texts: What exactly is Foreign Currency Indexation?

texts:
As I understand it, foreign currency indexation (FCI) is when a government pegs its currency to another (usually the dollar), and their central bank buys or sells dollars to maintain a stable exchange rate between the two.

The material I have to read for my class mentions FCI in the context of the Mexican tesobonos and other domestic debt that was issued linked to another currency.

I am unable to find a resource online or otherwise that can distinguish between the two possible answers I'm given to the question "What is FCI":
1. When a country issues debt in another country's currency
2. When a country buys foreign currency to lower the value of its currency

One seems incorrect because I don't see how the option hits at the fact that the currency is being pegged to the dollar (or another stable currency), and two seems wrong because it does not account for the other side of the equation (selling to increase which I would assume is functionally correct).

Any input or suggestions?


texts: Can i get rich if i apply the Black Scholes equation or other mathematics in economy?

texts:
Is it the Black-Scholes equation useful if i want to invest in stock market ?

how can i profit from using this equation in stock market ?


texts: Interest/Rental Rate is today's or tomorrow's MPK?

texts:
I recently posted and have since deleted a question regarding Exercise 2.1 in McCandless's "The ABCs of RBCs." The exercise involves deriving a first-order difference equation describing aggregate capital motion in a overlapping two-period generations model, and I could not solve it by using the definitions of $w_t$, $w_{t+1}$, and $r_t$ that I am accustomed to. It turns out that the exercise is easy to solve if you use the relationship $r_t = F_K(K(t+1), H(t+1))$ where $K$ and $H$ are aggregate capital and labor, respectively.

The reason I had so much difficulty with this exercise is that all of the economic theory I know dictates that $r_t = F_K(K(t), H(t))$, i.e. that today's interest/rental rate should equal today's marginal product of capital. Even this particular textbook says so a couple pages before the exercise in question. However, using that relationship yields an equation with no analytic solution for $K(t+1)$. If you use $r_t = F_K(K(t+1), H(t+1))$, i.e. that today's interest/rental rate is equal to tomorrow's marginal product of capital, the problem is solved with just a couple steps of algebra. But you can't just do that, can you?

If you need more context, I'm sorry that I deleted my previous question, but I had effectively shown 90% of the solution to the relevant exercise and I know that this site is not meant for giving homework solutions away. I hope someone can enlighten me on this particular stumbling block I've encountered, however.


texts: Slope vs elasticity of demand function - Is it the same thing?

texts: Do the slope of a linear demand function and the elastisicy of demand coincide when we use specific preferences for pricing. As a paradigm, if we consider the case of CARA normal preferences, by solving the proble of the represenative conumer, we know that the demand function is a linear one. In this case the slope and the elasticity of the demand function coincide, but is this the case in general?


texts: Solution to the Bellman equation is a fixed point

texts:
I have recently started studying dynamic optimization. I cannot quite wrap my head around the fact that the value function of the Bellman equation is a fixed point of a contraction mapping.
As far my understanding is rather naive: if the problem is finite, say:
$$\sum_{t=0}^T \beta^tu(c_t)$$
we construct the Bellman equation from the end, as if we knew the maximum possible value of the sequence in advance. Starting from the last period $T$, we just repeat the maximization by adding an optimal term reflecting current period utility $u(c_t)$, until we arrive to the period $0$. From here I can clearly see how contraction mapping works.
But the infinite case is not so easy for me to comprehend: I can only suppose, that, by iteration of the Bellman operator $(Bv)(x)$, we perform a "calibration" of the policy function until we find the value function (i.e. the maximum possible utility given our transversality conditions) $(Bv)(x)=v(x)$. Am I, at least, thinking in the right direction, or this idea should be understood in a different way?
Thank you in advance.
(Also, this is my first question on .stackexchange ever, and if there are any issues with presentation of my question, please, let me know)


texts: Which income dollar is taxed most heavily, including implicit taxation, in USA?

texts:
Income is often taxed implicitly by disqualifying deduction or government assistance. For example, if the recent proposal of "free tuition for kids of families making under \$125k" would pass the \$125,001-st dollar earned by the parents of 2 kids attending \$25k/year college would effectively reduce their after-tuition income by \$49,999, or 4,999,900% of that dollar.

Thus the question: which income dollar is currently taxed most heavily in USA, including both explicit federal+ssi+state taxation and implicit taxation by disqualifying deductions and assistance programs? How often it exceeds 100%?

EDIT:

famsy's answer convinces me that the question is too complicated. Therefore I'd like to amend it as follows:

Could you list realistic situations in which marginal income is taxed much more than 100%?

famsy mentioned hard cutoff in various welfare/HUD/etc benefits and a situation when a small marginal income led to \$30k of lost benefits. Assuming that the cutoff was set at the same amount that leads to implicit taxation of 3,000,000% on the disqualifying dollar.

Any other examples of that?


texts: Use of the term "effective" in economics

texts: I've seen the terms "effective demand" and "effective wages" bandied about in papers, but I'm not sure what these refer to. Please could someone explain both these concepts? Thanks!


texts: What were the liquidity requirements prior to Basel III?

texts:
I am investigating the impact of enforcing the Basel III liquidity requirements with a focus on the LCR. I have found some information about regulations in fore prior to Basel III in Sweden and Germany. However, it would be very interesting to know if there were any European countries where there were no or very little liquidity requirements prior to Basel III.

Do you know of any such examples?

Many thanks!


texts: What would happen if, hypothetically, money velocity would reach infinity?

texts: If, hypothetically, money velocity would reach an infinite speed, what would happen to that economy? If it would be infinite then it would mean that there would be infinite transactions and therefore Y would be infinite aswell? But infinite transactions would also be a sign of infinite demand and therefore the price would become infinite? Furthermore, if the money velocity is infinite, then it also would mean that every economic agent of the economy is in possession of the same amount of money and thus no wealth inequality would exist? I am curious to if there is a more solid theoretical answer to this and or what others think about this question.


texts: Which parts of health care can be considered market failures?

texts: The justification for public health care subsidies often involves declaring the health care sector to have market failures, for example infectious diseases being a public good and the customer having limited knowledge of the products. Are there any other aspects of health care that can be considered market failures, and under what justification?


texts: To profit from rolling, mustn't you be much more bullish or bearish than before?

texts:
Aren't you likelier to lose money from rolling, e.g. scenarios 3-5 below? How exactly can rolling profit you?

What if you aren't more bullish or bearish than before? What if you surmise that the underlying stock will attain only a certain range of prices, and de/in-crease no further?

I'll brainstorm three cases. Imagine that:

you bought a call. Your underlying asset's price hasn't risen above the spot price on purchase date.

you bought a put. Your underlying's price hasn't dropped below the spot price on purchase date.

In both cases, your call's and put's prices will have dropped, and you've lost money.

your underlying's price de/in-creases beyond the purchase spot price. Then all options' IV may rise. Then even puts at lower strike prices and calls at higher strike prices will cost more.


texts: Monopolies are just a mathematical misunderstanding

texts:
A little head-scratcher (and a good example why we should be careful with notation).

Consider a profit maximizing monopoly, that solves over price

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

Following the routine steps (see this post)

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

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

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

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

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

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

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


texts: The term "Most Favoured Nation" is misleading to me. Please explain

texts:
My understanding

If Country A extends MFN status to Country B with reduced tariffs for a product, then it must treat all other nations in the same way. By this WTO encourages multilateral concessions rather than trade-distorting bilateral concessions.

Question

What is the point of granting Country B, the MFN status if it's going to be the same for all countries? Also, the term 'Most Favoured Nation' is completely misleading here. Country A could have announced that it's going to reduce tariffs for that specific product to all WTO members rather than bringing Country B into the whole picture.

Please explain what's the point of a country granting another MFN status, and why does it apply to all WTO members if only two countries are involved here.


texts: How do we know a business is allocating resources correctly? If the answer is 'profitability,' why is monetary profitability the barometer?

texts:
To clarify, it's a two part question:

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


texts: Can absence of inflation be accounted for by a reconfigured class structure?

texts:
A previous and oft-heard question asked why no inflation results from the Fed pumping money into the economy.

Are we simply seeing a methodical wage suppression, thus no official "inflation," while prices soar in certain sectors dominated by "shareholders," non-wage income, and the "one-percent" or whomever?

The money moves first into the financial industry, where actual production investment is less attractive. It seems that as long as no money gets locked into "sticky" labor contracts, the Fed can pump away and the results are not deemed "inflation." The money does not cycle up in wages or wage-earner goods.

In other areas, however, we do see soaring prices: art, luxury goods, high-end urban real estate, philanthropic gestures, political campaign funding, ivy educations, high-tech medicine, hedge fund fees, dividend payouts, tax-avoidance cash hoards, stock bubbles, etc.

Can the absence of official "inflation" be explained in large part by the "disaggregation" of labor, middle-class debt, and a new class configuration since the late 1970s? More like a "redistribution" or even a "customizing" of inflation.


texts:
How exactly do you measure human capital for a given country and what numbers are included in that measure.

The reason why I ask is because im interested in simulating the Mankiw–Romer–Weil version of the solow Model.

Links to where I can get the data will be appreciated.


texts: Why does price drop as a result of increase in supply

texts:
According to the Law of Supply, if price increases, there is an incentive for producers to produce more, and therefore the quantity supplied increases. However, for an inelastic good, if there is a supply shock and supply significantly increases, why is there a drop in price? Can't the suppliers sell their product at the same or a higher price to increase total revenue?

Low price elasticity of demand, together with fluctuations in supply over short periods of time, creates serious problems for primary commodity producers, because they result in large fluctuations in primary commodity prices, and these also affect producers’ incomes. A good crop resulting in a supply increase leads to lower prices and lower farmers’ revenues. We come, therefore, to the ironic conclusion that a poor crop may be good for farmers because it increases their revenues while a good crop may be bad for them. Can't the farmers sell their product at the same or a higher price to increase total revenue?


texts: Simple worked-out example of computing future cashflows of other countries' assets?

texts:
I read through a research note from Bridgewater and a lot of the discussion centered on finding attractive cashflows of global stocks in USD terms. Here is a line for ease of reference:

Across a number of countries, the combination of prior currency
declines, equity declines, and rising interest rate differentials has
made their discounted future cash flows in USD terms very cheap (i.e.,
their unhedged assets). In the developed world, Japanese stocks
unhedged in USD terms are as undervalued as we’ve seen in decades.

