How to interpret Employment Elasticity in this text? In this VoxEU text, «Promising ideas for future research on the employment effects of minimum wages », how do I interpret the elasticity of employment?

I would think of it as percentual change in quantity of labour demanded over percentual change in minimum wage. However, if I google the concept, I get % change in employment associated with a % change in output. Ok, Factor Incomes = Expenditures = Output. However, although at a national level they are the same, at a micro level, I don't see how both definitions would equate...

Any help would be appreciated.

I'm citing the first two lines of the article you refer to (emphasis mine):

  The debate among researchers about the employment effects of minimum wages remains intense and unsettled. There is clear variation in the magnitude of estimated employment effects across studies, with the debate often being between an elasticity for low-skilled groups equal to (or indistinguishable from) zero, or an elasticity in the range of −0.1 to −0.2.

Mechanically, you can always compute elasticities of any two variables w.r.t. each other at an initial point $b$, which is defined as

$$\eta_{a, b} = \frac{\partial a(b)}{\partial b}\frac{b}{ a(b)}$$

Simply googling employment elasticity gives you

$$\eta_{employment, X}$$

where $X$ is the unknown. What is it, that employment is elastic towards?

The article makes clear that indeed, $a$ in this context is the employment rate, while $b$ is the level of the minimum wage.

Instead of googling, you could have looked at any of the studies cited in the article. The first sentence in Dube et al (2010) actually states that

  We use policy discontinuities at state borders to identify the
  effects of minimum wages on earnings and employment in restaurants
  and other low-wage sectors.

So they're interested in two related elasticities, one of which was the one you initially suspected. Their table 2 will give you some estimates of those elasticities.


Why is the Fed considering increasing interest rates? America's Fed Funds rate is below 1% and its growth rate is 3.9%. India's lending rate is approximately 9.5% and its growth rate is 5.1%.

India just dropped its lending rate while the US is considering increasing its own rates. Isn't this counterintuitive? Wouldn't the increase in the 'cost of capital' slow down the US economy?

The Fed recently decided not to raise rates because the economy is still recovering.  In theory, as unemployment goes down, it should start to increase inflation.  However, unemployment is low and inflation is also low.  This is probably because people have left the labor force and are no longer counted.  Having low interest rates does stimulate the economy but the Fed wants to raise rates, when possible, for several reasons.  Policy is supposed to be countercyclical so keeping low interest rates indefinitely could lead to inflation.  Also, low interest rates encourage investors to pursue more risky investments for higher yields which can cause bubbles and crashes.  Also, staying at low interest rates limits the Fed's ability to use monetary policy at the zero-lower-bound where they cannot stimulate the economy anymore by using conventional monetary policy.


Adam Smith and wage gap? Recently I was reading up on Adam Smith's economic philosophy of competition (i.e self interest) and division of labor.

While I understand (and agree) with Smith's commentary that free markets and division of labor spur innovation, production, and general well-being of the average individual, it appears that there isn't commentary on wage gaps.

I would assume that through specialization (and self interest) some labor is more valuable than others (e.g CEO salary vs factory worker salary). Couple this with competition and I would expect wage gaps to quickly form.

Does Adam Smith ever address the issue of self-interest, competition, and division of labor and any potential wage gaps that post risk to a healthy economy?

Yes, Smith addresses these issues in Book 1 Chapter 10 of The Wealth of Nations. Firstly, he notes that where two jobs are in almost every respect equivalent, we should expect them to pay the same wage:

  "THE whole of the advantages and disadvantages of the different employments of labour and stock must, in the same neighbourhood, be either perfectly equal or continually tending to equality. If in the same neighbourhood, there was any employment evidently either more or less advantageous than the rest, so many people would crowd into it in the one case, and so many would desert it in the other, that its advantages would soon return to the level of other employments. This at least would be the case in a society where things were left to follow their natural course, where there was perfect liberty, and where every man was perfectly free both to choose what occupation he thought proper, and to change it as often as he thought proper. Every man's interest would prompt him to seek the advantageous, and to shun the disadvantageous employment."

This is related to the observation made by MH.Q: if A and B are two equivalent jobs, but A pays more then everyone would rather work in A than B. This results in a shortage of labour in B and/or an excess of labour in A so that the wages converge by natural market forces and the wage gap disappears.

Most of the rest of the chapter is spent discussing reasons why we might diverge from this ideal of uniform wages. The need to compensate skilled workers for the cost of their education and for the chance that they will not be successful in their chosen profession, for example, are offered as key reasons why wages might differ. I recommend you take a look at the chapter to get a handle on Smith's thinking.

This reasoning still forms part of our understanding of the modern labour market: if the wage premium for a job is not sufficient to compensate a worker for the (opportunity) cost of training to do that job then workers will not become trained and there will be a shortage of labour in the industry. This will drive up prices by natural market forces.

More generally, we now understand that wage differentials are an important means by which the market informs participants about how they should act. An extremely talented person who could, in principle, tranin to perform any of a large range of difficult jobs has no way to know where society needs his/her talents most. But the market provides this information by providing a mechanism for prices (i.e. wages) to increase in areas where skilled workers are short relative to prices in areas where workers are plentiful. The true beauty of this market mechanism is that is simultaneously provides information about the needs for workers, and provides the incentives for workers to enter the appropriate industries.

Whatever problems the wage gap might cause in the economy, they must be weighed against the large efficiency gains that come from allocated talent where it is needed most.


using LOG in a econometric model I am a beginner at econometrics and I have to build a model explaining scholing (as dependent variable) by migration (independent variable) and a couple of covariables. I'm going to use fixed effects to do this.

Now my question is, where and why should I use a LOG? I already read a lot of questions and answers here but it didn't help me any further.

Should I log migration? Government expenditure on scholing? GDP/Capita? Literacy? Ratio of scholing?

The use of the natural $\log$ permits to obtain approximations of percentage changes instead of unit changes (assuming linear regression). For instance, the parameter associated with $\log$ of GDP per capita would give you the changes in education (in the unit you measured it, e.g., years) as a result of an increase of 1% in GDP per capita. Notice that if your dependent variable is also a $\log$ transformation, you'll obtain elasticities.
To conclude, it should be straightforward for you to understand that there is no reason to apply a logarithm on unordered variables, or on binary variables. Its use on ordered variables is up to you, as the economic signification of choice of the estimates is dependent on your interests.


Interest/Rental Rate is today's or tomorrow's MPK? I recently posted and have since deleted a question regarding Exercise 2.1 in McCandless's "The ABCs of RBCs." The exercise involves deriving a first-order difference equation describing aggregate capital motion in a overlapping two-period generations model, and I could not solve it by using the definitions of $w_t$, $w_{t+1}$, and $r_t$ that I am accustomed to. It turns out that the exercise is easy to solve if you use the relationship $r_t = F_K(K(t+1), H(t+1))$ where $K$ and $H$ are aggregate capital and labor, respectively.

The reason I had so much difficulty with this exercise is that all of the economic theory I know dictates that $r_t = F_K(K(t), H(t))$, i.e. that today's interest/rental rate should equal today's marginal product of capital. Even this particular textbook says so a couple pages before the exercise in question. However, using that relationship yields an equation with no analytic solution for $K(t+1)$. If you use $r_t = F_K(K(t+1), H(t+1))$, i.e. that today's interest/rental rate is equal to tomorrow's marginal product of capital, the problem is solved with just a couple steps of algebra. But you can't just do that, can you?

If you need more context, I'm sorry that I deleted my previous question, but I had effectively shown 90% of the solution to the relevant exercise and I know that this site is not meant for giving homework solutions away. I hope someone can enlighten me on this particular stumbling block I've encountered, however.

I found the problem, and now I feel dumb but I suppose I should leave the question up so people can know the potential pitfall and prepare for it better than I did.

The problem arose from me misreading (and clearly misunderstanding) the equilibrium conditions for the problem, where it states that the interest rate $r_t$ on loans issued today and paid back tomorrow is equal to $\text{rental}_{t+1}$, the rental rate on capital used tomorrow, which is of course equal to tomorrow's marginal product of capital. I had my problem set up with $r_t = \text{rental}_{t+1}$, which is incorrect. This means that yes, we should have $r_t = \text{rental}_{t+1} = F_K(K(t+1), H(t+1))$, which makes the exercise a simple algebra problem. I just had my subscripts all messed up!

Here's why $r_t = \text{rental}_{t+1}$ (summarized from text): If $r_t < \text{rental}_{t+1}$, then under perfect foresight (an assumption of the basic model in the given chapter), people will attempt to borrow infinitely to capture the profit of $\text{rental}_{t+1} - r_t$, and this condition cannot hold in equilibrium. On the other hand, if $r_t > \text{rental}_{t+1}$, then nobody will want to hold capital until the next term, instead attempting to lend all of their funds out.


Why Constant Returns to Scale Suggests Certain Relation I'm self studying intermediate macroeconomics by reading a textbook and I came across a relationship that I'm not quite sure how it is derived.

Let $F(K,L)$ be a production function where $K$ is capital stock and $L$ is the labor force. Assuming constant returns to scale, I'm not sure how to derive $$F(K,L) = F_K(K,L)K + F_L(K,L)L,$$ where $F_x$ denotes the partial derivative of $F$ with respect to $x$.

The result follows from Euler's Theorem on homogenous equations. This theorem states that if a function $f(x,y)$ is homogeneous of degree $\lambda$ then the following holds:

$\lambda f(x,y)= x \frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y}$

A (production) function with constant returns to scale is homogeneous of degree 1 by definition. The definition of constant returns to scale is basically the same as the definition of homogeneity of degree 1. That means $\lambda=1$, which proves the result you need.


conditional factor demand functions for capital and labor I don't how to put maths in here so using an image:

$$(\frac{r}{w} \frac{1-\alpha}{\alpha})*K$$
$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})[\frac{y}{a}(\frac{w}{r} \frac{\alpha}{1-\alpha})^{1-\alpha}]$$
$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})^{\alpha-1+1} \frac{y}{a}$$

$$\equiv (\frac{r}{w} \frac{1-\alpha}{\alpha})^{\alpha} \frac{y}{a}$$

Is that what you're looking for?  Just notice that between steps two and three, I inverted the part of K in parentheses and changed the exponent to account for the inversion.


