Variance of Quantile Regression I have been looking at quantile regression (since it is a much better method when trying to quantify welfare effects), and I am struggling with the following, standard model:

$\textbf{Model:}$

$y=x'\beta(u)$ where $u|x\text{~}Uniform\,[0,1]$ and for any $x,\, x'\beta(\tau)$ is a strictly increasing function in $\tau$.

For simplicity, assume $x=(1,x_1)$ meaning that we have one regressor and an intercept

$\textbf{Question:}$

What is $Var(y|x)$?

I cannot say how helpful this is for you but if your model is

$$y_i = a(u_i) + b(u_i)x_i, \;\; u_i|x_i \sim U[0,1] \;\;\forall i$$

Then

$$\text{Var}(y_i\mid x_i) = \text{Var}[a(u_i)\mid x_i] + x_i^2\text{Var}[b(u_i)\mid x_i] +2x_i\text{Cov}[a(u_i),b(u_i)\mid x_i]$$

which tells you that $y_i$ is conditionally heteroskedastic.
This can acquire a complicated integral expression if you use the "Law of unconscious statistician" and the fact the the denisty function of a $U[0,1]$ random variable is just unity:

$$\text{Var}(y_i\mid x_i) = \int_0^1[a(u)]^2du - \left(\int_0^1a(u)du \right)^2 \\ + x_i^2\cdot \left[\int_0^1[b(u)]^2du - \left(\int_0^1b(u)du\right)^2\right] \\
+2x_i\cdot \left[\int_0^1a(u)b(u)du - \int_0^1a(u)du\int_0^1b(u)du \right]$$


Rules of total differentials What are the rules of total differentials? I. e., given an arbitrary expression of which to take the total differential, what rules can be applied to arrive at the desired result, and how does one go about doing so?

Recall that the total differential $df$ of a function $f : \mathbb{R}^n \to \mathbb{R}$, $x = (x_1, \dots, x_n) \mapsto f(x)$, is defined as

$$df = \sum_{i = 1}^n \frac{ \partial f }{ \partial x_i } dx_i = \sum_{i = 1}^n f_{x_i} dx_i = \nabla f \cdot \left(dx_1, \dots, dx_n\right)^\top$$

Let $X$, $Y$, $Z$ be variables, and let $a$, $b$, $c$, $k$ and $n$ be constants. Then the following rules are valid:

$$\begin{alignat}{3}
dk & = 0 && \qquad \text{(constant rule)} \\
d(cX^n) & = cnX^{n-1} dX && \qquad\text{(power rule)} \\
d(aX + bY) & = a\cdot dX + b \cdot dY && \qquad\text{(sum rule)} \\
d(XY) & = Y \cdot dX + X \cdot dY && \qquad\text{(product rule)} \\
d(XYZ) & = YZ \cdot dX + XZ \cdot dY + XY \cdot dZ && \qquad\text{(product rule for three factors)} \\
d\left( \frac{X}{Y} \right) & = \frac{ Y \cdot dX - X \cdot dY }{ Y^2 } && \qquad\text{(quotient rule)} \\
d(X^{-1}) & = -\frac{ dX }{ X^2 } && \qquad\text{(inverse rule)} \\
d(X \circ Y) & = X'(Y) \cdot dY && \qquad\text{(chain rule)}
\end{alignat}$$

When evaluating around $(X, Y, \dots) = (X_0, Y_0, \dots)$ (e. g. around the steady state of a model), replace $X$ by $X_0$, $Y$ by $Y_0$ etc. in the above rules. For $X = X_0$ or $Y = Y_0$ respectively:

$$\begin{align}
d(cX^n) \biggr\rvert_{X = X_0} & = cnX_0^{n-1} dX \\
d(X^{-1}) \biggr\rvert_{X = X_0} & = -\frac{ dX }{ X_0^2 } \\
d(X \circ Y) \biggr\rvert_{Y = Y_0} & = X'(Y_0) \cdot dY
\end{align}$$

For $(X, Y) = (X_0, Y_0)$:

$$\begin{align}
d(aX + bY) \biggr\rvert_{(X, Y) = (X_0, Y_0)} & = a\cdot dX + b \cdot dY \\
d(XY) \biggr\rvert_{(X, Y) = (X_0, Y_0)} & = Y_0 \cdot dX + X_0 \cdot dY \\
d\left( \frac{X}{Y} \right) \Biggr\rvert_{(X, Y) = (X_0, Y_0)} & = \frac{ Y_0 \cdot dX - X_0 \cdot dY }{ Y_0^2 }
\end{align}$$

For ($X, Y, Z) = (X_0, Y_0, Z_0)$:

$$\begin{align}
d(XYZ) \biggr\rvert_{(X, Y, Z) = (X_0, Y_0, Z_0)} & = Y_0Z_0 \cdot dX + X_0Z_0 \cdot dY + X_0Y_0 \cdot dZ
\end{align}$$

As an example, consider the IS equation

$$Y = C((1 - t) \cdot Y) + I(i, E) + G$$

of an IS/LM model of a closed economy with a flat tax rate $t$. Take the total differential around the current state of the economy, using the rules above and setting $Y^v = (1 - t) Y$:

$$\begin{align}
dY & = d\left[ C((1 - t) Y) + I(i, E) + G \right] \\
& = d\left[ C((1 - t) Y) \right] + d\left[ I(i, E) \right] + dG \\
& = C_{Y^v} d\left[ (1 - t) Y \right] + I_i \, di + I_E \, dE + dG \\
& = C_{Y^v} \left[ Y_0 d(1 - t) + (1 - t_0) \, dY \right] + I_i \, di + I_E \, dE + dG \\
& = C_{Y^v} \left[ Y_0 (-dt) + (1 - t_0) \, dY \right] + I_i \, di + I_E \, dE + dG \\
& = C_{Y^v} \left[ (1 - t_0) \, dY - Y_0 \, dt \right] + I_i \, di + I_E \, dE + dG
\end{align}$$

References:

Chiang, Alpha C. and Kevin Wainwright, Fundamental Methods of Mathematical Economics, 4th ed., McGraw-Hill 2005, chapter 8.


The supply and demand of Virtual Products We know that the fundamental economic problem is scarce resources relative to unlimited wants. **Does this apply to apps and Ebooks?**They are essentially virtual products who have in theory have unlimited supply.

The book Information Rules by Google Chief Economist Hal Varian (with Carl Shapiro) deals with many issues raised by the particular features of the digital economy. In general, he finds you don't need new models, and that things are well approximated by high fixed and low or zero marginal cost of production.


What is the difference between budget constraint and budget line? Are those things mean the same thing or they are actually different?

One is an algebraic formula, the other is the geometric representation of that formula.

They are the same as much as a straight line and the equation describing said line are the same.


Non-viable Industry with demand curve above supply curve Say we have a supply and demand relationship, in which the demand curve does not intersect with the supply curve and the demand curve is situated above the supply curve. What phenomenon describes such a relationship, does such a phenomenon exist?

I was thinking maybe country $A$ has regulations in place such that suppliers cannot sell product $a$ for more than some amount $S$. Maybe there is an ethical issue such as underpaid staff associated with the production of the item, so consumers will not buy $a$ at such a low price. However this seems quite far fetched and I don't know whether such a scenario exists.

If we consider that no one wants an infinite number of any material thing other people can supply and that there are only a finite number of people/firms, the demand function should be bounded. That means that eventually the price people are willing to pay for one extra unit of the good will be zero, and assuming non-negative production costs at this point the supply curve will not be under the demand curve. So the situation you describe can only exist in theory.
However you can have examples where for large quantities the demand function is over the supply function, e.g., the market for ordinary air. People desperately need air (up to a limit), yet it can be supplied at zero cost (it is freely available, again up to a limit).


Luce Choice Axiom, Quantal Response Equilibrium How is the Quantal response equilibrium model influenced by the Luce choice axiom since Quantal Response equilibrium takes into account the rationality parameter ß and I dont see the mention of rationality perturbation in Luce Choice Axiom? And it would be of great help if anyone could post an example application of the Luce Choice Axiom. Thank You.

A few quotes from Jessie and Saari (2015) may be of interest.

Regarding Luce Choice Axiom (LCA):

  The effect of LCA is to endow each alternative with an intrinsic level of likelihood that is independent of the particular set from which it is chosen. Mathematically speaking, in Luce’s formulation, the choice axiom implies the existence of a weight function $v(A)$ for an alternative $A$ in which the probability of selecting $A$ can be written as
  \begin{equation}
P_T(A)=\frac{e^{v(A)}}{\sum e^{v(B)}}\tag{1}
\end{equation}
  where the sum in the denominator is taken over all alternatives in $T$ (Luce, 1959). Because function $v(\cdot)$ does not depend upon the set $T$, it defines an intrinsic weight of the alternative. An important special case is when $v(\cdot)$ is a linear function; here Eq. (1) defines the multinomial logit model.

Regarding Quantal Response Equilibrium (QRE) [in a $2\times2$ normal form game, where Row player chooses between Top and Bottom]:

  Instead of perfectly observing the payoffs for a given strategy, assume that the subjects perceive the expected value plus a stochastic term $\frac{\epsilon}{\lambda}$, where $\epsilon$ is a random variable and $\lambda$ is a magnitude parameter. In this framework, Row strategically chooses Top if
  \begin{equation}
E(\text{Top})+\frac{\epsilon_1}{\lambda}>E(\text{Bottom})+\frac{\epsilon_2}{\lambda}
\;\Leftrightarrow\; \lambda[E(\text{Top})-E(\text{Bottom})]>\epsilon_1-\epsilon_2. \tag{4}
\end{equation}
  That is, Row’s choice of a probabilistic strategy combines the actual expected values with a measure of how it is recognized. A common assumption about $\epsilon_i$ is that they are independent and identically distributed type-I extreme value random variables. In the general case of several strategies, the probability $p_i$ that strategy $s_i$ is chosen is given by
  \begin{equation}
p_i=\frac{e^{\lambda E(s_i)}}{\sum_j e^{\lambda E(s_j)}}.\tag{5}
\end{equation}
  This expression is identical to the LCA multinomial logit expression in Eq. (1) with  being a strategy’s expected payoff, with an emphasis on preserving the LCA structure.

