texts: Explain some All countries excluding residents in BIS Debt Securities Data

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In the BIS Debt Securities statistics:

In both column "issueresidence" and column "issuenationality" there is a category called "All countries excluding residents". I do not understand what it means. What is it used for? although I have read through the report going with the data.

Many thanks for your help!


texts: What is was the total corporate Income earned in the United States in 2014?

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What is was the total corporate income earned in the United States in 2014?

The question may seem simple, but I have been looking for a reliable source to inform me of this figure, and I hope someone out there can help me find a reliable figure and source.


texts: Is there a term for economic policy design built from minimizing per-household adverse impact?

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May be easiest to start with an example: let's say I'm looking to eliminate the mortgage interest deduction, but want to minimize the impact on households from doing so. I also want the change to be revenue-neutral, so I decide to offset the change with reductions to personal income tax rates.

The simplest way to do this would be to take the \$70B MID expenditure and reduce income tax rates across the board by \$70B / \$1.5T existing personal taxes, or ~5%. But MID currently benefits some income groups more than others, so this approach wouldn't minimize the adverse impact per household. To do that, we might look for the current distribution of MID benefit, and then tweak tax brackets accordingly optimizing for some loss function like median % reduction in after-tax income.

Is there a term for this type of policy design/analysis? It doesn't quite seem like Pareto optimality to me.


texts: Why are demand and supply curves shown as concave up?

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Why is it that demand and supply curves are typically shown in graphs, including in Econ 101, as concave up (i.e., convex)?

I know what it entails mathematically—that if $p(q_d)$ is a demand curve, $p''(q_d)$ is positive, and if $p(q_s)$ is a supply curve, $p''(q_s)$ is positive, but what’s the intuition for why that’s usually the case?


texts: Average ability conditioning on having accepted an offer

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There is a continuum of workers between 0 and 1. These have ability $\alpha\sim U[0,2]$. A firm offers them a salary $v$ and has profits
$$
\pi = (\rho \alpha-v) n(v)
$$
where $n(v)$ is the fraction of workers accepting the job at $v$ and $\rho>0$ is a productivity parameter.
Workers accept the offer if the salary is higher then the outside option $2\alpha^2$. Compute the expected profits of the firm.
I think share of people accepting the offer is (by uniformity of $\alpha$):
$$n(v) = \mathbb{P}[2\alpha^2 \leq v] = \mathbb{P}[\alpha \leq \sqrt{v/2}] = \sqrt{v/2}.$$
Expected profits are conditioned on acceptance and so is expected ability, hence:
$$
\mathbb{E}[\alpha \vert \alpha \leq \sqrt{v/2}] = \int_0^\sqrt{v/2}  \frac{\alpha f(\alpha)}{\mathbb{P}[\alpha \leq \sqrt{v/2}]}d\alpha = \frac{1}{4n(v)}\left[\alpha^2\right]_0^\sqrt{v/2}
$$
by definition of conditional probability.
I would like to double check that I am correct here and that average ability given acceptance is not simply the midpoint between $\sqrt{v/2}$ and 0 (i.e. ability is uniformly distributed between the proposed salary and 0). I think that this is incorrect, since acceptance is not uniformly distributed, conditioning on acceptance skews the distribution of ability observed after acceptance.


texts: Perfect competition: Finding short run equilibrium price?

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I am trying to self teach myself some Economics, I am using an old textbook given to me by a friend, which does not contain an answer key. I have run into the following problem and I was wondering if anyone could guide me (I don't want the answers, I just want to understand the method).

The firms in a perfectly competitive industry have a cost function given by:

$c(w_{1},w_{2},Y)= Y^{2} (w_{1}, w_{2})^{\frac{1}{2}} + 8$

Where $(w_{1},w_{2})=(4,25)$

The market demand in this industry is $D(p)=40-p$

The number of firms in this industry are $30$, I'm not sure if this ties in with this half of the question or not.

Anyways, what I have done so far is computed the total cost function:

$TC= 10Y^{2} +8$

From this point, how can I proceed onwards to find the short run equilibrium price?

I would appreciate it if anyone could offer some advice.

Thanks.


texts: What is the mix of maturities of outstanding US Treasury bonds called?

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What is the technical term for the mix of maturities of outstanding US Treasury bonds? Also, is there an "official" source for this information?

I tried searching to find out, but not knowing what the correct term for the maturity mix is, I got no hits.


texts: Mundlak Approach when panel data include time fixed effects

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What would happen when, starting from a panel data model with group fixed effects and time fixed effects I apply the Mundlak approach?

This is the model:

$ y_{i,t} = c + \beta x_{i,t} + \alpha_i + \delta_2 B2_t + \delta_3 B3_t +....\delta_T BT_t +\epsilon_{i,t} $

where $B_t$ are time dummies (time fixed effects).

Should I also include the sample averages for each $B_t$ so that the equation becomes:

$ y_{i,t} = c + \beta x_{i,t} + \gamma \bar{x}_{i} + \delta_2 B2_t + \delta_3 B3_t +....\delta_T BT_t +  \tilde{\delta}_2 \bar{B2} + \tilde{\delta}_3 \bar{B3} +....+\tilde{\delta}_T \bar{BT} +\nu_{i,t}$

wher $\bar{\bullet}$ denotes the sample average computed over each panel for variable $\bullet$.


texts: Labour-saving vs. Labour-augmenting technical change

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I've read a number of posts on the above topic but none refers to published empirical papers. Google searches have been hopeless. Does anyone know of any paper on empirical derivation of technical change indices?

A lot of papers use these terms interchangibly, there is a clear difference between them (labour-saving technical change stems from bias in technical chnage). Using some historical data, I am trying to establish if technical change has been labour-saving or labour-augmenting. However, I've yet to read an empirical paper on the topic.


texts: The Envelope Theorem, Some Workings/Substitution

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I have an application of the envelope theorem below, and would love some feedback on the steps taken to get from (2) - (3) and (3) - (4) and (4) - (5)
The overall question is: 'derive the marginal value for human capital in the second year' using the second-period value function, with parameters:

human capital $k_2$
savings $m_2$
consumption good price $p_2$
labour wage $w_2$
labour supply $l_2$

The value function is given:
(1)              $$V(k_2,m_2;p_2,w_2) = max_{c_2,l_2} u(c_2, l_2)$$
s.t $$ p_2c_2 = w_2k_2l_2+m_2$$
(2) With the budget constraint substituted into the objective we get:
$$V(k_2,m_2;p_2,w_2)=u(w_2,kl_2(k_2,m_2;p_2,w_2+m)/p_2,l_2(k_2,m_2;p_2,w_2)$$
(3) By the envelope theorem
$$\frac{dV(k_2;m_2;p_2,w_2)}{dk}= [\frac{d}{dk}u ((w_2kl_2+m_2)/p_2,l_2]_{l_2=l_2(k_2,m_2;p_2,w_2)}$$
(4) $$= [u_c((w_2kl_2+m_2/p_2,l_2)\frac{w_2l_2}{p_2}]_{l_2=l_2=(k_2,m_2;p_2,w_2)}$$
(5) $$=u_c(k_2,m_2;p_2,w_2),l_2(k_2,m_2;p_2,w_2))\frac {w_2l_2(k_2,m_2;p_2,w_2)}{p_2}$$
Screenshot uploaded for clarity


texts: Is the mid-market currency exchange rate something real? Or are bid and ask rates the real rates?

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Reading from this and other sources, it appears to me that there are three different ratios between any two currencies, namely

the bid rate
the ask rate
the real rate

My understaning is that the two primal ratios are 1 and 2, while 3 is just a derived quantity, specifically the mid-point between the former two. In other word, I understand that 1 and 2 are the two real, market-driven numbers, and that 3 is just a convenience to know where 1 and 2 roam in that specific historical moment.

Is my understanding correct?

In the following I just report my line of reasoning.

For instance, if I have an amount $A_1$ in one currency and I want to exchange it with another currency, I would receive the amount $A_2$ in this other currency, defined as

$ A_2 = E_{1 \rightarrow 2} A_1$

where $E_{1 \rightarrow 2}$ is the exchange rate.

If I change my mind and decide to convert $A_2$ back to the previous currency, then I will be given the amount $\overline{A_1}$,

$ \overline{A_1} = E_{2 \rightarrow 1} A_2 = E_{2 \rightarrow 1} E_{1 \rightarrow 2} A_1$

I've understood that, if we leave the time elapsed between the two operations aside (or if we do the two exchanges at exactly the same moment), we are sure that $\overline{A_1} < A_1$, because we are sure that in any given moment in time the following holds:

$E_{2 \rightarrow 1} < \displaystyle\frac{1}{E_{1 \rightarrow 2}} \tag{1}$

Is this true?

To me it seems obvious, since if $(1)$ had an equal sign, that would mean that I can freely exchange between currencies at zero cost (hence I could lose or earn money only as a consequence of the change of that unique rate over time due to other factors).


texts: Relationship b/w consumption & increase in interest rate

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Please help me clarify this-

Case 1 - If interest rates increase then people will save more to reap the benefits and will cut down on their consumption(C) so Consumption will fall.

Case 2 - Due to high interest rates - For every rupee saved, people's incomes will increase and their net wealth rises as a result of which consumption will increase.

so, Will consumption rise or fall with increase in interest rate? which case is likely to be more true and why? If we get an objective type question in exam which one should we mark?

Thank you so much for your help & support


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

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


texts: Does the Tax Allowance Benefit Everyone (Regardless of Their Income)?

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Note:

This question is in the context of the UK and its policies.

I understand that if your income is below the tax allowance (£11,000), you pay no income tax. However, I think my textbook is also trying to say that if your income is above the allowance, you only pay income tax on whatever is left after the allowance has been deducted from your total income. Is this true?

Oh, and I was also wondering if there was any difference between the 'personal tax allowance' and the 'tax allowance'.

Thanks


texts: Negative elasticity of substitution in a CES production function

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I have empirically estimated the elasticity of substitution parameter in the following model:
$$Y_t=[(A_1L_tK_{t})^{\rho} +(A_2M_{t})^{\rho}]^\frac{1}{\rho}  $$

here, $Y_t$ is output, $A_i$ is a factor-augmenting technology index, $K, L$ and $M$ are factors of production and the elasticity of substitution is $\sigma = 1/(1 - \rho)$. I estimated $\rho$ combining the logorithmised form of the above function and its FOC conditions in a system of nonlinear equations.

I am getting $\rho>1$ which gives a negative elasticity of subsitution, $\sigma<0$.
I am now struggling to put a plausible interpretation on this result; theoretically, the lower bound for $\sigma$ is 0.

I am guessing that I could still interpret the negative $\sigma$ as an evdience that factors are strong complements. Would this be a correct interpretation?


texts: regression method for data that contain a number of observation for several years

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I have a data set about 125 companies. For each company I have the salary and some other variables about the top 5 managers in each company.
One observation contains the top 5 managers in each one of the 125 firms  from 2010 to 2018, so every company has the data for its managers for each year.
For some companies some years are missed or it is for less than top 5 managers.
I want to check the effect of a regulation that occurred in 2016, and my question is :

Is it OK to do linear regression for the observations before 2016 at once ?,
I am not sure about that because every year has the same companies with the data of that year.