Which one is most distortive? Income tax, Poll tax, Land tax, or VAT?

Georgist argue for land taxes.

I think jizya is a form of poll tax.

VAT? I don't know.

I don't like income tax but can't really articulate why it's so bad.

Which one, for the same amount of revenue, reduces a country's GDP?

It seems that thrifty people will like VAT and spendthrift people will like income tax. Am I correct?

Would encouraging spending or encouraging investing a form of distortion?

I think in this case the typical economist's answer prevails: it depends. Taxes are distortive in so far as they prevent valuable economic activity from taking place.

Income taxes make working less attractive and therefore reduce the supply of labour. In an economy that is already labour constrained the distortion of income taxes can thus be significant. If, in contrast, land is a valuable but scarce resource land taxes will be distortive as well.

You're right that VAT is a consumption tax, and thrifty people won't mind such taxes typically. It is not  true that non-thrifty people won't mind income taxes because if we tax away their income they have nothing to spend! Taxes on interest or capital on the other hand won't be a much of a direct problem for the non-thrifty consumers.

Taxes on investment are distortive because they prevent valuable investments from taking place. This is the main argument put forward for lowering the taxes for the super rich in the US. As their income comes from investment lowering their taxes will spur investment. In how far this actually happens and whether the money is actually invested in the US is a different matter.

As a final point: some taxes are actually improving things by preventing economic activity. Environmental taxes like a tax on CO2 should in principle curb CO2 emissions and in that way correct distortions rather than introduce them.


How can intermediate goods and final goods be differentiated? The calculation of GDP(using expenditures) is: $C+I+G+Xn$,

where we calculate the spending on final goods and services within a country. However, how exactly are final and intermediate goods differentiated when calculating spending?

For instance, if one firm sells a product to another firm that adds to that same product and sells it again, how exactly do governments account for this when calculating GDP?

While @M3RS is correct that value added is another approach to computing GDP that handles the final vs. intermediate goods problem more aptly, within the context of the expenditure approach, you would effectively be measuring spending by who's buying it, and this measure is fundamentally imperfect. For example, flour sold by a cooking supply company to a bakery is likely to be counted as an intermediate good. Flour sold at a retail store is likely to be counted as a final good. But, it could be that a relatively small scale bakery buys flour at Costco (I used to work at a wholesale club, and we supplied a lot of small businesses). In that case, despite efforts by the government not to double count, it's really unavoidable. This is why value added is generally better for avoiding double counting.


Proof of monotonocity of preferences Question from Intermediate Microeconomics by Hal Varian:
"We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously?"
What I've done:
Preferences in the indifference curve can be represented using utility function and all the bundles that are indifferent are assigned a single value. And each value of the utility function also represents a fixed point on the diagonal line drawn through the origin. So, if one indifference curve intersects the diagonal line n times (say), then (n-1) points belong to different indifference curves and thus it would mean that the indifference curve in question has intersected another indifference curve, which is fundamentally not possible.
Does it prove the statement satisfactorily?

Let me pick up the discussion in the comments.
Consider any diagonal through the origin. Suppose it intersects some IC more than once. Pick two of these points and call them A and B. Because they are on a straight increasing line, one of the bundles, say B, has more of both good 1 and good 2. By monotonicity, bundle B should be preferred over A, which contradicts the statement that they are on the same IC.

If that is what you mean, your intuition is correct. However, there seems to be a jump in your argument: By saying
"if one indifference curve intersects the diagonal line n times (say), then (n-1) points belong to different indifference curves" you seem to be already assuming that the statement to be shown is correct and the n intersections could not exist in the first place.


Separation of base and momentum effect I am calculating YoY change in macroeconomic variables (inflation, industrial production etc.). However this growth is distorted by low base of last year. Currently I am using 2 year cagr to adjust for the base effect. Is there a better statistical method to separate the base effect and momentum.

For a "stable" base, you can use any average of previous years that "makes sense", that is an average with minimal variance and give an explicit explanation
If the last year doesn't deviate from that average then it is unnecessary

To demonstrate the momentum effect you can use a moving average, in that case there is no meaning for the base and edge cases are normalized


Piketty's Return on Capital How exactly does Piketty et al's method (as in his book) for computing the interest rate over time and countries work?

I know that they use reported tax returns, and that some criticize them for also using increase in housing values even if households didn't benefit from that through selling them (only an increase in book value).

So how does their method work in detail: Infer capital stock $k_t$ at $t$ through capital tax reports in $t$, look at interest accrued in $t+1$ through capital tax reports $Rk_{t+1}$, and then compute $r$ as $Rk_{t+1}/k_t$?

And what are potential advantages and disadvantages of this methodology compared to the traditional way?

Although I'm not sure that Piketty ever directly discusses the exact definition of $r$, he does make it clear indirectly. On page 52 of the hardcover English-language edition of his book, Piketty declares his "first fundamental law of capitalism":

Piketty obtains the share of income $\alpha$ from capital in national income from the income side of the national accounts, dividing "capital income" by national income. The capital share $\alpha$ is just the inverse of the aggregate labor share of income, on which there is an extensive literature. (Of course, there are several methodological choices that must be made when defining these concepts, and some of Piketty's choices differ from choices elsewhere.)

When finding $\beta$, Piketty appears to take the aggregate value of capital from respective countries' national accounts as well (though alternative sources are needed for older values). There is lots of information on the relevant choices in the technical appendix of Piketty and Zucman (2014), which is the basis of most discussion of $\alpha$ and $\beta$ in the book.

Since Piketty makes clear that $r=\alpha/\beta$, his definition of $r$ for a given year is essentially
$$r=\frac{\alpha}{\beta}=\frac{\text{aggregate capital income taken from national accounts}}{\text{aggregate value of capital taken from national accounts}}$$
Note that this actually does not (directly) involve tax data. Tax data is the basis of much of Piketty's other work, but not this.


Deriving equation for income offer curve Sorry if this is a basic question, however I have no idea on how to derive an equation for an income offer curve. All the explanations I'm getting is the graphical one where you just connect the different optimum points. It would be really helpful if someone can explain how do you derive an equation for such given any utility function.

What I have derived here is more appropriately called Engel curve.


Why are European countries happy to be outside Eurozone? In EU countries like Poland, Czech Republic, Hungary, etc, people are happy that they are not in Euro zone and Euro crises like that of Greece do not affect their economics.

However, some European currencies outside the Eurozone are pegged to a narrow band around the Euro, so their values largely change in line with the Euro's. So, what is the difference if we call a currency Euro or something else, when its value is changing by Euro crises?

For example, what is the advantage of currency in Czech over Slovakia now?

I largely agree with mathtastic, but I think it is necessary to add something.

When joining a monetary union a country does indeed lose its power to conduct monetary policy. However simply not being able to reduce the interest rate was not the main issue that Greece and other countries faced because of being in the Eurozone. This is because the ECB lowered interest rates (almost) down to the zero lower bound.

To adequately address your question we have to distinguish advantages of a country from having its own currency while in a crisis, vs. advantages from always having had its own currency in the first place.

Reasons why it is helpful to have your own currency when a crisis has already hit:

The issue in this case was the impossibility of devaluation of the currency. One way to understand the Greek crisis is as a current account crisis. Not only was the government over indebted, but the country as a whole. That is to say that there was a too large trade deficit for too long. The trade deficit creates a sort of debt that the whole country owes to other countries in total and was a main point of focus in the debates about Greek debt. You might have heard the issue of competitiveness being cited as a factor in the Greek crisis, which simply means the impossibiliy of the Greek economy to export sufficiently. You may have also heard about "living above their means" or "BMWs going to Greece financed by German money". All this refers to the trade deficit, i.e. the current accuont crisis.

To help itself out of this current account crisis, Greece would have to reduce its trade deficit, i.e export more and import less. If Greece would have had its own currency, a natural reaction to the crisis (without any government intervention even required) would be that Greece's currency loses value. Hence its exports are cheaper which leads to more exports and its imports are more expensive, which leads to less imports. In this way Greece would have an easier time dealing with the crisis and could also "grow its way out of the crisis" - policy advice often heard in this whole debate.

In addition to reducing the trade deficit, a currency devaluation would have helped Greece's economy grow and help with debt service, because the private and public sector were over indebted and not in a position to borrow. This means that domestic demand was very low, so foreign demand- i.e. exports- would have to pick up the slack.

Now, you might say that Greece could export more by simply reducing its prices even without currency devaluation. This is in theory true and is indeed what was recommended and what was attempted in Greece. You can look this up under the term "internal devaluation". However there are several problems with this. First of all it is easier to simply devalue the currency (one price adjustment) than to reduce prices of all export goods (many price adjustments). Furthermore, price decreases mean deflation, which brings with it further problems and is hard to combat later on, when it is no longer desired. A term to look up for more information on this would be "deflationary spiral". Third and perhaps most importantly is the issue of "downward nominal rigidity". This is the empirically observed phenomenon that nominal prices tend to not go down as much as they should or at all, i.e. are rigid in going downwards. This come perhaps from money illusion. It is easier to inflate away workers' wages than to actually reduce them, because the former doesn't cause any protest, while the latter does. Although this is not rational, it happens. Hence it is very difficult to reduce prices and export more (i.e. be more competitive) without an own currency.

This is the reason many countries are likely happy to have their own currency. As to why they are happy despite possibly being "pegged" to the Euro, is because they can break that peg much more easily than Greece if they wanted to.

Reasons why it is helpful to have your own currency before a crisis hits:

For information on how it could have come to such a loss of competitiveness in Greece I can recommend looking up the "Balassa-Samuelson effect", although this may not be the whole story.

Personally, I am not totally convinced by the conventional wisdom, especially popular in European media, that if Greece were to return now to the Drachma that things would be better. This is because their debts may then legally still be denominated in Euro and after the inevitable devaluation of the Drachma against the Euro (the whole point of having the Drachma now) would cause the debt burden to increase even further. For more on models where such effects are present see so-called "third generation currency crisis models".

