What would be the economic impact of the "fair tax" plan? So I read about an interesting proposal about completely replacing income tax with a heavy national sales tax of about 30% (23% inclusive to compare to income tax).

I was thinking about what the impact of this would be. On one end, income goes up both because people would want to work more and they get to keep everything they earn.

On the other end, prices go up because of the sales tax. I was also learning that spending is crucial for short term economic growth, so that may hurt. But does the laffer curve apply to sales tax as well? People may buy more frequently if it went down, increasing tax revenue. I know the laffer curve is unreliable, but it was just a thought.

Is this thinking process correct, or would the fair tax be a complete disaster? I apologize I just got interested in economics so I don't know much.

Well, one advantage to a sales tax is that it affects everyone (even those who don't pay income taxes). However, some people may see that same fact as a problem. This problem lies in analysis of the equity of the tax. When we consider every single person being taxed 30% on everything they buy, we need to think about how that affects different income groups. Lower income groups spend a much larger portion of their income on consumption, which means that they will be taxed relatively much more heavily than high income groups. This fact alone is enough to discourage this sort of action because the government tries to encourage saving in the lower income groups (so they can move up to higher income levels). This is one large reason why a tax like this may not be as fair as the name makes it seem.

Another piece of information that must be considered is the incidence of the tax. As we know, the incidence of a sales tax depends upon the relative own-price elasticities of supply and demand. This means that in a market with very inelastic demand (such as cigarettes or oil), the buyer is paying most of the tax whereas in a market with elastic demand the sellers would pay most of the tax. This fact would make it so that different industries would end up paying a different amount of the sales tax compared to one-another. For example, an oil company would end up paying much less of the percentage of the tax than a company making a selfie stick. This, again, seems to be unfair.

FairTax is not intended to increase or decrease the taxation rate, therefore costs of products should stay roughly the same.  For example, without income tax, a family might keep 10% more of their income and prices might fall 20%.  But then purchases are taxed at 30% and the net cost to a family remains the same.  The only exception is the cost of compliance, which would be eliminated (goodbye 70k pages of tax code), and would lower costs overall.  You can see more about this from a study conducted by Dale Jorgenson.
Laffer Curve applies, but again, the FairTax is not intended to increase or decrease taxes.  Therefore, the question of whether taxes should be increased or decreased for short term economic growth (or some other reason) is a question for taxation as a whole and is not related to the FairTax specifically.  FairTax rate may be increased or decreased by congress just as any other tax.
Would the FairTax be a disaster? According to Arduin, Laffer, and Moore, the FairTax would result in "Higher total economic output, More savings, Higher take-home pay for workers, Faster employment growth, Greater rewards to investing that directly lead to more capital formation, Lower mortgage rates and, consequently, beneficial impacts for the housing market, and, A more efficient and stable tax revenue system" - "the FairTax has a great deal to offer as a proposed tax replacement system and is a marked improvement over our current tax regime." https://fairtax-structure-psyclone.netdna-ssl.com/client_assets/fairtaxorg/media/attachments/56c4/b2b9/6970/2d22/4c5e/0000/56c4b2b969702d224c5e0000.pdf?1455731385

A little more on compliance costs:  The Tax Foundation estimates that, "Americans spent over 3.24 billion hours, which is about 369,858 years, preparing and filing tax returns in 2012. Considering individual, business and employment taxes, this costs $37 billion annually in compliance cost for federal taxes alone."  The FairTax essentially eliminates this waste.

Debunking some of the other responses:

  "Lower income groups spend a much larger portion of their income on
  consumption, which means that they will be taxed relatively much more
  heavily than high income groups."

Not only is this conclusion false, but the converse is true.  Under the FairTax, a prebate would ensure that those at poverty level would pay zero tax.  Under the FairTax, lower income groups would be taxed very little (if at all).  https://www.youtube.com/watch?v=UPm9BaihZIM

  an oil company would end up paying much less of the percentage of the
  tax than a company making a selfie stick. This, again, seems to be
  unfair.

This is also false.  Under the FairTax, all businesses pay zero tax.  Businesses collect the tax and are compensated for the cost of collecting the tax.  This ensures the taxes are paid fairly by individuals and the "incidence of tax" is not applicable.


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

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

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

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

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

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

because official government published inflation statistics are just as artificial as the fiat currency value they intend to measure. according to those statistics, "a loaf of bread" has gone up in price dramatically in the last 100 years.  but realistically, i think it would have cost hundreds of dollars to get a loaf of bread of the same quality and consistency as cobblestone bakery's "million dollar white bread" way back in 1916. that simple everyday example doesn't even begin to account for the price of important stuff like pharmaceutical grade penicillin.

it is unfortunate that people use the word "real" to refer to inflation-adjusted numbers, as if they are somehow more realistic. life is getting better due almost exclusively to technological advancement. that advancement makes everyone richer. arguably, it has been more useful to centralized systems (e.g. governments and large corporations) in the past few thousand years. however, i for one am hopeful that the next few hundred years will be characterized by more decentralizing technology (e.g. the internet, bitcoin, etc.) that will be more beneficial to the "common man".


Why is the stock market always rising? I asked myself: How is it that the stocks are always rising? How is money generated every year so that the value of a company rises?

I mean, at some point there is a finite amount of money in the system, isn't it? Right now people assume that the stock market is overheated and not many sources are left where money can come from to make it rise even higher.

Now my question is: How and where is money coming from? I know, people invest, but at some point they take money from point A to B and don't create it.

Is there a basic book out there which explains the basics? Not for dummies but also not for experts who assume to know everything. Maybe a pragmatic economics book?

How is it that the stocks are always rising?

Because companies generate value.

  How is money generated every year so that the value of a company rises?

It isn't. Money is a measure of value, it is not value itself. Suppose you spend the day making a painting that's worth 100 dollars. You added one hundred dollars' worth of value to the economy, but you didn't add any actual dollars to the economy. There's no need for there an extra 100 dollars to be created for you to make the painting. If the market capitalization of a company rises from 10 billion dollars to 11 billion dollars, the amount of money that people are willing to pay for the company has increased, but the amount of money that exists hasn't increased.

  I mean, at some point there is a finite amount of money in the system

Well, the money supply is generally increasing, but that's separate from the rise of stock prices.

"Where Does Money Come From?" is what you need I believe:

  Where Does Money Come From? reveals how, contrary to public perception, the bulk of today's money supply is created and allocated by commercial banks in their role as providers of credit. The authors argue that this system is inherently unstable, with little effective regulation of how much credit is provided or whether it is used for productive or speculative purposes. Based on detailed research and consultation with experts, including from the Bank of England, Where Does Money Come From? reviews theoretical and historical debates on the nature of money and banking and explains the role of the central bank, the Government and the European Union. This Second edition includes new sections on Libor and quantitative easing in the UK and the sovereign debt crisis in Europe.

The book also contains a lot of references for further reading.


Extension on the suspension of national debt ceiling So I just want to make sure i got this right,

The national debt ceiling was suspended, i.e. the government can now freely spend until Dec.8, which they "say" was for providing $15bn in hurricane relief.

But lets face it, the treasury was running out of "extraordinary measures" to keep the debt below the ceiling, thus the extension. Source -> http://www.businessinsider.sg/us-debt-20-trillion-how-much-2017-9/?r=US&IR=T

The debt increased by 317 billion. But that aside, I want to get into the economics fundamentals. What does this mean for the dollar?

So foreign debt is increased, I am assuming the USD is going to plummet if expectations of quantitative easing to pay off the debt increases?

Debt is between US govt and The Fed.

If the Fed reset the debt back to 0 and bail out the govt, nothing changes. The next debt epoch starts.

Viscious if my understanding is correct. No other govt in the world has this freewheeling !!


When a central bank buys government securities, is this exactly equivalent to printing money? When a country's central bank buys that same country's government securities, is this exactly equivalent to printing money?
There seems to be no agreement on this.
Federal Reserve FAQ:

Is the Federal Reserve printing money in order to buy Treasury securities?
No.

Carlo Cottarelli (2017, Ch. 7 "Printing money"):

central banks, by printing money, can help governments spend more than they collect in taxes. The difference (the deficit) can be bridged by borrowing not from private savers but from the central bank, primarily through the central bank’s purchase of government securities. Public debt increases, but if the securities are held by the central bank, any interest paid to it goes back to the government, which receives its profits even in countries where the government formally does not own the central bank. In other words, the portion of public debt held by the central bank is not to be regarded as real debt, at least not in the immediate future. This is essentially what has happened to varying degrees in many advanced countries, which have continued to run sizable deficits since 2008.

Who is correct? (Or, why the seeming disagreement?)
Concrete example: Say John is hired to mow the White House lawn for \$100. What then is the difference between the following two scenarios?

The US Treasury prints a \$100 note, then uses it to pay John.
The US Treasury issues a \$100 bond that the Fed buys, then uses the \$100 deposited in its account to pay John.

I don't know if you are aware that you are using the word "print" abusively but:

  The U.S. Treasury controls the printing of money in the United States. However, the Federal Reserve Bank has control of the money supply through its power to create credit with interest rates and reserve requirements.

Source : https://www.investopedia.com/ask/answers/082515/who-decides-when-print-money-us.asp

Thus both are correct. Clearly a CB does not increase the money supply by creating credits in order to buy governments securities.

It does so with other goals in mind, such as forging economic cycles, maintaining financial stability, reconfiguring the debt market and/or stimulating money multipliers in the national economy.

