texts: Is "normal distribution" a good choice for modeling future inflation rates?

texts: I have a financial model that generates future values for a present sum of money based on its growth by investment minus inflation adjusted expenditure. Rather than use fixed rates for growth and inflation (say over the next 20 years), I'd like to use a range with a probability distribution. e.g. inflation "normally" distributed between 1 to 5 percent (90% confidence). Question is, is a normal distribution a good choice for modeling future inflation rates? Or does the history of inflation point towards some other distribution?


texts: Trade-off between "extent of controls" and "quasi-experimental"

texts:
I apologize in advance for a long and possibly misworded question. I am trying to get to something but I am not exactly sure how to explain it. Hopefully, you can bear with me and provide me with some guidance.
I am interested in the trade-off between observational studies with a large set of controls and quasi-experimental studies with fewer controls.
I often see quasi-experimental papers that (try to argue they) get some almost exogenous variation, but at the expense of having fewer data points and fewer control variables. For example, you often see people rely on a new state-law to induce changes in a treatment-variable. To analyze the treatment, they then use a yearly county-level panel-data over, say, a 10 years period including the adoption of the law. Looking within this single state over that a period may allow them to argue that the variation is almost exogenous. But it leaves them with few county-controls to mitigate for possible endogeneities (e.g., in the case of US counties, because yearly county data is only available from the ACS for counties of more than 65,000 people). That is, their claim to exogeneity relies mainly on the quasi-experimental nature of the treatment, and little on controls (conditional exogeneity).
Another option would have been to run a purely observational study with a larger set of controls and put more of the weight of causal inference on getting closer to conditional exogeneity (given a more comprehensive set of controls). For example, one could consider variation in the same treatment-variable and look at a larger selection of counties from across the US for which a larger set of controls is available (e.g., counties with more than 65,000 people for which a wide array of yearly controls are available from the ACS).
Of course, all non-experimental studies will typically be biased. When trying to study the causal effect of a treatment in a non-experimental way, we can rarely eliminate biases altogether. We can only try to reduce endogeneity biases.
My point is that, in trying to do so (reduce biases), there is often a trade-off between a more quasi-experimental setting with fewer controls, and a more observational one with more control. In the first case, causal claims rely mainly on studying situations that are as close as possible to a random experiment (because once that fails, we don't have many controls to pick up the tab and mitigate endogeneities). In the second, causal claims rely more on getting as close as possible to conditional exogeneity. Each approach is exposed to different risks of biases. In the first case, biases come more predominantly from the treatment not being exactly exogenous. In the second, they come more predominantly from omitted variables.
These days, it seems like econ is choosing the first side of the trade-off: Your chances at publishing a quasi-experimental study with even a few extra controls tend to be much larger than your chances at publishing a more observational study with a wide array of controls.
My question is: Has anyone studied this trade-off in a more or less systematic way, e.g., through Monte Carlo simulations? Do we have any sense, even in a particular case, of how the two sources of bias trade-off? For example, assume a particular distribution for the data and suppose that you plan on running a Diff-in-Diff based on a common trend assumption, but with no access to extra controls to ensure conditional common trends. As anyone looked into how much violation of the common trend assumption (i.e., how much correlation between the dependent variable and some controls) makes the Diff-in-Diff estimates more biased than a simple OLS that incorporates even a subset of the controls?


texts: The largest difference is that the NYSE is an auction market and the Nasdaq is a dealer market. In the former, the highest bid for a stock is matched with the lowest asking price. In the latter, buying and selling happens in split seconds electronically through dealers. Could someone be more illustrative about the prhase ``the highest bid for a stock is matched with the lowest asking price" with some paradigm?


texts: Smaller variance of estimators in matrix sense

texts:
When comparing asymptotic variances, you usually conclude that a covariance matrix A is more efficient whenever the difference B - A ≥ 0 (where ≥ 0 means that the difference is a positive semidefinite matrix).

However, this comparison involves all elements in the matrices - both the diagonal elements (asymptotic variances of each beta estimator) and the off-diagonal ones (covariances between estimators) -, while we are usually interested in estimators for a particular beta coefficient having small standard errors.

Could anyone explain why is this method preferred to a comparison that entails only the diagonal elements? Could it be the case that some diagonal element is smaller in B while B - A ≥ 0?

Thank you!


texts: How can I obtain State level Investment in the US?

texts:
How can I obtain investment level data by state in the US?

I want to analyse how Public investment vs Private Investment responded to TFP shocks on a state level, so I am looking for Gross Private Domestic Investments, Residential and Non Residential investments for each state.


texts: Replacing Value-added Tax with more Income Tax

texts: What would be the effect on the economy if all VAT / sales tax was removed, but income tax was increased to compensate so that the government has no change in income?


texts: Why debt/equity ratio is limited to between 0 and 9

texts:
Is there any economic reason that debt/equity is limited to between 0 and 9 as in the picture below?

This research examines the impact of the law on firms' financial flexibilities.


texts:
A general return on investment (ROI) formula is:

\begin{equation}
\text{ROI}=\frac{\text{Net Profit}}{\text{Total Investment}}.
\end{equation}

But if you think about an investment that requires some sort of down payment, thus it is deemed as leverated return on investment (LROI), what would be a sensible way to compute such return? Specifically, I am interested in having $\textit{down payment}$ in the denominator. Think of a construction project or home investment.

\begin{equation}
\text{LROI}=\frac{\text{?}}{\text{Down Payment}}.
\end{equation}

Any suggestions?


texts: Do countries have to run on deficits? What is their possible economic future?

texts: Do countries have to run on deficits? Is their future to behave and act like big companies that produce goods and services?


texts:
Say I have €1000 (or $1000) on a bank account. What is that money really?

Is it a value stored on some computer at the bank where I have the bank account, a value stored at the central bank of the currency (in the case of the euro the European Central Bank) or something else?

And if it is just a value stored on a computer somewhere, why do we give it so much worth?


texts: Why can't countries print another country's currency?

texts:
Counterfeiting money is clearly a difficult thing for individuals, but surely a country should have no problems counterfeiting another country's currency. Why don't countries do it? For example, for the US to exert pressure on North Korea (or vice versa), it could conceivably print lots of North Korean Won and use that to cause hyperinflation in North Korea. Similarly for Greece to dig itself out of its debt crisis it could just print USD or any other major currency, and convert that into Euros.

My best guess is that this isn't done because it's an act of war, but countries are apparently willing to sling cyberweapons at each other, in which case I don't understand why they don't also do this, at least on a small scale.


texts:
Basically I need to replicate Hartley's 'A User's Guide to Solving Real Business Cycle Models' (http://www.econ.ucdavis.edu/faculty/kdsalyer/LECTURES/Ecn235a/Linearization/ugfinal.pdf). Specifically, I want to simulate the dynamical system implied by the model which is specified as follows:

where $c$ is consumption, $h$ is labour supply, $k$ is capital, $z$ is the autoregressive technological process, $y$ is the output and $i$ is investment.

I simulate it using the following logic: say at time $t$, everything is at steady state and all the values are 0, from which we have $k_{t+1}$. Then, at $t+1$ by giving a shock to the system through $\varepsilon$, i solve for $c_{t+1}$ and $h_{t+1}$ (as I have the 'shocked' $z_{t+1}$ and previously obtained $k_{t+1}$. Then, I plug those two to retrieve the rest, namely - $y_{t+1}, i_{t+1}, k_{t+2}$ and repeat the process.

Unfortunately, I get an explosive process which doesn't make sense:

I also include R code that is used to simulate this:

n<-300

data.simulated <- data.table(t = 0, zval = 0, cval = 0, hval = 0, kval = 0, yval = 0, ival = 0)
data.simulated <- rbind(data.simulated, data.table(t = 1, kval = 0), fill = TRUE)

for (ii in 1:n){

  ##initial shocks
  eps <- rnorm(1, mean = 0, sd = 0.007)
  zt1 <- data.simulated[t == ii - 1, zval]*0.95 + eps
  kt1 <- data.simulated[t == ii, kval]

  ##solve for ct, ht
  lmat <- matrix(c(1, -0.54, 2.78, 1), byrow = T, ncol = 2)
  rmat <- matrix(c(0.02 * kt1 + 0.44 * zt1, kt1 + 2.78 * zt1), ncol = 1)

  solution <- solve(lmat, rmat)
  ct1 <- solution[1, ]
  ht1 <- solution[2, ]

  ##now solve for yt1 and kt2 and it1
  yt1 <- zt1 + 0.36 * kt1 + 0.64 * ht1
  kt2 <- -0.07 * ct1 + 1.01 * kt1 + 0.06 * ht1 + 0.1 * zt1
  it1 <- 3.92 * yt1 - 2.92 * ct1

  ##add to the data.table the results
  data.simulated[t == ii, c("zval", "cval", "hval", "yval", "ival") := list(zt1, ct1, ht1, yt1, it1)]
  data.simulated <- rbind(data.simulated, data.table(t = ii + 1, kval = kt2), fill = TRUE)
}

a <- data.simulated[, list(t, cval, ival, yval)]
a <- data.table:::melt.data.table(a, id.vars = "t")
ggplot(data = a, aes(x = t, y = value, col = variable)) + geom_line()

Sy my question is simple - is the system specified in the paper is inherently unstable and ergo the results, or did I make a mistake somewhere?


texts: Is there book or research on economically sustainable design of town or village?

texts:
I'm looking for a book which may help to design a self-sustainable small  settlement, which can maintain its own economy with limited connections to the outside world. Prefereably it should answer questions like:

What population is sufficient for such a town or village?
How to model microeconomics of such a settlment?


texts: How to engineer the economic system, so that an individuals self interest leads to fulfilling collective interest

texts:
So it is said that Adam Smith said that self interest leads to collective interest.

This is obviously not the case. We do not have a society that maximises the collective good*.

My question is, Is there a way to engineer society such that self interest will lead to a collective interest?

*It can be argued that the very poor are not as poor as they were a short time ago, but this is not what I am asking about.


texts: Simultaneous Equation Models for Estimating Demand for a Good

texts:
Suppose in an economy there are $G$ available goods $X_1,...,X_G$.  We can formulate a system of $3G+1$ equations as below:

$$Q^d_g = A_{g1}+A_{g2}P_g+\mathbf{A}_g\mathbf{Z}^d_g+u_g\quad(g = 1,...,G)\quad(1)$$
$$Q^s_g = B_{g1}+B_{g2}P_g+\mathbf{B}_g\mathbf{Z}^s_g+v_g\quad(g = 1,...,G)\quad(2)$$
$$Q^d_g = Q^s_g\quad(g = 1,...,G)\qquad\qquad\qquad\qquad\qquad\quad(3)$$
$$\sum_{g=1}^GP_gQ^d_g = I\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad(4)$$

Here $Q^d$ is quantity demanded, $Q^s$ quantity supplied, $P$ price, $\mathbf{Z}^d$ and $\mathbf{Z}^s$ are vectors of other variables (assumed exogenous) relevant to demand and supply respectively, $I$ is available income (also assumed exogenous), the $A$'s and $B$'s are parameters (vectors if in bold), and $u$ and $v$ are error terms.

