Articles about police complaints for a lit review? I'm doing a research paper about how different cities have different quality of police service. I want to do a regression where the dependent variable is number of sustained complaints per 10 officers that year received by that agency. But maybe there is a better measure. I want to avoid using crime as a measure of police quality though, because I think crime is only partly affected by police service in the area.

Anyway, the thing I need to do first of all is get an idea of other work people have done in this area. And this area to me would be analyzing markets for public police, analyzing police service quality, analyzing demand for police service and whether it relates to quality of police service- same with supply, analyzing changes in police force for different cities, identifying factors that improve/diminish city-wide quality of police service.

Could someone suggest articles about measuring the quality of police service in a city? Or equilibrium quantity of police service in a city? Or things related to what I want to research? Especially if they do not focus on crime?

I found these articles about measuring the quality of service of a police department:

  Chen, Chien Min et al. 2013. The police service quality in rural
  Taiwan. Policing: An International Journal of Police Strategies &
  Management 37 no. 3:521-542.

  Editorial Desk. 1983. A Better Report Card for the Police. The New
  York Times (Late City Final Edition), February 11.

  Slothower, Mary, Peter Neyroud, Lawrence W. Sherman. 2015. Tracking
  Quality of Police Actions in a Victim Contact Program: A Case Study of
  Training, Tracking, and Feedback (TTF) in Evidence-Based Policing.
  International Criminal Justice Review 25 no. 1:98-116.

Then I found this about productivity and trust.Sort of has to do with supply side, and a little about the quality of service.

  Brown, Sarah et al. 2015. Employee trust and workplace performance.
  Journal of Economic Behavior & Organization 116 (August): 361-378.


Solow model golden rule with my exact answer In a perfectly competitive Solow economy with physical capital accumulation, population growth and a Cobb-Douglas production function, show that the “golden rule” steady-state would be reached if at every period aggregate consumption coincides with the aggregate labour income.

Let production function $$F(K_t,L_t)=K_t^aL_t^{1-a}$$

$$max[c^*=f(k^*)-(δ+n)k^*]$$ with respect to $k^*$

Then $MPK=a(k^*)^{a-1}$

So $k_G= (\frac{a}{(δ+n)})^{1/1-a}$ which is golden rule level of capital stock per capita.

Now calculate consumption at golden rule level

$$c_G=f(k_G)-(δ+n)k_G$$
$$c_G=(k_G)^a-(δ+n)k_G$$

$$c_G=(\frac{a}{(δ+n)})^{a/1-a}-(δ+n)(\frac{a}{(δ+n)})^{1/1-a}$$

$$c_G=(\frac{a}{(δ+n)})^{a/1-a}[1-(δ+n)(\frac{a}{(δ+n)})]$$

$$c_G=(\frac{a}{(δ+n)})^{a/1-a}[1-a]$$
$$c_G=k_G^a[1-a]$$

Ow consider to calculate wage

$w=f(k)-kf’(k)=(1-a)f(k)$

Then,

$$c_G=k_G^a[1-a]=w_G$$

$$c_G=w_G$$

Now consider aggregate version,

$C_G/L=W_G/L$

so,

$C_G=W_G$

I am confused at the aggregate transformation.

I add this question with its answer in order to contribute to the website. Thus, I will be glad if you add your opinions about my solution as well.


How did the Exchange Rate Mechanism work? The Exchange Rate Mechanism was introduced by the European Economic Community in 1979.

It fixes the Exchange rates between currencies to a specific margin.

But how does it do this?

How the system operated changed over time.

This Bank of England paper does a review of the literature. Rather than give an inaccurate summary, I will let you look through it.


What are different ways of specifying utility and decision making? This question is related to this question about the Machina paradox and about the expected utility model. In this question, I'd like to know a little more about various or even competing ways of specifying utility and decision making. It'd be nice if we could formulate a list of different formulations. To start, I suppose there is the Von Neumann–Morgenstern expected utility model, Savage's subjective expected utility model, or Prospect theory.

Is there anything else that is commonly used?

This won't get at individual choice, but how about evolutionary approaches? Perhaps this isn't what you are looking for, but one way to model decisions is to wander from the rational paradigm entirely. All changes in behavior are driven by natural selection, and so an equilibrium is based on stability.

  In a symmetric normal form game, an evolutionarily
  stable strategy is a (possibly mixed) strategy with the following property: a population in
  which all members play this strategy is resistant to invasion by a small group of mutants
  who play an alternative mixed strategy.

Text reference: Sandholm (2010)

Edit: Wanted to add some more exotic models, inspired by @CompEcon. These are interesting models for temptation, inconsistency, etc because you can get at internal conflict by seeing a DM as the unification of multiple parts.

Dual-Self Model of Impulse Control (Fudenberg and Levine 2006)

The Brain as a Hierarchical Organization (Brocas and Carrillo 2008)


Why is there Ricardian equivalence in Ramsey's model, but not in OLG? Why is there Ricardian equivalence in Ramsey's model, but not in OLG?

I am looking for an intuitive explanation.

Ricardian equivalence essentially means the timing of taxation doesn’t matter. Ramsey models are typically infinitely lived agent (or can be formulated as such) models with no heterogeneity. OLG models have age heterogeneity, so if people live for k periods an agent born in period 0 receiving a transfer in period t < k to be financed by a tax in period t+j, t+j > k, they don’t live to face the tax and the transfer is a permanent increase in income. Similarly, a person born in period k does not receive the transfer and views the tax as a permanent decrease in income. In an infinitely lived agent model (here a Ramsey model), the agent will always live to see both the transfer and the tax.


Is there any standard measure of economic significance? One measure is to look at standard deviations. If a one standard deviation increase in X leads to a more than a 0.5 (or 1, or ⅓, or whatever) standard deviation increase in Y, then we say that X has a economically significant effect on Y.

Is this standard? And if not, what other measures are there to formalize the notion of "economic significance"?

Imagine the basic linear regression setup:

$Y_i = \alpha + X_i \beta + \epsilon, \epsilon \sim N(0,\sigma^2)$

Holding everything else fixed, increasing $\sigma$ will increase the standard deviation of  $Y$ and therefore, for a fixed relationship between $X$ and $Y$, eventually move the relationship between them to economic insignificance by the standard you present. But the relationship might still be quite economically important. It might be better to instead ask about the standard deviation effects on $\sigma_\hat{Y}$, the standard deviation of the fitted values of $Y$, to ask if the effect is large relative to the total variation that can be explained by the model.

In accounting, they use a concept of immateriality which seems quite similar to economic insignificance. That might be a helpful definition for some problems.
This quote from Signifying Nothing: Reply to Hoover and Siegler by Deirdre N. McCloskey and Stephen T. Ziliak may also be helpful:

  The sheer probability statement about one or two standard errors is
  useless, unless you have judged by what scale a number is large or
  small for the scientific or policy or personal purpose you have in
  mind. This applies to the so-called "precision" or "accuracy" of the
  estimate, too, beloved of Hoover and Siegler — the number we calculate
  as though that very convenient sampling theory did in fact apply.


Linear Regression Assumptions of Homoskedasticity When I studied linear regression analysis, one of the assumptions taught was that of homoskedatiscity. I understood that homoskedasticity was required for significance testing on the coefficients. Then in my econometrics class, my professor said that we actually don't need homogeneity assumption since it was too strong. Instead, in order to conduct hypothesis testing on the coefficients, we could use "t-robust test" or Wald test.

So then why is homoskedasticity still widely assumed and taught in linear regression class? How do I reconcile these?

For the same reason you're taught the very simple supply and demand model of perfect competition in econ 101. It's not that it's wrong, it's a simplification of the real world and a good place from where to start. Once you've mastered the basics, you can learn more advanced topics. Heteroskedasticity isn't that advanced of a topic tho, most undergraduate students who take a second econometrics course get to learn about robust tests and all that.


The marginal cost function is meaningful only when the produced quantity is normalized The cost function depends on the number of produced items.

Let the value of the cost function C be in hundreds of thousands $ and the quantity is in 1,000,000 items, thus q = 1 indicates 1,000,000 items and q = 0.000001 indicates 1 item.

The marginal cost at a certain number of items (say 1560 items corresponding to q = 0.00156) is in one hand interpreted as the cost of an additional produced item (so it is the cost of the 1561th item), and from another hand it is the derivative of the cost function

$\frac{\partial \text{C(q)}}{\partial q}$ and then applying q to be 0.00156.

I see a good approximation for $\frac{\partial \text{C(q)}}{\partial q}$ to be $\frac{\partial \text{C(q)}}{1additionalitem}$ since 1 additional item is (0.001561 - 0.001560) which is an infinitly small quantity suitable to be considered as ${\partial q}$.

But what if in some other case, q actually represented just item units and not normalized item numbers e.g.:

q = 1 indicates 1 item, q = 1560 indicates 1560 produced items, and so on, so in this case $\frac{\partial \text{C(q)}}{\partial q}$ can't be $\frac{\partial \text{C(q)}}{1additionalitem}$ since 1 additional item is (1561 - 1560) which is 1 and not an infinitly small quantity.

would it be possible then to use the derivative of the cost function?

What I'm saying is that considering the marginal cost to be the derivative of the cost function is conditioned by having q a normalized value of a very big number of produced items. Do you agree?

I am not sure I understand your question but if I do, then I do not agree.

Marginal cost is defined as the derivative of the cost function. If the producible units are too large then marginal cost is less likely be a good approximation of non-marginal cost changes. The importance of this is that the derivative of an estimated cost function will probably not correspond to the real cost increase when non-marginally increasing the output.


Tit-For-Stat Strategy Best Replies Let $\delta\in(0,1)$ be the discount factor. Consider the stage game in the infinitely repeated prisoner's dilemma game:

The goal is to derive conditions on $\delta$ such that the symmetric tit-for-tat strategy profile is a Nash equilibrium.

To recall, tit-for-tat is when a player cooperates (here plays Yield, $Y$) the first round and then every round after copies the action of their opponent the second round.

I am told that if A is playing tit-for-that then B's best possible replies would be to alternate between $N$ and $Y$ (playing $N$ first), to always play $N$, or to play tit-for-tat himself resulting in both players always playing $Y$.

We compute the expected payoffs of each depending on $\delta$ and then figure conditions on $\delta$ so that $B$ should play tit-for-tat. As the payoffs are symmetric, these conditions provide $A$ should also play tit-for-tat given $B$ is and we have a Nash.

My only question is why it must be that these are the only best possible replies. Why might not $B$ have some periods where he plays $N$ for a while then switches to only cooperating? Or vice versa. Or anything outside of these three.