Can anyone tell me if it is Ok to do that or help by advising another regression method


texts: Ok to normalize GDP change by population change?

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Does it make sense to normalize change in real GDP by the contemporaneous change in population?

I'm interested in this calculation for the following reason. Suppose real GDP increases. I'd like to know what was the population increase that corresponded to this increase. I could then compare two distinct geographic regions, specifically two states in USA during a given time period. If one state increased real GDP by A dollars per person (as calculated above) while another increased it by B dollars per person, then I could declare that the first state was, in a sense, more productive or more efficient.

If g was the growth rate in real GDP and r was the population growth rate, I could alternatively calculate (1+g)/(1+r) and compare states according to this measure. A comparison based on this ratio is essentially the same as a comparison based on g-r: Just perform the algebraic division and subtract a 1 to get g-r. However, I feel that g-r doesn't have the same intuitive appeal as the method described in the previous paragraph. A numerical calculation on actual data shows that the two measures have a low correlation (of 0.2) ....

The method in the first paragraph produces numbers that are on the same footing as GDP per capita and moreover, these calculations can be compared to GDP per capita for an intuitive understanding.

For example, during 2010-2014, the change in real GDP divided by the change in population was 108,000 dollars in USA whereas 2014 GDP per capita was 49,000 dollars. For Pennsyvlania, the calculation resulted in 320,000 dollars versus GDP per capita of 47,000 dollars. For California it produced 114,000 dollars vs GDP per capita of 54,000 dollars.

Here's how I think about it. In 2010, USA real GDP per capita was 45,000 dollars or thereabouts. From 2010-2014, each person that was added to the population corresponded to a real GDP increase of 108,000 dollars.

To get fancy, if there hadn't been any population increase, real GDP might have grown by a certain amount. If we could estimate that amount, we could subtract it from the aforementioned 108,000 dollars and then say with more confidence that each person that was added to the population "caused" real GDP to increase by that much.

By analogy, imagine a 100 men were laying bricks (GDP) on top of one another. Each man could lay 10 bricks per hour. Now, 3 younger, stronger men are added to the workforce who can lay bricks at the rate of 50 per hour. The calculation that I am proposing would produce a number analogous to 50 which could then be compared to the number 10 so as to distinguish between the previous stock of labor and the new stock.

If you'd like to replace population with employed population, that would be fine ... It's has a secondary role in my question.


texts: Solving Utility Maximization with Lagrangian

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I know how to solve the 2 variable constrained optimization problem using MRS = MRT, but I also want to make sure I understand how to do it with the Lagrangian method.
So if I have the following problem
$U(x) = \alpha\ln(x_1) + (1-\alpha)\ln(x_2)$
with $p_1x_1 + p_2x_2 = w$
I got the answer using the MRS = MRT method as $x_1 = \frac{w\alpha}{p_1}$ and $x_2 = \frac{w(1-\alpha)}{p_2}$.  I am a bit confused on how to set up the Lagrangian.  Here's what I did
So $L = \alpha\ln(x_1) + (1-\alpha)\ln(x_2) + \lambda(w - p_1x_1 - p_2x_2) + \mu_1x_1 + \mu_2x_2$
$\frac{dL}{dx_1} = \frac{\alpha}{x_1} + p_1\lambda + \mu_1 = 0$
$\frac{dL}{dx_1} = \frac{1-\alpha}{x_2} + p_2\lambda + \mu_2 = 0$
$\frac{dL}{d\lambda} = w - p_1x_1 - p_2x_2 = 0$
$\frac{dL}{d\mu_1} = x_1 = 0$
$\frac{dL}{d\mu_2} = x_2 = 0$
Here is my issue here.  If I assume $x_1$ and $x_2$ cannot be 0 and I somehow assume $\mu_1$ and $\mu_2$ are 0, then I can solve it pretty easily.  I then just equate the $\lambda$ in the first two equations and then plug into the budget constraint like in the MRS = MRT case.

However, what gives me the right to make $\mu_1$ and $\mu_2$ equal to 0?  Is this the correct approach?  When are they not 0?

I heard in order to use the Lagrangian method, some "conditions" need to be satisfied.  What conditions need to be satisfied?  How do I verify this?  Is this related to differentiability?

Is there some restrictions on what $\lambda$ and $\mu$ can be?

Thanks!


texts: What do game theorists think of behavioural economics?

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Though behavioural economics has been popularized over the past decade in both industry and pop culture, it seems that not much has changed with regard to the standard economic definition of  rationality.

This is because for the most part (in my view and experience with my professors) it seems to have been irrelevant or unconvincing for the game theorists who deal with very similar theory to the behavioural economists. This is where a "super-micro" theory of consumer and prodoucer behaviour is generated and analysis takes place.

Now im not a huge fan of behavioural economics, but points like discontinous time preferences and prospect theory are useful for adding a degree of realism to models.

This all being said, (except for a few articles on behavioural game theory) why has a large chunk of young game theorists decided to stay away from "behavioural" elements?


texts: Solow Model, Growth rate of K/L and Y/L in steady state

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I have been given the following setup:

$$ Y=K^\theta (AL)^{1-\theta }$$

Where Y = Output, K = Capital, L = Labour and A = Productivity.

$$ \frac{\dot{L}}{L} = n $$
$$ \frac{\dot{A}}{A} = g $$

The Capital Accumulation Equation has also been given as:

$$ \dot{K} = sY - \delta K $$

Using this, I have calculated expressions for capital per worker and output per worker in the steady state as:

$$ \frac{K}{L} = A(\frac{s}{n+g+\delta })^{\frac{1}{1-\theta }} $$

$$ \frac{Y}{L} = A(\frac{s}{n+g+\delta })^{\frac{\theta }{1-\theta }} $$

The next questions asks: Calculate the growth rates of capital per worker and output per worker that will hold as the economy moves along a steady state growth path.

This is confusing because I was under the impression that growth of capital and labour is the steady state is 0, and then therefore growth of K/L and Y/L should also be 0. However this seems wrong and I believe the answer should be g. Can anyone help please?


texts:
From investopedia: "YTM is the total return anticipated on a bond if the bond is held until it matures"

I have also seen this interpretation used in other sources however this seems wrong to me.

More specifically the I don't see how the anticipated rate of return can be independent from the cost of capital.

What I get from the math is that YTM expresses the cost of capital required for the net present value to be zero.

If the YTM is low then I can probably use a higher discount rate when calculating the present value of the bond. But using a higher discount rate than the YTM, by it's definition means a lower present value and therefore a negative net present value.

If the YTM is high enough then I will most likely use a lower discount rate, meaning a  higher present value and therefore a positive net present value.

Is my understanding correct?


texts: Ordering of bundles for which the axioms of transitivity, continuity, strong monotonicity and convexity are valid

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Let there be two bundles which are obtained from the sequences $x^n = (x_1,x_2)= \left( 2 + \frac{1}{n},5 \right)$ and $y^n = (y_1,y_2) = \left(4 + \frac{2}{n}, 5 \right)$. Is it possible to obtain an ordering of the bundles such that the axioms of transitivity, continuity, strong monotonicity and convexity are respected?

My attempt:

Suppose the preference relation $\succsim$ is lexicographic.

It can be seen that $$4 + \frac{2}{n} > 2 + \frac{1}{n}, \,\, \forall n \in \mathbb{R}_+ $$
Furthermore, at the limit: $$ \lim_{n \to \infty} y^n = 4 > 2 = \lim_{n \to \infty} x^n$$

which means, given that $\succsim$ is lexicographic, that $y \succ x, \forall n \in [1,\infty)$, even at the limit. Therefore, $\succsim$ is continuous.

Furthermore, since $y_1 > x_1, \forall n \in [1,\infty)$, $y_2=x_2, \forall n \in \mathbb{R}_+$ and $y \succ x$, $\succsim$ is also strongly monotonic.

Let $z^n = \left(1+\frac{1}{n},5\right)$. In an analogous manner, since $\succsim$ is lexicographic, $x^n \succ z^n$ and $y^n \succ z^n$ and thus $\succsim$ is also transitive.

Now, let $k^n = \left( 2 + \frac{1}{n}, 4 \right)$ and $$ \begin{align}\tau &= \lambda \cdot x^n + (1-\lambda) \cdot y^n, \lambda \in (0,1) \\ &= \left(4-2\lambda + \frac{2}{n} -\frac{\lambda}{n}, 5 \right) \end{align} $$

Since $x^n \succsim z^n$ and $y^n \succsim z^n$, in order for $\succsim$ to be strictly convex we must have $\tau \succ k^n$, which implies that:

$$ 4-2\lambda + \frac{2}{n} - \frac{\lambda}{n} > 2 + \frac{1}{n} \therefore  2 \cdot (1-\lambda) > -\frac{1}{n} \cdot (1-\lambda) \therefore 2 > -\frac{1}{n} $$

which is true for all $n \in \mathbb{R}_+$.

Thus, the ordering found when considering $\succsim$ to be a lexicographic preference relation is transitive, continuous, strongly monotonic, and convex (strictly convex).

Is my answer correct?


texts: Why not just look at the money supply to calculate inflation?

texts: I see a lot of debate about the right measure to use to determine inflation -- apparently the CPI overstates it, etc. Why not just subtract the GDP growth rate from the money supply growth rate (or to be more accurate, divide 1+R by 1+r)? In the long run, it's supposed to predict inflation perfectly, yes?


texts: When was fractional reserve banking introduced?

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According to Wikipedia's history of banking article:

  Modern banking practice, including fractional reserve banking and the issue of banknotes emerged in the 17th century.

The article on fractional reserve banking seems to suggest that the Bank of Amsterdam is the earliest example:

  In the past, savers looking to keep their coins and valuables in safekeeping depositories deposited gold and silver at goldsmiths, receiving in exchange a note for their deposit (see Bank of Amsterdam). These notes gained acceptance as a medium of exchange for commercial transactions and thus became an early form of circulating paper money. As the notes were used directly in trade, the goldsmiths observed that people would not usually redeem all their notes at the same time, and they saw the opportunity to invest their coin reserves in interest-bearing loans and bills. This generated income for the goldsmiths but left them with more notes on issue than reserves with which to pay them. A process was started that altered the role of the goldsmiths from passive guardians of bullion, charging fees for safe storage, to interest-paying and interest-earning banks. Thus fractional-reserve banking was born.

But it does not state that, nor does the article on the Bank of Amsterdam.

I imagine the exact details might be murky, but I'm looking for a summary of the recognized possibilities. What organizations are candidates for the earliest fractional reserve banking system, and when did they begin their fractional reserve banking?