A CB (theoretically)(and indirectly) buys government securities in an inflation-neutral manner $\iff$ no money printed $\iff$ it uses the existing "stock of (scriptural) cash".

The difference between your two scenarios is the notion of debt. Strongly putting aside the fact that your ex-nihilo first scenario literally makes no sense without a credit underlier.

Both are right.
the FED is indeed not printing anything; i assure you no green notes were made in this process. it's all electronic and the accounting checks out of course.
the first part of the comment you highlight is a big shortcut, the second which deals with seigniorage is more in tune with reality so let's start with that. The Fed has a around 4T of interest yielding instruments on it's own balance sheet and thus it does receive cash interest for those (the coupons that come with them). this money is then partially sent to states/federal level in the US. in switzerland for example the cantons get everything. so in this sense, the CB's actions have resulted in the generation of cash but you can see that 1. the amount is a few %'s of what was issued initially and second, it takes a lot of time and ifs and buts for these few %s to find their way into the real economy, hardly helicopter money.
Now that being said let's go back to the first part of the paragraph,even if the fed wasn't there to buy them there is so much money going around these days that we would have easily found another buyer for these securities in exchange of an interest rate that would only marginally be higher (a rule of thumb from chair bernanke was that QE resulted in a reduction of 1% to the term premia)
http://archivesofeconomichistory.com/webdata/magaz/020514121439VolumeXXIII_No1_2011.pdf


What's wrong with the "airline marginal cost pricing" argument? This is a very common argument found in introductory classes and texts. Here's Mankiw's version:

Thinking at the margin works for business decisions as well. Consider an airline deciding how much to charge passengers who fly standby. Suppose that flying a 200-seat plane across the United States costs the airline \$100,000. In this case, the average cost of each seat is \$100,000/200, which is \$500. One might be tempted to conclude that the airline should never sell a ticket for less than \$500. But a rational airline can increase its profits by thinking at the margin. Imagine that a plane is about to take off with 10 empty seats and a standby passenger waiting at the gate is willing to pay $300 for a seat. Should the airline sell the ticket? Of course, it should. If the plane has empty seats, the cost of adding one more passenger is tiny. The average cost of flying a passenger is \$500, but the marginal cost is merely the cost of the bag of peanuts and can of soda that the extra passenger will consume. As long as the standby passenger pays more than the marginal cost, selling the ticket is profitable.

Do airlines actually do anything like the above? I think they don't as I have frequently been on planes with mostly empty seats (even before the current pandemic).
Mankiw says the marginal cost of another passenger is "tiny". Let's say it's \$30. Then if a flight has some empty seats 24 hours before scheduled take-off, why doesn't it offer the seats for say \$50 each and fill them all up? Why is it that, in practice and contrary to the above argument, the airline will usually prefer to leave the seats empty?
What, if anything, is flawed or incomplete about the above argument?

One possible answer is that Mankiw's argument takes consumer demand for airline tickets as fixed and given. I would speculate that cheap last-minute tickets are a substitute good for regularly priced tickets, and that if enough people came to prefer them, demand for regularly priced tickets would fall and the airlines would lose revenue. In other words, instead of paying full price, too many customers would deliberately hold out for the heavily discounted tickets.
This is the same reason why so many stores destroy their obsolete/stale inventory instead of selling it cheaply or donating it, and is an example of a perverse market incentive, as it leads to unnecessary waste.

It's a useful theoretical example illustrating the difference between fixed and marginal costs. And airlines totally do things like that--think of all the last minute 'discount' tickets sales. Airline tickets 'spoil' like fruit--after the flight date, they are useless. So an airline has every incentive to sell a ticket for every seat they can, regardless of the price.
But it misses the point that it's the average cost that determines the feasibility of the route. Selling half the tickets for seven hundred and half the tickets for three hundred still manages the average. So does selling one ticket for $100k and the rest for a penny.


Why min AC = min SRAC at the minima of AC curve? At the lowest point of long run average cost curve AC, the SAC is also at its minimum and that is not the case with any other SAC curve bounded by the envelope. Why is that?

Short-run implies that some decision variable cannot be free set, it is fixed for a time (in the short-run). In the long-run all variables may be freely set. Let us denote the fixed variable by $x$. This can take different values, so there is a family of short run cost functions is $SC(x,q)$.
Given a value $q$ let us denote the cost minimizing value of $x$ by $x^*$, i.e.
$$
x^* = \arg\min_x SC(x,q).
$$
Cost minimization implies that in the long-run this will be the chosen value of $x$, thus
$$
C(q) = SC(x^*,q) = \min_x SC(x,q).
$$
Dividing by $q$ we get
$$
AC(q) = SAC(x^*,q) = \min_x SAC(x,q).
$$
The above holds for any $q$.

This result comes from the "zero-profit" condition used to define long run equilibrium in this model.
Recall the fact that in the "firm" part of the model, the marginal cost curve intersects with the average total cost curve at the minimum of the average total cost curve. Since marginal cost is the individual firm's supply curve, it follows that when price equals the minimum of total cost, the firm produces the quantity at the crossing point and has zero profit. A higher price will give the firm positive profit since P > ATC, so Revenues > Costs. A lower price will give the firm negative profit since P < ATC, so Revenues < Costs.
Long run equilibrium is defined by the number of firms being at the level that gives each firm zero profit. Thus the long run supply curve must be at the zero-profit price level, i.e. the minimum of average total cost.


Explanation Rational Expectations I am struggling understanding the concept of rational expectations. Can someone explain in simple words the concept of rational expectations? Does someone know a good (online) source explaining rational expectations?

The concept of rational expectations can indeed be confusing.

One of the nicest pieces that I read online on rational expectations is the following:

https://economictheoryblog.com/2012/05/18/rational-expectations

It very nicely describes the concept of rational expectations in very simple words.

The most important thing one needs to understand is that rational expectations do not imply that all people act optimal under all circumstances, it rather implies that people behave optimally given the information they have.

I will provide an actual answer because I strongly believe that embedding the rational expectations (RE) assumption into macroeconomic models is ridiculous.

I will try to crystalize this in a concise way. Anytime we try to use a macroeconomic model to forecast outcomes we are actually creating a model that incorporates, via probability distribution, all possible outcomes. RE assumes that nothing unforeseen occurs (it is whenever nothing unforeseen occurs that rational agents can act optimally) and that rational agents are then able to compute profit maximizing choice paths. Further, any behavioral deviations necessarily produce sub-optimal paths for choice variables. This is akin to assuming that all economic actors know the model governing the DGP within which they operate. And this yields (2): agents can only form RE whenever they know the true specification of the economic model governing their world and its exact parameterization. You decide for yourself if you think these are good assumptions.

This yields an extreme (and perhaps dangerous) system of thinking; the supposition that economic models ought to consistently provide reliable quantitative predictions about future outcomes, for example. It is also ironic that modern macroeconomists micro-found current models to attain quantitative predictions over an ordinal outcome.

See the work of Roman Frydman. A good starting point is "Towards an Understanding of Market Processes: Individual Expectations, Learning, and Convergence to Rational Expectations Equilibrium". AER, 1982.

You might also look into the behavioral and experimental macroeconomics literature.

edit: I will add --  Evans, G. W. and G. Ramey (2006) Adaptive Expectations, Under parameterization and the Lucas Critique. Journal of Monetary Economics for assertion (2)

edit2: My memory was incorrect and erik (below in comments) is correct. Frydman didn't win the NP. It was his co-founder of his institution at Columbia university Edmund Phelps.


Does non-binding price ceiling effect the market? If the Price of a commodity is 1 dollar and this price is the equilibrium price. At this price, the quantity demanded & supplied is 100(KGs). If government sets the price ceiling of 10 dollars, What would be the effects on the market?

My curve for this question is:

No there is no impact at all. A price ceiling of $10 means that the price cannot go above $10. Since the equilibrium price is already below $10 the creation of a price ceiling will not effect anything at all.

It is called an ineffective ceiling because it is precisely that, ineffective.

No impact at all. Hence the term "non-binding".


Which foreign workers in USA who send remittances to family are getting the best bang for their buck? There are probably a lot of ways to measure that, but I want to measure it like this: Foreign national workers grouped by country of origin, which group sends the most money per capita in remittances?

That way it's kind of like saying they have the most income per capita after living expenses.

Maybe that means the skills they brought to USA are getting the best return compared to other groups.

It doesn't say anything about how far that remitted money goes in the origin country. So bang for buck is referring to getting paid in the US, not spending it abroad.

I'm not sure where to start searching for this information. I googled around but just found ads for remittance companies.

A good start would be The Economics of Migrants' Remittances by Hillel Rapoport and Frédéric Docquier. They both work extensively on this topic. In this paper, they review the  theoretical  and  empirical  economic  literature  on  migrants' remittances.

They review six theories decomposed into two broad categories individualistic motives (altruism, exchange, inheritance, and the strategic motive) and two types of familial agreements (on insurance and investment).

In all of these six theories, except one, migrant's income is indeed a very good predictor of remittances. However, other motives matter and may differ across "foreign national workers grouped by country of origin". For instance, some societies are more altruistic than others, and assuming  that  altruism  decreases  with  time  of arrival, the size of remittances should be negatively related to this variable in the altruistic case.

They also predict contrasting effects concerning the distance from family. For instance, in the inheritance theory, the amounts remitted are expected to be closely related to the probability of receiving inheritance in the origin country. If, as they assume there is a negative correlation between the distance from family and the probability of receiving inheritance, a Mexican worker will remit more than an Ethiopian worker, other things being equal. This could even be true if the Ethiopian worker has "the most income per capita after living expenses".

