How do I find out which form of utility function is being used? Can someone tell my how i can figure out which type of utility function the following maximization problem has. It is for an overlapping generations model.

$$\underset{x'}{\max} x'\big(E_t (P_{t+1}+δ_{t+1})-(1+r^f)P_t\big) - \tfrac{\gamma}{2} x'Ωx $$
Where:
$x'=$ portfolio of shares

$E_t (P_{t+1}+δ_{t+1}) =$ expected future payoff

$\gamma =$ agent i risk aversion

$Ω=$ covariance matrix

I would call this a mean-variance utility function. The agent likes higher mean values, which is the first term, but trades that off against higher variance, which is the second term.

If the random variable of interest is normally distributed with mean $P_{t+1} + \delta_{t+1} - (1+r^f)P_t$ and covariance matrix $\Omega$, and if the agent has constant absolute risk aversion utility, such as $u(w) = 1-e^{-\gamma w}$, then maximizing that utility is equivalent to maximizing mean-variance utility. Here are some details I found with a quick google search.


What does the Federal Reserve intend to do with bonds it has purchased under QE? In New York Magazine's interview with investor Mike Burry (made famous by The Big Short), he claims Quantitative Easing has left the Federal Reserve with an extraordinarily high leverage ratio:

  What makes you most nervous about the future?

  Debt. The idea that growth will remedy our debts is so addictive for politicians, but the citizens end up paying the price. The public sector has really stepped up as a consumer of debt. The Federal Reserve’s balance sheet is leveraged 77:1. Like I said, the absurdity, it just befuddles me.

What are numerator and denominator in that leverage ratio? What are the Fed's options for what to do with all of the assets it has purchased? Is it even clear what it intends to do?

The leverage ratio, as always, is a ratio between liabilities and equity. It has really no significance, as the liabilities of the Fed, which are mostly dollars, need not to ever be paid back.

Only in the case of inflation would the Fed need to reduce its balance sheet (i.e., sell the public debt or MBS). Do note that the profit of the Fed goes back to the government, thus the debt that is sitting there is an asset and liability of the government at the same time, canceling out. That is, the net debt decreases as the Fed buys bonds from the market. You may also view it as inflation or a money tax that pays back the debt.


Convergence in probability and convergence in distribution Im a little confused about the difference of these two concepts, especially the convergence of probability. I understand that $X_{n} \overset{p}{\to} Z $  if    $Pr(|X_{n} - Z|>\epsilon)=0$ for any $\epsilon >0$ when $n \rightarrow \infty$.

I just need some clarification on what the subscript $n$ means and what $Z$ means. Is $n$ the sample size? is $Z$ a specific value, or another random variable? If it is another random variable, then wouldn't that mean that convergence in probability implies convergence in distribution? Also, Could you please give me some examples of things that are convergent in distribution but not in probability?

I will attempt to explain the distinction using the simplest example: the sample mean. Suppose we have an iid sample of random variables $\{X_i\}_{i=1}^n$. Then define the sample mean as $\bar{X}_n$. As the sample size grows, our value of the sample mean changes, hence the subscript $n$ to emphasize that our sample mean depends on the sample size.

Noting that $\bar{X}_n$ itself is a random variable, we can define a sequence of random variables, where elements of the sequence are indexed by different samples (sample size is growing), i.e. $\{\bar{X}_n\}_{n=1}^{\infty}$. The weak law of large numbers (WLLN) tells us that so long as $E(X_1^2)<\infty$, that
$$plim\bar{X}_n = \mu,$$
or equivalently
$$\bar{X}_n \rightarrow_P \mu,$$

where $\mu=E(X_1)$. Formally, convergence in probability is defined as
$$\forall \epsilon>0, \lim_{n \rightarrow \infty} P(|\bar{X}_n - \mu| <\epsilon)=1. $$
In other words, the probability of our estimate being within $\epsilon$ from the true value tends to 1 as $n \rightarrow \infty$. Convergence in probability gives us confidence our estimators perform well with large samples.

Convergence in distribution tell us something very different and is primarily used for hypothesis testing. Under the same distributional assumptions described above, CLT gives us that
$$\sqrt{n}(\bar{X}_n-\mu) \rightarrow_D N(0,E(X_1^2)).$$
Convergence in distribution means that the cdf of the left-hand size converges at all continuity points to the cdf of the right-hand side, i.e.
$$\lim_{n \rightarrow \infty} F_n(x) = F(x),$$
where $F_n(x)$ is the cdf of $\sqrt{n}(\bar{X}_n-\mu)$ and $F(x)$ is the cdf for a $N(0,E(X_1^2))$ distribution. Knowing the limiting distribution allows us to test hypotheses about the sample mean (or whatever estimate we are generating).


How does one calculate compensating variation for multiple price change? For a single variable price change,

$$CV = - \int_{p_x^o}^{p_x^f} x_H(\rho,p_y,v^o)d\rho$$

$x_H$ is the Hicksian demand function for good $x$. What happens if both prices change? How does one calculate this? What about for an $n$ dimensional price vector where all the prices are changing?

Please give an example using double integrals.

I think the good way to do that is to introduce the Expenditure function which awesomely solves your problem.

The Expenditure function gives the money one has to spend to achieve a given level of utility, given a utility function $u$ and the vector of prices $p$.

$e(p,u^*)=min_{x \in \mathbb{R}_+^n,u(x) \geq u^*}p \cdot x$

Then you can express your compensating variation in two equivalent ways:

$CV=e(p_1,u_1)-e(p_1,u_0)=e(p_0,u_0)-e(p_1,u_0)$ where $p_0$ and $p_1$ are the old and new prices and $u_0$ and $u_1$ are the old and new utility. One can note that it can be translated as: if given $CV$ in compensation for the change, then the consumer would be indifferent to that change.


Is scalping tickets harmful? IMHO, scalping tickets is no different from legitimate arbitrage unless manipulative.

Iirc, arbitrage increases surplus and hindering scalping is setting a price ceiling which leads to deadweight loss or something like that.

So why do some states ban scalping tickets?

I'm assuming that such states think there is some perceived harm to their economy. Strangely enough, why tickets? Why not bags, clothes or phones?

There is a good Planet Money episode on ticket scalping; I recommend it.

The reason for banning ticket scalping has nothing to do with economic harm, and everything to do with making the arts (or sports, whatever) accessible to people of more-modest means. Consider the fact that artists could, if they wanted, just auction off all the seats to their shows, capturing all the surplus and putting scalpers out of business.*

If artists did this, however, lots of people wouldn't be able to afford to see popular artists perform. Many artists (the Planet Money episode uses Kid Rock as an example) want to try to make sure that their fans have a reasonable shot at attending, which means that they want to price the tickets low... but the only way this can work is if resale is illegal.

It's been suggested that artists (again, the same goes for sports teams) might benefit from making low-priced tickets available to fans for two reasons: because they plan on selling stuff to people once they're inside, and because an artist-fan relationship is hopefully not just a one-shot transaction. The idea is that fans who can attend the occasional show might be more likely to buy recordings, merchandise, and tickets in the future, providing the sort of long-running support that can keep an artist viable over many years.

  [P]erformers who undercharge their fans can paradoxically reap higher profits than those who maximize each ticket price. It’s a strategy similar to the one employed by ventures like casinos and cruise ships, which take a hit on admission prices but make their money once the customers are inside. Concert promoters can overcharge on everything from beer sales to T-shirts, and the benefits of low-priced tickets can accrue significantly over the years as loyal fans return.

*For the most part— there's some amount of resale that is sort of frictional, which arises from people not being able to attend a show and unloading tickets so they don't just eat the full cost, etc.


What is the real reason for china's stock market crash (August 2015)? I have read douzons of explanations and they all basically claim the following:

  China's stock market continued to boom despite the country's increasingly gloomy economic outlook, and this eventually created a bubble that popped.

The above sentence cannot be more vague and although everyone claims it's true, no one seems to give an explanation for why it is true.

Why is there a bubble? what is a bubble? Can someone explain to me in more depth how would a booming stock market accompanied with a slow growth economy create a crash?

Stock prices predominantly are a quantification of the company's future growth and profit prospects. These are expectations, and are partly based on how the specific company performs currently and has performed in the recent past, but also on what the "general economic outlook" looks like (expectations again): if it is "gloomy", we expect that this will constrain even the best of companies.

A usual "stock market bubble" is a situation where there is a unabated inflow of new investors (so new money, available to buy stocks, flows in the market), and where the general tendency of the prices of the stocks is to rise, and at a fast rate.

Experience has taught us that even in a sample of a few hundred companies, there is no way that the majority of them will excel in economic performance at the same time. So the "short-term general tendency of stock prices to rise" must come either from positive expectations on the "general economic outlook" (rather than the assessment of each individual company separately), or from a "Ponzi-scheme" climate, which is often the case at least in new stock markets in emerging economies: investors demand to buy stocks simply because they believe they will be able to quickly sell them at a higher price to somebody else, irrespective of what the "economic fundamentals" are, as regards actual economic performance. This fuels stock prices which in turn represent a signal to outsiders that indeed, they too can come in and play this game.

The thing with Expectations is that they may have no inertia: they can swing abruptly. So if in the middle of such a rising-stock-prices trend (which already may not be based on the actual economic performance, as said), comes a change of Expectations for the gloomier, suddenly investors "see" that the prices are over-inflated. The inflow of willing investors to buy at even higher prices suddenly stops, and those with the papers in their hands (but not with the money) start to accept lower and lower prices in order to reduce the damage. And this too happens fast.  And this is when "the bubble bursts".


Proxy for debt service? I'm trying to get info on debt service relative to GDP for Morocco. I know these sorts of figures exist for the US, Japan, etc., since a few authors use them, but Trading Economics does not seem to have anything on that and they did a pretty good job of recouping all the available info from the two most reliable sources (central bank and statistics institute).

Are you aware of a good proxy for debt service (i.e interest + amortization) for the public/private sectors?

There is data available on debt service for Morocco. You do not need a proxy. Google is your friend. These are some hits:

Trading Economics 1
Trading Economics 2
World Bank
Open Data for Africa
Central Bank of Morocco (open 2015 pdf, and search "debt service", and you will get the nominal value).


Best econometric models to fit when there is no control group? I am trying to study the effects of a program, where everyone gets treated. I have 50% of the population in t and the rest of the 50% in t+1 period. I understand this gives me a slight opportunity of creating a control group for just one time period and run something like DID. Or I can run a Segmented TS analysis.