Instead of calling the three strategies you named the "best possible replies", I would say that they are the most salient replies. As you mentioned, there are many other potential responses to a tit-for-tat strategy. It turns out that what best responds to a tit-for-tat strategy is also a tit-for-tat strategy. Every other strategy will produce a lower payoff than using the tit-for-tat.

Consider the sequence of outcomes generated by each of the three strategies you mentioned (played by $i$ against the other player's tit-for-tat):

Tit-for-tat ($s_i^T$): $(Y,Y)$, $(Y,Y)$, $(Y,Y)$,  $\dots$
Alternating ($s_i^A$): $(Y,N)$, $(N,Y)$, $(Y,N)$, $\dots$
Always $N$ ($s_i^N$): $(Y,N)$, $(N,N)$, $(N,N)$, $\dots$

Note that all four possible stage-game outcomes are observed. As a result, if a player $i$ is playing any other strategy $s_i^O$, her payoff $u_i(s_i^O,s_j^T)$ can be expressed as some convex combination of the payoffs from playing either of the above three strategies. That is, there exists $\alpha,\beta\in[0,1]$ with $\alpha+\beta\le1$ such that, for any $s_i^O\in S_i$,
\begin{equation}
u_i(s_i^O,s_j^T)=\alpha u_i(s_i^T,s_j^T) +\beta u_i(s_i^A,s_j^T) +(1-\alpha-\beta)u_i(s_i^N,s_j^T).
\end{equation}

Now if you established that $u_i(s_i^T,s_j^T)\ge u_i(s_i^A,s_j^T)$ and $u_i(s_i^T,s_j^T)\ge u_i(s_i^N,s_j^T)$, which I assume you have done, it must follow that $u_i(s_i^T,s_j^T)\ge u_i(s_i^O,s_j^T)$ for any other strategy $s_i^O$.


If all firms in an economy are in monopolistic competition with constant elasticity of substitution, can they profit-maximize at $MC=MR=AC$? Suppose all firms are monopolistically competitive with constant elasticity of substitution. Can they profit maximize at the quantity point $MC=AC$ (So $P \neq MC$ but $Q$ is set at where $MC=MR=AC$ is established)?

By constant elasticity of substitution, I mean that $\epsilon = -(\partial Q_j/\partial P_i)/(Q_j/P_i)$ is constant for $\forall i \neq j$ where $i,j$ refers to firms, $Q$ refers to quantity, and $P$ refers to price.

The long-run picture for a firm in monopolistically competitive industry should look like this:

The level of production is pinned down by where MR=MC. Price will be equal to AC at that point, so the firm has zero profits.

If the firm was producing at the point where MC=AC, it would have positive profits, which would encourage entry into the industry, shifting the demand in and reducing profits to zero.


Are Open Market Operations a Gift to the .1%? My Background
I was an Economics major a long time ago and I don't work in a related field.  I have this question that's been nagging me.  I hope somebody can answer the questions at the bottom.

Background Information
During Open Market Operations, the Fed buys or sells Treasuries in order to effect certain desired results such as changing the interest rate or changing the money supply.

To pump more money into the economy, the Fed will buy tons of Treasuries.  In other words, banks and other entities will give their Treasury papers to the Fed and in return, the Fed gives cash to the banks.  Then, this cash eventually finds its way into the local economy, spurring economic activity.

My Questions

When the Fed sells and buys Treasuries from banks, aren't the banks getting an enormous gift?  When I say gift, I mean that it's almost like free money.  When the Fed buys Treasuries, it announces what it will do and then buy in massive quantities which will inevitably drive up the value of Treasuries.  Banks are now selling their Treasuries for much higher prices than it was just a few days ago.  Isn't this a great deal for them?  How can they say no?
The second largest beneficiaries of the Fed's purchase of Treasuries aren't the common masses but are the large institutional investors who have a lot of money to begin with.  They are suddenly getting loans at extremely attractive rates and terms.  Is this preferential treatment (aka gift) very fair?  Can't we create a different system of loans so it's not so skewed towards the wealthiest .1%?

I strongly believe that Open Market Operations are absolutely an indispensable tool for the Fed to manage the economy.  But, that's not point though.  My point is that although it's necessary, doesn't Open Market Operations extremely favor the financially wealthy?  Trickle-down economics may work here but history has told us repeatedly that it's not very even-handed.  The money that flows to the average American is much less than what the people at the top get.

Is my description of this process correct?  Are Open Market Operations a large gift to the banks and the large investors that receive the initial loans?

Yes they are "gift" (or rather a stimulus), but not exclusively to the 0.1%. There's basically "trickle down" by inflating the M2 money supply, i.e. bank loans, which hopefully include loans to companies where the "average guys" work.

So in theory, banks have more funds to lend, at a low rate of interest, encouraging households and businesses to borrow. [...]
The Bank of England estimates that ultra-low interest rates and QE meant that the average household's income was £9,000 higher than it would have been by 2018.
It argued that younger people actually benefitted most, as they were more likely to be in work and reliant on wages for income.
By contrast, savers, who tend to be older, received negligible return on their money.

It's also true that QE and cheap credit in general have been a boon to the those well off, fueling asset prices (and not just stocks, but also real estate etc.)

But the starkest impact of QE has been on wealth, the value of assets, from housing to pensions.
The money received by financial institutions in return for bonds sometimes got diverted into other investments - bulking up the prices of the value of shares or property, benefiting those already at the top of the tree the most.
Shares in the FTSE 100 index have, on average, more than doubled in value over the past decade. [...]
property prices have risen by 43% over the past decade - far more than they would have done in the absence of the emergency injection of funds.
So they've vastly outpaced earnings growth; buying your first property and moving up has got even harder.
A 30-something today is less likely to own property than their great grandparents.

This is for the UK but the effect of QE and cheap credit have been pretty much the same everywhere.
So yeah, if you want to be a cynical Marxist, you  could say QE has created even more "wage slaves" than before, i.e. an increase in wealth inequality in some sense. The ECB hower disagrees with such a conclusion:

Quantitative easing in the euro area through the ECB’s asset purchase programme (APP) has stimulated economic activity and asset prices, affecting income and wealth inequality among households. It has decreased income inequality, mostly by reducing the unemployment rate for poorer households, but also, to a lesser extent, by increasing the wages of the employed. Quantitative easing has also helped to reduce net wealth inequality slightly through its positive impact on house prices.

Meh. There's a more rounded review of the research on the effect of monetary policy on inequality in an open access paper. Basically the effects on inequality seem to be ambiguous or modest at best.

Our review suggests that empirical research on the effects of conventional monetary policy on income and wealth inequality yields mixed findings, although there seems to be a consensus that higher inflation, at least above some threshold, increases inequality. In contrast to common wisdom, conclusions concerning the impact of unconventional monetary policies on inequality are also not clear cut.

And it also features a quote from Bernanke:

the effects of monetary policy on inequality are almost certainly modest and transient. (Bernanke, 2015).

N.B. When you say "trickle down doesn't work" (with respect to inequality), you're probably mixing the jars with the fiscal policy, i.e. tax cuts... which might be good separate question, although it might have been asked here before. Fiscal policy is generally considered the main "tweaking knob" for inequality.


Is there a comprehensive list of all market failures ever discovered? I'm looking for a complete run down of all different kinds of market failures;

Wikipedia has a list but I'm not sure if there might some obscure kinds of market failures that Wikipedia is missing. Are there types of Market failures that are not mentioned in this the standard textbooks/wikipedia?

Wikipedia: "Market failures are often associated with time-inconsistent preferences, information asymmetries, non-competitive markets, principal–agent problems, externalities, or public goods."

Market failures often arise due to deviations from the classical assumptions of economics (e.g. Perfect Competition, Perfect Rationality, Perfect Information, Unbounded Computational Capacity, ...etc). There are lists of well-documented and studied market failures and the factors driving them (monopoly is sometimes considered a case of market failure); however, there cannot be an exhaustive list as that would be equivalent to placing a bound on the number of ways people can behave unexpectedly


Evidence on economic impact of 2015 European refugee/migrant influx At the time of writing (September 2015), Europe is dealing with a large influx of refugees/migrants. Many are fleeing violence in Syria and elsewhere, others come from Africa and the Middle East in search of economic opportunity.

I am interested in knowing what is the current state of the art in understanding the net economic impact of these inflows for the recipient countries in North Western Europe? I am interested in impact along a wide range of dimensions, growth, employment, etc.

In particular, I am interested in evidence that allows us to account for the specific demographic and skills profiles of these migrants. Assuming that the migrants reflect the typical UK asylum seeker, some demographic information can be seen here. The majority are male, between 20 and 50. At least in the current "crisis", the majority of migrants appear to be muslim, if that is of any consequence. I was not able to find information about skills.

I didn't see the evidences on the recent European immigration, but the event is similar to the Mariel Boatlift story in Card (1990):

  The Mariel immigrants increased the population and labor force of the Miami metropolitan area by 7 percent. Most of the immigrants were relatively unskilled: as a result, the proportional increase in labor supply to less-skilled occupations and industries was much greater. Nevertheless, an analysis of wages of non-Cuban workers over the 1979-85 period reveals virtually no effect of the Mariel influx. Likewise, there is no indication that the Boatlift lead to an increase in the unemployment rates of less-skilled blacks or other non-Cuban workers. Even among the Cuban population wages and unemployment rates of earlier immigrants were not substantially effected by the arrival of the Mariels.

That's for a 7% shock. In contrast, Europe experience a 0.1% shock in labor supply. Maybe the only difference we'd find will be in the areas where immigrants settle densely.

For more reading:

Card, “Immigration and Inequality”;
Card, “Is the New Immigration Really so Bad?”

In general, economists suggest that low-skilled natives suffer a bit from an influx of low-skilled immigrants (but again, we're talking about large numbers, >1% of population):

http://www.igmchicago.org/igm-economic-experts-panel/poll-results?SurveyID=SV_5vuNnqkBeAMAfHv


Compute evolution of a distribution over time We have a population of people with different age $a$, time is indexed with $t$. There is a rate at which people die, $d(a, t)$. For simplicity, ignore births. I want to compute the evolution of the distribution of ages over time.

