List of theoretical models of learning What are the most advanced theoretical models about  "learning" such as learning-by-doing or learning from others?

Overall, learning in economics spans different areas. Here there is a largely incomplete list:

One of the pioneers of "learning" in economics is Arrow with his 1962 paper. In his paper, Arrow discusses the economics implications of theories about learning in social psychology. The main focus here is about firms "learning" over time. (For a recent survey of models within this literature: Thompson, 2010)
In the same year (1962), G.S. Becker adds another milestone. Becker's paper is a must read. From the point of view of individual agents, learning is an investment: it involves immediate costs and gives future gains. It raises the question of why firms should pay money for training their workforce in competitive markets (i.e., wages equal marginal costs). It also makes an important distinction between "general" (reusable) and "specific" knowledge.
Following up on Becker's work, a large literature in labor economics (e.g., Rosen, 1972) pushes the same question a little bit further. This literature culminates in Acemoglu and Pishke (1999) paper showing that market frictions are a possible explanation for firms paying for training.
A more recent literature has started to look at "learning" from a wholly different point of view: how people learn to play games. This literature originates from the results of many experimental works showing a number of anomalies in behavior compared to theory. A standard reference here is the book "Learning in games" by Fudenberg and Levine. (The book is somewhat old and there is much of research going on in this area. So I am not sure what would be an updated reference.)

Can you help me create a better list? I am looking for either area of work I have overlooked (e.g., is there something in behavioral literature?) or more advanced references for each of the listed topics.

If you aren't interested in learning from a game and decision theoretic perspective, I'm not exactly sure why you're posting on an economics forum. Because that's what learning really is, from an economics perspective. AI really breaks down into three subfields: logical, behavioral, and machine learning. The logical subfield deals with logical reasoning, automated proof-writing, automated conjecture making, and such. Behavioral AI is really more in line with theoretical economics- game theory, decision theory, mechanism design, etc.

Machine learning is really what constitutes mainstream AI research nowadays. This is really due to the fact that we now have the resources and tools to better deal with big data, rather than a philosophical revelation or technical breakthrough. Hot topics in computer science are very industry and money driven (as a theorist, I would argue too much so). Machine Learning really boils down to applying a stochastic process and refining a model. There isn't so much learning going on, just enhanced stupidity that works well sometimes. That's not to dismiss Machine Learning, but we should call it what it is.

I would definitely recommend AI, Machine Learning, and Evolutionary Game Theory, though. Russell and Norvig is the established classic AI text, and it has sections on Machine Learning as well. Link: http://aima.cs.berkeley.edu/

Evolutionary Game Theory uses similar techniques as Machine Learning. It relaxes the assumptions of Neoclassical Game Theory. Agents need not be perfectly rational. They can have imperfect information and adjust their strategies myopically. The game is played repeatedly. We then see how "mutation" (such as human error or experimentation) in enough agents drives changes in equilibrium. So we have a dynamical process to select equilibria in games. We can apply dynamics such as the imitation dynamic, the best response dynamic, etc. Weibull (https://mitpress.mit.edu/books/evolutionary-game-theory) and H. Peyton Young are both good introductions (https://www.amazon.com/Individual-Strategy-Social-Structure-Evolutionary/dp/0691086877/).

I took a seminar in Economics this past spring, the first half of which was Evolutionary Game Theory. We went through a bunch of papers as well; a subset of the following. One paper I enjoyed was Competitive Behavior in Market Games: Evidence and Theory. It showed that as the number of agents was made sufficiently large, that evolutionary forces drove the Nash equilibrium to the Walrasian equilibrium (under certain assumptions). This provides a behavioral motivation for the study of r-fold replica economies in the general equilibrium setting.

Mark E. Schaffer (1989): “Are Profit-Maximisers the Best Survivors?” Journal of Economic Behavior and Organization, 12, 29-45.

Mark E. Schaffer (1988): “Evolutionarily Stable Strategies for a Finite Population and a Variable Contest Size,” Journal of Theoretical Biology, Vol. 132, No. 4, 469-478.

Hehenkamp, B., W. Leininger, and A. Possajennikov (2004): “Evolutionary equilibrium in Tullock contests: spite and overdissipation,” European Journal of Political Economy, Vol. 20, 1045–1057.

Duffy, J., A. Matros, and T. Temzelides (2011): “Competitive Behavior in Market Games: Evidence and Theory,” Journal of Economic Theory 146, 1437-1463.

Kandori, M., G. Mailath, and R. Rob (1993): “Learning, Mutation and Long Run Equilibria in Games,” Econometrica, 61, 29-56.

P. Rhode, and M. Stegeman (1996): “A Comment on ‘Learning, Mutation, and Long-Run Equilibria in Games’,” Econometrica, 64, 443-449.

W. Sandholm (1998): “Simple and clever decision rules for a model of evolution,” Economics Letters, 61, 165-170.

Young, P. (1993): “The evolution of conventions,” Econometrica, 61, 57-84.

Young, P. (1993): “An Evolutionary Model of Bargaining,” Journal of Economic Theory 59, 145-168.

M. Saez-Marti and J. Weibull. (1999): “Clever agents in Young's evolutionary bargaining model,” Journal of Economic Theory 86, 268-279.

Matros, A. (2003): “Clever Agents in Adaptive Learning”, Journal of Economic Theory, 111, 110-124.

Ellison, G. (1993): “Learning, local interaction and coordination,” Econometrica, 61, 1047-1072.

Glenn Ellison (2000): “Basins of Attraction, Long Run Equilibria, and the Speed of Step-by-Step Evolution,” Review of Economic Studies, 67 (1), 17-45.

Bergstrom, T. and Stark, O. “How Altruism Can Prevail in an Evolutionary Environment.”

American Economic Review, May 1993 (Papers and Proceedings), 83(2), 149-55.
Eshel I., L. Samuelson and A. Shaked (1998): “Altruists, Egoists, and Hooligans in a Local Interaction Model,” The American Economic Review 88(1), 157-179.

Matros, A. (2012): “Altruistic Versus Egoistic Behavior in a Public Good Game,” Journal of Economic Dynamics and Control 36, 642-656.

Robson, A., and F. Vega-Redondo (1996): “Efficient Equilibrium Selection in Evolutionary Games with Random Matching,” Journal of Economic Theory, 70, 65-92.

Josephson, J., and A. Matros (2004): “Stochastic Imitation in Finite Games,” Games and Economic Behavior, Volume 49, Issue 2, 244-259.


Do trade policies have to change after Brexit? Being part of the EU is surely not the only way to participate in a free trade market. Could the UK continue with the same policies despite not being part of the EU?

The UK do it the "Norway way" this would mean they are part of the
European Economic Area, they need to pay into EU budget (roughly 80% of current pay) but
have no Seat in Brussels)
The Switzerland way - bilateral deals and roughly 50% of the
Norway way costs.
Lone Member of WTO.

In any way, Britain would gain the freedom to make its own trade deals (how about TTIP?!).


Equilibrium Price - OLS Regression I have asked another question related to price elasticity, which pretty much left me with this problem:

I want to analyze the factors influencing the price of a product. The underlying assumption is that of a classic market equilibrium situation where the price equals the point of demand=supply. Now - how do I model such equilibrium prices and estimate the estimators correctly? How do I treat the problem of simultanious equations in this specific case? And can I simply use OLS regression in the case of price-unelastic demand since price is only included in the supply function?

I already tried reading the relevant chapters in some of the most common pieces of literature (Wooldridge etc.), but I just do not fully understand how to effectively solve the issue.

The goal is to construct a simple linear regression formula that looks like this:

$P_{t}=\beta _{0}+\beta _{1}X_{t}+\varepsilon _{t}$

where P = Price is the dependent variable.

I am sorry for bothering but I am trying to understand this topic for weeks now and I just need some basic explanation on how to solve this issue. I am really thankful for any comment/answer that sheds some light on this. The more I think about it, the more confused I get.

The same factor affect how a product is supplied and demanded in different ways. If you want to model what the effect of change in a given independent variable has on equilibrium as a whole you need convert both your equations to a single reduced form equation.

If you have two equations a supply and demand equation both of the forms:
$$P_s=\alpha_0+\alpha_1X_i+\mu_i$$
$$P_d=\beta_0+\beta_1X_i+\epsilon_i$$

for estimating how $X_i$ affects equilibrium price set $P_s=P_d$

$$\alpha_0+\alpha_1X_i+\mu_i=\beta_0+\beta_1X_i+\epsilon_i$$

$$X_i(\alpha_1-\beta_1)=(\beta_0-\alpha_0)+(\epsilon_i-\mu_i)$$

letting the terms $(\alpha_1-\beta_1)$,$(\beta_0-\alpha_0)$ and $(\epsilon_i-\mu_i)$ be equal to $\gamma_1$,$\gamma_0$ and $z$ respectively we solve and find that the effect of $X_i$ on equilibrium price is:

$$\gamma_1=\frac{\gamma_0+z}{X_i}$$
based on this formula we see that the
coefficents value actually changes based on the the amount of $X_i $ provided.  Using this method you can get an accurate estimate of your factor's influence on equilibrium price and see how it changes.


Is there really a Nash equilibrium in this example? I was watching this video on Coursera and worked out the example before the solution was presented. The example begins at 4:20
The presenter says that the Nash equilibrium is achieved with 2,2 at the bottom right but I don't see it. My solution shows no Nash equilibrium.

I have two 1, 3* with the * asterisk representing the preferred value of player, P2 in the 3rd (Right) column.
I have two 3*, 1 on the bottom row (Down) for player, P2 because if P1 picks Down, the best outcome is achieved with 3 when P2 picks Left or Middle.

What am I missing here? All my other values agree with the example except for the 3 row and 3rd column.

The Nash equilibrium is indeed (down, right).
Note that your chart has helpfully underlined the max value among all possible strategies each player can play, conditional on what the other player plays. The steps on the graph  are useful as well: If no numbers are underlined in a cell, that strategy set is strictly dominated by something else. If one number is underlined, one player will want to unilaterally deviate.
Assume the players play (down, right):

P1 will not want to play up or center as their return will be 1 in those cases
P2 will not want to play left or middle as their return will be 1 in those cases

You can try this for any other cell with underlined values and see one player will be better off deviating. For example, in (up, middle) P2 would prefer to deviate to (up, left), then P1 would deviate to (center, left), P2 to (center, middle), P1 to (middle, up), etc.
FYI: the equilibrium should be referred to by its strategy rather than its values.


increased demand but no increase in price? I am teaching myself basic economics and I'm trying to understand supply and demand.
Recently, in my country, there was news of a strike by the petroleum suppliers. Expectations of an impending fuel shortage increased demand. (as evidenced by the long queues at petrol stations).

