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

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

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

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

This would look something like this:

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

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

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

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

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

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

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

The branch of microeconomics that you seem to be looking for is the study of externalities—activities that have side-effects that (positively or negatively) effect the welfare of others. The Wikipedia article on the topic is here.

Any good introductory/undergraduate level textbook will have a treatment of this topic. For example, Hal Varian's "Intermediate Microeconomics: A Modern Approach" (which would be my recommended first port of call) has a chapter on externalities. A slightly more specialised treatment can be found in a textbook on so-called public economics such as "Intermediate Public Economics" by Myles and Hindriks.

These books also contain examples of how goods with externalities can be formally modeled.

Alternatively, because externalities are a standard element of the economics curriculum, a Google search for "Externalities lecture notes" will turn up lots of freely-accessable PDFs that give a good overview.


What is the point of a constant (thus known) inflation rate? I have read somewhere (attributed to Milton Friedman) that a good practice of monetary policy is to maintain a constant inflation rate (of 3% per annum, say). What is the point of that? If everyone knows the constant inflation rate, would they not factor that in when pricing goods and thereby effectively eliminate the inflation?

As a toy example, suppose the Feb maintains the money supply $M(t)=M(0)e^{at}$ at time $t$ for some constant $a$ known to people. Then people will price the goods (including debts) $P(t)=P(0)e^{at}$ at time $t$ where $P:=(p_1,p_2,\cdots,p_n)$ is a vector of prices for $n$ goods. Then the ratio of the prices $P/p(1)=(1,\frac{p_2}{p_1},\cdots,\frac{p_n}{p_1})$ remains the same. What is the point of the targeted inflation?

I can think of one justification in a particular scenario for setting a target but of the money supply rather than of inflation which is the increment in price. If we know the quantity, so to speak, of the economy is growing at $Q(t)=Q(0)e^{at}$. Then it makes sense to increase the money supply as described above, so that people can still price the goods at $P(t)=P(0)$. But this is no price inflation. Besides, if the money supply is held constant and the quantity grow rate is known, people can just price the goods at $P(t)=P(0)e^{-at}$ and the price ratio still remains unchanged. I do not see the harm in price deflation.

The possible flaw in this setup is that the "speed" of the diffusion of the physical monetary supply amongst the non-bank entities is no greater than the "speed" of the transaction. We can eliminate this flaw and achieve infinite monetary diffusion speed and simultaneity of inflation by bringing all transactions onto digital platforms. People can set their algorithms to increase the prices at the target rate.

This question is related but different from the question Is zero inflation desirable?. The latter asked about the effect of keeping inflation at zero. My question asks whether targetting an inflation rate not necessarily zero that is to be known to all people is any different from zero inflation and its desirability.

As I understand it, your question is the following:

Assuming that the rate is inflation is known by all in advance, does it matter what rate of inflation we set?

The answer to this question is 'yes'. For one thing, even if inflation is predictable, it transfers resources from holders of cash to the government or monetary authority ('seigniorage'). As a result, people may try to hold less cash, which means they need make more trips to the bank (leading to 'shoe leather costs').

Thus, contrary to the supposed lesson of your 'toy model', perfectly predictable inflation can have real effects.

However, you are right to emphasise that the importance of predictability: unpredicted inflation often has effects that predicted inflation does not. For example, consider the common claim that an increase in inflation is good for borrowers and bad for lenders. If unpredicted, that is certainly true. But if predicted by all in advance, one might expect the increase to simply drive up nominal interest rates, leaving the real interest rate unchanged.


How to prove that a concave production imply that the input requirement sets are convex? According to page 7 of this slide, "A convex production set Y implies that the associated input requirement set V(y) is convex".
How can one go about proving it?

Start with definitions:

Production (possibilities) set: $Y$ which you know is convex
Input requirement set: $V(y)=\{\mathbf{x}:(y,−\mathbf{x})∈Y\}$

On page 7. you can see: $\mathbf{y}\in Y$ and $\mathbf{y'} \in Y$ which then implies $t\mathbf{y}+(1-t)\mathbf{y'} \in Y$.

Hint 1:

   Remember that: $\mathbf{y}=(y,−\mathbf{x})$ !

What does it mean that $Y$ is a convex set?

   $Y$ being a convex set means that if $\mathbf{y}=(y,−\mathbf{x}) \in Y$ and $\mathbf{y'}=(y,−\mathbf{x'}) \in Y$ then $t(y,−\mathbf{x})+(1-t)(y,−\mathbf{x'}) \in Y$ as page 7. would suggest.

Okay, but what does that actually mean?

   $t(y,−\mathbf{x})+(1-t)(y,−\mathbf{x'}) \in Y \implies (ty+(1-t)y, -t\mathbf{x}-(1-t)\mathbf{x'}) \in Y \implies (y,-t\mathbf{x}-(1-t)\mathbf{x'}) \in Y $

Which is just equivalent of saying that:

   $t\mathbf{x}+(1-t)\mathbf{x'} \in V(y)$ because both $\mathbf{x}$ and $\mathbf{x'}$ are in $V(y)$. (Look: second definition)


How does a refinance allow a mortgage to be repaid? A textbook I'm reading states (talking about the years leading up to the financial crisis):

  As long as housing prices increased, these mortgages were secure: the
  borrower
      rapidly accumulated equity in the house that could be taken out in a refinance,
      allowing the mortgage to be repaid.

How would this work exactly? I know that many people took out home equity loans, but I'm not exactly sure how accumulated equity would end up making liabilities easier to pay back.

Say you buy a house for \$100. This is paid with:

A \$10 down payment (from your own cash). (This is your equity.)
A \$90 loan from a bank at 10% annual interest. (We call this a mortgage loan or more simply a mortgage.)

Notice you're paying a relatively high interest rate of 10% on your mortgage, perhaps because the bank is not very confident that you'll be able to repay the loan.

Say that overnight, the value of the house rises by \$50 to \$150. Now your equity has also risen by \$50, from \$10 to \$60. You can now refinance your mortgage and ask the bank to lower the interest rate on your loan, say to 5%. You are certainly happy to do this refinancing because you'll pay a lower interest rate. And the bank might be willing to oblige because it is now more confident that you'll repay the loan.


Intertemporal choice with possibility of death Here is the setup:
Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period $1$, and during this period his sub-utility function is given by:
$$u(c_1) = \log c_1.$$
The individual is alive in period $2$ with probability $p$, and if he is alive, his state sub-utility function is given by
$$u(c_2) =\log c_2$$
and if he dies, he receives the fixed utility level $B$. Suppose he has access to a perfect capital market and discounts the future at rate $\beta$. His endowment is given by $(\omega_1, \omega_2)$.

I have a few questions about how to approach this problem. The first question is: do we assume he can die with debt/excess savings at the end of period $1$? If I assume that $p=0$ (dies with certainty), I get that he takes out a loan $s= \frac{\omega_2}{1+r}$ in the first period. Does this make sense, i.e., do we assume that even if he dies he gets an endowment of $\omega_2$ to pay off his debts? This result would correspond to $c_2 =0$.

The second question is about the fixed utility level. Should this be interpreted as, if he dies, he gets utility $u(c_1) + B$? Or $u(c_1) + \beta B$? Or that we assume his total lifetime utility from consumption is $u(c_1) = B$?

Thanks!

It is safe to assume that if the consumer passes away, his creditors get his endowment. This actually happens in real life. $B$ should obviously be zero. As far as the second period is concerned you can represent it as a von Neuman-Morgenstern utility from the lottery:

$\beta u(c_2)$ with probability $p$ and $0$ with probability $1-p$.

I.e. $U(c_1, c_2) = log(c_1) + p\beta log(c_2).$


In what way specifically are US CEO's able to engage in rent-seeking and exploit corporate governance to increase compensation? I've seen videos where Prof. Stiglitz mentions CEO compensation associated with rent-seeking:

https://youtu.be/b7wIw1VNjSk?t=29m58s
https://youtu.be/heOVJM2JZxI?t=41m28s

I looked on the web and saw a story about how government subsidies meant for workers are absorbed by the executives and that the company's lobbyists are seeking these rents. However, I don't understand how exactly that's done. What are some examples?

I also remember seeing an interview with either him or Prof. Krugman where they mentioned that CEO's are able to exploit the structure of corporate governance (using the board of directors) to artificially increase their compensation. How exactly is this done if it does occur?

Pre-Sarbanes-Oxley it was common for CEOs to nominate the members of the board of directors of their firms. A sub-committee of the board would determine the CEO's compensation, so a CEO could choose people loyal to him (even employees working under the CEO) for the board and those people could boost his compensation. And if they did not do so, he might also ensure that board members that failed to boost his pay did not serve renewed terms. In addition, they could potentially ensure that even when performance was poor that the compensation was high. Sarbanes-Oxley, along with changes from the major US stock exchanges, required independent nominating and compensation committees for boards of directors. It is generally seen in the literature that these rule changes curtailed this practice. However, some dispute that this was ever an economically important channel for self-dealing.


What if only the government could create money? If I understand correctly, under the dominant system of fractional reserve banking, many (all?) private banks can create money by lending.  See, for example, Implications of abolishing Fractional Reserve Banking on mortgages and interest rates.  So, money created when people (or other entities) go in debt, and destroyed when those debts are paid back.

Some organisations, such as Positive Money, advocate there would be considerably advantages if we step away from this system, and only the government could create money.  Quoting from their website:

  History has shown that when banks have the power to create money, they create too much in the good times, causing financial crises, and then create too little money in the bad times, making recessions and unemployment even worse. They put most of the money that they create into house price bubbles and speculation on financial markets, and only put a small amount into businesses outside the financial sector. We simply don’t think that banks, with all their incentives and need to maximise their profits, can be trusted with something as powerful as the ability to create money. And it’s not enough to regulate them, because regulators have already failed to keep them under control, and there’s no reason why they should get it right this time around. We need to stop banks being able to create money. Instead, we want to see the power to create money transferred to a democratic, accountable and transparent process (...)

