Do the republican tax cuts cost more than forgiving student loan debt? It is alleged by this article in the Guardian that the republican tax cuts cost more money than the total student loan debt bubble. The accuracy of this claim was briefly discussed in this post via the Skeptics stack-exchange; the comments on this post also suggest moving the discussion to this forum.

Can someone provide more details to clarify the answer as to whether the republican tax cuts cost more or less than forgiving total student loan debt?

While many folks treat reductions in government revenue as equivalent to spending, they’re not actually the same thing. Tax cuts don’t “cost” anything. Tax cuts represent less money coming in, while government spending (such as repayment of student loans) represent more money going out. So your first thought when seeing the two things treated as if they were the same should be “somebody has an agenda here” and to view anything that follows with a skeptical eye.

That said, it’s certainly valid to ask whether the tax cuts decrease government revenue by more than the cost of the repayment of student debt.  The short answer is “nobody knows” because both things represent such huge financial transfers that they would distort the economy.

Nobody denies that tax cuts increase economic activity — the question is by how much.  Many Republicans argue that tax cuts increase economic activity by so much that they “pay for themselves” because the smaller slice of a much larger pie works out to more overall. Most Democrats dispute this.

Similarly, nobody denies that government spending stimulates the economy — the question is by how much. Democrats often argue that government spending is a more effective (or at least more fair) way of stimulating the economy, than letting businesses (or the wealthy) hold onto the money and spend it themselves. Republicans dispute this.

Every facet of this issue is so politically charged, and what little hard data exists is so up to interpretation, that I don’t think you’ll really get the kind of definitive answer you’re probably after.  The bottom line is that it’s not really possible to conduct the kind of controlled experiments necessary to come to a solid conclusion. Which isn’t to say that people can’t make very reasonable (or persuasive) guesses. Just be aware that they are, in fact, guesses — and politically motivated ones, at that.


Swanson and Williams (2014): restricting based period response to one I would like to replicate the results as in Swanson and Williams (AER 2014): "Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates"
https://www.aeaweb.org/articles?id=10.1257/aer.104.10.3154.
However, I don't understand their specification for equation (9) (p. 11)
$\Delta y_{t} = \gamma^{\tau_{i}}+ \delta^{\tau_{i}}\boldsymbol \beta \boldsymbol X_{t}+\varepsilon_{t}$ in the paper. "Where $\gamma^{\tau_{i}}$ and $ \delta^{\tau_{i}}$ are scalars that are allowed to take on different
values in each calendar year $i$". $t$ indexex days and $\Delta y_{t}$ is the chagne in yield, $\boldsymbol X_{t}$ is a set of macroeconomin data surprise. They wrote

"We normalize the $\delta^{\tau_{i}}$ so that they have an average value of unity from 1990–2000, ..."

What chould they mean that the coefficients have an average value of one? Could it mean simply set $\delta^{\tau_{1990}} = 1$, $\delta^{\tau_{1991}} = 1$ ... $\delta^{\tau_{2000}} = 1$?
They have also posted their MATLAB code on the (bottom of the) website. But I still don't fully understand the specification. Would be nice if someone can help me out here.

I'm no empiricist (surprise), but skimming through the paper, I'm pretty sure that just means that the $\delta^{\tau_i}$'s are chosen so that

$$ \frac{1}{11}\sum_{i=1990}^{2000} \delta^{\tau_i} = 1 $$

as I stated in a comment above. This assumption is necessary in order to separately identify (estimate) $\delta^{\tau_i}$ and $\mathbf{\beta}$.

Without this assumption, all you are able to estimate is $\delta^{\tau_i}\mathbf{\beta}$, so you need additional assumptions to solve for the two factors separately.


Two-year difference-in-difference model design Is there some literature about two-year difference-in-difference (DiD) models? Suppose a policy was implemented in 1982, but not strictly enforced among all people. Can I still estimate a DiD model using the data only from 2012 to 2016?

Is there some literature about two-year difference-in-difference (DiD) models?

Of course.
The traditional two-group/two-period DiD design was quite popular 25 years ago, though it's less common today to find evaluations where entities are observed in only one time period pre- and post-shock. DiD methods hinge on the graphical exhibition of common group trends before program exposure. You cannot possibly demonstrate this, visually or statistically, with less than three pre-treatment time periods. Serial observations pre- and post-treatment is not necessary, but is very much preferred. In my opinion, your study is likely to be met with skepticism if you do not observe individuals for a sufficient number of time periods before your treatment of interest.

Suppose a policy was implemented in 1982, but not strictly enforced among all people. Can I still estimate a DiD model using the data only from 2012 to 2016?

No.
Unless I misunderstood your question, the immediate policy adoption year is 1982. If you were to restrict your time series to the years from 2012 to 2016, then by definition, you're only observing entities in the post-policy phase. This assumes the policy has persisted until 2016. Unless the policy was rescinded and reintroduced in the interval you referenced, then you cannot possibly conduct a DiD evaluation. Assessing treated and untreated entities post-policy is a posttest-only evaluation. A posttest-only design is not considered a DiD evaluation; you must observe entities pre- and post-shock.
But suppose, for example, a completely new policy is introduced in between the years you referenced (e.g., 2014). Before its introduction, all individuals are untreated. Once it is instituted, only a subset of individuals will be eligible. The individuals affected by the policy comprise your treatment group, while all non-affected persons comprise your control group. At a basic level, the 'classical' DiD approach requires you to observe a treatment group and a control group at least one year before and at least one year after your policy. If you do not observe any pre-event data, then you must model the effect of the policy in a different way.


Sum of residuals in multiple regression equals 0 I understand that in multiple regression
$$\sum_{}^{} X_{i,j}\hat{u}_{i} = 0 $$
 but I do not understand how my textbook says that if we include the intercept in the regression ($X_{i,0} = 1$)then we get:
$$\sum_{}^{} \hat{u}_{i} = 0$$

Completing the notation with the indices
$$
\forall j: \sum_{i=1}^{n} X_{i,j}\hat{u}_{i} = 0.
$$
As you say, if $X_0$ is the constant then
$$
\forall i: X_{i,0} = 1.
$$
Inputing $j = 0$ into the first equation
$$
\begin{align*}
\sum_{i=1}^{n} X_{i,0}\hat{u}_{i} & = 0 \\
\\
\sum_{i=1}^{n} 1\hat{u}_{i} & = 0 \\
\\
\sum_{i=1}^{n} \hat{u}_{i} & = 0.
\end{align*}
$$


Wages in Solow growth model with savings = 0 I am trying to understand the change of wage rate and rental rate in the Solow growth model with s = 0. It is clear that capital per capita will approach 0 (due to depreciation of capital). Also is clear to me the fact that the rental rate will rise because of decreasing marginal returns assumed on the production function. Since factors are paid their marginal products in case of Constant Returns to Scale, rental rates rise.
I am confused about the marginal product of labor overtime in a general setting. For example if I take $F(K,L)=K^aL^{1−a} ,0<a<1$ , then I can see that marginal product of labor will fall if we assume constant or increasing labor force. But I am unable to show this for a general $F$ with CRS.

Let
$$Q = F(K,L)$$
Assume
a) $F(K,L)$ exhibits consant returns to scale.

We need this to aggregate from the individual firms to the total.

b) Price taking behavior  and

c) Profit maximizing behavior

from the part of the firms.

Then, throughout the dynamic process,
$$w = \frac {\partial F(K,L)}{\partial L} \equiv F_L$$

i.e. the wage is equal to the marginal product of labor. For clarity, write

$$\frac {\partial F(K,L)}{\partial L} \equiv h(K,L)$$

$$\dot w = \frac {d}{dt}\frac {\partial F(K,L)}{\partial L} = \frac {d}{dt}h(K,L)= \frac {\partial h(K,L)}{\partial K}\dot K + \frac {\partial h(K,L)}{\partial L}\dot L$$

$$\implies \dot w = F_{KL}\dot K + F_{LL}\dot L$$

Assume  further

d) complementarity of inputs, $F_{KL}>0$, and

e) diminishing marginal productss (not in the temporal dimension but in the static dimension, due to diminishing rate of returns), $F_{LL}<0, F_{KK}<0$.

Then, if

$$\dot K <0, \dot L\geq 0  \implies \dot w <0$$

The same treatment wil give us

$$\dot r = F_{KK}\dot K + F_{KL}\dot L  >0$$


How does an elastic Money Demand affects the effectiveness of fiscal policy? From my notes:

'The elasticity of Money Demand reduces the impact on the interest rate of the increase in government spending...'

My question is: if the Money Supply is inelastic, the elasticity of Md wouldn't matter, because the Md would just shift up/down by the same amount regardless of its slope, and it is the shift that determines the change in interest rate, which doesn't fit with my notes.

Maybe another way to put it is: does the elasticity of Money Demand affects how much it changes in response to a change in government spending? If so, how?

a small rise in interest elasticity shifts the equilibrium position of IS-LM CURVES to the right


Question about gordon growth and expected stock prices I have problems understanding the solution to the following question and would like to ask if you could help me with the interpretation?

  A house is an asset which generates a benefit to its owners: a stream
  of housing services in the future. Similarly a stock generates a
  stream of dividends in the future. One measure of the value of this
  housing service is the rent one would have to pay on an equivalent
  house. For the purposes of this assignment, assume $D_{t+1}$ is the rent
  you have to pay over the next year (we know this number at time $t$),
  and $P_t$ is the price of the house today. The return on housing is
  $r_{t+1} =  (P_{t+1}+D_{t+1}-P_t)/Pt$. If the discount rate and growth rate of rent were constant, this setup satisfies the Gordon equation, $P_t = D_{t+1}
/ (r – g)$, where $r$ is the expected return on housing and $g$ is the growth
  rate of rent. You can ignore issues about taxes and transaction costs
  on houses.

  Suppose the Gordon equation were correct. In this world, looking at a
  specific city over time, suppose we start out at $D_{t+1} = \$10,000$ a
  year, $P_t =\$200,000$, $r$ is $10$% and $g$ is $5$%. Over time, would the
  price be constant, rising, or falling?

If I plug in the numbers into the Gordon formula I get $P=10.000/(10\text{%}-5\text{%})=200.000$.
Thus the price stays constant.

However the answer is:

  Since the expected return is $10$% but the “divided yield” is only $5$%,
  the price has to rise $5$% a year.

Could someone explain me if there is a way to understand the solution using the Gordon growth formula or some other intuitive approach?

Thank you very much in advance!

Plugging in the numbers into the Gordon's growth formula does not tell what will happen to the price of the house -it just verifies that the numbers given do satisfy the formula.

To see what will happen to the price in the future, you have to go to the definition of the return on an asset

$$r_{t+1} =  \frac {P_{t+1}+D_{t+1}-P_t}{P_t} = \frac {\Delta P_{t+1}}{P_t} + \frac {D_{t+1}}{P_t} \tag{1}$$

The right-hand side now is clearly "Asset percentage appreciation(Capital Gain) + rate of return on asset value" which is indeed the Total Return on an asset expressed in percentages.

