texts: How to find corner Pareto efficient allocations

texts:
I have some troubles in understanding how to find Pareto efficient allocation that are on the frontier of the Edgeworth box. I mean, the interior ones, can be found using the equality $MRS_A = MRS_B$, where $A$ and $B$ are the two agents of our pure exchange economy, whereas I cannot find anything about frontier allocations.

Is there any mathematical procedure I can use or it is only something I have to deal with using intuition (using the definition of Pareto efficiency I mean).

To be clearer, I cite an exercise from my workbook where there are two agents with preferences $u^A(x_1,x_2) =\sqrt{x_1x_2}$ and $u^B(x_1,x_2)=x_1+3x_2$, and endowments $\omega^A=(1,0)$ and $\omega^B=(0,1)$. The question is to identify the Pareto set.

This is the solution, where the blue lines are the Pareto set.


texts:
One of the things I've experienced as a graduate student is really the lack of math being a main factor in holding me back from approaching more advanced materials in microeconomics and macroeconomics. Often I find myself playing a lot of catchup. I primarily express this with reference to the lack of training in proofs based mathematics.
My question is: as economics educators what is the rationale for not exposing students to proof based mathematics at the undergraduate or masters level? (a basic intro to proofs class can go a long way).
Note: this question excludes those programs that are specialized PhD stream feeders.


texts:
If the Federal Reserve acts as a lender of last resort and steps in to prevent bank runs, then how do banks still fail?
Do they only step in if the bank is solvent but in emergency need of funds?


texts: Indifference curves and equivalence classes

texts:
Last week in class, my professor described indifference curves in the context of modelling consumer choice with multiple goods. He defined a partial-ordering operator $\prec$ and an equivalence operator $\sim$ to manipulate tuples that satisfied the budget constraint problem. So far, so good.

But then we went on to explore the behavior of indifference curves and I noticed that the $\sim$ was assumed to be reflexive, symmetric, and transitive. We learnt that indifference curves never intersect and that there is a completeness property that says that for all the tuples in our domain space belong to an indifference curve.

At this point, indifference curves looks like textbook equivalence classes to me, but I would like confirmation and perhaps some context from an economics perspective.

First of all, why not call them "equivalence classes" or openly saying that "indifference curves are equivalence classes". Second, does that mean that if I prove something about equivalence classes, then it automatically transfers to indifference curves in the context of this economic model?


texts: Continuous rational and monotone preference relation implies $x\succsim0$?

texts:
I updated my proof to a general version as follows: please share your thoughts & 2cent. Thanks

Show a monotone continuous complete preorder on $\mathbb{R^L_+}$ has  $y\geq x\rightarrow y\succsim x$.

  Point of Clarification
   $X=\mathbb{R^L_+}$
   Preorder means the usual reflexivity and transitivity.
   Complete means for any $x,y\in X$, have $x\succsim y$ or $y\succsim x$
   Continuous means the relation is preserved under limits.
   Monotone means for any $x,y\in X$, if $y\gg x$, then $y\succ x$.
   $\succ$ and $\sim$ are respectively asymmetic and symmetric parts of $\succsim$

Outline of Proof
 Go through two cases: (1) $y\gg x$. Easily get the result by definition. (2) Some components are equal while else y is strictly greater x. Use continuity where you add a sequence of small positive $\epsilon$ to y, making it a sequence $y^n_\epsilon$ where for every n, $y^n_\epsilon\gg x$ $\forall n$.

  Proof
   Suppose $\succsim$ is a monotone, continuous, complete preorder on $X=\mathbb{R^L_L}$.
   Case (1) $y\gg x$ (i.e. $y_i>x_i$ $\forall i\in B=\{1,\dots,L\}$).
   By definition, $y\succ x$, which implies $y\succsim x$.
    Case (2) $y_j=x_j$ for some $j\in B$. For $\forall k\not=j,k\in B, y_k>x_k.$
   For some $\epsilon>0$, let the sequence $\epsilon^n\in\mathbb{R^L_+}$ such that $\epsilon_j=\epsilon$, $\epsilon_k=0$.
   Denote the sequence $y^n_\epsilon=y+\epsilon^n$.
   Then, for any $\epsilon>0$ and $\forall n$, $y^n_\epsilon\succ x$, hence $y^n_\epsilon\succsim x$.
   By continuity of $\succsim$, $$\lim_{\epsilon \to 0} {y^n_\epsilon} = y$$
   Hence, $y\succsim x$. $\blacksquare$

 OLDER VERSION

My question is what is the valid reasoning behind that continuous rational and monotone preference relation implies $x\succsim0$. I have put a proof below and would appreciate if you share your 2 cent on the validity/rigor of the proof. Thanks!

Suppose $x\in\mathbb{R^+_L}=\{x\in\mathbb{R^L}:x_l\geq0$ $\forall l=1,\dots,L\}$.

Claim: For every $x\in\mathbb{R^+_L}$, monotonicity implies $x\succsim0$.

Proof:

(1) Suppose $x=(0,\dots,0)$.
Then, $x\sim0$ is possible.

(2) Suppose $x\gg y$. Then, by Definition of monotone preference, $x\succ y$ is possible.

(3) Suppose $\exists$ some $j$ such that $x_j>0$ and $1\leq j\leq L$.Then, I have the following process of elimination:

$x\succsim0$ is possible.
$x\succsim0$ and $0\succsim x$ $\iff x\sim0$ is possible.
$x\succsim0$ but not $0\succsim x$ $\iff x\succ0$ is possible.
$0\succsim x$ but not $x\succsim 0$ $\iff 0\succ x$ is impossible.

The single preference relation that is common in all three scenarios is $x\succsim0$.
Hence, for every $x\in\mathbb{R^+_L}$, monotonicity implies $x\succsim0$. Q.E.D


texts: Pricing optimisation when elasticities are positives?

texts:
I’m performing some exercises in order to get the optimal price of some product such a potato chips, biscuits, drinks, etc. (I’m taking price per unit and sales in units) But I’ve found that some of them have positive elasticities. This can makes sense for me, as if some biscuits brand is not so successful (in sales), price can decrease in order to be more attractive and on the other hand, I you have increase in demand, you can growth your price. But under this scenario, how can I establish an optimal price? I’m using a log-log model to obtain elasticities.
Also, at this scenario taking into account cross-elasticities would make sense? By example, how can biscuits influence chips’ sales?


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

Research Link

EDIT

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


texts: Diff-in-diff: Handling correlations within group-level treatment using microdata

texts:
Question: What are my best options for handling group-level correlations in a panel differences-in-differences model using StataSE 14.2?

Background: I have a Differences-in-Differences (DiD) design where a policy (subsidised primary healthcare) was rolled out to different age-groups (k=4) in different years. Like many DiD designs, my model faces the issue of individual-level outcomes (unmet need for a doctor in past 12 months; binary) and group-level treatment, which means there will be (1) correlations within age*year clusters, and (2) serial correlation between age-groups across years.

Ie. UNMETigt = αi+ αg + αt + γgt + βTREATgt + δCOVARSigt + εigt

While I haven't yet obtained access to the panel data, I imagine my Stata code might start from a basis of something like:

xtset id year
xtreg unmet L.i.age##L.i.year + L.treat + L.covars

Currently, this code does not account for the fact that treatment does not vary by i. I am aware that clustering by age*year will bias least-squares standard errors due to serial correlation for age-groups across years. I am also mindful that clustering solely by age-group to remove the time component will only leave me with four clusters, which is insufficient to estimate the correlation without bias. The literature I have consulted appears to cast doubt on the suitability of Stata's cluster option given serial correlation and few clusters (ie, Angrist & Pischke, 2008)

Question: What are my best options for handling group-level correlations in a panel differences-in-differences model using StataSE 14.2?

(1) One option in the literature is to correct the standard errors for first-order serial correlation at the group-level, using an AR(p) structure along the lines of Hansen (2007). I haven't seen any Stata modules that do this, but does anyone else know of one or something similar?

(2) Another option I've seen is block bootstrapping, which bootstraps the SEs by age-group akin to Cameron, Gelbach & Miller (2008). Would this involve simply specifying the option: vce(bootstrap, cluster(age)), or have I misunderstood?

(3) Is there a better approach I'm missing?

Apologies if I've missed something self-evident! I'm new to this form of analysis.


texts: Impact of working capital constraints onto output

texts:
I'm looking for empirical evidence (optimally from natural experiments, as described below) of the impact of working capital constraints onto firm output, and the differentials of firm size.

I suppose that generally, stricter working capital constraints are bad for output, and typically these constraints are stronger for smaller firms (measured in output) and younger firms. However, I couldn't manage to find (a) paper(s) to establish that fact yet.

Where by working capital constraint I mean something along the lines of Kiyotaki&Moore (1997)

$$L, K: f(wL, rK) \leq \psi(F(K,L))$$

, for example, for some constant $\psi_0$,

$$wL + rK \leq \psi_0 \cdot F(K,L)$$

where $F(\cdot)$ is the production function, and $f$ and $\psi$ can be whatever.

I have, in other environments, seen that some people take bank liquidity to approximate $\psi$ and argue that for example the last recession was a natural experiment on a change of $\psi$.

So, one type of useful regression table would be (on the firm level)

dependent variable: output
independent variables:
Increase of financial constraint (here, decrease of $\psi_0$)
Dummy for firm size (or different size bins)
And/Or: Dummy for firm age (or different age bins)
additional controls

One example would be Chodorow-Reich (2014, QJE). The two downsides with that paper are that

He uses employment, not output as dependent variable (but that's tolerable)
He does not actually list the coefficients on the dummies for size. He just includes them as controls.


texts: What does it mean for a technology to have a $|\rho|<1$?

texts:
Nowadays, when trying to model (log)technology $a_t$, I've seen many times the following: $a_t = \rho a_{t-1}+\epsilon$, where epsilon is given a certain probability distribution. What does it mean for $|\rho|<1$? I know that in this way, the time series is stationary. My question is related towards more the interpretation. With such a $rho$ does this mean that our technological discoveries are being lost in time? We're forgetting our past? or That the discoveries give a surge of increase in 'productivity', but then the 'productivity' decreases...

Any help would be appreciated.


texts:
In Mankiw, N. (2012). Principles of Macroeconomics (6th ed.)., on pg 456 Mankiw says "The amount of oil used to produce a unit of real GDP has declined about 40 percent since the OPEC shocks of the 1970s."

