What does efficient and inefficient innovators mean? I have been reading through this article about Innovation Indexes.

In this, I have come across the terms: "Efficient Innovators" and "Inefficient Innovators" in this plot:

So, what do they mean? And how are they calculated/determined?

My understanding of this chart is based on the Global Innovation Index 2015 report. Definitions are not explicit however.

They compute an Innovation Efficiency Ratio as the ratio of the "Output Sub-Index" score  over the "Input Sub-Index" score (definitions of these scores are presented in Figure 1). It is designed to assess the effectiveness of innovation systems and policies. In other words, this ratio shows how much innovation output a given country is getting for its inputs. Based on Table 1, all the countries with a ratio over the median (.71) appear to be considered as "efficient innovators".

For instance, Angola and Côte d'Ivoire do not show significant innovation input and  output  results,  yet  their  efficiency ratios appear high because their outputs outweigh their inputs on a low level.


Applications of Optimal Transport in Economics The 1975 Nobel Prize winner in Economics was Kantorovich who reformulated the optimal transportation theory of Monge and applied it to optimal resource allocation. The Wasserstein distance is central to this optimization model.
Can anyone familiar with optimal transport give an overview of some of its applications to economics? maybe beyond just moving mass/products to separate destination points. It's hard to understand how production, consumption and pricing comes into the picture compared to non-economics optimal transport.
If they even are still in use, how have these methods been developed and improved for economists in recent publications?

Optimal transport methods are very much still in use in economics. The show up in two-sided matching with side-payments, contract theory, hedonic pricing, partial identification in econometrics, and a couple of other areas. You can find an excellent overview of economic applications in the 2016 book Optimal Transport Methods in Economics by Alfred Galichon.


Is a universal basic income possible in the United States? Is a universal basic income or unconditional demogrant possible in the United States? (For the sake of specificity I have focused the question on the US, though the question is certainly interesting in all settings.)
It seems that without some restructuring, the answer is no. But, in order to entertain the idea (and pushing politics aside), what programs could/would be cut in order to fund a reasonably sized basic income? What size of basic income could be afforded, if any? How would tax rates have to change?

Of course the answer depends on the size of the basic income. It would be interesting to see how the answer would change for multiple values.

This is a good question. To be concrete, I think it's easier to pick a single number - this is arbitrary, but I'll go with the figure of $10,000 offered in the proposal by Charles Murray (one of the most prominent conservative supporters of a universal basic income). I'll assume that this is offered to every adult in the US age 18 and over, expanding slightly on Murray's 21 and over proposal.

This would be about 85% of the average poverty level for a single individual, just above 50% of the poverty level for a single parent with two children, and (at $20,000) about 85% of the poverty level for a family of four with two parents and two children.

The direct budgetary cost of this program, of course, is easy to calculate: it is the number of Americans age 18 and over, times \$10,000. There are about 245 million American adults currently, making this cost \$2.45 trillion. This compares to total federal government expenditures that are currently about \$4 trillion. (See this NIPA table for some figures.) Remarkably, the sum of "government social benefits" and "grants-in-aid to state and local governments" (the latter of which is almost entirely grants for social programs like Medicaid) is currently about \$2.4 trillion. Hence, to a first approximation, we could say that the federal government could afford the $10,000 UBI given its current budget if it eliminated all other existing transfers.

How plausible is this? Not very. More than 75% of the federal government's transfer spending is on three programs: Social Security, Medicare, and Medicaid. This spending is overwhelmingly concentrated on the elderly, with some also on the disabled (SSDI and Medicaid) and children (Medicaid). Taking away these programs and replacing them with the basic income, which is distributed evenly throughout the adult population, would surely leave these groups receiving far less in total than they currently do. This would be politically near-impossible to push through, and any sudden change would be dubious on policy and moral grounds too. (Even if one doesn't like the distribution of transfer spending embedded in these programs, millions of people have planned their lives around it.)

This is just one case of a basic point - which is that unless one plans to achieve massive savings through improved administrative efficiency or improved work incentives, any reallocation of the existing transfer pie will involve offsetting winners and losers. Since existing transfer recipients (aged, disabled, poor children, etc.) are targeted for a reason, such a shift may be quite painful. Moreover, any improvements in administrative efficiency are unlikely to be large enough to save much money; the more likely source of savings would be improved incentives, particularly relative to the dysfunctional disability system and perhaps current overspending on health care. But I haven't seen a case made that these would be anywhere near large enough to make a UBI work within the current budget without large losses to some existing party.

On a more positive note, I should mention that the headline cost of the UBI may not be quite as bad as it looks. Since the current tax-and-transfer system embeds very large implicit marginal taxes on some beneficiaries, it would be possible to replace these with higher explicit marginal taxes to claw some of grant back, without incurring additional distortions at the margin. That said, these high marginal taxes are heavily concentrated in certain segments of the population (e.g. single parents with children). The US tax-and-transfer system currently makes heavy use of tagging, which saves money at the expense of potentially perverse social incentives (conservatives have complained about incentives for low-income parents to avoid marriage for years). Doing away with tagging could limit these particular bad incentives and concentrated high marginal rates, but necessitate moderately higher marginal rates throughout the population.

Finally, if it is not realistic to eliminate existing transfers, we can think about how difficult it would be to establish a UBI through increased taxation. If (given the substantial existing transfers to the elderly) we limited the \$10,000 to adults below age 65, we are down to a population of about 200 million and cost of \$2 trillion. Since personal consumption expenditures are currently about \$12 trillion, (unrealistically) assuming a constant tax base these \$2 trillion could be raised through a 24% VAT with 70% coverage. This would be quite high, but not totally out of line with international norms. Furthermore, since current GDP is about \$17.5 trillion, and additional \$2 trillion in transfer spending (again unrealistically assuming constant GDP) would increase the US's overall tax intake as a share of GDP by 11.5 percentage points. This would make the US similar to the typical European country, still below states like Denmark, Sweden, and France with the highest taxation.


Could lexicographic preferences on N^2 be represented by a utility function u: $N^2$ to $Z$? I got this question on a homework:
Could lexicographic preferences on $N^2$ be represented by a utility function u: $N^2$ to $Z$?
I've heard countless times that lexicographic preferences can't be represented by a utility function. But would anything change if u: $N^2$ to $Z$?

If it is a lexicographic preference on $R^2$, the question sounds weird and I don't know if it can be represented by a utility function from $N^2$ to $R$. The domain of the utility should be the same as the domain of the preference relation, otherwise they cannot represent each other for sure.
Now suppose that, you mean, we have a preference on $R^2$, but we are only taking some data from the $\mathbb R^2$, for example only those data in $N^2$, and see that if we could represent those $N^2$ data by a utility defined on $N^2$. This way, I think the problem becomes more interesting and meaningful.  (Ok, so now the question is edited this way.)
If it a lexicographic preference on $N^2$, I think it can be represented by a utility function from $N^2$ to $R$.
The proof should be obvious in this case. A simple construction suffices.
If you have further questions on this case, please do let me know in comment.
Now let's think about the case of $u:N^2\to Z$. This problem becomes more complicated. To solve this problem, you first need to get used to the proof that a lexicographic preference on $R^2$ cannot be represented by utility function with $R$ as codomain. By applying the same method, you'll see that a preference on $N^2$ cannot be represented with a utility with $N$ as codomain. Then going from $N$ to $Z$ will not take much efforts.


Why are real median household incomes stagnant? This image shows US real median household income.

It seems remarkable for its lack of growth over the last 20 years. This has been the subject of much political debate (around the "1%" and "occupy Wall Street" movements, etc.) but I am interested in more objective economic analysis of this phenomenon.

Given that people are better educated and are working with better technology (which should make them more productive), and that the real economy has grown more generally, what economic theories can explain the lack of growth in real median household income?

The metric of median household income is also used by others to argue the presence of income inequality:
https://en.wikipedia.org/wiki/Income_inequality_in_the_United_States#Causes
However, it seems that it is not only the median but also the mean that stagnates:

(I used family instead of household income because I could not find a time series for mean household income.)
If the problem was only one of inequality then the mean income should still increase.
I think there are several reasons why median household income seems to stagnate.
First of all I think there is a visible upward trend that is only somewhat masked by the 2008 financial crisis. Granted this trend is still smaller than the increase of productivity. Why median household income grows at a slower pace than before is still a question.
I think the problem arises because neither the number of households nor their distribution is constant.
Changing size of households
One thing that I believe has an effect is that [average household size has decreased over the period you are looking at][3].

(I had some trouble opening the Census Bureau's xls files.)
So while total household income has in fact increased it is now divided between more numerous, smaller households making both the mean and the median smaller.
Changing composition of the US labor force
Another reason might be immigration. According to [this site][6] (I don't know if the statistics are reliable, there are a lot of links on the site I consider to be politically biased) the mean immigrant income is lower than the mean 'native' income. This is not surprising, immigrants need time to adjust and build the social networks necessary to get good jobs. Depending on the measure of productivity you use this can mean that while productivity in any given industry increases the weight of low-productivity industries increases as well. Thereby immigration may decrease mean and median income.
Note that this does not imply anything about the effect of immigration on the welfare of 'natives'. I am not claiming that the median household income of 'natives' is increased or decreased, I am pointing out that the weights used in the calculation are shifting.


Multiple regression. How do I plot a multiple regression graph? Shall it be a many dimensional plane(equals to number of explanatory variable)? Or will be the line for each beta, since the slope or beta is the partial derivative of y(explained) with respect to that particular x(explanatory)??

In principle it's a plane for 2 independent variables or a hyperplane for more. An exception is when your independent variables are a continous and a dummy variable. In that case the dummy basically changes to the intercept only so you could show two lines with different intercepts.

A work around if you have 2 continuous independent variables is to show the relation between the dependent and one independent for several values of the other independent.


Are there any other rational preference relations without utility function representations, besides Lexicographic? It seems like lexicographic isn't that "special". Like yes it is special in that supposing it has a utility function gives you a bijection from the rationals to the reals, but I mean unique in some sense. I know that it satisfies a bunch of nice properties, but it still feels like there should be plenty of other (rational) preference relations that don't have utility representations.

Yes, there are many. Here are some examples :

Consider the weak preference relation $\succsim$ defined over $\mathbb{R}^2$ as:

Example 1

$(x_1, y_1) \succsim (x_2, y_2)$

if and only if

either ($x_1+y_1 > x_2 + y_2$) or ($x_1+y_1 = x_2 + y_2$ and $x_1 \geq x_2$)

Claim : $\succsim$ cannot be represented by a utility function.

Proof : Suppose by contradiction that there existed a utility function $u$ representing these preferences. For each $a > 0$, we have $(a, 0) \succ (0, a)$, and therefore, $u(a, 0) > u(0, a)$. We can therefore assign to $a$ a non-degenerate interval of values satisfying the above inequality
$I(a) = [u(0, a), u(a, 0)]$. For any $a > b > 0$, all commodity bundles generating utilities in the interval $I(a)$ are strictly preferred to those in the disjoint interval $I(b)$ and should therefore be assigned a greater utility level. Then in each of these intervals we can pick a distinct rational number in increasing order to represent preferences. Since $a \in \mathbb{R_{++}}$, there are uncountably many such intervals, but set of rational numbers are countable. This results in a contradiction.