Suppose we want to estimate demand for good $X_1$. Two methods that might be considered are:

Method 1: Use equations (1), (2) and (3) for $g=1$ only, that is, ignore the equations for the other goods and the income constraint. Use (3) to eliminate $Q^s$. Then estimate (1) within the remaining system of two equations using two-stage least squares (2SLS), on the basis that the equation is overidentified.

Method 2: Use the whole system of $3G+1$ equations. Use (3) to eliminate $Q^s_g$ for $g=1,...,G$. Then estimate, using a suitable estimator, the system consisting of (1) and (2) for $g=1,...,G$, treating (4) as a cross-equation restriction.

Question: What would be the most suitable estimation technique for Method 2, and what advantages might it offer over Method 1?

Method 2 of course is rather impracticable as it is unlikely that all the necessary data could be collected.  So the point of the question is to understand what if anything is lost by Method 1 (relative to what might theoretically be obtained by Method 2).


texts: China - US Trade War: Holes in this analogy?

texts:
I have recently listened to a podcast by Peter Schiff concerning the China - US trade war. Schiff to me is an interesting chap; he always puts an interesting spin on things. However, from time to time his rhetoric is very predictable. I knew going into the podcast that he would be pessimistic about the US situation, however I think he may have gone too far with this analogy. I'm paraphrasing here, but it's almost word for word, I'm just condensing:

  To understand who would "win" the trade war between the US and China, let's imagine a simpler model. Suppose there is an imaginary island that has 4 people on it: 1 American and 3 Chinese people. Let's say they have to survive on this island somehow. One Chinese person is tasked with going out and fishing. Another Chinese person is tasked with foraging for fruits and other edible plants. The third Chinese person is tasked with preparing and cooking the food. So what does the American do? Well, he simply eats! Now he doesn't eat everything, he leaves enough for the three Chinese people to sustain themselves, but the American does get the lion's share. This illustrates the precariousness of the US economy; should the Chinese ever decide to kick the US off the island, they have the skills they need to survive. And by analogy, the Chinese can win the trade war since they are making a lot of useful things whereas America's economy is primarily consumption.

It sounds kind of absurd when simplified this way, but I think Schiff has made some excellent points (in a rather humurours way to boot). Let us concede that trying to predict who will "win" the trade war (might be more a lose/lose) is a very speculative matter, so let's cut Schiff some slack. It's not easy to take a risk and stake one's reputation. With that said...

Question: Are there any glaring errors in this analogy? Is there a way to make the analogy more realistic?

My personal critique:

The notion that the Chinese do all the work so the American can gorge himself and get hardly anything in return for themselves seems over the top. When America consumes Chinese products, China is getting USD in return, which is the world reserve currency and they can use that to buy or invest in anything in the world. Surely that's worth something. Of course, it's true that the RMB has been climbing the currency rankings in the past few years, but still, there are limitations on RMB denominated options.
There are certain sectors that America is adept at. America has a powerful agriculture sector that produces much of the worlds wheat and a handful of other crops.

That's what I have so far. I would like to find other errors in Schiff's analogy. If possible, I would like to improve on his analogy and make it more realistic.


texts: Why did American share prices fall sharply on February 5, 2018? What are the major contributing factors to this?


texts: Will banks in the US continue to offer CDs?

texts: Earlier this year, the Fed abolished the reserve requirement. My understanding was that the motivation for banks offering CDs was because the Fed didn't impose reserve requirements on CDs, so banks could lend out more of deposits held as CDs than deposits held in other, lower interest forms. Given that CDs no longer provide an advantage to banks over normal accounts in this respect any longer, why do banks have any incentive to keep offering CDs? Is there another reason banks offer CDs?


texts: Regarding a consumption aggregator: How do I differentiate under the integral sign?

texts:
Let $\varepsilon>1$ and let $$C_t\equiv\left(\int_0^1C_t(i)^{(\varepsilon-1)/\varepsilon} \, di\right)^{\varepsilon/(\varepsilon-1)}$$ denote a consumption basket in time period $t$, where $C_t(i)$ is consumption of good $i\in [0,1]$. In e.g. new Keynesian models we want to differentiate $C_t$ with respect to $C_t(i)$ for some $i\in [0,1]$ so as to solve a utility optimization problem. In my lecture notes, and in many texts on this subject, it is said that $$\frac{\partial C_t}{\partial C_t(i)} = \frac{\varepsilon}{\varepsilon-1} C_t^{1/\varepsilon} \frac{\varepsilon-1}{\varepsilon} C_t(i)^{-1/\varepsilon}.$$ Does anyone know how this differentiation is accomplished? This is my question I want answered. Below I will outline how I have thought about this question.

I am prone to thinking that it is wrong. For using the chain rule I would say that the answer is the following. $$\frac{\partial C_t}{\partial C_t(i)} = \frac{\varepsilon}{\varepsilon-1} C_t^{1/\varepsilon} \left(\frac{\partial}{\partial C_t(i)} \int_0^1C_t(i)^{(\varepsilon-1)/\varepsilon} \, di\right),$$ which, when asssuming that the function is such that we may differentiate under the integral sign, I get $$\frac{\partial C_t}{\partial C_t(i)} = \frac\varepsilon {\varepsilon-1} C_t^{1/\varepsilon} \left(\int_0^1 \frac{\varepsilon-1} \varepsilon C_t(i)^{-1/\varepsilon} \, di\right).$$ Now, using the mean value theorem for integrals it would be possible to say that $$\int_0^1 C_t(i)^{-1/\varepsilon} \, di = C_t(j)^{-1/\varepsilon}(1-0)$$ for some $j\in (0,1)$, and insert this result above and then get a similar result to what was shown in my lecture notes. However, this would lead us to considering another good $j$ not necessarily equal to good $i$.

The reader may think that I am confusing the symbol '$i$' in the integral, for the same symbol used when differentiating with respect to $C_t(i)$, and that I should, when differentiating, consider a good $i_0$, and then perform the following differentiation: $$\frac{\partial C_t}{\partial C_t(i_0)} = \frac{\partial }{\partial C_t(i_0)} \left(\int_0^1 C_t(i)^{(\varepsilon-1)/\varepsilon} \, di\right)^{\varepsilon/(\varepsilon-1)}.$$ This may be so, but I do not know how to get the desired result from this, and if I take this approach, I would say that the derivative is equal to $0$ (!) as the integral is just a real constant if $t$ is fixed, which it is.

It is sometimes said that we may differentiate the integral just mentioned by looking at the integral as beeing a sum. What they mean by this, I do not know. Maybe they represent the integral as the limit of a Riemann sum, which it is, and write $$\frac{\partial }{\partial C_t(i_0)} \int_0^1 C_t(i)^{(\varepsilon-1/\varepsilon} \, di = \frac{\partial }{\partial C_t(i_0)} \lim_{n\to\infty} \sum_{k=1}^n C_t(\xi_k)^{(\varepsilon-1)/\varepsilon}(i_k-i_{k-1}),$$ with $i_0=0<i_1<\cdots < i_{n-1}<i_n=1$ and $i_{k-1}\leq\xi_k\leq i_k$ for each $k=1,2\ldots,n$. When the authors write that we should look at the integral as beeing a sum, this must be it. But differentiating this sum with respect to $C_t(i_0)$ would in the best cases (i.e., when we can do differentiation inside the limit) be equal to $\lim_{n\to\infty}\frac{\varepsilon-1} \varepsilon C_t(i_0)^{1/(\varepsilon-1)} \cdot (i_\alpha - i_{\alpha-1})$ for some $\alpha\in\{1,2,\ldots,n\}$ such that $i_{\alpha-1}\leq i_0\leq i_\alpha$; the problem now is that $\lim_{n\to\infty}\frac{\varepsilon-1} \varepsilon C_t(i_0)^{-1/\varepsilon}\cdot (i_\alpha - i_{\alpha-1})=0$, which is consistent with modern advanced real analysis (to my knowledge) in the sense that if we just increase or decrease the value of $C_t(i)$ at one $i=i_0$, then the value of the integral will not change, and hence the derivative should be $0$ (i.e., no change in the value of the integral for a change in $C_t(i_0)$).

Note: These problems occur when studying e.g. the so called "Dixit-Stiglitz aggregator".


texts: Gini coefficients and median / mean income ratio

texts: Simple question: If the GINI coefficient (market incomes) goes up, is it a necessary feature that the mean income rises relative to the median?


texts: Does creating more jobs actually help the economy as a whole?

texts:
So I recently came across an interesting point on why NASA isn't a waste of money, and it basically stated how NASA supports thousands of jobs, creates community events, and uses a part of its budget as the salary of some of the smartest people on the planet. But is this a huge impact?

Whenever a large company is created, it creates hundreds maybe even thousands of decent paying jobs. But does this only benefit the people who are working in that company? Or does it benefit the community as a whole (in terms of economic success)?


texts: The value of money in a model economy. Has this been addressed?

texts:
Consider the following question:

"Given a simplified economy which produce and trade some products A,B,C etc... with N agents and a total money supply of M. What will be the price of A, B, C as measured in units of that money?"

It seems to me that this is one of the most fundamental questions in economics and yet I am struggling to find any papers that address it. I guess there may be some agent based models out there which address it but I don't know what keywords or phrases to use in a search. Any ideas?


texts: What is the difference between VAT and corporate tax

texts: Many times I hear that VAT (value added tax) is a "good" tax, while corporate tax is a "bad" tax/ However, both taxes take a cut from the difference between the income of a company and its expenses, and seem therefore to be economically equivalent. Can anybody explain the difference to me?


texts: In the eyes of a normal citizen, what difference does it make if my country has debt or no debt?

texts:
I got curious about this because I happened to pass by a list of countries with zero debt. Country debt seems like a major thing, but for a non-economics major like me, I don't exactly understand the implications of a country having debt.

More tax? Less progress? Exports are more necessary?

What difference does it make, for a normal citizen, if his/her country has debt or no debt?


texts: Why can't we control for squares and quadratics of predicted values in regression?

texts: If my goal were prediction (e.g. of propensity scores), why couldn't I control for higher order terms of the model equation? For example, why not estimate the model and then control for squares and cubes of the predicted values in a second stage and get an even better estimate of the correct predicted values (rather than just a test of functional form)? I know the standard errors would be wrong but couldn't I bootstrap the process?


texts:
I teach Politics and I've been asked to prepare a course which includes a lot of financial data because it covers recent international financial crises.
I've been trying to use IMF statistics, but I find them rather confusing. For instance, if I want to know a country's deficit, I find three different options:

And when I look up GDP, I have a bewildering number of options to choose from (I've highlighted the one that makes more sense to me):

Is there any rule-of-thumb method for a lay person to use these statistics? Alternatively, is there any other source in which the data is comprehensive but simplified?
Thank you so much in advance!


texts: Why is Keynes attacking the (neo)classical theory of interest rates on the grounds that it is indeterminate?

texts:
I do understand that he argues that in order to draw the loanable funds supply curve, you have to already know the volume of income, i.e. production, and therefore the interest rate in advance.
But why couldn't you just test for coherence in the following way?
Assume a level of income. Draw the corresponding loanable funds supply curve. Calculate the interest rate at the intersection of the supply and the demand curve, i.e. the interest rate for which the capital market clears. Determine if the income level corresponding to this interest rate is indeed the income level we assumed in the first place. If it is, this interest rate is an/the equilibrium rate, if it's not, it's not.
Is there anything wrong with this argument?


texts: Definition of strictly convex preference

texts:
Let $x,y\in X$.
Does strictly convex preference (which implies that the utility is strictly quasiconcave) mean that:
$x\succsim y$ implies $\alpha x+(1-\alpha)y\succ y$ for any $\alpha\in (0,1)$?


texts: Who said that growth would stop because of satiation?

texts:
I have a vague recollection I am unsuccessfully trying to find an exact reference for.