  The $\frac{\epsilon}{\lambda}$ form of the stochastic term in Eq. (4) makes it reasonable to treat $\lambda$ as a measure of “rationality”. This is because with small $\lambda$ values, the random terms dominate; indeed, with $\lambda=0$ (Eq. (5)), the subjects are completely insensitive to differences in expected value, so strategies are selected from a uniform distribution. In contrast, the effect of the random terms diminish as $\lambda\to\infty$, which means that the subjects become increasingly responsive to payoff differences; in the limit they reach the Nash equilibrium.


What are the economic perspectives regarding the game of salary negotiations? Apologies if I use non-economic language to explain what I suspect is a practical application of economics. I have no formal education in economics whatsoever but hoping you guys/girls might be able to help. :)

I'm the managing director of a company in which we run appraisals every 6 months. Each time we negotiate salary I have in my mind's eye this picture...

Assuming the 'correct' salary for an employee is 70k, there's an incentive to offer slightly more. 'Slightly more' because there's some error in estimating the market rate and the costs of getting this wrong are high. I've added a staff churn costs of £20k/yr for getting this wrong based on loss of knowledge, morale, recruitment costs and what I refer to as a 'change incentive' for the replacement employee. The change incentive is the amount you must offer a new employee beyond their current rate (market rate?) to discount the loss of familiarity and to take on the risk of joining a new employee.

Belief 1 - Underpaying employees is much more costly over the long term once staff churn is taken into account.

Belief 2 - the employee has better information about their value - based on them being nearer the information about their skills, positive contributions and self interest in the literal sense.

Belief 3 - salary expectation in job adverts are positively skewed to discount against the risk and transaction costs to the employee of change. Nobody switches to an identical salary unless it's a sideways move. Anecdotally, I've heard advice to change jobs every few years in order to raise your salary faster. Humans tend to be unnecessarily risk adverse and you can give yourself a competitive edge by overcoming this bias.

Belief 4 - primary information source for market value are job adverts and job offers. These overvalue for the reasons in belief 3.

Belief 5 - Protracted and/or aggressive salary negotiation is costly in itself. If there's a big discrepancy it can create feelings of being undervalued.

Belief 6 - Employees will be content and thus likely to remain with the company if they feel they are receiving the market rate.

Assumptions: the company is otherwise a pleasant place to work.

In my particular industry, I'd consider low staff churn rates and high staff morale as being a distinct and powerful competitive advantage. The figure of 20k churn cost is probably conservative.

In England, where I live, the cultural norm is for the company to either start the negotiation or more commonly simply state what the pay rise is going to be. This is followed by a period of watching how much they squeak squirm with dissatisfaction. Given the beliefs above and an industry where staff churn is costly, I'm inclined to lean in the other direction and either let them begin the negotiation or even more radically, simply request what their salary should be; as is common for sellers of other types of good. Salary negotiation seems to me to be unique in that the buyer of the good (their labour) dictates the price and then watches to see if the supply vanishes (resigns).

Is it an optimal strategy in salary negotiations to let the employee decide?

I will provide a simple game-theoretic modelling of the situation.
A new year starts and a company wants to make a wage-increase offer to an existing employee. Let $e$ be the employee's current efficiency and the corresponding wage $h(e)$ (which, represents an increase over previous wage). Let $v$ be the premium observed in the market for new hires (so if the employee goes to another employer he will earn $h(e) + v$). Let $c$ be churn costs (recruitment plus loss of efficiency etc) to the current employer, if the employee leaves and needs to be replaced.

This is a sequential game so we have to use the extensive form.

A) Firm offers a wage

First, the case where the firm ($F$) offers a wage and the employee ($E$) decides what to do:

The first outcome refers to the firm's cost, the second to the employee's wage. We have assumed that if the employee is offered the new hire premium it stays with the firm.
Let $p_l$ be the probability that the employee will leave if he is offered $h(e)$ only. The firm faces the following expected costs:

$$EC [h(e)] \equiv EC_{A1}= (1-p_l)h(e) + p_l[h(e)+v+c] = h(e)+p_l[v+c]$$

$$EC [h(e)+v] \equiv EC_{A2} = h(e)+v$$

Then in order for the firm to nevertheless offer $h(e)$ it must be the case that

$$EC_{A1} < EC_{A2} \implies h(e)+p_l[v+c] < h(e)+v$$

$$\implies p_l < \frac {v}{v+c}$$

and it should offer $h(e) + v$ if the inequality points to the other direction.

Let's move now to the OP idea, to tell the employee to ask for a wage. Here we have

B) Employee asks for a wage

Here too the first outcome is the firm's cost. We have allowed for the possibility that the employee asks only the efficiency wage. This is crucial.

Since we are in the "decision about the process structure" phase, we assign some probability $p_e$ that the employee may actually ask for just the efficiency wage. This is important.
It is also important to note that, assuming that the employee has asked for $h(e) + v$, while the criterion for whether the firm should accept or counter-offer only $h(e)$ has exactly the same expression as before, we are looking at a different probability. Here the firm must decide whether the employee is "bluffing" (he does not have an offer from another firm), or not. This is a different probability than the previous one. Here, the firm has additional information (for better or for worse), and so it has to make a difference assessment. Call the probability of not bluffing $p_c$.

We have that

$$p_l < p_c$$

because the former is a conditional probability of the same event ("the employee leaves"), while the latter is the unconditional probability. Keep this inequality for later.

Assume that the firm has estimated somehow ("if the employee asks for $h(e)+v$ there is $p_c$ probability that he will leave if I counter offer $h(e)$ only).
If this is estimated, then the firm already knows what it will do if the employee asks for the new hire premium -and it will depend on the specific values of the various quantities here.

So given an estimate for $p_c$ we are looking at two possible expected costs for the firm
B.1. The firm will counteroffer $h(e)$
here the expected cost is

$$EC_{B1} = p_eh(e) + (1-p_e)\cdot [(1-p_c)h(e) + p_c(h(e)+v+c)]$$

$$=  h(e) + (1-p_e)p_c(v+c)$$

B.2. The firm will accept $h(e)+v$

$$EC_{B2} = p_eh(e) + (1-p_e)(h(e) +v) = h(e) + (1-p_e)v$$

WHAT STRUCTURE TO CHOOSE?

Now we want somehow to compare the two structures and select the one that is more profitable for the firm. This requires to examine various cases characterized by the relation between the various probabilities.

CASE 1 : $p_e = 0 , p_l < p_c < v/(v+c)$

Here the firm will offer $h(e)$ in structure $A$ (so expected cost $EC_{A1}$), and will counter-offer $h(e)$ in structure $B$ (so expected cost $EC_{B1}$).
Given the assumed values of the probabilities we have that

$$EC_{A1} = h(e)+p_l[+v+c] < h(e) + p_c(v+c) = EC_{B1}$$

an so we should stick with the traditional structure $A$ where the firm offers first a wage.

CASE 2 : $p_e = 0 , p_l  < v/(v+c) < p_c$

Here the firm will offer $h(e)$ in structure $A$ (so expected cost $EC_{A1}$), but will accept $h(e)+v$ in structure $B$ (so expected cost $EC_{B2}$).
Given the assumed values of the probabilities we have that

$$EC_{A1} = h(e)+p_l[v+c] <  h(e) + v =EC_{B2}$$

and again we should stick with structure $A$.

CASE 3 : $p_e = 0 ,  v/(v+c) < p_l  < p_c$
Here we compare $EC_{A2}$ with  $EC_{B2}$
$$EC_{A2} = h(e)+v  = EC_{B2}$$

No winner here, but overall we see that
the incentive to adopt structure $B$ hinges on whether the employee may after all ask only for $h(e)$. ($p_e>0$ is necessary but not sufficient condition to adopt structure $B$).

CASE 4 : $p_e > 0 , p_l < p_c < v/(v+c)$

Here too we compare $EC_{A1}$,with $EC_{B1}$ but with $p_e>0$ so

$$EC_{A1} = h(e)+p_l[v+c] < >h(e) + (1-p_e)p_c(v+c) = EC_{B1}$$

We stick with structure $A$ if $p_e < (p_c -p_l)/p_c$, and we adopt structure $B$ if the inequality runs the other way.

CASE 5 : $p_e > 0 , p_l  < v/(v+c) < p_c$

Here we compare  $EC_{A1}$, with $EC_{B2}$ but with $p_e > 0$

$$EC_{A1} = h(e)+p_l[v+c] <  h(e) + (1-p_e)v = EC_{B2}$$

as one can verify. So here we stick with structure $A$.

Finally

CASE 6 : $p_e > 0 ,  v/(v+c) < p_l  < p_c$

Here we compare $EC_{A2}$ with  $EC_{B2}$
$$EC_{A2} = h(e)+v > h(e) + (1-p_e)v = EC_{B2}$$

and we should go with structure $B$.

VERBAL SUMMARY

1) If we expect that employees will always ask for the new hire premium if they get to ask first, then we should stick with the structure where the firm offers first a wage.  (Cases (1,2,3)

2) If there exists a positive probability that the employees may just ask for $h(e)$ then :
2a) If the firm will stand by $h(e)$ in any case and structure, we should keep the structure where the firm offers first a wage if $p_e < (p_c -p_l)/p_c$ (Case 4)
2b) If the firm will go for $h(e) + v$ in any case and structure, we should choose the structure where employees ask first (Case 6).
2c) If the firm will play differently in the two situations, we should keep the structure where the firm offers first a wage. (Case 5).

As is usually the case reality is more complex than that: negotiations may have more rounds, and the firm and the employee may not even agree on $h(e)$ although such disagreement is less common than "accepted wisdom" would have it.

But the general feeling I get from all the above analysis is that the main reason I would consider implementing a structure where employees "ask first" is if I thought that there exists a high enough probability that they won't ask for the new hire premium -and still, if at the same time I think that they won't try to bluff (i.e. I expect $p_c$ to be close to unity), again it would be likely preferable to stick with the traditional model.


Difference-inDifference model with Discontinued Treatment I have a situation where I observe two groups A and B for three years. Group A never received any treatment. Whereas group B received treatment in year 2 only. I can estimate the impact of the treatment by using only years 1 and 2 data with standard difference-in-difference approach. I am also interested in estimating the impact of discontinuation of treatment.
If I use year 2 and 3 data only, the treatment happens in period 2 and the treatment and control groups are not comparable. Would it be okay to use all three years of data and treat the "discontinuation of treatment" as second treatment?