Now,by plotting the supply and demand curves, it seems apparent that an increase in demand would lead to an increase in equilibrium price and equilibrium quantity. However, in reality, during this time, none of the petrol stations increased the price of petrol. Is this because of government regulation of prices or due to some other factor?
Thanks

Such a situation can be explained in the following ways:

If supply is perfectly elastic (horizontal supply curve), then an increase in demand does not increase the price. It's highly unlikely that supply of petrol here is perfectly elastic. This could be the case under perfect competition with constant marginal costs of petrol. However, typically petrol has increasing marginal costs. Alternatively, it could be the case with constant marginal costs and Bertrand competition (price competition, with few firms) meaning they also set prices equal to marginal costs as in perfect competition.
There may be costs to increasing the price. So-called menu costs make prices sticky and therefore changes are not as often as we expect. E.g. if you're a restaurant and want to increase prices, you have to reprint all menus, which may not be worth it for a temporary demand increase. However, this is probably not tbe case in your example.
When setting the price before the shortage was announced, the increase in demand was expected and the price already set accordingly high. Was there an increase in the price (shortly) before the announcement? If not then the next explanation is the only possibility.
Government regulation of the price.


Consider the following production function $Q=min \left(\frac{L}{2a}, \frac{K}{4b}\right)$. Let $w$ and $r$ be the wage and rental rate respectively The cost function associated with this production function is
$A) 2awQ\\
B) 4brQ\\
C) (wa + 2br)Q\\
D) None\; of\; the\; above$

What I have tried is:
We have the cost function $wL+rK=C$.
Since, here, the goods are perfect compliments, therefore, $\frac{L}{2a}=\frac{K}{4b}$.
Putting the value of $L$ in cost function we would get $\left(\frac{K}{2b}(wa+2br)\right)=C$.
Which would be C option if $Q$ can taken as $\frac{K}{2b}$.
But I'm not sure about that.
 Please confirm?

The steps to optimally go from the Production function to the Cost function is to solve the cost-minimization problem for the firm, which determines the input mix given prices and some level of output, and in turn allows us to express one input with respect to the other (in this simplest two-inputs case).

When the production function is of the Leontief variety, optimal input mix is indeed determined by the equality stated by the OP, since by simple reasoning, any amount of one input above the amount satisfying the equality will incur the cost to  buy it but not any extra output.

Inserting the equality

$$\frac{L^*}{2a}=\frac{K^*}{4b} \implies L^* = \frac {a}{2b}K^*$$

into the cost function we get Cost expressed as a function of one of the inputs only, $C^* = g(K^*)$

In order to eliminate it too, we turn again to the production function which can also be expressed as a function of one input at the optimal solution,

$$Q = h(K^*) \implies K^* = h^{-1}(Q)$$

Inserting $h^{-1}(Q)$ into the Cost function we obtain

$$C = g\left[h^{-1}(Q)\right]$$

where also the various exogenous constants and prices will be present. In fact, this is easier done when the production function is Leontief, than when it is Cobb-Douglas for example, and so it should be easy for the OP to arrive at the correct solution.


Human Capital Vs TFP I'm interested in familiarizing myself with some of the intra-debates that have occurred over the years, having to do with Mankiw, Romer, Weil (1992) and Klenow, Rodriguez-Clare (1997). Some argue that TFP growth can sufficiently account for cross-country variations in output per capita. Others argue that we need a model of Human Capital.
I am just interested in reading about, and catching up with the literature on this.
Are there any papers or books that you guys can recommend?
Thanks

Romer (1986): Increasing Returns to Long Run Growth
Lucas (1988): On the Mechanics of Economic Development
Romer (1990): Endogenous Technological Change
Jones (1995):  Time Series Tests of Endogenous Growth Models

These are all classic papers in this vein of endogenous growth and questions of cross-country convergence/divergence.


Jokes in Economics; Challenging Assumptions in the Dismal Science We've delved into questions about the history of economics. We've pondered what the most important equations in economics are. But in every science, academic culture inevitably forms a special set of ideas that further our understanding of the most fundamental ideas we use in our work: jokes.

Jokes are only funny if they set you up to have a false assumption about the material at hand, and then subvert it. In this way, jokes can be used to reveal underlying assumptions we economists might take about the world that are very well absurd, but important nonetheless to moving towards more sophisticated models. Even within mainstream economic schools, ideas like using cardinal vs. ordinal utility, or utilitarianism itself can be contentious. John Rawls's veil of ignorance or Nozick's more libertarian epistemology? Are sticky wages really realistic?

What are some jokes you have encountered that would be useful for addressing an underlying assumption of an economic theory, or economics itself?

(Any further recommendations for improving this question are appreciated. It can even be a community question if that would be best.)

Not to suggest that this should become a list of the best econ related https://xkcd.com/552/ and http://phdcomics.com/comics.php but I always really liked that one:


Are all points on the Long Run Average Cost (LRAC) curve productively efficient? The definition of productive efficiency is that any given output is produced for the lowest possible cost.

In the short run, only the minimum point on the SRAC curve is productively efficient - this makes sense because at any other output, the firm could move to a different SRAC curve that would give a lower cost for that output.

However, the LRAC is, by definition, the envelope of all SRAC curve - it shows the cheapest way to produce any given output.

Agree / disagree?

If true, why is it that so many economics sources claim that "productive efficiency is achieved when the firm produces at the lowest point of its AC curve"? Is it simply that firm decisions are perpetually taken in the short run?

The statement
"In the short run, only the minimum point on the SRAC curve is productively efficient"
is false.

Suppose producing 1 unit of a good costs 5 dollars. 2 unit costs 8, x>2 units costs 5x. Clearly AC is minimal if you produce 2 units.
But perhaps I do not want two units of the good, only one. Why spend the extra 3 dollars on the second good? Producing only 1 unit is also efficient in this case.

Note that this does not contradict your definition
"The definition of productive efficiency is that any given output is produced for the lowest possible cost."
The given output is 1 unit, and it is produced for 5 dollars, not 7 or 8, so there is no waste. Your definition does not say anything about per unit costs.

My example is also consistent with the definition of productive efficiency that I know.

  Productive efficiency is a situation in which the economy could not produce any more of one good without sacrificing production of another good.

Sidenote:
 Perhaps you are confusing productive efficiency and minimum efficient scale of production?


Can data from discrete choice experiments be used to predict models be used to predict willingnes to pay by specific individuals? I am not an econometrician, but noticed that discrete choice experiments are often used to determine willingness to pay for products with specific characteristics and prices. However, these average prices seem to be reported for the average person in that sample, not being specific to specific groups of individuals. For example, by looking at the results I can't tell how that willingness to pay for a given product/price combination varies across individuals with a different socio-economic background, gender, education, etc.

Getting more specific: what would prevent one from taking a reasonably large dataset with a discrete choice experiment and develop a machine lerning model to predict willingness to pay for individuals with specific characteristics?

In principle it would be possible to do so. In fact this is exactly what we do if we convert a marginal effect at the mean to a willingness to pay. We calculate it for the average person in the dataset.

One can also distinguish the average WTP by subgroups and socio-economic characteristics such as gender. The reason why academic papers do not often go beyond that (I guess) is that the predictions become so specific that they are hardly interesting anymore. Who would be interested in the willingness to pay of say "a 27 year old male with 12 years of education, an annual income of 24000€, voting republican and an interest in violent video games"? What about when he is 28 years old? Given that these models are typically non-linear their WTPs are going to be different.

Moving to a practical point of view price discrimination at such detailed level is impossible at the moment and for a number of products it may even be illegal (insurance is an exception).

Finally, a problem with any contingent valuation problem is that is willingness to say rather than willingness to pay. This is less of a problem in markets for goods with which the participants have experience with the good in question, but there will always be a bit of hypothetical bias.


How to see that upper-semicontinuity and supermodularity are equivalent in a supermodular game context? One requirement for a supermodular game $(I, \mathbf S, \mathbf u)$ is usually presented in two ways (e.g. in this note):

  For $i \in I$, $u_i$ is supermodular in $S_i$, when $s_{-i}$ is fixed, i.e. for $s_i, s_i' \in S_i$
  $$u_i(s_i \vee s_i', s_{-i})+u_i(s_i \wedge s_i', s_{-i}) \geq u_i(s_i , s_{-i})+u_i(s_i', s_{-i})$$

Or

  For $i \in I$, $u_i$ is upper-semicontinuous, i.e. for $\alpha \in \mathbb R$
  $$\{s_i \in S_i \mid u_i(s_i, s_{-i}) < \alpha\} \text{ is open.}$$

But they're obviously different. The former endows $S_i$ with an order structure, while the latter requires the equipment of a topology. How to understand this difference?

Your observation about topology and order is somewhat inaccurate. First definition make use of partial order on $S_i$ while the second make use of topology on it, but both structures are almost always specified by the assumption, that $S_i$ is a sublattise of $R^n$ and so it is equipped with usual subspace topology and partial order. This is the first point in the definition in the material you have referred to. So this worries are misplaced.

However there is some indications (see, for example, chapter 4 in Supermodularity and Complimentarity by Topkis), that the requirement of upper-semicontinuity is stronger and implies the first one. I'm not ready to provide an accurate proof, however.


Present-bias vs future-bias There is a huge literature in economics that studies time-inconsistencies in decision-making and that consistently finds that individuals make present-biased choices in a variety of contexts: we do not save enough for retirement, we procrastinate at work, we invest too little in our human capital, we drink and eat too much, we exercise too rarely, etc. It is widely accepted in our profession that human beings are distracted away from their long-term goals by their short-term impulses.

At the same time, a major theme in philosophy and literature (that goes back to Greek philosophy) is our inability to enjoy the present moment. According to this view, we are constantly dreaming of future imaginary pleasures and unable to satisfy ourselves with our present situation. An archetypal example is someone who always sacrifices the present for a mid-term goal (graduating, earning money, buying a house, getting tenured, ...), who always believes that she will enjoy life once the goal is achieved but who always finds a next step - and who realizes that too late. In the economics terminology, this person's most important decisions (work-life balance for instance) are actually future-biased.

I am aware that both phenomena are difficult to compare since the first one is extensively documented quantitatively whereas the second one is more speculative. But it strikes me that our view of intertemporal trade-offs is so dramatically different from what philosophers and psychologists think.