My question:

What would be the consequence if only a single institution, accountable to the national government, had the ability to create money?  Assume that this institution would use a more or less objective set of criteria to determine how much money to create, for example, in order to meet particular targets.

Edit: A commenter requested more background motivation why this question is specifically about banks.  Allegedly, the system leads to increasing house prices and debts, along with other problems.  My question here is not whether the issues that Positive Money are correct in attributing those problems the current system of private banks creating money; regardless of their correctness, my question is, as stated above, what the consequences would be of having only a single government-controlled institute create money.

When you dig down, this questions is very nearly a duplicate of this:

Implications of abolishing Fractional Reserve Banking on mortgages and interest rates

but based on the comments, it seems that the connection isn't obvious.

This question asking about what would happen if only a government institution could create money, but equally you say the proposal is not to have a fixed money supply.  They are, in practice, the same thing.

The central bank makes the money base, M0, and then the banks create the money supply, with some multiplier to this.  In a full reserve system, that multiplier is 1.0, and so the money supply is always equal to the money base.

In your question, we consider having a M0, but also have a state run bank that chooses the money multiplier to some number, that may or may not be 1.0.

From that point on things become almost identical - it doesn't really matter from the point of view of the economy, whether you make M0 ten times larger or smaller, if you offset it with changing multiplier.  It should be the total money supply that matters - the money base never leaves the central bank, and so may be thought of as a "construct" onto which the monetary system is hung.  The important point is that the government gets to directly control the money supply.

Before the era of quantitative easing, when a central bank wanted to increase the money supply, they lowered rates and that increased the multiplier.  With quantitative easing, they simply increase M0 and force the money supply up in a 1:1 ratio.  Either works (for a given value of "work").

There is, however, one very important difference:

With full reserve banking borrowing money is very expensive - it is economically the same as capital
With a state run lending bank, borrowing could be done at any rate the government chooses, including at an economic loss.

So, in your system, you could have a state run bank, that effectively subsidises business and/or people's mortgages using money raised from taxes or elsewhere.  This would be like an extreme version of the UK forcing RBS and Lloyds to increase lending.


What is the difference between constant elasticity of substitution and elasticity of substitution? What is the difference between constant elasticity of substitution and elasticity of substitution? Are these formulas related? How are they different concepts? I just did a whole problem set involving these and got the right answers. But my thought process was all math. I don't feel like I understand them economically. And that's what I want explained.

By CES, I mean
$$U(x,y) = A \left(\alpha x^{-\rho} + (1-\alpha) y^{-\rho}\right)^{-\frac{1}{\rho}}$$

By ES, I mean

$$\sigma = \frac{\mathrm{d}\log \left(\frac{x}{y}\right)}{\mathrm{d}\log \left(\frac{U_y}{U_x}\right)}$$

Well, you didn't get the math all right, otherwise you might have seen it yourself!

By Elasticity of substitution, you should refer to

$$ \sigma(x,y) = \frac{\mathrm{d}\log \left(\frac{x}{y}\right)}{\mathrm{d}\log \left(\frac{U_y}{U_x}\right)} $$

Then, constant elasticity of substitution is a property of a function $U$ such that for some constant $\bar \sigma$,

$$ \sigma(x,y) = \bar\sigma \, \forall y, x$$

That is, the elasticity doesn't depend on $x,y$. What you showed as $U$ is a function that has exactly that feature. If you compute $\sigma(x,y)$ (do it!), you will see that

$$ \sigma(x,y) = \bar\sigma = \frac{1}{1+\rho}$$

That is, the elasticity of your $U$ function is constant for any allocation. Hence, we refer to that class of function (for different $\rho$) to Constant-Elasticity-of-Substitution-Functions (with share parameters $\alpha$). Cobb-Douglas preferences would be a special (limiting) case of that, with $\sigma(x,y) = 1$

Example

Say, we produce happiness ($U$) with apples ($x$) and oranges ($y$). Lets look at the allocation $\{5,1\}$. We only have one orange, but we would really want more. Hence, we are willing to give up 2 apples to get one orange, and we would be indifferent:

$$ U(5,1) = U(3,2)$$

It is very easy to substitute apples with oranges, we have a high elasticity of substitution.

Now look at the allocation $\{1,6\}$. Do you think that you would again be willing to lose $40\%$ of $x$ to get an increase of $50\%$ in $y$? Is it true that

$$ U(1,6) = U(0.6, 12)$$

If yes, that means that the elasticity of substitution of $U$ (or my rather handwaving approximation to it) is the same at the two allocations $\{1,6\}$ and $\{5,1\}$. If that was true for all possible allocations, $U$ was CES.

There are some reasons why you would think some preferences are perhaps not CES: For example, if $x$ and $y$ are good complements. Then, when you have little of $x$, you're willing to give up a lot for the other, but that elasticity might decrease the closer you are to equality between the two inputs.


(Macro)econometrics book recommendation I am looking for good econometrics books for self-study.
I am strongly interested in macroeconomics and monetary economics/policy, so that I try to build up knowledge in econometrics especially for these fields.
At first I am looking for a basic introductory book but also for a book, which covers time series methods, VAR and so on (so macroeconometrical topics in general, I guess).
Applications are more interesting for me than pure theory, so the book(s) shouldn't be too theoretical.

Some more information about me: I study mathematical economics on graduate level and I bring prior knowledge in (measure theory based) probability theory.

Maybe one of you guys could help me :)
Thanks in advance!

For a first look at econometrics, I would recommend Stock and Watson, Introduction to Econometrics. Not only does this book cover the basics well, it gives good, clear treatment of causal inference in econometrics. It covers time series topics, including VARs. For more advanced treatments, I would suggest Fumio Hayashi's Econometrics.

If you feel like you have a grasp on these, you could then look at econometrics books that deal more specifically with macroeconomics. I like the book Structural Macroeconometrics. Others include Methods for Applied Macroeconomic Research and Applied Macroeconometrics.


What does "endogeneity of the industry structure" means? Dong,2019,page 899 documented that:

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

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

Broadly speaking endogeneity means that something some variable is determined within model as opposed to outside it. More narrowly in econometrics it means correlated with the error term (Wooldridge, (2009). Introductory Econometrics: 4ed. p. 88). These meanings are related since one will often lead to the another.
In this paper they actually use it in both meanings.

From economic literature we know that industry structures (e.g. whether industry is monopoly, duopoly, oligopoly, monopolistic etc.) depends on institutional setting and laws as well  (e.g. see discussions of this in Belleflmame & Peitz Industrial Organization Part IV). Moreover, it is often further argued that in turn laws that country implements also depend on "economic conditions of a firm’s country" (Dong, 2019).  So what they mean is that industry structure will not be just given by some exogenous parameters such as let's say availability of local natural resources (this could be an exogenous force that could determine if industry is a monopoly e.g. if there is let's say only 1 viable diamond mine then this would be exogenous factor leading determining market structure to be a monopoly). Rather, here the market structure is shaped by the leniency programs that affect cost of collusion and in turn the leniency programs likely depend on economic conditions (e.g. a country with less problem with cartels might have less anti-trust laws).
Dong (2019) throughout the chapter in previous paragraphs Dong repeatedly states that they are dealing with endogeneity because it could be a valid critique of identification strategy (i.e. their empirical model). Consequently, they also mean it in more narrow way that it would mean that in their regression of margins on those leniency laws the leniency laws would be correlated with error term. In fact, this is why Dong says that they dealt with it by using leniency index from 1990s - using past ('lagged') values instead of contemporaneous one's is a common econometric technique to deal with endogeneity in an empirical model.


Is money lent by central banks to private banks counted in MB or M1? If a bank borrow money from a central bank but keeps it as a reserve instead of lending it to someone else, is it counted in the monetary base (MB) or money supply measure M1, using US definitions ?
Maybe that case just doesn't happen.

EDIT: A related question: if every debt is paid back (including money lent by central banks), does MB remain constant (which could not be the case according to the answer to the previous question) ?

Yes, it is in both but we have to be careful not to double count:

  The Fed’s definition of M1 is the sum of (1) currency outside bank
  vaults, (2) traveler's checks of nonbank issuers, (3) customers’demand
  deposits at commercial banks (with minor deductions), and (4) other
  checkable deposits, like negotiable order of withdrawal (NOW) and
  automatic transfer service (ATS) accounts. Basically, this is currency
  held by the public plus demand deposit balances outside the Fed. M2
  consists of M1 plus (1) savings deposits (including money market
  deposit accounts), (2) small-denomination time deposits (less than
  $100,000), and (3) balances in retail money market mutual funds.
  Individual retirement account (IRA) and Keogh account balances are
  excluded from M2. Excess reserves, required reserves, clearing
  balances held at the Federal Reserve banks, and the like, are
  components of the Fed’s monetary base but would constitute
  double-counting of the same factors if included in M1 and other
  monetary aggregates. Such accounts are readily spendable media of
  exchange (transaction accounts), but counterparts of these accounts
  already are included in M1, for example, as components of customers’
  demand deposits at commercial banks. The quantities of liquidity to
  fear for inflationary consequences are either monetary base or M1/M2,
  but not both simultaneously.

The Problem of Excess Reserves, Then and Now (Todd (2013))

What is the monetary base?

