Mixed dominance game theory I don't quite understand here, how exactly is the strategy $(\sigma_1(U),\sigma(M),\sigma_1(D))=(0,1/2,1/2)$ dominates $U$ since if you look at the first column, $5$ is greates than $3/2+4/2=1.5+2=3.5$ . I'm guessing i'm doing something wrong. Could someone please tell me what i'm doing/thinking wrong?

The text says domination is "in the game remaining after one stage of elimination".

In stage one, column L can be eliminated. As this is exercise b., I am guessing that was exercise a.


Buying/selling bonds more than once Suppose the government of a country issues a bond. A certain bank buys that bond:

The bank loaned a certain sum of money to the government.
The government has to pay interest every x intervals of time and the face price at the maturity date to the bank.

What if the bank sells that same bond that it bought to the public. What happens then? If I buy the bond:

I give a sum of money to the bank
The bank now has to pay me interest and the face price at the maturity date?

What happens to the government in the equation?

If the bank sells me the bond they bought from a municipality, I am now simply entitled to the bond's remaining cash flows from the municipality. The price I pay for the bond from the bank is equivalent to the discounted present value of all remaining cash flows.


Can we successfully pursue the goals of environmental sustainability and reduction of income inequality at the same time (and, if so, how)? Environmentalists tell us to reduce our carbon footprint by, among other things, reducing our traveling and consumption of long-hauled goods. But people living in small-market export-oriented countries, as a result, may and are expected to have a hard time coping with such a drastic change in consumers' preferences (keep in mind, it's often developing nations). For example, about a third of Sri Lanka's GDP is just tourism and tea.

In Denmark the government is both pursuing policies aimed at environmental sustainability as well as income equality. If one country can do it it must be logically possible. So the answer is: yes we can!!


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

Because what Trading Economics states to be M0 is not really M0 but the monetary base (MB). Compare the data in their graph with the data from the Fed (e.g. here). These are some of the values from the monetary base (variable BOGMBASE):

2016-09-01  3735888
2016-10-01  3572132
2016-11-01  3629770
2016-12-01  3531565
2017-01-01  3595455
2017-02-01  3746401
2017-03-01  3856260
2017-04-01  3821654
2017-05-01  3774390

They correspond roughly to the ones in the TE graph.

Whilst M1 is indeed larger than M1, the monetary base does not need to be. This is the entry in the Wikipedia article for monetary supply in the US:

M0: The total of all physical currency including coinage. M0 = Federal Reserve Notes + US Notes + Coins. It is not relevant whether the currency is held inside or outside of the private banking system as reserves.
MB: The total of all physical currency plus Federal Reserve Deposits (special deposits that only banks can have at the Fed). MB = Coins + US Notes + Federal Reserve Notes + Federal Reserve Deposits
M1: The total amount of M0 (cash/coin) outside of the private banking system plus the amount of demand deposits, travelers checks and other checkable deposits

A similar entry from the Fed website indicates that M1 does not include the whole of MB. The relevant quote is:

  The monetary base is defined as the sum of currency in circulation and reserve balances (deposits held by banks and other depository institutions in their accounts at the Federal Reserve). M1 is defined as the sum of currency held by the public and transaction deposits at depository institutions (which are financial institutions that obtain their funds mainly through deposits from the public, such as commercial banks, savings and loan associations, savings banks, and credit unions).

It follows that the data from Trading Economics is misleading. It might be worth pointing this out to them.


Which measure of total loans is more relevant to Financial Stability? I am writing a paper on the financial stability of the banking sector. One factor im looking at is the amount of new loans or credit issued (credit growth). I have two different total loan measures. One measures the total loans by their utilisation while the other measures them by the credit lines spoken. Which measure would be more appropriate when regarding the financial stability of the banking sector? Im tending towards using the total credit lines which have been spoken.

Measuring the total loans by their utilization rate is more effective in determining the financial stability of the banking sector. These 'utilized' loans are IN EFFECT, aka, in use and simultaneously have a risk factor. Un-drawn data is not that useful because it might never be drawn and therefore pointless when determining stability measures.

My reason for saying this stems from the hard data perspective. You have hard, real data when measuring the total loans by their utilization rate. You have theoretical(not hard data, and there-fore theoretical risk factor) utilization rates when it comes to "spoken" credit lines available but not necessarily drawn.

Hope this helps.


Update of Fed mandate(2020) - "shortfalls of employment" In this Fed link, it's stated that 1 of the most important changes in the document describing the Fed mandate/framework, is

On maximum employment, the FOMC emphasized that maximum employment is
a broad-based and inclusive goal and reports that its policy decision
will be informed by its "assessments of the shortfalls of employment
from its maximum level." The original document referred to "deviations
from its maximum level."

Does "maximum employment" mean potential rate of employment?
In what way does the substitution of "deviations" for "shortfalls" change the mandate?

First, this is not change in mandate, Fed cannot just change its mandate unilaterally, as the mandate is given to Fed by US congress (see this Fed Richmond essay on that)  this is just change in its goals in pursuit of their current mandate.

Does "maximum employment" mean potential rate of employment?

According to Fed 'maximum employment' means:

Maximum employment is the highest level of employment or lowest level of unemployment that the economy can sustain while maintaining a stable inflation rate.

So taken at face value this would mean that by 'maximum employment' they mean  non-accelerating inflation rate of unemployment (NAIRU).

In what way does the substitution of "deviations" for "shortfalls" change the mandate?

It does not change the mandate at all, it changes the Fed's goals in pursuit of their current mandate. A deviation by definition means either positive or negative change from the target (eg unemployment being either above or below their target). If they only look at a shortfall from the target level that would mean they are only concerned if unemployment is above the target but not if it is below.


U.S. Bureau of Economic Analysis, when was that created? I thought that GDP in the United States was computed by the Bureau of Labor Statistics, but I find that now it is made by the "U.S. Bureau of Economic Analysis" which I never heard of.

For how long has been case? Has this agency always been responsible for GDP? If not, when did it start?

Bureaucratic history time! Yes, this agency (and its predecessors) have always been responsible for GDP; GDP was created a couple decades after the Department of Commerce and the Department of Labor split up.

The full answer is that the Bureau of Economic Analysis (BEA) was created in 1972 as a bureau in the Social and Economic Statistics Administration (SESA), then made an autonomous bureau within the Department of Commerce in 1975, with the abolishment of the SESA.

When the BEA was created in 1972, it was created out of the Office of Business Economics (itself an autonomous unit) in the Department of Commerce. In turn, the Office of Business Economics was established in 1945 inside another autonomous unit, that parent unit being the Bureau of Foreign and Domestic Commerce.

It was during the period of the Bureau of Domestic and Foreign Commerce (housed in the Department of Commerce) that GDP was created (in part by the work of Simon Kuznets on a measure of national income), but the agency preceded this by many years.

The Bureau of Foreign and Domestic Commerce, for its part, was transferred to the the Department of Commerce when the DoC was created in 1913 (by splitting up the Department of Commerce and Labor into two separate cabinet departments). It had previously been within the Department of Commerce and Labor, and was known as the Bureau of Statistics prior to 1912.

The Bureau of Statistics in the Department of Commerce and Labor was created out of the Bureau of Foreign Commerce (housed in the Department of State), and the Bureau of Statistics (housed in the Department of the Treasury). Each of those bureaus also had other names during the 19th century, but we've probably already gone way further back than you had intended.

This history thanks to the National Archives.


Is cash(currency) a security and a debt instrument? I know that cash is a financial asset and securities are defined as tradable financial assets, so cash is a security, right?
Another thing I'm wondering is that whether cash/banknote is a debt instrument or not. On wikipedia it is defined as one of a debt securities.

I don't think cash could be described as a security... one of the characteristics of securities is that they have imperfect (if very high) liquidity and provide a return (be it fixed or variable). Cash is the definition of liquid and inherently provides no return - you could earn interest on cash by depositing it in a bank but then you are creating a debt obligation in effect - the cash inherently, as in cash in a physical safe, generates zero return nominal by definition. You could think of cash as a debt security where a debt is theoretically placed on the issuer. But: in practice the debt is impossible to pay. You cannot bring a bill into the fed and demand they honour it. So I suppose it would be a debt security in the theoretical sense but it lacks almost all properties of debt securities:
cannot be repaid in practice, never intended to be repaid, perfectly liquid etc, and it has a value that cannot be expressed in terms of anything but itself.


What happens to consumer surplus and profits as firms get more information in Hotelling's duopoly model? In the Duopoly on the line [0,1] with customers uniformly distributed, with firm A on the 0 side and firm B on 1's side, we know that if the firms have no information about the customer, there will be no price discrimination, and the market will be divided into segments [0, 0.5] and (0.5, 1] buying from A and B respectively. If the exact points at which the customers divide is not important, will notate this as [A, B].

If the firms know which half of the line the customer is from, then (loosely speaking) the profits decrease, as the Segments get partitioned not into [A, B], but into [A, B, A, B] with lots of competition going on. Consumer surplus also decreases as there is some inefficient buying.

But what happens when the information increases? Namely, the information of the segment that the customer is from increases from 2 in the previous case, to a large number N. At the limit, this is equivalent to perfect information. Would I be correct to guess that competition gets more fierce in every segment, and so both profits and consumer surplus decreases? Or will we revert back to [A, B]?

In the question above, I was looking for an intuitive answer, not one based on calculations and best responses. But what if I wanted to find the exact equilibrium price and profits at the limit (that is, the firms have perfect information about where the customer is from)?

The article Quality of Information and Oligopolistic Price
Discrimination by Liu and Serfes covers this topic in great detail. It also has a rather nice literature review.


