Muth exposition of the rational expectations hypothesis I am reading in statistical decision theory and stumbled upon the rational expectations literature (rationality with incomplete information->dynamic problem->N.L Stokey->husband). The assumption that subjective expectation approximates the objective probabilities without adaptive learning seems almost ridiculous if one considers that the whole enterprise of statistics is to learn from the past to infer about the future.

Nevertheless, as explained clearly in the answer to another question, Muth (1961) proposed the hypothesis of rational expectations as a purely descriptive model, to facilitate explanation of certain market behavior, however unrealistic it might be to generalize this hypothesis to all behavior.

Please refer to the full text of the paper.

If I understood it correctly, section 3 of the paper is an exposition of how such a rational expectations hypothesis, as the author proposed and shortly justified in section 2, can be applied to analyze several market situations.

I had difficulty understanding the reasoning around equations 3.3-3.4. In particular:

  Referring to (3.3) we see that if $\frac{\gamma}{\beta}\neq-1$ the rationality assumption (3.4) implies that $p_t^e=0$, or that the expected price equals the equilibrium price.

What does the last part of the sentence mean? That equation (3.4) holds? How can $\frac{\gamma}{\beta}\neq-1$, $p_t^e\neq0$ and equations (3.3) and (3.4) hold together?

If I understand his exposition as imposing the rational expectations hypothesis (equation 3.4) on the market equilibrium price (equation 3.3), then the solution would be that either $\frac{\gamma}{\beta}=-1$ or that $p_t^e=0$. What does this mean? Or is he trying to show something else?

Muth assumes a model of

  "...short-period price variations in an isolated market with a fixed
  production lag of a commodity which cannot be stored".

It is useful to remember that the model's equations are expressed as deviations from equilibrium values. So in a bit more clear notation than the original (a star denotes long-run equilibrium value)

$$\begin{align} & D_t-D^* = -\beta (p_t-p^*) & {\rm (Demand)}\\
& S_t-S^* = \gamma (p^e_t-p^*) + u_t & {\rm (Supply)}\\
& D_t = S_t,\;\; D^* = S^* & {\rm (Market \;Equilibirum)} \end{align}$$

Production is determined one period before, based on expected future price, but final supply is also subject to random shocks, $u_t$, with $E_{t-1}u_t =0$. $p^e_t$ is expected price but we have not yet make any assumption on how it is formed, or to what is equal.

Eliminating quantities through market equilibrium we obtain

$$p_t-p^* = -\frac {\gamma}{\beta} (p^e_t-p^*) - u_t \tag {3.2}$$

Taking expectations conditional on time $t-1$ we obtain

$$E_{t-1}p_t-p^* = -\frac {\gamma}{\beta} (p^e_t-p^*) \tag {3.3}$$

Rearranging and subtracting $p^e_t$ from both sides we see that equation $(3.3)$ leads to

$$p^e_t-E_{t-1}p_t = (1+\gamma/\beta) (p^e_t-p^*) \tag {3.3a}$$

If  $\gamma / \beta =-1$ we obtain, without making any assumption on how expectations are formed but as a solution to the model, that $p^e_t=E_{t-1}p_t$. But this is uninteresting, being a very specific configuration of demand and supply responses. Assume then that $\gamma / \beta \neq -1$.

Then this way to write the relation (not in Muth's paper), shows clearly that if $$p^e_t \neq E_{t-1}p_t \implies p^e_t \neq p^*$$
and that
$$p^e_t = E_{t-1}p_t \implies p^e_t = p^*$$

Throughout the paper Muth treats $E_{t-1}p_t$ as the theory's prediction, a best prediction (and it is, in the sense of being the minimizer of mean squared error of prediction). Given this Muth argues as follows: if "market expectations" $p^e_t$ (i.e. some concept of "average", "prevailing" expectations) were not equal to the "best" prediction, then recurring pure-profit opportunities would exist, for someone that used $E_{t-1}p_t$ as his own expectation, while all others used some other expectations formation rule. But, is it reasonable to argue that the market as a whole is outperformed by some "wise man"? Is it reasonable to argue that the firms and the businessmen and any other people whose livelihood depends on the workings of this specific market, would not really try hard to be as efficient and as accurate as possible regarding their predictions? It doesn't sound too convincing, especially since we are talking about the collective wisdom of all market participants here.

So making the assumption $p^e_t = E_{t-1}p_t$ (i.e. imposing the RE Hypothesis) appears reasonable, and this leads to

$$p^e_t =p^*$$

(remember the right-hand side is long-run equilibrium price, not next-period's - we are not looking at period-by-period perfect foresight here).

Now use this result on the initial equations describing the market, and eventually obtain the determination of the short-run equilibrium price as

$$p_t = p^* -(1/\beta)u_t$$
This happens because we have imposed REH. In other words the imposition of REH brings about the result that current equilibrium price remains "attracted" and "chained" to long-run equilibrium, fluctuating randomly but not explosively.

Also we have

$$p_t = p^e_t -(1/\beta)u_t$$

which also means than in unconditional expected-value terms

$$E(p_t) = E(p^e_t)$$

"On average" (intertemporally), the price expectation will equal the actual price.

In one move Muth obtained two extremely powerful results:
a) Markets do not explode
b) Market participants on average and "as a whole" predict correctly.

And really, if markets did tend to explode rather than not explode, they would not be around for thousands of years, as they are. And if market participants were predicting consistently poorly, we would have seen much more personal financial ruins than we do.

What REH does not do well, is in helping model and analyze short run and transitional dynamics. It remains a long-run concept, a "long-run view" if you will, and this is why Adaptive Learning emerged, and this is why we are currently researching (in a frenzy), other expectations formation hypotheses.


Two-good economy, can we tell if the demand of good 1 rises or falls when the price of good 2 rises (price of 1 is constant)? Suppose we have a two-good economy, and we know that good 1 is a normal good. Can we then make any meaningful observation about the demand for good 1 when we change the price of good 2 and keep the price of good 1 constant?

Check out the demand functions for three cases:

CES Utility
Leontief Utility
Cobb-Douglas Utility

You should be able to see that the first case gives you that demand for good 1 increases, the second case demand for good 1 decreases, and in case 3 it is unchanged.


What is the difference between knowledge-based and R&D? So far, I always thought that knowledge-based companies and R&D companies were the same. But recently our TA mentioned that they are different, I've searched a lot to find the differences between them but the more I searched the less I found.

I would really appreciate if someone told me the difference between these two kind of companies.

A knowledge-based company sells products or services that are primarily knowledge-based. This doesn't have to be new knowledge - it can be existing knowledge.

An R&D company earns its way by developing new knowledge.


Why is the Fed worried about short term interest rates going negative? I refer to the following article: https://www.bloomberg.com/opinion/articles/2021-02-25/negative-interest-rates-could-be-trouble-unless-fed-acts, notably the following paragraph:

Market observers worry that this wall of liquidity could push short-term interest rates into negative territory. Although no one can be sure of the ramifications, this could prove disruptive to money-market mutual funds and to the functioning of short-term lending markets more generally. The surge in reserves will also add to banks’ assets, potentially causing them to bump up against regulatory leverage requirements, which limit the ratio of their total assets to equity capital. This, in turn, could cause some banks to pull back from lending against securities, potentially triggering yet another disruption in the “repo” market, a crucial source of financing for hedge funds, investment banks and many other institutions. Banks also might take steps to encourage households and businesses to take their deposits elsewhere.

How does negative short term interest rates disrupt the repo market in any way?

Market observers worry that this wall of liquidity could push short-term interest rates into negative territory.

Fed pays interest on excess reserves (IOER) as a tool of monetary policy since late 2008.
https://www.clevelandfed.org/newsroom-and-events/publications/economic-commentary/2015-economic-commentaries/ec-201502-excess-reserves-oceans-of-cash.aspx
The "wall of liquidity" would increase excess reserves. Fed can pay interest on those reserves so the IOER rate does not have to go negative unless Fed decides to try that experiment as a tool of monetary policy.
Negative interest rates are the same as paying a net fee for keeping deposits or other investments at the bank or central bank. Extra central bank liquidity does not motivate banks or the central bank to charge fees. Banks charge fees to compensate for a loss or lack of net interest income. Central banks might try to make interest rates negative as a tool of monetary policy.
Repurchase Agreements with Negative Interest Rates:
https://www.newyorkfed.org/research/current_issues/ci10-5.html
Negative rates on repo mean the lender will pay interest to obtain the security collateral. This implies that investors would rather hold certain securities, which are under shortage, instead of other financial assets. One needs some case studies and/or theories which demonstrate or predict that a surplus of excess reserves somehow triggers a shortage of securities in repo markets. However if Fed imposes negative interest rates on reserves that is a different analysis.


Solution of overdetermined system of moment conditions In Hayashi Econometrics, page 207-8, ex3 (see hint), he says that even if a population moment conditions (GMM setting) system is overidentified it still has a solution, while the sample moment conditions system cannot.
I'm having a hard time understanding this.
Any help would be appreciated.
By the way, I've also posted this question on CrossValidated. I hope there's no problem.
Edit: Check Jayk answer in CV. ;)

Here's a little discussion that might help.

The population version has a solution because it is assumed to have a solution. You can see that this is the case from assumptions 3.1 (linearity), 3.3 (orthogonality conditions), and 3.4 (rank condition for identification). You can see the derivation of this fact from equations (3.3.3) and (3.3.4).

Now, you'll notice the population version having a solution implies that
$$
\text{rank}\left( \Sigma_{xz} \right )
= \text{rank}\left(\left [\Sigma_{xz} \mid \sigma_{xy} \right ]\right ),
$$
as discussed in exercise 5 of section 3.3. In the hint they note that the population version has a solution when
$$
\left [\Sigma_{xz} \mid \sigma_{xy} \right ]
$$
is of rank $L$. If it has rank $L+1$, it will not have a solution. In the hint, they say that this is a set of "equality conditions." This is referring to the fact that one of the columns must be a linear combination of the remaining columns. This is a very hard condition to satisfy. In many models, this condition will hold with probability zero. This is because the data has to come out so that the equality condition holds perfectly.

On the other hand, the condition that the sample version $S_{xy}$ of $\sum_{xz}$ be of full column rank is a set of "inequality" conditions on the matrix. Because they are inequality conditions on the matrix, they are much easier to satisfy by chance.

In conclusion, $S_{xy}$ will have full column rank for sufficiently large $n$ because the conditions are inequality conditions which occur with probability larger than zero. However, to have a solution we need $\left [S_{xz} \mid s_{xy} \right ]$ to have rank $L$. But because this is an equality condition on the matrix, it only occurs with probability zero.

Search Keywords: Solutions, Exercise 3, section 3.4 Hayashi Econometrics


Why is fiscal deficit always shown as a percentage of GDP? If the probable reason is because it must reflect the government's ability to pay back the deficit, wouldn't government income be a better indicator, rather than GDP?

In short: yes, it very well might be and this has been argued by some (see, for example: http://www.forbes.com/sites/jeffreydorfman/2014/07/12/forget-debt-as-a-percent-of-gdp-its-really-much-worse/#29b8530f6e0c).