I also realize that there may have been organizations which did so a long time before it became an established practice. If that's the case, please mention those organizations, but please also summarize who the early pioneers of our present system of fractional reserve banking are.


texts: Triple Difference model using Repeated cross-sectional data

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I have a repeated cross-sectional data from the Demographic and Health Surveys. And I want to run a triple difference model, along the lines of Yelowitz (1995). My identification strategy is such that variation comes from the state of residence of the respondent (1, if state s enacted the policy, & 0 OW), treatment status of the respondent (0,1, naturally we don't have perfect compliance) in the state, and thirdly from the year of the treatment being administered (1 if treated between 1997-1999 and 0 otherwise).
The model then would be pretty standard
$Y_{iast} = \gamma_{st} + \lambda_{at} + \theta_{as} + \delta D_{sat} + X_{iast} \beta + \epsilon_{iast}$
I was under the impression that simply adding dummy variables and then interacting them would suffice. However, given that I am using cross-sectional data, would that mean I would have to convert this into a panel? I find this incredibly confusing since I do not have a dynamic dataset, and all measures are collected at the time of the survey and only one thing changes over time --  the treatment status based on the year of treatment.
I created a dummy variable = 1 if the respondent was treated between 1997-99 and = 0 otherwise. I am not certain if I am getting the right treatment effects here. Also this does not help me understand the parallel trends assumption, rather it further confuses me.
My question is if I wanted to look at the treatment effects of a respondent who was treated in a state with policy = 1 during 1997-99 then wouldn't a single dummy be enough rather than transforming cross sectional data to panel? Thank you!


texts: Why are second price auctions preferred if they don't maximize expected revenue?

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The reasoning usually given for why you would use a second price auction (SPA) as opposed to a first price auction (FPA) is that FPA encourage underbidding while SPA encourage truthful bidding. That is, bidding your true value is a weakly dominant strategy in SPA, whereas in FPA, bidding below your true value is the dominant strategy. See this question.

My question is: why does it matter to the seller whether people bid truthfully or not? Initially, I thought that since SPA induce truthful bidding, they also maximize expected revenue for the seller, which is why a seller would use SPA.  But, according to the revenue equivalence theorem, FPA and SPA generate the same expected revenue. So, shouldn't it not matter to the seller what auction they choose? Why would a seller prefer SPA -- which are generally harder to explain -- if it doesn't generate higher expected revenue?

I can think of three possible explanations:

There's a mismatch between theory and the real world. Maybe in theory SPA and FPA should generate the same revenue, but in practice they don't. If so, is there any empirical research that shows this?
The seller's goal is to collect information rather than to maximize revenue. Maybe the seller has a product and they don't know how much to sell it for. In that case, an SPA could help them generate an accurate demand curve.
To benefit the buyer. If there's no cost to the seller in terms of revenue, but a benefit to the buyer, a seller might want to use SPA. But this leads to the question: why does the seller care about helping the buyer? Maybe in order to encourage more buyers to participate in the auction? And, possibly encouraging more buyers to enter the auction would raise the expected revenue from the auction, if those new buyers were higher bidders.

Since SPA are so common in online advertising (google adwords) and eBay, they might be the most widely used auction there is today. So, I'm wondering why sellers prefer them to FPA. Is any of these explanations on the right track?


texts:
Reading through Robert Solow's 1956 paper, entitled "The Theory of Economic Growth", I was hoping to find his fundamental difference equation. I was wondering if the following equation is indeed that very equation, $$\dot{r}=s(r)F(r,1)-nr.$$
In my textbook, the fundamental difference equation is given by $$\dot{K}=f(K,L)-\delta K. \tag1$$
I am having a bit of trouble reading through Solow's paper (am a novice at economics), and was wondering if someone can locate the equation that is similar to $(1)$.


texts: What is the difference between Net Present value and present discounted value when periods are given in infinity $\infty$ . Both are then equal to $\frac M r$?


texts: competitive equilibrium with density functions

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Assume there are two competitive markets for goods a and b. Each consumer will either purchase one unit of a and none of b, or one of b and none of a. Consumers never consume both goods. Utilities are as follows:

$u(x,t) = 1.25 - 0.4t$

$u(y,t) = - (t-0.6)^2$

Valuations are for single units.

Assume the consumers are uniformly distributed over the interval [0.6,1.6] and in the initial allocation of goods, each with $0.6 \leq t \leq 1$ owns a unit of x and each with $t$ in $1.1 \leq t \leq 1.6$ own one unit of y. Find the competitive equilibrium.

What is throwing me off here is how to include the probability density of the initial distribution of goods.


texts:
I am trying to reconcile the derivation of a demand equation with what I actually run in an OLS model. After solving  $$max_{x_1,x_2}U(x_1,x_2)= \alpha ln(x_1) + \beta ln(x_2)$$ subject to $$p_1x_1+p_2x_2=m$$ I get the familiar derived demand equation $x_1^*=p_1m\frac{\alpha}{\alpha+\beta}$. So far, this lines up with intuition. I see a price, an income, and some parameters. However, for a lot of goods that are estimated in the literature via OLS, economists also include demographic information like race, age, and sex. How can this be justified by the demand equation? The only two options I see are that income or the parameters are functions of these variables. Typically, most data sets will have some measure of income observed so that rules income out, and leaves only the parameters. Does this mean when I write an OLS equation like this $$X_i=\beta_0 + \beta_1 M_i + \beta_2demographics_i$$ I am somehow implicitly imposing that my $\alpha$ and $\beta$ from above are functions of demographics?

Thanks for any input. I'd also really appreciate any papers/articles that talk about this topic specifically, so far I haven't had any luck finding them.


texts:
It is possible for the interest rate to affect the expenditure with consumption. An increase in the interest rate could, in principle, lead to increases in savings and, that way, to a decrease in consumption, given the income level. Suppose that consumption is, indeed, reduced by an increase in the interest rate. How will the IS curve be affected?
Considering the following equation for the IS curve:
$$
Y=C(\overbrace{Y−T(Y)}^{+})+I(\overbrace{r}^{-})+G+NX(\overbrace{Y}^{-})
$$
I assume it would be changed to
$$
Y=C(\overbrace{Y−T(Y)}^{+}, \overbrace{r}^{-})+I(\overbrace{r}^{-})+G+NX(\overbrace{Y}^{-})
$$
And thus, what was
$$
\frac{dY}{dr} = \frac{dI(r)}{dr} < 0
$$
now is
$$
\frac{dY}{dr} = \frac{dC(Y-T(Y), r)}{dr} + \frac{dI(r)}{dr} < 0
$$
and, therefore, the curve now is more downward-sloping than before.
Is this right? Kinda feels like I am missing some indirect effect.
Thanks!
EDIT: I was on the right track, but not correct. The trick is to apply the total derivative.
Going from $Y = C(Y-T(Y)) + I(r) + G + NX(Y)$, we have:
$$
\operatorname{dY} = \underbrace{\frac{\partial C(\cdot)}{\partial Y}}_{\equiv C_Y > 0} \cdot \operatorname{dY} + \underbrace{\frac{\partial I(\cdot)}{\partial r}}_{\equiv I_r < 0} \cdot \operatorname{dr} \therefore \operatorname{dY} - C_Y \cdot \operatorname{dY} = I_r \cdot \operatorname{dr} \Leftrightarrow \boxed{\boxed{\frac{\operatorname{dr}}{\operatorname{dY}}\bigg\vert_{IS} = \frac{1-C_Y}{I_r} < 0}}
$$
Now, with the new equation, we have:
$$
\operatorname{dY} = \underbrace{\frac{\partial C(\cdot)}{\partial Y}}_{\equiv C_Y > 0} \cdot \operatorname{dY} + \underbrace{\frac{\partial C(\cdot)}{\partial r}}_{\equiv C_r < 0} \cdot \operatorname{dr} + \underbrace{\frac{\partial I(\cdot)}{\partial r}}_{\equiv I_r < 0} \cdot \operatorname{dr} \therefore \operatorname{dY} - C_Y \cdot \operatorname{dY} = (C_r + I_r) \cdot \operatorname{dr} \Leftrightarrow \boxed{\boxed{\frac{\operatorname{dr}}{\operatorname{dY}}\bigg\vert_{IS'} = \frac{1-C_Y}{(C_r + I_r)} < 0}}
$$
Since $|C_r+I_r| > |I_r|$, the IS curve is now flatter and thus the income responds more to changes in the interest rate than before.


texts: Bernoulli transformation in " A Close Form Solution to the Ramsey model" by Smith (2006)

texts:
I am trying to understand the way Smith arrived from (1) and (2) to (6) and (8).

Could anyone give me a hint? Thank you!

  It is well known that the dynamics per capita consumption $c$ and capital $k$ are determined by the following pair of differential equations:
  \begin{eqnarray}
\dot{k} &=& k^\alpha - \delta k - c \tag{1} \\
\frac{{\dot c}}{c} &=& \sigma(\alpha k^{\alpha - 1} - \delta - \rho) \tag{2}
\end{eqnarray}
  A Solution

  The system of equations (1)-(2) is dauntingly nonlinear. To approach a solution, define the capital-output ratio (a Bernoulli transformation) by $z = k^{1-\alpha}$ and the consumption-capital ratio by $x = c/k$. Using these  transformations the system can be rewritten as
  \begin{eqnarray}
\dot{z} &=& (1-\alpha)[1 - (\delta + x)z] \tag{6} \\
\frac{{\dot x}}{x} &=&  \frac{\sigma \alpha - 1}{z} + \delta (1 - \sigma) - \rho\sigma + x \tag{7}
\end{eqnarray}
  The Bernoulli transformation converts the capital accumulation equation [Equation (1)] into the linear, albeit non-autonomous, differential equation in Equation (6). Despite this simplification, the system still does not allow an analytical solution. Equation (7) is still non-linear.

  Suppose, however, that $\sigma = 1/\alpha$. In that case $z$ disappears from Equation (7), and the system becomes recursive: Equation (7) reduces to
  $$
\frac{\dot{x}}{x} = - \frac{\delta(1- \alpha) \rho}{\alpha} + x \tag{8}
$$
  while $z$ evolves according to Equation (6), given the forcing process $x$ determined in Equation (8). This is a simple, autonomous logistic equation.

Citation: Smith, William. (2006). A Closed Form Solution to the Ramsey Model. Contributions to Macroeconomics. 6.


texts: What happens to a company whose share price goes down to very little over dividend loss?

texts:
This is a bit of an edge case scenario.

Let's say you have a company that is very profitable (and pays very high dividends off the profit) but has little/no growth potential.

The company decides to slash the dividends significantly (to the point that the total yield is super low, lower than most other equity) in order to pay significantly higher wages/benefits to their headcount.

Presumably, the share price of the company would plummet drastically, as nobody would want to own the shares (zero dividend + zero growth means you're better off investing in a savings account, at least outside of negative interest rate countries).

What happens to that company's finances longer term?

Their valuation just shrunk to almost nothing, but they aren't bankrupt as they still have the same cash flow, same same business, same outstanding debt and same profits as before - they merely redirected the profits from dividends to headcount costs.

(let's ignore real-world implications such that the company may start experiencing growth out of better publicity, employees using extra earnings to purchase their products ala Henry Ford-UAW parable, etc...).


texts: How does the Federal Reserve remove money from circulation?

texts:
I was watching a video about what gives money its value, and they say it's the total number of bills in circulation.