What is William Nordhaus' contribution to the economics of climate change? I'm trying to understand more about the economic repercussions of climate change. I'm unfamiliar with the specifics of the work of William Nordhaus, but it's been predicted in several instances that he will very likely win the economics Nobel prize in the near future* (forbes, nytimes, wsj, npr, marginal revolution). He is most famous for his work on the economics of climate change (which include some estimates of the social cost of carbon).
To clarify with question, what are the merits of William Nordhaus' work that have won him this attention? Was he merely the first to devote serious attention towards a rigorous estimate of the social cost of carbon? Or is there more?
*Update: Nordhaus was awarded the prize in 2018, along with Paul Romer.

Summary
Bill Nordhaus has made several significant contributions to the economics of climate change. That's something of an understatement. His contributions are not just in the pricing of carbon; they but span microeconomics, macroeconomics, (econometric and other) modelling, the philosophy of economics, and the economics of innovation.
Modelling
He's been one of several key figures in the development of integrated assessment modelling - see for example his paper in Science, An Optimal Transition Path for Controlling Greenhouse Gases, from 1992. Such modelling became a cornerstone of the Stern Review (through Chris Hope's PAGE model), and is a live and ongoing area of development at several major universities.
Philosophy
He's been a significant contributor to the discussions about how to design more meaningful measures of economic welfare, including his 1972 book chapter with James Tobin, Is Growth Obsolete: the discussions about what economic growth is, and the necessity of capturing the value of what we now call natural capital and well-being, have been core to the evaluation of the potential damage costs of anthropogenic global rapid climate change.
Innovation
He's "carried out extensive research on the determinants of technological change" - the words (p38) of the International Association of Energy Economists, which awarded him their 2011 "Outstanding Contributions to The Profession Award": this work has been important in the discussions about climate change mitigation, for example with regard to induced innovation, and learning curves for decarbonisation technologies.
Energy resources
There's also his 1973 discussion of the allocation of energy resources, which remains pertinent to the discussion of climate change mitigation today, though the forecasts about dominant technologies turned out to be a mix of prescient and ... less prescient.
And finally
His full CV is here, and shows both the breadth and depth of his interests.
So while it's fair to say that his discussion of the application of a Pigouvian tax to greenhouse gas emissions is significant, it's just one part of a much larger body of work on the distortions caused by system boundaries that were drawn far too narrowly within neoclassical economics; and possible remedies to those distortions.


Market with changing number of goods and services In the General Equilibrium framework of Arrow, Debreau and others, there are a fixed number of commodities, which I feel is a valid assumption in the short run but maybe not in the long run.
Over time, new products are introduced and old products seize to exist in the market. What are some models that address such markets? What are the welfare implications?
On a somewhat similar line, for example a smartphone was not available for most people earlier, but not only that, many people didn't even imagine such a device. Was the smartphone in their Choice Set earlier? If not, and if the introduction of the smart phone changes the Choice Set, can the welfare of a consumer before and after the introduction of the smart phone be compared (does it even make sense), as the preference relation is usually defined for a particular Choice Set?

I think the best candidate would be monopolistic competition as introduced by

Dixit and Stiglitz (1977) Monopolistic Competition and Optimum Product Diversity,

in which two models are introduced. One central theme was product variety and the endogenous determination of the number of product varieties.
There are many models formulated within the monopolistic competition framework in diverse areas of economic theory including

International Trade (Krugman)
Economic Geography (Henderson,Fujita,Krugman,Venables)
Economic Growth (Smulders, De Groot)
Macroeconomics (see for example Blanchard and Kiyotaki 1987)

The welfare analysis has centered around the question whether there is too much or too little product variety in equilibrium. The problem is that there are counteracting forces in equilibrium. Because of setup costs, revenues may fail to cover the costs of a socially desirable product. As a result some products may be produced at a loss at an optimum. This force tends towards too few products. On the other hand firms hold back output making price higher than marginal costs, which gives an incentive to entry, which creates a tendency towards too many products.
The different models therefore vary with respect to whether the first best social optimum is a case of too many or too few varieties depending on the specifics of the model and how the influence the balance of the counterveiling forces.
A representative selection of the literature on monopolitistic competition is collected in book

Brakman and Heijda (2003) The Monopolistic Competition Revolution in Retrospect,

chapter one of which has a textbook example of a general equilibrium monopolistic competition model ala Dixit and Stiglitz.


The factor elasticities from a Cobb-Douglas function in Romer's macroeconomy book Good night, I'm reading the Romer's macroeconomy book in the page 42, "A complication" section title. The begin of third paragraph say:

  This is not a general property of production functions, however. With Cobb–Douglas production, the elasticity of substitution between inputs is 1.  ...

I understand that the factors elasticity of sustitution is defined like $El_x(y)=\frac{d\,\ln(y)}{d\,\ln(x)}$ in this case will be $El_K(L)=\frac{d\,\ln(L)}{d\,\ln(K)}=\frac{d L}{d K}\frac{K}{L}$.
From Cobb-Douglas simplest function $Y=K^\alpha L^{1-\alpha}$ we have, for $Y=const$, $K=(YL^{\alpha-1})^{1/\alpha}$ then
$$\frac {d K}{d L}=\frac{ \alpha - 1}{\alpha}\left(\frac{Y}{L}\right)^{1/\alpha}$$
now replacing in the formula:
$$El_L(K)=\frac{ \alpha - 1}{\alpha}\left(\frac{Y}{L}\right)^{1/\alpha}\times\frac{L}{K}$$ operating we have
$$El_L(K)=\frac{\alpha-1}{\alpha}$$
like $El_L(K)=\frac{1}{El_K (L)}$ then $El_K (L)=\frac{\alpha}{\alpha-1}$.
The point is that this values are unequal to one.

Am I interpreting wrong the affirmation? Thanks for your help.

This is not the elasticity of substitution formula. The correct one is, between factors, $K,L$

$$\sigma = \frac{\mathrm{d}\log \left(\frac{K}{L}\right)}{\mathrm{d}\log \left(\frac{F_L}{F_K}\right)}$$

This expression can conveniently be worked as follows:

$$\frac{\mathrm{d}\log \left(\frac{K}{L}\right)}{\mathrm{d}\log \left(\frac{F_L}{F_K}\right)} = \frac {(L/K)[d(K/L)]}{(F_K/F_L)[d(F_{L}/F_{K})]}$$

$$=\frac {LF_L}{KF_K} \cdot \frac{d(K/L)}{d(F_{L}/F_{K})}$$

In the Cobb-Douglas case we have

$$ \frac {F_L}{F_L} = \frac {1-a}{a}\frac {K}{L} $$

so

$$d\left(\frac{F_{L}}{F_{K}}\right) = \frac {1-a}{a}d\left(\frac{K}{L}\right)$$

Substituting both expressions we have

$$\sigma = \frac {L}{K}\frac {1-a}{a}\frac {K}{L} \cdot \frac{d(K/L)}{[(1-a)/a]d(K/L)}=1.$$


Why would foreign asset purchases by PBOC temper yuan appreciation? Suppose the PBOC buys a bunch of dollar-denominated bonds, using its dollar reserves. All else equal, what effect should this have on the yuan-USD exchange rate? And why? It amounts to trading non-interest-bearing foreign assets for interest-bearing ones, but I am having trouble seeing whether or why it might cause the yuan to depreciate.

Quote...

"Suppose the PBOC buys a bunch of dollar-denominated bonds, using its
dollar reserves. All else equal, what effect should this have on the
yuan-USD exchange rate?"

Quote...

" I am having trouble seeing whether or why it might cause the yuan to
depreciate".

All else is not equal. To return to the original quantity of USD money held it will buy some USD from commercial banks, issuing renminbi in order to do so. Issuing renminbi will have the tendency to cause it to depreciate.


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

One possible flaw in your reasoning is your assumption about what happens to bond prices when there are capital inflows.  For example , suppose that the Bank of England has fixed short term interest rates at 1%, and that the yield of 5yr gilts is also 1%.  Then there is a sudden unexpected rise in the Bank of England rate to 1.5%, resulting in capital inflows to Sterling investments and thus a rise in the FX value of the pound.  However, the short term interest rate is still 1.5% because it is fixed by the BoE, and the 5yr gilt yield is likely to settle at a yield much higher than 1%, depending on the reason for the interest rate raise.  If the BofE says there will be a series of hikes, this yield could settle at 2% or higher.  If the BofE says it is a ‘one and done’ hike, it could settle lower, say 1.25-1.50%.  These numbers are all made up, the point being that it is unlikely that the bond yields stay at 1% when the BofE has raised its short term rate, which appears to be an assumption you made.


Search model with firm decision I am wondering if there is any work in search models that discusses firm behaviors. Most common search models that I am familiar with talk about the job seeker's threshold rule. Is there any model that discusses similar firm threshold rule, in investment in capital, effort etc.

The Neo-Schumpeterian literature models firm behavior with "an search and select" approach. Nelson and Winter (2009) where the pioneers in the subject, it is a pleasant and interesting reading.

Nelson, Richard R.; Winter, Sidney G. An evolutionary theory of economic change. Harvard University Press, 2009


Conditional independence and no correlation I have a question regarding basic econometrics.
Consider the model
$$y_i=\alpha +\beta x_i +u_i$$

I understand that assumption 4 of the linear regression model states

$$[1] \quad  E(u|x)=0$$

However, I often see this condition written as:

$$[2] \quad E(ux)=0$$

Are these two things equivalent? I see that if [1] and $E(u)=0$ then we get [2]; however I don't understand why [2] would imply [1].

[2] does not imply [1]. [2] and $E(u)=0$ imply $cov(u,x)=0$, which is about linear independence. [1] is stronger, as it refers to any type of dependence.

The classic counterexample to show this is $x=u^2$ over a symmetric domain. These are dependent yet linearly independent.

The R code below shows this:

set.seed(1)
u <- runif(100, min = -1, max = 1)
e <- rnorm(100, mean = 0, sd = 0.1)
x <- u^2 + e

plot(u,x)
abline(lm(x ~ u)) # Yields an R^2 of 0.006539

cov(u,x) # Yields 0.01206663

The plot is, where the black line represents the regression line:

Read more about this here.