  In economics, the monetary base (also base money, money base,
  high-powered money, reserve money, outside money, central bank money
  or, in the UK, narrow money) in a country is defined as the portion of
  the commercial banks' reserves that are maintained in accounts with
  their central bank plus the total currency circulating in the public
  (which includes the currency, also known as vault cash, that is
  physically held in the banks' vault).

  The monetary base should not be confused with the money supply which
  consists of the total currency circulating in the public plus the
  non-bank deposits with commercial banks.

Wikipedia: Monetary base

This is how it works:

  Creating Money through the Discount Window.  When a bank needs new
  reserves to support loans and investments it has already made or
  anticipates making, it ordinarily borrows from other banks at the
  Federal Funds rate.  But during times of stress, which are reflected
  by a shortage of liquidity in many banks, the whole banking system
  needs new reserves — hence the Fed's discount window. When a bank
  borrows funds overnight from the Fed's discount window (at an interest
  rate the Fed sets, called the discount rate), the bank's reserve
  account at the Fed is credited with the amount borrowed (and the Fed
  adds to its assets the additional amount owed to it by the borrowing
  bank).  Since the borrowing bank gets new reserves and no other bank
  lost reserves, net new reserves have been created for the banking
  system as a whole.  If the amount is also \$10 million, the banking
  system as a whole has a new capacity to expand loans and deposits by
  as much as \$100 million.  Thus, the Fed's open market purchases and
  discount window loans have the same ultimate impact on the money
  supply, at least until the discount window loans are repaid.

How the Fed Creates Money (McTeer and Villarreal (2008))


What does Leverage ratio mean in context of Banking sector and how is it different from CRAR? There are several definitions of Leverage Ratio in context of Banking Sector but it seems like it is no different from CRAR (Capital Adequacy Ratio), could someone explain what's the real difference between both concepts.

Leverage ratios are typical simple ratios of debt to equity while capital adequacy ratios are usually risk weighted.

  The capital adequacy ratio, or CAR, is a metric applied specifically
  to banks, while a common leverage ratio is used by investors to
  evaluate virtually any type of firm they choose to examine. The CAR is
  used to assess the financial risk a bank is exposed to through its
  existing loans. The ratio is risk-weighted and expressed as a
  percentage of the total exposure. ...

  Not simply a single leverage ratio, but rather several financial
  leverage metrics may be utilized to gauge a business's financial
  health. Two of the most commonly considered leverage ratios are the
  debt-to-equity ratio and the long-term debt-to-capitalization ratio.

What is the difference between the capital adequacy ratio and the leverage ratio?

Source: Investopedia


Does dollar cost averaging actually have any advantage over one time investment? Some banks promote savings plans by stating that investing a fixed amount of money in regular time intervals minimizes the average buying price or the downside risk (dollar cost averaging). Since the regular saving amount is fixed, they claim that, when the stock price is low more shares will be bought, and when the price is high fewer shares will be bought, so in total, you will buy more shares when they are cheap and fewer when they are expensive, hence investing more efficiently.

Although this seems to be a valid argument, intuitively (at least for me) it still feels rather like some sort of fallacy than a sound investment strategy, however I cannot show exactly why. So my question is whether there is an actual mathematical proof that dollar cost averaging has a definite advantage over one time investment (or the opposite)? To be precise, is it really possible to somehow reduce risk and keep the same expected return (or raise expected return and keep the same risk) using this stragegy?

The seminal academic criticism of dollar cost averaging on many specifications of economic conditions is A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy (Constantinides (1979)). You might also be interested in these papers:

  Dollar Cost Averaging is an investment system that is widely advocated
  by brokerage firms and mutual funds. In its best known form, an
  investor seeking to put a lump sum into risky assets is counseled to
  invest the money over a period of time in equal installments in order
  to avoid the devastating effect of a market fall immediately after a
  single, lump-sum investment. Using graphical analysis, historical
  stock market returns, and Monte Carlo simulations, this article
  demonstrates that no such benefit accrues to a Dollar Cost Averaging
  Strategy. Two alternative strategies, optimal rebalancing and buy and
  hold achieve better performance in all three analyses.

Nobody gains from dollar cost averaging analytical, numerical and empirical results (Knight and Mandell (1993))

  Some studies find the dollar-cost averaging investment strategy to be
  sub-optimal using a traditional Sharpe ratio performance ranking
  metric. Using both the Sortino ratio and the Upside Potential ratio,
  we empirically test four investment strategies for alternative asset
  investments. We find the relative ranking of dollar-cost averaging
  remains inferior to alternative investment strategies. (JEL G1, G11,
  N2)

An empirical examination of the effectiveness of dollar-cost averaging using downside risk performance measures (Leggio and Lien (2003))

  The widespread practice of dollar-cost averaging (DCA) amongst the
  investing public, has puzzled most financial economists, ever since
  Constantinides demonstrated the dynamic inefficiency of this
  strategy under very general conditions. This enduring phenomena has
  forced researchers, such as Statman , to suggest behavioral
  explanations for DCA's popularity, predicated on the prospect theory
  of Kahneman and Tversky .

  In this paper we reexamine the payoff structure of DCA via
  continuous-time financial mathematics and then ask the question: Is it
  possible to reconcile the theory and practice of dollar-cost
  averaging?

  To answer this question, we take a slightly different approach to the
  issue by using the tools of stochastic calculus and Brownian bridges.
  We demonstrate that engaging in a dollar-cost averaging strategy is
  akin to purchasing a zero strike arithmetic Asian option on the
  underlying security. In other words, people who engage in dollar-cost
  averaging are implicitly purchasing a path-dependent contingent claim.
  We then prove that the expected return from this exotic option — i.e.
  the DCA strategy — conditional on knowing the final value of the
  security will uniformly exceed the return from the underlying security
  for all sufficiently large volatilities.

  This leads us to argue that investors may be dollar-cost averaging
  because they have "target prices" for the underlying asset price. The
  strategy of dollar-cost averaging would then exceed the returns from
  lump-sum investing, based on their subjective conditional expectation.
  In fact, the more volatile the underlying security, the greater is the
  benefit to dollar-cost averaging — conditional on knowing the final
  value — which is consistent with common practice.

A CONTINUOUS-TIME REEXAMINATION OF DOLLAR-COST AVERAGING (MILEVSKY and POSNER (2003))

  Dollar Cost Averaging is a strategy for purchasing equity securities
  that is widely recommended by professional investment advisors and
  commentators, but which has been virtually ignored by academic
  theorists and textbook writers. In this paper we explore whether the
  strategy is but another instance of irrational behavior by individual
  investors, or whether it is an investment heuristic that has survival
  value in an environment in which security prices exhibit mean
  reversion behavior that has only belatedly been recognized by academic
  theorists. Our evidence supports the view that the uninformed
  individual investors who follow this strategy in purchasing individual
  stocks to add to an existing portfolio are better off than if they
  followed the ‘rational’ strategies traditionally recommended by
  academics.

Dollar Cost Averaging (Brennan, Li and Torous  (2005))


Where the economic growth of a society come from? I'm thinking about value generating. I hear it a lot in a innovation context, i.e. one should create a new product that a lot of people want to buy.

I can see how a new product can value more than the sum of its parts, but I don't understand how this can increase the wealth of a society.

The point of view that raised this question for me was: let's say a person can spend only what she earn as wage, so when a new product come out, this product is competing with all the pre existing products, someone should lose to someone else to win.

Where the economic growth of a society come from?

I can see how a new product can value more than the sum of its parts, but I don't understand how this can increase the wealth of a society.

The wealth of society, in material sense, consists of what it can produce. Production of more products or services is the wealth. Economic growth is by definition a continuous increase in production. In fact the way how we most commonly measure economic growth is to just measure output per person by measuring GDP per capita.

Wealth is not money, money is just a measurement stick for value, storage of that value, and tool to simplify exchanges, but it’s not wealth in itself. However, because it is so ubiquitous many non economists equate it with wealth itself but that is just ‘money illusion’. If you would have billion \$ but could not buy even a loaf of bread with it you would be poor compared to a person with 0 dollars who has access to any goods or services they wish.

  let's say a person can spend only what she earn as wage, so when a new product come out, this product is competing with all the pre existing products, someone should lose to someone else to win.

In competitive market economy people  earn approximately what is their marginal product. When you go to work you either create goods or services for someone directly or indirectly and in competitive market you will get for that money equal to the worth of your marginal product. If you can produce more with  the same or less inputs you will also earn more money.

The reason why for example Solow-Swan model shows that economic growth depends on technology is that technology makes people continuously more productive year after year and allows them to produce more. This increases production is the real wealth, but besides that if people are more productive they also get pay more.

In real life not all markets are competitive so the above holds only approximately but empirical evidence shows that real wages indeed track net productivity over long term.

Besides increases in technology endogenous growth theory suggests that also savings rates and support for basic R\&D and human capital can accelerate economic growth. The mechanism there is different than in Solow model but ultimately again what delivers growth is how the above boosts the productivity and output.


Wouldn't reducing Fed Balance Sheet lead to Inverted Yield Curve? BACKGROUND

I am involved in finance, but by no means an economist. I've been reading Ben Bernanke's "The Courage to Act" and have become interested in QE1 and QE2. Currently, I am trying to understand the Fed's Balance sheet reduction.

NOTE: Apologies if some of my assumptions/questions are misguided

ASSUMPTIONS

QE was a fiscal strategy to lower long-term interest rates
Fed bought Treasury securities and Mortgage-backed Securities to reduce long-term interest rates
Fed is currently looking to reduce Balance sheet to raise long-term interest rates to pre-recession levels (including short-term interest rates)
The Fed is looking to raise short-term interest rates first, then long-term interest rates

QUESTION(S)

If the Fed raises short-term interest rates, but keeps long-term interest rates low, wouldn't this create an Inverted Yield Curve?
Aren't Inverted Yield Curves an indicator of recession?
Why isn't it better to raise on long-term interest rates first, and then raise short-term interest rates?

