texts: How PMI is the best leading economic indicator and how to retrieve it?

texts:
From Bloomberg Market Concept, PMI (Purchasing Managers' Index) is the best leading indicator that alerts to forthcoming turning points in real GDP growth. For example, PMI fell to its low point and started to recover well in advance of GDP falling to its low point and then rebounding. I am wondering why PMI is the BEST leading indicator but GDP growth?
I dig further to see if I can download the data for this index from this post, I click on the link and see only one line. I am wondering what country this PMI line stands for, and how to collect time-series PMI for all countries.


texts:
The given explanation about how subsidies unintentionally can result in resources being wasted does make sense to me. However, I just wanted a second opinion on my take on this.
To me, it seems like a very trivial claim with no little relevance in the real world. Can't this be easily avoided if, let's say, we let the said farmers consume the resources they want initially. Then, the government only releases subsidies if they deem the amount of resources used as appropriate and necessary.
All in all, please inform me of any aspects I might be missing in interpreting the given picture or any shortcomings in my "solution" to this.


texts: Can anyone help me understand the Motrtensen-Pissarides model?

texts:
I am seeking help with the Mortensen-Pissarides model in discrete time? Basically, I was given the following in class example (which we didn’t complete do to time constraints associated with the end of the semester).
Our workers Bellman Equations are as follows:
$V_u=b$$+\frac{aV_e+(1-a)V_u}{1+r}$ and
$V_e=$$w+\frac{\lambda V_u+(1-\lambda)V_e}{1+r}$ respectively
With $V_u$ and $V_e$ are expected utility values for unemployed and employed worker(s). a (∈ (0,1)) is the job-finding rate, b (> 0) is the unemployment benefits, r (> 0) is the real interest rate, w is the wage; and λ (∈ (0, 1)) is the job-destruction rate.
find the law of motion of the unemployment rate, given a and $\lambda$
Suppose that w is set to the reservation wage. Describe the condition that $V_u$ and $V_e$ must satisfy in this case. Then, given the values of b, a, λ, and r, compute the equilibrium values of $V_u$ and $V_e$.
My professor didn’t have time to explain this concept, but said it would be super important if we intend to take the next highest macro course my universities grad school offers. Essentially this is a solve for yourself equation for summer vacation, but I am lost. Can any one show me what to do?


texts: Do people really care about higher moments?

texts:
I have heard that people often handle uncertainty using point estimates not probability distributions. However, I have been unable to find any evidence for this in the heuristics and biases literature. I was wondering if anyone could point me to some relevant papers?

To clarify, there is no question whether some people have some beliefs about the higher moments of distributions. However, it would not shock to me to learn that when (for example) considering by how much the stock market will rise tomorrow, people form a point estimate (perhaps using historic averages) but do really not think about the uncertainty surrounding their estimate.


texts:
This is in reference to https://fred.stlouisfed.org/series/M2
My question is how can i calculate the M2 value on per capita basis? Do i just divide it with the population by year?


texts: Balance of payments and the free floating exchange rate system

texts: I am a beginner economics student and recently, I have been learning about how balance of payments surpluses are important for a country to control the value of its currency using its accumulated foreign reserves. In the case of the free floating exchange rate regimes (e.g. Russia), by default, the foreign reserves account is empty. This makes perfect sense since the country does not need any reserve assets to manipulate the value of the currency. Does that mean to say that the balance of payments position is always "neutral" (i.e. neither deficit nor surplus) for a country with a freely-floating exchange rate regime and that the BOP position is irrelevant for such a country since the current account and capital and financial accounts automatically balance each other?


texts: Forming of consumption habits in dynamic equilibrium model?

texts: I just have a question, if you know an example where the consumers form a habit about their consumption in a perfect competition setup. I found this paper by Fuhrer, but it does not solve the it in a proper setup.


texts: Would it be correct to use exchange rates of the biggest trading partners to the dollar as an explanatory variable?

texts:
I'm trying to study the relationship of general macro factors and their effect on credit in the private sector.

The country in question has a fixed exchange regime with the dollar, would it be correct to use exchange rates of the country's biggest trading partners to the dollar as an explanatory variable.

I'm not sure if should be regressing on the absolute figure of credit, or the year to year change in credit. My reasoning for the latter is that since I'll be using GDP growth rate, CPI based inflation, it's best to see how their changes effect changes in credit. If that's the case, should I use changes in oil price and the stock index, or their yearly averages?


texts: why significance of lag variables are often not reported in VAR model papers, but just IRFs?

texts: I am reading this VAR model paper https://www.rieti.go.jp/en/publications/summary/15030006.html which does not report the regression results of the VAR model, but just IRFs and historical variance decomposition. This is just one of many such papers. Why is that the case? I agree IRFs are important for finding indirect effects. But why significance of lag variables are not reported in most VAR papers.


texts: What international payment systems do exist?

texts:
I recently read up on the Society for Worldwide Interbank Financial Telecommunication (SWIFT). As faar as I understood it was up until recently the only provider of a system to exchange money internationaly between different entities.

(There are other national systems)

Now I saw that china is developing its own system called Cross-Border Inter-Bank Payments System (CIPS). This system is still using SWIFT to communicate with certain entities but can also connect them directly.

Also the Instrument in Support of Trade Exchanges (INSTEX) is beeing created by France, Germany and the UK. This system is not connected to SWIFT and currently only allows goods to be traded.

Did I understand it right that those systems are partwise competitors and are there more such systems?


texts: What does the elasticity say about the fraction of total cost used on input 1?

texts:
A firm have the following production function
$$
y=x_{1}^{\alpha} x_{2}^{1-\alpha}, \quad 0< \alpha < 1
$$
$w_1>0$ is the cost of input 1 and  $w_2 > 0$ is the cost of input 2.

(1.1) Derive the input demand functions.

I have done that and I get

$$
x_{1}^{*}\left(w_{1}, w_{2}, y\right)=\left(\frac{\alpha}{1-\alpha}\right)^{1-\alpha} w_{1}^{-(1-\alpha)} w_{2}^{1-\alpha} y
$$

$$
x_{2}^{*}\left(w_{1}, w_{2}, y\right)=\left(\frac{\alpha}{1-\alpha}\right)^{-\alpha} w_{1}^{\alpha} w_{2}^{-\alpha} y
$$

I'm confident in this result.

1.2 What is the elasticity of $x_2^*/x_1^* $with respect to $w_2/w_1$?

$$
\begin{aligned}
E &=\frac{\partial x_{2}^{*} / x_{1}^{*}}{\partial w_{2} / w_{1}} \frac{w_{2} / w_{1}}{x_{2}^{*} / x_{1}^{*}} \\
&=-\frac{1-\alpha}{\alpha}\left(\frac{w_{2}}{w_{1}}\right)^{-2} \frac{w_{2} / w_{1}}{x_{2}^{*} / x_{1}^{*}} \\
&=-\frac{1-\alpha}{\alpha}\left(\frac{w_{2}}{w_{1}}\right)^{-1} \frac{x_{1}^{*}}{x_{2}^{*}} \\
&=-\frac{1-\alpha}{\alpha} \frac{w_{1}}{w_{2}} \frac{w_{2}}{w_{1}} \frac{\alpha}{1-\alpha} \\
&=-1
\end{aligned}
$$

(1.3) What does the above elasticity say about the fraction of total cost used on input 1?

$$\frac{w_1x_1}{w_1x_1+w_2x_2}$$

I'm lost here.
I do not know how to answer this question.


texts: Does the VCG algorithm work for any bundle valuation function?

texts:
Assume we have $n$ buyers of $|M|=m$ items in a combinatorial auction.
So as we know, we can use the Vickrey-Clarke-Groves (VCG) algorithm to allocate bundles of items to buyers as best as possible. However, each player $i$ has a value $v_{ij}$ for every single item $j$ and a value $v_i(S)$ for each bundle of items $S \subset M$.

My question is as follows: can we always use the VCG algorithm to find the best solution to this problem, even when the $v_i(S)$ function is non-additive, for example if $v_i(S) = \max\limits_{k \in S} v_{ik}$? (So in this case, player $i$ values a bundle of items as much as its most valued item, no matter how many items are in the bundle)


texts: What does these "strategy notations" mean?

texts:
In a sequential game, where there are 8 pizzas.

Player 1 decides number of pizzas he wants. Let's call it S1 (strategy of player 1), and S1 = 5 means player one decided to get 5 pizzas.

Then player 2 decides number of pizzas he wants, and player 2 knows what player 1 decided. Let's call it S2 (strategy of player 2), and S2 = 5 means player two decided to get 5 pizzas.

If the S1 + S2 > 8 then both players get 0 pizzas.

Else, the players get the number of pizzas that they decided to get, also player 1 gets S1 pizzas and player two gets S2 pizzas.

In "solutions" to exercises to an assignment about strategies, they have written the following:

S1* and S2* are "Nash equilibrium" strategies of the player 1 and player 2.

Find all the Nash equilibrium in pure strategies in this sequential game.

(1) S1* ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8} and
S2*(S1) = 8 - S1   if   S1 = S1*,
S2*(S1) > 8 - s1   if   S1 > S1*,
S2*(S1) ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8}   if   S1 < S1*

What does it mean that S1 > S1* or S1 < S1*

It means The player 1 decides a number of pizza which is greater than 8?

What does the notations above mean?


texts: Does economic theory support the notion that the wealth of the wealthy is based on the poverty of the poor?

texts:
Almost any discussion about poverty and wealth and income inequality at some point includes arguments based on the premise that the wealth of the wealthy is causally related to the poverty of the poor; more specifically, there often seems to be a tacit agreement that the former causes the latter.

This is the basis for many arguments about distributional justice and in particular the notion that inequality is unjust per se or simply socially inefficient. I am however not interested in the discussion of any ethical questions regarding this issue, as this would motivate primarily opinion-based responses. Instead, I would like to know if there exist any (mathematical) models which support the common assumption that the same economic processes which make the wealthy wealthy also make the poor poor.


texts: Is there any scientific proof that 2%-3% target inflation rate is ideal?

texts:
There are a couple of central banks (RBA, Federal reserve for example) that use inflation rate as a key indicator to regulate their official cash rates.

Those target inflation rates usually range from 2%-3%.

This is taken from federal reserve's official website:

  Over time, a higher inflation rate would reduce the public's ability to make accurate longer-term economic and financial decisions. On the other hand, a lower inflation rate would be associated with an elevated probability of falling into deflation

World has changed in the past 10 years or so:

World's prevailing overnight cash rates have plunged from 3%-20% in the 20th century to 0%-3% in the past 5 years.