I was wondering if there is any better way?

If you dont want to used DID, a simple cross sectional analysis would do with the addition of a dummy variable to indicate whether the individual was treated in period $t+1$ or not (implying they were treated in period $t$

for example if you were trying to see if  test scores of students change depending on when they have their class on monday or tuesday. your data set would be:

$$
\begin{array}{c|lcr}
n & \text{Test score} & \text{IQ} & \text{Class on monday} \\
\hline
1 & 60 & 80 &0\\
2 &80 &65 & 1 \\
3 & 90& 70 & 0
\end{array}
$$

By the incorporation of dummies you can just use regression methods for cross sectional data.


Utility Theory/Marginal Rate of Substitution: Can the marginal rate of substitution be calculated for a point of the budget line? This a person's budget line with various points, and their consumption, C*, and their endowment e, which is worth $5000 (unimportant). Also shows is their initial indifference curve. The difference curve and budget line intersect at e and e'.

Question: Why is the marginal rate of substitution of a, on the budget line, greater than C*?

I've been told any point that lies to the left of C* (the consumption optimum) has a marginal rate of substitution higher than the one at C* which is equal to the price ratio. Similarly, any point which lies to the right of C* has a marginal rate of substitution less than the one at C* which is equal to the price ratio.

The second indifference curve that C* would form part of is not shown in the diagram.

Why can I know the marginal rate of substitutions of points on the budget line if the marginal substitution is calculated on an indifference curve? Or, in this case, the MRS of C* is calculated by equating the slope of the indifference curve to the slope of the budget line. More to the point, how can I arrive at the answer that the MRS a > MRS C* if MRS can only be calculated on for a point on the indifference curve and not for a point on the budget line? Wouldn't all points on the budget have the same MRS implied by the line's slope?

There is something simple I'm not seeing.

Your claim that "MRS can only be calculated on for a point on the indifference curve and not for a point on the budget line" reveals a misunderstanding. Note that every point lies on some indifference curve. So each point on the budget line also lies on some indifference curve. We also know that all indifference curves are convex, since the utility function has Cobb-Douglas form.

At $C^*$, the optimal bundle, the indifference curve has to be tangent to the budget line, so it has the same slope as the budget line. At point $a$ the indifference curve (by convexity) intersects the budget line from above and therefore must be steeper than the budget line. Thus the MRS at $a$ is larger than the MRS at $C^*$.


Intuition behind Real Money Demand and Real Money Supply Standard undergraduate textbooks begin with an exposition of the  money market with the following equilibrium condititon:

$$\frac{M^{s}}{P}=L\left(R,Y\right)
$$

In the above, the LHS is what is defined as "Real Money Supply", and the RHS is defined as "Real Money Demand". My question is the following: does the fact that we divide the LHS by the price level render these two quantities in units of goods? Intuitively, I think these quantities represent the number of goods that can be bought for a given amount of nominal money. What are the units of these quantities?

They're in monetary units! Let's say an economy has a money supply of $100$ $mu$ and a price level of $1$. Another economy has the same money supply but a price level of $1.5$. Which economy has the bigger real money supply? The first, obviously. In the first hypothetical economy, you can think of the average transaction as one involving smaller amounts of currency. Real money demand will of course depend on nominal income $Y$. An increase in nominal income makes people demand more money because there's more transactions to be made.


How are low/middle/high classes defined mathematicaly? I am only looking for mathematical references. I think this belongs to econometrics but am not sure nor where to look at it specifically. I suspect the definition is given with some kind of weighted average where income and number of people with similar income are computed.

Actually there is no single agreed upon definition of low middle and high class. For example, Pew research center uses the following definitions:

  “Pew Research defines middle-income Americans as those whose annual household income is two-thirds to double the national median. For a family of three, that ranges from \$42,000 to \$126,000 in 2014 dollars.
  The lowest-income group earned \$31,000 or less for a family of three while the lower-middle group earned between \$31,000 and \$42,000 in 2014, according to Pew Research. At the most affluent levels, upper-middle-income, three-person households earned between \$126,000 and \$188,000, with the highest-income households topping \$188,000 in 2014 earnings.”

In economics research on income distributions usually people don’t explicitly define what low middle or high class is but rather they calculate deciles of income distribution and then also 99percentile and 99.9 percentile (that is the very rich and ultra rich).

But really you could define it in multiple ways splitting it by quartiles where the lowest quartile is lower class two quartiles in middle are middle class and upper quartile is upper class would also make sense. Saying lower class is just lowest 10% and upper class highest 1% and everything in between is middle and upper middle class could also make sense etc. So the ‘best’ way how to measure it is to certain degree arbitrary and different measures could be appropriate in different settings.


Why is a Normal Yield Curve a sign of a healthy economy? I think the question is pretty self explanatory. I'm just trying to understand the logic behind why an upward sloping yield curve indicates a good economy?

The prevalent hypothesis for the normal slope of the yield curve is due to a combination of the expectations hypothesis, and a liquidity premium.
Recall what the yield curve is measuring- it graphs Yield to maturity against a bond of maturity t, for different time horizons t. This yield to maturity is generally thought of as the interest rate.
First, the assumption is that we hold constant the risk profile of the bonds in question- think of just looking at the yields of T-Bills for different horizons.
The expectations hypothesis is straightforward: it specifies that the yield to maturity (upto an approximation) of a two year bond is the average of the current yield and the expected future yield. As such, if the yield curve is flat, this would mean that the interest rates are not expected to change. Generally speaking, the yield curve is upward sloping. This can still occur under constant interest rate expectations, because people have a preference for liquidity. As such, not having liquidity for 2 periods is more costly than 1, and hence this premium is reflected in a liquidity premium on the yield curve. However, if the yield curve has a sharp upward slope, the economy is expected to do well. This is because first, output is positively correlated with interest rates. This is, in part, due to the fact that a boom is correlated with increased spending, leading to inflation, and the government controlling money supply (inflation) by raising interest rates.


Long-term interest rate and stock market correlation What correlation is there between (1) long-term interest rates and (2) the stock market valuation? Please provide a simple intuitive explanation.

For example, as I understand it from recent news reports, rising long-term interest rates put pressure on the stock market. Why?

Many organisations borrow money to purchase shares (trading on margin). Their enthusiasm for doing this will depend on the interest rate. So lower interest rates means more borrowing for purchasing shares, which means prices rise.

A similar thing happens with other stuff that people tend to buy with borrowed money - like housing.


Why can we write any lottery as a convex combination of the degenerate lotteries? I know that a degenerate lottery is a lottery that yields outcome $n$ with probability $1$ and I also know the definition of convex combination: given $x_{1},x_{2}, \cdots ,x_{n} \in \mathbb{R}$, a convex combination of these points is a point of the form $\alpha_{1}x_{1}+...+\alpha_{n}x_{n}$ such that $\alpha_1+...+\alpha_n=1$.

But I am quiet confused about why we can write any $L=(p_1,...,p_n)$ as a convex combination of the degenerate lotteries $(L^1,...,L^n)$. Can someone please explain this for me? Many thanks!

Pick any set of non-negative $p_1,\dots,p_n$ such that $p_1+\cdots+p_n=1$. The convex combination of degenerate lotteries $L^1,\dots,L^n$ with the $p_i$'s can be written as
\begin{align}
p_1L^1+\cdots+p_nL^n&=p_1(1,0,\dots,0)+\cdots+p_n(0,\dots,0,1)\\
&=\bigl(p_1(1)+p_2(0)+\cdots+p_n(0),\;\dots,\;p_1(0)+\cdots+p_{n-1}(0)+p_n(1)\bigr)\\
&=(p_1,\dots,p_n).
\end{align}
This is just a lottery $L=(p_1,\dots,p_n)$.


Concept for "when a mechanism exists which can be exploited, people will exploit it" I dimly recall a concept, I think defined by an economist, although I cannot remember the details or context.  I think an example--apocryphal or not--was welfare recipients who would have more children in order to qualify for more welfare.  I know that's a controversial example and am not claiming that the    phenomenon is real or wide-spread, but it's just to give a sense what the concept is that I'm searching for.

In general the concept is something like: although you may create some sort of financial or political mechanism to serve one purpose, if people can use it for unintended personal gain then they will.

I was wondering if anyone can name the concept for me so that I can research it further.  Also if anyone knows relevant literature from Economics or Social Science journals or academic publications, I'd appreciate it.

I think the broad principle you are looking for is: people respond to incentives.

This is an important principle (some would say the most important in economics), with many implications and corollaries. But I think the particular implication you're looking for is unintended consequences.

So in your example, welfare was intended to alleviate poverty. However, because people respond to incentives, welfare has the unintended consequence that some people have more children.

(Other similar terms you may be thinking of: Cobra effect, perverse incentive.)


Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic? As we know that $Q*P=const.$ for Cobb-Douglas preferences, we can thus conclude that $\frac{dQ/Q}{dP/P}$ is always $-1$:
$$
QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P}
$$

Yes.
I have to include at least 30 characters in an answer, so let me repeat: Yes.


How to evaluate whether the synthetic control is good enough I'm using the synthetic control method to evaluate a state-level policy (using synth package in Stata). I've read the seminal ADH papers on CA tobacco & Germany reunification, but I still don't know exactly how to decide if the constructed synthetic state is a good fit. What we do at the moment is looking at the graph - to see if there's overlap between the synthetic and the real state. However, I feel this is not a very "robust" way...

Is there any measure that we can use or test on?

Edit:

After reading through reply (and papers mentioned again), I have another related (but maybe a bit nuanced) question on what to expect at the time of (or immediate after) intervention.

As shown in the two following figures from ADH (2010) and ADH (2015), there is a small effect in the same year of the intervention for CA tobacco Propostion 99, while in the Germany reunification study, the gap only becomes noticeable 2 years later. In some other papers using SC, there is an immediate effect (such as Cavallo et al. (2013)). I suppose as long as there is a consistent story to support the results, the short-term effect size of the intervention will not invalidate the fitness of synthetic control?

This is an excellent question, but unfortunately with no (yet) agreed upon answer.

Many authors such as in those seminal papers use cross-validation for this. This is basically what is implied in the ADH (2015) paper on German unification. If the synthetic control is good the MAPE (mean absolute prediction error) and RMSPE (root mean square prediction error) should be quite low. Additional cross-validation where the pre-treatment period is split into training and testing period is so far the common way to go, although there is no agreed upon value of how low the prediction errors should be, just that lower is always better.