Is there any attempt in economics to reconcile both views? For instance, are you aware of a study that finds that people are future biased? Any reference or thought about this topic would be greatly appreciated. Thanks!

The tradeoff between work and leisure has been extensively studied.
I would start with the wikipedia entries on labor supply:

  https://en.wikipedia.org/wiki/Labour_supply
  https://en.wikipedia.org/wiki/Labour_economics#Neoclassical_microeconomic_model_.E2.80.94_Supply

If you are looking for more complex articles, Heckman in particular studies this, but it is econometrically heavy for undergraduates.

Note that there are two different effects you are asking about. First, you are looking for an economic explanation or model of why people find themselves regretting the amount of work they are doing after the fact. Depending on how you define regret, this can be modeled by allowing the agents to be surprised by their own mortality or other statuses.  They will, after the fact, wish they had not valued the money so highly!

Secondly, you are looking for agents who explicitly value money tomorrow more than today. Awkwardly, the literal interpretation of this will not get the behavior you are looking for. If agents actually valued having money tomorrow more than today, they would never spend money and only save it! But, it is perfectly possible that agents value the money in the future too much, just not more than today.  If this still describes what you are looking for, you should take a look at inter-temporal choice, particularly hyperbolic discounting.

  https://en.wikipedia.org/wiki/Intertemporal_choice

To help exemplify this second point, let us consider the case of normal discounting rates $\beta$, where each period is worth a fraction of the prior period, say $\beta=1/2$ the value. The value from now to forever is:

  $=1*0.5^0+1*0.5^1+1*0.5^2+....$

  $=1/(1-0.5)=2$ by infinitely repeated fractions.

But what if $\beta$ is greater than 1? Say $\beta=1.1$?

  $=1*1.1^0+1*1.1^1+1*1.1^2+...1*1.1^{999}+...$
  diverges to $\infty$ by sum of infinitely repeated values, a sign of problems to
  come.


Why switch from Gold to Fiat If I'm not mistaken, gold was used in early days of USA.

Why did we switch to fiat, i.e dollar bills. Originally they were backed by gold, so why not keep gold?

I'm just trying to understand basics of why USA switched to dollars (even if they were gold backed).

Thank you

When recession strikes, it's prone to the currency equivalent of "bank runs" where everyone attempts to trade in their paper money for gold at once, causing a drastic reduction in the money supply, rising of interest rates, and the dreaded deflationary spiral. In the face of a recession, you want the opposite to happen.

During the Great Depression, every major currency abandoned the gold standard, and the time of abandonment is seen as being correlated with their subsequent recovery. The U.S. abandoned it for good in 1971 while the economy was facing stagflation and foreign countries were demanding to exchange their U.S. dollars for gold, of which we didn't have enough gold reserves to fully satisfy.

A fiat currency gives policymakers many more tools to stimulate the economy to meet their objectives. Tying your currency to gold limits the extent to which you can expand your money supply. And don't forget that under fractional reserve banking, it's the banks that create most of the money supply, not the Fed.

On top of that you're prone to sudden random money supply expansions due to new mining windfalls, wasting a commodity that otherwise could be put to use in the real economy, and have to deal with the increased transaction costs of shipping and storing physical gold.

http://www.bloomberg.com/news/articles/2011-08-04/the-nixon-shock


long run growth of money supply I am trying to understand how the money supply (bank deposits + currency) grows over time. That's the end goal. This is the first part of my awful struggle.
I'm superconfused, and almost everything I have read has made it worse.
Linked directly below is the first thing on this topic that made any sense to me, so I'm treating it as my starting point.
https://www.bankofengland.co.uk/quarterly-bulletin/2014/q1/money-creation-in-the-modern-economy
My understanding is like this:

most money creation is done by commercial banks when they make loans
*each instance of loan issuance is directly responsible for a temporary increase of the money supply
*these issuances, in aggregate, are indirectly responsible for most of the growth of the money supply over time

Question : Is what I wrote above accurate? It seems logical, but I can think of an equally logical way in which it is wrong, hence my confusion. If correct-ish, please read on:
So I am looking at the loan as having 3 parts:

part 1: The bank makes me a loan. Bank deposits increase, and thus the money supply increases.
part 2: case 1: My account is credited, and I can spend it. But I don't. I just like that it is there.
part 2: case 2: My account is credited, and I use the money to fund some productive activities today, but I do things I would have done anyways, say, tmrw. Maybe I was impatient. Or derived utility from the today-ness.
part 2: case 3: I use the loan to fund additional productive activities (more than I had initially planned for today), without changing my plan for tmrw and tmrw+.
part 3: I pay back the loan, removing this loan's direct contribution to the money supply.

I guess what I'm getting at is: Is there some connection to the bank making loans, and those loans being used to fund additional productive activities* than otherwise possible (say, given the agent's initial budget constraints), and long run growth in the money supply? Ie. You can go to the bank and get a loan pretty fast - faster than prices can change. So having that extra money means you can do more stuff. That extra stuff, is that the key here?
Or am I just way off base?
*Like, say I had an apple farm and I was planning on hiring someone, Bob, for day labor for \$200 to help me pick the apples and sell them. I thot I'd have 500 apples to sell at \$1 each. So I estimated I'd get \$500 revenue with \$200 labor making \$300 profit. But it turns out I have 750 apples to pick. Me and Bob can pick and sell a max of 500 apples, so if I want to sell more apples, I need more help, but I can't afford it and it's day labor so I need the money by the end of the day. So I borrow \$200 from the bank, and hire an additional person for the day, Helen, and we pick all 750 apples. I make \$750 revenue w \$400 labor costs, so I make \$350 profit. So bc I took out the loan and used it to do productive things, I have more profit and Helen made a day of wages.
** If someone sees fit to answer, ideally, I'd like some math. Or if there is some model that can show the players (consumers, firms, banks etc.) and their interactions, that would be great. Supergreat, even.
That is all for now

Question : Is what I wrote above accurate?

There is a bit more nuance to it but 1-3 points are 'corect-ish'.

I guess what I'm getting at is: Is there some connection to the bank making loans, and those loans being used to fund additional productive activities* than otherwise possible (say, given the agent's initial budget constraints), and long run growth in the money supply?

Not in the long-run. There is a relationship between growth of money supply and economic activity but not in the long-run only in the short run. This is because in the long run prices are flexible and they will quickly adjust to increase in money supply (see further discussion of that in any standard macro text like Blanchard et al Macroeconomics ch 8-10).

If someone sees fit to answer, ideally, I'd like some math. Or if there is some model that can show the players (consumers, firms, banks etc.) and their interactions, that would be great.

It is possible to describe this with a model that is built upon individual interactions of consumers, firms and so on, but that would take too much space as even very simple micro founded macro models are quite large. For example, a basic microfounded (i.e. explicitely including interaction between households, firms etc) macro model introduced Woodford, M. (2011). Interest and prices, takes over 30 pages and that is a graduate text that does not explain basics that one would probably have to cover to explain it to someone with no economic training. Consequently, let me offer more concise model (which will not have qualitatively different results from more nuanced microfounded model) where I will skip description of individual interaction of individuals and just directly impose assumptions on behavior of aggregates that could otherwise be derived from individual interactions of individuals and firms (if you want more nuanced models look at above mentioned Woodford ch 3 or at Romer Advanced Macroeconomics Ch 6, 7 and 11).
Thus I will introduce simplified model based of above mentioned Blanchard et al. Let us start by description of money market. The money market can be described using:
$$M/P = L(Y,i) \tag{1}$$
Where $M$ is money supply, $P$ price level (so $M/P$ is real money supply), $L$ is money demand, $Y$ is real output and $i$ interest rates.
The money demand will be given as follows:
$$L= f_1 Y - f_2 i \tag{2}$$
Because money demand will increase with economic activity, and decrease with interest rates. This is what would normally be microfounded, but I will just assume it as a shortcut without proving it. However, intuitively it is not unreasonable assumption, when aggregate output (which is economically also equal to income) increases there is more economic activity so people will demand higher real money balances as there will be more transactions in the economy. Next if the interest rate is high people will demand less loans and thus also money, and will save more and thus hold less money balances.
Next, goods market will be given by:
$$Y = C + I +G \tag{3}$$
where $C$ is consumption, assumed to follow $C=c_0 + c_1 (Y-T)$ with $0<c_1<1$. Where $Y-T$ is income after taxes. Again aggregate consumption would typically be derived based on individual interactions, but it is reasonable to assume people consume more if their disposable income increases.
$I$ is the investment assumed to follow $I = \bar{I} +d_1 Y- d_2 i$. Once again this would normally be microfounded, but it is reasonable to say that investment increases when output increases, and investment decreases when interest rate $i$  increases as it is harder for firms to get loans and so on.
Finally $G$ is government spending, there will be no additional assumptions on its behavior for your question it is not relevant.
So given above assumptions we will have:
$$Y = c_0 + c_1 (Y-T) + \bar{I} +d_1 Y- d_2 i +G \tag{4}$$
Solving for $Y$ so we get expression for goods market equilibrium yields:
$$Y = \frac{1}{1-c_1 -d_1}\left( c_o + \bar{I} + G - c_1T \right)  - \frac{d_2}{1-c_1-d_1} i \tag{5} $$
Now finally, in an economy from a macro perspective both the goods market equilibrium and money market equilibrium above must be also in equilibrium together.
Recall that money market equilibrium was given by equation (1) substituting (2) into (1) we get:
$$  M/P=f_1Y−f_2i \tag{6}$$
Solving 6 for $i$, substituting into $5$  and once again solving for $Y$ so we isolate output we get:
$$ Y = \frac{1}{(1-c_1 - d_1) \frac{f_2}{ d_2} + f_1} \frac{M}{P} + \frac{1}{1-c_1-d_1}+d_2 \frac{f_1}{f_2} \left( c_o + \bar{I} + G - c_1T \right)  \tag{7} $$
Examining how $Y$ varies with respect to real money balances we get that:
$$\frac{dY}{d(M/P)} =  \frac{1}{(1-c_1 - d_1) \frac{f_2}{ d_2} + f_1} \tag{8}$$
So indeed increase in amount of money will increase output, in fact there even be multiplier effect because the higher the output is the more demand for money there will be etc.
However, note the above does not hold in a long run. This is not captured by the brief and simplistic model above but while in short run we can assume $P$ is fixed, in a long run $P$ will most certainly not be fixed, and in fact it will increase in response to increase in $M$ (see discussion of that in Blanchard et al ch 9). Hence, in a long run increase in money supply cannot stimulate output (which would via multiplier stimulate more demand for money and again more output). Consequently, and answer to your question is no (although I am not sure what you mean by long run - in economics long run is defined as time period where $P$ if flexible and can adjust).
In addition the reason why we can observe increase in money supply over long periods of time is that central banks try to maintain price stability, which many of them define as a yearly inflation of around $2\%$. For that to happen money supply needs to constantly increase as well. Consequently, even though it is correct to say that private banks create most of the money in our economic system, the central bank is ultimately ultimately in control in how much money is being created. They do this either through bank regulation, interest rate setting or by control of monetary base - this is also explained in the McLeay Radia, & Thomas (2014) you provide link to in your Q. If a central bank would be hell bent on it and would purposefully want to keep $M$ constant, they could do it (by unreasonably hiking interest rate, regulating borrowing in a such way as to make it nearly impossible etc). Conversely, if central banks think there is not enough money supply in the economy they can increase it regardless of bank lending (e.g. direct purchase and monetization of government debt). Note here that central bank can actually do this even without using private banks. For example, central bank can buy government debt which creates new money. Thus central bank can always move money supply wherever it want's to in principle (even if private banks would not want to lend).