Example 2

$(x_1, y_1) \succsim (x_2, y_2)$

if and only if

either ($\min(x_1,y_1) > \min(x_2,y_2)$) or ($\min(x_1,y_1) =  \min(x_2,y_2)$ and $x_1+y_1 \geq x_2 + y_2$)

Claim : $\succsim$ cannot be represented by a utility function.

Proof : Suppose by contradiction that there existed a utility function $u$ representing these preferences. For each $a > 0$, we have $(a+1, a) \succ (a, a)$, and therefore, $u(a+1, a) > u(a, a)$. We can therefore assign to $a$ a non-degenerate interval of values satisfying the above inequality
$I(a) = [u(a, a), u(a+1, a)]$. For any $a > b > 0$, all commodity bundles generating utilities in the interval $I(a)$ are strictly preferred to those in the disjoint interval $I(b)$ and should therefore be assigned a greater utility level. Then in each of these interval we can pick a distinct rational number in increasing order to represent preferences. Since $a \in \mathbb{R_{++}}$, there are uncountably many such intervals, but set of rational numbers are countable. This results in a contradiction.


Do free-trade economies typically offer any protection for domestic markets? The aimed-for outcome of the protectionist could be said to be the shielding of domestic markets from competition with an "unfair" advantage. For example, an emerging economy might have non-existent workers' rights enabling lower production cost.

However, discussions surrounding naive protectionist policies typically descend into "define a biscuit" type arguments. In short: the difficulty in defining the boundaries of tariffs quickly turns arguments to farce.

But there must be other, better ways to achieve the desired outcome. I have read that in the early 2000s Germany "protected" its intra-EU car sales by ensuring EU emissions regulations were closely aligned with the emissions of their own diesel engine technology making market entry by (for example) American cars with big petrol engines more difficult. Whether this is apochryphal or not, the point remains.

Do free-trade economies typically endeavour to protect themselves in ANY way, or does "free mean free" in the minds of these legislatures?

I think the (or at least, a) relevant concept is that of non-tariff barriers to trade. Wikipedia has a nice summary.

Let me quote a couple of sections from the article:

  Non-tariff barriers to trade (NTBs) or sometimes called "Non-Tariff Measures (NTMs)" are trade barriers that restrict imports or exports of goods or services through mechanisms other than the simple imposition of tariffs. The SADC says, "a Non-Tariff Barrier is any obstacle to international trade that is not an import or export duty. They may take the form of import quotas, subsidies, customs delays, technical barriers, or other systems preventing or impeding trade." According to the World Trade Organisation, non-tariff barriers to trade include import licensing, rules for valuation of goods at customs, pre-shipment inspections, rules of origin ('made in'), and trade prepared investment measures.

-

  According to statements made at United Nations Conference on Trade and Development (UNCTAD, 2005), the use of NTBs, based on the amount and control of price levels has decreased significantly from 45% in 1994 to 15% in 2004, while use of other NTBs increased from 55% in 1994 to 85% in 2004. [...] The need to protect sensitive to import industries, as well as a wide range of trade restrictions, available to the governments of industrialized countries, forcing them to resort to use the NTB, and putting serious obstacles to international trade and world economic growth. Thus, NTBs can be referred as a new of protection which has replaced tariffs as an old form of protection.

So regulatory and similar barriers to trade have become widespread—often as a way to circumvent restrictions on protectionism.


Costs of transportation I assume that it makes sense to ask for the energy costs of transportation of different goods per weight and volumetric mass density, depending on the means of transportation (truck, train, ship, etc.) and on the distance of transportation.

I assume that there are either data or plots for this, but I don't know where to find them. A typical plot I'm looking for would answer the question:

  How much energy (including losses) does it take to transport one
  metric ton of good X (having volumetric mass density $d$) by train for
  100 resp. 1000 miles, today and 100 years ago?

In case you don't find this question (or approach) sensible, please tell me why.

Background: I'm planning a data visualization project of transportation of all kinds of goods. One part of the project will be the routes of transportation: along which paths and for what distances are which volumes of goods transported? (On a global and a local level.) Another part shall be the costs of transportation (to which finally will also count the costs of lifting goods, e.g. in a harbour, but maybe these are negligible).

The paper "The impact of scale on energy intensity in freight transportation" by Gucwa and Schaefer has some of the information you need. Figure 5 from that paper is presented below:

The site ShipMap.Org has a data visualisation of shipping routes, where you can filter by type of freight.

(Disclosure: these are all colleagues of mine except Gucwa)


K-step ahead forecast of VAR(2) I am trying to determine how to write the K-step ahead forecast of a VAR(2), with two variables, as a weighted average of its mean and last observations. I understand that one must use companion form, but am unsure of how to derive the weights from it. Any guidance is much appreciated. Thank you.

I'm not a VAR specialist, but it could go along the following lines.
First write the VAR in companion form:
$$
X_{t+k} = A + B X_{t+k-1} + E_{t+k-1}.
$$
Where $t$ is the last observation, $E_j$ are the errors and $A$ and $B$ are fixed coefficients.
Then solving recursively:
$$
\begin{align*}
X_{t+k} &= A + B X_{t+k-1}+ E_{t+k-1},\\
&= A + B(A + B X_{t+k-2} + E_{t+k-2}) + E_{t+k-1},\\
&= (I + B)A + B^2 X_{t+k-2} + B E_{t+k-2} + E_{t+k-1},\\
&= (I + B)A + B^2(A + BX_{t+k-3} + E_{t+k-3}) + B E_{t+k-2} + E_{t+k-1},\\
&= (I + B + B^2)A + B^3 X_{t+k-3} + B^2 E_{t+k-3} + B E_{t+k-2} + E_{t+k-1},\\
&= \ldots\\
&= A \sum_{j = 0}^{k-1} B^j + B^{k} X_t + \sum_{j = 0}^{k-1} B^j E_{t+k-j-1}
\end{align*}
$$
Then taking conditional expectations and using $\mathbb{E}(E_j|X_t) = 0$, gives:
$$
\mathbb{E}(X_{t+k}|X_t) = A \sum_{j = 0}^{k-1} B^j + B^{k} X_t.
$$
If we let $k \to \infty$ and if $B^k \to 0$ (i.e. the process is stable) we have that:
$$
\mathbb{E}(X_{t+k}|X_t)\to \mathbb{E}(X_\infty) =  A \sum_{j = 0}^\infty B^j = A(1 - B)^{-1}
$$
Substituting $A = \mathbb{E}(X_\infty) (1- B)$ gives:
$$
\mathbb{E}(X_{t+k}) = \mathbb{E}(X_\infty)(1- B) \sum_{j = 0}^{k-1} B^j + B^{k} X_t.
$$
This is a weighted sum of $\mathbb{E}(X_\infty)$ and $X_t$. In fact a weighted average as the weights add to the unit matrix:
$$
(I - B) \sum_{j = 0}^{k-1} B^j + B^k = \sum_{j = 0}^{k-1} B^j - \sum_{j = 1}^{k} B^j + B^{k} = B^0 - B^{k} + B^{k} = I
$$


Why are the formulas for price elasticity of supply and demand the same in intro microeconomics? I get that they are both gauging responsiveness, but I don't particularly understand why they are the same formula.

The elasticity is a very general concept. Consider an arbitrary function

$$y=f(x_1,x_2, \cdots , x_n) $$

The elasticity of $y$ with respect to $x_i$ is

$$ e_{y,x_i} = \frac{\partial y}{\partial x_i}\frac{x_i}{y} $$

It measures the percentage change of $y$ when variable $x_i$ changes by 1% - a measure of responsiveness, as you say. It can be applied to anything, including the demand and the supply, where you get the common concepts like own-price, cross-price, income elasticity, etc. The sign of the elasticity is given by the sign of the derivative, which depends on the function $f(\cdot)$.

Elasticities applied to functions other than standard demand and supply abound. For example, individual factors of production, relative factors of production, investment, taxation, preferences, city size, et cetera.


Why did it take so much QE by the ECB to raise the Eurozone inflation to 2%? From 2015 to 2018 the ECB increased the money supply by around 20% (around 6% y/y), with a GDP increase rate under 1%. Yet the inflation rate remained under 2%. A back-of-the-envelope calculation would expect a much larger inflation rate (around 5% or more). What happened?

UPDATE: here is my calculation: using a quantity of money model: $Y P = v M$
where $Y$ is the GDP, $P$ is the price level, $v$ is the money velocity and $M$ is the money supply, then the inflation (rate of variation of $P$) is the rate of variation of $M$ less the variation of $Y$, that is about 6% - 1% = 5%

Because commercial banks have used injected liquidities to consolidate their balance sheet instead of stimulating demands by creating credits (that did not previously exist when they make loans). This is called the money multiplier effect. The multiplier was somehow blocked (to ~$1$) because of their precaution behaviour, and so was the money velocity.

On March 10, 2016, the ECB has even considered the possibility of giving 200€ per month and per person to stimulate inflation. And this with the main idea of circumventing the commercial-bank system. This unconventional monetary policy is called monetary helicopter.


Gold coins as currency? My question is about gold standard. But not the version I always see mentioned (trading bills for gold at a set price). I mean having gold coins in circulation.

For example, new currency consists entirely of gold coins (various sizes/purity diluted with worthless metal). The ratio is 1¢/mg with coins ranging from 1 cent to 100 dollars (worth roughly 5x that in current money). The 100 dollar coin maybe being pure gold (quarter-sized, used mostly for saving).

This system seems to have a few good advantages. Simple to understand, minimal inflation (I think), people owning real value instead of worthless paper/plastic being trusted etc. How well would this system function and what possible problems are there with it?

Here are three types of money:

Commodity money: goods of value are used as money (e.g. gold in your example, or cigarettes in a prison),
Representitive money: money is still based on a commodity but, instead of actually using that commodity in exchange, they use pieces of paper that can be exchanged for the commodity (e.g. the gold standard),
Fiat money: money with no intrinsic value, which is trusted by people because they government tells them it will be the official medium of exchange into the indefinite future (e.g. the modern US dollar, British pound, Euro, etc.).

A fourth type that is emerging (e.g., in the form of Bitcoin) has no intrinsic value and no official backing from government. It is accepted in exchange solely because people believe that will be able to spend it again in the future.

The physical burden of physical money

Firstly, there is a serious practical problem associated with commodity money in its purest form, namely that transporting and storing the money is difficult and expensive. If I want to buy a house, am I supposed to work around with half a million dollars worth of "stuff" in a briefcase and hope nobody steals it? What if I want to buy a book from Amazon? Do I have to send them some gold coins in the mail?

At the very least, these considerations are going to compel people to use representative rather than commodity money.