However had they not had the Euro in the first place, like the "happy" European countries you are mentioning, then their debts would have likely never been denominated in Euro in the first place and could more easily pay that debt through a currency devluation / inflation.

Another reason countries are happy to not have had the Euro in the first place is because the Euro created interest rates for Greece's public debt that were too low than what they should have been. This means the government became over-indebted, which lead to the problems we see today. Had the interest rates been (correctly) higher the government would have perhaps borrowed less and not too much. This is to say that due to the Euro (and the false positie expectations caused by it) the "price signal" was not working so well. Other countries that never adopted the Euro did not experience such a loss of information from the price signal.


Causes of trade deficit: Multiple views I am trying to understand the causes and macroeconomic implications of running a trade deficit in the United States, and I came across a few different views on this topic.  I'd like to know if there are studies that try to understand the root-cause of this trade deficit.

First, I understand that trade deficits aren't necessarily a bad thing, and it all depends on the context.  Since the trade deficit reflects the difference between savings and investment, whether it's good/bad depends on what the excess investment is being used for, and whether the investments will reap benefits in the future.

That said, my focus is on trying to understand what is causing the current trade deficit to increase; I see there are different views:

US is consumption driven, and our consumers/government are spending beyond their means.  That is, there is a huge demand from the US economy, which is causing us to import more than we export, which is causing the deficit.  If we cut that spending, it will reduce the trade deficit [1].
East Asian countries (especially China) are experiencing a "saving glut" and instead of investing in their own country, they are exporting their capital to the US and parking it in safe US-Treasury investments.  It is this capital inflow to the US that is widening the trade deficit [2,3].

[1] https://www.washingtonpost.com/opinions/everything-you-need-to-know-about-trade-economics-in-70-words/2017/05/05/a2b76a02-2f80-11e7-9dec-764dc781686f_story.html?noredirect=on

[2] https://carnegieendowment.org/chinafinancialmarkets/77009

[3] https://www.federalreserve.gov/boarddocs/speeches/2005/200503102/default.htm

Qualitative evidence for (1):

Our savings rate, measured as fraction of saving to GDP is lower than what it was in 1950s--1970s: https://fred.stlouisfed.org/series/W207RC1Q156SBEA
Our federal deficit is widening, and taxes aren't enough to cover the government expenditure.

Qualitative evidence for (2):

China is a net exporter, and continues to be competitive by taking steps to prevent RMB from strengthening against the dollar.
Savings rate in China is a high fraction of their GDP, relative to the US: https://tradingeconomics.com/china/personal-savings.
The interest rates in the US are historically low, which is because there is a lot of demand for US treasury from abroad. Quoting from [2]:

  Interest rates suggest very strongly that capital isn’t sucked into the United States from abroad, but rather is pushed into the United States from abroad.

I see a bit of truth in both sides of the story.  US is consumption driven (not necessarily a bad thing), and China has high savings, probably because of a host of factors such as culture (savings minded), more income inequality (rich save more of their income than the poor), etc.

I have two main questions:

What is the direction of causality?  Is US consumption driving the trade deficit, or is foreign capital inflow driving US consumption?  I'd appreciate any academic citations that argues one way or another quantitatively.
If it's capital inflow driving US consumption, then why doesn't US just use the cheap loans to repay its current debt?  Isn't it in US's control to decide what to do with the capital we get -- why spend it?

Often a good answer consist the most of shedding light on some aspects of the terms of the question itself. I hope a couple of remarks could be useful.
About causality, the fact is that current deficit implies reserves exit from USA, which only can be supported by reserves entering, otherwise resulting in a diminishing stock of reserves, eventually exhausting it. A capital-account superavit --net inflow of capital-- represents an inflow of reserves, in that sense financing trade deficit (see Economic Report of the President, 2004). Letting aside causality --which can be very complex and call for other matters-- both imbalances are bond to present themselves simultaneously. In other terms, the fact that trade deficit and capital superavit pop up strongly correlated doesn't mean a causality. I suspect --sorry again for the lack of evidence-- that there's no causality there indeed. Instead, those paths suggested in the question about rates of interest or foreign exchange rates could be more promising sources of explanations, probably besides productivity and cost structures (again, see Conclusions in Economic Report of the President, 2004). It would be an example of third -unknown- causal factor.
About repaying the debt with capital inflows, we have to keep in mind that those capital inflows are new debt. For example, see Kirabaeva, Koralai & Razin, Assaf. (2010). Composition of Capital Flows: A Survey, NBER Working Paper Series. Aside with debt-instruments, capital inflows also comprise equity-instruments, i.e. Foreign Direct Investments and equity purchases. Depending on the context, even the last ones could also be considered national 'debt', as it represents foreign ownership of 'local' firms.
Interestingly, the "US's control to decide what to do with the capital we get" reflects the conflation in an unique agent "US" which in practice is a set of --millions of-- firms, consumers, authorities... There is no central control on the employment of all those flows, even though all those agents are acting, and controlling, in the USA, in that sense all them constitute "US's control".


Mixed Strategies in Bayes Nash Equilibrium (Bayesian Battle of the Sexes). Shouldn't it depend on $p$? I have a question about calculating mixed strategies in a Bayes Nash Equilibrium in a simple 2-player bimatrix game. To demonstrate the issue, consider ``Bayesian Battle of the Sexes.'' Suppose P1 faces a P2 whose type is unknown with probability $p$. An example is below in which $p=.5$.

Here's what's surprising to me. If you calculate the mixing strategy for P1 by making sure that P2 is indifferent, you wind up with P1 mixing strategies that don't depend at all on $p$. This seems strange to me.
If P2's type is more clear, shouldn't the optimal mixed strategy shift to anticipate this?
End of question. Addendum: The game above apparently has two mixed strategy EQMs:

P1 mixes $(\frac{1}{3},\frac{2}{3})$, P2 left mixes (0,1), P2 right ($\frac{2}{3},\frac{1}{3}$).
P1 mixes $(\frac{2}{3},\frac{1}{3})$, P2 left mixes ($\frac{2}{3},\frac{1}{3}$), P2 right (0,1).

Like I said, this doesn't seem to depend on $p$ (the probability of facing the first type).
Also: Shouldn't this game have an odd # of EQM? I thought this was a rule of thumb. I am contemplating the idea that there's a third equilibrium that mixes the two above.

Suppose player 1 chooses a mixed strategy such that the left type of player 2 is indifferent between C and H. There is a unique mixed strategy that does this. The same mixed strategy, however, does NOT make the right type of player 2 indifferent. Loosely speaking, this is simply because the preferences of the left type are exactly those of the right type switched around. Thus it is impossible for player 1 to make both types indifferent simultaneously. Therefore, the probability $p$ plays no role when choosing a strategy such that at least one of them is indifferent.
This also indicates why there are exactly two equilibria.


Is it theoretically possible for a singular national currency to exist under a free banking system? Free Banking is a proposed monetary system, usually by Austrian Economists, as an alternative to the prevalent Central Banking system. Under this arrangement, commercial banks would issue their own banknotes rather than by a Central Bank. The total quantity of banknotes and interest rates would be dictated by market forces. Free Banking is said to have existed historically in several countries such as the US, Canada, Scotland and China.
The question I'm wanting to ask is concerned mainly with the issue of currencies in this proposed arrangement. Suppose, India tomorrow decides to scrap the RBI (its Central Bank) and move to Free Banking system where banks would issue paper money backed by gold. Would that mean its national currency i.e. the Rupee, would cease to exist because commerical banks would issue their own forms of currencies (Currency X issued by Bank A, Currency Y issued by Bank B and Currency Z by Bank C)? In other words, would multiple currencies (each being issued by a commerical bank) be existing in India then rather than one single national currency i.e. Rupee? Is it possible for India to have a Free Banking arrangement with one singular national currency?
Also, if several competing private currencies are to exist in one country, would each bank be willing to accept the currency of the other? How did historical examples of Free Banking function regarding this issue?

Is it possible for India to have a Free Banking arrangement with one singular national currency?

Under free banking you would only end up with single currency if one bank manages to become a monopoly on issuing the currency. That is possible, although at least historically it did not occurred under free banking systems. Also this would be in essence equivalent to central banking system with only difference that the central bank would not be government institution.
Also, for full disclosure,  I am mainstream economist and not fan of idea of free banking (which is a fringe idea that very few economist support, and it would likely be very inefficient monetary arrangement)  but to my best knowledge of the position of free banking advocates, they advocate free banking because they don't like monopoly on money so ideally the system should be operated with multiple currencies.
However, If the free banking currencies are backed by gold (which was true for most historical free banking systems but does not necessarily need to be part of the system as you can have fiduciary free banking) then even if they technically use different currency they are all in some sort of 'monetary union'. This is because even if they can still vary the number of banknotes redeemable per ounce of gold (and hence the value of individual notes) the exchange rates between the banks is essentially fixed by value of gold which is in practical ways virtually equivalent of being in monetary union (see Eichengreen & Temin, 2010).

Also, if several competing private currencies are to exist in one country, would each bank be willing to accept the currency of the other?

If the free banking banks operate under gold standard then they would have to because in essence what gives value to the money is gold. Lets say hypothetically that under such arrangement bank A would refuse to take money of bank B. Well all you would have to do is just to convert your bank B banknotes to gold and get bank A banknotes for that gold so it is not like bank A can stop you from converting the money.  In addition why would bank that wants to attract customers (and their gold) impose this extra administrative burden on its customers?
If there would some fiduciary free banking then there likely would be floating exchange rates for each banks money and when you would be going to another bank you would just have to pass through exchange rate like when you want to put money in foreign bank. Here I suppose it would be more doable for bank to impose restrictions on other banks money if they would want to - but again question is why would they want to restrict new customers coming to them?

How did historical examples of Free Banking function regarding this issue?