So is there any scientific proof that 2% inflation rate (or 2%-3% in RBA's case), is still the optimum target in today's low interest rate regime?


texts: Confused by the Term "Welfare Relative to Full Information Welfare"

texts:
This is a question comes from Field Exam in Advanced Economics Theory (Jan 2016) from UCB Econ Dept. In the first problem (Q1), it asks:

  b) How does welfare relative to the full information welfare depend on $\alpha$ and $\delta$?

I have never seen such expression before. What does the phrase "welfare relative to the full information welfare" mean?

My wild guess is to set up the total welfare as a function of $\alpha$ and $\delta$? Thanks in advance.

Edit 1.

I am asked to "type the question out so that we don't have to follow a link to see it." So here it goes:

  Consider a two period bargaining model in which an uninformed buyer makes
  offers. If there is trade in period 1 the payoffs are ${\alpha}q-p$ for the buyer and $p-q$ for the seller where $p$ is the price and $q$ is the quality and ${\alpha}.0$. We assume the realization of q is only known to the seller and drawn from a Uniform $(0,1)$. If instead they trade in the second period their payoffs from a time zero perspective are ${\delta}({\alpha}q-p)$ and ${\delta}(p-q)$ for ${\delta}\in [0,1]$ and if they don't trade they get 0.

  a) Show that the equilibrium will be characterized by two cutoff types
  $q_1({\alpha};{\delta}) \in [0,1]$ and $q_2({\alpha};{\delta})\in [q_1,1]$ such that types $q < q_1$ trade in the first period and that types $q$ such that $q_1\leq q \leq q_2$ trade in second period and finally types above $q_2$ do not trade.

  b) How does welfare relative to the full information welfare depend on $\alpha$ and $\delta$?(If you find this hard to do analytically, at least work out a few examples with low and high values and explain)

  c) Assume ${\alpha} = 1.7$ and ${\delta} = 0.8$ and suppose that with probability ${\gamma}$ in the second period another buyer arrives in the market in which case, they both simultaneously submit offers to the seller. How does welfare relative to the full information welfare depend on ${\gamma}$? (Do only the ${\gamma} = 1$ case if you are short on time.)


texts: Why does the stock price of listed firm matter for that firm?

texts:
As the title hints, why would the stock price matter for a firm?

Which are -in rough terms- the channels that a firm's stock price influence it?


texts: Why will Australia increase its interest rate only after the US increases its interest rate?

texts:
According to this article, Australia will increase its interest rate only when the US increases its interest rate.

The Aussie dollar (AUD) keeps going down, which is not very good for importing businesses. Why doesn't the Reserve Bank of Australia increase the interest rate right now rather than just wait for the US to increase first? What is the point?


texts: Does brain drain really affect a nation's growth trajectory?

texts:
Take India as an example. India has been losing most of its bright minds to the west. India also ranks low in development. I would like to get a definitive answer to this cause-effect type question.

If India had somehow ensured that its talented people could not leave the country or If India had prevented its bright and ambitious minds from getting enticed and seduced by the west, would those bright minds have been forced to figure out how to improve India's infrastructure thereby resulting in India's development?

Or is it the other way, i.e., a nation's development is mostly (>80%) decided by the quality of its political leadership? The quality of Indian polity has been really bad since 1947. This is not a judgment but a plain fact. So is it that even if we had retained the bright ones they would have made no difference to India's future?

Could you give a data-intensive answer with stats? Do give intuitive arguments also to back it up.

My thesis is that a nation's polity decides the economic fate of the nation, not its talent pool because talent can be trained by the government of the day whenever it wants to. In India, people are not talented because they are born so talented but because competition forces that in the over-populated society. So my claim is that the fact that Indians have become so successful in the USA where they hold key policy-making positions should not be a cause of alarm. Had they been in India also, they could not have made any difference. And whenever the nation's polity improves, the nation will create any amount of required talent it requires just like monkeys can be trained any time you want them to perform in a circus.

Is my thesis wrong? I hear strong views on both sides and i cannot just make up my mind as to which side to follow. Please don't just give subjective answers/opinions (i know i have!). Provide some rigor and facts.


texts: How to take the derivative and show that MPL in the Solow model is equal to real wage w

texts:
I am taking macro course this Fall and my calculus is quite rusty. So in the lecture notes they derive the following:
$$MPL = dY/dL = d(ALf(k))/dL = Af(k) + ALf'(k)  (-K)/(L^2  A) = A(f(k) - kf'(k)) = w$$
Specifically, I don't quite understand how they got $Af(k) + ALf'(k) (-K)/(L^2  A)$ from $d(ALf(k))/dL?$
Honestly, I am stuck at this point and guess will be doing a lot of differentiation like this during the entire course.


texts:
I'm having some confusion with using the terminology of MRS. For example, let's take up this question:

  If good 1 is a “neutral,” what is its marginal rate of substitution for good 2?

The answer is:

  Zero—if you take away some of good 1, the consumer needs zero units
  of good 2 to compensate him for his loss.

The question is asking for the MRS of good 2. The answer interprets this question as "how much of good 2 will one need to give up for a loss in good 1?". In that case, it is, of course, 0. But, you can just as easily interpret the question as: "How much of good 1 will one need to give up for a loss in good 2?" -- in which case, the answer is infinity -- the consumer would not want to give up any amount of good 1 for a loss in good 2.

In a different question, this was asked: "What is your marginal rate of substitution of \$1 bills for \$5 bills?". And the answer was "5". So, in this question, the good after the word "of" (\$1 bills) is what you're giving up. In other words, the answer is the answer to the question: "How many \$1 bills would you give up for a \$5 bill?" So this answer interprets the question in completely the opposite way.

To phrase it more clearly, when someone asks:

  What is the MRS of good 1 for good 2?

How should I interpret it? Is it "how much good 2 you would give up for an increase in good 1?" or "How much good 1 you would give up for an increase in good 2?"


texts: How is monetary policy fair in the current economy?

texts:
I've just read Money Creation in the Modern Economy, an article published by the Bank of England.

This article brings about a lot of questions in my mind. This article talks about money being created through commercial bank loans, and that central banks only have the authority to set interest rates or to employ quantitative easing in order to stimulate the economy. Loans being repaid should theoretically destroy the money that was created and balance the books, but inflation grows in that economy as banks earn interest (and in this case, the interest is actually the money that never existed, assuming that they destroy the rest of the money paid back).

So, my questions is:

How is this fair for every other constituent in the economy who has earned money the hard way, by working and not by generating it so freely like interest returns on loans do for commercial banks?

How is inflation fair, as populations increase and every time someone gets a bank loan, new money is added to the economy over time as they pay back that loan, and everyone else's currency is de-valuated?

Consider country X which has one constituent named Roger who works at a commercial bank in X and, coincidentally is also the president of X. He gets a loan from his bank for 100 dollars (with an interest rate of 5%), however, in his economy, only 100 dollars of money exists as actual currency and he has 0 dollars in his bank account. He will never be able to pay off his interest rate of 5% without getting another loan. His bank or state will coincidentally not be able to pay him his wage over time without printing new money from a central bank or giving his bank a loan, or, perhaps a bail-out. All this interest will do is inflate the economy, and you can only fight interest with interest.

Now apply this concept to our current economic system on a macro level, and it feels to me like it will ultimately fail as a system, because inflation can only combat inflation for so long until the price of every asset reaches infinity.


texts: How to justify the treatment and control groups for Difference-In-Difference with staggered implementation of laws?

texts:
A. Background:
Dong, 2019 and Dasgupta, 2019 used the same way to generate the treatment and control groups because they all learn about the impact of the same laws on different dependent variables. I retrieved the information on how Dasgupta, 2019, p. 2596-2597 create their sample as below:
The baseline identification:
$Y_{it}$ = $\alpha$ + $\beta$ $(Leniency Law)_{kt}$ + $\delta$$X_{ikt}$ + $\theta$$_t$ + $\gamma$$_i$ +$\epsilon$$_{it}$ (1)
where $i$, $k$, and $t$ index firms, countries, and years respectively. $X_{ikt}$ is a vector of the different firm, country, and industry control, while $\gamma$ and $\theta$ are firm and year fixed effects.
The variable of interest here is $(Leniency Law)_{kt}$. Dasgupta, 2019, p. 2597 documented that this variable equals 0 before the passage of the leniency law in country $k$, and 1 afterward. They follow a standard difference-in-difference approach with staggered implementation of laws (Bertrand, 2003) to construct the treatment and control group.
B. Author's description:
Dasgupta, 2019, p. 2597 said that

the treated group comprises all firms that are headquartered in
countries that have passed a leniency law by year t. The control
group comprises firms in countries that never adopted a
leniency law in our sample period and firms headquartered in countries
that adopted a leniency law at some later point of time.

C. Discussion:

Whether the control group includes firms in countries that implemented this law at some earlier point in time? My understanding is: for example, from Table 2, Dasgupta, 2019, p. 2599, Korea passed the laws in 1997, therefore, the control group including all firms in all countries not implementing this law from 1995 to 2002, including the US.
From my point of view, it should be the case because based on this identification, firms in the US will not be affected by the laws passed in Korea based on this identification strategy so these US firms from 1995-1996 and 1998-2002 can be control observations for Korea. But if this is the case, why do they need to write down "adopted a leniency law at some later point of time"? Because in Korea case, the word "our sample period" means "1995-2002" already.

Does it mean that only $(Leniency Law)_{kt}$ of the treatment group after the laws being passed received a value 1? Other than that, the control group and the treatment group before the laws being passed receive a value of 0?

Imagining two cases: (1) Both Germany and Brazil implemented this law in the year 2000 and (2) Only Germany implemented this law in 2000. So whether the numbers of observations of the control groups for these two cases are identical?

Australia and Belgium passed the law in 2003 and 2004, accordingly. So, firms in Malaysia only exist once in the control sample? I mean, whether one observation can be the control for many treatments in this DiD setting? (meaning no duplicate control observation).