(Evolutionary Game Theory) Argue informally there can no longer be an ESS in which only b is played Here is a problem in evolutionary game theory: (So the term I am using should be familiar for people in this field)

The game is called 'Clever Mutants' which is a symmetric two-player game:

For this game, I have managed to find three symmetric Nash Equilibria.
They are $(a,a), (b,b)$ and $((1/4,3/4),(1/4,3/4))$, in which the first two are evolutionary stable (ES) and the last one is not.

  Now, suppose that mutants have a 'secret handshake'. That is, suppose
  that mutants can recognize other mutants and play different pure strategies against normal
  and mutant opponents. For example, a mutant could play $b$ against another mutant but
  play $a$ against a non-mutant. Argue informally there can no longer be an $ESS$ (Evolutionary Stable Strategy) in which
  only $b$ is played.

I don't know how to argue for that statement, even informally. Can someone help me, please? Thanks so much.

The "secret handshake" idea was first formalized in economics by Robson (1990).

Suppose initially the equilibrium is $(b,b)$. Since the normal population cannot recognize the mutants, they'd always play $b$.

When the mutants enter the population, because they can recognize their own kind through a secret handshake, they can play $a$ against one of their own (when there is a secret handshake), and play $b$ against the normal population (no secret handshake). This way, the mutants are getting $3$ each time they meet another mutant and $1$ each time they meet a normal. Therefore, the mutant's strategy is a best response to the normal's strategy, but a better response to itself than the normal's strategy is. As a result, the normal's strategy fails to be evolutionarilly stable.


If PPP Exchange rate is 0.291, what does that mean? I've normalised deflators for countries A and B. If the Price level of Country A/ Price level of country B = .291, does that mean that on average for every dollar a person in Country B spends, for the SAME thing in country A it only costs about .291?

S =  P1 / P2  ; P1=Price at country A's currency for good X,

P2=Price at country B for the same good X and S is equal to the exchange rate of currency #1 and currency #2.

This formula measures the difference between the two countries’ rates of inflation and the cost of commodities will drive changes in the exchange rate between the two countries.

this relates the change in two countries’ inflation rates to the change in their exchange rate.

for every 1.00 dollar spent on the good X in country B, it takes  .29 cents to obtain the same good X in in country A buying it with country A's currency.

So if S doesn't match the exchange rate between the two countries for good X then one of the country's currency's is devalued.

As countries with higher levels of inflation are likely to end up with their currencies devalued

https://www.investopedia.com/updates/purchasing-power-parity-ppp/


GDP(Expenditure view of GDP): /Why aren't investments categorized as non-final goods? My understanding is that consumption = consumption of final goods = whatever consumers buy from companies (with an adjustment for export-import-process + maybe housing is slightly different (not important here). So if you were to buy a fully US-made table it wouldn't really matter that first one company plants and harvests the tree, another then buys the whole tree and transforms it into useable wood (cuts into useable sizes, sorts out bad parts, possibly treats wood etc), and then the last step somebody buys that wood and assembles a table. The only thing that matters is when this table is actually sold to an private customer (for 100\$ or whatever)(assuming its directly sold by the joiner and leaving out dedicated retailer).
So far seems somewhat understandable that only the use of the activity to real persons/consumers would ultimately be relevant and seen as economic productivity (use being measured by $spent). However I don't understand why some expenditures made that are called "investments" still increase GDP (and aren't lumped in with other precursors as non-final goods)?(1)

(1)(Maybe expenditures that are classified as investments, like a new production machine, can be seen as not directly tied to a specific output-product (unlike e.g. a concrete amount of wood bought per output-table to be assembled into a table)? But i would not see why this is directly relevant when measuring the quality/productivity of the whole economy as GDP probably should (just because somebody invests into something doesn't mean that's reasonable, e.g. investing into gold-plated machines etc or just machines not fit for their intended use, while you could somewhat reasonably argue that everythng bought by customers should be defined as a useful product and GDP-increasing because apparently the customer found it useful and satisfying customers is ultimately the purpose of the economy?
Also where would that leave sandpaper and similar things? (Machines detoriating very little with each table produced, wood deterioirating/disappearing completely (into the table), and sandpaper in between depending a bit on luck with the wood and not clear whether its more non-final good or investment))

Well first of all the story why we only record final consumption is not completely straight - it’s not because we only care about activity of “real person” or consumer. But because counting it all the way would mean we double count the value of the good.

For example imagine the following situation. A wood is produced and sold for 15\$ to furniture company and then furniture is sold to consumers for 30\$. Well it’s not that we don’t care about the 15\$ because it was bought by company, but because the 15\$ value is already “hidden” in the value of the final good. Counting both would give you value of 45\$ but thats double counting the 15\$ is already "hidden" in the final price (of course final price could be sometimes lower if the second business by mismanagement manages to destroy value - i.e. producing something with lower value then value of the inputs - then you would want to record only the final price still to account for the fact that the process destroyed part of the old value).

Even when business purchases something which is not used for further consumption it counts as final good, purchasing catering for some firm celebration would be reflected in consumption since the catering is final good.

However, while we can’t really count let’s say wood that will later (same year) be used for furniture production we can count spending on machinery because there would not be any double counting since it’s not like you just modify the machine and sell it later as some final good.

This is because GDP basically tries to measure output at current prices. You can do that either by income approach since by definition output is equal to income or by spending approach because all output is going to be used or “spent” in one way or other. Investment also represents spending the produced output so it should definitely be there.

The same question you are asking about gold plated machines can be asked about any final good. If a consumer wants gold plated PC instead of normal PC is that any less or more rational than business owner wanting gold plated machine? The answer is if you want to assume people are rational the business owner will only invest in golden machine if that’s somehow relevant to business process otherwise it would be outcompeted away by other business. If you want to relax the rationality assumption then why should we assume consumers are rational and business not? If we count irrational purchases by consumers we should not discriminate irrational investment.

Regarding the auxiliary question about depreciation. Depreciation actually is not reflected on GDP because it is Gross Domestic Output. However, there is also NDP - net domestic product that controls for depreciation.


Typical Growth Model Social Planner Problem Consider the following social planner's problem, hand-waving the usual assumptions on the preference, technology, endowment, and inelastic supply of labor:

$V(k_o^*)= max_{\{c_t,k_{t+1}\}_{t=0}^{\infty}}\quad \sum\limits_{t=0}^\infty \beta^t U(c_t)$

s.t. $\quad c_t+k_{t+1}=f(k_t)+(1-\delta)k_t$, $c_t,k_{t+1}\geq0, k_o=k_o^*$

$\textbf{My Question}$:

(Q1) Is the following a correct description of what happens in $t=0,1$?

(a) The economy starts with the given preference, technology, and endowment $k_o^*$.

(b) The planner chooses how much to put into the production and leave as to carried on as undepreciated capital to the next period. In other words:

(i) A fraction of $k_o^*$ is devoted to into the technology $f(\cdot)$.
(ii) The rest is simply carried onto the next period with the penalty of depreciation .

(c) Still in $t=0$ and with (b)-(i), the technology produces $y_t$.

(d) The consumer makes a choice as to how much to consume and invest from $y_t$ as $c_t+i_t=y_t$

(e) In $t=1$, the capital stock for tomorrow is defined as, $k_1=(1-\delta)k_o^*+i_t$, how much you left over from the initial capital stock to be carried over to $t=1$ plus how much you decided to leave out from the production as investment.

(Q2) In the social planner's problem, we have control vectors as a sequence of $c_t$ and $k_{t+1}$. These are two distinct control vectors, because the sequence $\{c_t\}_{t=0}^\infty$ requires the decision to be made after what you get from the production within the same period, but the decision of how much of the capital stock to have tomorrow involves how much of the capital stock today you will leave to be carried over to tomorrow in addition to the investment decision. For example, if for some reason, the capital stock is perishable, this $\delta=1$, our choice variable would be only $c_t$ as $c_t$ determines the level of $i_t$, which in turn determines the level of $k_{t+1}$, correct? Is $k_{t+1}$ not a control variable?

Q1: Your bullet point (b) is not how we usually interpret capital, it is usually not assumed that $k_0$ is divided between $k_0^p$, and $k_0^s$ the capital we use to produce and the capital we store for next period. Instead, we assume all the capital is used for production, but using it for production does not delete it,  it only depreciates it. For example, if you use your machines to produce pizza that does not mean that they are obsolete to be used next period.

If you want you could add to the model that un-used capital does not get depreciated, but it is an easy exercise to show that under very general conditions it will never be optimal to leave capital un-used.

So I do not agree with your interpretation in (e), typically $k_1=(1-\delta)k_0+i_0$.

Q2: This question is not particular of the dynamic model you present, but I think that the infinite sequences are messing up with your intuition.

Consider this simple example. If I say that you can choose to buy chocolate (at a price of \$2) or cheese (at a price of \$4), but you only have \$10 dollars (sorry this are rough times :P ), it is clear that if you are to spend all your money on these two goods, then choosing how much chocolate to buy, immediately pins down how much cheese you will buy. However, the fact that this is true does not change the nature that both amounts of chocolate and cheese are your choice variables. The budget constraint may allow you to re-formulate this problem as one where you only choose how much chocolate to buy (since cheese would be implicit), but this will only be a technique to simplify the original problem.

Something similar happens here. So to be concise, both sequences $\{c_t,k_{t+1}\}_{t=0}^\infty$ are control variables even if they have a simple linear relationship between them through the law of motion.


Does bond yield always equal the prevailing bank interest rates? Does a bond's yield (principal and coupon rate) always equal the bank interest rate?

Each fixed income instrument has an interest rate implied by a transaction price, and these prices can move in different directions.
The FRED website has a list of some of the more important interest rates in the United States:
link to FRED. However, these are mainly “generic” yields, which are based on fitting a curve through traded bond quotes. For example, the “10-year Treasury bond” yield shown on the website is going to be close to the the market yields of Treasury bonds/notes that are near a 10-year maturity, but there are spreads between them.


