Economics' position in the hierarchy of sciences (hard vs soft) As a student of Economics, I often listen to the claim that Economics is a "soft science" and that its results may not be too reliable etc. The explanations are often based on personal opinion.
I have newly come to know that rigorous academic literature exists that uses bibliographic and other data to rank sciences based on their "hardness", following Comte's idea of a hierarchy of sciences.
Wikipedia cited this as an empirical investigation of the hierarchy of sciences--
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3694152/
While I find this analysis useful, it does not specifically tell us where Economics lies in the hierarchy (it does find evidence of a hierarchy based on 5/6 factors like clusters in reference graphs, length of paper etc). In most of the results, it clubs all of the social sciences together. In one of the charts, it has a category "Economics and Business", which appears to be near the other social sciences in the hierarchy. But I am not sure where Economics alone (not clubbed with business or other social sciences) will stand in the hierarchy.
Another paper tries to specifically find Psychology's place in the hierarchy--
https://journals.sagepub.com/doi/10.1037/1089-2680.8.1.59
I wanted to know, if there are any such studies that specifically tell us about where Economics stands in the hierarchy-- whether it is closer to the natural sciences or the social sciences?

There is actually no clear cut consensus on where Economics belongs (although it is fair to say most would likely put it into category of social science). Some authors consider it to be science, some social science, some even moral science, and some even argue it should have its own category.  A good paper that tries to answer this question for economics is  Hudson (2017).
According to the author:

Is economics a science or a social science? Arguments have been made for both orientations, i.e. that economics is a social science (Frey 1999), a science (Frey 1999) and even a moral science (Schabas 2009). In terms of sciences it has been linked with physics, with many physicists doubling as, or transforming into, economists and a subpart of physics, econophysics, specifically evolving which deals with economics (Stanley et al. 1999). There are also links with biology (Marshall 1920; Daly 1968). Frey (1999) argues economics is a social science as it is part of those sciences which deal with actual problems of society, i.e. it is the subject matter which makes it a social science. However, he also points out that in practice economists tend to fill the journals with axioms, lemmas and proofs, i.e. they adopt what they perceive as a scientific, and particularly a mathematical, methodology. Mayer (1980) argues that economists act as though economics is a hard science and this is reflected by their sophisticated use of mathematics. However, he then goes on to argue that econometrics is not sufficiently advanced to enable us to test theories as a hard scientist would.

The literature review above is good place to find out the different views on what economics is. In addition the paper itself is not just a literature review but also itself tries to answer the question by examining how similar economics is to other fields. Hudson (2017) further concludes:

With respect to the question posed in the title of this paper, our view, in part informed by these results, is that the subject matter of economics places it clearly as a social science, but many in the discipline act as if it were a science. Economics has gradually developed into an interdisciplinary subject that uses scientific methods, for example setting out and formally testing hypotheses, and particularly a mathematical approach, to solve social science problems. This dual aspect may explain why it fails to fit neatly with either as in fact it combines elements of both. It is a social science pursued with more quantitative rigour than much of the rest of the social sciences. This emphasis on technique then pushes economics and economists away from the other social sciences and in some sub-disciplines towards maths. Placing economics as a science, emphasises technique above subject matter. But there is then a danger that technique becomes an end in its own right, rather than a means to an end, i.e. a vehicle which allows a more refined analysis of economic issues which have wider relevance. Often, for example when developing a new econometric technique which subsequently becomes widely used, this is justified. But sometimes this is not the case, which helps explain the relative isolation of the discipline as noted earlier. This does not mean that economists should abandon their quantitative focus, but that they should always strive to ensure that their work contributes, directly or indirectly, to an understanding of a real world issue. This is consistent with Frey’s (1999) observation that economics is part of those sciences which deal with actual problems of society, but that most economists attempt to imitate the sciences and that economics can be regarded as a branch of applied mathematics. It is also consistent with the view that that economics, particularly neoclassical economics, is the most mathematical of the social sciences (Porter 1996).

However, I would not take the above conclusion immediately at face value (author also cautions against that) since the cluster analysis done there could not take into account everything what you would ideally want to and it focused only on research in one country (UK). As you can see since this is still being debated and articles about this published in 2017 this is still not completely settled question (although to be fair most would likely classify it as a social science). Also, as noted in the excerpts above the issue is that economics is quite close to the border between social and hard sciences (some authors say it is social science that acts like hard science or draw parallels with biology) making it difficult to classify.

PS: Actually the Comte's 19th century idea of 'hierarchy of the sciences' is problematic in itself.  The problem is that a field on its own cannot be neatly put into such hierarchy because it consists of many sub-fields that are heterogenous. For example, when it comes to fields like game theory economics can run lab experiments while in astrophysics researchers have to rely almost solely on observational data.
Consequently, once you break fields into sub-fields you will find that subfields from various fields can be on top of the hierarchy while other subfields from the same fields can end up at the bottom.


Are there any economic theories around the concept of companies focusing on that which is easier to calcuate? A lot of the organisations I have worked for have focused on that which is easy to calculate.

For example, direct cost savings are often easy to calculate, but analysing the wider implications of a cost cutting exercise are complicated.

A company might save money on their IT budget if they reduce the number of printers they use and this is relatively simple to calculate. However, the implications for productivity of having fewer printers is much more complicated and is often ignored (in my experience).

Are there any economic theories that investigate this effect?

Your question is ultimately one about information flow in networks under conditions of imperfect and incomplete information. I like your distinction between "easy" and "hard" to calculate - it's a good rubric for problem classification.

I believe that work being done on complexity theory and information flows can help shed some light on how to think about the issue. Cesar Hidalgo is a leading thinker in this field and has assembled some very interesting tools in the context of global trade (the Atlas of Economic Complexity being one). At the level of organizations, there would be an additional layer of complication arising from behavioural anomalies in decision-making that tend to bias human beings in favor of decisions cast in terms of simple data sets with clear narratives. This is the other side of the coin to Nassem Talib's "narrative fallacy", and of course, any study of behavioural biases must also include some time spent with the work of Kahneman and Tversky.


Suppose I have a preference satisfy all basic assumptions, how to show consumer problem solution is unique The preferences are complete, transitive, continuous, strictly monotone and strictly convex

The textbook says it is because
 (1) Budget Set is compact so that a solution exists;
 (2) B is convex and the utility function representing this preference is strictly quasi-concave

What if I have no information on budget set, that is, I don't know what properties B might have. Can all arguements above still hold?

Can I use the strict increasing utility function to prove the solution is unique? Since a preference with all these assumptions ensures a continuous, strictly increasing and strictly quasi-concave utility function. Then by contradiction, there can not be two or more maximization point of utility function.

In that case you would still have a problem showing the existence of a solution. Without existence, it makes little sense to think about uniqueness. The reason a continuous utility function (implied by some of those preference assumptions you gave) has a maximum at all is because a continuous function achieves a maximum somewhere on a compact set, which in this case is B.

Luckily, we don't really have to imagine scenarios in which we have no information about the budget set. This is not some abstract set, but rather something very concretely defined as:

$B(p,w)=\{x \in \Bbb R_{+}^{n}: px \leq w \}$,

where $p$ is the price vector, $x$ is the demand, $w$ is the budget and $n$ is the dimension of the vector.

Luckily, this is always compact.

So, no, you cannot show there is a unique solution, because in that case you can't show there is a solution in the first place (using standard tools).

However,  you are correct in thinking that uniqueness itself does not hinge upon the compactness of the budget set.


Number of observations in different panel data regressions Given a balanced two-period panel data, with lets say 1000 observations on 500 individuals.

When you estimate a pooled OLS regression and first-differences regression is there a standard in the economics literature on how you should report number of observations.

It seems most natural for me to report 500 observations in the case of first-differences.

This might seem trivial. But better follow any standard if it exists.

It is conventional to report both the total number of observations (1000 in your case) and the number of groups (500 in your case). If you want or are allowed to report only one number as the number of observations, it is suitable to report 1000 for POLS because POLS doesn't mind the fact that it is a panel data set. For FD, it is slightly confusing to me to say that the number of observations is 500. I would probably ask again of the writer what 500 means.


Externalities - First order conditions I am currently reading the book "Microeconomics: Principles and Analysis" by Cowell on my own. I'm reading the externalities chapter, and i found an interesting example:

There are just two firms: firm 1 is a polluter and firm 2 the victim. Firm 2 (the victim) makes an offer of a side-payment or bribe to firm 1. The bribe is an amount that is made conditional upon the amount of output that firm 1 generates: the greater the pollution, the smaller is the bribe; so we model the bribe as a decreasing function β(⋅).

The optimization problem is

My question is how did they arrive at those FOC's?

UPDATE:The second part of this optimization is to look at the problem from firm 1 perspective, it follows like this:
Now look at the problem from the point of view of firm 1. Once the victim
firm makes its offer of a conditional bribe, firm 1 should take account of it. So
its profits must look like this

This is from F.A.Cowell - Microeconomics - Principles and Analysis p.444-445

To make sure it's completely explicit: superscripts below are indices referring to either firm $1$ or firm $2$.

The choice variables in this problem are $\mathbf{q}^2$ and $\beta$. Notice that $\mathbf{q}^2$ is a vector of $n$ quantities. That is to say, $\mathbf{q}^2=\left(q_1^2,q_2^2,\ldots,q_n^2\right)$.

$(13.9)$ is just the derivative of the objective function $(13.8)$ with respect to $q_i^2$. Notice that you can rewrite the objective function $(13.8)$ as $$ p_1q_1^2+p_2q_2^2+\cdots+p_iq_i^2+\cdots+p_nq_n^2-\beta\left(q_1^1\right)-\mu_2\Phi^2\left(q_1^2,\ldots,q_i^2,\ldots,q_n^2 ,q_1^1\right) $$

Differentiating this with respect to $q_i^2$ and setting that equal to $0$ gives us $$ p_i - \mu_2 \frac{\partial\Phi^2 \left( \mathbf{q}^2,q_1^1 \right)}{\partial q_i^2}  = 0 $$

In Cowell's notation, $\Phi^2_i$ is just the derivative of $\Phi^2$ with respect to $q_i^2$.