Denote the mass of people at or below age $a$ by $F(a,t)$

$$ F(a,t) = \int_0^{a} m(\tilde a,t) d\tilde a $$

Ultimately, I am after some Kolmogorov forward equation, that is, the solution for

$$ \partial_t F(a,t)$$

My approach Let $f(a, t)$ denote the density of people at age $a$ and point in time $t$. I will start with a discrete time approximation and let $\Delta$ go to zero. At each discrete point in time,

$$ f(a+\Delta, t+\Delta) = (1-P(a, t))f(a, t)$$

where $P(a, t)$ is the discrete time analogue of $d(a,t)$. As I'm going to let $\Delta\to 0$, I can approximate $1-P$ with $1-\Delta d)$:

$$ f(a+\Delta, t+\Delta) = (1- \Delta d(a,t))f(a, t)\\
\frac{f(a+\Delta, t+\Delta) -f(a,t)}{\Delta} = -d(a,t))f(a, t)\\
(\partial_t + \partial_a)f(a,t) = \lim_{\Delta\to 0}\frac{f(a+\Delta, t+\Delta) -f(a,t)}{\Delta} = -d(a,t))f(a, t)\\
$$

I can integrate both sides w.r.t. a and get

$$ \partial_t F(t, a) = - f(t, a) - \int q(t, a) f(t, a) da \\
\partial_t F(t, a) = - \partial_a F(t, a) - \int q(t, a) \partial_a F(t, a) da $$

I know that $\partial_a q(t, a) = q(t, a) (1-q(t, a))$. However, that doesn't really help me with solving the integral. Is there perhaps another angle to attack this problem? Or did I miss something?

Here's my best guess. I haven't checked to thoroughly if this is right, but maybe it will help.

Evolution of population density

I understand the model as follows. $f(a,t)$
is the density of people of age $a$ at time $t$. Suppose at time $t=0$, the density of the population is $f_0(a)$. To model the aging process as well as the mortality rate, the density $f$ must evolve over time so that it satisfies the condition that you derived. Thus, $m$ must satisfy the following partial differential equation
$$
\frac{\partial f}{\partial t} + \frac{\partial f}{\partial a} + d(a, t) f(a,t) = 0
$$
and the initial condition
$$
f(a,0) = f_0(a).
$$
I believe that PDEs of this form can have relatively straightforward solutions depending on the functional form chosen for $d$. Here are some cases.

Case 1: Constant mortality rate, $d(a,t) = d_0$.

Suppose a constant mortality rate, $d(a,t) = d_0$. Then (using Mathematica),

DSolve[
 {D[f[a, t], t] + D[f[a, t], a] + d0 f[a, t] == 0,
  f[a, 0] ==  f0[a]},
 f[a, t], {a, t}]

results in

{{f[a, t] -> E^(-a d0 + d0 (a - t)) f0[a - t]}}

So, as we can see, this gives a simple solution
$$
f(a,t) = \exp\{-a d_0 + d_0 (a-t)\} \cdot f_0(a-t)
$$
Case 2: Log Mortality, $d(a,t) = \log(a+1)$.

Here we have

DSolve[
 {D[f[a, t], t] + D[f[a, t], a] + Log[a+1] f[a, t] == 0,
  f[a, 0] ==  f0[a]},
 f[a, t], {a, t}]

which results in

{{f[a, t] -> (1 + a)^(-1 - a) E^t (1 + a - t)^(1 + a - t) f0[a - t]}}

This also gives a simple solution
$$
f(a,t) = (1+a)^{-a-1} e^t (1+a-t)^{1+a-t} \cdot f_0(a-t)
$$

Case 3: The general case

For the case where we do not yet specify $d(a,t)$,

DSolve[
 {D[f[a, t], t] + D[f[a, t], a] + d[a, t] f[a, t] == 0,
  f[a, 0] ==  f0[a]},
 f[a, t], {a, t}]

gives us (in TeXForm for clarity)

$$
\begin{align*}
\left\{\left\{f(a,t)\to \\
   \text{f0}(a-t) \cdot \\
   \exp \left(\int_1^a
   -d(K[1],K[1]-a+t) \, dK[1]-\int_1^{a-t} -d(K[1],K[1]-a+t) \,
   dK[1]\right)\right\}\right\}
\end{align*}
$$


If the (direct) utility is concave in all goods, is the indirect utility necessarily concave in wealth? Suppose that the direct utility $u(x_1,...,x_n)$ is concave in each of its arguments.  Does this imply that the indirect utility $U(w,p)$ is concave with respect to $w$? If all goods are normal than this can proved. e.g. using Lagrange multipliers.  But, is it true in general?

One can assume that $u$ is differential as many times as necessary.

Thanks.

Your statement does not seem to be true for normal goods either. A counterexample:
$$
U(x_1,x_2) = (x_1x_2)^{\frac{2}{3}}
$$
By the Cobb-Douglas property the optimum bundle given $w,p$ is
$$
(x_1,x_2) = \left(\frac{w}{2p_1}, \frac{w}{2p_2}\right),
$$
so both goods are normal. The indirect utility is
$$
U(w,p) = \left(\frac{1}{4p_1p_2}\right)^{\frac{2}{3}}w^{\frac{4}{3}}.
$$
Here $w$ is raised to a power higher than 1 so $U(w,p)$ is convex in $w$.


Are strict dominance solvable games weakly dominance solvable? Okay consider a game $G$ if a strategy $s_i$ has the following property we call $s_i$ the strictly dominant strategy

$$u_i(s_i,s_{-i})>u_i(s_i',s_{-i}) \\ \forall s_{-i} \ \forall s_i' \epsilon S'_i$$

Where $s_{i}$ indicates the strategies of players other then $i$ in the game and $S'_i$ is the set for strategies of player $i$ except the specific strategy $s_i$

Now let's look at the definition of a weakly dominant strategy

if a strategy $s_i$ has the following property we call $s_i$ the weakly dominant strategy

$$u_i(s_i,s_{-i})≥u_i(s_i',s_{-i}) \\ \forall s_{-i} \ \forall s_i' \epsilon S'_i \ and \\ \exists s_i' \epsilon S'_i \ such \ that: \ u_i(s_i,s_{-i})>u_i(s_i',s_{-i})$$

Okay I believe from these two definitions we can derive that any strictly dominant strategy $s_i$ is also a weakly dominant strategy

Definition of strict dominance solvable is as follows :

A strict dominance solvable game is a game where the equilibrium outcome is strict dominance equilibrium.
A weakly dominance solvable games is a game where the equilibrium outcome is weakly dominance equilibrium.

So It seems like then a strictly dominance solvable game is always a weakly dominance solvable game. Am I wrong?

You're right. Let $s^*=(s_1^*,\dots,s_N^*)$ be the equilibrium of a strictly dominance solvable game. Then by definition,
$$
u_i(s_i^*,s_{-i})>u_i(s_i,s_{-i})
$$
for all $i$, all $s_i\ne s_i^*$ and all $s_{-i}$. This implies that
$$
u_i(s_i^*,s_{-i})\ge u_i(s_i,s_{-i})
$$
for all $i$, all $s_i\ne s_i^*$, all $s_{-i}$ and with strict inequality for at least some $s_i$ (in fact, for all $s_i\ne s_i^*$). This makes $s^*$ an equilibrium satisfying the weak dominance solvability criterion.

Your quoted definition of strict/weak dominance solvability makes me a little uncomfortable though. I'd say

  A game is strict (or weak) dominance solvable if the process of iteratively removing strictly (or weakly) dominated strategies leads to a unique outcome (i.e. only one strategy for each player survives).


Distribution of firm sizes and firm age What are public sources for US firm/plant sizes, in order to characterize the firm size distribution? And what are stylized facts about the firm size distribution: What does it approximate to?

Somewhat related: What about the firm age distribution? That is, the distribution of firms given their age. I understand the latter is a soft concept in the data, but are there first-order approximations for age, and how does its distribution look?

Compustat Annual is used in Gabaix and Landier (2008). A famous stylized fact is the power-law distribution (by Gabaix again) of firm sizes. But power-law claims have been criticized as resulting from poor measurement.


Why does a positive output gap imply workers working overtime? From Investopedia, "A positive output gap indicates a high demand for goods and services in an economy, which might be considered beneficial for an economy. However, the effect of excessively high demand is that businesses and employees must work beyond their maximum efficiency level to meet the level of demand."
And from Lumen: "when the economy is above full employment, then the unemployment rate is less than the natural unemployment rate and real GDP is greater than potential. Operating above potential is only possible for a short while, since it is analogous to workers working overtime."
Why do these websites claim that a positive output gap is not necessarily good? The unemployment rate is less than the natural unemployment rate (full employment rate) if the cyclical unemployment is lower, which means the economy is in an expansion. This means that more people have jobs, not the same workers are working more hours like these sites say, right? I understand that expansions are temporary, and there isn't always going to more output than expected, but why is having real GDP > potential GDP bad?
From what I know, potential GDP is the amount of output of an economy when everyone who should have a job has a job. During an expansion, people who normally couldn't get a job, has jobs because there are more jobs. This increases output. And so Real GDP > Potential GDP. That's it. I don't know why there would be a higher demand for goods, I don't get why workers would need to work overtime.
Can someone please clarify? Thanks!
Links:
https://www.investopedia.com/terms/o/outputgap.asp#:~:text=An%20output%20gap%20indicates%20the,be%20either%20positive%20or%20negative
https://courses.lumenlearning.com/wm-macroeconomics/chapter/natural-unemployment/#:~:text=The%20economy%20is%20considered%20to,equal%20to%20the%20natural%20rate.&text=By%20contrast%2C%20when%20the%20economy,GDP%20is%20less%20than%20potential

A fisherman usually works 50 hours and catches 50 kg of fish every week. So let's say that his potential (or "natural") output is 50 kg of fish.
Now suppose his boss orders him to work 80 hours per week and catch 80 kg of fish. This 80 kg of fish is his real output and exceeds his potential output of 50 kg. This is not necessarily a good thing and is probably not sustainable:

He may prefer to work less (have more leisure rather than the consumption goods that his additional work can buy).
He and his fishing rod may be overworked and thus wear out more quickly.

A definition of potential GDP:

Potential gross domestic product (GDP) is a theoretical concept that means different things to different people. To some, it reflects a world in which every worker is matched with the perfect job, every good idea is implemented, and the bad ones are ignored. In this world, resources are allocated optimally with no distortions from the tax code, information frictions, or suboptimal government policies.†

I would add also that potential GDP at any moment is that which can be sustained over the long term, holding constant resources and technology at that given moment.

†This idealized definition isn't actually used to get estimates of potential GDP. Instead, such estimates are simply obtained by smoothing out GDP fluctuations.
If this idealized definition were actually used, then it would in practice be quite impossible for real/actual GDP to ever exceed potential GDP.


The Fed has a $4.5 trillion balance sheet: where did they get that money? Who paid for that $4.5 trillion balance sheet?

https://www.cnbc.com/2017/09/19/hedge-fund-titan-ray-dalio-says-to-succeed-in-markets-you-need-to-bet-against-the-consensus--and-be-right.html

"Money" in this case is a liability of the Federal Reserve - mainly reserve balances held at the Fed, but also curency in circulation (which was largely stable).