Next it is also argued that examining if the trend in the countries from donor pool that are assigned non-zero weights and seeing if the pre-treatment trend in those donor countries seem to match the pre-treatment trend of treated country similar way as you would do for DiD (Difference in Differences) as argued here.

Lastly, as crazy as it may seem, yes visual inspection is actually recommended as well.

Beside the above you should also conduct sensitivity analysis by systematically trying to vary the number of countries in the donor pool and see if the resulting synthetic control has still a good fit. That's again also done by ADH 2015 and you will find it in almost all studies as well. Publishing your weights is also considered good practice.

Of course, doing a proper cross-validation is difficult if you have small pre-treatment sample. I was once working on a synthetic control study at one of the euro-system member's central bank with few colleagues where we had very short pre-treatment period due to data constraints. Instead of doing cross-validation we decided to just test whether the real pre-treatment series is statistically significantly different from the synthetic series using couple of non-parametric tests. When we presented the results and methodology at a workshop no objections to that were raised, and there were some very excellent econometricians present in the room. However, beside central bank's brief the study was not published because the results were not very interesting as placebo test showed results were not significant and we decided to abandon the project since we judged chance of publication to be low so the idea never got proper peer review, so take that as you will.

Response to edit:

as with classical DiD there is always an issue of potentially delayed effects or anticipation effects that would bias the result. However, in this case the authors argue that the increase after the reunification was actually part of the effect and not delayed effect. As the authors say:

  Our estimate of the effect of the German reunification on per capita GDP in West Germany is given by the
  difference between the actual West Germany and its synthetic version, visualized in Figure 3. We estimate that the
  German reunification did not have much of an effect on
  West German per capita GDP in the first two years immediately following reunification. In this initial period, per
  capita GDP in the synthetic West Germany is even slightly
  lower than in the actual West Germany, which is broadly
  in line with arguments about an initial demand boom
  (see, e.g., Meinbardt et al. 1995). From 1992 onward,
  however, the two lines diverge substantially. While per
  capita GDP growth decelerates in West Germany, for the
  synthetic West Germany per capita GDP keeps ascending
  at a pace similar to that of the prereunification period.

However, arguably this is a weak point of the paper.

Otherwise, if there would be a genuine delay in the effect you would have a problem that could be solved similarly as with DiD by identifying the 'correct' date where the treatment started to have an effect and identify the pre and post treatment period based on that.


Why is the annual transferred money worldwide quite different? The source below says
"According to this document from the US Treasury, SWIFT handles about \$5 trillion per day, or given about 250 business days per year, about \$1.25 quadrillion dollars a year.".
How much money is wire transferred every year worldwide?

However this source below says
"Worldwide, 230 million people send \$500 billion in remittances each year".
https://qz.com/775159/theres-a-500-billion-remittance-market-and-bitcoin-startups-want-in-on-it/

Why is the annual transferred money worldwide quite different?
Could you tell me the correct figure?

There is no contradiction here as not every transfer is a remittance.

  remit
  late Middle English: from Latin remittere ‘send back, restore’

It is my understanding that the word remittance is usually used to describe transfers by foreign workers to their home countries. From Wikipedia:

  A remittance is a transfer of money by a foreign worker to an individual in his or her home country.

These transfers may be conducted via SWIFT. As such they make up a small part of all SWIFT traffic, which would also include domestic payments, international business transfers, etc. So it is quite possible that the yearly volume of remittances is $\$5 \cdot 10^{11} $ whereas the yearly volume of SWIFT transfers is $\$1.25 \cdot 10^{15} $.


Is 'full employment' synonymous with 'the natural rate of unemployment'? Is the phrase 'full employment' synonymous with the phrase 'the natural rate of unemployment'? Parkin, et al. (2010) seem to use these two terms interchangably in chapter 20, but looking up these two terms in the Oxford dictionary of economics (Black, Hashimzade & Myles 2009) shows two different meanings: Black, Hashimzade and Myles state that 'full employment' relates to the equilibrium point in the labour market, whereas 'the natural rate of unemployment' is a Keynesian concept which looks at the level of unemployment given constant inflation.
My interpretation of this is that 'full employment' is a classical concept, whereas 'the natural rate of unemployment' is not, because it seems as if the latter varies according to the rate of inflation (a nominal variable).
EDIT: The answers I have gotten so far are incorrect in that they say that 'full employment' means '100% employment'. This is incorrect because full employment actually takes into account frictional unemployment. I quote two dictionaries on the definition of full employment:

A situation where the labour market has reached a state of equilibrium, so that those in the active labour force who are willing and able to work at going wage rates are able to find work, and the only remaining unemployment is frictional unemployment.
(Black, Hashimzade & Myles 2009)

The following definition comes from The Economist

Jobs for all that want them. This does not mean zero unemployment because at any point in time some people do not want to work. Also, because some people are always between jobs, there will usually be some frictional unemployment. Full employment means that everyone who wants work and is willing to work at the market wage is in work. Most governments aim to achieve full employment, although nowadays they rarely try to lower unemployment below the nairu: the lowest jobless rate consistent with stable, low inflation.

The Economist goes on to define frictional unemployment as

That part of the jobless total caused by people simply changing jobs and taking their time about it, because they are spending time on job search or are taking a break before starting with a new employer. There is likely to be some frictional unemployment even when there is technically full employment, because most people change jobs from time to time.

In South Africa, unemployment is defined as those people who are actively seeking work, but who have not found work. Frictional unemployment seems to be a looser concept: the citizen wants work, but is happy to give up their previous job. It may be entirely possible for them to get work, just that it's taking them a while to secure their next contract. For this reason, one cannot say that an economy with a surplus of jobs is not at full employment.
References
Black, J, Hashimzade, N & Myles, G. 2009. Oxford dictionary of economics.  3rd edition. New York: Oxford University Press.
Parkin, M, Kohler, M, Lakay, L, Rhodes, B, Saayman, A, Schöer, V, Scholtz, F & Thompson, K. 2010. Economics: global and Southern African perspectives. Cape Town: Pearson.

Full employment is a more general term, which has much less implication than natural rate of employment. My experience reading a lot of economics papers is that careful authors do not mix the two concepts.

Stricto sensu, full employment should mean 100% of the workforce is employed. But when we are talking about periods such as the trente glorieuses, the term is often used to mean "very low unemployment", which Keynesian economists associate with natural rate of employment. Politicians will most certainly never use the later, while economists may not always be very careful about which one they use.


How exactly does QE affect the value of the USD? A lot of people on the Internet refer to quantitative easing (QE) as a form of "legal money printing" when it is actually not. As such, many of these folks would thus erroneously say that QE leads to devaluation of the currency as a result of the increase in the supply of physical money. This is clearly not correct as QE increases electronic credit (in the form of their reserves) in commercial banks (as banks provide treasury bills and mortgage-backed securities in exchange), which they can then lend out to borrowers who require these funds.

QE aims to lower interest rates in the economy. I was wondering if the mechanism by which QE effects a devaluation of the currency is through the lower interest rates? That means to say, does QE cause the USD to depreciate because the lower interest rates disincentivises financial investments in the US. Hence, the demand for the USD falls as a result of less investors seeking for USD to buy US financial assets.

QE actually can increase money supply in the economy. We have different measures of money supply ranging from $M0-M4$. QE is not physical printing of banknotes so it does not expand $M0$ but it can expand wider money supply.

Following, the St. Louis Fed definition the QE is defined as:

  large-scale
  asset purchases—in the hundreds of billions of dollars range—of, for example, mortgage-backed securities
  and Treasury securities.

To the extent that these securities are bought with newly created bank reserves (which you even in your question assume) they will actually increase money supply measures beside the most narrow one which only includes physical notes and coins. In addition QE is supposed to also encourage banks to lend more which also further expands money supply.

In fact increase in the money supply is what is supposed to bring interest rates down as interest rates are determined at money market as you can see on the graph below taken from Blanchard et al. Macroeconomics an European Perspective.

Furthermore, when we talk about devaluation we are talking about currencies with fixed exchange rate. Dollar is not under fixed exchange rate regime.  Here it is more correct to talk about depreciation not devaluation (see the explanation of differences here).

The value of currency on foreign exchange depends on both money supply and interest rate. A simple basic classroom monetary model of exchange rate can be expressed as:

$$S= m-m_f -\phi (y-y_f)+\lambda(i-i_f) $$

Where $S$ is the exchange rate $m$ is the log of money supply, $y$ log of real output, $i$ interest rate and $f$ denotes foreign country. So QE can lead to depreciation through both its direct effect on money supply and through its effect on interest rates, however whether dollar depreciates or appreciates depends also on what the other economy, relative to which we value dollar, does.


Partial production function question Hi everyone, I am learning about the partial production function. I don't understand why a tangent it drawn next to the curve; I get that it shows the MPL. Does this mean diminishing marginal product of labour will be reached eventually? Also, it is always assumed that K0 is constant in partial production function?

Thank you

The tangent lines are drawn because they are trying to get you to think about the magnitude of the slope at each point on the production function. The marginal product of labour is the derivative of the production function, and will look like a decreasing function when drawn graphically, starting off with high values for low levels of labour, then decreasing to low values for high levels of labour. This corresponds to how the slope of the production function starts off steep and then gets flatter. Because the gradient decreases, this is called 'diminishing' returns.

We assume capital is constant when looking at this graph.


Log-linear version of the uncovered interest rate parity I am trying to derive the log-linear version of the uncovered interest rate parity under complete asset markets.

I know that the UIP condition is given by

$$(1+i_t)=(1+i^*_t)\frac{S_{t+1}}{S_t}$$

I have seen in papers that the log-linear version is simply given by

$$\hat{i}_t-\hat{i}^*_t=\hat{S}_{t+1}-\hat{S}_t$$

but I cannot see how this is derived. According to me, the log-linear version should be

$$\frac{i}{1+i}\hat{i}_t-\frac{i^*}{1+i^*}=\hat{S}_{t+1}-\hat{S}_t$$

Could someone please write down all steps to obtain the log-linear version of the UIP?