The use of Debt/GDP is the current international norm, but Debt/Tax revenue might very well be a better, more concise option. Using Debt/GDP might be because it has been common to compare countries to each other with GDP or GDP/capita and having GDP as a factor relates the debt to these measures.

It can also be argued that in the end the whole population of a country is responsible for paying their country's debts, so in an extreme situation it's not just the government's income which might be used to pay off debts.


Did the Nixon shock cause skyrocketing real estate prices in the US? Ca. 1970 the prices of real estate started skyrocketing in the US: Real estate prices chart. Same with gold: Gold prices chart.

So my conclusion is that real estate did not increase in value, it was the USD that decrased its value.

Further my theory is that Nixon taking US out of the gold standard in 1971 was what caused this. I assume that after this the US started printing a lot of dollars and paid down their foreign debt with the new less valuable dollars.

Looking at gold values is simply cherry-picking. From 1970 to 1980, the CPI went from 38.8 to 82.4, an increase of 112%, and an annualized rate of 7.8%. Your chart shows housing prices increasing about 200%, an annualized rate of about 11.6%. So while most of the price increase was due to inflation, there are 3.8 percentage points that remain unexplained.

One can also compare the dollar to other currencies. While the $/£ rate fluctuated a lot in this period, from 1970 to 1980, overall the dollar actually strengthened against the pound slightly, and from 1970 to 1976 its strength more than doubled. The Yen exchange seems to show the opposite trend, however.


Does the envelope theorem hold at a corner solution? Suppose we have the following production function:

$$F(L,K)=\max_{L_K}H(L,L_K,K)=\max_{L_K}\left[(L-L_K+1)^\alpha(L_K+K)^{1-\alpha}\right]=(L-L_K^*+1)^\alpha(L_K^*+K)^{1-\alpha}$$

With the constraint $L_K\in[0,L]$.

We know that $$\frac {dH}{dL_K}=\alpha(L-L_K+1)^{-1}H+(1-\alpha)(L_K+K)^{-1}H=0$$
Hence the value for $L_K$ at which the derivative is zero is $L_K^0=\frac {(1-\alpha)(L+1)+\alpha K}{1-2\alpha}$. And the optimal value $L_K^*$ is:
$$
L_K^*=\begin{cases}
L_K^0 &\text{ if } &0<L_K<L &(1)\\
L&\text { if } &L<L_K^0&(2)\\
0 &\text { if } &L_K^0<0 &(3)
\end{cases}
$$

It is clear that if $L_K^*\in(0,L)$, (case $(1)$ ), then the envelope theorem holds:

$$\frac d {dL} F(L,K)=\frac \partial {\partial L}H(L,L_K^*,K)=\alpha(L-L_K^*+1)^{-1}\cdot F(L,K)$$

Moreover, in the third case (3), it is also clear to me that the envelope theorem holds. However, I am not so sure about the second case (2). I would say that the envelope theorem does not hold in this case, because if we substitute $L_K^*$ back into the original production function, we get
$$F(L,K)=1^\alpha(L+K)^{1-\alpha}$$
And the derivative with respect to $L$ in this case is
$$ (1-\alpha)(L+K)^{-1}\cdot F(L,K)$$

For the envelope theorem to hold in case 3, this would require $\alpha= (1-\alpha)(L+K)^{-1}$, which Almost-Always doesn't hold.

But the reason this confuses me is that in this question I was referred to this paper, which has a theorem that states:

So my question is:

Am I right that the envelope theorem doesn't hold when $L_K$ is at a corner solution?
Does this contradict the theorem, or do I misunderstand the theorem? If not, is the theorem correct?

First, you made a sign error in the computations. After correcting for your error, a crucial hypothesis you miss is that $X$, the choice set, does not depend on the variable $t$ in the theorem (with the notations of the theorem). To apply the theorem properly, the interval $[0,L]$ should not depend on $L$.

A) The sign error

$$\frac{\partial H}{\partial L_K}=-\alpha (L-L_K+1)^{-1}H+(1-\alpha)(L_K+K)^{-1}H=0$$
We define $L_K^0= (1-\alpha)(L+1)-\alpha K$.

B) Why we could think the envelop theorem's result may fail

Presuming that $0<\alpha<1$, there are four possible cases.

(1) $L_K^0\in [0,L]$. One can check the objective function is concave, thus $L_K^*=L_K^0$.

(2.i) $L_K^0\notin [0,L]$ and $H(L,0,K)< H(L,L,K)$. Then $L_K^*=0$.

(2.ii) $L_K^0\notin [0,L]$ and $H(L,0,K)> H(L,L,K)$. Then $L_K^*=L$.

(2.iii) (just to be exhaustive) $L_K^0\notin [0,L]$ and $H(L,0,K)= H(L,L,K)$. Then there are two solutions, $0$ and $L$.

In case (1), $$\frac{\partial F}{\partial L}(L,K)=\frac{\partial H}{\partial L}(L,L^*_K,K)+\frac{\partial L^*_K}{\partial L}.\frac{\partial H}{\partial L_K}(L,L^*_K,K).$$
The second term of the right-hand side is equal to zero thanks to the first-order condition. This is compatible with the envelop theorem's result for an interior solution.

In case (2.i), $F(L,K)=H(L,0,K)$ and so $$\frac{\partial F}{\partial L}(L,K)=\frac{\partial H}{\partial L}(L,0,K).$$
This is compatible with the envelop theorem's result for a corner solution here.

In case (2.ii), $F(L,K)=H(L,L,K)$ and so $$\frac{\partial F}{\partial L}(L,K)=\frac{\partial H}{\partial L}(L,L_K=L,K)+\frac{\partial H}{\partial L_K}(L,L_K=L,K).$$

We have to be cautious about the notations here, $\frac{\partial H}{\partial L}$ means the partial derivative corresponding to the first argument, and $\frac{\partial H}{\partial L_K}$ to the second one. The second term of the right-hand side is nonzero, which does not fit with the envelop theorem's result.

C) Why it actually does not fail

Write the problem as $F(L,K)=\max_{x\in [0,1]}H(x,L,K)$, with
$$H(x,L,K)=(L-x L+1)^\alpha(x L+K)^{1-\alpha}.$$
This problem is equivalent to the initial one.
The key difference is that the interval $[0,1]$ does not depend on $L$ or $K$. This is the reason why we can apply the envelop theorem, whereas it was wrong to apply it before.

We can check that the case (2.ii) is compatible with the envelop theorem, we have $F(L,K)=H(x=1,L,K)$ and so $$\frac{\partial F}{\partial L}(L,K)=\frac{\partial H}{\partial L}(x=1,L,K).$$


How did Portugal draw down their interest rates on pubic debt? I notice that Portugal had a very high interest rate on its national bond issues back in 2012 but since then it has drawn down significantly:

How were they able to decrease the interest rate?

1.- The government imposed an austerity program and, in exchange, received assistance from the IMF and the EU.

2.- The ECB made it clear that it would do whatever as necessary to save the Euro, even buying sovereign bonds of Euro countries.

3.- A general improvement in financial conditions around 2013 throughout the world let to a decline in default premia.


Are there any analysis of what is the net benefit of NASA program to US economy? I am looking for some study that tries to calculate whether the NASA program on a net basis benefits the US economy. The program is very expensive, but it generates lots of patents, research, jobs and other things that must have some value for the US economy.

I had a look, and there's not a alot, and not much that is current. The problem is, the question (What is the impact of NASA on the economy?) is too big and too difficult to measure. I think you'll have better luck by focusing on particular angles to this question.
For example, when referring to the impact of NASA, this could be anything from impacts on the aerospace industry, manufacturing industry, procurement, R&D, IP and patents, services and local economies at the different NASA sites, during different time periods, etc.
I'm sure you've already done some searches, but in case you haven't tried this, have a look at Google Scholar, and see if any of your search results bring up papers that a) sound topical and b) are widely cited.
For papers that fit both criteria, click on the "Cited by..." link and you will find a list of all papers that reference this result, from which you can get a better idea of different research angles people have taken, as well different key words that you can use to look for what you ultimately are trying to answer.
Below I list the titles of a couple of relevant papers to get you started. Try entering them yourself into Google Scholar and have a look at where they have been cited.  Good luck!

"Assessing the full effects of public investment in space"
"Evidence from Patents and Patent Citations on the Impact of NASA and Other Federal Labs on Commercial Innovation"
"Economic Effects and Spin-offs in a Small Space Economy: The Case of Canada"
"Measuring the Economic Returns from Successful NASA Life Sciences Technology Transfers"
"Estimating the Impact of Shuttle Launches on Regional Economic Activity"


Interpreting coefficients with Delta ln as independant and dependent variables Imagine we have a DGP such that

$$
\Delta \ln y_{it}=\beta\times\Delta\ln x_{it}
$$

How do you interpret the $\beta$ coefficient, since it is expressed in an approximation of a growth rate?

Thanks for your help

Your equation can be re-written (through the properties of logs) as:

$$
\ln(y_{it} / y_{it-1}) = \beta\ln(x_{it} / x_{it-1})
$$

So it becomes a log-log regression equation.  In this form, it means that if we change the ratio of $x_{it}$ to $x_{it-1}$ by one percent, the ratio of $y_{it}$ to $y_{it-1}$ will change by $\beta$ percent, on average.  In other words, if $x_{i}$ grows by one percent between two periods, $y_{i}$ is expected to grow by $\beta$ percent in that same time span.


Matlab: Solow Model Convergence of capital I am currently trying to create a while-loop which iterates the evolution of the capital stock until it converges on the n-th digit. As I am still quite new to Matlab I face a lot of problems. I would be very thankful for any kind of help.
Here is my code:
% Model parameters
alpha = 1/3;    %
s     = 0.2;    % Investment rate
delta = 0.2;    % Depreciation rate
n     = 0.02;   % Growth of labor force
g     = 0.01;   % technological progress

eps  = 1;
k(1,1) = 0.5;
i=0;

while  eps >= 1.0e-5
    t = t+1;
    k(1,t) = (1/((1+n)*(1+g)))*((s*k(1,t-1)^alpha+(1-delta)*k(1,t-1)));
     z = k(1,t);
    z1 = k(1,t+1);
         kdif = z1-z ;
          eps = max(abs(kdif));
    i = i + 1;
  if i >= 300
    break;
  end
end

Since, I was urged to present an answer for didactic reasons to which I totally agree, I will provide the full set of corrections to avoid any ambiguity.
% Model parameters
alpha = 1/3;    %
s     = 0.2;    % Investment rate
delta = 0.2;    % Depreciation rate
n     = 0.02;   % Growth of labor force
g     = 0.01;   % technological progress
eps  = 1;
k(1) = 0.5;
t=1;

while  eps >= 1.0e-5
    t = t+1;
    k(t) = (1/((1+n)*(1+g)))*((s*k(t-1)^alpha+(1-delta)*k(t-1)));
    z = k(t);
    z1 = k(t-1);
    kdif = z-z1 ;
    eps = max(abs(kdif));
   if t >= 300
     break;
   end
 end


How do Gini coefficients correlate with the cost of higher education? Are there any studies that explore the higher net present value (NPV) of education in countries with higher Gini coefficients?