As a preface to my answers, I want to point out that bond yields are set in the market. We can think of bond yields as being (roughly) the sum of the expected path of short rates over the life of the bond, plus a term premium.

QE may or may not have lowered term premia (which would lower yields), but that is not enough for the Fed to completely set interest rates independent of what bond market participants expect the path of short rates to be.

The Fed may want to keep bond yields low when raising rates, but bond market participants will not want to own bonds that they expect to lose money on. Therefore, it would be extremely difficult for the Fed to keep bond yields down if they are in the process of raising short rates. As a result, it is difficult for the curve (overnight - bond maturity) to invert when rate hikes are expected.
Yes, inverted yield curves have been historically associated with recessions in the United States. This is an indication that the bond market is pricing future rate cuts. (The curve will have difficulties inverting if short rates are zero, as has been the case in Japan.)
The raising of bond yields is done by people who expect rate hikes, not by a Fed decision. Since the private sector does not exclusively borrow on a short-term basis (for example mortgages), this presumably has an effect on the economy. As a result, it is part of the "transmission mechanism" from the policy rate to the economy, and so it is not really better or worse than raising the short-term rate.


Percentage of workforce change, with two PPFs A hypothetical economy produces two goods, X and Y. The performance (yield) for every worker is steady, and every worker for Y can produce 10 units of product. If $L_x+L_Y=200 $ (meaning that the total workforce is 200):

(My problem is in (d), everything else is just assisting so you get a better view of the problem)

-a) How many units can every X worker produce?

-b) Find the equation of the first production possibilities frontier (PPF)

-c) Find the equation of the second production possibilities frontier (PPF)

-d) If the technology of the production and the performance of workers for X and Y did not change, what was the change of the workforce between the first and second PPF?

My tries:

-a) If $L_Y=0 \to Y=0$ then $L_X=200$ and for $Y = 0 \to X=400$, so every worker for X can produce $\frac{400}{200}=2$ units

-b) For $y = λx+β \Rightarrow ... \Rightarrow y = -5x+2000$

-c) As the two equations are parallel, $y' = -5x + β' \Rightarrow ... \Rightarrow y' = -5x+2500$

-d) Now for d, where my problem is situated, my try is that the percentage change must equal = $\frac{2500-2000}{2000}100= 25$% but even if that's the correct answer I can't fully understand why this would be the case. What does the $β$ and $β'$ have to do with the workforce? I can't seem to be able to wrap my head around it. Can anyone help me?

The fact that you are getting a correct answer in D using your method is purely due to algebra and cancelling off of common terms.
Let us first see why the answer is actually 25% :
So why does a PPF shift? A PPF Shifts because of either a change in technology or change in resources. The question clearly states that there is no change in the technique of production or output per worker. This means the change in PPF is due to change in resource - which in this case is Labour.
Now in order to find % change in the labour force, consider that if the entire labour force is used in the production of the good Y ( which is what points on Y-axis denote )
Previous Production = 2000, New Production = 2500 [ from intercepts of your equations ]
Since we know that there has been no change in per-unit labour output hence it remains 10.
Thus Previous total labour force = 200, New total labour force = 2500/10 = 250 .
You can easily compute and see that percentage increase is 25%
Your method:
% change = $\frac{2500-2000}{2000}100= 25$
if you simply divide the numerator and denominator by 10 (which is output per work for y), you get what has been done and explained above.


Question Regarding 'Potential Output' I am learning about potential output. We have been told that it is the amount of output that an economy can produce when using its resources, such as capital and labour, at normal rates/maximum capacity. How could an expansion occur if using resources at maximum capacity is considered 'normal'?

Any answers would be greatly appreciated, thanks!

Potential output is the level of output achieved when all resources are employed and put to their most productive uses, and which can be sustained over the long term.

Expansion beyond the current level of potential output usually occurs through technological progress. This is a catch-all phrase that includes the invention of new machines, better education, improvement of workers' skills, etc.

It can also occur through an expansion of the labor force and capital stock (i.e. more workers, more "machines").

Another way it can occur is through overheating. A concrete (but not common) example of overheating would be if we forced everyone to work say 20 hours a day — this might achieve a temporary boost in output, but this is probably not sustainable over the long term. Similarly, we can overwork our machinery, livestock, and other capital goods, but again this would probably not be sustainable.

A more common example of overheating is during a speculative boom -- say a property boom, when due to overoptimism and other factors, we might have a period of a few years when new properties are built at a frenetic pace, so that potential output is exceeded. This, again, is not sustainable.


Effect of minimum wage on higher levels of pay Suppose the minimum wage increases to \$$x$. Is there any evidence on the effect (if any) this is likely to have upon the wage profile of workers higher in the hierarchy, who are already paid more than \$$x$?

My question is inspired by the following comment from the Financial Times (paywalled link):

  As an employer with an annual payroll of around £650k pa the impact of the introduction of the minimum wage in 1997 led us to pay our lowest paid staff ( casual bar staff back then on about £3ph ) the increased minimum wage so they at least benefited. Everyone else higher in the hierachy ( full timers, supervisors, asst managers, managers) all suffered because at every opportunity ( as people left and needed to be replaced) we tried to replace these higher paid staff with the same caliber person but on lower wages. And we were successful at dong this; and we had to be because we could not afford our overall wage bill to increase. So in 2000 I was paying a General Manager 35k a year. Now I can find and pay a general manager 25k pa and thats a massive nominal decline over 15 years. So the real impact of the minimum wage introduction in the real world of small husiness was to pay the lowest casual staff a little more but most of the higher paid staff ended up being paid less .

Is there any evidence to support the claim that the described response is a widespread phenomenon?

This phenomenon is sometimes called "wage compression" because the range of wages is compressed by the minimum wage laws.
One paper on this subject is The Impact of the Minimum Wage on Other Wages


Is there still allocative efficiency when a subsidy is placed on a good? An answer schedule for a practice exam I am doing states that when a subsidy is placed on a a good by the government, there is a loss of allocative efficiency.

I have also learnt from this video that when supply and demand change, the market will still be allocatively efficient, although the amount of consumer and producer surplus will change. However, the video does not take into account dead-weight loss.

When a subsidy is placed on a good by the government, there is obviously a loss in welfare due to the dead weight loss. By my question is this: is there still a point of allocative efficiency in the market of a good with a subsidy, or is there no longer allocative efficiency at all when there is a dead weight loss?

allocative efficiency occurs whenever total market surplus is maximized. This occurs whenever price is equal to the ‘free market’ equilibrium price. There is no surplus of goods at this equilibrium price. There is no DWL at this equilibrium. If there exists DWL, the market is not operating at the 'free market' (as phrased in a comment below) or the ‘unfettered’ equilibrium and the market is not allocatively efficient. To be clear, this market will still operate at some equilibrium. However, this equilibrium will not be efficient.


Application of Intermediate Value Theorem for General Equilibrium Here's a problem restated from Ross Starr's General Equilibrium Theory.

  Consider a two-commodity economy with an excess demand function $Z(p)=(Z_1(p),Z_2(p))$. The price space is $p \in P = \left \{ p | p \in \mathbb{R}^{2}, p \geq 0, p_1 + p_2 =1 \right \}$. Let $Z(p)$ be continuous, bounded and fulfill Walras' Law as an equality, that is $p_1Z_1(p)+p_2Z_2(p)=0$. Assume $Z_1(0,1)>0$, $Z_1(1,0)<0$, $Z_2(0,1)<0$, $Z_2(1,0)>0$.
  Use the intermediate value theorem and Walras' Law to show that the economy has a competive equilibrium. That is, demonstrate that there is a price vector $p* \in P$ so that $Z(p*)=(0,0)$.

And I have a hint: Characterize $Z(p)$ as $Z(\alpha , 1- \alpha)$ for $0 \leq \alpha \leq 1$. Use the intermediate value theorem to find $0 \leq \alpha \leq 1$ so that $Z_1(\alpha , 1- \alpha)=0$. Then apply Walras' Law.

I'm having problem finding $\alpha$, how could I find it?

A stronger hint: Write $p_2=1-p_1$, so that $Z(p)=Z(p_1,1-p_1)$. Use the conditions $Z_1(0,1)>0,Z_1(1,0)<0$ etc. and the intermediate value theorem to argue that there exists a $p_1^*\in(0,1)$ such that $Z_1(p_1^*,1-p_1^*)=0$.


A question about the exchange economy The question I am given is the following: Consider an economy that has only three goods, mineral water, orange juice, and wine available in ﬁxed amounts, and three agents, A, B and C. So in this economy agents have no money initially. There are perfectly competitive markets for these three goods. The agents are not allowed to hold any negative amount of goods. Answer the following questions.

(a) Suppose that A owns all the mineral water, B owns all the orange juice, and C owns all the wine. A only likes orange juice, B only likes wine, and C only likes mineral water. What are the equilibrium prices for mineral water, orange juice and wine and the equilibrium quantities consumed by each individual?
(b) Now suppose that A owns everything and A only likes drinking orange juice, both B and C own nothing, both B and C like drinking wine only. Discuss the equilibrium quantities consumed by each individual.
(c) Now suppose that A equally likes these three goods, B equally likes the mineral water and orange juice, but does not like wine at all, and C only likes wine. Without considering who owns mineral water, orange juice, or wine initially, what allocations are Pareto optimal?

My question is about sub-questions (b) and (c). For (b), if A owns everything and B and C own nothing, apparently there will be no trade. So what is the point for asking this question? For (c), if there is no utility function, how could I tell what is Pareto optimal? I really wish someone could teach me how to answer this kind of question and show me some examples. Thank you, and I wish you a happy new year.