But we have assumed (and the numbers given verify the initial condition), that Gordon's formula holds so

$$P_t = \frac {D_{t+1}}{r-g} \implies P_t(r-g) = D_{t+1} \tag{2}$$

Substitute $(2)$ into $(1)$ to get

$$r_{t+1} = \frac {\Delta P_{t+1}}{P_t} + \frac {P_t(r-g)}{P_t} = \frac {\Delta P_{t+1}}{P_t} + r-g \tag{3}$$

Now, reasonably we should identify "expected (total) return per period" $r$ with "total return next period" $r_{t+1}$.

Then  $(3)$ becomes

$$r_{t+1} = r = \frac {\Delta P_{t+1}}{P_t} + r-g \implies \frac {\Delta P_{t+1}}{P_t} = g \tag{4}$$

which in our case, means that the value of the house will appreciate $5$% per year. Intuitively, since expected Total Returns are $10$% and what we get out of the house as income ($D_{t+1}/P_t$) is $5$%, the other component of Total Returns, house price appreciation, must cover the distance between the two, which is another $5$%.

Note: Whether this increase in price refers to "asking" price or "equilibrium" price is another matter that involves a more elaborate modelling of the situation.


Basel affecting the bank behaviour? In EU, Banks have changed their behaviour lately, e.g. as acting liquidity providers to certain markets like notes etc.

Introduction of Basel III is probably one reason (tighter capital and liquidity requirements). Due to new stress tests, some of European banks are seen to be in bad shape.

Anyhow, Basel III is not yet finished. How banks are expected to change their lending or market making behaviour during the end of this decade? Is it possible to estimate, what sectors are going to get hurt?

Interesting question. Indeed, Basel/I,II,III-type regulation changes the behavior of banks, that´s probably the goal of said regulation.

Its possible that their market behavior with respect to "notes" (which notes?) has changed.

bason on the typical Modigiliani/Miller intuition, it seems that there is no reason why Basel/type regulation will affect a sector or another. The main effects are in changing how firms get financed. If banks are expected to hold senior debt, then firms are more likely to issue senior debt. This changes how funds are intermediated from savers to investors, but in principle it should not change which sectors are financed. It should only affect how they are financed, with equity, preferred, junior debt, senior debt, senior collateralized debt, etc.


How do I fill gaps in my data? In my study, I have 5 independent variables which contains 21 observation each. However one of my independent variables have 3 gaps. What should I do?

e,g

I would need to know the effect of education to inequality and I would like to conduct standard OLS method. However, I have one unbalanced data which have gaps unlike the rest of the data... what should I do?
per say in 1997 (no data) 1998 (0.2345) 1999 (no data) 2000 (0.3453) and then from 2001 - 2017 it has continuous data....should I just drop it and start from 2001?

Friend,

This situation that requires an imputation method that you must pick from.   Dealing with missing data is a sensitive matter.  Depending on which way you choice to handle missing observation will impact your project and in this case (with observations less than 100) could make your analysis poor/basis.

Here are some popular options:

Impute the value of the missing data
Remove a variable which has a lot of missing data and use other variables which measure similar aspects of the characteristics being studied.
You could create a regression model to impute missing values.
You can use the average (caution when using this method as there may be other variables in your data set that may be dependent).
Duplicate the previous or nearest value.

Here is a website on some tips: http://www.real-statistics.com/descriptive-statistics/missing-data/

Here is a working paper on the subject: liberalarts.utexas.edu/prc/_files/cs/Missing-Data.pdf

Missing values is delicate subject.  Use caution and always, always, always DOCUMENT WHAT YOU ARE DOING, because others want to know and it makes your work so much better.


Meaning of "Federal Reserve’s various liquidity facilities" and something more I've found this link of San Francisco Fed. In it, it's stated that the Federal bank began «paying interest on reserves held against certain types of deposit liabilities.(...) This was important for monetary policy because the Federal Reserve’s various liquidity facilities initiated during the financial crisis caused upward pressure on excess reserves and placed downward pressure on the Federal funds rate. To counteract these pressures, on October 6, 2008, the Federal Reserve Board announced that it would begin paying interest on depository institutions’ reserve balances.»

I need help on clarifying the sentence in bold. Which facilities were those? What's the problem on an upward pressure on excess reserves, and downward pressure on the Federal funds rate?

Any help would be appreciated.

Downward pressure on the Federal funds rate means bringing interest rates down even further (to ~0%).

Upward pressure on excess reserves likely means increased incentive for banks to build up excess reserves. The part about reserves is bit ambiguous. After reading the article a couple of times, this is what I make out of the paragraph (my comments are in bold):

  This was important for monetary policy because the Federal Reserve’s
  various liquidity facilities initiated during the financial crisis
  caused upward pressure on excess reserves (provided banks with cash to increase reserves) and placed downward pressure
  on the Federal funds rate (lowered the interest rate to the target level ~0). To give  Fed a tool to counteract these pressures in the future when they decide to exit QE and tighten the monetary policy, on October
  6, 2008, the Federal Reserve Board announced that it would begin
  paying interest on depository institutions’ reserve balances. Paying interest on reserves gave the banks incentive to increase the reserves at the time. In the future, lowering interest rate paid on reserves would create downward pressure on excess reserves.

I found a footnote next to "Federal Reserve’s various liquidity facilities" part of the sentence leading to a page describing these facilities:
Credit and Liquidity Programs and the Balance Sheet. It looks like a detailed technical description of QE programs Fed implemented after the 2008 crisis.


What will I see of the €545 from TTIP? According to this TTIP paper, a European family of four will see their annual disposable income increase by €545 on average:

  These gains can also be translated into household
  disposable income. One of the most widely quoted
  figures from the CEPR study is its estimation that
  a European family of four would see their annual
  disposable income increase by an average of €545
  per year as a result of the agreement. This figure
  takes account not only of increases in wages and
  other household income but also price reductions.

If on average all European households gain €545, does my purchasing power actually increase? If not (what I presume), why is this seen as an advantage?

Interpreting the paper you linked:

  a European family of four would see their annual
  disposable income increase by an average of €545
  per year as a result of the agreement. This figure
  takes account not only of increases in wages and
  other household income but also price reductions.

This means that price changes have been taken into consideration and so this income change is already corrected for any inflation. It is possible that a trade deal results in more disposable income, for a basic example see Ricardo's theory of comparative advantages.

I can't say how this figure was arrived at by the paper because no explanation is given.

The following has very little to do with your question, it is more of a reaction to what I perceive to be your anti-TTIP stance. If I am mistaken, apologies.
I find that people who don't like TTIP focus on strange things even though there are some valid critiques. The paper you linked says that the gains are a result of, among other causes, a

  more aligned regulatory systems agreed
  under the TTIP

Some critiques claim that the regulatory system will be closer to US regulation which favours companies over consumers. In terms of patent rights it may also not be optimal, though the effect of patent systems on long term growth is unclear anyway. I find that these are valid worries. Even if TTIP does decrease prices (which I think it will) there may be hidden costs. I don't know if there are, but I think it should be this that is scrutinized about TTIP.


Inflation vs Deflation Why is in flation preferable to deflation?
I appreciate this is largely due to the fact that deflation causes a large decrease in demand as people continually wait for prices to decrease, but if anyone has finer points I would be grateful.

I wouldn't necessarily agree that inflation is universally preferable to deflation. Each has positive and negative consequences. Inflation hurts savers, deflation hurts current consumers. A little inflation (let's say, 2% per year) is useful -- if nothing else, it helps deal with wage stickiness. Deflation, on the other hand, would be a godsend for a country like Venezuela where prices have been growing incessantly.

This is all to say that there isn't a single rule for inflation vs deflation. The broader economic context is critical.


Private Investment Impact on Bond Yields From Japan to the US to Germany, we are currently seeing longer term bond yields falling at an alarming rate.

I tune into a fair bit of economic commentary, and can often come to some sort of understanding of the factors that commentators say are at play in the current situation. But one I struggle with is the idea that weak private investment is a factor in declining yields.

Can somebody please explain why this is the case? Is the idea that weak private investment leads to weaker GDP growth, which leads to weaker inflation, which leads to higher bond prices? Or is there something else at play here?

I think you've answered your own question. Not only would lower inflation be a factor in lower bond yields but also consider that a lower level of demand for loanable funds for private real investment means lower corporate bond yields. That view is cited in the following Larry Summers quote taken from this economics.stackexchange.com question on secular stagnation...

  Think about what the world was like when General Motors or AT&T or
  Exxon or IBM were iconic companies. They were issuing debt. They were
  investing on a massive scale to expand capacity and to build networks.
  Now think about iconic companies of today like Apple and Google. They
  have more cash flow, fundamentally, than they know what to do with.
  And the result of that, of course, is an excess supply of savings.
  Another way to approach the question is to say, what's happened to the
  relative price of durable equipment, either producer equipment or
  consumer equipment, appliances? And the answer is those prices have
  gone way down. Well, when those prices go way down it means a given
  unit of savings goes much further.

  All of that, it seems to me, operates to reduce real interest rates


Empirical means of discerning "economy" and "bubble" In the news lately and in previous administrations, one of the most popular sound bytes I've heard was: "so and so is not growing the economy, he's growing the bubble." As with much sensationalism in the news, this is a rather normative statement. What I want to investigate is:

Question: what is a positive statement that can be said for the same argument?

Seeing as the federal reserve themselves have openly said they have no formal definition of a "bubble" and we can take it all the way back to the tulip mania days, but I think it's still interesting to see what is the most persuasive quantifiable metric that would suggest if the bubble is growing or if the economy itself is growing.

My best attempt One metric I noticed was in America home ownership is down and yet the real estate prices are increasing, suggesting that the valuation of homes is from the speculation of a wealthy few. Now, I concede this is only representative of one part of the economy, to see the bigger picture we would have to include more industries. Perhaps the same technique, but using a composite basket of such metrics?

You are probably not far off the mark. While there may be no consensus what a bubble is, one proposed definition is

Unusual changes in single measures, or relationships among measures (e.g., ratios) relative to their historical levels. For example, in the housing bubble of the 2000s, the housing prices were unusually high relative to income.
For stocks, the price to earnings ratio provides a measure of stock prices relative to corporate earnings; higher readings indicate investors are paying more for each dollar of earnings.

I'm not aware of [more] composite measures... but I'm not sure it would be very useful either. Generally one wants to know where exactly the problem is (whic sector) when there's a bubble.
Although Wikipedia doesn't seem to mention this, there's obvious caveat to such a method. Quoting from a fairly cited review of Camerer:

Any apparent bubble could be evidence of a variable which affects intrinsic value but is not observed by the econometrician.