How would one measure that?

That's unfortunately just kind of dropped at the end of a chapter as the second to last sentence in a five paragraph side note about OPEC, and I've been curious for years now if that reduction was because the mix of energy supply changed (rise in natural gas consumption?), or production is simply more energy efficient, or what.

Can someone clarify the claim, the process, or point toward primary sources (US EIA maybe?), rereading this book has reminded me how frustrating that bit was.


texts:
I am reading Money Power book, from 1932 (http://www.worldcat.org/title/money-power-and-human-life/oclc/3783026). The author explains how the War Loans in the UK worked.

He says that the government offered a bond at, say, X% interest rate. Then, banks offered some of their clients a loan of credit, at a cost of X-1%, which had to be tied to such bond. This is, clients would "buy" the bond with credit money. This was a sound business for the client, which would make 1%, and the bank, which would receive X-1% almost risk-free (bond was a collateral).

It occured to me, that this practice could be quite common. Is it? For example, say a poor country is selling a bond, which pay high interest rates. Then I could go to the bank and ask them for a loan, backed with the bond as collateral, and use that money to buy that loan. The bank would agree to do so, and we would both benefit.

Is this legal? Is it cheating? Does this happen?


texts: There seems to be a lot of fear that a Brexit will have a very bad impact on both the European and the British economy. Why would this be, does a Brexit imply that there will be less trade between EU-countries and Great-Brittain, why is this?


texts: Does the Fed/SEC have tools to address shock-propagation from correlation of fund flows?

texts:
Premise
In 2017, passively invested assets totaled 37% of mutual funds and ETFs;  by 2021 this number is closer to 50% if not more. After the market downturn in (March) 2020, the Fed updated their research paper which evaluated potential risks to financial stability stemming from passive investing:
https://www.federalreserve.gov/econres/feds/the-shift-from-active-to-passive-investing-potential-risks-to-financial-stability.htm
The piece does not have a strong position on the question, citing mixed empirical findings for the affirmative and negative as well as unclear causality. However, let's briefly play devil's advocate and imagine a worst case scenario:

Passive assets under management (AUM) increases above some tipping
point, decreasing the heterogeneity of investors and inducing a
systemically huge non-diversifyable risk (Ben-David, Franzoni,
Moussawi (2017))
Upon a risk event, the large degree of comovement of fund flows and
stocks would propagate shocks
As price insensitive players, passive investors simply redeem at
market price, yet as active managers have incentive structures not
to sell at distressed levels, the dilemma in so many words becomes:
what happens when passive wants to sell and there is not active to
buy?

Under more benign assumptions, active may simply benefit from distortions caused by passive, but in the extreme scenario we are assuming in this article, perhaps monetary policy may need to have a playbook to prevent a financial crisis. I'm not going to pretend to know exactly all the mechanics of what would happen if events 1, 2 and 3 unfold (market goes to zero, liquidity crises, ect), but that's besides the point. For the purposes of the question, let's just assume this scenario can unfold.
Question
Assuming the Federal Reserve / SEC wants to address the risks outlined above, what macroprudential tools would be relevant and what could be done ad hoc?


texts: Is the Federal Reserve issuing money in a fair way?

texts:
Basic logic says that, once a central bank is issuing new money for increasing the money supply, the money should be distributed fairly between all the citizens, and that means giving them all an amount equal in proportion to their income (say a 5% of their annual income for achieving a 5% inflation). So they should give the money to the government, and then the  government either distributes the money or it builds public infrastructure that everyone benefits from. Most likely, this is the way the Eastern European countries experienced inflation in the 1990's.

Conversely, when the Fed decides to remove a certain amount of money from the economy, the Government should tax everyone in a fair way (the rich should pay more than the poor) and then give the money to the Fed to burn it. Or to burn it directly, without even giving it to the Fed.

Instead, the Federal Reserve has some sophisticated and arcane ways to move the money, beyond the comprehension of the general public. The Fed and the banks are involved into actually owning those newly issued money, and that looks really strange.

This article says:

  When the Fed wants to expand the money supply, it buys a security -- let's call it Asset A -- from a bank. Then it electronically transfers money to that bank.

Therefore, if the Federal Reserve decides, it can issue new money and buy and own half of the assets in the USA for free whenever they want. The newly issued money get to the banks, and depending on the decision of the banks to use the money or not, they can create inflation - or not. They can give those money in astronomical bonuses to their top executives and those people can send the money to Switzerland for example - therefore no inflation.

Is there something important that I'm missing?


texts: What was "Pareto's proof of the immeasurability of utility"?

texts: Wong (1978, 2002, Foundations of Paul Samuelson's Revealed Preference Theory), repeatedly refers to "Pareto’s proof of the immeasurability of utility". What was this proof?


texts: Why a current account surplus is bond to lead to an appreciation of a currency?

texts:
I have got some confusion in trying to explain why a trade surplus is going to lead to an increase in the exchange rate. The usual logic goes as follows.

Export X > Import M
Demand for the country's currency increase
Appreciation happens

What confuses me is step 2. Why the demand for the country's currency increase? I know that there is certainly a high demand for the country's currency because money is needed to buy its exports, but the demand is high does NOT mean the demand is INCREASING. Why can't the demand for the currency just stay high, but constant, so foreigners can get their needed money to buy exports?


texts: Macroeconomics 101 Problem: Aggregate Demand Changes

texts:
Consumer spending initially rises by 5 billion for each 1% increase in household wealth.  Investment spending initially increases $20 billion for each 1% decrease in real interest rate. The multiplier is 4.

If house household wealth decreases by 5% and real interest rate falls by 2%, (1) in what direction and by how much will aggregate demand shift at each price level. (2) In what direction and by how much will it eventually shift.

$$\quad -5\% \quad \text{in} \quad HH\quad { Y }_{ d }\text{ } \Longrightarrow \text{ } -$25\text{ }\text{billion in}\text{ } C$$

$$\quad -2\%\quad \text{in}\quad i\text{ } \Longrightarrow \text{ } +$40\text{ }\text{billion in}\text{ } { I }_{ g }$$

If I treat aggregate demand the same way as aggregate expenditure (is this right?), then with government spending and exports constant, the initial change is

$$-$25\quad billion\quad +\quad $40\quad billion\quad =\quad +$15\quad billion$$

and for the long term we use the multiplier,

$$\Delta C\quad =\quad -$25\quad billion\quad \times \quad 4\quad =\quad -$100\quad billion$$

and

$$\Delta I\quad =\quad $40\quad billion\quad \times \quad 4\quad =\quad $160\quad billion$$

So the long term change is +$60 billion? (i.e. curve shift out to the right)


texts: What exactly is on the Fed balance sheet?

texts:
All the rage these days is how crazily big the Fed's balance sheet has grown. Looking on federalreserve.gov, I can see its value topped up ~6,573,136 millions USD (~6 trillion USD).

Fine, but is there an exhaustive list of all the assets on this balance sheet? Loans? Bonds? Cash? Equities?


texts: Deriving the New Keynesian Phillips Curve (NKPC)

texts:
I have a question regarding the NKPC. I would like to know if it is possible to derive the NKPC from a sticky prices model, without making assumptions regarding the production function firms face. I am trying to estimate an open economy NKPC. As far as I am concerned, much of the extensions of the NKPC for the open economy involve substituting the commonly used Cobb-Douglas function for  another one which explicitly incorporates imported goods. Some examples of this approach are  Galí and López-Salido, Balakrishnan and López-Salido,  and Rumler. However, almost all of the the derivations of the NKPC assume that firms face a Cobb-Douglass production function, as you can see in Gali and Gertler, Galí and López-Salido, Balakrishnan and López-Salido, Romer, and Galí. Wouldn´t there be a contradicction if (this is the approach followed by Balakrishnan and López-Salido), one assumes that firms face a Cobb-Douglas function but at the aggregate level one assumes a different production function, such as a CES production function that incorporates imported inputs? I am having trouble with reconciling the assumption of different production functions. Because of this apparent contradiction, I thought that, if it is posibble to derive the NKPC from a sticky prices model without assuming a Cobb-Douglass production function (or any other production function for that matter), I could easily bypass the problem.  Hope I made my case clear. Thank you in advance!
P.S. I know that Rumler derives a NKPC assuming just a CES  production function. However, I havent been able to understand exactly how he estimated the coefficients of his model nor what variables he actually used. For an undergradute such as me, estimating such a model seems to be out of reach. However, if someone is willing to give me a hand, I would really appreciate it. Thank you!


texts: Empirical Study of Auctions with Limited Data

texts:
I have limited real auction data which I am trying to see if I can do any empirical analysis. The data consists of auction type (i.e., forward or reverse), protocol (e.g., Vickrey, Dutch, English, etc.), winning bid value, 2nd highest bid, length of auction and number of bidders. The dataset is large (~500+ for each protocol). I do not have bid-level information (e.g., how the bids are distributed for each auction) which really limits what I can do with the data.

As you see, the problem is that I do not have bid-level data (e.g., how each bidders were bidding). I had two ideas originally:

Determine whether bidders are bidding according to the Bayesian
Nash strategy but I don't think it is possible to establish a
distribution of valuations since I do not have bid-level data.
An analysis of the Revenue Equivalence Theorem by examining the
actual seller revenue for each protocol versus the expected revenue
but not sure if this is possible.

Any suggestions or suggestions of past studies will be greatly appreciated!


texts: Positive examples of central bank interest rates adjustments policies

texts:
I'm looking for sources, maybe scientific articles, that study the effectiveness of central bank interest rate adjustments. Specifically, I'm looking for some kind of a proof by example, where a country which had stable policies regarding the adjustments in a larger period of time received consistent results in the effects of these adjustments; especially when adjusting for global crises.

Which countries are best examples for a positive role of adjusting central bank interest rates?


texts: Theories that complement/contradict prospect theory?

texts:
Kahneman and Tversky's prospect theory, which they developed to contradict expected utility theory, is obviously an interesting result.