I recall watching an interview of Jacques Attali about a new book of his (maybe 6 or 7 years ago) where he mentioned scholars who once (around 1700?) were convinced that economic growth would stop, not because of limits to technological progress, but because of satiation.

As I recall it, the argument from these scholars was something like "we may be able to produce 10 times more food, but there's only so much food an individual can eat in a day, so we'll never get to such levels of production because of a lack of demand".

Of course, we know that these scholars missed a number of important points, the main one being that growth occurs not only through producing more of the same old good, but by increasing the quality of these goods and by creating entirely new goods (which can easily break the satiation argument).

I am not interested in a discussion of the argument per se. Rather, I am looking for precise references (if any) to people who actually argued (or maybe are still arguing) about the purported "satiation" limit to growth.

Bonus points if someone can point me to Attali's interview or to the book where he mentions these people.


texts: Diminishing mariginal utility and risk preferences

texts:
Diminishing marginal utility is a concept only in cardinal utility theory rather than ordinal utility theory. As diminishing marginal utility implies a concave shape of the utility function, does it necessarily mean that agents with diminishing marginal utility must be risk-averse (also has a function with a concave shape)?

Does cardinal utility theory assume the law of diminishing marginal utility in all of this theory? Could you have increasing marginal utility within cardinal utility theory?


texts:
Maybe this is a well-known fact that I have somehow overlooked or forgotten etc., but I found myself curious recently if there are any conclusions about WARP holding over different dimensions for a given choice structure.

So, if I have a utility function, $N$ agents, $L$ commodities and price vectors in $R^L_+$, and I want to determine if WARP holds here, is it enough to assume that $L=2$ and prove WARP. Meaning, is it true that if WARP holds for $L=2$ it also holds for $L=N$, $N \in \mathbb{N}$

Edit : I feel like I should add that I know, generally, proving something for a specific case does not allow one to generalize the result. However, there are unique cases where such proofs can work. The first example that comes to mind is that whenever the excess demand function is homogeneous of degree zero we can reduce the problem to the simplex and it is sufficient to show that only n-1 markets clear.

Why I am asking?

I am trying to determine whether or not WARP holds for an adaptation of the (1999) Fehr & Schmidt Inequality Aversion utility function. I thought it might be easier to do by considering $L=2$


texts: Why is the long-run average production cost not necessarily the same as the minimum average total cost?

texts: As you can see from the graph, the LRATC doesn't touch the SRATC curves when they're at their minimum. Why is this so?


texts: Should one remove trend from time series before testing for cointegration?

texts:
Should one remove trend from time-series before testing for cointegration? I guess no, but I couldn't find any answers yet.
Also is it necessary to remove trend before estimating a VAR model if the trend is the same across the variables like in the plot below?


texts: Cyclicality of Real Wages? Counter, pro or acyclical?

texts:
Is the real wage counter or pro- cyclical? I've read in some textbooks that the real wage is mildly pro-cyclical, but I've also found some papers stating that it's acyclical.

So, which is it? Also, if the real wage is pro-cyclical, does that mean that there's some sort of price rigidity, i.e., the economy is not always on the Price-Setting curve?


texts: Relevance of government liabilities to GDP

texts:
After Malaysia's national debt was [reassessed][1], its totaled $250bn along with other government liabilities.

Now, I'm having trouble understanding the direct relevance of the ratio of goverment debt to gross domestic product, in Malaysia's case.

Namely, in the article it is stated that its 80 percent of Malaysia's gross domestic product. Why is this statistic important? That is, why should I care about the total government liabilities of Malaysia's being 80% of its gross domestic product.

In the case of Turkey, [it][2] is mentioned that companies based in Turkey are suffering under the weight of the foreign debt amounting to some $300bn. The comparison to the countries GDP is then made again; "\$300bn is more than a third of GDP".

Again, what gives a measure on the relevance of that the foreign debt is more than a third of GDP?

How does this measure differ from country to country?

[1]: Malaysia leader on a mission (Hannah Beech and Richard C. Paddock, Sa-Su 16th of June 2018)

[2]: Pillow talk; surrender your dollars, urges President Erdogan (The Economist, 16th of June 2018)


texts: Should Prices (or Price Indices) be modelled with deterministic trend?

texts:
I always face a dilemma on whether to assume prices to have a time trend or not while modelling. It is also partly a statistics problem. Let me explain. Assume I have time series, $y_t$ of price of a commodity which on plotting appears to be having an upward slope (which is after all true for majority of items).
When I apply unit root test without drift, the result is non-rejection of unit root. However, if I include a drift term, the result is rejection of unit root.
Now, if the true process is random walk without drift, inclusion of drift is very likely to incorrectly reject the null (below is a simulation study that shows that if the true process is pure random walk, inclusion of drift rejects the null around 34% of times). The red-line is the distribution of t-statistic when ADF test is applied with drift, and blue-line when applied without drift (which is the true process).

(the vertical line is the 0.05 quantile value for DF-distribution - blue curve)
Now if the series did have a time trend (without unit root), ADF test (without drift) almost never rejects the null of unit root.
Hence the dilemma. My take is that the answer (whether trend is stochastic or deterministic) has to come from theory. So the question boils down to Why should prices have a deterministic trend? What economic dynamics would justify modelling the series as, say AR(1) process with time trend?
Code:
'%>%'=magrittr::'%>%'
n=1e4
tt_coef = 0.1

ar1 = function(phi, n=1000, tt=0, tt_coef=0,sd) {
  y = numeric(1000+100)
  for (i in 2:length(y)) {
    y[i] = phi*y[i-1] + tt*tt_coef*i + rnorm(1,mean = 0, sd = 1)
    }
  return(tail(y,n)) # first 100 observations burned to remove impact of initial condtns
}

samples_tt = replicate(n,ar1(phi = 0.7,tt = 1, tt_coef = tt_coef, sd = 8),simplify = F)
df_stats_tt = lapply(samples_tt, function(x) urca::ur.df(x,lags = 0,
                                                         type = 'none')@teststat) %>%
  unlist()

samples_rw = replicate(n,ar1(phi = 1, sd = 1),simplify = F)
df_stats_rw = lapply(samples_rw, function(x) urca::ur.df(x,lags = 0,
                                                         type = 'none')@teststat) %>%
  unlist()

df_stats_drift = lapply(samples_rw, function(x) urca::ur.df(x,lags = 0,
                                                            type = 'drift')@teststat[,1]) %>%
  unlist()

sum(df_stats_drift<quantile(df_stats_rw, probs = 0.05))/n
sum(df_stats_tt < quantile(df_stats_rw, probs = 0.05))/n

plot(density(df_stats_drift), type = 'l', lwd = 2,
     col = 'red', main = 'DF-Distribution', xlab = '')
lines(density(df_stats_rw), type = 'l', lwd = 2, col = 'blue')
abline(v = quantile(df_stats_rw, prob = 0.05))
legend('topleft', legend = c('Without Drift', 'With Drift'),
       col = c('blue', 'red'), lwd = 2, bty = 'n')


texts: Set of rationalizable strategies for this 4 x 4 matrix

texts:
I would like to find the set of rationalizable strategies for this 4x4 game:

The first thing I did was try and find all PSNE. I found two, the ones I bolded.
Thus, my answer to this question is that the set of rationalizable strategies for Player 1 is {T, Y} and the set of rationalizable strategies for Player 2 is {B, C}.
Is this answer correct?


texts: Why people respond to surveys like that of Purchasing Managers' Index?

texts:
A lot of data, including indexes, rely on surveys. For example, Purchasing Managers' Index.

(1) Why people answer these surveys (is there any benefit)?

(2) How to make sure the data is correct? What if people randomly fill in the survey, or intentionally give incorrect data?


texts: Does the law of motion remain constant in a rational expectation model? Does it constantly change in a boundedly rational agent framework?

texts:
Is the following true?

The rational expectations hypothesis also implicitly assumes that the law of motion of the economy does not change, which actually is a self-fulfilling assumption as long as all agents behave rationally. However, this is not longer true in models that introduce boundedly rational agents.


texts: What is the most general definition of “the core” in game theory?

texts:
I’ve seen definitions of “the core” that rely on some specific assumptions, such as that the game is one of a transfer of resources, or that there is “transferability of utility” (presumably intending to capture the notion of money being the source of this).

But what is the most general definition of the core? Can we talk about the core of any arbitrary game, or does the concept fundamentally only work for specific types of games?


texts:
For a highschool economics/mathematics interdisciplinary essay I will use the Lagrange multipliers and deriving formulas that find the maximum. Could some one maybe suggest any (utility) functions that have 3 (also 4) variables (doesn't matter if it has constants).
Thanks in advance!


texts: Where can I find UK stock data over the last 70-80 years? Preferably adjusted to to the inflation.


texts: Why is there less price transparency in some industries (especially healthcare) than in others?

texts:
To give a specific pair of contrasting examples:

If I search for homes for sale in say Michigan, I can quickly see the listed price for each home. (See e.g. Zillow.) Sure, there might be taxes, commission, fees, discounts, etc., but the final price I pay will almost certainly be within ±50% of the listed price I see.
But if I search for an assisted living or adult foster care home (for the elderly) also in Michigan, I am unable to find a single home that lists any price on its website, Facebook page, or anywhere else. Instead, every single home asks you to call or email them, or arrange for a tour. I have no idea what I'll have to pay, even very roughly, perhaps not even to an order of magnitude. I truly have no idea if the cost per month will be \$1,000, \$5,000, or \$10,000.

Unfortunately, from my brief search, there doesn't seem to be much research by economists on this topic (but let me know if I'm mistaken).

Here are some possible explanations I've considered:

Price transparency tends to be decreasing in price.

This might be generally true, but fails to explain why there is so much less price transparency in healthcare than in real estate.

In healthcare, there is much more uncertainty and variation as to what each patient will end up costing.

But each healthcare facility does have standard rates for particular items, such as "a standard type X blood test", "a brain MRI in Machine #566", "a 24-hour stay on Bed #125", "a month's long stay in Room #351" (excluding all miscellaneous costs). Just like any restaurant or business has standard rates for particular goods and services.

The difference is that most restaurants and other businesses do publish these prices, while healthcare facilities do not.

Why is it advantageous for healthcare facilities to keep these prices shrouded in secrecy? Why have market forces not forced them to reveal these prices (in contrast to other industries)?

The US healthcare industry is perhaps exceptionally egregious. But I think it is also generally true in most countries that there tends to be much less price transparency in healthcare than most other industries. Why is this?

