income function or direct compensation function).
By definition it is defined as:
$$m(\text{p},\text{x})\equiv e(\text{p},u(\text{x}))$$
Hal Varian writes in Microeconomic analysis (page 109):

it is easy to see that for a fixed $\text{x}$, $u(\text{x})$ is fixed, so $m(\text{p},\text{x})$ behaves exactly like an expenditure function: its monotonic, homogenous, concave in $\text{p}$, and so on. What is not so obvious is that when when $\text{p}$ is fixed, $m(\text{p},\text{x})$ is in fact a utility function.
The proof is simple: for fixed prices the expenditure function is increasing in the level of utility: if you want a higher utility level, you have to spend more money. In fact, the expenditure function is strictly increasing in $u$ for continuous, local non-satiated preferences.
Hence for fixed $\text{p}$, $m(\text{p},\text{x})$ is a monotonic transform of the utility function therefore itself a utility.

Does this (the bolded statement) mean that we essentially convert our consumer's budget constraint/budget line into his indifference curves when prices are fixed?

$m(\mathbf p,\mathbf x)$ specifies the minimum amount of money required for a consumer to attain the same utility as consuming bundle $\mathbf x$, taking prices $\mathbf p$ as given. In other words, since all bundles on the same indifference curve as $\mathbf x$ have the same utility value, and to achieve this utility, one needs at least an income of $m(\mathbf p,\mathbf x)$, we can thus establish a one-to-one mapping between utility levels and income levels. As utility is ordinal, we could as well use income as our utility measure.

This does not, however, suggest that the consumer's budget line is converted to her indifference curve; the two remain distinct objects. To see this, consider a two-goods case. With fixed prices, the slope of the budget line is $p_2/p_1$, which is constant for all $\mathbf x$'s. In contrast, the slope of the indifference curves is generally a non-constant function over $\mathbf x$:
\begin{equation}
\frac{\partial x_2}{\partial x_1}=\frac{\partial e(\mathbf p,u(\mathbf x))/\partial x_1}{\partial e(\mathbf p,u(\mathbf x))/\partial x_2}=\frac{MU_1(\mathbf x)}{MU_2(\mathbf x)}\,.
\end{equation}

The money metric utility function simply changes the unit of utility measurement from utils to dollars, which is legitimate thanks to the ordinality of utility. It does not change the underlying mathematical objects in any substantive way, though.