But, after their experiments has anyone tried to completement the theory? Or to contradict it?


texts: prodest package in R, TFP growth estimation

texts:
I have a question regarding the results and its transformations received from prodest package estimation. So, the dataset is available here  https://drive.google.com/file/d/1aedWYABus1fQjKWxkOmYOmxv-qSja7hF/view?usp=sharing. My code is the following:
remove(list=ls())

library(plm)
library(dplyr)
library(ggplot2)
library(prodest)
library(estprod)
library(broom)
library(pdynmc)

pckg<-c("plm","readxl","dplyr","ggplot2", "broom","prodest", "estprod")
install.packages(c("plm","readxl","dplyr","ggplot2", "broom","prodest", "estprod"))
lapply(pckg, require, character.only = TRUE)

# Set the working directory
setwd("C:/Users/vadya/Desktop/baka")

# Downloading the survey data
Data <- read.csv("LV.csv", header=TRUE, sep=",")
str(Data)

Data$ID<-as.numeric(as.factor(Data$ID))

summary(Data)

# Creating a panel data frame
PData <- pdata.frame(Data, index = c("ID","Year"))

pdim(PData)
pvar(PData)

DataA <- Data %>%
  filter(NACE == 'A' & Year < 2014) %>%
  filter(VA > 0, L > 0, K > 0, M > 0) %>%
  select(ID, Year, L, VA, K, M) %>%
  summarise(ID = ID,
            Year = Year,
            l = log(L),
            va = log(VA),
            k = log(K),
            m = log(M))

####################################################################################################################################
mod2LP <- prodest::prodestLP(DataA$va, fX = DataA$l, sX = DataA$k, pX = DataA$m, idvar = DataA$ID, timevar = DataA$Year,
                             R = 100, cX = NULL, opt = "optim", theta0 = NULL, cluster = NULL, tol = 1e-100, exit = FALSE)
mod2LP
omegaLP <- prodest::omega(mod2LP)
summary(mod2LP)
summary(omegaLP)

mod2OP <- prodest::prodestOP(DataA$va, fX = DataA$l, sX = DataA$k, pX = DataA$m, idvar = DataA$ID, timevar = DataA$Year,
                             R = 100, cX = NULL, opt = "optim", theta0 = NULL, cluster = NULL, tol = 1e-100, exit = FALSE)

mod2OP
omegaOP <- prodest::omega(mod2OP)
summary(mod2OP)
summary(omegaOP)

mod2ACF <-  prodest::prodestACF(DataA$va, fX = DataA$l, sX = DataA$k, pX = DataA$m, idvar = DataA$ID, timevar = DataA$Year,
                                R = 100, cX = NULL, opt = 'optim', theta0 = NULL, cluster = NULL)

mod2ACF
omegaACF <- prodest::omega(mod2ACF)
summary(mod2ACF)
summary(omegaACF)

mod2W <-  prodest::prodestWRDG_GMM(DataA$va, fX = DataA$l, sX = DataA$k, pX = DataA$m, idvar = DataA$ID, timevar = DataA$Year,
                                   cX = NULL, tol = 1e-100)
mod2W
omegaW <- prodest::omega(mod2W)
summary(mod2W)
summary(omegaW)

####################################################################################################################################

After using the omega function I receive the summary statistics of the TFP estimation. However, if I want to assign this omega function output to another object, I end up with matrix of randomly assigned numbers (I guess so). Hence, the problem is that my dataset is from 2011 till 2019, and I need to get the change of the TFP YoY or, basically the growth of it for each entity separately YoY. Would really much appreciate your suggestions since I tried a lot of things (including changing the overall function prodest in order to get the TFP assigned to each firm in each year, but nothing really helped).


texts: Who really benefits from economic growth?

texts:
In recent social protests, I have heard the claim that the economic growth benefits only the rich: they become richer while most people become poorer.

To check whether this claim is realistic, I looked for data relating economic growth (measured by the increase GDP) and real wages. I found this blog post, which shows that in the UK in 2008-2014, there has been positive economic growth while the real wages were declining.

The writer offers several explanations to this phenomenon, but they may be specific to the UK. So, my question is: what are some other examples of economic growth that comes together with decreasing real wages?

In general, what are examples of economic growth periods, in which few people benefit while most people become poorer?


texts: Can I normalise the Dixit-Stiglitz price index to 1?

texts:
I've built a model that I am trying to solve in Matlab. The model has Dixit-Stiglitz preferences and $m$ goods, so admits a price index of the following form:

$ P = \bigg[ \sum_m p_m^{1-\varepsilon} \bigg]^{\frac{1}{1-\varepsilon}} $

I would like to normalise this to 1. That is, everything in my model would be in terms of the final goods basket. However, the goods prices are already determined by the following well-known equation

$ p_m = P^{1-\varepsilon} \bigg[ \frac{I}{Y_m} \bigg]^{1/\varepsilon} $

where $I$ is total income (you can think of it as $\sum_m p_m Y_m$) and $Y_m$ is production of good $m$.

Furthermore, given a set of wages and rental rates (supplied as a "guess" for Matlab's fsolve), the FOCs already (over)identify the capital and labour levels, and so $Y_m$ is determined, pinning down $p_m$. It seems like I can't set the price index $P =1$?

What shall I do? Shall I include the $P-1=0$ equation in my Matlab solver (adding to the overidentification issues!)? Shall I calibrate $\varepsilon$ to ensure $P=1$? Or do you have any other advice?

Thank you so much!


texts: What is the correct economic term for beneficial "transaction frequency"?

texts:
I am not an economist but I am trying to track down and understand an economic principal (and/or theory) that I think is called "transaction frequency" but when I go searching on that term I find only similar phrases so obviously I am in error. Below is the best way I can describe what I am looking for.

This is related to what is commonly called in the media "wealth inequality".

I remember about a year ago seeing a video that talked about the economy and how transactions (buy/sell exchanges) help it. Sadly I cannot find that video (and if it used invalid terminology maybe that is a good thing).

What the video presented was that there is a spectrum of transactions defined by the two variables of transaction size and transaction frequency. The video asserted that wealthy individuals (top 20% of the population) tend to make transactions that are large in size but relatively few in the scheme of things (such as multi-million dollar investment buys). Conversely, the video asserted that individuals in the vast majority (80%) of the population mostly make small size transactions in fairly high frequency (i.e.: tens of millions of every day retail & service purchases). Finally the video asserted that it is each transaction -- no matter what size -- that "benefits" the economy and that this means that more money in more hands causing more transactions is much more beneficial to the economy than the relatively few large investments.

Now like I said I am not an economist so I do not know if these assertions are accurate or accepted. I do not even understand exactly how a transaction "benefits" the economy. However if I am ever to achieve understanding then I need to know what it is I am trying to research and thus this question.

Thank you for any information on this matter.

PS: I have often heard statements like "Each 1 dollar spent generates an additional X.XX dollars in economic activity." (Is there a name for this concept?) so perhaps that is what the video was attempting to suggest as the "benefit" of each transaction?


texts: What would be the effects of an expiration date on currency?

texts:
Let's say we introduce a monetary system where each piece of money is printed with an expiration date - a year, perhaps.

I'm imagining something rather different from inflation (although I do not know whether it would actually behave much differently) :
With inflation, the entire money supply gradually devalues at some set rate.
With an expiration date, there is no devaluation for a while, and then a sudden drop. However, at that point (and in fact for quite some while already) there will be new money in print, which will still have the same value the old money would have had a day ago (plus/minus the undoubtedly still existing inflation rates on top of that, but unless that's somehow important in this, let's ignore that for the purpose of this question.)

So the setup would essentially be a government infinitely printing money BUT to prevent hyperinflation, old money is suddenly and permanently lost from the economy. Presumably the printing rate would roughly coincide with the expiration date such that, at any given, about the same amount of money (plus/minus external demand but let's ignore that as well) is available. It may just suddenly change owner.

What will happen, short- and long term? (Obviously short time a lot of things, like savings plans and how banks work would have to significantly change or they would downright fall flat, but after a while, assuming our hypothetical government wouldn't just frightenedly revert the laws after two years of resulting economic failure or something, a new economy would build around these new restrictions. What would that be like - without delving too deeply into pure speculation. Are there useful models adaptable/built for such a situation?)


texts:
What is the difference of Financial Economics and International Economics? Why, How? What are the implications of these differences?

Will a model of international economics suddenly become a model of financial economics if I simply change the names?

Apples, Bananas, Carrots, Drupes are named Financial Products A, B, C and D.

England and France are named investor E and investor F.

I saw myself repeating the same exact basic math and coming to the same conclusions, different names notwithstanding.

Both are Arrow-Debreu general equilibria. I can't understand the differences besides there necessarilly being money in financial economics.


texts: Additional components in utility functions (behavioral economics)

texts:
I am looking for a term describing the second part of a utility function in behavioral economics and related disciplines.

For example, Thaler (1983) describes a utility function that could be simplified like

$u_i=\overline{p}-p \pm v(p^*-p)$

with $\overline{p}$ valuation of the good, $p$ price of the good, and $v(p^*-p)$ the so-called transaction utility; the utility gain/loss from making a bargain or being ripped off.
Similarly, a simplified Fehr-Schmidt utility (1999) function consists of

$u_i=(\overline{p}-p)-\alpha (p^*-p)-\beta (p-p^*)$.

with the second and the third term of the utility function describing negative preferences for inequity.

Thaler calls the first term "acquisition utility" and the second term "transactional utility". Is this a consensus in (behavioral) economics, i.e., could we call the second/third part of Fehr-Schmidt "trabsactional utility" or is there another, better term for this second part of utility that is added to the "classical" utility?

Do you know of a paper comparing these terms? I only do so with respect to fairness (Fehr, Schmidt, 2006; Clavien, Chapuisat, 2016).

...

Clavien, Christine; Chapuisat, Michel (2016): The evolution of utility functions and psychological altruism. In: Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 56, S. 24–31. DOI: 10.1016/j.shpsc.2015.10.008.

Fehr, Ernst; Schmidt, Klaus M. (1999): A Theory of Fairness, Competition, and Cooperation. In: Quarterly Journal of Economics 114 (3), S. 817–868. DOI: 10.1162/003355399556151.

Fehr, Ernst; Schmidt, Klaus M. (2006): The Economics of Fairness, Reciprocity and Altruism – Experimental Evidence and New Theories. In: Foundations, Bd. 1: Elsevier (Handbook of the Economics of Giving, Altruism and Reciprocity), S. 615–691.

Thaler, Richard (1983): Transaction Utility Theory. In: Advances in Consumer Research 10 (1), S. 229–32.


texts: Black-Scholes - Theta formula Futureoption Currencyoption

texts:
I cannot figure out how the theta-formula would look like for a future option and a currency option.

I know the formula and understand it for an ordinary stockoption - but not for future-option and currency option.