Like any other entity, the Fed creates liabilities by issuing them. It did this by buying bonds in the open market (mainly Treasury and mortgage securities).

The seller of the bond (more likely, its bank) will get a deposit ("money").
The Fed gets an asset (the bond).

As people have found out, there is little to stop the Fed from doing this. They get matched assets and liabilities, and the assets it buys pays a higher rate of interest than its liabilities.

Other entities have to worry about funding risk when conducting such trades -- others may fear bankruptcy, and not lend them money. Very few people worry about the central bank running out of money.


What are some growth theories that are considered the most correct at the moment? In under grad intermediate macro classes they often teach the Solow model. While intuitively it makes sense, it seems like it no longer is really taken seriously anymore (I could be wrong).

From my understanding (which could I be wrong of course), there appears to be a move toward more endogenous growth theories that try to explain technology growth rather than taking it as a constant like the Solow model.

Can anyone provide me some examples of growth models that, at the moment, are considered the most complete or correct?

Oded Galor's interesting work on Unified Growth Theory subsumes the Solow model, the Malthusian model and endogenous growth theories in a very stylized way. This model is of course "long term" and ignores institutions.

It is a OLG model where the main problem from the household side is a choice between quantity versus quality of offspring (human capital intensity or number of children), increasing human capital is costly. From the factors side there is a fixed factor land, that plays the role of the Malthusian restriction when technology growth is non existent or low, human capital, and a labor augmenting technological or productivity factor that grows exogenously, this is understood as technological progress.

The model generates a first malthusian trap, that is only escaped after there is some population reduction shock (think black death) or some technological shock. Then the Solow stage, and then a endogenous growth phase. Population dynamics plays a vital role, in the malthusian stage population is stagnant and dependent on the fixed land factor, then in the second stage it grows exponentially and in the third stage households choose quality over quantity and the population decreases. Think of Middle Ages, 20th century US and Japan in this century respectively as examples of this stages.
Anyway I am a little rusty and it is not my field but this work is amazing.
Slides: Unified Growth Theory and Comparative Economic
Development


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.


Investors in index funds pay lower taxes, but higher taxes on dividends? Doesn't the second para. beneath contradict itself? Don't the boldened words contradict each other?

       So let’s pick up where we left off a few chapters ago.
Recall that the net annual return was 7.8 percent for the average equity fund over the past 25 years and 9.0 percent
for the S&P 500 index fund. With the high portfolio
turnover of actively managed funds, their taxable investors
were subject to an estimated effective annual federal
tax of 1.2 percentage points per year, or about 15 percent
of their total pre-tax return. (State and local taxes would
further balloon the figure.) Result: their after-tax annual
return was cut to 6.6 percent.
      Despite the higher returns that they earned, investors
in the index fund were actually subjected to lower taxes,
largely derived from their dividend income. The extremely
low costs of index funds consume less dividend income
relative to actively managed funds, resulting in higher dividend
yields and, therefore, higher taxes on dividends.

John Bogle's The Little Book of Common Sense Investing, 10th Anniversary Edn. Pages 87, 88.

Doesn't the second para. beneath contradict itself? Don't the boldened words contradict each other?

No, not necessarily. English is high context language and the passage above is a bit ambiguous but there is no necessary contradiction here.

Despite the higher returns that they earned, investors in the index fund were actually subjected to lower taxes, largely derived from their dividend income

This likely refers to the fact that in the US,  dividends from long term investments are subject to lower capital taxes than let's say capital gains that you get via trading (see article about it here)
The next passage here:

The extremely low costs of index funds consume less dividend income relative to actively managed funds, resulting in higher dividend yields and, therefore, higher taxes on dividends.

when talking about higher taxes likely just refers to the fact that in the US the higher your income the higher income tax you pay. US has progressive capital income taxes (at least on the paper due to loopholes effective tax rates might not always be). In addition since taxes are payed as a fraction of your income even if there would be flat $10\%$ tax on capital income, if your income \$10000 you will pay more taxes than when your income is \$1000, so your tax bill will higher when your income is higher.
This being said again the passage is highly ambiguous so it is not clear what the author means, but it is not necessarily a contradiction.


Could anyone here be able to explain gambling addiction and its debt with Microeconomics theory? I am a research master student in Cognitive and Clinical Neuroscience, with the specialization/track Neuroeconomics and have to come up with a master thesis subject soon. I was thinking about gambling addiction and had some ideas of first theoratically explaining it with utility functions that are risk-seeking and use Arrow-Pratt measure of risk aversion. Does anyone have other theories in mind that can contribute to the microeconomical explenation of gambling addiction? Or perhaps someone having a "theory" of their own? I would love to see some ideas from others to get some inspiration!

It seems to me that the topic is related to rational addiction: Individual preferences for consuming $x_t$ are conditioned by their past consumption $x_{t-1}$. See for instance:

Becker, G., and Murphy, K. (1988). A Theory of Rational Addiction. Journal of Political Economy, 96(4), 675-700.


How compensating balance works? Assume a clothing store needs a 100,000 line of credit (LOC) to
  manage its operating cash flow each month. The store plans to use the
  LOC to make inventory purchases at the beginning of the month, and
  then pay down the balance as the store generates sales. The bank
  agrees to charge a lower interest rate on the LOC if the clothing
  store deposits a $30,000 compensating balance. The bank loans the
  clothing store’s compensating balance to other borrowers, and profits
  on the difference between the interest earned and the lower rate of
  interest paid to the clothing store.

From https://www.investopedia.com/terms/c/compensating-balance.asp

Why can't the bank provide only 70,000 loan to the clothing company at an adjusted equivalent interest rate?

I can't see the value of compensating balance.

The short answer is that the bank could do that, but it prefers to hold the $30,000 as collatoral on the LOC since presumably this clothing store is a relatively high-risk client.


Forecasting quarterly EUR/USD exchange rate My aim is to forecast the one-quarter ahead EUR/USD exchange rate. I have constructed a regression model with the following as explanatory variables: exchange rate in the previous quarter, EUR/USD futures price, American and European GDP growth rate, inflation rate, return on stocks, interest rate on 3-month govt. securities, current account balance, net financial account balance and dummies for the inversion of EU and US yield curve. All the explanatory variables are at one-quarter lag. The input data file could be found here.

I am getting spurious results - all these variables are coming out to be insignificant but surprisingly the R^2 is more than 90%.

Is OLS not a good technique for forecasting exchange rates? If not, then which other techniques could be used?

There are many methods to forecast exchange rates- look at the series of influential papers by Meese and Rogoff for a primer (https://scholar.harvard.edu/files/rogoff/files/51_jie1983.pdf).

To answer your particular question- what you describe seems to be driven by  multicollinearity. For instance, returns on stocks will be correlated with the inflation rate if they are nominal,  CAB and FA balance will be related to both the GDP growth rate as well as the interest rates etc. To test whether your results are susceptible to multicollinearity in the variables, try Variance Inflation Factor type tests.


How do U.S. treasury yields impact yields of other sovereign debt markets? I read somewhere that when the U.S. Treasury yields rise, it will also have a "gravitational pull" on yields of other sovereign debt markets. For example, when the U.S. Treasury yields rise, the German bund yield will also rise. Is it because when US yields rise, sovereign bond investors will move out of lower yielding Eurozone sovereigns into US Treasuries? Can someone please explain the relationship or transmission mechanism?

For free-floating sovereign borrowers (e.g., Japan, Canada, UK, and the euro as a bloc (the member countries are pegged versus each other), short-term bond yields are largely determined by the expected path of the policy rate (plus a small term premium).
For longer-term bonds, one can debate how value is determined, but forward rates are generally smooth, so they can be interpreted as rate expectations and a term premium as well.
This means that bond yields ca diverge: e.g. look at Japanese bonds versus other sovereigns from 1995-2008 (at which point other countries converged at levels near Japan’s).
However, we see correlations between markets, which is not unexpected.

Central bankers might set domestic rates as a spread versus another currency, like the USD.
The business cycle is global, and new information about the outlook is thus correlated across markets.

This explains why short-term movements often are in the same direction, yet there are no reliable “rules” (since that would imply guaranteed trading profits).


Why would a commercial bank borrow from another commercial bank instead of the central bank?(more questions inside) 1) In my textbook, it is said that overnight rate is quarter of a percent below the bank rate, so does it mean that if bank rate is 5%, then overnight rate is 4.75%? What is the point of borrowing from the central bank then if it is cheaper to borrow from another commercial bank?
2) Is overnight rate the same as federal funds rate?
3) It is also said that if the overniht rate is too high, it discourages commercial banks to borrow from the central bank, why?

Yes, the “overnight rate” in the inter-bank market would be 4.75%, based on that description. The idea is that banks borrow from each other, not the central bank; the central bank is just providing back up facilities to cap the interbank rate. The objective is that banks need to convince other private sector entities that they are solvent, and not just the central bank.
The most important inter-bank market for domestic USD transactions is the Fed Funds market, but there is also the London inter-bank market.
This question was vague. Keeping the lending facility at a higher rate than the inter-bank rate keeps banks borrowing from themselves, for the reason noted earlier. The spread matters, not the absolute level (which was possibly implied by the question).


Find quantity from price elasticity I have $P_1 = 24$, $Q_1 = 800000$, $P_2 = 32$ and price elasticity $e = -8$ and need to find the function $P(Q)$.

I guess I need to find $Q_2$ by

$$
\frac{(Q_2-Q_1)/Q_1}{-(P_2-P_1)/P_1} = -8 \Leftrightarrow Q_2 = \frac{8800000}{3}
$$

But does it make sense that the quantity will be so much higher by a price increment and thus not follow the law of demand? I know that $e = -8$ is a high price elasticity but this is quite extreme I think.

You have that price elasticity is defined by:

$$\varepsilon_{d} = -\frac{\partial Q}{\partial P}\frac{P}{Q} \approx -\frac{P}{Q}\frac{\Delta Q}{\Delta P}$$

Initially we have $P = P_{1}$ and $Q=Q_{1}$ and after the perturbation we have $\Delta P = (P_{2} - P_{1})$ and $\Delta Q = (Q_{2} - Q_{1})$, therefore:

$$-\frac{P_{1}}{Q_{1}}\frac{Q_{2}-Q_{1}}{P_{2}-P_{1}}=-8 \implies Q_{2}-Q_{1}=\frac{8Q_{1}(P_{2}-P_{1})}{P_{1}}$$

And therefore:

$$ Q_{2}=Q_{1}+\frac{8Q_{1}(P_{2}-P_{1})}{P_{1}}=\frac{8800000}{3} $$

This is so large, partly because the price elasticity is so large, but also probably because of the error in the finite difference approximation method over such large changes in $P$.