Please note that any successful explanation must explain why there is less price transparency in some industries (especially healthcare) than in others (real estate, airfare, food, cars, car repair, university tuition, etc.).


texts: competitive equilibrium, Walrasian equilibrium, Walrasian auction

texts:
There are several sellers holding some indivisible goods, and several potential buyers with different valuations for these goods.  I need to calculate the Walrasian equilibrium in this scenario, but first I need to understand what exactly is a Walrasian equilibrium. So I am looking for a short, formal, operational definition of this term.

Wikipedia just links to a page about General equilibrium theory, which is very long and verbal, but I couldn't find there a formal definition of a Walrasian equilibrium.

This page also hints that a Walrasian equilibrium is similar to Competitive equilibrium, but I didn't understand whether they are identical or different, and if they are different - what is the relation between them?

There is also a page about a Walrasian auction, but again, I am not sure what is the relation between this and a Walrasian equilibrium?

The definition in the about.com dictionary looks promising: "An allocation vector pair (x,p), where x are the quantities held of each good by each agent, and p is a vector of prices for each good, is a Walrasian equilibrium if (a) it is feasible, and (b) each agent is choosing optimally, given that agent's budget. In a Walrasian equilibrium, if an agent prefers another combination of goods, the agent can't afford it."   But, they do not define what they mean by "feasible".

I would very much appreciate an orderly explanation of the relation between all these different terms.


texts: Does RBC models pin down equilibrium output, amount of labor and capital without initial condition?

texts:
In ordinary equilibrium models, we can pin down equilibrium quantity by supply-demand functions.

Is this the same in RBC models?  Can we pin down equilibrium output and amount of labor and capital without initial conditions with stochastic variations? Or do we need initial conditions (time $0$ conditions) for labor and capital?


texts: Deriving a demand curve from a Cobb-Douglas utility

texts:
Probably a daft question but I derived an equation for a demand curve from a general Cobb-Douglas utility function $$U(x,y)=\beta x^{\alpha}y^{1-\alpha}$$ given a budget constraint $$M=xP_x+yP_y$$ and found that the quantity of $x$ demanded would be $$x=\frac{\alpha M}{P_x}$$.

which surprised me in that this function is independent of the price of good $y$. I see some references on these pages which suggests that I didn't make any spectacular  errors but, my elementary understanding is that the demand curve is a functions of many thing, not least the price  of other related goods. Now surely goods $x$ and $y$ are substitutes to some extent?

Now, my question is this, is my understanding of this essentially correct and, what sort of utility functions would generate demand curves $x=f(P_x, P_y, M, etc)$?

Thank you


texts: Is there an externality if someone buys all stock of some merchandise? On one hand, if they buy all of everything and there's still demand then they've taken it away from other people. On the other hand, it kind of feels like that should be accounted for in the supply curve, and it's not an externality so much as the producers not having known the correct supply curve?


texts: Is there consensus on why inflation is not rising?

texts:
I find it kind of odd that we are not experiencing any significant inflation recent years despit the low rates and quantitative easings.

Is there a consensus why this is the case among economists? If not, what are the mos popular explanations?

I am refering to countries in weastern EU and USA.


texts: More privileges to the rich and less rights for the poor in the Great Depression?

texts:
I would like to know if in the Great Depression (1930s) the government of US and other Western governments increased the taxes for the poor or if they reduced the incomes and the rights of the poor.

I recently realized that, at least since the Irish Great Famine (1845-1852) until today, the governments' response to economic troubles was to reduce the taxes for the rich and/or to increase their privileges and to increase the taxes for the poor (or to reduce their incomes, which is basically the same thing) and/or to reduce the rights of the poor.

As for the rich, I have already found that the government's reaction was to increase their privileges:
"The government did little to address the growing maldistribution of wealth. In fact, government action worsened the problem. Andrew Mellon (1855–1937), secretary of the treasury under Presidents Harding, Coolidge, and Hoover, was one of America's richest men. He saw to it that tax cuts for the wealthy passed through Congress in the 1920s, helping the rich retain even more of their wealth. When workers tried to organize and use unions and strikes to improve their wage and health benefits, the government was hostile to such activities."
Link

So I would like to know more about this tactic of addressing poverty by increasing poverty and inequality and to what extent it was applied in the Great Depression


texts: How much does a person donate to charity unintentionally

texts:
I am wondering if it's possible to estimate what percentage of a person's salary ends up in a charity even if that person never donates?
I am not an economists and I am not sure if that is a valid argument, but it seems to me that if some percentage of population is constantly donating say 10% of their income to charity, then some of other people's income will become part of that 10% due to circulation of money.
Also, governments of developed countries often spends some small percentage of budget on foreign aid so part of income goes there. If we take an average person from a developed country, like UK, would it be possible to estimate how much that person's salary contributes to charity? Is this even a correct way of thinking?


texts: Profit maximization problem using linear regression (pooled OLS)

texts:
I'm currently on a university assignment where I'm stuck more or less in the middle. I have to answer the following problem:

Suppose you are interested in estimating the production function for agricultural output (as in the seminal article  Mundlak 1961).  You have access to data for a large number of farms $i$ for $T \geq 1$ time periods. The
production function you want to estimate is:

\begin{equation}
y_{it} = x_{it}\beta + \alpha_i + \epsilon_{it}
\end{equation}

where $y_{it}$ is log-output, $x_{it}$ is log-labour (a variable input), $\alpha_i$ is log-soil-quality (a fixed input) and $\epsilon_{it}$ is rainfall (a random input). Each farmer knows the price of output $P_t$, the wage rate $W_t$, and the soil quality of his farm $\alpha_i$. However, as the
econometrician you only observe ($y_{it}$, $x_{it}$). Assume that $\epsilon_{it}$ is $iid$ and independent of everything else in the model.

Solve the farmer’s profit maximization problem assuming he sells output
at a common (across farmers) market price $P_t$ and pays common
wages $W_t$. (Hint: It may help to write down the production function in levels instead of logs.) For notational convenience, assume $Ee{^{\epsilon_{it}}}  = \lambda$. Does the labor demand depend on $\alpha_i$? Explain the economic intuition behind the result.

This is the preceeding task which is answered as follows:

$$y_{it} = x_{it}\beta + \alpha_i + \epsilon_{it}$$ is log of the production function. So production must be

$$Y_{it} = A_iX_{it}^\beta\cdot u_{it}$$

found by taking exponential
$$\exp(y_{it}) = \exp(x_{it}\beta + \alpha_i + \epsilon_{it})$$

and defining $Y_{it} = exp(y_{it})$ $X_{it}=\exp(x_{it})$ and $A_i = \exp(\alpha_i)$ and $u_{it} = \exp(\epsilon_{it})$.

Profit max problem is then

$$ \max_{X_{it}}\Pi_{it} = P_t A_iX_{it}^\beta\cdot u_{it} - W_t X_{it} $$

Given the iid character of $\epsilon_{it}$ and the farmers knowledge the expected profit is the same with $\mathbb E[u_{it}]$ substituted for $u_{it}$:

$$ \max_{X_{it}}\mathbb E [\Pi_{it}] = P_t A_iX_{it}^\beta\cdot \mathbb E [u_{it}] - W_t X_{it} $$

The solution for labour demand is
$$X_{it}^\star= \left(\frac{P_tA_i \mathbb E [u_{it}] }{W_t}\right)^{\frac{1}{1-\beta}}$$

higher price, soil quality and expected rainfall are all expected to increase marginal revenue of labor and therfore increase labor demand for a given wage.

Here's the question on which I am stuck:

Under what assumption can you recover a consistent estimate for $\beta$ by running (pooled) OLS? Based on what you found in (1a) do you think this assumption is violated in this case? (no proof required)

Would anyone give me some hints on how to tackle this task?
Extremely glad for any help!


texts: Solving an OLG model, value function iteration vs. projection (chebyshev polynomial)

texts:
I can't decide between using value function iteration or projection on chebyshev polynomials.

I'm inclined to use projection, however I need to compute (for welfare analysis) the value of the value function at some specific age.

Using the decision rules computed by projection and derived from FOCS is it possible to compute the expected lifetime discounted utility?


texts: Why would mortgage rates go up if interest rates go down?

texts: What reasons or scenarios could cause a case where mortgage rates would rise if interest rates(federal funds rate) fall? Is that even possible?


texts:
Mankiw & Whinston (1986) show that the market may contain too many firms. The intuition is that if a firm charges a suboptimal high price, a rival has a demand curve that is "too high" and can also enter the market. This is socially suboptimal if both firms incur fixed costs and have the same marginal costs, because one firm could as well supply the total quantity alone with the same variable costs but lower total fixed costs.

What I don't understand is: Why are fixed costs needed for this resultat? Fixed costs might as well be absent. Then a suboptimal high price might allow a rival with higher marginal costs to enter the market. Note that the entrant might not even produce the same product but an imperfect substitute.

The result is somehow related to the tradeoff between increasing returns to scale and variety (see Meade, 1974) and product selection in monopolistic competition (see Spence, 1976).

If possible, a graphical representation of the answer would be much appreciated.


texts: Change in price and income using the Slutsky equation

texts:
Quantity bought is given by
$$
q(m,p) = 0.02 m - 2 p
$$
where $q$ is number of bottles bought, $m$ is income and $p$ is price per bottle.

If income is $m = 7500$ and price is $p = 30$, the number of bottles is
$$
q(7500,30) = 0.02 \cdot 7500 - 2 \cdot 30 = 75 \cdot 2 - 60 = 90
$$

Now if price rose to $p = 40$, how much income would I need in order to buy the same amount as before the price change?

I would just solve $q(m,40) = 90$ with respect to $m$, i.e.
$$
q(m,40) = 0.02 \cdot m - 2 \cdot 40 = 90 \Leftrightarrow m = \frac{90 + 2 \cdot 40}{0.02} = 8500
$$

But apparently, I should have used the Slutsky equation, so the answer is something like
$$
\Delta m = q \Delta p = 90 \cdot (40-30) = 900
$$
so the new income is $7500 + 900 = 8400$.

But with an income of $m = 8400$ and price $p = 40$, I cannot afford 90 bottles since $q(8400,40) = 0.02 \times 8400 - 2 \times 40 = 88$, So why is this solution correct?

Why is my solution incorrect and how is $\Delta m = q \Delta p$ related to the Slutsky equation?


texts: How did reducing the employment gender gap impact the US economy?

texts:
Premise
In the United States, women have been replacing men in the workforce, or rather were from sometime prior to 1976 until the mid-90's. (The general upward trend is from the recent recession, sorry, I'm recycling a graph from another presentation).

Presumably, this occurred when a more qualified woman got a job over a male counterpart as women entered the workforce.
Given that, one would expect the economy to grow substantially as overall productivity rose.
Yet US GDP growth did not appear to outpace the world over that period, since not all the world liberalized their gender roles simultaneously.