Concerning the future-option i think there would be a very slight modification - probably just replace the S (stock) with the future price. But I dont know if the interst-factor on the right-handside should be removed or not?

Concerning currencyoption - I know how to calculate the price but not the theta here either. I have googled a lot and cannot see any formulas in John C Hulls book (Option Futures and other derivatives).

But heres the formula for calculating the theta for a stockoption.
X = Strikeprice, S = Stockprice, q = divident, r = interest, T-t = Time to Maturity, and  sigma is volatility.


texts: Are symmetric equilibria continuous with respect to the payoff matrix?

texts:
Assume a two player symmetric game where the payoff for the row player is given by:
$$
A = \left( \begin{array}{cc}
a_{1,1} & a_{1,2} &\cdots & a_{1,n}\\
a_{2,1} & a_{2,2} &\cdots & a_{2,n} \\
\vdots & \vdots & \ddots & \vdots\\
a_{n,1}&a_{n,2}&\cdots &a_{n,n}
\end{array} \right)
$$

We denote by $\Delta$ all probability vectors over $[n]$.

A symmetric equilibrium for the game is a vector $a\in \Delta$ such that
$$\forall x\in \Delta: x^tAa\leq a^tAa$$

Assume we increase the value of some specific coordinate $i,j$ by a variable $t$. Denote the new matrix by $A(t)$.

  Assuming $A$ is non-singular, is the change in the symmetric equilibrium continuous in $t$?

I'm aware that the question might not be enough well-defined, as there could be more than a single equilibrium for $A$, but is there necessarily a symmetric equilibrium for $A(t)$ which converges to the symmetric equilibrium for $A$ as $t\to 0$?


texts: Non-uniqueness of iterated elimination of weakly dominated strategies?

texts:
In the lecture, my professor said "when we eliminate weakly dominated strategies, you might end up with different equilibria depending on
the order of deletion!"

Can anyone give me an example?


texts: Is America economy, Connecitcut's economy, and the global in general recovering and better than the year 2008?

texts:
Please answer all three if you can.  I live in Connecticut, America, and of course global trade and economies matter as we are becoming more global from technology.

December 2007 the markets crashed hard and 2008-09 was the actual defined recession.  Worst we ever had (not depression, recession).  By GDP growth definition we did recover.  BUT living in Connecticut I've seen things differently so sorry if it sounds opinionated but I'm trying to put facts together from research and forum answers.

GE Headquarters is leaving CT and moving to Boston, meaning hundreds of high paid jobs leaving and the taxes are switched to everyone else yes?  Our governor has been called the worst, and we only have 3 million people which is down a lot in past years.  That means less business and money which is not good.  Taxes are already higher than almost every other state...BUT my question is are we recovering because form what I've read the answer is yes.  But if a huge job supplier is leaving and tax burdens increase, how can CT ever recover?

The same for America.  Unemployment is like 5% but most of these jobs at least where I am on the East Coast are part time fast food/retail jobs.  Good for kids maybe, but full time employment and good pay even start at $11 or $12 an hour is better than a father supporting his family on a 20 hour a week mcdonalds fry cook.  So is this really a recovery (maybe definition) but has it really gotten better?

Not just here...but the rest of the world as well?  All I hear is bad stuff about Europe, debt crisis, Greece.  What's going on?  No blame game what is going on for sure that we know?


texts:
Marginal cost is defined as "the change in the total cost that arises when the quantity produced is incremented by one unit." And given a total cost function $C(q)$ that's differentiable, the marginal cost is the derivative, $C'(q)$. But if I were given $C$ and asked the cost that arises when the quantity produced is increased from 2 to 3, I would simply calculate $C(3)-C(2)$; no need to bring calculus into the picture.  In general, $ C(3)-C(2) \neq C'(2)$. For example, if $C(q) = q^2$, then $C(3)-C(2) = 5$, but $C'(2) = 4$.

Thus my question is:
Why is the derivative used to represent marginal cost instead of the difference?

Note: I thought this question must've been what's being asked here, but evidently not; there what's being asked is (essentially) why $C'(3) \neq C(3)-C(2)$.


texts:
A person with a current wealth of 100,000 who faces the prospect of a 25% chance of losing his or her 20,000 automobile through theft during the next year. Since there is no upside to this event and E(gain) = 0.25*(-20000) + 0.75*0 = -5000
This would mean we all take insurance against unfair bets in life. Is this conclusion correct?


texts: Link between recession and decline in investments

texts:
I recently followed MIT online lectures for economy and I found this - one of the reason for investments decline in recession is bad expectations about economy -----> leading to Higher capital output ratio -------> lower Investments

How does bad expectations leads to higher capital output ratio and then why does that translates into low investments?
My thoughts - Bad expectations about economy might cause firms to severely cut their production. Since, output gets lower and output being in the denominator makes the whole fraction to be bigger so we get higher capital output ratio and that discourages investments because cost of capital is high so with the lower output it would be hard to pay off the loans. Is my reasoning correct? Is it conceptually sound? Am I thinking clearly and simple yet effectively? I am not sure about the answer neither with my line of reasoning.

You're welcome to critique my thoughts and lead me to correct answer or you can share your own views or answer about it (and I guess that would be way better and conceptually sound)

Thank you so much for your time. Grateful!


texts: Have social accounting matrices and input output models fallen out of fashion? if so, why?

texts: My perception may be uninformed but 'worldwide' I believe collection of official data on input output tables of economies dont seem to be keeping up with the times. Im aware that compilation of such data sets is difficult hence the large time gaps between releases but I would think that 5 years or so would suffice. examples of countries where such data are up to date would be much appreciated


texts:
What would be the I.C of this function? $u(x,y)=\min(x,√y)$
I understand since it is a perfect complements case it should be "L" shaped but I wanted a more detailed graph.


texts: Simulating the economy - is it an active field of research?

texts:
The question revolves around another motivating question: How does economics become more effective at predicting the behavior of the macro economy? For example, how does economics develop methods that allow it to predict with some certainty, more certainty than current methods provide, that a recession in country A will occur?

How much is simulation used by economists and institutions? I know that the Federal Reserve in the US conducts bank 'stress tests', which are a sort of simulation. I'm wondering if this approach has been expanded and scaled to answer other sorts of economic questions.

Are there any institutions or researchers developing simulations as a core part of their research?


texts: Using US foreign tax policy to offset a raise in interest rates

texts:
I am an amateur economist at best, more a person with an economic BS looking to explore data science (I will be using python). I have a theory that I want opinion on that will allow the Fed to raise the interest rate while offsetting the lose in domestic investment by lowering or eliminating the repatriate tax laws.

My assumptions are that raising the interest rates will lower investment overall, lower the money supply, and decrease demand.  That lowering the repatriate tax laws will have American firms import a higher level of liquid capital, spur domestic investment, and create jobs.

Ultimately I want to make a formula with as little dependencies as possible where $f(x)+g(y)=0$. $f(x)$ will be the effect on the economy due to the interest rate and $g(y)$ will be the effect of the tax. So if you raise the interest rate $f(x)$ then you must lower the repatriate tax rate $g(y)$.

My questions are:

1) Are you aware of a study like this?

2) Are my assumptions correct?

3) Any advice would be greatly appreciated such as data sources, economic papers on parts of what I am trying to do, possible factors to include.

4) Just looking at it, does it seem logical?


texts: Is it better for low-income people to live in the countryside where it's cheap or in the city where there are more services?

texts: Supposing someone is struggling to pay the rent in an urban area, and they don't have anything tying them down to any one place, would it make sense to move to a rural area where the rent is much lower? Or are cities generally better for low-income people because of the services like food banks, etc.?


texts: Mathematical analysis of an economic model - stuck in calculations

texts:
I'm not sure if it's more economic than mathematical question but it's about analyzing a model from economics so I'd rather ask it here.

There's a model with two goods, 1 and 2. The first one has both consumer demand ($D_1(P_1)$) and the government demand ($G$, the variable is predefined externally). The second one has only $D_2(P_2)$.

The supply functions for both goods are: $Q^s_{1,2}=S(P_1,P_2)$ (some quantity of good 2 is used in good 1 production and vice versa) The supply quantity of good 1 increases when its own price $P_1$ increases but decreases when there's an increase in $P_2$ (as the costs increase). Also own effects dominate, so $\frac {\partial S_1}{\partial P_1} > |\frac {\partial S_1}{\partial P_2}|$ in absolute terms. The same is true for $S_2$. Again, I'll write out all the equations below for more clarity:

$$Q^d_1 = D_1(P_1)+G$$
$$Q^d_2 = D_2(P_2)$$
$$Q^s_1 = S^1(P_1, P_2)$$
$$Q^s_2 = S^2(P_1, P_2)$$

Where I got stuck is in calculation of $\frac {\partial Q}{\partial G}$ for $Q_1, Q_2$ (the change in $Q_1$ or $Q_2$ after a change in G). The only thing that comes to my mind is:

$$\frac {\partial D_1}{\partial P_1}*\frac {dP_1}{dG} + 1 = \frac {\partial S^1}{\partial P_1}*\frac {dP_1}{dG} + \frac {\partial S^1}{\partial P_2}*\frac {dP_2}{dG}$$ for $Q_1$, but how to calculate the $\frac {\partial Q_1}{\partial G}$ from here?


texts: Determining the capital return from the investment in dynamic firms and their growth

texts:
According to Tech Tour Growth 50, an organization that identifies the. young firms valued between one hundred millions and one billion dollars and which benefits ("chiffre d'affaires" increase by 50% a year) there 284 of such firms in Europe and 833 in United States where the injected funds are five times higher. If 5*284>833 does it means that the return on investing in Europe is greater than in United States ?

I am not sure about the title I have to my question

Information provided by "l'Europe, le continent au plus fort potentiel de licornes" from Les Echos, a French newspaper about Economy


texts: Are unit root tests necessary or useful on small samples of time series data?

texts:
I have a 16 year time series (annual frequency with 16 observations). I will conduct an OLS regression. In this setting do I need a unit root test?

Do you have additional suggestions for things that I should do to pre-analyze my data?


texts: Creating a tailored sample from panel data

texts:
As a small part of a project, I have been asked to tailor a large panel dataset I have built into a form that is more comparable to one specific country.

So I have done the following:

Look at the ranges of my dependent variable, explanatory variables and controls for the country of interest.

Drop any firm-time observations that fall outside the ranges of any of these variables.

Run my regression on the truncated sample.