Additionally, do any of these studies include the impacts of economic mobility as a reducing factor of the NPV or price of higher education?

I think this gives an answer reasonably close to what you're looking for (from the NYTimes article, "In climbing the income ladder, location matters," featuring research by Raj Chetty, Emmanuel Saez, and others).

The team of researchers initially analyzed an enormous database of earnings records to study tax policy, hypothesizing that different local and state tax breaks might affect intergenerational mobility.
What they found surprised them, said Raj Chetty, one of the authors and the most recent winner of the John Bates Clark Medal, which the American Economic Association awards to the country’s best academic economist under the age of 40. The researchers concluded that larger tax credits for the poor and higher taxes on the affluent seemed to improve income mobility only slightly. The economists also found only modest or no correlation between mobility and the number of local colleges and their tuition rates or between mobility and the amount of extreme wealth in a region.

(emphasis added)
Note that the study is primarily about income and social mobility, but they also mention that tey find modest or no correlation between tuition rates and amounts of extreme wealth in a region.


Does the law of supply reject rise in total revenue for goods with elastic demand? If demand for a product is elastic( consider the case when the price is low ), lowering the price further increases total revenue.

However, as per the law of supply, low prices cause suppliers to supply less of this elastic demand product.  There will be a shortage and price must increase back to equilibrium price.

Doesn't the law of supply invalidate "total revenue rises with price drops on goods with elastic demand"?

There is no contradiction.

The law of supply simply indicates a supply curve is upward sloping.  There is no prohibition against the curve itself moving so that it intersects demand in another location, so long as the slope remains positive.


Optimisation using value function I have the following optimisation problem:

max $E_{0}\sum_{t=0}^{\infty}[log(c_{t}) + log(m_{t})]$ subject to $y + \frac{M_{t-1}}{p_{t}} + R_{t-1}\frac{B_{t-1}}{p_{t}} = c_{t} + m_{t}+b_{t}+\tau_{t}$

Where lower case letters indicate real variables and $R$ is the gross nominal interest rate.

I am trying to solve this using the value function approach but I am having a difficult time understanding what the state variable should be in this case. I tried using wealth as the state and formulated the following value function:

$V(a_{t}) = \max_{c_{t}, m_{t},b_{t}} [u(c_{t},m_{t}) + \beta V(a_{t+1})]$

where $a_{t} = y+ \frac{M_{t-1}}{p_{t}} + R_{t-1}\frac{B_{t-1}}{p_{t}} $ and initial values are assumed to be given. My problem now is that I don't know what to substitute for $a_{t+1}$. I have tried forwarding the left-hand side of the budget constraint (i.e $a_{t+1} =  y + \frac{m_{t}}{\pi_{t+1}} + R_{t} \frac{b_{t}}{\pi_{t+1}})$ and then differentiating w.r.t c,m and b but my results are very strange. Furthermore, if I have understood correctly, I also have to find $V_{a}(a_{t})$ which I cannot do with this substitution.

I am trying to learn this using Walsh's book and in his example, the budget constraint has capital which appears on both sides of the budget constraint, this allows him to re-write capital as a function of $a_{t}$. I tried to do the same but with real balances;

From the budget constraint I can write $m_{t} = a_{t}-c_t-b_t-\tau_t$

So, $V(a_{t}) = [u(c_{t},m_{t}) + \beta V(y + \frac{a_{t}-c_t-b_t-\tau_t}{\pi_{t+1}}) + R_{t} \frac{b_{t}}{\pi_{t+1}} ]$

Again I differentiate w.r.t c,m and b and this time my results are looking less crazy but still not correct. I get:

(c) $u_{c} - \beta V_{a}(a_{t+1})[\frac{1}{\pi_{t+1}}] = 0$

(m) $u_m + \beta V_{a}(a_{t+1})[\frac{1}{\pi_{t+1}}] = 0$

(b) $\beta V_{a}(a_{t+1})[\frac{R_{t}}{\pi_{t+1}} - \frac{1}{\pi_{t+1}}] = 0$

And lastly, $V_{a}(a_{t}) = \beta V_{a}(a_{t+1})[\frac{1}{\pi_{t+1}}] $

The final condition implies that $u_{c} = V_{a}(a_{t})$ which is similar to Walsh's answer but I can't seem to obtain a form of the Fisher equation and money demand function from my workings.

There is also the equilibrium condition $c_{t} = y-g$ but I have no idea when to impose it.

Any thoughts on what I have done incorrectly?

Starting with your original equation:

$max_{c_t, m_t, b_t} E_0\sum_{t=0}^\infty U(c_t, m_t)$

s.t.

(1) $y+\frac{m_{t-1}}{1+\pi_t}+\frac{1+i_{t-1}}{1+\pi_t}b_{t-1}=c_t+m_t+b_t+\tau_t$

Here: $R_{t-1} =1+i_{t-1}$ and $1+\pi_t=\frac{P_t}{P_{t-1}}$

Note that in this problem, you have have two state variables, $m_{t-1}$ and $b_{t-1}$, and your main issue have been that you have bunched these together. your Bellman should be:

$V(m_{t-1},b_{t-1})=max_{c_t, m_t, b_t} U(c_t,m_t)+E_t\beta V(m_t,b_t)$

s.t. (1)

You can here use your contstraint to get rid of one control, or you can solve it using the lagrangian. If you use your constraint to substitute for $c_t$, your updated problem becomes:

$V(m_{t-1},b_{t-1})=max_{m_t, b_t} U(c_t(y, m_{t-1}, b_{t-1},m_t, b_t, \tau _t),m_t)+E_t\beta V(m_t,b_t)$

For clarification:

$c_t(y, m_{t-1}, b_{t-1},m_t, b_t, \tau _t)=y+\frac{m_{t-1}}{1+\pi_t}+\frac{1+i_{t-1}}{1+\pi_t}b_{t-1}-m_t-b_t-\tau _t$

FOCs:

$[b_t$]: $-U_{c_t}+\beta E_tV_{b_t}=0 $

$[m_t]$: $-U_{c_t}+U_{m_t}+\beta E_tV_{m_t}=0$

Envelopes:

$[b_{t-1}]$: $U_{c_t}\frac{1+i_{t-1}}{1+\pi _t}\implies V_{b_t}=U_{c_{t+1}}\frac{1+i_t}{1+\pi _{t+1}}$

$[m_{t-1}]$: $U_{c_t}\frac{1}{1+\pi _t}\implies V_{m_t}=U_{c_{t+1}}\frac{1}{1+\pi _{t+1}}$

You should be able to combine these equations such that you find the demand for money. To me, your equilibrium condition (along with the fact that no capital is present in the set-up) impies that there is no saving in real variables, and hence you have nothing that can pin down the real interest rate, and you therefore lack information to find the fisher equation.


CES production function application problem I'm currently trying to do some estimations using the micEconCES package in R by Henningsen/Henningsen (2011). My issue is that I am not very familiar with R and I'm trying to implement my own dataset to get the estimations with the package. They authors of the paper created this data set for the estimations.

R> set.seed( 123 )
R> cesData <- data.frame(x1 = rchisq(200, 10), x2 = rchisq(200, 10), x3 = rchisq(200, 10), x4 = rchisq(200, 10) )
R> cesData$y2 <- cesCalc( xNames = c( "x1", "x2" ), data = cesData, + coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) )
R> cesData$y2 <- cesData$y2 + 2.5 * rnorm( 200 )
R> cesData$y3 <- cesCalc(xNames = c("x1", "x2", "x3"), data = cesData, coef = c( gamma = 1, delta_1 = 0.7, delta = 0.6, rho_1 = 0.3, rho = 0.5, + nu = 1.1), nested = TRUE )
R> cesData$y3 <- cesData$y3 + 1.5 * rnorm(200)
R> cesData$y4 <- cesCalc(xNames = c("x1", "x2", "x3", "x4"), data = cesData, coef = c(gamma = 1, delta_1 = 0.7, delta_2 = 0.6, delta = 0.5, rho_1 = 0.3, rho_2 = 0.4, rho = 0.5, nu = 1.1), nested = TRUE )
R> cesData$y4 <- cesData$y4 + 1.5 * rnorm(200)

The ﬁrst line sets the“seed”for the random number generator so that these examples can be replicated with exactly the same data set. The second line creates a data set with four input variables (called x1, x2, x3, and x4) that each have 200 observations and are generated from random χ2 distributions with 10 degrees of freedom. The third, ﬁfth, and seventh commands use the function cesCalc, which is included in the micEconCES package, to calculate the deterministic output variables for the CES functions with two, three, and four inputs (called y2, y3, and y4, respectively) given a CES production function. Now in my paper I'm trying to estimate the CES function for the U.S. at the Aggregate Level for the two input case with capital and labor. So what I did is I gathered data from the World Bank Data Base from 1990-2015, where I used Gross Fixed Capital Formation for capital and total Labor Force for Labor.

The authors did f.e. a non linear estimation the following way

R> cesNls <- nls( y2 ~ gamma * ( delta * x1^(-rho) + (1 - delta) * x2^(-rho) )^(-phi / rho), + data = cesData, start = c( gamma = 0.5, delta = 0.5, rho = 0.25, phi = 1 ) )
R> print( cesNls )

Now I want the exact same thing for my own data Set which is called Data_Extract_From_World_Development_Indicators. So what I did is firstly

R> ceslan <- cesCalc( xNames = c( "GrossFixedCapitalFormation", "LaborForce" ), data = Data_Extract_From_World_Development_Indicators, coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) )

So i replicated

R> cesData$y2 <- cesCalc( xNames = c( "x1", "x2" ), data = cesData, coef = c( gamma = 1, delta = 0.6, rho = 0.5, nu = 1.1 ) )

All I did was changing the name of the Dataset and replaced x1 and x2 with my two variables for capital and Labor.

Afterwards I tried to do the non linear estimation

R> cesulan <- nls(y2 ~ gamma * (delta * GrossFixedCapitalFormation^(-rho) + (1-delta)*LaborForce^(-rho))^(-phi / rho), data = Data_Extract_From_World_Development_Indicators, start = c(gamma = 0.5, delta = 0.5, rho = 0.25, phi = 1) )

Now this is where my Problem is: I dont know what variable is meant to be y2 in my dataset. I can see in the formula that y2 ~ gamma *... so ist plotted against the rest of the term, but I dont know what Kind of value I need to plug in there. Does anyone have any advice?

Your y2 needs to be the output associated produced with those inputs. Given that you have a CES production function and you use World Bank Country data as inputs, you need output of the countries in that specific year. Typically we use GDP as a measure of output at country level. You can get it a.o. from the World Bank.


Can you use more than one instrumental variables in an Econometric model? Can you use two instrumental variables $z_1$ and $z_2$ at the same time for $x_1$ and $x_2$, in the following regression model

$y=a+bx_1+cx_2+dX_{other}+e$, where

$y$ is the explained variable,

$x_1$ and $x_2$ are two variables of interest that you want to study but are endogenous,

$X_{other}$ are other exogenous control variables,

$e$ is the error term.