The second first-order condition is the derivative of the objective function with respect to $\beta$. Since $\beta(\cdot)$ is a decreasing function of $q_1^1$, we can also think of $q_1^1$ as a decreasing function of $\beta$. (Formally, $q_1^1$ is the inverse of $\beta$, which is well-defined since $\beta$ is decreasing. Intuitively, if firm $2$ conditions their bribe on firm $1$'s level of output, then firm $1$'s output choice also depends on the amount of the bribe.)

Thus, applying the chain rule, the derivative of the objective with respect to $\beta$ is $$ -1 -\mu_2\frac{\partial\Phi^2 \left( \mathbf{q}^2,q_1^1 \right)}{\partial q_1^1} \frac{dq_1^1}{d\beta}=0 $$
which, unfortunately, isn't quite the same as in Cowell. Notice however that $\frac{dq_1^1}{d\beta}<0$, so perhaps he is using the absolute value of that derivative to get rid of the minus sign in front of $\mu_2$.


What exactly is Foreign Currency Indexation? As I understand it, foreign currency indexation (FCI) is when a government pegs its currency to another (usually the dollar), and their central bank buys or sells dollars to maintain a stable exchange rate between the two.

The material I have to read for my class mentions FCI in the context of the Mexican tesobonos and other domestic debt that was issued linked to another currency.

I am unable to find a resource online or otherwise that can distinguish between the two possible answers I'm given to the question "What is FCI":
1. When a country issues debt in another country's currency
2. When a country buys foreign currency to lower the value of its currency

One seems incorrect because I don't see how the option hits at the fact that the currency is being pegged to the dollar (or another stable currency), and two seems wrong because it does not account for the other side of the equation (selling to increase which I would assume is functionally correct).

Any input or suggestions?

A currency can be indexed but so can a bond. An indexed bond is one where the coupons and principal are indexed to another currency (the U.S dollar in the case of Tesobonos) at the spot rate in effect at the time of issuance. So you actually pay in the local currency but how much you pay depends on the prevailing exchange rates when payment is due.

A bond can be indexed without a currency being indexed. It is typically a way, much like a foreign currency denominated debt issuance, to remove local inflation and exchange risk from debt issuance.


When a tax is imposed on the sellers, the price of the good rises. So, why doesn't the demand curve shift? A tax imposed by the government on the sellers would drive up the price of the good. I understand that the supply curve will shift upwards due to this but the won't the demand curve also shift downwards due to the increase in price of the good?

I think you're confusing quantity demanded, and the demand curve.

The demand curve tells you how much quantity should be demanded at each price point. Therefore changes in price should change the quantity demanded, not shift the curve. You want to think of this in terms of demand and supply shocks.

For example:

Imagine it was discovered that bananas gave you super powers. Now the ability to supply bananas hasn't changed (no supply shock), but the desirability of bananas at any given price point has increased (demand shock).

An increase in price due to taxation has not impacted the desirability of goods at any given price point. It simply changes the price point.


Delay in the transmission of knowledge to poorer countries Assume the world consists of two regions, the North and South with the following production functions and technology lags in the south by $\tau$ years:
$$ Y_N = A_N (t) (1-a_L) L_N; \; \; \dot{A}_N = a_L L_N A_N (t)$$
$$ Y_S = A_S (t) L_S  ; \; \; A_S = A_N (t - \tau) $$
The growth rate of output per worker in the North is $3 \% \; year^{-1}$ and if $a_L \simeq 0$, what $\tau$ must be for output per worker in the North to exceed that in the South by a factor of 10?

For output per worker in the north to exceed that in the south by a factor of ten:
$$ 10 = \frac{Y_N/L_N}{Y_S/L_S} = \frac{A_N(t)(1-a_L)}{A_S(t)} $$
with $a_L \simeq 0$ this goes to
$$ \to \frac{A_N (t)}{A_N (t-\tau)}$$
My book says this is equal to $e^{0.03 \tau}$
Could someone explain where this last result comes from please?

By the notation used, labor quantity appears to be constant. Then the only source of growth of output is the growth in $A_N(t)$, and they will have the same growth rate. Take logarithms and then time derivatives on the output per capita equation to see this.
Then remember introductory differential equations on how to express $x(t)$ as a function of $x(0)$ and a constant growth rate. And don't forget to explicitly solve for the 10-factor difference required, at the end.


Skepticism about the claims of instrument variable validity/exclusion through a statistical test—the Arellano-Bond Test I am an applied researcher and occasionally come across papers that have panel data and that use dynamic models with both a fixed-effects term and lagged DV (or multiple autoregressive terms):
$y_{it} = \beta_0 + B_1X_{it}+\alpha y_{i(t-1)}+\delta D_{it} + \lambda_i + \gamma_t + \epsilon_{it}$
where $i$ denotes the panel unit and $t$ denotes the time dimension.  The parameter of interest is $\delta$ and $D_{it}$ denotes a binary treatment.  When the number of time periods is small, such a model cannot be estimated using OLS because of Nickell's bias.
One approach I have seen people use is to employ higher lags as instruments.  The identifying assumption is usually stated as no serial correlation between higher-order error terms.
Is it correct to take this assumption of no serial correlation as the exclusion restriction, i.e., the IV affects the final outcome only through the instrumented variable? If yes, then how does this square with the general point that causality/exclusion cannot generally be established with statistical tests such as the Arellano Bond Test, which statistically tests for the null hypothesis of "no autocorrelation," and proceeds if there is a failure to reject the null for higher orders?
In Mostly Harmless Econometrics (book), Angrist & Pischke write (p. 245):

The problem here is that the differenced residual, $\Delta \epsilon_{it}$, is necessarily correlated with the lagged dependent variable, $\Delta Y_{i(t-1)}$, because both are a function of $\epsilon_{i(t-1)}$. Consequently, OLS estimates of (5.3.6) are not consistent for the parameters in (5.3.5), a problem first noted by Nickell (1981). This problem can be solved, though the solution requires strong assumptions. The easiest solution is to use $Y_{i(t-2)}$ as an instrument for $\Delta Y_{i(t-1)}$ in (5.3.6).10 But this requires that $Y_{i(t-2)}$ be uncorrelated with the differenced residuals, $\Delta \epsilon_{it}$. This seems unlikely, since residuals are the part of earnings left over after accounting for covariates. Most people’s earnings are highly correlated from one year to the next, so that past earnings are also likely to be correlated with $\Delta \epsilon_{it}$. If $\epsilon_{it}$ is serially correlated, there may be no consistent estimator for (5.3.6).

Angrist & Pischke make no reference to the Arellano Bond Test to establish the validity/exclusion of the IV.  Instead, they make qualitative arguments as I generally see with IV models used for other types of data generation processes.
Does the Arellano Bond (AB) Test really establish exclusion/validity?  Or, is it merely a diagnostic that may be used as a secondary argument along with primarily qualitative arguments for exclusion.  If the AB test is merely a diagnostic, how should one evaluate research studies that assert identification on the basis of the AB test?  (i.e., the AB test fails to reject the null of "no autocorrelation" but qualitatively, one may have reasons to believe that there should be a correlation but the current sample does not show it).
NOTE: Slightly edited version cross-posted on https://stats.stackexchange.com/questions/490747/skepticism-about-the-claims-of-instrument-variable-validity-exclusion-through-a

If yes, then how does this square with the general point that
causality/exclusion cannot generally be established with statistical
tests...

It seems to me that "[exogeneity of IV] cannot generally be established with statistical tests" does not imply that it cannot be tested in specific cases. In this (very specific) context, the exogeneity claim rests on absence of serial correlation, which in principle can be tested as a null.

Or, is it merely a diagnostic that may be used as a secondary
argument along with primarily qualitative arguments for exclusion?

I would agree with you there. A non-rejection of the no-serial correlation null is by itself insufficient to establish exogeneity.
(If, hypothetically, the null hypothesis is presence of serial correlation, then yes, but such tests seems statistically unfeasible.)


Need examples for confusion about rent-seeking. Who is the seeker and what is the rent? Please answer assuming I have no background in economics. I keep coming across this term in various articles (Example) but get more confused every time I look up what it means.
I have read about the concept of economic rent and how it is different from colloquial use of the word rent. But it still doesn't help because the definition of economic rent is too technical for me :(
Here's an example of rent-seeking from Wiki:
An example of rent-seeking in a modern economy is spending money on lobbying for government subsidies in order to be given wealth that has already been created.
Who is the rent-seeker in this example? And what is the rent - the money spent for lobbying or the subsidy availed?
It'd be great if someone can give a few more diverse examples (like where the State is rent-seeker or an individual businessman is rent-seeker). More importantly, please break down the example by who is the rent seeker and what is the rent. Thanks!

Rent-seeking

Has no single agreed-upon definition (see the many definitions below).
Is a fancy synonym for "bad for society" (see especially Tullock, 1989 below).
Sometimes (but not always) refers specifically to lobbying (your example seems to be following this usage).

(In light of the above, my opinion/recommendation is that everyone should simply avoid using the term rent-seeking. If one simply means "bad for society", then one should just say that. If one is thinking of "lobbying", then one should just say that. However, I don't expect that my recommendation will be adopted because rent-seeking has the advantage of being an unfamiliar and technical-sounding term that helps writers sound more intelligent than they are.)

Krueger (1974) introduced the term rent-seeking:

In many market-oriented economies, government restrictions upon economic activity are pervasive facts of life. These restrictions give rise to rents of a variety of forms, and people often compete for the rents. Sometimes, such competition is perfectly legal. In other instances, rent seeking takes other forms, such as bribery, corruption, smuggling, and black markets.

Gordon Tullock credits himself with introducing the concept in 1967. Tullock himself gives various definitions of the term:
Tullock (1989):

My suggestion is that we use the term “rent seeking” (and I always have) solely for cases in which whatever is proposed has a negative social impact.

Contradicting himself, Tullock (1987):

‘Rent seeking’ refers to the investment of resources in efforts to create monopolies.