Thank you very much

It’s derived as follows. First start with original equation.

$$(1+i_t)=(1+i^*_t)\frac{S_{t+1}}{S_t}$$

Take natural logs of both sides:

$$\ln(1+i_t)=\ln(1+i^*_t)+\ln(S_{t+1}) -\ln(S_t)$$

Now you just use the following:

$$s_t=\ln(S_t)$$

And use the well known fact that for small values of $i$ the following approximation holds:

$$\ln(1+i)\approx i$$

And rearrange to get

$$\hat{i}_t-\hat{i}^*_t=\hat{s}_{t+1}-\hat{s}_t$$

PS: Also actually the equation you derived is not log-linearized as it’s not linear in its log parameters


Does open source software contribute to GDP? Does open source software contribute to the GDP of a nation? If yes then how, and how does it depend on the increase in usage? For instance, would an increase in the usage of open source software increase GDP, or would it decrease GDP?

Open source software does influence GDP in a number of ways, both positively and negatively.  The net effect of greater open source usage will depend on the economy, I think particularly on whether the economy produces or imports most of the closed-source software that is being displaced by greater open-source usage.

Here are some of the mechanisms by which open source software influences GDP:

People still pay for some open source software through donations, a mechanism very similar to the purchase price of closed source software.  E.g. the Mozilla Foundation received $4.5 million in contributions in 2015 (see p4).
Companies provide a wide range of services that rely on open source software.  In some cases this is closer to closed source development (e.g. Red Hat), where companies pay to use software systems -- even though the underlying software is open source, they pay for an "enterprise solution".  Maybe 90% of web servers are open source, but companies are still paid to provide those servers, same with companies providing virtual machines.
The use of open-source software by companies or workers that could not afford closed-source equivalents improves productivity and probably therefore GDP.
Most obviously, the use of open source software replaces some closed-source software reducing the purchase and production of closed-source software.  More closed-source development is paid, so this would reduce GDP in the country where the closed-source software is made.

As I mentioned, whether an increase in open-source usage is likely to increase GDP probably depends primarily on whether most closed-source software is domestically produced or imported.  If closed-source software is domestically produced, and this production is partly replaced, GDP could go down, unless this if offset by open-source-related services.  However, if closed-source software is mostly imported (the case in the vast majority of countries worldwide), only the value addition in wholesale and retail shows up in GDP.  Using open source instead will free up foreign exchange that can be used elsewhere.  If a chunk of this buys capital goods instead, that should boost GDP in the medium term.


What does it mean to identify structural shocks in macro models? What does it mean to identify structural shocks in macro models? Sometimes, it seems to mean just disentangling VAR innovations into 'structural' shocks which may or may not have any economic interpretation. Here, people use Cholesky decomposition and so on.
Other times, it seems identifying structural shocks mean imposing economic interpretation on the structure shocks you identified using for example the Cholesky technique. As an example, one may identify the stochastic component of the federal funds rate in a SVAR model as a monetary policy shock by assumption or by using some rigorous way as in Gali who identifies technology shocks step by step. But he could have impose it, right??

A great up to date treatment that I keep coming back to is Ramey (2016). It discusses identification in both articles you refer to.
The short answer to your question is that obtaining structural shocks is always based on theoretical reasoning and assumption imposition including in both of your examples (e.g. Christiano Eichenbaum Evans (1999), Gali (1999)).
On page 5 Ramey writes:

I  view  the  shocks  we  seek  to  estimate  as  the  empirical  counterparts  to  the  shocks  we  discuss  in  our  theories,  such  as  shocks  to  technology,  monetary  policy,  fiscal  policy,  etc.  Therefore,  the  shocks  should  have  the  following  characteristics:

(1)  they  should  be  exogenous  with respect to the other current and lagged endogenous variables in the model;

(2) they should be  uncorrelated  with  other  exogenous  shocks;  otherwise,  we  cannot  identify  the  unique  causal  effects  of  one  exogenous  shock  relative  to  another;  and

(3)  they  should  represent  either  unanticipated movements in exogenous variables or news about future movements in exogenous variables.

Any shock satisfying (1) - (3) can be used to make statements about the causal effect of an unexpected change to a variable on contemporary and future values of all variables in the model, which is the main goal of contemporary econometrics.
It seems that in earlier times researchers were more cavalier with identification, which is reflected in for example the oirf procedure in STATA, which will happily estimate "causal" effects based on orthogonalizing the residuals from the reduced form model, but this reasoning appears to be outdated. I think its contemporary version are  sign restrictions a la Uhlig (2005), which also stem from theory.


Is my solution to finding the Hicksian demand correct? Maximize $x_1^{1/2} + x_2^{1/2}$ subejct to the budget constraint Maximize $x_1^{\frac{1}{2}} + x_2^{\frac{1}{2}}$ subejct to the budget constraint $p_1x_1+p_2x_2=m$
Setting up the Lagrange and finding the first-order conditions:
$L(x_1, x_2, \lambda)=x_1^{\frac{1}{2}} + x_2^{\frac{1}{2}}+\lambda(p_1x_1+p_2x_2-m)$
$\frac{\partial L}{\partial x_1}=\frac{1}{2}x_1^\frac{-1}{2}+\lambda p_1=0$
$\frac{\partial L}{\partial x_2}=\frac{1}{2}x_2^\frac{-1}{2}+\lambda p_2=0$
Equating these,
$2p_2x_1^\frac{-1}{2}=2p_1x_2^\frac{-1}{2}$
Solving for $x_1$ and $x_2$, we get
$x_1=\frac{p_2^2x_2}{p_1^2}$
$x_2=\frac{p_1^2x_1}{p_2^2}$
Substituting these into the budget constraint and solving to find the Hicksian demand ($x^*(p,m)$),
$p_1x_1+p_2x_2=m$
$\frac{p_2^2x_2}{p_1}+p_2x_2=m$
Solving for $x_2$,
$x_2(\frac{p_2^2}{p_1}+p_2)=m$
$x_2^*=\frac{m}{p_2}.\frac{p_2}{p_1+p_2}=\frac{m}{p_1+p_2}$
We do the same thing for $x_1$ and we get
$x_1^*=\frac{m}{p_1+p_2}$
We now have the Hickdian demands, substitute these into the objective function to get the indirect utility function and by duality, we know, $V(p,E(p,u))=u$,
$V(p,m)=(\frac{m}{p_1+p_2})^\frac{1}{2}+(\frac{m}{p_1+p_2})^\frac{1}{2}=u$
Solving this to find m,
$\frac{2m^\frac{1}{2}}{p_1^\frac{1}{2}+p_2^\frac12}=u$
$m^\frac{1}{2}=\frac{u}{2}(p_1^\frac{1}{2}+p_2^\frac{1}{2})$
$m=[\frac{u}{2}(p_1^\frac{1}{2}+p_2^\frac{1}{2})]^2$
Finally we also know by duality that $E(p,V(p,m))=m$, therefore
$E=[\frac{u}{2}(p_1^\frac{1}{2}+p_2^\frac{1}{2})]^2$
To find the Hicksian demand we use Shephards Lemma (take the partial derivative of the expenditure function)
$\frac{\partial E}{\partial p_i}=2.\frac{u}{2}(p_1^\frac{1}{2}+p_2^\frac{1}{2}).\frac{1}{2}.\frac{u}{2}.p_1^\frac{-1}{2}$
Simplifying this
$h_1^*=\frac{u^2}{4}.p_1^\frac{-1}{2}(p_1^\frac{1}{2}+p_2^\frac{1}{2})=\frac{u^2}{4}(p_1^\frac{-1}{4}+p_2^\frac{1}{2})$
Is this correct? (I've tried to make each of my steps really clear so this is easy to follow)

Here is what I am thinking (and i could have made a mistake since CES algebra is a bit tedious)
First you have the MRS condition from Lagrange which boils down to
$$p_1 x_2^{\rho-1} = p_2 x_1^{\rho-1}$$
from here I always aim to reconstruct the utility function (because it is a constant equal to the max utility or in this instance you know it will satisfy constraint and be u). So to get the utility function to appear I do this
$$p_1^{\frac{\rho}{\rho-1}} x_2^{\rho} = p_2^{\frac{\rho}{\rho-1}} x_1^{\rho}$$
I then add $p_1^{\frac{\rho}{\rho-1}} x_1^{\rho}$ to both sides
$$p_1^{\frac{\rho}{\rho-1}} x_2^{\rho} + p_1^{\frac{\rho}{\rho-1}} x_1^{\rho}= p_1^{\frac{\rho}{\rho-1}} x_1^{\rho}+p_2^{\frac{\rho}{\rho-1}} x_1^{\rho}$$
and isolate
$$p_1^{\frac{\rho}{\rho-1}}( x_2^{\rho} +  x_1^{\rho})= (p_1^{\frac{\rho}{\rho-1}}+p_2^{\frac{\rho}{\rho-1}} )x_1^{\rho}$$
utility function appears on LHS and I impose constraint
$$p_1^{\frac{\rho}{\rho-1}}u= (p_1^{\frac{\rho}{\rho-1}}+p_2^{\frac{\rho}{\rho-1}} )x_1^{\rho}$$
finding
$$\frac{p_1^{\frac{\rho}{\rho-1}}}{(p_1^{\frac{\rho}{\rho-1}}+p_2^{\frac{\rho}{\rho-1}} )}u=x_1^{\rho}$$
which reduces to
$$\frac{p_1^{\frac{1}{\rho-1}}}{(p_1^{\frac{\rho}{\rho-1}}+p_2^{\frac{\rho}{\rho-1}} )^\frac{1}{\rho}}u^\frac{1}{\rho}=x_1$$
Inserting value of $\rho = 1/2$ I get
$$\frac{p_1^{-2}}{(p_1^{-1}+p_2^{-1} )^2}u^2=x_1$$


Oil Price Chart Scale I found the axis on the following graph of crude oil prices over 1950-2015 from MacroTrends surprising.

The y-axis labels are 20, 40, 60, 80, 100, ...but they are not equidistant. Why?

Usually, when people use non-equidistant axis, it is because they want to emphasize some variation more than others. For example, if most of your data is between 0 and 1, but you have one outlier on 100, then an equidistant axis would make it hard to analyze most the variation, because it emphasizes the wrong parts.

In this case you have a log-scale, which is a simple nonlinear axis that (in general) emphasizes small values over larger ones. Whether that makes sense with oil prices, is - to me - unclear.


What is the standard error on quarterly GDP figure? The government and media seem to judge whether it is in a good economy right now based on its quarterly GDP figure.

However, I wonder how its figure is trustworthy. Even if the quarterly GDP is +1.2%, the actual figure should be +0.3 to +1.9% in 95% CI. Or -0.8% to 3.0%. Or something like that. But the point is that it should never be at the exact point, especially given that the figure is frequently updated later.