The problem of debasement

Where commodity money has been used historically, it has been exposed to the problem of "shaving". Since the currency is intrinsically valuable, there is an incentive to shave a tiny amount off of each coin (such that the difference is indistinguishable from normal coin wear) and melt those shavings together into a piece of precious metal that can be sold. You can read more about this here.

Takes away some valuable policy tools

Imposing a commodity money would take from the government some valuable tools to deal with economic shocks. In particular, it reduces the ability of the government to use monetary policy to reduce the real effect of economic downturns. For example, during the most recent recession, major governments engaged in "quantitiative easing", which saw them creating new money to stimulate the economy. This would be much more difficult if creating new money meant having to dig a significant quantity of gold out of the ground of another country.

Additionally, it is not obvious how big/genuine the advantages you describe are. For example, here is a plot of US inflation:

Note that inflation tended to have higher peaks and be much more volatile during the first half of the C20 than in recent years. But that was exactly when the gold standard was in effect and the value of currency was directly tied to a physical commodity. Also, deflation was more common then, which is problematic because deflation has a number of damaging effects on an economy. Modern policy makers are better able to regulate the money supply to control inflation and keep it around the low and stable levels thought to be optimal.

People might be more willing to trust commodity money. But they would have to overcome concerns about counterfeiting and debasement. Recent experience from the last half century has been that people in stable democracies are, in fact, quite willing to trust fiat money.

Edit in response to comment:

It's true that precious metals are sufficiently valuable that large quantities are not needed to make most payments. But the problem remains that (a) if I am carrying them around to make payments then I am subject to a new source of  theft/loss that is less acute with electronic financial balances; (b) insisting on a physical commodity money makes it hard to transact remotely (e.g. buying goods online or remitting money to pay for bills or an invoice); (c) businesses regularly need to spend, store, and move money on the order of millions or sometimes billions; often across borders or oceans. Moving from a world in which money can be stored and moved at essentially zero real cost, with essentially zero delay, to one where we are burning real resources to move physical stuff around would be a huge technological step backwards.
I don't understand what you mean about debit cards. Your whole question started out with "...not the version I always see mentioned (trading bills for gold at a set price). I mean having gold coins in circulation..." i.e. we are talking about commodity money, not representative money. Yes, debit cards fix the problem of physics, but they also mean we aren't talking about commodity money any more. Having a debit card you can hand to your bank in exchange for gold is really equivalent to having a US dollar banknote that you can hand in to exchange for gold.
Yes, the US dollar has lost a lot of its purchasing power. But that's a good thing! There are numerous economic benefits to a low (but positive) stable rate of inflation. Inflation per se is not bad, it only becomes problematic when we have either very high levels of inflation, or when the rate of inflation is not stable (both were true under the gold standard).


A guide to hyphenation in economics? In the econ literature, what is the convention when it comes to (not) hypenating some common terms like:

first(-?)best, second(-?)best,...
best(-?)response?
...

The Economist suggests that "There is no firm rule to help you decide which words are run together, hyphenated or left separate" so I thought people here could be more aware of the conventions in econ than people, say, at http://english.stackexchange.com.

Plamen Nikolov of Binghamton University presents a brief treatment of this in "Writing Tips For Economics Research Papers". He notes that there are two basic rules of economic usage:

  "Long run" (without a hyphen) is a noun. "Long-run" (with a hyphen) is
  an adjective. Same with short(-)run. and "Saving" (without a terminal
  s) is a flow. "Savings" (with a terminal s) is a stock.


How to prove a generalised function is quasiconcave? I have a question I have been asked to solve:
Given that $(a_1, a_2,...,a_n)\in R_{++}^n$ and $(x_1, x_2,...,x_n)\in R_{++}^n$, and $A>0, \mu >0, p \neq 0$, if there is a function $f(x)=A(a_1x_1^p+a_2x_2^p+...+a_nx_n^p)^\frac{\mu}{p} \space \space \forall x \in R_{++}^n$, show that function $f$ is a quasiconcave function over $R_{++}^n$ when $p \in (0,1]$.
I understand that to show a function is quasiconcave, it needs to satisfy this definition:
$f:_+^→$ is quasiconcave on $_+^$ if and only if $∀,∈_+^$ and for all $\in(0,1)$
$f(+(1−))≥\{f(),f()\}$
I am wondering how I would use this definition to show that a generalised function $f$ is quasiconcave, or if I should be approaching this from another concept/definition.

Note first that the function $r\mapsto A(r)^{\mu/p}$ is strictly increasing on $\mathbb{R}_+$. When you look at the minimum in the definition of quasi-concavity, you can therefore ignore this part and it suffices to show that the function
$$(x_1,x_2,\ldots,x_n)\mapsto a_1x_1^p+a_2x_2^p+...+a_nx_n^p$$
is quasi-concave. Actually, the function is even concave. The sum of concave functions is concave, so it suffices to show that the function
$$(x_1,x_2,\ldots,x_n)\mapsto a_ix_i^p$$
is concacave for each $i=1,\ldots,n$.


Mechanism design when the set of feasible decisions depends on types Q : Can the tools of mechanism design be applied when the set of feasible decisions $D$ depends on the types $\theta$?
For example, when $d \in D$ represents the total funding allocated toward some good and $\theta_i$ represents the funds $i$ has available, $D = \{ d | 0 < d < \sum\limits_i\theta_i\}$.
Q : If not, is there some other approach that analyzes this sort of scenario?

Yes, they can, because the utility function typically depends on the type. A particular action unavailable to a type can be modelled as that action yielding so low utility that it is never chosen no matter what other players do. Then apply standard mechanism design to the appropriately modified utility function.


How does the fractional reserve banking system work? I would like to understand better exactly how this works. I have heard a lot recently (particularly since the 2007-08 crash and Occupy movement) about money creation in particular (usually with a very negative bias). However, these descriptions often only go so far into it and I am curious whether it is really so bad once one has the full picture.

I'd like to go through a simple example and point out where I am unsure what is actually supposed to happen.

So, we have one Bank, with perhaps two customers. Alice and Bob. Alice has deposits at the Bank worth £500. Bob has £100 at this bank. A total of £600 of deposits, which the bank is liable make available to the customers at any time. The Bank has £5000 worth of its own capital. Totaling £5600 cash held (I realize that the banks' capital and the deposits are not the same - capital is an asset and deposits are a liability, for one - but this sum represents the full reserve amount, yes? The money which would be used if needed to serve depositors requests for withdrawal). We will say that the capital ratio is 10%. As I understand it, this makes the total lendable capital at the bank £5000 + £450 (Alice) + £90 (Bob) = £5540. I am pretty sure I am correct in my understanding so far.

So, Bob owes Alice a lot of money. He needs to pay her £1000. So, he takes out a loan at 5% interest. The Bank decreases its lendable capital by the amount of the loan, so it can now only loan a further £4540, however it still technically possesses the full £5540 as the £1000 loan is "new" money. Naturally, Alice now deposits Bob's £1000 payment in her account. The banks total deposits now sit at £1600, the amount it is holding is now £6600. Due to the new £1000 deposit on Alice's account, £900 is added to the lendable capital. Making it £5440. Is this correct? So far - besides the amount of lendable capital against which "new" money may be created - no deductions have been made. In addition, the £1000 loan is considered an asset that the bank owns.

So, now, the loan has eventually accumulated £80 interest and Bob manages to complete his payments to the bank. Bob pays the bank £1080 in total. Here is where I am most confused. What happens to this amount? I have heard people talk about "money destruction", implying that the bank quite literally throws away the £1000 originally lent to Bob. But somehow I find that hard to believe, and I am further confused because people mention removing it from circulation - presumably simply not making any use of it - as being the mechanism by which it is "destroyed". However, I do not believe it can be effectively removed completely from circulation, as the bank would surely either invest it or use it to make more loans, no? If indeed the money is not really destroyed, the bank has effectively just made £1080 out of nothng, right?

Perhaps I have gone wrong somewhere in my accounting. I have a Software Engineering background so a lot of this is very new/alien to me. I am just very interested in understanding it. I feel like if something is hard to believe (such as many of the claims made about money creation) it usually is for good reason, so I just wanted to understand the full picture for myself.

The bank hasn't made £1080 out of nothing. Bob paid that money into the bank. It wasn't in the bank earlier, and it is in the bank now. Alice's account has been increased by £1000. And the bank has £80 extra that it earnt by lending to Bob.

It's helpful to distinguish the money that the bank holds, from the amount of money in the whole system, and from the amount of money the bank owns.

£1080 has left the rest of the system, and entered the bank.

The bank's own capital starts at £5000 and finishes at £5080 (ignoring any interest it's paid to Alice, and its operating costs).

Alice's account starts at £500, and finishes at £1500.

Bob's account starts and ends at £100.


Marginal Utility vs Cost of production I have a confusion.
Marginal utility is always decreasing and people will not be happy to pay 2 times of price for 2 times of a coffe but I guess the price of producing 2 times of coffe will be the same as producing one unit.
So in this case why this does not cause companies to have less profit from that particular product? Why companies still try to sell as much product as possible while they cannot charge you same amount. (In this case double the price vs double the coffe)

The premise of the question is simply false. Companies do not maximize $Q$ they maximize profit.
For example, consider trivial case of a monopoly. The demand is given by $Q = 10-p$ so demand decreases with price. Now let us suppose the monopoly has constant marginal costs $c(Q)' = 2 \implies c= 2Q$. Given this the profit function of monopoly will be given by:
$$\Pi = p Q - 2Q = (10-Q)Q -2Q$$
With FOCs:
$$ 10 -2Q -2 = 0 \implies Q^*=4 $$
So in this case the monopoly would produce exactly 4 units of products no more no less. The exact quantity of products will be different in different market structures (e.g. duopoly, oligopoly, monopolistic competition, perfect competition), and under different parameters (e.g. demand parameters costs),  but generally in all of them there will be some profit maximizing $Q$. So the premise of your question is false. Of course, firms won't just produce goods to dump them into garbage and to loose profit.


Find equilibrium price using excess demand function Consider an economy with two agents. There are two goods, x and y. Agents' preferences are Leontif ones as follows:
$u_1(x,y)=\min(x,4y)$ and $u_2(x,y)=\min(x,y)$.
Initial endowment for 1 is (2,4), for 2 is (4,2)
The problem asks me to use the excess demand function to find the equilibrium price and show that there are infinitely many equilibria with that price. The problem also asks what is the cause of such multiplicity of equilibria.
I tried this many times, but I always get that the equilibirum price is (1,-1/2), which is impossible.
Any help is appreciated.

Let $m_i$ be the market value of the endowment of player $i\in\{1,2\}$.
In optimum player $i$ spends everything such that $p_x x_i + p_y y_i =m_i$.
And because of the preferences in optimum also $x_1 = 4 y_1$ and $x_2=y_2$ holds.
You use that to get 2's demand as $x^*_2 = \frac{m_2}{p_1+p_2}=y^*_2$ and a similar bur slightly different formula for $4 y^*_1 = x^*_1$.
The excess demand would be this demand minus the endowment. The sum of excess demands is zero in equilibrium.
In equilibrium, $x_1^*+x_2^* =2+4$ and $y_1^*+y_2^* =2+4$, which you can both use to calculate an equilibrium price ratio. Any price combination with that ratio clears the market.