If you have endogeneity between a dependent variable and error term the use of Instrument variables are the way to go.

as long as $\mathbf{COV}(x_1,z_1)\ne0,\mathbf{COV}(x_2,z_2)\ne0,\mathbf{COV}(z_2,e)=0$ and $\mathbf{COV}(z_1,e)=0$ you can do so.


Effects of finding infinite gold reserve Suppose an infinite reserve of gold was found. What would be the consequences to the economy in general. Would it have major negative effects?

The gold  will be free. (price 0 not anymore rare).

banks and others institutions will found others stuff for having reserve. ( platinum, silver, grains, maybe one day water ).


Effects of Robotics on the overall marginal propensity to consume Basically we know that poor and middle class workers have a high marginal propensity to consume as compared to rich people. Assuming that all of their jobs will be done by robots, and  only a few consumers with jobs are left, won’t the overall spending decrease and thus result in a sort of recession? This is if we assume that Rich people who know robotics have a lower marginal propensity to consume and a higher marginal propensity to save. What is your view?

If your assumption that "only a few jobs are left (primarily high-skill)" is true, then there are roughly two options:

people without jobs become redundant, meaning they will not reproduce anymore and disappear (pretty much as it happened to the horse). Here you end up with a society of a much reduced size, which will surely happen through some form of recession, or long stagnation period (kind of like a convergence to a new steady state. Naturally, this is very unlikely to happen in democracies (horses could not vote). An alternative is for many of the jobless to emigrate, but automation being a global force, this is just delaying the problem.
the few remaining jobs are shared among the people. As Keynes forecasted almost 90 years ago, technology could make a 15-hours working week possible. Thus, the fewer hours of work available can be shared among the population (which would require some re-skilling effort). Although I am skeptical this will ever happen in capitalism, at least it averts a big recession.
taxation becomes much more progressive, taxing the rich to provide subsidies to the jobless. An "extreme" form this could take could be the Universal Basic Income, or the Negative Income Tax, favourite of Friedman. Since robotics is to increase productivity and increase profits (by lowering the labour share), an UBI could be finances via taxation on profits. On the one hand, giving income to the rest of the population is likely to generate more demand for products and services, leading to more job creation and growth. On the other hand, these taxation systems could be combined with some form of "unproductive" work, like volunteering, community work, etc. There is plenty of evidence that employment is important for mental and social wellbeing (e.g. here), so simply providing income might not lead to socially desired outcomes. As Voltaire said,

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

In all three options (explicitly and drastically in the first option), fertility is likely to endogenously adapt to these changes, just as it has done so in the past. Likewise, political ideas also adapt to technological and cultural changes, so things like UBI, which before were not feasible, might become socially accepted. The call for UBI from some of the very rich might partly reflect this (or an instinct response of those benefiting from capitalism to save it from a potential crisis/revolution).

Having said all this, I would dispute your assumption that there will be no jobs for the low/middle skilled individual. Under alternative assumptions the three options mentioned above might not be the most likely options anymore.


A Special Case of Difference-in-Differences I remember reading a paper where the Difference-in-Differences was a bit special, but I had forgotten the details. My recollection was

Two time periods, specifically one time period before treatment and one time period after treatment.
The "treatment" was such that all firms had to comply with a certain share of a variable X.
The treatment group consisted of firms with very low (or zero) share of X before the treatment, and
The control group consisted of firms with a share already close to the required share of X before the treatment.

The idea was that the treatment group received most of the shock, while the control group was little affected.
Do you know a paper that uses such a framework?

Take a look at Ch 5 of Mastering Metrics (Angrist and Pischke) or their earlier "Mostly harmless econometrics".


Percentage/proportion of published papers with DSGE models I remember reading a few years back an article that showed an interesting graphic with the percentage/proportion of published papers with DSGE models across time. I've tried searching, but I get so many results related to DSGE, but not to what I'm looking for...

I'm looking for a reference with that graph.

You may have been thinking of a chart originally from The Economist Nov 24th 2016 article "Economists are prone to fads, and the latest is machine learning" though I cannot see it there.  There is a copy of the chart visible at Noah Smith's blog

It shows an analysis by The Economist of the key words in working-paper abstracts published by the National Bureau of Economic Research, with lines for laboratory experiments, randomised control trials (RCTs), difference-in-differences, regression discontinuity, machine learning or big data, and DSGE


Why do riskier investments pay more? I'm talking about bonds, stocks, and the sort.

I understand that an individual investor that's planning to invest, say, 50% of his savings, may require a higher expected gain to go for a riskier investment.

However, if risk can be diversified away, wouldn't people with enough money, even if they are risk averse, choose the investment opportunities with highest expected value and diversify among them? Wouldn't then any investment with higher-than-average expected value be flooded with money until they almost don't pay more?

Is it that...

most risky investment options are too correlated to allow for almost all of the excess risk to dissolve?
risk premiums only happen in markets with limitted access or that don't work like the ideal 101 market in a relevant way?
some other reason?

(1) You have already correctly pointed out that correlation makes it difficult to diversify away all the risk.

(2) You have also correctly alluded to the fact that most people are risk averse and hence that risky products tend to have a risk premium.

(3) What you have not mentioned -- and what I think is most important in the real world -- is the uncertainty premium.

The distinction between risk and uncertainty is usually credited to Frank Knight (1921, pp. 43–48).

Where we can quite precisely calculate probabilities and expected values, such as with lottery tickets and roulette wheels, we have risk. Where we cannot, such as with most real-world events, we have uncertainty.

Example. Asset $A$ pays $\$100$ with probability (w.p.) $1$ and so has expected value $\$100$.

Asset $B$ pays $\$300$ w.p. $0.5$ but loses $\$100$ w.p. $0.5$. So, the expected value of $B$ is: $$0.5 \times \$300 + 0.5 \times (-\$100) = \$100.$$

Each asset has the same expected value $\$100$.

(2) Nonetheless, because most people are risk averse, most people would prefer $A$ to $B$. That is, they'd be willing to pay more for $A$ than $B$. Or equivalently, $B$ would command a risk premium.

But any such risk premium should be small in the real world, since in the real world, as you've pointed out, there will probably be (i) ways to diversify away the risk; and also (ii) sufficiently many risk-neutral or risk-seeking individuals who bid away the risk premium.

(3) But the real world is rarely like the above example, which involves risk. The real world usually involves uncertainty:

Example. Asset $C$ is a US government bond that will pay out $\$100$.

Asset $D$ is a stock that -- based on your data, models, and analysis -- you expect will pay out $\$300$ w.p. $0.5$ but lose $\$100$ w.p. $0.5$.

Again, each of assets $C$ and $D$ has expected value $\$100$.

But now, even if you're risk-neutral, you'd probably prefer $C$ to $D$. That is, you'd pay more for asset $C$ than asset $D$. Equivalently, asset $D$ has an uncertainty premium.

The reason is that you do not (and should not) completely trust your data, models, and analysis. There are fundamental limits to your knowledge over and beyond mere risk -- we may call such epistemological limits uncertainty.


GDP per capita and trade relationship There's a lot of literature describing the relationship between growth and trade, but I'm not sure what conclusions I can draw from GDP per capita (specifically) and trade in one particular year for multiple countries. The graph is a regression I ran, so the red line demonstrates a positive relationship between the two variables in that year. But I'm also confused because the R squared value is very low, indicating a weak relationship. Is this because I have included too many countries in the test or because of the many other factors playing a part? Apologies as this question is probably quite stupid, but I'm very confused.

The task: "The United Kingdom government has asked you to write a report on the relationship between gross domestic product (GDP) per capita and trade openness. In particular, they would like to know whether the sum of exports and imports as a percentage of GDP had a positive effect on GDP per capita in 2015. To allow you to do this, they make available data on GDP per capita, exports of goods and services and imports of goods and services. GDP per capita is measured in constant 2010 United States dollars and exports and imports are expressed as a percentage of GDP."

The reason that relationship weak is that there is a whole lot more influencing GDP than just trade. Not included in this analysis are things like commodity prices, types of exports, quality of institutions in a country, population. Countless others.

If you wanted to test the hypothesis that countries with higher levels of trade tend to be larger, you probably have. With such a simple analysis, it's probably hard to get much more than this.


What is the calculable effect of counterfeiting on an economy? I'm curious whether one can numerically calculate the effect that counterfeiting has on an economy.

As I understand it, counterfeiting essentially amounts to theft of the wealth of everybody holding units of that currency. For example, say you have an economy with 100 units of currency currently circulating. Bob creates 100 fake units of currency. If he does nothing but leave them in his safe, then the economy is unaffected. However, if he spends all of them, he will get goods and services in exchange for nothing of value. This is the theft. Him introducing his 100 fake units into the economy doubles the money supply, which will eventually more or less lead to a doubling in the price of everything (but not necessarily).

So now, if Dave had 10 units of currency his purchasing power was X. However, after the counterfeiting and doubling of the money supply and thus more or less doubling of prices, his purchasing power is X/2. Likewise for anybody who was holding that currency.

So, is it correct to say that in an economy with X currency units, counterfeiting and spending Y fake units is equal to theft of Y/(X+Y) of the wealth of the economy?

e.g. Given 100 legit units and counterfeiting and spending 200 units, 2/3rds of the wealth was stolen?

If not then what is the effect?

I'm adding this as a separate answer because it's quite independent of my other answer.

We've agreed that if there are X dollars existing and you counterfeit Y dollars, then you've stolen Y/(X+Y) of the value of those X dollars.

This assumes you do your counterfeiting all at once, and without warning.

If instead you do your counterfeiting slowly over time, or if it can be anticipated, then there's an additional effect:  people try to rid themselves of money holdings in order to avoid being stolen from.  (That is, they try to trade dollars for goods before the dollars lose value.)

This is costly to the moneyholders, with no offsetting benefit to anyone.  One way to see that it's costly to moneyholders is that they now own less money, which makes their lives less convenient.  A different way to see that it's costly to the moneyholders is that the rush to trade money for goods bids up prices, which lowers the value of money.  (These are not two different costs; they are two different ways to think about the same cost.)

So in this case, you have stolen more than Y/(X+Y) of the value of originally existing money, but kept somewhat less (because by the time you get to spend your dollars, they're worth less than dollars were worth at the outset).  The difference between what you steal and what you keep simply dissipates.


How does the Fed measure the shadow banking sector in the US? It's apparently popular to say on TV [at 2:20 in that clip] that the Fed has no idea what's going on in shadow banking sector. To what extent is that true? (I could ask this on Skeptics as well given format/claim, but I suspect I'll get better answers here).

Or, polemics aside, how does the Fed measure the shadow banking sector in the US?

Well before going to measurement I think it’s appropriate to start by definition. The term shadow bank is not always 100% consistently applied but most often the a shadow bank is defined as follows:

  Shadow banks are financial intermediaries that conduct maturity, credit, and liquidity transformation without explicit access to central bank liquidity or public sector credit guarantees.

This is how you see shadow banks defined a lot in research (and also other definitions come close). Moreover, this is definition used in research coming from Fed such as  this paper from NY Fed or this paper from St Luis Fed for example.