Basically a problem of confounding variables, as far as I understand it.
As a putative example (of the latter), Camerer gives:

An example might be the Hong Kong stock market, which rose l0 times in value
between 1970 and 1973, then dropped 75% in a year. These enormous price swings
might indicate a bubble or fad, or they could be rational swings based on changing beliefs about what will happen when Hong Kong reverted to China after the British lease expires in 1997.

More examples like that are supposed to be given in a paper by Flood et. al (cited by Camerer), but I haven't read it.


Could someone please explain the proof of Hotelling's lemma? According to https://en.wikipedia.org/wiki/Hotelling%27s_lemma,

the maximum of the firm's profit at some output is given by the minimum of the difference between the profit and the revenue.

However, it does not sound right, as the difference of difference of the profit and the revenue is the negative of the cost of the input. The minimum would correspond to the maximum cost for input incurred. How would the maximum of the fir's profit at this point?

Also what does it mean by "at some output y*(p)"? Is y*(p) fixed here?

Well done for spotting this one. It is (was) simply a wrong statement. It is indeed the maximum and not the minimum of the expression as (was in the past) stated in the wikipedia article.

Then the maximum of this expression is the maximum of $-C$ (Cost) which is equivalent to the minimum of $C$, and the equivalence with maximum profit holds under duality.


How exactly does elasticity relate to slope? My book (Goodwin's Microeconomics in Context, pg. 117) states the following about price-elasticity of demand:

  Given two demand curves that go through a specific point on graphs with the same scale, the flatter demand curve will represent the relatively more elastic demand and the stepper one the relatively less elastic demand.

I have actually two questions about this:

1) Will the flatter demand curve be more elastic at any given point (for any given value of $p$) or just at the point that both curves pass through?

2) How can we show this mathematically using the definition of elasticity as  $$\epsilon=\frac{dQ}{dp}\frac{p}{Q}$$?

Thanks very much in advance.

The two demand functions $D_1(p),D_2(p)$ cross at the point $(Q,p)$. Their respective elasticities at price $p$ are
\begin{align*}
\epsilon_1(p) & = \frac{\text{d}D_1(p)}{\text{d}p}\frac{p}{D_1(p)} \\
\\
\epsilon_2(p) & = \frac{\text{d}D_2(p)}{\text{d}p}\frac{p}{D_2(p)}.
\end{align*}
However since both function cross at the point $(Q,p)$ we know that
$$
D_1(p) = D_2(p) = Q.
$$
But then
$$
\frac{p}{D_1(p)} = \frac{p}{Q} = \frac{p}{D_2(p)}.
$$
Meaning the only difference between their elasticities is $\text{d}D_i(p)/\text{d}p$, which is their slopes.

As for your 1. question, the conditions are not clear. Is the 'flatter' curve only 'flatter' locally, or for every price $p$? If you only mean locally, then no, the statement is only valid in the intersection point $(Q,p)$.


How to test for Granger causality? I am trying to test if $a_t$ granger causes $b_t$:

$$a_t=\rho_1+\phi_{11}a_{t-1}+\alpha_{11}b_{t-1}+\beta_{11}c_{t-1}+u_{1t}$$

$$b_t=\rho_2+\phi_{21}a_{t-1}+\alpha_{21}b_{t-1}+\beta_{21}c_{t-1}+u_{2t}$$

$$c_t=\rho_3+\phi_{31}a_{t-1}+\alpha_{31}b_{t-1}+\phi_{31}c_{t-1}+u_{3t}$$

I am trying to use an F test.

However, should be null be: $\phi_{21}$ = 0.

Or do I also need to set: $\beta_{21}$ = 0 because a impacts b through c.

This site https://www.statisticshowto.com/granger-causality/  shows about conducting the F-test for granger-causality.     It also talks about  alternative Tests.

"If you have a large number of variables and lags, your F-test can lose power.

An alternative would be to run a chi-square test, constructed with likelihood ratio or Wald tests. Although both versions give practically the same result, the F-test is much easier to run."


Slutsky matrix computed from budget shares In Haag et al. 2009 Testing and imposing Slutsky symmetry in nonparametric demand systems, the authors claim that the Slutsky matrix can be computed from share functions expressed in terms of logged prices and logged wealth.
In particular they claim that, let $p$ and $w$ be logged prices and logged wealth.
$s_{ij}=\frac{\partial{b_i(p,w)}}{\partial{p_j}}+\frac{\partial(b(p,w))}{\partial w}b_j(p,w)+b_j(p,w)b_i(p,w)-\delta_{i,j}b_i(p,w)$
where $\delta_{i,j}$ is the kronecker delta function that says that in the diagonal terms we have to substract $b_i(p,w)$.
He claims that this is the Slutsky matrix in unlogged prices terms, but how can this beif everything is in terms of shares. I have tried to derive it myself but I cannot reproduce what they have, but maybe I am making some mistake. The authors cite Mas-Colell et al. do you know the exact reference in the book they only provide the general reference.
Reference:Haag, B. R., Hoderlein, S., & Pendakur, K. (2009). Testing and imposing Slutsky symmetry in nonparametric demand systems. Journal of Econometrics, 153(1), 33–50.

In all indexed references to the Slutsky matrix in Mas-Collel et al. no such relation can be found. It is my impression that the authors meant that the expression they write conveys the same information and restrictions with the original, being a scaled version of it.

I will use indices $i$, $k$, and write the logarithm explicitly in order to avoid confusion.

$$\frac {\partial b_i}{\partial \ln p_k} = \frac {\partial (x_ip_i/w)}{\partial \ln p_k}$$

Get liberal with partial differentiation, think of it as a differential, which gives

$$\partial \ln p_k = \partial p_k/p_k$$

Insert above to get
$$\frac {\partial b_i}{\partial \ln p_k} = p_k\frac {\partial (x_ip_i/w)}{\partial p_k} = \frac{p_ip_k}{w}\cdot \frac {\partial x_i}{\partial p_k}$$
and rearranging

$$\implies \frac {\partial x_i}{\partial p_k} = \frac{w}{p_ip_k} \cdot \frac {\partial b_i}{\partial \ln p_k} \tag{1}$$

So we have expressed the first term of the usual Slutsky element in terms of logarithmic derivatives of budget shares. For the second component we have

$$\frac {\partial b_i}{\partial \ln w} = w\frac {\partial (x_ip_i/w)}{\partial w} = w \frac {(\partial x_i/\partial w)p_iw - x_ip_i}{w^2} = p_i\frac {\partial x_i}{\partial w} - b_i$$

rearranging and also multiplying by $x_k$ we get

$$\frac {\partial x_i}{\partial w} x_k = \frac {x_k}{p_i}\frac {\partial b_i}{\partial \ln w} + \frac {x_k}{p_i} b_i$$

Multiply and divide each element by $p_kw$:

$$\frac {\partial x_i}{\partial w} x_k = \frac {x_kp_kw}{p_ip_kw}\frac {\partial b_i}{\partial \ln w} + \frac {x_kp_kw}{p_ip_kw}  b_i$$

$$\implies \frac {\partial x_i}{\partial w} x_k = \frac {w}{p_ip_k}\frac {\partial b_i}{\partial \ln w}  b_k + \frac {w}{p_ip_k}  b_ib_k \tag{2}$$

Combining,

$$(1),(2) \implies s_{ik} = \frac {\partial x_i}{\partial p_k} + \frac {\partial x_i}{\partial w} x_k \\
=\frac{w}{p_ip_k} \cdot \frac {\partial b_i}{\partial \ln p_k} + \frac {w}{p_ip_k}\cdot \frac {\partial b_i}{\partial \ln w}  b_k + \frac {w}{p_ip_k}\cdot  b_ib_k $$

$$\implies s_{ik} = \frac{w}{p_ip_k} \Big(\frac {\partial b_i}{\partial \ln p_k} + \frac {\partial b_i}{\partial \ln w}  b_k +  b_ib_k\Big) \tag{3}$$

The term in the big parenthesis is what the authors give as the off-diagonal element of the Slutsky matrix. The scaling factor $\frac{w}{p_ip_k}$ is symmetrical, so the expression in the big parenthesis nevertheless reflects the same symmetry conditions as the usual $s_{ik}$ terms.

If you apply the same method for the diagonal elements you will get the $-b_i$ term.

This form of the Slutsky matrix I believe is old story, and it has come about for purposes of econometric estimation of demand systems. For example, in Theil, H., & Clements, K. W. (1980). Recent Methodological Advances in Economic Equation Systems. American Behavioral Scientist, 23(6), 789-809. we find this form of the Slutsky elements, which the authors call "elements of the Slutsky matrix" without any "explanation" as to why the textbook expressions are scaled.

But I would advise to go ahead and e-mail the authors asking for clarifications.


Can you set $C / P^{\eta}$ to be the numeraire in a NK model? Consider a static model with CES demand. Real aggregate demand is
$$
C = \left(\sum_j c_j^{(\eta-1)/\eta}\right)^{\eta/(\eta-1)}
$$
and labor supply is inelastic, so the budget constraint is
$
\sum_j p_j c_j = W
$
and the demand function is
$$
c_j^{*} = \frac{C P^{\eta}}{p_j^{\eta}}
$$
where
$$
P = \left(\sum_j p_j^{1-\eta} \right)^{1/(1-\eta)}
$$
is the ideal price index. Can I set $C P^{\eta} = 1$ as my numeraire so that $c_j^{*} = p_j^{-\eta}$? More generally, what is required of a numeraire?

I'm going to answer my own question. Consider multiplying all prices and income (i.e., the wage) by a common factor $\lambda>0$. The new ideal price index is just $P' = \lambda P$. The new wage is just $W' = \lambda W$. So real expenditure, $C' = W'/P' = W/P = C$, is invariant. The "numeraire" should now be $C' (P')^{\eta} = \lambda^{\eta}$, hence prices relative to the new "numeraire" should now be $p_j' = p_j \lambda^{1-\eta}$, not $\lambda p_j$. That's a contradiction---$CP^{\eta}$ is not a stable unit of account.

Another way to see the problem is that demand is no longer homogeneous of degree zero in prices and income under this normalization: $(c_j^{*})' = \lambda^{-\eta} p_j^{-\eta}$, so $(c_j^{*})' / c_j^{*} = \lambda^{-\eta}$.


Are real wages a good measure of economic progress? Why do we tend to use Real GDP Per Capita instead of the real wage? What is the issue of using the real wage instead?

Thee are several issues including what happens about incomes that are not wages, but the main one is

  Not everybody earns a wage

This is an issue for the self-employed (especially in agricultural subsistence economies), but it is also an issue in economies with large numbers of dependants, especially the very young or the very old

It also raises the issue of the employment of women: increasing the proportion of women working will tend to boost total GDP and GDP per capita even though it can in some circumstances reduce average wages if the women entering the job market earn less than men already there

There are also cyclical issues: there have been recessions where unemployment has increased substantially but wages of those still working have been less immediately affected; there have been other recessions where the reverse pattern has predominated.  In both cases GDP per capita has fallen and the economy is obviously weaker than it was before the recession


Question on subgame perfect equilibrium Consider a world of complete information with two agents X and Y and two time periods 1 and 2.