The Federal Reserve can print or remove money from circulation. But if somebody owns that money, they can't just take that money away right?  So how do they take money out of circulation?  Is there a limit on how much they can take out?


texts: When plotting a demand curve for a good, lets say carrots with price on the y-axis and quantity demanded on the x-axis. A shift any determinant of demand other than price of carrots results in a shift of the curve. Let us say that determinant in question is income. National income increases and as a result demand for carrots increases (as carrots are a normal good). The shift for an increased demand is referred to as a 'shift to right'. However is this not a vertical shift up. A vertical shift up of the demand curve means that for the same price people will demand more and for the same quantity people will pay a higher price. Is 'a vertical shift up' and 'a shift to the right' just different ways of describing the same movement or does a 'a shift to the right' achieve something different that I have not understood.


texts:
Suppose we assume that production function has a Cobb-Douglass form:
$$Y=A\times K^\alpha\times L^\beta,$$ where $Y$ is output (GDP), $A$ is Total Factor Productivity and $L$ is labor. By log-linearizing the production function we have:
$$y=a+\alpha k+\beta l,$$ where $y=log(Y)$, $k=log(K)$ and $l=log(L)$. Hence, the model that we empirically estimate can be written as:
$$y_t=a+\alpha k_t+\beta l_t+\epsilon_t,$$
where $\epsilon$ is the error term. Suppose applying OLS we have the estimated parameters, i.e. $\widehat{a}$, $\widehat{\alpha}$ and $\widehat{\beta}$.
Question Does only $\widehat{a}$ refer to $TFP$, or the $TFP=\widehat{a}+\epsilon$? As far as I know, $\epsilon$ is also called Solow residual. Please elaborate.
Thanks!


texts: Are prices part of total factor productivity?

texts:
I am trying to understand how production is related to income/profit and where do prices enter. Suppose there is a single firm with a Cobb-Douglas production technology:
$$Y=AK^{\alpha}L^{\beta}$$
Where do prices come into this? I see this being related to whether $Y$ is expressed in units of output or in monetary value (total revenues?). If the former, I would think this means that only $Y\times p$ gives the firm's profit, if $p$ stands for price of output. But if this is the case, can we "absorb" prices into total factory productivity and rewrite everything as:
$$\pi = Y\times p = pAK^{\alpha}L^{\beta} = \tilde{A}K^{\alpha}L^{\beta} $$ where $\tilde{A} = p\times A$?


texts:
I would like to hopefully get some insights on the Anscombe and Aumann Expected utility.

I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers preferences over not pre-determined lotteries or risky outcomes.

However, I don't manage to rationalize this way the Anscombe and Aumann expected utility, although I believe I understand the proof.

Particularly, I would like to know how I can rely heuristically the 'state space' and 'probability spaces' (other than being antecedent and image of the Aumann act).

Also, sometimes 'objective probabilities' are evoked as well as an explanation with horses, that I don't get.

Sorry for this confusing message and thanks a lot!


texts:
A seller owns a single unit of an invisible good. It is worth $v(s)$ to a buyer, where
$s ∈ R^+$ is the quality of the good. The function $v(·)$ is strictly increasing and strictly concave with
$v(0) = 0$. Quality is chosen by the seller, and the cost of providing a good of quality $s$ is given by a
function $c(s)$, which is strictly increasing and strictly convex with $c(0) = c
'(0) = 0$ and $c'(0) < v'(0)$.
(Implicit in this description is the assumption that the buyer’s preferences are quasilinear is some good
other than the one being traded.)

There are many parts to this question, but I'm most concerned about the step up. Which asks write down the first-order conditions to find the pareto optimal quality that maximizes the sum of the utilities and confirm that it is positive.

I'm thinking that the utility functions are as follows:

$u_B(x,s)=x+v(s)$

Where $x$ is dollars spent on anything besides the good that is being traded (like the composite commodity theorem)

$u_S(s)=v(s)-c(s)$

The utility of the seller would just be the value they can sell the good for minus it's cost?

Thus,
$max_s(u_B+u_S)=v'(s)+v'(s)-c'(s)=0$

This results in the following equation:

$2v'(s)=c'(s)$

Which doesn't make sense because of the assumptions of the first derivatives in the statement of the problem. So I'm not quite sure what I am doing wrong. Any assistance would be greatly appreciated. Thanks in advance!


texts: Is a social choice aggregation rule defined for a set of weightings over the set of voters (N)?

texts:
In Christian List's Stanford Encyclopaedia entry Social Choice Theory (2013, https://plato.stanford.edu/entries/social-choice) he says that:

  "an aggregation rule is defined for a fixed set of individuals N and a fixed decision problem, so that majority rule in a group of two individuals is a different mathematical object from majority rule in a group of three."

I was wondering if, in a similar way, social choice aggregation rules are defined for a set of weightings over N? In other words, does a disagreement regarding how to weight the voters entail a disagreement regarding aggregation rule?

E.g. let's say that N = {voter-1, voter-2}. Furthermore, you and I both favour a lexicographic dictatorship. The only difference is that you favour a lexicographic dictatorship which ranks voter-1 over voter-2, and I favour a lexicographic dictatorship which ranks voter-2 over voter-1. Strictly speaking, do we agree on aggregation rule, or do we disagree?

Any help would be greatly appreciated! :)


texts: Total cost function and (dis)economies of scale

texts:
I'm really confused about how I'd tackle this.

I have an equation, $TC(Q) = 100Q + 20Q^2 + 3Q^3$.

And I'm trying to find where the economies of scale, diseconomies of scale and constant return to scale occurs.

My instinct would be to take the derivative of that function, and then set it to 0, and then see what the values to the left and right of 0 are which would be the slope and allow me to see depending on whether or not they're positive or negative whether it's an economy or diseconomy of scale.

Is this along the right road?


texts:
So i have this question on leverage and cost of capital:

Leverage and the cost of capital Gamma Airlines has an asset beta of 1.5. The risk-free interest rate is 6%, and the market risk premium is 8%. Assume the capital asset pricing model is correct. Gamma pays taxes at a marginal rate of 35%. Draw a graph plotting Gam- ma’s cost of equity and after-tax WACC as a function of its debt-to-equity ratio D/E, from no debt to D/E = 1.0. Assume that Gamma’s debt is risk-free up to D/E = .25. Then the interest rate increases to 6.5% at D/E = .5, 7% at D/E = .8, and 8% at D/E = 1.0. As in Problem 21, you can assume that the firm’s overall beta (βA) is not affected by its capital structure or the taxes saved because debt interest is tax-deductible.

The answer sheet is this ( only a part of the table is shown)

..

I understand how they got to the RA and how it doesn't change according to the capital structure.

I also know how to calculate D/V from D/E.

The problem is that i dont seem to understand which formula I should use to calculate RE.

If , for example, i use this formula

RE=RA+(RA-RD)D/E for D/E equal to 0.10 i get

RE=0.180+(0.180-0.06) · 0.10 = 0.192 which is not 0.1941.

Then which formula should i use ?

R=rf+B(rm-rf)?

Why do i need to calculate DV?

Somebody please explain how i can get accurate results of RE using which formula? Thanks i greatly appreciate it.


texts: Calculating the Competitive Equilibrium in a pure exchange economy with 3 comodities and 2 agents

texts:
Consider a pure exchange economy with three commodities and two households with individual endowments
$e_{1}=(1,2,3) \text { and } e_{2}=(3,2,1)$
respectively, and utility functions
$u_{1}\left(x_{11}, x_{12}, x_{13}\right)=x_{11}+2 x_{12}+3 x_{13} \text { and } u_{2}\left(x_{21}, x_{22}, x_{23}\right)=3 x_{21}+2 x_{22}+x_{23} $
respectively.
Which of the following is the competitive equilibrium price vector?
Options:
(A) (3,2,3)
(B) (1,1,1)
(C) (1,2,1)
(D) None of the above
My attempt:
First I tried solving the optimization problem of the first agent
$ max \hspace{0.5 cm} u_{1}\left(x_{11}, x_{12}, x_{13}\right)=x_{11}+2 x_{12}+3 x_{13} \\ \text{subject to} \hspace{0.5 cm} p_{1}x_{1} + p_{2}x_{2} + p_{3}x_{3} = 3p_{1} + 2p_{2} + p_{3}\\
 $
I took three cases:
Case 1:
$
\frac{p_{1}}{1} > \frac{p_{3}}{3} > \frac{p_{2}}{2} \hspace{0.5 cm}  \text{or} \hspace{0.5 cm}  \frac{p_{1}}{1} > \frac{p_{2}}{2} > \frac{p_{3}}{3} \\  \text{Here I took the price level of a good i and divided it with the marginal utility of that } \\ \text{good. From this I concluded that the optimal bundle in this case should be:}   \hspace{0.5 cm} (0,\frac{p_{1}}{p_{2}} + 2 + 3\frac{p_{3}}{p_{2}},0) \hspace{0.5 cm} \\ \text{Now I took other cases as well where I took  the price relation as follows:} \hspace{0.5 cm}  $
$ \frac{p_{3}}{3} > \frac{p_{2}}{2} > \frac{p_{1}}{1} $
But the problem becomes very complicated and difficult to solve. Can somebody guide


texts: Where one can see the world economy sectors comparison by value?

texts: I'd like to know which economy sectors in the world are the biggest. Does such statistics exist? If so, how accurate and up to date is it? If not, what can be used instead?


texts: Strategic form: mixed strategy nash equilibria?

texts:
The question I am dealing with is:

  Find all Nash equilibria in pure or mixed strategies.

This is what I have done so far..

Pure strategy nash equilibria

By observing best responses, the PSNE are $(u2,l2)$ and $(d2,r2)$

Mixed strategies

Solving for $\tau$:

$10\tau +2(1-\tau) = 5\tau +8(1-\tau)$

$\tau^{*}=\frac{6}{11}$

Solving for $\sigma$:

$10\sigma +2(1-\sigma)=5\sigma+8(1-\sigma)$

$\sigma^*=\frac{6}{11}$

Therefore: $(\tau^*,\sigma^*)=\left(\frac{6}{11},\frac{6}{11}\right)$

The correct answer is apparently:

  $(\tau^*,\sigma^*)=\color{red}{(1,1)},\color{red}{(0,0)}$ and
  $\left(\frac{6}{11},\frac{6}{11}\right)$

It seems that the correct answer has omitted my pure strategy nash equilibria. I also don't know how to get $(1,1)$ and $(0,0)$. Any chance you could help me out?

Thanks.


texts: Is there any overlap between evolutionary and behavioral game theory

texts:
Evolutionary and Behavioral game theory are two different techniques. Both seem to be inspired from biology. So is there any overlap between their theory?