You presumably should be using all 3 years for the data. Given that you had the appropriate conditions for diff-in-diff (parallel trends), and you're looking at a standard case of the treatment only being relevant in treated periods (no lagged effects), then the additional data should not hurt your estimates.  Additional years of untreated data will help you more appropriately measure the de-facto difference between the two groups, and therefore more precisely measure the effect treatment.
Take a look at panel data and difference-in-differences application - you add fixed effects for all $t$ and all $i$, and create a DiD variable for the the interaction of the treatment and control variable.  It doesn't, under ideal conditions, matter what the timing of treatment is.  If you do have a reason to believe there are lagged effects you should, of course, account for that with lags/leads of treatment, which I believe the other answer is concerned about.


VaR and rating for commercial banks I would like to know if there exist a database where Value at risk of commercial banks are.

Beyond that if there is a connection between the rating from agency (as S&P, Fitch etc..) and the VaR of banks. And where I can find references of that.

I restrict myself to credit rating for Banks only.

There are different solutions, in bold are my preferred one.

To have just an idea about single banks register a free user account to rating agencies as S&P, Fitch, Moody's and type the bank of interest. Also history in some cases is available. (this solution is just per bank and slow)

Database Compuststat via Wharton (WRDS subscription), not free. Only S&P historical ratings, but with a complete database after you insert the correct tags of interest. Download via web, or with external software R, Matlab, etc.
Bankscope (new Orbis bank), not free via web or WRDS subscription. Fitch ratings but they are not able to be saved to file due to restrictions (just to that manually). Very user-friednly database and historical data too.
Thomson one banker, not free. A complete overview of ratings can be seen bank for bank with historical view. But it is not possible to get it in batch for historical ratings for all the banks in one shot. Slow but complete.

Other databases can be Datastream (not free and partially historical data ), Bloomberg (current and historical ratings data but one company at time).

There are also other database but after some research I managed to get them.


Why use marginal rather than average tax rates in incentive analysis? Why do tax analysts worry about marginal tax rates, not average effective rates, in looking for incentive effects of taxes

People make decisions based on how the decision will change things.  If I work an extra \$1000 worth of time, then I have to pay $\$1000 * \text{marginal tax rate}$ in taxes.  The average rate is irrelevant to that calculation.  It's a little more complicated than that in that the marginal tax rate may change over that \$1000.

The only time that the average tax rate would matter would be if I were asking at the beginning of the year if it would make sense to not work at all that year.  But I can reach the same result with marginal tax analysis and not be restricted to the beginning of the year.  The marginal-based analysis already has to handle things like the marginal rate changing.

The average tax rate provides useful information so seldom that there's no real point in using it.

The marginal rate tells us how a change from the status quo will affect things.  If my marginal rate in the example is 25%, then I can make an extra $750 by working that extra.  Is that more or less than my value of my leisure time?  That's a real decision.


Publishing in conferences and then journals In economics, it is very common for researchers to submit papers to conferences before submitting their papers to journals. Are there any cases in which submitting a paper to a conference makes submitting the same paper (or a similar one) to a journal more difficult? If so, what are the warning signs?

To take a random example, this conference says that they publish submitted papers as peer reviewed conference proceedings. Would that be an issue if one wanted to subsequently publish a paper in a journal?

In my experience peer reviewed proceedings are okay but if its a partner journal its not. I actually have fairly recent experience with this because one of my papers that I just submitted to a journal was published at one conference as a part of peer reviewed conference proceedings. Since, I am young scholar myself I also first consulted this with both my mentor and I actually even send an email to my target journal asking if submitting paper to that conference counts as prior publication that would disqualify it from publishing there and they said its okay they dont count that as prior publication. However, it would not be okay if the publication would be in actual journal (if the conference has a partnership with one) - the website you linked mentions this.

But in case the conference is partnered with some journal and this is not just proceedings they wont publish there your work without your consent - at least that is my experience. Last summer I send one other paper to a conference organized in my home country and they were also having similar opportunity as the conference you linked here and actually they selected my paper to be in the journal but since its a local publication I declined and they were fine with it - at least to my best knowledge (although probably try to first send an email to the conference organizers).

Also when I was inquiring about this generally more experienced professors told me its usually positive to have your paper been already in peer reviewed proceedings. They told me that reason for that is that most journals dont have double blind peer review. Hence the reviewers can actually google you and some might think that if your paper was accepted at a good conference and already been peer reviewed once then it is of high quality, although I suppose the converse could be true with bad conference. This being said I only have two papers under my belt so maybe take this advice with a grain of salt, but I think the advice of the more experienced professors at my uni should be solid, some of them have quite impressive publication records.


Taylor rule and optimal monetary policy In a New Keynesian model, under the assumption of sticky prices, we need to express the monetary policy through an equation in order to close the model made of New-Keynesian Phillips curve and dynamic IS curve.

I've read that an easy choice is to use the so called Taylor rule, which express the interest rate as a function of inflation (and possibly a random component). But, I've read that it is a suboptimal choice because it is something exogenous, whereas if we endogenously compute the optimal monetary policy we can reach a better result.

My question is why using a Taylor rule when we know it is not optimal to do that?

I'm not sure I fully understand what you mean by computing it endogenously? The nominal interest rate would be endogenous in the NK framework because the output gap and inflation are endogenous. There'd be feedback between nominal interest rates and inflation, which both feed into each other for example. So in that sense I'd consider the approximation of interest rate policy using a Taylor rule as entailing that interest rate policy WAS endogenous wrt. the output gap and inflation.

As for why we'd use the Taylor rule as opposed to some more complex but accurate approximation for interest rate policy... well I can only suppose that the Taylor rule is a sufficiently good approximation such that the marginal benefit of adding more complexity / accuracy is minimal and perhaps less than the computational cost of doing so. There comes a point where you start to prioritize parsimony more and more. Perhaps this is the motivation.


Price elasticity of demand in the point of economic equilibrium The function of demand is:\begin{align*} D(p) = 66-3p-p^2 \\\end{align*}
The function of supply is: \begin{align*}S(p) = 4p^2+8p-114\\
\end{align*}
The task is to find price elasticity of demand in the point of economic equilibrium.

I have found out that the equilibrium price is 5 and equilibrium demand is 26.

I also have a formula that states that $E = k * P/Q$
, where $P$ - equilibrium price, $Q$ - equilibrium demand and $k$ - coefficient  of $S(p)$ slope

How to find $k$ or are there another methods to solve this task?

Your formula is overly simplified.

The elasticity is supposed to be "how much does supply change if the price changes". Now, the natural way of looking at this is $S'(p)$, the derivative of $S$. However, the units of that are hard to make use of. Hence, we normalize $S'(p)$ by multiplying it with $P/S(p)$, hence getting the "percentage response of $S$ to a percent change in $P$".

Long story short, your $k$ should satisfy

$$ k = S'(p)$$

Note that this is the price elasticity of supply. For the price elasticity of demand, you would instead use $D'(p) P / D(p)$.


Can budget lines be discontinuous? It's been awhile since I've taken introductory microeconomics. I read budget lines can be discontinuous awhile ago but am suspicious as to such a concept being discussed in intro micro classes particularly calling them budget 'lines'.

The problem:

  Say Jill likes food and clothing. Jill has 200 to spend on food and clothing. One unit of food costs \$1 while one unit of clothing costs $2.

Budget line is 200=F+2C

  Say Jill receives an 80% discount on food but it applies up to 100 units.

New budget line is 200=0.2F+2C for 0-100 then same as old for 100 onward?

So it's discontinuous? So it's not really a budget 'line' right (though piecewise, it's a line, I guess).

I guess the discount holds for the 100 first units of food even if she buys more than 100. Therefore the new budget line is
\begin{equation*}
\left\{
   \begin{array}{ll}
   & 200 = 0.2 F + 2C \text{ if } F < 100 \\
   & 200 = 0.2 \times 100 + F-100+2C \text{ otherwise }
   \end{array}
\right.
\end{equation*}
which is continuous.


How does a central bank create the money used for quantitative easing or lowering the value of their currency? Up until last week, the Swiss central bank used Francs to buy Euros, in an effort to lower the value of the Franc; today the European central bank announced that it would use Euros to  buy bonds in order to fight deflation.

I assume that the central banks "create" the money used for these programs electronically. I would like to understand how this works. Can a central bank simply by fiat change its holdings of its own currency, and then use this new money in any way they please? Do they later have to "pay back" this money to balance the books, or can they simply forget about it?

Or more concretely: if the ECB buys bonds with newly created electronic money, and these bonds later default, would that be a problem for the ECB or could they laugh it off?

Short Answer

  Can a central bank simply by fiat change its holdings of its own currency, and then use this new money in any way they please?

Theoretically it can, if you don't mind destroying credibility and the economy in the process. In modern economies there are regulations in place that make this impossible. So no.

  Do they later have to "pay back" this money to balance the books, or can they simply forget about it?

If they keep "printing" new money and keep paying back old money in perpetual, the net effect is not having to pay back. So the US government can afford US\$19T of debt. But technically they have to pay back. See long answer below.

  Or more concretely: if the ECB buys bonds with newly created electronic money, and these bonds later default, would that be a problem for the ECB or could they laugh it off?

ECB can laugh it off, but Draghi can't, and certainly Eurozone can't either.

Long Answer

First you have to look into the process of money creation. Let's say you provide an ounce of gold bar (asset) to the Fed, in exchange the Fed will pay you an equivalent sum for your gold,  the current market price, say US\$35. The gold is now in the Fed's reserve (it is called Federal Reserve for a reason). Archaically, you can redeem your gold bar with US\$35.

However, note that debt instruments (i.e. bonds) are also assets. Therefore the government can issue short-term bonds to the Fed that the Fed will put in its reserve, and hand the cash to the government. The book is still balanced because the bonds in reserve are now "disabled", just like you cannot use your gold bar anymore when it's in reserve. But there will be more liquid cash in the market, cash that can be used to do other things, such as investment. When the bonds mature, the process is reversed. Furthermore, the interest (profit) earned from the government bonds will also be remitted back to the government, so the book is still balanced even when interest is taken into consideration.