You can find nice accounts of how the system worked in writings of 18th century economists such as for example in Adam Smiths Wealth of Nations. I will only give very brief summary here.
The system developed as an extension of commodity money. Before paper bank notes people used gold/silver (or other metals) coins across Europe. However, travelling with coins is dangerous so people would put them in banks and get 'bank note' of their gold balance that they could get at any other branch of the bank on demand. Since these banknotes were as good as gold/silver coins people started using them instead of the coins.
Under free banking every bank issued their own notes but since the value of note dependent on the gold you can get they could be easily exchanged with each other. If banks A note entitled you to 1 ounce of gold but bank B note entitled you to 2 ounces of gold you would only accept 2 banks A notes for 1 banks B note. Later one as the system developed there were also dedicated exchanges for money issued by various banks.
However, the above is only very rough and crude and simplistic description. The system worked bit differently across different countries since back then there was much less standardization and uniformity when it comes to ways how financial institutions operate (at least relative to present day). For example, the US free banking system was relatively more regulated than lets say the Scottish or Swiss one (see Kenneth (1988) or Kroszner & Randy (1995)).


Are opportunity costs synonymous with economic costs? I was working on a question that asked the opportunity costs of going to college per year given that college tuition is $ x $ and the salary per year is $ y $. The answer given is $ x + y $.

I thought that economic costs is given by: $$ \text{Economic costs} = \text{Accounting costs} + \text{Opportunity Costs} $$

Here, the accounting costs would be the explicit cost of tuition, while the opportunity cost would be the implicit cost of wages foregone.

Is my conclusion correct? Or is economic costs synonymous with opportunity costs?  (Which makes opportunity cost equal to the total cost, explicit + implicit)?

In economics, we argue that there is only one correct way to think of costs. And so, the adjectives economic or opportunity in front of the word cost are actually superfluous — the terms cost, true cost, economic cost, and opportunity cost are all exact synonyms.

Note. If they are superfluous, then why do we use these adjectives?

One reason is to strongly emphasize that other conceptions of "cost" that accountants and other non-economists use (e.g. accounting costs, historic costs) are not quite correct.

Another reason is that in practice, it may be difficult to figure out what the true cost or opportunity cost is. And so in practice, economists will — despite what they themselves teach in Econ 101 — often use the term cost in some narrower, incorrect sense.


Why doesn't the ECB implement the same fiscal and monetary policy that the FED used to save the US economy? If the Fed managed to save the US economy with their liberal expansionary policy, why doesn't the ECB follow suit if it is much more efficient in reducing unemployment etc?

Also, why did Quantitative Easing work to better effect in the US compared to so far in Europe?

The ECB faces a unique challenge in that the Eurozone is a monetary union without a fiscal union. Because each country has autonomy over their own fiscal policy and there is no separate Eurobond, it is unclear which countries' bonds the ECB would buy to perform Quantitative Easing. In the US this is easy because of the presence of US Treasury Bonds that  the Federal Reserve can readily purchase.

Also, since the Eurozone is composed of so many different economies, the main goal of the ECB is inflation control. It is extremely hard to set a blanket policy to cover the whole Eurozone when there are so many different economies in different states right now. Setting an interest rate very low or performing quantitative easing over the whole Eurozone, which is very hard because of the lack of fiscal union, would undoubtably be good policy for countries like Greece and Portugal, but would be the wrong policy for a country like Germany that currently has a strong economy.


Can increase of NEER cause higher inflation? I´m trying to find siutable econometrics model for explaining inflation during financial crisis and after. My final model shows that if NEERnominal effective exchange rate) increases, the inflation increases too.

NEER is undertaken from Eurostat when increase of NEER means appreciation.

I´m not sure if this means increase above 100-> appreciaton. Or if any increase (for example from 78 to 80) means appreciaton.

I don´t know how to explain this model. Do anybody have any idea how the NEER works and why there is positive relationship between NEER and Inflation?

Thanks for any advice.

Here are my quarterly data for NEER: eurostat

An increase in the index from one point in time to a later point indicates a nominal appreciation over that period

Standard economic theory might suggest that would lead to lower prices than without such an appreciation, since imports would be cheaper and demand for exports could reduce

The Czech Krona was devalued at the end of 2013.  An article published a year later by the Czech National Bank suggests it thought it achieved the aims, saying

  Without having depreciated the exchange rate, deflation would have been significant, at least -1%, meaning that the Czech economy would already have entered deflation for an extended period. However, thanks to the exchange rate depreciation, the threat of deflation caused by a lack of demand and a downturn in the economy passed. Despite a significantly greater anti-inflationary effect abroad than was expected at the end of 2013, core inflation returned to positive values after nearly five years.

and this is consistent with standard economic theory

But if you want a rationalisation of why a currency appreciation may not have happened during a financial crisis, try thinking of a world where interest rates are tumbling worldwide and where carry-trade investors looking for nominal yield invest in countries where nominal interest rates are higher, possibly caused by higher inflation.  Such a country might see higher inflation than other countries and at the same time an appreciating currency.  The appreciating currency may then attract momentum investors, with the flood of money pushing interest rates lower than would be suitable to control inflation (especially if the country wanted to keep its exchange rates more stable), and the combination of more money and reducing interest rates could lead to higher inflation

To a small degree this may be what has happened in the Czech Republic more recently: it had slightly positive interest rates (until summer 2017, when they started to be increased) while the Euro area has had zero or negative short-term interest rates, and has seen an appreciation in the Krona against the Euro.  There could be other explanations


Consumer Preference when Consumer only consumes $A$ or $B$ Let's say Sally either wants to coke or pizza, but never both.

I am aware of the standard consumer preferences, such as Perfect Complements as well as Perfect Substitutes.

But I have never heard of the above case regarding Sally. Is there a particular name for this preference type?

If Sally only prefers A or B but not both, this could be an example of Independent Goods. These are goods that are neither complements nor substitutes, and changes with one good generally do not affect the other.

However, with the information about Sally's preferences, it sounds to me like it could also be an example of Cross-Category Substitute Goods. These are goods that can substitute (imperfectly) for one another. Consumers may find one good more satisfying than the other based on their individual preferences and utility function.

  i.e. perhaps Sally wants a slice of pizza or Coke, and both cost \$1.
  She prefers the taste of Coke so she generally chooses it, but one day the price of Coke goes up to \$2. She
  may be satisfied to a similar degree purchasing pizza until the price
  of Coke comes back down. On a different day, she may want to purchase 2
  pizzas for the same amount as 1 Coke. There are many possible outcomes with
  cross-category substitutes.

It's a little unusual and subjective, because both goods in the example are in consumable food/drink categories, but one good satisifies hunger and the other good satisfies thirst. Thus, it's hard to think of one being a replacement for the other unless one thinks of them both being sweets or snack items. (One common example uses a chocolate chip cookie and a chocolate chip granola bar in place of Coke and pizza.)

If this isn't the exact term you're looking for, I hope this helps you on the right track at least.


PPP / currency evaluation An economics book has the following example:

In the USA, a Big Mac sells for 1 USD, while in Germany it sells for 3 EUR.

The "fair" FX relation would therefore be 1 USD = 3 EUR. At the FX market, however, the FX relation is 1 USD = 2 EUR.

The author now concludes that the EUR is undervalued. But I think that's wrong, the EUR is overvalued here, isn't it?

Your conclusion is correct here. Since at the current FX rate you can buy the burger cheaply at an equivalent rate of 2 EUR in the US. So basically, if you live in Germany and want to buy a Big Mac, you are better of buying the Big Mac from the US since via the FX rate you will still have 1 EUR left(if you started with 3 EUR) and hence this will increase the demand of the USD in the foreign exchange market and hence

USD should appreciate in the future => USD in undervalued => EUR is overvalued.


How to interpret Marginal Cost values? The Marginal Cost (MC) of an additional unit of output is the cost of the additional inputs needed to produce that output.
Here is one of the formulas for calculating marginal cost:

$\ MC=\Delta CF\div\Delta output$

For example, suppose it costs  €1600 to produce 100 units and €2300 to produce 200 units. MC = €7

What does it mean to have the marginal cost equal to 7?

What does it mean to have the marginal cost equal to 7?

It means that, at the current size of your production capabilities, if you want to produce one more unit of your product, you will have to spend 7 Euro.

This, MC value is a quantitative description of the cost you pay if you want to adjust your initial production plan to a larger output and it is determined by your production capacities.

Here is an example:

You have a bus company and your service is to offer a one way trip from point A to point B, every day at a given hour. Now, your buses have 50 seats and your total cost for the trip is 100 Euro (fuel, road taxes, etc). In addition to that your licence says that  you have to provide additional bus if the passengers are more than 50. In this case, if you have 49 passengers and in the last minute there is a reservation for one more seat, your marginal cost is effectively zero, however, if there are two reservations in the last minute and the total number of passengers is now 51, the 51th passenger's marginal cost is 100 Euro, because you need a second bus only for him.


How low can interest rates go? How deeply negative? Ten years ago, negative interest rates were an impossibility, an intellectual curiosity. Now it's a common policy.
Just read a claim that there is still an absolute lower bound, even if it happens to be a little bit below zero. But having had one certainty smashed, I'm curious--what stops rates from going even further below zero?
The Bank of Japan has had very low rates for a very long time, partially made possible by the deflationary environment. Even if the money in the bank doesn't earn very much interest, it just buys more over time.
What happens if the whole world goes the way of Japan, with constant and sustained deflation? Ie, assuming all government bonds carry a negative coupon.
Say global economy that is deflating at -.06, is -.05 still  the 'real world lower bound' of interest rates?  Can a lower bound be said to meaningfully exist, or is there only the spread between the rate of deflation and the interest rate?
I think the economics frame of this is that the nominal rate is -.05, but less deflation -(.06), the actual interest rate is .01?
So I guess my actual question is: Is there a lower bound for nominal rates? Or are very negative rates possible as long as they are less than the rate of deflation?
(I am not an academic economist. Pardon my lack of jargon).

Your question contains several incorrect premises, hence before providing an answer I will first correct those misconceptions as any discussion based on incorrect premises cannot be  very productive.
Correction of Misconceptions

Ten years ago, negative interest rates were an impossibility, an intellectual curiosity.