I was wondering whether there are any serious cons of this approach - particularly given that my method will include only a subset of the observations for some firms. Bear in mind that this is meant to provide a rough and ready indication rather than be a super robust exercise.

Many thanks for your help.


texts: Is lowered probability of spending equals savings?

texts:
This a really basic one and logic says: Yes given enough iterations.
But I am looking for validation

Situation: There is a 7% probability of expenses of 1000 occurring. I have a tool that then applied to the process has a 95% probability to reduce the chance of expenses occurring by 58-78% (mean at 60%).
How do I calculate savings?


texts: Questions of the type "What do you think other people would think?"

texts:
For a study in the adoption of new technology, a student and I are developing a questionnaire that will poll domain experts on their opinions of what their colleagues would think about benefits/drawbacks of adopting a particular technology. This is research in social science/business but not strictly game theory, and as we are not economists, we don't know the literature.

Have economists/game theorists investigated questions of the type What do you think other people would think? If several experts can, say, draw technology acceptance distribution functions that reflect their own beliefs about the community's attitude toward a particular strength or weakness of a new technology, then the geometrical average of those distribution functions could be a starting point for inquiry into ranking the relative importance of a set of several strengths and weaknesses. Has this been done before? By whom?

We are not asking for a tutorial here, just a pointer to where should we should start looking for prior art.

Full disclosure: I asked this question on SE/Psychology and Neuroscience and did not receive meaningful answers.


texts:
I have the following system of equations

$$ \rho V(u, \epsilon^i) = F(u, \epsilon^i) + V_u(u, \epsilon^i)g(u, V(u, \epsilon^i) + \lambda^i \left(V(u, \epsilon^{-i}) - V(u, \epsilon^i)\right)$$

with $i \in \{0,1\}$, so that $\epsilon$ can take two values and $g(u, V)$ known and initial $u(0), \epsilon$ given. $g(u,V)$ is the law of motion for $u$, $\dot u(u, \epsilon^i)$ if you will - but it depends on the value of $V$. This looks like a HJB, but crucially, there is no optimization involved.

This is a macro-labor model, where the amount of job openings depends on the value of a filled position ($V$), which is why the law of motion for $u$ (unemployment) depends on the equilibrium value of $V$.

How could I compute (numerically?) the value of $V$ that solves this ODE?


texts: Reason for SMEs in the European Union employing the bulk of people?

texts: Is there any specific reason why SMEs in the European Union employ the vast majority of people in general as well as in certain industries? Are they exempt from certain regulatory burdens such as certain labour laws, for instance minimum wage legislation?


texts:
The normal supply and demand models take the supply and demand of a particular good and show that the equilibrium price is where the two curves intersect.  At this point, all the people below the equilibrium point value the good as worth less than the price; on the other hand, all the people above the equilibrium point value the good as worth more than the price; people at the equilibrium point value the good at the price value.
In my mind, following this logic, everyone should want to "purchase" a free good.  But that is not necessarily the case.  For example, in an undergraduate program, the university will give away t-shirts, pens, etc. to the students for free.  However, not all of the students will want these items.  However, since the price is free, it seems that everyone should want them.
How do we reconcile both of these observations?


texts:
Someone asked a simple question: when wages increase, why don't companies just raise prices such that it cancels out the wage increase?

Of course, this isn't what happens in real life since real wage growth exists. But what's the best way to intuitively explain why that's the case?

A simple explanation could be that the demand curve shifting outward due to higher wages leads to an increase in quantity and price, but that's just from looking at lines on a graph.


texts:
Question:

What my did is

I proceed this question until that point. But, I will be happy if help me to solve this question.

Thank you.


texts: Is this formula for net present value correct?

texts:
I have been presented with this formula for the net present value:
$$NPV  = I_o + \sum \frac{F_t}{(1+r+p_t)^t},$$
where $F_t =$ net cash flow for period $t$; $R=$ required ret of return; $I_o=$ Initial cash investment, and $P_t=$ inflation rate during period $t$.
Although I've been told it is an industry standard, I don't get it.

Why does rate of return increase with time? I assume it is constant - if I want 8% return each year, I assume it comes from inflation adjusted value, so the term should be out of the brackets
"Initial cash investment" pharsing suggest the value will be positive, but I assume it has to be negative, otherwise it wouldn't make sense to sum initial investments with inflows.

Any comment will be appreciated, thank you!


texts: Does non-monotonicity imply non-satiation always? Why or why not?

texts: I understand that monotonic preferences imply non-satiation. But I am not sure 100% if non-monotonic functions always have satiation. An intuitive and mathematical explanation would be very helpful.


texts: What possible reasons could make arbitrage impossible between some markets?

texts: What could prevent arbitrage (not necessarily risk-free) between some markets even when price differences exist?


texts: Finding labor supply function from equation of labor market

texts:
The supply side of the labour market is given by the following set of
equations:
Utility of worker is given by $$U = L^{\frac{1}{2}}C^{\frac{1}{2}}.$$
Real wage $w = 5$,
T-Max = 40 hours,
Investment Income (Fixed) = 100

Now assume that the real wage increase from 5 to 8; assuming labour
supply to liner line, find the equation of the labour supply function using
two discrete points?


texts: I do not quite get a phrase that I read in the Financial Times today.

texts:
"a share that has fallen by 95 per cent has fallen by half since it has fallen by 90 per cent"

Can you explain the logic behind that?


texts: Regional disaggregation of a national input-output table

texts:
I am trying to disaggregate a "national" input-output table into three regions using Simple Location Quotients (SLQs) and RAS balancing. In particular, I'm trying to use the "Two region logic with more than two regions" technique (Miller & Blair, Section 8.6.3).

I am not able to get the target $\textbf{u}$ and $\textbf{v}$ margins to be consistent with each other, which is preventing me from applying RAS. I suspect that something rather obvious is eluding me, and I'd be grateful for advice.

To make this concrete, please see some dummy values below.

"National" IO table $A^n$:

         c1       c2
id
c1 0.161368 0.000001
c2 0.004815 0.047835

Total output by sector $x$:

id
c1    422428
c2    508800

Whence inter-industry flows $Z$:

         c1       c2
id
c1 68166.22     0.28
c2  2034.17 24338.67

Table of total outputs, by region {$r_1$, $r_2$, $r_3$}, by sector {$c_1$, $c_2$}:

          c1        c2
id
r1  30624.97  62497.83
r2 329614.70 415367.70
r3  62188.33  30934.47

As per the textbook, I'm looping through each region in turn, calculating the outputs:

          c1        c2
id
r1  30624.97  62497.83
R  391803.03 446302.17

and LQs for regions $r$ and $R$ (not $r$), and applying the LQs to $A^{n}$ to obtain $A^{rr}$ and $A^{RR}$:

       c1     c2
id
r1 0.7250 1.0000
R  1.0000 0.9746

This gives $A^{r_1r_1}$ and $A^{RR}$ respectively:

         c1       c2
id
c1 0.116988 0.000000
c2 0.004815 0.047835

         c1       c2
id
c1 0.161368 0.000001
c2 0.004693 0.046622

I subtract $A^{r_1r_1}$ and $A^{RR}$ from $A^{n}$ to obtain $A^{Rr_1}$ and $A^{r_1R}$  respectively:

         c1       c2
id
c1 0.044380 0.000000
c2 0.000000 0.000000

and

         c1       c2
id
c1 0.000000 0.000000
c2 0.000122 0.001214

I convert these input coefficients to flows using the regional outputs, and use these as the first block of the marginal matrices. For this example, I obtain $\textbf{u}$ and $\textbf{v}$ as follows:

       c1     c2
0    0.00   0.00
1   47.87 541.64
2    0.00   0.00
3   36.58 365.76
4 3049.71   0.01
5    0.00   0.00

         0    1       2    3      4      5
c1 1359.14 0.01 1310.71 0.01   0.00   0.00
c2    0.00 0.00    0.00 0.00 117.39 580.08

However, when I check for consistency, I obtain the following "collapsed" matrices:

        c1     c2
c1 3049.71   0.01
c2   84.44 907.40

        c1     c2
c1 2669.85   0.01
c2  117.39 580.08

which are clearly different.


texts:
So I am currently stuck on the following problem:

Consider a representative agent model where the representative consumer has preferences given by $$\sum_{t=0}^{\infty} \beta^t \ln(c_t)$$ where $0<\beta<1$ is the consumer's subjective time rate of preference and $c_t$ is consumption at time $t$. The consumer is endowed with one unit of consumption good at $t = 0$. The consumption good can be stored costlessly across time. That is, consumption at $t$ follows $$x_{t+1} = x_t - c_t$$ where $x_t$ is the available consumption at the beginning of $t$ and $x_0=1$.

Solve for the equilibrium sequence of $[c_t]_{t=0}^\infty$.

Now the first thing that throws me off that is away from a traditional model is that leisure is completely missing from the consumer's preferences. Next I rearranged to find for $c_t$ which is seen from $$x_{t+1} = x_t - c_t$$ $$x_{t+1} - x_t = -c_t$$ $$x_t - x_{t+1} = c_t$$ $$-{\mathit{\Delta}}x_t = c_t,$$ but given the negativity are we summing negative values?


texts: Cost-optimal p2p-trade in a community of households

texts:
I’m trying to solve the following problem and I’ve been working on it for a long time already:
I want to optimize electricity-costs in a smart grid. There’s producer and consumer households in the grid. Trades are just possible in between producer and consumer households.
The smart grid consists of 200 households.
The Trading price of a household-pair is something like that:
Electricity price = price – possible price reduction (equation  1)
Where price is a constant and possible price reduction depends on parameters for each household-trading pair.
That means optimizing the electricity price (eq. 1) is possible by maximizing possible price reduction.
I want to optimize the electricity price for the community and not from a single household perspective.
I defined the possible price reduction function for a household-pair as:
P(Ci,Pi) = x * value1 + value2 + value3
Pi = producer household
Ci = consumer household
P(Ci,Pi) = household trading pair

As for x=1 value 2 and value 3 are mostlikely really small. The variable kind of depend on each other.
More information
Value 1
Value 1 is the same for every possible household pair.
But x depends on the distance (d) of the households Pi and Ci.
If d < 10 km:
    x = 1

If d> 10 km:
    X = 0

Value 2
Value 2 depends on the difference of the price zones of the household pair. So for each possible pair value 2 will be different. The price zone important for value 2 will be called zone A.
So value 2 for the Pair (P1,C1) would be:
Value2 =zoneA(P1)-zoneA(C1)
Zone1 depends on the location of the households.
Value 3
Value 3 also depends on the households price zones. It depends on a different price zones which we’ll call zone B.
So value 3 for the Pair (P1,C1) would be:
Value3 =zoneB(P1)-zoneB(C1)
Zone 3 also depends on the location of the households.
At the moment I’m looking at the problem as a transport problem for bipartite graph case.
Interpreting households as nodes of a graph and individual price functions in between households as edges.
I want to compare different useful algorithms, pick the best fitting one and implement that in python.
How would you guys interpret the problem and what are your suggestions for useful algorithms for that case?
Thanks in advance.


texts: Connection between negative interest rates and negative bond yields

texts:
In an answer to one of my other questions: Why does falling global bond yields signal coming deflation, the answerer states:

  Whereas central banks set rates by policy, long term bond yields are determined by the market (i.e., supply-demand equilibrium). An inverted yield curve signals recession and implies rates are set too high relative to market expectations. If central banks set rates in positive territory when long term bond yields are negative, they will de facto force the yield curve to invert.