Solution Method for Infinite-Horizon Maximization Problem Full disclosure: this problem was part of a final exam that none of our class could really solve definitively. Below the general form is a specific utility function we worked with that I'll try to replicate my work for. Any help on the solution method would be good; specifically, it seems Euler's equations/steady states would be better for this particular form of question rather than using a Bellman, but any guidance on either method would be appreciated.

Suppose a representative agent is solving

$$
\begin{align}
& \max_{\left\{ c_t, w_t \right\}^\infty_{t=0}} \sum_{t=0}^\infty \beta^t u(c_t) \\
& \text{s.t.} \\
& w_t = Rw_{t-1} - c_t \\
& c_t \geq 0 \\
& w_t \geq 0 \\
\end{align}
$$

For all $t$, and $w_{-1}$. Additionally, $0 < \beta < 1$, $R > 1$.

$c_t$ is consumption at time $t$, and $w_t$ is wealth at the end of time $t$. $\beta$ is a discount factor.

Let
$$u(c_t) = \phi \mathrm{e}^ {\theta c_t^p}$$
where $\phi, \theta, p$ are constant parameters.

  My first question is what values of the constants $\phi, \theta$, and $p$ are needed to ensure that $u(c_t)$ are strictly increasing and strictly concave in $c_t$, for all values of $c_t$. Later on the problem asks us to assume those above conditions.

So taking the first and second derivative of $u(c_t)$ gives us:

$$
\begin{align}
u'(c_t) & = \phi \theta p c_t^{p-1}\mathrm{e}^ {\theta c_t^p} \\
u''(c_t) & = \phi \theta p(p-1) c_t^{p-2}\mathrm{e}^ {\theta c_t^p} + \phi \theta ^2 p^2 c_t^{(p-1)^2}\mathrm{e}^ {\theta c_t^p} \\
& = \phi \theta p c_t^{p-1} \mathrm{e}^{\theta c_t^p}\left[ \frac{p-1}{c_t} + \theta p c_t^{p-1} \right] \\
\end{align}$$

So $u'(c_t) > 0$ in order to satisfy the strictly increasing constraint. $u''(c_t) < 0$ must be true for strict concavity. I suggested that $\phi, \theta > 0$ and $p = 1$ for this to be true. I'm not sure how this ugly second derivative can be simplified to find the appropriate conditions.

After doing this, we had to express Bellman's equation and Euler's equation for the problem.

Bellman:

$$\boxed{V(w) = \max_\tilde{w} \left[ \phi \mathrm{e}^{\theta (Rw - \tilde{w})^p} + \beta V(\tilde{w})\right]}$$

Euler:

$$\boxed{\sum_{t=0}^\infty \beta^t (Rw_{t-1} - w_t)^p = \cdots \beta^t (Rw_{t-1} - w_t)^p + \beta^{t+1}(Rw_t - w_{t+1})^p + \cdots }$$

Finally, we got to say that $\beta \cdot R = 1$. We were then asked to find the value function and optimal decision rules for our choice variable(s). I used the Bellman to try to solve the problem, where I guessed the function form of the value function:

$$V(\tilde{w}) = F \mathrm{e}^{M\tilde{w}} + H$$

where $F, M, H$ are undetermined coefficients. After substituting this into the Bellman and putting in appropriate arguments, taking the derivative to get an optimal choice, substituting the optimal choices back into the Bellman, I got stuck trying to solve for $F, M, H$ in a way that would give me a sensible consumption choice at the end.

The little trick with $\beta R = 1$ is supposed to make consumption constant across all periods, so I assume that the point of getting the Euler's equation is so we can solve it using steady states and make life easier, but my algebra there hasn't borne any fruit either it seems.

  For the dynamic programming method, have I set the functional form of the value function correctly? If not, what should be the guess? And finally, how does all the nasty algebra work out?

  For the steady states method, what does the path of wealth look like? Does it end up constant as well? (I suppose that question applies for the Bellman approach as well.)

(If it's pedagogically interesting or useful--or if you don't trust that I'm not begging for homework help--I can show my work for both methods.)

Please let me know if anything is unclear.

Your first question (regarding constraints on the parameters) can be answered through first and second derivative analysis. In order to satisfy strictly increasing, we need $u'>0$ and to satisfy strictly concave, we need $u''<0$. What does this actually mean?

$$u'(\frac{}{})=\phi p\theta c_t^{p-1}e^{\theta c_t^p}>0$$
Since we know that $c_t^{p-1}e^{\theta c_t^p}>0$ automatically, this reduces to:
$$\phi p\theta>0$$
Next:
$$u''(\frac{}{})=\big[\phi p\theta (p-1) c_t^{p-2}+\phi p\theta c_t^{p-1}\big]e^{\theta c_t^p}<0$$
Because we know that $e^{\theta c_t^p}>0$ and $\phi p\theta c_t^{p-1}>0$, this must mean:
$$\phi p\theta (p-1)c_t^{p-2}<0$$

By virtue of $(1)$ and the fact that $c_t^{p-2}>0$, we know that:
$$p-1<0$$
or
$$p<1$$
Now,  what we can do is think about it critically. If $p=0$ then utility does not change when consumption changes. This is clearly untrue. If $p<0$ then utility decreases when consumption increases which also seems incorrect. Therefore, our condition for $p$ is:
$$0<p<1$$
Now, what does this mean for $\phi \;\text{and}\; \theta$? It means:
$$either\quad\phi , \theta>0\quad or\quad \phi ,\theta<0$$
Now, this looks like a typical exponential utility function, so we know that in these cases, both the coefficient for the exponent and the coefficient in the power will be negative (I will not bother proving this as I am sure it is somewhere in literature). Therefore we have the following three conditions for the parameters:
$$0<p<1$$
$$\theta <0$$
$$\phi <0$$

Now, the next step is to show that we do in fact have constant consumption. Taking our Euler Equation approach, we substitute in the constraint and take two terms in the sum,
$$...+\beta^t\phi e^{\theta (Rw_{t-1}-w_t)^p}+\beta^{t+1}\phi e^{\theta(Rw_t-w_{t+1})^p}+...$$
Differentiating w.r.t $w_t$ and doing some simplifying, we get:
$$(Rw_{t-1}-w_t)^{p-1}e^{\theta(Rw_{t-1}-w_t)^p}=\beta R(Rw_t-w_{t+1})^{p-1}e^{\theta(Rw_t-w_{t+1})^p}$$
Substituting consumption back in, we get:
$$c_t^{p-1}e^{\theta c_t^p}=\beta Rc_{t+1}^{p-1}e^{\theta c_{t+1}^p}$$
Now, since it is specified that $\beta R=1$ in the problem, we can see that the only way this equality holds is if $c_t=c_{t+1}=c^\star$

What does this mean for wealth? Will wealth also be constant? Well, let's conduct a thought experiment and suppose not. Suppose wealth increases each period ($w_{t+1}>w_t\;\forall t$). This implies that as $t\rightarrow \infty$, we will see wealth grow to be infinite as well, which is wasteful and would not satisfy the transversality condition. Now suppose wealth is decreasing ($w_{t+1}<w_t\;\forall t$). We can clearly see that eventually we will not have enough wealth to sustain constant consumption. Therefore we can see that $w_t=w_{t+1}=w^\star$. Now, what are the relationship between these two? Well, going back to our condition for wealth, we can see
$$w^\star=Rw^\star-c^\star$$
Rearranging, we get:
$$c^\star=(R-1)w^\star$$

Because we have steady state wealth, we know that $w^\star=w_0$

Now, knowing that we have steady state consumption, we know our utility function will be the same value for every period (discounted by $\beta$). So our value function simply becomes:

$$V(w)=\frac{\phi e^{((R-1)w_0)^p}}{1-\beta}$$

Therefore, we do not need to use the method of undetermined coefficients to find the value function.


How does low population growth increase the effect of accumulated wealth This passage comes from page 10 of the translation of Thomas Piketty's book Capital in the Twenty First Century:

  If the rates of population and productivity growth are relatively low,
  then accumulated wealth naturally takes on considerable importance,
  especially if it grows to extreme proportions and becomes socially
  destabilizing.

Why does low population growth exacerbate the effect of accumulated wealth?

Intuitively, I would think that an increasing population would mean more potential employees, thereby allowing already wealthy people to more easily offer low wages. By contrast, I would intuitively think that low population growth, and the resultant scarcity in employees, would force the wealthy individuals to offer higher wages.

Piketty's essential argument is that when the $r$ is the rate of return to wealth and $g$ is the economic growth rate, you will see wealth and economic power concentrate in the hands of the few when $r \gt g$. This presumes that the wealthy will reinvest their returns from wealth rather then spending it on consumption.

Low productivity improvements will lead to low growth in GDP per capita, and combining this with low population growth will then lead to low growth in total GDP, so these combined will lead to smaller values of $g$ than seen previously when both productivity and population were growing more quickly.  This is probably not particularly controversial.

Harder questions include

the impact of low productivity improvements and low population growth on $r$, and therefore on whether the gap between $r$ and $g$  would in fact widen
empirical evidence of whether $r \gt g$ has been true historically and globally
whether further concentrations of wealth may in future change $r$
whether Piketty's preferred solution of global wealth taxes and taxes on very high incomes (designed to reduce $r$) might also have an effect on $g$, and if so then in which direction and by how much


Does the concept of Capitalism increase the net wealth? I am currently going through a video by Peter Schiff from the occupy Wallstreet period where he is talking with the protestors at the time. I'm pretty early in the video and Mr. Schiff makes the following statement

"The way a capitalist gets rich is by enriching everybody else" - Schiff (4:21)

I take the above to mean that "Capitalism increases the net wealth of everyone. This is something that I have personally heard before, but never looked into. So, I tried to google the following

Does capitalism cause a net increase in wealth

What I was looking for was essentially an Econ101 level explanation of possibly the argument for and against this but the different links that appeared were:

How Capitalism Actually Generates More Inequality - evonomics.com
Is Capitalism To Blame For Inequality? - inequality.org
ECONOMICS AND CAPITALISM - capitalism.com

Which all by their article or website name alone seem like they would be biased.
So I ultimately want to pose the question here in two points. Firstly, did I interpret Schiff's own quote properly? Secondly, what is the basic Econ 101 explanation for the above-bolded statement?

Here is a graph of labor productivity per hour for the United States since WWII.

This is fairly typical of capitalist economies. Even Karl Marx and revolutionary socialists recognize that increasing labor productivity is a general characteristic of capitalism. So yes, the pie keeps getting bigger and bigger as a result of this in combination with population growth.
The question of inequality is a somewhat separate one. If the whole pie is growing big enough, the absolute size of my slice can grown even if my relative share as a percentage of the whole is getting smaller. In other words, the total wealth of society keeps increasing, and so in absolute terms, even the poorest see some benefit. In relative terms, that gets more complicated.