I would imagine it would be rather rigorous to set out to find exact data and unpack it step by step, so maybe we can just use fictional data: "Japanese Stock A" fictional interest rate at x%, ect. I'm merely interested in the logic.
Question
Can someone provide a fictional worked out example that shows what 'computing future cashflows in USD terms' looks like? At least for me, the way the paper posed the idea in a very high level manner, it's a bit hard to follow.


texts: Ordinal axiomatization of proportional division

texts:
A proportional division is a kind of fair division in which a resource is divided among $n$ partners with subjective valuations, and each partner receives a share which is worth for him at least $1/n$ of the total resource value.

This definition is cardinal in nature: it relies on the assumption that each partner has a numeric value function which is unique up to scaling.

Suppose that all we know about the partners is that they have an ordinal preference relation. Is there a natural way to define the notion of proportional fairness in this case?

I thought of several possibilities myself, but I would like to know if something like this has already been done in the literature.


texts:
The costs of running a university are $C = F + m_{1}*q_{1} + m_{1}*q_{1}^{2} + m_{2}*q_{2} + m_{2}*q_{2}^{2}$ where $ q_{1} $ is the number of students taking courses during the academic year and $q_{2}$ is the number of student taking summer courses. How large are the economies of scope that result from offering courses throughout the year, and how do they vary with the number of either type of students?

This is a question in a old exam I am trying to understand, I have no solution or answer. I only know about this way for economical scope $\frac{ C(Q_{1}, 0) + C(0, Q_{2}) - C(Q_{1}, Q_{2}) }       {    C(Q_{1}, Q_{2})    } > 0$ , which I dont know if could be used for this question, or how to use it in this question.


texts: Why doesn't an import quota or tariff affect net capital outflow?

texts:
Given:
NX = NCO.
How can it be argued in the standard model of an open economy (e.g. https://slideplayer.com/slide/12862696/) that NCOs stay unchanged when a quota is placed on imports?
It seems that in one place in the textbooks we state NX=NCO is a "biblical truth" but then when we apply the open economy model we say that NX increase has no effect on NCO.
If there is a restriction on imports this must increase NX. Which must move NCO to the right or cause a shift along the curve (I wouldn't know which).
This would also seem logical, a protectionist economy is not one that foreign investors would want to invest in. Therefore they would remove their investment (NCO increases).


texts:
In the 'chicken' game, (stop,go) and (go, stop) are the two pure strategy Nash equilibrium profiles. If the game is played once, does it make more sense to use the rationalizability solution concept? The way I think of it is, that if we can't correctly predict the rival's action, then we might end up not coordinating. Thus, although Nash equilibrium gives a sharper prediction, rationalizability is more realistic to use, given that crashes do happen!

Any thoughts?


texts:
Consider the growth model with inelastic labor supply, full depreciation, log utility and CRS technology with the Bellman equation be defined as follows:
$$V(k)=\max(log(k^\alpha-k')+\beta V(k'))$$
st $$k\geq0\ \text{and}\ \theta k^\alpha-k'\geq0$$
As a guess I have used the usual $V(k)=a+bln(k)$ substituted on the Bellman and have derived $k'=\frac{k^\alpha\beta b}{1+\beta b}$. From this I have found the $k_{ss}=(\frac{1+\beta b}{\beta b})^{1/(\alpha-1)}$ called the non-trivial SS
This is the first SS while the other is $k_{ss}=0$
My question is how can we use the policy function to show that the system converges to the non-trivial steady steady state given any $k_0 > 0$


texts: Difference between multinomial logit and conditional logit

texts:
I'm trying to decide whether to run a multinomial logit or a conditonal logit (McFadden, 1973). I have data from a choice-based conjoint study in which each of the respondent's choices was between a pair of products with varying characteristics, including price. Each of the characteristics is a continuous variable, if that matters. I want to estimate a marginal willingness to pay for each of the characteristics. Typical explanations of how the two models differ are as follows:

  Multinomial logit models a choice as a function of the chooser's characteristics, whereas conditional logit models the choice as a function of the choices’ characteristics.

By this logic, I would lean towards a conditional logit given that I'm trying to estimate a marginal willingness to pay for each characteristic. On the other hand, the values I estimate for this depend entirely on the preferences of the respondents, so you could say that I'm really estimating something relating to the preferences of respondents, rather than anything innate about the choices' characteristics.

Does anybody have a more crisp understanding of the differences between the models and/or reflections on which would be more appropriate in this setting?


texts: Can someone please explain or provide some useful link on factors affecting setting prices of mobile telephony services?


texts: Timeline of comprehensive NIPA revisions

texts:
I have been fruitlessly searching for a list of dates of comprehensive National Income and Product Account revisions.  Clues I have found so far: The Bureau of Economic Analysis  website says the 1999 revision was the 11th one, and there have been three more since then - 2003, '09, and '13.

From the Philadelphia Fed's vintage datasets it looks like there were comprehensive revisions in 1975, 1985, 1991, and 1995.  This still leaves several unaccounted-for revisions.  Is there an online source for this information or should I hunt through old print copies of the Survey of Current Business?

Thanks

edited to remove acronyms


texts:
I am working on undergrad research in econometrics and am seeking some advice/help in terms of finding data sets and picking variables. I have an idea chosen for my topic, but I need to make a official proposal including a rough linear regression equation to turn in to my teacher soon.
My topic idea is to observe the causes for recent decline in female labor force participation in the US. I am hoping this topic is not too broad. Initially, I was going to look at whether campaign spending impacted voter share in Senate races from 2012 data sets, but I find this idea a tad boring and would like to make my new idea work if possible.
My ideas for variables include the obvious: age & teen participation rates (16-24), race/ethnicity, educational attainment, children, martial status, avg weekly hours worked, etc. However, I wanted to also see if the increase in opioid addiction in the US could also be having an impact on labor force participation specifically for women, as well as paid family leave benefits in the US vs other countries and labor force participation of immigrant women.
So with all said, does anyone have any suggestions for me both as to whether this topic is viable as a project in my course, as well as where I could find the data for such a topic? I have been reading a lot of literature on the topic, but having a hard time finding actual data sets that I could use for regression.
Thanks!


texts: Did the dollar depreciate when Trump won the election?

texts:
I expected the the dollar to briefly depreciate against all currencies when Trump won the election (in 2016), but I have just learned that it briefly appreciated against some. It depreciated against the Euro and Pound, but appreciated against the South African Rand and Australian Dollar. Why did the Rand and AUD depreciate against the dollar?

Source

Source

Source


texts: Why wouldn't an arbitrageur who shorts an overpriced security, and longs a substitute company, break even?

texts:
A Random Walk Down Wall Street (2015 11 ed, but an 2019 ed. is upcoming). p. 249 Top.

  Suppose irrational investors cause an oil company security to become overpriced relative to both its fundamental value and its peer oil companies. Arbitrageurs can simply sell the overpriced security short and buy a similar substitute oil company security. Thus, the arbitrageur is hedged in the sense that favorable or unfavorable events affecting the oil industry will influence both companies. A rise in the price of oil that makes the shorted security rise will make the arbitrageur’s long position rise as well.

Why wouldn’t this arbitrageur just break even, especially after transaction costs?
Case 1 of 2: The oil industry improves.
Then as written overhead, the substitute oil company's and shorted security's price rise. The former causes the arbitrageur  to gain money, and the latter  to lose money.
Case 2 of 2: It tumbles.
Then the substitute oil company's and shorted security's price drop. The former causes the arbitrageur  to lose money, and the latter  to gain  money.


texts: Interpretation of largest inverse root in a stationary time series

texts: Let's consider a stationary time series that can be modelled with an AR(p). I know that the cumulative effect of a shock is given by$$ \frac{1}{1- \sum^p \theta_i}, $$ where $\theta$ are the coefficients of the lag polynomial.I was wondering if there was any interpretation ( excluding stationarity) for the biggest (inverse) root in case of a shock to the time series.


texts: Is there any reliable data on what % of the UK population currently earn less than £17,300 annually?

texts:
According to the Living Wage Foundation the "real living wage" in the UK is £9 an hour

Which assuming a 37 hour week & rounding to the nearest whole GBP amounts to £17,375

  Formula used ((9*37)/7)*365.25

I don't know how many hours a week or what the annual figure is that the LWF assumes or uses so I've had to just pick a number (37 hours a week in this instance) & calculate from there, so if anyone can provide the correct number of hours (or better yet their annual rather than hourly rate) please do.

I've spent a fair amount of time cruising the ONS & other sites trying to come up with an accurate figure for what % of people earn less than this but simply can't find anything (so far) to provide it.

So does anyone have this figure or a site they could direct me to that has this information?


texts: Using margins after probit estimation to equal probabilities between almost identical individuals

texts:
I'm considering a Probit model for the probability that a student will finish the course based on their hours of study, age, sex, origin, how they passed the previous course and labor market situation for students.

probit finish hours age women inmigrant previous_courses

Now with these estimates, I have to compute the number of hours of study necessary so that the probability of completing the course of a student who works is the same as that of another student with identical characteristics but who does not work.

I know I have to use the command margins but I can't figure out how. Any clue?

Thanks in advance!


texts: Why did the Swiss National Bank abandon its currency peg so suddenly?

texts:
There are many theories about why the Swiss National Bank (SNB) abandoned its currency peg a few days ago.

My question is more specific:  why did they make the change so sudden?  Why not reduce the peg to 1.19 (Francs needed to buy one Euro) one month, 1.18 the next month, and so on, until a reasonable balance is found, taking into account all of the factors that the bank would want to consider in targeting an exchange rate?

Disambiguation update: Some of the commentary/responses below maybe should be directed at the following related questions:

Why did some call maintaining the peg "expensive"?
Why did the SNB decide to end the currency peg?


texts: Which countries invest their state pension in their stock market and its effects?

texts:
I apologise in advance if this is not the right stack exchange site to ask this question.

China has started investing its state pension fund in the stock market on full scale recently.

I know Norway has a pension fund which is built from its profits from oil profit. Canada also has a fund.

I am wondering how common this is? What are the effect on the stock market or economy as a whole when the government take such action?


texts: what are some unique features of heterodox economics?

texts:
I've been reading up a bit on heterodox economics as well as watched some of the lectures online and quite frankly, I'm having a hard time figuring out whats are the unique features of this school of thought.

Meaning that it seems to me (as of now) one can learn about uncertainty from standard economics textbooks and read up on Marxian economics and seemingly find little to be gained from this approach.Though I could be not very open minded in this regard.