Quantitative easing is similar. In addition to government bonds, the central bank is now allowed to buy a set quantity of financial instruments that it normally wouldn't have access to, in the same exchange mechanism as stated above. QE allows central banks to (directly) influence interest yield of other instruments, in addition to the usual interbank interest rate which is already close to zero. A lower interest rate makes investment more attractive, which drives the economy. Now that there is more cash in circulation, exchange rate falls, which makes foreign direct investment attractive because US assets cost less in foreign currencies's perspective.

Now, what if the bonds default? Let's suppose there are US\$100 out in circulation, backed by US\$100-equivalent of reserves. If US\$20 of the bonds default, the value of the US currency in circulation will drop in value accordingly in terms of exchange rate. i.e. nominally the dollar notes still say US\$100, but the actual purchasing power will drop to only US\$80.

Suppose that initially US\$20 of reserve is in bond and US\$80 is in gold. When you reason further, had it been a fixed exchange rate system, once the bonds default, if the owners of the US\$40 of gold rush to redeem their gold at a fixed rate, the reserve will now be worth US\$40. The remaining US\$60 in circulation will now have only \$40/\$60 (= 2/3) of its initial purchasing power (compare with 80% purchasing power right after the default). If all US\$80 of gold reserves is redeemed, the remaining US\$20 in the market will worth US\$0. This is one of the reasons why fixed exchange rate won't work: Once there has been a default and people rush to redeem the reserves, hyperinflation follows.)


is it possible to find PPP monthly data? For most of the databases, monthly PPP data is not provided. How it can be possible to find monthly PPP data?  i mean PPP(exchange rate) conversion factors.
Thanks

That doesn't exist. Gdp is quarterly.

There are no short term indicators like that on a global levels.


CARA Coefficient Calculation Consider the following scenario:

A consumer with CARA (constant absolute risk aversion) claims that she is indifferent between "getting ＄2400 for sure" and "getting ＄5000 or ＄0, each with 50% possibility".

I know that a consumer has CARA if and only if the vNM utility function is an affine transformation of $-e^{-\lambda x}$, where $x$ is the prize of the gamble. I was wondering how I could solve for the coefficient $\lambda$, given the above scenario.

To do so I wrote down the following equation:

$e^{-2400\lambda}=\frac{1}{2}e^{-5000\lambda}+\frac{1}{2}e^{-0\lambda}$

It is clear that $\lambda=0$ should be a solution to it. However, I found that this could not be the case, as $\lambda=0$ means risk neutral, which is controversial with the consumer's claim.

What should be the correct way of solving it? I think I must have made some stupid mistakes here but I couldn't figure it out.

(For reference, this is actually Problem 6.2 in Kreps' textbook - any suggestion or hint would be much appreciated.)

Implementing the "affine transformation", let $$u(x) = A-B\exp\{-\lambda x\}$$

Then we want to solve $(x_1 = 2400, x_2 = 5000)$

$$A-B\exp\{-\lambda x_1\} = \frac 12 \Big[A-B\exp\{-\lambda x_2\}\Big]+\frac 12 \Big[A-B\exp\{-\lambda \cdot 0\}\Big]$$

$$\implies A-B\exp\{-\lambda x_1\} = A - \frac 12B - \frac 12B\exp\{-\lambda x_2\}$$

$$\implies \frac 12B -B\exp\{-\lambda x_1\} + B\frac 12\exp\{-\lambda x_2\} =0$$

$$\implies -\frac 12 +\exp\{-\lambda x_1\} - \frac 12\exp\{-\lambda x_2\} =0$$

and we verify that $A,B$ do not matter.

This is a non-linear function in one variable, and a computer algorithm should be used to find the possible solutions. In this particular case, trial-and-error by hand (or naive graphing in a spreadsheet) may mislead, because, as the posted solution by the OP in a comment shows, the non-zero value for $\lambda$ that satisfies the equation is very small, $\lambda = 0.0032$.

So if one tries to graph the function in a spreadsheet, it must specify very small increments for $\lambda$ otherwise it will miss the small interval for which the function becomes positive for strictly positive values of $\lambda$, and then falls to zero and negative values again.

Making matters worse,the values of the actual prizes are too large numerically when inserted into the exponential function, and so the increments for lambda should be even smaller, if one would want to "see" the solution in a spreadsheet.. For example to use the actual levels of the prices as coefficients of the equation, one needs to specify increments of the order $10^{-5}$.

One could input the prizes in hundreds or in thousands... (the solution in the link posted in the comment uses hundreds), which allows for larger increments.


Net Positions vs Gross Positions as they Relate to the Current Account What is the difference between say, gross asset and liability positions and net asset and liability positions? I mean these terms in the particular way that Cavallo and Tille use them in their 2006 paper "Could Capital Gains Smooth a Current Account Rebalancing?" Can they be expressed as an accounting identity? The key factor in this paper is that gross asset positions change but NFA positions are kept constant. This is true by construction, but how? I could understand this if I just understood generally how net and gross positions are different.

The assets and liabilities are what make up what is called the International Investment Position, often broken down into three main parts:

Direct investment: subsidiaries abroad or domestic companies with foreign owners, where their full profits or losses count as overseas income for the balance of payments
Portfolio investment: foreign shares and bonds or domestic shares and bonds owned by foreigners, where the dividends and coupons count as overseas income for the balance of payments
Other investment: including foreign bank accounts and loans, where the interest counts as overseas income for the balance of payments; there are also derivatives and reserves

When these are added up, the amounts involved are big league (to channel President Trump).  At the end of 2016 the US had gross assets abroad worth about USD 24 trillion and gross liabilities to foreigners worth about USD 32 trillion, each more than US annual GDP. (The UK gross positions are even more extreme)

The net International Investment Position is simply the difference between gross assets and gross liabilities, so with the US having a net liability of about USD 8 trillion at the end of 2016

One might naively think

having a persistent current account deficit might lead to steadily widening net liabilities as financial flows need to balanced current account flows
having a net liability could lead to a deficit on income flows (if you owe more you might pay more), making the current account deficit difficult to close even if trade in goods and services moved into balance

That was not what was observed in the paper and so two rationalisations were offered

US assets abroad seemed to be paid a higher rate of return than US liabilities to foreigners for specific reasons
US assets overseas had been revalued over time (for reasons such as exchange rate changes or market price changes) so the net position had not exploded

The rest of the paper speculated that this sort of process could lead to a smoother transition to a current account balance than one might otherwise naively think, especially if accompanied by currency depreciation.  It combined this with some mathification and a toy numerical illustration


Is loss in tax revenue a negative externality? I was thinking about how online gambling could cause numerous governments to face a reduction in tax revenue from conventional gambling, upon which taxes do apply in most countries.

If governments do face such a loss in tax revenue, would such a loss in tax revenue be considered a negative externality?

In my view yes, it would be considered an externality. An externality is said to occur when a production or consumption decision of an individual has an unintended consequence on the consumption or production of someone else.

The analysis of externalities usually does not include governments, considering only production and consumption, but one can think of the government as a firm that produces public goods like law and order and national defense.

In that case the decision of the individual to use online gambling rather than conventional gambling has an unintended effect on the production possibilities for the government. Now that the government has less revenues, it can produce less public goods.

When a person goes for online gambling rather than conventional gambling they do not intend to reduce the overall provision of public goods, they just went for online gambling because it was more convenient/cheaper etc.


How does excessive consumption in an area decrease tax revenue? Source: p 156, Urban Geography (2009; 3rd ed) by Michael Pacione

  The main ideological battle is between pro-growth
  and anti-growth factions. The pro-growth ideology
  proclaims that more development results in increased
  population, greater aggregate sales, more local tax
  revenues and more local jobs, owing to increased local
  spending. Benefits therefore flow to those who need
  employment and those in favour of lower taxes.
  The
  anti-growth ideology emphasises the other side of the
  coin: development brings more people to an area than
  local institutions can service, thus any $\color{darkred} { \text { downward trend
in taxation  }   }$  is overcome in the later stages of growth
  by the need for $\color{green} { \text { greater fiscal expenditure  }   }$.

1. How does excessive consumption in local institutions cause a $\color{darkred} { \text { downward trend
in taxation  }   }$? Excessive consumption ought to be boost tax revenue?

2. The last sentence seems to contradict the  anti-growth ideology. Please clarify? I am guessing that the anti-growth ideologues want to avoid $\color{green} { \text { greater fiscal expenditure  }   }$; so why do they reject a growth (or overgrowth) in consumption?

Actually the text does not state that consumption leads to a downward trend in taxation, but actually the other way around--

According to the text, anti-growth ideology says that low taxes do indeed lead to development, mainly focusing on population increase, but that this population growth will strain local institutions, meaning public services like emergency response, sewage services, etc.

Greater fiscal expenditure would be required to expand these services to accommodate the increased population.

During its explanation of the anti-growth ideology the article is not referencing increasing consumption of private goods, such as at local businesses, but rather of public goods as explained above.


Is DARA utility implying CRRA most of the time? The Wikipedia page on risk aversion states that a "Constant Relative Risk Aversion implies a Decreasing Absolute Risk Aversion, but the reverse is
not always true". Let me decompose this statement in two parts:

1/ "Constant Relative Risk Aversion implies a Decreasing Absolute Risk Aversion."

A simple example is the log utility function, $u(c) = \ln(c)$, with $c>0$ satisfies the DARA because the utility function is positively skewed $\left(u'''=\frac{2}{c^3} >0\right)$ and implies a Relative Risk Aversion equals to $1 \left(=-c\frac {u''(c)}{u'(c)}\right)$.

2/ "but the reverse is not always true".

I am wondering if this is the most frequent case? Or if most of the time DARA utility functions also exhibit CRRA?

I would be grateful if you can illustrate your answer with some utility functions.

Let me turn my comment into a quick answer:
Using the notation of the article you quoted $A(c)$ is the absolute risk aversion and $c A(c)$ the relative risk aversion. If $A(c)$ is decreasing, the preferences fulfill DARA. If $c A(c)$ is constant, the preferences fulfill CRRA. If CRRA holds, then $A(c)$ must be decreasing in $c$.

If we take any $A(c)$ such that $c A(c)$ is decreasing and $A(c)$ is positive, then $A(c)$ will also be decreasing. In this case, the preferences are both DARA and DRRA. You asked whether DARA implies CRRA in almost all cases. From this analysis, it seems to be rather the case that CRRA is the exceptional case.