Person X only lives in second period.

Person Y lives in 1st and 2nd periods both.

X and Y are each endowed with and exogenous income I which can be allocated between consumption in both periods.

$s_Y$ = Y’s saving and  $0\le s_Y \le I$

$c_{1Y} $ and $c_{2Y} $ are the agent Y’s first and second period consumptions respectively.

The A gent X’s preferences are altruistic for Y. After observing the saving of Y, $sY$,X determine how much his endowment $tX$ to transfer to Y for $t_x\in [0,I]$

$c_{2X}$ the agent X’s consumption in period 2.

Utility functions Y and X are respectively

$$V_Y= ln(C_{1Y}) + bln(C_{2Y})$$

$$V_X=ln(C_{2X})+a *V_Y$$

where a is positive and $a*b\ge 1$ and $b\in (0,1)$

What is the su game perfect equilibrium levels for $t_X$ and $s_Y$?

If $S_Y$ is the amount saved by $Y$ in the first period, and $T_X$ is the amount transferred by $X$ to $Y$ in the second period, then $X$'s payoff as function of his choice $T_X$, taking as given $Y$'s choice $S_Y$ is
$$\ln(I - T_X) + a\left(\ln(I-S_Y) + b\ln(S_Y+T_X)\right)$$

$X$ will choose $T_X$ by solving the following problem :
$$\max_{T_X \geq 0} \ \ \ln(I - T_X) + a\left(\ln(I-S_Y) + b\ln(S_Y+T_X)\right)$$

First-order condition for optimality is:

$$\frac{1}{I-T_X} =\frac{ab}{S_Y + T_X} $$

Solving it for $T_X$ we get,

$$T_X = \frac{abI-S_Y}{ab+1}$$

This is the best response transfer function of $X$.

Now we solve $Y$'s utility maximization problem in period 1, taking as given $X$'s best response function of period 2.

\begin{eqnarray*} \max_{S_Y\geq 0} & & \ln(I - S_Y) + b\ln\left(S_Y + \frac{abI-S_Y}{ab+1}\right)\end{eqnarray*}

which can be rewritten as

\begin{eqnarray*} \max_{S_Y \geq 0} & & \ln(I - S_Y) + b\ln\left(I+S_Y\right) + b \ln\left(\frac{ab}{ab+1}\right)\end{eqnarray*}

Solving it we get
$$S_Y^* = \max\left(\frac{(b-1)I}{b+1}, 0\right) $$

Since $b \in (0, 1)$,
$$S_Y^* = 0$$

Consequently,
$$T_X^* = \frac{abI}{ab + 1}$$


if the richest 85 people give away all their money? I once heard a fact that the richest 85 people are as wealthy as half the world's population put together. My question is, what does that mean?

Does it mean that there is some feasible method in which these 85 people can double the wealth of half the world's population? What would happen if they decided to do so? How would they go about doing this?

It seems safe to say that the bulk of that wealth consists of equity (stock) holdings, not "money." (For example, Bill Gates owns a lot of share of Microsoft.)

Let's assume that the top 85 people wanted to redistribute their wealth voluntarily.

If they tried selling that equity all at once, the price of the equities would likely collapse (who would pay a lot of money for those shares, if everyone know that they were selling all at once?) The amount of money to redistribute would be a lot less than the current estimate of their wealth (which uses the current stock prices). The logistics involved with the transfer would probably consume most of of the transferred wealth. (If it were easy to transfer wealth to individuals in poorer countries, aid programmes would have been more effective than seen in practice.) That is, some people would be wealthier, but it would likely be intermediaries skimming off the cash transfers.
Logistically, there would be no way to transfer all of those shares to half the world's population. (They would need something like a brokerage account.) And even if that were somehow accomplished, the recipients would likely dump their shares, and their value would collapse. Brokers would probably end up getting all of the value from their transaction fees.

In other words, there would presumably be a transfer of wealth, but it would be a lot less than what is implied by current market prices.

This of course raises the obvious question of why they would do this voluntarily; the top 85 richest people did not get that way by dumping their wealth on random strangers.


Can you please help me find this topic in Mechanism design/Rational choice theory? When I was in university, I remember studying some kind of topic in adv microeconomics where someone gives you three options, where one is obviously worse and is put there just to deceive you so that you don't pick the one with greater utility. Could you please help me remember the name of this fallacy/dilemma/theorem and what is the best strategy to solve this problem?
Thanks a lot

I think you're referring to the decoy effect. A popular example of this is the Economist subscription puzzle, popularized in Dan Ariely's TED Talk (starting at 12:22).


Probability of the event knowing that I received no informations First I want to thank you if you pay attention to my post. I apologize if it seems elementary to you, note that I searched a lot an answer before posting.

I have a particular informational framework where there are 3 events denoted A, B, C.

A= This guy is cool.

$\overline{A}$= This guy is not cool

B= Someone is here

$\overline{B}$= No one is here

C= He tells me if he is cool

$\overline{C}$= He does not tell me if he is cool

P(A), P(B) and P(C) are the probabilities associated with these events.

I assume that if the person who can advise me is not here, she cannot tell me something.

What is the probability that this guy is cool given the fact that no one is telling me something?

I propose the following formula:

$P(A|\emptyset)=\frac{p(A\cap B \cap \overline{C})+p(A\cap\overline{B})}{P(\emptyset)}$

Where $P(\emptyset)=P(A\cap B \cap \overline{C})+P(\overline{A}\cap B \cap \overline{C})+p(\overline{B})$.

Knowing the Bayes rule the previous equation bothers me because it contains a kind of union between events on the numerator. Maybe this is because there is a kind of redundancy between event B and C. My question is, is it the correct formula to compute the conditional probability in this framework?

Thank you

The right denominator should be $P(\bar C)$, and the right numerator should be $P(A\cap \bar C)$ since $\bar C$ is the event of no receiving information, either because the guy is not there or the guy is there but gives no information. The denominator should not depend on the true state of his "coolness".

An easy way to picture this problem is by doing a diagram. Think of a square and divide it in half, say vertically where the mass (or probability) in the left side represents $P(A)$ and complementary probability in the right. Then divide the square in another half, say horizontally, so that the mass in the top half represents $P(B)$. each of the resulting smaller squares contains the mass of each of the possible intersections between these two events. Finally, you can divide the top half (created in the second step) in half (say horizontally again) where that top part represents $P(C)$, and the bottom part (from this last line up to the bottom of the square) represents $P(\bar C)$. Clearly, $C$ does not intersect with $\bar B$ and $\bar C$ contains $\bar B$, as desired. And you can clearly visualize the probability you are trying to calculate.


How could the economic cost of the world not speaking the same language be estimated? While languages are fun and add color and flair to cultures and make the world a more interesting place, they also have a cost. Beyond the monetary costs of translation/editing/proofreading, interpretation, multi-language signage and so on, there are well-documented instances when minor translation errors have caused serious international crises resulting in loss of life and/or of business.

What are some methods of estimating the (current or historical) global cost of language diversity? (I would like to limit the question to just the cost - language diversity also has benefits, such as tourism, or economic activity pertaining to language training.)

To measure the costs of different people speaking different languages, researchers use a "linguistic distance" metric, see for example this paper. However, measuring the cost of linguistic diversity appears to be challenging. Some effects are shown along the following lines.

Impact of linguistic distance on international trade

In this paper, they construct new series for common native language and common spoken language for 195 countries, which they use together with series for common official language and linguistic proximity in order to draw inferences about

the aggregate impact of all linguistic factors on bilateral trade,
the separate role of ease of communication as distinct from
ethnicity and trust, and
the contribution of translation and interpreters to ease of communication.

Results show that the impact of linguistic factors, all together, is at least twice as great as the usual dummy variable for common language, resting on official language, would say.

Impact of linguistic distance on international migration

In this paper they examine the importance of language in international migration from multiple angles by studying the role of linguistic proximity, widely spoken languages, linguistic enclaves and language-based immigration policy requirements. To this aim they collect a unique data set on immigration flows and stocks in 30 OECD destinations from all world countries over the period 1980–2010 and construct a set of linguistic proximity measures.

Results: Migration rates increase with linguistic proximity and with English at destination. Softer linguistic requirements for naturalisation and larger linguistic communities at destination encourage more migrants to move. Linguistic proximity matters less when local linguistic networks are larger.

This paper on the Costs of Babylon—Linguistic Distance in Applied Economics
may also be relevant.

Impact of linguistic distance on literary translations

Interestingly, one of the latest Freakonomics Radio episode is called "Why Don't We All Speak the Same Language? (Earth 2.0 Series)". There are 7,000 languages spoken on Earth. What are the costs — and benefits? They quote (with references)

  There's also the roughly \$40 billion a year we spend on global
  language services — primarily translation and interpretation. And
  another \$50-plus billion a year spent learning other languages.

Useful references

Victor Ginsburgh and Shlomo Weber, Culture, languages, and
economics, in Victor Ginsburgh and David Throsby, eds.,  Handbook
of the Economics of Art and Culture, vol. 2, Amsterdam: Elsevier,
2014.
Victor Ginsburgh and Shlomo Weber, How Many Languages Do We Need? The Economics of Linguistic Diversity, Princeton, NJ: Princeton University Press, 2011


What is a good AUSTERITY indicator? I am writing a paper on European poverty and I am using a treatment control setup
similar to Difference-in-Difference methods.
Now, since the data I am using is rather recent, I would like to condition on "austerity levels", i.e. I would like to make sure that countries in the control group and those in the treatment group are equal in terms of austerity that has been employed.

This is what I have so far:

First of all I defined austerity as umbrella term for the following:

Public wage and employment cuts
Cuts in welfare expenditure
Rescaling labour protection institutions
Changes in pension age
Cutting the minimum wage
Ad-hoc tax rises

First, I thought about using GDP change as a measure. Oviously, there might be a host of other reasons
why GDP changes, especially when there has just been (or there still is) a large economic downturn (defined by declining GDP).

Then, I thought of social welfare spending as an indicator. However, welfare spending might also (and indeed does)
increase in times of crisis, because more people might become unemployed and need support, even though the individual height of the
help has decreased. Moreover, different countries might have chosen completely different approaches to
austerity. E.g. Italy has chosen to increase the tax burden, to change the pensionary system and to fight inefficiencies in taxation and government,
while Latvia has primarily chosen to cut down public salaries (sometimes by 50%), while Greece seems to try both desperately.
That means that it is not so clear that austerity always reflects the same way and especially that social welfare spending is a bad proxy.