Question
Why is that?
Is there a flaw in the reasoning, or were the effects simply not visible at the scale I've looked because the data was too volatile or confounded by external factors.
I'd be interested in any studies that dealt with this topic and offered potential causal mechanisms for breaking the presumed link between (again, the presumed) increased efficiency, and output growth.
Thanks!
Sources:

LNS10000001 - Civilian noninstitutional population, male
LNS11000001 - Civilian labor force, male
LNS10000002 - Civilian noninstitutional population, female
LNS11000002 - Civilian labor force, female
Google


texts: Derive optimal wage in New Keynesian-Calvo wage stickiness

texts:
Following Costa, 2016 in page 96, developing the labor variety optimal wage decided by the household, the FOC is:
$$0=E_t\sum_{i=0}^\infty(\beta\theta_w)^{t+i}\left\{\psi_W\left[L_{t+i}\left(\frac{W_{t+i}}{W_{j,t}^\ast}\right)^{\psi_W}\right]^\varphi L_{t+i}\left(\frac{W_{t+i}}{W_{j,t}^\ast}\right)^{\psi_W}\left(\frac{1}{W_{j,t}^\ast}\right)+(1-\psi_W)\lambda_{t+i}L_{t+i}\left(\frac{W_{t+i}}{W_{j,t}^\ast}\right)^{\psi_W}\right\}$$
I can reach this equation, nevertheless in the next equation from the book, the term $\left(\frac{W_{t+i}}{W_{j,t}^\ast}\right)^{\psi_W}L_{t+i}$ is factored and cancelled out since the other side of the equation is $0$. My question is whether this is valid, since $W_{t+i}$ and $L_{t+i}$ are functions of the infinite series since they're indexed with $i$, then I would like to know if this is algebraically valid, or if it's a mathematical typo. And if it's valid, how can I derive the next equation, where the mentioned terms are cancelled out.
Thanks!
PD: If it helps:
-This is how $L_{j,t+s}$ is defined: $L_{j,t+s}=L_{t+s}\left(\frac{W_{t+s}}{W_{j,t}^\ast}\right)^{\psi_W}$.
-$W_{j,t}^\ast$ is not a function of the summation (check the indexes).
-The idea is to obtain a closed expression for $W_{j,t}^\ast$.


texts: Application of 'Fermi's Golden Rule' to Economics

texts:
Wikipedia says:

  'Fermi's golden rule describes a system which begins in an eigenstate, ${\displaystyle |i\rangle } |i\rangle$ , of an unperturbed Hamiltonian, $H_0$ and considers the effect of a perturbing Hamiltonian, $H'$ applied to the system. If $H'$ is time-independent, the system goes only into those states in the continuum that have the same energy as the initial state. If $H'$ is oscillating sinusoidally as a function of time (i.e. it is a harmonic perturbation) with an angular frequency $ω$, the transition is into states with energies that differ by $ħω$ from the energy of the initial state.
  'In both cases, the transition probability per unit of time from the initial state ${\displaystyle |i\rangle } |i\rangle$  to a set of final states ${\displaystyle |f\rangle } |f\rangle$  is essentially constant.'

Does anyone know of an Econ paper which uses this? Alternatively, what might an application of it be?


texts: Where can I find research on the impact of informal/unregulated suppliers on prices and externalities?

texts: I am looking for research and papers on the impact of informal/unregulated suppliers on market prices and negative externalities. I am particularly interested in the manufacturing sector.


texts: Dynamics of interest rates, exchange rates and bond prices within the UIP

texts:
There are already a few questions about the workings of the UIP and the exchange rate. What I have basically taken from those discussions is that one always has to distinguish between the spot rate and the expected future rate.
Let's take the UK as our domestic country and the US as a foreign one, making the exchange rate E_t = X $/£. If the UK increases its interest rate, the spot rate will, ceteris paribus, increase due to capital flows into the UK. Now, since the UK interest rate is still above the US interest rate, one would expect the pound to depreciate versus the dollar, i.e. the future expected exchange rate would decrease. This was just to establish my understanding of the UIP, in case my reasoning is flawed in some way.
The point that after the capital flow into the UK and the spot rate increase, there is still an interest rate differential, is crucial for my reasoning that follows below.
What I don't understand is how the future expectations part of the UIP can be reconciled with the relationship between interest rates and bond prices. Let's take again the above example. If the UK increases its interest rate above the US interest rate, there will be a flow of capital from the US into the UK, because UK bonds promise higher returns. This, in turn, will drive those bond prices up. On the other hand, because people will sell US bonds, the prices of US bonds will go down. Now, since interest rates and bond prices are inversely related, the flow of capital into the UK and the increase in bond prices will drive the interest rates on those bonds down. At the same time, the flows of capital out of the US and the decrease in bond prices will drive the interest rates on US bonds up. This will cause both interest rates to equalize again.
What I fail to understand now, is why we would still expect a future depreciation of the pound / appreciation of the dollar, if the interest rate is already equalized in the first place due to the relationship with bond prices. Because in order to use the UIP, there must be an interest rate disparity that will cause the currency of the country with the higher interest rate to depreciate in the future.
Somewhere there must be a flaw in my reasoning, but I fail to see where. My guess is that it has something to do with the time dynamics involved. However, in the usual understanding of UIP dynamics that I have described in the first paragraph, the spot rate adjusts immediately after the increase in the interest rate due to capital flows into the UK. So if these capital flows are taken as an "immediate action" after the interest rate change,
bond prices would have to adjust immediately likewise, and the interest rates would have to be equalized again. This would also make sense as the UIP assumes perfect capital mobility.
Can someone see where I fail to consider something?


texts: How are recessions even possible if its impossible for banks to lose money?

texts:
When a bank issues a loan, the money must end up with another bank. Therefore, the banking system as a whole can never lose money. Only the dumb banks which make loans that arent repaid can ever lose money.
Therefore, is a recession only possible if there is a divide between "smart" and "dumb" banks? Is it the case that, in any recession caused by bad loans, there must always be at least one smart bank somewhere that is profiting and solvent? Since the money has to go somewhere it seems there always has to be at least one bank that is least dumb and ends up with all of the money from others. In fact, the only reason m2 would fall at all is a composition effect whereby the dumb banks are more leveraged and fail.


texts:
I'm a little confused by the following question and answer provided by MRU:

Fruit farmers pay beekeepers for their honeybees’ pollination
services. Honeybees provide an external benefit to fruit farmers.
However, fruits provide an external benefit to the beekeepers because
their honeybees need fruits. Which external benefit is larger:
honeybees’ external benefit to fruit farmers and fruits’ external
benefit to beekeepers?

Their answer:

Honeybees’ external benefit to fruit farmers is larger

This seems like the least fitting answer to me.  The fruit farmers pay the beekeepers for their services, so the benefits they get from this relationship are mostly accounted for by the cost.  However, beekeepers don't have to pay the farmers for the benefit their bees get from pollinating their plants, so this benefit is an external benefit that farmers give to beekeepers.  Am I misunderstanding something here?


texts:
China has fabricated its GDP in the past. Which are the real-world repercussions of doing so?

Let me pose an scenario: If China were in a recession (say, -1% for two quarters), but posts 1% for both, which would be the consequences, if the world acted in accord with those figures? Would it impact variables like currency value? Inflation? Interest rates? SHCOMP? Trade surpluses that don't match the published GDP?


texts: What is the main difference between FDI and short run capital inflows/outflows? I feel like both are quite similar in their nature but I don't understand the distinction between the two fully. Many thanks!


texts: Who was the inventor of Utility function?

texts:
To my knowledge, the idea of representing weak-order with a function dates back to Cantor. So my questions are:

1) Was Cantor the first person to rigorize these kinds of representation?

2) Were there anyone in the ancient world who (though not rigorously) developed the idea of representing social choice or preference by a function?


texts: How net capital outflow is equal to net exports suppose I export a car to US and in return i got few thousand dollars then instead of acquiring any asset abroad i decided to bring money back to my home country by exchanging dollar with local currency. Can any one clear my confusion?


texts: Does money neutrality mean that nominal GDP (output) changes following changes in money supply?

texts: If money neutrality stipulates that only nominal variables will be affected following changes in money supply, then does this mean that following such money supply changes, real GDP remains unchanged while nGDP changes, as changes in money supply causes changes in price levels, and nGDP is by definition real GDP (which is unchanged) * price level deflator?


texts: Inclusion of firms on the efficient frontier of a Production Possibility Set

texts:
I'm working through Cooper's Data Envelopment Analysis, and they are going over Production Possibility Sets.

They present 9 firms, each with two inputs and one output:

Graphically it easy to see why firms (E,D,C) make up the efficient frontier, however I am struggling to find a mathematical motivation for the inclusion of firm D? How do you show its input/output ratios warrant its inclusion algebraically as opposed to graphically.


texts: How can successful small caps outperform large caps, when they become large caps?

texts:
For example, pretend that some S&P 600 corporation succeeds and profits, like some biotech discovers multiple cures to disease like cancer. Assume that its market capitalization then skyrockets enough that it becomes a large cap and joins the S&P 400 or S&P 500.

Wouldn't it join either of the larger S&P indices? Are there reasons that it'd choose to remain S&P 600?

If so, then this former small cap has become a large cap. So how can small caps historically outperform large caps after recessions?


texts: What does it mean "non-Walrasian" or "quasi-Walrasian"?

texts:
In a recent NBER workshop, Robert Hall started a discussion with his first slide summarizing the macro literature.

I am not very familiar with either DMP model or New Keynesian model and have no idea about any of his statements in this slide. Can anyone explain them without going to the very detail of the models?


texts: I'm looking for literature in new keynesian model adaptation to model price shocks. I'm aware of Blanchard, Olivier, and Jordi Gali.  2007.  “The Macroeconomic Effects of Oil Shocks: Why Are the 2000s So Different from 1970s.”  NBER Working Paper No. 13368. Do you know other adaptations of the new keynesian model in this way or from the exporting country view?


texts:
I apologize if this question is very basic. I have the following plain vanilla Instrumental Variable model.

$Y=\alpha+X\beta+\varepsilon$

$X=\delta+Z\gamma+\eta$

$\varepsilon\perp\eta,\quad Z\perp\eta \quad$ true

I am interested in testing $\varepsilon\perp X$, that is, whether X is a valid instrument for the first equation (very informally stated, one might say I want to test whether $X$ is exogenous, or whether I need to instrument $X$ with $Z$)

My idea is: estimate the IV model using 2SLS or GMM, using both $X$ and $Z$ as instruments, and then perform a Sargan/Hansen test. My guess is that the test's power will depend on how strongly $Z$ predictx $X$ (that is, on how relevant of an instrument $Z$ is for $X$). In 2SLS, the first stage will fit perfectly and the test will be basically a test of whether the OLS residual are orthogonal to $Z$. Is this reasoning correct? Is the Sargan/Hansen test a valid test for $
\varepsilon\perp X$?


texts: Difference between IS curve viewed by Keynes and by Friedman

texts:
In my economics lectures, we are going through Keynes vs Friedman. As far as I got we have a downward sloping IS curve in the IS-LM model. We get this curve from the Keynesian cross when the rate of interest decrease and plant expenditure/investment increase and thus output grows. However, my lecturer also mentioned Keynes trying to criticize monetarism says that IS curve can be perfectly inelastic, therefore outward shift in LM won't affect the output much but will reduce the interest rate, whereas Friedman side has IS curve as usual downward sloping, thus making investors interest rate elastic. How is this possible? Seems like I am missing something, could you help?