When does the Divine Equilibrium refinement coincide with that of Perfect Sequential Equilibrium? In signaling games, it seems that the Cho Kreps refinement (intuitive criterion) is the go to refinement for eliminating bad sequential equilibria. Divine equilibrium and perfect sequential equilibrium are also interesting refinements though. It seems more common that these are compared to Cho Kreps. Are there any interesting examples comparing the differences between perfect sequential and divine equilibrium? I've never seen the two concepts discussed together.

Some input:

In Cho, I. K., & Kreps, D. M. (1987). Signaling games and stable equilibria. The Quarterly Journal of Economics, 179-221, Banks & Sobel's Divine (and Universally Divine) equilibrium concepts are presented in Section IV.4 as a stand-alone concept.
On the other hand Grossman & Perry's Perfect Sequential Equilibrium concept is just mentioned in Section IV.5 which has the title "Never a weak best response".

In the Banks, J. S., & Sobel, J. (1987). Equilibrium selection in signaling games. Econometrica, 647-661. paper on Divine Equilibrium, page 654 (near the end of Section 3), we read "(...) This condition is more restrictive than universal divinity because (...)" , "this condition" being "never a weak best response".

So it appears that Perfect Sequential Equilibrium (PSE) is a stronger equilibrium filtering criterion than Divine Equilibrium. This accords with

Theorem 2 of Banks & Sobel : Every signaling game has a divine equilibrium
to be contrasted with Section 4. of the Grossman, S. J., & Perry, M. (1986). Perfect sequential equilibrium. Journal of economic theory, 39(1), 97-119. paper introducing PSE, where they show by means of an example that a Perfect Sequential Equilibrium may fail to exit.

A paper that applies both concepts is Beggs, A. W. (1992). The licensing of patents under asymmetric information. International Journal of Industrial Organization, 10(2), 171-191.. In Section 3.2 a result is derived by an appeal to the PSE concept. Then the authors note that, given an additional condition, they could obtain the same result by an appeal to Divinity. This agains shows that PSE, when it exists, is stronger than Divine equilibrium. Here too an example is offered for a case when the PSE does not exist.


Wouldn't an unconditional basic income lead to an inflation that negates its effect? There are several version and denomination for a basic income. In this question, I will call unconditional basic income the situation were all citizens of a country receive regularly a lump-sum of money, independently of their age, their employment status and job,etc. I will assume that, at the moment the basic income is  instituted, it is larger than the poverty threshold. I am also assuming that the basic income is not a substitute of other welfare subsidies.

The concept is gaining popularity these days, and for many reasons, economical or philosophical.

My understanding of offer and demand is that, if people can pay more for a product and are willing to do so, then prices will increase. So, it seems that, after the introduction of the basic income, there will be mechanically a large inflation.  In a short time, people with no job and that relied mostly on the welfare system will be poor again. Worse, people with low income will be closer to the new poverty threshold.

My questions:
1) What natural mechanical effects prevent an over-inflation after the introduction of a substantial basic income? By natural, I mean any direct or indirect effects of the sole introduction of the basic income.

2) If an inflation cannot naturally be avoided, what measures are usually suggested together with the introduction of the basic income?

Edit: my question is close but not an exact duplicate of this question. In the example of the other question, $A$ would receive $30$ and $B$ would receive $90$ for an unconditional basic income of $30$. If the two questions are equivalent, please explain.

Theoretically basic income might have a tendency to increase inflation. But that largely depends on how much is the basic income provided. Usually, the idea of basic income itself means that it is 'basic' and is just sufficient for a subsistence. With such an income level, the problem of inflation does not crop up really.
However, basic income might have other serious problems with crowding out due to large government spending and the disincentive to work and hence loss of productivity.

Even if we suppose, there is a large basic money disbursement which can cause inflation, then I think it should not be unconditional. Usually, such plans are in the form of guaranteed employment programs, buying of ration from designated stores and many more measures. However, I still feel these measures are not for tackling inflation rather the disincentive to work.


Are all constant-sum games games of pure conflict, or only zero-sum games? The title essentially says it all. I am asking since I came across the following statement: “Zero-sum games are also known as games of pure conflict”. This seemed to imply that zero-sum and pure conflict are synonyms, which confuses me since I figured that all constant-sum games should be games of pure conflict, by definition.
So, are all constant-sum games games of pure conflict or are there some constant sum games that do not follow this rule?

For most purposes, there is no difference between (two-player) zero-sum and constant-sum games. One usually assumes in game theory that players maximize expected utility. Payoff functions are von Neumann-Morgenstern utility functions. One does not change the preferences induced by such a payoff function if one adds or subtracts a constant. One can, therefore, transform every constant-sum game into a zero-sum game without changing preferences and behavior.


Economic interpretation of Returns to Scale There are three possible types of returns to scale: increasing returns to scale, constant returns to scale, and diminishing (or decreasing) returns to scale. If output increases by the same proportional change as all inputs change then there are constant returns to scale (CRS). If output increases by less than the proportional change in all inputs, there are decreasing returns to scale (DRS). If output increases by more than the proportional change in all inputs, there are increasing returns to scale (IRS).

What are the economic interpretation of constant returns to scale, decreasing returns to scale, increasing returns to scale? In other words, what means and how it can be interpreted if the economy has a specific type of returns to scale?
Thanks!

Since the OP has labeled their question "Economic Interpretation of Returns to Scale":
The economist mostly responsible for spreading the use of mathematical rigor in economics, Paul Samuelson, who also never lost sight of the essence of economics, writes as follows in "Foundations of Economic Analysis" (1947, Enlarged Edition 1983), p. 84 (emphasis mine):

The problem of homogeneity of the production function is one about
which much controversy has raged. It has long been held on
philosophical grounds that product must be a homogeneous function of
the first order of all the variables, and if this is not so, it must
be either because of "indivisibility" or because not all "factors"
have been taken into account.
With regard to the first point, it is clear that labeling the absence
of homogeneity as due to indivisibility changes nothing and merely
affirms by the implication that "indivisibility" does exist, the
absence of homogeneity.
With respect to the second point, we may reverse the Aristotelian
dictum and affirm that anything that must be true self-evidently
("philosophically"), intuitively -i.e. by conventional definition of the terms involved- that such a principle can have no empirical
content. It is a scientifically meaningless assertion that doubling
all factors must double product. This is not because we do not have
the power to perform such an experiment; such an objection is of
course irrelevant. Rather the statement is meaningless because it
could never be refuted, in the sense that no hypothetically
conceivable experiment could ever controvert the principle enunciated.
This is so because if product did not double, one could always
conclude that some factor was "scarce".

"Principles that have no empirical content" can be seen, and used, as methodological / modeling choices.
For example declaring that a production function $Q = F(K,L)$ has constant returns to scale (homogeneous of first order/degree, or "linearly homogeneous"), is equivalent to declare that we understand the symbols $K$ and $L$ as capturing all forces affecting the level of output.
Samuelson goes on to write

...the expression "factor of production"... has been used in at least
two senses... First it has been used to denote broad composite
quantities such as "labor, land and capital". On the other hand, it
has been used to denote any aspect of the environment which has any
influence on production. I suggest that only "inputs" be explicitly
included in the production function, and that this term be confined to
denote measurable quantitative economic goods or services... So
defined the production function need not be homogeneous of the first
order.

The profession has implemented his suggestion exactly, and this is why we see models with decreasing or increasing returns to scale. But in light of the above wise comments, we must keep in mind that, say, a production function with increasing returns to scale does not reflect some real-world impressive technology that can more than double output if we only double inputs. It is just a methodological / modelling choice we have made, following Samuelson's suggestion.
A way to justify Samuelson's suggestion as regards what to include in the "production function" construct, is that he essentially suggests to include those output-affecting factors related to which the firm has a strong degree of control and decision making over their quantities employed.

Responding to comments by the OP

Thanks for the answer! Summarizing Samuelson's points I understand the
following: if we are able to capture all forces affecting production,
than the production function is homogenous of first order. However,
since we are not able to measure all inputs/factors, then it is
reasonable to assume that the production function is not linearly
homogenous. If so, then I assume that the production function is never
linearly homogenous, because K and L are measurable, but A (TFP) is
never measurable.
Aside from that, from your answer I assume that there is no strong
ground to find any economic interpretation of the returns to scale,
since it is merely methodological/modeling choices, right?

Don't confuse data availability on a factor with symbolic representation of a factor. So one could in principle say that $A(TFP)$ are "all other factors" and so we have constant returns to scale, but then $A(TFP)$ would become a catch-all concept devoid of any economic meaning.
Returns to scale are indeed a methodological/modeling choice so they do not have "intrinsic" economic interpretation. But they affect the results of the model. As such, they are effective, because they indirectly reflect the existence (or not) of factors that will not enter a specific model quantitatively.
So choosing diminishing/constant/increasing returns to scale will reflect the knowledge/belief of the researcher as to whether there is some important factor that affects output and stays out of the model. So in a sense the represent an aspect of the model that has this indirect economic meaning.


Question on Fama-French Three Factor model I am currently taking an econometrics course, and the final assignment in that course is to write a research paper using econometric ideas. I have read Fama and French paper on the three-factor model and was impressed by the model. I would like to write my research paper using the same methodology for the Hong Kong stocks and see if I get the same results.

I am wondering if it's possible for me to run regression using the same data sets that Fama and French used in the model on the U.S. stocks. It will help me to see if I am on the right track. If I get the same numerical values and results as theirs, it shows that I am doing it correctly. Then I can use the methodology to the Hong Kong stocks.

Here is the link that helps you replicate Fama-French 1993 paper.


Why wasn't the wage of the entrepreneur included in explicit costs? I was solving an economic problem (I was calculating explicit and implicit costs) and noticed one interesting thing:
In the said problem, the entrepreneur set himself the wage of 10 000 rubles AND in the solution said wage was NOT included in explicit costs. But his old wage (before he started his own business) was included in implicit costs(By the way, his old wage was 12 000 rubles).
This puzzles me because although he owns the business, he's also its employee. And if he is his own employee, his wage must be accounted as a wage of any other employee. I don't think that an accountant would make an exception for him. Besides, if he decreased his own wage, then expenses of his business would decrease and consequently, its profit would increase.

Entrepreneur's wages are his return from his investment (his labour, leisure time, etc.) and his current wages are implicit costs. You need to be able to differentiate between accounting and economic profits to understand why this is so. This can be explained with an example.