Thirdly, I thought of the height of government debt as a proxy, the logic being:
countries which are highly indebted might be forced to cut down on the welfare state.
Again, this is a rather weak predictor for austerity, simply looking at some examples:
Latvia, with a public debt of 40% of GDP in 2012 had to go through a multilateral bailout, while
Germany, with a public debt of about 80% was involved in many bailouts in the recent years.

What I came up with in the end is the following:
the 10 year government bond interest rates show how much confidence financial markets have in the country in question, moreover high interest rates
simply force the country to save, in order to stand a realistic chance of being able to service the debt in future.
Therefore, conditioning on the 10-year government bond interest rate should be able to control for at least some of the austerity effects.

My problem is that I didn't find many recent year studies using a treatment control approach for aggregated data, and even less which would describe
the choice of the right austerity indicator and I am not really trusting my logic.
It seems like I am missing something or that I am making life somewhat too easy.

I would be really interested in hearing your thoughts and your critique, or in the best case someone knows a well-established austerity indicator.
Thank you in advance!

Best wishes

If it is about European Union, it would make sense to look at austerity as a response to the debt crisis. I would measure austerity not as the level of government debt, but as the change in levels of government debt from year to year. The slower the government debt (as a share of GDP) increases, the more austere are the budget policies of that country.

Also, if you have access to state budget deficits data, it would be a very convincing measure of austerity in my opinion. The less is the budget deficit, the more austere is the budget policy.


Database for Monthly GDP Can anyone point me to a source of monthly GDP? So far I only find yearly and quarterly. I need it for the period of Jan/1999-Jan/2015 for USA, Japan, the Eurozone and UK.

Thank you!

For the US there is a firm that calculates something from monthly data that the quarterly Bureau of Economic Analysis (BEA) GDP data is also based on: http://www.macroadvisers.com/monthly-gdp/


Literature on factors affecting number of houses built Is there any existing literature on the various factors affecting the number of houses constructed in a particular city over, say, a given month? Factors might include: quality of housing stock, a lagging value of housing sale price, house price to earnings ratio.

Preferably, I would like to see literature that describes the relative importance of these factors, perhaps by running a regression--so that way, when I do my own regression on the factors, I can compare the magnitude and direction with existing research.

Anything related to this would be useful too; for example, if there is no paper which predicts the number of houses built, then something which gives, say, a utility yield for constructors would be helpful.

It won't help much with the high frequency variation of interest to you but this is a famous and important paper on this topic:

  I process satellite-generated data on terrain elevation and presence
  of water bodies to precisely estimate the amount of developable land
  in U.S. metropolitan areas. The data show that residential development
  is effectively curtailed by the presence of steep-sloped terrain. I
  also find that most areas in which housing supply is regarded as
  inelastic are severely land-constrained by their geography.
  Econometrically, supply elasticities can be well characterized as
  functions of both physical and regulatory constraints, which in turn
  are endogenous to prices and demographic growth. Geography is a key
  factor in the contemporaneous urban development of the United States.

The Geographic Determinants of Housing Supply (Saiz (2010))

This paper may also be useful:

  The long-run price elasticity for alternative specifications of new
  housing supply is estimated using U.S. annual data for 1950 through
  1994. The basic model expresses residential construction as a linear function of new housing price and the prices of construction inputs.
  Long-run elasticities range from 1.6 to 3.7, suggesting that new
  housing supply is price elastic. Residential construction responds to
  both the real interest and expected inflation rates, but other
  construction cost variables perform poorly. However, the results are
  sensitive to the time-series processes underlying the variables. A
  modified model that expresses residential construction as a function
  of changes in input prices, rather than their levels, produces a
  long-run elasticity of about 0.8 and a significant inverse
  relationship between new housing supply and the construction wage
  rate.

The Long-Run Elasticity of New Housing Supply in the United States: Empirical Evidence for 1950 to 1994 (Blackley (1999))


How reliable is BLS / JOLTS data on quits? I'm looking at the Job Openings and Labor Turnover Survey (JOLTS). It also allows you to disentangle separations between layoffs and quits. The data comes from surveys, i.e. is self reported.

There's several reasons why the quit/layoff data may be misreported, e.g.

Quits that anticipate layoffs, will bias up the number of quits
Firms might not care / not know  exactly, and assume it was a quit/layoff (direction ambiguous)
Responder may purposefully or subconsciously try to defend the firm's image, and misreport

Importantly, there's no reason that the aforementioned reasons should average out to the true data, or that the bias is constant over the business cycle.

Since there are many studies that actually rely on layoff versus quits - is there a study on the reliance of this data?

Here is a short lists of study’s that looks at the on the reliance of JOLTS data as well as make comparisons to other similar data sets.

Analysis of JOLTS Research Estimates by Size of Firm October 2012-
 Katherine Bauer Klemmer
https://www.bls.gov/osmr/pdf/st120060.pdf

ADJUSTED ESTIMATES OF WORKER FLOWS AND JOB OPENINGS IN JOLTS-  Steven Davis,  R. Jason Faberman, John Haltiwanger, Ian Rucker (2018).
http://faculty.chicagobooth.edu/steven.davis/pdf/MS_ch5_StevenDavis-et-al_p315-370.pdf

Help-Wanted Advertising and Job Vacancies- Rob Valletta – Federal Reserve San Francisco
https://www.frbsf.org/economic-research/publications/economic-letter/2005/january/help-wanted-advertising-and-job-vacancies/

UNDERSTANDING ONLINE JOB ADS DATA  - Anthony Carnevale, Tamara Jayasundera, Dmitri Repnikov
https://cew.georgetown.edu/wp-content/uploads/2014/11/OCLM.Tech_.Web_.pdf

Reliability of JOLTS Estimates
https://www.bls.gov/jlt/jltreliability.htm


Fisher Effect - inflation and stock return This is my understanding:

Fisher effect posits that expected nominal returns on any asset would move one-for-one with expected inflation. That is, when expected inflation increase, the nominal return on stock would also increase, is this correct? Besides, based on the theory, inflation would also cause nominal interest rate (the rate which dividend is discounted to the present to obtain stock price -Present Value Model) to increase, which would decrease stock price.

My problem:
The two conclusion above contradicts and I'm confused. Can anyone point the mistake of my thoughts? or PVM and fisher effect cannot be viewed together?

It’s simpler if you start with a bond. If the yield increases (expected return), the price goes down. Future returns are higher, but if you were holding it before the price change, you get a capital loss. Your return to maturity will still be the previous (lower) yield; the capital loss acts as a drag on the future expected returns.

If we assume that the only thing that changes in the stock valuation, an increased discount rate causes a fall in price, with a higher expected return later.

However, the situation for equities is more complicated. The fair value is the discounted value of future cash flows. If expected inflation is higher, why are not the cash flows also higher? Therefore, you need to model the relationship between cash flows and inflation.


Why can Iceland setup and maintain a single-payer system but Vermont can't? Vermont apparently tried to setup a single-payer healthcare system, only to have various healthcare and pharmaceutical companies threaten to ruin them if they did so, at which point Vermont, a state not large enough to take them on, backed down.

Despite this, countries like Iceland have single-payer systems, and don't have to deal with things like nonsense pharmaceutical price gouging despite having only around half the population of Vermont, and six billion dollars less in GDP.

Why is it that Iceland can setup a single-payer system, but Vermont couldn't? What does Iceland have that Vermont doesn't? And how can these differences be generalized such to explain what the requirements are for a state, or country, or healthcare providing NGO to be able to run a single-payer system?

From what Wikipedia tells me on the Vermont case, the Vermont government feared increases in costs and taxes from such a reform. In the end, it boils down to what people/voters/decision-makers are willing to pay for a health care system they believe to be good for the people. Scandinavian countries provide lots of top-class public services (health care, child care, education) but also collect the highest tax rates in the world. Apparently, political will and public opinion in Iceland were willing to accept the price attached, which was not the case in Vermont. Beyond, it is possible that the move from the previous system was less drastic in Iceland, requiring fewer things to change.


Do local taxes help in paying back foreign debts? I always wonder if increasing local taxes could help countries in paying off the foreign debts?

I think taxes generate income in local currency. While foreign debts (from IMF, World Bank etc.) are to be paid in USD. How could this help out?

If you actually raise local tax it would help you can just convert the money raised with local tax into the currency in which the debt is. For example, if UK has some debt in Euros they can raise taxes in pounds and just exchange them at an exchange rate for euros and pay down their euro denominated debt.

However, it would not be possible to pay the foreign debt by just printing the local currency as that would lead to depreciation of local currency and hence its exchange rate.


Example which violates weak pareto and non dictatorship Can you give an example of a social choice rule and a social welfare function that violates the conditions of Weak Pareto criterian and non dictatorship simultaneously?

Such an example does not exist.

Suppose non-dictatorship is violated. WLOG, let individual $1$ be the dictator among $n$ individuals. That is, the social choice function always selects an alternative that ranks highest in $1$'s preference, i.e. $$f(\succ_1,\dots,\succ_n)\in\arg\max\{\succ_1 | x\in X\}.$$

For weak Pareto efficiency to also be violated, we must have two alternatives $y,z\in X$ such that $y\succ_iz$ for every $i=1,\dots,n$, but the social choice function chooses $z$, i.e. $f(\succ_1,\dots,\succ_n)=z$. Yet this clearly contradicts the above condition of dictatorship, in that $z\notin\arg\max\{\succ_d | x\in X\}$.


Will the goods market be in equilbrium along the AD curve? This is a question which was asked in the entrance to Jawaharlal Nehru University's (New Delhi) entrance for their post-grad program specializing in International Economics in 2014.

Which of the following is true regarding the relation between IS and AD curves?

a) The commodity market must be in equilibrium along the IS curve but it may not be in equilibrium along the AD curve.

b) An increase in government spending will shift the IS curve but not the AD curve.

c) The steeper the IS curve, the steeper the AD curve.

d) A horizontal shift of the AD curve is typically greater than a horizontal shift in the IS curve due to crowding out.

I'm pretty sure the answer is A but I cannot find enough matter to convince my friends who are convinced it's D. Please help!

Definition: The Aggregate Demand curve shows the combinations of the price level and level of output at which the goods market and assets (money) markets are simultaneously in equilibrium. This definition proves option a) incorrect. The correct option is d)


interest rate and money supply When the interest rate increases, I learned that money supply decreases because people put their currency back in banks in forms of assets and tend to save more, spend less.

However, money supply includes deposits as well as currency. So what I'm really curious about is whether a rise in interest rate actually decreases money supply.

Doesn't a rise in interest rate just decrease the ratio of currency in the economy and increase the ratio of deposits in the bank, the sum (deposits + currency) remaining the same? So shouldn't money supply technically stay the same?

Maybe this helps: The interest rate is the price of money. If the supply of something goes down, while the demand stays the same, the price moves up. So if the supply of money were to go down, the interest rate would go up, if the demand for money stays the same.