So how much standard error is it considered to include?

Good question!

I've never seen standard errors reported alongside official figures (e.g. here for US, here for UK). You would expect they could calculate/report them, since GDP is computed from samples (so randomness is explicitly involved in the design). It is more common to see standard errors reported for GDP forecasts though. For example, check Figure 2.1 of the latest Bank of England Inflation report (data here).

Regarding GDP, what is very common however is the publication of revised figures. That is something both the US and UK include in their quarterly reports (see links above), and also common in many (in not all) countries. Comparing actual and revised figures gives you an idea of the uncertainty involved on preliminary estimates. For example, in the release notes for quarterly GDP of the US economy (see link above), towards the end there is a section called "Updates to GDP", which contains:

  BEA releases three vintages of the current quarterly estimate for GDP:  "Advance" estimates are
  released near the end of the first month following the end of the quarter and are based on source data
  that are incomplete or subject to further revision by the source agency; “second” and “third” estimates
  are released near the end of the second and third months, respectively, and are based on more detailed
  and more comprehensive data as they become available. [...]

  The table below shows the average revisions to the quarterly percent changes in real GDP between
  different estimate vintages, without regard to sign.

The Bank of England also provides its estimates of the past uncertainty (what they call "backcast", in opposition to "forecast"). This is available in the last sheet of this dataset.

Another interesting example comes from the Euro Area. Eurostat produces quarterly "Preliminary GDP flash estimates" for the Euro Area for selection of periods: 30, 45, and 60 days after the end of the quarter. As the page states, there is "a trade-off between timeliness and accuracy". An example of subsequent revisions are:


Effects of Eliminating Government Controls on Supply (organ donation) I was having a discussion with somebody about organ transplants.   I gave the free market pov that allowing the sale of organs would greatly increase the supply, and the all-in price would come down greatly if everybody knew that they (or their heirs) could profit by making their organs available (it might even encourage a few people to adopt a healthier lifestyle in order to not destroy a valuable asset, and maybe encourage businesses - like financial middlemen - to get into the game).
The person I was discussing with agreed with the argument -- in theory -- but countered that it was unfair that a rich person would have a better opportunity to get a transplant and that, indeed, a poor person's best (and maybe only) chance was to use the current lottery system.
My question -- does anybody know an example of something analogous to human organs whose supply was controlled, whose cost was extremely high and supply very low, and then became available on the market and as a result became readily available because of increased supply and/or lower price?  My one possible answer is the abolition of rent controls.  I was hoping for an example that was more understandable to my friend.  Perhaps certain items that were, by law, exclusively available to the aristocracy in the past, and that later became something that everybody was able to afford.

The Iranian organ market
It might be worth looking into the organ market in Iran. Unlike in other countries, it is legal to sell your kidney to patients who need a new one. The process is regulated and charities actively help pay for patients who cannot afford to pay the donor themselves.
The result is that a kidney, which would cost more than $100.000 on the global black market can be bought for a few thousands of dollars. This also highlights an overlooked problem with the concern that a free market would put rich people in front of the line. The fact is that very rich people can always find a way to acquire the goods they want. If they do it illegally, they can hire expert lawyers to get them out of trouble.
The example of Iran shows that allowing people to sell their organs for profit will lower the barrier to entry to the point where middle class people could conceivably afford one. It also becomes possible for charities to afford to buy organs for the poor. This would not be possible if they were to pay the black market price or wait indefinitely to win the waiting-list lottery.
https://en.m.wikipedia.org/wiki/Kidney_trade_in_Iran


From Discrete to Continuous time: Total Differential I'm trying to derive an HJB from a discrete time setting. At some point, I am left with

$$ \lim_{\Delta\to 0} \frac{v(c_{t+\Delta}, u_{t+\Delta}, t+\Delta) - v(c_{t}, u_{t}, t)}{\Delta}$$

and am not sure what to do. If $\Delta$ was only in one argument, this would be a partial differential. My hunch is that this is the total derivative in $t$, but I dont know how to show that.

How do I proceed with the expression above?

You can separate your function in three terms by writing
\begin{align}
& v(c_{t+\Delta},u_{t+\Delta},t+\Delta)-v(c_t,u_t,t) = \\
& v(c_{t+\Delta},u_{t+\Delta},t+\Delta)-v(c_t,u_{t+\Delta},t+\Delta) \\
+ & v(c_{t},u_{t+\Delta},t+\Delta)-v(c_t,u_t,t+\Delta) \\
+ & v(c_t,u_t,t+\Delta)-v(c_t,u_t,t)
\end{align}
When you divide by $\Delta$ and take the limit $\Delta \rightarrow 0$, the first expression converges to $\dfrac{\partial v}{\partial c} \dfrac{dc}{dt}$, the second expression to $\dfrac{\partial v}{\partial u} \dfrac{du}{dt}$, and the third expression to $\dfrac{\partial v}{\partial t}$. Therefore your total derivative equals
\begin{equation}
\dfrac{\partial v}{\partial c} \dfrac{dc}{dt} + \dfrac{\partial v}{\partial u} \dfrac{du}{dt} + \dfrac{\partial v}{\partial t}
\end{equation}


What are the pros and cons of a "long stock, short call" position compared to a "short put"? The profit-loss diagram for the "long stock, short call" position and the "short put" position are almost exactly the same, except that for the former, you may be able to profit more when the stock goes up as, in addition to the premium collected from selling the option, you also get to profit from capital gains and dividends from ownership of the stock. Additionally, you are able to allow for a greater decrease in the stock price before you start incurring a loss. However, to take two positions, there may be more transaction costs compared to just taking a "short put" alone. Are there any other pros and cons that I have not considered?

The primary consideration in practice is that the initial investment is larger if you are long the stock, and thus consumes more balance sheet.
The next consideration is that if you don’t hold to maturity, the implied volatility exposure is opposite (and the associated greeks) for the positions.
After that, there are only voting rights, jurisdiction-dependent tax issues, and the reality that one instrument might be mis-priced.


How many people in the world were living below 15 dollars a day in the last decades? The question I really want to make is if poverty is decreasing of increasing worldwide, but since I guess there is no way to objectively define poverty, that question doesn't fit in here. I was always suspicious that when they release the poverty statistics, they always release the extreme poverty figures and not the poverty figures. For example, recently I found people living under 10 dollars a day either was increasing or it's stagnant (green line, as if they weren't poors). So this leads me to believe poverty is conveniently defined as for showing "poverty is decreasing worldwide". That's why I would like to know if there is a way to figure out how many people leaves under 15 dollars (or any other figure between 10 to 15 dollars, if you like) which according to my country statistics for poverty it would be poverty. By seeing the green and blue lines in this graph the best guess is it's increasing, but I don't have data to sustain that assumption.

So the question is, how many people in the world were living below 15 dollars a day in the last decades?

Most of the "official" statistics compiled in international organisations use some thresholds like the one shown in the graph. Common for instance are the one by the World Bank (data here and report here).

Therefore, unless you find such data already computed, it is not possible to tell.

There is one imprecise alternative though. You can use this online tool to compute global poverty based on any threshold you like (using annual income in £). For example, 15 US dollars correspond to roughly to £11.64 (as of 31/08/17, 13:25 BST), which amounts to a yearly (365 days) income of £4,250, which yields:

As the FAQ explains, this analysis is based on data from the World Bank, is valid for 2008, and assumes a population of 6.69 billion. Therefore, based on the above result, 5.34 billion people lived below $15 a day in 2008. This is "sort of" consistent with the data in the graph you posted, in my opinion.

Unfortunately, such analysis is only valid for 2008.


Is Adam Smith's "stock" an archaic version of "capital"? In The Wealth of Nations, Adam Smith uses the word "stock" many times, but not with the meaning we ascribe to it today (supply of an asset, inventory). I take it that he refers to capital, as in a businessman who deploys capital into a business.
For instance:

Such parts only of the produce of land can commonly be brought to market, of which the ordinary price is sufficient to replace the stock which must be employed in bringing them thither, together with its ordinary profits.

Is my assessment correct?

Сельскохозяйственные продукты могут, в виде правила, поступать на
рынок только в таком количестве, чтобы обычная цена их была достаточна
для возмещения капитала, необходимого для доставления их туда, и для
оплаты обычной прибыли.

This is the same place, but from Russian translation of the book. Here "stock" was translated as "капитал", which is a Russian word for "capital".
So, I think yes. It seems that you're right.


How to draw the indifference curves for $u(x,y) = min(2x,y)+ y?$

I don't understand how we can plot it. I know that there's going to be minimum so I am familiar with the cusp shape of perfect complements. But this looks like a quasilinear utility function. So how can I systematically plot it?

https://www.desmos.com/calculator/m3yzlrz1rs

Here, as you can see when $2x>y$, $U=y+y=2y$ (Right hand side to the line of kink of $2x=y$
and when $2x<y$, $U=2x+y$
So, the Black curve denotes the utility function of 10 level of utility but you can draw for any with the kink line as $2x=y$.


What is the relationship between indirect utility function and the expenditure function? What is the relationship between indirect utility function and the expenditure function? Explain what accounts for this relationship.

This classic picture from Mas-Colell, Whinston & Green should help you:


Decision Theory Question: Existence and uniqueness of the certainty equivalent of p Let $X = (x_*,x^*)$ be an interval in the real line and denote by $\Delta(X)$ the set of simple probability distributions on $X$. Consider a preference relation $\succcurlyeq$ on $\Delta(X)$ that satisfies the axioms of expected utility theory. If $\succcurlyeq$ displays monotonicity with respect to first order stochastic dominance and risk aversion then for all $p \in \Delta(X)$ the certainty equivalent of $p$ exists and is unique.

Sketch of the proof:

1) We define the certainty equivalent of lottery $p$: $CE_p \sim \int_{X}u(x)p(x)dx$

2) We know that if $p$ FOSD $q$ then $p\succcurlyeq q$

3) Because of risk aversion: $\int_{X}u(x)p(x)dx \leq u(\int_{X}xp(x)dx) =u(p)$

4) We want to show that $\exists$ a lottery, call it $s$ such that $CE_p \sim s$; in this respect (from 3 above) we know that $p \succcurlyeq s$; We then pick a particular lottery $q$ such that $p \succcurlyeq q$

5) Since by assumption $\succcurlyeq$ on $\Delta(X)$ satisfies the axioms of expected utility theorem (in particular continuity) there exists a unique $\alpha$ such that  $\alpha p + (1-\alpha) q \sim s$ ( see MWG p. 177). We therefore proved that $\exists$ a compound lottery $s$ that is the certainty equivalent of lottery $p$.