I cannot see the mechanism as to why if central banks set rates in positive territory when long term bonds yields are negative how this will cause the yield curve to invert.


texts: Can Dynare solve general equilibrium (GE) models with non-convex adjustment costs?

texts:
I know that Dynare (which sits on top of Matlab) can solve many kinds of dynamic stochastic general equilibrium (DSGE) and overlapping generations (OLG) models. I also know that Dynare can handle some sorts of adjustment costs. For example, I have seen convex adjustment cost examples in Dynare. In particular, The Macroeconomic Model Data Base provides on the order of 50 models compatible with Dynare and the user manual indicates several models (e.g. NK_IR04 and US_NFED0) with quadratic (a type of convex) adjustment costs.

Can Dynare solve models with non-convex adjustment costs like An equilibrium model of lumpy housing investment (Iacoviello and Pavan (2008)) or Housing and debt over the life cycle and over the business cycle (Iacoviello and Pavan (2013))? Non-convex has a specific mathematical meaning, but in the context of these papers it indicates that adjustment costs that are not proportional to the amount of adjustment. Instead, the adjustment costs have a fixed-cost proportional to the current asset value.  However, there are other forms of non-convex adjustment cost. If Dynare can solve any model with any sort of non-convex adjustment costs that is of interest.

If models with these adjustment costs can be solved with Dynare, please provide an example or a link to an example (if possible).  If Dynare currently cannot solve these models is there any published code that can do so? Even sample code for a specific model solution rather than a general product like Dynare would be helpful.

More details on non-convex adjustment costs:

I draw my language here from a
A Model of Housing in the Presence of Adjustment Costs: A Structural Interpretation of Habit Persistence (Flavin and Nakagawa (2008))

  At the instant the house is sold, the household pays a transactions
  cost proportional to the value of the house sold, so that wealth also
  changes discontinuously....The housing model developed in Section I
  invokes a fourth set of assumptions: utility depends nonseparably on
  nondurable consumption and on housing, nondurable consumption is
  costlessly adjustable, but housing is subject to a nonconvex
  adjustment cost ($\lambda > 0 $).

Perhaps this language is non-standard but that's a quote from a paper in the AER, and when I've discussed it with others people seem to know what I'm talking about. The two mentioned papers don't use that language but do have the same rough form, that transaction costs are not increasing in the degree of the adjustment but rather that any use of adjustment (other than a small bit, perhaps for depreciation or unit improvement perhaps) triggers a cost related to the state variables instead of the control variables. The paper On the Nature of Capital Adjustment Costs (Cooper and Haltiwanger (2005)) seems to use nonconvex adjustment costs in the same way in a firm capital setting.

  Building upon the analysis of Abel and Eberly [1999], Cooper,
  Haltiwanger and Power [1999] and Caballero and Engel [1999], during
  periods of investment plants incur a fixed adjustment cost. Generally,
  these non-convex costs of adjustment are intended to capture
  indivisibilities in capital, increasing returns to the installation of
  new capital and increasing returns to retraining and restructuring of
  production activity. These fixed adjustment costs represent the need
  for plant restructuring, worker retraining and organizational
  restructuring during periods of intensive investment


texts: What are the effects of the increase/decrease in stock options after an IPO?

texts:
Research :

As far as I can understand :

Stock options are used to increase the capital of companies to realize some projects
Shares are divided into two categories :

o    Free float (which is the part of shares important for my next question)
o    Locked-in stock

For the free float, it’s easy to understand. Public investors can earn money by playing with stock prices.
For the company it’s harder for me to understand.
    When a company wants capital to run projects, she can do an IPO. The initial price depending on the financial situation.

Question :  What are the effects of the increase/decrease of stock prices after that IPO ?

For exemple : Initial stock price was 20 dollars and public investors paid 20 dollars which got into the capital of the companies. If stock price is now 25dollars, company won’t earn 5dollars more. So what’s the point for the company to be devalued after an IPO if she got the amount of capital she wanted ?

Attempt :

I saw only 2 easy solutions :
-   If company wants to increase capital a second time, she needs to have a big value on the market to reduce the dilution of control.
-   If company is too much devalued, she can be acquired by concurrents.
If company doesnt decrease too much and doesnt want to increase capital again, she has no point regarding the increase/decrease of her stock prices, right ?


texts: Definition of "simple situation" is ambiguous

texts:
"Simple” situations (where it is easy to predict which strategies will be chosen by the different agents):

Each participant has a strategy that outperforms all others regardless of the strategies adopted by its partners.

How can everybody have a strategy that outperforms everybody else's strategy?


texts: Applying Economic Principles to Other Studies

texts:
I was recently reading this article about some research that was done concerning the illegal killing of elephants.  There were two quotes that caught my attention:

  ...illegal killing [of the elephants] increased markedly after 2008 and was correlated strongly with the local black market ivory price and increased seizures of ivory destined for China...

and

  ...Illegal killing rates were strongly correlated with black market ivory prices in the Samburu ecosystem...

In the article, the correlation is treated as a previously unknown fact that was "discovered" by the research team and appears to be one of the major finds of the study.

However, it does not seem like the researchers can take credit for this "discovery."  It seems that an economist can reach the same conclusion by a much simpler method:

Increased seizures of ivory reduce the supply of ivory on the market.
Since the supply of ivory has decreased and the demand has remained constant, the price of ivory will increase.
The higher price will motivate individuals to enter the ivory market as suppliers (which, therefore, will lead to more elephants being killed).

Is there a particluar reason as to why the economic principles of supply and demand were not applied to this study in order to more rapidly reach this result?


texts: What would a negative externality diagram look like if the initial price is equal to 0 and then increased with tax?

texts:
The price of plastic bags in Scotland has been increased from free to 0.05 pounds sterling. How would I represent the negative externality decrease using a diagram in such a situation?

This is what I have so far. I'm not sure that it is correct.


texts: Fama Macbeth and double clustering presents inconsistent results

texts:
I have a large unbalanced panel data with 460 firms and 1259 days. The model I would like to run is below

$$
Y_{it} = \beta X_{it} + \alpha Z_{t} + \epsilon_{it}
$$

where $Y_{it}$ is stock return, and $Z_{t}$ are Fama French 3 factors, and $X_{it}$ are variables of interest.

I run Fama Macbeth (FM) and double clustering to correct for the standard error, but two models give inconsistent results,i.e., $\beta$ is significant in one model, and not in the other.

I understand that Fama-MacBeth technique
was developed to account for correlation between observations on different firms in the same time point,
not to account for correlation between observations on the same firm in different time points. Traditionally, it should run cross section regression at each time point, then average estimates along time $T$. But in my case, due to the inclusion of $Z_t$, I have to run time series regression first since otherwise, $Z_{t}$ are not identifiable. In this case, does FM actually correct for correlation between observations on the same firm in different time points?

More importantly, does the inconsistent result mean that my results are not robust? Under my case, can I argue one is more appropriate than the other? Can the unbalanced data structure contribute to the inconsistent results?

I'm using fm and cluster2 command on this page Stata command


texts: Why Does Deficit Spending Work Without a Liquidity Trap?

texts:
My understanding  is that in a functioning economy, the financial market clears when the nominal interest rate is above zero. It is only when it reaches zero that a liquidity trap occurs and the government must engage in deficit spending to borrow the money pooling in the financial market and make sure it is spent.

My question is this: Why would increased government deficit spending shift the AD curve when we are not in a liquidity trap situation? Every dollar that is spent by the government will have to be borrowed from somewhere - households. This would decrease their consumption by the exact same amount government spending increases.


texts: Whats the rationale for using taylor series in economics?

texts:
I've been reading about the translog production function and know its really just a log-log production function approximated using a first order maclauren series.

Why not just leave the function as is? What economic interpretation or use does taking taylor series do for us?


texts: Static Profit Maximization Short Run Shut Down Decision

texts:
In considering whether to stay open or shut down in the short run, a firm compares its revenues to its “avoidable costs”. We usually think of these avoidable costs as variable costs, but of course they could be fixed. This is where I have a thought experiment question:
Suppose we are looking at profit over a month. It is negative. You are considering if you are at least covering avoidable costs. How do we consider capital cost?
Case 1: You rent the factory and the lease is not flexible. This is a sunk cost.
Case 2: You own the factory. Your best alternative is to rent your factory out. If you shut down, you can easily find a replacement (assume no transaction cost). Then this foregone rent is an avoidable cost.
Case 3: This is where it gets tricky for me. You own the factory and no rental market exists. However, you can easily sell the factory if you shut down. So in my mind this is avoidable and the foregone rent (user cost of capital) is the relevant cost. But this doesn’t consider future profits unless we assume that the firm can buy back the factory in the following period when/if prices rise again. This seems incorrect.
That seems to be a downfall of static maximization. How would you propose thinking about this last scenario? Why don’t we consider dynamic profits when discussing shut down decisions?


texts: Computing the continuous time survival rate

texts:
We have a population of people with different age $a$, time is indexed with $t$. There is a rate at which people die, $d(a, t)$. For simplicity, ignore births. I want to compute the evolution of the distribution of ages over time.