Now, to reduce the money supply and with that to keep an economy from overheating, the central bank could just collect dollar bills and keep them in a vault for later use. Less money, means higher interest rates, means less investment, means less heat in the economy. However, it is easier for the central bank to simply change the price it charges banks borrowing from it overnight. This is just one of three policy tools that the bank uses, the other two being open market operations and reserve requirements. By increasing the price of money, the effect is similar to a change in the money supply, so that the central bank effectively reduces the money supply.

Hope this helps. Have fun studying this! I really enjoy the topic, even though I still know way too little about it!


Definition: What Is The "Trend Growth Rate"? I am a bit unsure about how the "trend growth rate" is defined in macroeconomics. Is it to correct to say that if a time series $\{y_t\}$ may be decomposed as $$y_t=d_t+c_t,$$ where $d_t$ is a deterministic trend and $c_t$ a cyclical component, then $$(d_{t+1}-d_t)/d_t$$ is the "trend growth rate", i.e. the growth rate in $y_t$ assuming $c_t=0$? And if it can be decomposed as $$\log(y_t)=d'_t+c'_t,$$ with another trend and cyclical component, then $$[\exp(d'_{t+1})-\exp(d'_t)]/\exp(d'_t)$$ is the "trend growth rate", i.e. the growth rate in $y_t$ assuming $c'_t=0$?

Sometimes I feel that the definition is $(d_{t+1}-d_t)/d_t$ and $(d'_{t+1}-d'_t)/d'_t$ in the two cases, referring to the growth rate in the trend component and not to the growth rate in the dependent variable $y_t$ ignoring the cyclical component (i.e., setting $c_t=0$ for all $t$).

That is, I interpret "trend growth rate" as the growth rate in $y_t$ ignoring the cyclical component. Is that a correct interpretation?

Any time series can be decomposed in four terms:

trend: the underlying change in the variable if no other factor is present. In the simplest case, think of an upward slopping line. The growth rate of this trend is it's slope.
cycle: the cyclical component of the series, defined by ups and downs like a wave, with a certain "frequency" and "amplitude". Think of this like a wave.
seasonal component: usually a within year cycle. The standard textbook example is that of ice cream sales, which pick up in summer. This is different from the longer cycle described above, and perhaps less smooth (e.g. as ice cream sales are low 3/4 of the year)
noise: natural randomness due to measurement errors or other unobserved yet minor factors, including shocks (e.g. a very hot weather in a week, increasing ice cream sales)

For a series $y_t$, this is something like

$$ y_t = d_t + c_t + s_t + e_t $$

Importantly, all the variables are defined in the same units by construction. E.g. if this is GDP, they are all in value added units (real, nominal, whatever).

A general case of a decomposition is (assume just trend and cycle):

$$ f(y_t) = d^{'}_{t} + c^{'}_{t} $$

In this case, the trend growth of $f(y_t)$ is the growth rate of $d^{'}_t$. But this is not the same as the trend growth rate of $y_t$.

Consider an example. Let us construct a series $y_t$, where $d_t=d_0(1+g)^t$ and $c_t=sin(t)$, and $y_t=d_t+c_t$. This is a trend-cycle decomposition where the growth rate of the trend is $g$:

$$ \frac{d_{t+1}-d_t}{d_t} = \frac{d_0(1+g)^{t+1}-d_0(1+g)^t}{d_0(1+g)^t} = \cdots = g $$

Now, transform the process into log, and let us postulate a new decomposition:

$$ \log y_t = D_t + C_t $$

where $D_t = D_0(1+G)^t$, and $C_t$ is an unknown function. This is by definition correct, but $C_t$ might be an irregular, perhaps not algebraically defined function (like $sin(t)$). In this new case, it is correct, by definition, that the trend growth rate of the log of $y_t$ is $G$, computed with the standard formula.

The central question is: can we find a general method to calculate the trend growth rate of $y_t$ ($g$) using only some transformation of $D_t$? (as in your attempt using the exponential). In other words, can we use only $D_0(1+G)^t$ to obtain $g$?

(Here I highlight the point of why would you ever go down this route, if you can decompose $y_t$ in levels and solve your problem immediately; but anyway, let us continue).

The answer seems to be negative. It is trivial to see that

$$ e^{D_0(1+G)t} e^{C_t} = d_0(1+g)^t + sin(t) $$

where you cannot find a direct function between $G$ and $g$ which does not involve the use of $C_t$ and $sin(t)$. In other words, you need to use the information of both decompositions to solve the problem. But this is circular. To make the link between logs and levels, you need to make the decomposition in levels. But if you do the latter, the answer is there already. No need to go further.

Finally, consider the very special case where the series $y_t$ only has a constant growth rate (trend):

$$ y_t = d_t = d_0(1+g)^t $$

Then,

$$ \log y_t = D_t = D_0(1+G)^t = \log \left(d_0(1+g)^t\right) $$

The following formula recovers the original growth rate of $y_t$ in terms of the trend from the series in log:

$$ \dfrac{e^{D_{t+1}} - e^{D_t}}{e^{D_t}} = \frac{d_{t+1} - d_t}{d_t} = \cdots = g $$

The result can be generalised to any $f(y_t)$, where the transformation of the growth rate calculation has to be $f^{-1}(\cdot)$.


Influential Theory in the Economics of Poverty As far as I can tell, research on the economics of poverty is very empirically driven, and this is probably appropriate. What kind of economic theory has been developed though? I'd also be interested in theory of some influence too. To avoid wholly opinion-based answers, let's measure influence by how the theory directed other research or anti-poverty measures. As an example, I know papers have been written on the theory of poverty traps, but I'm not sure that concept is a contribution from theorists so much as some theorists developed a model for what might have already been an empirical observation. Are there any cases where concepts started in theory?

Links to papers are good, but the question is also about history to some extent, so it would be nice if you can show a trail of this paper influenced that paper or this policy.

To extend @Majoko's comment, you may be very interested in the book Poor Economics which discusses many of the issues you note. It specifically discusses issues with theory, and of course has a lot of empirical work to back it up.

Perhaps on the other end of the spectrum is general equilibrium theory applied to poverty and the developing world. you should really look into Robert Townsend's work. His "Thai Project" is a massive dive into some of the questions you're asking. A reasonable place to start is probably with his books.

As an aside, I was originally hooked on his work by his fantastic application of microeconomic general equilibrium theory in The Medieval Village Economy, which has sadly gone out of print (although I see there are now some used copies finally selling for less than $70, which is nice). He takes very sparse data and asks what theory might be able to tell us -- then very carefully and purposefully walks the reader from a most basic model through many extensions to explore important possible variations of the medieval experience. It's really an excellent example of applied general equilibrium work, and how theory might still be tested/explored with little data.

This isn't my area of research, but I'm very interested to see other answers appear here.


Derivation on p.99 of Salanie, The Economics of Taxation (2nd edition) Starting on p. 98 of Salanie's "The Economic of Taxation" (2nd edition), it explains

  To probe it more rigorously, let us define the utility of taxpayer $w$ when he claims to have productivity $w'$:
  $$
V(w', w) = u(C(w'), Y(w'), w).
$$
  For the mechanism to be revealing, $V$ must be maximal in $w' = w$. Assume that all functions are differentiable and that income $Y$ is positive. Then we have the first-order necessary condition
  $$
\frac{\partial V}{\partial w'} (w, w) = 0 \tag{NC1}
$$
  and the second-order necessary condition
  $$
\frac{\partial^2 V}{\partial w'^2}(w,w) \leq 0 \tag{NC2}.
$$
  Differentiating (NC1) gives us
  $$
\frac{\partial^2 V}{\partial w'^2} + \frac{\partial^2 V}{\partial w' \partial w} = 0
$$
  ...

My question is this: How do we arrive at the last equation from (NC1)? If I differentiate
$$
\frac{\partial V}{\partial w'} (w', w)
$$
with respect to $w$, don't I just end up with $\frac{\partial^2 V}{\partial w'\partial w}$? Likewise, if I differentiate with respect to $w'$, I end up with
$\frac{\partial^2 V}{\partial w'^2}$. What am I missing?

Why are you doing $\frac{\partial^2 V}{\partial w'^2}$ ?

Even if it is said that $w^{'}=w$ at the optimum, it should be taken different when you differentiate it for first order conditions. So, you differentiate it according to $w^{'}$ and $w$.


Estimating $TFP$ using Cobb-Douglas production function Suppose we want to estimate total factor productivity (TFP) under time series framework. Let assume that the production function is given in the Cobb-Douglas form, i.e.
$$Y_t=A_tK_t^\alpha L_t^\beta,$$
where $A_t$ is the total factor productivity (TFP), $K_t$ is capital stock and $L_t$ is labor. After log-linearization the empirical model is given (time series are $I(1)$, therefore we take in the first-difference)
$$\Delta ln Y_t=\mu+\alpha \Delta lnK_t+\beta \Delta  ln L_t+\epsilon_t,$$
where $TFP_t=\widehat \mu+\widehat \epsilon_t$;$\widehat \mu$ is average factor productivity and $\widehat \epsilon$ is the deviation from average over time.
Questions

In the above specification, by construction, $\mathbb{E}\widehat \epsilon_t=0$ (moment condition). It means that by estimating the above specification yields to $TFP_t=\widehat \mu+\widehat \epsilon_t$, which hasn't any trend (upward- or dawnward-sloping). However, it is natural to assume that $TFP_t$ time series can have a time trend. If no, what is the economic interpretation of no-trend in the $TFP_t$? Is it possible to derive time-trend in the $TFP_t$?
What is the interpretation of the estimated $TFP_t$?
Suppose the estimated $TFP_{2020}=2$ or $TFP_{2019}=3$, how these numbers can be interpreted?

Thanks in advance!

If you want to control for some deterministic trend you could add a trend term to your equation. For example, if you think there is a linear trend you can add $\gamma t$:
$$\Delta \ln Y_t= \mu+ \gamma t + \alpha \Delta \ln K_t+ \beta \Delta \ln L_t+\epsilon_t.$$
However, this being said since the equation is already estimated in first differences you have to assume there is a trend in the growth rate of TFP not just in TFP.
Regarding the interpretation, the TFP itself is unitless and there is no agreed upon measurement but higher is better. What studies usually do is not to look at TFP itself but at its growth. So in this case if TFP in 2020 is 2 and TFP in 2019 is 3 the growth rate would be $\frac{2-3}{3}=\approx -0.3$. That would mean that economy technologically regressed somewhat between the two years.
This being said one has to be very careful when interpreting TFP as its estimates can also partially reflect changes in returns to scale, markups due to imperfect competition, or gains from sectoral reallocations (see this World Bank brief). This is especially problem when you look at an aggregate data rather than at firm level panel data.