What are the general assumptions about interest rate in a restatement of Quantity Theory of Money by Friedman? and what are the assumptions that Keynes made regarding interest rate?


texts: How can I obtain monthly unemployment by ethnicity by state for the US?

texts: Grateful for any help, thoughts and direction.


texts: Demand Curve Price not perfectly elastic

texts:
I'm trying to make the argument that our Sales go up when prices for all our Products are 30% off. Which I believe should be our new Regular Price. but our Demand Curve doesn't support this. Should I be setting up the demand curve differently? on a per product basis? or package size?

I sell our food product in different package sizes
2oz, 4oz, 9oz , 16oz 3.5lb
Normalized the time our products were at that price.


texts:
How does the companies set up utility function for its own purposes?

In another word, what is the types statistics data that is usually consider and statistical method being used to set up these functions? Just name the types of methods and types of data out.

I heard that the function itselves is always to be a secret of a company but why are they always different between different companies?


texts: Deriving log-linearized equilibrium in Galí (2019)

texts:
I am reading the Paper "The effects of a money-financed fiscal stimulus" by Galí (2019).
I am trying to derive the log-linearized equilibrium as given in equations (15)-(22). I believe I am able to derive all equations expect for equations (17) and (20). I suspect that equations (12) and/or (13) should be used in deriving at least one of (17) and (20) (and possibly both).
Does anyone have any idea how to proceed?


texts: Gapminder's Dollar Street and the role of self-supply

texts:
I find it quite hard to get a clear picture of what the income numbers in Gapminder's Dollar Street tell. How to compare \$27 in Burundi with \$10,098 in China? What would it mean that the family in Burundi is 500 times "poorer" than the family in China?

There are two aspects that are unclear to me:

Wouldn't it be a better measure (than income is) to quantify how much of the money one needs to lead a "normal healthy" life one has at ones disposal (in percent)? How is this measure called?
What about self-suppliers (what many families in poorer countries are)? They own and need less money (income) than others do, but how is the value of their self-supplying work measured?

In the context of self-supply: Wouldn't "belongings" be a better measure than "income"?


texts: Compensated demand function for perfect complement indifference curve

texts: For example, the indifference curve for goods $A$ and $B$ is $min$. How should I express its compensated demand function if the quantity of A does not depend on its price because of the zero substitution effect?


texts: How can the replacement level fertility be 2.1 everywhere in the world?

texts: Common sense would indicate that the replacement level fertility of Norway ought to be lower than that of Sudan due to fewer children dying there. Why, then, is the replacement fertility rate universally taken as 2.1?


texts:
If I have data that is on some level, say industry-county-year, and a certain treatment, say a regulation change in some states in certain years. Is it possible to run a Dif-in-Dif on the industry-county-year level and cluster by states? Or do I overestimate my statistical significance if I don't aggregate my data to the state level first? If it is not necessary, are there any advantages to aggregating?
And would clustering be a problem if only one state is treated? Thus, if there would only be 1 treatment cluster and ~50 control clusters.


texts: Multiplant Monopoly With Third Degree Price Discrimination

texts:
I am trying to do an exercise with a Monopoly Firm with 2 production plants that supplies 3 different markets.

I know how to do every case (Multiplant monopoly or third degree price discrimination), but since this exercise combines both cases, I dont know how to solve it.

Can anyone tell me how to proceed? This are the costs for every plant, and the demand for each market, for clarification.


texts: Calculating natural rate of unemployment

texts:
I have sample data on unemployment rate in a market and am looking to calculate the natural unemployment rate. The natural unemployment rate I obtained is constant over a time period, which is not a realistic assumption given the fluctuations we observe in labor force, employment.
As per the keynesian relationship between unemployment and inflation, the natural rate is defined as rate when inflation is stable or change in inflation is 0.
Pandas DataFrame:

import pandas as pd
import numpy as np
import random

df = pd.DataFrame({
                   'Date_Col': pd.date_range(start='1/1/2010', periods=40, freq='3M'),
                   'unemployment': np.random.uniform(5,12,40),
                   'Inflation': np.random.uniform(1,3, 40)
                  })

df['Change_Inflation'] = df['Inflation'].pct_change(periods=1)

# Drop first row
df1 = df[2:len(df)]
df1

I fit the following regression model to obtain estimates and calculate the natural level of unemployment:
change in inflation = b0 + b1 * unemployment + e

Substituting, change in inflation = 0, and solving for unemployment, the natural unemployment rate = b0/b1. The rate I obtained is for entire time period, this isn't realistic as there are significant supply side fluctuations in labor force. Therefore, I'd like to calculate the natural rate for each time period. How would I do so?


texts: Can the endowment point be the competitive equilibrium?

texts:
Quoting from MWG p.519, Chapter 10: Pure Exchange, The Edgeworth Box

  ..., any intersection of the consumers' offer curves at an allocation different from the endowment point $\omega$ corresponds to an equilibrium..."

Does this mean that the endowment point can never be an equilibrium or that the crossing of offer curves there is not enough to guarantee that?


texts: proof of uniqueness of Dominant strategy equilibrium

texts:
This exercise is from book: Steve Tadelis, Intro to game theory, chapter 4 exercises.

Prove: If the game $\Gamma= \{N,\{S_i\}^n_{i=1},\{v\}^n_{i=1}\}$ has a strictly dominant strategy equilibrium $s^D$, then $s^D$ is the unique dominant strategy equilibrium.

My attempt:

Proof by contradiction: Suppose $s^D$ were not the unique DSE. Then $\exists s'^D\in S'^D$ such that $v(s'_i,s'_{-i})\geq v(s_i,s_{-i})$ where $s'_i,s'_{-i}\in S^D$ and $s_is_{-i}\in S^d$. But this contradicts the assumption that $s^D$ is the DSE.

Would this be correct?


texts:
I'm not sure how to determine the range for which a shadow price is valid.

You might be able to skip straight to the question here.

I've been introduced to it using the following approach in 2D.

Context

Given an optimal solution which is at a corner, there are two intersecting
lines. Say that these lines represent the following inequalities

\begin{equation}
  \begin{aligned}
    2K + 3S & \leq 10 \\
    K + 2S & \leq 6 \\
    Z & = 30K  +  50S
  \end{aligned}
\end{equation}

Then the shadow price is the change in the objective function, $Z$, when the
right hand side of an inequality is changed by one unit.

Computing this for the second equation is done as follows:

\begin{equation}
  \begin{aligned}
    2K + 3S & \leq 10 \\
    K + 2S & \leq 6 + \Delta\\
  \end{aligned}
\end{equation}

Then subtracting the second equation from the first twice

\begin{equation}
  \begin{aligned}
    S & = 2 +  2 \Delta
  \end{aligned}
\end{equation}

Therefore

\begin{equation}
  \begin{aligned}
    K &= 2 - 3 \Delta
  \end{aligned}
\end{equation}

And the objective function can be written as

\begin{equation}
  \begin{aligned}
    30K + 50S &= 30(2 - 3 \Delta) + 50(2 + 2\Delta) \\
    &= 160 + 10 \Delta
  \end{aligned}
\end{equation}

And the shadow price is found from $z(1) - z(0)$, where $z(\Delta) = 160 + 10
\Delta$ which gives $10$.

Therefore the shadow price is 10.

But how do I compute the range for which this is valid? I can get through the
algebra here pretty easily, but there's little meaning to it.

Question

How do I determine the range for which I can adjust the second inequality such
that the difference made to the objective function is $10 \times
\text{adjustment}$.


texts: Why does average variable cost = marginal cost for this function?

texts:
I was hoping someone could explain the following. Suppose the short-run total cost function is TC = 50 + 12Q. Which of the following statements is true at all levels of production?

The correct answer given was that MC = AVC

Could someone explain to me why please?


texts: Are there any effective research efforts into combating wealth inequality?

texts:
There seems to be no "correct" answer in combating wealth inequality; however, we should attempt to use different methods to combat inequality in cities, then counties, then states, then countries.

However, Politics is a huge barrier. Politicians are afraid to make any drastic efforts.

I don't want to sound opinionated so I won't ask, "What are the best ways to combat wealth inequality". Instead, I will ask, "Are there any effective research efforts into combating wealth inequality"?

I also made a similar post on wealth distribution (for you to see) but the question was deleted for being too broad.


texts: First and Second Order Lagrangian-Multiplier Conditions for Optimization

texts:
The Statement of the Problem:

Let $f,g$ be two functions on $\mathbb R^n$ and assume $\nabla f $and$ \nabla g$ are nonzero everywhere. Write the first and second order Langrangian-multiplier conditions for the following two problems:

$$(1) \text{ minimize } f(\mathbf x) \text{ subject to constraint } g(\mathbf x)=b $$

$$(2) \text{ maximize } g(\mathbf x) \text{ subject to constraint } f(\mathbf x)=c  $$

Given a solution $\mathbf y$ to first and second order conditions for the minimization problem $(1)$, for some value of $b$, set $c=f(\mathbf y)$ and consider the maximization problem $(2)$; when is $\mathbf y$ a solution to this problem as well?

My Questions:

I believe I have the first-order conditions for $(1)$:

$$ \frac{\partial \mathcal{L}(\mathbf x)}{\partial x_i} = \frac{\partial f(\mathbf x)}{\partial x_i}-\lambda \frac{\partial g(\mathbf x)}{\partial x_i}=0$$

But what are the second-order conditions? I know that, in order to minimize $f$, $\mathcal{L}$ must be convex and that the constraint set must be convex, but are those the "second-order conditions"? If so, how do I determine them? By way of bordered Hessians? That doesn't seem right. Anyway, any help here would be appreciated. Thanks!


texts: Production Set: Not satisfying Free Disposal Assumption

texts:
I saw the figure which satisfies the free disposal assumption in Mas-Colell, Whinston and Green (1995), but wondering if there is a figure that DOES NOT satisfy the free disposal assumption? Any leads will be great.
Thanks!


texts: Is the Convex Combination of Two Pareto Optimal Allocations Also Pareto Optimal?

texts:
I am studying for my qualifiers, and I ran into this question from a previous year's exam.

$\textbf{Question:}$

Consider a two-consumer two-good pure exchange economy. Both preferences are locally non-satiated and convex. Prove or disprove the following statement: if $(x_1,x_2)$ and $(\hat{x}_1,\hat{x}_2)$ are two different pareto optimal allocations, then the convex combination, $(\alpha x_1+(1-\alpha)\hat{x}_1,\alpha x_2+(1-\alpha)\hat{x}_2$ MUST also be pareto optimal for any $\alpha\in(0,1)$.

I believe the statement is true, and here is the work for my proof below.