Are revealed preferences normative or positive notion? I always thought from my understanding of the terms normative and positive that revealed preferences are a positive concept. For example, saying Anakin prefers grass to sand (i.e. $U(g)\succ U(s)$) is a positive statement.

My thinking is as follows:

It’s a value free statement
It’s empirically objectively testable statement. We can just make an experiment where we give Anakin choice of sitting in sandy room vs grassy room and observe preference.
Independent observers would agree on the observed outcome Anakin picking the grassy room.

However, I encountered an opinion that since all preferences derive from underlaying values they are all strictly normative and considering them positive even in the strict sense of revealed preference is a fallacy.

Is the opinion correct? If the opinion is not correct how would you refute it? Just by stating my points 1-3?

Also I tried to find some sources that would discuss this but google scholar just gives me results that are unrelated to this philosophical issues. I looked in Julian Ress’ philosophy of economics, and Hausmanns anthology but I could not find satisfactory answer there either. Are there any good references for this issue?

However, I encountered an opinion that since all preferences derive from underlaying values they are all strictly normative and considering them positive even in the strict sense of revealed preference is a fallacy.

There's a logical inconsistency here which might help see why it's not a good way of looking at the issue.  What is the key element that is purportedly revealed by dividing the universe into "things normative" and "things positive"?  I would suggest that it is determinism - matters of a positive nature correlate by way of fully deterministic, structurally-modelable processes that are discoverable through repeated experiment.  Think physics - laws guide observables, observables reveal the laws, the laws can be used to predict future observables.  If a tree falls in a forest and no one is around to hear it, physics tells us that it still makes a sound.

Matters of a normative nature correlate only to the extent that a system of "norms" has been set up to enforce them.  Think ethics - morals guide behaviour, behaviour reveals morals, but can morals - absent a normative framework - be used to predict future behaviour?  No - because morals themselves can change, because agents are capable of deception, and because agents may not even have perfect knowledge of their own preferences. Crucially, morals alone are no guaranteed predictor of unexamined human behaviour.

So, I'd argue that your friend's opinion is logically inconsistent because it is a contradiction: in order for it to be true that all preferences derive from underlying values, it must be true that values influence behaviour in a deterministic way according to underlying laws that are, in principle, discoverable through experiment.  That's a pretty weighty claim, in my opinion not at all borne out by the preponderance of evidence - but if it were true, it would mean preferences are in fact positive!

Whether preferences are normative or positive then depends on the assumptions about the agent.  We usually want them to be positive so that we can math about them, and so we make a whole bunch of assumptions about homo economicus that - if true - support that assumption.  But of course, we know that homo economicus is a fiction. So we might suspect that our theory on preferences is at best a useful benchmark to provide context for understanding how people actually behave.


In an intertemporal (2-period) consumption model, why is the investment rate independent of discount factor? In lecture, my professor defined the following 2-period consumption model:
$c_i = $ consumption in period $i$.
$y =$ endowed income in period 1.
$r = $ interest rate in perfect credit markets.
$h = $ money invested in period 1.
$w(h) = $ period 2 return on money invested in period 1.
$U(c_1, c_2) = u(c_1) + \beta u(c_2)$ an additively separable utility function with discount factor $\beta$.
Then the budget constraint is $$c_1 + \frac{c_2}{1+r} = y - h + \frac{w(h)}{1+r}$$ so the Lagrangian for utility maximization is $$L = u(c_1) + \beta u(c_2) + \lambda \left( y - h + \frac{w(h)}{1+r} - c_1 - \frac{c_2}{1+r} \right).$$ But then $h^*$ is determined entirely by one of the first order conditions, $$L_h = \frac{w'(h)}{1+r} - 1 = 0,$$ which is independent of $\beta$.
My professor said that this means "patient and impatient people invest the same amount $h^*$, maximizing the net present value of income." Mathematically, I understand why this has to be true, but intuitively it doesn't make sense. If $\beta = 0$, for example, shouldn't we invest $h=0$ because all consumption in the future provides 0 utility? Why doesn't similar reasoning apply to very small $\beta$? And why would we be trying to maximize the NPV of income if income in the first period provides more utility than income in the second period?

This idea is known as the Fisher separation theorem.
Without the investment opportunity to transfer $h$ units of present day value into $w(h)$ units of future value, the perfect credit market gives us the intertemporal budget constraint of
$$
c_1 + \frac{c_2}{1+r} = y,
$$
which can be represented by a straight line.

Without knowledge of the consumer's preferences, it is not possible to say what the optimal $(c_1,c_2)$ is here. But we can say with certainty, that the higher the budget line is, the more options the consumer has, and assuming monotonic preferences she will be better off.
Now the yield curve $w$ of the investment opportunity allows us to shift the basic credit market budget line. Starting from the lower right point of $(y,0)$ (i.e. not putting money into the credit market at all) we can reach cash flows $(y-h, w(h))$.

But by also putting some money into the credit market (or borrowing), one can reach other cash flows as well. These always transfer $x$ units of present value into $x(1+r)$ units of future value (in case of borrowing $x$ is negative), so they are always paralel to the original budget line, but instead of starting from $(y,0)$, they start from the point $(y-h, w(h))$ where $h$ is the size of the investment.
The optimal investment size is the one that reaches the highest budget line:

The idea is that given perfect credit markets one can separate consumption behavior and investment behavior. The higher the net present value of my cash flow, the better of I will be once I adjust my cash flow via the credit market to my intertemporal preferences (this is where $\beta$ matters). Thus I need to make investment decisions that maximize the present value of my cash flow, and I do not have to take anything else into consideration, e.g., the timing of the payments.

A mathematical tidbit:
In the above example, given the optimal $h$ (assuming it is an interior point) the budget line is tangential to the orange curve depicting the possible investments, so we have
$$
w'(h) = 1 + r,
$$
the marginal yield from the investment and the credit market are equal. This is equivalent to the final equation in your question.


Efficiency conditions for externalities I have a 2 consumer 2 goods economy. Both the goods produce an externality for the other consumer, therefore, they are a part of the other's utility function. How do I show that despite the externality, the equilibrium is efficient?

You cannot show this because it is not always true. Consider the following situation:

Two consumers (Romeo (R) and Juliet (J))
Two goods (Apples ($A$) and Chocolates ($C$))
Romeo's endowment is $(a = 1, c = 0)$ and Juliet's endowment is $(a = 0, c = 1)$
Preferences are given by $u_R(a_R, c_R, a_J, c_J) = a_R + 2a_J $ and $u_J(a_R, c_R, a_J, c_J) = c_J + 2c_R $

Observe that Romeo only cares about apple consumption and Juliet only cares for chocolate consumption. Even though Romeo likes apples himself but he loves to see Juliet consume his favorite fruit twice as much. Similarly, Juliet prefers to watch Romeo consume the chocolate than consuming it by herself. The only Pareto efficient allocation in this economy occurs when Romeo offers the apple to Juliet and Juliet gives her chocolate to Romeo i.e. $(a_R, c_R, a_J, c_J) = (0, 1, 1, 0)$.

The competitive equilibrium in this economy is defined as $(p_A^*, p_C^*)$ and an allocation $(a_R^*, c_R^*, a_J^*, c_J^*)$ satisfying the property that both consumers choose their best bundle taking prices and other individual's choice as given. Since both can only choose for themselves and not for the other person they'll both end up buying what they like i.e. Romeo will buy only apples and Juliet will buy only chocolates. So endowment allocation $(a_R^*, c_R^*, a_J^*, c_J^*) = (1, 0, 0, 1)$ is the only competitive equilibrium and is supported by any price vector $(p_A^*, p_C^*)$ satisfying $p_A^* > 0, p_C^*> 0$. Clearly it is not efficient.


Will a Guaranteed minimum income not eventually just be crowded out by inflation? That is, if we implement a guaranteed minimum income, would inflation not eventually rise to a point where it is essentially useless? I would expect prices to be adjusted knowing people have a certain amount of money available. Any explanation would be helpful!

I will not discuss fairness (for example employers gains versus employees gains and bargaining power) principles as you did not ask about those.
Is "crowding out" the right phrase here?
Even if inflation lessens the effect of a minimal income there may still be an effect. Imagine that there are two people, $A$ with an income of 0 $B$ with an income of 60, so total income is 60. The government issues a minimal income of 30 so $A$'s income is changed to 30, total income is changed to 90. If this has no real effect on the economy then all prices rise accordingly, that is they rise by 50% because that is by how much nominal incomes haved changed. However if you adjust for this 150% price level, $A$ still can buy goods in value of $\frac{30}{1.5} = 20$ while $B$ can buy goods in value of $\frac{60}{1.5} = 40$. So there could at least be a redistribution effect as previously $A$ could not buy anything and $B$ could buy more things.
One concern is that inflation may not be even. Only the income of poor people will be raised hence demands for goods poor people buy will rise but demand for goods consumed by rich folks will not change. As a result the poor may experience larger inflation than the well to do, making the redistribution of incomes one between only poor people. The lines between poor and well to do here are murky. If (due to inflation) a pop-tart costs \$10 then people will buy quality food unless it is even more expensive. If a pop-tart's price rises to \$1,000 people will buy caviar unless its price is also raised.
A hope of governments implementing such policies is that (aside from fairness and solidarity principles) a minimal wage will also help minimum wage earners be more financially secure. Some studies have shown that in extreme poverty you make worse decisions and are less productive simply as a result of stress. If this is indeed a main effect then a minimum wage (or a higher minimum wage) can increase overall productivity. Thus inflation will not be the only effect of the policy but also an increased number of goods will be produced.


Impact of a reduction of distortions in a flat consumption tax I ask about the survey results of some prominent Australian economists shown here (Which is a similar Australian-centric version of the very interesting IGM Forum Surveys). The results of the survey surprised me as it isn't what I was expecting.

“Increasing government revenue collected through the Goods and Services Tax (GST) by removing exemptions (such as food, health and education) is better than achieving the same extra revenue by increasing the GST rate while retaining the existing exemptions.”

My question is, is there any empirical or other research on the impact of transition from a distortionary to a less distortionary tax which could be applied to the Australian case?

There is theoretical work on the matter in general. In fact, many standard models of optimal consumption taxation will typically yield a distortion that is increasing and convex in the rate of taxation. This means that increasing a tax on a good from 5% to 6% results in higher distortion than increasing it from 2% to 3%. Following this logic, it is better to tax many goods at a low rate than to tax few goods at a high rate, as the distortion would be smaller. This means that removing the exemptions (taxing goods with a currently lower rate of taxation than the rest) is better than increasing the tax rate on previously taxed goods (since they have a currently higher rate than the exempt goods). To conclude, it means that the distortion from taxing exempt goods, which would mean going from 0% to e.g. 20%  (assumed current VAT in Australia) is lower than going from 20% (current tax rate on non-exempt goods) to 40%, or so.