3rd Degree Price Discrimination I came across a True/False question in my economics problem set:

  Is the following statement true or false?
  "A monopolist can practice
  third-degree price discrimination in the two markets it serves.
  Quantity demanded at any positive price is always higher in market 1
  than in market 2. Therefore, when the monopolist profit maximizes, it
  will certainly charge a higher price in market 1 than in market 2."

The answer is false. However, I do not understand why it is false.

I considered two cases, case 1 where the monopolist charges both markets a uniform price. If the monopolist practices price discrimination, profits will increase for the monopolist, and price charged in market 1 will be higher than market 2.

Case 2 is where only market 1 (since it is the "strong" market) is served under uniform pricing. By price discriminating, monopolist will also serve market 2 as it generates profit, and price in market 1 is higher than in market 2.

Why then is the statement false? Am I missing out another case?

Any help is greatly appreciated! Thank you.

Here is a counterexample (i.e. an example showing that the given statement is false). Assumptions:

The cost of producing each unit of the good is \$1.
All consumers are exactly identical, with each consumer willing to pay up to \$10 for one unit of the good. (Also, each consumer is willing to pay at most \$0 for a second unit of the good.)
Market 1 has 200 consumers, while Market 2 has 100. (And so, it is true that "quantity demanded at any positive price is always higher in market 1 than in market 2."†)

Since all the consumers are exactly identical, the profit-maximizing price in both markets is simply the maximum each consumer is willing to pay, namely \$10 (and the producer will produce 300 units of the good). Thus, it is false that the monopolist "will certainly charge a higher price in market 1 than in market 2".

†This statement is actually wrong. At a sufficiently-high price, the quantity demanded of a good in any two markets will be equal to zero. To correct this statement, one would either change "always higher" to "no lower" or append to the start of this statement "if quantity demanded is non-zero, then ..."


Where's a good place to find Information on Non-OCED countries? I'm looking for Private Savings (Sp), Investment (I), Taxes (T), Government Spending (G) for India.

The IMF Data, the UN Country Data or the World Bank Open Data should be good data sources covering a wide range of countries.


Why do game theorists use a discounted payoff of this form? Excuse the click-baity title. I notice the discounted payoff in the game theory literature usually takes the form

$$\sum_{t=1}^\infty\lambda(1-\lambda)^{t-1}R_t$$

This differs from the discounted payoff in the other dynamic optimization settings, e.g., see the Bellman equation in control theory.

Why the difference?

In my experience, it's mainly just for cleanliness for results.

Consider an infinite horizon repeated game, with discounted payoff representation (where I use $\delta = (1-\lambda)$ in your notation)
$$
(1-\delta)\sum_{t=0}^{\infty}\delta^t R_t
$$
where $0 < \delta < 1$.

Suppose I play a strategy that gives me the same payoff, say $a$, for each period $t$. Then,
$$
(1-\delta)\sum_{t=0}^{\infty}\delta^t a = (1-\delta)\frac{a}{1-\delta} = a
$$
which is cleaner than
$$
\frac{a}{1-\delta}
$$
As a side note, multiplying the utility by a constant does not change preferences, so we keep the inherent preferences the same.


Books friendly to self-studying Industrial Organization I'm currently an undergraduate freshman looking for resources to self-read Industrial Organization. I've read Varian's undergraduate book cover-to-cover and have a decent understanding of basic game theory, and I own the book
Industrial Organization: Theory and Applications by Pepall-Richards-Norman

Is there another book that would be better for someone who wants a rigorous treatment of IO that is mathematically advanced but theoretically digestable, or is this one optimal? (By the time I begin to self-read, I'll have finished most of baby Rudin).

While taking Industrial Organization I remember working with:

Strategies and games: theory and practice by Dutta
Introduction to industrial organization by Cabral
Industrial organization: theory and applications by Shy
Industrial Organization: Markets and Strategies by Belleflamme and Peitz

The first two are rather introductory while third and forth are more advanced (getting into greater detail with a little bit more advanced maths). You can probably find them online if you try.

And on top of that, I really enjoyed The Economics of industrial organization by Shepherd. It is way older than the others but still made quite a good read.


Number of firms in Long Run In a competitive market, is it possible to know the change (increase/decrease) in number of firms in the Long run with a positive shift in demand for increasing costs case?

Yes, it is possible. In the long run, firms enter until they break even. Suppose firms are symmetric. Then for each firm the break even condition is that the average costs equal the price. This is because the price is equal to the average revenue. The average revenue is given by $px/x=p$ where $p$ is price and $x$ is quantity. If revenue equals costs on average, then there are no profits left to be made and this is the equilibrium number of firms.

Further, in a competitive market, price equals marginal costs. Hence, the break even condition there is also price equals marginal costs. Alternatively, in this case the condition is Average Costs equal Marginal Costs. From this condition you can find the break even quantity. From there find the break even price, by setting price=marginal costs. Then plug in the break even price and quantity into the demand function to determine how many firms must enter until the market equilibrium price and quantity are equal to the break even price and quantity. The result is the long run equilibrium number of firms.

Note that the question is only reasonable in the presence of fixed costs. If there are no fixed costs, the long run number of firms is infinite and we have a trivial answer. However, the treatment of this topic in textbooks as well as academic papers alwa assumes the presence of fixed costs.


What are the arguments against a zero corporate tax? I've read a title in the news proposing a zero corporate tax. Thinking about it I couldn't figure a good reason against.

Why couldn't a country just set the corporate tax rate for firms to zero and then tax any gain obtained via negotiating shares or receiving dividends? Tracking the latters seems way easier (via a digital national registry of ownership and trades and mandating disclosure of dividends ) than burdening firms with complicated tax codes and the state with the burden of chasing them.

I am sure I am missing some theoretical and real world complications, so please, enlighten me.

It is possible to structure business entities in most if not all countries as pass through structures (e.g., limited liability corporations, sole proprietorships, or general partnerships).  Such entities are not taxed at the corporate level.  Tax liability instead flows through to the principals who own not shares but partnership interests.

Your question should therefore be restated: what advantage is there to reducing the corporate tax rate to allow shareholders to pay less tax than if profits flowed through to their personal income tax returns?

The answer to that question is data-dependent.  In some economic environments, it is useful to encourage corporate investment through corporate tax cuts.  We are not in such an environment today, however.  There is now a very wide and deep literature on how corporations have been saving more than they have been investing since the 2007-09 financial crisis.  Corporations have been hoarding cash or distributing capital to stockholders in the form of dividends and share buybacks more than they have been investing in future productivity and profitability growth.  Corporate tax cuts would therefore likely increase wealth inequality because they would flow through to already wealthy shareholders.

The only argument for reducing the corporate tax rate today has to do with international competitiveness.  The top tax rate for U.S. corporations is 35%.  In Ireland it is 18%.  If you ran a giant multinational, you might want to "invert" and re-domicile to Ireland or any other lower-taxing country.  The U.S. tax code has so many loopholes that through clever use of intercompany debt, net operating loss carryforwards, and operations overseas, it is possible bring the effective tax rate for a U.S. domiciled multinational closer to 10-15% over longer time horizons.  We should obviously attempt to set corporate tax policy to limit inversions, but many companies already pay less than they would if they were headquartered overseas.


What does this condition for a profit of a firm exist mean? What is the intuition behind this?

Let $Y=zF(K,N)$ be a production function.
For a profit to exist Indana conditions must hold and :

$$\frac{∂^2zF(K,N^d)}{\partial K \partial N} > 0$$

I understand all the conditions intuitionally, but I can understand this one mathematically but can't understand even what is meant by $\frac{∂^2zF(K,N^d)}{\partial K \partial N} > 0$. What does this being greater than zero imply?

It means the impact of changing labour on the marginal product of capital is positive. IE if you increase labour MPK will increase and also if you increase labour MPL will increase.


Equality, Taxes & Business Growth First, I'm not an economist - just a regular Joe interested in a small part of the subject.
Second, I apologize if this is a better question for the 'politics' stack exchange, but I figured I might get a more thorough/technical answer here.

The question: What is flawed with the following scenario (i.e. what are the downsides or why is it not realistic)?:

A government's tax model is hard on the wealthy. For simplicity's sake, let's say it caps an individual's annual income (total via employment, capital gains, gifts or anything else) to $1,000,000 USD. So if they make more than that, the rest goes to taxes (or same-year purchases, I suppose) - no exemptions for this tax bracket.
The government invests the additional taxes into education - providing high quality, cheap/free high level education. In theory, boosting the education level of the country as a whole - and hopefully stimulating innovation, etc.
Other taxes flow back into businesses - incentives to start and run small businesses. This could keep the markets competitive (plus, no business 'too-big-to-fail' or gross monopolies). Since owners/stakeholders wouldn't profit beyond a point, the focus may go to social/science/tech advances (making a name for one's self), giving back, etc. They could also hire more, use more services, and otherwise stimulate the economy that wat. I suppose you'd need some 'business savings account' to allow large businesses to have a safety net as they could otherwise become unstable.

Anyway, maybe it's just me, but it seems like making $1M/year would still make for a fantastic living and one you could retire on quickly. You'd still see people making 20x what others earn, so the point isn't to completely flatten the social scale, just even it out.