What would the determinant of the input-output matrix represent? What is the intuition? I know that the determinant of a 2x2 matrix represents the oriented area of the parallelogram represented by the vectors in the matrix. For 3x3 or higher order matrix it represents the oriented volume. I am trying to get such an intuitive understanding of the determinant of the input-output matrix used in macroeconomics. What could it represent? Does it represent the size of the economy? We usually measure the size of the economy by measuring it's GDP. If it represents the size of the economy, could this determinant be a better measure of the size of the economy than GDP?

Your conjecture seems unlikely. For example the unit matrix would show an economy where no new goods can be produced (it takes 1 unit of something to make 1 unit of that same thing). Yet the determinant of this matrix is 1. If we were to multiply the $3 \times 3$ unit matrix by say 10, the new determinant would be a 1000. But the economy did not get better, if anything it got worse.


When can one read the general theory of employment,interest and money? I am a first-year undergrad econ student and was interested in reading Keynes' book. in the preface, Keynes pointed out that the text deals in the abstract and is meant for his fellow economists. After reading a few chapters its become quite clear that he wasn't kidding. there so many theories and ideas that I am not familiar with and most of the ideas are criticised more than they are explained.

So my question is: what prior knowledge do I need to possess to understand the book? Any books you can recommend to acquire said Prior knowledge?
and lastly is the book even worth reading?

I don't think you should read it at any point in your carrer, honestly. It is severily outdated, ambiguous and overall not worth the time and effort put into reading it.

Try Screpanti & Zamagni's An Outline of the History of Economic Thought. Undergraduates do better when studying the works of economists who have been dead for decades as what they are, historical curiosities.

If you are really bent on reading the General Theory and/ or pretend to research history of economic thought, then I'd say after you go through an intermediate macroeconomic theory course you're good to go.


How is the matching principle implemented with double entry accounting? I understand that the accounting matching principle requires incurring the expense in the same period as the revenue.  But I'm confused how one would go about doing this in double entry accounting.

For example, imagine in 2016 I pay a subcontractor \$50,000; and, in 2017, I finish the work and issue an invoice for \$80,000.  Now, since I didn't invoice for the work in 2016, I can't show the 50k as an expense, but rather an asset; only in 2017 do I move it from an asset to an expense.

Does that mean that every expense in the chart of accounts needs to have a matching asset category? For example, if I have an expense "Subcontractor", I need to have an asset "Accrued Subcontractor"? None of the chart of accounts I've seen have such a repetition, and it seems unwieldy and error prone.

And, if I don't have the same level of detail in my Assets as the Expenses, then, when it becomes time to move them from Assets to Expenses, where will I get that information?

If I invoice based on cost-plus-fee, won't I have a chicken and egg problem? When I look at the cost of a project, there won't be expenses until I invoice? So how will the costs show up?

A great example would be to give the general ledger entries for my exact scenario.

It appears that you mix up the timing of invoicing with the timing of accrual of an expense or a revenue. There exist special Balance Sheet accounts that do not affect the P&L (with names like "Next-period Expenses" in the Assets side or "Next-period Revenues" in the Libailites/Equity side, depending on the country of course) which you use in order to account for such transactions, where invoicing does not track step-by-step the creation of costs and revenues. Small companies use these usually only when they "trespass" the fiscal-year time-boundary. Big companies may use them month-per-month.
In your specific example, assume that even by accounting standards, you are not entitled to recognize revenue in the current year, because, say, there are clauses in your contract that affect the economic substance of the deal. Still, your subcontractor invoices you now. You will credit the subcontractor account, and you will debit, not expenses, but "Next-period Expenses", and it will be a component of your Assets in the coming Balance Sheet.

Next year, when you will invoice your customer, you will credit this account and you will debit the relevant expense account, thus recognizing in the P&L the expense in the same period that you have recognized the revenue.

Assume that the subcontractor offers software development services and that your Accounting system has the Expense account "Third Party software Development services". Then in the ledger will see this year

\begin{array} { r  r  r |}
  \hline
\hline
  \text {Account Description} & \text {Debit} &  \text{Credit}\\
  \hline
\text{Next-period Expenses} & 50 &  \\
\text{Accounts Payble} &  &  50\\
\hline
\end{array}

If you also pay the subcontractor then you get

\begin{array} { r  r  r |}
  \hline
\hline
  \text {Account Description} & \text {Debit} &  \text{Credit}\\
  \hline
\text{Accounts Payble} & 50 &  \\
\text{Cash Deposits} &  &  50\\
\hline
\end{array}

Next year, when you invoice the final customer we have, to recognize the expense

\begin{array} { r  r  r |}
  \hline
\hline
  \text {Account Description} & \text {Debit} &  \text{Credit}\\
  \hline
\text{Third Party software Development services} & 50 &  \\
\text{Next-period Expenses} &  &  50\\
\hline
\end{array}

which makes the balance of "Next-period Expenses" zero,

and the revenue of course

\begin{array} { r  r  r |}
  \hline
\hline
  \text {Account Description} & \text {Debit} &  \text{Credit}\\
  \hline
\text{Accounts Receivable} & 80 &  \\
\text{Services sold} &  &  80\\
\hline
\end{array}

There are more complicated situations of course, for example, when you are entitled to recognize part of the revenue now, even though you have not invoice your customer, but I  leave them as a practice opportunity for you.


Deriving and using the pricing equation I'm a mathematician who's trying to learn some economics from Cochrane's Asset Pricing book.

I don't have any background in economics.

In chapter 1, he derives the basic pricing equation
$$ p_t = \mathbb{E}_t \left[ \beta \frac{u'(c_{t+1})}{u'(c_t)} x_{t+1}\right] $$
as follows:

Consider the problem of
$$\max_{\xi} u(c_t) + \mathbb{E}_t \left[ \beta u (c_{t+1}) \right]$$
where
$$c_t = e_t - p_t \xi, \qquad c_{t+1} = e_{t+1} + x_{t+1}\xi$$.

The pricing equation is the first order condition of this optimisation problem.

In words, you're trying to maximise your utility by buying some number $\xi$ of an asset with a random future payoff $x_{t+1}$ that sells for $p_t$ today. $e_t$ and $e_{t+1}$ are your original consumptions levels.

It's weird to me that even though the equation is a formula for $p_t$, both sides of the pricing equation depend on $p_t$. Namely, the denominator
$u'(c_t) = u'(e_t-p_t \xi) $ is actually a 1-to-1 function of $p_t$. So I feel like the formula tells me how to find $p_t$, given that already know what $p_t$ is.

The first application Cochrane presents is the risk-free rate.
Here $x_{t+1} = R^f$ is known at time $t$ and $p_t = 1$. Therefore

$$R^f =  1/\mathbb{E}_t \left[ \beta \frac{u'(c_{t+1})}{u'(c_t)}\right] $$

But $c_{t+1} = e_{t+1}+R^f \xi$ so there's no randomness inside the expectation. How can we go on to then assume that consumption growth $c_{t+1}/c_t$ is lognormally distributed, when it appears to be a constant?

In next application, the discount factor $m = \beta \frac{u'(c_{t+1})}{u'(c_t)}$ is treated as the same across different assets. But $c_t$ and $c_{t+1}$ are my optimal consumption levels for a given single asset, so I would expect $m$ to vary across assets.

So my question is, is it possible to reconcile the derivation of the pricing equation with the way it's applied in the examples?

As regards the first question, the "$p_t=...$" expression is conceptually and qualitatively useful because, at the optimum, it relates price with consumption and expectations. Mathematically it is an implicit function of course, so it is not a "closed-form solution" to "tell us how to find $p_t$".

Cochrane acknowledges this as he writes in p. 6

  "We have stopped short of a complete solution to the model, i.e., an expression with exogenous items on the right-hand side. We relate one
  endogenous variable, price, to two other endogenous variables,
  consumption and payoffs. One can continue to solve this model and
  derive the optimal consumption choice $c_t , c_{t+1}$ in terms of more
  fundamental givens of the model. In the model I have sketched so far,
  those givens are the income sequence $e_t , e_{t+1}$ and a specification of
  the full set of assets that the investor may buy and sell. We will in
  fact study such fuller solutions below. However,
   for many purposes one can stop short of specifying (possibly wrongly) all
  this extra structure, and obtain very useful predictions about asset prices
  from (1.2), even though consumption is an endogenous variable."

Regarding the first example, the "no-investment consumption" sequence $\{e_t\}$ is in general considered random, due to factors unmodeled at this introductory level, like an income stream that is affected by exogenous random shocks etc, so the use of the expected value relates to the existence of $e_{t+1}$  in there.

Regarding the second example, Cochrane writes p. 7 (my emphasis)

  "In this context, equation (1.4) is obviously a generalization, and it says something deep: one can incorporate all risk corrections by
  defining a single stochastic discount factor—the same one for each
  asset—and putting it inside the expectation. $m_{t+1}$ is stochastic
  or random because it is not known with certainty at time $t$. The
  correlation between the random components of the common discount
  factor $m$ and the asset-specific payoff $x_i$ generate asset-specific
  risk corrections."


Does RBC models pin down equilibrium output, amount of labor and capital without initial condition? In ordinary equilibrium models, we can pin down equilibrium quantity by supply-demand functions.

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

The stock of capital in the RBC model is a predetermined state variable, meaning that the capital $K_t$ available at time $t$ was determined at time $t-1$. Usually we have an accumulation relation of the form
$$K_t = I_{t-1}+(1-\delta)K_{t-1}$$
When solving an RBC model starting at time $t=0$, we must exogenously assume some initial capital stock $K_0>0$ to get the model started, since we don't explicitly consider what happened at time $t=-1$.

Labor, on the other hand, generally is not specified ahead of time. Instead, in many RBC models the household has an exogenous certain time endowment, perhaps normalized to 1, and then "leisure" $L_t=1-N_t$ is the amount of time remaining after "labor" $N_t$. Leisure then enters into the utility function just like consumption. (An equivalent and common alternative is to directly put labor $N_t$ as a "bad" into the utility function.)