QUESTION: Am I missing any detail in the proof?

Your notation is a bit misleading: it would be better to write $\mathbb{E}u(p)$ or $U(p)$ for the expected-utility associated with $p$ instead of $u(p)$, and $u(\mathbb{E}p)$ for the utility of the expected value of $p$. Formally $u$ is defined on $X$ and not on $\Delta(X)$.

Regarding your proof, it seems to me that: $(i)$ you don't explain how to find $s$; $(ii)$ you don't find a certainty equivalent, because $s$ is a lottery. What you want to find is a sure monetary prize, i.e. a degenerate lottery, that the decision-maker values equally as the lottery $p$.

For instance, you can notice that, by the monotonicity of $u$,
\begin{equation}
u(x_{*})\leq \int_{X}{u(x)p(x)dx} \leq u(x^{*})
\end{equation}

In addition, the function $u:x \rightarrow u(x)$ is continuous. Therefore, by the intermediate value theorem, there exists $CE_p \in [x_{*},x^{*}]$ such that $u(CE_p) = \int_{X}{u(x)p(x)dx}$.

For the uniqueness, imagine that $CE'_p$ is another certainty equivalent of $p$, i.e. that $u(CE'_p)=u(CE_p)$. Since $u$ is strictly increasing (which can be seen as a consequence of the monotonicity with respect to first-order stochastic dominance), we obtain $CE'_p=CE_p$.

Notice that you don't need risk aversion to prove the result, but further implies that $CE_p \leq \mathbb{E}p$.


Comparing GDP contractions between Russia and US I was reading Rogoff's piece on the Russia's economic outlook, and in a paragraph, he states

  The shock to the real economy has been severe, with Russia suffering a decline in output in 2015 and 2016 comparable to what the United States experienced during its 2008-2009 financial crisis, with the contraction in GDP totaling about 4%.

I'm wondering how did they reach this figure. I was trying to redo the calculations, this time with OECD data on GDP, but none of the figures obtained are comparable - I just did $GDP_{t+1}/GDP_{t}=1+gr$ For Russia, I got 6-7%, and USA 2-3%,  depending whether we use GDP or GDP per capita.

Any help would be appreciated.

In Rogoff's article (at least current version) the first sentence you quote links to IMF's World Economic Outlook Database.

My guess is that when he is referring to output he means Gross domestic product, constant prices. Looking up the numbers in the database we have 63038.4 billions of 2011 rubles in 2014 and 61097.5 in 2016 which translates to 3.1% decline (negative growth).

If I use per capita numbers than that also gives 3.1% decline which I guess is "comparable" to 4% decline.


Central Banks, Large Scale Asset Purchases and Inflation First, the overview:

With the fractional reserve system, money/credit is primarily created through loans on deposits but the bank is required to maintain their deposits up to a certain amount (roughly 10% I think).  The other primary avenue of money creation is by the Federal Reserve printing money, but there is severe reservations on printing money given past episodes of hyper inflation, though recent events with quantitative easing and large scale asset purchases, the Fed's balance sheet has reached over 4 trillion dollars.  The Fed has stated that any profits accumulated from these assets will be reinvested into new securities when they mature and any additional profit will be deposited into the treasury.

Here is my question:

If the federal reserve were to regulate the banking industry so that fractional requirements were raised to something like 50% on all future deposits, that would have an appreciating effect on the dollar since the rate of increase in the supply of dollars needs to keep up with the growth of the economy every year.  If the Fed offsets this appreciation with additional asset purchases by printing money, the Fed's revenue/balance sheet would increase... and over time that excess profit could start to make up the overwhelming portion of the fiscal budget (which could take decades or centuries)...  Historical issues with the central bank funding the budget have always resulted in hyper inflation, but with this work around, where the funding of the budget was not coming from the direct printing of money but from the profits from security purchases as they matured, hyper inflation would be avoided, right?

Please explain why this is a bad idea...  In theory the banking system wouldn't have a noticeable impact since, as additional money is created to offset the increased fractional requirements, that money will be deposited into the banking system (where else would it go) increasing holdings and increasing the money available to be lent out...

This is in essence what the Japanese have been doing with paying off Government debt in order to prevent their currency from appreciating naturally (instead of raising reserve requirements), right?

Response (wasn't allowed to respond at length so I'm making an edit to my original post):
Lending would have "some" reductions, but it wouldn't be as severely impacted as it would if it weren't offset by more asset purchases, purchases that are then deposited into banks, expanding the monetary base which then expands the amount to be lent out...  There's also the argument that, by replacing tax's with the profits from maturing assets, there would be a stimulating effect on GDP, which would cause the dollar to appreciate, which would then require more printing or lending to maintain stable prices... though of course it would take a significant amount of time for profits on maturing assets to become a sizable portion of the fiscal budget, but of course the FED isn't purchasing securities with the idea of maximizing revenue so I'd imagine their rate of return could get a little better if they really tried and this where to become a primary mandate...

I'm definitely not saying raising the supply of dollars increases their value, the opposite actually...  My argument says raising reserve requirements would reduce the supply of dollars, but printing would offset this reduction, maintaining the equilibrium.  I suppose an implicit assumption I didn't spell out was that the amount of dollars printed would not equal the number of dollars no longer being lent out since fractional banking has the multiplier effect, i.e. today one dollar created by the FED is equivalent to 9~10 dollars lent out in the banking system.

Here is my question:

  If the federal reserve were to regulate the banking industry so that
  fractional requirements were raised to something like 50% on all
  future deposits, that would have an appreciating effect on the dollar
  since the rate of increase in the supply of dollars needs to keep up
  with the growth of the economy every year. If the Fed offsets this
  appreciation with additional asset purchases by printing money, the
  Fed's revenue/balance sheet would increase...

Reserves are essentially a deposit at the Federal Reserve by banks. Banks have a minimum required level of reserves; anything beyond that are excess reserves. As a result of "Quantitative Easing", American banks already have large amounts of reserves. Raising the reserve requirement would just change the status of the reserves from excess to required, and could easily have little effect on the economy. The precise effects of Quantitative Easing on the economy are debated, but they are certainly not very obvious.

In other words, a policy very similar to raising required reserves was already tried, and had little observable effect.

One thing to keep in mind that reserve creation is distinct from bank money creation. When a bank extends a loan, it creates an asset (the loan) and a liability (the deposit) simultaneously. This step is done independently of existing reserves, or central bank activity.

However, this deposit creation creates a need for extra reserve holdings (during the next reserve accounting period). If excess reserves exist in the banking system, the bank can just go out and borrow the reserves from other banks. That is, lend first, get reserves later. If excess reserves do not exist, the central bank has to create some - if it wants the inter-bank rate to remain under control. Otherwise, some banks will fall short of regulatory requirements, and are effectively illiquid, and will be willing to borrow at extremely high rates to meet regulatory requirements. In other words, reserve creation follows deposit (bank money) creation.

(In case it is not obvious, once the Federal Reserve creates reserves, about the only way they can be destroyed is by currency (notes and coin) withdrawals, or by net tax payments being transmitted to the Treasury. An individual bank can transfer/lend them to another bank, but this does not change the amount outstanding. Therefore, the Fed was able to force an increase of reserves without raising requirements.)

Textbook descriptions of fractional reserve lending tend to be oversimplified. Only some accounts are covered by reserve requirements, and banks have been working techniques to minimise their costs for decades. A lot of "money" is in other money market instruments ("shadow banking") which are not covered by reserve requirements. Raising reserve requirements has the effect of making regulated banks less competitive versus their shadow banking competitors.

Setting a reserve requirement of 50% (for example) would mean that a bank might have to issue a \$50 bond in order to be able to make a loan of \$100 safely. (It has to finance the massive amount of reserves that are imposed on the asset size of its balance sheet.) It would be borrowing in the bond market in order to leave money on deposit at the central bank at the overnight rate.

Balance sheet assets:

\$100 loan; and
\$50 reserves.

Liabilities:

\$100 deposit; and
\$ 50 bond.

The spread on the \$100 loan would have to be increased to make up for the negative spread on the \$50 in reserves (versus the bond). The banking systems ability to lend would be largely crippled, and firms would be forced to switch to alternative sources of financing. If firms cannot get financing, they cannot invest or hire more people, and that makes capitalists and politicians unhappy.

The main economic effect of required reserves is that it is a means of forcing banks to lend to the central bank at a low rate. Until the Fed was given the right to pay interest on reserves in 2008, banks received no interest, and so reserves were an interest-free loan to the government. Even if reserves pay interest, it is at an administered rate set by the central bank (which effectively becomes the short-term risk-free rate). Banks have no choice but to accept that rate of interest, whereas Treasury bill/bond rates are set in auction. (In practice, Treasury bill rates trade close to the policy rate.)

This policy of forcing banks to lend to the government (via the central bank) is often called "financial repression." This matters more for countries with poorly developed bond markets, but the U.S. Treasury can lock in low rates for a very long time without much difficulty.

  and over time that excess profit could start to make up the
  overwhelming portion of the fiscal budget (which could take decades or
  centuries)... Historical issues with the central bank funding the
  budget have always resulted in hyper inflation, but with this work
  around, where the funding of the budget was not coming from the direct
  printing of money but from the profits from security purchases as they
  matured, hyper inflation would be avoided, right?

What percentage of bonds are purchased by the central bank is not an issue. The Bank of Japan has been holding large amounts of Japanese Government Bonds for years, and inflation has not budged. The key is that the deficit is very large (working from memory, some cases were 30+% of GDP), and they were often associated with losses of productive capacity. In other words, the big deficits were the problem behind hyperinflation; a central bank buying existing debt is just a reshuffling of government liabilities.

Attempting to run "too large" deficits and trying to use central bank purchases of bonds reserve requirements to control inflation will not work in the long run. The velocity of money would just increase as people move towards shadow banking. If done for a long enough time, people can just switch over to using a foreign currency, which is usually a critical step towards hyperinflation.

In summary, running a deficit of 1% of GDP and having the central bank buy all the debt (monetising it) is not going to have much of an impact on inflation. (The recent experiments in quantitative easing provide a test case.) Running a deficit of 30% of GDP is probably going to cause serious inflation (unless the country switches over to rationing, such as in World War II), and what the central bank does with its balance sheet is not going to make a big difference.