This all being said, what are some of the unique features of heterodox economics that one wouldn't necessarily be exposed otherwise?


texts: What is meant by an inflation rate spoken in the typical news?

texts:
The news usually says that inflation for a certain month is say $2.57\%$.  It is never said relative to what.  Should I assume that is relative to the previous month?
If that's so, then the more inflation rises, the more likely the percentage reported will be small and eventually negative --- otherwise, inflation would be rising exponentially.
Wouldn't be more useful if we would look at inflation since the a certain historic mark?  In the US, for example, shouldn't we look every day how much money the dollar has lost its value since 1917 or 1971?


texts: What's the name of this pairwise price-setting scheme?

texts: Two siblings inherit equal shares of a house. To decide who gets to live in it, they each bid what they think the other half is worth. The person with the higher bid gets it, and pays the other sibling halfway in between the bids. Therefore, everyone gets better than their bid: the seller receives more and the buyer pays less. Does this scheme have a name?


texts: Fast way to write out the utility optimization problem for a Cobb-Douglas function?

texts:
In my last problem set, I had to solve both the Utility Maximization Problem (UMP) and Expenditure Minimization Problem (EMP)  for a Cobb Douglas utility function. Recall, Cobb Douglas is defined as
$$U(x,y) = x^\alpha y^\beta$$

I can compute the EMP or UMP. I can then find the other by "duality". But writing the problem was very tedious and messy. I ended up with an indirect utility function like this

$$v(p_x,p_y,m) = \left(\frac{\alpha m}{p_x}\right)^\alpha \left( \frac{\beta m }{p_y}\right)^\beta$$

and doing the Lagrangian was kind of clunky with all this multiplication going on.

Is there a simpler way to write the problem that can save me time / effort?


texts:
Question:

  A choice rule $C$ satisfies path independence if for all $A, B \in 2^X \setminus \emptyset$, $C(A \cup B) = C(C(A) \cup C(B))$. Prove that if $C$ is nonempty and rationalizable, then $C$ satisfies path independence.

My attempt:

Since $C$ is rationalizable, there exists a preference relation $\succeq$ such that $C = C_{\succeq}$. Now let $A, B \in 2^{X} \setminus \emptyset$ and $x \in C(A \cup B) = C_{\succeq}(A \cup B) \subseteq A \cup B$. So $x \succeq y$ for all $y \in A \cup B$. Since $C(A) \cup C(B) = C_{\succeq}(A) \cup C_{\succeq}(B) \subseteq A \cup B$, then $x \succeq y$ for all $y \in C(A) \cup C(B)$, hence $x \in C(C(A) \cup C(B))$, which shows that $C(A \cup B) \subseteq C(C(A) \cup C(B))$. Now let $x \in C(C(A) \cup C(B)) = C_{\succeq}(C_{\succeq}(A) \cup C_{\succeq}(B))$, which implies that $x \succeq y$ for all $y \in C(A) \cup C(B)$. But if $y \in C(A) \cup C(B)$ then this means that $y \succeq z$ for all $z \in A \cup B$. By transitivity, we have $x \succeq z$ for all $z \in A \cup B$, so $x \in C(A \cup B)$. So, $C(C(A) \cup C(B)) \subseteq C(A \cup B)$. Therefore, together we have $C(A \cup B) = C(C(A) \cup C(B))$.

Is my proof correct?

Furthermore, can anyone provide an example of a nonempty choice rule that satisfies path independence but is not rationalizable?


texts: Given Cobb-Douglas production functions for 2 factories (same owner), how will the owner produce $y$?

texts:
So my question is this:
A company owns two factories, A and B, each with the following production functions:

$f_A(x_1,x_2)=x_1^{\alpha}x_2^{1-\alpha}$

$f_B(x_1,x_2)=x_1^{\beta}x_2^{1-\beta}$

Now assuming that $\alpha=1/2$, $\beta=3/4$ and $w_1=w_2=1$ (prices on the input market), how will the company choose to produce $y$?

I've solved the two production functions for the following demand functions:

$\textbf{x}_A(\textbf{w},y)=\left(yr_1^{\alpha},yr_1^{\alpha-1}\right)$
  with $r_1=\dfrac{w_1(1-\alpha)}{w_2\alpha}$

$\textbf{x}_B(\textbf{w},y)=\left(yr_2^{\beta},yr_2^{\beta-1}\right)$  with $r_2=\dfrac{w_1(1-\beta)}{w_2\beta}$

And the expenditure functions:

$c_A(\textbf{w},y)=w_1yr_1^{\alpha}+w_2yr_1^{\alpha-1}$

$c_B(\textbf{w},y)=w_1yr_2^{\beta}+w_2yr_2^{\beta-1}$

Now, I am no sure how to determine how the company will produce $y$. If I insert the values above I get some weird numbers.

Any help would be much appreciated!

Thanks.


texts: Can you provide a reference regarding a revealed preference test(s) of rational inattention models, as proposed by Sims, ergo, using a mutual information measure as the cost of putting attention. And if possible can you briefly explained it. A link that explains the model is given here http://sims.princeton.edu/yftp/Gerzensee/info.pdf


texts: Estimating the rental rate of capital from data

texts:
Take the classic optimization problem of the neo-classical firm:

\begin{equation}
 \begin{array}{*2{>{\displaystyle}r}}
 \mbox{maximize (over $K, L$)} & f(K, L) - RK - WL
 \end{array}
\end{equation}

The first order condition equates the marginal product of capital with the rental rate of capital $R$.

Which raises the question...

How do macroeconomists typically estimate a time series for the rental rate of capital using U.S. data?

(Disclaimer: I don't do macro, but my curiosity has been sparked.)

One approach is to use financial market data to get $R_t$, use another first order condition that the rental rate of capital equals the nominal interest rate plus depreciation (i.e. Hall and Jorgensen). Backing a rental rate out of financial market data is not obvious though! In financial markets, prices vary based upon risk and time.

time dimension: Long-term rates are typically higher than short-term rates. When macro-economists and macro-models talk about the rental rate of capital, what's the time frame?
risk dimension: Eg. callable bonds have high yields than non-callable bonds. Debt and equity may have different expected returns based upon risk.
inflation dimension: A fixed nominal rate is a stochastic real rate depending on realized inflation, and the expected real rate is the nominal rate minus inflation expectations. The real rental rate would add back inflation expectations.

A completely different direction is taken by Casey Mulligan where he sticks entirely with Bureau of Economic Analysis (BEA) data.

I don't follow this literature, and I don't have a sense of the range of approaches that are considered sensible in modern, empirical macro.


texts:
Bear with me - this is a long question. But I did do few of the parts, but I'm posting it because it seems necessary that you know what I previously did. Sorry for the "length"! Answers are given in blockquotes.

MAC = Marginal Abatement Cost MDF = Marginal Damage Function

1) A policy maker is faced with the following MDF from the emissions of nitrous oxide: MDF = 1000 E (where E = tons of emissions). Research leads the policy maker to perceive that the industry MAC function is MAC = 130,000 – 1000E.

a) What will be the perceived economically efficient target of emissions?

  Efficient target would be the situation where
  MDF = MAC
  | 1000E = 130,000 – 1000E

  E = 65

b) What is the emissions fee that generates that target?

  Emission fee = MDF = 1,000E = 1,000 × 65 = 65,000

c) What is the aggregate level of permits that generates that target?

  Aggregate level of permit = MDF × E = 65,000 × 65 = 4,225,000

d) If there is a thick market for permits, what will be the market price of a permit?

e)The actual MAC is MAC = 150,000 – 500E. Find or show the cost of an error from using an emission fee.

f) The actual MAC is MAC = 150,000 – 500E. Find or show the cost of an error from using cap and trade.

Could someone help me figure out on how to do part d, e and f?


texts:
Suppose player $1$ and $2$ are playing a simultaneous move game where with continuous strategies $x_1$ and $x_2$. The Cournot equilibrium is $x_1^*,x_2^*$. The following diagram purports to show that in a sequential game, player $1$ benefits from deviating (upwards) from $x_1^*.$

The isoprofit curve maps the level of $x_1$ onto $x_2$ such that each combination
generates player $1$'s Cournot equilibrium profit $\pi^*$.

How exactly does this diagram show that player $1$ benefits by player $x_1+\epsilon$, where $\epsilon>0$?


texts: I am looking at the imf interest rate data page for Sweden right now. There are two different interest rate indicators named "Central Bank Policy Rate" and "Money Market Rate". I know what policy rate is but I have no idea about money market rate. Their monthly values are really similar but not exactly the same. What is "money market rate"? If I would have used money market rate instead of policy rate to compare different interest rates of different countries would that be sound?


texts: Comparing & contrasting decision problems and normal games

texts: I am trying to compare and contrast between decision problems and normal games. Are there any key concepts I should know? Any help would be greatly appreciated.


texts:
I learned that inflation can be a result of more loans or debt. When there are too much borrowers in the country, people will have more money to spend and the amount of products is the same so prices will increase.

This does not make sense to me because for each new borrower, there is a new lender. Number of borrowers equals the number of lenders. So, when someone has more money to spend, the lender has less to spend. What can cause inflation?


texts:
I am trying to find Nash Equilibrium of an auction with two bidders in which the highest bidder wins the object but both bidders pay the losing bid. Here every bidder follows the same bidding strategy β which is a strictly increasing and differentiable map from values to bids.

I am unable to find the Nash equilibrium of the game. Can someone help me with this? Is this some kind of standard Auction?


texts:
In India, primary deficit = fiscal deficit - interest payments accrued on loans

one view is it should be as HIGH as possible because that would mean we are borrowing not to pay interest payment but for investment, wealth creation.

another view is it should be low because that would mean that you are not borrowing anymore to meet your expenditure.

I tried to search on the Internet but it aggravated the confusion as one of the leading newspaper in India remarked in one of its articles -“The rise in primary deficit is not the sign of a healthy economy. It means the government is spending more on interest payments instead of creating wealth.” I just couldn't understand this statement.
Never been this confused in economics. Please guide.


texts: Can I refine the set of equilibria in a signaling game to the sender-optimal outcome?

texts:
Main question: I've been reading about communication games a lot, and I'm wondering if there are good criteria to select between two separating-ish equilibria. I think of a separating equilibria as coordination equilibria among types. So, if we grant that these types successfully coordinate, why wouldn't we grant that they coordinate to a sender-optimal (in a Pareto efficient among senders sense) equilibrium? That is, suppose there is a single sequential equilibrium where all senders do strictly better than in the remaining equilibria. What arguments are there for selecting this equilibrium?