Hint:

These exercises seem to be encouraging you to think about the First Welfare Theorem, and whether it will hold. Recall the theorem which states that if markets are competitive (price takers), markets are complete (full information), and that consumers are locally non-satiated, then every competitive equilibrium should be Pareto optimal.

For each sub-question, there is at least one agent whose preferences are not locally non-satiated. For part (b), you are correct that there will be no trade. That is, you are at a competitive equilibrium. You should discuss if the allocation is Pareto optimal. If the allocation is PO, prove it, and if not, show a counterexample.

For part (c), you do not need to know the utility functions of each agent to do this question. Since we only care about utility up to a monotonic transformation, you can in theory make up a utility function that fits agent A's description. In this case, all three drinks are perfect substitutes, so you can express agent A's utility as

$$u_A(m, j, w) = m + j +w$$

Or any monotonic transformation of that. But this is not necessary. You can solve (c) with just the definition of a Pareto optimal allocation and some intuition. Hope this helps.


What does "survey of panel" mean? In one of my marketing slides it says: The diagnostic potential of micro test market is low because no survey of panel possible; the diagnostic potential of simulated test market is high.

I think the diagnostic potential is in regard to product positioning.

What does "survey of panel" mean here?

A panel survey is a kind of longitudinal study.

In effect the survey sample (known as the panel) is asked repeated questions over time.  This allows the measurement of change over time for the units of analysis.

For example you could measure unemployment by taking a random sample of the working age population and asking them whether they are working or looking for work.  Later you could take a different random sample, and get a new number at the later date. This would be a series of cross-sectional studies and could give you an estimate of the net change.

With a panel survey, you could ask the same people at different times, giving you an estimate of gross employment flows and other more interesting details of change over time.  The difficulty is that some members of the panel might leave, and if this departure was related to the question of interest then it could bias the results. In addition, even if the panel was typical at the start, it might cease to be in future simply because all its members had become older.


Is It Possible for a Country to have a Gold Standard without a Fixed Price of Gold? It is my understanding that at the beginning of the 20th century, many, if not most, countries had a monetary system that was based on a gold standard. However, by the end of the 20th century, most countries had abondoned it.
(1) Is it possible to have a gold standard without a fixed price of gold?
(2) Are there any countries left today which tie their currency directly to gold or some other precious metal?
Thank you.

(1) Is it possible to have a gold standard without a fixed price of gold?

No, with some provisions. First, I presume here we are talking about the price of gold in terms of currency not its relative price (relative to other goods and services) which was always allowed to fluctuate. Gold standard by its definition requires that money is fixed to gold at some fixed rate. If that does not hold it would not be a gold standard. However, the fixed rate can be changed overtime. For example, government could decide that one day the fixed rate will be 10 USD for 1 ounce of gold another day it will be 15 USD for 1 ounce. But this is not the same as having floating price for gold.

(2) Are there any countries left today which tie their currency directly to gold or some other precious metal?

No. Depending on what you count as country, the late  Islamic State in Iraq and al-Sham (ISIS) had rolled out a trimetallic currency (see Oxnevad 2016). Their currency was to be made directly from gold, silver and copper hence would be directly tied to those commodities. Although, by international community it was never recognized by anything more than a terrorist group, it would probably satisfy the Max Weber's definition of state during mid 2010s. However, that likely would no longer be applicable presently after they lost all their territory to Iraq and Syria.


How are you supposed to calculate overhead expenses? I'm doing a college assignment (creating a software product) in Computer Science and have been given a template for the part of the report about economics. At one moment it states the following:

To calculate overhead expenses we must multiply our overall salary by the coefficient of overhead expenses.

And later in the text it assumes that this coefficient is 1.2 without any context or explanation. This makes absolutely no sense to me. Am I missing something or is it wrong? If it is wrong, how am I supposed to calculate overhead expenses if every reasonable expense is already accounted for?

Estimating overhead expenses by applying a coefficient to salaries can make sense in some circumstances.  In an organisation which is mainly office-based, overheads may consist mainly of the costs of office space, office running costs (electricity, cleaning, etc), computer equipment and support, and (depending on the local jurisdiction) payroll-related and property-related taxes. Using a fixed coefficient will always be an approximation to actual costs, but sometimes it can be a fairly good one, especially if the organisation has a fairly "flat" structure with most staff being on similar salaries and having similar office and computing needs.

In a manufacturing organisation with much capital equipment this approach would be inappropriate.


What benefits do OPEC countries obtain by cutting oil supply? It is unclear to a economic novice like me why OPEC is not cutting down production and raising oil prices. I have read several journalists commenting upon this on the internet but perhaps an economist can explain this current fact better.

The OPEC scenario is quite well described by a market with Cournot Competition. That is, while collusion would lead the highest total profits to the sum of the participants, each invididual participant would gain by increasing his production a little bit.

Without observing the quantity of each participant and proper enforcement, that's the outcome the model predicts - and reality concurs.


SPNE and Pareto Optimality "The SPNE of a sequential game might not necessarily be Pareto Optimal"

I understand the definitons of Nash Equilibria and Pareto Optimality and that these are not synonymous concepts. An example in reference to this question would be a Firm-Union Wage Setting Game, in which there might be $w$ offers which provide greater payoffs to both the firm and union.
Please share some other examples for the same. Thanks!

Proof of "the SPNE of a sequential game might not necessarily be Pareto Optimal"?
I don't get it, your example is a proof of this statement. So what else do you need?

If you need another example, just take the prisoner's dilemma, and turn into a sequential game with imperfect information. Then, the NE is equal to the SPNE and you have an equilibrium without Pareto optimality


Elasticity, link between demand and supply I have a exercise with the corresponding answer, but i don't get it:

  Suppose there's a better wheather this year and the size of the harvest of soy increased a 60%. The demand curve for soy did not change. The price of the soy dropped a 20%. We can conclude that the elasticity of demand is -3.

Is this true? Under what circumstances? Why? Thank's a lot!

Example

if p = -1%

and the production increase is +2%

elasticity is -2

[2/-1 = -2]

Our exercise

if this is true

when p = -20%

and production is 60% more

elasticity is -3

[60/-20 = -3]

To sell the 60% more the price has to decrease, if it decreases of 20%, the ratio among products sold (+60%) and price decrease (-20%) is equal to -3.

So, elasticity is the ratio among variation in quantity (60%) and variation in price (-20%) = -3.


What may have caused these blips in the value of Euro vs. US dollar I was looking at the USD/EUR exchange rates a few minutes ago (Saturday evening, Eastern Time Zone here in USA) at xe.com and noticed some sharp blips on it from earlier today.

The graph looked as shown below.

The times (on the X-axis) are in the GDT/UTC timezone but these fluctuations are from activity caused during Saturday. Notwithstanding that I assumed that the exchanges are closed on Saturday, the blips are interesting because the value after the blip is the same as before it.

Are these blips caused by

some algorithmic trading happening during the weekends, or
perhaps something in how xe.com calculates the currency rates, or
something else?

I’d go with (2j, something with how they calculate exchange rates. If you note the scale, the blips are abeolutely small, so there was just some small glitches.

I am only somewhat familiar with currencies, but the spot markets use market makers. (Currency futures are traded on exchanges, but the chart should be labelled as futures if that were the case.) Series like this are based on some kind of “average” of quotes. The period shown is outside “normal” trading hours (currency markets are global, so trading hours reflect that), and there is no reason to update quotes, so the level is mainly stable.

Any number of things could cause the small glitches. For example, if one of the dealers shuts down their system temporarily, it could move the average. Or there could have been some out-of-hours activity that caused one dealer to move quotes, and then snap back into line with the other dealers after the activity passed.


Why are trade deficits considered unfair? President Trump has accused Germany and China of unfair trading practices over trade deficits.

What is unfair about trade deficits?

This may be economics 101, but in my naive eyes every time a trade is done it is done deliberately because both sides believe there is a profit to be made. Hence, each time American companies give money to Chinese companies in exchange for goods and thus enhance the trade deficit,  this would presumably be to the advantage of both the USA and China.

You don't see Apple accusing Samsung of unfair trading practices because Apple bought Samsung screens but Samsung didn't buy Apple batteries in return.

Note that I am not asking why trade deficits are considered bad. Though I don't understand that either, my question how deliberate trade can be considered unfair stands even if trade deficits are bad as a whole for one country.

You are correct.  Trade deficits are not unfair, although it is hard to define unfair in an economic sense. No one is forced to trade and trade represents a consensual agreement.

The strongest economic argument for considering trade deficits unfair is so-called dumping, which is a form of unfair competition. That is when firms sell goods abroad at below a normal price in order to drive out the local competition in the long run. As the foreign businesses would make losses doing so, it only works if the foreign governments subsidize those firms. That is why subsidies leading to unfair competition are banned according to the World Trade Organization rules. In the case of the steel tariffs imposed by the U.S., dumping by China was used as an argument, although there was no evidence of China conducting steel dumping and China isn't even one of the main exporters of steel to the U.S.

Another reason is that a trade deficit means that foreign firms are doing better than domestic ones, thereby threatening the jobs of domestic workers. However, for this to happen  consumers must be voluntarily buying those foreign products. If foreign firms offer a much better and/or cheaper product, then a trade deficit is great for consumers, but bad for domestic workers who produce those goods. In this case, trade still represents an overall net increase in welfare, but there are winners and losers. If the winners (consumers) would compensate the workers who lost their jobs, everything would be fine. If they do not it could be considered unfair, although it is not the foreign country being unfair in this case.