Why was Swiss National Bank in red by keeping fix exchange rate to Euro? When I read news about the action of Swiss National bank of not keeping fix ration to Euro any more, I read in all articles, that it was too expensive for Swiss National Bank to keep the fixed exchange rate. I don't really understand how can it be expensive. Swiss N.B was printing Swiss Franc and selling it for Euro? Right? How can be expensive printing and having Euro for free?

From a central bank's point of view, printing money isn't free.  Each 1 CHF created costs exactly 1 CHF - that is, it appears on the bank's balance sheet as a liability.  They owe that 1 CHF to someone (the person they bought the Euros off - a bank).  And whenever you owe someone money, there is always the ultimate belief that you can pay it back.  Lose that and the bank fails, and the currency fails.

With central banks this isn't clear cut, since the money can only be "paid back" by destroying it, but the trust in fiat money relies on the solvency of the central bank.  A sort of, "so long as you could pay it back, I'll never ask you to".

The SNB had been buying so many Euros (and other currencies) that it was sitting on foreign reserves worth about 85% of Swiss GDP.  In the process it did make a lot of profit, but that can only go on so long.

In theory, if the SNB could have held out forever, then it could have beaten the ECB, and when the Euro eventually strengthened, unwound its position as a profit.  But that would have involved the SNB conducting massive quantitative easing in the mean time, in order to supply the world with sufficient CHF to meet demand.  Given that Switzerland is somewhat smaller than the Eurozone, it would have been a battle it was destined to lose.

Given that they knew they would likely lose eventually, it is better to lose now, when you only have 85% of GDP in Euros, than to lose later on when you have 850% of GDP in Euros!

Of course having a central bank that is completely screwed, would weaken the CHF, but they only want moderate weakness, no complete destruction of the currency!


Slope of the Budget Line When we try to maximise utility constraint to a budget. We find the utility function or indifference curve which is having the budget line as tangent. So for solving a question we can equate the slope of budget line with the slope of a indifference curve and we will get the maximising utility coordinates.In many of the text books they equate ratio of prices with the tangent slope, but the slope of the budget line is negative where as the relative prices are positive. How does this work ? Why are they not considering the - sign of budget line ?

They do consider it. The precise mathematical formulation is usually
$$
-\frac{p_1}{p_2} = \text{MRS}(x_1,x_2)
$$
or
$$
\frac{p_1}{p_2} = \left| \text{MRS}(x_1,x_2) \right|
$$
in the basic cases, when MRS is a negative number (the slope of the indifference curve at basket $(x_1,x_2)$).


Why would a CBDC (Central Bank Digital Currency) be good for the economy? I've read about CBDC, how it could be a cryptocurrency like digital payment system, that could replace fiat currencies. But what I don't get is what value would it give to the economy?
Someone who works at a Central Bank explained to me, that by holding the a currency in your own crypto wallet, and not not as a deposit in a commercial bank, the commercial bank's balance sheet would shrink significantly. By shrinking, it could lend out less money with higher interest rates, and could disrupt the complex commercial banking system in a bad way.

There is good summary (with references) of the benefits of CBDCs on Wikipedia.
With respect to banking sector disruption see this 2018 report by the Sveriges Riksbank. It finds that

while a given outflow of retail deposits into e-krona
reduces banks’ liquidity portfolios and worsens their funding
profiles, banks can normally control this outflow via deposit rates.
Banks can also issue more market funding to restore their liquidity
and funding profiles.

That said,

The exact features of an e-krona can, however, be controlled by the
policy maker. In sum, we do not find any decisive argument against the
issuance of an e-krona when studying financial stability effects on
banks.


How to find data about earning per share of S&P 500 I am working on a small project regarding PE ratio of SP500,for which I need historic earning per share data of SP500. I searched finance yahoo, but it has only prices data. Could anyone tell me the website where one can obtain it?

A Google search turns up sites like

http://www.wsj.com/mdc/public/page/2_3021-peyield.html
http://www.multpl.com/table?f=m
https://www.macrotrends.net/2577/sp-500-pe-ratio-price-to-earnings-chart
https://ycharts.com/indicators/sp_500_pe_ratio

which slightly disagree about whether the current trailing ratio is just above or just below 20


Does more variable input cause marginal product to decline? Previously, I believed that after a certain point, additional variable input results in a decline in productivity. For example, if you hire too many waiters, they will eventually get in the way of each other, resulting in a decline in productivity.

However, I read online (https://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=marginal+cost+and+law+of+diminishing+marginal+returns) that "The law of diminishing marginal returns means that increased production of a good requires more and more of the variable input. For example, the first 50 units of production can be had with only 5 workers. However, the next 50 units might required an additional 10 workers. "

But doesn't this contradict with the law of diminishing returns? The law states that as more and more of an input is used, there is a point at which the increase in output is at a decreasing rate. So is the website wrong? Wouldn't increasing even more variable input decrease production even more?

For example, at a car factory, at some point after hiring many workers, productivity decreases. Isn't the website stating that the solution to this is hiring even more workers, which is counter-productive?

The two statements are similar.

For the website example, you could say that the marginal product of the first 5 workers is 50 units. For the next 5 workers, however, you could deduce that the marginal product is less than 50 units (otherwise "the next 50 units" would require exactly 5 workers, not 10 workers).

The website is merely stating that, in order to get the same number of outputs (in this case 50 units) you need to hire proportionally more inputs. To judge whether this is counter productive requires knowledge about the price you could sell these products, etc.


What does the Leontief Inverse represent? (Intuitive Meaning or Real World Concept) I encountered that nobody, even my profs and lecturers so far, has an intuitive way to explain what the Leontief inverse represents. Does somebody here?

As most people here would know, it goes:

$\ x=Ax+y $ where $x$ is the output and $y$ the final demand. So

$\ x - Ax =y $

$\ x (1 - A) =y $ or

$\ x = (1-A)^{-1}  y  $ or

$\ x = Ly $

While $A$ is clearly the proportion of total output that comes from intermediate value exchanges and not from transactions to final demand $1 - A$ should be the proportion of total output caused by final demand. However $L = (1-A)^{-1}$. So what would this be? The inverse proportion of what in total output is related to final demand? You can also just say of course $L$ represents the multiplier or scaling factor of how $x$ responds to changes in $y$, but that is not what I am asking for. I wonder if there is any real world interpretation possible on what L represents. Or is it an entirely abstract multiplier?

Something you didn't mention is that

$x = Ax + y$

means that to produce one unit of $x$, you use $A$ unit of $x$. E.g. you need electricity to produce electricity.

Under the condition that $1>|A|\geq0$

$(1-A)^{-1} = \sum_{k=0}^\infty A^k$

Which allows us to write

$x = Ly = \left(\sum_{k=0}^\infty A^k \right)y$

Thus, for one unit of $y$, your (scalar) $L$ expressed as an infinite sum can be interpreted as the length of the engaged auto-production chain.

A little illustration

Note that all of the above can be generalized in matrix terms, i.e.

$\boldsymbol{x} = \left(\boldsymbol{I} - \boldsymbol{A}\right)^{-1}\boldsymbol{y}$

where $\boldsymbol{x}$ and $\boldsymbol{y}$ are column vectors and $\boldsymbol{I}$ and $\boldsymbol{A}$ square matrices. Each $\boldsymbol{x}$'s component may (or may not) require some of its own production as well as some units coming from other sectors, i.e. from $\boldsymbol{A}\boldsymbol{x}$. In this case,

$\left(\boldsymbol{I} - \boldsymbol{A}\right)^{-1} = \sum_{k=0}^\infty \boldsymbol{A}^k$ is true if and only if all of $\boldsymbol{A}$'s eigenvalues have absolute value smaller than $1$. $\left(\boldsymbol{I} - \boldsymbol{A}\right)^{-1}$ can be useful if you want to know how any variation -- of $y$ admitedly, but also of anything else, say, a tax -- propagates through a (co-dependent) sectorial chain.


What are the arguments against the rational expectations hypothesis? I believe the rational expectations hypothesis says that agents in a model bear expectations that are the same as mathematical expectations.

Under what circumstances does this hypothesis become questionable? What are the usual arguments against this hypothesis?

The Rational Expectations Hypothesis (REH) is an hypothesis about aggregate expectations. I believe it is illuminating to post here a lengthy quote (part 2) from Muth (1961) paper where REH originated (bold letters are our emphasis):

  2. THE "RATIONAL EXPECTATIONS" HYPOTHESIS
   Two major conclusions from studies of expectations data are the following:
  1. Averages of expectations in an industry are more accurate than naive models and as accurate as elaborate equation systems, although
  there are considerable cross-sectional differences of opinion.
  2. Reported expectations generally underestimate the extent of changes that actually take place.

  In order to explain these phenomena, I
  should like to suggest that expectations, since they are informed
  predictions of future events, are essentially the same as the
  predictions of the relevant economic theory (We show in Section 5 that
  the hypothesis is consistent with these two phenomena). At the risk of
  confusing this purely descriptive hypothesis with a pronouncement as
  to what firms ought to do, we call such expectations "rational." It is
  sometimes argued that the assumption of rationality in economics leads
  to theories inconsistent with, or inadequate to explain, observed
  phenomena, especially changes over time (e.g., Simon 1959). Our
  hypothesis is based on exactly the opposite point of view: that
  dynamic economic models do not assume enough rationality.

  The hypothesis can be rephrased a little more precisely as follows: that
  expectations of firms (or, more generally, the subjective probability
  distribution of outcomes) tend to be distributed, for the same
  information set, about the prediction of the theory (or the
  "objective" probability distributions of outcomes).

  The hypothesis asserts three things: (1) Information is scarce, and the economic
  system generally does not waste it. (2) The way expectations are
  formed depends specifically on the structure of the relevant system
  describing the economy. (3) A "public prediction," in the sense of
  Grunberg and Modigliani (1954), will have no substantial effect on the
  operation of the economic system (unless it is based on inside
  information). This is not quite the same thing as stating that the
  marginal revenue product of economics is zero, because expectations of
  a single firm may still be subject to greater error than the theory.

  It does not assert that the scratch work of entrepreneurs resembles
  the system of equations in any way; nor does it state that predictions
  of entrepreneurs are perfect or that their expectations are all the
  same. ...

I believe that it should be clear from the above that:
1) REH  is not an assertion about each separate individual, but about the properties of the "prevailing" expectation produced by the black-box combination of individual expectations.  In other words the REH is assumed, without really making any assumptions about individual rationality.