For a reference, see for example slide 30 (and a few before) in this slide set I found online. Its from Mankiw's Microeconomic Principles.

This however does not take into account any "fairness" considerations or welfare implications for the case of households not being able to afford enough food as a result. So the standard theory may not apply in cases where taxing food at all may lead to starvation, as starvation is not considered. However this is likely not the case anyway for such a rich economy as Australia that has other means of providing welfare (incl. food) to the needy.


Where to start learning economics as a mathematician? I study pure mathematics at university and I'm looking to get into economics, with pretty much no background knowledge about it.

Are there good sources to learn from with a decent mathematical background in mind, or should I just start learning from "normal" sources, like watching video lectures from introductory courses, which don't assume much mathematical knowledge? Preferably, I'd like to embrace economics without those limitation.

McCloskey's Applied Theory of Price is somewhat legendary as a model of clarity. It is, sadly, no longer in print. However, a PDF is available here: http://www.deirdremccloskey.com/docs/price.pdf. The level of mathematical sophistication in this book (like in most good economics!) is not that high, but the book gives a deeper look at the important concepts than is to be found in most extant introductory undergraduate texts.

If you really want a more mathematically formalised treatment then you are going to have to turn to graduate-level econ books. For microeconomics, the classic text of choice is Microeconomic Theory by Mas-Colell et al.

If you do go down the more formal route, I would urge you not to give up on simpler treatments altogether; they're great for building intuition. More than a decade of experience in economics has taught me that good intuition built through simple models is often far more valuable than a less intuitive understanding of a more sophisticated model.


what is the interpretation of $\beta_{ij}$ in the translog production function? The translog production function is defined as the following.
$$\ln y=\alpha_0+\sum_{i=1}^n\alpha_i \ln x_i+\frac{1}{2}\sum_{i=1}^n\sum_{j=1}^n\ \beta_{ij}\ln x_i\ln x_j $$

I know it is a approximation of the CES production function and simplifies to  being a logged general cobb douglas production function when every $\beta_{ij}=0$.

however in cases where every (or even a single) $\beta_{ij}\neq0$ what interpretation does it take on?

i.e. I know $\alpha_i$ is interpreted as an "output elasticity", what is $\beta_{ij}$ interpreted as?

You may interpret $\alpha_i$ as the output elasticity regarding input factor $x_i$, keeping other factors $x_j, j\neq i$ constant. $\beta_{ij}$ is an indicator for complementarities in production, i.e. how much does the addition of one percent of both factors $x_i$ and $x_j$ add to $y$. Since there is the factor 0.5, and since $\alpha_i$ and $\alpha_j$ are relevant too, the interpretation is not that straightforward.


Could food storage prevent a depression? In Genesis chapter 41 Joseph interpreted the dreams of Pharaoh about 7 years of plenty and 7 years of famine which resulted in saving Egypt from famine, among other things.

I think this is a great economic feat to say the least. But it brings up so many economic questions about the scenario and how it might play out under different economic models and policy decisions.

First off, nowadays can a big enough food storage keep a city or a nation from going into an economic depression? Which economic models might I use to analyze the situation? The Great Depression included the Dust Bowl, and a lot of hunger, and it makes me wonder what difference a gigantic food storage could have done.

Egypt in that Bible story was experiencing a famine though, and economic depressions don't seem to be caused by famines necessarily. So is food storage only applicable during a famine?

Keep in mind that during the 7 years of famine in the Bible, there was still a negative production shock that more than likely produced a heavy recession for some of those seven years as workers tried to reallocate their labor to something more useful than agriculture. A recession merely represents a fall in final goods production. The grain that was saved up doesn't represent production for that period (rather it would be for the previous seven years of economic boom). The grain stored up represents savings rather than production.

It doesn't look like Joseph or Pharaoh told the people that the famine was coming (imagine the panic), so workers wouldn't have predicted the change in permanent income, and their intertemporal substitution would be much smaller because of the error in their adaptive/rational expectations. Joseph merely used taxes (one-fifth of each year's harvest) to engage in consumption smoothing.

So to answer most of your questions, food storage doesn't prevent negative output shocks. It merely is a hedge against them. Arguably most people should try to have emergency savings of their own to hedge against recessions of their own, but especially in America, we are not very good at saving money. We also have a lot of population who live paycheck to paycheck, and are liquidity constrained, unable to consumption smooth according to their predictions in permanent income, even if they want to.


Pesaran's CCEP estimator in eviews I intend to use Pesaran's (2006) common correlated effects pooled (CCEP) estimator. However, I'm not yet very familiar with advanced econometrics and advanced use of eviews. More specifically I want to estimate this model:
\begin{equation}
y_{it} = \alpha_{i} + \beta_{1}x_{1,it} + \beta_{2}x_{2,it}+\gamma_{i}F_{t}+\epsilon_{it}
\end{equation}
in which $F_{t}$ is an unobserved common factor and $\gamma_{i}$ is a country-specific factor loading. We were taught that $F_{t}$ can be proxied by:
\begin{equation}
F_{t}=\frac{(\bar{y_{t}}-\bar{\alpha}-\beta_{1} \bar{x}_{{1,t}} -\beta_{2} \bar{x}_{{2,t}}-\bar{\epsilon}_{{t}})}{\bar{\gamma}},
\end{equation}
in which $\bar{y_{t}} = \frac{1}{N}\sum_{i=1}^{N} y_{it}$, and $\bar{\gamma_{}}=\frac{1}{N}\sum_{i=1}^{N} \gamma_{i}$, with $N$ the number of cross-sections.

Substituting the second equation into the first yields:
\begin{equation}
y_{it} = \alpha_{i}-\frac{\gamma_{i}}{\bar{\gamma}}+\beta_{1} x_{1,it} +\beta_{2} x_{2,it} +\frac{\gamma_{i}}{\bar{\gamma}}\bar{y_{t}} - \beta_{1} \frac{\gamma_{i}}{\bar{\gamma}} \bar{x}_{1,t} -\beta_{2}\frac{\gamma_{i}}{\bar{\gamma}}\bar{x}_{2,t}+\epsilon_{it}-\frac{\gamma_{i}}{\bar{\gamma}}\bar{\epsilon_{t}}
\end{equation}
or with $\alpha_{i}-\frac{\gamma_{i}}{\bar{\gamma}}=\alpha'_{i}$ and $\frac{\gamma_{i}}{\bar{\gamma}}=\gamma'_{i}$:
\begin{equation}
y_{it} = \alpha'_{i}
+\beta_{1} x_{1,it}
+\beta_{2} x_{2,it}
+\gamma'_{i}\bar{y_{t}}
- \beta_{1} \gamma'_{i} \bar{x}_{1,t}
-\beta_{2}\gamma'_{i}\bar{x}_{2,t}
+\epsilon_{it}-\gamma'_{i}\bar{\epsilon_{t}}.
\end{equation}

To estimate this in eviews, I had the following idea

The cross-sectional averages $\bar{y_{t}}$, $\bar{x}_{{1,t}}$, and $\bar{x}_{{2,t}}$ can be easily calculated from the dataset. I would use cross-sectional fixed effects to estimate all $\alpha'_{i}$. Next, I would need $N$ terms to estimate all $N$ $\gamma'_{i}$. To do this, I would include these $N$ terms: $\gamma'_{A}\bar{y}_{t}dum_{A} + \gamma'_{B}\bar{y}_{t}dum_{B} + ... + \gamma'_{N}\bar{y}_{t}dum_{N}$, in which each capital letter denotes one of the $N$ cross-sections and the dummy variable takes the value of $1$ once for each cross-section. Then, for each averaged explanatory  variable, $\bar{x}_{1t}$ and $\bar{x}_{2t}$, I would include these $2 \times N$ terms: $\beta_{1}\gamma'_{A}\bar{x}_{1,t} + \beta_{1}\gamma'_{B}\bar{x}_{1,t}+ ... + \beta_{1}\gamma'_{N}\bar{x}_{1,t}$ and $\beta_{2}\gamma'_{A}\bar{x}_{2,t} + \beta_{2}\gamma'_{B}\bar{x}_{2,t}+ ... + \beta_{2}\gamma'_{N}\bar{x}_{2,t}$.

So, to sum up, my suggested input for eviews (to estimate with cross-sectional fixed effects) is the following:
y = c(1)*x1 + c(2)*x2 + c(3)*y_avg*dumA + c(4)*y_avg*dumB + c(5)*y_avg*dumC + ... + c(1)*c(3)*x1_avg + c(1)*c(4)*x1_avg + c(1)*c(5)*x1_avg + ... + c(2)*c(3)*x2_avg + c(2)*c(4)*x2_avg + c(2)*c(5)*x2_avg + .....

In this equation:

c(1) = $\beta_{1}$;
c(2) = $\beta_{2}$;
c(3) = $\gamma'_{A}$;
c(4) = $\gamma'_{B}$;
c(5) = $\gamma'_{C}$.

These are my questions regarding this estimation:

First of all, confirmation of the correctness of my derivation would be welcome;
Would the estimation in eviews I suggest do the trick?
If so, should I include an intercept in the fixed-effects estimation?
If not, is there an alternative procedure to implement the CCEP estimator in eviews?
The estimated error terms should be $\epsilon-\gamma'_{i}\bar{\epsilon}$, is this structure automatically obtained? Or should this be imposed one way or another?
The same question for $\alpha'_{i}$: it should equal $\alpha_{i}-\frac{\gamma_{i}}{\bar{\gamma}}$. Should this condition be imposed, or is it automatically fulfilled when inputting my suggested input in eviews;
Other suggestions regarding the use of CCEP estimator in eviews are certainly welcome.

Any help, also partial answers, is appreciated!

The technique described in the question is almost correct. Consider a panel data set consisting of three cross-sections ($a$, $b$, and $c$) and three time-periods ($1$, $2$, and $3$). Let y denote the column vector with the observations of the dependent variable, x the column vector with observations of the first explanatory variable, and z the column vector with observations of the second explanatory variable. They take these forms respectively:

$\textbf{y} =
\begin{bmatrix} y_{a1} \\ y_{a2} \\ y_{a3} \\  y_{b1} \\ y_{b2} \\ y_{b3} \\ y_{c1} \\ y_{c2} \\ y_{c3} \end{bmatrix}$
; $\textbf{x} = \begin{bmatrix} x_{a1} \\ x_{a2} \\ x_{a3} \\  x_{b1} \\ x_{b2} \\ x_{b3} \\ x_{c1} \\ x_{c2} \\ x_{c3} \end{bmatrix}$;  $\textbf{z} = \begin{bmatrix} z_{a1} \\ z_{a2} \\ z_{a3} \\  z_{b1} \\ z_{b2} \\ z_{b3} \\ z_{c1} \\ z_{c2} \\ z_{c3} \end{bmatrix}$.

Let $\bar{y}_{i} = \frac{1}{3}(y_{ai} + y_{bi}+y_{ci})$, with $i = 1, 2, 3$, and equivalently for $x$ and $z$: $\bar{x}_{i} = \frac{1}{3}(x_{ai} + x_{bi}+x_{ci})$ and  $\bar{z}_{i} = \frac{1}{3}(z_{ai} + z_{bi}+z_{ci})$, both for  $i = 1, 2, 3$.