Definitions by some other writers:
Hyde & Borzutzky (2016):

political rent-seeking—the pursuit of unearned income streams by lobbying government for market privileges

Henderson (2008):

People are said to seek rents when they try to obtain benefits for themselves through the political arena. They typically do so by getting a subsidy for a good they produce or for being in a particular class of people, by getting a tariff on a good they produce, or by getting a special regulation that hampers their competitors. Elderly people, for example, often seek higher Social Security payments; steel producers often seek restrictions on imports of steel; and licensed electricians and doctors often lobby to keep regulations in place that restrict competition from unlicensed electricians or doctors.

Parson (2004):

the using up of real resources in an effort to secure the rights to economic rents that arise from government policies.

Bateman & McAdam (2003):

the act of trying to improve personal income at the expense of someone else, rather than by increased work or productivity

Khan (2000):

a person gets a rent if he or she earns an income higher than the minimum that person would have accepted, the minimum being usually defined as the income in his or her next-best opportunity ... Rents may take the form of higher rates of return in monopolies, the extra income from politically organized transfers such as subsidies, or the extra income which comes from owning scarce resources, whether natural resources or specialized knowledge. ...

Rent-seeking is the expenditure of resources and effort in creating, maintaining or transferring rents.

Black (1997):

Spending time and money not on the production of real goods and services, but rather on trying to get the government to change the rules so as to make one's business more profitable. This can take various forms, including seeking subsidies on the outputs or the inputs of a business. or persuading the government to change the rules so as to keep out competitors, tolerate or promote collusion between those already engaged in an activity, or make legally compulsory the use of professional services.

Rutherford (1995):

Monopolizing activity. This is much criticized as it produces a social waste rather than a social surplus.

Murphy, Schleifer, & Vishny (1993):

any redistributive activity that takes up resources

Pearce (1992):

The use of real resources in an attempt to appropriate a surplus in the form of a rent. An industry may use resources to lobby a government to impose a restriction such as a TARIFF on an imported good, so that the factors of productions in the industry earn payments in excess of their TRANSFER EARNINGS as a result of the higher market price for the good, which they produce. Consumers suffer two losses from rent seeking; the loss of CONSUMERS’ SURPLUS from the higher price and the loss of output from the resources devoted to rent-seeking. Resources may subsequently be devoted to rent protection. In international economics a related, though different, concept has been developed with the name, directly unproductive profit-seeking (DUP).

Bannock, Baxter, & Davis (1992):

Behaviour that improves the welfare of someone at the expense of the welfare of someone else. The most extreme example of rent-seeking behaviour is that of a protection racket, in which one group betters themselves without creating any welfare-enhancing output at all. Not all examples are criminal, however: the behaviour of labour or management when they put more effort into increasing their share of turnover, rather than into increasing the total volume of turnover, can be described as rent-seeking.


Proving that constant absolute risk aversion and relative risk aversion implies independence of initial wealth I was able to prove that for a portfolio with one risk-free asset and one risky asset, if the Arrow-Pratt measure of absolute risk aversion is constant (i.e., constant absolute risk aversion, CARA), then the dollar amount invested in the risky asset does not depend on the agent's wealth. Similarly, with constant relative risk aversion (CRRA), the proportion of wealth an agent invests in the risky asset also does not depend on the agent's wealth.

Now, how can I prove the more general statement that with CARA and $N$ risky assets, the amounts of wealth invested in each of the $N$ risky assets is independent of the agent's initial wealth? As well as the analogous statement for CRRA?

The foundation for my exposition comes from Mas-Colell's examples in Ch. 6.

The maximization problem for your specific question can be generalized pretty easily. Consider the case with one risky asset and one riskless asset. Let $\beta$ be the wealth invested in the safe asset, normalized to 1 dollar per dollar invested. Let $\alpha$ be the wealth invested in the risky asset, which has some random payout $z$ such that:

$$\int z \ \text{d}F(z) > 1$$

So that the mean return is greater than the riskless asset. So we express our maximization problem as:

$$\max \ \int u(\alpha z + \beta) \ \text{d}F(z) \\
\text{s.t.} \quad\alpha + \beta = w$$

You can take advantage of the fact that $w - \alpha = \beta$ $\implies \alpha z + \beta = w + \alpha(z - 1)$ and find first order conditions. If $u$ is concave (risk averse) then Kuhn-Tucker FOCs which combine to make:

$$\int u'(w + \alpha(z - 1))\cdot(z - 1) \ \text{d}F(z) = 0 \quad \text{iff} \quad \alpha \in (0, w) $$

So for the generic case, you can do the same setup with $N$ risky assets and one riskless asset that is better than whatever other riskless assets are out there. Let's normalize it again to payout of 1.

So the maximization is now:

$$\max \int u(\alpha_1 z_1 + \cdots + \alpha_N z_N + \beta) \ \text{d}F(z_1, \cdots z_N) \\
\text{s.t.} \quad \alpha_1 + \dots + \alpha_N + \beta = w$$

Notes:

If you have already done the easy case, this general case should not be so bad, just some more work. For other readers, I'll state the definitions of constant absolute and relative risk aversion below, respectively.

$$r_A(x) = -\frac{u''(x)}{u'(x)} = n \quad \forall x$$
$$r_R(x) = -\frac{x \cdot u''(x)}{u'(x)} = n \quad \forall x$$


get statistics about the research intensity of an industry I want to know how much research is conducted in an industry in order to be able to say Industry X is more research intense than Industry Y.

For industry categorization I use the NACE classificiation.

I know that research intensity per se is an indicator which can be calculated as:

Ultimately, I want to be able to say, that some industries are more welcome to conduct R&D projects.

Please let me know, if there are any more suitable indicators than R&D intensity. Someone (informally) told me, that R&D intensity is out of fashion, and that IPP (intellectual property products) would be more suitable. However, I am not sure about that.

Perhaps someone with more expertise on the matter can answer your question more directly, but in the mean time:

In the literature on innovation, it is fairly common to use patent data to measure the intensity of innovation activity.

Here are Aghion et al (2005) on their approach:

  "There is a large literature on measuring innovation intensity, with the most commonly used measures being R&D expenditure and patenting activity. We use the average number of patents taken out by firms in an industry, and to reflect the
  heterogeneous value of patents, we weight each patent by the number of times it has been cited by another patent. These data are generated by matching the NBER patents database to accounting data on firms listed on the London Stock Exchange
  (from Datastream). Our sample includes all firms with names beginning "A" to "L" plus all large R&D firms. After removing firms involved in large mergers or acquisitions and those with missing data, we have an unbalanced panel of 311 firms spanning seventeen two-digit SIC codes over the period 1973-1994. We also have information on citations to and from each patent, which enables us to construct a count of citation-weighted patents. We take the average value of citation-weighted patents of firms within each industry (SIC code) in each year. We do not observe a sufficient number of firms in all industries in all years, so our resulting industry level panel is also unbalanced with 354 industry-year observations."

The latest version of the patent database to which they refer can be viewed here. Aghion et al.'s data is available here.


Best formula for price depending on amount What is the best formula of price of the product depending on amount. I mean "best" in psychological, marketing, stock rotation, profit maximizing, etc sense (any of them or all together, if possible).

Say, I often see that prices on Coca Cola bottles growing not as fast as volume of them.

I sure there is the best formula, invented by psychologists or derived empirically then proved in use.

I think your expectation that a "best" formula exists is very unreasonable.

There is no "best" car design, there isn't a formula to design the fastest airplane with total weight $x$ and there is no easy formula that will give you the best price in general situations.

Sciences have a lot of unsolved optimization problems. Economics, psychology and most sciences involving humans have a lot of seemingly unknown variables, further complicating things. So while there are some principles which you can base your pricing strategy on I have never heard any reasonable person claim that a general best price mechanism exists and I don't think it does.


Illustrating difficulty to find dominant strategies: series of simple one-shot two-players games For a game theory class I am prepping, I am looking for simple mathematical puzzles that can easily be presented as one-shot 2-players simultaneous games in which one of the players has a dominant strategy. The puzzle is to find the dominant strategy.

My goal is to interactively illustrate how "games are not equal in the face of dominant strategies": Although standard game theory predicts that players will play dominant strategies when they have one, dominant strategies can be more or less easy to identify in different games, which may lead players to play dominant strategies more often in some games than others.

I would like to do so by putting students in the shoes of the player who has a dominant strategy in a series of games in which the dominant strategy is increasingly hard to find.

Note that the game of Nim is excluded because it is neither one-shot nor simultaneous. The games could for example (but do not have to) look like this:

  The other player will choose and integer $y$ satisfying property $P_1$ (e.g., $y$ is contained in some subset of integers). You must yourself choose an integer $x$ satisfying property $P_2$. You win if $f(x,y)$ (e.g., $x+ y$) satisfies property $P_3$.

My question is: can anyone provide a series of games that would do the job?

Desirable qualities of the series are:

Ideally, the series should contain between three and four games.
Games should be easy to explain.
Games should be "truly interactive" in the sense that the other player can actually influence the outcome (no "The other player will choose $y$. You must choose positive integer $x$. You win if $31^3+33^3+x^3 = 76^3$.")
Games should be as "entertaining" as possible (sorry, I know this is subjective).
The progression in the difficulty to find dominant strategies should ideally come from dominant strategies becoming more and more "clever", as opposed to checking an increasing number of "cases" (sorry, I know this too is subjective).
I should be able to explain why the dominant strategy is what it is in class relatively quickly (I.e., ideally dominant strategies should be of the kind "hard to find, but easy to understand once you know what it is")

Start with the following matrix.
$$ \begin{matrix}1 && 0 && 0\\
1 && 1 && 0\\
1 && 1 && 1  \end{matrix}$$

You will choose a $1$ in the matrix and change it to a $0$. The other player will choose a $0$ and change it to a $1$. Your goal is for the resulting matrix to have an even determinant. The other player's goal is for the resulting matrix to have an odd determinant.

Hover over the box to find out the dominant strategy:

   Change the $1$ in the bottom left corner to a $0$.