Above is how he grouped the control and treatment based on his identification, but on page 2600, Dasgupta, 2019, section 3.1 said that "control firms are all firms in the same industry in countries that had not passed a leniency law in the 7 years surrounding the event date". This identification confused me because now we have one more dimension about the industry. I am wondering why they did not put it right in the baseline identification but instead in results section? What is the reason behind that?


texts: Macroeconomics Textbook on New-Keynesian models

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

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

Edi:
Check the link found here


texts: Combining Difference-in-Differences with Matching Methods When Parallel Trends Are Met in Unmatched Data

texts:
I'm running a difference-in-differences (DID) regression on panel data as follows:

$$ Y_{it} = \beta_{0} + \beta_{1}Treat_{i}\times Post_{t} + \mathbf{\Pi}\mathbf{X}_{it} + \tau_{i} + \gamma_{t} +\varepsilon_{it}$$

where $\tau_{i}$ and $\gamma_{t}$ are company and year fixed effects, respectively. $Treat_i$ equals 1 for treated companies and 0 for control companies and $Post_t$ equals 1 for years 2010-2012 and 0 for years 2007-2009. These main effects are subsumed by the fixed effects. $\mathbf{X}_{it}$ is a vector of control variables. Standard errors are robust and clustered by company. $\beta_1$ is the difference-in-differences estimator that I'm interested in.

When I run the regression as is, the parallel trends assumption appears satisfied, i.e., when I replace the $Post_{t}$ in $Treat_{i}\times Post_{t}$ with separate year indicators, the coefficients for the pre-intervention years are not significantly different from zero. The post-intervention years are also not significantly different from zero (consistent with the fact that the estimated $\beta_1$ in the original regression is not significant).

However, the pre-intervention dependent variable and control variables differ substantially between the treatment and control groups. This motivates me to utilize a reweighting technique which results in an improved counterfactual. Specifically, I use entropy balancing (Hainmueller, 2012), although I don't think the particular matching method will be relevant to my question (e.g., it might be easier to imagine that I use propensity score weights). I include the average pre-intervention values of the dependent variable as well as other covariates as the conditioning variables. When I run the same regression as above but include the entropy weights, the parallel trends assumption is also satisfied but now the estimate of $\beta_1$ is significant.

My question is this:

Since the parallel trends assumption seems to be satisfied in both the original DID and in the DID combined with matching, is there a reliable source that justifies using the matching DID over the original DID? The first three papers cited below seem to suggest that the DID combined with matching provides more accurate estimates because it reduces bias, but I am not familiar enough with the literature to be sure that I am interpreting these papers correctly.

Edit: I'm digesting Ferraro and Miranda (2017) some more and my sense is that an insignificant result may be the result of heterogeneous treatment effects (p310): "...the constant treatment effect is hard to believe when the treated and untreated units, despite having similar trends, have very different levels of fixed characteristics (like home size and age) that affect water use." Any thoughts on this would be greatly appreciated.

Citations:

Imbens, Guido W. and Jeffrey M. Wooldridge. 2009. Recent
developments in the econometrics of program evaluation. Journal of
Economic Literature 47, no. 1: 5-86.

Ferraro, Paul J., and Juan José Miranda. "Panel data designs and estimators as substitutes for randomized controlled trials in the evaluation of public programs." Journal of the Association of Environmental and Resource Economists 4, no. 1 (2017): 281-317.

Heckman, James J., Hidehiko Ichimura, and Petra Todd. 1997. Matching as an econometric evaluation estimator: Evidence from evaluating a job training program. Review of Economic Studies 64 (4): 605–54.

Hainmueller, Jens. "Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies." Political Analysis 20, no. 1 (2012): 25-46.


texts: How the long lives of oil platforms can account for the volatility in oil prices?

texts:
I have a question that asks me to explain how the fact that oil rigs/platforms last for a very long time increases the volatility in oil prices.

To me this does not make sense (I just can't understand how having a long lasting asset, effectively making their operations more efficient and less costly, could possibly increase the volatility of prices)

Any help would be amazing, thank you :)


texts: Latent Variable Models such as Harrison and Rutstrom (2008)

texts:
I'm working with some experimental data on choice under uncertainty and trying to use a method similar to RISK AVERSION IN THE LABORATORY (Harrison and Rutstrom, 2008).

I am pretty sure that one of the explanatory variables used to estimate the  $\mu$ and CRRA parameter is an upper bound.  Does anyone have a good link to some literature on these kinds of latent variable models with errors in variables with a known distribution, e.g., gamma?


texts: Semi Annual Deposit that earns 5% Compounded Quarterly

texts:
I was asked:

  A man planned to endow 1000000 USD to his son on his son's 21'st
  birthday. How much is his semi-annual deposit in a special account
  that earns 5% compounded quarterly if the first deposit was made when
  the son was 4.5 years old?

Answer is 16640.20 USD

My Solution:

Comparing Effective Rates:

$${ ER_{semiannually} = ER_{quarterly} }$$
$${ (1+i_{semiannually})^{m_{semiannually}} - 1 = (1+i_{quarterly})^{m_{quarterly}} - 1 }$$
$${ (1+i_{semiannually})^{2} - 1 = (1+0.05)^{4} - 1 }$$
$${ i_{semiannually} = 0.1025 }$$

Get the number of periods for Semi-Annual Payment

$${ 21-4.5 = 16.5 {yrs} }$$
$${ n = 16.5 \times 2 = 33 payments }$$

I am going to use the formula for Future Worth of Annuity since it is equal payments

$${ F = A\frac{ (1+i)^n - 1 }{i} }$$

Wherein

$${F = 1000000}$$
$${A = ? }$$
$${i = 0.1025 }$$
$${n = 33 }$$

I get an Annuity of 4265.165002

What am I doing wrong? is it not Future Annuity? Are my interest rates correct?

--
P.S. this isnt homework; this is for a board exam review in mechanical engineering. I don't know why they include finance/accounting in the "Engineering Economics" section but I have no solid background in business mathematics.


texts:
I'm absolutely not from firm financing and look to read up on the subject, but mostly onto empirical stuff.

Standard questions would be:

What is the ratio of firms that finance themselves with bank loans?
How does this vary with firm size?
What's the duration of these loans?

Is there some handbook chapter or something similar for this?


texts: Why are break-even and shut down points based on average cost?

texts:
I understand the basic idea of break-even and shut-down points, where break-even is the price at which revenue covers all economic costs, and is located where the marginal cost equals to average cost. And that shut down is the price where revenue just covers variable costs (it is where marginal cost equals average variable cost).

My question, why are taking in to account average cost and average variable cost, rather than just total cost and just variable cost? Why is shut down point where revenue equals average variable cost rather than just variable cost or total cost, and why is break even where marginal cost equals average total cost, not just total cost or variable cost?

Thank you


texts:
I have two variables that are non-stationary and contain stochastic trends. I used the Hamilton filter( an improvement over the HP filter) to remove the trend and isolate the cyclical component. My question is can I use these filtered variables (i.e. the cyclical component of the original data) in a standard OLS regression? Although the variables are now stationary will the application of the filter bias the estimates or generate spurious regression results? I know this is the case with the HP filter, although the Hamilton filter should correct for that.
The reason I am doing this is because I want to preserve the long-run properties of the data for my analysis. If I first difference the data to make it stationary all of that long-run information is lost. I am trying to figure out the best way to preserve the long-run information while making the variables stationary. Any other suggestions are welcome.
Thanks in advance!


texts: Ordinal utility and monotonic transformations

texts:
If u(x) is an ordinal utility function that represents the (weak) preference relation R, then
(a) any strictly monotonic transformation of u(x) also represents $R$, or
(b) any monotonic transformation of u(x) also represents $R$.
Which is the right proposition, (a) or (b)?

I thought that (b) is the right answer, but when I looked up various online sources I found both definitions, so I'm no longer sure.
I thought (a) cannot be right, because the condition for a monotonic transformation is usually formulated as a conditional: F is a strictly monotonic transformation of u if the following holds: (1) if $u(x)>u(y)$, then $F(u(x))>F(u(y))$. But that doesn't deal with the case (2) $u(x)=u(y)$, which represents xIy. Wouldn't $F(u(x))>F(u(y))$ be compatible with (1) and (2), but represent xPy? Thinking about it, however, it seems that the same as (1) with "greater than or equal" wouldn't do it either. Are the monotonicity conditions formulated as biconditionals? I'm confused.


texts:
Majority Rule will induce non empty choice set if individual preferences are single peaked

Is this statement true? I have some trouble in understanding the meaning of 'single peakedness' in context of this statement. Does choice set here imply that we need to find the, say, favorite alternative amongst the given ones? I understannd that Majority Voting is riddled with intransitivity. What does 'non empty' choice set imply ?

What I understand is that for single peaked alternatives, individual has a particular alternative of his choice and the alternatives that are away from the peak would be preferred less.
My concepts seem to be quite shaky. Please bear with me.


texts: Exponential Moving Average smoothing factor

texts:
I learn best my reading about a concept and then trying to implement it using math and a programming language.

Right now, I'm trying to implement an Exponential Moving Average indicator, but I'm sort of stuck on the smoothing factor. What I've come up with:

$$\frac{1}{N}\sum\limits_{k=0}^N \alpha^{k} P_k$$
Where N is the window of days in consideration, k loops through the days, $ \alpha $ is a smoothing factor and P is the price.

What should I use for a smoothing factor? Is there any general guidelines? And am I even near the final product?


texts: What are the main long-standing Keynesian economic programmes in Western nations?

texts: Much of US military spending is more easily rationalised as a job-creating programme than a form of defence, e.g. vehicles Congress funds despite Pentagon insisting it doesn't need or want them or have anywhere to store them. Part of the reason the US spends far more on the military than other Western nations (3.3% of GDP vs 2% or less) is that, in the United States, the military is an especially socially acceptable source of welfare. As a UK citizen I find this plausible, but it occurs to me that I have no idea what the UK government spends money on as much for the jobs as for the apparent application. Which leads to my question: what forms of spending do different Western nations use with Keynesian motive?


texts: Question about misperception in IS-MP model

texts:
Why is these steps happens one after another in IS-MP Model if MP curve is a horizontal line? Also, is this preventable?

a) Policymakers believe the slow-down in growth is caused by a
negative aggregate demand shock...

(b) ...so they lower the Real interest rate R.

(c) In truth, the IS curve never shifted...

(d) ...so the great inflation happened.


texts: What are the advantages of using euro for Greece?

texts:
Theoretical benefits of using unified currency are well known and described in many places like
https://www.economicshelp.org/europe/benefits-euro/
However, reality (or more comprehensive analysis) shows that euro gives advantage to countries with strong economy like Germany and creates additional difficulties for countries with weak economy like Greece.
Quick description is here https://www.investopedia.com/ask/answers/09/euro-introduction-debut.asp

The German economy was relatively prosperous by 2012, and European
monetary policy was far too tight for weaker economies. Portugal,
Italy, Ireland, Greece, and Spain all faced high debt, high interest
rates, and high unemployment. This time, monetary policy was too tight
rather than too loose. The only constant was that the euro continued
to work in favor of Germany.