Are the two complementary to each other in some way or instead they overlap with each other? Specific examples in real-world domain would be helpful.


texts: Behavioral responses of tax policy on labour supply ( first time doing Difference in Differences)

texts:
I am trying to estimate the causal effects of the The Working Income Tax Benefit (WITB) on the labour supply of married women in Canada. The WITB is essentially equivalent to the EITC.
I am looking at two years in the Survey of Labour Income and Dynamics (SLID), 2006 and 2011. The WITB was implemented in 2007. The SLID is essentially equivalent to the Panel Study of Income Dynamics (PSID) in that it reports the labour market activity of individuals, which is what I'm concerned with.
I was able to retrieve the datasets online using ODESI. (I used "person files") I am using the .dta files.
I would like to conduct a Difference-in-Differences (D-i-D) regression and 1) estimate the probability that the individual was working, and 2) estimate how many hours the individual worked, given that the individual was working.
For 1) I will be using "alhrp28" which denotes annual hours paid during the year of observation.
For 2) I am interested in looking at "alfst28" which tells us labour force status during the year of observation. alfst28 corresponds to four values, "em" (employed), "Un" (unemployed), "No" (Not in Labour force), and ".c"
So the first thing I did was that I loaded both datsets into STATA using the "use" command. I noticed that the number of observations from 54,000 to 47,000 once I loaded the data for both years.
From here, I am stuck...not sure how to move forward.
I found some notes online and they say I need to generate a time dummy. But, I am a little confused. I am using panel data for the years 2006 and 2011.  Do I need to generate a time dummy and run preliminary regressions before doing DiD?
The notes also say to separate treatment from control. I have been asked to do this using high school education. (I realize this doesn't work so I need to discuss why in my write-up).
Do I generate a "treated" variable in STATA?
And, for 2), what commands can I use to condition on whether the individual was employed?
**Note : I have taken graduate level econometrics, and time series. But, my knowledge of causal inference and things like maximum likelihood is quite poor.
Thanks


texts: Questions about the future of macroeconomic modeling and the role of simultaneous equation systems

texts:
I started to study about macroeconomic modeling and I am interested in the following questions. I understand that there are no definite answers to these questions. But I am interested in the opinion of local experts.

Is there a future for DSGE models after the 2007 crisis?

Will DSGE models be replaced by agent-based models?

Does it make sense to study and use in practice the econometric systems of (simultaneous) structural equations after Lucas critique in today's realities?

I would appreciate a reasoned answer and a constructive discussion.


texts: what is the difference between normal OLS simple linear regression and Canonical cointegrating regression?

texts: what is the main difference between simple linear regression and Canonical cointegrating regression. Why we should use Canonical cointegrating regression instead of OLS?


texts: What would be the effects of large wage subsidy paid directly to workers by the state?

texts:
What would happen if the government started paying working people directly to their accounts a monthly subsidy equal to: (net domestic product/total annual manhours)*manhours worked by the worker this month?
Would that equalize the wages across the economy, since companies can reduce labor costs to zero therefore always outcompete a company with high salaries?
Presumably people would still work hard to earn extra income, but it wouldn't be much higher than the base subsidy. Perhaps 1:1.
Would this drive up inflation?


texts:
Consider the following version of the stochastic Ak model written as a Bellman equation:
$$v(A,k)=max\ log(c)+\beta E[v(A',k')|A]$$
$$s.t\ k'+c\leq Ak$$ and non-negatitvities.
$A$ is a stationary first order Markov process. $E[\cdot|A]$ denotes the expectations of · conditional on $A$. We assume that $\beta\in(0, 1)$.
Now we can also show that the value function $v$ can be expressed as $$v(A,k)=\frac{log(k)}{1-\beta}+v(A,1).$$
If we denote $E[v(A',1)|A]$ as $D(A)$, which is a constant (i.e., is only a function of the exogenous parameters of the model and the realization of the stochastic process A, but is not a function of the endogenous variables). Use this and the new equation to substitute into the maximization problem in the Bellman equation. We should get a simple maximization problem in $c$ and $k$.
And what the solution is given as $$v(A,k)=max\ log(c)+\frac{\beta}{1-\beta}log(k')+\beta D(A).$$
Could someone show the steps behind this derivation


texts: Can one bank be the correspondent bank of itself?

texts:
http://www.investopedia.com/terms/c/correspondent-bank.asp

Correspondent bank is like a delegator in a country to operate on behalf of the delegatee who doesn't normally has established business in that country.

However, I heard that for some bank groups, one subsidiary can be the correspondent bank for another subsidiary, especially in the area of clearing. Let's say Deutsche Bank Italy can be the correspondent bank for Deutsche Bank North America.

Does it imply that Deutsche Bank Italy can hold a Nostro account in Deutsche Bank North America or vice versa.

I wonder why would these kind of relationship considered as correspondent? What are the limitations/benefits for banks operating in this way?


texts: Consider the following production function $Q=min \left(\frac{L}{2a}, \frac{K}{4b}\right)$. Let $w$ and $r$ be the wage and rental rate respectively

texts:
The cost function associated with this production function is
$A) 2awQ\\
B) 4brQ\\
C) (wa + 2br)Q\\
D) None\; of\; the\; above$

What I have tried is:
We have the cost function $wL+rK=C$.
Since, here, the goods are perfect compliments, therefore, $\frac{L}{2a}=\frac{K}{4b}$.
Putting the value of $L$ in cost function we would get $\left(\frac{K}{2b}(wa+2br)\right)=C$.
Which would be C option if $Q$ can taken as $\frac{K}{2b}$.
But I'm not sure about that.
 Please confirm?


texts:
Considering that markets open in different time zones, in general the opening and closing times are different.
I suppose that a stock market opening later (in the same day) receive information on the other markets opening earlier.

I think I should take into account this if I want to implement i.e. Granger causality analysis and I have daily stock indices prices. What could be a proper method to approach the problem?


texts: What is the relationship between Marshallian demand and Two-Stage Least Squares Estimation Procedure

texts:
I was reading Varian, and he gives an example of how to find the quantities demanded using a CobbDouglas utility function with observable data, and a question arose: what is the relationship between this approach and simply doing a two-stage regression for price and demand?
Does the Marshallian demand and the regression approach answer different questions?
Does one solve a problem that the other cannot solve?


texts: Was Adam Smith correct about the relative marginal productivities of capital in agriculture, manufacturing, and trade?

texts:
Adam Smith (1776):

No equal capital puts into motion a greater quantity of productive labour than that of the farmer.

After agriculture, the capital employed in manufactures puts into motion the greatest quantity of productive labour, and adds the greatest value to the annual produce. That which is employed in the trade of exportation, has the least effect of any of the three.

In modern language, we might write the above as
$$MPK_{\text{Agriculture}}>MPK_{\text{Manufacturing}}>MPK_{\text{Trade}}.$$
Has there been any research proving/disproving the above assertion (in the context of 18th-century Britain)?


texts: Does the law of supply reject rise in total revenue for goods with elastic demand?

texts:
If demand for a product is elastic( consider the case when the price is low ), lowering the price further increases total revenue.

However, as per the law of supply, low prices cause suppliers to supply less of this elastic demand product.  There will be a shortage and price must increase back to equilibrium price.

Doesn't the law of supply invalidate "total revenue rises with price drops on goods with elastic demand"?


texts:
I have the following task:

At some moment of time (1953), the government of a country (Israel) signs an agreement with
another country (West Germany) stipulating that West Germany would pay reparations to Israel
during the following N years. For simplicity assume that N is large enough, that the amount or
reparations is proportional to Israeli output, and that the economy of Israel reaches the new steady
state while the reparations are stil paid.

Need to use Solow model. But I really do not understand what the change will happen. Probably it is the same as an increase in s. Help is needed.


texts: Is there any way to sufficiently cover the cost of a UBI?

texts:
Note: I'm talking about the cost of a UBI, and the cost only. Not the social benefits, or the political barriers, or all that stuff. Just the cost.

If you've been following American politics for a while, then you've probably heard of Andrew Yang. He wants to give everyone over 18 and under 65 $1000 every month, free and clear, and no questions asked.

However, how do we (or in this case, the government) pay for it ($2.4+ trillion)?

On his site, Andrew Yang suggests the following:

500 billion saved from welfare programs (you either chose UBI or current benefits)
100 billion saved from healthcare related needs
800 billion generated from a VAT
600 billion from economic growth

This all adds up to $2 trillion.

500 billion saved from welfare. Okay. Another $800 billion generated from a tax. Okay.

But what about the $100 billion saved from healthcare needs? Is that an actually reason, which studies to back it up?

Also, at what point do we keep some of that money as profit?

So with all of these factors combined - can we fully pay for a UBI?


texts: Is there a folk theorem for repeated games on networks?

texts:
Games on networks have been studied extensively, however, I was not able to find a folk theorem for games on networks. Is there one or can it be derived from an already existing folk theorem?

With games on networks I mean games in which the payoff of the stage game only depends on the actions of the direct neighbors in a network. Simple examples for that would be the the majority game (in which the payoff depends on the number of neighbors that play the same action as you are) or a prisoner's dilemma played with each neighbor.


texts: Where can I find historical (very old) USD printing data?

texts: Where can I find historical/very old USD printing data? Charts can be useful, but I want numbers. It is for a project.


texts: Cleaning data for DSGE model estimation: An and Schorfheide (2007)

texts:
In Herbst and Schorfheide "Bayesian Estimation of DSGE Models", in the appendix named "Data Sources", they show several formulas relating the empirical data which should be used for the model.

Here's a snapshot from the book.

I've taken the data from the FRED. One can notice that the observations were taken monthly for some variables, and for others were taken quarterly. Some begin in the 40's, while others begin in the 50's.

However, the formulas in the book assume the same time period $t$. Hence, what I did was to discover the intersection of the dates of all observations, i.e. quarterly data beginning from the 50's,  and cleaned the data accordingly.

Now, I'm using the formulas in the book to create those new variables, namely per capita real output, annualized inflation, and federal funds rate.

My doubt resides on whether my procedure was correct.


texts: Implications of abolishing Fractional Reserve Banking on mortgages and interest rates

texts:
Suppose for a moment that someone with legislative power decides to abolish Fractional Reserve Banking and passes a law that forces banks to only lend the money they own, that is M0.
What would be the economy-wise implications of such a change in the long run and what in the short run? In particular with such a criteria in mind as mortgages, interest rates and dispossessions.


texts: Why can't price level be negatively correlated with money demand?

texts:
Source: p 585, Economics, 3 Ed, 2014, by NG Mankiw, MP Taylor

  Although many variables affect the demand for money, one variable stands out in importance: the
  average level of prices in the economy. People hold money because it is the medium of exchange. Unlike
  other assets, such as bonds or stocks, people can use money to buy the goods and services on their
  shopping lists. How much money they choose to hold for this purpose depends on the prices of those
  goods and services. The higher prices are,
  the more money the typical transaction requires,
  [1.] and the more
  money people will choose to hold in their pockets and bank accounts.
  [2.] That is, a higher price level (a lower
  value of money) increases the quantity of money demanded.

I doubt 1 and 2 that feels too absolutely certain. (They're also restated, but rephrased, on pp 683 and 705.) Why must 1 and 2 be true?

Abbreviate Prior Money as PM, i.e. consumers' money held 'in their pockets and bank accounts' before the price rise.

Suppose that higher prices $\implies$ more money needed for each typical transaction. But even facing  a higher price level, consumers may already possess enough PM to transact, and so needn't more money.

Moreover, even with enough PM for their regular purchases, the price rise may cause consumers to spend less. Then money demand would DEcrease.


texts: Risks asscoiated short term stimulus as interest rates approach zero

texts:
TL;DR
Government interest rates are approaching zero.