Is there a good way of assessing an estimated absolute value of a currency? If we want to figure out the strength of a currency relative to another currency, we look at the exchange rate between the two. However, I'm wondering what is the most accurate way of assessing the absolute value of a currency?

I suppose commodities or gold could be used, but there can be variations on the value of those over time (i.e if there is a new use for gold in electronics, the value is obviously going up.) So have economists found a better way?

Actually there is an effort by IMF that indirectly offers a common unit of measurement to express the value of the major world currencies homogeneously.

It's called SDR (Special Drawing Rights) sometimes abbreviated as XDR. It's a sort of meta-currency whose value is calculated as follows:

  The value of the SDR in terms of the U.S. dollar is determined daily
  and posted on the IMF’s website. It is calculated as the sum of
  specific amounts of each basket currency valued in U.S. dollars, on
  the basis of exchange rates quoted at noon each day in the London
  market.

  The basket composition is reviewed every five years by the Executive
  Board, or earlier if the IMF finds changed circumstances warrant an
  earlier review, to ensure that it reflects the relative importance of
  currencies in the world’s trading and financial systems IMF website


Research around the free-rider problem when the resource is taken away? Today, Wikipedia is again running a donation drive in an attempt to raise more money. Their requests seem to occur more frequently each year. I would guess that 99.99%+ of Wikipedia users never donate, and yet continue to use the service. The existence of Wikipedia as a resource certainly isn't "free," as servers cost money. I wondered what all of the free-riders would do if Wikipedia were to run out of funding and not exist as a resource anymore.

Can anyone share some insight/examples around what happens in a given microeconomy in which the "free" good - the existence of which results in the free-rider problem - is taken away? Is there a sudden rush from the free-riders to pay, and then after some time, donations regress to their original mean?

This may not be exactly what you're looking for, but your question reminds me of the work of Elinor Ostrom, who (along with Oliver Williamson) won the Nobel in Economics for her work on what academics in the field call 'the commons'.

Here's a good place to start reading about her work. Check under 'Popular Information' and 'Advanced Information' in particular for details about her work.


Currency Values, Developing Economies and Balance of Trade For a developing economy like India, where balance of trade is negative, is it good to have a weak dollar or a strong dollar?

Dollar value increases (Rupee, the local currency, weakens), imports (especially of oil) are done at an extremely high price, that leads to pressure on inflation and people (Central Bank etc.) are concerned. Personally as an exporter, we are a viable business today primarily because of a strong dollar, if the currency remained where it was two years back, our business would have made great losses and probably even shut down.

My thought process is if the local currency becomes very weak, imports would become expensive; while some imports like oil cannot be avoided, many other goods that are imported today would become viable to be produced locally, this means lesser imports in the long run, and similarly since exports would produce more revenue, more businesses would become viable and hence in the long run exports would increase.  This would eventually result in positive balance of trade and the effect would be a positive spiral.

Given the short term inflationary shock and long term benefits of employment and thereby prosperity, is it generally better if the Central Bank doesn't interfere in currency devaluation and lets the Market find its own equilibrium.

The primary question stems from the worry that it is a common conception in India that with a strong dollar the country will be doomed.

If my argument is weak, can anyone explain why?

Currency values change relatively slowly over time, partly due to differences in the rate of expansion of the money supply over time between different countries, and partly due to changes in the terms of trade.

If we compare the Indian Rupee with the US dollar. M2 for the US dollar roughly doubles every 10 years, the Rupee is going up roughly 5 times in the same period. The Indian M3 measure is equivalent to the US M2 measure (M measures vary considerably between countries in what is being measured.)

US Dollar M2
Indian Rupee M3

This is why the Rupee is getting progressively weaker, and will continue to do so, especially if balance of payments are also negative. The ratio of rupees:dollars is increasing, and so the value of rupees in dollars is falling, as the market tries to maintain equilibrium.

When the central banks intervene in the currency markets, they essentially use their position to alter the relative value by buying/selling as appropriate. However, in this case they can only do this if they have foreign currency to sell, and with a negative balance of payments, and a rapidly expanding money supply, they are essentially in the position of standing on the sea shore and telling the tide not to come in.

While all of the above is the monetary side of things, as an exporter you're standing on the trade side of the equation, and what you say is quite correct. All things being equal, over time local producers will step in to provide the imports that are now too expensive, exports will flourish, and the situation should reverse itself as you explain. However, that implicitly assumes that money supply expansion rates are broadly similar, and that clearly isn't the case. Unless and until the Indian central bank gets its banking system under control, and slows down the expansion in the money supply, you can essentially rely on continuing inflation, and a weak currency.

It continues to be an open question in Macro-Economics as to what the 'right' degree of monetary expansion is. However, there is a very strong correlation between countries with low expansion rates, Germany for example, and economic strength. There are a lot of negative effects within the economy when inflation rates are too high due to monetary expansion, fundamentally because it leads to widespread distortion of the price signal.


Do wages differ in two perfectly competitive labour markets? I understand that within a single labour market, the wages would be the same between two workers as firms and workers are both wage takers, but what about when there is more than one perfectly competitive labour market: if the labour market for jobs A and B are both perfectly competitive, would the workers in A earn the same as the workers in B, provided that the two jobs are not the same?

This will typically depend on if people can switch between the two markets. If switching is possible then the marginal worker has to be indifferent between working in market A and market B and this equalizes the wages in the two markets. This also assumes you mean wage rates and not wage bills. Wage bills also depend on hours worked per worker, and that decision need not be equal across industries because of sorting and other reasons.

If people can't switch between markets it can, but doesn't have, to be that wages do not equalize. Consider two workers on two different islands with residents that don't trade or even meet. Even if labor markets on both islands were perfectly competitive, it needn't be that their wage rates were equalized.


Any research done on relationship between fertility rate and wealth? I am discussing about evolution theory with a philosophy student and she observes that wealthier families tend to have fewer children, which kind of goes against natural selection, i.e. the genes of smarter/healthier people do not necessarily pass along the generations.

Now I am thinking:

Is there really such a pattern? If yes,
Does it vary across different environments (e.g. developed vs developing countries)?
What is the economics explanation?

References to papers are very welcome.

I am not sure how to tag this question, feel free to edit.

Population changes slowly over time but has large effects in the long-run.
Here are some well-studied facts about fertility:

Before the industrial revolution, the rich had more surviving children than the poor.
The transition from stagnation to economic growth is accompanied by a demographic transition from high to low fertility.
Today, both within and across countries, rich and educated mothers have less children than poor and unskilled ones.
Most of the literature finds that the income of the father positively affects fertility, while the income of the mother negatively affects fertility.

Economists would stress that one explanation among others is Parents' income: Opportunity cost of child-rearing time is high for high income/education mothers. They are other reasons.

David de la Croix works on this topic and offers interesting lectures on Fertility, Education, Growth and Sustainability here. You will find references for the above facts and other reasons for the decline in fertility.

An academic reference is: De la Croix D. and M. Doepke, Inequality and growth: why differential fertility matters, American Economic Review, 93, 1091-1113, 2003.


How would one take advantage of this arbitrage opportunity? I have a quick question about how arbitrage works. Let's say that there are two investments:

Invest in a two-year zero
Invest in a one-year zero and then reinvest into a forward contract from year one to year two.

The no arbitrage principle theoretically states that since one could make unlimited money, these two investment strategies must be priced equally.

I am a little confused as to how one would take advantage of this arbitrage opportunity. Suppose investment 2 costs more than investment 1. I suppose I would have to somehow borrow money and sell investment 2, take that money and put it in investment 1, and then pay back investment 2? I'm really not sure who I would be borrowing from and how I would be able to sell. If someone could give me a step-by-step process on how to take advantage of a hypothetical arbitrage opportunity, that would be greatly appreciated.

Hi: Don't think of a specific case. Just think of investment A and investment B and assume that the return on both investments is the same. Also, assume that investment A costs more to invest in than investment B. In that case, you would sell some amount, X, of investment A to Mr. Pushover and buy the same amount, X, of  investment B with the proceeds from Mr. Pushover ( and you'll have a little left over since A costs more than B. Call  what's left, L, for leftover ).

Then, when the investment horizon is complete, you pay Mr. Pushover the return with the return that you made from investing in B.

But,  now you still have L left so you made L with no risk. That's the arbitrage. I hope that helps. To summarize, if two investments return the same thing, they have to cost the same thing or else there's an arbitrage.


Extreme Value Theorem in Economics Would appreciate some thoughts on proving the existence of a solution (a maximum) in an applied context.
Suppose the objective function is one of maximising utility:
$$\max\Sigma\beta U(C_t)$$
Subject to some constraints on resources, say:
$$\\C_t+K_{t+1} = F_F(K_F,E_F,S_t)$$
Where the constraint is the economy's resource constraint, inclusive of current consumption $C_t$ and investment possibilities $K_{t+1}$, set equal to the production function $F_F$, which includes arguments on capital $K_t$, energy, $E_t$ and the emissions stock $S_t$ (i.e. emissions affect production costs).
The extreme value theorem states 'that a continuous function throughout a non-empty compact set will have a max (min. respectively)'.
In this respect, my questions is: what are the requirements for the feasible set of solutions to be on a compact set?

non-negativity of variables?
terminal conditions on the variables (i.e. they are all exhausted in the future)?

Would appreciated some thoughts, for sure.