2) It has as much to do with  the "internal consistency" of the economic model itself, because by construction and without any economic assumptions, $E(X\mid I) = X+ e,\; E(e\mid I) =0 $.

The fact that the predominant economic model framework has been that of the "representative" (identical) consumer, nevertheless blurred the distinction between the aggregate expectation, and individual expectations on aggregate variables. This provided shallow "micro-foundations" to the REH, (shallow because it is not really micro-founded, that which essentially assumes away the need to aggregate), but also, it moved the debate into the arena of individual expectations formation and whether individuals use information efficiently or not, which raised valid objections as those mentioned in the answer by @EnergyNumbers.

But really, at the individual level, the hypothesis that individuals use the mathematical expected value comes essentially from Expected Utility theory, that predates the Rational Expectations, and has a debate on its own (also here in Economics.SE)

Another set of "arguments against" the REH (which gave very interesting literature), was collected early on in the book "Individual forecasting and aggregate outcomes - Rational Expectations examined" 1983 R. Frydman and E. Phelps (ed). Of which I mention two:

1) Being an equilibrium concept, REH requires co-ordination of expectations formation (which is really not that realistic) or properties of Nash-equilibrium: this last insight gave us "Eductive Expectations" and some really thoughtful works by Roger Guesnerie.

2) The second one, which became rather more widely spread than Eductive Expectations, is "Adaptive Learning" (see "Learning and Expectations in Macroeconomics" By Evans and Honkapohja, 2001).
Adaptive Learning pointed out that REH assumes that economic agents know the structure of their environment perfectly. So in Adaptive Learning models we have the first systematic approach to model uncertainty : as economists, so economic agents do not know the environment perfectly, and they have to estimate it and learn it gradually (hence "adaptive learning"). In this strand of literature, "learning" is done through econometric methods, mainly least-squares (which is a very intuitive least-distance mathematical approximation method). Roughly speaking, here agents' expectations are not the expected values, but the estimated expected values. This creates much more interesting and realistic dynamics, that some times may converge (someday) to an REH equilibrium (which makes Adaptive Learning a "selection mechanism" for the sometimes multiple REH equilibira), or to some other point, not predicted by REH.

Research into the issue of aggregate expectations formation and modeling is currently exploding, see for example another Frydman & Phelps (ed.) book, "Rethinking Expectations" (2012), in parallel with the emerging "Post-Walrasian" direction in Macroeconomics (see D. Colander (ed). Post-Walrasian Macroeconomics 2006).


Derive the cost function for a Homothetic production function I'm having trouble understanding the steps in showing that a Homothetic production function's cost function must be expressible in the form $C(w, q) = a(w)b(q)$.

Since the production function is homothetic, I know that the optimal cost minimizing input ratio given the same input costs must be exactly the same for different quantities of output i.e.

$$
\frac{H^j(w,q)}{H^i(w,q)} = \frac{H^j(w,q')}{H^i(w,q')}
$$

Rearranging this we arrive at the ratio:

$$
\frac{H^i(w,q)}{H^i(w,q')} = \frac{H^j(w,q)}{H^j(w,q')}
$$

This makes sense because in order to the maintain the input ratio constant, we would need both cost-minimizing inputs to increase by the same factor when going from $q$ to $q'$. However, the proof then states that "for the above to true it is clear that the ratio must be independent of w, thus, setting $q' = 1$"

$$
\frac{H^1(w,q)}{H^1(w,1)}= \frac{H^2(w,q)}{H^2(w,1)} = \cdots =\frac{H^m(w,q)}{H^m(w,1)} = b(q)
$$

and so

$$
H^i(w,q) = b(q)H^i(w, 1)
$$

The steps after this to get to $C(w, q) = a(w)b(q)$ is pretty understandable and straightforward for me.

However, what I don't understand is how you can clearly see that the ratio must be independent of w. Surely the ratio just states that for a given w the inputs must increase by the same factor/ratio. But how does that imply that the ratio has to be exactly the same for all w?

Edit: for those who are asking, this comes from an exercise question in Frank Cowell's textbook: Microeconomics: Principles and Analysis.

There must be an error in your proof.  Where does your proof come from?
The part "for the above to true it is clear that the ratio must be independent of $w$," cannot be True.  Your ratio must be independent of $q$ but not of $w$.
Take for instance the Cobb-Douglas case (which corresponds to a homothetic production function) for a counter example. See Diewert or Chambers for a proof of your result:
Chambers, Robert G., 1988, Applied Production Analysis, Cambridge University Press.
Diewert, E., 1982, "Duality approaches to microeconomic theory", in Handbook of Mathematical Economics, Volume 2.
In the Cobb Douglas case, the production function $$q=x_1^\alpha x_2^\beta$$ yields the first order conditions $$\frac{w_1}{\lambda}=\alpha\frac{q}{x_1}$$
$$\frac{w_2}{\lambda}=\beta\frac{q}{x_2},$$ so that optimal input demand satisfy (in your notations) $$\frac{x_1}{x_2}=\frac{\alpha}{\beta}\frac{w_2}{w_1} \equiv \frac{c_1(w)}{c_2(w)},$$ which is independent of $q$ and implies (show it) that $$x_1=H^1(w,q)=c_1(w)b(q),$$ $$x_2=H^2(w,q)=c_2(w)b(q).$$ It follows that the cost function $$c(w,q)=w_1H^1(w,q)+w_2H^2(w,q)=a(w)b(q),$$ with $a(w)=...$. A similar derivation holds for the more general homothetic case, because by definition of homotheticity, the production technology can then be written as $$y=f(x)=g(h(x))$$ where h is homogeneous of degree one...


Data mining in econometric modelling Would I be "mining the data" in a time series analysis if I add more lags than theory suggests? For instance, for annual data analysis, it is recommended that two lags would be sufficient to capture the dynamic interactions among the variables and account for potential serial correlations. Similarly, in models that use quarterly data, using four lags is a norm. However, in many instances, there is a conflict between what theory says and what one could observe in actual data.

Just wondering if it amounts to "data mining" when I augment the model with more than 2 lags of annual data. Assume the lag order is selected using an information criterion.

The critical points here are the phrases "it is recommended that...", and "using four lags is a norm". "Recommended" and "norm" based on what? On a specific prevailing theoretical model, or on past experience with the specific kind of data? If it is the latter, you do not conflict with any economic theory, if you try something different.

This is also a good example of the need to arrive at a synthesis where the model is both theoretically supported and also statistically adequate (consult the works, especially the books, of prof. Aris Spanos on this important methodological matter).


Help understanding this inclusive capitalism proposal Robert Ashford has written about his proposal for a better, inclusive capitalism, but I don't understand the method. For example, take a look at this article. All is very obscure. It seems to be about paying workers with shares, but I don't quite understand it. Why would companies expand their shares? That lowers their price. Can't see how this would work. Is anyone familiar with his proposals?

Robert Ashford has written about his proposal for a better, inclusive
  capitalism, but I don't understand the method. For example, take a
  look at this article. All is very obscure.

  Can't see how this would work.

The article is altogether too sketchy, idealistic, contradictory, very flawed, with too many unfilled gaps and motley elements. Much of it sounds like campaign promises, but a "broader distribution of capital acquisition and income" is not the panacea the article purports.

Initially, the authors admit that "production generally becomes increasingly more capital intensive" (p.70) and that "capital [keeps] doing an ever-increasing portion of the total work" (p.71). Despite that, the authors "predict" that a broadening of capital acquisition will lead to "fuller employment of labor" and that "the present demand [...] [of] employment would increase" (p.71) (even by virtue of the market's anticipation of that broadening!), that it "should be reflected in increased employment of labor" (p.73).

That twist is unrealistic and makes no sense. Simply put, it would be absurd for a profit-maximizing agent to invest on labor even though (or despite that) he knows that labor keeps being increasingly replaced by capital.

The principle of decreasing marginal utility strikes the authors' presumption that higher levels of income will consistently lead to greater demand of goods and services. The authors purport that, unlike the "Keynesian analysis", binary growth would continue materializing in the long run. But they do not (and cannot) articulate how their proposal would overcome the decreasing marginal utility in the long run, or why this would be any different in the aggregate. In short, the authors appear to ignore the notion of oversupply.

The article posits that its so-called "binary economic approach" can also enhance "the prospects for achieving environmental sustainability" (p.70). But then it admits that it is optimistic and doubtful that "binary growth would in the aggregate be greener growth[,] because [...] too many people may also prefer to spend their enhanced capital income on brown rather than greener products and services" (p.73). The article ends up requiring an "active role" from the government "with respect to [...] environmental sustainability issues" (p.73).

The article also goes from the initial premise that its proposal would require "no government command" (p.70) to proposing that the government embrace an "active role" in defining where to promote a "qualified" binary financing"  as well as to determine which producers shall be subjected to "more stringent [standards] than [the] mandatory standards imposed on all producers" (p.73). That governmental active role also includes the implementation of a "credit reinsurance entity modeled after the FHA home loan reinsurance program" (p.74).

The article is so poorly written and so incongruous that it significantly hurts the "prestige" and value of the authors' credentials (listed at the end: J.D. & Ph.D. holders). The only thing for which I would praise the article is the call for a reduction of tax rates. Putting aside the terrible "quality" of the article, it appears as if one team of authors wrote pages 70-71 and their opponents wrote pages 73-74.


How to predict income n years after graduation using income dataset with age, but not graduation year? I'm trying to predict the income of graduates of certain Master's programs n years after graduation, using the American Community Survey individual level dataset to calibrate my equation. It gives me observations of individuals listing their income, age, degree program, and other variables, but doesn't tell me years since graduation or years in the workforce. How can I best predict income n years after graduation?

I'd like my final product to be a regression equation of the form:

income_year_n = starting_salary(many variables) * (1+rate_of_raises)^n

My initial approach is along the lines of:

The youngest people with this degree are 23 years old. They all must have graduated the previous year. Use them to calibrate the starting_salary function.
The next youngest group is 24. They must either have one year of experience, or have just graduated. I know roughly the proportion for each, because I know how many 23 year olds there are in the dataset, but I don't know which are the new graduates and which graduated last year.
The next youngest is 25, this group has either 0, 1, or 2 years of experience, and I know the proportions for each.

And so on. This feels like the beginning of an approach that would work, but I can't figure out how to go from this data to a regression equation that predicts income after a certain number of years.

Any ideas? I know there's no perfect solution, I'm looking for a close-enough hack to actually use the equation in the real world. Anything would be greatly appreciated, thanks a ton.