To sum up, migrant's income is a crucial variable but other variables, which may differ by country of origin, may also be of first-order importance to understand remittances.

It would undoubtedly be India, as enormous segments India's tertiary educated class come to the US to work as programmers for 120k.

https://en.m.wikipedia.org/wiki/List_of_ethnic_groups_in_the_United_States_by_household_income


How do government purchases crowd out the private sector? I am curious about how government purchases crowd out the private sector (if it does). If we look at a graph of the composition of US GDP, it seems that government purchases and investment are somewhat negatively correlated. It's obvious during WWII that government purchases skyrocketed while investment shrank significantly.

I am wondering about the intuition behind why this happens. If I had to guess, it's because at a given snapshot in time, the capital and labor in the economy is limited, and if the government is spending more money to use capital goods and labor, then there are less capital goods to go around for the investment. Is that line of thinking correct?

Just to add some more besides the answers above:
Short answer: by influencing interest rate.
Explanation:
In the post Keynesian literature what has come to be appreciated a lot is that government purchases, backed by increased government debt, increases interest rate. Why? Well, that's in itself an interesting explanation and perhaps should be a separate question (interesting, because contrary to what people think that "more govt borrowing means more govt bonds in the market, means lower bond prices and hence higher interest rates" is not at all a satisfactory explanation).
Private investments are assumed to be a function of interest rate. So some of the investment projects (particularly, those at the margin) that were earlier profitable may not be anymore due to increase in interest rate.
This is what is essentially, crowding out of private investment.
This does not require the assumption that Savings have to be fixed. Instead, in Keynesian framework, what happens is that $Y, S, C$ all goes up (because crowding out is not necessarily full, depending on the interest elasticity of money demand - slope of LM curve). It's just the share of $G$ increases and that of $I$ decreases.
Coming to your assessment that historically, at least during some periods, $I$ and $G$ have been found to be positively correlated. Indeed, investment is not just a function of interest rate. It is also a function of sentiments of future of the economy. When govt's start building infrastructure or take measures to improve supply constraints it boosts the confidence in the economy and encourages investment.
That doesn't make concept of crowding out incorrect. Because the concept is applicable when, ceteris paribus, $G$ increases.
Lastly, your own idea that "the capital and labor in the economy is limited, and if the government is spending more money to use capital goods and labor, then there are less capital goods to go around for the investment." is the somewhat closer to the classical view. This assumes that economy is at its full potential and there are no rigidities in the labour market. Without going into details, this view over the year has been seriously challenged. However, it should still be considered as an alternative explanation.

Can a fully-financially-sovereign central government use its monopoly power of currency insurance to purchase up a massive amount of real resources, therefore making it such that there are fewer available for the private (non-government) sector to purchase? Yes. That is possible. If you call that crowding out, then crowding out is possible.
If, however you’re talking about any and all government spending “crowding out“ private sector lending based on the assumption of “loanable funds,” then, no, this kind of crowding out does not exist. The idea of loanable funds assumes that there is only a finite pile of money available to both the government and private sector, from which they can “borrow.”
As long as the real resources are available for purchase, federal government spending crowds in (augments) private spending. This idea of crowding out is false and predicated on three other false ideas. Briefly, it incorrectly assumes that:

the central government is a user of its own currency,
banks are revenue/reserve constrained (loanable funds), and
the interest rate is an axiomatic function of the free market.

The truth is that:

the central government issues currency every time it spends (even when it sells bonds, which is very misleadingly called “borrowing”),
banks issue credit every time they lend, and
the interest rate is a policy variable of the Fed’s FOMC board. (They change it because they want to change it.) Further, since the central bank has the infinite capacity to purchase and sell bonds on the open market, they therefore have infinite control over the market interest rate.

In summary: Real crowding out is possible, financial crowding out is not.


Interest rates and economic growth Are interest rates the cause of economic growth?

For example there is no money in the system and bank a is lending company A a loan Y with X interest.

how can company A pay back the loan Y with interest X when the system is just loaded with loan Y?

My conclusion is the Loan Y can only be paid back with interest when the economic is growing by other loans?

Let's consider a simpler example.

You have 10 apples. With that, you can eat $x$ apples and "invest" in the rest $10-x$ apples, plant them, and each would yield two apples tomorrow. Let's say that with some optimization, you decided to eat 4 apples, saving the other 6 apples so that you could have 12 apples tomorrow. GDP would grow by 2.

Is this a result of "interest rate"? No. There's not even a bank here.

Now imagine that there is a bank that ask you to deposit your apples there for a day. What would you demand in return? 2 apples tomorrow for every apple you save today. That's the interest rate. The assumption is that the borrower can do something at least as productive with the money he/she borrowed, and the apples would go to those who can most efficiently use them.

I would like to say the pay back of interest rates in a debt monetary system can only be served with new debts?

Initial state: no money in the system
First step: Bank A is lending the first loan X with interest rates I to company A.
Second step company A is buying productions from Company B at the amount of X.
Third step company B is buy products from company A.
Forth step: Company A is paying back Loan X but it can’t pay interest rates I because in the System was just amount X.

Where does Company A get the interest I.
In my opinion only through new debts?


What is the difference between risk, uncertainty and ambiguity I am trying to pin down the difference between risk, uncertainty and ambiguity.

As I understand, when behavioral economists talk about choice under uncertainty, they mean choice when agents face risk (known probability distribution over a range of outcomes) versus ambiguity (unknown probability distribution). So uncertainty is a blanket concept that can be broken down into risk and ambiguity. See for example Dannenberg et al (2014).

I also understand there is a debate on the meaning of these terms going back to Knight (1921) and Ellsberg (1961). Are there any competing definitions to the one above?

Here is a decision-theoretic formalization of your definitions.

The usual framework to talk about objective risk is the situation where a decision-maker expresses preferences over objective lotteries. Formally, if $X$ is a prize space, objective lotteries are defined as elements of the space $\Delta(X)$ of probability distributions (usually with finite support) over $X$. For instance, the decision-maker might be asked to form preferences between the lottery that offers her/him an apple with probability 0.3 and an orange with probability 0.7, and the lottery that offers her/him an apple with probability 0.5 and an orange with probability 0.5. The standard result in that area (von Neumann-Morgenstern theorem) delivers a representation that identifies the agent's attitude towards objective risk (her/his utility function), while the probabilities are given as a primitive of the model.

The usual framework to talk about ambiguity is the situation where a decision-maker expresses preferences over uncertain acts. Formally, if $X$ is a prize space and $S$ is a state space, acts are mappings $f:S \rightarrow X$ from $S$ to $X$. For instance, the decision-maker might be asked to form preferences between the act that offers her/him an apple if Novak Djokovic wins the 2017 Australian Open and an orange otherwise, and the lottery that offers her/him an apple if Andy Murray wins the 2017 Australian Open and an orange otherwise. The standard result in that area (von Neumann-Morgenstern theorem) delivers a representation that identifies both the agent's probabilistic beliefs regarding the states and her/his attitude towards risk (her/his utility function).

There is a third widely used concept, usually called Anscombe-Aumann acts or horse races, which associates both objective lotteries and uncertain acts. Formally, given a prize space $X$, an Anscombe-Aumann act is a mapping $f:S \rightarrow \Delta(X)$ that associates an objective lottery to any state in $S$.

Notice that the definitions of objective risk and ambiguity are to some extent subjective. The fact that risk is called "objective" relies very much on the assumption that the decision-maker agrees with the underlying probability model. For instance, if you observe the outcome of a coin toss, you might believe that heads happen with an objective probability of 0.5. It is implicitly imposed in the theory that the decision-maker agrees with this statement.

Regarding ambiguity, you might yourself believe that the act "receive an apple if Novak Djokovic wins the 2017 Australian Open" is very ambiguous because you have no idea on how to compute a subjective probability for this event. That said, another decision-maker might very confidently believe that Djokovic has a 74% chance of winning the tournament, in which case she/he does not perceive this act as ambiguous at all. Ambiguity is a subjective notion, which is given by people's preferences and behavior and not by the choice situation itself.

Let's talk about layman terms.

Ambiguity is lack of explicit context. A cook are are given flours, eggs, sugar, salt, spices. If you ask the cook to "make food out of it", this is ambiguity.

Uncertainty is random outcomes cause by ambiguous instruction/direction.
E.g.  Use above ambiguous instruction, the results can be a pasta, cakes, biscuit, charcoal, etc.  The outcome is "uncertain".

Risk is all possible tangible accessible "bad" outcome/events by probabilities associate to specific activities, depends on context.
E.g. When you lies the flat ground, your chances of falling is low.  But, that doesn't mean you can't fall : what if the earth below you break apart due to earthquake.  (winks)


Do the stock performances of various companies have a measurable correlation with exchange rate? For example if the values of big companies in a country decrease, will the value of that country's currency measurably decrease?

A company valuation is merely in paper. It is similar to  economist eating shit jokes. When the stock price of a big company drops, it "suppose to" hurts the shareholder who bought it on high.

When I say "suppose", because intervention does happens to "too big to fail" company. In worst case, government hold too much "interest" in big company that might issue bonds(AKA print money) to bails out the entity, as what happens to Asian financial crisis, and USA subprime loan financial crash.

IMHO, details real world example falls under TL;DR; category. There is countless global example.