One can prove the existence of such optimal plans using the extreme value theorem of Weierstrass, but it requires some advanced math.
Here is a toy version of the model without energy and emissions. Both the instantaneous utility functions $u:\mathbb{R}_+\to\mathbb{R}$ and the production function $f:\mathbb{R}_+\to\mathbb{R}$ are assumed to be continuous and nondecreasing. Moreover, $u$ is assumed to be bounded (!). There is given initial capital stock $k_1\geq 0$. The space of feasible consumption and production plans is defined as $$F=\big\{(c_1,k_1,c_2,k_2,\ldots)\mid 0\leq k_{t+1}\leq f(k_t-c_t)\}, k_t\geq c_t\geq 0\big\}.$$
$F$ describes all feasible paths of consumption and capital.
This set is a nonempty compact subset of $\mathbb{R}^\infty$ endowed with the product topology. Here is why: By Tychonoff's theorem, the set $$\prod_{t=1}^\infty [0,f^t(k_1)]^2$$ with $f^0$ the identity function $f^{t+1}=f\circ f^t$ is compact and $F$ is a subset of this compact set.  By definition, all coordinate functions are continuous. Each of the relevant inequalities defines a closed set and $F$ is, therefore, a closed subset of a compact set and, therefore, compact itself. Also, the plan that never invests and consumes everything is in $F$, so $F$ is nonempty.
The utility function $U:F\to\mathbb{R}$ given by
$$U(c_1,k_1,c_2,k_2,\ldots)=\sum_{t=1}^\infty \beta^t u(c_t)$$
is well-defined and continuous in the product topology. Since the utility function is bounded, $U$ will always be finite and, therefore, well-defined. To see that it is continuous, note that since $u$ is bounded, there exists for each $\epsilon>0$ some $T$ such that the utility of any two paths that only differ at times later than $T$ can differ by at most $\epsilon/2$. Since all coordinate functions are continuous, if the two consumption plans are close enough in the first $T$ coordinates, they will differ at most by $\epsilon/2$. So if the paths are close enough at finitely many coordinates, the corresponding utility will be close enough. So $U$ is continuous in the product topology.
So $U$ is a continuous function on the nonempty compact set $F$. By the extreme value theorem of Weierstrass, $U$ takes on a maximum at some point in $F$ and such a point is an optimal plan.
You can find a more general proof of the existence of optimal plans along these lines in the book "Dynamic Programming in Economics" by Le Van and Dana. The assumption that $F$ is increasing is not needed, you can replace the product of intervals that includes $F$ by bounding it with the largest values that can be produced instead of the one that comes from always reinvesting capital. That $u$ is bounded was assumed to guarantee that $U$ is finite. One can replace this by an assumption that guarantees that the instantaneous utility cannot increase to
fast along a feasible path.


Solving Euler Equation for standard DSGE Models I am studying a rather standard DSGE Model with a standard Utility function $U = f(c_t, n_t, M_t)$ subject to a budget constraint. Now, tosolve the intertemporal optimization problem I have, or everyone has, to deal with an expectation term; often similar to $E_t \left[\lambda_{t+1}\right]$, where $\lambda_t$ is the standard Lagrangian multiplier. Is there an anlytical trick to solve this? It seems to me the that usually the Expectation is just erased (without a justification) or studied using MLE estimators or Kalman Filters and surrogates.
Thanks to whoever can enlighten me on the issue.
Cheers

Edit 1:
$\max_{c_t, n_t, i_t, M_t, K_t, B_t}{\mathbb{E}_t}\left[ \sum_{t=0}^{\infty} \beta^t \left( \log{(c_t^i)} - \gamma_i(n_t^i)^{2}+ \log \left(\frac{B_t}{P_t} \right) \right) \right]$
under the constraint:
$\frac{M_t}{P_t}+ c_t + i_t +  \frac{B_t}{P_t(1+r_t)} \leq u_t n_t + \frac{Q_t}{P_t}K_t + \frac{B_{t-1}}{(1+\pi_t)P_{t-1}} +\frac{M_{t-1}}{(1+\pi_t)P_{t-1}}$
The issue is wrt to a term which comes up in both the maximisation wrt to Bonds and Money: $\beta {\mathbb{E}}_{t}\left[\frac{\lambda_{t+1}}{(1+\pi_{t+1})}\right]$ - how could I solve it? (with theother terms it would lead $ c_{t}^{-1}=\beta {\mathbb{E}}_{t}\left[\frac{c_{t+1}^{-1}}{(1+\pi_{t+1})}\right]$

It really depends on the problem. As to why it would disappear, sometimes you can express the multiplier in terms of variables at the present or past, as in $\lambda_{t+1}=\lambda_{(c_t,n_t,M_t)}$ , which means it's an expectation over values that are known at that time. Therefore, you have $E_t[\lambda_{t+1}]=E_t[\lambda_{(c_t,n_t,M_t)}]=\lambda_{(c_t,n_t,M_t)}=\lambda_{t+1}$

But, as said above, it depends on the problem.


Minimum sample size for cross-sectional RDD I haven't done a regression discontinuity design (RDD) before. I know it requires a large sample size for identification, thus I fear that my sample size is not large enough.

The study is cross-sectional, not longitudinal.
Entire sample size is around 1000, and the sample size around the cutoff point is around 100.

Is it enough for a cross-sectional fuzzy RDD?

What is the "minimum" sample size and "good-enough" sample size for cross-sectional fuzzy (sharp) RDD?

I've run RDDs on similar sample sizes and got the paper accepted at a respectable conference. It's important to run McCrary Density Tests on your sample to look for people using knowledge on the treatment assignment rule to manipulate results and - even more important - to have a clear identification strategy, a qualitative justification for what you're doing.


Sources for macro economic forecast data I need data for these long run(atleast 10year forward) macroeconomic parameters from 2000, meaning I need forecasted data as in 2000 for 2010 so I can backtest my model with actual realised data:

Long run aggregate gdp growth

Long run population forecast by age groups

Long run inflation forecast

Current account deficit forecasts

Kindly provide me all available sources to such data.

GDP: If I remember correctly, Congressional budget office offers 10-12 yr forward potential gdp every quarter, from which you can derive predicted potential growth.

PopGrowth: U.S. Census has this data

Inflation: Fed Res/Philidelphia provides inflation forecast

Account deficit: All the sources for 5 or more years forecast in int. trade are either proprietary or highly unreliable. Best of luck in your search.


A question about a derivation in Gali's Monetary Policy book In Chapter 3 of Gali's famous Monetary Policy book, he measures the effects of a monetary policy shock.

The interest rate rule is:

Then a shock $v_t > 0$ occurs.

He proceeds to measure how this affects $y$, $\pi$ and $r$ (output, inflation, and real interest).

As you would expect, $y, \pi$ go down, $r$ goes up. However, he then derives the following equation, which measures what happens to the nominal interest rate:

However, I simply cannot for the life of me figure out how he derives this equation. I mean, I totally get that he's just using the Fisher equation. But why doesn't he go back to the interest rate rule from the first picture and use that? Why is he suddenly ignoring his own rule and relying fully on a basic identity like the Fisher equation?

As mentioned in the comments your question is not possible to answer as it is, but you should know that in macroeconomic models of growth exogenous shocks are measured by log-linearising equations around their steady state and then calculating impulse responses (that is, the magnitude and persistence of a shock to the variables of interest). This must be precisely what your book shows you, and unless you become familiar with macroeconomic modeling this question will hardly be answered any better than it is on your book.


Inverse/negative relationship between investments and interest rate The investments (I) have a negative relationship with interest rate (r)
$$
I = e-f \cdot r.
$$

So $e$ can be interpreted as a minimum level of investments while $f$ can be interpreted as how much the interest rate (r) affects the investments (I) negatively.

I don't understand why an increment in interest rate (r) implies a negative effect on the investments (I).

I thought that my investments would become more valuable if the interest rate increases, so from my point of view, people would be more interested in investing if the interest rate increases.

I guess I have misunderstood something.

The investment I earns income in the future. This income can be compared to the risk free rate of interest in the market to determine whether the income earned on I exceeds the opportunity cost of investing in I.

When interest rates rise, it is more worthwhile for an investor to purchase risk free bonds rather than invest in I. This decreases the demand for I, hence its price decreases.


Why did the EUR/USD go down immediately when the Fed cut interest rate? I was following the Fed’s decision on interest rates. I thought if there is an interest rate cut, the EUR/USD will go up but contrary to that it went down on 07/31/2019 immediately after the decision to lower interest rates. Some sites claim that the Fed didn't cut enough (50 basis points) as opposed to the actual cut of 25 basis points. I have been following the news for almost 3 months and no one expected a 50 basis point cut. Is there something I am missing?

One possibility is that although market participants had generally expected a 25-basis-point cut, they had also assigned a small probability to a bigger 50-basis-point cut.

And so, when it was confirmed that the cut would be 25 rather than 50 points, market participants then reacted accordingly to this (mild) surprise by strengthening the USD.

Edit: Actually, a bigger factor may have been the Fed's failure to promise more stimulus/rate cuts in the coming months (as some/many may have hoped).

For example, Wall Street Journal:

  Stock markets sold off and the dollar strengthened Wednesday afternoon after Fed Chairman Jerome Powell disappointed investors in his post-decision news conference when he didn’t more explicitly ratify expectations of additional stimulus in the months ahead.


Speed of convergence of output on the balanced growth path Find how quickly $y$ converges to $y^*$ in the vicinity of the balanced growth path
  $$ y=Y/AL=f(k); \; y^*=f(k^*) $$
  They suggest the hint, write $k=g(y)$, where $g(\bullet)=f^{-1}(\bullet)$.)

  $Y$ is product output; $AL$ is effective labour; $K$ is capital; lowercase letters are divided by $AL$ (e.g. $y=Y/AL$); $k^*$ is the balanced growth path of capital.

This is problem $1.11$ in Advanced Macro by Romer.  I have tried looking at Lagrange Inversion Theorem, and applying the above get to the first order Taylor series centered around $k^*$

$$ \displaystyle g(y) = k^* + \lim_{k \to k^*} \left( \frac{y-f(k^*)}{1!} \right) \frac{d^0}{dw^0} \left( \frac{k-k^*}{f(k)-f(k^*)} \right) $$

but since $y=f(k)$ and the zeroth derivative is the function itself, we get the following cancelation:

$$ = k^* + \lim_{k \to k^*} \frac{f(k)-f(k^*)}{f(k)-f(k^*)}(k-k^*) $$

$$ = k^* + \lim_{k \to k^*}(k - k^*) = k^* $$

Which doesn't tell us anything ... Do we need to look at the second order derivative?