From my experience, there may also be illogical reasons that people consider trade unfair, which I discuss below.

When a country runs a trade deficit that means that it is consuming more than it produces. The country consumes at least as much as it produced and then a bit from what other countries produced too. When that happens, a country is essentially borrowing money from the rest of the world, because consuming more than you have is like spending more money than you have. That is what people mean when they say the U.S. owes a lot of money to China. In this sense many people who take out a loan with a bank to buy something think it is unfair that they have to pay it back. That could be one way in which deficits are considered unfair.

Another way in which deficits are considered unfair is by comparing a country to a business, which is wrong and leads to wrong policy. A business wants to maximize profits, so it would like to sell more goods than it buys. The business fails otherwise. In this sense, a business seeing other business succeeding where it fails might think it is being treated unfairly. As discussed, however, a trade surplus just means that you are lending money to the rest of the world. That may be good for some time, but only if you eventually get it back, i.e. eventually run a deficit. So for a business, perpetually making profits is a good thing. For a country, a perpetual surplus forever is not welfare enhancing.


Complete Markets in Continuous Time In the standard discrete time economies with a finite number of states, $n$, a complete markets economy is simply an economy with $n$ independent assets (Think Ljunqvist and Sargent Chapter 8).  This is because $n$ independent assets is sufficient to span the set of states tomorrow.

I had a discussion with a professor last week in which he stated that one of the conveniences of continuous time when thinking about asset pricing is that within a continuous time economy one can get complete markets simply with a risk-free bond and a risky asset (independent) for each Brownian motion in the economy.

He explained it as we talked, so I think I mostly understand it, but was wondering if someone would mind writing down the details?

I will probably spend a day or two this week on it (depends on some of the properties of the differential calculus), so if no one else answers the question then hopefully I can provide a satisfactory answer.

I am the last person that should be answering continuous time questions like these, but if there's no one else I guess I'll give it a shot. (Any correction of my dimly remembered continuous-time finance is very welcome.)

My impression has always been that this is best interpreted as a consequence of the martingale representation theorem. First, though, I'll loosely establish some notation. Let the probability space be generated by the $n$ independent Wiener processes $(Z_t^1,\ldots,Z_t^n)$. Let there be $n+1$ assets, where the value of the $i$th asset at $t$ is given by $S_t^i$. Assume that asset $i=0$ is a riskfree bond $dS_t^0=r_tS_t^0dt$,  while assets $i=1,\ldots,n$ are each risky and are driven by the corresponding $Z_t^i$:
$$dS_t^i=\mu_t^idt+\sigma_t^idZ_t^i$$
Assume there is a strictly positive SDF process $m_t$ normalized to $m_0=1$, such that $m_tS_t^i$ is a martingale for each $i$ (basically the definition of SDF) and where
$$dm_t=\nu_t dt+\psi_t\cdot dZ_t$$
(I use $\cdot$ as the dot product, which will be convenient.)

Finally, let the $n+1$-dimensional vector $\theta_t$ be our portfolio at time $t$, such that net worth $A_t$ is given by $A_t=\theta_t\cdot S_t$. Assume that $A_0$ is fixed and that further we have
$$dA_t=\theta_t\cdot dS_t$$
Now I'll state the objective, which captures the essence of complete markets. Suppose that the world ends at time $T$, and that we want net worth $A_T$ to equal a certain stochastic $Y$, which can depend on the full history up until time $T$. Suppose that $A_0=E_0[m_TY]$, so that in a world with complete markets we could (at $t=0$) use our initial wealth $A_0$ to purchase the time $t=T$ payout $Y$. In the absence of these direct complete markets, the question is whether there is nevertheless some strategy for the portfolio $\theta_t$ that will allow us to obtain $A_T=Y$ in all states of the world. And the answer, in this setting, is yes.

First, one can calculate $d(m_tA_t)=\theta_t\cdot d(m_tS_t)$. Thus $m_tS_t$ being a martingale implies that $m_tA_t$ is a martingale. Thus we have $A_T=Y\Longleftrightarrow m_TA_T=m_TY$ iff
$$m_tA_t=E_t[m_TY]$$
for all $t\in[0,T]$. Note that this is true for $t=0$ by assumption; hence to get equality it is only necessary to prove that the increments are always equal on both sides.

Now the martingale representation theorem comes in. Since $E_t[m_TY]$ is a martingale, we can write
$$E_t[m_TY]=E_0[m_TY]+\int_0^t \phi_s\cdot dZ_s$$
for some predictable process $\phi_s$. So we need to be able to show $d(m_tA_t)=\phi_t\cdot dZ_t$. Writing
$$d(m_tA_t)=\sum_i (m_t\theta_t^i \sigma_t^i +A_t\psi_t^i)dZ_t^i$$
we see that we need $m_t\theta_t^i\sigma_t^i +A_t\psi_t^i=\phi_t^i$ for each risky asset $i=1,\ldots,n$, which we can invert to give the needed portfolio choice $\theta_t^i$:
$$\theta_t^i=\frac{\phi_t^i-A_t\psi_t^i}{m_t\sigma_t^i}$$
The riskless asset portfolio choice $\theta_t^0$ can then be backed out from $A_t=\theta_t\cdot S_t$.

The intuition here is simple: we need to always have $A_t$ adjust to maintain the equality $m_tA_t=E_t[m_TY]$, but both the expectation on the right and the SDF $m_t$ on the left are moving in response to the driving processes $dZ_t^i$. Hence we need to pick a portfolio $\theta_t$ such that $dA_t$ precisely offsets these movements and the equation continues to hold. And we can always do this as long as locally, our assets span all the risks $dZ_t^i$ -- which can happen more generally, even for $n$ correlated assets as long as their increments are locally linearly independent. (The case here of $n$ risky assets each drien by an independent Brownian motion is a special one.)


Does control system engineering have a place in economics? Do central banks use some form of engineering-style PID control systems/feedback loops to implement monetary policy?

I'm an electrical engineering student taking microeconomics/macroeconomics and a lot of it, at least in terms of government policy to control inflation and interest rates, seems applicable to control systems engineering. However, I can't find a great deal of hard literature about it.

Just as a for instance, one could use PID control to set an output, say inflation rate, to follow a specific course or remain steady given certain inputs, say GDP or interest rates or productivity, and given external disturbances, say Brexit. And even if the controller can't prevent catastrophes altogether, it can dampen the response so that sudden and jerky crashes are smoothed out.

Why or why not does economic policy use established control theory? If it does, what applications can this be seen?

Thanks in advance!

Economists have been exploring control theory applications to macro economics for decades. For example, here is a 40 year-old research paper written in 1976 on the topic.

top of page 2 (also numbered 171)

  In the past decade, a number of engineers and economists have asked the question: "If modern control theory can improve the guidance of airplanes and spacecraft, can it also help in the control of inflation and unemployment?"

Non-linear adaptive human behavior, uncertainty and governmental decentralization of control (i.e., democracy) are the main reasons I believe control theory has not become a more common tool for policy makers. Economics is simply not an exact science. Whereas engineering is more so. So control theory is more useful in the engineering discipline.


Why would governments sell bonds when the economy is in recovery? China confident of meeting 2020 fiscal targets, CGTN, 7 August 2020.

The article states that China is selling "special government bonds".

Why do this? Especially when economy is just recovering?

What is the direct effect on the economy, both in the short and long terms?

The article pretty much answers this:

China has issued 100 billion yuan (about 14.1 billion U.S. dollars) of special government bonds for COVID-19 control measures in a bid to support local infrastructure construction and epidemic prevention and control, the senior official added.
It is set to counter the downward pressure on economic growth, expand tax and fee reduction policies to help enterprises tide over hard times, and strengthen budget balance to mitigate the adverse impact of the epidemic on fiscal revenue growth.

Even if the economy is doing better, it is expected to otherwise be below their growth targets.
(If you have a more specific question, you should re-phrase your question accordingly. If you want to find someone with expertise on Chinese government policy making (not me!), I am unsure how many read this website.)


"Tightness" of political elections and public attention Are there any empirical studies on political elections that focus on the "tightness" of the race and how much attention the election receives from the public (or perhaps voter turnout).

By "tightness" I mean ex ante probabilities of winning the election are not too different among the candidates.

I suspect that tight races should be able to garner more public attention, but I would like some evidence to back this up.

Yes, you should look at the regression discontinuity literature in political economy that uses close elections as the identification strategy. For example, see http://sekhon.berkeley.edu/papers/CaugheySekhonRD.pdf  and http://www.polmeth.wustl.edu/media/Paper/EggersetalRDD.pdf


Primary dealers in treasury auctions When the treasury or equivalent institution of a country auctions of government bonds there is frequently (i.e. in most countries) some sort of restriction on who can participate. The term primary dealers refers to agents who participate in this primary auction with the intent of reselling the acquired bonds on the secondary market. Usually there is a gap between the bond price (or implied interest rate) of the primary and the secondary market so this is profitable.

Some papers on the phenomenon:

VALUING DEALERS' INFORMATIONAL ADVANTAGE: A STUDY OF CANADIAN TREASURY AUCTIONS (JStor access needed)
Who Buys Treasury Securities at Auction

What benefit if any does the treasury derive from this setup, i.e. restricting auction access?

(As requested in comments)
Primary dealers have a privileged position, so there is value in being registered as a primary dealer.
The Treasury or Central Bank can impose standards of behaviour (e.g. an expectation of reasonable participation in all bond auctions or open market operations) as a condition of maintaining that registration. There are rules such as https://www.newyorkfed.org/markets/pridealers_policies.html and you will find sections such as

The New York Fed expects a primary dealer to:

participate consistently as counterparty to the New York Fed in its execution of open market operations to carry out U.S. monetary policy pursuant to the direction of the FOMC;

provide the New York Fed’s trading desk with market commentary and market information and analysis helpful in the formulation and implementation of monetary policy;

participate in all auctions of U.S. government debt; and

make reasonable markets for the New York Fed when it transacts on behalf of its foreign official account holders.