What are the risks to borrowing large sums in the current enviroment? Would inflation occur?
Full Story
I was recently reading an article about Rishi Sunak's (UK Chancellor) aim to rein in public spending in the UK post pandemic, the implication being he was planning to do this much earlier than other countries.
Since the interest rates are so low borrowing appears very cheap. Conventional gilts (fixed interest) make up 75% of the UK government portfolio and the interest rates on these are approaching zero (see graph above). There is strand of thought that government ought to borrow lots while it can, this opinion appears to be widely held. The spending so far is short term stimulus such are furlough payments, not medium/long term investment.
Inflation
A turbo charged economy with low unemployment could lead to higher demand, higher prices and then inflation. However for countries hit hard by the pandemic unemployment is high (5% in the UK) and likely to increase as furlough measures are removed.
The Question
What are the risks to continuing to borrow large amounts ($100Bns)to spend on short term stimulus right now?
What economic reason would there be to not do so?


texts: How to define durable/non-durable good industries? For example, is the industry of  Wholesale and retail trades defined as durable good industry? Thanks in advance.


texts: What is the economic purpose of increasing the minimum wage?

texts:
It is generally accepted among economists that minimum wage warps the equilibrium point between the supply and demand of labor by instituting a price floor and increases unemployment for unskilled laborers (while increasing the wage for the individuals who continue to work).
However, I have noticed that politicians continue to advocate an increase in the minimum wage.  Politics and political maneuvering aside, is there an economic reason as to why a higher minimum wage would benefit the economy?


texts:
I am using Mishkin's textbook "Economics of Money, Banking and Financial Markets." On the chapter on financial crises, the authors list a number of factors that could trigger a crises.

One factor is An Unanticipated Decline in the Value of the Domestic Currency. I quote "Because of uncertainty about the future value of the domestic currency in developing countries (and in some industrialized countries), many nonfinancial firms, banks, and governments in developing countries find it easier to issue debt denominated in foreign currencies rather than their own currency. This can lead to a financial crisis in a similar fasahion to an unanticipated decline in the price level.  With debt contracts denominated in foreign currency when there is an unanticipated decline in the value of the domestic currency, the debt burden of domestic firms increases.• Since assets are typically denominated in domestic currency, there is a resulting deterioration in firms' balance sheets and a decline in net worth, which then increases adverse selection and moral hazard problems along the lines just described."

I don't get the logic. The authors are a bit vague: a decline in the value of the domestic currency perhaps means a depreciation relative to other currencies. Now, if that is correct, if there is uncertainty about the future value of the domestic currency, why would firms issue debt denominated in foreign currencies? If domestic currency is expected to appreciate, then only does it make sense (forgetting uncovered interest parity for now). Am I thinking correctly about this?

Thanks!


texts:
Walras has available 24 hours per day. He has to alloacate this 24 hours between leisure $(L)$ and work. His utility function depends on leisure and the composite good $(C)$ and is given by $U=LC$. Work pays him a wage of 1 dollar per hour and this is his only income.

What is his optimal choice of $L$ and $C$ ?

I understand that $MRS=C/L$ and it should be equal to the price ratio. Is it 1 or 2?
I am confused whether budget constraint is $C+L=24-L$ (in this case price ratio is 2). Can someone clarify this?


texts: Imports/Exports in the equation of exchange

texts: From the equation of exchange: $MV=PY$, where $M$ is the money aggregate, $Y$ is the real output, $P$ is the price level and $V$ is the velocity of money, we derive $\% \Delta M + \% \Delta V = inflation + growth\ rate$. How will these equations be affected by inclusion of imports/exports, and international financial transactions?


texts: Can a weaker currency be used to offset lower productivity of labour in an economy?

texts: Can a weaker currency be used to offset supply-side (specifically low productivity of labour) problems of an economy to restore international competitiveness?


texts: Writing the core as the intersection of pareto efficient outcomes of all coalitions

texts:
I have been reviewing general equilibrium models and was trying to find an efficient method for computing the core of a cooperative game. I was taught this topic in a very poor way so I believe I still have some conceptual errors.

Here is a thought I had:

Suppose we are in an economy with three consumers, $A$, $B$, and $C$, with utility $u_{i}(x)$ defined over bundles $x \in \mathbb{R}^{2}$ and endowments $\omega_{i}$ for $i = A, B ,C$. I want to compute the core for this economy.

I know the core must satisfy:
\begin{align}
u_{A}(x_{A}) &\geq u_{A}(\omega_{A})\\
u_{B}(x_{B}) &\geq u_{B}(\omega_{B})\\
u_{C}(x_{C}) &\geq u_{C}(\omega_{C})\\
\end{align}
i.e. the core must be individually rational. So let $$D =\{ x \in \mathbb{R}^{2} : x \text{ is individually rational for $A$, $B$ and $C$} \}$$ I also know that the core is a subset of the pareto efficient outcomes, so let $$E =\{ x \in \mathbb{R}^{2} : x \text{ is pareto efficient} \}$$ Now here is the part I am not sure about: I know that the core is also not blocked by any two-person coalition. I think this means that any core allocation is pareto efficient for any two-person game. Thus I define:
\begin{align}
F_{1} =\{ x \in \mathbb{R}^{2} : x \text{ is pareto efficient in the cooperative game with only $A$ and $B$ } \}\\
F_{2} =\{ x \in \mathbb{R}^{2} : x \text{ is pareto efficient in the cooperative game with only $A$ and $C$ } \}\\
F_{3} =\{ x \in \mathbb{R}^{2} : x \text{ is pareto efficient in the cooperative game with only $B$ and $C$ } \}
\end{align}

Here are my questions:

Is the above analysis correct?
Can I write the set of core allocations $\mathcal{C}$ as $$\mathcal{C} = D \cap E \cap F_{1} \cap F_{2} \cap F_{3}\text{?}$$
Can this method of solving be generalized to a game with $n$ players and $m$ goods?

Let me know if anything is not clear!


texts: Flat Term Structure and Immunized Portfolio Strategy

texts:
The current term structure is flat at 2%. You have a liability of $500,000 per year for the next five years. You decide to form an immunized portfolio.

  a) Describe your exact strategy if you invest in one through five-year zero-coupon bonds.

What I did is

$$
D_{\rm funding}=w_1(1)+w_2(2)+w_3(3)+w_3(3)+w_4(5)+w_5(5)
$$

but does $D_{\rm funding}$ equal to 5? what does it equal to and how do I solve this equation


texts: How does high U.S. federal debt affect its citizens?

texts:
My apologies if this is a silly question. My background isn't in economics, though wish I had some.
During the 2008-9 financial crisis, federal debt increased significantly and there was a small talk between my friends on how this much debt is unprecedented and the U.S. will collapse unless something is done to reduce it.
It turns out (at least from what I experienced), is that nothing really changed. Debt increased much more now and the economy seemed to be doing fine until COVID-19 erupted.
Recently a stimulus package has been released to alleviate the economy affected by COVID-19. More debt is added and I'm wondering how is the U.S. government just be able to print money without side-effects? (at least for now?)
My understanding back then was that an increase in government debt implies increase in tax but the tax actually got reduced when the Trump administration took charge.
Sources

Federal Debt: Total Public Debt as Percent of Gross Domestic Product
Federal Debt: Total Public Debt
Tax Cuts and Jobs Act of 2017


texts: Difference between equilibrium and k-rationalizability

texts:
I'm reading a Structural Models of Nonequilibrium Strategic Thinking: Theory,
Evidence, and Applications by Crawford, Costa-Gomes and Iriberri. They write the following:

  In two-person games, a player can find his set
  of k-rationalizable strategies via k rounds of
  iterated strict dominance, without the need
  for fixed-point reasoning. Thus, k-rationalizability is cognitively less taxing than equilibrium, especially for small k.

K rationalizable strategies are those that survive k-rounds of iterated strict dominace (for n=2 player games). For n >2, k-rationalizable strategies are those that survive k-rounds of iterative never best response elimination.

What is meant by fixed point reasoning here? Is there a difference between fixed point reasoning and iterative never-best-response elimination?

Relevant section is Section 2.2 found on page 12.


texts:
Let $F(K,L)$ be a production function with variables $K$ for capital and $L$ for labor.

The slope of the $F(\overline K,L)$ ($K$ taken constant) is defined as the marginal product of labor ($MPL$) such that:

$$MPL=F(K,L+1)-F(K,L)$$

Most production functions have a positive decreasing slope due to diminishing marginal product and therefore are not straight lines. How is the $MPL$ formula still valid? Isn't that the same formula to find a gradient $m$ of a line (i.e. $\frac{y_{2}-y_{1}}{x_{2}-x{1}}$)? If we take any function whose representation isn't a line, its slope at a certain point is equal to the slope of the tangent at the point and not the formula for the gradient $m$.

Also, supposing the given formula for $MPL$ is true, shouldn't we also have $MPL=\frac{\partial F}{\partial L}$?


texts: Income Elasticity of Demand for Higher Education

texts:
My model has been given as:
$$\ln (H_ed) = 18.08 -  0.53\ln Pop -2.01 \ln Distance + 0.47\ln RGD $$

Where (Hed) is higher education, pop is population, and RGD = Real GDP per capita.

I have been asked to find the "income elasticity of the demand for higher education".

As there are no income variables in this model, I am unsure of where to look for the income elasticity.


texts: Proof of nestedness of subgame perfect equilibria

texts:
Below is a lemma which I believe to be true and which I would like to use to derive other results

  Take any two games in extensive form (complete information) $\Gamma$ and $\Gamma'$ differing only through their collections of information sets $\mathcal{H}$ and $\mathcal{H'}$. Suppose that for each decision node $x$ in the set of decisions nodes $\mathcal{X} = \mathcal{X}'$, $H(x)$ is a finer partition of the set of actions $c(x) = c'(x)$ than $H'(x)$.

  Then for ever subgame perfect equilibrium outcome of $\Gamma$, there exists a subgame perfect equilibrium of $\Gamma'$ with the same outcome (but the converse does not need to be true).

I could try to write a complete proof but this seems to be basic enough a statement and I don't want to re-invent the wheel (or fail to pay tribute to former proofs). So my question is:

Do you know of any reference where that result is proven (or maybe disproven in case I got something wrong)?

Edit : I am only interested in pure strategies equilibria.


texts: What are some helpful online tools (databases, etc..) for economic analysts?

texts: More specifically, I'm looking for a online database of US economic statistics that is regularly updated. Most of my searches result in older data, that is not particularly useful for what I need it for. I'm needing to make many cross references with it, for instance, comparing the unemployment rate of two cities/regions.


texts: Textbook for industrial organization without calculus

texts: I'm planning to teach an undergraduate course in industrial organization. Calculus is not a prerequisite. I also want to avoid doing too much game theory in it so as to not be duplicative of a similar course offering in game theory. Any recommendations on textbooks?


texts: A basic question about supply and demand graph

texts:
i have some basic knowledge on economics ,and i had an argument with a friend ,so  my question is this , as we all know
(If we ignore all the outside factors) that the price of any product is governed by it's quantity in the market. So the more from that product existing in the market the lower the prices and vise versa.
Is there a method or formula that works backwards i mean from the price of that product you can find the quantity that represented in the market ??