The basic contrast is that capital is a stock while labor is a flow. We can choose the level of investment flow $I_t$ in each period, and the stock $K_t$ (which we can no longer control once we've reached time $t$) reflects the accumulation of past investment flows $$K_t = \sum_{s=0}^\infty (1-\delta)^s I_{t-s-1}$$
Meanwhile, labor $N_t$ is a flow that the household can choose optimally at time $t$.

Things becomes more complicated in a model with either (A) human capital or (B) search frictions. With (A) human capital, the effective supply of labor is partly a stock, since it reflects past flow investments in human capital; whereas with (B), the number of ongoing employer-employee relationship is a stock that reflects accumulated matches. Neither of these are present in the baseline RBC model, however.

Instead, the baseline RBC model is essentially the Ramsey growth model augmented with a stochastic process for TFP and endogenous labor supply. In this model, capital $K_t$ is the only endogenous linkage between periods.


What are the advantages and disadvantages of the IS LM model? How does the IS-LM model help economists in the day to day analysis of the economy? There are just too many assumptions that are not there in the real world.

The best economic models make useful predictions with as little complexity as possible -- in other words, they make assumptions that aren't "true" in the real world, but make predictions that nevertheless turn out to be true.

For instance, advocates of the day-to-day use of the IS-LM model such as Paul Krugman point to the analysis of liquidity traps as an important case where its users have proved to be right where many other analysts have made bad predictions.

From "What I Mean When I Talk About IS-LM (Wonkish)":

  Those of us who understood IS-LM and took it seriously declared in advance — in late 2008 and early 2009 — that big deficits and huge increases in the monetary base would lead neither to soaring interest rates nor to soaring inflation. This was very much not what many influential people were saying: there were widespread forecasts of soaring rates and soaring inflation. Later, there were many people denying that austerity would have negative effects on output.

He provides a more detailed explanation of an IS-LM analysis of liquidity traps (and a few other insights that the model provides).


Understanding at a quote about externalities in law and economics that something is an externality is partly a statement about physical reality and partly a statement about the legal system.

What does this mean? I assume the aspect of externality being a physical reality problem is just people only care about self interest so externalities can occur. However I don't understand how something is An externality could be a statement about legal rule.

You don't give the source of the quote, but presumably what is meant is this.  Whether X's production or consumption of a good affects Y (in a physical way such as smoke from X's factory or noise from X's playing loud music, not merely through the workings of the price system) is a matter of fact.  On the other hand, whether X is required (assuming a negative effect) to bear the costs of the harm to Y, is a matter of law.  The implication seems to be that an externality is present only if the law does not so require.

However, some writers would exclude the legal aspect from the definition of an externality.  Baumol & Oates, for example, state (quote found here, top of page 5):

  "An externality is present whenever some individual's (say A's) utility or production relationships include real (that is, nonmonetary) variables, whose values are chosen by others (persons, corporations, governments) without particular attention to the effect's on A's welfare."

An advantage of this type of definition is that it avoids the implication that an externality is no longer present when it has been addressed by law as above. Instead, we can say that the externality is still present but has been internalized.


How exactly could you protect your debt, by enclosing it in larger debts with better security? I don't understand the notion below of "enclosing"  or "including" the 2nd bad debt into the 1st more secure debt. If you already owe the larger debt with larger security, then haven't you spawned a new separate bad debt that you're now trying to protect?

How exactly did debtors enclose their second bad debt into their first debt?

I, not the source, boldened everything below. Google Answers: Origin of use of verb 'to hedge' as in 'hedge a bet'

Hedging a bet comes from the same linguistic roots as hedging a field. The idea of a hedge as a defence or enclosure making something secure is the starting point for the image of hedging bets. "Hedge" as a metaphor for making one's bet safer, by enclosing it within another [I boldened.], less risky bet dates back to the seventeenth century. "To secure oneself against loss (on a bet etc.) by betting etc. on the other side." This sense of "hedge" dates from 1672 according to the Oxford English Dictionary (OED).

hedge (v.) | Origin and meaning of hedge by Online Etymology Dictionary

late 14c., "make a hedge," also "surround with a barricade or palisade;" from hedge (n.). The intransitive sense of "dodge, evade, avoid committing oneself" is first recorded 1590s, on the notion of hiding as if in a hedge. That of "insure oneself against loss," as in a bet, by playing something on the other side is from 1670s, originally with in; probably from an earlier use of hedge in meaning "secure (a debt) by including it in a larger one which has better security" (1610s). Related: Hedged; hedging. The noun in the wagering sense is from 1736.

'Hedge your bets' - meaning and origin.

It began to be used in relation to financial transactions, in which a loan was secured by including it in a larger loan, in the early 17th century. Initially, the phrase associated with this form of hedging was 'hedging one's debts', for example, John Donne's Letters to Sir Henry Goodyere, circa 1620:

"You think that you have Hedged in that Debt by a greater, by your Letter in Verse."

Inky Fool: How John Donne Invented the Hedge Fund

That's the first recorded usage of the phrase hedge in meaning to secure a bad debt by making it part of a larger one for which better security has been obtained. Although this was the first common financial use of hedging.
From that sense of making your debts safe, came the idea of hedging in your bets by betting on more than one horse which pops up in 1672. From there you get the idea of finding two near-identical things at different prices, buying the cheaper and shorting the dearer. And thus the hedge fund.

(Please note that is guesswork based on the linked text.)
From the Inky Fool page:

Then, in the early seventeenth century John Donne promised a chap called Sir Henry Goodere that he would send him a letter in verse. He didn't get round to it, and to make matters worse Goodere wrote him one, which meant that Donne really owed him. Or, as Donne put it in an apologetic letter:

I owed you a Letter in verse before by mine own promise, and now that you think that you have hedged in that debt by a greater by your Letter in verse, I think it now most seasonable and fashionable for me to break.

John Donne already owed him a letter, then that obligation for a letter got rolled into a larger obligation.
This is obviously a non-financial obligation. To what extent we can extend this to finance, an existing debt is rolled into a larger new loan, with the new loan having better collateral than the old. In a modern context, it would be something like rolling a credit card debt into a home equity line.
(The only other interpretation I can think of - which does not fit this example - would be to reduce risk in a book of loans by diversification. I.e., replace riskier loans with ones secured by stronger collateral. This would not be considered “hedging” by modern portfolio managers, but it might match a loose interpretation of “hedge your bets.”)


Could indexation of wages help Argentina? In Argentina we experience one of the largest inflation rates of the world.(please click the top of the inflation rate column to order by inflation rate).

This is a large problem that causes stress and uncertainty to very big numbers of people. Periodically, indeed every year, there is a fight with the government called "paritarias" (spanish) in wich we agree, to put it more simply than it really is, by how much percentage the salaries will increase.

The government inflation rates are not credible. Big parts of the population, specially those opposed to the FPV, don't believe those are the inflation rates, they say they are higher in reality.

I was thinking to myself that maybe we could implement a system wich automatically raises wages according to inflation, at least for certain workers such as public teachers, that already have very established tasks and amount of hours of work per week assigned.

Then I read this article and though this is what i was looking for!

The article describes a process exactly to what I was thinking:

  Indexation is a technique to adjust income payments by means of a
  price index, in order to maintain the purchasing power of the public
  after inflation

But then I thought to myself: Actually our government, (I suspect since I'm ignorant about economics ), uses inflation, by creating money to pay it's debts (to the government officials it's salaries for example) so they are not going to want to raise the salaries at the same time as inflation, but try to wait as long as possible, because they save money. In the article says how the pain is passed from workers to the state:

  When a government decides to index wages of government employees to
  inflation it is to transfer the risk of inflation away from government
  workers onto the government.

What "helping Argentina" means: Increasing happiness of it's inhabitants in general. That's my way of viewing if a certain policy decision is ought to be taken. I focusing of making the public workers happier. In that sense, then yes, automation would be better for them.

It seems that you answered your own question?

If the government's estimation of inflation rates are not credible, how can the government effectively index to inflation?

In any case, the first best solution to inflation in the long run is almost entirely an independent, competent central bank that has the capacity to raise interest rates, limit the money supply, and bring inflation under control. (And have a government that doesn't interfere with the central bank.)


Price Elasticity of Demand for Positive Price Increases What does it mean when the price elasticity of demand  %Qd/%P is greater than one?  Typically I hear that it means the demand is elastic since if, say, the price decreases by 1% the demand for the good increases by more than 1%.  But what happens if %P is +1% and %Qd still increases by more?  Sure, this is elastic, but does it give us any more information?  I can't see why %Qd/%P > 1 makes sense in this case.

Except of the purely descriptive aspect, "elastic demand", or more accurately, regions of the demand schedule where demand elasticity with respect to price is higher than unity, in absolute terms, is linked to the basic monopoly theory, since the monopolist maximizes profits at a point of the demand schedule where "demand is elastic".

Define the demand point-elasticity with respect to price as

$$\eta = \frac {\partial Q }{ \partial P}\cdot \frac {P}{Q} \Rightarrow \frac {\partial Q }{ \partial P} = \eta \cdot \frac {Q}{P} \tag{1}$$

Note that algebraically, the elasticity is a negative number, with the sign indicating the direction of influence, since $\partial Q / \partial P <0$.