This is the correct way to get the CCEP estimator allowing for one common factor, as in the model described in the question:
\begin{equation*}
\begin{split}
\begin{bmatrix} y_{a1} \\ y_{a2} \\ y_{a3} \\  y_{b1} \\ y_{b2} \\ y_{b3} \\ y_{c1} \\ y_{c2} \\ y_{c3} \end{bmatrix} = \beta_{1} \begin{bmatrix} x_{a1} \\ x_{a2} \\ x_{a3} \\  x_{b1} \\ x_{b2} \\ x_{b3} \\ x_{c1} \\ x_{c2} \\ x_{c3} \end{bmatrix}+\beta_{2}\begin{bmatrix} z_{a1} \\ z_{a2} \\ z_{a3} \\  z_{b1} \\ z_{b2} \\ z_{b3} \\ z_{c1} \\ z_{c2} \\ z_{c3} \end{bmatrix}+
\gamma_{a} \begin{bmatrix} \bar{y}_{1} \\ \bar{y}_{2} \\ \bar{y}_{3} \\  0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix}
+\gamma_{b} \begin{bmatrix}  0 \\ 0 \\ 0 \\ \bar{y}_{1} \\ \bar{y}_{2} \\ \bar{y}_{3} \\  0 \\ 0 \\ 0 \end{bmatrix} +
\gamma_{c}  \begin{bmatrix}  0 \\ 0 \\ 0 \\  0 \\ 0 \\ 0 \\ \bar{y}_{1} \\ \bar{y}_{2} \\ \bar{y}_{3}  \end{bmatrix} \\
- \beta_{1}\gamma_{a} \begin{bmatrix} \bar{x}_{1} \\ \bar{x}_{2} \\ \bar{x}_{3} \\  0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix}
- \beta_{1}\gamma_{b}  \begin{bmatrix}  0 \\ 0 \\ 0 \\ \bar{x}_{1} \\ \bar{x}_{2} \\ \bar{x}_{3} \\  0 \\ 0 \\ 0 \end{bmatrix}
-\beta_{1} \gamma_{c} \begin{bmatrix}  0 \\ 0 \\ 0 \\  0 \\ 0 \\ 0 \\ \bar{x}_{1} \\ \bar{x}_{2} \\ \bar{x}_{3}  \end{bmatrix}
-\beta_{2} \gamma_{a}  \begin{bmatrix} \bar{z}_{1} \\ \bar{z}_{2} \\ \bar{z}_{3} \\  0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{bmatrix}
-\beta_{2} \gamma_{b} \begin{bmatrix}  0 \\ 0 \\ 0 \\ \bar{z}_{1} \\ \bar{z}_{2} \\ \bar{z}_{3} \\  0 \\ 0 \\ 0 \end{bmatrix}
-\beta_{2} \gamma_{c} \begin{bmatrix}  0 \\ 0 \\ 0 \\  0 \\ 0 \\ 0 \\ \bar{z}_{1} \\ \bar{z}_{2} \\ \bar{z}_{3}  \end{bmatrix} \\
+ \phi_{a} + \phi_{b} + \phi_{c} + \mu_{it}
\end{split}
\end{equation*}
Here, $\phi_{a},\ \phi_{b},$ and  $\phi_{c}$ are cross-sectional fixed effects and $\mu_{it}$ a well-behaved error-term that does not require any restrictions.

An interesting remark is that if the six $\beta$s that appear together with the $\gamma$s are not restricted to be equal to each other and equal to the first two $\beta$s,   more than one common factor is allowed.


Log-linearisation Euler Consumption Equation I am trying to log-linearize the Euler consumption equation in Gali's book. He says:

  A log-linear approximation of $Q_{t}= \beta E_{t}[(\frac{C_{t+1}}{C_{t}})^{-\sigma}(\frac{Z_{t+1}}{Z_{t}})(\frac{P_{t}}{P_{t+1}})]$ (1)

I spent all of last night trying to learn log-linearization so this might be why my answer isn't correct but here is my attempt:

I re-write $Q_{t}=\frac{1}{1+i_{t}}$ and thus (1) becomes:

$1= \beta E_{t}[(1+i_{t})(\frac{C_{t+1}}{C_{t}})^{-\sigma}(\frac{Z_{t+1}}{Z_{t}})(\frac{P_{t}}{P_{t+1}})]$

Taking logs of both sides (I'm assuming I can ignore the expectation operator, although I'm not really sure why):

$0=ln(\beta) + ln(1+i_{t})- \sigma[ln(c_{t+1}) - ln(c_{t})] + ln(z_{t+1}) - ln(z_{t}) + ln(P_{t}) - ln(P_{t+1})]$ (2)

Approximating around the steady state values:

$0=ln(\beta) + ln(1+i^{*})+(\frac{1}{1+i^{*}})(i_{t}-i^{*})- \sigma[ln(c^{*})+(\frac{1}{c^{*}})(c_{t+1}-c^{*}) - ln(c^{*}) - (\frac{1}{c^{*}})(c_{t}-c^{*})] + ln(z^{*}) + (\frac{1}{z^{*}})(z_{t+1}-z^{*}) - ln(z^{*}) - (\frac{1}{z^{*}})(z_{t}-z^{*})+ ln(P^{*}) + (\frac{1}{P^{*}})(P_{t}-P^{*}) - ln(P^{*}) - (\frac{1}{P^{*}})(P_{t+1}-P^{*})$

That was quite messy but hopefully you see what I am doing, a simple first order approximation around the steady state. Next I used equation (2) to cancel some terms. I was left with:

$(\frac{1}{1+i^{*}})(i_{t}-i^{*})- \sigma(\frac{1}{c^{*}})(c_{t+1}-c^{*}) +  \sigma(\frac{1}{c^{*}})(c_{t}-c^{*}) + (\frac{1}{z^{*}})(z_{t+1}-z^{*}) - (\frac{1}{z^{*}})(z_{t}-z^{*})  + (\frac{1}{P^{*}})(P_{t}-P^{*}) -  (\frac{1}{P^{*}})(P_{t+1}-P^{*}) = 0$

Re-writing in terms of deviations from steady state:

$\tilde i_{t} - \sigma \tilde c_{t+1} + \sigma \tilde c_{t} + \tilde z_{t+1} - \tilde z_{t} + \tilde p_{t} -  \tilde p_{t+1} = 0$

I can re-arrange this in terms of $\tilde c_{t}$ and put in expectation operators but my answer does not match with Gali's. He says:

  $c_{t} = E[c_{t+1}] + \frac{1}{\sigma}(i_{t} - E_{t}[\pi_{t+1}] - \rho) + \frac{1}{\sigma}(1-\rho _{z})z_{t} $

First of all, I don't understand where $\rho$ came from since it is not in (1). Furthermore, am I making a mistake in my linear approximation? Should I not have used (2) to cancel terms?

I just learned log-linearization so my method might be quite naive. I simply "logged" both sides, used first order Taylor approximation around steady state, cancelled terms from the "logging" step and solved for consumption.

Any assistance is greatly appreciated!

To simplify matters, let's call the right-hand side of your starting equation $X_t$ Then, I start just like you did with

$1 = X_t$

The difference between your solution and Gali's is that you took the Taylor expansion around

$\log(1)=0=log(X_t)$  which implies that also the steady state equals 0, so we can simply subtract it to get log-differences,

whereas Gali used

$1 = \exp(\log(X_t))$ with steady state $1=\exp(\log(X^*))$

Let's define $x_t=\log(X_t)$.

By definition of the Taylor expansion this gives

$T(1) = \exp(x^*)+\exp(x^*)(x_t-x^*)$

Note that the exponential function is identical to its derivative. We know that $\exp(x^*)=1$ from above, so we can simplify to

$T(1)=1+(x_t-x^*)$

At this point, you are correct that the $\rho$ cancel out. Instead of defining $\hat{x}_t=x_t-x^*$ but Gali chooses to replace $\rho=\pi +\sigma \gamma-i$, which is the steady state condition, which is why $\rho$ stays on the paper.

Note, however, that the "approximation error" from taking log differences instead of Gali's approach is tiny, i.e. for $\beta=0.99$ it is only $-\log(0.99)\approx 0.01$

Have a look at appendix 2.1 of Gali's book! It is quite complicated, but together with this post, I hope you get it!


How can one compute the CPI All items index from the component indexes? How can one compute the CPI All items index given the CPI energy index and the less energy index? I used the relative importance as component weighted value but it isn't true.

I'm afraid that with the information you state, this is impossible.

Say there are three items in the CPI: housing, food, and energy. Define the weight of each component in total CPI, weight which can vary over period, as $w_{h,t}$, $w_{f,t}$, and $w_{e,t}$ respectively. By definition, they add up to 1. Similarly, define the CPI series of each item as $P_{h,t}$, $P_{f,t}$, and $P_{e,t}$ respectively.

The CPI index for all but energy goods, $P_{hf,t}$ is given by:

$$ P_{hf,t} \equiv \frac{w_{h,t}}{w_{h,t}+w_{f,t}}P_{h,t} + \frac{w_{f,t}}{w_{h,t}+w_{f,t}}P_{f,t}$$

Although you know $P_{hf,t}$, you do not know any of the other 4 terms, for each period. As such, this is an undetermined system. In the case of a CPI with $N$ items, the system has $2(N-1)$ unknowns.

If weights are constant, you cannot get much further either. Say that you have $T$ number of periods. Then, you have a system of equations like

$$ A_{t} = bX_{t} + cY_{t} $$

where only $A_{t}$ is known. This is also undetermined. You can only write $X_{t}$ as a function of $Y_{t}$, $b$ and $c$. (and viceversa).

A second best approach?

You have one option though. You could compute the "vector distribution" of the all-CPI index. To see this, notice that the total price index, $P_{t}$ is

$$ P_{t} \equiv w_{h,t}P_{h,t} + w_{f,t}P_{f,t} + w_{e,t}P_{e,t} $$

This is equal to

$$ P_{t} = (w_{h,t}+w_{f,t})P_{hf,t} + w_{e,t}P_{e,t} $$

But weights add up to one. Therefore,

$$ P_{t} = (1-w_{e,t})P_{hf,t} + w_{e,t}P_{e,t} $$

Or better:

$$ P_{t} = P_{hf,t} + w_{e,t}(P_{e,t}-P_{hf,t}) $$

Now, since you know the CPI index for energy-only ($P_{e,t}$) and for all-but-energy ($P_{hf,t}$), you could compute $P_{t}$ for a given assumption on the energy weight on total CPI. You can, for instance, look into other similar countries and see how much this weight is. Or look for related information on this respect. This number cannot be wildly different across countries. So you can still get a rough idea of general CPI.


Abenomics and the Japanese VAT tax hike Abenomics seems to me like a straightforward and modern plan of economic reflation through monetary easing and some attempt at structural reform.