$\textbf{My Proof:}$
By pareto optimality of $x_i$ and $\hat{x}_i$:
$$\not\exists\; x_i^\star\; s.t.\; u_i(x_i^\star)\geq u_i(x_i)\;\forall i\; \text{and}\; u_i(x_i^\star)> u_i(x_i)\;\text{for at least one }i \;\text{or}\;u_i(x_i^\star)\geq u_i(\hat{x}_i)\;\forall i\; \text{and}\; u_i(x_i^\star)> u_i(\hat{x}_i)\;\text{for at least one }i$$
$$\implies\;u_i(\alpha x_i)\geq u_i(\alpha x_i^\star)\;\forall i\;\text{and}\;u_i((1-\alpha)\hat{x}_i)\geq u_i((1-\alpha)x_i^\star)\;\forall i$$
$$\implies\not\exists\;x_i^\star\;s.t.\;u_i(\alpha x_i^\star+(1-\alpha)x_i^\star)\geq u_i(\alpha x_i+(1-\alpha)\hat{x}_i)\;\forall i$$
$$\text{and}\;u_i(\alpha x_i^\star+(1-\alpha)x_i^\star)> u_i(\alpha x_i+(1-\alpha)\hat{x}_i)\;\text{for at least one}\;i$$
$$\implies (\alpha x_i+(1-\alpha)\hat{x}_i)\;\text{is pareto optimal}$$
$$\blacksquare$$

This proof seemed almost too easy, so I'm wondering if it is correct/rigorous.


texts: Matlab: Solow Model Convergence of capital

texts:
I am currently trying to create a while-loop which iterates the evolution of the capital stock until it converges on the n-th digit. As I am still quite new to Matlab I face a lot of problems. I would be very thankful for any kind of help.
Here is my code:
% Model parameters
alpha = 1/3;    %
s     = 0.2;    % Investment rate
delta = 0.2;    % Depreciation rate
n     = 0.02;   % Growth of labor force
g     = 0.01;   % technological progress

eps  = 1;
k(1,1) = 0.5;
i=0;

while  eps >= 1.0e-5
    t = t+1;
    k(1,t) = (1/((1+n)*(1+g)))*((s*k(1,t-1)^alpha+(1-delta)*k(1,t-1)));
     z = k(1,t);
    z1 = k(1,t+1);
         kdif = z1-z ;
          eps = max(abs(kdif));
    i = i + 1;
  if i >= 300
    break;
  end
end


texts: Econometrics - Why does adding a dummy varaible improve my Ramsey RESET test result?

texts:
As I understand, the Ramsey RESET test (although called ovtest on Stata), is not actually a general test for omitted variable bias. Rather, it is a test for misspecification. Specifically, if the model is properly specified, "no nonlinear functions of the independent variables should be significant when added to the estimated equation". So now I'm confused because after estimating three models, I get these results.

So according to this, the null of no omitted variables (or no misspecification) will be rejected for the first two but not the last (at 5% sig. level). Yet, the translog is essentially the log-log with higher powers of the independent variable, so I'm confused as to what to conclude from this. I'm inclined to say that the dummy variable was an important omitted variable, but then again RESET is not a general test for OVB.

Perhaps also worth mentioning is that I am assuming I can conduct the ovtest as a test for endogeneity to check the OLS assumptions (because this is the only relevant test we were taught that isn't the 2SLS/Wu-Hausman).


texts: Who originated the term "deadweight loss" and when?

texts: I am looking for the first use of the term "deadweight loss."  Any suggestions either as to who it was who first used it or how to search for it?


texts:
Anyone would like to help me show the following ( or a book/paper reference would be a great help)
" The price  elasticity of demand is equal to $\sigma$ for the demand function of CES preference, $d(p_i,I,P)=\dfrac{p_i^{-\sigma} I}{P^{1-\sigma}}$, where $P=\left(\sum_{j=1}^N p_j^{1-\sigma}\right)^{\dfrac{1}{1-\sigma}}$ and $I=\sum_{j=1}^Np_jx_j$."
The formula for the price elasticity of demand is given by $\epsilon_i(p_i,I,P)=-\dfrac{\partial d(p_i,I,P)}{\partial p_i}\dfrac{p_i}{d(p_i,I,P)}$.
I have tried many times but couldn't get the desired answer. Thank you very much in advance.


texts: Interpreting coefficient in the disutility function as disutility tolerance?

texts:
I am studying a model that relates incentives (money) and a set of actions.

Let $f(x) = k\frac{x^2}{2}$ be the disutility function of the agent, where $x$ is the level of effort that the agent is exerting and $k$ is set exogenously. I found that if $k > \theta$, $\theta$ is also set exogenously, then the incentive plays an insignificant role at determining the set of actions.

How should I interpret that?

My own interpretation is that the agent has low intention to exert a high level of efforts that even being compensated, they would not exert the necessary level of actions.

Am I right? How can microeconomics interpret the coefficient $k$? I understand that it is the marginal disutility, but it does not sound very practical. Can anyone please give me some reading/intuition behind the disutility function?

Updated: I am thinking of using the work: disutility tolerance but I cannot find any literature on the term.


texts: Some issues with HRS (Health and Retirement Study) data

texts:
I am using the 1992 HRS (Health and Retirement Study) dataset. The
codebook is available at
http://hrsonline.isr.umich.edu/modules/meta/1992/core/codebook/14_h1.htm

I am trying to construct the share of HRS respondents that lost their
job because of business closure (see the variable 3612 at the link
reported above). I cannot understand what is the meaning of: 1.
Checked 5. Not checked

What happened to these respondents? There is a note about checking
just below the question but I still do not understand what "Checked"
and "Not Checked" actually mean.

Finally, the total number of observations in 1992 are 12652. In fact,
including all answers, we have that there are 12652 observations
(i.e., the summation of the possible answers reported below).

        V3612 Code  Frequency
        ---------------------
                0        6338
                1        1175
                2         222
                5        4888
                9          29

It seems that both respondents that were "checked" by the interviewer
and respondents that were "not checked" by the interviewer DID NOT
ANSWER the question. Am I correct?


texts: How are PPP, nominal exchange rates and inflation related?

texts:
This Forbes article discusses how changes in the market exchange rate can be used to estimate an inflation rate thanks to the principle of purchasing power parity (PPP).

Can someone distill this process a little better? I can follow the steps mentioned in the article, but the underlying principles are still not clear to me.


texts: Causal Interpretation of $\beta_1$ with a Dummy explanatory variable

texts:
Suppose you run a regression (over the entire sample) of hourly earnings $Y$ with an intercept and a binary variable $D$, where $D$ takes on a value of $1$ if the individual has a college degree and $0$ otherwise:
  $$Y=\beta_0 + \beta_1D+U$$
  with $E(U|D)=0$. Does $\beta_1$ admit a causal interpretation?

My instinct says yes since the zero conditional mean implies zero covariance, which then gives unbiasedness and consistency for $\hat{\beta_1}$. But the solution says otherwise:

  We should not expect $\beta_1$ to admit a causal interpretation here: If $U$ captures all unobserved factors which determine hourly earnings, it should not be the case that $E(U|D)=0$ as $U$ should include some measure of ability which we would expect it to be correlated with $D$. $\beta_1$ simply captures the average difference in hourly earning between grads and non-grads.

Can someone please explain to me how my intuition was wrong?


texts: price elasticity: Linear regression low r square

texts:
I faced an interview question for a job where interviewer asked me suppose your r square is very low (between 5 to 10%) for a price elasticity model.

How would you solve this question? Anything that a typical econometrics guy would do?

Edit: I have posted this question in stats.stackexchange.com forum for understanding this problem from the perspective of model diagnostics and feature engineering


texts: What is consumer debt and how could it make businesses vulnerable?

texts: Consumer debt is the obligation to pay for the credit that the customers have used. But, how can tapping out more credits make business more vulnerable?


texts: advice on econometric or methodological approach of my master thesis

texts:
For my master thesis, I am studying the effect of input trade liberalizaion on Research and development decision depending on firms' financial constraints in India. I have a firm level database from 1991 to 1997 (before the asian crisis).

At a first step, I run a baseline regression with Research and development dummy as a dependant variable and input tariff, output tariff, interacted term between input tariff and importer status and some control variables. This works fine. A decrease in input tariff increases the probability to R&D. I used a fxed effect logit model and a linear probability one.

At a second step I use Rajan and Zingales's external financial dependance. I split my sample into high constrained firms and low constrained firms and I run the exact same model for the two groups (i.e R&D dummy as dependant variable and same explicative variables). I find that the highest constrained do more research and development. I compare the two coefficients in front of input tariff variables.

At a thrid step, I use an endogenous financial variable constructed from my database = leverage ratio. This is a robustness check for rajan and zingales' method When I slipt my sample into two groups high constrained and low constrained using leverage ratio, I find the opposite, the highest constrained are doing less research and development.

Do you have any advice for me to improve my work?


texts: Why do game theorists use a discounted payoff of this form?

texts:
Excuse the click-baity title. I notice the discounted payoff in the game theory literature usually takes the form

$$\sum_{t=1}^\infty\lambda(1-\lambda)^{t-1}R_t$$

This differs from the discounted payoff in the other dynamic optimization settings, e.g., see the Bellman equation in control theory.

Why the difference?


texts: Second order partial derivative and cross second-order partial derivative

texts:
I'm following a paper (Full text available here!) where at some point (pag.17 and 20) the author get the following derivative:

$$\frac{\partial V}{\partial L}=Y-X\frac{dY}{dX}=\alpha X^{-\frac{c}{b}}Y^{\frac{1}{b}}$$

where: $Y=\frac{V}{L}$ and $X=\frac{K}{L}$

Then, starting from this he calculates the partial derivative with respect
to L and the cross second-order partial derivative (the partial derivative with respect to K), whose results are shown below:

$$\frac{\partial^2 V}{L^{2}}=-\frac{\alpha }{bL} X^{-\frac{c}{b}}Y^{\frac{1}{b}-1}\left ( X\frac{dY}{dX}-cY \right )$$

$$\frac{\partial^2 V}{dKdL}=\frac{\alpha }{bL} X^{-\frac{c}{b}-1}Y^{\frac{1}{b}-1}\left ( X\frac{dY}{dX}-cY \right )$$

I was stuck trying to derive these latter derivatives. Is there anyone who can help me with this? Thank you so much!


texts: Quarterly regression, year-fixed effects

texts:
I am trying to inspect the heterogeneous effects of a USA-based shock on a panel of countries using quarterly panel data. My variables of interest are the USA-based shock (which has only temporal variation and is mildly serially correlated) and the interaction of this variable with another variable that has cross-sectional and temporal variation too. My question would be whether it makes sense to include year-fixed effects in this regression?
I mainly worry about something like controlling for a downstream variable (subtracting part of the effect of the US shock with the year-fixed effects).


texts: Impact of technology shock on hours worked in basic RBC model - short and long run with logarithmic preferences

texts:
First off, I apologise if, in the following, I do not present the model adequately - I'm at an intermediate level of the study of economics. My question is at the bottom.

Anyway, consider a basic RBC model, where there are a large number of representative firms and infinitely-lived agents, who behave according to the rational expectations and permanent income hypotheses.There is perfect competition. We also assume that agents know exactly what will happen in the future.

The model presented mathematically:

The consumer's problem:

$max\sum_{t=0}^{∞}β^t[u(c_t)+v(1-h_t)]$

s.t. $\sum_{t=0}^{∞}βR^{-(t+1)}c_t=A_0+\sum_{t=0}^{∞}βR^{-(t+1)}w_th_t$

where $β=$ the discount rate; $R^{-1}=\frac{1}{1+r}$, $u=$ a function representing the value of consumption, $v=$ a function representing the value of leisure, $h_t=$ hours worked

The firm's problem:

$max{π=A_t}f(K_t,h_t)-w_th_t-r_tK_t$

We assume all savings are invested in capital, so we have:

$K_{t+1}=(1+r+δ)K_t+w_th_t-c_t$

where $δ=$ depreciation rate of capital.