Consider the following communication game. Receiver payoffs are the second number in the pair. There are six types of senders, with payoffs given as the first element of the pairs. I will show there is a pooling equilibrium and at least two partial separations. I'm wondering what kind of techniques can be used to argue in favor of either separating equilibrium. One is sender-optimal and the other is receiver-optimal.

$$\begin{array}{l*{6}{c}r}
             & Action \;B & Action \;L & Action\;R& Action\:LL & Action\;RR & \\
\hline
type\;B & (0,3) & (1,2) & (1,2) & (2,1)& (2,1) \\
type\;L & (0,2) & (1,3) & (1,2) & (2,0) & (2,2.25) \\
type\;R & (0,2) & (1,2) & (1,3) & (2,2.25)  & (2,0) \\
type\;LL & (0,1) & (1,2) & (1,0) & (2,3) & (2,1) \\
type\;RR & (0,1) & (1,0) & (1,2) & (2,1) & (2,3)  \\
type\;H & (0,0) & (1,0.9) & (1,0.9) & (2,3.1)  & (2,3.1)  \\
\end{array}$$

Let their be a prior distribution on types $\pi$ where $$\pi(B)=.3,\pi(L)=\pi(R)=.2, \pi(LL)=\pi(RR)=.1, \pi(H)=.1.$$

In a pooling equilibrium, the receiver will take action $B$ for expected payoff $EU_2(B) = .3(3) + .4(2) + .2(1)=1.9$, edging out $EU_2(L)= .3(2) + .2(3) + .2(2) + .1(2) + .1(.9)=1.89$.

However, there are partially separating equilibria.

Separation 1
Let types $L,LL$ "ask" for action $L$, types $R$ and $RR$ "ask" for $R$ and then $B$ and $H$ mix 50/50 between the two signals. Let the messages be $l$ and $r$ with the natural interpretation.

So $EU_2(L\mid l)\Pr(l)=.15(2) + .2(3) + .1(2) + .025(1)=1.125=EU_2(R\mid r)\Pr(r)$

So the receiver earns $2.25$ in expectation. The senders are better off too.

Separation 2
But let's consider another kind of separation. Types $R$ and $LL$ always send a message $ll$, "asking" for action $LL$. Types $L$ and $RR$ send $rr$, asking for action $RR$. Again, $B$ and $H$ randomize evenly.

Then, $EU_2(RR\mid rr)\Pr(rr)= .15(1) + .2(2.25) + .1(3) + .025(3.1) = .9775=EU_2(LL\mid ll)\Pr(ll).$ The expected payoff is 1.955 because each message is received half the time.

Responding to $rr$ with action $R$ and  $ll$ with $L$ yields a lower payoff of, so the separation, being jumbled with types $L$ and $RR$ pooling, isn't useful for taking the "correct" actions $L$ or $R$ as the receiver would like.

It seems to me that this last equilibrium is more robust. There are two separating equilibrium, which require coordination. Granting that senders can coordinate, why wouldn't they coordinate in the sender-optimal way?

I'm wondering if any methods exist that would refine the equilibrium set to exclude the receiver-optimal separation. The first pooling equilibrium might be said not to be neologism proof.

Neologism proofness is defined in section 3 of this paper. Roughly, there must not be an additional (off path) message such, that if observed, the receiver could form beliefs and a rational strategy based on those beliefs such that all who sent the message are strictly better off relative to the proposed equilibrium and those who didn't weakly prefer the proposed equilibrium outcome. I'm guessing that won't work here, because you have to consider two neologisms ($ll$ and $rr$) at once to eliminate separation 1, which requires collusion essentially. But are there any other ideas?


texts: The current economic in the US is very complex and uncertain. Is it possible to see the precise steps that the Fed uses to make its decisions? Why did they choose a rate of that amount and not another amount?


texts: Subgame Perfect Equilibrium in Baye, Shin (1999)

texts:
The following is taken from Baye, Shin (1999)
Consider a contest over a prize valued at 1 with symmetric players $1$ and $2$ who exert a level of effort $x_1$ and $x_2$ respectively. Effort cannot exceed $2/3$. Profit ($\pi$) of player 1 is
$$\pi_1=\frac{x_1-\frac{x_1x_2}{2}}{x_1+x_2-x_1x_2}-x_1$$
The simultaneous-move equilibrium is (denoted with superscript $*$)
$$x_1^*=x_2^*=1-\frac{\sqrt{2}}{2}$$
The profit for each is
$$\pi_1^*(x_1^*,x_2^*)=\pi_2^*(x_1^*,x_2^*)=\frac{\sqrt{2}-1}{2}$$
And we have that the best response of player $2$
$$R_2(x_1)=\frac{2x_1-\sqrt{(-2x_1^2+4x_1)}}{2(x_1-1)}$$
However, suppose that player $1$ 'moves' before player $2$. Then, player $1$ would deviate (upwards) from $x_1^*$, presumably, because player $2$ would reduce it's level of effort, and it would receive more of the prize. How does one show this?

In the article, Baye and Shin consider the new Stackelberg equilibrium $\pi_1^s$ where they show that $\pi_1^s(x_1^*+\epsilon)>0$ for some $\epsilon>0$. Specifically
$$\pi_1^s(x_1^*+\epsilon)-\pi_1^*(x_1^*+x_2^*)=\frac{\sqrt{1+2\epsilon\sqrt{2}-2\epsilon^2}-1-\epsilon\sqrt{2}+2\epsilon^2}{\sqrt{2}-2\epsilon}>0$$

I've tried replicating their result by seeing how $x_2$ changes with $x_1+\epsilon$ and substituting $x_1+\epsilon$ and the new value of $x_2^s$ into $1$'s profit function, but I fail to reach their result.


texts: What would you call a real market that is close to perfect competition?

texts: I want to explain perfect competition to students using a few practical examples without going into much of the theory. But I want it to be theoretically accurate and I don't want to claim that those are examples of 'perfect competition'. I am thinking about calling it 'near perfect competition', but I wonder if there is a conventional term for a market that is close to perfect competition. This wikipedia article mentions 'close-to-perfect competition' but I'm not sure if that's a conventional term.


texts:
I am new to Dynare++ and I have really quick question I cannot seem to find the answer too.

What is the difference between these two commands and why is the output different?

!dynare++ --per 20 --sim 3 file_name.mod

dynare file_name.mod

In the first command its unable to find steady state values based on my initial values and in the second it can. Why?

Here is the mod file of the basic RBC model I want to simulate with the first command. I can do so with the second, but not the first.

var c, l, k, w, r, y, i, z;
varexo eps;

parameters beta, delta, alpha, a, rho, rbar, wbar;

beta=.99;
delta=.025;
alpha=.33;
a=1;
rho=.9;
rbar=1/beta+delta-1;
wbar=(1-alpha)*(alpha/rbar)^(alpha/(1-alpha));

model;
//Inter-Euler
1/c=beta*(1/c(+1))*(1+r(+1)-delta);
//Intra-Euler
a/(1-l)=w/c;
//H.H. Budget Constraint
k=w(-1)*l(-1)+(1-r(-1)-delta)*k(-1)-c(-1);
//Firm FOC Capital
r=exp(z)*alpha*exp(z)*(l/k)^(1-alpha);
//Firm FOC Labor
w=exp(z)*(1-alpha)*exp(z)*(k/l)^(alpha);
// Production Function
y=exp(z)*(k^alpha)*(l^(1-alpha));
i=y-c;
z=rho*z(-1)+eps;
end;

initval;
k=((wbar/a)/(wbar*(1+1/a)-(r+delta)*(alpha/rbar)^(1/(1-alpha))))*(alpha/rbar)^(1/(1-alpha));
c=wbar*(1-((wbar/a)/(wbar*(1+1/a)-(r+delta)*(alpha/rbar)^(1/(1-alpha)))))/a;
l=(wbar/a)/(wbar*(1+1/a)-(r+delta)*(alpha/rbar)^(1/(1-alpha)));
w=wbar;
r=rbar;
y=(k^alpha)*(l^(1-alpha));
i=(k^alpha)*(l^(1-alpha))-(wbar*(1-((wbar/a)/(wbar*(1+1/a)-(r+delta)*(alpha/rbar)^(1/(1-alpha)))))/a);
z=0;
end;

shocks;
var eps;
stderr .02;
end;


texts: How does economic theory handle full automation of production resulting in full unemployment?

texts:
As advances in robotics and artificial intelligence continue, one possible outcome is a laborless economy, in which capital (means of production) is the dominant factor in production, by multiple orders of magnitude.  Looking at the current system, it would seem to me that a steady progression toward full automation within the bounds of the current market structure would lead toward an ever increasing concentration of wealth amongst those that possess capital.  (coincidentally, this seems to be occurring)  The end result of this, in my mind, seems to be a collapse of capitalism, in which supply curves are vertical, demand curves are horizontal, and they intersect near 0.

Now there are proposed solutions, which seem to move toward socialism, in general.  In this question, I am not seeking one of these solutions, but rather, theory.

My question is, it seems that traditional economic theory relies on { capital, labor }.  How does economic theory handle a zero-labor scenario, in which the capital is essentially a black box that outputs products?


texts: Is there a name for this type of CES look-alike utility function?

texts:
I do not know whether the following utility functions are used a lot but I was wondering whether there was a common name for this type CES like utility function
$$u(z) = \left[  \left( \sum_{j \in J_1} z_{j}^{\alpha_1}\right)^{\rho/\alpha_1} + \left(\sum_{j \in J_2} z_{j}^{\alpha_2}\right)^{\rho/\alpha_2} \right]^{1/\rho},$$
perhaps it is simply an instance of the CES?
The utility function is defined over two non-overlapping groups $J_1$ and $J_2$ of goods $z_j$. The goods from the two groups are weighted diffrently in the inner CES part by $\alpha_1$ and $\alpha_2$ respectively.


texts: Why is the martingale factor a martingale in Hansen's 2012 Dynamic Valuation Decomposition?

texts:
In this question, I'm continuing to explore the tools used/presented in Lars Hansen's Econometrica paper "Dynamic Valuation Decomposition within Stochastic Economies" (2012).

This might be an easy question, but I can't quite see it. In the paper linked above, the factorization is presented in which one component is a martingale.
See p. 937. On this page it presents this formula and says

  Given a solution to (21), I construct a martingale via
  $$
\widetilde M_t = \exp(-\rho t) M_t \left [ \frac{e(X_t)}{e(X_0)} \right ]
$$
  which is itself a multiplicative functional.

Maybe it's easy, but I just don't see right away how to show that $\widetilde M_t$
is a martingale. How can I show this?

NOTE: This question is related to the following two questions:

Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/eigenvector
Example of the change of measure proposed in Hansen (2012)


texts: What could happen if a country changes their currency rate constantly?

texts:
Introduction

Imagine this random country. "Yolistan", it is a new country that appeared after a war/revolution/independence/whatever.

The currency it's the "Yolo"

Yolistan needs to import resources to start again the industry, for some time they are not able to produce enough raw materials so they decide to change their currency rate to 1:2 (Yolo/Dollar) to favor Imports.

The First Question is,

Where could this country acquire dollars at such rate or how they do it?