There is clear answer how leaving euro may help Greece -
https://www.quora.com/How-would-leaving-the-euro-for-the-drachma-benefit-Greece
However no clear explanation how Greece benefited from EURO.
My understding was that Greece replaced national currency with euro because of some kind of euphoria rather than argumeted decision. And I can't see any clear evidence that it was wise. Maybe I'm missing something.
The question is about using EURO instead of national currency [for Greece]. Not about pros/cons of being part of EU. Countries like Sweden or Polad being part of EU use their own currencies and do not have plans to replace them with EURO.
More generic question why whould goverment of a country with weak economy want to lose control on monetary policy and replace (or link to) national currency with external currency.


texts: Why is the inverted yield curve a good predictor of impending economic recession?

texts: The inverted yield curve has often been cited as a good predictor of impending economic recession. What are the reasons to explain why is it a good predictor? Is the inverted yield curve a cause or symptom of recession?


texts: Clarification about Market Structure Oligopoly or Monopoly

texts:
As per the definition i found in the internet,

Oligopoly, in which a market is run by a small number of firms that together control the majority of the market share.
Monopoly, where there is only one provider of a product or service.

Consider this situation in a country.

There are 4 main bus operators in this country. A,B,C and D and some individual bus owners.

The bus fare is controlled by a national body.
Some particular bus owners  who has AC installed in the bus, charges a 0.2$ extra per route.

In the above scenario in what classification would you put the transport sector of this country. Is it a monopoly as the price is regulated by a single body? or is it an oligopoly as the market share is dominated by these four main company.

Further more for my upcoming exam if I get a question on Market structure of this country transport system how can I elaborate?


texts: Are there any studies that show that "Affirmative Action" hurts the economy?

texts:
Are there any studies that show that "Affirmative Action" (an action or policy favoring those who tend to suffer from discrimination, especially in relation to employment or education) hurts the economy?

Based on personal research/reasoning, I believe that "Affirmative Action" could hurt the economy, but I would like to do more research on the subject.  Any links to (credible) studies showing that "Affirmative Action" hurts the economy would be greatly appreciated.


texts:
In Australia, ~10% of our salary goes into a compulsory retirement savings scheme. I have chosen the default option for young people, which involves a relatively balanced split between stocks, investment in property and a bit of cash.

I have been working for 2-3 years, so have a small balance in my super account.

I am not sure whether I should cheer on the stock market going up (increases the value of my existing 2 years worth of investments), or when it goes down (allows my fortnightly contribution to buy more units of stock, which will/may then go back up later.

I suppose ultimately, this boils down to "If a stock index deviates from its long term average, would a rational economist forecast that:

a) The rate of change of the index will eventually return to the long term average, meaning I should cheer the bull.

b) The value of the index will eventually return to where it would have been if the deviation did not take place and the rate of change stayed at the long term average the entire time (cheer on the bull)"

P.S. I am aware of the common theory in economics that crossing one's fingers does not impact the future direction of the stock market either up or down. I simply refuse to accept this as truth ;) But feel free to pretend this is a question for interest's sake only without any actual implications.

Also, apologies if this belongs in personal finance. I don't believe it does, because it is more intended as a theoretical question around general trends in stock markets and economies than as actual advice for someone's stock choices.


texts: How much did it 'cost' slave-owning nations to emancipate the slaves as a percentage of GDP?

texts:
According to this article in the Guardian the UK Treasury tweeted in 2018:

  "Did you know that in 1833, Britain used £20 million pounds - which amounted to 40% of the UK GDP to buy freedom for all slaves in the Empire. The amount of money borrowed for the Slavery Abolition Act was so large that it wasn't paid off until 2015. This means that every living British citizen paid for ending the slave trade."

To which one angry British citizen, Lexington Wright, tweeted back:

  "So basically my father, and his children and grand-children have been paying taxes to compensate those who enslaved our ancestors and you want me to be proud of this fact? Are you f****** insane???"

The Guardian adds as commentary to this exchange:

  Few people in the 1830s would have seen it this way. Compensation was a mechanism of ending a system that millions of people had come to regard as abhorrent and a national disgrace. The abolitionists agonised over it ... the only people who saw a positive in it were the people who spent three decades campaigning for it and would be the beneficiaries of it - the slave owners.

They go on to add:

  The slave owners not only recieved compensation from the British Taxpayer they won another concession, the euphemistically named 'apprenticeship' system. What this meant was that slaves were forced to work on the fields for another further six years without pay after the abolition of slavery.

The above is the background to the following questions:

Q. The compensation was paid for emancipating slaves in the Empire. How much of this was paid for the top five slave-owning nations? Who are they, and how many slaves were emancipated?

**Q. How much was this worth as a percentage of the top slave-owning nations GDP at that time? And in particular, the USA?

Q. Was any additional monies paid by any of those nations governments as compensation?

Q. How did they come up with the figure of £20 million pounds - was this solely based on the market values of slaves at the time or were other factors taken into consideration?

Q. How would one cost the six years of unpaid work by emancipated slaves and how much did this come to?

There are a number of questions but they are all interlinked and prompted by the initial tweet. I can ask them separately if people wish.


texts: Deriving the Euler equation from a Continuous Time Dynamic Programming Problem (HJB)

texts:
Solving for the Euler equation in discrete time is farily straight forward with the use of the Benveniste Scheinkman theorem. However for the following standard Ramsey model:
$$\max \int_{0}^{\infty}e^{-rt} u(c(t))dt$$
subject to:
$$u(c(t))=\ln(c(t))$$
$$\dot{k}(t)=Ak^\theta-\delta k(t)-c(t)$$
the problem is simple if I use the Hamiltonian however if I write the Hamilton-Jacobi-Bellman equation for this:
$$rV(k(t))=\ln(c(t))+V'(k(t))\dot{k}$$
I have no clue how to get started. How would one go about solving for the Euler Equation using the corresponding HJB equation?


texts: VCG mechanism with a minimum payment threshold

texts:
Suppose that we want to find a socially-optimal allocation in the following setting:

There are $n$ firms and $m$ workers.
Each firm $i$ needs one worker and has value $v_i$ for having a worker (any worker).
Each worker $j$ needs one job and has value $v_j$ for having a job (at any firm).

The values are private and we look for a truthful mechanism. The first attempt is VCG, however, it might run a deficit. For example, if:

there are 5 firms with values are 5,4,3,2,1
there are 4 workers with values 4,3,2,1

then VCG says that the 4 high-value firms are matched to the 4 workers, each firm pays 1 (its externality on the 5th firm) and each worker pays -2 (his externality on the 4th firm). So we have a deficit of 4.

A simple solution here is to declare that there will be no negative payments. Apparently the mechanism is truthful: if there are more firms than workers then all firms pay a positive price and all workers pay 0, and vice versa if there are more workers than firms.

My question is: in what other cases is it possible to modify the VCG mechanism like that, by adding a "minimum payment"?


texts:
The utility function for goods can be modeled using something like the exponential utility:

$$B(x)=\frac{1-\exp(-ax)}{a}$$
with $a>0$.

So that marginal benefits are modeled as being within $[0,1]$:

$$B'(x) = \exp(-ax)$$

This would look something like this:

So far, so good. Now, in the production of this good, there are costs, because there are bads which are produced as byproducts (think pollution) that we would like to model.

I am not from economics. I just think a project I am working on would benefit by us studying and using whatever is used in micro.

What are some good utility function for bads (no pun intended) or for costs?

Or if you could recommend some good textbook that covers this with enough mathematical rigor that would be fine as well. From Google Books, I have seen this could be a good bet, but it doesn't let me look at it without buying it:

Microeconomic Theory And Applications - Page 84
Agarwala S K - 2008
If we want more industrialisation we have no option but to
accept more pollution as well. Industrialisation leads to rise
in utility level while pollution leads to fall in utility level
It makes the ICs upward sloping to the right. GoodY (Bad) GoodY
...

It seems like it has a nice discussion on how to model bads/costs. Would you recommend it?

ps: I just realized maybe I could use $C(x)$ as being $B(x)$ but with $a<0$ for what I want...


texts: How to model the change in fossil fuel price?

texts:
What is the best way to model fossil fuel prices? I am trying to build an energy-economic model and changes in fuel prices are an important part of the model. I need to know how to model them. Any ideas?

I would like to forecast the changes in fossil fuel price (oil and gas basically). As this is part of an energy model which takes into account those economical trends


texts:
Has Stack Overflow an overall positive impact on programmers productivity?

On one side, it takes time and effort to ask and answer questions -- thus decreasing productivity.

On the other side, more and more programmer questions are answered and easily found through Google. This allows many programmers to find solutions to their problems quicker than ever before, thus increasing productivity.

Has Stack Overflow been economically beneficial to programmer productivity? If so, can this be quantified in terms of money?

Note: I've asked this related question on Skeptics.SE, but it turns out there is no peer-reviewed research on the matter.


texts: Is falling inflation in India one of the reasons for the Nifty crossing the 10,000 points mark?

texts: Recently the Nifty crossed the 10,000 mark for the first time. At the same time inflation in India is falling. My question is whether the fall in inflation in India one of the reasons for the Indian stock market doing well?


texts: Ranked choice preference with ties - Arrow's Impossibility Theorem

texts:
My question relates to my understanding of Arrow's Impossibility Theorem and ranked choice.  It seems to me that the requirements on social choice functions are too strict. A social choice function cannot result in ties. This sounds unreasonable to me.
Let two voters with preferences $a > b > c > d$ and $a > c > b > d$. It seems that any "reasonable" choice function would choose $a > b = c > d$. Any other output would be making an arbitrary distinction between $b$ and $c$. So my question is: if we relax the output of our social choice functions to allow for ties, is there a social choice function that satisfies Arrow's criteria? Is there proof that no such function exists?
As an addendum, I tried a "trivial" such function but it doesn't seem to work.
Let $f$ a social choice function which if every voter prefers $c_1 > c_2$ then in the final output $c_1 > c_2$; otherwise $c_1 = c_2$.
This seems to fail by the transitivity of ties. So, for two preferences $a > b > c$ and $c > a > b$ then $a > b$ but $c = a$ and $c = b$ which is a contradiction. If we were to choose, $a > b = c$ we would be violating the independence of irrelevant alternatives. As, if we were to delete $b$ the result "should" be $a = c$. Is there a way to work around this?


texts: Would a major wealth redistribution cause a major inflation?

texts: I've seen a video on wealth distribution on the US where perceived, "desired"(by the majority) and actual income distributions are shown. I've been thinking what would happen to the purchasing power if such a distribution was attained. How much could the supply increase to balance the huge amounts of money that were just being invested and accumulated and will now be spent on consumer goods? If an inflation would occur, is it possible to estimate it?


texts: Dynamic programming: verification principle

texts:
Consider the Gale cake problem with $u(c) = log(c)$, so that the problem becomes:$$\max_{x}\sum_{t=0}^{\infty} \beta^{t}log(x_t-x_{t+1})\: sub\: 0<x_{t+1}\leq x_t,\: x_0>0\ given$$

It is pretty easy to show that the function $v:(0,x_0]\rightarrow\mathbb{R}$ given by $v(x)=A+B\:log(x)$, where $A=\frac{\beta}{(1-\beta)^2}log\beta+\frac{1}{1-\beta}log(1-\beta)$ and $B=\frac{1}{1-\beta}$ is a solution of the Bellman equation. I also know that it is the value function of the cake problem but the classic verification principle, i.e. $\lim_{t \to +\infty} \beta^tv(x_t) = 0$ is not met.