Update:
I saw a gold graph once and the price was changing according to time not the quantity. And people start to draw as they call it trend lines (upward and downward ) so if the trend is up they call it Supply if the trend is down it is a demand graph, is this right ? Is there  a way to find the quantity of gold that traded in this example from the graph it self ? Of course we still ignoring the other factors that could change market direction we talk only supply and demand.
Maybe it is a silly question .... sorry.


texts:
Is there any well known study that links government debt to tax rates? I have been searching the literature for some time now and haven't found any.

More importantly, could government debt track tax rates?


texts: Why is my elasticity of substitution wrong?

texts:
I am calculating elasticity of substitution for the following production function:
$$F(K,L) = A(aK^{-\gamma}+bL^{-\gamma})^{-\mu/\gamma}$$
where $A, a, b, \mu, \gamma$ are constants. $A, a, b, > 0$, $\mu \neq 0 $ and  $\gamma \neq 0; \gamma>-1$.
We learned in our course that to calculate elasticity of substitution we should first calculate marginal rate of substitution and then calculate elasticity with respect to $K/L$. I calculated MRTS to be:
$$MRTS = \frac{b}{a} \left(\frac{K}{L}\right)^{\gamma+1}$$
Then I try to calculate the elasticity of the above with respect to $K/L$ which gives me:
$$EL_{MRTS_{K,L}} = \frac{d MRTS}{d (K/L)} \frac{K/L}{MRTS} \\ = \frac{b}{a} (\gamma+1)\left(\frac{K}{L}\right)^{\gamma} \left( \frac{K/L}{\frac{b}{a} \left(\frac{K}{L}\right)^{\gamma+1}}\right)  \\= \gamma +1$$
However, the textbook says the correct answer is $\frac{1}{\gamma+1}$. I think I just made some small mistake somewhere because the answer provided by book is just an inverse of my answer. But I don't know where I am making the mistake.
Please could someone help me with this? Thanks.


texts: Examples of the use of Vector Autoregressive Models

texts:
I am self-learning Vector Autoregressive Models currently, and have practiced on a few datasets. But I wanted to read some actual research papers that use VAR, so that I get an idea of the level of rigour in their use in actual research or the practical sides to be kept in mind to use them.
When I searched "Vector Autoregressive Models" or its variants in Google Scholar, it displays papers about VAR. I wanted to read papers which apply VAR to answer different questions, such as in monetary or fiscal policy etc. maybe.


texts:
I've been reading a book on a Kaleckian economics model, but there is a recursive function that has been bothering me. Can anyone provide some insight into why the equation why designed like this?

Quote from the book:

  $Y = \min\{aE, uK\} \quad (1.1)$

  Equation (1.1) denotes the fixed-coefficients production function, where $u$ denotes output; $E$, employment; $K$, capital stock; $a = Y/E$, labor productivity; and $u = Y/K$, the output-capital ratio. In the following analysis, we assume that the capital-potential output ratio is unity. From this, we can regard the output-capital ratio $u = Y/K$ as the capacity utilization rate.$^{4)}$
  ...

  $4)$ The capacity utilization rate $u$ is defined as $u = Y/Y^*$, where $Y$ denotes the actual output and $Y^*$ denotes the potential output. The capacity utilization rate is decomposed into $u = (Y/K)(K/Y^*)$, where $K/Y^*$ denotes the capital/potential output ratio and captures the production technology. If we assume that $K/Y^*$ is constant, then $u$ and $Y/K$ change in the same direction. From this, we can regard the output/capital ratio as the capacity utilization rate. In this chapter, for simplicity, we assume that $K/Y^* = 1$. Therefore, we obtain $u = Y/K.$

I assume $a$ and $u$ are the fixed coefficients. But even if we suppose $uK < aE $ then since $u = Y/K$, we should have $uK = aE$, or is that wrong? If correct, why do we use use the minimum operation?

Here is the digital book. Quote from page 20.


texts: what is the Relationship between Zero nominal interest rates and liquidity traps

texts:
So I'm reading mankiw"s principles of economics and I'm in the chapter about the influence of monetary and fiscal policy on Aggregate demamd.
The part about nominal Interest rates and liquidity traps left me confused and I didn't really understand what it meant. Can anyone elucidate the role of short run interest rates and their effect on the economy?
More specifically, can anyone explain this particular paragraph:

"Some economists have suggested that the possibility of hitting the zero lower bound for interest rates justifies setting the target rate of inflation well above zero. Under zero inflation, the real interest rate, like the nominal interest, can never fall below zero. But if the normal rate of inflation is, say, 4 percent, then the central bank can easily push the real interest rate to negative 4 percent by lowering the nominal interest rate toward zero. Thus, moderate inflation gives monetary policymakers more room to stimulate the economy when needed, reducing the risk of hitting the zero lower bound and having the economy fall into a liquidity trap."


texts: I do not quite understand the statement "total variable cost is the area under the marginal cost curve" Does it means MC inserts at the AVC at the lowest point (see picture)? But why AVC is drawn and not TVC?


texts: If we have a condition where employment is lead by the wages does it mean that a wage reduction will cause unemployment?


texts:
Suppose two players play the following game:

\begin{array}{cc}
  & L & R  \\
U & 1,1 & 0,0 \\
D & 0,0 & 4,4
\end{array}

Is there any way to compare the top-left Nash equilibrium with the bottom-right one? Is there any way to distinguish between two equilibria and to define which one is "better"?


texts: Newly issued shares are sold on the stock market?

texts:
When a company issues new shares in order to raise it's capital, can it sell those shares on the stock market? Or they have to be sold outside of the stock market?

I mean in general, rules can differ from one country to another.


texts: What is the iff condition for a preference with linear Engel curves (all Engal curves are linear)?

texts:
If we restrict the consumption at $\mathbb R_+^n$, then it seems like we are implicitly assuming that the Engel curve pass through the origin, so the iff condition would be homothetic preference.

However, if we let $x\in\mathbb R^n$, other classes of preference would also give linear Engel curves. For example, those represented by a quasi linear utility in two dimensions: $u(x)=x_1+f(x_2)$; in this case, the Engel curves are parallel lines.

It could be assumed that, as in the standard consumer theory, the preference is non-satiated and continuous, so the indifference sets are curves.


texts: Why is the tat-for-tat strategy a Nash equilibrium in infinitely repeated games?

texts:
Why is the tat-for-tat strategy a Nash equilibrium in infinitely repeated games, but not a Nash equilibrium in a finite scenario? Specifically for this matrix:

Assume higher payoffs reflect higher utility. It's a prisoner's dilemma situation.

Since tit-for-tat assumes we start at (Honor, Honor), and play the strategy that the other player last played in future rounds, I don't really see why it's a Nash equilibrium in an infinite scenario and not a finite scenario.

In a finite scenario (e.g. one round), wouldn't the players end up at the NE (Cheat, Cheat) because they follow their self-interest? And in an infinite scenario, wouldn't they end up at (Honor, Honor) (not a NE) assuming the discount factor is high enough?

Any clarity appreciated!


texts: Can we know what mainly caused the latest US manufacturing slump?

texts:
Reuters says (Oct 1, 2019):

U.S. manufacturing activity tumbled to a more than 10-year low in September as lingering trade tensions weighed on exports, further heightening financial market fears of a sharp slowdown in economic growth in the third quarter.
The survey from the Institute for Supply Management (ISM) on Tuesday came on the heels of data last week showing a cooling in consumer spending in August. The economy’s fading fortunes have been attributed to the Trump administration’s 15-month trade war with China, which has sapped business confidence and undermined manufacturing.
Ironically, manufacturing has borne the brunt of the trade tariffs, which the White House says are necessary to protect industries from what it says is unfair foreign competition. President Donald Trump blames the Federal Reserve, in particular Chair Jerome Powell, for the manufacturing sector’s malaise.
“As I predicted, Jay Powell and the Federal Reserve have allowed the Dollar to get so strong, especially relative to ALL other currencies, that our manufacturers are being negatively affected,” Trump wrote on Twitter shortly after the ISM survey was published. “Fed Rate too high. They are their own worst enemies, they don’t have a clue. Pathetic!”
[...]
“It couldn’t be more ironic that the trade tariffs done to bring factories back from overseas, are actually shutting down production at existing plants here in the U.S.” said Chris Rupkey, chief economist at MUFG in New York. Machinery manufacturers said demand was “softening on some product lines, backlogs have reduced, and dealer inventories are growing.” Electrical equipment, appliances and components makers noted that the “economy seems to be softening,” adding that “tariffs have caused much confusion in the industry.”

So we have two competing narratives here, not necessarily mutually exclusive:

Trump says the manufacturing slump is due to US interest rates being too high
Others blame the trade war(s) started by Trump

Is there any economic analysis that can shed more light on this, or is it just going to be a matter of competing opinions?
(The Eurozone manufacturing also shrank as did the UK's.)


texts: Is there empirical evidence on usability of Cobb-Douglas production function?

texts:
I am trying to estimate a simple Cobb-Douglas production function $Y=AL^{\alpha}K^{\beta}$
on US data and get an unrealistic estimate of $\alpha$ and a high p-value for $\beta$.
Structure of regression is as follows:

$\frac 1 Y \frac{\mathrm dY}{\mathrm dt} = \frac 1 A \frac{\mathrm dA}{\mathrm dt} + \alpha \frac 1 L \frac{\mathrm dL}{\mathrm dt}
+ \beta \frac 1 K \frac{\mathrm dK}{\mathrm dt}$

and assuming technological growth constant:

$\text{growth}_Y = a_0 + \alpha\cdot \text{growth}_L + \beta\cdot \text{growth}_K$

I have the following output of linear regression in R:

\begin{array}{lllll}
 &\text{Estimate}\quad & \text{Std. error}\quad & \text{t value} & \mathrm{Pr}(>|t|) \\
\text{(Intercept)}\ & 0.008256 &   0.006070 &  1.360  &  0.186    \\
growth_L  &  1.388552  & 0.283867  & 4.892 & 5.47\mathrm e^{-05}\ ^{***} \\
growth_K   & 0.194165   & 0.255572  & 0.760  &  0.455 \\
\\
R^2 = 58\%
\end{array}

Estimate for the coefficient in front of $\text{growth}_L$ ($\hat\alpha$) seems unrealistically high (1.388552) and estimate for coefficient for $\text{growth}_K$ ($\hat \beta$) has high p-value (0.455).

Before running the regression I excluded outliers (observations outside 2.5% and 97.5% for growth_gdp, growth_L and growth_K).
I also checked correlation between growth_L and growth_K and it is 42% which is not that high to impact stability of coefficients of the regression that much.

Unfortunately I could not find a simple and reproducible analogue of the above analysis.

My questions are the following:

Is there an empirical analysis of simple Cobb-Douglas function producing realistic estimates of coefficients? So that I would understand my key mistakes
If not, what would be the simplest form of production function which could be supported by empirical analysis?