It seems like this would result in:

A more just society where the bottom 40% of the nation controls MORE than 1% of the wealth. Obviously you'll still have bums, drug addicts, etc. but that's a reality everywhere so unless it worsens the problem I wouldn't consider that a flaw; and perhaps a rehabilitation system could be funded.
Create a more robust economy as you'll have a lot of businesses competing and lots of educated people pushing the limits and as stated before, perhaps looking to higher-minded goals than the bottom-line.
A higher standard of living on average - as more people would be educated, employed and contributing to society.

So again - why doesn't this work? What are the downsides? Or is this just the wrong stack-exchange?

Thanks!

To provide some input (which I do not necessarily endorse), the Tax Foundation has used its "Taxes and Growth" (TAG) model to estimate/simulate the effects on USA Economy of Thomas Piketty's proposal that the tax rate for very high incomes should rise to $80$%.
The results can be found on a report freely downloadable from here.

Their Key Findings are (quote)

  1) If ordinary income were taxed at the top rates of 80 and 55 percent, our model estimates that after the economy adjusts, total
  output (GDP) would be 3.5 percent lower, wage rates would drop 1.6
  percent, the capital stock would be 7.4 percent less, and there would
  be 2.1 million fewer jobs.

  2) If capital gains and dividends were taxed at the new tax rates along with ordinary income, the economic damage would be much worse.
  GDP would plunge 18.1 percent (a loss of $3 trillion dollars annually
  in terms of today’s GDP), the capital stock would be 42.3 percent
  smaller than otherwise, wages would be 14.6 percent lower, 4.9 million
  jobs would be lost, and despite the higher tax rates, government
  revenue would actually fall.

  3) Although Piketty’s proposed income tax increase may appear to target only upper-income taxpayers, all income groups would suffer
  from the economic fallout.

  4) Our model estimates that the after-tax incomes of the poor and middle class would drop about 3 percent if the higher rates do not
  apply to capital gains and dividends and about 17 percent if they do.

The reasons that I say that I do not necessarily endorse the above results is that the report provided, although produced by a "Michael Schuyler, PhD" is not a scientific paper -so we do not know what assumptions and structure does their "TAG" model incorporates.


How to explain negative correlation between quantity sold and expenditure on advertisement? I have received the following dataset from our economics Professor. It has 15 observations and 4 variables - 'qsold' (quantity sold of product X), psn (price of X), pcb (price of a substitute product Y), adv (expenditure on advertising of X). I am supposed to derive a demand function (qsold = B0 + B1 (psn) + B2 (pcb) + B3 (adv)). Now theoretically, all three independent variables are supposed to have a relationship with qsold, however, I am supposed to explore only linear relationship, so, I tried to fit the following model.
df1
qsold   psn pcb adv
1183    1361.97 1405.78 3.22
974 1520.49 1369.17 3.39
1179    1361.43 1448.71 4.03
1258    1159.67 1465.12 3.91
1161    1297.74 1383.93 3.46
1052    1362.44 1450    3.64
992 1447.25 1404.4  3.55
1213    1316.93 1418.03 3.81
1133    1365.97 1391.95 4.21
1001    1283.92 1403.11 4.22
1221    1329.34 1428.9  3.38
1137    1278.41 1426.81 3.89
1112    1466.21 1442.68 3.65
1025    1355.73 1359.79 4.25
1277    1377.06 1455.03 3.35

lm(formula = qsold ~ psn + pcb + adv, data = df1)

Residuals:
    Min      1Q  Median      3Q     Max
-118.47  -31.59   12.42   39.46   92.43

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  635.4451  1240.7873   0.512   0.6187
psn           -0.5897     0.2647  -2.228   0.0477 *
pcb            1.1835     0.6650   1.780   0.1027
adv         -103.7231    62.7722  -1.652   0.1267
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 72.57 on 11 degrees of freedom
Multiple R-squared:  0.5764,    Adjusted R-squared:  0.4609
F-statistic:  4.99 on 3 and 11 DF,  p-value: 0.02004

In the output above, only psn is significant (based on t stats). Our Professor told us that we should consider only significant coefficients in the demand function. I am finding it difficult to agree with. In this case, if I consider only psn in my demand function, I am perhaps violating the null hypothesis, which is based on F stats (that all coefficients are 0). Also, if I consider only psn I am essentially negating the combined effect of all three variables, and basically choosing a different model that what I fitted.

adv has a negative coefficient, which is against my theoretical understanding. As I have read that it has a positive correlation with the quantity demanded. How can I explain this relationship?

If possible please cite literature, which I can refer. Also, please note collecting data for other variables, increasing sample size, or fitting non-linear models is not a possibility.

In the output above, only psn is significant (based on t stats). Our Professor told us that we should consider only significant coefficients in the demand function. I am finding it difficult to agree with. In this case, if I consider only psn in my demand function, I am perhaps violating the null hypothesis, which is based on F stats (that all coefficients are 0). Also, if I consider only psn I am essentially negating the combined effect of all three variables, and basically choosing a different model that what I fitted.

It is important to take into account significance because you cannot directly observe data generating process. Regression does not tell you what $\beta_0, \beta_1 ... $ are, it tells you what they appear to be based on fitting line that minimizes the sum of squared residuals through data. Yes in expectations (provided all OLS assumptions hold) $E[\hat{\beta}] = \beta$ but this result only holds in the limit as the number of observations go to infinity (see discussion in Verbeek. A Guide to Modern Econometrics or really any econometrics textbooks for more details).
In this particular case the $F$-stat (with 3 an 11 degrees of freedom) is 4.99 which is sufficient to reject the null of joint insignificance i.e. $H_0: \beta_0 = \beta_1 = ... \beta_k = 0$ so that is not a problem.
However, you cannot reject the null hypothesis that $\beta_3$ (effect of advertising) is zero. Consequently, just taking the results of the regression you present at face value (which is not necessary always appropriate in real research but might be in classroom setting), the correct answer would be "advertising has no significant effect on quantity sold, we cannot reject the hypothesis that the true effect of advertising is 0".

adv has a negative coefficient, which is against my theoretical understanding. As I have read that it has a positive correlation with the quantity demanded. How can I explain this relationship?

This could be because you have some reverse causality. Demand equations are endogenous systems and should be modeled with simultaneous equations, not just simple regression (see this explanation for how to do that in R). Using simple multivariate regression in such cases is likely going to result in biased coefficients.
Possibly when demand is low firms ramp up spending on advertising, while when demand is high and firms quickly sell their inventory they might  not want to spend extra money on advertising. This creates reverse causality issue which biases the $\beta_3$ estimates that no longer give you accurate effect of adv  on $y$ (quantity sold). It is possible that advertising spending increases sales, but higher sales are simply associated with less spending and the second effect from sales $\rightarrow$ adv simply dominates.
This being said you mention that this is an exercise imposed on you by your teacher not real research. It is possible your teacher just wants to test if you can interpret coefficient estimates properly not if you understand concepts such as reverse causality (if you did not covered this in your class then probably your teacher is not interested in discussion of that). You should ask your teacher about their expectations regarding the answer.


Why use empirical macroeconomic models when they are not policy invariant (Lucas Critique)? With high probability this question is duplicate, and I tried to find one already in the community, but I was unsuccessful.

According to the Lucas Critique, in its more general terms, the problem with empirical macroeconomic models is that they are not invariant to policy changes, and hence we cannot take any policy conclusions out of them.

My question then is why do we still use them?

Any help would be appreciated.

The response to the Lucas Critique was the emergence of RBC and DSGE models. Using microeconomic foundations of macro models we can simulate how behavior changes when policy changes and only estimate "deep" structural paramateres that are not policy variant. Before microfoundations we were estimating models where the estimation included the actions of people. With microfounded models today we try to seperate the actions. This was not possible in older models as we actually did not consider how people act or react, whereas microfoundations tell you how people would react.

However this is a difficult task as once you introduce agents that actively think about their actions you must take into acount their future expectations, which are unknown. One way to deal with this are rational expectations.

A further issue is that such models predict reactions that are quicker than in the data. If agents are perfectly rational, have perfect foresight and all information, they react quickly and perfectly. The solution to this today is to add frictions that slow these reactions down. However old models that we used to estimate (think about IS-LM and especially AS-AD models) also have the huge issue that people are too stupid (only adaptive (backward looking) expectations, do not take information into account when forming expectations, don't think about what may come in the future) and this is partially a piece of the Lucas Critique. Now we have the problem that people are too smart or super-rational. Some models (see models where some fraction of agents are "Rule of Thumb Consumers") now also assume that some agents are fully rational (many indeed are) while some just are backward looking (as in the normal IS-LM or AS-AD model), as a balance of the two things to generate a more realistic picture.

As for the critique of rationality: In many experimental micro studies rationality fails. However this does not tell us how many small deviations from rationality aggregate, which is what macro is interested in. It may occur that from many different deviations in different directions that in aggregate rationality is still a good approximation.

Furthermore approaches have been developed now to deviate from rational expectations. These are very difficult to solve though. One interesting way is to assume people are rational, but do not have all the information, which is a reason most people make mistakes. These are models of information frictions. Key words: Rational Inattention (e.g. Sims) and Inattentiveness (e.g. Reis). Another related approach includes Learning Models.

To summarize: we try to have models that are immune to the Lucas Critique. These often require rational expectations to be solved, but other approaches are also being developed.


When can economists claim to "understand" an event or phenomenon? It's a common refrain that economists still don't have a solid grasp of the causes of business cycles (in particular, the Great Depression), despite decades of serious study. What would it take to say that this (or another event/phenomenon -- economic growth, the collapse of the Soviet Union, the causes of inequality) is "understood"? Are any key questions in economics "solved"?

Some additional questions for discussion- Can economists say that they "understand" something when they can craft policy to manipulate it as desired? Does the ability to predict phenomena constitute "understanding"? Is something "understood" when there is a broad consensus in the profession?

I'm not sure there is a correct answer to this question (or if there is, we don't understand it yet!), but here's a first shot at an answer:

Even if you look at the natural sciences, there is a process whereby ideas are refined over time. In the 17th century people 'understood' mechanics thanks primarily to Newton. But that didn't mean Einstein couldn't improve on the theory with relativity. One approach would then be to say that we never really understood mechanics in the first place, we were just confused until Einstein came along. But that binary view of understanding sets a very high threshold that economics may never meet; indeed, by that standard it might very well be that humanity never truly understands anything. I think most good scientists would be very cagey about ever describing a problem as solved—theories cannot be proven correct, only 'not disproven' and subsequently improved.