While it's still early, it looks like many of the predicted effects of this approach have begun to materialize:  unemployment is lower, earnings are higher, currency has deflated resulting in a rise in exports and improvements to corporate earnings.  Capital has, unfortunately, accumulated on corporate balance sheets rather than re-entered the economy, but even this is a known effect of easing.

One thing I don't understand (aka my question) is:  why did the Japanese government seek to raise consumption tax (VAT) during this process?

It would seem that the whole point of easing is to stimulate productive money circulation, and implementing a consumption tax when consumers are likely to suffer in the initial stages from currency devaluation seems very counterproductive to the cause.  If the government actually needed the funds then surely there were other approaches available (borrowing or deferred taxation) which would have had less negative impact on the overall easing programme?

Everybody seems to be worried about the raise in the consumption tax, and how it has thus far crippled the efforts to bring the Japanese economy out of stagnation. But Japan has 200% of DGP in public debt, and it cannot leave its public finances go south, not even temporarily.

My impression is that it was the choice to lower corporate tax and "in exchange" increase V.A.T. (perhaps under the impression that it was low, if they looked at European Union levels). Demand was supposed to strengthen through direct transfers, while lowering corporate tax is to boost business initiatives, towards investment but also give some added room to increase wages (to help demand).

We' ll see. Up to now, it doesn't go very well.

ADDENDUM

That the increase in the Sales Tax had as its target to take care of the public finance side of the equation is clearly stated in the IMF-report on the matter, in which we read

  "The consumption tax rate increase in April to 8 percent was a major achievement, but is only a first step towards fiscal
  sustainability...The second consumption tax rate increase in 2015 to
  10 percent with a uniform rate should be confirmed. Raising the tax
  rate further at a moderate pace would help establish fiscal policy
  credibility. Staff estimates that fiscal consolidation in 2015 would
  slow growth by ½ percent, leaving growth in 2015/16 still above
  potential under the baseline."

A quick journalistic take can be found here.


Aggregate production function, factor shares and cointegration When estimating an aggregate production function you fit your data to a selected functional form of the production function, derive the parameters and inference from there.

My question is, is there a reason for testing for cointegration (i.e. Engle & Granger method) of the production input variables' time series data? What is the extra information you could derive from, for example, VECM analysis of such cointegrated variables, apart from their long-term relationship?

Intuitively, you test for cointegration because if two variables are cointegrated, they represent only a "one dimensional" family of data points - even if you have a million data points from that sample, they will all fall close to the same subspace, and in general that will mean that you will have many values of parameters for your regression problem which will give a good fit (spurious regression).

Consider the linear regression case - say that you have $ y = Ax + \varepsilon $ as your regression problem, where $ x $ is a column vector, $ A $ is a row vector and $ y $ is a real number. Let's say further that the "structural" relationship we are looking for is $ y = Bx $, where $ B $ is also a row vector. Take an extreme case of cointegration - $ x $ is $ 2 $-dimensional, and we have a linear relationship between its coordinates, i.e $ x_2 = c x_1 $ for some constant $ c $. In this case, any linear functional $ A $ which is equal to $ B $ when restricted to the subspace spanned by $ (1, c) $ will give a perfect fit, and the regression won't be able to distinguish between them. (There's a one dimensional family of such functionals, i.e row vectors $ A $.)

What VECM analysis does is to take advantage of deviations when the relationship is not perfect. In real econometric applications, you never have a relationship that's as clean as $ x_2 = c x_1 $ (or $ y = Bx $) for your entire dataset - cointegration allows for transitory white noise in the linear combination $ x_2 - c x_1 $. If the variance of the white noise is relatively small, a standard regression will still return similar $ R^2 $ values for many different operators. Instead, what you do is look at first differences: a good fit should also fit these, i.e we should have

$$ Ax_{t+1} - Ax_t \approx y_{t+1} - y_t $$

where the subscripts denote the time of observation. Running the regression this way allows you to capture the white noise in the cointegration process and use it to your advantage - it's a way of capturing the information which a naive linear regression is going to miss.


Econometrics for currency valuation? Different assets have different motivations and components for price determination. For example, an equity stock price might be considered to be include the value of underlying company, its potential for future growth, and its value as a store of wealth (kind of like a Yap stone).

The price of a currency would seem to be largely determined by the balance of trade with the country or countries involved. For example, if there is a net interest in buying the products of a country, then its currency will be in demand and the price will decrease, but if the citizens of the country are net buyers of foreign goods, then the price will tend to decrease. Thus, it is self balancing, because as long as the net buying of foreign goods continues, the value of the currency will decline reducing the amount they can buy, until it becomes so low that the country is forced to become a net seller, and the value of the currency begins to increase again.

Is there an econometric method for valuing currencies that takes such factors into account?

Yes, the earlier answer about currency value gives some links, including a link to an IMF publication that presents models (methods) with some notes on how to calibrate them and further links to literature. There they describe among others also the macroeconomic balance framework that takes into account the internal and external balance at the same time.


Vegetarians vs shoppers of humane meat/eggs/dairy - Who has the biggest impact on the factory farming meat industry? I apologize for not being able to word this in a non subject specific way.

So, for people who don't support widespread factory farming practices, there are people that abstain from meat completely, and then there are those who buy humane sources, such as cage free/organic/grass fed whatever. These terms differ by definition and enforcement by region, but for the sake of the argument please assume a best case scenario.

So, I have heard non-meat eaters claim they make the most impact by not supporting the meat industry at all.

I have also heard that they have no impact, since they are simply not a part of the market, and that meat eaters who buy 'humane' meats have much more of an impact because they are still buying meat, but putting it towards a minority practice helping it grow and showing demand for it.

I would appreciate a mathematical summary/explanation, as I'm not sure which explanation is correct.

I don't think there is right or wrong. Here is an example of what could be behind some of these arguments.

Let us assume that there are two buyers in the economy: Singer and Foreman. Foreman enjoys meat but he prefers humane meat (other things equal). Let $V$ be the value that Foreman derives from a unit of humane meat and $v$ the value from normal meat.

Singer is a consequentialist and has as a goal to reduce the meat consumption. Singer is willing to pay $1\$$ to reduce the total consumption of meat in unit and $\beta\$<1$$ to reduce the total consumption of humane meat. If Singer was alone, he would simply refrain from eating. Because Singer is a consequentialist he does not care who eats the meat (this simplifies the analysis).

Now, suppose that there are scale economies in the production of humane meat so that the first unit costs $C$ and the second costs $C'$, while the production of normal meat has constant returns and the marginal cost is $c$. Both markets are competitive.

If $V-C<v-c$, then in isolation Foreman would buy normal meat. Singer would have a disutility of $1$. If Singer buys humane meat then Foreman would do so too if
$V-C'>v-c$ (which may be possible since $C'<C$). Singer would then have a disutility of $2\beta+C'$ (the price of the meat plus the total disutility of two units). If $2\beta+C'<1$, then Singer judges the world to be better if he buys humane meat and he proceeds to do so.

Thus, if activists consider 'humane meat' to be much better than normal meat and there are substantial scale economies in its production, they may prefer to buy it as a way of inducing others to do the same. If they have agent-specific morality (e.g. they prefer a world in which others buy meat than a world in which they buy meat but they have the same world consumption), then participating in the humane meat market may be a less desirable option.

Finally, notice that there are other ways in which Singer could improve the world. For instance, he can buy stock in humane meat consumption and swallow the losses that come from selling at a price $p=c+V-v<C$. This gives Singer a disutility of $\beta+(C-c)-(V-v)$ which is lower if $\beta$ is sufficiently high.

(For simplicity I assume that Singer does not consider Foreman's consumption of utility as deserving moral praise so he does not include Foreman's extra utility in his computation. If he did, then buying humane meat would be even more desirable.)


UK unemployment for July 2016 Why was the UK unemployment rate in July 2016 lower than forecasted by the Bank of England?

I would guess that this Is due to the variance that exists in the tool used to make predictions about unemployment in the economy known as  Okun's Law. As stated on wikipedia as:

  The gap version of Okun's law may be written (Abel & Bernanke 2005) as:

  ${{\displaystyle (Y-{\overline {Y}})\over{\overline {Y}}}=c(u-{\overline {u}})}$

  where

  ${\displaystyle Y}$ is actual output

  ${\overline {Y}}$ is potential GDP
  ${\displaystyle u} $ is actual unemployment rate
  ${\displaystyle {\overline {u}}}$ is the natural rate of unemployment
  ${\displaystyle c}$ is the factor relating changes in unemployment to changes in output (Econ John: This is also known as the "Okun Coefficient")

From the Usefulness section on wikipedia

  Through comparisons between actual data and theoretical forecasting, Okun's law proves to be an invaluable tool in predicting trends between unemployment and real GDP. However, the accuracy of the data theoretically proved through Okun's law compared to real world numbers proves to be generally inaccurate. This is due to the variances in Okun's coefficient. Many conclude that information proved by Okun's law to be acceptable to a certain degree. Also, some findings have concluded that Okun's law tends to have higher rates of accuracy for short-run predictions, rather than long-run predictions. Forecasters have concluded this to be true due to unforeseen market conditions that may affect Okun's coefficient.

  As such, Okun's law is generally acceptable by forecasters as a tool for short-run trend analysis between unemployment and real GDP, rather than being used for long run analysis as well as accurate numerical calculations.

Hope this helps.


Is utility in neoclassical economics a circular argument/concept? Neoclassical economics as a utility function that represents a consumer's preference ordering over a choice set.

Joan Robinson criticized utility for being a circular concept:

  "Utility is the quality in commodities that makes individuals want to
  buy them, and the fact that individuals want to buy commodities shows
  that they have utility"

This criticism is similar to that of the philosopher Hans Albert who argued that the ceteris paribus conditions on which the marginalist theory of demand rested rendered the theory itself an empty tautology and completely closed to experimental testing. In essence, demand and supply curve (theoretical line of quantity of a product which would have been offered or requested for given price) is purely ontological and could never been demonstrated empirically.

In my understanding, the neoclassical economics is based on utility. So if this concept is no testable, and circular, how neoclassical economics can explain anythings?

I'm not saying the system can not predict anythings, because if we record a lot of behaviors, we can certainly predict some behavior by comparing similar patterns (it's mainly the logic behind machine learning). But we should not call that a theory neither an explanation.

I end up with those interrogations:

Is utility a circular definition?
The theory has falsifiability?

Related content

As I'm exploring this question, and will add some content I stumble upon that I think add some context.

https://fixingtheeconomists.wordpress.com/2014/02/17/joan-robinsons-critique-of-marginal-utility-theory/

Let's be clear--the concept of utility is both unfalsifiable (as a singular proposition) and useful.

Joan Robinson is right, of course: Utility as a definition is circular. If you read a textbook that discusses the foundations of economic theory (such as the popular graduate text by Mas-Colell, Whinston, and Green), then you start not with utility, but with preferences. You would characterize an individual as being defined by a "preference relation" which describes, for every pair of potential allocations (i.e., sets of goods), which they prefer.