To my best knowledge there is no unified measure/indicator that’s being recorded (like let’s say GDP/inflation). Rather like this literature review from NY Fed mentions people take the definition of shadow bank and then calculate the proportion of for example financial liabilities hold by shadow banks relative to ordinary banks or other types of financial institutions. Maturity and credit transformation calculated as proportion per type of bank is also used. In wider research I have seen other measures as well.


How are purchasing power parity (PPP) conversions computed? How are purchasing power parity (PPP) conversions computed?

I guess that goods' and services' prices are compared across different countries/currencies. However, there are services such as healthcare or university education that some countries (e.g, EU countries) provide as universal rights and are "free" (paid by "taxes"), whereas within other countries those services/coverages are to be paid directly by people. So I don't know how these important differences are taken into account when computing PPP conversion.

The calculation of PPP is a very complex, resource consuming task. As you can imagine, coming up with a single number comparing countries relative purchasing power means many assumptions have to be taken (i.e there is a trade-off between realism and simplicity).
The most comprehensive documentation relating the methodology behind PPP can be found in this World Bank website. Here I just give a brief idea of what's going on. Check the documentation for further clarity (particularly Chapter 4).
The calculation of PPP goes in stages. First, data on prices of individual products within a basic heading (a macro category, e.g. food) is computed. From here, relative prices for each product across two countries are computed, and aggregated at the basic heading level using a geometric mean. An example is given in Table 1 of Chapter 4, copied below:

Then, an important issue is product choice. Comparability depends on products being relatively homogeneous in both countries, so that table above can be filled in completely. This requires an adjustment for product quality when necessary (e.g. mobile phones), part of which is adjusted using hedonic regression (see page 15+ of Chapter 4). Additionally, products must be representative on each country, simply defined as (see point 7 in Chapter 11 for a technical definition):

A representative product is one that is purchased in relatively large quantities in a country.

Several mechanism are used to adjust for imbalances among these two factors (including weights).
The list of problems continues. Which price to include? As the documentation states:

The price at which any single good or service is purchased is liable to vary considerably during the course of a year and also between different locations, especially in large countries. In these circumstances, the PPPs for individual products have to be defined as ratios of average prices.

Finally, Chapter 8 deals with Government services like health and education, There is a differentiation between individual services (household consumed) and collective services (public goods). Most of education and health as services provided to the individual is the former, whereas others like R&D in education and health is the latter. See Box 1 in Chapter 8 for a complete list.
The valuation of these services is an issue. A quote in extenso might help here:

Most of the individual and collective services produced by government are non-market services.   They are either provided free to individual households or the community as a whole or they are sold at artificially low prices that do not reflect their costs of production.   As there are no market prices the value of the government’s current expenditures on non-market services has to be estimated in the national accounts by the current value of the inputs used to produce them.  Similarly, as there are no market prices the PPPs also have to be estimated indirectly using other data.  The same problem arises when trying to measure changes in the prices of government services over time within a single country.
The solution usually adopted in both international and intertemporal price and volume indices is to compare the prices and volumes of the inputs used in the production of non-market services instead of the prices and volumes of the outputs.  When the PPPs compare input prices the resulting expenditure data when converted into a common currency compare the volumes of the inputs used up in the production of non-market services in different countries.   Input volume indices inputs can provide close approximations to output volume indices but only if the ratios of outputs to inputs, i.e., productivity levels, are the same in different countries.    This may often not be case.   PPPs based on input prices are therefore second best measures that are necessitated by the lack of output prices

See the chapter for more details.
In conclusion, there is an attempt to provide homogeneity across goods and services. But there are many reasons why perfect comparability might not be achieved. In the case of government services, if inputs do not reflect outputs homogeneously across countries (partly due to productivity differences, as highlighted above), this will affect PPPs.


Macroeconomic model or knowledge base representing connected industries in the world I'm looking for data (model, Expert system, knowledge base) that describes how different industries and countries interact with each other. And the nature of the relationship between them.
An example of such a relationship could be the recent covid-19 crisis.
The crisis forced countries to close the borders, which affected travel, and hospitality industries in a negative way. But the lockdown and people's inability to go shopping led to profits of shipping companies.
Is there a database/API/graph or any source of data showing this kind of connection between industries and the nature of that connections? Some books research papers discussing such a model?
Some question that might be answered with this data:

What will happen if say, Belgium (or any country), would force 'iron curtain' on itself and stop all economic activity with the rest of the world. What industries, in the world, might be affected?
What industries will be affected if the USA banned oil production?
What industries rely on Maritime transport? If for some reason only 10% of all Maritime transport will be operational what industries will increase their profit and what industries register a loss?

The other question is, knowing that the world is infinitely complex, is it even possible to have such a model, even on the macro level?

is it even possible to have such a model, even on the macro level?

Yes, it is entirely possible. There are large scale general equilibrium models that would be able to answer those sort of questions. For example, the questions you are asking could be answered with dynamic stochastic general equilibrium (DSGE) models.
Namely, you want some large-scale multisector DSGE model (there are smaller versions where you will lump multiple sectors together), such as the multisector DSGE model used by  Antosiewicz & Kowal 2016 for investigating effect of CO2 emissions reductions mandated by policy on the economy. In fact based on your description you likely want to go even bigger and include more equations - that is still doable, once you know how to make 2 sector DSGE model adding more sectors is just question of having data and enough time (usually large and detailed DSGE models are built by large teams not individuals).
You would likely want to first start by studying some simple cases though. Macroeconomic Theory a Dynamic General Equilibrium Approach by Wickens is good introduction.
Alternatively, you could also model it via old school input-output tables in some sort of Leontief model, but that would likely be less accurate than the above. However, if you are planning to do this just for fun that would be easier.

Is there a database/API/graph or any source of data showing this kind of connection between industries and the nature of that connections?

This sort of question cannot be answered with raw data. For example, if data would show that there is 500 mil ton of fish imported into Belgium from outside, you can't just assume that Belgium will have this amount of fish less because under autarky Belgium could increase its production of fish at the expense of other industry so you always need some model for tracking all the effects through the economy.
As for data, you have to be more specific. There is no single 'uber'-economics-dataset that would have all economic data in the world. For most EU countries you could get necessary data from their statistical offices. For example, for the Netherlands you would likely be able to find most data you need if not all at CBS (it is hard to say unless you precisely specify the model).


Does Progressive Taxation Actually Follow The Decreasing Marginal Value of Wealth? From my understanding, the application of a progressive income tax (increasing rate based on income level) follows from the assumptions of: "Equal Sacrifice" - everyone's "sacrifice" should be the same, and the "Decreasing marginal value of wealth" - the actual value inherent in receiving an additional unit of money is less for someone with more money.
My question is, then, to what extent do modern progressive income tax systems match money's "actual" quantity/value curve? Presumably this curve is something that could be estimated/calculated/measured, correct? But as far as I'm aware, no modern taxation system is set with respect to any theoretical or actual quantity/value curve for money.

tl;dr
No they do not for several reasons:

Your post is based on misinformation, I know of no work on optimal income taxation that would aim to 'equalize sacrifice' (heck you would not find such philosophy even among most relevant moral/political philosophies). Consequently, the whole premise is false, and you would not even expect to see arguments in favor of implementation of and implementation itself of such tax system.
Even if your question would be rephrased to whether governments generally set marginal tax rates as dictated by optimal taxation literature the answer would be again negative. Generally speaking, politicians for better or worse are simply not interested in optimizing income tax rates (from societal perspective - of course, they likely do optimize it in a way to curry political favors).

Correction of Misinformation in The Question
Let me first address some misconceptions/misinformation in your question before answering the question:

From my understanding, the application of a progressive income tax (increasing rate based on income level) follows from the assumptions of: "Equal Sacrifice" - everyone's "sacrifice" should be the same, and the "Decreasing marginal value of wealth" - the actual value inherent in receiving an additional unit of money is less for someone with more money.

This is incorrect understanding of optimal taxation literature.

We are talking about optimal income taxes so marginal value of wealth does not even enter the calculation here. Optimal income taxation is as the name says about optimizing income taxation, and thus what enters optimal income taxation problems is marginal value of income.

From my understanding, the application of a progressive income tax (increasing rate based on income level) follows from the assumptions of: "Equal Sacrifice"

I am not sure where you (mis)heard the above, but it is extremely inaccurate statement.
They are based on the following optimal non-linear tax function which comes from the seminal works of Mirrlees (1971) (who in fact got Nobel Prize in Economics for this contribution), Diamond (1998) and Saez (2001). The optimal marginal income tax will be given by:
$$ \frac{T'(z_n)}{1-T'(z_n)} = \left( 1 + \frac{1}{\epsilon_{lT}} \right)\frac{\int (1-b_m)f(z_m)dz_m}{1-F(z_n)} \frac{1-F(z_n)}{z_nf(z_n0)}$$,
with $b_n \equiv \frac{\Psi'(u_n)u_c}{\eta}+ nT'(z_n) \frac{\partial l_n}{\partial \rho} $.
I wont go over every single term in the formula as this would turn this answer into a book but broadly speaking the first part $\left( 1 + \frac{1}{\epsilon_{lT}^*} \right)$ is given by elasticity of labor supply to income taxes and you can think of it as an 'efficiency' parameter, the second part $\frac{\int (1-b_m)f(z_m)dzm}{1-F(z_n)}$ tells us what the marginal benefit of redistribution is and this marginal benefit factors in underlying actual welfare which is captured by $b_n$ which depends on both utility of consumers and the societal utility function,  and finally $\frac{1-F(z_n)}{z_nf(z_n0)}$ is the part that captures the relative magnitude of distortions created by this taxation. Again since we are talking about improvements in actual underlying utility what the aggregate price level is does not matter.
Now utility does enter the problem via $b$, but there is no principle of equal sacrifice or anything like that.

It is correct to say that people with concave utilities will have diminishing marginal utility of income (they will also have diminishing marginal utility of wealth but this is optimization of income taxes not wealth taxes). However, this has almost no effect on the progressiveness of optimal tax rates and actually does not affect the shape of marginal tax rate schedule that much.
What is far more important is what is the societal welfare function which assigns welfare weights to each individual. Here most commonly used societal welfare functions are (e.g. see Saez 2011):

A) Utilitarian social welfare function -  This social welfare function is based on the idea that poorer people value on a margin 1 dollar more than richer people - but by no means it implies 'equal sacrifice'. As a matter of fact if there would be no efficiency cost to taxation a utilitarian would make all incomes completely equal since if there is any person anywhere with higher income than someone else that means aggregate utility could be increased by moving that dollar from higher income person to poor person. Utilitarians  are not trying to make sure everyone sacrifices equal utility - they care about maximizing total utility.
B) Rawlsian social welfare function - This is based on Rawlsian MaxMin idea which states that it is moral to maximize the welfare of the poorest members of society (Rawls (1971), Theory of Justice p. 152). This welfare function gives welfare weight of 1 to the poorest member of society and everyone above zero (of course, in process of redistribution someone else becomes the poorest one - don't interpret this in a way that all redistribution goes to single person). Tax systems based on this function are as far from idea of equal sacrifice as possible. This social welfare function literally does not give a damn about sacrifice of anyone else than a poorest member of society and taxation and redistribution will occur to the point that it generates so much distortions that government is simply not able to make a positive redistribution (in terms of welfare) to the poor anymore.
C) Charitable conservative/Libertarian social welfare function - This one is typically also based on MaxMin criterion with a twist that although poorest still get welfare weight of 1 people who are not poorest also get some non-zero welfare weights (Atkinson 1995 and Diamond 1998). Again nothing to do with idea of equal sacrifice when it comes to utility.