In the selection process, the New York Fed will evaluate a prospective primary dealer with these expectations in mind.

In effect primary dealers provide liquidity and information and markets even at times of crisis, which comes at a cost, one which countries such as the USA think is worth paying to get the increased financial stability it brings.


Zero Economic Profit and opportunity cost? In microeconomics textbook, there is always this notion of zero economic profit in perfect competition. We know that when people gets negative economic profit, they often leave the market. What I wonder is if there exists some NPOs that competes in everyday markets (such as food markets because it sounds like doable), earning say zero accounting profit, meaning negative economic profit. If there do exist, why aren't they driving other for profit competitiors out? Is this because not much people are investing or what?

Theoretically it is possible but only if the non profit organization operates at a cost which is lower than all other existing as well as expected new players as in a free market anybody with a much lower cost can enter and offer a price lower than the NPO and still earns a profit. And what about other NPOs in the same field. If they have a lower cost they will certainly offer a lower price. Secondly the NPO should accepted by the consumers. Practically speaking the market has many more complexities such as existence of brands and the information that price suggests. A lower price means lower quality which may not be accepted by the consumers. For example I may start manufacturing and selling mobile handsets at zero profit but still I might not drive Apple out of the market. Also, the world is not much perfect. To start I would have to install a capacity that can produce at a cost lower than the existing players and then offer a lower price to drive them out.

But still you can have examples of apparent monopolies in markets say for example 'online information'. What do you think Wikimedia is ? It is an NPO.


Principles of Economic Reasoning: How Are Expected Costs and Benefits Distinct from Ethical and Moral Judgments? This question relates to principles of economic reasoning in a non-financial context:
How are economic principles applied to non-financial models, such as a democratic election?
One may reverse the assumption and ask how benefits and costs in a financial context would be evaluated without recourse to making ethical and moral judgments?
For brevity one may describe an ethical philosopher as a person who makes an effort to answer two questions:

What is good?
How should one act to cause the good?

Terse principles of economic reasoning might be stated as follows:

Maximum benefits are good.
One should act to maximize benefits and minimize costs in the social context.

Public good would be an effort to maximize benefits and minimize costs for a group of individuals. Private good would be an effort to maximize benefits and minimize costs for each individual while interacting with members of the social group. Edit: Pareto efficient outcomes occur when no one is worse off.
How then is economic reasoning distinct from more general efforts to determine what is good and how one should act to cause the good? If people demand government solutions to social problems and economists debate the costs and benefits of different types of government institutions then is this not a political, ethical, and moral debate which cannot be resolved via recourse to an independent economic reasoning skill?

The following is simply not accurate statement about economics:

Terse principles of economic reasoning might be stated as follows:

Maximum benefits are good.
One should act to maximize benefits and minimize costs in the social context.

In order to answer this question, and see why the statement is inaccurate, it is important to recognize that inquiry in economics (an other sciences as well), can be split into two categories:
Positive Economics: Positive economics deals with questions of what is. For example, what is the elasticity of demand for market for potatoes? What is the effect of rising minimum wage on employment? etc. (see Mankiw Principles of Economics pp 27.). Most economics as practiced today (in academic research) is positive economics.
Normative Economics: Normative economics deals with question what ought to be? If we estimated a differences-in-differences model that shows small increases in minimum wage do not significantly affect employment should we increase it or not? (ibid. Principles of Economics). Normative economics is mostly dealt with in public economics or in practical public policy.
Now it is plain to see that positive economics and research about positive economics simply does not concern itself with maximum benefit or whether one acts to maximize benefits and minimize costs (from moral perspective that is).   When we model rational behavior of profit seeking firm  in positive inquiry we are not implying that firm should act that way - we are attempting to just be descriptive and describe the behavior of firm.  When we say people are trying to maximize their utility (or when behavioral economists tell us sometimes they don't) we are not claiming this is moral thing to do or they should behave in such way. This is done without any moral judgement or prejudice similar way as physicist would describe motion of a gas or planets (of course, the precise techniques will differ but in principle on fundamental level there is not much difference).
Hence already from onset we can safely say that whole corpus of positive economics is  distinct from making any moral or ethical judgements so let us turn our attention to normative economics.
Normative economics deals with ethical and moral issues but not by any means in such overtly reductionist way as suggested in the 'terse principles' you stated.
Normative economics will nowadays start with recognition that although economics originated in moral philosophy* it is no longer part of it and we economists are not anymore specialist in moral philosophy (of course, a person can have multiple specializations one can be both economist and moral philosopher the same way as one can be biologist and moral philosopher, or as someone who can be both physicist and chemist at the same time). Consequently, when we make normative inquiry we won't start by trying to deduce what is moral or not from first principles.
Rather in normative economics we start by looking at past work of moral philosophers and moral frameworks that are already developed (yes sometimes those moral philosophers happened to also be economists - e.g. Adam Smith - theory of moral sentiments, Amartya Sen - Capability and Well-Being etc.). The three widely popular moral frameworks used across public econ literature are moral philosophies based on Rawls' theory of justice, classical liberalism and utilitarianism but there are of course many more different frameworks used (see Ross (2014) Philosophy of Economics for short overview).
In both Rawls theory of justice or classical liberalism the objective is neither to maximize benefits or minimize costs in either private or social context (see Rawls (1971)
A Theory of Justice; Nozik  (1974)  Anarchy, State, and Utopia). Rather a Rawlsian economist would recommend to conduct economic policy in accordance with maxmin principle i.e. maximize welfare of the poorest member of society and nobody else (although once you raise one person someone else becomes the poorest so Rawls is not implying to take care of only one person). A classical liberal/libertarian economist would favor any policy that minimizes the use of force and coercion by state (even if it would not necessary maximize utility - classical liberals are not utilitarians). Utiliterians would indeed want to maximize benefits and minimize cost in terms of utility.
However, note in athe above cases it is not really the economist who postulates what is good or bad. Rather the economist will defer to moral philosophers. Furthermore, when doing normative economics an economist will not necessary even pick a side. Vast majority of the corpus of public economics literature usually makes comparative analysis that takes into account several different moral  philosophies. For example, in optimum income taxation literature people routinely estimate optimal taxes and transfers using Rawlsian, utilitarian, classical liberal (also known as conservative - due to US politics where conservatives tend to be economically libertarian) or other welfare function (see Saez 2001 as an example of a study that does this).
Of course, ultimately in a democracy it will be people to decide which social welfare function society adopts, and people should decide based on their own values and moral principles. I think most economists nowadays humbly acknowledge this.
This being said economists are also people and most people love discussing politics and moral philosophy so many economists will frequently make statements that go way beyond even normative economics. Some will even dabble in moral philosophy more professionally. This is not unique to economics. You will find many physicists such as Einstein for example who at some point started to dabble in moral philosophy. While in case of physics it can be easy for people to make distinction in economics this can be more difficult due to the historical roots in moral philosophy that economics has but that does not make 'principles of economic reasoning' any more close  to it.

* I am specifically putting emphasis on 'moral' as it can be argued no science can be divorced from metaphysics and other branches of philosophy that deal with epistemological questions (see Ross cited above).  How do we even know we can know anything? Is there even such thing as a 'fact' or 'objective truth'?


Perfectly elastic supply How would you algebraically write a perfectly elastic supply?

Will it be infinite at price = 4? (The choice of the number 4 is completely arbitrary)

Yeah, that's pretty much it for any horizontal or vertical line:

P = p0


intuition behind the blanchard kahn conditions? In order for a DSGE model to have a unique solution, it is required to satisfy the Blanchard Kahn conditions. However, these conditions seem very abstract to me.

Is there an intuition behind the blanchard kahn conditions? Why does a DSGE model have a unique solution iff the number of unstable eigenvalues at the linearized steady state is equal to the number of control variables?

The condition that unstable eigenvalues equal in number the control/decision/non-predetermined variables is equivalent to the requirement that a model possess the "saddle point property".

Of more interest is why economists generally want their models to possess such a property, something that holds for the DSGE models.

In Economics we call models with the saddle point property as "saddle path stable"; a mathematician would disagree. From a mathematical point of view these models are unstable, because there is a unique path to the fixed point/equilibrium. It should then be evident why such models are characterized as unstable: the slightest perturbation will push the dynamics off the unique path to equilibrium, never to return... enter human will and purposeful action by economic agents: we keep the model on the unique path on purpose, in order to fulfill the optimization conditions that describe our will and desires. In other words, going to the fixed point is the optimal thing to do from a utility-maximization point of view. And if a shock happens we forcefully "jump" back on the saddle path (that may have changed or stayed the same due to the shock), correcting the course of the economic system by will and decision.

Consider now a model that is mathematically stable proper. It means that it does not matter where we start, and it does not matter what we do, we will end up in the long-term equilibrium. Hardly an appropriate model to reflect the observed human affairs, or decision-making.

And decision-making is structurally an unstable phenomenon, mathematically speaking. This may help glean a bit more intuition: to possess "as much decision-making as needed" in order to have a unique way to go to the fixed point, we need the model to allow us to actually decide optimally on the number of variables the model premises say that we can decide upon, no less and no more: so, as many unstable roots as "unstable"(decision) variables.

If the unstable roots are less than the unstable/decision variables, the model does not give us the "degrees of freedom" we need - it is "too stable", hence the many solutions: it is mathematically stable. Boring.