A large company stock can be jack up by speculation. Say a company issues  10 millions stock with $1 face values. If a willing buyer trade 100 stocks with $1.50, and subsequent buyer keep buying 100 stocks and jack it to $50, it doesn't mean the company "values" sudden shoot up from $1 x 10 millions = $10 millions  to $50 x 10 millions($500 millions). This WILL NOT create extra $490 millions to the economy, nor to the money supplies.

Without government money supplies and cheap loan rates, it is impossible to create such speculation. In addition, without increase money supplies, not hot money flow into a country, foreign exchange will always stay in a stabil level.

Example of high stock values and insane inflation

Zimbabwe stock market compare stock value.

Examples of bubbles crash and NO bailout made, no apparent inflation

Dot Com bubbles.
Enron, Worldcomm scandal.

Example of bubbles crash. Country bail out cause higher inflation

Asia pre 2007 economy crisis stock value

Example of crash and bail out inflation flow to other country.

USA QE. Speculator borrow cheap money and speculate outside US. Hot money cause many Asian country company stock shoot up without fundamental.


Why do government jobs provide better benefits than industry jobs? I've noticed how government jobs in the US are known to have generous pensions, healthcare plans, vacation time, etc. as compared to the corresponding job in the private sector. (I haven't actually done any comparisons specifically, but it's something that many people say, so I am assuming that this belief is true.) Why is this the case?

Someone may answer with, "This is because government workers have unions, which push for better benefits." But why can't the industry employees form unions as well, and thus receive equivalent benefits?

I'll describe in turn five potential explainations:

Risk aversion interacting with the tax code
Is this true when we control for worker attributes?
Lack of incentives for cost control
Solving turnover, training and other HR problems
Political economy: unions and politicians

Risk aversion interacting with the tax code

I've heard it argued (but not empirically substantiated) that because government positions generally offer very low risk of job loss they attract risk adverse people.

All other things equal, relatively risk adverse people like relatively generous insurance and have a greater precautionary savings motive against negative shocks. Because retirement savings, health insurance, and to a lesser extent, life insurance have tax advantages when purchased through the employer, this risk aversion would interact with the tax advantage to induce a high level of retirement savings, health, and life insurance. Disability insurance is not tax advantaged, but employer-run plans do help solve some of the adverse selection problems associated with stand alone disability plans and so they too have an incentive to be employer provided and more generous in government positions for similar reasons.

Is this true when we control for worker attributes?

That all said, I'll echo @rocinante's point that among some sub-populations of workers, it isn't clear that government benefits are particularly extensive. My reading of the Are government employees overpaid? literature is that highly educated or skilled government workers do not typically appear overpaid (in a Mincer regression residual sense) relative to their private sector counterparts, and this includes measures of income and benefits. And elite financial and IT firms are often famous for their lavish benefits of meals, profit sharing, and low cost health care. However, part of the story there is that wages are higher in those fields and benefits are generally increasing in wages (if only because so are the tax advantages). It may be surprising to hear this but the average education and age of a public sector worker is substantially higher than in the private sector, explaining some of the higher wages and higher benefits.

Lack of incentives for cost control

So while it may well be true that, as @kbelder says, public sector employers have less of an incentive to hold down benefits, they have less of an incentive to hold down wages too, at least in conventional wisdom government employee benefits are more different from private sector benefits than the wages are, so that leaves us with a remaining puzzle beyond poor cost containment incentives.

Solving turnover, training and other HR problems

@rocinante's point about turnover is also a good one. We can think of the employee-employer relation as a sort of investment that pays returns while employment persists. Any situation where the initial employer investment (e.g., in training, background checks, customized equipment) is large relative to the immediate payout is one in which the employer is going to want to incentivise the employee to stick around until that investment is repaid. Pensions, which back-load compensation have a powerful incentivizing effect towards retaining staff under these circumstances.

Similarly, when positions require idiosyncratic human capital (extensive expertise and training not useful for other employers), this makes the employee strongly value continuing the employee relationship, and if government employers particularly require this sort of expertise (say maintaining ICBMs) then employment protection benefits may be another efficient way to attract staff without paying higher wages.

Political economy: unions and politicians

Finally, two more reasons from a political economy angle. First, unions may not just get better benefits because they have more power and influence but also because the people who run unions wish greater power and influence. To those ends, higher wages give them less than retirement and benefits programs which require wealth and staffing to be run by the union. Second, benefits, particularly defined benefit pensions, can be opaque in their true costs. Since politicians have to answer in elections to the public, HR strategies that please government employees (like high defined benefit pensions) but appear to be low cost to the public (again like high defined benefit pensions) therefore are relatively attractive to the politicians that administer the government.

Private companies are usually too small to promise the kind of long term pension systems that the government offwrs.


Is there any empirical evidence for the so-called "law" of diminishing returns The "law" of diminishing returns is usually "demonstrated" with made-up examples (programmers working on a software, farmers acquiring land...), but rarely on evidence. Is there any empirical research on actual data to acknowledge and quantify this law?

The above chart is from Agroecosystems, nitrogen-use efficiency, and nitrogen management by Cassman KG, Dobermann A, Walters DT, and it deals with this sort of question quite extensively for those interested in all the gory details.

There isnt any data because we can demonstrate this fact by the production of anything by holding the number of laborers fixed and increasing the amount of equipment.

Its an logic which holds in reality and thus generates a theory.

You can do it with seeing how many cookies you can bake cookies in an hour with different resources. If its just you, increasing the number of ingredients may increase your yeild or even having another oven may speed up your time. However at some point there will be no gain from getting more ingredients or more equipment- you're simply limited by what you have.

Now what would be interesting is checking if wicksell's law holds (i.e. $\frac{\partial F^2}{\partial K \partial L} \geq 0$) however this is also logically sound.

Bottom line we can demonstrate it, but its logically consistent enough for us to take it for granted.


Okun's law nominal GDP growth Does Okun's law also work for nominal (not real) GDP growth?

Does Okun's law work at all?

It was an empirical observation of the relationship between unemployment and an estimate of the "output gap" (the relative difference between actual GDP and potential GDP)

To the extent that the relative difference between actual GDP and potential GDP may be the same whether calculated using nominal GDP or real GDP, then the relationship should hold either in both cases or in neither. Otherwise the argument becomes one of saying that the output gap is affected by inflation


What is the point of all the models in an economics degree? I am a student of Economics doing my masters degree and I have to say I am a bit tired of all the models.

On the one side, there is these models where I can see how they are derived, which always seems to be a mixture of using the Lagrangean with some - often rather unconvincing - assumptions. But I kind of fail to see the deeper meaning. For example how do New Keynesian (or RBC) models help me understand the real world?

How would they be used in practice - is it reasonable to assume they could forecast inflation, growth or interest? It seems like these things are inherently impossible to predict.
Do they help me understand how they work? The understanding I have about them comes more from non-mandatory applied courses and my personal readings about past financial crisis etc.
But probably most importantly, do I believe anything that comes out of them which I did not assume already before? Certainly not.

Or the Solow model, how is the fact that some countries seem to have followed a path that vaguely resembles that assumed by the Solow model a justification for its validity? Drawing a simplified picture of a human doesn’t help me understand why they became sick.
There is extreme cases like Barro's model of Ricardian Equivalence which seems like either the world's most boring circus trick or an attempt to fool policy-makers without basic maths skills.

On the other side there is a few cases where I would say my understanding improved with models in a way it would not have without, e.g. the notion of externalities, Pigouvian taxation or comparative advantage. But I have to say - given the countless pages of Lagrangeans I have set up, hours I have spend maximising profit functions and arguments I had in my head trying to find ways to justify some micro axioms - this is not a lot.

Don't get me wrong, I am fascinated by the study of the Economy and everything it relates to, I just don't see how a lot of what we learn is actually a helpful tool. I am a good student and neither looking for an easy way out, nor do I want to rant about studying. I am just looking for some motivation where this all leads. Can somebody explain to me what the deeper meaning of economic modelling is and why we give it this much attention?

And yes I know all models are wrong, but how are they useful?

Models are more than just math. Model is a simplification of a reality that allows you to study the underlying mechanisms. Models do not need to be mathematical. Many people actually create models without even realizing it. For example, if someone says "minimum wage will not lead to unemployment" that person is actually having a model even if they never present any mathematics. Such person definitely does not take into consideration full reality - every choice of every single individual, movement of every atom and so on.

Hence, whether you use mathematics or not you are using some model anytime you are describing any mechanism, such as x causes y, or there is such and such relationship between x and y because of this or that. Thinking otherwise is just self-deception as no human mind can take into account full reality when examining any issue. You have to simplify whether you do it with math or without. However, I get that at the heart of your question is why economists use mathematical models, but I wanted to highlight that there is no way of escaping models.

Mathematical modelling has advantages over plain text.

Dani Rodrick put it best when he said:

  We need the math to make sure that we think straight--to ensure that our conclusions follow from our premises and that we haven't left loose ends hanging in our argument. In other words, we use math not because we are smart, but because we are not smart enough.

  We are just smart enough to recognize that we are not smart enough. And this recognition, I tell our students, will set them apart from a lot of people out there with very strong opinions about what to do about poverty and underdevelopment.

Hence the reason why economists use mathematical models is that they are tremendously helpful in disciplining your thinking and by forcing you to say exactly what you mean. Written text is imprecise, words can have double meaning, people can easily cover up unsound logic by good use of literary devices or appealing to your emotions all of which can cloud your judgement.