What has the major impact on whether tax system is progressive or not actually does not depend that much on either of the above mentioned but primarily on the shape of income distribution.

For example, early Mirrlees (1971) and Tuomala (1984) simulations based on assumption of log-normal distribution yielded regressive (but approximately linear) marginal tax rates even under maxmin or utilitarian scenarios (e.g. see example below).

The true reason why modern optimal income taxation shows that tax system is progressive is that we later empirically discovered that log-normal distribution does not fit data nicely because income distributions seem to have pareto-tail (e.g. see Saez 2001). If we switch from log-normal income distribution to log-normal distribution with pareto tail suddenly we get progressive tax rates as you can see below under both utilitarian and maxmin scenario (the marginal tax rates are high for poor due to redistribution but average tax rates are progressive here).

So the premises of your question are prima facie wrong. Even though it is probably at least in principle possible to derive some new social welfare function that would be about  equal sacrifice, I know of no published research or even famous economist advocating such principle. The shape of an optimal marginal income taxes is primarily determined by shape of income distribution, different moral philosophies typically stretch or squeeze it or move it up and down (of course, one can create arbitrary moral philosophy and some would probably change a shape itself significantly but that is not what you will see with the usual ones).
Answer

My question is, then, to what extent do modern progressive income tax systems match money's "actual" quantity/value curve?

If I reinterpret this question about asking whether modern progressive income tax systems match the ones prescribed by optimal income tax calculations, the answer is that they simply generally don't. If they do it is often by accident rather than an intent.
For example, below you can see simulation of utilitarian and Rawlsian optimal marginal tax schedules in the Netherlands compared to the real observed ones from Zoutman et al (2012):

First as you can clearly see the utilitarian optimal marginal tax rate is completely different from the real observed one (although they intersect at 1 point).
Second, the optimal income taxation under Rawlsian scenario also intersects the real marginal tax rates only at a single point, although here above about 80000 euro income the optimal marginal income taxes are more close to the real observed ones, they still not match, and below 80000 euro they completely diverge.
The result that you see above for the Netherlands is not unique (it is not possible to go over all literature and all simulations in scope of SE answer but I never seen work that would show real life progressive marginal tax rates match the optimal ones), even though many countries have different tax codes in most countries you will get match between optimal marginal income tax schedule and real marginal income tax schedule at best at a single point (in case they cross) but often not even that. This is typically explained by the fact that taxes are determined via democratic processes so we should not even expect them to match anything what is predicted by optimal taxation literature. In fact, as shown and argued by Zoutman, Jacobs & Jongen (2016) real world tax systems are often set up to give some extra weights to middle/upper middle class and this is argued to be due to their political importance.


How is the Solow residual measured? In the Solow model, we have the Solow residual often referred to as the level of technology A.

More particularly : \begin{equation} Y(t) = [K(t)]^{\alpha}  [A(t)L(t)]^{1-\alpha} \end{equation}

Here it is defined as "is the portion of output not explained by the amount of
inputs used in production" though there's an explanation of its fluctuations, I still do not understand how it is calculated.

This paper from the National Bank of Belgium does leave me a bit confused because several measurements are said to be used but it sometimes sounds as if one took the total output for a year and substracted what wasn't explained directly by labour and capital, to obtain the residual?

I'm not really sure how it is measured and where said measurements even come from,

Can someone point me to an answer?

Thanks for your time,

Nate

Below please find a portion of a lecture slide a professor of mine used last year. Please note that $\gamma_{\tilde{y}}$ denotes per-capita output growth, $\gamma_{\tilde{k}}$ denotes per-capita capital growth and $\alpha(t)$ denotes the income share of capital. $R(t)$ - the Solow residual - can then be easily computed.

The production function you have stated was the one we used for this example. So it can be applied here directly.

Source: "Growth and Business Cycles" lecture by Professor Gerhard Sorger, University of Vienna


finding the returns to scale of a production function Find the returns to scale for he following production function- $(x_1 + 1)^.5 (x_2)^.5$

My attempt,
Let $f(x_1,x_2)=(x_1 + 1)^.5 (x_2)^.5$
And $g(x_1,x_2)=(x_1)^.5 (x_2)^.5$
Now,
$(x_1 + 1)^.5 (x_2)^.5$
$>$
$(x1)^.5 (x_2)^.5$
Therefore,
$f(x_1,x_2)>g(x_1,x_2)$
Or, $f(tx_1,tx_2)>g(tx_1,tx_2)$ for some t>0
$>(tx_1)^.5 (tx_2)^.5$
$=t(x_1)^.5 (x_2)^.5$
$=tg(x_1,x_2)$
The function g exhibits constant returns to scale. The function f being bigger than it should exhibit increasing returns to scale. The answer given, however, is decreasing returns to scale. Where am I wrong? Thank you in advance.

What you have proven is that $$f(tx_1, tx_2) > tg(x_1,x_2)$$

which translates "scaled $f$ is higher than some other, homogeneous function $g$ scaled by the same factor". This does not prove anything about the returns to scale related to $f$, although I can see why it may appear otherwise.

You can go in reverse, starting from

$$tf(x_1,x_2) = t^{0.5}t^{0.5}f(x_1,x_2)=...$$

and compare to $f(tx_1, tx_2)$.

Also beware about the following: what are the permissible values for $t$ when returns are not constant? Are you sure we should obtain the result for $t>0$, or maybe we examine the property for a smaller interval?


Are the figures quoted in this liblabcon's blog post accurate? (topic: UK banks) Background

With regards to the UK government.

I have recently been involved in a debate stemming from figures mentioned in this blog post (the blogger was advocated by Occupy London's facebook page and verifying the level of "over-sensationalism" portrayed in the post would make or break my relationship with them both).

Here are the bare bones of what the blog post claims:

  Bankers cost this country £456.3bn in fraud.

  People on the dole cost this country £1.6bn in fraud.

  0 bankers are sent to prison for fraud.

  6000 people on the dole are sent to prison for fraud (/yr).

  Politicians had to bail the bankers out with £1.2tn, leaving the
  next generation with 3 times more tuition fees to pay.

I did post (twice) on that blog post, asking for citations, but they have not yet replied. So I turn to Stack Economics for the first time for help with either verifying/debunking two claims (100 rep points is not from involvement on stack:economics):

Questions

(i) Where (if anywhere) does the £456.3 billion come from?

(ii) Where (if anywhere) does the £1.2 trillion come from?

Source:- Bankers cost this country £456.3bn in fraud

  In the UK, where the government bailed out Royal Bank of Scotland Group Plc (RBS) and Lloyds Banking Group, the total outstanding support explicitly pledged to Britain’s banks stood at 456.3 billion pounds ($730 billion) at the end of March, or 31 percent of GDP, the National Audit Office said in a July report. The amount was down from a peak of 1.16 trillion pounds.

Source:- Politicians had to bail the bankers out with £1.2tn, leaving the next generation with 3 times more tuition fees to pay.

  The Treasury has pledged to spend £1.2 trillion on the bail-out since the crisis began. But the real outlay has been much smaller. By March it was committed to spending £456.33bn: £123.93bn in loan or share purchases, which required an actual cash injection from the government to the banks, and £332.4bn in guarantees and liabilities. It costs taxpayers up to £5bn a year just to service the loan that the crisis incurred.

The idea seems to be more to create noise rather than putting facts into perspective. The 2 lines in isolation are damning, but when you read the whole thing it seems to make a bit more sense. Seems more at fear mongering rather than putting the facts into perspective.


Name for a slightly-stronger than Nash Equilibrium? As I understand it, a Nash Equilibrium is a fixed point in strategy profile space, in the sense that it is not to any individual player's advantage to deviate from said strategy profile.

Is there a name for the (slightly stronger) equilibrium condition whereby it is to every individual player's disadvantage to deviate from said strategy profile? If so, what is it?


When estimating a basic macroeconomics model, why is goodness of fit with labor data not often dealt with? So when dealing with not-too-complex RBC models or New Keynesian models, we often arrive with a few final reduced-form equations, and as far as I know, we use these equations to estimate the model. For Gali's simple New Keynesian model we have consumption Euler equation, New Keynesian Phillips Curve and some form of Taylor rule.

But it seems that when estimating them, labor data (for example, labor $N_t$ in production function $Y_t = A_tN_t^{1-\alpha}$) seems to be dropped and not compared with model's prediction that can be inferred from coefficients and how reduced-form equations got derived.

Why is this comparison not often done? This seems to be an important indicator for a model..

It's somewhat public knowledge that Macroeconomic models don't fit labor data without

High Frisch Elasticity (but Rogerson, Prescott try to argue for that)
Preference shocks (but, as Chari, Kehoe, McGrattan (AER 2006?) show, we cannot really understand these properly
Search&Matching with weird parametrization or assumed wage rigidity
Some other spooky thing going on that helps fitting the data

So since we know it doesn't work out, why feel bad about posting the correlations and make everyone feel bad? :)

If it were to work out, surely post it though.


Utility function is given as U(x1, x2) = 10x 0.5 1 + 5x2 Given a utility function $U= {10x^{0.5}} + 5y$, calculate the MRS and explain its economic meaning.

The MRS I calculated is $\frac{1}{\sqrt{x_1}}$, but I can't really understand it's economic meaning or how to derive its indifference curve. Some help please?

The MRS represents the rate of exchange between goods x and y that would leave the agent indifferent to trading the two. It is the slope of the indifference curve for a given value of utility U.

To derive the indifference map (the set of indifference curves), take U constant in the utility function, and solve for y in terms of x. You can check if your MRS calculation is correct by taking the first derivative of your indifference map function.


Preference over lotteries without independence axiom Suppose a set of $N$ outcomes can be ranked in the following order: $1\succ 2\succsim\cdots\succsim N$. Further, suppose a decision maker has preference over lotteries over these outcomes. Assume the preference over lotteries is rational, continuous, but not necessarily consistent with the independence axiom.

Does it follow that the best lottery in this case is the degenerate lottery $(1,0,\dots,0)$?

What if the independence axiom is violated?

No, not necessarily. Without the independence axiom (or something else to replace it) there is not much you can infer about preferences over (non-degenerate) lotteries from knowing preferences over outcomes only.

For instance, let $p^L_n$ be the probability of outcomes $n \in \{1, 2, 3\}$. Then preferences  over lotteries $\succeq^*$ represented by the utility function

$$U(L) = p^L_1 + \beta [p^L_2p^L_3],$$

are continuous  and rational, but do not satisfy the independence axiom. For $\beta$ large enough, it is not even the case that $(1,0,0)$ is the best lottery, although $(1,0,0) \succ^* (0,1,0)$ and $(1,0,0) \succ^* (0,0,1)$.