Yolistan(yolos) wants to buy Iron from the US(dollars) do they pay is Yolos or they have to buy dollars first?

After some time of importing goods, now they are able to supply themselves so they change the Yolo to 2:1 (Yolo/Dollar) to favor Exports

The Second Question,

"What happens to their economy and currency if that country changes the rate constantly to favor Exports/Imports?

Thanks for the interest in this question.


texts:
I understand that taxes (Pigovian taxes) can be used to steer the economy in a certain way. For example, if you increase the taxes on things related to cigarettes, the price increase will decrease the demand. Or, if you put a carbon tax, the industry will try to produce its products in a carbon-neutral way in order to keep the prices - hence demand - on the same level, which will transform the economy in a more green one.
However, why don't we also pay money to industries that have a negative carbon footprint?
I mean, while producing your product, if you either capture some carbon or product something that can be used to capture carbon, you are directly doing a "good" to the society. Wouldn't this also incentivize companies not just to have a zero-carbon footprint but instead to have a negative footprint?
Are there any examples of such policies?


texts:
$y_t = B_0 + B_1t$

I have proved $B_0 = \bar{y} - B_1t$

I have found $B_1 = \frac{\sum_{t=1}^T t \cdot (y_t - \bar{y})} {\sum_{t=1}^T t \cdot (t - \bar{t})} $

However I'm supposed to have $B_1 = \frac{ \sum_{t=1}^T y_t \cdot (t - \bar{t})} {\sum_{t=1}^T t \cdot (t - \bar{t})} $

Was just wondering if anyone could point out where I'm going wrong?


texts: Approximation to a second order partial derivative

texts:
Let's say we want to approximate a second order differential:

$$ \partial_{aa} V(a)$$

Now, say we have a grid of values for $A$, where the step size is $\Delta$, $i$ is the index on this A grid, and we define the short hand notation

$$V_i \equiv V(A_i)$$

Achdou et al (page 13, equation 35) then compute the approximation to the second order differential on the grid at a point $i$ as

$$\partial_{AA} v_i =  \frac{v_{i+1} - 2v_i + v_{i-1}}{\Delta^2}$$

They don't explain why, and I can't follow here. Could someone provide me with the rough ansatz for why this is the case?


texts: Are principal payments on government bonds included in normal budget spending?

texts: If I look, for example, at the UK government's Autumn 2017 budget document the spending piechart has a wedge which says 'net debt interest £41bn'. I notice the wording says 'interest' and not something like 'net debt servicing' or 'interest and principal'.  The government has to repay the principal amount of the bond when it matures.  My question is are these prinicpal payment included in normal budget spending?  If not where are they accounted for in government finances?  Thank you.


texts: Difference between Negotiable Instrument and Financial Asset

texts:
So here are the two pages I was reading to try and understand :

Negotiable Instrument
and
Financial Asset

Confusion started as both pages use Certificates of Deposits(CDs) as an example.So a CD is both a financial Asset and a Negotiable Instrument ?

Considering the other examples of negotiable instruments like cheque, draft,money order, traveler's cheque I understand that these instruments are basically used to make payments from one person to another or access money from your own account.

And financial assets like stock,bonds,or bank deposits are well, just assets, that is your money kept secured or invested somehow in some place and you might earn a profit from it regularly or use it to bear various expenses. Basically it's your property.

But then, how can CDs be both? Are they financial assets that can be transferred to other people if deemed necessary? Because those articles clearly mention one thing that Negotiable instruments can be transferred. Then bonds,stocks etc can be Negotiable Instruments too? Can't we have someone else as a nominee in those?

This is very confusing please explain. Thanks.


texts: Does anybody know, any (advanced/classic) textbook that combines game theory with differential equations in mathematical economics. Specifically, I an interested in asymmetric information problems.


texts:
I was searching online for some notes on how to draw a Pareto curve on income distribution. That's when I came across Pareto chart which is a bar diagram and is used in quality control.
Are these the same and are both curves drawn using the same method?
Kindly help.


texts: Why did the rate of money supply growth accelerate from 1993-96 in the United States?

texts:
Even though the rate of growth in the monetary base decelerated — and the money multiplier decreased for the most part — from 1993-96 in the United States, the growth rate of the M2 money stock still progressively sped up. How is this possible?

Reference to second graph:

https://www.alt-m.org/2016/07/21/why-the-money-multiplier-remains-so-low/


texts: What am I doing wrong in the derivation of Bass diffusion model?

texts:
I've been deriving Bass diffusion model and keep consistently finding a different result than Bass' original answer. To make things worse, every single link in the Google results page just copies the Bass original solution, while I am finding the different one. You don't have to know the model, just let me show you the math part, so you can check my solution.

The premise:

We have two formulations of the hazard rate --- as Bayesian conditional probability and as a linear function:

\begin{equation}
 \frac{f(t)}{1-F(t)} = p + q F(t)
\end{equation}

where $f(t) = \frac{dF(t)}{dt}$. This gives the following differential equation:

\begin{equation}
 \frac{dF(t)}{dt} = (1 - F(t)) (p + qF(t))
\end{equation}

My solution

Using Chain Rule, we rewrite this as:

\begin{equation}
 \int \frac{dF(t)}{(1-F(t))(p+qF(t))} = \int dt = t
 \label{eq:diff}
\end{equation}

Notice that:

\begin{equation}
 \frac{1}{(1-F(t))(p+qF(t))} = \left( \frac{1}{p+q} \right) \left( \frac{q}{p+qF(t)} + \frac{1}{1-F(t)} \right),
\end{equation}

substituting this to the above equation, implies:

\begin{equation}
 \int \frac{q}{p+qF(t)} dF(t) - \int \frac{-1}{1-F(t)} dF(t) = (p + q) t
\end{equation}

integrating yields:

\begin{equation}
 \log (p + qF(t)) - \log (1 - F(t)) = (p + q) t
\end{equation}

using log properties:

\begin{equation}
 \log \left( \frac{p + qF(t)}{1 - F(t)} \right) = (p + q) t
\end{equation}

or:

\begin{equation}
 \frac{p + qF(t)}{1 - F(t)} = e^{(p+q)t}
\end{equation}

cross producting the fraction yields:

\begin{equation}
 p + qF(t) = e^{(p+q)t} - e^{(p+q)t} F(t)
\end{equation}

finally:

\begin{equation}
 (q + e^{(p+q)t}) F(t) = (e^{(p+q)t} - p)
\end{equation}

or:

\begin{equation}
 F(t) = \frac{e^{(p+q)t} - p}{e^{(p+q)t} + q}
\end{equation}

The problem:

But Bass, somehow found the following:

cancelling out my answer does not yield Bass' answer. The unnecessary $q$ is ruining everything.

Can you please help me with this inconsistency?

Thank you.


texts: Could someone please explain the proof of Hotelling's lemma?

texts:
According to https://en.wikipedia.org/wiki/Hotelling%27s_lemma,

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

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

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


texts: What Taylor approximation is used in this equation?

texts:
In Wickens' Macroeconomic Theory book, in page 48(1st edition), the author states that by doing a taylor approximation we get the following result.

Why is that? What approximation did he use?
I've tried several to linearize the fraction $\frac{(1+\eta)^{\sigma}}{\beta}$ around those values, but I don't get the same...


texts: Why politicians choose Mega Projects in developing countries?

texts:
kindly forgive me if this doesn't belong here. I just thought probably it's suited here.

Why do politicians choose mega projects in developing countries instead of spending more on health and education?

Also, are there any noted academics who work in this area.

Kindly enlighten.


texts: Where can I find an interactive graphic showing the development of countries?

texts: I remember once finding a graphic which let you slide back and forth, showing how third world countries had developed over time. It would be really handy to find it again, but I've tried all the keywords I can think of and it's not coming up.


texts: Concave utility functions corner solution explanation

texts: I seem to not be getting this. Could someone explain me the mathematical way to show a concave utility function [like (ax^2+by^2)] subject to a budget constraint has a corner solution. I get the economic intuition behind it but not the mathematical part behind it.


texts: Suppose the state raises taxes in order to internalise externalities. Doesn't the consumer have to pay the additional external costs then, because the prices are raised due to the taxes?


texts: If thera are two firms and both of them have constant returns to scale production function. Will the aggregate/industry production function still be the sum of individual production functions. How does CRS effect the aggregate production function of industry?


texts: What's the role for official intervention in the Balance of Payments?

texts:
If the Balance of Payments (BP) is defined as
$$BP=\text{Current Account}+\text{Capital Account}$$
where:
$$\text{Current Account}=X-M+\text{Net Income Interest}$$
and
$$\text{Capital Account}=\text{F}-\Delta \text{R}$$

Assume current account is positive, and $\text{Net Income Interest}=0$ for simplifying. Then there are 2 remaining ways for the balance of payments to be theoretically equal to zero:

1)$\text{F}<0$ and $\Delta R=0$ i.e. by home country acquiring foreign assets, or

2)  $\text{F}=0$ and $\Delta R>0$ i.e. by the domestic Central Bank (CB) to increase their foreign exchange rate reserves.

Why would there be a need for official intervention by having the domestic central bank (CB) to increase its foreign reserves, if there was no buying of foreign assets ($\text{F}=0$), of ?

Any help would be appreciated.


texts:
I am trying to understand how the Fed effects the fed funds rate. Here it says:

  Once the Federal Open Market Committee deems that economic conditions
  warrant a change in the money supply through specific open market
  operation, the command to buy or sell a specific amount of U.S.
  Treasury securities is passed down through the New York Fed President
  to what is called the Domestic Trading Desk of the New York Federal
  Reserve Bank. The Domestic Trading Desk is then responsible for
  implementing the conducting the actually trades. It does this sending
  messages to a selected group of about 30 securities dealers who
  specializing in the U.S. Treasury securities. These dealers have 15
  minutes to respond back with a indication of their willingness to buy
  participate in the exchange of securities. Some dealers are willing,
  others are not. In fact, the "open" part of open market operations
  means that the trades are open to any of the securities dealers
  willing to participant. The Domestic Trading Desk then has 5 minutes
  to respond back to the each of dealers that the terms of the exchange
  is acceptable.

  Once all parties have agreed on the exchange terms, the resulting
  transactions work much like any other. If the Fed buys, then it
  collects the securities from the dealers in exchange for checks. If
  the Fed sells, then the dealers collect the securities from the Fed in
  exchange for checks. In both cases, the checks are cleared much like
  any of the millions of checks process each day.

So the Fed manipulates the reserves of banks in order to increase or decrease fed funds, and it uses open market operations to do this. I am curious, though: what if in the case of "raising rates", the Fed wants to sell securities but no bank wants to buy them? And, why wouldn't a bank buy securities anywhere else?