How do we know a business is allocating resources correctly? If the answer is 'profitability,' why is monetary profitability the barometer? To clarify, it's a two part question:

How do we know a business allocates resources efficiently?
Assuming the answer to above is: "profitability" Why is is 'monetary' profitability taken to be synonymous with efficiency of resource allocation?

A firm has a business plan. From its perspective, resources are allocated “correctly” if they achieve its business plan. However, it is entirely possible that the business plan makes no sense, e.g., it is supplying a product far in excess of what customers are willing to buy. For public companies, equity market analysts attempt to project the effectiveness of those business plans. The volatility of equity prices is an indication that this is not easy.
A single project is typically evaluated with discounted cash flow analysis. (Similar to this question answer: government analysis) This gives us a project-level profitability measure, but we really need to evaluate the global business plan.
The issue is that “profitability” is somewhat vague: on what horizon? It is entirely possible for a firm to invest in projects to build capacity but those initial projects have very low profits (or even losses) during its growth years. However, the hope is that the firm is very profitable when it has reached its target size. Unless we wait, we cannot be sure whether this strategy will generate future profits or not.


Is there a theory about investors' behaviour during bubbles? As far as I can see there are two senses in which it's 'rational' for an investor to buy during a bubble.

The investor has erroneously overvalued the value of the stock/commodity.
The investor is aware that it's a bubble and is overvalued, but believes he can make a profit by selling before the bubble bursts.

There are also 'irrational' explanations, such as the investor being caught up in the hype, or fearing missing out.

The question is, is investor behaviour during bubbles well studied, and are there models explaining it?

The investor has erroneously overvalued the value of the stock/commodity.

Here is a prominent paper that models irrational bubbles:

  This paper attempts to formalise herd behaviour or mutual mimetic
  contagion in speculative markets. The emergence of bubbles is
  explained as a self-organising process of infection among traders
  leading to equilibrium prices which deviate from fundamental values.
  It is postulated furthermore that the speculators' readiness to follow
  the crowd depends on one basic economic variable, namely actual
  returns. Above average returns are reflected in a generally more
  optimistic attitude that fosters the disposition to overtake others'
  bullish beliefs and vice versa. This economic influence makes bubbles
  transient phenomena and leads to repeated fluctuations around
  fundamental values.

Herd Behaviour, Bubbles and Crashes (Lux (1995))

The investor is aware that it's a bubble and is overvalued, but believes he can make a profit by selling before the bubble bursts.

Bubbles, rational expectations and financial markets (Blanchard and Watson (1982)) is a famous paper on this subject.

  This paper investigates the nature and the presence of bubbles in
  financial markets. Are bubbles consistent with rationality? If they
  are, do they, like Ponzi games, require the presence of new players
  forever? Do they imply impossible events in finite time, such as
  negative prices? Do they need to go on forever to be rational? Can
  they have real effects? These are some of the questions asked in the
  first three sections. The general conclusion is that bubbles, in many
  markets, are consistent with rationality, that phenomena such as
  runaway asset prices and market crashes are consistent with rational
  bubbles. In the last two sections, we consider whether the presence of
  bubbles in a particular market can be detected statistically. The task
  is much easier if there are data on both prices and returns. In this
  case, as shown by Shiller and Singleton, the hypothesis of no bubble
  implies restrictions on their joint distribution and can be tested. In
  markets in which returns are difficult to observe, possibly because of
  a nonpecuniary component, such as gold, the task is more difficult. We
  consider the use of both "runs tests" and "tail tests" and conclude
  that they give circumstantial evidence at best.

Here is another:

  We present a model in which an asset bubble can persist despite the
  presence of rational arbitrageurs. The resilience of the bubble stems
  from the inability of arbitrageurs to temporarily coordinate their
  selling strategies. This synchronization problem together with the
  individual incentive to time the market results in the persistence of
  bubbles over a substantial period. Since the derived trading
  equilibrium is unique, our model rationalizes the existence of bubbles
  in a strong sense. The model also provides a natural setting in which
  news events, by enabling synchronization, can have a disproportionate
  impact relative to their intrinsic informational content.

Abreu and Brunnermeier (2003)

[I]s investor behaviour during bubbles well studied, and are there models explaining it?

Yes, this is a huge literature with probably thousands of papers and hundreds of books written about it. Here is a technical book on the subject:  Asset Pricing under Asymmetric Information: Bubbles, Crashes, Technical Analysis, and Herding,
 These books are more historical than theoretical: Manias, Panics and Crashes: A History of Financial Crises, This Time Is Different: Eight Centuries of Financial Folly, Irrational Exuberance.


GMM Estimation of a parameter from Intratemporal Euler of capital constraints I'm trying to estimate $\lambda$ from this intratemporal Euler equation:

$\left[ \dfrac{C_t^{-\sigma}}{C_t^{*-\sigma}} \dfrac{P_t}{S_t P_t^*} \right]^{\lambda} \left[ \dfrac{\bar{P_t} Y_t - \Delta (FR_t)}{P_t C_t} \right]^{1-\lambda}  = 1 $

Log-linearizing this gives: (done in paper)

$\Rightarrow \lambda \left[ \sigma (c_t - c_t^*) - \ln (RER) \right] = (1-\lambda) \left[ y_t - c_t - \ln (P_t / \bar{P_t}) - (fr_t - fr_{t-1}) \right] $

Now, there are a bunch of assumptions and approximations taken into account, but at the end of the day, I will have data on all the macro variables, and my project is to estimate the values of $\lambda$ for different countries (FYI: $\lambda$ represents the presence of risk sharing).

I've heard that there exists GMM methods for such estimations, but Hayashi only has a small section of intertemporal Euler equation GMM work. I was wondering if you guys could advise me on how I can estimate for this $\lambda$ parameter, or perhaps some guideline as to where I can look. Just to note again, I will have all the variables' data. :)

Thanks!

To elaborate on what has been said in the comments already, using GMM based on Euler Equations generally involves uncertainty that motivates some sort of expected orthogonality between a moment equation and some instruments. Here is a common example of a "Consumption-Based Asset-Pricing Model" (see, for example, Campbell, 1993, 1996) posted by Dave Giles:

A representative agent chooses a consumption time-path to maximize expected discounted utility

$E\left[\sum_{i=0}^\infty\beta^i U(c_{t+i})|\Omega_t\right]$,

where $\Omega_t$ is the information set at time $t$, subject to the inter-temporal budget constraint,

$c_t + p_tq_t = r_tq_{t-1} + w_t$, for all $t$.

The optimal consumption path satisfies:

$p_tU'(c_t) = \beta E[r_{t+1}U'(c_{t+1})|\Omega_t]$, for all $t$

Which gives the Euler equation:

$E[\beta(r_{t+1}/p_t)[U'(c_{t+1}) / U'(c_t)]|\Omega_t] - 1 = 0$.

He then imposes the CRRA utility function $U(c_t) = c_t^{1-\gamma}/(1-\gamma)$, making the Euler equation become

$E[\beta(r_{t+1}/p_t)(c_{t+1}/c_t)^{-\gamma}|\Omega_t] - 1 = 0$.

This yields the moment equations:

$E[\{\beta(r_{t+1} / p_t)(c_{t+1} / c_t)^{-\gamma} - 1\}z_t] =
 E[E[\beta(r_{t+1} / p_t)(c_{t+1} / c_t)^{-\gamma} - 1|\Omega_t]z_t] = 0$

with $z_t$ a vector of instruments belonging to $\Omega_t$.

In this scenario, the uncertainty referred to is captured in the expectation operator over the information set $\Omega$. Notice that the interpretation of $\Omega$ motivates which instruments to use in the estimation.

Takeaway: if you want to use Euler equations to motivate GMM, you need some kind of uncertainty. Use uncertainty structure to decide instruments.

Sources

Campbell, J. Y., 1993. Intertemporal asset pricing without consumption data. American Economic Review, 83, 487-512.

Campbell, J. Y., 1996. Understanding risk and return. Journal of Political Economy, 104, 298-345.


Substitution effect when price of both goods change by the same percentage I am trying to grasp the concept of income- and substitution effects.

The way, I've understood it, the decomposition bundle is found, at the original indifference curve, where the slope equals that of the new budget line.

Does this mean that if the price of both goods (assuming a simple model of 2 goods) change by the same percentage, the substitution effect is zero? As the slope of the budget line will remain unchanged.

This seems to intuitively make sense to me, but I would greatly appreciate a 100% confirmation, that this is correct.

Thank you!

Consider the budget line with 2 goods:
\begin{equation}
p_xx+p_yy=m
\quad\text{or}\quad
y=\frac{m}{p_y}-\frac{p_x}{p_y}x,
\end{equation}
where the relative price is $\frac{p_x}{p_y}$.

Suppose now both goods become $10\%$ more expensive (e.g. due to a $10\%$ tax on them). Then the budget line becomes
\begin{equation}
1.1p_xx+1.1p_yy=m
\quad\Leftrightarrow\quad
p_xx+p_yy=\frac{m}{1.1}
\quad\text{or}\quad
y=\frac{m}{1.1p_y}-\frac{1.1p_x}{1.1p_y}x=\frac{m}{1.1p_y}-\frac{p_x}{p_y}x
\end{equation}
where the relative price is still $\frac{p_x}{p_y}$. From the equations, we see that a uniform percentage change in prices produces a pure income effect ($m$ drops to $m/1.1$), but no substitution effect, since the relative price remain the same after the change.


Which measure to check in analysis (p-values or $R^2$)? In an analysis e.g. OLS regression which measure would you look at?

$R^2$, $adjusted-R^2$ or $p-value$?

How would you consider a regression with p-values >0.15 but with an $R^2$ of 40%?
In general in economics, what have you seen?

R-squareds and p-values give different information. For example, suppose that you regress birth weight on mother's smoking. The p-value tells us whether the association is indeed nonzero (in the statistical sense), and the R-squared tells us how much of variation in birth weight is explained by mother's smoking.

p-value > .15 and R-squared 40% would mean that (1) we can't say that the association is nonzero (2) but the explanatory power for the given sample is quite large. The two neither reinforce each other nor are contradictory.


What is Q in the quantitative theory of money? I am testing the quantitative theory of money for South Africa. QP = Mv. It is fairly clear what M and P are (broad money, or M1, price index, etc). But I am puzzled with Q. Is it GDP or does it include also intermediary inputs?

The idea of the theory is that prices depend on the amount of money and the quantity of "goods and services". But since companies and people also pay for intermediate goods and services, I think I need to consider also intermediate inputs and not only final goods and services, as in GDP.

Any ideas? Thank you very much!

Assume there are two agents in an economy, $A$ and $B$, (and some costless transaction mechanism). Per time period, agent $A$ produces alone quantity of intermediate good $q_A$. Agent $B$, thorugh a company where it is shareholder, buys this quantity, the company inputs also some other intermediate good , say $q_B$, and the two together through a production function result in a final good quantity $(q_A,q_B) \to Q$. $Q$ is then bought by agent $A$ and agent $B$ as consumers, at price $P$. $PQ > p_Aq_A$ since it embodies a larger amount of productive resources (assume no inflation, which is not essential here).