This makes text  harder to actually analyze analytically. For example, even in moral philosophy - the least mathematical field I can think of, to fully analyze argument made in text and determine whether it makes sense you have to often resort into translating it from plain English into symbolic logic - which is form of math. Mathematics itself is just a language based on logic, that's also why in mathematics we often talk of equations as sentences or statements.

When you reduce model to set of mathematical expression you are forcing yourself to make your own thinking bare. You cannot easily conceal faulty logic anymore. You can argue that math can be used to 'fool policy-makers' as you put it but you cant easily fool other scholars with math while with text you can easily fool both policy makers and scholars.  My argument here is not that the math is bullet proof, as argued by Romer some scholars can try to mislead with using "mathiness", but lying with math is much much more harder than lying with text.

Models actually do help predict what will happen. First, do not confuse prediction with forecasting. For example New Keynesian model predicts that if there will be sudden shock to demand wage rigidity will lead to higher than natural level of unemployment - that is a prediction but its different from forecasting as the prediction is based on the ceteris paribus conditions while the word is constantly changing.

Predictions that model make can be useful in itself for several reasons. Predictions actually allow us to test whether one theory is superior than another. In fact the only way of testing a theory is to test its prediction against empirical observations. If someone has elaborate theory written in text that says that minimum wage does not affect employment and other person will make equally compelling case in text against that how will you decide which person is right?

One way how to do that is to turn the first person text into a mathematical model. The person says that minimum wage does not affect unemployment? Okay that means he postulates the following relationship:

$$ U(w_{min}) = a + bw_{min}$$ where $b=0$

Now converting the thinking of that person into mathematical model actually allows us to test it - we can based on the model above construct regression of unemployment on minimum wage:

$$U = \beta_0 + \beta_1 w_{min} +\epsilon $$

and test whether the first person was correct by testing the null hypothesis of $\beta_1=0$ against alternative hypothesis $\beta_1 \neq 0$.

Predictions also allow us to do counterfactual analysis. We can ask ourselves what would happen if in the presence of wage rigidities government increases spending during the recession. New Keynesian models provide you with framework to think analytically about such questions and fully explore all their logical conclusions.

Does this mean that math is the only way of studying economics? No. Of course, every individual is different. Some people are visual learners, some people are auditory learners.  Some students respond better to narration than to math. Moreover, as you yourself admitted math helped you to understand some problems so it worked for you well at least a couple of times. While you might have learned better most concepts by reading about them  other student might have completely opposite experience.

Moreover, depending on your career choices you might end up not using most of the math in real life. However, a master degree especially if its master of science and not just master of arts is often a stepping stone (at least in the Europe) towards PhD or more academic career in policy institutes or government institutions where you will need the math if not directly then at least indirectly to understand new advances presented in academic journals. For example, even routine psychologists must have some statistical understanding if they want to keep up to date with new techniques to help their patients as in order to see if some technique is better than other some testing has to be done. Otherwise you will be just at mercy of trusting what authors say in conclusions, or some intermediary like academicians who like to blog for wide audience etc.

Furthermore, you should not interpret anything I said above as saying math is the only way of doing economics or that narrative analysis is useless. Sometimes narrative analysis can be more nuanced, and with some problems we might not even yet discovered ways how to model them mathematically in satisfactory way. However, models and especially mathematical models are incredibly important tool in any economist's toolkit.

Although I am sure many mathematical models have an actual use, another historical reason for the many mathematical models in economics is to make economics appear more like a hard science like physics or chemistry.

UPDATE

Because of the downvotes and the request below I will provide a quotation to backup this claim.

Jerome Kagan: The Three Cultures: Natural Sciences, Social Sciences, And The Humanities In The 21St Century


Practical advice for calculating optimal prices The company I work for is interested in making the pricing for its products more quantitative.  I researched the topic and I found some theory for calculating optimal pricing in Microeconomics texts and the "Pricing and Revenue Optimization" text by Phillips.
I have an engineering background and the theory makes sense to me, but I can't find any good material about how to implement these calculations in practice.
Here are some more specific questions

Calculating the optimal price requires a price-response function (seems very similar to a demand curve) associating price with demand.  The material I've read assumes that this function is known, but I can't find any good material about how to fit a price-response function in practice.  I've found some vague advice about using survey data, but it doesn't seem that practical or specific to me.  Are there some more specific and established methods for fitting a price-response function?  Maybe from historical transaction data?

Calculating the optimal price requires a cost function associating production quantity with cost.  I can imagine calculating this by accounting for raw material and labor costs in the manufacturing plant, but would appreciate if there's a more formal way to do this.  Maybe a complete tally of the costs I can sum up.

I imagine that any estimates of the price-response function and the cost function will have error.  Is there an established way to quantify the error and its impact on my pricing calculations?  This isn't addressed by the resources I've found.  Pricing of my company's products will have a large impact on revenue and I don't want to just fly by the seat of my pants.

Are there established methods for simultaneously optimizing the prices of a portfolio of products given a manufacturing quantity constraint?  The plants are constrained by the quantity of product they can produce.  The Phillips text has some theory on constrained pricing for one product, but not a portfolio of products.

Any advice is greatly appreciated!  Or even simply some insight as to whether optimal pricing theory is useful in practice, or sharing any war stories of actually implementing optimal pricing.

A price-response function differs from a demand curve. A price-response function appears in a model where prices are selected by the firm, instead of output. A demand function appears when firms are price takers and cannot influence the price of the product on the market. They will have to sell it at whatever the going rate is.
I will try to answer the questions but they will be very general answers, hopefully they are useful.

The price-response function can be estimated from historical data. I don't know what you mean by transaction data. But if your company is a manufacturer of stuff then transactions could mean the cost of your raw materials and intermediate goods purchases. Then it is possible to estimate a price-response function from this. But it is important to remember that the price-response you estimate is based on your own companies pricing strategy in the past. If your company has made mistakes in it's pricing before, how will estimating this price-response function help that? I think it is better to use a method that takes data from the entire industry instead and benchmark your company against that.

You don't need to do this in very much detail. Just setup your problem generally. Such as, Production Function = Y = F(x1, x2, ...) and cost function = C = G(x1, x2, x3, p1, p2, p3). Solve that problem, what do you end up with? Focus on estimating what is needed in that function in reduced form. I would think what you need is a good measure of your marginal costs.

Estimating the price-response function will certainly have error. But that depends on a lot of things: data availability, model specification, measurement error, etc. You can benchmark against other studies in your field or outside your field instead of trying to removing error completely. You can eventually compare the model's predictions against out-of-sample values.

Unless there is some interdependency between the production of these products within the factories, this should not be a problem I think. For instance, are these products made in the same factories? Does the production of one affect the other? If not, you can get probably get away with solving the problem for each product's price response separately.


What is the best example social norm effect economy? Here is my example.

I read the paper called "Social norms and Energy Conservation" (2010) by Hunt Allcott, about the energy conservation of households by providing them with the amount of energy individual household use and their average neighbor's energy usage. The first thing is this research discover at the first place that household did not use the best efficient method to conserve the energy. Interesting things are 1 ) the adding reference descriptive social norm for society to adjust 2 ) not only people decrease their energy usage toward that descriptive social norms but some who below average adjust toward social norm level.

So what are the another phenomena social norm affect individual decision ?

Well, it sounds like the paper is drawing a conclusion between behavioral responses towards energy consumption when they're shown public averages.

There's a problem with that paper -- unless it makes specific reference to this:
- How does he/she derive causation between variation in electricity and 'social norms'? I don't see social normality being the primary influence.

Separately there are psychological effects at play like:

• Bystander Effect, Social Loafing, Diffusion, and Moral disengagement

That very much could be at play, confounding the entire study. What if I chose to increase energy expenditures 'just' because I see that the averages aren't 'that bad.'

"Everyone else is saving well, so I can go heavy and not hurt the environment as much..."

This incentive and what I understand as the one described in the paper where people conform to a standard norm are different.

But if you're doing some homework and need some 'answer': there are many, cigarettes are very heavily advocated against right now. Someone would choose to change their habit of smoking because 'it's currently less acceptable.


Dynamic programming, optimal consumption-savings (finite horizon) problem Let $w_t$ denote a consumer's wealth at time $t$ and $c_t$,
the amount she chooses to consume, so her savings exiting this time period are $w_t-c_t$. Given this savings decision, her savings $w_{t+1}$ at time $t+1$ are determined by a random process in which $w_{t+1}=\alpha w_t$ or $w_{t+1}=\beta w_t$, where $\alpha,\beta$ are postitive constants, each with probability $\dfrac{1}{2}$ and independent of past rates of return on her savings. At time $t$, when she is choosing $c_t$, she knows $w_t$ but she doesn’t know
anything about future returns except the probabilistic law just given; she does know her past consumption decisions, of course, and past rates of return. Considering a log utility, i.e. $u(t)=ln(c_t)$ and assuming that the consumer is impatient, so that he discounts future utility by a factor $b$ each period, where $0 < b < 1$, then the consumer's decision problem can be written as follows:
$$v(c_t)=\max_{c_t \geqslant 0}\sum_{t=0}^{T}b^{t}u(c_t)$$

If the consumer can not borrow, then what is the optimal consumption level for the consumer?