This is not true at all. Clearly empirical research shows that there were periods when interest rates in some countries were slightly negative. For example, Kugler, P., & Rich, G. (2001) show that Switzerland had slightly negative interest rate in late 70s. That is about half a century ago and the paper itself is 20 years old and this was well known. So your statement is just factually not true.
In fact negative interest rates and possibility of thereof enjoyed periodic waves of interest, the most early ones dating all the way back to early 20th century (See Ilgmann, C., & Menner, M. (2011) and sources cited therein).

Just read a claim that there is still an absolute lower bound, even if it happens to be a little bit below zero. But that's premised on an inflationary world.

One cannot prove a negative but I study macroeconomics for quite some time and I have never seen anyone saying that zero lower bound (ZLB) or even effective lower bound (ELB) are premised on inflationary world. I would like to be corrected if anyone economist ever made such claim, but I doubt it and even if some do this is definitely not any claim that would be generally held by mainstream macroeconomists.
Answer

And in an economy that is deflating at -.06, is -.05 still still the 'real world lower bound' of interest rates? Can a lower bound be said to meaningfully exist, or is there only the spread between the rate of deflation and the interest rate?

ZLB or even ELB does not depend on deflation or any arbitrary rate of deflation. ZLB or ELB exists independently of what the rate of inflation/deflation is in the economy. ZLB or ELB as pointed by @BrianRomanchuk in his excellent +1 comment refer to the bounds on nominal interest rates, and even more specifically nominal interest rates on deposit accounts. Real interest, or even other nominal interest rates  (such as rates implied by ECB's long-term repo operations (LTROS) rates see The Economist for explainer) can be arbitrarily negative.
The reason why ZLB or ELB exist is the existence of cash. Due to existence of cash - which is equivalent to financial paper with implicit zero nominal interest rate - there must be some ELB. Since cash and money on deposit accounts are theoretically perfectly fungible the limit on nominal interest rates should be zero. Of course in real life there are issues such as storage costs. Even without negative interest rates you are willing to pay bank to keep your money safe and as a result the interest rates can become slightly negative (Ilgmann, C., & Menner, M. (2011)).
However, slightly negative does not mean arbitrarily negative. There will be point where the nominal interest rate is so negative nobody will be willing to hold money in deposit accounts. This is trivial just consider an extreme case of negative $-1000\%$ interest rate. Would you hold any money on deposit account under such punitive negative nominal interest rate? I think not! Of course, this raises question what is actually the true ELB if not zero. The studies show that while this effective lower bound will be below zero, it can only go very little below zero - reasonable estimates are around $-1\%$ being maximum (see Hills, T. S., Nakata, T., & Schmidt, S. (2019) and sources cited therein).
Now are there some ways how this issue could be dealt with? Actually yes! Both ZLB and ELB can be easily abolished by abolishing cash. If people do not have choice of withdrawing their money from bank then interest rates can be arbitrarily negative (see Buiter 2009; Buiter 2005; Yates 2004, and Ullersma 2002, for reviews on the relevant literature). Unfortunately, it seems that most societies are not ready to give up cash yet, since despite of support for abolition of cash among  experts this idea is not widely embraced by politicians.


Inverting price functions and their conditions/intervals If I have demand functions

For $P<15$:

$$
Q(P) = 700-40P
$$

For $P>15$:
$$
Q(P) = 400-20P
$$

If I invert them, I get the price functions

For $Q<100$:
$$
P(Q)=20 - (1/20)Q
$$

For $Q>100$:
$$
P(Q)=17,5 – (1/40)Q
$$

I know how I get the expressions, for instance, $Q = 700 - 40P \Leftrightarrow 40P = 700 - Q \Leftrightarrow P = \frac{700}{40} - \frac{1}{40} Q$, but I don't how the conditions $P < 15$ can change to $Q < 100$.

Notice that if you plug in $P=15$ into either of the $Q(P)$, you get

$$Q(P) = 700-40P = 700 - 40 \cdot 15 = 100$$

$$Q(P) = 400-20P = 400 - 20 \cdot 15 = 100$$

So you can take the exercise further and see that when $P < 15$, then $Q > 100$ (notice the direction of the inequality is changing; the more expensive a good, the less consumers buy of it)


Competitive equilibrium in an exchange economy with lexicographic preferences I am really stuck with this problem and not able to approach it. Any help will be much appreciated.

I tried to draw edgeworth box with initial endowment point. I do know that for competitive equilibrium, tangency condition must be met such that both utility curves are tangent at equilibrium point. But here, i am not able to identify utility curves. Please help.

Consider an exchange economy with two agents,1 and 2 and two goods X and Y. Agent 1's endowment is (0,10) and Agents 2's endowment is (11,0). Agent 1 strictly prefers bundle (a,b) to (c,d) if,either a>c or {a=c and b>d}. Agent 2 strictly prefers bundle (a,b) to (c,d) if min{a,b} > min{c,d}. For both agents, we say that bundle (a,b) is indifferent to bundle (c,d) if, neither (a,b) nor (c,d) is strictly preferred to each other.

Q. This exchange economy has:
a)one competitive equilibrium allocation.
b)two competitive equilibrium allocations.
c)infinite number of equilibrium allocations.
d) no competitive equilibrium allocations.

Answer : a

The preferences of agent $A$ cannot be represented by any utility function and the prefeences of $B$ not by a differentiable utility function, so forget calculus approaches.

Since $A$ has strictly monotone preferences, we must have $p_1>0$ and $p_2>0$ for every equilibrium. Also, $A$ is always willing to give up any amount of good $2$ to get more of good $1$. So he will spend his wealth on good $1$ with consumption of good 1 equal to $10 p_2/p_1$. Also, we know that $B$ must consume both goods in equal amounts, so you just have to plug the equality $x_1^B=x_2^B$ in the budget constraint (justification here). Then you have the demand for both goods and can calculate their excess demands. Since only relative prices matter, you can normalize by, say, setting $p_1=1$. Since both agents will spend their whole wealth, Walras' law applies, and in order to find an equilibrium, you just have to find prices under which the excess demand for one of the goods (your choice) is zero. If you find a unique solution, you have found a unique equilibrium (note that demand is unique given prices).


How a country buy stuff from other countries? and what is its means of exchange? I was thinking about this scenario, where a country X wants to buy some toys (worth of 100$) from country Y. both of them have their own currency-- not USD. So, now, how does the exchange happen between X & y?

will the country X print 100$ equivalent of X's currency and convert that into US Dollars? or will country X exchange gold worth of 100$ to buy those toys from Y?

P.s. If I sound too dumb, its OK, I can handle that, am new to economics & trade.

In general one country cannot just print currency of other country. At least not legally, I suppose some countries could engage in counterfeiting.

A country has to go to foreign exchange market where they purchase the currency of the other country first and then make the transaction in that currency. In practice the foreign exchange market is ‘accessed’ just by making bank transfer where banks converts the money at the current exchange rate, same as you would when you order stuff from other country on internet or when on vacation.

Gold was used in international trade before modern age where gold and silver was kind of an universal currency. The only difference was in the gold and silver content of the coins so once that was accounted for, for all practical purposes, countries were basically in a monetary union - in fact Euro is often compared to gold standard see Eichengreen and Temin’s work on this  here. But this system is no longer used as it’s impractical to ship gold between countries when floating exchange rates can do the same if not even better job with just paper fiat money.


'One Unit Change in the Explanatory Variable' I have a conceptual question in terms of econometrics.

I understand for example that the primary goal of econometrics is to use estimated parameters to calculate the average change in the dependent variable conditional upon a unit change in the independent/explanatory variable(s).

However, may I ask if this 'unit change' is represented by the standard deviation, or in fact is representative of a 1% change?

Any feedback/discussion on this would be appreciated,

Best,

You can use summary statistics to compare the one unit change to the standard deviation and could say that it represents a 1, 1.2 2 etc. standard deviation change. For example, if in the regular form:
$$y_i=\beta_{0}+\beta_{1}x_i+u_i$$
say $\beta_{1}=6$ and from your summary statistics, the standard deviation of $y$ is 3, you could in turn explain the coefficient as: "A one unit change in $x$ is associated with a 2 standard deviation change in $y$, ceteris paribus".

To interpret the unit change as a 1% change, you can convert the coefficient to read it in terms of percents relative to the levels of $x$ and $y$ or, to much more convenience, you can run the model in log-log form:
$$\log(y)_i=\beta_{0}+\beta_{1}\log(x)_{i}+u_i$$
In this form, $\beta_{1}$ is the percentage change in $y$ from a 1% change in $x$. Exactly what you are looking for!
$$\beta_{1}=\frac{\%\Delta y}{\%\Delta x}$$
where the denominator is usually a 1% change.


Static Profit Maximization Short Run Shut Down Decision In considering whether to stay open or shut down in the short run, a firm compares its revenues to its “avoidable costs”. We usually think of these avoidable costs as variable costs, but of course they could be fixed. This is where I have a thought experiment question:
Suppose we are looking at profit over a month. It is negative. You are considering if you are at least covering avoidable costs. How do we consider capital cost?
Case 1: You rent the factory and the lease is not flexible. This is a sunk cost.
Case 2: You own the factory. Your best alternative is to rent your factory out. If you shut down, you can easily find a replacement (assume no transaction cost). Then this foregone rent is an avoidable cost.
Case 3: This is where it gets tricky for me. You own the factory and no rental market exists. However, you can easily sell the factory if you shut down. So in my mind this is avoidable and the foregone rent (user cost of capital) is the relevant cost. But this doesn’t consider future profits unless we assume that the firm can buy back the factory in the following period when/if prices rise again. This seems incorrect.
That seems to be a downfall of static maximization. How would you propose thinking about this last scenario? Why don’t we consider dynamic profits when discussing shut down decisions?

In the short run, you cannot sell your capital. To do so would be a violation of "short run" and would instead be the "long run".
Case 3 (and I would also contest Case 2) are outright forbidden by the definition of short run.
I would note that your question has a lot of narrative to it - which is good in some cases, but you want to keep the literal definitions in mind, not all actions you describe are valid options in the parameters you've established. Optimization is, at its heart, a simple fact of math.