An alternative view would therefore be that understanding is measured on a continuous scale so that partial understanding is recognised and new discoveries refine that existing understanding. One might then define something as (at least partially) understood when

  Economists share a broad professional consensus on the matter.
  The consensus view is consistent with available empirical data.
  The consensus view represents a meaningful contribution over and above the knowledge that might be expected of a lay-person.

An issue for which economics performs better on all three dimensions might be said to be better understood.

Something like the effect of a rent ceiling, the role of adverse selection in a market, the potential benefits of free trade, or the static welfare effects of monopoly appear to be fairly well understood (at least by social science standards) because economists are in broad agreement, these things are not well-understood in society at large, and economists' views on these issues are generally bourne out empirically.
Things like the effects of a fiscal stimulus, the dis-employment effects of a minimum wage, or the dynamic relationship between competition and innovation seem to be less well-understood because economists frequently disagree on these issues—both with each other and with the data.

The rationale for the three components of the definition is as follows:

Consensus is not a direct measure of understanding. But I include it as a proxy to get at the fact that there are some areas of economics in which seemingly convincing theories that match some aspects of the data quite well are in direct conflict with alternative theories that also do well in some respect. It seems like having two conflicting views on an issue that you are not able to reconcile ought to be penalised in any measure of understanding.
Obviously, economics is an empirical undertaking—it aims to describe and explain empirical phenomena. A description of or explanation for a phenomenon that is not consistent with data is clearly not part of a good understanding of that phenomenon.
This criterion is aimed at getting at the idea that economists have been especially successful in improving upon a common sense understanding of the world in some areas. In these areas, economists might be viewed as having a particularly good understanding relative to society at large. Consider two examples: (i) a monopolist will charge more when demand is less elastic; (ii) two countries can benefit from trade even when one of them has an absolute advantage in every good. Both are issues that economists agree on, but (i) is common sense whereas (ii) is utterly counter-intuitive. The definition is designed to capture the idea that understanding (ii) is more meaningful because society depends upon economists to figure such things out. Society could probably figure out (i) without economists' help.


Simple General Equilibrium Model of Public Goods: Intuition? We assume a two person economy, denoted by person A and B. Good y is an ordinary private good, and each person begins with an allocation of this good given by $ y^{A*} $ & $ y^{B*} $ respectively.
Each person may consume some y directly or devote some portion of it to the production of a single public good, x. The amounts contributed are given by $y_{s}^{A}$ and $y_{s}^{B}$, and the public good has production function defined by
$$
x=f\left(y_{s}^{A}+y_{s}^{B}\right)
$$
Resulting utilities for these two people are given:
$$
\begin{array}{c}{U^{A}\left(x, y^{A *}-y_{s}^{A}\right)} \\ {U^{B}\left(x, y^{B *}-y_{s}^{B}\right)}\end{array}
$$
The necessary conditions for efficient resource allocation in this problem consist of choosing the levels of public goods subscriptions ($ y^{A*} $ & $ y^{B*} $) that maximize, say, A’s utility for any given level of B’s utility.
The Lagrangian expression is
$$
\mathscr{L}=U^{A}\left(x, y^{A *}-y_{s}^{A}\right)+\lambda\left[U^{B}\left(x, y^{B *}-y_{s}^{B}\right)-K\right]
$$
where K is a constant level of B's utility. The first-order conditions for max are
$$
\begin{aligned} \frac{\partial \mathscr{L}}{\partial y_{s}^{A}} &=U_{1}^{A} f^{\prime}-U_{2}^{A}+\lambda U_{1}^{B} f^{\prime}=0 \\ \frac{\partial \mathscr{L}}{\partial y_{s}^{B}} &=U_{1}^{A} f^{\prime}-\lambda U_{2}^{B}+\lambda U_{1}^{B} f^{\prime}=0 \end{aligned}
$$
A comparison of these two equations yields
$$
\lambda U_{2}^{B}=U_{2}^{A}
$$
and when substituting into the preceding equation the end result is:
$$
\frac{U_{1}^{A}}{U_{2}^{A}}+\frac{\lambda U_{1}^{B}}{\lambda U_{2}^{B}}=\frac{1}{f^{\prime}}
$$ or more simply,
$$
M R S^{A}+M R S^{B}=\frac{1}{f^{\prime}}
$$

  For such goods, the MRS in consumption must reﬂect the amount of y that
  all consumers would be willing to give up to get one more x, because
  everyone will obtain the beneﬁts of the extra x output. Hence it is
  the sum of each individual’s MRS that should be equated to dy/dx in
  production (here given by $ \frac{1}{f'} $).

Q: I follow the order of operations mathematically but don't understand the bolded statement.

You can take MRS as the willingness to pay (Take the other good in MRS as money). If the good is a private good that costs 3, your willingness to pay should be 3 because you are buying it for yourself. However, a public good is used by all payers, so we only need the sum of the willingnesses to pay to be equal to 3. (You are simply splitting the bill)


Why would a cash-rich company borrow money? I have read that Apple Computer issues corporate bonds.

Considering that it has $200 billion in cash, and the company complains it has been unable to spend its enormous amount of cash, why would they be issuing corporate bonds?

You are right that it seems strange why a cash-rich company is borrowing. In the case of Apple, the money that they are borrowing is being used to pay dividends to shareholders. The reason why they aren't using their \$200 billion is because doing so would cost them tens of billions of dollars in taxes. The current US tax code taxes corporations at 35% when they bring money they made overseas back to the US (this is called repatriation). So while, Apple has \$200 billion on the surface, \$180 billion of that is sitting overseas and can't be used to pay shareholders. It is cheaper for them to borrow money to pay dividends, than incur the huge tax costs associated with repatriation.

In general, however, borrowing is also attractive to firms today since interest rates are so low. If you can borrow at 4%, and expect to earn a return of 8% on that capital, taking on debt seems like a good deal. Therefore firms flush with cash still may borrow if they feel the return they can earn on the borrowed money is greater than the cost of interest.

Check out this article from Bloomberg for more information on the Apple case: Bloomberg Article


What are the identification problems in measuring peer effects? I am currently writing my bachelor thesis on peer effects. However, the more I read about the identification problems (I read e.g. Manski, Moffitt, Angrist, Goldsmith et al.), the less I understand. I particularly have a problem with understanding how endogenous selection affects my estimates (omitted variables? Selection bias?) and understanding the correlated unobservables/ related errors in variables and the endogenous membership problem and how or whether they relate to each other.

I know this is a lot but any help is appreciated!!! Thanks a lot!!!

Well, imagine you don't know how students are grouped. Maybe better students are deliberately grouped together, for example. Then your estimation is clearly biased. You'd basically reach the conclusion that classes with better students are better.

Peer effects are hard to identify with observational data because similarities in the behavior of peers could be due to peer effects or to selection into peer groups based on common unobserved characteristics, or to factors that affect all peers in a peer group.

To do a proper estimation we need a quasi-experiment, preferably a true experiment. Because in such context you indeed know that student allocation is random, so there's a clear causal link and possibility to separate the treatment effect from homophily and confounding factors.

Angrist and Pischke's Mostly Harmless Econometrics is a must-read for anyone interesting in working in this topic. Angrist (2014) discusses this matter in more depth and this NBER digest may help you with the intuition.


Does deflation mean drop in asset prices? Usually when inflation rises the stock market rises with it. The second point i want bring your attention to before i ask my question is when there are stimulus measure enacted by the government, thereby increasing the government deficit and there being a corollary between government spending and asset prices.

If there is a scenario where the economy enters a period of deflation, does this necessarily mean that asset prices will depress? Or could this be avoided where asset prices stay the same or keep rising ?

One would need access to stock price index data to make definitive statements. There are probably studies doing such analysis. However, I will make some rather safe generalised comments.

Firstly, we should expect differences in behaviour between the gold standard era and the present, as well as between developed and developing markets.

My expertise is with floating currency, developed countries. And the following statements appear safe to say.

Other than Japan, there has been no extended period of falling CPI (“deflation”) outside of recessions/global crises in the floating currency era. Pre-2020, that deflation was mainly due to falling oil prices, core CPI remained positive.
Stock markets tend to fall in recessions, for many reasons. Most modern recessions have been associated with financial crises, and leveraged investors needed to cover positions. This means that stock prices can be lower than fundamentals.
The deflation in Japan was extremely mild, and I would guess that there were some periods of rising stock prices (although the Japanese stock market was in a secular bear market after the bubble pop in the early 1990s) coinciding with deflation. Someone with access to Japanese financial data would have to verify
what happaned.

As such, we have no real guidance for what sort of “deflation” can happen in a floating currency sovereign. However, it is very hard to see what significant difference a deflation of -1% has versus an inflation of 1% for equity valuations (with those rates being similar to historical post-1990s experience). Stocks could rise and fall based on the moods of stock investors. The difference in expected nominal growth rates can easily be counter-acted by lower discount rates.


How can a consumer economy possibly be sustainable? Some consumer economies

In 2017, the United States household final consumption expenditure (HFCE) is $13t, which is 68% of its GDP.
In 2017, the United Kingdom has a HFCE of 1.7t, which is 66% of its economy.
In 2017, Hong Kong has a HFCE of 228b which is 68% of its economy.

Source: Wikipedia
What is consumer economy?
A consumer economy is an economy driven by consumer spending unlike production exports like industrial economies.
While I fully understand how consumer economy works in microeconomics (basically everything is the same and perfectly normal) and noted that US is an exception to the norms of international economic norms (since it's the owner of USD), I would like to be enlightened on how a consumer economy is possibly sustainable in terms of balance of trade, …aside from waiting for miraculous FDI injection

How can I continuously consume without running out of money&resources? (assuming this nation is not a Juche/Soviet)
Does this not eventually cause a devaluation of your national currency if you keeps on importing more than you export?
Is it OK for me to conclude that consumer spending is bad, we should save as much as possible like Singapore, China and Japan and focus on exports to make as much incoming money as possible?

GDP is, by definition, basically only consumption and government spending.  That's why you see consumption reported as such a high % of the overall number.  Gross Output (GO) is a more comprehensive measure of economic activity, and on that measure household consumption is closer to 35% of the economy.  A "consumer economy" isn't one in which most economic activity is in the form of consumption of imported goods — there is plenty of production going on in such countries, as well.  More production than consumption, in fact (since many of the goods produced are used by other businesses, and often not counted in GDP figures.)