$\underline{Note:}$ The problem is based on David M. Kreps' microeconomic theory book, but it is adjusted to be a finite horizon problem. Kreps, in his book, solves this problem in a fuzzy way for $T=3$, that is not obvious to me. However, due to the fact that I know little of dynamic programming, since I am in the begining of examining this topic, I would appreciate it, if someone could provide a solution in the finite horizon. If the problem is not set in a rigorous way, I would be glad too to see somene making any appropriate change. I beleive that it is a classic problem in the field of economics.

Your value function is as follows:
$$
V_t[w] = \max_{c_t \in[0,w]} \left\{u(c_t) + \frac{1}{2}V_{t+1}[\alpha(w_t - c_t)] + \frac{1}{2}V_{t+1}[\beta(w_t-c_t)] \right\}
$$
with the terminal condition
$$
V_{T}[w_T] = \max_{c_T \in [0,w_T]} u(c_T)
$$

So, we can solve this via backward induction. Clearly, at the final period $T$, since $u$ is monotonic, we consume everything, so $V_T[w_T] = u(w_T) = \ln(w_T)$.

Let us now consider one period previous, so period $T-1$. The value function is:
$$
V_{T-1}[w] = \max_{c_{T-1} \in [0,w_{T-1}]} \left\{u(c_{T-1}) + \frac{1}{2}V_{T}[\alpha(w_{T-1} - c_{T-1})] + \frac{1}{2}V_{T}[\beta(w_{T-1}-c_{T-1})] \right\}
$$
We already know what $V_T[\cdot]$ is, so substituting,
$$
V_{T-1}[w] = \max_{c_{T-1} \in [0,w_{T-1}]} \left\{u(c_{T-1}) + \frac{1}{2}u(\alpha(w_{T-1} - c_{T-1})) + \frac{1}{2}u(\beta(w_{T-1}-c_{T-1})) \right\}
$$
considering the case $u(\cdot) = \ln(\cdot)$,
$$
V_{T-1}[w] = \max_{c_{T-1} \in [0,w_{T-1}]} \left\{\ln(c_{T-1}) + \frac{1}{2}\ln(\alpha(w_{T-1} - c_{T-1})) + \frac{1}{2}\ln(\beta(w_{T-1}-c_{T-1})) \right\}
$$
Take first order conditions, and we can get optimal $c_{T-1}^*(w_{T-1})$.

Then we have solved what $V_{T-1}[\cdot]$ is! We can then do the same procedure by considering $V_{T-2}$. Repeat until we get to $V_0$.

EDIT to reflect comment.
You now know that $c^*_{T−1}(w_{−1})=\frac{\alpha\beta}{1 + \alpha \beta}w_{T-1}$.
Plugging back into $V_{T-1}$, we have solved for the value of $V_{T-1}$,
\begin{align}
V_{T-1}[w] &= \ln(\frac{\alpha\beta}{1 + \alpha \beta}w_{T-1}) + \frac{1}{2}\ln(\alpha(w_{T-1} - \frac{\alpha\beta}{1 + \alpha \beta}w_{T-1})) + \frac{1}{2}\ln(\beta(w_{T-1}-\frac{\alpha\beta}{1 + \alpha \beta}w_{T-1})) \\
&=\ln(\frac{\alpha\beta}{1 + \alpha \beta}w_{T-1}) + \frac{1}{2}\ln(\alpha(\frac{w_{T-1}}{1 + \alpha \beta})) + \frac{1}{2}\ln(\beta(\frac{w_{T-1}}{1 + \alpha \beta}))
\end{align}

Finally, lets now go to $T-2$. The value function is
$$
V_{T-2}[w] = \max_{c_{T-2} \in[0,w_{T-2}]} \left\{\ln(c_{T-2}) + \frac{1}{2}V_{T-1}[\alpha(w_{T-2} - c_{T-2})] + \frac{1}{2}V_{T-1}[\beta(w_{T-2}-c_{T-2})] \right\}
$$
We just solved what $V_{T-1}$ is! Plug it in, and repeat.

This expression will probably blow up quite quickly, so it will be a pain to solve analytically.

I still can't comment, so this is not another answer it is adding some math to the given answer
Since

$ Log X*Y = log X + log Y $

$ Log(X ^ i) = i * log X
$

So substituting

$
Ln Z +1/2 Ln X + 1/2 Ln Y = Ln (z * Srqt(X*Y)) $

will simplify the expression a lot, but I have to reduce it in handwritten form because I'm writing from a phone now

You will reach

$ max [ w*(w-c)]  $

which clearly happens at

$ c=w/2 $

(try any values)

2- Also, are you sure of ur use of the term "dynamic programming"???

3- And I don't understand from where came the term

$ [ Alpha*Beta / (Alpha*Beta +1)] $  , that's why I substituted twice (in the original formula before this reduction too)

4- Finally,  I don't see why didn't u substitute
    $ V(t) = u(t) $   from the beginning to simplify things?
I simplified ur formulas mathematically, but I don't get how u reached the EQ (I admit I'm not specialized in ur field I came for an interdisciplinary problems).
I get that

$ Saving(t) = Return_of_Saving(t-1) + w(t)- c(t) $
Then u say her expected wealth "w" at time t+1 is an average of two values. So
$ W(t+1)= (alpha + beta) /2 * W(t) + Income(t+1) - C(t+1) $
 - that u have to add a factor for the decrease of money value & the increase of prices with time, that's ur "b" in the maximization formula right?

Anyways, if u don't care to explain just be informed of these logarithmic relations & use them to simplify


Why don't economists recommend voluntary childlessness to fight poverty? Please see the titled question. Poverty obviously demands pressing  solutions, let alone a stopgap. Dasgupta beneath refers to "the best Desta’s world can do": isn't Voluntary childlessness and Antinatalism more effective and instant? Kids who play and scavenge in garbage, and who live in sewers may argue that it was better never to have been born. Harms of their existences are obvious:

For those who still crave children, why isn't adoption recommended?  I refer only to educating the indigent;  anything involuntary like eugenics  is unethical.

Dasgupta, Partha. Economics: A Very Short Introduction (2007).
p. 159 Bottom

In a moving discourse on the character of poverty at the 2001
Plenary Meeting of the Pontifical Academy of Social Sciences,
Vatican, Justice Nicholas McNally of Zimbabwe urged us all to see
poverty as a sense of fatalism to ever-increasing economic
hardships in a changing, and elsewhere an often progressive, world.
At that same meeting, the political scientist Wilfrido Villacorta
suggested that the term ‘poor’ when applied to countries is perhaps
no longer useful; that countries ought perhaps now to be classified
in accordance with some such term as ‘progressive’, so that we may
ask if they have the institutions, policies, and civic attitudes in place
to enable people to improve their lot. Perhaps the best Becky’s world
can do for Desta’s is to offer financial and technical assistance so as
to promote and support local enterprises – including those

p. 160

involving education and primary health care – that people there are
all too keen to create even as they see from a distance how people
elsewhere have been able to improve their conditions of living. And
perhaps the best Desta’s world can do for Becky’s is to alert it to the
enormous stresses economic growth there has put on Nature. There
is, alas, no magic potion for bringing about economic progress in
either world. [I bolded]

p. 102

Gender inequalities
The considerations I have just outlined can’t on their own explain
the persistence and magnitude of household inequalities in the poor
world. In a notable article, the demographer Pravin Visaria
observed that the female–male ratio in India had shown a decline
since the Indian Census of 1901; worse, it has been considerably less
than 1. According to the most recent census, there are 93 women to
every 100 men in India. In the rich world today, the ratio is 106 to
100. In answering a question the epidemiologist Lincoln Chen
posed in response to Visaria’s finding, namely, ‘Where have the
women gone?’, he and his collaborators collected gender-based
mortality and anthropometric statistics from villages in the Indian
sub-continent and discovered male bias in the allocation of food
and health care in poor households. The suspicion is that parents
not only practise female infanticide, but also withhold postnatal
health care so as to reduce the number of girls in the household. [I bolded]

Economics: The User's Guide. p. 334.

 Inadequate childhood nutrition, lack of learning stimulus and sub-par schools (frequently found in poor neighbourhoods) restrict the development of poor children, diminishing their future prospects. Parents may have some control over how much nutrition and learning stimulus their children get – and some poor parents, to their credit, make great efforts and provide more of those things than do other parents in similar situations – but there is a limit to what they can do. They are by definition under great financial stress. Many of them are totally exhausted from juggling two or three insecure jobs. And most of them had a poor childhood and poor education themselves.

Despite the initial shock value provided for the question, and the high possibility for this question to become heated, political, or otherwise delve into an off-topic conversation, I will do my best to provide an answer to this question.

  Voluntary childlessness would be a functionally ineffective suggestion. This is not only too vague a suggestion to be widely useful or create policy for, but there are better focuses for economists to study in order to fight poverty.

If adults are practicing female infanticide for cultural or economic reasons, would these adults seriously consider simply not having children if you ask them? If adults are withholding post-natal care in particular circumstances, then how is this an economic failure rather than a moral one? If we are focusing on the family unit, and argue that every family has its own smaller market economy in who provides what sort of labor for the family, then shouldn't we argue that each family economy should be informed on how to make better choices, and be restricted from making unethical choices such as murder?

In some cases, maybe a family might consider not having kids if they can't support them. The consideration for whether someone will have a reasonable quality of life of course is subjective. In some parts of America there is extreme poverty, same as there is in India or China or many other countries. Yet happiness or "utility" has always been a subjective experience, and families continue to have children in these conditions.