Implications for currencies pegged to USD of Chinese devaluation? I get the general implications that exist for both US-Chinese exports/imports. However, considering that some currencies are pegged to the USD, would there be any effect and if so what?

Thanks

Let's take Lebanon as a country that pegs to the USD and examine the implications of Chinese devaluation on Lebanese imports and exports.

First step is to recognize that what matters for the trade balance is the real exchange rate, not the nominal exchange rate. We need to examine the nominal exchange interrelationships first. The second step is to examine the inflation differential, under different hypothetical scenarios.

Nominal Exchange Rates:

Since the Lebanese pound is pegged to the USD, if China devalues their currency and exchange rate used to be 100 Renminbi for 1 USD, now 120 Renminbi for 1 USD, by definition (of devaluation and peg) the nominal exchange rate between China and USA will change, but the nominal exchange rate between USA and Lebanon will not.

Inflation:

Assuming zero inflation, for simplicity, in all 3 countries, then the
Chinese goods and services will now look cheaper to Americans and
cheaper to Lebanese. In turn, American and Lebanese imports will now
look more expensive to Chinese people.
Assuming China has a 30% inflation rate, while USA and Lebanon have 0
inflation rate, then the fact that the inflation rate differential
between China and USA is 30%, while the Chinese nominal exchange rate
was devalued by only 20%, implies that in real terms, the Chinese currency (relative to both the USD and Lebanese Pound) has
actually appreciated by approximately 10%=30%-20%, leading to Chinese exports looking more
expensive to Americans and Lebanese, and American and Lebanese
imports looking cheaper to the Chinese.
Assuming US inflation rate to be zero, and Chinese inflation rate to be 30% while Lebanese inflation rate to be 5%, we are in a situation where the Chinese currency was devalued, as before, by 20% but the inflation differential (25%=30%-5%) overwhelms the devaluation (25%>20%) hence the Chinese Renminbi has actually appreciated 5% relative to the Lebanese pound, rendering Chinese exports more expensive for Lebanese people. Lebanese exports will now look cheaper to Chinese people.


Including (demand) price elasticity in a price regression model I am wondering how to include price elasticity (demand side) in a linear price regression model that is based on asuming price is the result of demand=supply.

Constructing a price regression under the asumption of price inelastic demand is pretty straight forward, since you do not have the problem of dealing with simultaneous equations. Yet, I cant wrap my head around how to implement the asumption of price elastic demand in a simple linear price regression.

Thanks in advance for any kind of comment on that problem!

The incorporation of a price elasticity in your regression requires that your dependent variable, quantity,  be logged as well.

Take an example of a basic demand side equation including two independent variables

$$Q_d=\beta_0+\beta_1 P+\beta_2 S+\mu$$

where $Q_d$ is quantity demanded, $P$ is the price of the good in question and $S$ is the price of a substitute.

To incorporate price elasticity in this regression you have to log your dependent $Q_d$ and then log price $P$ as well.

$$\ln(Q_d)=\beta_0+\beta_1 \ln(P)+\beta_2 S+\mu$$

Only via this framework can we calculate elasticity, given by $\beta_1$.

In terms of calculating equilibrium we would require the use of simultaneous equations where supply $Q_s$ is logged.

However this calculation of percentage change in $Q$ can be transformed easily by specific equilibrium quantity by using basic algebra such as:

1.$$Q_d=Q_s=Q^*$$
2.$$\ln(Q_d)=\ln(Q_s)=\ln(Q^*)$$
3.$$\mathrm e^{\ln(Q_d)}=\mathrm e^{\ln(Q_s)}=\mathrm e^{\ln(Q^*)}$$
4.$$Q_d=Q_s=Q^*$$

The same steps can be followed when calculating $P^*$.

Hope this helps.


Relationship between strong and weak axioms of revealed preference I keep seeing these following facts just asserted while reading:

Let W = weak axiom of revealed preference
Let S = strong axiom of revealed preference
Let C = the commodity vector

$W \iff S$ when $C \in R^2$
$W \not\to S$ when $C \in R^i, i>2$

I can't find the 1958 paper by Rose that most other papers cite but I am interested in the proof for 1.

My thoughts about it:

I think that any agent whose demand struct satisfies W for a two-dimensional commodity space must have rational preferences. Since his preferences are rational, his demand structure must satisfy S.
Is this roughly correct?

My questions:
1. Anyone have a reliable link to Rose's paper?
2. Anyone have a reliable link to any alternative sources?

If we are in $R^2$ and we have that xRy, is it true that the euclidean distance from the origin to x must be greater than the euclidean distance from the origin to y? If so, is it possible to use this property to show that $W\iff S$ in $R^2$?

The only journal that published it is behind a paywall:
http://www.jstor.org/stable/2296210?seq=1#page_scan_tab_contents but check your school library access for it.

The proof is pretty complicated and is based on an induction argument. When I've tried to link SARP and WARP, I've only ever found references to his paper.


Do reserves at Bank of Canada count as money? I read the following three statements concerning M1 and M2 in Canada:

a) "M1 consists of currency held outside the banks and chequable deposits of individuals and businesses."

b) "M1 does not include currency held by banks, and it does not include currency and bank deposits owned by the government of Canada."

c) "M2 consists of M1 plus all other deposits."

My questions about these quotes are:

1) Does "currency and bank deposits owned by the government of Canada" in (b) mean currency and deposits at the Bank of Canada? If not, are these deposits just deposits by the Canadian government at some other bank? And where does the government of Canada keep its currency?

2) If the above ^^ is correct that these are currency and deposits at the Bank of Canada, does "M2 consists of M1 plus all other deposits" in (c) imply that while deposits at the Bank of Canada are part of M2, currency held by Bank of Canada (ie its reserves) are not part of M2, ie Bank of Canada's reserves are not money?

1) Does "currency and bank deposits owned by the government of Canada"
  in (b) mean currency and deposits at the Bank of Canada? If not, are
  these deposits just deposits by the Canadian government at some other
  bank? And where does the government of Canada keep its currency?

Yes. The Canadian Federal Government consolidates its deposits in a single account (managed by the Receiver General) at the Bank of Canada. It does not bank elsewhere.

"Currency" in this context refers to Canadian bills and coins (and not foreign currency reserves). These are liabilities of the Canadian Federal government itself. Normal accounting practice is to net to zero any liabilities "owned" by the issuer on its own balance sheet.

  2) If the above ^^ is correct that these are currency and deposits at
  the Bank of Canada, does "M2 consists of M1 plus all other deposits"
  in (c) imply that while deposits at the Bank of Canada are part of M2,
  currency held by Bank of Canada (ie its reserves) are not part of M2,
  ie Bank of Canada's reserves are not money?

Once again. "currency" here means Canadian dollar bills, and they are liabilities directly issued by the Bank of Canada. This currency represents bills and coins that have been minted, and not distributed to private banks (or returned by banks). These are not considered "reserves" under any definition of "reserves." These notes/coins only enter the money supply when they are shipped to private banks.

(Note that Canada abolished bank reserve requirements -- the requirement for private banks to hold deposits at the central bank based on a percentage of their deposits. As such, "reserves" is no longer a meaningful term, you would need to be more specific - e.g., foreign currency reserves. If that is what you mean, foreign currency reserves are not normally considered part of the domestic money supply, except perhaps in cases where the country is "dollarised.")


Which are the different Schools of Economic Thought? It would be great to have a brief but comprehensive list of current (e.g. Austrian) and defunct (e.g Mercantilism) schools of thought in Economics. I think an ideal answer would include:

the defining features of the school, which enable it to differentiate it with the rest.
major authors/writers behind the school.
key papers/books/textbooks presenting/defending the ideas of the school of thought.

Note: To order the discussion and avoid very lengthy answers, I suggest we have one school of thought per answer (like they do in other forums, like TeX).

Post-Keynesian

Post-Keynesianism (PK) is based on the criticism of the so called "Keynesianism", which according to PKs is not loyal to core Keynes ideas. As such, this school of thought aims to be called the "true" Keynesians.

The criticism starts with the workhorse model of Keynesianism, the IS-LM model, developed by Hick in a 1937's article, right after Keynes magnum opus. According to Minsky (a prominent PK), this is

  an article which ... misses Keynes’ point completely’ (Minsky, 1969, p. 225)

Later in life Hicks acknowledge this, by stating that his model

  was Walrasian rather than Keynesian in origin (Hicks, 1981, p. 142)

Given this background, PK has the following core features in its method:

emphasis on disequilibrium rather than equilibrium (as in IS-LM).
rejection of rational expectations. Agents can make inaccurate estimates of future based on present information without need to be either fully rational or incredibly naive.
against microfoundations. PKs argue that "emergent properties" of a system, arising from the interaction of individuals, means a system cannot be understood from a simple extrapolation of the properties of a few agents (e.g. representative firm and household).
the use of Leontieff (fixed proportion) production functions. PKs reject the marginalist theory, and argue that the latter is empirically inconsistent (e.g. Blinder, 1998).
Money is not neutral. This is a straightforward Keynesian argument, also present in IS-LM. Modern approaches highlight the crucial role of banks in endogenous money creation, which is not dependent on reserves (e.g. Moore, 1979).
Government has an important role in stimulating aggregate demand. Also in line with IS-LM, PKs argue that effective demand is what matters for economic activity. Say's law is therefore rejected.

Some early authors of this discipline are Michael Kalecki, Joan Robinson, Nicholas Kaldor, Luigi Pasinetti, and Piero Sraffa. More recent authors include Wynne Godley, Steve Keen, Frederic S. Lee, and Marc Lavoie.

A recent introduction to PK can be found in Godley and Lavoie (2007). There is also a very comprehensive two-volume Oxford Handbook of Post-Keynesian Economics.

Sources: own research, and Keen (2013).


Literature / Evidence on Cash Hoarding of Firms I have received anecdotal evidence (heard stories) about many firms hoarding cash (liquid assets) post 2008 and not spending it despite availability of many projects with positive NPV. However, when I tried to find some research / data on this matter, I couldn't dig out too much.

I know that one can use compustat to get a grasp on liquid assets that firms have. Is there any other data on this matter? What papers would be starting points to read up on the related literature?