How Do I Calculate the After-Tax Equilibrium Quantity of a Supply and Demand Graph? Suppose the supply of a good is given by the equation $Q_S = 360*P_S - 720$. And the demand for a good is given by $Q_D = 960 - 120*P_D$. The government decides to levy a tax of \$2 per unit on the good, to be paid by the seller.

And I must find the equilibrium quantity of the curves, after the \$2 tax has been taken into account for. I know the equilibrium quantity is 540 before the tax based on the following calculations:

$Q_S=Q_D$
$360P-720 = 960-120P$
$480P = 1680$
$P = 3.5$
If we sub in 3.5 into both equations ($Q_S$ and $Q_D$) then we get 540.

Therefore, the equilibrium quantity is 540 before taxes have been taken into account. However, I am unsure how to figure out the equilibrium quantity after the tax.

Does anyone know how to go about solving this issue?

All help is appreciated.

Implementing @dismalscience comment suggestion, the unit tax burdens the suppliers. So the demand schedule is not affected, only supply. How? Since the tax is fixed per unit sold (and not a percentage charge), then the slope of the supply curve should not change. Therefore what remains is an upwards shift, that will lead to increased equilibrium price-decreased equilibrium quantity. The algebra should lead one to

One could see this as a fixed shift in overall (not just production) marginal cost: the quantity has the same production marginal cost as before -but now "$2" is added as an obligation per unit, to cover the tax.


Macroeconomics Textbook on New-Keynesian models I'm looking for textbooks that explain the New-Keynesian models, without taking shortcuts on the mathematics, that would go in depth on the derivations of the formulas. I appreciate rigour, and clarity above all else. If intuition is supplied, it would be perfect.

I find Jordi Galí's book on monetary policy is not good at presenting the model, specially by not explaining the mathematical assumptions (which are not simple details...)

Edi:
Check the link found here

Michael Woodford's book Interest and Prices, while it may not be explicitly New Keynesian, may have some of the rigor you're looking for applied to this class of models.

A more direct alternative would be New Keynesian Economics edited by Mankiw and Romer. While it's a collection of papers not a textbook, if you're looking for underpinnings of New Keynesian models this'd be a good place to start. Also "The Science of Monetary Policy: A New Keynesian Perspective" by Clarida, Gali and Gertler.


Game theory vs Experimental economics What are the main differences in the methods of game theory and experimental economics? Which method is better suited to analyze strategic behavior?

They're complementary to each other.

With the development of Behavioral Game Theory, canonized in Camerer's 2003 textbook, the current paradigm of game theory 1 is converging towards making theories about how people play games, and test them, most often with experiments.

Wither Game Theory, Fudenberg & Levine, 2016


Public Debt as Percent of GDP My question relates to calculation total debt as percent of GDP (quarterly). Since debt is a stock and GDP is a flow, I can understand calculation it on an annual basis but not quarterly.

Even if the measure calculated is total debt at a point in time as a percentage of annual GDP, the frequency with which it is calculated could be quarterly. Taking quarter 1 2018 as an example, debt would be the total at end of that quarter.  GDP might relate to the last available full year, ie 2017, or to the year ending in that quarter, ie from quarter 2 2017 to quarter 1 2018.

A chart of such quarterly data for the US may be viewed here.


Locational Marginal Pricing when different prices and when the same? I am kinda confused about this YouTube video.

So the LMP with no constraints is the same in both nodes. For me it was the same because I used those offers from node 1 also in node 2 and we chose the highest offer because also those companies who wanted to sell it for 35$ will not say no if you buy it from them for 42 dollars and we do this because it is the easiest way to calculate the price so everyone is happy.

Now later in the video (from 1:48-2:37 min) the price is different in each node because of the transmission constraint. Why? I mean I still just used the third package with 38$ per MWh because it is cheaper for node 2, why would I still let node 1 pay for that?

okay meanwhile I got the answer to this:

the main idea behind LMP is to reduce the marginal cost of the WHOLE system.... therefore it is cheapier if you select those offers that way....

calculations:

38 * 600 + 48 * 600 = 51600

if we would do it as I thought makes more sense:

36 * 400 + 48 * 800 = 52800

as you can see even though the price seems to be more fair for node 1 now in total the costs increased from 51600 dollars to 52800 dollars


In the context of banking, how (if at all) do the terms 'capital', 'net worth', and 'equity' differ? In banking, are the three terms capital, net worth, and equity simply identical and exact synonyms?

If not, how do they differ?

(Aside: And what about in other contexts? For example, does the same hold more generally in corporate finance? What about in economics in general? I believe in economics, capital is usually used to refer to something quite different.)

Consider this...

A bank's capital is used to finance the purchase of assets. Those assets are mostly loans made to households and businesses and governments. When a loan is made the bank is "buying" the future payments of the borrower. This suggests the whole right side of the balance sheet is capital because it takes the entire right side to finance the purchase of all of the left side. Some of the capital is the bank's own debt or equivalently, the liabilities, which is owed to depositors and bond holders. The remainder of the capital is called equity which is what the common and preferred shareholders own. The value of all the shares or of all the "stock" (as in stock market) is the equity. Stockholders and shareholders and equity owners are the same thing. Confusingly "the stock in a business" is the assets (in blue on the left) but the "stock" (also known as the shares) are the smaller part called equity (in teal on the right). In order to control all the assets (in blue) you have to own the equity (in teal) so that is why the word "stock" is used to refer to the teal part and also the blue part.

Net worth is assets minus liabilities so it is the same thing as equity. "Net worth" is the usual term when speaking of the equity of an individual or a household. When speaking of the equity of a company sometimes stock market participants call it "book value".

I don't think non-bank companies think of these terms any differently than banks. In any company there is the distinction between physical capital which is always on the left side, and financial capital which are the two parts on the right side. If the company has some cash or other valuable paper on hand then there is also some financial capital on the left side (held as an asset).

The above diagram is useful in the context of accounting and finance but less useful in the context of economics.

I think economists use the word capital to refer to an accumulation of value, in other words assets. In economics capital has the connotation of being an accumulation rather than a flow. For example savings are an accumulation of a flow of income. (Capital) accumulations can be land, structures, equipment, software, patents, copyrights, and human capital (skilled people and educated people), and other assets.


Is there an economic reason why employees don't share salary information with each other? In Western society, one's salary is often a taboo topic and people tend to not tell other people what they earn.

In China by contrast, I have been told that asking one's salary is fairly normal social discourse.

It seems that employees being aware of each other's salaries would be an advantage, as they have more information about what the organization is willing and able to pay.

Is there an economic reason why people don't reveal their salaries, or is this entirely a cultural taboo?

dwjohnston,

To answer your question briefly: no, because it is rather a social or psychological matter than it is an economic matter.

There is already asked a good question about this subject in The Workplace community: https://workplace.stackexchange.com/questions/15397/why-is-discussing-pay-such-a-taboo-how-can-i-get-people-to-talk-about-concrete/15431#15431

Feel free to read the (also good) answers. The answer section also contains some handy tips and tricks that you and your co-workers could try.

I hope this will be useful for you.


is endogeneity a problem in the first-stage regression in a two-stage least square regression? We have this model:
$$D=\alpha_1+\gamma_1 Z + \epsilon_1$$
$$Y=\alpha_2+\gamma_2 D + \epsilon_2$$
Notations are as usual: Y is the outcome, D is the treatment, Z is the instrument
Two conditions for instrument variable to work in the literature: relevance (there is a correlation between Z and D) and exogeneity (no correlation between Z and error term $\epsilon_2$)
However, it seems no one cares about endogeneity in the first stage regression, which is the correlation between Z and $\epsilon_1$. Why is that the case? I have never seen any applied micro paper addressing this.

Yes it is a problem. The first stage itself has to satisfy the same assumptions that standard OLS would and $cov(Z,\epsilon_1)\neq 0$ would violate them (see A Guide to Modern Econometrics by Verbeek).
Furthermore, actually the two conditions you mention are not enough. The instrument should also not be 'weak', that is the first stage should have $F$-statistics above $10$ (as a rule of thumb). Also the instrument should have an effect on $Y$ only through $D$ - the so called exclusion restriction (see Mostly Harmless Econometrics by Angrist and Pischke).


Updated International patent protection index from Park (2008) Park (2008) provides an international patent protection index between the years of 1960-2005 with 5 years intervals. I was wondering if an updated version of such an index exist?

Apparently not. A 2015 article by the author uses his index to evaluate economic growth across country and time, stopping in 2005, same as the index in the original paper. And yet, many of the other variables are in principle available for more recent years.

The first best here would be for you to contact the author. He might be in the process of updating his index. Actually, if you look into his working papers, you can see he is doing some work on patents. Even more, there he offers some (more updated) data on copyright and Trademark. You might contact him to know better what this is.

The second best is that you expand the index yourself. For example, you can use the data just mentioned. Alternatively, you can use the subcomponents of this or this index (e.g. property rights or investor protection). There are more indexes here (e.g. intellectual property protection), and here.

One way to do this update is to take the original Park's series, and see which one of the above match its better (higher correlation, for instance). From here you obtain your "proxy". Then, simply extend Park's index with the newest data on this proxy. This is simply an exercise of "concatenation".


Microeconomics, deriving demand equations from utility unction Utility function: U=X+XY and I=XPx+YPy
Good Y is a composite good, so Py= 1

What would be the demand function for good X?

I got Mux=1+y and Muy=x and since Mux/Px=Muy/Py

1+y/Px=x/py

so that I=XPx+(Xpx-1)Py---> X=(I+Py)/(Px(1+Py)

Is this correct? Or am I supposed to set Py= to 1 in the calculations so that it would instead be X= (I+1)/2Px?

Also, would it be correct to say that these are substitutes? And good X is a normal good?

You're right in that $\frac{1+y}{p_x}=\frac{x}{p_y}$. This implies that $yp_y=xp_x-p_y$, and using this in the budget constraint $I=xp_x+yp_y$ yields
$ I =xp_x+xp_x-p_y=2xp_x-p_y$ or

$$x=\frac{I+p_y}{2p_x}.$$

In order to determine whether these goods are gross substitutes (or complements), you need to compute $\frac{\partial x}{\partial p_y}$ and observe that this is

$$\frac{\partial x}{\partial p_y}=\frac{1}{2p_x}>0.$$

This means that increases in the price of $y$ are associated with increases in the consumption of $x$, a behaviour that corresponds to gross substitutes.