Thanks,


texts: In my understanding, M2 includes M1 and M1 include M0. However, I checked the money supply here and used the "Compare" function to compare the money supply of m0 with money supply of m1, and found that the money supply of M0 is higher than that of M1. How come?


texts: When can one drop time subscripts? Example from Angrist and Kugler (2003)

texts:
Not the first time I am asking myself, but in this paper they actually start with a time dependent maximisation problem and then drop all time subscripts.
Background: They have profit maximisation problem that reads
$$
\Pi = \phi^{t} \sum_{i=0}^\infty \left \{f[\theta_{g}(N_t,I_t)] - w_{Nt}N_t - w_{It}I_{t}-\lambda C_N N_{t-1}\right\}
$$
where $\Pi$ is profits, $\phi^{t}$ is discount factor, $f[\theta_{g}(N_t,I_t)$ is output, $N_t$ and $I_t$ is different type of labour, $w_{Nt}$ and $w_{It}$ the respective wages, and $C_N$ a firing cost for the $\lambda$ workers that are replaced in each period.
Steps: They write "Adjustment costs are linear and there is no aggregate uncertainty, so time subscripts can be dropped and the objective simplified to be:"
$$
\Pi = (1-\phi)^{-1} [f(\theta_{g}) - w_{N}N - w_{I}I- \phi \lambda C_N N ]
$$
Question: I only knew this step with the Bellmann equation were you simplify the infinite horizon problem into basically a timeless problem of finding the optimal policy function, but here it seems to be literally just dropping the dimension like that. Does anybody know more generally when one can simplify a problem like this? This question interests me also more generally because I see many papers writing basically immediately version 2 of the problem and not considering optimizing the sum of the profits through time.
Reference: Angrist, J. D., & Kugler, A. D. (2003). Protective or counter‐productive? labour market institutions and the effect of immigration one unatives. The Economic Journal, 113(488), F302-F331.


texts: What is the maximum number of characters in a currency symbol?

texts:
In the program I am writing, I need to show a currency selector. I would like it to display currency symbols. For this, I need to know what is the longest, in characters, currency symbol (or rather what the maximum length can be, if there is any limitation).

E.g. USD, EUR, RUB all use single-character symbols: $, €, ₽. I initially assumed that it will always be one character. But I am obviously wrong, as e.g. Polish zloty symbol is zł.


texts: Is the equity lending involved in naked short-selling structurally equivalent to fractional-reserve banking?

texts:
Fractional-reserve banking consists in banks lending out more money than they
actually possess. This can also be seen as "money creation", or at least "money
substitute creation"-- the claim on the bank (e.g. checking account deposit)
is practically equivalent to cash-in-hand.
A short-seller borrows shares in a stock, sells them on the market, buys them
back later, and returns them to the lender. This becomes a "naked short" if the
borrowed shares "do not exist", i.e. are "share substitutes" credited to a
short-seller's account without being backed by specific shares. Thus
naked-shorting relies on a practice of "fractional-reserve brokerage".
Fractional-reserve banking is widely accepted while naked-shorting is widely
considered unethical and is in most cases illegal. This confuses me because,
per the above logic, they seem to be the same practice, just with a different
asset class. In both cases, an abstract financial asset in the form of a claim
on a backing asset (bank cash reserves or broker-held equities) is "created
from thin air". In both cases, the existing stock of the asset in devalued by
the creation of extra units, i.e. inflation.
Am I missing something? Are fractional-reserve banking and fractional-reserve
brokerage, for lack of a better term, "structurally equivalent"? If not, what
are the important differences in their economic effects?


texts: When can the fiscal multiplier be negative?

texts:
I am looking for a case study or data which shows a negative (fiscal/spending) multiplier effect.

Does anyone know a study where this is analyzed?


texts: Why do government jobs provide better benefits than industry jobs?

texts:
I've noticed how government jobs in the US are known to have generous pensions, healthcare plans, vacation time, etc. as compared to the corresponding job in the private sector. (I haven't actually done any comparisons specifically, but it's something that many people say, so I am assuming that this belief is true.) Why is this the case?

Someone may answer with, "This is because government workers have unions, which push for better benefits." But why can't the industry employees form unions as well, and thus receive equivalent benefits?


texts: The characteristic feature of indifference curve is that it will not touch the X axis or Y axis. But as a special case it will touch the Y axis if the combination is between Money and Commodity. "If money is taken on Y-axis, then IC curve can touch oy-axis" here we have taken 'money' on Y-axis and 'commodity' on X-axis. Here my doubt is could we use indifference curve for one commodity? If so please explain me with an example.


texts: In credit easing, how do central banks avoid allegations of unequal treatment?

texts: In credit easing, central banks purchase private assets such as corporate bonds. How do central banks choose which corporate bonds to buy? If the central bank buys bonds of one company but not those of another, wouldn't that result in allegations of favoritism? How do central banks choose which private assets they are going to buy without causing allegations of unfair treatment?


texts: Question about the "No Dictator" Criterion in Arrow's Impossibility Theorem

texts:
I have a question about Arrow's impossibility theorem. I'm not sure I understand exactly what is meant by the "no dictator" criterion. Does the presence of a "dictator" mean that across all possible combinations of individual preference orderings for N individuals, the same person's preferences will always match the group preference ordering exactly? Or does it simply mean that across all possible combinations of individual preference orderings for N individuals, there will be some individual for each one of those combinations whose preferences match the group preferences exactly, but that individual doesn't necessarily have to be the same for each combination?

If the former, I can clearly construct a counter-example that (I think) satisfies the other two criteria (unanimity and independence of irrelevant alternatives). For example:

Combination 1:

Person 1: A > B > C

Person 2: B > A > C

Person 3: C > A > B

Group preference: A > B > C

Combination 2:

Person 1: A > B > C

Person 2: B > A > C

Person 3: B > A > C

Group preference: B > A > C

In this example, Person 1 is the "dictator" in combination 1, but not in combination 2. Therefore, by the first definition above of "dictator" there is no dictator in this system (I'm also assuming I haven't violated the other two criteria: someone please point out if I have). If we're going by the second definition of "dictator" above, sure, this system has a "dictator" under each combination, but this doesn't seem like an appropriate definition to me. If the ballot changed with new issues to rank (e.g. A*, B*, and C*) these "dictators" might not hold sway anymore, so are they really "dictators" in the sense we normally think? Or is it just happenstance that their preferences happened to align with the group preferences one time? Obviously, there's something about the theorem that I'm not understanding, so if someone could please clarify that for me I'd be very appreciative. Thanks!


texts: What statistical techniques can be used for measuring price elasticity

texts: I know that linear regression is used for calculating price elasticity. If my objective is to estimate the parameters of a causal relationship, can i use machine learning techniques like Random Forest or lets say ARIMA with regressors? Has anyone done this before? I tried searching in jstor.org but didn't find any.


texts: Labour Productivity Growth and Reallocation of Labour

texts:
Using a shift-share methodology, labour productivity growth can be arise from productvity growth within a sector (within effect) or reallocation of labour to sectors with higher productivity (reallocation effect).

1)

However we know that Productivity = Real Value-added / Employment.

So won't an increase in employment in a sector result in a fall in the sector's productivity and hence overall productivity?

2) Based on
http://www.ilo.org/wcmsp5/groups/public/---ed_emp/---emp_elm/documents/publication/wcms_143163.pdf

  employment intensity is the direct inverse of labour productivity

So does this mean the government should not employ policies to reallocate labour to higher productivity sectors?

It will be good to refer me to some paper that address these questions


texts:
I have a question involving optimal consumption bundles for quasi-linear preferences. Utility is given by

$$U(x_1,x_2) = 16\sqrt{x_1} + 2x_2$$

and $p_1 = 8, p_2 = 4, I = 30$.

What I have so far is

$$8x_1 + 4x_2 = 30$$ and

$$MRS = -\frac{4}{\sqrt{x_1}} = -\frac{p_1}{p_2} = -2$$

Solving that I get $x_1 = 4$, but plugging that into the budget equation results in a negative value for $x_2$. What am I doing wrong here?


texts: How does changing the Bank of England base rate work?

texts:
If we assume the demand for money (D above) is fixed in this position (for the purposes of this question), and supply (S) is fixed in this position, then how can the BoE change market interest rates (to influence inflation) using the base rate alone? Is this an invalid assumption?

And if changing the base rate changes the interest rate, why doesn't the BoE also need to adjust the money supply every time it changes the base rate to maintain equilibrium as in the diagram above?

It looks to me as though the BoE can only change market interest rates (and influence inflation) by changing the money supply - which I think is what I read the US Fed does?

I have no idea, and am really confused about how the central bank plays a role in the money market equilibrium in the diagram above, and how it actually influences inflation. Any clarification or insight would be greatly appreciated.

For the purposes of my exam, I know that 'the BoE increases interest rates to curb inflation as costs of borrowing rise etc....' and 'quantitive easing means increasing the money supply to encourage lending, lowering interest rates etc....' but I'm struggling to appreciate how the mechanism actually works.


texts: Bellman equation corresponding to stochastic EZW recursive utility

texts:
A bit of a basic question maybe, but I am confused how to write down the Bellman of this recursive utility function based on Epstein-Zin-Weil preferences and some stochastic constraints.
$$
U_t = \left \{(1-\beta) C_t^{1-\frac{1}{\eta}} + \beta[E_t(U_{t+1}^{1-\gamma})]^{\frac{1-\frac{1}{\eta}}{1-\gamma}}\right \}^{\frac{1}{1-\frac{1}{\eta}}}
$$
It already looks like a Bellman equation, Any pointers?


texts: How to deal with misspecification of models in Macroeconomics?

texts:
I'm wondering what methods are used in economics, specially in macro, to deal with model misspecification.

I've already searched the web, but I may be missing some methods. Therefore, I ask you for some help.


texts: What are exactly considered resources in modern economics?

texts:
I'm taking a basic course in economics and I'm trying to understand what the term "resources" really mean in this context.
Reading this article, I found out that in classical economics, resources are usually divided in 3 categories: Land, Labour and Capital.
Anyway, while watching some videos, often I see enterpreneurs as another possibile type of resource.
Now, is this an addition of modern/present economics?