Then, using the fact that the three markets of the model clear (goods, labour, capital), and assuming constant returns to scale, we have three equilibrium conditions (after some maths):

$u'(c_t)=β(1+A_{t+1}f_1(K_{t+1},h_{t+1}-δ)u'(c_{t+1})$ - intertemporal savings/consumption choice

$\frac{v'(1-h_t)}{u'(c_t)}=A_tf_2$ - consumption/leisure tradeoff

$K_{t+1}=(1-δ)K_t+A_tf-c_t$ - law of motion for capital

What I'm interested in is what happens to hours worked when there is a positive technology shock with logarithmic preferences. I have already shown that the income and substitution effects cancel each other out in the steady state of the model - but supposedly, in the short run, the substitution effect dominates the income effect with logarithmic preferences. Can someone explain this to me why and show this to me mathematically?


texts: Migration wage differential, Borjas (2013) textbook

texts:
Basic calculus question here! I started reading the textbook Borjas, G. J. (2014). Immigration economics. Harvard University Press and am confused already with the first result.
Background: He frames the migration decision in terms of wage differences between two countries $i \in \{0,1\}$ in each country (home is 0)
$$
log (w_i) = \mu_i + v_i
$$
where $\mu_i$ is the average wage in home and potential destination and $v_i $ is an i.i.d normally distributed random variable with mean 0 and variance $\sigma^{2}$. If $i=1$ is destination country, then migrant will pay a cost $C$ to move there.
Calculation: Okay, the simple algebra is then to combine these elements into an index
$$
I = log \left(\frac{w_1}{w_0+C} \right) \approx (\mu_1 - \mu_0 - \pi) + (v_1 - v_0)
$$
with $\pi = C/w_0$.
Steps: So I did some log manipulations (see below) and think I arrive at this if the $log\left(1+\frac{C}{w_0}\right) \approx log\left(\frac{C}{w_0}\right)$. Is this an approximation one does? If yes, do you background at to why? Or is the simplification different?
$$
log \left(\frac{w_1}{w_0+C} \right) = log (w_1) - log(w_0+C) + log(w_0) - log(w_0) = log (w_1)  - log(w_0) - log\left(1+\frac{C}{w_0}\right) = e^{log(\mu_1 + v_1)} - e^{log(\mu_0 + v_0)} - e^{log\left(1+\frac{C}{w_0}\right)} \approx (\mu_i - \mu_i - \pi) + (v_1 - v_0)
$$


texts: Depreciation vs. obsolescence in RBC and New Keynesian DSGE models

texts:
A common calibration for depreciation rates within RBC models is to assume 10% depreciation rate (based on NIPA stats, for instance). This implies a half-life of about 6.5 years. But this estimate seems a little low for advanced economies where capital is often in the form of computerized technology etc, which would seem to depreciate at a much faster rate (say 25% pa, implying a half-life of more like 2.5 yrs). Further, with technological advance you have the problem of obsolescence - the useful life of a capital good may end long before it depreciates away fully using the 10% pa rate. There is an element of unpredictability around obsolescence as well.

How can this be accounted for within RBC and DSGE models? Would obsolescence pose a problem for calibrating a model assuming delta is approx. 10%?

Thanks in advance,

R.


texts:
I have a question about the gravity equation. In the Feenstra textbook, on page 144, it is stated that

  In the monopolistic competition model [...] the countries are completely specialized in different product varieties. Trade in these product varieties is referred to as intraindustry trade...

On page 145, it is stated that

  Then it follows that a good produced in any country is sent to all other countries in proportion to the purchasing country's GDP.

To formalize this, consider a multicountry framework where $i,j=1...C$
  denotes countries and $k=1,...N$
  denotes products. Let $y_{k}^{i}$
  denote country $i's$
  production of good $k.$
  Since prices are the same across all countries, we normalize them to unity, so $y_{i}^{k}$
 actually measures the value of production. The total GDP in each country is measured by $$Y^{i}=\sum_{k=1}^{N}y_{k}^{i}$$
  and world GDP is $$Y^{W}=\sum_{i=1}^{C}y^{i}.$$

Here is where I am confused. I was under the impression that each country produces a single variety of the differentiated good. In that case, the total GDP in each country should just be $$Y^{i}=y_{k}^{i}$$
  where $k$
  is specific to $i$.
  In other words, I understand the statement as each country producing just one variety of the same good. I believe this is an incorrect interpretation for two reasons:

If that were the case, the number of goods should actually be $C$,
not $N$.
(It could be that $C=N$
but the author does not specify this)
The GDP
by the product would be $y_{k}^{i}$
but by the expenditure approach would be $Y^{i}=\sum_{k=1}^{N}y_{k}^{i}$.

Confronted with the likely possibility that my interpretation is fallacious, I don't know what the alternative interpretation is. What else could the statement “countries are completely specialized in different product” varieties mean?


texts: Monotonicity of second price auctions with bidder-specific reserve prices

texts:
I am having difficulty understanding the problem below:

Given CDFs $F_1, ..., F_n$, prove that the allocation rule of a second-price auction with bidder-specific reserve prices is monotone. The item is rewarded to the bidder with the highest bid that meets his reserve price. The reserve price of bidder $i$ is $r_i = _i^{-1}(t)$ where $_i$ is the virtual valuation function

$$\phi_i(v_i) = v_i - \frac{1 - F_i(v_i)}{f_i(v_i)}$$

and $t$ is chosen such that

$$Pr\left[\max_i _i(v_i) \ge t\right] = 1/2.$$
Since the virtual valuations are determined before the auction (if I understand it correctly), how does the reserve prices affect the monotonicity of the allocation rule? The behavior is still the same: if you keep on increasing your bid, you'll have a higher chance of getting the price. How should I go about this?


texts: Research on the link of QE and increased economic activity

texts:
Im looking for good literature of quantitative easing and the effects on economic actitivty.

from a modelling perspective
Any empirical research?

What I am thinking of, is how much of an effect does QE actually have for citizens?


texts: If someone goes for a haircut, does it increase GDP?

texts: If I go for a haircut, am I causing the GDP to rise because consumption is rising?


texts: What are the assumptions behind calculating the market equilibrium from supply and demand curves?

texts:
Imagine that there are 5 buyers (B1,...,B5) with maximum willingness to pay as follows:

B1 = $5
B2 = $4
B3 = $3
B4 = $2
B5 = $1

Imagine that there are 5 sellers (S1,...,S5) with minimum selling prices as follows:

S1 = $5
S2 = $4
S3 = $3
S4 = $2
S5 = $1

I now present two hypothetical situations:

SITUATION 1: Each buyer is matched to the seller with the corresponding price.

In this case, the quantity traded = 5 units

SITUATION 2: Match B1 with S5, B2 with S4, B3 with S3, B4 with S2 and B5 with S1.

In this case, the quantity traded is equal to 3 units since the last two trades cannot happen.

DISCUSSION AND QUESTION

Obviously, these are two extreme situations. However, it seems to highlight an interesting point, namely, what assumptions do we have to make about "reserve prices" of buyers and sellers, and the way they interact with each other, in order for us to be able to calculate the equilibrium point? In other words, there seems to be more than meets the eye with the idea of calculating the equilibrium point from the supply and demand curves alone.


texts: Characterising a set of outcomes containing the collection of pure strategy Nash equilibria

texts:
Consider a game with $N$ players, each indexed by $i=1,...,N$. Every player $i$ has to choose a $J\times 1$ vector of actions $a_i\equiv (a_{i,1},...,a_{i,J})$ where each $a_{i,j}$ can be zero or one. The payoff of each player $i$ is $u_i(a_i, a_{-i})$, where $a_{-i}$ denotes the actions of the other players.
A pure strategy Nash equilibrium (PSNE) of the game is $a^*\equiv (a_1^*,...,a_N^*)$ solving
$$
(1) \quad a_i^*\in argmax_{a_i\in \{0,1\}^J} u_i(a_i, a^*_{-i}) \quad \forall i=1,...,N
$$
Note that if $a^*$ is a PSNE, then
$$
(2) \quad \text{If $a^*_{i,j}$=0, then } u_i(a^*_i, a^*_{-i})\geq u_i(a^*_i+\{a_{i,j}=1\}, a^*_{-i})\\
 \quad \quad \text{If $a^*_{i,j}$=1, then } u_i(a^*_i, a^*_{-i})\geq u_i(a^*_i+\{a_{i,j}=0\}, a^*_{-i})\\
\forall i=1,...,N \quad \forall j=1,...,J
$$
where $a^*_i+\{a_{i,j}=1\}$ denotes $a^*$ where $a^*_{i,j}=0$ is replaced by one; $a^*_i+\{a_{i,j}=0\}$ denotes $a^*$ where $a^*_{i,j}=1$ is replaced by zero.
Claim: Assume that ties are zero probability events. Then, an action profile $a$ satisfies (2) if and only if
$$
(3) \quad a_{i,j}=1\{u_i(a_i+\{a_{i,j}=1\}, a_{-i})- u_i(a_i+\{a_{i,j}=0\}, a_{-i})\geq 0\}\\
\forall i=1,...,N \quad \forall j=1,...,J
$$
Question: Let $A$ be the set of PSNE. Let $B$ be the set of $a$ satisfying (3). Is $A\subseteq B$? If $B$ is empty, then $A$ is empty?


texts: Efficient social allocation awards item to the highest valuer in a sponsored search auction. Whom is it optimal for?

texts:
In mechanism design, for example in the case of a single item auction, we often assume that a socially efficient outcome is to allocate the good to the bidder with the highest valuation of that good. In the case of a sponsored search auction, we want the items (slots on the sponsored search space) to be handed out in such a way that the most valuable slots go to the bidders with the highest valuation of the same slots.

In the sponsored search auction case, whom is the allocation optimal for? The bidders, or the web user, or both? If it is optimal for the web user, why?


texts:
In France, one of the presidential candidate said that the European Central Bank should purchase the public debts of the country and transform it into a perpetual debt (this is a literal translation, I don't know if there is a specific word for that in English).

Since I have very little knowledge about economics and how the ECB works, I find it very unlikely that a bank can just purchase the entire debts of a country.

I would like to know if this is really possible and if so, what exactly is a "perpetual debt"?


texts: Econometric test for detecting change from trend stationary to stationary process

texts:
I am stuck with the following problem from research. Is there an econometric test which detects change from trend stationary to stationary process.

I tried to search for this but the literature is quite vast. Can somebody point to the relevant literature ?

Any help is appreciated.


texts: What are some further readings in Econometrics you recommend?

texts:
I've reached the end of my Econometrics courses for the undegraduate level at my university, but I would like to continue learning. I hope I could get some recommendations for further reading. I present a summary (off the top of my head) of what has already been covered in my courses:

OLS, Multiple OLS, heteroskedasticity
Time series, autocorrelation, ARDL
Pooled model, fixed effects, random effects
IVs, Diff-in-diff, Probit, Tobit
Fuzzy and Sharp RD

As well as the relevant tests for each case. I'm also familiar with Econometric theory on matrix form.