Misleading vertical axis in foreign exchange graphs analyses? The market for a currency typically has the y axis labelled as (currency1/currency2) where currency1 is the currency in which the demand and supply is for. If this is the case, wouldn't it mean that a vertical movement upwards along the vertical axis mean that the currency is in fact depreciating rather than appreciating? For example, if a point on vertical axis is originally at £3/1USD and a movement upwards along the vertical axis to a point where £5/1USD, does this not mean that the pound has depreciated? I'm curious all of a sudden because I've always been told and analysed the currency market as one where any upwards/downwards movement on the vertical axis represents appreciation/depreciation, but the example I've just given seems to conflict with this. I've also found various sources where a movement upwards along the vertical axis shows an appreciation, such as in the pic below, which is how I've always viewed the market until just now.

The convention in finance is that any currency pair "currency1/currency2" is to be interpreted as the number of units of currency2 needed to buy one unit of currency1, or alternatively, as the number of currency2 you get from selling one unit of currency1.

For instance, as of 13th of Match of 2017, the currency pair rate of exchange between the £ and the US $ (GBP/USD) was roughly 1.22. This means that you need 1.22 US dollars to buy £1.

Under this convention, a fall/increase in the GBP/USD means a depreciation/appreciation of the British Pound with respect to the US Dollar.

So, using your example, if the GBP/USD goes up from 3 to 5, then the British Pound appreciates with respect to the US Dollar.

By contrast, the convention in economics is to define the exchange rate as £x/\$1, meaning that you need x British Pounds to buy 1 US Dollar, or that you can sell 1 US Dollar for x British Pounds.

Under this convention, an increase/fall in £x/\$1 means a depreciation/appreciation of the British Pound with respect to the US Dollar.

In other words, the interpretation is exactly the opposite.


Can a CES parameter be negative? I estimated the CES function (https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution) using national accounts data for France. I got (using notation in wikipedia):

a = 1.19
r = -0.48

so the term next to capital is negative (-0.19). Is this possible? What does it mean? I don't see anywhere in that website a restriction on the sign of "a". My textbook does not state restrictions either. Is it fine? Or is it a problem?

Any thoughts on the issue?

To elaborate on my comment above, whether there's a "restriction" on the possible values of $a$ depends on your assumptions about the production function.

If you assume that all inputs into the production function contribute positively to the final output, then it must be that $a \in (0, 1)$.

Since you estimated the parameter, you might want to check the confidence interval of the estimated parameter. You can do a one-sided test if $a < 1$, for example.


How does corporate income tax apply? I am very confused regarding the corporate income tax. Please explain me the following scenario:

"Teddy Bears Company" buys stocks of 1000 euro (VAT added). Then, in 1 month sells everything with 1500 euro and makes a profit of 500 euro.

Where comes the income tax? On the profit of 500 euros or on the income of 1500 euros?

"Income tax" for corporations means "profit tax". The 1.500 euros is never called "income" but "Revenue", or "Net Revenue", or "Net Sales turnover" or something similar. But never "income" -"income" is equivalent to "profit", for companies or professionals. (*)

"Profits" are calculated as "Net Revenues minus tax-deductible expenses".

"Net Revenues" means revenues without taking into account any Sales tax (like the V.A.T is).  This is what the "net" signifies here.

So the tax rate will be applied to the 500 euros in your example.

--

(*) When a professional says "my income is 20.000 EUR" he means "revenues minus professional expenses". When filing a tax-return, he will be taxed on the 20.000 EUR, minus any "living-expenses" tax deductions provisioned for natural persons (like maybe health care etc).

When a person that only works as an employee states "my income is 20.000 EUR", then he has not deducted any expenses from his wages, because it is considered that this person has no professional expenses, only "living" expenses.


A question regarding eurodollar futures rate I am reading a paper, and cannot understand this part. In the second line, it is said that
the pay off on this futures contract equals one minus the current annualized 3 month LIBOR rate in the contract expiration month.
Right after the sentence, however, the equation is using a policy rate of the central bank. Shouldn't r_t+n be a LIBOR rate instead of policy rate?
Please explain why if anybody knows about this.

In theoretical literature LIBOR rate and central bank's rate (for example Fed's fund rate) are often used interchangeably (see many examples in    Freixas and  Rochet: Microeconomics of Banking).
The reason why they are used interchangeably is that there is quite a strong proportional relationship between them and LIBOR rate depends on the Fed's fund rate. Hence:
$$r_{\text{LIBOR}} = f(r_{\text{Fed}})$$
In fact they are approximately equal so that:
$$r_{\text{LIBOR}} \approx r_{\text{Fed}}$$.
You can see that this holds in real life pretty well from the graph below based on Fred data. Also as explained here the correlation between them is almost 1. Hence, for purposes of theoretical modeling we will often just simplify and say that $r_{\text{LIBOR}} = r_{\text{Fed}}$ even though in reality this holds only approximately (there is really no point in explicitly modeling $r_{\text{LIBOR}} = f(r_{\text{Fed}})$ - models are meant to be simplified version of reality).


Why do ARM rates rise in recessions? Economic theory says that interest rates fall in recessions. If they rise from risk then that defeats the theory. Why do ARM rates rise in recessions?

First lets correct some misconceptions  "Economic theory says that interest rates fall in recessions." Economic theory (at least mainstream economic theory) does not say anything like that.
In fact in IS-LM AS-AD model, which is one of the workhorse models of modern macro, during recession if central bank would be passive and not do anything in recession interest rate would increase. This is because when an economy enters recession, demand for liquidity increases but the supply of credit decreases and hence ceteris paribus interest rate should increase.
Second, while adjustable rate mortgage (ARM) interest usually increases at the beginning of a recession it will usually quickly starts falling as data show. The reason for this is that in real world ceteris paribus condition is not realistic. During recession central bank will not be passive but it will actively try to stimulate economy by lowering its interest rates and by injecting extra liquidity into the economy which affect all other interest rates in economy including ARM and put downward pressure on them. Hence the interest rates will tend to eventually fall during recession as a result of central bank intervention if the intervention is successful.


Finding Cobb-Douglas Hicksian Demand using Duality I'm trying to follow the in-text examples from Mas-Colell. I can confirm I have the correct first order-conditions and hence the Marshallian demand functions for Example 3.D.1: $u(x_1,x_2) = x_1^\alpha x_2^{1-\alpha}$ subject to the budget constraint, $p_1x_1 + p_2x_2 =w$. By going through the example and taking Lagrange, I found the Marshallian demands to be $x_1(p,w)=\frac{\alpha w}{p_1}$ and $x_2(p,w)=\frac{(1-\alpha) w}{p_2}$. Fine.
The part I'm having difficulty with is finding the Hicksian demand, we know from 3.E.4 that $x(p,w)=h(p,v(p,w))$, where $v(p,w)$ is indirect utility, it's made clear that we can find indirect utility by substituting our Marshallian demand functions into $u(p,w)$.
I attempt to find v(p,w) by substituting the Marshallian demand for $x_2$ into the $u(x_1,x_2)$ : V(p,w)=
$(\frac{\alpha w}{p_1})^\alpha [ \frac{(1-\alpha)m}{p_2} ] ^{1-\alpha}$
To quote the notes given to me by my tutor, 'Marshallian is Hicksian if we substitute utility by indirect tility function:
$x^*(p,w)=h^*(p,V(p,w))$
I've reached a bit of a dead end here, I have the indirect utility function, but don't know how to get the Hicksian demand.

You have found the value function $V(p,I)$ which in your case is given as
$$V(p,I) = \alpha_1^{\alpha_1}\alpha_2^{\alpha_2}\frac{I}{p_1^{\alpha_1}p_2^{\alpha_2}},$$
where $\alpha_2 = 1- \alpha_1$ and $I$ is income.
The Hicks demand is a function of the utility level denoted $u$. An agent facing prices $p$ and income $I$ gets utility $V(p,I) = u$. Therefore you can set
$$u = \alpha_1^{\alpha_1}\alpha_2^{\alpha_2}\frac{I}{p_1^{\alpha_1}p_2^{\alpha_2}},$$
and invert to solve for $I$ in order to get
$$\frac{p_1^{\alpha_1}p_2^{\alpha_2}}{\alpha_1^{\alpha_1}\alpha_2^{\alpha_2}}u = I,$$
which is the expenditure function. You can insert this in your Marshall demand
$$\frac{\alpha_j I}{p_j} = \left(\frac{\alpha_j}{p_j}\right)\frac{p_1^{\alpha_1}p_2^{\alpha_2}}  {\alpha_1^{\alpha_1}\alpha_2^{\alpha_2}}u = h^\star(p,u).$$
Or in the case of $J$ goods: You have CD preferences with well known Marshall demand
$$(1)\ \  x^\star_j(p,I) = \frac{\alpha_j I}{p_j} \Leftrightarrow \frac{x_j}{\alpha_j} = \frac{I}{p_j},$$
and the utility function is
$$(2) \ \ U(x) = \prod_j x_j^{\alpha_j} = A \prod_j \left(\frac{x_j}{\alpha_j} \right)^{\alpha_j},$$
where $A := \prod_j \alpha_j^{\alpha_j}$ the constant $A$ serves the purpose of making the algebra somewhat easier. Inserting from (1) in (2) gives you value function
$$V(p,I) = A \prod_j \left(\frac{I}{p_j} \right)^{\alpha_j} = \frac{AI}{\bar p},$$
where $\bar p:= \prod_j p_j^{\alpha_j}$ and $I$ is constant across goods hence not bound by index so when $\sum_j \alpha_j = 1$ it $\prod_j I^{\alpha_j} = I$. From here you isolate income to get
$$\frac{\bar p}{A}V(p,I) = I$$
you then insert this in Marshall demand to get
$$x^\star(p,I) = x^\star\left(p,\frac{\bar p V(p,I)}{A}\right) = h^\star(p,V(p,I)).$$
Knowing the Marshall demand $\alpha_j I/p_j$ insert $\bar p V(p,I)/A$ with $V(p,I)$to get
$$h^\star(p,V(p,I)) = \frac{\alpha_j}{p_j} \frac{\bar p V(p,I)}{A} ,$$
let $V(p,I) = u$ to get
$$h^\star(p,u) = \frac{\alpha_j}{p_j} \frac{\bar p u}{A} = \frac{\alpha_j}{p_j} E(p,u),$$
where $E(p,u)= \frac{\bar p u}{A}$ is expenditure function (this follows from the fact that we arrived at $\bar p u/A$ as an expression for income by inverting the value function).