Assume that you currently work for a dentistry. You are now considering operning your own practice. You may earn 100,000 per year as an entrepreneur. The running business costs are, say, 40,000.

Step 1. Calculate Explicit costs.
Explicit costs: rental, utility, admin etc. costs = 40,000.

Step 2. Accounting profit. Accounting profit = Revenues−Explicit costs = 100,000 - 40,000 = 60,000. Looks good!

But these calculations consider only the explicit costs. Since running your practice means leaving your current job where you are earning $40,000, your current earnings will be opportunity costs or things that you sacrifice to get the next best alternative. Thus, your current salary is an implicit cost to your business. You will compare implicit costs and potential profit from the new business (your net earnings from the new business).

Step 3. You need to subtract both the explicit and implicit costs to determine the true economic profit: 60,000 - 40,000 = 20,000.

Note that, here, your wages are not explicit costs; as the owner of the business you are receiving return on your investment in the form of wages.


ARIMA - reason for + MA term I have 2 questions regarding ARIMA.

1st: How do we get the MA component - the et's (as we want to regress yt on lagged yt and also et and lagged et's)? If I want to regress yt on lagged yt's, I have them. But I do not have et and lagged et's.
2nd: what is the advantage of including et's in the regression - why is it better (if it is) than simple AR regression? Are there some efficiency gains from adding et terms?
Thank you

The MA terms are lagged errors (you don’t need to fetch them manually - for example in R you can use Arima function which does this for you and any program/language will have this basic function as mentioned +1 answer of @RichardHardy in +1 comment of @Dayne).
For example, following Verbeek (2008) A Guide to Modern Econometrics 4th ed pp 261 ARMA(p,q) in general form can be written as:

$$y_t=\theta_1 y_{t−1}+ … + \theta_p y_{t−p} + \epsilon_t+ \alpha_1 \epsilon_{t−1}+…+ \alpha_q \epsilon_{t−q}$$

The distinction between the effect of AR coefficients and MA coefficients is that they model fundamentally different forms of relationships with past realizations. AR terms model autocorrelation of the dependent variable - that is relationship with its own past realizations. MA terms model dependence on the errors that model made in the past. These have different implications for how persistent the series is.

I think it is best to visualize this. Here are two pictures I took from the above mentioned Verbeek from pages pp 260-261.
On this first picture you can see effect of autocorrelation in AR(1) process when $\theta=0.5$. You can see that even though we have only single AR term it’s effect is persistent across several periods.

However, let’s consider now case of MA(1) process where $\alpha=0.5$. As you can see clearly below the effect is seen only for one period.

The advantage of including MA terms (provided that they actually should be there and you are not adding them just for heck of it), generally speaking, are that you will more accurately model the persistence in your model, you will have better fit and more accurate forecasts than otherwise. It is always important to get the right functional form functional form as wrong functional form can even bias the results. I mean on a very basic level (and I am oversimplifying here) this is like asking why we sometimes use $\ln y = \alpha + \beta \ln x + e$ instead of $y = \alpha + \beta x +e$ it is because we want to get the functional form right so there is no misspecification in the model.


What does liberal economic theory say about monopolies? Ludwig von Mises in his book "Liberalism: In the Classical Tradition" writes that in liberal economic the monopolies are rare and have a tendency to disappear.

For an onlooker like me, however, his arguments sound not convincing, they give an impression of topics specially selected for polemics. For example, he doesn't explain the causes of the Great Depression (which is a standard argument against liberalism for his opponents).

Moreover, I would say, his style is strangely focused on examples, he seems to carefully avoid mathematical language, where chosen notations and premises give a possibility to deduce general statements from other general statements. As a result, his examples look like special cases which do not cover the whole picture. The examples that he gives look good, but a feeling appears that there are other, uncomfortable examples, which go unnoticed.

On the other hand, what happens in the real economy does not confirm his scheme well, for example (this is commonplace in the political debates in modern Russia) the "liberal reforms" of 1990-2000-ies led not to capitalist relations but directly to a feudal society with highly monopolized economical and political life.

I want to ask you if there exist theories/books/articles where the accusation against Liberalism --

  Liberalism leads to monopolies

-- is discussed in detail with convincing references, examples, and conclusions?

EDIT 29.09.2018. Gentlemen (and ladies), still I would like someone to enlighten me. Where do monopolies come from? Are they a result of state intervention, or do they arise by themselves, without a public policy? Where is this all described (i.e. which reading could you recommend)? If the school of Mises died, what does the rest of the economic science say about it?

EDIT 08.07.2019. I'd like to add this question: are there any ways to deal with monopolies except the government intervention?

Monopoly and competition are one of the central topics in microeconomics, so there many theories on the source of monopoly, and they are not universally applicable.  Government intervention is certainly one possible source of monopoly, but there are many others.

I don't think I could give a general answer that does the question justice, so I will just give links to some of the topics are related:

Cournot competition
Economies of scale
Network effect
Diamond search paradox
Monopolistic competition
Market contestability

The general area is known as industrial organization.  The classic text is Jean Tirole's "The Theory of Industrial Organization", though I think this only covers a small fraction of the topic.


Why do expectations of inflation decrease SRAS (Short Run Aggregate supply)? If firms and workers expect the prices to rise, the short run aggregate supply will shift to the left to SRAS2.
  (https://www.albert.io/blog/what-shifts-aggregate-demand-and-supply-ap-macroeconomics-review/)

In other words, the SRAS will DECREASE. But why? Especially considering that firms react with increased output supplied to inflation in the short run. According to theory of sticky prices such reaction happens because many firms with flexible output prices see increased inflation as chance to rip additional profit in the short run. So why would they decrease quantity supplied at all possible price levels (i.e. shift SRAS to the left) when they expect inflation to increase?

That’s because you are confusing inflation expectation (increases in prices in the future) with just inflation (i.e. increasing prices now). If aggregate prices increase quantity produced would increase. However, an expectation of price increases in future shifts supply curve to the left as businesses will prefer just to hold on the inventory today and sell it in the future at higher price. If you have an apple and you get option of selling it today for 10e or week after for 50e you will probably prefer the latter (ignoring potential behavioral effects such as hyperbolic discounting and assuming rationality). This will shift the supply of apples in the short run to the left.

Similarly when it comes to aggregate demand higher inflation expectations would actually increase demand, because if you expect prices to be high in the future you want to buy stuff you want now.

You should be very careful not to confuse inflation expectations and inflation they work completely differently.


What is the definition of: 'commodity space'? I have seen the concept of commodity space being used multiple times in economics, in particular within microeconomics, but I could not find a general definition of it.
Based on the examples that I have seen, I would guess that it is a vector-space of n-dimensions, in which every dimension coincides with one specific commodity. Furthermore, n is equivalent to the cardinality of the set of commodities.
Is this understanding correct? Is there even a universal understanding of a commodity space?

Yes, a commodity space is the set of all possible commodity bundles. The simplest Micro 101 example is typically the nonnegative quadrant of $\mathbb{R}^2$, but in general equilibrium theory it is often assumed to be infinite-dimensional since there are infinitely many commodities (each good is differentiated by time and space, etc.).


Uncertainty and Pareto efficient policies There are two economic agents $i\in \{1,2\}$ with state dependent utility $u_{is}=-(x-b_{is})^2$ where $x\in R$ and $b_{is}\in R$ is bliss point of $i$ in state $s\in\{1,2\}$. Assume $b_{1s}\lt b_{2s}$ for $\forall s\in\{1,2\}$. State $s\in\{1,2\}$ occurs with probability $\pi_{s}$. We denote $U_i(x_1,x_2)=\pi_1u_{i1}(x_1)+\pi_2u_{i2}(x_2)$.
Ex-post Pareto efficient policies in state 1 and 2, $x_1^*$ and $x_2^*$ respectively, I found them to be as follows:
Any policy in $[b_{11},b_{21}]$ is ex- post Pareto efficient in state 1 and any policy not in $[b_{11},b_{21}]$ is ex-post Pareto inefficient in state 1. Hence $x_1^* = z$, where $z$ is any $z\in [b_{11}, b_{21}].$ By similar arguments $x_2^* = z$, where $z$ is any $z\in[b_{12}, b_{22}].$
But how would we characterize ex-ante Pareto efficient policy pairs, ${x_1^*,x_2^*}?$

Pareto efficient allocations can be found by maximizing a weighted average of the utilities of the agents. Let $\lambda$ be the Pareto weight for agent 1 and $1 - \lambda$ the weight for agent 2 (where $\lambda \in [0,1]$). This then gives the following problem:
$$
\max_{x_1, x_2} -\lambda \left[\pi_1(x_1 - b_{11})^2 + \pi_2(x_2 - b_{12})^2\right] - (1-\lambda)\left[ \pi_1 (x_1 - b_{21})^2 + \pi_2 (x_2 - b_{22})^2\right].
$$
The first order conditions with respect to $x_1$ and $x_2$ give:
$$
\lambda \pi_1 2(x_1 - b_{11}) + (1-\lambda) \pi_1 2(x_1 - b_{21}) = 0\\
\lambda \pi_2 2(x_2 - b_{21}) + (1-\lambda) \pi_2 2(x_2 - b_{22}) = 0.
$$
Simplifying gives:
$$
x_1 = \lambda b_{11} + (1-\lambda) b_{21},\\
x_2 = \lambda b_{21} + (1-\lambda) b_{22}.
$$
So $x_1$ and $x_2$ are weighted averages of the bliss points.


Measurement for the downstream use of a commodity I am looking to find a measurement that would tell me the size of the market of the downstream use of some particular commodity. For example, salt or wheat would be used by many companies downstream. Mangoes on the other hand will be used by less firms downstream. Therefore, there is a larger downstream market for salt and wheat. Are there existing measures that have been used to measure the size of downstream market of some particular commodity? If not, do you have any suggestions on how to build one?

If you are looking for certain commodity data from the US.  The USDA Economic Research Service has data on market size of certain commodities.  But I am not sure about firm level data.

https://www.ers.usda.gov/data-products/commodity-costs-and-returns/

There measures include cost and return estimates are reported for the United States and major production regions for corn, soybeans, wheat, cotton, grain sorghum, rice, peanuts, oats, barley, milk, hogs, and cow-calf. The series of commodity cost and return estimates for the U.S. and regions is divided into two categories: Recent and Historical estimates.