**I've seen that often "modern" and "classical" economics are interchangable attributes referring to the same thing: the view of economics started with the works of Adam Smith


texts: Marginal Rate of Substitution for perfect complements

texts:
I have come across the following problem:
Determine the marginal rate of substitution MRS(x1, x2) at point (x1, x2) = (5,1) for the following function:
u(x1, x2) = min(x1, x2).
The solution is that the MRS is undefined at that point.
However, I don't understand why that is. With this utility function, we get an income expansion path that goes exactly 45 degrees from the origin, because the two goods are alway consumed in equal quantities.
And as far as I know, the MRS of such a function (u(x1, x2) = min(αx1, βx2)) is only undefined at the exact angles of these curves, i.e. where x2 = (α/β)x1. In the problem at hand, however, we have x2 < (α/β)x1, i.e. 1 < 5.
Shouldn't this mean that the MRS at the point (5, 1) is actually 0 and not undefined?


texts: Is there an economic term for decreased demand due to expected decrease in price due to a product's value lasting for a finite amount of time

texts:
So, at work we are doing a charity bake sale.

Lunch hour is long gone. An email was sent out offering everything at half price.

I imagine decreased demand as everyone knows they have to get rid of it all by the end of the day, therefor everyone will expect the price to decrease further, therefor people will not buy due to the expectation of lower prices when an item is only of value for a finite amount of time.

Is there an economic term to describe this situation?


texts: If I want to create my own currency model what would be the best basic options / things / ideas I need to look into?

texts: First of all, I am from a IT background and currently writing my thesis on a system in which I am have to create a model of a nation. So to run the economy in this simulation (for now you can understand it as a simulation), I need appropriate economic models and monetary policy. I have done my reading on the basics of monetary policy and how central banks are responsible to control the inflation and deflation of currency. And also, I am aware of the gold reserve which now is more like a fractional reserve system. I do understand that the purpose of my project strongly matters in this case, but for a start, a very basic model would be enough. I already am familiar with crypto currencies like Bitcoin, Ethereum etc. Also, this system is run by computer so it's human error / politics proof, or a bit more like an ideal system. So, it would be great to have your insights/opinions on how should I design the currency and the economic model.


texts: How to Calculate the productivity multiplier?

texts:
Given a Cobb Douglas

$Y_t = A (K_t^\alpha L_t^{1-\alpha}) $

$ K_{t+1} = sY_t + (1-\delta) K_t$

How do we get the multiplier on productivity to be equal to $ \frac{1}{1-\alpha}$?
I understand that if productivity increases, output increases, thus we get more capital and thereby more output and so on. But I can't reach this multiplier.

My Attempt:

If have x increase in A,
then
$Y_t=(1+x)A (K_t^\alpha L_t^{1-\alpha})  $

That is an x increase in Y.

$ K_{t+1} = s(1+x)A (K_t^\alpha L_t^{1-\alpha})  + (1-\delta) K_t$

$Y_{t+1}=(1+x)A * K_{t+1}^\alpha *L_{t+1}^{1-\alpha} $
$Y_{t+1}=  (1+x)A * (s(1+x)A (K_t^\alpha L_t^{1-\alpha})  + (1-\delta) K_t)^\alpha  * L_{t+1}^{1-\alpha} $

I think the increase here should be $x * \alpha $ but I can't see it.
so that for a unit increase in productivity i.e x=1;
 $\Delta Y  =  1 + \alpha + \alpha^2 +... =\frac{1}{1-\alpha} $

Also in the steady state we  have,
 $ Y = A^\frac{1}{1-\alpha} * \frac{s}{\delta}^\frac{\alpha}{1-\alpha} * L$
taking logs we have that percentage change in A increases Y by $\frac{1}{1-\alpha}$.


texts: Measure of New Firms Born in Each Period

texts:
In an economy with stochastic overlapping generations of firms, how do we easily understand the measure of new firms born?

The set-up states:

"In each period, measure $\rho\in(0,1)$ of new firms are born and are endowed with net worth $w_0>0$. Firms survive to the next period with probability $(1-\rho)$ and hence the measure of firms alive in every period is 1."

$\textbf{My Question:}$

What is the measure of firms?
How does the measure of firms relate to the firm's survival probability onto the next period?

I think I am not understanding clearly when the author uses these related but distinct terms. Can someone explain easily?


texts: Strictly increasing function transformation

texts:
I have utility function given by:

$U(x_1, x_2) =
  \begin{cases}
                                   x_1+x_2 & \text{if $x_1+x_2<6$} \\
                                   6 & \text{if $6\leq x_1+x_2\leq10$} \\
                                   x_1 + x_2 & \text{if $x_1+x_2>10$}
  \end{cases}$

If I transform this to this:

$F(U(x_1, x_2)) =
  \begin{cases}
                                   U(x_1, x_2)+4 & \text{if $U(x_1, x_2)<6$} \\
                                   10 & \text{if $U(x_1, x_2)=6$} \\
                                   U(x_1, x_2) & \text{if $U(x_1, x_2)>10$}
  \end{cases}$

Is it strictly increasing function transformation?

Thanks guys


texts: Subsidies Incidence on Producers and Consumers

texts: When calculating the incidence on producers and consumers using a demand and supply curve is dead weight loss a part of the incidence? I know that for example the producer's incidence is a rectangle with a height of the old supply curve price at the new equilibrium quantity minus the new equilibrium price. What I'm not sure about is the width of the rectangle. I know it should start at the y-axis, but I'm unsure of where to stop. The original equilibrium quantity? Or the new equilibrium quantity? If I were to extend the rectangle to the new equilibrium quantity then dead weight loss is included. Is this correct?


texts: Convert data in current US dollars to constant international dollars (PWT)

texts:
I would like to convert a nominal GDP series in US dollars to real GDP at constant PPP using Penn Wold Table (PWT) version 10.0 (see here).
So far, I managed to get the real GDP at current PPP. Using the variable name conventions from PWT, if the nominal GDP series in US dollars is Y, then Y/pl_gdpo is the real GDP at current PPP (i.e. cgdpo).
The aim is to get rgdpo, namely the real GDP at constant PPP.
Thanks in advance.


texts: If a company buys a robot, it's part of investment. If a person buys a car, it's part of consumption. Why?

texts: As I understand it, a company buying a robot -- something that depreciates over time and will eventually break -- is included in investment because it provides a long term benefit (increase in GDP). But then why is a car considered consumption? It also depreciates over time (though not in a year) and provides long term benefits to GDP.


texts: Python vs R (vs Stata): the old battle revisited

texts:
I am an avid Python user. I know Stata but I'm not a pro. I don't know R. I do econometrics (mostly time series, but also cross-section and panel), and statistics, and Python seems quite sufficient in meeting my needs.

I know that economists (at least old schoolers) are mainly using Stata and statisticians mostly R.

I read here and there that 1) R's libraries are superior to Python's, and 2) when it comes to visualization nothing can beat R's ggplot.

My questions are:

a) What are examples of econometric/statistical analyses that can be easily done in R but not (as easily or at all) in Python?

b) Is visualization in R really superior to Python? In what sense: less coding, ease of coding, more intuitive, or the quality of the final output?

c) Where will you put Stata in this comparison?


texts: How does domestic demand affect the domestic currency's value

texts:
If an economy grows, due to a tax reduction for example, how does that affect the exchange rate?

My logic would be that reduced taxes put more money into people's pockets, which they then use to buy more stuff. If all of that stuff were produced domestically, nothing were to happen to the exchange rate. If some of that stuff were to be produced in other countries and imported, those importing the goods will want to exchange the domestic currency for their foreign currency. That would increase demand for foreign currency relative to domestic currency and thereby decrease the value of the domestic currency.

However, as the economy grows other country's producers will want to buy into the economy's market, for which they will need that country's currency and increase demand for it. That will drive the currency up.

Therefore: What effect is stronger in response to domestically motivated economic growth? Is it the depreciating effect of imports or the appreciating effect of new entrants or am I missing something entirely?


texts: Why offer curves of a power plant are stepwise increasing?

texts:
I was wondering why the supply curve of a power plant in the auction for the Day-Ahead Market is stepwise increasing and not a continuous function with first and second derivative strictly positive.
I am thinking of a gas plant (CCGT), the amount of fuel to be used can be adjusted continuously and not discretely, am I wrong?


texts: Government spending/borrowing difference/ national debt increase disparity

texts:
My background in economics is non-existant, I'm just doing some research before the UK general elections and am having some difficulty in understanding certain data.

Assuming the figures found in this and this link are accurate, the UK government spent £714 Billion in the 2014 fiscal year. They generated £619.8 billion in public revenue in the same year. I'd assume the difference between these figures, £94.2 billion, is what they needed to borrow to make up the difference. But the website lists the UK national debt to be of magnitude £1258 billion in 2014 and £1185 the year before, meaning that only a total of £73 billion was borrowed in reality.

Moreover, the HM treasury PESA (page 19) gives public sector current expenditure in 2014 to be ~£666 billion, which is over £45 billion more than what they generated from public revenue. Even if the statistic of £619.2 billion is incorrect, and the government actually generated exactly the £666 billion spent, the difference £714-£666 billion=£48 billion is less than the amount by which the national debt rose in the 2014 fiscal year. I can't get the figures to match up!

Finally, from what I've learned today, government borrowing works by having banks etc. purchase bonds which the government pay interest on, and then in a certain number of agreed years pay the purchaser back what they paid. The statistics for government spending in the second link above show £47.4 billion being spent on interest. However, I can't find any account of the original loans being paid back. That is, surely some of the bonds the government sold should mature each year, requiring them to pay the owner of the bond the original amount they sold it for?

Apologies for my economic naivety.


texts:
After testing for cointegration with Johansen test using the following code

[h,pValue,stat,cValue,mles] = jcitest(ret,'model','H1*','lags',4,'display','params')

I received this output:

Data: prices
Effective sample size: 56
Model: H1*
Lags: 4
Statistic: trace
Significance level: 0.05

r  h  stat      cValue   pValue   eigVal
----------------------------------------
0  1  40.5214   35.1929  0.0161   0.3350
1  0  14.6781   20.2619  0.1453   0.1667
2  0  5.4670    9.1644   0.1580   0.1091

So it rejects no cointegration. So I am running the VECM with rank 1 restriction:

B = mles.r1.paramVals.B % Cointegrating relations with rank = 1 restriction

I get the following output:

r = 1
------
A =
-0.6259
-0.2261
-0.0222

B =
0.7081
1.6282
-2.4581

B1 =
0.0579 1.0824 -0.8718
0.1182 0.4993 -0.5415
0.1050 0.1667 -0.1600

B2 =
-0.5462 2.2436 -1.7723
-0.1518 0.6605 -0.6169
-0.1610 0.5966 -0.5366

c0 =
2.2351

c1 =-0.0366
0.0872
0.1444

How would I interpret this output and how do I move forward after estimating the parameters? (I have only displayed the r=1, and these are not the actual results, by I couldn't find any explanation behind them)


texts:
I have a question that asks to find $\frac{\partial K}{\partial L} $
from $Q=cL^aK^b$, when $Q$ and $c$ are constants. It lists 4 answer choices but I’m just not sure how to approach it. Implicit function theorem? Chain rule... any help or suggestions would be appreciated.
--Update--
Well I thought about this some more and think I got it:
The total differential can be written as:
$$dQ=\frac{acK^b}{L^{1-a}}dL+\frac{bcL^a}{K^{1-b}}dK=0$$
dividing by $dL$ and c and moving terms, gives
$$\frac{aK^b}{L^{1-a}}\frac{\partial L}{\partial L}=-\frac{bL^a}{K^{1-b}}\frac{\partial K}{\partial L}$$
Dividing though by $L$ and $K$ and expressing it in terms $\frac{\partial K}{\partial L}$ gives:
$\frac{\partial K}{\partial L} = -\frac{aK}{bL}$,
which I hope is correct.


texts: Estimation of point-identified Dynamic Discrete Choice models with moment inequalities

texts:
I'm trying to understand and implement in code the method in Bajari, Benkard, Levin (2007). The first stage is clear to me, as well as how to forward-simulate to obtain an estimate of the value function. What I don't get is:

What are the moment conditions? In the paper, the moments are expressed as the difference of the simulated value employing the policy obtained from the first stage, and some other policy:

For example, I tried choosing N randomly selected states and obtaining the simulated value for simulated paths of length T, by using the first-stage policy and some perturbed version of that policy. Is this one way of generating moment inequalities?