How should i proceed to actually show that $v(x)$ is the value function of the problem?


texts: Why does the US consider non-farm payrolls when looking at employment levels? What are the reasons for not including farms? Are the workers too transitive, does it not contribute in a certain way to economy which is undesirable to measure? Other countries seem to have similar ways to measure employment levels which suggests farms payrolls are problematic.


texts: What are some theoretical explanations for deviations from the efficient market hypothesis?

texts:
According (the semi-strong form of) the efficient market hypothesis, the price of an asset should reflect all publicly available information about the 'fundamental value' of that asset. The reasoning is that if there is some public information that suggests the price is below the fundamental value then people will have an incentive to act on this information and buy more of the asset. This increase in demand will cause the price of the asset to rise, closing the original price-value discrepancy.

This reasoning seems intuitively plausible, but significant price-corrections during the recent recession seem to suggest that markets had systematically priced in a manner inconsistent with underlying fundamentals. What academic theories (i.e. published or in working papers) have been advanced (and by whom) to explain why the efficient market hypothesis might fail? Is there much of an empirical consensus on the validity of the efficient market hypothesis in the literature?


texts: Lack of historical data for calibration of probability of default

texts:
It is a known fact that default rates seem to exhibit cyclic behavior. Most probability of default models use one-year averages of default rates to calibrate the models. The one-year averages should be observed long enough to take into account the effects of a full business cycle. But what if historic data does not do back far enough to explain the effects of a full business cycle?

I guess one could link macro economic factors to default rates and extrapolate. Then the value should be somewhat cycle neutral. But from what data could there be extrapolated? Also S&P and Moody's default rates go back to the 1980's but are they representative in all case to extrapolate from? And I do wonder, how do financial institutions make 'artificial' data to represent full business cycles? Thanks for any suggestion or help.


texts: Walras's Law V.S Say's Law- Is there a difference?

texts:
I've been going over the concept of Walras's Law and often references to Say's Law. I've heard and have seen online that they are really the same thing however by looking at the definitions I notice a common difference.

  Walras’s law:
  “For any price vector $p$, we have $()≡0$; the value of the excess demand  is identically zero.”

  Where excess demand $z(p)$ is defined as:
  $$z(p)=\sum_{i=1}^n(x_i(p,m)-\omega_i)$$
  where $x_i(p,m)$ is our marshallian demand for good $i$  and $\omega_i$ is the initial endowment of good $i$.

Conversely,

  Say's Law:
  "aggregate production necessarily creates an equal quantity of aggregate demand" (from Wikipedia).

  or $$Q_s(p)=Q_d(p)$$

Would it be safe to say that Walras's Law makes reference to only consumer demand (which is transferred through a market and is not "consumed" by the firm themselves via inventory investment), While Say's Law is a statement regarding both demand by consumers and producers regardless of whether or not it goes from producers to consumers or producers back to themselves in form of inventory investment?

The rationale for this argument comes from the fact that we do conciser inventory investment to be included in demand even though it does not change hands in a market.


texts: Microeconomic rationale for UIP (uncovered interest rate parity)

texts:
The key idea behind UIP is that as for all common financial instruments, the "law of no free lunch" should also hold for currencies. However it differs from traditional replication-based no-arbitrage conditions like CIP in that there is no obvious argument for why the exploitation of opportunities when it does not hold true necessarily depletes all such opportunities, thereby making "free lunches" rare in a world of rational investors.
Concretely, the currency of a country with a relatively higher interest rate needs to gradually depreciate to offset the positive earnings potential. What mechanism drives this gradual depreciation?
I've heard that there are models on this issue but have not been able to locate the literature.
Thanks for all suggestions!


texts:
It's frequently useful in physics and engineering applications; are there any applications in theoretical economics? (If not, were there any attempts at incorporating CA that just never caught on?)

See http://en.wikipedia.org/wiki/Complex_analysis.


texts: Limits to Quantitative Easing Programmes

texts:
I have been reading recently on the quantitative easing programmes by the ECB and the BOJ, see http://www.cnbc.com/2016/04/07/what-the-bank-of-japan-boj-will-do-now-that-negative-rates-have-disappointed.html, and, http://www.bloomberg.com/news/articles/2016-04-21/ecb-to-start-buying-corporate-bonds-in-june-as-part-of-stimulus.

The ECB will be expanding its current programme to include corporate bonds and  it is being suggested that the BOJ may give up on negative interest rates and possibly could buy japanese equities instead. It seems that these central banks are just working their way up the risk asset spectrum. My question is where do these asset buying programmes stop (penny stocks/distressed debt?)? Also what happens to these assets, surely if they sit on the central banks books it could go bankrupt like a commercial bank? Moreover, what could cause these asset buying programmes to be abandoned/fail?


texts: why is Fed creation of fiat money valid?

texts:
some people suggest that the government prints money to pay its bills and that the increased amount of money in circulation lessens the value of $1.   i hope to get an explanation of why both assertions are false and suggest the following:
the Federal Reserve Bank (Fed) inserts money into the economy thru loans. at least two questions arise

presumably if all loans were paid back, there would be no money in circulation.   but corporations borrow money to build products and others borrow money to buy those products, hence a never ending cycle.  so Fed balance sheet every expected to
be zero (i.e. no outstanding loans)?   and what happens to the money in circulation from defaulted loans?

the "value" of money is presumably based on supply and demand.  this presumably counters the idea that the more money in circulation reduces its value because as the population and economy grow, there is a greater need for money, maintaining its value.   when an economy shrinks, the fed makes fewer loans and as loans are paid back, the amount of money in circulation is reduced.   further, much more money is needed in circulation today than in colonial times (as an example) simply because there is a greater population and need for money (or the economy has grown).

are these concepts correct and do they explain/justify fiat money?  what concepts are missing from a more comprehensive understanding?


texts: Why does the government need to control interest rates?

texts:
Context
As far as I understand, economic cycles are mostly dependent on the amount of demand (which is influenced by money supply, which is in turn influenced by the availability of credit). Since credit dwarfs cash as a % of total currency, credit is by far the most important driver of money supply.
In general, the government controls interest rates to slow down an overheating economy, or to expand a slowing economy.

Question
My question is, why do we need government to control interest rates? Assuming banks are rational and want to make money, wouldn't banks tighten credit rules in the midst of an overheating economy? If banks sense that debts are too high, wouldn't it make sense for them to increase interest, or stop lending to risky customers to avoid customers that default on their debts? I don't see why government is any more qualified at controlling interest rates than banks themselves. You could argue that banks are greedy, but at the same time, they're smart and have a long-term view. If a bank loaned money in an overheating market, they wouldn't be in business for too long.

Thanks!


texts: Can't Derive Expectation in Second Price Auction

texts:
I'm working on a SPA where we solve:

$\max_{\beta \ge 0} Pr\{Winning\}[v - \mathbb{E}(b^{[2]} \ | \ b^{[2]} \le \beta)]$

We assume all beliefs on bids are independently and identically distributed on $[0,1]$ given by CDF $F(b)$.

$b^{[2]}$ denotes the second highest bid.

I've found $Pr\{Winning\} = Pr\{\beta \ge b_1, \ldots , b_n\} = F(b)^N$

In my lecture notes we are given:

$\mathbb{E}(b^{[2]} \ | \ b^{[2]} \le \beta) = \frac{1}{Pr(b^{[2]} \le beta)} \int_0^{\beta} bdF(b)^N$

I'm assuming this comes from $P(A|B) = \frac{P(A \cap B)}{P(B)} $, but can't quite figure it out. Especially the $F(b)^N$ in the integral.


texts: Currency Peg or Currency Substitution/Dollarize?

texts:
Why would a sovereign state choose an exchange rate peg over the demonetization of the local currency, replaced by hard currency?

In the case of the West and Central African CFA Francs, France has an obligation to support the peg to the Euro. Would it not be more advantageous for both parties to facilitate the distribution of Euros throughout the CFA Franc area instead?

Considering Ecuador's and Zimbabwe's experiences, it would appear demonetization is the end result of very dramatic currency crises and never really a choice. But it seems to have all the advantages of a peg (stability, trade facilitation, etc) without any of the disadvantages (currency speculators, need to maintain reserves, etc).

What am I missing here?

EDIT

A brief description from Wikipedia of the conditions in Ecuador leading up to the official adoption of the USD in 2000.

And for Zimbabwe, an article from the BBC describing the well-known hyperinflation the country suffered through before abandoning it's currency.

There are a few more links I wanted to include, but unfortunately my rep is too low.


texts: Is there an economic reason why employees don't share salary information with each other?

texts:
In Western society, one's salary is often a taboo topic and people tend to not tell other people what they earn.

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

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

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


texts: Could leisure be considered a Giffen good?

texts: One of my microeconomics fellow students asked this and it got me thinking. The leisure demand curve is a mirror of the labour supply curve. In the section where the Income Effect is greater than the Substitution Effect, would leisure be considered a Giffen good as well as an inferior good? Because the price of undertaking leisure is your wage.


texts:
I can solve most utility maximization problems using my mathematical knowledge .... but not when it comes to Leontief preferences. I do not have a book to lean on (am self-studying), so would really like some help. How does one solve a general maximization problem like $$\max [\alpha x_1, \beta x_2, \gamma x_3] \ \text{subject to } \ \lambda_1 x_1 + \lambda_2 x_2 + \lambda_3 x_3 = M$$
where $M$ is income and $\lambda_i$ is price for good $i$?