I am not sure if this is exactly what you are looking for but this is a good start.  One can also call their office for additional information.


If protectionism is injurious to a state, is the success of mercantilist China in spite of its protectionist measures? If protectionism is injurious to a state, is the success of mercantilist China in spite of its protectionist measures?

Furthermore, if the academic consensus is that most instances of protectionism are akin to using self-harm in retaliation to a perceived offensive measure, why is it still so prevalent (for example the EU Common Agricultural Policy)?

References:

  Protectionism is used for a number of reasons, some of which are
  outlined here, but is generally acknowledged to be ineffective and
  harmful to a country’s economic interests in the longer term. This is
  because it prevents the mutual gains from trade being realised, and,
  by restricting competition, limits the incentives for firms to improve
  their efficiency.

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/43315/11-718-protectionism.pdf

  Our main conclusion is that, in all the scenarios we consider,
  protectionism is not an effective tool for macroeconomic stimulus.

https://www.nber.org/papers/w24353

I am not an expert on this issue, but pending an expert's answer on this matter, here are my two cents.

1. It is not true that there is a consensus that protectionism is almost always a bad thing for a country.

Many slightly non-orthodox economists (e.g. Dani Rodrik, Chang Ha-Joon) have pointed out that protectionism is a perfectly good strategy that many developing/industrializing countries have adopted, including the US in the 19th century, Japan and Korea in the 20th, and now China in the 21st.

I believe Rodrik and Chang's main argument for protectionism in this context is the infant industry argument. Another argument is the second-best argument. See this other answer of mine.

2. China's protectionism has been selective.

In my vague impression as a non-expert, in most industries in which China exports heavily (except perhaps steel), there has been little protection and great competition. Think for example of clothing and the electronics manufacturing base centered around the Pearl River Delta and Shenzhen. These are industries in which every cost advantage and innovation are ruthlessly and instantly seized upon, to the advantage of both producers and consumers (including consumers around the world).

I believe the IT industry is where China engages most heavily in protectionism. As is well known to the man on the street, many technology platforms like Google, Facebook, and YouTube do not operate in China either because they have been outright banned or because of the onerous censorship requirements. The result is that local substitutes have flourished (Baidu/Sogou for search, WeChat/Weibo/QQ for social media, Tudou for video, Taobao/Alibaba for ecommerce) and Tencent and Alibaba are among the worlds largest firms, even though most people outside China may know little of them.

But perhaps the greater bone of contention is China's "theft" of intellectual property (IP). As an explicit/implicit condition of entry, tech firms trying to enter China are usually forced to hand over their IP.

Again, these are merely my vague impressions and hopefully an expert can back these up or correct me with more concrete facts and statistics.

3. One argument against protectionism is that it provokes retaliation, which can be damaging.

However, for the past many decades, the many countries to which China exports have shown great restraint and retaliated little. These are for reasons that I am not sure about and which I hope an expert will explain. (Perhaps this is simply the same restraint that has been somewhat shown -- not always consistently and often arbitrarily -- to other developing countries in the past.)

This is now changing with the aggressive trade war launched by Trump and there are now indeed fears and perhaps even signs that China may be suffering as a result of this trade war. Huawei and ZTE are two Chinese companies that have suffered heavily from the US's uncertain on-and-off bans in the past year.

This however is to not to say that Trump's trade war is the best approach. See for example this recent piece by the right-wing, pro-trade Cato Institute ("Disciplining China’s Trade Practices at the WTO - How WTO Complaints Can Help Make China More Market-Oriented", Nov 2018). I think many economists would agree that if China does indeed engage in protectionism and one wishes to retaliate, then the means of retaliation should be through multilateral, rules-based organizations like the WTO, and not unilateral, arbitrary trade wars such as those currently being undertaken by Trump.

4. Your example of the EU Common Agricultural Policy.

I think economists are almost universally agreed that protection for agriculture in rich countries is bad for most parties (the only beneficiaries being the farmers who receive the subsidies). I have never come across any modern economist defending any such policies.

Besides, I am not aware that China engage in much agricultural protectionism and indeed, I don't think this is what people think of when talking of China's protectionism. (Recently China has imposed heavier tariffs on pork and soybeans imports from the US, but these I believe are merely strategic retaliatory measures against Trump's trade war.)


By buying stocks, am I as an individual measurably affecting the economy? I know that participating in an IPO is directly helping the company, because my money is going straight into their bank account. I know that the stock market as a whole has an effect on the economy. However, what would be the measurable effect of me buying $1,000,000 of, say, Amazon? They've already IPO'd, so it's just a million of my dollars getting spread out between other random people who were selling regardless of whether or not I, personally, am buying. I guess all it does is create a slight upward pressure on the stock? Can the effect of that upward pressure be quantified in some way that means something to a layman, e.g. "it creates 1 new job in the US" or "it's equivalent to spending a million on arbitrary consumer products"?

From an aggregate level, the only direct income effect is that you will have paid a brokerage fee, which is part of the financial sector’s revenue.

After that, all that has happened is a rearrangement of an existing financial asset. If the seller uses the proceeds to purchase goods and services for consumption, that could be attributed to the purchase, although that might be a stretch.

The seller may also pay capital gains tax, and since they need a buyer to sell, that could be pinned on the purchase.

The effect on the price is hard to judge. In the short term, there might be some effect (although it would be negligible for a large cap firm), it will not really matter in the long run, if we assume that prices drift towards the fair value determined by corporate profitability.


Why is the consumption line and 45degree line's intersection not the equilibrium income level? The question is as below

The answer is A. I understand why it is A, but do not understand why it isn't C. Doesn't the point where the consumption line and 45 degrees line intersect represents the equilibrium income level?

For most people consumption does not equal income. Many consume less (they save) and others consume more (they take on debt) than they earn. In an economy with financial markets and heterogeneous consumers, discounted lifetime income should equal discounted lifetime consumption, but there is no reason why consumption should equal income at every point in time.


Quantity restriction in model with fixed factor of production I'm trying to see the effect of a restriction on production in a model where one factor of production is perfectly elastic and the other is fixed.
Specifically, suppose the production function is Cobb-Douglas: $y = k^\alpha l^{1-\alpha}$. Then cost minimisation gives
\begin{align}
k &= \left(\frac{\alpha}{R} \frac{W}{1-\alpha} \right)^{1-\alpha} y \quad \quad \quad (1) \\
l &=  \left(\frac{1-\alpha}{W} \frac{R}{\alpha} \right)^\alpha y \quad \quad \quad (2)
\end{align}
where $R$ is the price of $k$ and $W$ is the price of $l$. The goods market is perfectly competitive, so price equals marginal cost:
$$
p = \left(\frac{R}{\alpha}\right)^\alpha \left(\frac{W}{1-\alpha}\right)^{1-\alpha}. \quad \quad \quad (3)
$$
Demand for the good is given by
$$
y = \frac{\phi}{p} \quad \quad \quad (4)
$$
where $\phi$ is a parameter. Equations (1) - (4) give four equations in the six variables $y, k, l, p, R, W$. Now suppose $k$ is perfectly elastic and $l$ is perfectly inelastic, i.e.
$$
R = \bar{R} \quad \quad \quad (5) \\
l = 1 \quad \quad \quad (6).
$$
I can solve these six equations in six variables. But now suppose I want to introduce a quantity restriction, $y \leq \bar{y}$ (where $\bar{y}$ is sufficiently low as to be binding). To avoid an overdetermined system, which of the six original equations do I drop? Alternatively, do I redo an optimisation equation, including this extra constraint, so that there is an additional Lagrange multipler variable?
Intuitively, I think that the price $W$ of the inelastic factor of production $l$ will be bid up, but I'm not sure how this mathematically arises.
Thanks!

Summary The equilibrium wage will decrease. The reasoning is that, due to the output constraint, total labour demand will go down. Then because of the fixed labour supply (and the fixed price of capital), this makes it that the equilibrium wage falls.
Derivation
We have the first order condition for the (aggregate) labor demand.
$$
l = (1-\alpha)^\alpha W^{-\alpha} R^\alpha \alpha^{-\alpha} y \tag{1}
$$
Take first the case, where there is perfect competition and no output restrictions. Then equalising (inverse) demand and (inverse) supply for the output market gives:
$$
\begin{align*}
&\frac{\phi}{y} = p = R^\alpha \alpha^{-\alpha} W^{1- \alpha} (1-\alpha)^{1- \alpha}. \\
\to &y = \phi R^{-\alpha} \alpha^\alpha W^{\alpha-1} (1-\alpha)^{\alpha-1} \tag{2}
\end{align*}
$$
Subsituting $(2)$ in $(1)$ gives:
$$
l = (1-\alpha)^{2 \alpha-1} W^{-1} \phi
$$
This is the (aggregate) demand for $l$. Labour supply equals $1$ so equilibrium on the labour market requires that:
$$
\begin{align*}
&1 = (1-\alpha)^{2 \alpha - 1} W^{-1} \phi,\\
\to &W = (1-\alpha)^{2 \alpha - 1} \phi. \tag{3}
\end{align*}
$$
This is the equilibrium wage.
Plugging $(3)$ back into $(2)$ gives the equilibrium output.
$$
\begin{align*}
y &= \phi R^{-\alpha} \alpha^\alpha (1-\alpha)^{\alpha-1} (1-\alpha)^{(2 \alpha-1)(\alpha-1)}\phi^{\alpha-1},\\
&= \phi^\alpha R^{-\alpha} \alpha^\alpha (1-\alpha)^{2\alpha(\alpha-1)}
\end{align*}
$$
Notice that we do not need to consider ourselves with the equilibrium on the capital market as $R$ is fixed.
Now the alternative with a fixed supply (use subscripts $f$ for the equilibrium prices). If $\overline{y} < y$ then the price on the output market will be given by:
$$
p_f = \frac{\phi}{\overline{y}}.
$$
The price will no longer equal marginal costs but will be higher. Then aggregate labour demand will be equal to:
$$
l = (1- \alpha)^\alpha W_f^{-\alpha} R^\alpha \alpha^{-\alpha} \overline{y}.
$$
Setting this equal to aggregate supply (which equals 1) gives the equilibrium wage if output is restricted:
$$
W_f = (1-\alpha) R \alpha^{-1} \overline{y}^{1/\alpha}.
$$
Then:
$$
W_f < W,\\
\iff (1-\alpha) R \alpha^{-1} \overline{y}^{1/\alpha} < (1-\alpha)^{2 \alpha-1} \phi,\\
\iff \overline{y} < \phi^\alpha (1-\alpha)^{2\alpha(\alpha-1)}R^{-\alpha} \alpha^\alpha = y
$$
So the wage on the restricted market is lower as we assumed that $\overline{y} < y$.