I think you're looking for false precision, here.  "Years since graduation" is already a step function with an essentially arbitrary cutoff (should it really matter to your model that much if somebody is one day shy of being at the end of +1 years, versus one day into +2 years?  the actual difference is a few days.)

Just use age minus 23, or just use age in your model.  It shouldn't impact things that much either way.


Recursive Substitution in Time Series Would appreciate some guidance on a matter of recursive substitution, where we have the AR model:
$$y_t = \alpha +\theta_1y_{t-1}+ u_t$$
And
$$E(y_t)= \mu_t$$
Where:
$$\mu_t = (1+\theta_1 + \theta_1^2+..+\theta^{t-1})\alpha+\theta^ty_0$$
It follows by recursive substitution we get:
$$y_t = \mu_t +(u_t +\theta_1u_{t-1}+\theta^2u_{t-2}+...+\theta^{t-1}u_1)$$
And subsequently:
$$E[y_t] = E[\mu_t]+ E[(u_t +\theta_1u_{t-1}+\theta^2u_{t-2}+...+\theta^{t-1}u_1)]= \mu_t$$
Would someone be able to explain how the step concerning recursive substitution is obtained, moving from line 2,3,4?


Can money flow from Firms into the Financial Market in the Circular Flow? In Macroeconomics, we learn that the circular flow diagram is a simple economic model that illustrates the flows of goods and services through the economy. Can the arrow that connects the "Financial Market" sector of the economy to the "Firm" sector be double-headed?

Traditionally, in the class, I've learned that Firms borrow money from the financial market to make investments in capital (so the arrow is always pointing from the Financial Market to the Firms), but I've never seen a situation where money flows from the Firms into the Financial Market.

Can this occur? And if so, can you give an example of when?

Thanks!

Yes! I put together this sketch to show it

For example

Households can save money in banks, which inject money into the financial market
They are later compensated the form of a rate of return
Firms can borrow money
Later they need to pay an interest. This way the money flows from the firms back to the financial market


Why do central banks increase their rate to fight inflation? It was top news a week ago that Bank of Ukraine increased its rate to 30%.
And the news said they did this to fight inflation.

But I don't understand one thing: isn't the increased rate of "money printing" of the central bank only aggravates the problem? How is it supposed to reduce inflation?

From Monetary Policy:

  There are several monetary policy tools available to achieve these
  ends: increasing interest rates by fiat; reducing the monetary base;
  and increasing reserve requirements. All have the effect of
  contracting the money supply; and, if reversed, expand the money
  supply.

Increasing rates makes it more expensive to borrow and thus slows economic growth where the US in the early 1980s would be a good example to see the recession that was had at the hand of high interest rates at the time.


Where to get historical intraday trading data from? I have started to learn about trading and would like to play around with historical data. I therefor need a dataset, that provides intraday values, not only opening, high and low prices for a specific day and time. I would like to query a web service, db, whatever like this:

getPrice($isin, $date, $time)

Unfortunately I can't find anything or maybe I am just using the wrong search words on google. Yahoo Finance, etc. only provides opening, high and low data which is not sufficient for my need. Specifically I am looking for historical SMI futures data:

http://www.eurexchange.com/exchange-en/products/idx/smi/SMI--Futures/19444

Product ISIN CH0008616432

Underlying ISIN CH0009980894

I already had a look at:

www.xignite.com
www.quandl.com

which looked promising, but again they do not provide intraday values.

I work at Quandl and we have intraday data here: https://www.quandl.com/vendors/as

The databases include S&P 500 One Minute Bars, NASDAQ 100 One Minute Bars, Dow Jones Transportation Average One Minute Bars, Dow Jones Industrial Average One Minute Bars and Dow Jones Utilities Average One Minute Bars.

The databases cover five years of history and include OHLCV data and all additions, removals and changes to the index.

You can use our API with every dataset. Each database has a section explaining API usage and bulk download. You can also check out our detailed API documentation here: https://www.quandl.com/docs/api

Hope this helps!

Also, we apologize for the shortcomings of our site's search features - we are working very hard to improve this to better help users find the data they need.


What Was the Accuracy of Macro Model in the Phillips' Machine (MONIAC)? One of the most interesting  economic 'artefacts' featured on the campus of my alma mater is the Philips' machine or Monetary National Income Analogue Computer (MONIAC) pictured below.
MONIAC was a hydraulic computer, with a rudimentary macroeconomic model, build by none other than William Philipps as a part of his dissertation. MONIAC could be used to visualize and even predict several macroeconomic variables depending on its calibration (such as interest rates or prices resp. inflation).   The machine was originally intended just for classroom use (Bissell, 2007), but eventually several research/policy institutes around the world decided to commission the machine as well (for example New Zealand Institute of Economic Research bought one). This makes me wonder if the machine was ever accurate enough to be useful outside classroom (e.g. research/policy analysis/forecasting). Since it is based on rudimentary macroeconomic model I would expect relatively large forecasting errors.
I tried to do research on the MONIAC's accuracy but I am finding conflicting reports. According to Wikipedia:

To their surprise, Phillips and his associate Walter Newlyn found that MONIAC could be calibrated to an accuracy of 2%.

but no reference to the work where Phillips and Newlyn made the claim is provided.
I dug bit deeper and managed to find paper (Bissell, 2007) that claims the MONIAC's accuracy was reportedly only $\pm 4\%$ but again the claim is not directly supported by citation. In the next paragraph the paper cites Newlyn (1950) so I thought it might have the answer (since Wikipedia mentions Newlyn as well) but it turned out it does not mention any number for the accuracy of the machine.
This leads me to my question, is there any primary source in the economic literature for the accuracy of the MONIAC? If so what level of accuracy does it report?

Phillips himself claims writing about Moniac like machines in 1950: "The accuracy obtained depends on the precision with which the machines are constructed, but there is no difficulty keeping it within about $\pm$ 4%" (p.284)
The article also points out that at the time of writing he was still building the MONIAC at LSE, but had already constructed one in Leeds. I suppose the LSE version turned out to be accurate upto 2%, and hence the conflicting informaton.
Economica, New Series, Vol. 17, No. 67. (Aug., 1950), pp. 283-305. Here's a link

Two unrelated fun-facts:
The MONIAC features in Terry Pratchett's Discworld novel: Making Money. As always in Pratchett's novels there are a lot of references to roundworld reality: introduction of paper money, outsourcing, inflation due to money dilution and many others
The Dutch have an expression "To have money like water" which in the Dutch context obviously means to have lots of money. The MONIAC is one of the few cases where it can be interpreted literally.


Update of value function in continuous time - HJB When solving (numerically, by value function iteration) a dynamic programming problem in discrete time, such as

$$V_1(a) = \max_{c} \ u(c) + \dfrac{1}{1+\rho}V_0(a')$$

we maximize with respect to the control variable and get a first order condition that we then plug back into the functional equation shown above. The result of this step, $V(a)_1$, will then be used on the RHS of a second iteration

$$V_2(a) = \max_{c} \ u(c) + \dfrac{1}{1+\rho}V_1(a')$$

and we repeat this process until $V(a)_n-V(a)_{n+1}<\epsilon$.

My question is how does the update of the value function work in continuous time?  I have been working on a paper that uses continuous time dynamic programming, so the Bellman equation looks as follows

$$\rho V_n(a) = \max_{c} \ u(c) + \dfrac{\partial V_n(a)}{\partial a}da_t \quad (*)$$

where the transition equation is represented by $da_t$. From what I have seen, the update of the value function is done by calculating $\Delta$:

$$ \Delta = \ u(c(a^*)) + \dfrac{\partial V_n(a)}{\partial a}da_t(a^*) - \rho V_n(a)$$

where $u(c(a^*))$ and $da_t(a^*)$ represent the control and transition equation as functions of the optimal policy. That is, we maximize the RHS as in the previous example (the discrete time case), but then we subtract $\rho V(a)$ from both sides. Then updating the value function is done as follows:

$$V_{n+1}(a) = V_n(a) + \Delta$$

How can this be so? I would have thought that I would just use the maximised RHS of (*) and plug back in a new iteration. How come the other method is the correct one?

You iterate towards a fixed point, so you want to reach a situation where plugging in your current iterated value produces itself. Now using your notation, we are told that we should calculate

$$V_{n+1}(a) = V_n(a) + \Delta$$

where

$$\Delta = \ u(c(a^*)) + \dfrac{\partial V_n(a)}{\partial a}da_t(a^*) - \rho V_n(a)$$

Insert the second into the first to see what the iteration rule is:

$$V_{n+1}(a) = V_n(a) + \ u(c(a^*)) + \dfrac{\partial V_n(a)}{\partial a}da_t(a^*) - \rho V_n(a)$$

When you reach a point where

$$V_{n+1}(a) = V_n(a) $$

(or $\epsilon$-so)

It will mean

$$\rho V_n(a)= \ u(c(a^*)) + \dfrac{\partial V_n(a)}{\partial a}da_t(a^*) $$

which is what you have to satisfy.

Some stars etc may have to be adjusted in the above, for a fully consistent notation.


How do I determine PED from price consumption curve with slope of zero? Given a budget for two goods $x_1$ and $x_2$, a fixed price for good 2 and three prices for good 1 with the corresponding optimal amount of good 1 ($x_1$), I like to calculate the PED for good 1.
By looking at the three given points, I know that the price consumption curve for good 1 is a horizontal curve, i.e. the slope of the price consumption curve seems to be zero (connecting the three points).
Since I know the price ratio, I also know the MRS for the three given points.
So I have to find $x_1(p_1, p_2, m)$, where $p_2$ and $m$ are known constants, in order to determine $\partial x_1(...)/\partial p_1$.
What is the correct approach to this problem?

Since you have discrete datapoints and want to calculate PED, you will have to make assumptions, like "the data represents the general behavior of the consumption function". (You can also get more data or throw your hands up in despair.)
If you know that price has no effect on the quantity demanded, you can apply the PED formula, and get a very specific number for PED.


What is the difference between Stochastic game and Bayesian game ? I was studying definitions of Stochastic and Bayesian game and it appears that Stochastic game is a generalized form of Bayesian game. Could anybody please explain the fundamental differences between Stochastic game and Bayesian game and imperfect information and incomplete information games ?

In a Bayesian game, information is incomplete. To cope, players have beliefs about the state of the game. In a sense, each player strategizes as if the game was as he or she believes. So each player operates in his or her own world. And if every player plays a Nash equilibrium in one's own world, that's a Bayesian Nash equilibrium.

In a stochastic game, the information about the current state of the game may indeed be public. At a given time step, the next state is determined by the current state, the strategy profile played at that time step, and some stochastic process (like a Markov chain, for example).

We can have a stochastic Bayesian game where information is incomplete and there is a stochastic switching device like a Markov chain.