Let $m(a, t)$ denote the mass of people at age $a$ and point in time $t$. I will start with a discrete time approximation and let $\Delta$ go to zero. At each discrete point in time,

$$ m(a+\Delta, t+\Delta) = (1-P(a, t))m(a, t)$$

where $P(a, t) = exp(-d(a,t)\Delta)$ is the discrete time analogue of $d(a,t)$. As I'm going to let $\Delta\to 0$, I can approximate $P$ with $(1-\Delta d)$:

$$ m(a+\Delta, t+\Delta) = \Delta d(a,t)m(a, t)$$

Issue Already here I'm having trouble understanding what happened: $\Delta d(a,t)$ denotes the mass of people who died during $\Delta$ at age $a$ and time $t$. Shouldn't this be negatively affecting the mass of people alive? I was expecting something along the lines of

$$ m(a+\Delta, t+\Delta) = (1- \Delta d(a,t))m(a, t)$$


texts: Calculating price elasticity by asking a "this" or "that" question

texts:
Let's say 2 goods exist: A for 10 and B for 20 (B is more premium in this example)

If I decrease the price of both goods by 10% and ask:

"Do you prefer A for 9 or B for 18 "

What sort of insights (elasticities, etc.) would I be able to get from this? I figure the usual arc elasticity is not possible for this, since the units are discrete.

Is it also possible to get other insights if I lower the price of the premium product more than the cheap product? i.e.:

"Do you prefer A for 9 or B for 17?"

Or even lower the price of the cheap product more than the premium, i.e,

"Do you prefer A for 8 or B for 18?"

I'm thinking about any insights that I can get from asking these sorts of questions, but the traditional equations of elasticity don't seem to apply.


texts: GDP simple question got me confused: the sale of a capital asset

texts:
a) Delta Air Lines buys a new jet from Boeing for 200 million dollars.

b) Delta Air Lines sells **one of its jets to Kim Kardashian for 100 million dollars.

So..

a) $200 million investment, purchase of the final good, so GDP increased by 200 M

b) No change, but why? Even if the had bought the plane for 50 million and made profit by selling it to Kim? Here's my in length answer I am not too certain of:

Does not change. Why? This good was already included in GDP. It was produced and sold. It has not been modified by Delta Air Lines, thus absolutely no value added to this plane.  It is simply the ownership transfer of a good that was bought. However...Wasn't that a service? I mean, Delta made it EASIER for Kim to buy a plane. They provided a service, so a profit would be added to GDP...NO?


texts: Unilateral transfers in the balance of payments

texts: In the secondary income account, unilateral transfers like unconditional foreign aid are recorded but aren't every transaction double-entry to make the balance of payments equal 0. What is the other entry in the KAFA to account for these unilateral transfers?


texts: Income/Wealth Inequality; Why does it matter?

texts:
I have attempted to answer this question on my own through reading books, blog, and other economic pieces of literature but they all fail to articulate why wealth or income disparities matter. Now obviously leveraging slave labor or paying someone literal pennies is an issue. But why does the disparity of wealth between say the middle class and the top 1% matter?

From what I have studied it seems cultivating a competitive market (fair prices for goods and housing), managing inflation, and ensuring a strong currency is really what is necessary. Given these things everyone would be able to buy and sell goods or services and still be able to squirrel some money away for retirement. What am I missing?


texts: What does "endogeneity of the industry structure" means?

texts:
Dong,2019,page 899 documented that:

We estimate Export Market Leniency Laws as the weighted average of the passage of leniency
programs in all other countries, excluding the country in which the firm is headquartered:
$$ \text{(Export Market Leniency Laws)}_{jkt} = \sum_k w_{kj}L_{kt}, $$
where $k$ denotes any country other than country $k$, $j$ denotes a three-digit SIC industry, and $t$ denotes the year. $w_{kj}$ is the share of the three-digit SIC industry $j$’s exports from country $k$ to any other country $k$ out of all of the exports from industry $j$ in country $k$ in 1990. $L_{kt}$ is an indicator
variable that takes a value of one if country $k$ passed a leniency program by year $t$, and zero otherwise. To avoid any endogeneity of the industry structure, we base the weights on the data in year 1990. The variable ranges from zero when none of the foreign countries that receive any exports from the firm’s industry have passed a law to one when all of the foreign countries with exports from the firm’s industry have passed leniency programs.

I do not understand what does "endogeneity of the industry structure" means in this context, and why we need to base the weights on the data in year 1990 to avoid this issue?


texts: What is the effect of Quantitative Easing on the US budget deficit?

texts: Is the deficit getting larger because of QE?


texts: Does the US stock market tend to rise after natural disasters?

texts:
It seems counter intuitive that markets would rise after a huge disaster that probably affects multiple industries like oil or produce.

For example, can someone explain why the US markets actually rose in the days following hurricane Harvey?

Edit: changed title to include natural disasters as a whole.


texts: Mathematics of the income and substitution effects

texts:
I have recently been learning about the concept of utility and the indifference curve. I am having some problems understanding the effects on consumption of two goods $X$ and $Y$ of a change in the price of $X$. I understand what the substitution effect generally means. It refers to a substitution of the good $Y$ for the good $X$ that has now become more expensive. Graphically, it is represented by a shift along the indifference curve from point $e$ to point $e^{'}$.

The scenario given in the diagram is as follows: Income $M$ = $ {$100}$ while original prices are at $p_x$ = $ {$10}$ and $p_y$ = $ {$10}$ The three downward-sloping lines seen in the diagram are the so-called "budgetary constraints". The original budgetary constraint line that is tangent to point $e$ has equation $Y = \frac{M}{p_y} - (\frac{p_x}{p_y})X$. However, I am unsure how the two other budgetary constraint lines are derived. The effect here is a doubling of the price of $X$ from $ {$10}$ to $ {$20}$. Hence, I would think the straightforward effect is that the the gradient of the budgetary constraint line changes from $-1$ to $-2$ but that is not what is directly observed. In fact, there is also a change in the vertical intercept of the budgetary constraint line.

Can someone help to explain to me why the substitution effect leads to consumption at point $e^{'}$ and why the income effect leads to consumption at point $e^{*}$?

The example is taken from the book Economics with Calculus by Michael C. Lovell (Chapter 4, p. 152).


texts: Is There a Good Companion for Theory of Moral Sentiments

texts: I am reading "The Theory of Moral Sentiments" by Adam Smith. There's a lot of technical, and/or dated language. Is there a good companion to read this with?


texts: OPEC's market share strategy: What is the benefit of market share in a fungible market?

texts: Coverage of the recent fall in oil prices frequently mentions OPEC's decision to defend their market share, sacrificing price in the process. I understand how market share is important from a marketing perspective: strong brand loyalty gives a firm power to charge a premium over similar products. However, since oil is fungible, what is the benefit of maintaining market share? When I buy oil today, I don't care who I bought it from yesterday, right? What is the benefit OPEC receives by maintaining market share?


texts: Global Macro Investing textbooks and reading list

texts:
What is a good reading list for Global Macro investing? What does Bridgewater, Bervan Howard, Soros, AQR etc. use to teach their staff about macroeconomic investing?

Let us assume a top-class education at the undergraduate level in economics, maths, and economic history so as to avoid the common recommendations of not very useful introductory texts.

Note: Global Macro Investing involves expressing views on commodities, rates, FX, Real Estate, Equities and other asset classes using ownership, futures, or options to find relative value and generate alpha on a global basis.

For example: Short USDTRY on asset outflows from turkey due to geo-political risk and US tightening cycle compared to TRY printing/easing.


texts: Why did large denomiations exist in the early 20th century?

texts:
In the early 1900s, you could buy a newspaper for 5 cents, a pound of apples for 10 cents and the average salary was about \$40 a month.

Nowadays, an issue of the NYT costs \$2.50 , a pound of apples can cost \$1.15 per pound and the median monthly income is about \$2,200.

Today, it makes sense to have a \$100 bill, we can spend it all on a meal at a restaurant and you would need a few of them to pay rent or make a car payment. But in 1900, I can't imagine anything that could be bought with a $100 bill. Perhaps rent? Or a worker's wages?

Compared to the average salary in 1900, a \$100 bill would be the comparable to a $5,500 bill. I can't imagine anything costing that much money today that would justify producing such a highly valued denomination.

My question is: why did we produce \$100 bills in the early 1900s, when there was probably no practical use for them? And also, did people carry $20 bills around in their wallets or were these considered big money?


texts: Europe not self-sufficient in terms of food requirements and consumption?

texts:
An acquaintance once told me that Europe is not self-sufficient in terms of food consumption as it does not have enough farmland and farmers to produce enough for all its people, especially in terms of things such as wheat and meat consumption, and hence must rely on the United States to provide such supply such food products in exchange for other products. His claim is that such dependency and exchange of goods is due to the fact that Europe is not and could never be self-sufficient in terms of food production.

Is this true?

Thanks.


texts: Export is high sensitive to external income. How can be this explained?

texts: I am estimating an export equation, where dependent variable is export and independent variables are exchange rates, external income and other controls. Each coefficient is an elasticity. The results of regression suggest that export is substantially sensitive to external income with elasticity coefficient higher than 6. How this finding can be explained, what are the possible underlying factors which force to such a high sensitivity? I think that this is because of lack in non-price competitiveness in export.


texts: When Balassa-Samuelson effect increases, real exchange rate depreciate?

texts: I researched several literatures related with Balassa-Samuelson effect and according to literatures, as Balassa samuelson effect increases, real exchange rate appreciates. However according to the literature (The real exchange rate of euro and Greek economic growth by Gregory T. Papanikos) , as BS effect increases 10%, the the real exchange rate falls by 4.8%. I could not find any reasonable explanation for this argument. Why this happens?


texts:
As a quantitative analyst and armchair economist I have seen little reason to do qualitative analysis as done in the other social sciences.

However I keep running into these rather wordy analyses of economic issues (primarily from social research organisations) which are constantly pushed and presented as holding the same weight as those presented by the quant camp.

I don't want this to turn into a rant and if this question is opinionated please close it.

My question is: Where does qualitative analysis fit in formal economic research?


texts: Do you have a list of books about the evolution of the banking sector?

texts:
I'm looking for interesting books to read about the banking sector.

Topics:

Changes in the banking sector,
Adaptation of financial services in the digital age,
European and US banking regulations
The efficiency of banking supervision,
Convergence of banking and insurance sector.

Thank you in advance for your suggestions.

French/français :

Avez-vous une liste de livres au sujet de l'évolution du secteur bancaire ?

Je suis à la recherche de livres intéressants à lire au sujet de l'économie bancaire.