If the unstable roots are more than the "unstable" variables, we cannot control the model through our decision making, and it will explode/implode.


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

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

Anyone know where to find these data?

I just faced the same problem and found the solution:

Use this code in R:

input Stata file

library(foreign)
child <- read.dta("C:\child.iq.dta")

Code found here:(https://www.statmethods.net/input/importingdata.html)

You need the double " \ " if you're using R.
read.dta("    ") Type the exact folder with data ending. Be careful to use common characters, otherwise R could have problems finding the folder. In my case I just saved the files on C:\.

This way you can access all Data.

I'm using the latest R-Studio version.

I hope I could help you!


Central Bank Balance Sheets and foreign bonds I have a question relating to central bank's balance sheets, taken from Krugman and Obstfelds' "International Macroeconomics" textbook.

They mention that when the central bank purchases foreign bonds, the domestic money supply increases. This is paid for with domestic currency.

My question is: how does this look like in practice? So say the Fed buys the government of England's bonds. Will they convert it first to pounds? Or would Bank of England sell the bond for dollars? I am struggling to understand how the increase in purchase of foreign bonds increases domestic money supply.

Any help is much appreciated.

It happens in reality, pretty much as described in the book, not far from what you wrote

Say that the fed would like to buy UK bonds. Since UK bonds are issued in pounds, in order to buy them, the Fed will have to 1st buy pounds, in exchange for dollars, which didn't previously exists.
In this case, more dollars will enter circulation, and the money supply will rise.
In parallel, the dollar exchange rate will increase against the pound, that is the dollar will weaken.

Its the same logic that  domestic bonds: buying domestic government bonds, in exchange for previously non-existing dollars, would increase money supply.

In today's free capital markets, there isn't any essential difference between the two, because of arbitrage:
In the case of buying foreign bonds, and rising pound rate, euro holders, for example, for them rates remained unchanged , will buy dollars to sell pounds, until a new euro rate will be set.

Similarly, a local increase in inflation, due to purchasing domestic bonds, will effect exchange rates, as local currency value would fall.


What are the pros and cons of eliminating corporate taxes? I recently heard a story on npr about economic policy changes that both liberal and conservative economists definitively agree on.  Among other things, complete elimination of corporate taxes was mentioned.

I'm curious to know more about what the consequences of such a policy would be, both positive and negative.
Particularly, i want to know how this could possibly benefit the middle and lower echelons of society, not just the wealthy.  I'm curious if there are any benefits to the government as well, since they stand to lose income by this change.

I'm not looking for answers appealing to political ideology or speculation.  I want solid answers backed up by sound theory and empirical evidence.

The first and most important insight here is to recognize that burden of taxation (the incidence) need not fall on the entity taxed. Economist Herb Stein is famous for having quipped (on the subject of the corporate income tax):

  "...that it’s as if people think that if the government imposed a tax on
  cows, the tax would be paid by the cows."
  Are Taxes on Corporations Taxes on People?

The corporation may front the money, but ultimately that money comes from customers, employees, vendors, creditors, and equity holders. Miller and others have written down models where corporate shareholders bear the burden but it doesn't have to be that way.

So to assess the consequences of eliminating the corporate income tax, we really want to know who pays (bears the burden of) the corporate income tax. To the extent that it is the providers of capital of the firm who bear the burden, we might assume that lowering the corporate income tax would act like an income tax cut for the rich. But there are simple models where customers pay some of the corporate income tax, such as if domestic and foreign products (as well as investments) are perfect substitutes, then (immobile) labor pays all the burden of the corporate income tax. Unfortunately, the issue of incidence remains murky despite decades of work on the subject.

Regardless of who pays, it is clear that enormous resources are devoted to corporate income tax avoidance probably because corporations have so many more opportunities for tax avoidance than individuals do, due to their complexity, multi-territoriality, and general scale and scope. If eliminating the corporate income tax freed most of those resources invested in corporate taxation preparation and avoidance (on the order of \$150 billion by two estimates just in compliance costs, ignoring strategically wasted resources), resources amounting to something like half of actual corporate income tax revenue would be usable for other activities. Free up those resources and you can make everyone better off, at least in principle. You might for example create a revenue neutral increase in dividends, capital gains, and interest taxation to offset the corporate income tax cut. This could leave beneficiaries of current spending essentially unaffected while the holders of current capital in taxable accounts would be a bit worse off and tax-free accounts (retirement, charities) slightly better off from the direct effects of the tax changes. But since their compliance costs fell massively, there might be enough to make everyone better off.

The bottom line is that that the corporate income tax is a expensive way to gather tax revenue from rich people and we are not sure it even does get money from rich people. The corporate income tax can plausibly harm non-rich people in the process. Taxing the income of the rich directly, if that is the end goal, is much more efficient. The resulting efficiency gains can be split between the rich and poor. Even if you don't particularly want to tax the rich, a more efficient tax policy means  tax rates can be lowered. So there is something for a liberal and conservative economist alike to love with this tax reform.

Here are a couple of papers that suggest that higher corporate income taxes induce corporations to have more debt and less equity (greater leverage), although there is some evidence that reducing these taxes would not reduce leverage in the short run.

  ...low tax rate firms lease more, and have lower debt levels, than high
  tax rate firms

Debt, Leases, Taxes, and the Endogeneity of Corporate Tax Status

  The results suggest that taxes have had a strong and statistically
  significant effect on debt levels. For example, cutting the corporate
  tax rate by ten percentage points (e.g. from 46 to 36%), holding
  personal tax rates fixed, is forecast to reduce the fraction of assets
  financed with debt by around 3.5%

Do taxes affect corporate debt policy? Evidence from U.S. corporate tax return data

  ...we show that taxes have a first-order effect on capital structure.
  Firms increase leverage by around 40 basis points for every
  percentage-point tax increase. Consistent with dynamic tradeoff
  theory, the effect is asymmetric: leverage does not respond to tax
  cuts.

As Certain as Debt and Taxes: Estimating the Tax Sensitivity of Leverage from State Tax Changes

If I can recall papers that estimate the costs of tax avoidance and excess burden of taxation I'll add them as well. Suggestions welcome.


What is the mechanism that triggers a stock price change? When discussing with my son basic economics (how the price is driven by demand, among others), I came to wonder which exact mechanism triggers a price change in a stock exchange.
In everyday life, prices are fixed (in practical terms) by the provider (a shop for instance). The consumers either buy it or not, which can drive the provider to lower the price (or not). In any case, there is a trigger (the decision of the owner to set a price) that probes the market.
What is the equivalent in a stock market? Specifically, what exact mechanism modifies the price to get a reaction of the ones who would like to buy or sell stock? I understand that globally the demand drives the price, but once the price is, say, 10 EUR - what triggers a change?

Is it a random mechanism ("we, the stock exchange organization, will fluctuate the price around 10 EUR to see whether more will buy or sell")?
Or an offer is done by some of the ones who would like to sell or buy ("I will ask around to buy for 9 EUR and see if someone sells", or "I will set the price of my share to 11 EUR instead of 10 and see if someone buys from me"?)
Or something else?

I won’t discuss the fundamental reasons why stock prices change (discussed in another answer), but the mechanics (roughly) work like this. (Real world is more complex, since there are multiple exchanges, and high frequency trading.)
An exchange matches orders from buyers and sellers. The sensible way of making an order is to put a limit price on it. So you either make a bid up to a maximum price, or sell at a minimum.

If your order cannot be matched to an existing order, it is added to the queue of orders. There is a list of bids (buy orders) and offers (sell orders), which are ordered by price. E.g., if the highest bid is to buy at \$90, a bid at \$100 is better and is added to the front of the queue. (If the order price matches an existing price, the orders are processed first-in, first-out.) No transaction has happened, so there is no recorded stock price change. (Exchanges report the best bid/offer, which might change.)
If your order can be matched (either you pay as much as someone is willing to sell at, or sell at a price people are willing to pay), you buy/sell at the prices specified by the existing orders. E.g., if there were orders to buy 100 shares each at \$100 and \$90, and you are willing to sell 200 at \$90, you first sell at 100, then 90. The pricing history will note the transactions, and the price drops.

Other orders are “market orders,” where you buy/sell at the best offer/bid. In the era of high frequency trading - where the prices move extremely fast - this is surprisingly risky. A market order can be considered to be a bid with a limit of infinity (!) or a sell at 0 (which explains the risk, if orders can jump extremely rapidly). In a market where most orders are market orders, they will account for most of the transactions - limits are set not to trigger a transaction, rather they wait for a market order.
One thing that is often not appreciated is that professional traders will continuously monitor their open orders. They will remove them and add them back at new prices in response to news. This means that the prices can jump without any buying or selling: people can adjust prices without there being any transactions. This effect means that it is safest to think about prices as being set based on traders’ views, and not some mechanical supply and demand effect based on buying and selling flow numbers.


How much money has the Fed printed? The Federal Reserve is the bank of banks in the US. While it cannot force banks to change their rates in order to monitor the economy, it has several other ways to influence. One way it by printing money.

Please forgive my questions, whose answers seem easy to be found online. It's a hot topic, so it's very hard to get validated information.

Questions:

Is the amount of money printed open knowledge?
Where to get a history profile of how much money has been printed by the Fed?
How validated is the info you provide, and in what sense?

The Fed’s liabilities (technically broader than the true monetary base but arguably more relevant depending on your definition of “money printing”) are released weekly in their H.4.1 release. They appear in Table 4. Right now they are about 6.3 trillion dollars, up almost 2.4 trillion from a year ago.

They’re “validated” in the sense that the Fed has internal controls, external third-party auditors, and is subject to regular Congressional oversight.

Yes, you can find a time series from the St. Louis Fed’s FRED service.