Some (not all!) preference relations are rational, which means that they are both complete (you have a well-defined preference over any pair of allocations), and transitive (if you like A more than B and B more than C, you like A more than C). A subset of those preference relations can be represented by a utility function (again, not all--the classic example is lexicographic preferences).

So a utility function is really just a thing that represents some underlying preferences. The statement "Steve's preferences are accurately modeled by a utility function" are not restrictive enough to be tested in any practical way. Rationality in general is hard to test as well, as you can always explain away seeming rationality violations with unusual preferences.

Instead, you should think about utility as a framework, not a theory. It's a language for developing theories. For example, you can describe Friedman's Permanent Income Hypothesis without invoking utility at all, but describing it in terms of utility is a lot clearer and simpler!

As an aside, the blog post you linked to is utter tripe, from a guy who seems to love bashing economics while not actually knowing all that much about it. I would avoid him like the plague.


Is there any widely accepted downsides for Cuban system? The Cuban political, social and economic systems under communism are known for having a good medical system and high quality medical workers. Cuba also has a good educational system. The country also provides most public services (as is typical in communist or formerly communist countries).

Some fragilities of the Cuban system include patients leaving the country to obtain medical care to obtain higher-paying employment opportunities and other life conditions.

Notwithstanding, are there any disadvantages of the Cuban economic and social system that are largely accepted by:

University literature
Actual speeches of the Cuban government
Cuba-based media
Media interested in Cuba but based in foreign countries

Those downsides could be of any form, like poverty, corruption, bad quality or quantity in first-need objects....

EDIT:
To narrow down the question and make it more specific:

Is Cuban economy mainly based on what government provides, or have Cubans enough purchase power to buy "what they want"?
Did company-based economy develop? Like if I want to create a company for a specific application, it is feasible?
Is food available for middle Cuban classes at correct prices?
Are importations possible or too expensive ? If not, why are they expensive: transportation costs, government taxes?

The Cuban system is widely criticized. Particularly by people who experienced it.

(Aside: In fact, this is consistent with the general trend that people who have actually lived under Communist, Socialist and Marxist systems tend to condemn those systems. And the only people who tend to praise such systems are people who never lived under those systems yet favor imposing those systems on others against their will.)

roughly 1 in 10 of all Cubans choose to live in the U.S. (despite the extreme hardship of making that migration)
roughly only 1 in 100,000 Americans choose to live in Cuba (despite the relative ease of making that migration and many of whom are FBI fugitives, avowed Communists and members of other radical leftist organizations)

Notwithstanding the above observations and statistics, let's study two of the question's premises.

  Cuban medical system is as far as I know well known for the quality of its formation and the medical workers and doctors it gave. Cuba has also a good educationnal system.

While it is true that the medical system has been praised. Many criticize the praise as being inaccurate. For example, this research paper from the University of Miami in 2007 cites:

  My own research, however, suggests that the unequivocally positive descriptions of the Cuban health care system in the social science literature are somewhat misleading. In the late 1990s, I conducted over nine months of qualitative ethnographic and archival research in Cuba. During that time I shadowed physicians in family health clinics, conducted formal and informal interviews with a number of health professionals, lived in local communities, and sought to participate in everyday life as much as possible. Throughout the course of this research, I found a number of discrepancies between the way the Cuban health care system has been described in the scholarly literature, and the way it appears to be described and experienced by Cubans themselves. [emphasis mine]

Further, the author writes:

  After just a few months of research, however, it became increasingly obvious that many Cubans did not appear to have a very positive view of the health care system themselves. A number of people complained to me informally that their doctors were unhelpful, that the best clinics and hospitals only served political elites and that scarce medical supplies were often stolen from hospitals and sold on the black market. Further criticisms were leveled at the politicization of medical care, the unreliability of health data and the overall atmosphere of secrecy surrounding the prevalence of certain infectious diseases such as HIV and tuberculosis.

We know that Socialist, Communist and Marxist regimes are not transparent with their information. So many consider the official reports of the quality of Cuba's health care system to be unreliable at best.

Perhaps the most objective indictment of the Cuban system, however, is to look at migration patterns into and out of the country.

In 2017, the Migration Policy Institute reported findings that:

  Cubans have been among the top ten immigrant populations in the United States since 1970, and in 2016 were the seventh largest group. Nearly 1.3 million Cubans lived in the United States in 2016,

Further, they report:

  Compared to the overall foreign- and U.S.-born populations, Cubans were less likely to be proficient in English, had lower educational attainment, and earned lower household incomes.

Researching migration patterns in the opposite direction: from the U.S. to Cuba, I found this Wikipedia article which estimates there were nearly 2,000 to 3,000 Americans living in Cuba in 1998. And that many of them were FBI fugitives, avowed Communists and members of other radical leftist organizations.

The fact that roughly 1 in 10 of all Cubans choose to live in the U.S. (despite the extreme hardship of making that migration) and roughly only 1 in 100,000 Americans choose to live in Cuba (despite the relative ease of making that migration) is a very objective and quantitative indictment against the Cuban system in addition to the more qualitative indictments provided from the above sources.


Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)? My understanding of local non-satiation is that increasing your allocation of one good by a marginal amount increases utility. Suppose your utility takes the following form:
$$U(x,y)=x^\alpha y^\beta$$
and your initial endowment is $(0,0)$. Now, if you increase either good without increasing the other, your utility does not increase. Does this mean that your utility is not locally non-satiated?

No.
Cobb-Douglas utility is monotonic and monotonicity implies L.N.S.
The issue here is that you're only considering edge cases. You've correctly reasoned that edge points are not more desirable that the origin. However, LNS simply claims that there exists a more desirable bundle within the open epsilon ball of your allocation under consideration (and this is true for all allocations). So given any epsilon, an open epsilon ball centered at the origin will necessarily contain an allocation where both elements are strictly positive.
To see this, pick an epsilon and draw the epsilon ball around the origin. It should become fairly obvious what's going on.
Hope that helps.


loanable funds theory: why is the supply of loanable funds equal to saving (+ dishoarding + new money)? It seems that the loanable funds theory suggests that all that is saved is supplied in the market for loanable funds. This makes sense when we are talking about 'household saving' (i.e. household income minus consumption). This money will be put on a savings account (or used to buy bonds), and if not, counts as hoarding per definition. I have a hard time grasping why it would be true for 'firm saving'. Let me explain what I mean by that: Assume a production volume of 1 million $ in a given period. Assume further that 800.000 are paid out as wages and that 500.000 of those are consumed. Overall saving is 500.000, household saving is 300.000. It's obvious that the households will want to loan out those 300.000 (and in the case that they hoard some of this money, it constitutes hoarding, i.e. negative dishoarding, and gets subtracted from the supply of loanable funds = saving + dishoarding + newly created money). But I don't understand why the firms would supply the remaining 200.000 as loanable funds. Is there some assumption that profits are rules out in principle, i.e. that production has to equal household income? I'd be very grateful for some clarification, thx in advance.

Does saving increase the supply of credit? Critique of loanable funds theory.
http://wer.worldeconomicsassociation.org/files/WEA-WER-4-Lindner.pdf

In the first step, the concepts of “saving” and “credit” will be clearly distinguished using simple accounting. It will be shown that credit is not limited by anybody’s saving and that no one has to abstain from consumption in order for a credit to be provided. Also, it will be shown that financial saving (an increase in net financial assets) through a reduction in expenditures reduces other economic units’ revenues and thus their ability to spend and save. Using the concept of excess demand and supply, it will be shown that excess saving does not lead to an excess supply of credit − which would lower interest rates − but to an excess supply of goods, services and/or labor which will lower prices and production. How interest rates change is not determined by excess saving: They could increase, stay the same or decrease. Finally, it will be argued that the identification of saving with the  provision  of  credit  is  likely  to  stem  from  the  invalid  application  of neoclassical growth models to a monetary economy.

The  present  paper  shows  that  the  underlying  view  of  the  “saving  finances  investment”  doctrine implies that the amount of loans that can be lent in a period is limited by the amount of saving in the same period and that, consequently,an abstention from consumption (and other spending) is necessary for more credit to be available for investors. This view is the basis of loanable funds theory (Robertson, 1936;Ohlin, 1937a,c,b;Tsiang, 1956). It will be argued that this view is deeply flawed. Using simple accounting rules in the vein of Stützel (1978;1979) and Lavoie and Godley(2012), the paper will first clarify the difference between saving and the provision of credit: saving changes an economic unit’s net worth which the provision of credit does not. The provision  of  a  credit  only  changes  either  the  composition  of a unit’s  financial  assets or the length of its balance sheet, but not its net worth. Second, it will be shown that loanable funds theorists commit a fallacy of composition  when  they claim  that household financial saving  increases aggregate investment  in tangible assets.

In recent history Paul Krugman defends the use of loanable funds model in online debates with other economists. The statistical measures in the United States have two components called national income and product accounts (NIPA) and flow of funds accounts (FFA). These debates seem to revolve around what role the interest rate(s) play in the dynamic increase or decrease of production, income, and financial instruments. There does not seem to be any deterministic role for interest rates and the financial accounts are not directly linked to the NIPA accounts because there are accounting methods to re-value assets, to depreciate assets, to recognize casualty losses, and introduce other discontinuities in the financial sectors. In short there is no simple deterministic mechanism to link financial saving and investment in a complex credit-driven economy.


Existence of 'best' and 'worst' lottery How can 'the best and worst lotteries exist when the set of outcome is finite and the rational preference relation satisfies independence axiom' be proven?

Hint
Let $\{1,2,\dots,N\}$ be the set of outcomes. Without loss of generality, let $1\succsim 2\succsim\cdots\succsim N$. Let $\mathbf e_i$ denote the degenerate lottery that assigns probability $1$ on outcome $i$ and $0$ on the rest. Note that any lottery $L=(p_1,\dots,p_N)$ can be written as a compound lottery $p_1\mathbf e_1+\cdots+p_N\mathbf e_N$.
Since lottery $\mathbf e_i$ amounts to getting outcome $i$ for sure, we must have
\begin{equation}
\mathbf e_1\succsim \mathbf e_2\succsim \cdots \succsim \mathbf e_N.\tag{1}
\end{equation}
Successively applying the independence axiom to $(1)$, you'll obtain $\mathbf e_1$ as (one of) the best lottery and $\mathbf e_N$ as (one of) the worst.


Sequential games and Perfect Bayesian Equilibrium Reading the paper http://www.sciencedirect.com/science/article/pii/002205319190155W
I came up with the following question.

Given that this paper deals with games in which players move simultaneously, the formula in (1) of Definition 3.1 makes perfectly sense. If someone considers sequential movements of the players, how Definition 3.1 (and hence formula in (1)) would change?

Any good reference about "sequential moving" games?

As Fudenberg and Tirole note, the fact that they assume players move simultaneously does not matter:

  This specification is more general than
  it may appear, because the set of feasible actions can be time and history
  dependent, so that games with alternating moves are included.

Moreover, all actions are observable by all players, so the definition would be unchanged by the assumption that moves are alternating.