The profit function of a monopolist is

$$\pi = P\cdot Q(P) - C(Q(P)) \tag{2}$$

The first-order condition for a maximum with respect to price is

$$\frac {\partial \pi}{\partial P} = 0 \Rightarrow Q + P\frac {\partial Q }{ \partial P} - MC\cdot \frac {\partial Q }{ \partial P} = 0 \tag{3}$$

Inserting $(1)$ into $(3)$ we have

$$Q + P\cdot \eta \cdot \frac {Q}{P} - MC\cdot \eta \cdot \frac {Q}{P} = 0$$

$$\Rightarrow 1 + \eta - \eta \cdot \frac {MC}{P} =0$$

$$\Rightarrow - \eta \cdot \frac {MC}{P} = -\eta -1 $$

$$\Rightarrow  |\eta| \cdot \frac {MC}{P} = |\eta| -1$$

$$\Rightarrow P^* =  \frac {|\eta|}{|\eta|-1} MC \tag{4}$$

$(4)$ is essentially an implicit relation since $\eta$ is a function of price also, but it provides a specific insight: Since we naturally expect that price will be positive, we see that we must have $|\eta| >1$: the price will necessarily be set at a level where "demand is elastic", i.e. at a point on the demand schedule where the point price elasticity of demand is higher than unity, in absolute terms.


Any Resources for Micro Comprehensive Exams? I'm currently preparing for a first year microeconomics comprehensive exam and have been looking for good resources for a while. Ideally, I was looking for any school site that has a list of (and links to) their old micro comps with solutions.

We cover what I'd imagine is a pretty standard course- a half semester each on partial equilibrium, general equilibrium, social choice and game theory; though all that's needed is any overlap between those and whatever the other school's comp covers.

Again, sorry if this isn't the right place, but if anyone has any sources off-hand, I'd very much appreciate it!

I know Harvard posts its past comprehensive exams: https://economics.harvard.edu/pages/past-general-exams. I imagine many other schools would have such resources available to the public as well. You'd just have to do a little bit of Googling to find out.

However, I doubt that any of these past exam questions would have solutions available (and they should not be). You should try the questions on your own. If you're stuck, discuss the issues with your classmates/friends/professors. You're also welcome to ask questions here, but be sure to following our policy on homework questions and the general guidelines of this site.


Have UK exports (goods and services) to Ireland declined in value since 2011? Where can I find the relevant Office Of National Statistics data on UK exports to Ireland? I want to know if the value of UK exports to Ireland has declined since 2011 and if so, does anyone know why that might be? I understand the reasons that UK market share in Ireland has decreased, but I'm in interested in why the total value may have decreased (or not). Thank you.

The ONS Balance of Payments Pink Book gives the following figures for UK exports to Ireland (£million).  The figures in Euros would be different, as would Irish reporting of the numbers, but there seems to have been a sharp drop in services exports from 2012 to 2013.

2016 data is due to be published in October 2017, though trade in goods numbers may already be available

 £m     Goods Services  Both
CDID    QDJJ    FYVJ    LGIA
2011    18223   11475   29698
2012    17234   11615   28849
2013    18592    8780   27372
2014    18104    9288   27392
2015    16764    9321   26085


Raise/Lower Seller Fees on Platform - Expected Seller Behaviour? Say there is a marketplace company that facilitates buy/sell of digital content (i.e. marginal cost = 0). And that content is somewhat substitutable but not completely so. As an example, for a particular category of digital goods we see the majority of sellers pricing at $100, while some price lower and higher based on whether their good is clearly much higher quality (or has more inclusions or whatever) or lower if lower quality/less inclusions/more simple.
The marketplace levies a commission on the sellers, say 30% of the sale value.
And now the marketplace decides to increase the fee to 40%.
How would the sellers respond?
Do they just soak up the extra fee? Do they pass it through to customers?
The marginal cost of additional unit sold is zero. The company is somewhat of a market leader (but by no means the only option for buyers).

I sell digital books, and will discuss their particular situation. I do not know whether what I describe applies elsewhere.
I and have read a fair amount of discussions about how to price books. To what extent academic research would be referred to, it’s wherever marketing research ends up (business journals?), and not straight economic models.
The first thing to keep in mind is that for electronic books, there is “arbitrage” across platforms, and there is pressure by some stores to keep your price in line with other platforms. As such, if one platform changes their royalty payout, you have to either eat the lower revenue, drop the platform, or raise price across all platforms. If the platform is small, you might be able to just raise the price on that one platform, but that might anger customers. As such, the decision is complex. E.g., is it possible to stop using a platform? Is the lower revenue per unit on one platform enough to justify a global price hike?
After that, pricing is somewhat of a black art. Each market has its own conventions for pricing. For example, dollar prices often end in .99 (this convention is in fact enforced on one platform). Therefore, you cannot make small percentage adjustments to price (unless the price is large, which is rare for e-books).
After that pricing is relative to competitors, any paperback edition (where printing cost partly determines price), and how you want to position your book. For example, you might keep the price high if you are emphasizing the quality of your books. Once again, pricing is a marketing decision, since the sales price is far above the marginal production price.


In the eyes of a normal citizen, what difference does it make if my country has debt or no debt? I got curious about this because I happened to pass by a list of countries with zero debt. Country debt seems like a major thing, but for a non-economics major like me, I don't exactly understand the implications of a country having debt.

More tax? Less progress? Exports are more necessary?

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

1)  Debt matters because it smoothes (or unsmoothes) taxes over time, which matters because the deadweight loss from taxation is (roughly) proportional not to the tax rate, but to the square of the tax rate.

2)  Because family sizes are not homogeneous, government debt (which transfers the tax burden to future generations) can redistribute the tax burden across families.  (Think, for example, about a taxpayer with no kids, or a family that has just immigrated.)

3)  Government debt makes it easier to borrow --- it's better to pay 3% to government bondholders than 18% to your credit card company.  This is possible because the penalty for not paying your taxes is considerably more severe than the penalty for not paying your credit card bill.  (In effect, government debt resurrects the institution of the debtor's prison.)

4)  There are of course issues with misperceptions, where debt can make people feel either richer or poorer than they really are, depending on whether they underestimate or overestimate their future tax burdens, and so can affect consumption paths in either direction.


Utility Function in Consumer Credit I have been studying the area of unsecured consumer credit (consumer loans and credit cards) and credit scoring. My question is: can we have a utility function (either a lender's or borrower's utility) that can take both the borrower's credit score (probability of repayment) and loan limit (amount) as arguments in an explicit manner? What I have managed to get on the web are implicit functions of the form $f(x,y)$ e.g. on equation (1) in the article https://pdfs.semanticscholar.org/3207/55db4a277766043b5a1cb73f3b84df9cb613.pdf

Below is an example based on the general formulation in your linked article. This will very likely need a lot more fine-tuning. Moreover, the following example does not necessarily satisfy the theoretical properties laid out in footnote 16 of the paper. (You should check this.) Nevertheless I hope this could at least give you an idea of how to think about writing down an appropriate utility function that suits your purpose.

Consider
\begin{equation}
\Pi(d,q,\theta)=
\underbrace{\left[1+\mathrm e^{-(\alpha_0+\alpha_1 d+\alpha_2q+\alpha_3\theta)}\right]^{-1}}_{G(d,q,\theta)}
\biggl[d+\underbrace{\frac{a+bq-d}{\theta T}\left(\frac{1-(1+r)^{-\theta T}}{r}\right)^{\!\!-1}}_{M(L,q,\theta)}-q^2\biggr]\,,
\end{equation}
where

$d=$ down payment; $q=$ car quality; $\theta=$ creditworthiness; $L=$ loan amount
car with quality $q$ is priced at $p(q)=a+bq$, where $a,b$ are parameters to be estimated/calibrated
loan amount: $L=p(q)-d=a+bq-d$
probability of purchase $G(d,q,\theta)$ is modeled by a logistic distribution, which is parameterized by the variables of interest, and the $\alpha_i$'s are parameters to be estimated/calculated
$\theta T$ is the term of the loan, which is increasing in $\theta$
assuming repayment in each period is the same, i.e. $L/\theta T$, the PV of loan payment is $M(L,q,\theta)$, where $r$ is the periodic interest rate
cost of producing a car with quality $q$ is modeled by $c(q)=q^2$


Fisher Effect vs Quantity Theory of Money and how an increase in the money supply lowers interest rates? I was under the impression that in the long run, a larger money supply resulted in lower interest rates. According to the Quantity Theory of Money, see below figure, an increase in the money supply -> An increase in price levels.

Increasing price levels == increasing inflation rate.

Fisher Effect:

According to the Fisher Effect:

Nominal Interest Rates = Real Interest Rates + Inflation

Changes in the money supply should not affect the Real Interest Rate in the long term therefore there is a 1 for 1 increase in Nominal Interest Rates and Inflation in order to maintain the equation.

The Chart suggests that an Increase in money supply => Higher prices == Inflation, which i believed meant lower interest rates.

But the Fisher Effect seems to be suggesting the opposite, hence my confusion.

I would appreciate any help in clarifying this, thanks in advance.

ceteris paribus - other things staying the same

What happens with a changing money supply depends on what other things stay the same in your thought experiment. Possibilities might include:

If real interest rates stay the same but you manage to increase the money supply and inflation, then nominal interest rates must rise by definition.  Historically, nominal interest rates have been higher in inflationary periods than in periods of price stability or deflation
If nominal interest rates stay the same but you manage to increase the money supply and inflation, then real interest rates must fall by definition.  This is likely to lead to an inflationary spiral as people borrow cheaply in real terms, increasing demand and the money supply further and so pushing prices higher
If you force inflation to stay the same but you manage to increase the money supply excessively compared with that inflation, you may need other controls such as price regulation.  This could lead to shortages of goods or an asset price bubble, at which point things other than money become important while interest rates could become less relevant


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

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

This is how I'd approach the problem. Please point out any issues on this method as it is based on my own approach (I have no textbook to reference this to).