Sujets possibles :

évolution du secteur bancaire,
l'adaptation des services financiers à l'ère numérique,
réglementations bancaires européennes et américaines,
l'efficience de la supervision bancaire,
convergence du secteur bancaire et assurantiel.

Je vous remercie par avance de vos propositions.


texts: Why min AC = min SRAC at the minima of AC curve?

texts: At the lowest point of long run average cost curve AC, the SAC is also at its minimum and that is not the case with any other SAC curve bounded by the envelope. Why is that?


texts: I have this two charts of gold prices for the last 60 days. One is in Dollars and the other in Euros. Why they are not an exact match?


texts:
I am struggling a bit with understanding the meaning of capital ratios, and bank profitablity. It seems to me that capital requirements stipulate that a certain fraction of banks' risk weighted assets have to be held as equity. I get why that is the case: for any given value of assets, having more capital serves as a cushion against their falling values. The definition of bank capital is: $$E=A-L$$

Where E represents bank capital. Now, from a textbook I am reading, it says that banks don't like having high amounts of capital, as it reduces their potential profits. I don't understand what that means- doesn't having high amounts of capital mean that the bank is indeed very profitable (maximizing difference between assets and liabilities?)


texts: Why is the symmetric grim trigger not a Nash?

texts:
Consider the stage game:

Let $\delta\in(0,1)$ be the discount factor. Let $G$ be the symmetric grim trigger strategy profile. The payoffs are then

$$E_{A}(G) = E_{B}(G) = \sum_{i=0}^{\infty}3\delta^{i} = \frac{3}{1-\delta}. $$

If a player were to defect from $G$ at time $n$, they would be playing $N$ at time $n$ and every round after they would play $Y$ because that would maximize their stage game payoff given the other player is going to play $N$ forever. Let $G_{n}^{A}$ and $G_{n}^{B}$ be the strategy profiles were $A$ and $B$, respectively, defect from $G$ at time $n$ in this way. By symmetry, we have
\begin{align*}
E_{A}(G_{n}^{A}) = E_{B}(G_{n}^{B}) = \sum_{i=0}^{n-1}3\delta^{i} + 7\delta^{n} + \sum_{i=n+1}^{\infty}\delta^{i} &= 3\frac{1-\delta^{n}}{1-\delta} + 7\delta^{n} + \frac{1}{1-\delta} - \frac{1-\delta^{n+1}}{1-\delta} \\
&= \frac{3+\delta^{n}(4-6\delta)}{1 - \delta}.
\end{align*}
If $\delta \geq \frac{2}{3}$, then $E_{A}(G_{n}^{A}) \leq E_{A}(G)$ (and $E_{B}(G_{n}^{B}) \leq E_{B}(G)$) for all $n$ so it's not clear to me why the symmetric grim trigger strategy profile is not a Nash in this case.

My professor claims that $G$ is not a Nash for any $\delta$. I do not believe it.


texts: Facebook's Libra - Why would it vary in value

texts:
Facebook has come up Libra its version of crypto-currency.

The unique feature of Libra is the "reserve" which backs Libra. The reserve is supposed to be held in stable global currencies (USD, GBP, JPY and EUR).

For a Libra coin to be created and equivalent amount of local currency (based on exchange rate) needs to be transferred to Libra reserve. I am assuming that during this transfer the local currency is converted to USD/GBP/JPY/EUR and then transferred to the reserve.

Essentially for every Libra that is in circulation its equivalent amount is held in its reserve.

Given this, I am assuming that:

Libra would behave like Hong Kong dollar against USD and it would remain stable against USD, GBP, JPY and EUR
There would be volatility in the price of Libra against the local currency (except for USD, GBP, JPY and EUR).

Are these assumptions right?


texts: What are the problems of estimating gravity regressions with firm-level data or industry-level data rather than country-level data?


texts: Why wouldn't other firms follow suit if an individual firm decides to cut its price?

texts:
Why doesn't the demand curve an individual firm faces in a perfectly competitive market have the same elasticity as it does in a oligopolistic market?
Under perfect competition, if a firm increases its price fractionally, consumers will turn away from it and look for alternatives. On the flip side, if a firm reduces its price fractionally, it can capture the entire market. So why wouldn't other firms follow in footstep like they do in a oligopolistic market?


texts:
"European movements for degrowth, decroissance, are rooted in the idea
  that the perpetual growth assumption built into modern economics fails
  to take into account the depletion of natural capital. Hence the
  importance of sustainability."
  - The end of progress

What is natural capital?


texts:
What are the indicators of a country being in a financial crisis?

I would like to know both about the acute and recovery phase.

I am trying to make a point to our company that we are not growing despite the financial crisis being over.


texts: In a competitive equilibrium, can price of a commodity ever be zero?

texts: I don't think they can be, but I'm not very sure. Are their special cases where the equilibrium is competitive even when prices are zero?


texts: Can the major indice of an exporting nation decrease at the same time the currency devalues?

texts:
In the UK, the FTSE100 is achieving record highs at the same time the currency (GBP) is depreciating rapidly.

The media often correlate the two events by reporting that since the indice is made of 100 multinational companies who trade primarily in foreign currencies; a weak pound allows them to book larger profits after they trade back into the GBP domestically.

However, can the FTSE100 decrease at the same time the currency also decreases in value or must the two levers always go in separate directions?


texts:
I want to fit a time-varying VAR model to my data because of a structural break occurring midway in the sample. But I want to plot IRFs, not for the entire dataset, but for the pre-structural-break period (about 30 data points) and the post-structural-break period (also about 30 data points). Does anybody know a package or software that can do this?
I have found packages that can do something similar in R (but for a time-varying BVAR). So this does not work for me as the packages require that I use the pre-structural break period (or part of it) as training data for estimating the prior coefficients. Thus, it does not allow one to impose their own priors for the coefficients (without estimating them using the data points at the beginning of the sample). Consequently, it estimates BVARs just for the remaining sample, which in my case will be mainly periods after the structural break.
My best alternative so far is to break the sample and build a VAR model for each period - before and after the structural break. Maybe a BVAR, given that the data is short for both periods.


texts: Volatility of investment: Joint-Volatility of mutually independent variables

texts:
I´ve been trying to compute a volatility of invesment with currency hedging and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% volatility, we also know that the current volatility of a dollar toward our currency is 5%. We want to know the volatility of the whole invesment.

Can I compute as following? If so, what is the reason for adding the two deviations instead of mulitplying them considering the volalitity of an index and a currency are mutualy independent.

$$\sigma=\sqrt{(16^2)+(5^2)}$$


texts: Societal benefits of Securitisation (e.g. Asset Backed Securities)

texts:
I was reading about the benefits and harms of securitisation.  A research piece suggested "Reducing overreliance on the banking system" with 2 sub-points:

Corporates can access to the funding sources directly
Banks can distribute their existing risk and thus free up their balances to undertake more lending

I was wondering if the second point actually isn't valid if point 1 is true.  Considering a closed system, when the corporates get funding from investors directly instead of banks, although the banks free up their balance sheet (on the demand side), investors also pull out money from the banks at the same time (supply side).  In this sense, only point 1 is true (transfer of lending entity) where point 2 is not beneficial since there is actions in the supply side (provision of saving/deposit from investors).

Is my argument valid?  Discussions welcomed.


texts:
Found the following very interesting statement on bond prices,

"The yield on a risk-free government bond should equal the growth in nominal GDP since that represents the opportunity cost of holding a government bond both in terms of investment opportunities (real GDP) and the time value of money (inflation)"

http://globalfinancialdata.com/7-centuries-of-government-bond-yields/

Question) How does one square the circle of this statement and the "expectations hypothesis"?

Most significant factors in the price of a goverments bonds

Question)Is future growth or short term rates that determine longer rate? or are these two the same somehow?


texts: Concept for "when a mechanism exists which can be exploited, people will exploit it"

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

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

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


texts: How does one asses the impact of a proposed policy?

texts:
My State government is considering a new regulatory policy at the moment. We need to put together an assessment of the (likely) economic impacts of the policy. How do we do that?

I don't work for the state, I'm an outside volunteer.
I don't have any specific economics education.
I'm hoping to be able to put something meaningful together with just a couple of evenings of work.
There are a few other people whom I'm hoping will help.
At this point even knowing what to google could be a big step forward

The desired end result, I'm pretty sure, is a document saying "Given this trusted data, and these reasonable starting assumptions, and this comprehensible mathematical model, we expect to see about this many more or fewer jobs and about this much more or less business investment". Not knowing any standardized techniques, this feels like trying to forecast the effects of a river dam on next year's hurricanes.

There are a few components to the proposed rules, but they can be considered in isolation. The most important one would require (of large producers) a set rate of reduction of CO2 emissions, which currently have few if any regulations in our state. So, for example, opponents of the rules will want a forecast based on the assumption that activities which are currently emitting CO2 simply shut down instead of migrating to different technology; proponents will want a forecast based on the assumption that wind an solar installations ramp up perfectly.

I'm new here; feel free to edit the tags or question!


texts: Why do top professional sport players get usually paid so much?

texts:
I'd like to find an answer to this question as I can't see how something like this can be happening. I can see three reasons that they would earn that much but any of them if thought better is wrong.

1) They generate all the money they win. I don't deny that they generate lots of money, but news like this one: http://www.euroweeklynews.com/news/axarquia-malaga-east/item/126022-la-liga-clubs-threaten-strike, or this one http://www.forbes.com/sites/mikeozanian/2015/01/22/nba-adding-1-1-billion-of-debt-while-getting-its-best-credit-rating-ever/ make clear that there are going to be a lot of times where their salary is clearly overvalued, and according to only economic terms they should earn maybe something that's a third of their salary.

2) They generate the money on its own. I consider that also mostly false, if they generate that much is because mass media is always talking about them and showing them, if they wished they could take any other thing and with time put it on top being that thing much less expensive for them on the beginning.

3) What the do not earn economically , they earn in entertaining people and making them less aware of their problems, ok, so do a lot of other things, like computer games or books or whatever, and none of them get that much of hype usually, moreover, they are likely to be victims on piracy with a lot more frequency than, let's say, a televised sport event.

Maybe this is applied for other professionals like top actors or singers, but I don't know of such huge debts on their case, and I get the impression that there much more top sport players with huge winnings rather than actors or singers.

I'm not a economist, but I find this question intriguing, hope you can help me to understand why.

Thanks for your time.