What Is Social Security Invested In? As a self-employed business owner, I am paying approximately 15% of my income to social security, yet I keep hearing that they're "running out of money for it."  I'm a little confused about this: 15% is how much I currently save for retirement and over 25-30 years, it should fund my retirement comfortably and that's at a rate of around 8%.

I realize social security isn't invested in anything returning 8% or higher, but it's hard for me to imagine that they government is running low on money with my 15% of income (if I always made 60000 I would have paid 270000 into social security and at 3% interest, that's 8100 a year).

So where is my social security money going?

There are two ways to organise social security. One scheme is known as fully-funded social security. The alternative is called pay-as-you-go.

Fully funded schemes

Under a fully-funded scheme, the government collects regular payment from each member. These payments are invested until the member needs to claim (e.g. their pension), at which point the member receives payments from the invested money and the returns that it has generated. This corresponds to the situation you describe where your social security payments are sat in an investment somewhere waiting to go back to you.

Pay as you go schemes

This may be disturbing reading, so brace yourself!

Countries such as the UK and the USA do not use a fully-funded scheme. Instead, a significant portion of their social security provision operates on the basis of a so-called pay-as-you-go scheme in which the money paid by today's workers (e.g. you) is not invested at all. Instead, it is immediately spent on making social security payments to people who are currently retired. The hope is that today's workers, when they eventually retire, will likewise have their pensions paid from the social security contributions of their children (who will by then be working). And so the chain continues, each generation handing money directly to the last with little provision for self-sufficiency.

Assessment

The obvious problem with this is that the generation of 'boomers' now retiring is unusually large and had unusually few children. Moreover, that generation enjoys unprecedented levels of longevity, meaning that they are likely to claim far more out of the system than they paid in. All this means that current workers face a large burden paying the social security claims of the much larger generation that preceded them.

However, we are kind of stuck. If we want to switch to a fully-funded system then somebody has to get a very bad deal. Option 1: current employees have to pay twice (for their own fully-funded retirement and for the pay as you go claims of their parents). Option 2: current workers pay only for their fully-funded retirement and current retirees (who already paid for their parents' pensions) do not receive any pension at all. Neither alternative is very politically tractable.


What is Saddle Point Stability? What is saddle point stability and what sorts of functions or systems of equations give rise to such a thing?

For example, would we say that a two systems of stochastic difference equations that are interlinked give rise to an environment with saddle point stability?

"Saddle point stability" refers to dynamical systems, (usually systems of difference or differential equations), where the system has a fixed point, and there exists a single trajectory that leads to the fixed point.

It follows that from a mathematical point of view these systems are in reality unstable.

A 2 X 2 system is the standard example because one can construct intuitive two-dimensional phase diagrams to understand the properties and the behavior of the system over time.

For natural sciences, unstable systems are useless as models -the tiniest deviation, if not corrected, would lead to corner solution (elimination or explosion of the system).

But saddle-path stable systems have found important uses in economics, because this feature of theirs accommodates purposeful behavior. Assume that an economic system described by a set of difference equations was properly stable in the full mathematical sense. That would imply that no matter where we started, automatically the system would tend to its fixed point/long-run equilibrium. But this means that no matter what the economic agents did and how they interact, the system would settle in equilibrium... this does not sound very convincing once we accept that agents try to optimize their situation (in terms of utility, wealth, etc).

But if the system is "saddle-path stable", then agents track the trajectory followed, and if it appears to deviate from the one that leads to the fixed point, they purposefully change their own behavior in order to go back to the desired trajectory, since corner solutions are not optimal.

The standard example here is the basic growth model.


Removing a degree of freedom from relative utilitarianism Relative utilitarianism takes utilities as reported by agents, rescales them so that, for each agent, the alternatives have utility values between 0 and 1, and then chooses an alternative to maximize the (weighted) sum of the rescaled utilities. This forces an equality of sorts upon the agents as their utilities are all bounded on the same range. However, they can still express the degree to which they prefer A to B (relative to their preference of B over C) by making the gap between A and B larger (or smaller) than that between B and C.

Has anybody come across a mechanism like this except that, instead of rescaling reported utilities to a given range, we simply take the ordinal preferences expressed by the reported utilities and assign predetermined utility values (respecting the order).

That is, with relative utilitarianism:

$$ (10,4,2,0) \rightarrow (1,0.4,0.2,0) \text{ and } (100,9,1,0) \rightarrow
(1,0.09,0.01,0)$$

What I want to do is the following:

$$ (10,4,2,0) \rightarrow (10,7,5,2) \text{ and } (100,9,1,0) \rightarrow
(10,7,5,2)$$

The numbers in $(10,7,5,2)$ are irrelevant (they could be between 0 and 1) -- the point is just that they're the same across the two cases. Basically, I'm just extracting a preference order from the reported cardinal utilities and then slapping predetermined utility values on to them, respecting the order but not magnitudes in differences. Then, subsequently, I would choose an alternative to maximize the sum of utilities.

Two related questions:

Have you seen this done anywhere, either explicitly or implicitly?
Supposing you haven't, what would you call this?

One of the major criticisms you hear about classical economic frameworks is that ordinal utility is the only valid form of utility, because cardinal utility is just putting arbitrary numbers onto people's preferences. The thing is, cardinal utility is really not as fraught as heterodox schools (or even Austrian economists) might expect. Cardinal utility is only an expression of preference up to positive affine transformations, so as long as a utility function maintains the order of all the preferences, the utility functions represent the same preferences; cardinal utility just allows for us to express convexity/concavity along with it.

So when I see a system of utility such as this, it just looks like a normal monotonic transformation into the range $[0,1]$. The only problem with it is that it will normalize all utility functions considered into that range, and you might lose some information about the strength of preferences relative to other agents to each other. I'm not exactly sure what it would be used for.


How to build a Social Accounting Matrix from an Input-Output Table? I built an Input-Output table (IOT) with the industryXindustry format because I thought it was a building block to build a social accounting matrix (SAM). But now I realize that I can't transpose the data from the IOT into the SAM because the SAM requires an industryXcommodity format and does not support industryXindustry or commodityXcommodity flows.

So the question is, how am I supposed to transfer data from the IOT to the SAM? They are supposed to be one of the main sources of information to build a SAM...

Many thanks!

Sarah

IOTs are usually derived from Supply and Use tables, which have an industry by commodity format.  If you used these to derive your IOT, then you can use those to build your SAM, though note you need both the Supply AND Use tables for this. You end up with something that looks roughly like what you see on slide 7 here - with both commodity and activity (industry) rows and commodity and activity columns in your SAM.  If you have the data to support it, this is probably the preferred way to go about structuring a SAM.

However, if you only have an industry by industry IOT, you can still build a SAM from that (with additional data from the country's National Accounts or another source), and this approach is far from uncommon.  Instead of having separate activity and commodity rows and columns, you'll only have activity rows and columns, but you can still construct a SAM (though you may have to combine some of the non-IOT cells in your SAM to get the structure to work).  As an example to hand, here is a paper outlining the construction of a SAM for Scotland using an industry by industry format (as Scotland is a part of the UK, it also shows an approach to constructing a SAM using estimates when full National Accounts data outside the IOT are not available).


LIBOR rates: Are these monthly or yearly interest rates? If I have, for instance, a Libor security with maturity of one month, with interest rate $r$. Is $r$ the amount to be paid after one month, or is it the annualized interest rate?

(My gut tells me that it is the annual interest rate, but I have not found a source to confirm this.)

And if it is the annualized rate, how is the (actual) interest payment that is due after one month calculated? Is it $1+r/12$ or is it of the form $e^{r/12}$

To answer the first part, it's an "annualised" interest rate convention - like all other quoted interest rates. For example, if a one-month money market rates are unchanged at 4%, you would receive approximately 4% in interest after a year, or roughly 1/3% a month. (Note that those numbers are ignoring compounding, further details below.)

As for the calculations, things are complicated. The high level answer is that a monthly interest rate is roughly $r/12$, with $r$ being the quoted rate. This is a simple interest rate.

The true calculations are complicated by the nature of LIBOR. Technically, LIBOR (London Interbank Offer Rate) is a polled rate of "large" banks in a number of currencies. There are similar "fixes", such as Euribor (Euro area), TIBOR (Japan), CDOR (Canada). The polled rate is based on the money market convention in each currency for a certain class of interbank borrowing.

Interest rate calculations depend upon the daycount convention, and the calendar used. If we borrow on June 1st, one month later is normally July 1st. What happens if July 1st is a weekend or holiday? There are standard comventions in each currency that determine which days are holidays, and how to move the due date relative to such dates (before/after).

There are a wide variety of day count conventions that are used across markets. I believe that act/365 (GBP) or act/360 (other currencies) are standard. (Based on this ICE LIBOR document: link.) Anyone who needs to know the exact calculations should refer their queries to their banking counterparties, as there can be a large number of small modifications to the generic description I give below.

In act/360, the amount of interest is given by the quoted rate times the fraction (actual number of days in the lending period)/360. For act/365, the interest is given by the quoted rate times (the number of days in the period/365).

Therefore, if the one-month maturity period is 30 days in the future, and the currency uses an act/360 convention, the fraction used for the one-month rate is 30/360 = 1/12. However, it is clear that the true annual compounding rate will vary from compounding $(1+r/12)^{12}$ since months are not exactly 30 days, and the number of days in the year is either 365 or 366.


Data Request: Raw housing stock of particular city I want to get the raw number of units of housing stock that there is in a particular city in month $X$ of year $Y$ (even yearly data would be fine). This place shows yearly stock from 2010 onwards. Here shows data for every 10 years. This link makes me think there should be more yearly data since this has 2013 data.

Is there anywhere I can find a more comprehensive data set?

There really isn't high-frequency data out there for free, but bi-annual data are available from the Census American Housing Survey. The survey goes back to 1973, though data at the metropolitan area level don't go back that far. Also, the data are extrapolated from a sample, so caveats apply.