I know very little about this, but check out Jake Zhao's work. He's an AP at Stony Brook.

From the abstract,

  My model finds that 63% of the increase in corporate
  cash holdings can be accounted for by the increase in cash flow volatility.
  The increase in cash flow volatility observed in the data arises from a
  decrease in the correlation between revenue and operating expenses.

Accounting for the Corporate Cash Increase.

I imagine the references he includes will also be useful.

Edit: He uses compustat data.


Isn't money moving towards central bank in the long run? Central banks typically pumps money into the system by :

lending out to private banks
buying govt bonds

But in both these cases won't the central bank get back more money when it ends it's position (ie., initial money along-with the interest) and in the end more money from the system would get accumulated with the central bank.

A minor point, but central banks also pay for operating expenses. So they have to spend some of the surplus on salaries, building maintenance, etc. And they also get more surplus by printing physical money.

However in most countries it is included within the charter of the central bank that any surplus left over at the end of some period is to be transferred to the government treasury. The government is then free to spend this surplus.

This is one of the reasons for the seperation of the central bank and the government. If a government had control of the bank it could be tempted to instruct the bank to create a surplus and then use said surplus to finance government expenditures. This is deemed undesirable as it inreases inflation.

Should a central bank somehow end up with a deficit rather then a surplus it falls to the treasury to help them out (if needed).

You can read about details in the FED's charter:
https://www.federalreserve.gov/aboutthefed/section7.htm

The ECB also has a paper with some info on this. Point 2.1.:

  Overview of profit distribution and loss coverage
  In general terms, a central bank’s annual net profits (recognised positive and
  negative income, less operating costs) can either be passed on to shareholders
  (government and/or private sector) in the form of a dividend, or added to its financial
  reserves. In cases where a central bank has either both public and private ownership
  or only private ownership, the amount of profit that can be distributed to private
  shareholders is typically subject to a cap (ranging from 6% to 12% of the nominal
  value of the paid-up capital), while the remaining distributable profit, net of any
  transfers to equity (capital and reserves) goes to the government.


Relative risk aversion and lotteries exercise Given a consumer with a utility function, $u(w)$, and a wealth of $w>1000$. Assuming that the consumers relative risk aversion is constant and equal to 1, that is $R_r(w)=1$ for $w>0$, the consumer is facing a lottery that gives him 50% chance to win 1000 and 50% chance to lose 1000.

My question is, how much is the consumer willing to pay to avoid this lottery, and how does it depend on $w$? I can't seem to figure it out, and I really have no idea where to start.

You want the household to be ex-ante indifferent between taking the lottery and paying some $p$ and voiding it.

With van-Neumann-Morgenstein utility, the utility of taking the lottery is given by $$U_L(w) \equiv 0.5 U(w-1000) + 0.5U(w+1000)$$

Now, you're looking for a payment $p(w)$ such that $u(w - p(w)) = U_L(w)$.


Estimates for 'inflation expectations': the 'breakeven' rates. What are they? «Popular market measures of US inflation expectations are climbing sharply higher in the wake of this week’s Federal Reserve meeting, which analysts say hinted at officials being willing to tolerate higher inflation before tightening monetary policy more aggressively.

So-called “breakeven rates”, which are a rough estimate of expected inflation derived from comparing the yields of conventional and inflation-proof Treasuries, have jumped markedly this month, and have gone even higher since Wednesday’s Fed meeting»

Could you please explain how are these breakeven rates estimated? And why they can be a 'rough estimate' of expected inflation?

Any help would be appreciated.

Intuitively, this is the story: The interest rate on inflation-linked bonds (which means that the coupon payments are adjusted for inflation) can be seen as a real interest rate, because one is always exactly compensated for the realized inflation. Subtracting this real interest rate ($r$) from a nominal interest rate ($i$) gives the average inflation expectaction ($\pi^e$) over the period remaining before maturity. Just use the fisher-equation to see this: $r=i−π^e$.


Transformation of Cobb Douglas Utility So, I need to determine whether or not $u=x^{0.5}y^{0.5}$ exhibits the same preferences as $u'= log(x) + log (y)$. Any tricks I can use here? I've done the logarithmic transformation so that I now have $(0.5)log (x) + (0.5)log (y)$. My guess is, if I multiply these by $2$ I'll get $log (x) + log (y)$ and thereby proving that u and u' refer to the same preferences, but I'm not sure if this is correct?

Hint: how does a positive monotone transformation of the utility function affect the consumer's maximization problem?

Edit,

Suppose the optimal bundle for some agent with some utility function $u$ is given by $x^{*} = (x_{1}^{*},x_{2}^{*})$. Suppose then that I take the transformation of $u$ by some strictly monotone function $f$. I claim that $x^{*} = (x_{1}^{*},x_{2}^{*})$ is the optimal bundle for the new utility function $v = f \circ u$.

Suppose not, suppose that there is another bundle $\hat{x} = (\hat{x}_{1},\hat{x}_{2})$ such that $v(\hat{x}) > v(x^{*})$. But by the definition of $v$, we have $$\tag{In}\label{In} f(u(\hat{x})) > f(u(x^{*}))$$ Then, since $f$ is strictly monotone, it is invertible and so from \ref{In} we must have $u(\hat{x}) > u(x^{*})$, which contradicts optimality of $x^{*}$.

The $\ln$ function is one such strictly monotone function on domain $\Re_{+}$.


Is the contract curve orthogonal to the priceline? Consider an exchange economy with two consumers A and B, two goods x, y. Consumers have identical preferences $U=xy$. Total available endowment are $E_x$ and $E_y$.

This is the background of a homework question which does not ask but I got this question when I try to draw the Edgeworth Box.

I find the contract curve to be the diagonal of the Edgeworth Box, with slope $\dfrac{E_y}{E_x}$. I also find the price in this economy to be $\dfrac{p_x}{p_y}=\dfrac{E_y}{E_x}$.

Then I got confused that if we start from an endowment point (for example, at the bottom right corner) and trade to the contract curve to get an equilibrium, then the line we trade along is called the priceline right? And its slope should be $-\dfrac{p_x}{p_y}$ right? If I did all these correct, I find my priceline is not orthogonal to the contract curve.

It is more likely I made something conceptually wrong? Is the contract curve in this economy the diagonal?

You write that the slope of one line is px/py and of another is -px/py. Take a piece of paper and draw the line y=2x and y=-2x are they orthogonal (answer: no)? In particular case the lines y=x and y=-x are orthogonal.

If we regard it more formally, the vectors are orthogonal if the product is 0. Thus,

<1,-p>*<1,p> = 1-p^2

This is 0 only if p=1 or p=-1, i.e. if the quantities of the 1-st and 2-nd good are equal.

To take a loon on it. Consider the wealth distribution something like 1-st player: [5;
15], 2-nd: [25;5], thus ex=30,ey=20,px/py = 2/3, then it looks like this:

p.s. Calculations and plotting were made with pyEdgeworthBox package (I wrote it).


What model did the MONIAC use? Phillips designed a hydraulic computer to model the UK economy in 1949; 12-14 copies were built. What model did it compute with? How have modern models of the UK built on that work?

According to Bissell (2007),  MONIAC was based on a simple, first-order model of the dynamics of an economy (but authors also mention it could be recalibrated to higher-order models):

Let $u$ be the production flow, $v$ the consumption flow, $w$ the stocks and $p$ the price, all measured, for simplicity, from a base at which the system is in equilibrium. We have then, by definition, the identity
$$U-V={dw\over dt}$$
and three hypotheses,
$$\eqalignno{&\ \ u=lp\cr &v=mp}$$
and
$$w=np$$
where $l$ $m$, and $n$ are parameters.
If at time $t=0$, from equilibrium, there is a spontaneous change, $\Delta v$ in
consumption, then
$${dW\over dt}=u-(v+\Delta v)=(l-m)p-\Delta v$$
Also,
$${dp\over dq}={1\over n}$$
Therefore [after some manipulation] […]
$$n{dp\over dt}-(1-m)p+\Delta v=0$$
The solution of this equation,
$$p={\Delta v\over l-m}(1-{e}^{{l-m \over n}t})$$
gives the path of the induced price change. […]
This simple model could be further developed, in particular by making a distinction between working and liquid stocks, introducing lags into the production and consumption functions, and linking the demand curve for liquid stocks to the rate of change of price […].

The above is in its essence based on the idea of circular flow combined with some canonical Keynesian macroeconomics.
For example, just compare the diagram representation of MONIAC (picture on left from Media Archealogy wiki) to the circular flow diagram from contemporary Krugman's macro textbook (picture on the right). You will notice that there is some resemblance although they are not exactly the same.
This being said both MONIAC and circular flow diagram are didactic tools (MONIAC was used by central banks for some time, but the machine was originally intended just for classroom use). Hence the actual models do not directly build on this ideas even though they are connected.
Modern models that try to model economy such as dynamic stochastic general equilibrium (DSGE) models, relate to the MONIAC model only very superficially and don't build upon MONIAC model directly.


Measuring income effect before knowing substitution effect Suppose on the x axis we have shelter and on the y axis we have composite goods. Now, if the price of shelter increases, the optimal bundle changes from point A to point D. Standard textbook tells me to draw a line parallel to the new budget line B1, which is tangent to the indifference curve I0. In this way we can get the substitution effect. The income effect follows. My question is, can we reverse the two procedures and measure the income effect first by drawing a line parallel to the original budget line and tangent to the new indifference line?
Thanks!

You can definitely do so! There are two versions of the income effect. The one that you are referring to is called the Equivalent variation. The two ways of looking at the problem were introduced by Sir John Richard Hicks.
To see the impact of a price change in monetary terms, we ask how much money should have been taken before the price change to leave a consumer at the same utility level he attains after the price change.
This is the same thing as you had asked: can we reverse the two procedures and measure the income effect first by drawing a line parallel to the original budget line and tangent to the new indifference line?
I hope this has helped but if you wish to explore further, see the 'Consumer Surplus' chapter in Hal Varian's 'Intermediate Microeconomics'.