Okay so, in the book they looked at the first order taylor series of $\dot{k}$, so as @denesp said, we need the time here too!  So rather here we should look at the taylor series around $\dot{y}$

$$ \displaystyle \dot{y}(y) \simeq \left[ \frac{\partial \dot{y}(y)}{\partial y(k)} \bigg|_{y=y^*} \right] (y(k) - y(k^*)) $$

$$ \frac{\partial \dot{y}(y)}{\partial y(k)} \bigg|_{y=y^*} = \left( \frac{\partial \dot{y}(y)}{\partial k(t)} \bigg|_{y=y^*} \right) \left( \frac{\partial k(t)}{\partial y(k)} \bigg|_{k=k^*} \right) $$

First we look at:

$$ y=f(k) $$

$$\Rightarrow \dot{y} = \frac{d}{dt} f(k) = \frac{d f}{d k} \frac{dk}{dt} = f'(k) \dot{k} $$

We know the key equation of the Solow model is:

$$ \dot{k}(t) = s f(k(t)) - (n+g+\delta)k(t) $$

$$ \Rightarrow \dot{y} = f'(k) \left[ s f(k(t)) - (n+g+\delta)k(t) \right] $$

We take the derivative of this with respect to capital:

$$ \frac{\partial \dot{y}}{\partial k} = f''(k)\left[ s f(k(t)) - (n+g+\delta)k(t) \right] + f'(k) \left[ s f'(k) - (n+g+\delta) \right]$$

The value $k^*$ is the golden-rule level of the capital stock so:

$$ s f(k^*) = (n+g+\delta)k^* $$

And hence

$$ \left( \frac{\partial \dot{y}}{\partial k} \bigg|_{y=y^*} \right) = f''(k^*)*(0) + f'(k^*)\left[ s f'(k^*) - (n+g+\delta) \right] $$

Next we use the hint (not much of a hint, and rather misleading to begin with in my opinion)

$$ \left( \frac{\partial k(y)}{\partial y(t)} \bigg|_{k=k^*} \right) = \left( \frac{\partial y(k)}{\partial k(t)} \bigg|_{y=y^*} \right)^{-1} = f'(k^*)^{-1} = g'(y^*) $$

Plugging both of these in to our first order partial derivative:

$$ \frac{\partial \dot{y}(y)}{\partial y(k)} \bigg|_{y=y^*} = \left( f'(k^*)\left[ s f'(k^*) - (n+g+\delta) \right] \right) * \left( f'(k^*)^{-1} \right) $$

$$ = s f'(k^*) - (n+g+\delta) $$

since around the balanced growth path $s = (n+g+\delta)k^*/f(k^*)$ and putting

$$ - \frac{\partial \dot{y}(y)}{\partial y(k)} \bigg|_{y=y^*} = \lambda $$

$$ \lambda = (n+g+\delta) - \frac{(n+g+\delta)(k^*)*f'(k^*)}{f(k^*)} $$

With $\alpha_k = \frac{k*f'(k)}{f(k)} $ being the elasticity of output with respect to capital we obtain:

$$ \lambda = (n+g+\delta)(1-\alpha_k(k^*)) $$

So $y$ converges to its balanced growth-path value rate $\lambda$ the same as $k$ converges to $k^*$


Difference between Unit and Share? I was reading the ISO 10962 (the 2015 version) which classifies financial instruments.

In the Collective Invesment Vehicle (CIVs) they separe them in:

Standard Funds
Hedge Funds
REIT
ETF
Pension Funds
Fund of Funds
Private Equity Fund

In the fourth attribute of each one of that CIVs is "Security type and investors restrictions" and the possible values are:

Shares
Units

Question: What is the difference between both?

Investopedia

Mutual fund units, or shares, can typically be purchased or redeemed as needed at the fund's current net asset value (NAV) per share, which is sometimes expressed as NAVPS. A fund's NAV is derived by dividing the total value of the securities in the portfolio by the total amount of shares outstanding.

Open-end fund (wiki)

An open-end fund is equitably divided into shares which vary in price in direct proportion to the variation in value of the fund's net asset value. Each time money is invested, new shares or units are created to match the prevailing share price; each time shares are redeemed, the assets sold match the prevailing share price. In this way there is no supply or demand created for shares and they remain a direct reflection of the underlying assets.

Unit or share class (wiki)

Many collective investment vehicles split the fund into multiple classes of shares or units. The underlying assets of each class are effectively pooled for the purposes of investment management, but classes typically differ in the fees and expenses paid out of the fund's assets.

A share or stock is part of an individual company. Unit (Trusts) are a collection of different (and usually related) shares.

For example, I am currently investing in a Singapore Equity Fund. And this is known as a Unit Trust. And within the Singapore Equity Fund, my investment is made up of different company shares, e.g. the local bank shares, telecommunication company and some other companies.

And these Unit Trusts are usually managed by a Fund Manager who belong to a Fund Management Company (or known as Fund House). And there are many different Fund Management Companies in Singapore with their own expertise and knowledge.

Source: here


Is it correct to say that import tariffs are unilateral? Is it correct to say that import tariffs are unilaterally decided by the nation or bloc applying the tariff?

It depends on the importing country or bloc (X), and the country the import is coming from (Y), and the product category (Z).

If X is not a WTO member, and is not party to a trade agreement with Y, then tariffs can be set unilaterally.

If X is a WTO member (and has bound Z) or has signed a preferential trade agreement with Y that covers Z, then the tariff can be set unilaterally within (multilateral, bilateral or regionally agreed) limits.

If X is part of a free-trade agreement (or customs union) with Y that covers Z, then X is constrained to allow duty-free import.


If I want to create my own currency model what would be the best basic options / things / ideas I need to look into? First of all, I am from a IT background and currently writing my thesis on a system in which I am have to create a model of a nation. So to run the economy in this simulation (for now you can understand it as a simulation), I need appropriate economic models and monetary policy. I have done my reading on the basics of monetary policy and how central banks are responsible to control the inflation and deflation of currency. And also, I am aware of the gold reserve which now is more like a fractional reserve system. I do understand that the purpose of my project strongly matters in this case, but for a start, a very basic model would be enough. I already am familiar with crypto currencies like Bitcoin, Ethereum etc. Also, this system is run by computer so it's human error / politics proof, or a bit more like an ideal system. So, it would be great to have your insights/opinions on how should I design the currency and the economic model.

In fractional reserve banking the money supply goes up and down according to the rate of new money being created as new loans are made and the rate at which existing money is destroyed as loan (principal) is repaid. So your model needs to include some estimate of the mutual enthusiasm, between banks and their customers, for making new loans. This in turn will be a function of the interest rate amongst other things (IMHO most importantly, people's perception of the future trajectory of house prices).

BTW, I hope you're not assuming that the money supply is capped according to the money multiplier story. That's all completely wrong as the Bank of England confirm => here.

An alternative is full reserve banking where the money supply does not go up and down with loans/repayments. In this case new money can only be created by the government/central bank. This would be far easier to model. When looking at full reserve banking - don't be misled into believing that banks can not lend in such a system (as some textbooks may imply). Peer to peer lenders (e.g. zopa) are essentially full reserve banks and they exist already.


Questions on comparing GDP between various countries What is the difference between OER vs PPP? What fundamentally drives them? Shouldnt an arb opportunity exist and wouldnt that difference then go away? My understanding of OER is the official nominal exchange rate that is quoted by banks and is used by travelers to exchange money. PPP is an estimated exchange rate that is a function of the same good that is sold in different countries (causes being difference in costs/living standards). Is PPP the "real" exchange rate? For a given product, say a hamburger and OER rates of A:B of 10:1, let's say that we can buy 5 hamburgers in A at 20 units of A currency for a total value of 100 A dollars. If we bring them to B and in B, hamburgers are worth 3 units B currency, then our 5 hamburgers are now worth 15 B. If we use the OER to convert back to A, then we would have 150 A of value. Shouldn't this arb go away?
GDP numbers (nominal or real) from various countries are usually reported in their own currency. If one wanted to compare GDP between countries, one would have to use an exchange rate to convert to some common currency. What exchange rate should be used (OER vs PPP... and are there others?) and which GDP (nominal vs real) should be used? My intuition is that OER is usually use and its on nominal GDP (since real is usually indexed but its still possible to compare real by taking inflation and exchange rates into account based on difference between the two years that real GDP are indexed to?)
How do interest rates and inflation affect currency strength (in general?)?

Apologies if these are simple macro concepts. I have a limited understanding

Answer to question 1:

OER is an actual price set by the government. The real exchange rate or RER (That´s how people typically call it) is a ratio of prices of goods, as you mention.

The arbitrage does not go away because the goods in the RER calculation are not completely tradable. The PPP among tradable goods is closer to 1 (meaning the PPP exchange rate among tradable goods is closer to the OER). You can´t trade hamburgers, they get cold, mushy....

Moreover, goods and services are not the only thing being traded across countries. You also trade capital. So a country that is in vogue for international investors will see lots of demand for its capital, raising the price of everything denominated in its exchange rate. So its goods and services look expensive, but its not that things are in disequilibrium its just a disequilibrium in the goods and services part of the balance of payments, that is balanced by another disequilibrium in the capital part of the balance of payments.

Answer to question 2:

Use nominal GDP, in Dollars or in PPP Dollars. Use dollars if you care about dollars, for example if you want to figure out the likely market size for your good which is produced in the US. Use PPP dollars if you care about local living conditions. PPP adjusted (per capita) GDP is a good way to figure out (economic) living conditions.

Answer to question 3:

High rates should imply higher returns to investors that provide liquidity to the local economy, so they should be connected with a more appreciated currency. High inflation lowers the expected future value of the currency, so it should make holding the currency less desirable instead. This should lead to a more depreciated currency.

However, the answer quickly gets more complicated if you add expectations and monetary policy to the mix. For example, an increase in interest rates that will lead to an expectation of a slowdown in the economy and very low future rates might depreciate the currency; high inflation that will lead to an expectation of a big monetary policy contraction raising interest rates, might appreciate the currency.


Envelope Theorem in Hopkins and Kornienko (2010) This is from Hopkins and Kornienko (2010). In this model, $x$ is investments, $s$ is status, and $y=z-x$ is leisure, where $z$ is endowments. $x(r)$ is the optimal investment, and the relative investments determine the status in the model. Here they characterize the agent with the rank, $r$, and derive the reduced form utility. But, I am not quite sure about how the envelope theorem works here.