Really, everything I know about derivatives and slopes goes all out the window with this damn thing. If somebody told me what the prices and income were, the optimal choice, when there are only a few goods, could probably be found by just applying common sense, but what about the general case? Is there no general "formula" like there is for Cobb Douglas and CES functions? Is there some go-to method that we use in these cases?


texts: Kuhn Tucker optimization problem and game theory

texts:
Consider a game with two players, where each player i= 1 ,2 has preferences $u_i$= $s_i^a$$c_i^{1-a}$, where c_i is the consumption and $s_i$ is social interaction. $s_i$ is given by :
$s_i$ = $t_i$ + $t_{ij}*t_{ji}$, where t_i is time spend by player i alone, and $t_{ij}$  is the time player i spends with player j. Player i has to decide how much of his or her time T to allocate between work, having time alone, {t_i} and social interaction $t_{ij}$. Assume that for each hour, player i works, he or she earns the wage w and assume that the price of the consumption good $c_i$ is normalized to p=1.

i. Define the optimization problem for player 1. Write down the Kuhn-Tucker conditions and discuss these conditions. Explain why player 1 faces a strategic situation. Find the best response functions for player 1 and 2. Graph these functions.

ii.  There are some cultures that emphasize social interaction more than others. In this exercise how can I determine the role of '' culture'' if exists?

My solution is :

$$max s_i^a c_i^{a-1}$$

subject to $c_i$+w$s_i$=Tw and $s_i\le T$

Lagrangian

$$L(\lambda, \mu, s_i, c_i) = max s_i^a c_i^{a-1} -\lambda [c_i+ws_i-Tw]+\mu [s_i-T]$$

FOCs

$L_{\lambda}=0$ so, $c_i+ws_i=Tw$    (Eqn-1)

$L_{s_i}=0$ so, $as_i^{a-1}c_i^{1-a}$-$\lambda w$- $\mu=0$ (Eqn-2)

$L_{c_i}=0$ so, $(1-a)s_i^{a}c_i^{-a}$-$\lambda =0$ (Eqn-3)

Slackness condition : $\mu [s_i-T]=0$

If $s_i-T<0$ implies $s_i < T$ so $\mu =0$

Thus by equation (2), $as_i^{a-1}c_i^{1-a}$=$\lambda w$

By equation (3),  $(1-a)s_i^{a}c_i^{-a}$=$\lambda $

By equation (2)/(3), $(a/1-a)(c_i/s_i)=w$ implies $c_i={w(1-a)\over a} s_i$ (Eqn-4)

Equation 4 and 1, ${1-a\over a}ws_i +ws_i=Tw$ implies $s^*_i=aT$

Thus, $c_i^*=(1-a)wT$

In order to find the best response function

$s_i^*=aT$

$t_i^*+t_{ij}*t_{ji}=aT$

By equation 5, $t_{12}(t_{21})={aT-t^*_1\over t_{21}}$ and

$t_{21}(t_{12})={aT-t^*_2\over  t_{12}}$ equation (6)

When I plug (5) into (6)

$t_{21}(t_{12})={aT-t^*_2\over  (aT-t^*_1)/t_{21}}$

So,

$t_{21}={(t_{21}aT-t_{21}t^*_2)\over aT-t^*_1}$

$t_{21}aT-t_{21}t^*_1= t_{21}aT-t_{21}t^*_2$

$(t^*_2-t^*_1) t_{21}=0$

Each player faces a strategic situation because his best response depends on the others action. The term $t_{ji}$ determine by other players. Thus you have to choose your best response conditional on the others’ action.I really try to find the best response functions but i stuck at this point.

Thank you.


texts:
I've recently started my PhD and upon looking at my textbook (the sargent one) I found that it differed greatly from my Masters textbook (Romer) and in turn my undergraduate macro text (williamson).

What is perplexing is that for the most part the models taught in all three books deal with key questions of economic growth, labor markets and business cycles. However the approaches are very different and dont necessarily feed into eachother almost like each model stands on its own disregarding the method of the previous.

This is not my experience with micro, where it was very clear that more and more depth is uncovered using the same core models of consumers, firms and market structures.

This all being said, though i recognize the value of being exposed to so many different models as part of my academic training, holding them all on the same scale when analysing a phenomenon can be at times contradicting (i.e comparing the insight from infinitely lived households to overlapping generations models).

Bottom line: why are there so many different macroeconomic models that explain the same phenomenon.


texts: Datasets with pre- and post migration earnings

texts:
I am interested in computing the pre- and post-migration earnings of international migrants, especially those migrating from low income to high income countries (or vice versa).
The data should allow me to compute pre- and post-migration earnings for each individual (as opposed to having one group with earnings at home and another with earnings abroad).
I am aware of:

New Immigrant Survey
Latin American Migration Project (LAMP and MMP)
Migrating out of poverty
data used in some small scale studies for one country (e.g. Tonga)

Could anyone point out additional data sources?


texts: Is there a commitment mechanism which allows players to achieve pareto optimal solutions?

texts:
For any non-cooperative game, is there some commitment mechanism which will can guarantee that players chose a pareto-optimal solution?

Or, are there known conditions for this to obtain?

EDIT: I elaborate what I mean by "commitment mechanism" below:
Informally, I mean something like a "contract" that players can sign and are guaranteed to follow in the future.
So there is an additional round at the start of the game where each player, independently, decides to sign this contract (or not).

For instance, coordination in the prisoner's dilemma can be achieved by offering each player the option of signing a contract which states:
"If both players sign this contract, then I will cooperate".


texts: Compared to commodity markets, money markets move a lot. My guess is that commodity markets are less elastic due to fixed production costs. But I don't know if that is the correct explanation.


texts: Can an economy grow without its population growing?

texts: Assuming natural resources are not a limiting factor, can a country's economy keep growing if the country's population is not growing? What about the global population?


texts: Solution of overdetermined system of moment conditions

texts:
In Hayashi Econometrics, page 207-8, ex3 (see hint), he says that even if a population moment conditions (GMM setting) system is overidentified it still has a solution, while the sample moment conditions system cannot.
I'm having a hard time understanding this.
Any help would be appreciated.
By the way, I've also posted this question on CrossValidated. I hope there's no problem.
Edit: Check Jayk answer in CV. ;)


texts: How does interest rates impact investment

texts:
How does a decrease in interest rates decrease investment rates? This is how I believe a liquidity trap works, not sure if it is correct.

Thank you


texts: Non-constant returns to scale and competitive factor markets

texts:
I am having difficulties to understand the conclusion in bold below, taken from Frankel (1962):

  A  second  limitation  of  the  Cobb-Douglas  function  appears  when  it  is  fitted  to  historical  data.  All  improved  fit  generally  is  obtainable  if  the  exponents:  and  a  are  allowed  to  vary  freely  instead  of  being  constrained  to  equal  unity.  With  some  sets  of  data,  the  resulting  sum  of  the  exponents  has  differed  significantly  from  unity,  an  outcome  that  opens  the  door  to  economies  and  diseconomies  of  scale  and  that  leads  to  abandonment  of  the  convenient  assumption  that  factors  are  paid  their  marginal  products.

As I understand things, returns to scale is a technical issue, which might be independent on market conditions. Albeit not a reliable source, the same appears in the Wikipedia entry.

One interesting answer to this might come from the first answer here. However, the author is interested in competition among producers, in terms of the final goods price. Basically, that a natural monopoly (where IRS hold), has an average cost always below the marginal cost, so competitive market produces loses. But what prevents a natural monopoly to pay its factors their marginal products? You can think of a natural monopoly, or any other example of firms with DRS or IRS, in which they operate amid competitive capital and labour markets. I see no a priori reason why market forces would not lead these firms to pay the factors their marginal product.

To sum up: why IRS or DRS mean we should abandon competitive assumptions in the factor markets?


texts: Why do low labour and wage flexibility forestall a single currency?

texts:
The European Union: Politics and Policies (2017 6 edn). p. 77 Middle.

Please see the red line beneath. Doesn't low labour and wage flexibility befit a single currency? If labour and wage fluctuate, then a single currency would become unstable?


texts:
Monetary Policy, Inflation,
and the Business Cycle,
Jordi Gali,
Page 45
http://elib.peaceland.edu.ng:8383/greenstone3/sites/localsite/collect/peacelan/index/assoc/HASH0139.dir/doc.pdf

How does "ψ " convert to "MC"?

You can say Drago Bergholt solutions for Gali
http://bergholt.weebly.com/uploads/1/1/8/4/11843961/the_basic_new_keynesian_model_-_drago_bergholt.pdf
but Drago also didn't explain this change. (page 13 )

Sincerely


texts: Why don't governments exploit negative interest rates more than they currently do?

texts:
At the moment many governments, such as Finland's, are able to borrow money at negative interest rates. My question is: why don't they borrow as much money as possible while interest rates are negative?

The answers I have heard so far don't make sense.

  Governments avoid borrowing too much money because that would lead to spending more money

This doesn't make sense: they could borrow money and not spend it and just take the profit from the negative interest rate.

  Governments avoid borrowing too much money because they want to minimize the risk that a bank fails and loses their money

This doesn't make sense: they could take the money out as cash, pay people to guard it, and still make a profit from the negative interest rate even if the money was just sitting in a safe.

  Governments avoid borrowing too much money because there are limits to how much they can take out in loans in they won't to keep a healthy distance to those limits.

This doesn't make sense: if they borrowed money at a negative interest rate now, and just saved the money, they would be in a better position in the future compared to not taking the loan. (In all cases except when interest rates go even more negative in the future, in which case it might be beneficial to take the loans when the rates are lower - however, no-one is arguing that governments would be speculating like this).


texts: Ambiguous definition of Substitution and Income effect?

texts:
Consider the (schematic) indifference curve diagram of two good-quantities Q1, Q2:

According to Wikipedia we call the vector AB' the substitution effect and the vector B'B as the income effect.

I now wonder why I could not, instead of translating the tangent through B onto the lower indifference curve, translate the tangent through A to the higher indifference curve, thus denoting AA' as the income effect and A'B as the substitution effect.

Note that these two definitions do not coincide for (sufficiently) different shaped indifference curves.


texts: Interaction dummies estimates influence other estimates?

texts:
In page 311 of Gujarati Basic Econometrics, there's the following example for use of dummy variables, when we're interested in the interaction between two qualitative terms.