Consider this statement from Indian economist and Nobel Prize winner Amartya Sen:

  "There is considerable empirical evidence that even as people in many parts of the world have become richer, with much more income to spend in real terms than ever before, they have not felt particularly happier than before.1 "

As with all things this may not be universally true. Some studies find suicide rates are not sensitive to income or unemployment. 2 But what is a bad living standard for some is not an insurmountable living standard for others. Is it wrong for people to bring children into the world where they must overcome suffering? Answering this question requires imposing a hard standard for what standard of living is a basic right, which frankly, is not the intellectual right of economists over everyday people.

Responsible economists, if looking at this issue, would rather prevent the miniature market failures within the family unit. Sometimes, trying to make policy that greatly restricts choice at the small scale would be impractical, or too prohibitive to be ethical, as economists generally like to allow for individual freedoms. So economists tend to look at broader policy through taxes or social welfare programs to combat poverty. One thing that is clear is that to prevent the most egregious consequences of poverty, there must be a way to hold those accountable who commit atrocities such as female infanticide or other such actions.

  "It was mentioned in the last chapter that no major famine has ever occurred in a functioning democracy with regular elections, opposition parties, basic freedom of speech and a relatively free media (even when the country is so poor and in a seriously adverse food situation)....Despite China's greater economic success than India's in many economic fields, China - unlike independent India - did have a huge famine, indeed the largest famine in recorded history, in 1958-61, with a mortality count estimated at close to 30 million. Though the famine raged for three years, the government was not pressed to change its disastrous policies3"

If transparency and public accountability are required to prevent and act on national tragedies that greatly reduce welfare, then on the smaller scale, the culture within a community is what will determine whether poverty or crises of resources will be answered with some sort of aid or assistance, or whether they will be answered with more drastic measures.

One cannot ignore in this conversation that many modern economies actively encourage population growth. As mentioned above in the comments, some places like Communist China had a one-child policy to restrict population growth. That policy has been repealed in the face of the changing demographics that China is undergoing, where there will be a much larger proportion of older people who live longer. The one child policy was a contrived way of dealing with issues like food shortages. Because the government tried to completely control markets, they created weird market failures and dealt with them in ways that were clearly detrimental.

Does this mean policies such as giving tax breaks to those who marry or giving welfare based on household size are bad policies? Is there moral hazard in subsidizing child creation in some sense? First off, why do these policies exist? An economy can grow both with the creation of technology, and the creation of capital and labor which pair together at some "efficient" ratio, depending on the market. To perhaps oversimplify, growing labor is one of the ways of growing an economy and trying to keep it productive and competitive with other countries.

Thus, economists should study how welfare programs for families affect the incentives families have for working or having children, etc. Which they already do. A cursory search of the literature:

Maru, Rushikesh M. "Incentives and disincentives in the Indian family welfare program." Studies in family planning 17, no. 3 (1986): 136-145.
Knox, Virginia W., Cynthia Miller, and Lisa A. Gennetian. Reforming welfare and rewarding work: A summary of the final report on the Minnesota Family Investment Program. Vol. 8. New York: Manpower Demonstration Research Corporation, 2000.
Keane, Michael, and Robert Moffitt. "A structural model of multiple welfare program participation and labor supply." International economic review (1998): 553-589.
Dahl, Gordon B., Andreas Ravndal Kostøl, and Magne Mogstad. "Family welfare cultures." The Quarterly Journal of Economics 129, no. 4 (2014): 1711-1752.
Schoeni, Robert F., and Rebecca M. Blank. What has welfare reform accomplished? Impacts on welfare participation, employment, income, poverty, and family structure. No. w7627. National bureau of economic research, 2000.
Lundberg, Shelly, and Robert D. Plotnick. "Adolescent premarital childbearing: Do economic incentives matter?." Journal of Labor Economics 13, no. 2 (1995): 177-200.

At the end of the day, economists are not concerned necessarily with changing the minds of individual family members and encouraging them to not have children. A family may not even find this "optimal", as children are a source of not just future support into old age, but of companionship in a harsh world (and other non-pecuniary incentives). Energy is better directed at guiding the hand of government towards policy that can effectively alleviate poverty and increase the welfare of society as a whole.

Additional citations:

1 Sen, Amartya Kumar. The idea of justice. Harvard University Press, 2009. 272.
2 Andres, Antonio Rodriguez. "Income inequality, unemployment, and suicide: a panel data analysis of 15 European countries." Applied Economics 37, no. 4 (2005): 439-451.
3 Sen, Amartya Kumar. The idea of justice. Harvard University Press, 2009. 342.

Why don't economists recommend voluntary childlessness to fight
  poverty?

Because making that recommendation is unpopular, and the bulk of society does not seem ready to have a serious discussion about it. And at an individual level, nobody who wants to have children will change his or her mind solely on grounds of what economists suggest would be best for society.

Governments could certainly make a much better effort to avoid overpopulation, although that would entail striking much of the outdated and populist welfare mentality. In the U.S., many women living in poverty --with no studies and no job-- bear multiple children (in some cases, each impregnation being effected by a different man), and yet these biological parents are given no ultimatum from the welfare system. If further welfare benefits were conditioned on --say-- sterilization, "Human Rights" activists would make a huge scandal. To a greater or lesser extent, systemic deficiencies of that sort also exist in Africa and Europe.

Instead of voluntary childlessness, I think a more realistic, more embraceable option is to postpone childbearing. The era where the next generation was needed for helping --say-- in the farm is long gone. Now the ongoing increase of life expectancy and of automation require[s] people to enhance their skills set. The latter is much harder to attain if the young adult is already immersed in parenting obligations.

  For those who still crave children, why isn't adoption recommended?

I personally do not see it viable, but any elaboration in this regard is too susceptible to misinterpretations and requires weighing a multitude of factors. I will only point out that adoption does not address one root cause of the problem: That the system largely fails (or hopefully not so much now and I am just unaware of it) to prevent multiple unplanned pregnancies among individuals with high reproductive rates and living in extreme poverty.


Is wealth inequality actually a problem I have been searching around online, but cannot really find an answer to my question.

I can find a lot of material covering wealth inequality and how it has developed over time, but haven’t found any material to support my theory (or the opposite).

My question is: Is wealth inequality actually a problem? With this I mean the super wealthy vs the rest (if that makes a difference).

I will try to explain my thinking as good as possible. My theory is, that super wealthy people tend to not spend all of their money, they may invest it or set it aside.

Consider a scenario where an individual owns 99% of all the wealth (i.e. money, disregard stocks, bonds etc in this scenario) in an economy, but spends roughly the same as everyone else in the same economy, effectively “disabling” a huge portion of the wealth. Would the “poor” actually be affected by this negatively? Would prices on goods reflect that “effective” wealth, or the total wealth in said economy?

Another scenario could be where one person owns most or all shares in all companies in the economy, and everyone else living of of salary. Would this actually be a problem? I imagine that it is same as above scenario.

Obviously these are silly extreme scenarios, I was just trying to paint a bit clearer picture of where I am coming from.

If the super rich (or perhaps top 1%) have an average spending similar to everyone else in an economy, with the only difference that they own more wealth, would that actually be a problem; or perhaps in reality a smaller problem than how it is depicted in the media?

I am not looking for political standpoints, but a more fact based answer.

I think that you are more or less than correct in thinking that cash that is never spent (nor expected to be) may as well not exist. Thought experiment: suppose that, unbeknownst to you and everyone else, £1 million suddenly appears under your mattress. If you never discover the money, it is hard to see how it could change anything in a meaningful way.

There are some caveats, however. First, a game theoretic point: even if rich people never spend their money, threats to spend their money might influence outcomes. For example, they could pledge to donate lots of money to the political opposition unless the government does what they say. If this threat works, they will never need to pay out.

Second, a ‘non-economic’ point: money gives you options, and people might enjoy having options in itself (even if they don’t spend the money). One might object to the kind of ‘options inequality’ brought about by an unequal wealth distribution even if rich people never spend their cash.

Third, to bring us back to the real world, we should stress that, usually, rich people do consume more than poorer people. So while it might be interesting to discuss wealth inequality without consumption inequality, this is not a phenomenon which we are actually facing today.

Wealth inequality, if earned through merit and productivity have no economic problems.

https://www.hedweb.com/bgcharlton/evolpsych.html

However it have certain biological problems.

Humans instinctively want to be "richer" than the rest. Your girlfriend, pick the richer guys.

In other word, if your girlfriend want to choose between you and Bob, all the money that Bob earns reduce your happiness.

Hence, a lot of what happens in politic, is people complaining about inequality without even bother pointing out how they are made worse off.

They are not made worse off in anyway economically. However, instinctively, their ancestors have a hard time getting laid because someone else' are even richer.

Wealth inequality may lead to power inequality. Here, the rich don't just stay idle with money. They use their money to sponsor politicians that give them favor makes it even richer.

Samples:

US founding fathers say that people shouldn't inherit wealth (I think there is a question about it in politic stackexchange)
Ming emperor preventing merchants from sailing overseas because he fears merchants can end up being richer than him. Again, the emperor is not made worse off by those merchants. However, he prohibits anyway.

I strongly suspected that income taxes are made to create poverty instead of to pay for anything.

Some answers point out that many rich people don't spend their cash.

That is wrong. Rich people invest their cash. That cash is then lent to another people that use their cash. So all cash is always used.


How to demonstrate that a game always have a subgame-perfect equilibrium in pure strategies? If I have an specific extensive game, with only a finite set of strategies, how can I demonstrate that the game always have a subgame-perfect equilibrium in pure strategies? My first intuition was to show that in every subgame a pure strategy it's a solution to the problem (maybe not unique) and then there is always a pure strategies equilibrium. But I'm not sure.