Now, for the first transaction to take place, the buying of intermediate good $q_A$, we need quantity of money $M_A=p_Aq_A$. This quantity of money is now held by agent $A$. How much money we want, in order to facilitate also the purchasing by both consumers of the final good?

It will depend on what kind of transactions we envisage to the end of the cycle.  Agent $A$ already has $M_A = p_Aq_A$ with which he can buy part of the final good. If $B$ buys the good pior to any other interaction with $A$, then $B$ must also hold quantity of money equal to $M_B = PQ - p_Aq_A$.  So the total quantity of money needed, in this scenario, is $PQ$, and the intermediate goods do not enter the final equation of the quantitative theory of money.

Assume now that the only quantity of money available is $p_Aq_A$. What can we do to facilitate all transactions? Well, agent $A$ can buy first a part of the final good from company belonging to $B$, then the company will give the money to $B$ as dividends, and then $B$ will give the money to the company as consumer buying the rest of the final product. But in order for the transactions to happen sequentially as described, and be completed within the same time period as previously, money must "move faster". So in such a situation, the velocity of money will be higher than unity.

$$PQ = \left(\frac{PQ}{p_Aq_A}\right) \cdot M$$

where the term in the parenthesis is $\left(\frac{PQ}{p_Aq_A}\right)\equiv \mathbf v$, the velocity of money. But again, the "product" side of the equation will be $PQ$. No counting of intermediate goods.


Separating and supporting hyperplane theorems I am having trouble understanding  the separating and supporting hyperplane theorems. I've read what I can online but am just not able to develop any intuition. Can someone please give a basic outline of these theorems using economic context? And any graphical interpretations would be extremely helpful.

I will sketch a solution for your question on the separating hyperplane theorem together with one economic application to producer theory (for more details please look at MWG).

Theorem: Suppose $B \subset \mathbb{R}^N$ is a convex and closed and that $x \notin B$. Then there is a $p \in \mathbb{R}^N$ with $p \neq 0 $ and a value $c \in \mathbb{R}$ such that $px>c$ and $py < c$ for every $y \in B$

Application (Producer theory): Suppose the production set $Y$ is closed and convex. Then every efficient production $y \in Y$ is a profit maximizing production for some nonzero price vector $p \geq 0 $.

Sketch of proof:
Start with an efficient $y$ and define $P_y$ as the "better than" set with respect to $y$. This set is clearly convex (pick $y', y'' \in P_y$ and their convex combination is clearly "in it"). Next realize that because $y$ is efficient $P_y \cup Y = \emptyset$. We know have all the ingredients to apply our theorem above, and in particular $\exists p \neq 0$ such that $p y' \geq py'''$ $\forall$ $y' \in P_y$ and $\forall$ $y''' \in Y$. Because $y'$ can be chosen arbitrarily close to $y$ (remember $y' \in P_y$) we can straightforwardly show that $y$ is profit maximizing for $p$

Other "famous applications" that you may want to look at are:

1) The "Second Fundamental theorem of Welfare Economics

2) The saddle point approach to dynamic programming developed by Karlin and Uzawa.


Economic theory / papers on sovereign debt? I am an undergraduate student who does some research on sovereign debt and its sustainability.

Which papers are essential to understand how sovereign debt works and which implication it has for the economic policy of the country?

Carmen Reinhart from Harvard Kennedy School works extensively on these questions. She has a recent paper forthcoming  in the Journal of the European Economic Association, 2016, entitled "Sovereign Debt Relief and its Aftermath" with Christoph Trebesch. They study sovereign debt relief in a long-term perspective, using two distinct samples: 1920-1939, and 1978-2010. They published a short Vox-CEPR column on this research.

In their book, with Kenneth Rogoff, "This time is different" they address this question. They have also other interesting and good papers:

Reinhart, Carmen, and Kenneth Rogoff. "Dealing with Debt." Journal of International Economics 96 (July 2015): S43-S55.
Reinhart, Carmen, and Kenneth Rogoff. "Financial and Sovereign Debt
Crises: Some Lessons Learned and Those Forgotten." Financial Crises:
Causes, Consequences, and Policy Responses. Ed. Stijn Claessens, M.
Ayhan Kose, Luc Laeven, and Fabian Valencia. International Monetary
Fund, 2014.

Check also:

Reinhart, Carmen M., and M. Belen Sbrancia. "The Liquidation of
Government Debt." Economic Policy 30.82 (March 2015): 291-333.


Monopolies are just a mathematical misunderstanding A little head-scratcher (and a good example why we should be careful with notation).

Consider a profit maximizing monopoly, that solves over price

$$\max \pi = PQ(P) - C(Q(P)) \tag{1}$$

Following the routine steps (see this post)

we arrive at the important result that, at the profit maximizing price, the price elasticity of demand should be higher than $1$ in absolute terms, or lower than $-1$ in algebraic terms. Namely at the profit-maximizing price we have

$$\eta^* = \frac {\partial Q }{ \partial P}\cdot \frac {P}{Q} <-1 \Rightarrow \frac {\partial Q }{ \partial P}P <-Q$$

$$\Rightarrow \frac {\partial Q }{ \partial P}P +Q <0 \tag{2}$$

But $\frac {\partial Q }{ \partial P}P +Q$ is the derivative of $PQ(P)$ and $PQ(P) = TR$, Total Revenue. So $\frac {\partial Q }{ \partial P}P +Q = MR$, Marginal Revenue and we just obtained that at the profit maximizing price and in order to have elasticity greater than $1$ in absolute terms, we must have $MR^* <0$.

But we also now that at the profit maximizing point we have $MR^*=MC^*>0$.

So a solution does not exist, and therefore we conclude that monopolies are just a mathematical misunderstanding.

Now, I went into the trouble(?) to write this smirking post, I hope somebody will go into the few dozens of seconds required to write a clear answer to point out where the trick lies.

$PQ(P)=TR$, Total Revenue.

$\frac{∂Q}{∂P}P+Q$ is the derivative of $PQ(P)$ with respect to $P$.

$MR$, Marginal Revenue, is the derivative of $TR$ with respect to $Q$.

So in general $\frac{∂Q}{∂P}P+Q \neq MR$


If the price of oil and energy goes down, why does CPI go up? Today, StatsCan revealed that Canada's CPI rose by 1.3%. They are attributing it to lower energy prices, led by the fall in the gasoline index (down 12.6% since one year ago).

From my understanding, an increase in Canada's CPI means Canadian goods/services cost more CAD to purchase.

But if energy has become cheaper, why are things overall becoming more expensive to purchase?

Canadian prices will tend to rise when energy prices fall because Canada tends to export oil and import other things. As a major oil exporter, a fall in the price of oil decreases the value of the Canadian currency— because foreigners have less need to purchase Canadian dollars with which to buy oil— causing other things to be more expensive to purchase (due to an increase in the prices of imported production inputs and finished goods).

Incidentally, this is why the Canadian Dollar is known as a commodity currency.


Currency Value Formula I recently have gained interest in the way currency value is derived in crypto-currencies and have researched the ins and outs of supply and demand. Is there a particular mathematical formula to compute both the supply and demand curves based off of data. In other words what data is needed in order to come up with currency value. I understand that supply of course is just the unit amount of a currency that is available for consumption. Demand however seems to be a bit tricky in that its curve can be adjusted by more than one factor.

Research Link

EDIT

I am by no means attempting to argue the legitimacy of crypto-curriences because I think the value of bitcoin alone explains for itself how much we value it regardless of any real physical asset to back it up. I am merely asking by what means is that value derived.

This is a difficult question in that it is very difficult to prove that something is impossible. However, based on the types of analysis done in financial markets, estimating supply and demand curves is obviously difficult to do.

The usual methods for valuing assets in financial markets is to rely on some relative value versus a similar asset, or discounted cash flow. For a currency, we can compare the prices of similar items (hourly wages, goods prices) to get fair value. However, I am unaware of items sold at fixed prices in crypto currencies that would allow us to use a similar valuation method.

As for supply and demand, unless we have a reason to know that supply and demand curves follow some particular parameterisation, all that it says that for every buyer there is a seller. A price change can either be explained by the supply curve or the demand curve shifting (or both); we have no idea what happened. There is no clear method to go from observed transaction data to back out supply and demand curves.

For example, imagine there are a sequence of transactions at rising prices. Is that because there was an increased demand by buyers, or was it the result of existing owners being less willing to sell? Since every transaction has two sides, we have no idea. All we know for sure is that the price went up - which we could see by just looking at the time series of prices.

Furthermore, prices can change without any transactions. In the financial markets, prices jump on the release of economic or corporate news. This is much more easily interpreted as a change in fair value, rather than a shift in demand or supply curves.

Finally, it is unclear what a supply or demand curve represents. In the short term, a crypto currency supply is fixed (at least until the next coin is “mined”). How exactly can the quantity supplied or demanded change?

In other words, probably the only way to see whether “supply and demand” work is to build a model that works. I am unaware of any successful attempts in other asset markets to build such a model, so you have little guidance on how it could be done.

Addendum: It is difficult to control supply to keep an asset near a target level. Preventing the price from going up is easy, as you could just flood the market. Stopping the price from falling is difficult. You cannot destroy currency units held by people, and so you cannot reduce the amount outstanding. If people want to sell at a lower price, there is little you can do except buy the crypto up with some kind of currency reserves. (Which is how currency pegs are defended.) However, currency pegs tend to fail. (I believe some crypto currencies follow a backing strategy; I do not know how popular those currencies are are.)


Why do Higher Interest Rates attract Foreign Investors? I am reading the following Article at Investopedia which states

  Generally, higher interest rates increase the value of a given
  country's currency. The higher interest rates that can be earned tend
  to attract foreign investment, increasing the demand for and value of
  the home country's currency. Conversely, lower interest rates tend to
  be unattractive for foreign investment and decrease the currency's
  relative value.

I do not understand why Higher Rates would attract Foreign Investors, therefore unable to see how they can profit from it.

How does this work, and what are some of the common ways Foreign Investors use this to their advantage?

The answer lies in this part of your posted quote:

"The higher interest rates that can be earned tend to attract foreign investment, increasing the demand for and value of the home country's currency."

Foreign investors would be attracted to the higher interest rate if they are able to receive a better return on their investment than they would get from their local market.

It sounds like your confusion might arise from the fact that a higher interest rate would mean the borrower has to pay out more in interest. Your quote refers to investors, the party receiving the higher interest payments.

A common way in which foreign investors would use higher interest rates to their advantage is by borrowing money locally at a lower rate and investing it in foreign markets at a higher rate. Profits would be calculated based on the difference in interest on the money (in a simplified situation). A more realistic scenario would also  include exchange rate fluctuations and other variables.