Then, the paper refers to the true parameters as those that minimize the following target function:

I understand that the expected difference in simulated values is strictly positive according to Revealed Preferences, but I don't understand why the true parameters are the ones that minimize the function above. For example, if the value function becomes zero at any state and choice for a given set of parameters, the simulated values will be zero as well under any policy, even if the true parameters are not such.

Any help or reference of a concrete example will be greatly appreciated.


texts:
A central tenet of libertarianism is the notion of free association–being able to socialise and enter into contracts with people of your choosing, with the corollary of being able to refuse to do those things too. The obvious criticism of this would be that one could then refuse to sell to people based on their skin colour, sex, orientation, etc., which has a historical precedent pretty much all over the globe. Does this make economic sense, though, or does it represent a market failure?

To my non-economist eyes it looks pretty cut and dry. Say Alice has a widget store and decides to only sell to people in group A. Bob also has a widget store and sells to both groups A & B. Surely Bob should have a significant economic advantage here, allowing him to lower prices and stay competitive with Alice? Even if some group A customers would refuse to shop at Bob's, presumably more would be attracted to Bob's store for its lower prices?1

Even if social or legal pressures meant everyone had to segregate, would this not present a gap in the market to be filled by group B store-owners, who would then sell to the underserved group Bs, with prices presumably more in line with group B incomes (if they are also economically disadvantaged compared to group A), and with the profits more likely to be redistributed amongst other group B businesses?

It's a cliche that the libertarian answer to everything is that 'the market will fix it', but this does seem like a sitation where that should happen, unless government pressure countered market forces (e.g. if it was made illegal for group Bs to even open their own stores or buy stock from wholesalers willing to sell to them). Would the libertarian counter-claim be, then, that the existence of economic segregation can only occur when backed by state force?

1 However, this paper does suggest that '[d]iscriminators are on average willing to forego 8 percent of their earnings to avoid a coworker of the other ethnic type'.


texts: Show that conditional variance of error in linear probability model is heteroskedastic?

texts:
I have a problem that asks me the following:

" Consider the linear probability model, in which we specify the
regression equation to be linear in X,
E(Y |X = x) = Pr(Y = 1|X = x) = x'β
We can accordingly express the regression equation by Y = X'β + e with
E(e |X = x) = 0 for all x. Show that the conditional variance of e
given X = x depends on x, i.e., e is heteroskedastic. "

Intuitively, I visualise why this is the case - but cannot figure out how to demonstrate this formally. Could someone help?
Thanks in advance!


texts:
I am trying to understand what it means for an interest swap to be collateralized.
If for example, I am paying fixed to a bank and receive floating in return. Who is giving collateral to whom? and how is the amount of collateral calculated?
I read that: "swaps are collateralized at the onset and then collateral is called up or down depending of changes in the market value of the swap". Don't really understand what this means and I would appreciate an example.


texts: Proof of Criteria for Local Identification in Rothenberg (1971)

texts:
My question is regarding Theorem 1 (page 579) of Rothenberg (1971). It is associated with four assumptions given on the same page. But, I only have a question about a single step of the proof, so I don't think the entire context is necessary.

Definition 3: A parameter point $\alpha^0$ is said to be locally identifiable if there
exists an open neighborhood of $\alpha^0$ containing no other $\alpha$ in $A$ which is observationally equivalent
...
Assumption I: The structural parameter space $A$ is an open set in $\mathbb{R}^m$
...

Under Assumptions I-V given in the paper, we have

Theorem 1: Let $\alpha^0$  be a regular point of the matrix $R(\alpha)$. Then $\alpha^0$ is locally identifiable if and only if $R(\alpha^0)$ is nonsingular.

In the proof for one direction of the iff statement, the author begins by supposing $\alpha^0$ is not locally identifiable. This means ``there exists an infinite sequence of vectors $\{\alpha^1, \alpha^2, ..., \alpha^k,  ...\}$ approaching $\alpha^0$ such
that $g(y, \alpha^k) = g(y, \alpha^0)$ for all $y$ and each $k$.'' Then, the author later claims that
$$d_i^k = \frac{\alpha_i^k - \alpha_i^0}{|\alpha^k - \alpha^0|}$$
has a limit point $d$ on the unit sphere, and, ``as $\alpha^k \to \alpha^0$, $d^k$ approaches $d$.''
This does not make sense; I agree that there is a limit point but not that there is a limit.. As a counterexample, suppose $A = \mathbb{R}$, $\alpha^0 = 0$, and the infinite sequence was
$$\{\alpha^k \}_{k=1}^\infty = (-1)^n \cdot (1/n)$$
This sequence is valid because it approaches $\alpha^0 = 0$, while we can simply assume that the $g(y, \alpha^k) = g(y, \alpha^0)$ condition holds for all $y,k$ for the sake of contradiction. Using this sequence, we get
$$d^k = \frac{\alpha_i^k - \alpha_i^0}{|\alpha^k - \alpha^0|} = \frac{(-1)^n \cdot (1/n)}{(1/n)} = (-1)^n$$
which has limit points but no limit.
Is there an explanation for why the author assumes such a limit exists? I did not catch any other conditions on $\alpha$ in the paper that could make this step in the proof work.


texts: Question regarding social welfare in the presence of externalities

texts:
I am currently learning high school level economics and I do not understand how indirect taxation may increase net social welfare in the presence of negative production externality.

This is because, from analysis of welfare in the market diagram with linear demand and supply curves, I found that the social welfare gain due to a tax correcting a negative production externality is equivalent to the welfare loss to consumers and producers from the taxation itself (resulting in no net change in total welfare).

Theoretically, this can also be explained by the fact that taxation reduces the net satisfaction of consumers, firms, and government, but increases net satisfaction in the 3rd party.

My current understanding is that correcting externalities do not cause net welfare to change, but it allows the socially optimum level of resources to be allocated to production, answering the "what to produce question" and allowing the economy to benefit in the long run, but I'm not at all sure.


texts: Derivation on p.99 of Salanie, The Economics of Taxation (2nd edition)

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

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

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


texts: Verifying the constant elasticity of the demand model Q= aP^b

texts:
"It is well known" that the elasticity of $Q$ relative to $P$ is the constant $b$ in the equation $Q(P)=aP^b$. We can verify it using the convenient definition of elasticity $= \frac{dQ}{dP} \frac{P}{Q}$, we can verify it in Wikipedia.

Based on this, when I create a spreadsheet with parameters $b=-2$, $a=100$ and P ranging from 1-5 by 1 I expected to recover an elasticity of -2, where elasticity =  % change in Q/ % change in P.  This is not the case. Instead the elasticity  varies substantially as the % change in P varies.

I'm forced to conclude that 'constant elasticity' does not mean a fixed value regardless of the magnitude of the price change, but only invariant with regards to the value of price OR that I have a spreadsheet error.

I've pasted an image of the spreadsheet results below.  Obviously, without seeing the formulas, no one can verify that I don't have an error, but I'm hopeful that someone will give this a spin for themselves and get very different numbers and then I'll know my failure to verify the constant elasticity in this function is a spreadsheet error.


texts:
I find the yield curve for bond rates confusing. For example, the current yield curve for US treasuries is shown below:

The difference between the 10-year bond and the 30-year bond is tiny, just 0.15%. This seems like a negligible premium to receive for assuming an additional 20 years of risk.

Is there a theory that explains this counterintuitive (to me) condition?


texts: Looking for behavioral economics research about the redemption of gift cards

texts:
This is a long shot! I was wondering if anyone could point me to any behavioral economics or other economics research on perceived value, specifically I'm looking at why some people don't redeem activity gift cards before they expire.

My hypothesis is that time doing something else they choose, is perceived as better used than time doing the activity that the gift card pays for.

For context, some of these gift cards are are worth \$100 - $500 and generally the activity they pay for is chosen by the gift giver who would know about the likes and dislikes of the receiver.

I know this is quite general, but I'm working as an analyst in a company that sells gift cards and I would like to have some background research before I look to draw any conclusions from the data, I know that some people use them, some people don't  and I can see some patterns in variables in the two groups, but I'd like to bring some theoretical rigor to the analysis.


texts:
the title says it all. What is the relation between HICP and GDP. And will there be a high inflation just before recessions?

So the upper graph is the percentual change of the BNP from the last year, and same with the HICP that is under the first graph. The question is, how would you describe the relation between the GDP and HICP using the graphs?


texts: Why hasn't JPE formally retracted Emily Oster's article "Hepatitis B and the Case of the Missing Women" (2005)?

texts:
Amartya Sen (1992) argued that there were more than 100M "missing women" worldwide.
In "Hepatitis B and the Case of the Missing Women" (2005), Emily Oster argued

that hepatitis B can account for about 45 percent of the “missing women”: around 75 percent in China, between 20 and 50 percent in Egypt and western Asia, and under 20 percent in India, Bangladesh, Pakistan, and Nepal.

Oster was heavily criticized. And later, Oster et al published what amounted to a full retraction: "Hepatitis B does not explain male-biased sex ratios in China" (2008, 2010).
Klassen (2008) gives a short account of the above story.

What I found strange is that Oster (2005) still appears on the JPE website (and also JSTOR). There is no retraction, errata, or any other clue to the uninformed reader that there might be anything wrong with the article.
Why hasn't JPE formally retracted Oster (2005)?