If I differentiate $U(r)$ with respect to $r$ and suppress the arguments, I have that
$$U_x x' + U_y(y'-x') + U_s s'.$$
I know that $Z'(r) = \frac{1}{g(Z(r))}$, where $g$ is the density of $z$. This implies that the first term and third term and $U_yx'$ turn out to be zero to make the above equation equal to Equation (8). My understanding is that $U_x = U_s = 0$ since $x(r)$ is the optimal investment. But, I don't know how to explain the elimination of $U_yx'$. Can anyone give me some help?

From the first order condition for optimality, we know that (equation (4) in the paper):

$$U_x(x,Z(r)-x,S(r))x'(r) - U_y(x,Z(r)-x,S(r))x'(r) + U_s(x,Z(r)-x,S(r))S'(r)=0.$$

When differentiating ${\bf U}(r)$ with respect to $r$, we find your expression:
$$U_x(x(r),Z(r)-x(r),S(r))x'(r) + U_y(x(r),Z(r)-x(r),S(r))(Z'(r)-x'(r)) + U_s(x(r),Z(r)-x(r),S(r))S'(r).$$

Replacing the first equation into the last one yields
$${\bf U}'(r)=U_y(x(r),Z(r)-x(r),S(r))Z'(r).$$

Now, $Z'(r)=1/g(Z(r))$ which gives equation (8).


Can we get rid of banknotes and coins? this is more a theoretical question, nowadays with Internet, Debit/Credit cards and Cryptocurrencies, why should we keep printing/making more physical money?

granted not everybody has access to these technologies, but for the sake of this question, let's say every body does

Money will always be used for exchanges between nations. As a universal equivalent it will still be the best commodity for nation-to-nation exchanges and for measuring debts and credits between nations too.
Besides using alternative open source equivalents, such as cryptocurrencies, how would national banks manage to regulate inflation rates? This certainly is a critical point. Bitcoin for instance is a finite source of exchange: if it were to become a universal equivalent, virtually it would infinitely increase in its value, since the volume of the market exchange gets bigger and bigger.  Other cryptocurrencies tried solving this creating non finite sources, yet this still implies a arbitrary growth of the volume of available currency.


Profit maximization and returns to scale relation Suppose we have 2 inputs a and b , output is y=f(a,b).
In the long run, let us suppose profits are maximized at a* and b*.
Profit is py-wa-kb[p is price and w and k are constants]. Now for max profit, profit equals py-wa*-kb*.
Now for constant/increasing returns to scale firms, doubling input clearly doubles or more the profit which means there can be no finite a* and b* for such firms which does not make logical sense to me.
Where am i wrong?

Are you assuming a perfectly competitive market? If so, then a profit-maximizing firm with constant returns to scale (CRS) production can only feasibly earn zero economic profits as $P = MC$ in the long-run. If not, then either $P > MC$ and the firm continues to produce indefinitely until it hits capacity constraints or $P < MC$ and the firm ceases to operate since producing any units would be unprofitable (in which case doubling inputs would be even more unprofitable).

To see this, it's easiest to consider the firm's cost function $C(w, r, y)$. Since the firm's production is CRS, the firm's average cost of producing $y$ is constant and thus $C(w, r, y) = C(w, r, 1)y$. The firm's unconstrained profit maximization problem is thus

\begin{align*}
\max_{y} \prod = Py - C(w,r,1)y.
\end{align*}

Assuming an interior solution, the first-order condition is

\begin{gather*}
\frac{\partial \Pi}{\partial y} = P - C(w,r,1) = 0 \\
\implies P = C(w,r,1).
\end{gather*}

So at $P = C(w, r, 1)$, profits are zero and output $y$ is indeterminate. If instead $P > C(w,r,1)$, for instance, then we are no longer at an interior solution and it is clear that the firm will continue to produce and use more inputs up until capacity constraints bind.


Why are so many pharmaceutical drugs so expensive? In the US, the drug sofisbuvir, brand name sovaldir, and used to treat  liver disease hepatitis C, was launched with a price tag of $1000 a pill; and in the UK, the manufacturer Gilead recommended a twelve week course that costs £35,000.
There are roughly 160,000 people in the UK that require treatment and unprecedentedly the NHS chose to phase the drug in. This obviously has to do with the cost of the drug.
Why are so many pharmaceutical drugs so expensive?

Prices are high because drug firms have monopoly power, granted to them by the patent system. In addition the demand for the drugs is fairly inelastic because once you fall seriously ill you're often willing to pay a high price for the cure. If your insurance covers it, you won't even directly notice the price. So the companies can charge almost any price.

Now the patent system is there for a good reason: developing drugs is expensive and if not patented others may use your hard-obtained knowledge to their advantage, without paying for it. Therefore, if your patent is granted you get monopoly power for a while to recapture your investment, on the condition that when the patent expires the knowledge can be used by anyone.

There is no doubt that developing drugs is expensive but whether it justifies the prices charged is a different matter. The pharmaceutical industry is generally unwilling to reveal its costs for good reasons, and that makes estimating profit margins hard.

Part of the question is normative anyway because what would we consider "excessive" profit? What costs are justified when it comes to someone's health?

A fairly old article in the J of Economic Perspectives on this interplay can be found here:
https://www.aeaweb.org/articles?id=10.1257/jep.7.3.97

As for tags: microeconomics would certainly be better suited as would monopoly


Doubt about equivalence relation In class I was taking notes about equivalence relations defined as:

Given a generic relation $R$ on $X$, $xIy$ if both $xRy$ and $yRx$

Now, I don't really understand the following proposition:

If $R$ (the original relation) is reflexive and transitive, then $I$ (the derived relation) is reflexive, symmetric and transitive.

I understand this is an instance of $\succsim $ where the derived relations are $\sim$ and $\succ$, but the proposition holds only for the former (the strict preference obviously is not symmetric). Why is that so?

Also, how can I prove that $R$ having the two properties leads to $I$ having the same two properties + symmetry?

If both $xRy$ and $yRx$ $\forall x,y \in X$, then the indifference relation $I$ is symmetric by definition. Not all symmetric relations are equivalence relations. However, you are given that $R$ is also reflexive and transitive. So we have that $I$ is symmetric, reflexive, and transitive. Therefore $I$, or $\sim$, is an equivalence relation.

You can verify that $\sim$ is an equivalence relation by reading off the definitions of the three properties. $R$, or $\succsim$, is a (weak) preference relation, also known as a total preorder. Total preorders are transitive, complete, and therefore reflexive.

Keep in mind that reflexivity and transitivity does not necessarily imply symmetry: $R = \{(x,x), (y,y), (x,y)\}$ given $X = \{x,y\}$ is clearly reflexive and transitive but not symmetric because $xRy$ but not $yRx$.


Production choices in Hayek's theory of information-bearing prices As I understand the work of Hayek, he asserts that prices encapsulate the true societal worth of the item being sold by integrating the compound need for all of the ingredients and work which go into that item.

I get the notion that he concludes (though I cannot cite him verbatim on this) that in order to facilitate the greatest societal benefit one should produce what is most expensive and consume what is least expensive (which a rational actor would do anyway, thus providing a more explicit mechanistic argument for Smith's "invisible hand" notion).

While I totally see this playing out in the middle and low price ranges, taken to the letter, this concept would be a directive to try and produce not high-tech, but luxury goods.

I can't see this being of the greatest benefit to society, since the price of luxury goods (e.g. higher-end Montblanc stationary) derives not from the materials, and only marginally from the craftsmanship, but primarily from the brand identity and the rigidity of the niche (by virtue of which it is possible to keep supply low).

I'm wondering if someone who understands Hayek better than I do could either explain to me why this is in fact the choice which would best benefit society, or why this conclusion does not in fact follow from Hayek's theory.

Having mulled over this for a while, I think the answer is actually quite simple. While luxury goods might have some of the highest margins and highest prices per unit, they don't actually make the producers the most money because of the low quantities in which they are sold. So I think my summary might have been ill formulated. Instead of “produce what is most expensive”, a better summary would be “produce what is most profitable”.

Clearly luxury goods are not what is most profitable. Currently this would rather be high-tech services such as data analysis and reliable forecasts.


Best Response Functions for Cournot For a Cournot Duopoly game with Linear Demand functions, we need to find the optimal quantity of each firm such that profit is maximised. Given the linearity of the Demand curves, we will obtain a quadratic profit function. Since profit function is strictly concave and quasiconcave, we can ensure a unique maximum, i.e. a unique optimal quantity for the firm to produce. The above explaination is for a 'standard' game with Linear Demand function, say, $max(a-bq,0)$, with cost function, say, $C_i=c_iq_i$ for, say, a duopoly, $q=q_1+q_2$

What I need to understand is that if we have non-linear demand function, such that we cannot ensure a unique optimal quantity for profit maximisation (which would be the Best Response function), how would the Nash Equilibria or Equilibrium be obtained? That said, is it possible for a Cournot game, or for that matter, any game to have more than one Best Response?

I'm still a bit rusty on the concepts, please bear with me. Is what I'm trying to understand, right conceptually? What am I missing?

In general a best response function returns a set of best responses. This can be seen in much simpler games than Cournot.

To give a degenerate example, if a player is always indifferent between their strategies, their best response function will always return the set of all their strategies.

When you have best response functions that give sets with more than one element, Nash equilibrium happens when each player's play is contained in the other player's best response set.


Is Universal Basic Income compatible with free international trade? If one country introduces UBI, what prevents other countries from taking advantage of that and supplying cheaper (no need to finance a UBI scheme!) goods to the original country and outcompeting the local industries? Does UBI automatically mean high international trade tariffs?

There is nothing to prevent other countries "taking advantage" of an export market's UBI.  However, I don't think that that implies a country introducing a UBI would need to increase tariffs, and I have never heard this being advocated.

Since UBI hasn't been implemented on a large scale, there is little compelling evidence on what its effects will be, but a lot of speculation on what they might be.