Based on the information you have, you would run a regression of log output on log-labor, log-capital and log-human capital. This would give you a model like this.

$$\ln(Y)=\beta_0+\beta_1\ln(L)+\beta_2\ln(K)+\beta_3\ln(H)+\mu$$

in terms of a more "economic looking" equation, we take the expectation of this equation and take $e$ and raise it to the power of both sides giving us our production function.

$$\mathbb{E}[\ln(Y)]=\mathbb{E[}\beta_0+\beta_1\ln(L)+\beta_2\ln(K)+\beta_3\ln(H)+\mu]$$

$$\ln(Y)=\beta_0+\beta_1\ln(L)+\beta_2\ln(K)+\beta_3\ln(H)$$

Recall that we view $\beta_0$s the co-efficient on omitted variable $\ln(A)$ as the rate of technological change1,2
$$\exp\{\ln(Y)\}=\exp\{\beta_0+\beta_1\ln(L)+\beta_2\ln(K)+\beta_3\ln(H)\}$$

$$Y=A^{\beta_0}L^{\beta_1}K^{\beta_2}H^{\beta_3}$$

Using this form you can more comfortably  calculate elasticity of subsitution between $L$ and $K$. If your elasticity of substitution is greater than or equal to 1 you have a labor saving process, however if elasticity of substitution is less than 1, we either have a process which is either a Human capital augmented process of TFP augmented process 3.

Hope this helps

1. https://en.wikipedia.org/wiki/Solow_residual#Regression_analysis_and_the_Solow_residual

2. the actual "quantity" of $A$ can be calculated by
$$A=\left(\frac{Y}{L^{\beta_1}K^{\beta_2}H^{\beta_3}}\right)^{\frac{1}{\beta_0}}$$

3. this is of course assuming that either  $\beta_3>0$ and/or $\beta_0>0$.


Can inflation show up in assets without necessarily being reflected in classic inflation indexes? I have been having an argument with a friend of mine who obtained an economics degree in college. I have been arguing that increased money supply from the fed has led to inflation in asset prices, despite 'inflation' not really showing up in things like CPI. He argues that since Fed economists use CPI, I am wrong to even consider any other metric since I am not smarter or more knowledgeable than the fed. Is he right? Does inflating asset prices not really count as inflation?

Yes inflating asset prices does not count as an inflation generally speaking although your friend's explanation is incorrect.
Fed is not an authority that decides how inflation is defined. Inflation is generally in academic literature simply defined as (Lebow & Rudd, 2016)

Inflation measurement is the process whereby changes in the prices of individual goods and services are combined to yield a measure of general price change.

Assets are neither goods and services so they should not be considered at all if we talk about inflation generally.
This being said economists also sometimes use the inflation concept to measure change in price level of things other than goods and services. Price indexes that track asset prices and concept of asset price inflation does exist, but if an economic text, book, article etc talks about inflation they will mean inflation as defined above. When they are using other meanings of inflation economists will always add clarification like  asset price inflation etc. However, again if the discussion is just about inflation, without any other caveats it is about general goods and price inflation. Also this is not because Fed would decree so, this is just general economic terminology (Fed has power over methodology they use for their measure of inflation but they try to capture inflation as accurately as possible).


When and why did governments impose restrictions on money creation In many countries governments have made laws that bar themselves from creating money directly. Instead they have to go via a circuitous route involving the creation of bonds. This means that the government has to go into debt in order to create more money. The reason for this self imposed restriction seems obvious to me - it is a kind of advertising to prospective purchasers of government bonds. It says "don't worry about us devaluing your bonds through excessive money creation because we have written it in stone that we're never going to do that". If it wasn't for this assurance then government bonds would be harder to sell.

Whatever the reasoning - after many years being interested in this question I have never come across any official explanation. Surely somewhere there must be a record of how these restrictions came into existence. Where are these records?

In any healthy economy, the central bank is independent of the executive government. (Since the central bank can be thought of as part of the 'government', I want to be specific about which parts of government I am referring to—by "executive" I mean the body of people who are in power and who administer policies.)

This separation is in order to separate fiscal policy from monetary policy, as this makes it easier to achieve monetary policy objectives. Otherwise, the executive could enforce money creation merely to achieve some objective, such as increased government spending or a decrease of local-currency denominated debt, but this would send inflation skyrocketing. Instead, the executive (through the Treasury) sells bonds on the open market. Any entity is free to buy those Treasury bonds, and the price is determined by the market. (An executive that controls the central bank and forces them to buy Treasury bonds is not really independent of the central bank—it is just a show.) So, the Treasury selling bonds is how the executive raises money for itself, but it also increases the demand for money, so the central bank needs to be part of the group of entities that buy the bonds, in order for interest rates to remain unchanged. Needless to say, when the central bank buys bonds, it is increasing the supply of money.


Download original spreadsheet from Reinhart-Rogoff "Growth in a Time of Debt" I want to access the infamous Excel spreadsheet from Reinhart and Rogoff's 2010 paper "Growth in a Time of Debt". I see the paper here, and in the 2013 errata I see a link to the raw data, however I'm not an economist and I don't know how to find the data in the link (it looks very comprehensive). Also it doesn't have the spreadsheet, and I'd like to reproduce the error in that.

How do I find Reinhart and Rogoff's original 2010 spreadsheet from "Growth in a Time of Debt"?

I know this was a while ago now but here is the excel file.

UPDATE: As somebody highlighted this is not the original 2010 file, but it does include the key raw data and some helpful instructions.

Here is the link to the video of where I go through the process step - by - step: https://www.youtube.com/watch?v=ItGMz0ERvcw

Hope this helps,
EBW.

Excel file


just economic interpretation: Is every steady state a golden rule steady state? Is every steady state a golden rule steady state in solow model?

I know this question’s exact answer. I only want to ask for the following,

When know that at steady state $\dot{k}=0$

And in solow swan model $$\dot{k}= sk_t^a-(\delta + n+g)k_t$$

Since this equation is zero, I obtain the $$k_{ss}=(\frac{s}{\delta + n+ g})^{1/1-a}$$

When I maximize $$c_{ss}=f(k_{ss})-(\delta + n+g)k_{ss}$$ with respect to $k_{ss}$

I obtain the golden rule level $k_{gr}=(\frac{a}{\delta + n+ g})^{1/1-a}$

So,

$$k_{gr}=k_{ss} \iff a=s$$

That’s, saving rate is equal to capital share of income.

Otherwise, under different conditions, they are not the same.

What i want to ask that to what extent such a expression in the view of an economist is logical? This is true in terms of mathematical expression, but is it logical in terms of economic intuition  as well? If correct, What does this result say to me intuitively?

No. There are many steady state levels of per-capita consumption. The maximum of these is then defined to be the golden rule (steady state level of per-capita consumption).


Substitute a continuos variable with a categorical one in Linear regression I am pretty new to econometrics, and I am thinking about substituting a continuous variable (say assets for a company) with a categorical one containing a number based on which quintile the continuos value was (so 1-5). Obviously doing so I will lose some information however I was hoping that doing so would semplify the interepretation of an interaction variable made of the original continuos variable and of another continuos variable. Especially as I am going to plot a marginsplot (in STATA). I wanted to ear the opinion of someone more experienced and if this is a good/ feasible idea or it will backfire in some way.
Thanks in advance

You can use the continuous variable "Assets" as stand-alone, and use its categorical incarnation for the interaction term.
While we may be accustomed to use "automatically generated" interaction terms as part of ready-made functional forms like the translog, nothing forbids us to introduce selectively interaction terms in a regression setting, when we have an economic, structural argument as to why this specific interaction term is meaningful and why it belongs to the regression.
Therefore, using two different versions of the same variable is in principle acceptable as long as a solid argument can justify it.
From a technical point of view, it does not create any issues.


Why does the Solow Model matter for undergraduate students? I've been looking at the economics undergraduate curriculum and have been thinking and wondering as to what specific skillset we want to equip undergraduate students with in the working world.

One can think about this by thinking about the ideal career outcomes of economics undergraduates. Most undergraduates with economics degrees should ideally end up in two occupations* (ideally meaning that their education will correspond to a desired occupation):

Data Analyst (using exclusively data to identify actionable information)
Business Analyst (using data and qualitative information regarding the economic environment relevant to a given business to identify actionable information).

With these two ideal career outcomes in mind its very clear as to why intermediate microeconomics, econometrics and market macro makes a difference. However as to why the Solow Growth model is taught on the undergraduate level is a bit confusing for me and Im left with any satisfactory answer.This is a relevant question because its a part of the core undergraduate macroeconomics education so its relevant for even those not intending to go to graduate school.

In terms of specific career outcomes (it could be that this list is lacking) why is studying the Solow model relevant for the undergraduate student who does not intend to go to graduate school?

EDIT: Im not coming to say the solow model is useless, im asking why this is a part of the core economics curriculum. I myself am interested in economic growth in terms of understanding the economy and its fluctuations. Additionally I'm an economics educator not a student so these questions do come up in classes where im responsible to respond to them.

I disagree that:

a) The core curriculum should not include things that are relevant only for those pursuing graduate school.

b) A university degree should necessarily focus only on career outcomes for students.

c) There are only two relevant careers and therefore the only thing worth teaching is how to handle different types of data.

The core curriculum needs to provide a foundation for all future paths of students, which includes those going to graduate school.

Further, a university degree is foremost a scientific (or at times artistic) pursuit within a field and not a trade school. That is why professors are scientists (or at times artists) and not industry professionals. After a bachelor's degree a graduate should at least understand the basics of that field. Sure, many of those skills learned at university can partially be transferable to a job in the real world. However, that's a different story, which often does not involve the actual material learnt, but other skills learnt along the way, such as critical thinking and writing.

The Solow model is the foundation for beginning to understand economic growth and development. That is at the core of what the economics field aims to understand. Even  most policy debates will inevitably involve growing the economy or creating jobs. I would argue any student that is not interested in that question at all has no business studying economics. That is why the Solow model is in the core curriculum.

Lastly, there is a reason not everyone studies statistics and IT so that we can all become data analysts (for business or otherwise). The reason is that there are many other career paths.


Does a high positive output gap relate to high unemployment rates? I have read that high output gaps (GDP gaps) are directly related to high unemployment rates. However, I did not find any source clarifying whether this "rule" apply to both positive and negative gaps or just to one of them. I can see how this relate to recessionary (negative) gaps, but I am not sure about the inflationary (positive) gaps. Some articles say that positive gaps cause unemployment rates to fall, but I just found a graph showing a rise in such rates also when positive gaps increase:

Image source

As denesp said, you're looking at a graph with no output gap.