P.S. For the full reproducibility of the analysis below is more info on data and R code used in estimation of the coefficients.
I take data from OECD Economic outlook database

Variables used: GDPV – states for Real GDP, HRS states for hours worked per worker, LF – states for number of workers in Economy, KTPV states for productive capital stock. I calculated L as $LF*HRS$

Full R code and the input data set can be found at pastebin.


texts: Do open market operations permanently increase the money supply?

texts:
Suppose the Fed buys 1000 dollars worth of T-Bills in the open market to try decrease interest rates and increase the money supply. It does this by printing money and electronically increasing the sellers (a private bank) reserves by 1000 in exchange for the T-Bill thus boosting the private banks reserves and in this way the newly printed money has entered into the economy. Once the banks reserves have increased, the money multiplier process begins and the ultimate increase in the money supply is equal to 1000 dollars times the money multiplier. Depending on the money multiplier (that is, how willing banks are to lend that new money), the increase to the money supply could be only $1000 (in the case of no lending) or potentially a lot more. This much I understand as most textbooks describe the process fully.
But now what does the Fed end up doing with these T-Bills? Since they are T-Bills, they must mature within a year, so when they mature surely the government has to pay the Fed the face value of the T-Bill? The money the government uses to pay the Fed will then leave the economy and the money supply will not have changed ultimately. Even if the initial Fed purchase of the T-Bill had a high money multiplier and thus caused an increase in the money supply much larger than 1000, the government must pay the Fed with real currency or reserves at maturity. Thus, through open market operations, I can only reason that the money supply can increase at best only in the short term (maximum of 1 year when the last purchased T-Bills mature) and hence it does not constitute a permanent increase in the money supply. Also, when the government pays the Fed at maturity, this decrease in the money supply should lead to some deflation counteracting the initial boost that the open market operations were intended to do. So am I missing something or can open market operations only increase the money supply in the short term (being max 1 year assuming the Fed is purchasing T-Bills)? This reasoning would lead me to believe that quantitative easing can also only increase the money supply until the maturity date of the purchased government bonds (around 20 years) at which point the money supply must decrease to where it was before the quantitative easing began?
Any help on this would be most appreciated as all my textbooks describe how the Fed buys T-Bills and how this increases the money but not what the Fed ultimately does with these T-Bills and how that may or may not decrease the money supply.


texts:
If the only information we had about Goldie were that she chooses the bundle (6, 6) when prices are (6, 7) and she chooses the bundle (10, 0) when prices are (5, 5), then we could conclude that

a.
the bundle (6, 6) is revealed preferred to (10, 0) but there is no evidence that she violates WARP.

b.
Goldie violates WARP.

c.
the bundle (10, 0) is revealed preferred to (6, 6) and she violates WARP.

d.
neither bundle is revealed preferred to the other.

e.
the bundle (10, 0) is revealed preferred to (6, 6) but there is no evidence that she violates WARP.

My attempt:
Obvious conclusion to this question is that (6,6) bundle is preferred to (10,0) bundle when prices are (6,7) but when the prices are (5,5) everything is the other way round thus it violates the WARP whereas the correct answer as stated in the questionbank is A why is that?


texts: How have central banks been injecting currency after crises since 2007?

texts:
In an article by Jean-Michel Naulot about the 2007–2008 financial crisis, I read (my translation):

Although central banks had an exemplary reaction at the time of the [2007–2008] crisis, they subsequently carried out an unprecedented policy by massively and durably injecting currency into the financial system, as never before. A major part of these liquid assets was invested into risky assets and speculation. Private debt rose considerably again.
In the past 20 years, a fiendish debt feedback system has risen: as crises break, public spending is massively revived and tax revenue is reduced, hence public debt soars. Central banks keep interest rates low for extended periods of time and private debt rises considerably, especially in countries with high levels of inequality. Excessive private debt leads to a new crises, which drives public debt up, ...

The second paragraph suggests that public debt rises because of public spending programs and because lower tax revenue during hard times is not compensated by higher tax revenue during boom times. However the first paragraph suggests that there's more to public debt than public works (which benefits the public) and low taxes (which benefits whoever gets low tax rates). Where does the money that's “massively and durably injected” go?
Does this refer to stimulus packages? To governments compensating for defaulting financial institutions? Who's getting the money? Are these loans (that don't seem to be repaid) or gifts?


texts:
In my own studies I have noticed that many of the constrained optimization type questions that are often covered in intermediate/advanced microeconomics courses are seldom seen in more empirical types of work.

under what circumstances would I apply the use of the Legrangian multiplier to an real world problem?


texts: How to run Panel data analysis when data on the dependent variable is on a 5 year interval basis and that on independent variable is on yearly basis?

texts:
I am reading a paper which empirically tests if primary exports affect education attainment in LAC countries over the period 1965 to 2010. It uses percentage of secondary school enrollment as dependent variable. It mentions that data has been obtained from Barro and Lee (2013). But the problem is that Barro and Lee provide data for every 5 years
interval where as the data on primary exports is available on yearly basis. So I'm confused as to how can one perform the regression when the data on one of the variables are largely missing?
I'm using stata to perform the task.


texts: Why are lower cost retailers going bankrupt but premium chains are not?

texts:
In recent months, there has been a lot of talk of a "retail apocalypse". The increasing purchases on the internet have (supposedly) put pressure on storefront retailers. Payless is declaring bankruptcy and Sears has made public statements that suggest they may be facing bankruptcy shortly.

Nevertheless, luxury retailers like Nordstrom and the Hudson Bay Company, exactly the kind of companies I would expect to be most affected by internet sales cutting into their business, seem to be doing well.

Why would this be the case?

Note that my impression that higher-income consumers are more likely to use is the internet is born out by statistics (Pew Research report on internet use by income level.)


texts: Generalization of the Heckscher-Ohlin Model

texts:
The Heckscher-Ohlin Model is normally presented for the case of 2 countries, 2 factors of production and 2 traded goods, leading to statements that, subject to free trade and various other assumptions:

A country with a relative abundance of a factor will specialize in
and export the good whose production makes relatively intensive use
of that factor (the Heckscher-Ohlin Theorem).
The return to a factor will be equalized between the countries (the
Factor Price Equalization or Heckscher-Ohlin-Samuelson Theorem).

Do these results generalize, subject to the same assumptions, to cases with more than 2 countries, factors or traded goods, and what are good sources that treat this topic?  Of particular interest are cases with 3 factors: labour, man-made capital and natural capital.

I appreciate that the predictions of the Heckscher-Ohlin Model often differ from
empirical findings (eg the Leontief Paradox), but this question is about the model itself.


texts: Why doesn't economy of scale bring down prices of food?

texts:
I have little to no experience in economics and would enjoy a simple answer, if possible. Additionally, I base this question on subjective data, so I might be completely wrong in my assumptions.

EDIT: The title was deemed confusing. What I mean by "food" is any ready-to- or close to ready-to-eat meal. Restaurant meals definitely qualify, but so do frozen meals that might need a microwave/oven. I'm unsure about instant ramen, since I can hardly imagine enough people consuming enough ramen to create economic pressure on the rest of the food industry. Anything requiring attentive cooking disqualifies, so e.g. pasta is out.

Having some experience in preparing food for groups of people of up to 50, I could easily observe economies of scale working, driving the price per meal down as the number of participants (and thereby meals) increased. Roughly speaking, I'd spend about 3\$ on a meal for myself, 2\$/meal for 2-3 people, 1\$/meal for 10 people, and so on.

EDIT: I should emphasize I'm not asking about a specific price, but rather use them to show the difference between expectation and reality.

So I would expect companies preparing hundreds or thousands of meals per day (i.e. restaurants) to sell meals at comparably low prices. Now most restaurants don't work like that and prepare every meal when it's ordered and I'd assume customers pay because they value the experience more than the food itself.

But why aren't there any places selling decent meals for .5\$? My explanations don't quite satisfy me:

They do exist, it's called McDonalds. The prices aren't that low because there is an organizational overhead, at some point the number of people required rises linearly with the food that can be distributed. I'm not quite satisfied by this, because if it were driven by economics of scale, I'd expect similar concepts for better quality meals.
They do exist, they are called soup kitchens. At some point, the prices are just so low that demanding the actual price causes people to question it's quality. I.e. when selling food for .1\$/meal, people start wondering what's wrong with it. The only way people accept these prices is by acting as a charity, giving the meals away for free and generating money through donations, rather than meals sold. But wouldn't that mean there should be something like for-profit soup kitchens? I know a pay-as-you wish restaurant in my city, they rely heavily on economics of scale, and still invest about 4\$/meal.
Rent is the essential problem. A restaurant can only seat so many people, and prices
would drop drastically enough only at higher numbers. In that case, wouldn't bigger restaurants or restaurants owning their venue offer cheaper food?
In the thought of all of the above, the solution are frozen foods. Prepared in huge quantities at industrial scale, they may be shipped anywhere and are storable, even selling in stores is possible. Then again, the cheapest frozen food I know still costs around 1\$/serving (and is by no means a full meal). There is actually a company sponsored by the red cross delivering frozen meals to elderly people, which has prices starting at 3\$/meal.
People just don't accept cheap food. Though possible, there is a much stronger social component to eating, driving people to avoid low priced food as to avoid a status-penalty. But there are cheaper places (e.g. cafeterias) in existence, already associated with a status-penalty, so why would even cheaper food result in unbearable status penalties?


texts:
Recently I started to read again Brealey & Myers's "Principles of Corporate Finance" (an older edition I hold it since I attended to the university course on Economics and Corporate Finance as a part of the curriculum in Electronics Enginering at the University of Bologna), since I need to evaluate the profitability performance of some projects I am involved with. The two authors use the NPV method which assumes (more or less explicitly) the use of compound interest, perhaps familiar to all of us, and, en passant, mention the existence of the simple interest. Inspired by curiosity, I searched for applications where the interest rate is required to be simple, but I was not able to find anything outside examples in textbooks and lecture notes, so my question is: what are the uses of simple interests in current economy?
Edit on behalf of the comments. I am asking this question because I am curious to see some examples and understand the reason why, in these cases, the simple interest is used. In my understanding, the use of compound interest is extremely natural since it corresponds to the intuitive concept that the invested money (continuously) produces a cash flow that is implicitly reinvested (at least up to the moment when the intial investment + the interest has to be payed back), thus it implicitly generates a (continuous time) conpound interest rate: for the simple interest I am not able to imagine such an intuitive explanation.


texts:
I have a set of objects $A=\{a_1,a_2,a_3,\cdots,a_m\}$ and one player, who proposes a vector of valuations $t=(t_1~t_2~t_3~\cdots~t_m)$ for the $m$ objects. $T$ is the set of all such valuation types. Given $T$ I design an allocation function $$f:T\rightarrow [0,1]^m$$ and a payment function $$p:T\rightarrow \mathbb{R}$$
The mechanism $(f,p)$ is said to be Incentive compatible if $$t(f(t))-p(t)\geq t(f(t'))-p(t')~~\forall t,t'\in T~~~~~~~~~~~~(1)$$
One can easily derive from the above eqaution that incentive compatibility implies the following: $$t(f(t))+t'(f(t'))\geq t(f(t'))+t'(f(t))~~~~~~~~~~~~~~~~~~(2)$$
that is, $(1)\Rightarrow (2)$.

Is the converse ($(2)\Rightarrow (1)$) true?