Shouldn't we have different estimates due to the presence of the extra interaction term?


texts:
Suppose I have a set of units $n_i, i = 1,...,N$. One unit was receiving a treatment $n_j = 1$ at times $t=1$ to $t=\tau$. All other units never received the treatment so $\forall t, n_i=0,i\neq j$. At $\tau+1$ to $T=t,T>>\tau+1$, $n_j=0$.

Suppose the shock to $n_j$ is totally exogenous for simplicity.

Is there a causal framework that allows me to estimate the impact of $n_j=1$?


texts:
Hi  I needed some clarification on something. I have three variables:

$V_1$ which is an indicator of an interest rate risk premia
$V_2$ which is an indicator of a credit risk premia
$V_3$ which is an indicator of a liquidity risk premia.

While in theory the relationship of:
$$V_1 = V_2 + V_3$$ should hold; I'm struggling to find a good modelling technique that can decompose $V_1$ into subcomponents that relate to $V_2$ and $V_3$. I am searching for something beyond a vector auto-regressive model.
My question is would State space modelling help me in this decomposition.


texts:
I was reading about the debate about income inequality and I would like to know your opinion on the matter.

Basically, the positions are two: the classical one, which states that inequality is good for growth because it fosters innovation and investments and the most recent one, the one of IMF and OECD, which states that inequality causes a decrease in human capital investment among lower-income households, which prevent them to become earners or consumers in the future.

I read that both are supported by empirical evidence but there is skepticism about them (e.g. Chris Giles on FT).

What's your idea on the topic? Do you have any suggestion about literature/articles I can read about it?


texts:
How did 'crisis' spread through the financial system in '07-'08? Specifically, what is the process by which a subprime mortgage impacts the health of the credit markets as a whole? An explanation in the context of securitization would be appreciated.

I understand that subprime mortgages are sold to special purpose vehicles but the process is muddled from there.

I don't need a mathematical explanation, a clear conceptual explanation would be perfect.

Thank you!


texts: Why can the job offer have a negative relationship between salary and quantity of work?

texts: Excuse me the following question arose, is it possible that the job offer has a negative relationship between salary and the amount of work?


texts: Labor time and the exchange value (Marx). What about the quality of the raw materials?

texts:
Karl Marx writes in his book "capital", that the exchange value of a commodity is determined by the necessary average labor required to produce the commodity. The labor is measured in time.

Here's my question. There are different types of wood for the production of furniture. Why is furniture made of high-quality wood usually more expensive, while the amount of labor (measured in time) is independent of the wood quality? According to Marx, a table made of low-quality wood should be as expensive as a table made of high-quality wood (apart from negligible differences in the processing due to the wood quality). But this is obviously wrong.

What would Marx answer to this question?


texts: Is a lack of any barriers to entry a necessary condition for ensuring pareto optimality is reached?

texts: I understand that a competitive market is necessary for a market to equilibriate to a pareto optimal state, and that things like economies of scale, network effects, government restrictions, and government imposed costs can prevent reaching pareto optimality. But do other barriers like startup capital also prevent reaching pareto optimality? I would think the answer is no, since something like sunk costs can be amortized over all products sold by a market actor. Is this correct, or am I missing something?


texts:
Suppose we have a mechanism where a finite number of agents possess private information that is not drawn from a probability distribution.

The agents' types are given and fixed but agents only know their own type. As there is no probability distribution, players do not form any beliefs.

The agents' behavior is modeled as utility-maximizers and the utility functions are quasilinear in nature.

Does it make sense, from the above, to use as a solution concept the non-Bayesian Nash equilibrium (Nash, 1950)? If yes, could you please point me out to the right literature (some paper references)?

Thank you in advance.


texts: Calling 118 118 (UK) - A market failure?

texts:
Is the shocking cost of directory enquiry numbers in the UK a market failure, or the economy working perfectly well?

EDIT: I know that proponents of free markets often like to blame over-regulation or government interference for perceived problems in markets, so I wonder if anyone could point to some regulation that has caused this incredible series of price hikes.


texts: Analyse the data of two responses while having two different scales

texts:
I am working on data analysis these days and stuck on analysis when I have to compare the two kinds of responses.
First, I have data on the self assessment, I have asked students to rate them on a scale of 1- 5 (SD-SA) on 25 behaviors, what they think about themselves.

Than though a timed exercise, I have asked assessors to access them on same behaviors on the number of occurrence and also if the student shows anything against the behavior then a negative score is also given. The scoring is done is such a way that a student can get a maximum of 4 points if they show the behaviors many times and a minimum of negative 4 if they show against.

Now, for the purpose of comparison I want to analyse both the scores. Self assessment Vs Assessor scoring, so I want to know how can I do it? I want to measure the over/under estimation of self assessment or the assessor scoring.

Should I make the assessor score into a scale too? Where -4 to -1 is disagree, -1 to 1 is neutral and 1 to 4 is Agree?
I can't seem to make it a scale of 1-5 to have a uniform score.

I have asked the same question on Cross Validated. UPDATE: Question has been eliminated.


texts: Help understanding expression for continuous discounting

texts:
In footnote 3 of their paper "Patent Breadth, Patent Life, and the Pace of Technological Progress", O'Donoghue Scotchmer and Thisse take a discount rate of $r$ and write

  If the flow of profit $\Delta$ lasts for length $t$, the discounted profit is $\Delta(1 − e^{−rt})/r$.

Can someone explain where the expression $\Delta(1 − e^{−rt})/r$ comes from?

Whilst I am familiar with continuous time discounting, I have never seen it formulated in this way before. I would usually expect the expression for discounted profit to be $\Delta e^{-rt}$.


texts: What is the difference between knowledge and information?

texts: I believe this distinction may have been made by Hayek or some other Austrian.


texts: How are fund managers usually compensated against benchmark?

texts:
I have heard that fund managers who invest clients' wealth are usually compensated according to how well they perform against a benchmark.

What exactly is the (most typical) payoff function for fund managers as compensated against benchmark? E.g. the 20, 2 rule for hedge funds, what is the exact number over which they get 20 percent? Is it the amount that they earned more compared to what they would have earned if they just inveated in a benchmark index?


texts: Empirical Data on Demand for Minimum-Wage Jobs in the USA

texts:
The idea of a minimum wage and its effects in terms of supply and demand are well-known in mainstream economic theory.

I'm constructing an argument regarding the minimum wage, and what I'm curious about is whether there is actual empirical data that indicates that demand for minimum wage jobs is greater than their supply, and if so, by how much? I'm looking for data particular to the U.S., but if such data exists for other countries, that would be helpful too.


texts: WAPM and CRS across all production plans

texts:
In Hal Varian's Book "Microeconomic analysis" on page 35 he gives the following description of a profit maximising firm.

  ...If the firm is maximising profits, then the
  observed net output choice at price pt must have a level of profit at least as
  great as the profit at any other net output the firm could have chosen. We
  don't know all the other choices that are feasible in this situation, but we
  do know some of them-namely, the other choices $y^s$ for $s = 1,. . . , T$ that
  we have observed. Hence, a necessary condition for profit maximisation is
  that
  $$p^ty^t\ge p^ty^s$$
  for all $t$ and $s=1,...,T$

  We will refer to this condition as the Weak Axiom of Profit Maximisation
  (WAPM).

In the case of a firm which has a production function with one input and one output where $p=w$, such that $p$ is the price the output is sold and $w$ is the price of the input across all production possibilities sets. Can such a firm be called profit maximising at any level of output?


texts:
Consider the Correlated Random Effects model $y_{it} = \alpha + x_{it}\beta + \bar x \gamma + w_i + \epsilon_{it} $ where $x_{it}$ is a scalar explanatory variable.

The correlated random effects GLS estimator $ \hat \beta_{CRE} $ is the OLS estimator of $\beta$ in the quasi-demeaned regression

$\tilde y_{it} = \delta + \tilde x_{it} \beta + \bar x_i \rho + u_{it} $,

where $\tilde y_{it} = y_{it} - \theta \bar y_i , \tilde x_{it} = x_{it} - \theta \bar x_i $ and $\theta = 1 - (\sigma^2_\epsilon/ (\sigma^2_\epsilon + T\sigma^2_w))^{1/2} $

Question: I need to show that the residuals from the regression of $x_{it} - \bar x_i $ on a constant and $\bar x_i $ is just $x_{it} - \bar x_i $ itself.

Attempt: Regress $x_{it} - \bar x_i = \alpha + \bar x_{i} + \tilde r_{it} $ rearrange to get the residuals, $\tilde r_{it} = (x_{it} - \bar x_i) - (\alpha + \bar x_{i})$ I'm not sure how to proceed.


texts:
https://en.wikipedia.org/wiki/Tendency_of_the_rate_of_profit_to_fall

The tendency of the rate of profit to fall (TRPF) is a hypothesis in economics and political economy, most famously expounded by Karl Marx in chapter 13 of Capital, Volume III.[1] Economists as diverse as Adam Smith,[2] John Stuart Mill,[3] David Ricardo[4] and Stanley Jevons[5] referred explicitly to the TRPF as an empirical phenomenon that demanded further theoretical explanation, yet they each differed as to the reasons why the TRPF should necessarily occur.[6]

Now, I have some years trained as an economist; but, find the whole fuss around the TRPF somewhat strange. Marx lived in a time of a non-fiat economy. The inherent value of one kopiejek or what have you was based on how much bread it could exchange. Nowadays money is defined to be a unit of account maintained by trust in the FED. Hence, inflation targeting.

So, did Marx really miss the memo about credit? Can someone help me better understand where am I getting this concept wrong as so many think this is the cornerstone of Marxian economics.


texts: An index of the The Economist's Schools Brief series

texts:
I was wondering whether anyone might have an index of the articles that made up the The Economist's Schools Brief series that ran from 1975 to 1999 (with a brief refresh in 2013)?

They were an interesting set of articles that explained economic concepts (with a free market slant, of course, being The Economist) in an easy and accessible form.


texts: Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?

texts:
As we know that $Q*P=const.$ for Cobb-Douglas preferences, we can thus conclude that $\frac{dQ/Q}{dP/P}$ is always $-1$:
$$
QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P}
$$


texts: Gelman and Hill's Data on Effects of Child Support Enforcement

texts:
In Gelman and Hill's 2007 book, Data Analysis Using Regression and Multilevel/Hierarchical Models, chapter 11 begins the exploration of multilevel models. To do so, they introduce a data set that relates city level child support enforcement policies to individual outcomes. Because the treatment is at the city level, this serves to show how sometimes it is good to model the city level effects (at the higher level of the hieratchical model) and then model those as having effects on individuals (the lower level). I'd like to follow along but the data set doesn't seem to be in either of the two places on Gelman's website where he keeps data:

Data and software for the examples in the book
More data and software for the examples in the book. (Sorry we're a bit disorganized right now!)