To see why, observe that

$$ U(1,0,0) = 1, $$
$$ U(0,1,0) = 0, $$
$$ U(0,0,1) = 0, $$

However, for $\beta > 4$,

$$ U\left(0,\frac{1}{2},\frac{1}{2}\right) > 1 .$$

Violation of the independence axiom can be seen from the fact that, when $\beta > 4$,

$$ [1,0,0] \succ [0,1,0]  ,$$

although

$$ \left[0,\frac{1}{2},\frac{1}{2}\right] \succ \left[ \frac{1}{2}, 0, \frac{1}{2}\right]. $$


Cournot oligopoly - first-order condition I am reading an article that has this description of the first-order condition for a Cournot n-firm game:
Take $P(Q) = Q^{-1}$, $\pi_i(q_i, Q) = (Q^{-1} - c_i)q_i$.
Then the first-order condition for an interior profit-maximizing choice of $q_i$ requires that
$$ \frac{\partial \pi_i}{\partial q_i} + \frac{\partial \pi_i}{\partial Q} = Q^{-1} - c_i - q_iQ^{-2} = 0.$$
I am trying to understand why it is OK to simply take $\frac{\partial \pi_i}{\partial Q}$ ignoring the fact that $Q$ is actually a function of $q_i$. If I expand the term so that $Q = q_i + q_{-i}$ and take the partial derivatives $\frac{\partial \pi_i}{\partial q_i} + \frac{\partial \pi_i}{\partial q_{-i}}$, the solution is not the same as the one that is written in the article. Would appreciate any explanation.

Note :$Q = \sum_{i=1}^n q_i$.
Thus the optimisation problem of firm $i$ is:
\begin{align}
max_{x_i\in\mathbb{R}_+}\pi_i(q_i,Q)
\end{align}
where $\pi_i(q_i,Q) = \big(Q^{-1}(q_i;q_{-i}) -c_i\big)q_i$. Assuming interior solution, the first order condition is
\begin{align}
\frac{\partial\pi_i}{\partial q_i} + \frac{\partial \pi_i}{\partial Q}\frac{\partial Q}{\partial q_i} &= 0\\
\implies (Q^{-1} - c_i) + (-1)Q^{-2}q^*_i* 1 &= 0\\
\implies q^*_i &= Q(1-Qc_i)
\end{align}


What's a good textbook on International Trade? My professor for Int. Trade insists on using his unfinished notes as a basis for the class, so I'm looking for an alternative.

The syllabus goes as follows:

Gains from trade

Free trade equilibrium and offer curves

Applications of the basic trade model
Tariffs and welfare

Trade preferences

The Ricardian model

The hecksher ohlin model- fixed coefficients

The theory of international capital flows

As background: by this point we've had a few micro and macro courses, industrial organization, public economics, game theory, optimization, and linear algebra.

Thanks in advance

International Economics by Alan M. Taylor and Robert C. Feenstra is a good alternative, as International Trade by John Mclaren, which is more original.

If you look for a more advanced textbook, which discusses the underlying assumptions of the trade models, the reference is Advanced International Trade by Robert C. Feenstra.


Evaluation around steady state for a specific DSGE Model The following equations are taken from Ravenna, walsh: "Optimal Monetary Policy with Unemployment and Sticky Prices" (2011).

(i)$$\frac{Z_{t}}{\mu_{t}} = w_t + \frac{\kappa}{q_{t}} - (1-\rho)E_{t}(\frac{1}{R_{t}})(\frac{\kappa}{q_{t+1}}) $$

(ii) $$ w_{t} = w^u + (\frac{b_t}{1-b_t})(\frac{\kappa}{q_t}) - (1-\rho)E_t(\frac{1}{R_t})(1-p_{t+1})(\frac{b_{t+1}}{1-b_{t+1}})(\frac{\kappa}{q_{t+1}}) $$

$ \phi $...  wage replacement rate

$b_t$... surplus bargaining share of a worker

$Z_t$... exogenous productivity shock ($\bar{Z}=1$)

$\mu_t$... retail price mark up

$\kappa$... post of posting a vacancy

$\rho$... Share of matches $N_{t-1}$ that loses its jobs in t

$q_t$... probability that a firm will fill its vacancy

$\lambda_t$... marginal utility of consumption

$\frac{1}{R_t} \equiv \beta(\frac{\lambda_{t+1}}{\lambda_t})$

$p_{t+1} \equiv \frac{m_t}{u_t}$... job finding probability with $m_t$ matches and $u_t$ unemployed ones

$\beta$... discount factor

$w^u = \phi w $

Given the last identity, (i) and (ii) could be used to jointly solve  for $\kappa$ and $w$. At least this is suggested in the paper by the atuhors.

(ii) $w_t = \phi w_t + (\frac{b_t}{1-b_t})(\frac{\kappa}{q_t}) - (1-\rho)E_t(\frac{1}{R_t})(1-p_{t+1})(\frac{b_{t+1}}{1-b_{t+1}})(\frac{\kappa}{q_{t+1}})$

<=> $w_t = \frac{(\frac{b_t}{1-b_t})(\frac{\kappa}{q_t}) - (1-\rho)E-t(\frac{1}{R_t})(1-p_{t+1})(\frac{b_{t+1}}{1-b_{t+1}})(\frac{\kappa}{q_{t+1}})}{1-\phi}$

Put into (i) to eliminate $w_t$

$\frac{Z_{t}}{\mu_{t}} = \frac{(\frac{b_t}{1-b_t})(\frac{\kappa}{q_t}) - (1-\rho)E_t(\frac{1}{R_t})(1-p_{t+1})(\frac{b_{t+1}}{1-b_{t+1}})(\frac{\kappa}{q_{t+1}})}{1-\phi} +\frac{\kappa}{q_{t}} - (1-\rho)E_{t}(\frac{1}{R_{t}})(\frac{\kappa}{q_{t+1}}) $

<=> $\frac{Z_{t}}{\mu_{t}}(1-\phi) = (\frac{b_t}{1-b_t})(\frac{\kappa}{q_t}) - (1-\rho)E_t(\frac{1}{R_t})(1-p_{t+1})(\frac{b_{t+1}}{1-b_{t+1}})(\frac{\kappa}{q_{t+1}}) +\frac{\kappa}{q_{t}}(1-\phi) - (1-\rho)E_{t}(\frac{1}{R_{t}})(\frac{\kappa}{q_{t+1}})(1-\phi) $

Rearrange and solve for $\kappa$:

$\frac{Z_{t} (1-\phi)}{\mu_{t} ((\frac{b_t}{1-b_t})(\frac{1}{q_t}) - (1-\rho)E_t(\frac{1}{R_t})(1-p_{t+1})(\frac{b_{t+1}}{1-b_{t+1}})(\frac{1}{q_{t+1}}) +\frac{1}{q_{t}}(1-\phi) - (1-\rho)E_{t}(\frac{1}{R_{t}})(\frac{1}{q_{t+1}})(1-\phi)} = \kappa $

<=> $\kappa = \frac{Z_{t} (1-\phi)}{\mu_{t} \big(\big(\frac{1}{q_t}\big)\big[(\frac{b_t}{1-b_t})+(1-\phi)\big] - (1-\rho)\big(\frac{1}{q_{t+1}}\big)E_t\big(\frac{1}{R_t}\big)\Big[(1-p_{t+1})\big(\frac{b_{t+1}}{1-b_{t+1}}\big)+(1-\phi)\big]\big)}$

Evaluating this formula arount the steady state yields

$\bar{\kappa} = \frac{(1-\phi)}{\bar{\mu} \big(\big(\frac{1}{\bar{Q}}\big)\big[(\frac{b}{1-b})+(1-\phi)\big] - (1-\rho)\big(\frac{1}{\bar  {Q}}\big)\beta\Big[(1-\frac{\bar{M}}{\bar{U}})\big(\frac{b}{1-b}\big)+(1-\phi)\big]\big)}$

Since all this parameters and steady state values are well defined I am able to calculate the steady state value of $\kappa$ and hence the one of $w_t$ as well.

I wanted to simulate the related model in dynare. Having a look at the dynare code provided by the authors, I noticed that they made use of a totally diferent approach to calculate the steady state value of $\kappa$:

$AAk = \left[{\begin{array}{cc} 1-\phi(1-b) & -\phi b(1-\rho)\beta \bar{\theta}\\ 1-b & (1-\beta(1-\rho))(\frac{1}{\bar{Q}})+ b\beta(1-\rho)\bar{\theta}  \end{array} } \right]$

$BBk = \left[ {\begin{array}{cc} \frac{\phi b}{\bar{\mu}} \\ \frac{(1-b)}{\bar{\mu}} \end{array} } \right] $

$CCk = AAk^{-1}BBk$

$\bar{\kappa}=CCk(2)$

Where

$\theta_t=\frac{v_t}{u_t}$ measures the labor market tightness (relation of vacancies and job seekers)

I would like to know whether my derivation of the steady state value for $\kappa$ does make sense and how the authors of the paper derive it?
I have read the appendix to the paper aswell as the dynare code, but to be hones I do not have an idea of how they calculate $\kappa$.

The results of my calculation and the one of Ravenna and Walsh differ significantly.

I found the error in my derivation: I mistakenly supposet that the steady state of $p_t+1$ equals $\bar{\rho}$.
I did not recognize that p was different from $\rho$ because of the poor quality of my printout.
Reading the paper again on a screen I immediately spotted the mistake.


Why does the EU need a clearing centre to circumvent US sanctions against Iran? As reported here and elsewhere, the EU is considering the creation of a clearing house to keep trading with Iran despite US sanctions. Why is it not possible for the EU to conduct normal financial transactions with Iran without the involvement of US institutions?

Because the US has threatened to sanction European companies that trade with Iran.  Most European companies that are interested in trading in Iran also trade with the US, so would be vulnerable to various kinds of sanctions.


Textbook/Reading Suggestions for Urban Economics I have a pretty straightforward question. What sort of textbooks or graduate readings are there for urban economics that you would personally suggest and why? Preferably I would like one that has practice exercises/proofs in them that I can use. I've seen a few books that look like graduate texts out there, but don't know much about what's in them, so I figured some people here might.

Masahisa Fujita is considered as one of the most famous theorist in urban economics. He is one of the pioneers of the New Economic Geography. His book
Urban Economic Theory: Land Use and City Size, 1989, Cambridge is a master piece, laying down the theoretical foundations of urban economics. Also, you may read

Fujita, Masahisa; Krugman, Paul; Venables, Anthony J. (1999). The
Spatial Economy: Cities, Regions, and International Trade. Cambridge,
Massachusetts: MIT Press.
Fujita, Masahisa; Thisse, Jacques-François (2013). Economics of
Agglomeration: Cities, Industrial Location, and Regional Growth (2nd
ed.). Cambridge University Press.

Esteban Rossi-Hansberg from Princeton is a rising star in urban economics. You may check out his syllabus, which is pretty useful. He does not recommend any textbook, and provides a more modern approach.


difference between screening game and moral hazard game What is the difference between screening game and moral hazard game?

I know that in screening game, TYPE is not known by the principal, while in moral hazard game, EFFORT is not observed by the principal. But what is the key difference between two settings, rather than what we call it? I mean, effort can also be considered as type....