A positive output gap usually does lead to employment being higher than the natural rate (=unemployment is lower than the natural rate).

Reading these lecture notes might help: http://eml.berkeley.edu/~jaya/lecture/Econ1_lecture9.pdf


Prove that an estimator is consistent The following exercise is from Wooldrige:

Show that $\hat{\beta} =\frac{1}{N} \sum\limits_{i=1}^{N}\hat{u_i^{2}}x'x $ is a consistent estimator for $E(u^2x'x)$

by showing:

$$\frac{1}{N} \sum\limits_{i=1}^{N}\hat{u_i^{2}}x'x = \frac{1}{N} \sum\limits_{i=1}^{N}{u_i^{2}}x'x + o_p(1) $$

Where $o_p(1)$ is read "little oh p 1"

And we use the hints that:

1.) $\hat{u}_i^2$ = $u_i^2 - 2x_iu_i(\hat{\beta}-\beta) + [x_i(\hat{\beta}-\beta)]^2$

2.) $\hat{\beta} - \beta$ = $o_p(1)$

3.)Sample averages are $O_p(1)$  read as "Big Oh P 1"

4.) we assume all necessary expectations exist and are finite

I'm getting stuck with this. I know I must be missing some simple sort of substitution or there is some gap in my knowledge or understanding preventing me from making the necessary manipulations.

I would love if someone could walk me through this and explain the intuition a bit here.

I will provide another hint, more "primitive" than the one offered by @Anoldmaninthesea, for those that are not still very familiar with the "big-Oh/little oh" notation and arithmetic.

What we are examining here is a sum, which, following the first obvious "hint" given, is to be decomposed in three separate sums.

Now, we are interested in what happens to the value of these sums as the number of summands goes to infinity... In such cases, essentially we are looking if "we have enough "$N$"'s for the infinite sum to go in value to something finite (given the a priori assumptions), and if yes, whether this finite limit is zero or not.

Consider the middle sum

$$\frac{1}{n} \sum\limits_{i=1}^{n}[-2x_iu_i(\hat{\beta_n}-\beta)\mathbf x_i'\mathbf x_i] = -2(\hat{\beta_n}-\beta)\frac{1}{n} \sum\limits_{i=1}^{n}(x_iu_i\mathbf x_i'\mathbf x_i)$$

$(\hat{\beta_n}-\beta)$ was taken out of the sum because it does not depend on the index $i$. It does depend on $n$, since it is an estimator function and not a specific estimate, but not on $i$.
The assumptions of the model tell us what happens to $(\hat{\beta_n}-\beta)$, if it remains unscaled, as $n\rightarrow \infty$. As for the summands, $(\mathbf x_i'\mathbf x_i)$ is a $k\times k$ matrix, that does not include itself any sum. So it is finite (the fact that the random variables involved have possibly infinite support does not bother us -the probability that they will take the value "infinity" is zero). So it is only the whole expression $(x_iu_i\mathbf x_i'\mathbf x_i)$ that multiplies in cardinality as $n$ increases - and by the assumptions of the model we know things about $x_i$ and $u_i$ and what happens to the average of their product. Etc.

An unrelated example to show what this "how many $n$'s" business means is to consider, for example, a random vector like

$$\frac{1}{\sqrt n}\left(\mathbf X'\mathbf X (\hat \beta_n - \beta)\right)$$

We "know" that this random vector converges to a multivariate distribution, i.e. it neither converges to a constant, nor does it diverge. Can we see this in our primitive way? We would want a finite asymptotic variance. The asymptotic mean will be zero so we need only to examine

$$V_n=E\left[\frac{1}{\sqrt n}\mathbf X'\mathbf X(\hat \beta_n - \beta)(\hat \beta_n - \beta)'\mathbf X'\mathbf X\frac{1}{\sqrt n}\right] = E\left[\left(\frac{1}{n}\mathbf X'\mathbf X\right)[(\hat \beta_n - \beta)(\hat \beta_n - \beta)']\left(\mathbf X' \mathbf X\right)\right]$$

What is the problem with the above expectation? The first term wll converge to something finite and non-zero (per initial assumptions), the second goes to zero, the third goes to infinity(because it includes sums whose cardinality will go to infinity). So the expectation is still of undetermined fate. But if we multiply and divide by $n$ (we can do that, we have not yet send $n$ to infinity) we obtain

$$V_n= E\left[\left(\frac{1}{n}\mathbf X'\mathbf X\right)[n\cdot(\hat \beta_n - \beta)(\hat \beta_n - \beta)']\left(\frac{1}{n}\mathbf X' \mathbf X\right)\right]$$

Now things begin to clear: the first and second terms will converge to expected values, so they can be taken out of the external expected value:

$$V_n\rightarrow \left(\lim_{n\rightarrow \infty} E\frac{1}{n}\mathbf X'\mathbf X\right)\lim_{n\rightarrow \infty} E\left[n\cdot(\hat \beta_n - \beta)(\hat \beta_n - \beta)'\right]\left(\lim_{n\rightarrow \infty}E\frac{1}{n}\mathbf X' \mathbf X\right)$$

The middle term inside the expectation  is the (multivariate) "square" of $\sqrt n (\hat \beta_n - \beta)$. We know that this last one converges to a zero-mean random vector, so the limit of the expected value of its "square" is its asymptotic variance, which is finite. So we have the product of three asymptotically finite expected values, and so the whole expression is finite, and so the variance of the expression we started with is finite, and moreover, non-zero (by the usual initial assumptions of the model).


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

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

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

I might be wrong but from what you write, it seems you've been given a "classical" introduction to econometrics: You've covered IVs and Diff-in-diff but apparently only in passing, and causal inference does not look like it was the core of the classes you've taken.

If that's correct, then I would recommend reading:

Mastering 'Metrics (https://www.amazon.com/Mastering-Metrics-Path-Cause-Effect/dp/0691152845),
Mostly Harmless Econometrics (https://www.mostlyharmlesseconometrics.com/)

before reading anything else (e.g., Wooldridge or Greene, as referenced in E.Sommer's answer).


Nominal Growth rate above Nominal Interest Rate I'm reading Ray Dalio's "An In-Depth Look at Deleveragings", and at one point he's talking about central banks providing liquidity and credit support, and he states:

  "This produces relief and, if done in the right amounts, allows a
  deleveraging to occur with positive growth. The right amounts are
  those that a) neutralize what would otherwise be a deflationary credit
  market collapse and b) get the nominal growth rate marginally above
  the interest rate to tolerably spread out the deleveraging process."

I'm not sure I understand point b here. Could someone explain the interplay between nominal growth rate and nominal interest rate, and how they affect the deleveraging process?

Thanks!

I have not read the text in question (other than the quote), but I would guess that his logic runs as follows. If we are discussing the government, one common analytical concept is the primary fiscal balance - the fiscal deficit excluding interest payments. If the primary fiscal balance is zero, the change in government debt will equal interest costs. The assumption is that a primary balance of zero is in some sense neutral (that assumption could be questioned), nominal debt levels will grow at the nominal rate of interest (since the government needs to borrow to cover the interest payment).

If we then look at the debt/GDP ratio, we see that is the nominal interest rate is the same as the nominal growth rate of GDP, the ratio will be unchanged under that circumstance. However, if the nominal interest rate is less than nominal GDP, the ratio would fall.

However, it is unclear to me why growth rates being “marginally above”interest rates makes anything other than a marginal difference. That might be better explained elsewhere in his text.

There is a literature on the concept of fiscal sustainability, where the relationship between growth rates and interest rates is covered in nore depth. Trying to summarise that theory appears to be beyond the scope of this particular question, but that is a key word you could use to search for more details.


Doubt in understanding the advantages of Fixed Exchange Rate The author of my book writes:

ADVANTAGES OF EXCHANGE RATE
If exchange rates are fixed, then inflation may have a very harmful effect on the demand for exports and imports. Because of this, the government is forced to take measures to ensure that inflation is as low as possible, in order to keep businesses competitive on foreign markets. Thus, fixed exchange rate ensure sensible government policies on inflation.

I don't understand this point and would be grateful if someone could explain it, perhaps with a real world example.

Basically, if you are the government, its a way that you are telling everybody that they should believe your commitment to low inflation. They should believe you, because you'll hurt yourself a lot if you allow inflation.

More generally, economists sometimes talk about agent's ability to commit to a policy: say, governments might promise something, but its hard for investors to believe that they'll follow through. SO one way to solve this problem is that the government builds creates an institution, where breaking the promises hurts a lot.

The classical reference is Odysseus getting his crew to tie him to a mast so he would not throw himself at the sirens in the sea.  He is in effect choosing to bind his future self, curtailing his own freedom. The value of this is that it gives him freedom to do other things (travel along the siren infested waters and listen to their song).

A fixed exchange rate can serve such a purpose: The idea is that a country fixes the exchange rate. This fixed rate makes it very obvious and very costly to behave badly, say by printing money or increasing government borrowing. The fixed rate constrains the government from bad behaviour.

Of course, this decision is not free. In the case that you set a fixed rate and then you end up behaving badly, then the result is worse than if you had never fixed the exchange rate in the first place. (Imagine Odysseus drowning if he is tied and the boat sinks and he is unable to swim away.)


World economy and world trade What is the difference between the world economy and world trade? I have read in one book saying "US share in the world economy is 28% and in the world trade is 15%" (2008 edition though). Please explain. Thanks

"Trade", in economics, usually means trade between countries.  So if goods made in, say, the Netherlands are sold in Belgium, that counts as trade.  But if goods made in, say, California are sold in Florida, that doesn't count as trade.  Because the US is a large and populous country, it has a high proportion of internal transactions that count as part of its GDP, a measure of its economy, but do not count as trade.  Many smaller countries, on the other hand, will have a share of world trade exceeding their share of the world economy.