Anyone know where to find these data?


texts:
I am interested in understanding the differences between mainstream economics and marxist economics. For that, a guide about what is central to the marxist economic theory (not political or cultural theory) would be highly useful.

What are the core elements of Marxist economics?

PS: my emphasis on core aims to avoid this question being flagged as "too-broad". I also hope there is sufficient consensus within theorists in order to avoid being "primarily opinion-based".


texts: Net Present Value with investments in multiple phases

texts:
I am trying to calculate the Net Present Value for a theoretical project in which, unlike most examples in textbooks and on internet tutorials, investments do not only happen in t=0, but they also occur in later years.

My assumption is that investment expenditures occur at the beginning of each year, while operating expenditures (incomes minus costs) occur at the end of each year.

I have tried to illustrate that with the image below. The image shows the t=0 point, the 3 years considered in the analysis and the facts that the Investment expenditures (Inv) occur at the beginning of the year, while the operating expenditures (op) at the end.

My question then is, would the following formula be correct in order to calculate the total NPV of the project? Is it ok to discount the $Inv_y$ costs with the $(1+d)^{y-1}$ and the $Op$ with $(1+d)^y$?

$$NPV = - \sum_{y=1}^{y=3} \frac{Inv_y}{(1+d)^{y-1}} - \sum_{y=1}^{y=3} \frac{Op_y}{(1+d)^{y}}$$

For me, it makes sense since, for instance, the $Inv_1$ occurs "now", while the $Op_1$ occurs 1 year later. A similar thinking applies to the rest of the $Inv$ and $Op$ expenditures.

Any feedback will be greatly appreciated!


texts: Wages, capital: Substitution and Output Effects

texts:
Consider a CES production function $Y=f(K,L)$ with elasticity of factor substitution $\sigma>0$.

The substitution effect of higher real wages naturally implies a shift along the isoquant to more $K$. The rise in costs will reduce output. The total effect of $w \uparrow$ on $Y$ and $K$ is the sum of this substitution and output effect.

I'm interested in the link between the value of $\sigma$ and the strength of these two effects. Does anyone know a good reference, or lecture notes on the algebra of these effects in the CES context?


texts: Who paid the bill for cheap Chinese exports?

texts:
We have all enjoyed the flow of cheap Chinese imported goods, whether in the shops, or online.
The shipping costs from China have always seemed very low.
Now I see this note:

Got notification today that all USPS international GEPS contracts will be terminated September 31st.
This is all related to the Universal Postal Union agreement that allows Chinese sellers to ship products to the U.S. for less than it costs us to ship to the same state.
The administration has given the UPU an ultimatum, that they: either allow the USPS to set rates for China mail that arrives in the U.S., or the U.S. will officially leave the UPU on October 17th.
Either way, this means as of October 17, no more cheap Chinese shipping. They will have to pay the same domestic rates as us once their e-packets arrive here.
This is great news for U.S. sellers, especially eBay sellers.

My question is: Who paid the bill for cheap Chinese export shipping?


texts:
Should mean wages increase with inflation?
If not, why? Has this profound consequences in the redistribution of wealth?
(not an expert in economics...I apologise is the question is too naif)


texts: Taking the derivative of capital per effective unit of labor in the Solow model

texts:
I'm taking an intro macro course, and my calculus is pretty rusty.  I'm going through some lectures notes right now where they derive the growth rate of capital in the Solow model like so:

I'm wondering what the process is for getting to the very first step where they take the derivative with respect to time.  Generally, are there good resources for learning how to do this, as I imagine I'll be doing it a lot?


texts: Instrumental variable regression: How many interpretations?

texts:
I was reading Amemiya "Non-linear regression models" (1983) in which he says that

This statement should not be construed as a criticism of Theil's
interpretation. I know of at least  six more interpretations of 2SLS:
a certain interpretation works better than others when one tries to
generalize 2SLS in a certain way. Thus, the more interpretations, the
better.

Does anyone have any idea of what these 6 interpretations or at least just some of them may be?


texts: How does Marginal rate of substitution change?

texts: If you are at a point $(x,y)$ where your $MRS(x,y)=3z$, and you later exchange goods to be at point $(x-a,y+b)$, where your $MRS(x-a,y+b)=z$, can you conclude that you are one the same indifference cure, different one, or is there no conclusion possible?


texts: Monetary Policy and the Yield Curve PART ONE

texts:
As I understand it the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations.

I'm trying to understand how the yield curve is affected:

The Fed Fund rate is the overnight rate at which reserve balances, held by banks at the fed can be lent to each other. The shortest maturity that the treasury yield curve has is 1 month (no overnight). Are expectations regarding overnight fed funds rates reflected in the 1 month yields? I would suppose so, because if the government raises fed funds, their intentions are to influence and increase interest rates in general. Thoughts?

The discount rate is the interest the Fed charges other banks to borrow money. Does the 'discount rate' relate to the commercial paper listed here?. Am I correct in thinking that the discount rate refers to short term borrowing < 1year and that changes in the yield curve at maturities greater than 1 year may not be directly correlated to changes in fed funds or discount rates? (because these are not tools for influencing long term rates)

Finally I understand that changes in the curve at longer maturities may reflect the governments 'open market operations' and their buying and selling of US securities.

Any help solidifying this understanding would be much appreciated.

PART 2 TO THIS QUESTION HERE


texts: Do countries have an obligation to match their savings and consumption rate with that of the U.S.?

texts:
https://www.barrons.com/articles/europe-is-now-a-bigger-trade-villain-than-china-51558118723

The above articles state that trade imbalances are a bad thing and that if a government doesn't enact social and economic policies to make sure people are spending more instead of producing more it will lead to trade surpluses and these trade surpluses are a bad thing. The article mentions a decline in social aid spending and policies towards improving its manufacturing competitiveness. How does any of this make any sense? Is this just an opinion or do most economists agree with this assertion that countries should aim to reduce surpluses through consumption if a country like the U.S. has a major savings deficit?


texts: Kuhn-Tucker conditions in linear cost minimization

texts:
Suppose we have the production function $f: \mathbb{R}^{2} \to \mathbb{R}$ given by
$$
f(x,y) = ax + by
$$
and input prices $p_{1}$ and $p_{2}$, and we want to minimize the cost function $p_{1}x_{1} + p_{2}x_{2}$ such that $ax + by \geq \alpha$ where $\alpha \in \mathbb{R}$ is some production level.

Taking the Lagrangian
$$
\mathcal{L} = p_{1}x_{1} + p_{2}x_{2} + \lambda(\alpha - ax_{1} - bx_{2})
$$
and the Kuhn-Tucker first order conditions are $p_{1} - \lambda a \geq 0$ and $x_{1} \geq 0$ (but both can't be non-zero), $p_{2} - \lambda b \geq 0$ and $x_{2} \geq 0$ (without both being non-zero) and $\alpha - a x_{1} - bx_{2} \leq 0$ and $\lambda \geq 0$ (but both can't be non-zero).

How would we divide up our cases here to check whether we get a corner or interior solution? It's easy to see that the constraint has to be binding since we're minimizing cost and our objective function is strictly increasing in $x_{i}$, but how do we check the cases whether $x_{i} = 0$ or $x_{i} > 0$ for $i = 1$ or $i=2$ (or both).


texts:
I am new to investing on the market so I am doing some research and studying. From what I can tell, the purpose of a collar strategy for options trading is to protect your gains you've made on the underlying stock.

If you want to protect your gains, why would you not simply buy an OTM put?

Is the purpose of writing a covered call in a collar strategy to offset the premium cost of the put?

Edit: To clarify, why would you write a call to possibly cap your gain and lose your shares if your goal is to protect from loss?


texts:
Suppose we are given a set of observations on income $X_{i}$ and consumption $Y_{i}$ and we plot all the $(X_{i},Y_{i})$ on a graph. We want to draw a sample regression function as close as possible to the existing yet unknown population regression function. Why is it considered wrong to take $\sum \hat u_{i}$ as small as possible to draw our regression function?

My study book says that this method assigns "equal weights" to the $\hat u_{i}$ which is not accurate. However, I also agree with the least order square method.

Anyone have a specific example to show me that the normal summation method leads to bad estimation?


texts: The effect of structural unemployment on revenue from value added tax

texts: Bill Gates and European countries have shown favor for consumption/VAT taxes. The arguments given by proponents are often something along the lines that "we know how to tax certain items more than others in a way that has the least negative impact on the economy but still maintains the necessary amount of revenue". But this seems to me more of something an accountant would say rather than an economist. For example, the U.S. might have placed a higher consumption tax on metal washboards in the 20's than shampoos. (A sudden drop in washboard manufacturing causes structural unemployment). Then the electronic washer comes in making the revenue collected from washboards decrease rapidly. In other words, the value of an item often changes over time. How does the government respond to the loss in revenue in a timely manner? I couldn't find research on this so I feel like I am missing some assumptions.


texts:
Follow on to this question.

Using similar constraints:

  The constraints regarding the system I'm modeling are (and looking for a general solution to):

  Marginal Utility for every unit of a good must be positive (or zero), finite, and declining (though never to below zero).
  The available quantities of all goods must be finite, though they can be arbitrarily large.
  2.a There can be an arbitrarily large, though finite number of other goods in the system.
  Aggregate Utility must increase for all, while individual utility must decrease for all except one (the "monster") when a good of a certain class (let's say "cars") is transferred from any member of the group to the "monster".
  Condition 3 should be met for all transfers of "cars" from "innocents" (people not the monster) to the "monster", to the exhaustion of "cars" from the system.

The Difference

Let's replace the "monster" with a group of individuals, still in the minority.

Can a mathematical relationship be defined between their utility function over a good (x), and their representation in a population (p), that sets lower bounds for the existence of a class of "utility monsters".

For example, if members of the "monster" group a have function $u(x)=Ax+\frac{b}{x^2}$ and members of the innocent (i.e. non-monster group) have utility function $v(x)=Cx+\frac{d}{x^2}$, can we describe the ratio of $M:I$ (where $M$ is the size of the "monster" group and $I$ is the size of the "innocent" group) that allows $M$ to exist as a "utility monster" class solely in terms of $A$, $b$, $C$, and $d$?

This is basically a question in regards to constructing non-Pareto economies in simulation.