What happens to the money that the government is in debt from? Since nearly all countries are in debt except for four (http://www.therichest.com/rich-list/rich-countries/the-only-5-countries-in-the-world-living-debt-free/), where does all the money that the other countries no longer have go to? Surely these four countries can't be receiving it all.

This does not work like that. If you want to add-up all the debt in the world you will not end-up with 0.

Think about a situation in which I owe you \$100, you owe someone else \$100, and this someone else owe me \$100. Total debt would be \$300, even if another guy is debt-free.

Moreover, country debt (called sovereign debt) is not only owned by other countries but most of the world-debt, is owned by people, mostly through pension funds (and other investments). So even in a single-country economy, the country may issue some debt that consumers or firms can invest in. And the global amount of sovereign debt will be strictly positive.

Again most of the world-debt is privately owned and it may even be the case that those five countries you're talking about don't hold a single debt contract.


What happens when a subsidiary distributes its shares to its parent company? After a subsidiary company spins off from its parent and becomes public, what happens when the subsidiary distributes its shares to the parent firm's shareholders at some later time?

What I'm reading seems to suggest that the price of the subsidiary's stock will converge to that of its parent, but I'm not sure why. Can someone elaborate on this?

For context, I'm reading a paper on limitations of arbitrage that studies events where the market value of a parent company is worth more than that of its subsidiary.

The argument to have both share values converging is based on the fact that when the subsidiary redistributes the shares to the parent is similar to "unspining off".

The spin-off subsidiary is effectively being re-owned by the parent, becoming a part (a share) of the parent. As such, owning shares of the subsidiary becomes a proxy of owning shares of the parent.


How is the IS curve derived? The following diagram is included in my textbook as a means of deriving the IS curve.
Is it not the case that in the top graph, as output increases, interest decreases at a rising rate whereas in the bottom graph, as output increases, interest decreases at a falling rate. How are they compatible?

There is no inconsistency here. Following Blanchard et al. Macroeconomics an European Perspective (which is by the way same textbook where you got that picture from) the goods market can be described as:
$$ Y = C(Y − T) + I(Y, i) + G   \quad (1)$$
where, $Y$ is the output, $C$ consumption, $T$ taxes, $I$ investment $i$ interest and $G$ gov. spending. Then if we assume that consumption follows:
$$C = c_0 + c_1(Y − T) \quad (2)$$
and that investment function is given by:
$$I = \bar{I} + d_1Y − d_2i \quad (3) $$
then the goods market equilibrium will be given as:
$$ Y = \frac{1}{1-c_1-d_1}A - \frac{d_2}{1-c_1-d_1}i \quad(4)$$
where $A=[c_0 + \bar{I} + G − c_1T]$. Finally the IS curve is derived just by solving the above equation for $i$:
$$i = \frac{1}{d_2}A - \frac{1-c_1-d_1}{d_2} Y \quad (5)$$
Now this last expression clearly corresponds to the IS from the graph. As the equation lay bare the relationship between interest rate and output is still the same - lower interest rate is associated with higher output. The intuition behind negative relationship between
investment and the interest rate is determined by the fact that the higher the interest rate, the lower the incentive for a company to borrow to make new investment. Higher investment means also higher output $Y$ so the lower the interest rate the higher output will be.
Really the upper graph just plots the equation (4) although rearranged in different way and the bottom graph is the equation (5).  So the relationship was already negative and same in both upper and lower graph.  The graphs also might not be drawn to scale - they dont look to me like they are generated by specifying the underlying functions in lets say tikz picture in LaTex.


How can I write a conditional expectation of finite state markov process in matrix notation NOTE: This question is related to the econometric method explored in the following two questions:

Multiplicative factorization of stochastic growth time series--solving for an eigenfunction/eigenvector
Example of the change of measure proposed in Hansen (2012)

QUESTION: Suppose that $X_t$ is an $n$-state Markov chain with transition probability matrix $\mathbb P$ and realized values given by $n$-dimensional coordinate vectors. Suppose that $\{W_{t+1} \}$ is an iid sequence of multivariate normally distributed random vectors. How would I represent an equation of the form
$$
E[\exp(D'X_t + X_t' F W_{t+1}) e(X_{t+1}) \mid X_t = x] = \exp(\eta) e(x)
$$
as an eigenvector problem for a matrix $\mathbb M$? How can I represent $\mathbb M$ in terms of the primitives of the problem?

Let the $n$ states of the finite-state markov chain be denoted
by $\{x_1,...,x_n\}$ and let $\vec e = [e(x_1), ..., e(x_n)]'$.
Now,
first note that because $X_{t+1} \mid X_t$ is independent of $W_{t+1}$, we can write
\begin{align*}
\exp(\eta) e(x) &= E[\exp(D'x + x' F W_{t+1})] E[ e(X_{t+1}) \mid X_t = x] \\
  &= \exp(D'x + x' F F' x)\, E[ e(X_{t+1}) \mid X_t = x] .
\end{align*}
Then, because this must hold for all values $x= x_1, ..., x_n$, we
can assemble the following vector equation,
\begin{align*}
\vec e \, \exp(\eta)
  &=
\begin{bmatrix}
\exp(D'x_1 + x_1' F F' x_1)\, E[ e(X_{t+1}) \mid X_t = x_1] \\
... \\
\exp(D'x_n + x_n' F F' x_n)\, E[ e(X_{t+1}) \mid X_t = x_n]  \\
\end{bmatrix}\\
  &=
\text{diag} \begin{bmatrix}
\exp(D'x_1 + x_1' F F' x_1) \\
... \\
\exp(D'x_n + x_n' F F' x_n) \\
\end{bmatrix}
\, \mathbb P \, \vec e \\
  &=
\text{diag}(f)\, \mathbb P \, \vec e \\
\end{align*}
where $f = [ \exp(D'x_1 + x_1' F F' x_1),  ..., \exp(D'x_n + x_n' F F' x_n) ]'$
and $\text{diag}$ is the operator that takes a vector and places
it on the diagonal of a matrix where the off-diagonal elements are zero.
So, we can express the equation as a linear operator $\mathbb M$ on $\vec e$
with
\begin{align*}
\text{diag}(f)\, \mathbb P \, \vec e
  &= \vec e \, \exp(\eta) \\
\mathbb M \vec e &= \vec e \, \exp(\eta).
\end{align*}


How is workforce guaranteed in basic income system? After reading an article on wiki and watching the Ted video on basic income system in a society and even M.Zuckerberg talks about it, nobody really addresses the issue of the workforce availability.

If every person is guaranteed a basic income who is there left to work/be employed? I think only more ambitious people will work. What will motivate the rest of the people?

Brian's answer surely hit a major part of the issue - the level of the UBI. Yet, there are other aspects of the problem.

People like to work. There is a huge amount of sociological literature showing that people derive considerable non-pecuniary benefits from work, or alternative, that lack of work leads to several personal (and social) undesirables (for example, here, here, and here). As Voltaire said,

  Work keeps at bay three great evils: boredom, vice, and need.

Thus, many people will like to work. This is the supply side of the labour market.

Firms will still need workers. Provided capital and robots do not take over all jobs, firms will still require some workers. If the supply of labour across skill levels is not high enough, then either migration will occur (perhaps politically undesirable, but historically favoured by firms), or wages will go up. The latter will induce more people to work.

The key is, then, not only the level of UBI, but whether there will be enough jobs. Perhaps there will not be, at least not for the current working week. Maybe Keynes' prediction of a 15-hour working week might finally become true.


Log of a Negative Market-Book Ratio in a Regression Model As noted in this post, the book value of a company is its assets minus its liabilities.

I am reading this paper: "The price of sin: the effect of social norms on market" by Hong and Kacperczyk. One of the paper's hypothesis is that institutional investors are less likely to hold sin stocks. To demonstrate this, the following initial (Fama-Macbeth) regression was run as a benchmark:

$$IO \sim Logsize + Beta + LOGMB + PRINV + STD+ RET $$

IO is institutional ownership
Logsize is the market cap
Beta is the beta of the sector the stock belongs
LOGMB is the log of the market to book ratio.
PRINV is the inverse of price
STD is standard deviation of monthly return
RET is log of arithmetic of previous year's monthly return.

My question here is that, because the Market book ratio can be negative, how can we take log of this?

It is not specified in the paper how this is treated. I have the strong suspicion that it is likely any company with negative book value for whatever reason is ignored. Surely this would introduce some sort of bias. Does anyone know what is the standard practice?

Well the problem can be dodged by the use of some simple solution of just adding a constant to all values which circumvent issues of taking logarithms of negative numbers. Usually the mean is used as a centering point. If the mean is negative though some other number must be chosen.

Interpretation of such a transformed variable would be different from its regular logged counter part.

These are just some hunches on what could have been done. Its odd that methods aren't mentioned for this case.


An $n$-player prisoner's dilemma where a coalition of 2 players is better off defecting I'm interested in a game kind of like the prisoner's dilemma. The important thing about the 2x2 prisoner's dilemma is that it is efficient if all cooperate, but this is not an equilibrium, because both players have a dominant strategy to defect.

I have in mind a variant. Suppose $n$ players can choose to cooperate or defect. It is group efficient if all cooperate, but any player would like to defect from that. Further, any coalition of 2 (more generally $k$) players would prefer to defect together. So we could imagine payoffs $u(\text{all defect})=0$, and switching to cooperate increases all individual payoffs by 1, but at a private cost of $2+\epsilon$ (more generally $k+\epsilon<n$). So, it is always better for the group if someone cooperates, but only for a large enough group.

Is there a name for this kind of thing? Are there any papers or other resources that explore how this differs than the classic prisoner's dilemma?

A public goods game is a generalization of the prisoners dilemma that could cover this.

In a public goods game all players set their individual contribution level $x_i \in [0,\bar{x}]$ where $\bar{x}$ is a given positive parameter. Sometimes instead of an interval there are several discrete options to choose from. Player $i$'s payoff is defined as
$$
- x_i + c \cdot \sum_{j = 1}^{n} x_j
$$
where $c$ is a parameter such that $\frac{1}{n} < c < 1$. In these games it is individually rational to defect (set $x_i = 0$) but the Pareto optimal outcome is to cooperate (meaning $\forall i: x_i = \bar{x}$).

Seems to me that you could adapt this to your problem by narrowing the range of $c$ to $\frac{1}{n} < c < \frac{1}{2}$. In this case a player would prefer even dual defection to himself having to cooperate. Of course these games do not cover the whole game class you described, by they are part of it, and there is a lot of literature on public goods games, though mostly in behavioral economics.