First, it is important to observe that countries' cost bases already differ a lot in terms of firms' tax burdens and unskilled wage rates.  Countries with high taxes and high wages don't typically sustain them through protectionist tariffs.

Second, it is suggested that UBI may lower a lot of government costs, so that the impact on firms' tax burden would not be as large as you might expect.  For example, UBI would replace many benefits (e.g. job seeker and housing benefits) reducing administration costs, especially for means-tested benefits.  It is argued that it would reduce physical and mental healthcare costs related to poverty, which could be particularly important in countries like the UK that have free universal healthcare alongside substantial poverty.

Third, it is unclear what effect a UBI would have on wages.  Since workers' basic cost of living is (at least partially) covered, it is possible that wages could fall.  There would certainly be a political argument for reducing the minimum wage.  Depending on how the cost of UBI is distributed, this could more than offset the tax burden on firms.  It is also well established that a lot of traditional benefits result in very high effective marginal tax rates on part-time work (as earned income is offset by reduced benefits); a UBI is likely to improve the financial incentive for unemployed people to do small amounts of work in a lot of countries, even if wages were somewhat lower.

Finally, it is largely unknown how UBI might affect a country's comparative advantage and productivity.  For instance, some (not all) suggest that UBI would drive innovation by giving people the time and space to pursue an invention or start a business under less financial pressure.  This would lead to more value-added jobs, which is how countries typically manage to compete internationally while sustaining high wages and tax rates.


Was there any use of scoring rules in economics or finance before Hanson published about LMSR? Scoring rules arose in the field of meteorology, with the seminal paper published in 1950, but I can't find any references to their using in economics or finance until Hanson published in 2002. Half a century is a long time, so it seems unlikely that Hanson was the first to use scoring rules.

Is the problem just with my Google-fu or was Hanson actually the first? I'm betting on the former.

Hanson wasn't the first one.

"Scoring rules and the evaluation of probability assessors" by Winkler was published in the Journal of the American Statistical Association in 1969 wasn't published in an economics journal but already mentioned economic applications.

Other examples (probably also not the first publications in economics journals, but still earlier than Hanson) are:

Selten (1991), "Properties of a Measure of Predictive Success?" in Mathematical Social Sciences.

Selten (1998), "Axiomatic characterization of the quadratic scoring rule" in Experimental Economics.


Deriving demand function in case of multivariable utility functions with min and max structures Suppose I have utility function like this: $u(x_1,x_2,x_3)=min\{x_1,a-x_1\}\times min\{x_2,b-x_2\}+x_3$ where a and b are real numbers and $x_1\in [0, a]$ and $x_2\in [0,b]$. What will be a procedure of finding, for example, Marshallian demand $x(p,w)$?

My confusion: In case of more simple function without minimum or maximum structures I would simply use Lagrangian to define the demand. However, given function is not differentiable.

My question: can I apply Lagrangian here and, if so, how can I do it? If it is impossible to use Lagrangian in this case, what else sholud I do?

It is possible to use a Lagrangian to obtain your Marshallian demands, provided you break each min function up into two different pieces and remain wary of boundary solutions. So for example, if you impose the condition $x_1<\frac{a}{2}, x_2<\frac{b}{2}$ you can simplify your utility function to $x_1 x_2 + x_3$, and then solve for Marshallian demands that are valid when this condition holds. Once you've obtained your demand for this piece it's good practice to re-state your condition as a function of the parameters (a, b, w, and $\textbf{p}$) Then go back to your original utility function, impose an alternative condition and repeat to get a different piece of the demand. The demand function will be piecewise (and in this case it seems like it'll consist of quite a few different pieces). Good luck!


What is the difference between two stage least squares and instrumental variable regression? I'm doing independent study and I am having trouble understanding the difference between these two estimators.

I get that 2SLS is predicting the endogenous variable, and that instrumental variables are similar to proxy variables, but I don't get how one differs from the other.

The meaning of the words first

Some people use the word "IV estimator" to refer to any estimator that uses instrumental variables. To them, IV estimators contain 2SLS, LIML, k-class estimators, and others, so 2SLS is a special case of IV. For example, the title of Bekker's (1994, Econometrica) paper is "Alternative approximations to the distribution of instrumental variable estimators".

More traditional people mean by IV the particular instrumental variable estimator $(Z'X)^{-1}Z'y$ for the exactly identified case ($Z$ = instrument matrix, $X$ = regressor matrix, $y$ = regressand vector), and 2SLS is a generalization of IV to the overidentified case. But, as Paul says, 2SLS can be expressed as an IV estimator of this second sense because it is $(\hat{X}'X)^{-1} \hat{X}'y$, where $\hat{X} = Z(Z'Z)^{-1}Z'X$ is the instrument matrix.

I personally think it is very fine to leave the meaning of IV estimators ambiguous because the meaning is usually clear in the context and we need not rigorously distinguish them.

As for your question ...

It seems to me that the sentence "2sls is predicting the endogenous variable" means the first stage regression of the endogenous regressor on the instrumental variables (to get $\hat{X}$). The expression "instrumental variables are similar to proxy variables" looks more casual. Proxy variables (e.g., IQ for ability) can be used to solve the endogeneity problem. Instrumental variables are another way of solving the endogeneity problem. In that sense they are "similar".


What is the "bequest condition" in a finite-horizon discrete optimization problem? For a finite-horizon discrete time optimization problem, my textbook provides a condition called the "bequest condition", which I'm not familiar with. Specifically, where the state at time $t$ is denoted $x_t$, the bequest condition states that at the final state, $x_T$, it must hold that $x_T\geq \bar x$. What does this mean?

It is simply the terminal condition of the model. You do not specify the variable that x represents, but if it were, for example, capital, this would simply state that in the last period (since horizon is finite) there is a condition that states that capital must be greater or equal to some given amount (bequest --> legacy, you might find some sense in that word).
Again, you do not specify the model, but normally these types of conditions relate to either a simplifying assumption that allows you to solve models using certain methods (for example undetermined coefficient, iterative solution methods, etc.), or to some logical notion.


Does anyone here have experience with GARCH-MIDAS forecasting? I'm a masters student looking for a thesis topic. Please note, I'm studying Finance and whilst the econometrics component of my course is rather lacking when compared to a straight Econometrics degree, thanks to the internet there is a vast wealth of resources out there for me to try and grasp it on my own - with some friendly help along the way of course :)

I'd like to use the thesis as an opportunity to learn a new regression model. Specifically GARCH models used to forecast volatility.

As I understand it, the GARCH-MIDAS model (as described by Engle et. al 2013) can and has been used with daily stock return data and macroeconomic data (typically quarterly or monthly) to produce volatility forecasts that contain both long and short-run components.
The GARCH model encompasses the mean-reverting short-run fluctuations in volatility, whilst the MIDAS component captures the long-run effects.

This is what I gather from briefly looking over the paper late last night. Any corrections are welcome!

In terms of time-series experience, I can implement AR, ARDL, VAR and VECM models. I have never used ARCH, GARCH, or any of their variations; though as I said I would really like to learn.

I guess all I am asking is whether this is feasible option for me as a student with no formal teaching, but a desire to learn by himself. If so, can anyone point me to some books with practical expositions of the GARCH and MIDAS regression methods? I presume an understanding in each method separately would greatly aid combining the two.

Your thoughts and opinions would be greatly appreciated!

Sean Becketti has a very readable book called Introduction to Time Series Using Stata that has a chapter on (G)ARCH models. Unfortunately, it does not discuss mixed-data sampling (MIDAS), as that is a more advanced topic. I am not aware of any introductory treatment  of that material.


Have countries with a monopoly on a resource in an area ever established 1-company monopolies in that area to drive up price? Say its the 18th century and South America wants tea. Britain, for example could have a monopoly on the tea trade in the area. However if multiple British companies sell in the area they will drive eachothers prices down. So the British government could only allow 1 company to trade there, or force a merger between the companies, so they can trade as a monopoly and make more money which will be payed as tax to the British government. Has this ever happened, or is there a flaw in my logic?

Yes, you are describing the (British) East India Company.  A royal charter granted it a 15 year monopoly on English trade with "all countries east of the Cape of Good Hope and west of the Straits of Magellan".  Also noteworthy, "at the height of its rule in India, the British East India company had a private army of about 260,000 — twice the size of the British Army".


Is the opportunity cost under the supply curve? Is it correct to say that the opportunity cost is a particular point on the supply curve? And if so, why?

I understand what is going on with the opportunity cost with the production possibilities curve (how you give up more of one good when producing another), but I'm just not sure how it relates to the supply and demand curve, and area underneath the supply curve.

On this video, (https://www.youtube.com/watch?v=zEE-qOuo_Cw), at 3:15, he says that there is an opportunity cost more than $9. Why is this referred to as opportunity cost?

Opportunity costs occur for all suppliers. The lowest price at which supply occurs (agents willing to sell) is just above the lowest opportunity cost of the suppliers.

I would not describe it as a point on the supply curve. Because you will not offer something for sale unless it is greater than you opportunity cost. It is important to note that opportunity costs dictate the starting point and slope of the supply curve.

So presuming your opportunity cost for 1 unit is 10\$ you will only sell at 11\$ (opportunity cost + 1), another persons opportunity cost may be 12\$ and so they are only willing to sell at 13\$ hence the increase in quantity supplied as price rises, more and more people are willing to sell as their opportunity costs are covered and they can make a profit.


Long Term Economic Profit for Perfectly Competitive market When we consider a perfectly competitive market, in the short run we will run a firm if the total economic profit though negative till price is above shutdown point.In long run we will run at an equilibrium where total economic profit is 0. I am not able to understand why would we run a firm if the profits are negative or 0 ?

This is because we are talking about economic profit not accounting profit.
An economic profit takes into account opportunity cost. If you are skilled programmer that can earn $\\\$100000$ per year being employed at Google then doing something else like operating your own business incurs an opportunity cost of $\\\$100000$ per year.
Hence in this situation if the person would set up perfectly competitive business, the business would still record $\\\$100000$ accounting profit even if the economic profit would be 0.
Consequently, even in perfectly competitive business people have actual incentives to run those business.