Thanks

Moral hazard models feature agents' hidden actions (or these actions are not contractible). For example, a manager's contract cannot determine a wage contingent on the manager's effort, only contingent on other observable outcomes such as "success" / "no success" of a project.

The next two classes of models assume that actions are observable/contractible, but entail different costs to different unobservable types.

In screening models, a principal offers a contract to a privately informed agent. It is not an action, but an inherent type which is not known. For example, a seller does not know a buyer's willingness to pay. Taking the manager example, the principal would offer different contracts for different "manager types" (e.g., "motivated+productive" / "not motivated+unproductive") in which the "effort level" is already set (and by assumption is observable and contractible such as "hours worked"). Then manager types could self-select into the different contracts as working hours are less troublesome for the 'motivated type'.

Another interesting class of models are signaling models. Here the informed party moves first and offers the contract. Taking the same example, motivated managers would offer to work longer for a higher wage which they deserve as they are more productive. The unmotivated manager would love to pocket the higher wage, but the longer hours are too costly for him - so he would not offer such a contract.


A law against selling any house cheaper than it was bought for, what consequences would that have? I'm looking for a more general and principled answer and use Scandinavia today only as a sketchy example of the kind of scenario I'm asking about.

I live in Scandinavia where house prices has had an uninterrupted bubble boom during a quarter of a century now. Households are the most indebted in the world. Mostly of course in the form of housing loans. If the housing bubble would burst in Scandinavia as it has done in many other places the recent decade, certainly all banks will immediately be wiped out and millions of Scandinavians will become completely destitute for the rest of their lives with unpayable debts and no property to match it as a deep depression sets in.

Some key figures (for Sweden, not the oil country):

+7% housing prices on average per year since 23 years, with record increases the last couple of years.
0% growth in GDP per capita last 10 years (housing prices doubled anyway).
1.2% (positive) CPI-inflation since 10 years.
0.8% (positive) consumer housing loan now offered in ads without negotiation (after tax deduction) while central bank interest rates are stuck deep into
the negative.

Imagine that the government makes a law that forbids anyone to sell any housing at a lower price than what it was last bought for. Thus per definition the house bubble cannot burst, not legally anyway. And everyone is safe, the crash prevented and everyone will keep making millions simply by borrowing more for risk free "investing" in simply owning ones own house, right?

What would the negative consequences be and how would it play out?

That would be really, really bad.

Any house that loses value will be unsellable, and thus virtually worthless.

Most people living in such a house would be prevented from moving. They cannot sell it, since no one wants to buy an overpriced house, and they cannot afford buying another house with their capital already tied up in the current house.

A black market would appear, with people giving money back under the table. "Buy my house for 4M SEK and I'll refund 1M SEK under the table."

I can tell you one thing it won't do. It won't stop prices from ever falling.


The relation between the Black-Scholes model and quantum mechanics As an active participant on the Physics Stack Exchange I have, on several separate occasions, run into some vague remarks about the 'intimate relation' between the famous Black-Scholes model in economics and the Schrödinger equation that appears in quantum mechanics. In particular, people mention that path integrals (a certain technique that is very useful in quantum mechanical calculations) find many applications in economic settings.

I'd love if someone could make this connection clearer by

Explicitly (i.e. in equations) showing how the Schrödinger equation and the Black-Scholes equation are related
Discussing the use of path integrals in economics

I have more often heard of how the Black-Scholes equation is just the heat equation. You can find that information here. I haven't heard of a relationship between Black-Scholes and quantum mechanics before, but this post on the Physics stack exchange seems to have the details you're looking for. (Maybe you've seen this post before.)


What is fiscal impulse? I came across this term in the following paragraph and I could not comprehend what it meant.

  The new WPI series does not include any indirect taxes, which brings it conceptually closer to the producer prices and also removes fiscal impulse impact

This looks like a quotation from The Indian Express

WPI is likely to mean "Wholesale Price Index", similar to what is sometimes called the "Producer Price Index" and related to GDP deflators, but distinct from the "Consumer Price Index".

The exclusion of indirect taxes is presumably designed to avoid measuring price changes directly associated with India's introduction of a national Goods and Services Tax in 2017.


Bond market vs stock market during crisis Why does bond market not change as much as the stock market during financial crisis? On the picture we see the development of the two markets

Short answer:
A bond issued by a company is less risky than a share of the same company.

Longer answer:
A company is in bankruptcy if its assets are worth less than its obligations. In case of bankruptcy the assets are sold off in the market or by individual agreements with the creditors. Direct creditors are payed first. If there is any money left, bond owners are payed. Since the assets were worth less than the obligations, no money is left, shareholders get nothing.

So even if things turn bad, bond owners can expect reimbursement. (Unless the change in asset price was drastic they can expect a large fraction of their money to be reimbursed.) Stock owners can expect no money if the company goes bankrupt. Even worse, stock prices already go down if asset prices decrease, because the company will have less profits after meeting its debt obligations, and hence it can pay less dividends. Basically a stock owner is betting on high profits while a bond owner is betting on medium profits. During crisis most companies cannot expect high profits anymore and their prices fall accordingly. Most bond issuing companies still don't go bankrupt so bonds are less affected.


How can a country develop the skills of its population and have them stay? Suppose, I am a leader of a country, and a lot of my citizens go to the Gulf states (see 3.1, Page-09) to work as unskilled laborers. I see my population working abroad as laborers as a prestige concern of my country, and strategic baggage.
What can I do so that these laborers happily come back home, happily stay in their own country, and contribute to their own country's economy?

The brain drain is a difficult issue facing many countries around the world. Simply, they need something to come back to. Laborers generally leave countries because there is insufficient economic activity for them domestically. If a country wants to retain workers, they need to build up educational infrastructure, encourage foreign direct investment, and open up border to free trade. However, building domestic economic infrastructure requires skilled labor - the very laborers who generally leave for foreign markets. Its a bit of a catch-22.


Pure exchange economy: Given an initial endowment are multiple equilibria possible? Consider a pure exchange economy with two goods ($x_1,x_2$) and two consumers $A,B$. Both users have an initial endowment, $(\omega_1^A,\omega_2^A)$ and $(\omega_1^B,\omega_2^B)$ respectively. A price ratio $p^*$ is an equilibrium price ratio if after both users maximize their utility given their budget, that is $\forall i\in \left\{A,B\right\}$ they solve the problem
\begin{align*}
\max_{x_1^i,x_2^i} \ & U(x_1^i,x_2^i) \\
\\
\mbox{s.t. } & p \omega_1^i + \omega_2^i = p x_1^i + x_2^i,
\end{align*}
the maximizing bundles $(x_1^A,x_2^A),(x_1^B,x_2^B)$ are such that the markets are in equilibrium, meaning
\begin{align*}
x_1^A + x_1^B & = \omega_1^A + \omega_1^B \\
\\
x_2^A + x_2^B & = \omega_2^A + \omega_2^B.
\end{align*}

Suppose that $U$ fulfils the usual conditions of convexity, monotonicity (or local non-satiation, pick whichever you like) and continuity. Given an initial endowment is it possible to have two different equilibrium price ratios? The ideal answer would give a simple example, but non-constructive proofs are also okay. I am especially interested in examples where both equilibria are interior points of the Edgeworth-box.

A graphical representation of the problem:

Green is the set of Pareto-optimal points, red and blue are indifference curves, thin lines are budget lines.

Yes. The Debreu version of the Sonnenschein-Mantel-Debreu theorem guarantees that excess demand has to satisfy very little restrictions if there are as many consumers as commodities.

An explicit example of multiple equilibria in a $2\times 2$-exchange economy can be found in

  Shapley, L. S., and M. Shubik. “An Example of a Trading Economy with
  Three Competitive Equilibria.” Journal of Political Economy, vol.
  85, no. 4, 1977, pp. 873–875.

In the example, both consumers have even quasi-linear preferences, which are (necessarily for nonuniqueness) linear in different commodities.


Saddles and Rational Expectations. Language barrier preventing me to solve this exercise For the system
  \begin{align}
\dot{x} = x + y + 1\\
\dot{y} = 2x - y + 5
\end{align}

  (i) Find the fixed point.

  (ii) Transform the system into deviations from the fixed point. What are the characteristic roots of the transformed system?

  (iii) Derive the equations for the stable and unstable arms.

  (iv) Set the model up on a spreadsheet and plot, on the same graph, the following trajectories:

  (a) The trajectory from initial point (-2,4)

  (b) The unstable arm passing through the point at which $x=2$

  4th exercise page 172 in the "An Introduction to Economic Dynamics book"

Can anyone explain to me how do we solve - (ii) Transform the system into deviations from the fixed point. What are the characteristic roots of this transformed system ?

I simply do not understand the point of the exercise. Anyone care to explain what it wants us to do?

I am a Slovakian student, and the exercises in English are getting me stuck. Any help would be appreciated.

$\newcommand{\vect}[1]{{\bf #1}}$

Note that you can write the system in the form

$$
\dot{\vect{x}} = A \vect{x} + \vect{b}
$$

where

$$
\vect{x} = \left(\begin{array}{c} x \\ y\end{array}\right), ~~~~ A = \left(\begin{array}{cc} 1 & 1 \\ 2 & -1\end{array}\right), ~~~~~ \vect{b} = \left(\begin{array}{c} 1 \\ 5\end{array}\right)
$$

A fixed point $\vect{x}^*$ is a point for which $A\vect{x}^* + \vect{b} = 0$, which in this case is

$$
\vect{x}^* = \left(\begin{array}{c} -2 \\ 1\end{array}\right)
$$

Now define the variable

$$
\vect{z} = \vect{x} - \vect{x}^*
$$

and note that

$$
\dot{\vect{z}} = \dot{\vect{x}} = A\vect{x} + \vect{b} = A\vect{x} - A\vect{x}^* = A(\vect{x} - \vect{x}^*) = A\vect{z}
$$

That is,

$$
\dot{\vect{z}} = A \vect{z}
$$

What you need to do now is to find the eigen-decomposition of $A$


What is the relation beween Granger causality and Rubin's causality? Granger proposed a test for causality based on time series, is there any relation with the notion of causality by Rubin that seems prevalent on applied micro work. The latter deals with the notion of counterfactual and how we can use an experimental set-up to capture the expected value of this parallel world situation to infer about the average effect of the intervention.

In short, not really.  Prof. John Cochrane offers an astute example of Granger causality by stating that a weatherman Granger-causes the weather.  We know that a weatherman has no measurable role in causing the weather, but there is indeed an intertemporal correlation between what the weatherman says today and what happens tomorrow.


Money supply M0 and M1 data for students Its my first time on economics xchange. I am a student of M.Phil. Economics 1st semester. I am writing a term paper and I need some data.

I am looking for money supply M0 and M1 data for top 50 countries (preferably in USD) for the year 2000. My university has a subscription of http://www.tradingeconomics.com/. But that is only accessible in the university's library.

I am back home for vacations. So I wanted to ask if anyone knows of a resource where this might be available for students free or at a low cost. Or if someone of you can provide this data. Thanks.

I think one of the best websites for this rather general economic data is

https://fred.stlouisfed.org/

On the first look I found money supply data for many countries. Additionally, you can check the websites of national central banks, which usually have comprehensive data, especially on monetary time series.