Longitudinal microdata on house migration patterns I am looking for a database that has longitudinal microdata for housing migration patterns.

Optimistically, the data would look something like:

In 2006, Person #2341 made $X, was Y years old, and lived in a Z year old house. In 2007, Person #2341 moved houses.

This way, I can see if we can use microdata to predict if a person is going to move within a year using his information currently via a logit regression.

The ACS database almost works, but it is ex post facto; it tells you the person moved a year ago (so I would be using a persons current information to predict if he moved LAST year; not what I want). I want to know if the person will move the following year, and theres no way to do this using ACS since it doesnt track the same person year to year.

The US Panel Survey of Income Dynamics (PSID) has this  data,  at least if pre-tax income will do.

  We use the 1999-2009 Panel Survey of Income Dynamics to estimate household move probabilities as a function of, among other things, current housing equity. The lock-in effect supposes that mobility decreases with equity, particularly as equity becomes negative. We find that while owners do move less than renters, the move probability increases as homeowners become underwater. The propensity to move out of state in particular increases dramatically for sand state homeowners who have negative equity. There is no lock in effect from negative equity.

Mobility and Mortgages: Evidence from the PSID (Colson and Greece (2013))

The NLSY may also have this data.


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

To an extent yes, tracking the money supply is somewhat helpful in determining inflation, but there are other important factors to consider.

Productivity?

Say there was a massive crop failure and the same amount of money.  Food prices (and prices in general) would go up, right?

What is money?

Do we just count government money (monetary base)?  There are aggregates for that, but if you've accepted a check for services before you know that you also accept bank money which does not have a 1 to 1 relationship with government money.  So you have to include bank money to determine how much money is the economy.  But what types of bank money?  Demand deposits?  M1?  Interest bearing deposits M2?  M3?  This is subjective...but it helps to look at many aggregates.

What about foreign trade?

If you count the money supply do you include say dollars in the USA or dollars abroad as well?  In some cases dollars are used a medium of exchange abroad and don't really come home, so they don't influence domestic prices like domestic dollars do.

What about foreign exchange

Currencies compete, and because they are fiat there is always the possibility that one currency (especially a smaller one in a weakened state) will suffer a confidence crisis and crash.  This can influence prices, yet the amount of money in the economy can stay the same.

So truely, you need to look at many factors to figure out inflation.  All that being said though the supply of money is still something very important to keep an eye on.


Learning Suggestion to better understanding on Advanced Microeconometrics (Master Degree Level) I am studying master in Economics and currently taking the compulsory course of Econometrics in which I have problem in understanding the materials. It is a must for me to pass this course in current semester, but I have little confidence to succeed it with my knowledge at this time. The book used in the course is "Econometric Analysis of Cross Section and Panel Data" by Jeffrey Wooldridge.

I don't have the proper basic understanding of first three chapters in the book consisted of The Stochastic Setting and Asymptotic Analysis, Conditional Expectations and Related Concepts in Econometrics, and  Basic Asymptotic Theory. Therefore, it would be tougher to understand the following chapters.

So what is your suggestion for me to figure out this? Perhaps the beginner-friendly books of Statistics or Econometrics? Or other tips and trics?

Maybe some of you have experienced the same situation in the past, then you can share how you figured out and have done with this problem.

I appreciate for your help. Thanks in advance!

This youtube channel has excellent videos for metrics:

https://www.youtube.com/channel/UC3tFZR3eL1bDY8CqZDOQh-w


The Econometrics of the Stone Geary Production function The Stone-Gerry production function generally takes a form of:
$$f(x_{i})=\prod_{i=1}^n(x_{i}-a_{i})^{\gamma_i}$$

where $x_i$ represents all inputs in the model, $a_i$ is a constant representing the initial investment which does not contribute to production and $\gamma_{i}$represent output elasticies.

when running a regression and converting it into a production function (which was already discussed on the site) how should our inital regression look when we have constants $a_i$ included?

Stone-Geary production functions attempt to reflect the real-world observation that for production to be feasible, there exist minimum thresholds in the quantities of inputs employed. This is not about initial investment but that one cannot use miniscule levels of inputs and obtain "very little" output -for production to even begin, one needs input amounts above a certain threshold, dictated usually by technology. At the aggregate (market or macro level), perhaps this effect practically vanishes, but for firm-level data, this may be an important feature of actual production.

Assume that we have data for $i=1,...,n$ firms and we postulate the existence of a Stone-Geary production function

$$q_i=f_i(\mathbf x_i;\mathbf a_i) = A\prod_{j=1}^K(x_{ji}-a_{j})^{\gamma_j}$$

The model is non-linear in the parameters, and It will remain non-linear in the parameters even if we take the natural logarithms. So one could in principle consider Non-linear Least Squares (NLS) estimation using the above specification without taking logs, but it is advisable to do take logarithms, because it lends a "degree of linearity" in  the model which will only do good  to the NLS estimator and the iterative estimation algorithm that it will be used by the software, since no closed form solution exists. So we specify, for $K$ non-constant regressors,

$$\ln q_i =\ln A + \gamma_1\ln(x_{1i}-a_{1})+...+\gamma_K\ln(x_{Ki}-a_{K}) +u_i,\;\;\; i=1,...,n$$

where we want to estimate the gammas and the alphas plus the constant term... Note that the above specification assumes that the "thresholds" (the alphas) are the same for all firms, per regressor (they are not indexed by $i$). So in all we are estimating $2K+1$ parameters with a cross-sectional sample of size $n$ and we must have $2K+1 < n$.

Also, note that $A$ is the level of of output when all inputs exceed their threshold by one unit.

The NLS estimator requires starting values for the coefficients. For the gammas, one could run OLS by setting the alphas equal to zero and use the OLS estimates as starting values. For the alphas, one could start by setting them equal to zero, except if one has some idea about what they could be approximately.

A good thing of such an approach is that the estimated thresholds can be checked for plausibility, using existing knowledge about production processes, which provides a non-statistical test for the validity of the specification.

An open access paper discussing the approach with empirical applications can be found here.


why is aggregate demand equal to aggregate expenditure? AD is how much the people in market demand (or want to buy) goods and services. On the other hand, AE is actually how much they end up spending.

AD = AE = C+I+G+X-M

I can demand and not buy? wouldn't that make AE unequal to AD? so how can it be equal?

Please, help. Thank you!

When we say that AD=AE we don’t mean that aggregate demand function is equal to aggregate expenditure - we mean by that the actual total quantity (Q) demanded on the market given the aggregate prices at a specific period of time is equal to aggregate expenditure. Aggregate expenditure is equal to the sum of all spending on output (Q) sold in the economy at the given time.

They must be equal because the total quantity demanded is actually quantity that’s being purchased on the market - it’s not some hypothetical demanded quantity that’s not purchased.


Who exploits comparative advantage in international trade? Suppose that under autarky, Colombia makes coffee and cars at \$1 and \$2 each, and Japan makes coffee and cars at \$20 and \$10 each. Since Japan has a comparative advantage in car manufacture, the standard theory says that Colombia will import cars and export coffee.

However, I'm having a hard time imagining how this actually happens in practice. If I run a Colombian car business, why would I import cars from Japan, when they cost five times as much? Why not just buy cars at home?

In general, I see no reason why any business dealing in a single market should care about price ratios; they only see the absolute prices of a single good. For the trade to actually happen in this case, you'd either need a company that trades both cars and coffee (do those actually exist?) or government-controlled trade. Neither of these feel realistic.

If we can look at Ricardo's original example, the same problem appears. Ricardo is assuming that production across an entire country is synchronized in some way; his theory would work if a single business in each country controlled all production of all goods there. But I don't see how the logic holds if there are separate companies producing cloth and wine.

In real life, how are comparative advantages actually exploited?

It's fine to make a supposition that it costs Colombia twice as much to make cars as coffee, and Japan twice as much to make coffee as cars.  It's also fine to express these ratios in terms of the respective local currencies.

The apparent problem you describe only arises because you go beyond the above and express the costs in terms of a common currency (\$).  But in a situation of autarky, there is no way in which the exchange rates needed to convert prices in other currencies to \$ could be determined. Thus your supposition is incoherent.

The way in which comparative advantage would be exploited, given the ratios you describe and given free trade, is that the rate of exchange of Colombian to Japanese currency would adjust to a level at which, in both countries, Colombian coffee is cheaper than Japanese, and Japanese cars are cheaper than Colombian. The Colombian car business will then be able to benefit from comparative advantage while not needing to look beyond the relative prices of locally produced and imported cars.

Addendum:  If, in the past, two countries both used gold as a currency, this would not, given autarky, be equivalent to a common currency. Even if the gold were physically the same, it might just happen (eg for geological reasons) to be scarcer and therefore more valuable in one country than the other.  In the absence of international trade and of payment in gold for traded goods, there would be no mechanism to equalize the value of gold in the two countries.  It would therefore be feasible that the cost, in terms of their respective gold currencies, of producing every good would be higher in one country than the other.  Given free trade, however, the value of gold in the two countries would be equalized at a level at which some goods would be cheaper in one country and some in the other.  The mechanism for equalization would be that people and businesses in the more expensive (and therefore more gold-abundant) country,  taking their own rational decisions and without any need for central control, would import goods from the cheaper country, paying in gold and therefore causing an outflow of gold to the cheaper country.


Regression on a constant If I have observations of $y_{i}$ and $x_{i}$ which are i.i.d. I also have OLS assumptions such as $E(\epsilon_{i} \mid X_{i})= 0$, my qustion is:
If I project $y_{i}$ onto a constant $\mu$, that is, we have model
$y_{i} = \mu + \epsilon_{i}$. Does finding the OLS estimator $\hat\mu$ has anything to do with $x_{i}$? Because in my opinions, $x_{i}$ never emerges.
Thanks~

So basically the question is:
If I know the average ($\hat{\mu}$) of the daily temperatures ($y_i$) of last year, does that tell me anything about how many people were born ($x_i$) each day?

Unsurprisingly the answer is no.

The most you can get is the average of the $x_i$ series if you have the parameters of an unbiased regression between $x_i$ and $y_i$.