You could represent the game in simultaneous form (matrix) to see all possible equilibria. If there is only one, then that's your subgame-perfect Nash equilibrium (since there are no other equilibria). If there are multiple equilibrias in the simultaneous representation, the extensive form allows you to see if some paths would never be reached given the structure of the game.

Essentially, the extensive form "proves" which paths would never be reached through ruling them out. The one path that is reached is your SPNE. An SPNE has a more strict definition. There is really no shortcut around the arithmetic in the extensive form since the definition of SPNE forces you to check for the one viable path.


Are terrorists rational? Terrorism in general, and suicidal terrorism in particular, is
  popularly seen as “irrational,” but many economists and political
  scientists argue otherwise.

This quote is from Terrorism: The relevance of the rational choice model by Bryan Caplan. This paper has been published in 2006 in Public Choice. In relation with the recent terrorist attacks in Paris (Nov. 15), is there any new (economic) development on the question of the rationality of terrorism?

Edit: the title is intentionally short but by saying “is X rational?" I definitely mean "Can X be rationalized?"

I guess you might already know this, but I wanted to add a little detail to the other answers for the sake of any layman who comes here and gets the wrong end of the stick.

What is meant by rationality?

It is important to begin by saying that when economics use the term rational they have in mind a fairly precise definition that does not perfectly coincide with the way the word is sometimes used colloquially:

  We say that a decision maker is rational if

  s/he has preferences that are transitive and complete
  s/he acts in a manner consistent with optimization with respect to those preferences.

On the first bullet: suppose some one has to make a decision. We say that they have transitive and complete preferences if (i) they are able to rank the alternatives among which they choose from "most preferred" to "least preferred", and (ii) that ranking is internally consistent.

On the second bullet: A person acts in an optimal manner given their preferences if they choose the alternative that is 'most preferred' among the set of all feasible alternatives.

So are terrorists rational?

As others have noted, the literal answer to the question is that we can't really (empirically) verify that terrorists are rational. This is because observing one rational decision does not rule-out the possibility that the individual concerned made an irrational decision at some point in the past (or that they will make an irrational decision in the future). The best we can manage is to look for behavior that violates the two conditions above and take observations of such violations to be evidence of irrationality.

But, to address the spirit of the question: just because voluntarilly committing suicide and murder in the name of your beliefs may seem irrational in the colloquial sense does not mean that it is necessarily so. Indeed, if a person has carefully considered the alternatives available to them and decided that the option they find most attractive is to conduct a suicide attack then this behaviour is entirely consistent with rationality.

Rational terrorism in context

It is important to stress that there is no value judgement implicit in an eocnomist describing behaviour as rational. Just because something is rational behaviour does not mean that it is good or desirable or can be condoned. Rather, it just means that we think we have a systematic way of understanding why people might choose to behave in a certain way. Building a systematic understanding of a phenomenon is an important first step in deciding upon the best way to respond to it.

Terrorists are definitely rational. Each one of them maximizes their utility by blowing themselves up. Their preferences and utilities are defined by their beliefs, of course, not the reality of the situation. Their rationality is bounded, because they may not know that their beliefs are false or misguided.

The open question is how bounded is the terrorists' rationality. There are plenty of works out there, which I admit I haven't read, but Inside Terrorism by Bruce Hoffman looks to be a very popular one.


How does fed cutting federal fund rate affect student loan If fed cuts rate, it means it's cutting federal fund rate right? then why do loans like credit card and stuend loan? those aren't like Mortgage rate which the fed cuts its rate by buying MBS

The Fed funds rate is the rate at which commercial banks can borrow reserves on the overnight market (see this explanation at Investopedia). As such it affects all other interest rates banks charge since when they can borrow more cheaply they can also lend money cheaply to  consumers.
This affects among others also student loans (when they are provided by commercial banks - some places have government provided and subsidized $0\%$ interest student loans). However, of course if you already had a loan in a past it will only be affected if you took it at variable interest rate or if you are taking out a new loan, the fixed interest rate loans won't be changed retroactively.

The Fed doesn't cut mortgage rates by buying MBS. MBS didn't even exist until 1980s. The fed funds rates affects the rate at which banks can borrow from the fed, and hence the rate banks are willing to lend to people. Only in the case of the  adjustable rate mortgage (ARM) does the fed rate directly affect the mortgage rate. Almost all mortgages rates are fixed at origination. Refinancing changes the rate, but by replacing one mortgage with another--loaning someone new money at a lower rate to pay off the old loan.


Easterlin hypothesis In my understanding, the seminal contribution of Easterlin (1974) showed that within a single cross section, both within and across countries, happiness correlates positively with income. However, growth in income over time  within a country is not met with similar increases in happiness. Is my understanding correct?

The basic idea of Easterlin hypothesis is that 10 units of additional income does not require 10 units of additional happiness. The idea is close to the decreasing marginal utility of consumption.

Also, commiting suicides are less in countries where there are so many conflicts. Commiting suicide is more often in countries where prosperity level is higher.


How is the ARIMA model a valid approach for forecasting Economic Variables? Ive noticed the use of univariate forecasting methods (i.e the ARIMA model) employed in forecasting inflation (see references below).

How is this a valid approach in terms of forecasting economic variables? does this approach not omit the large amount of economic theory which determines how these variables are determined (i.e via equilibrium and interaction of variables other than themselves?)

1.https://scholar.harvard.edu/files/stock/files/forecastinginflation.pdf see pages 6-72.http://repository.graduateinstitute.ch/record/294965/files/HEIDWP05-2017.pdfhttp://repository.graduateinstitute.ch/record/294965/files/HEIDWP05-2017.pdf
3.http://www.unagaliciamoderna.com/eawp/coldata/upload/pakistans%20inflaction_arima%20model.pdf

So your question is basically asking why a purely statistical model would be better at forecasting than a model based on theoretical relationships. For example, think about a simple form of the ARIMA model i.e. an AR model where you're just using lags of the process to explain the process itself. Now think about what is contained in the lags of the process... If the true process (i.e. the DGP) is determined by theoretical relationships between other variables then these will automatically be included in the lag. So the ARIMA model is a statistical way of modeling the process to make sure you capture the statistical properties of the underlying relationship but does not necessarily provide an explanation for what is going on. In forecasting, especially when series are volatile and erratic, you often find that simple statistical models such as these do a better job since the underlying relationships may not be very stable or may be more complicated than any theory we can come up with. This is related to a recent article  which you may find interesting: http://www.sciencedirect.com/science/article/pii/S0169207017300997

I came across the answer to the validity of univariate modelling in economics (albet indirectly) from the book called A Rational Expectations Approach to Macroeconometrics. This answer is based on the material in the book, for a better understanding I reccomend actually going through it.

  In short the validity of ARIMA models is based on the assumption that the market is always in equilibrium or efficient1.

In order to understand how use of ARIMA models in Econometrics is a valid way to forecast economic variables, we must understand models which considers the case of for rational expectations (other wise referred to as efficient markets).

your standard efficient markets model is:

$$y_t=\tilde{y}_t+\sum_{i=0}^N\beta_i(X_{t-i}-X_{t-i}^e)+\epsilon_t$$
where:

$y_t=$ Economic variable of interest at time $t$ like unemployment or real output.
$\tilde{y}_t=$Natural rate or equilibrium of economic variable at time $t$
$\beta_i=$ coefficents.
$X_{t-i}=$ an aggreagte demand variable like money growth, Inflation or Nominal GDP growth.
$X^e_{t-i}=$ Anticipated aggregate demand conditional on knowing all  information at point $t-i$
$\epsilon_t=$ an error term

This model accounts for variability that can be present when a market does not have all information pertaining to $y_t$.

combining this formula using a specification used with the Lucas supply function:
$$\tilde{y}=\sum_{i=1}^N\lambda_iy_{t-i}$$

combining the two equations we get:

$$y_t=\sum_{i=1}^N\lambda_iy_{t-i}+\sum_{i=0}^N\beta_i(X_{t-i}-X_{t-i}^e)+\epsilon_t$$

This model tells us that if rational expectations hold,the relationship of  $y_t=\sum_{i=1}^N\lambda_iy_{t-i}$, thus providing validity for the use of uni variate models in economics.

For more reading on this topic, below is posted links to the three chapters which helped me:
1)http://www.nber.org/chapters/c10241.pdf
2)http://www.nber.org/chapters/c10243.pdf
3)http://www.nber.org/chapters/c10244.pdf

UPDATE: Upon Contacting Dr. Paul Middleditch on Twitter he says that the RHS variables must be replaced with a proxy which is normally the value of the previous period. ARIMA methodology satisfies such constraints.2

1. Mathematically this statement can be written as:
$$\mathbb{E}_m(X_t|\phi_{t-1})=\mathbb{E}(X_t|\phi_{t-1})$$

 where the expected value given by the market of $X_t$ conditional on $\phi_{t-1}$ the set of all available information at time $t-1$, is equal to the true expected value of $X_t$

It follows logically that $\mathbb{E}[X_t-\mathbb{E}_m(X_t)|\phi_{t-1}]=0$

2. a Youtube series he prodouced on rational expectations
https://www.youtube.com/watch?v=hMaJ0CMRNlk&list=PL1BUBmE-wKq_McDWvrAsiMygpupxOpvpg