As for whether $x$ is a normal good, you need to determine if increases in income are associated with increases or decreases in its consumption, so we calculate

$$\frac{\partial x}{\partial I}=\frac{1}{2p_x}>0.$$

As consumption of $x$ increases with $I$, we say that $x$ is a normal good (has positive income elasticity).


Why is it important to open up the economy before a cure for COVID-19? This is a multi-part question:

Why are we leaving quarantine so soon?
If it's to increase economic activity, why is it important to keep it so high?
At what point is economic activity worth more than thousands of people's health and livelihoods?

This is not economics question
healthcare, helping sick people are economic activity.
This is example of false dilemma. Economy activity such as food and health equipment production are important to save many people lives.


How to show the production function is concave in K and L but not strictly so? Suppose we have a production function with constant returns to scale. Let us denote it by $F(A,K,L)$ where $A$ is the technology, $K$ the capital and $L$ Labor. Further assume the first partial derivative of $L,K$ are both positive and the second partial negative. How to show the production function is concave in $K$ and $L$ but not strictly so?

This problem is from Acemoglu's Intro to Modern Economic Growth. I don't quite understand what it means to say the function is concave in $K$ and $L$. Do I need to show that $F(K,L)$ (treating A as constant) is concave? or do I show $F(K)$ and $F(L)$ are concave (treating L,A or K,A as constants)?

If it is the latter, it seems the problem seems trivial by the second derivative test.

So we want the Hessian to be NSD, so we need the PMs to alternate weakly.

$H=\begin{bmatrix} F_{kk} & F_{kl} \\
F_{kl} & F_{ll}
\end{bmatrix}~~NSD \iff~~~F_{kk},F_{ll}\leq0~~~\&~~F_{kk}F_{ll}-F_{kl}^2\geq0$

We are given that $F_{kk},F_{ll}<0$ so we need to figure out the cross partials.

Constant returns to scale implies that we have a homogeneous of degree 1 function:

$F(K,L)=KF_k+LF_l \implies  F_l=KF_{kl}+LF_{ll}+F_l~~ \&~~  F_k=LF_{kl}+KF_{kk}+F_k$

Now we can substitute these equations into the expression for the 2nd PM:

$\big(-\frac{L}{K}F_{kl}\big)\big(-\frac{K}{L}F_{kl}\big)-F_{kl}^2=0~~~~~$
 and we're done.


How did downgrading bonds contribute to Greek crisis? According to an article I read, one of the steps that was used to contribute to the Greek downfall was that bankers downgraded the bonds of the country. This immediately makes the interest rates (“yields”) on the bonds go up, making it more and more expensive for the country to borrow money or even just roll over the existing bonds.

I don't understand the impact this has.  Why it makes it more expensive for the country to borrow money?  And what is "roll over existing bonds"?

Also what are the warning signs in the economy that this is happening?  Is a weak currency one sign?

Here's a non-technical answer:

Bonds are a form of debt.  What the issuer is selling is essentially a promise to repay the principal (i.e. whatever price the buyer paid) and some interest to the buyer.  (Note: since we're talking about debt, you could also think of the buyer as a lender.)  In return, the issuer gets to use the money from the sale for whatever current projects needed funding in the first place.

Skirting some technical stuff, assume the yield is the same thing as the interest rate.  When lenders think there's a higher risk of not getting their money back, they'll either 1) not lend in the first place, or 2) if they do lend, demand higher a higher interest rate to compensate them for the higher probability of not getting repaid.

When someone downgrades your credit, it's a statement about you: they believe you're at a higher risk of not fulfilling your promise to repay the lender.  So any lender that does decide to take a risk and loan you money (i.e. buy your bond) is going to be in situation #2 above: they'll demand you pay more interest on the loan (here, higher bond yield) to compensate them for your riskiness.  That makes borrowing more expensive for you since you now have to pay a higher interest rate than you would have if you had better credit.

Rollovers are a type of reinvestment.

At the heart of the matter, credit downgrades happen when lenders lose faith in your ability to fulfill your promises.  This happens for a multitude of reasons.

As an example, S&P's 2011 downgrade of U.S. debt happened because they believed 1) that the pattern of running deficits most years might eventually put the U.S. at risk of not repaying (that is, the debt-to-GDP ratio might not be sustainable), and 2) that political leaders lacked a credible plan to tackle the problem.


Preparation for the rigors of an economics graduate programme I realize now that my undergraduate program is not nearly as rigorous as it should be - it required almost no math to complete. This is concerning because I've been accepted into a decent (top 30) PhD program. However, I (luckily) am also completing a degree in mathematics.

My question:

Can anyone recommend a good textbook(s) to help me bridge the gap between my non-rigorous program and a PhD program (level of rigor is whatever might be typical of a top 30 school??). I would also love any online resources such as video lectures, problem sets with solutions etc.

I looked at MIT's OCW but most of the courses beyond the principles do not include lectures, which was really disappointing.

I'd work my way through Microeconomic Analysis by Hal Varian (the PhD level one) and Mathematics for Economists by Simon and Bloom. You'll need both the micro intuition  of the former and mastery of the math bits of the the latter. You'll need thornier and more technical books at some point but these authors will hold your hand enough to work through them solo.


(Why) was von Neumann not a fan of the Nash equillibrium concept? Charles A. Holt and Alvin E. Roth's The Nash equilibrium: A perspective notes:
"In a personal communication with one of the authors, Nash notes that von Neumann was a “European gentleman” but was not an enthusiastic supporter of Nash's approach."

Is there any more information about why von Neumann had this attitude?  Or can we infer a reasonable answer?

Is there any more information about why von Neumann had this attitude?

There must be, but I have never seen it.

  Or can we infer a reasonable answer?

Here is one possibility based on hearsay among the Game Theory community.

Von Neumann thought that there was a sharp distinction between zero-sum games and other games.

In zero-sum games, there was no hope of cooperation. Therefore, it makes sense for players to engage in selfish, individualistic decision making. It is natural to assume that players choose what to do independently and with their best interests in mind. The resulting solution concept for such games is the concept of minimax equilibrium, which coincides with the concept of Nash equilibrium.
In other games, there is usually at least some room for mutually beneficial cooperation. It makes sense for rational people to talk to each other and try to find ways to cooperate. Hence, it is not evident that players must choose what to do independently and with only their best interests in mind. The way I've heard the story is that, for such games, Von Neumann favored the approach of Cooperative Game Theory in which decisions could be made collectively by groups of people.

I will add a further note. In the 1950s, there was no empirical evidence to support either hypothesis. In retrospect, we do see in practice that people often cooperate when they face prisoners' dilemmas. Also, the most widely cited field evidence supporting equilibrium behavior is from competitive settings that are close to zero-sum games (penalty kicks, tennis serves).


Does Nash Equilibrium predict the existence of vaccine reluctance? I was listening to a lecture on Nash Equilibrium, which stated that a Nash Equilibrium by definition occurs at a point that no players in the game have an incentive to change their strategy - everyone is playing their best response to everyone else. It occurred to me, though: it seems to me that 100% vaccination rate is not a Nash Equilibrium because herd immunity for a good vaccine would likely occur far earlier than that - once herd immunity is achieved, unvaccinated people would have far less incentive to change their strategy and get vaccinated.
Am I missing something, or does Nash Equilibrium occur at exactly the point where herd immunity is achieved - no one regrets their decision or wishes that they chose a different strategy, and no one has an incentive to change their strategy? (For any actual biologists reading, yes, I do realize that I'm being very simplistic about how vaccines and herd immunity actually works).
That being said, if I'm right about this, does game theory predict that some people would be reluctant to get the vaccine simply because they're "freeloading" (for lack of a better term) on people who already got the vaccine?

It depends on how you build the game. You may have games with several Nash equilibria, with a dominant strategy equilibrium (which is a special case of Nash equilibrium) or no equilibria at all.
Let us consider a game with 3 players, where herd immunity is achieved at 40% and where players incur a small cost for taking the vaccination and make a big gain when herd immunity is achieved. In this case you have 3 Nash equilibria (when 2 players decide to get the vaccine, nobody has an incentive to deviate).
In another game you may have 3 players who don't care about herd immunity, but that want to become immune (say the disease can come back at any time). In this case you have dominant strategy equilibrium: everybody gets the vaccine.
Finally let's construct a game with 2 players, where herd immunity is achieved at 40%. In this scenario players incur a small cost for taking the vaccination, and a bigger cost if they are the only player who takes the vaccination [1]. Again, herd immunity gives a gain. This can be modelled with a payout matrix such as:

PlayerA Vax
PlayerA No Vax

Player B Vax
1,1
2,-1

Player B No Vax
-1,2
0,0

then the game doesn't have a Nash equilibrium (you may have noticed that this is the same payout matrix of the prisoner's dilemma).
To answer your question, a game that includes vaccine reluctance may have several equilibria or none at all. Vaccine reluctance is an a-priori to your model, which can be factored in when building the payout matrix. Then you can analyze the game an try to predict possible outcomes.
[1] For instance if players are members of an anti-vax community/group, they may incur a reputation cost if other members don't get the vaccine.


Labour markets and supply-side policies: too much stress put on the WS push factors? In reading several macro textbooks, it seems that most of the supply-side policies tend to be focused on the labour supply side (wage setting curve), instead on the firm/labour demand side(price setting curve).

In most textbooks, this whole section is devoted to training programmes, wage accords, income policies, the degree of 'coordination' in unions of the economy, etc.

Almost very few pages,or paragraphs, are dedicated to price-push factors, for the exception of the usual chapter on the oil shocks in the late 70's, which can be seen as labour productivity shock. Almost nothing is said about improving competition, and whatever else can be considered as price-push factor.

Why is that? I maybe wrong, though.

Some may say that there's no too much stress, since the relevant policies are already studied in the field of Industrial Organization. However, my reply to this, is that there's also a field called Labour Economics where many of the effects of the policies for the WS curve are studied, and yet macro textbooks still cover them. Hence, there's clearly an unbalanced exposition in most macro textbooks...

I think it depends on the category of literature you're reading. The category of innovation literature has a lot about supply-side cost changes, and about related policies - you'll find lots of work on learning curves, technology diffusion, harnessing economies of scale. Frank Geels of Manchester does a lot of work on the theoretical side of this.

And there's broader literature on industrial policy and regulation too.