Interest Rates and Inflation According to the Fischer hypothesis, nominal interest rates increase with inflation, so that the underlying real interest rate is preserved.

One might then expect that if a nation A has a higher interest rate than another nation B, then the expected inflation for nation A will be higher than that of nation B. (Assuming the real rate of interest is the same accross nations as in the international Fischer hypothesis)

However, if a nation sets its interest rates by controlling money supply, then the nation can raise their interest rates by decreasing the supply of money. Wouldn't the decrease supply of money then lead to decreased inflation, rather than the increased inflation described in the Fischer hypothesis?

The fisher hypothesis, as well as related aspects of the neutrality of money hypothesis, are typically argued only to operate in the long-run, with changes in money supply having short-run effects which are modeled with monetary disequilibrium theories.

So, a nation sells bonds in exchange for liquid assets denominated in its currency and then holds onto those assets, reducing the liquidity in their economy. As a result, at short-run levels of demand, that currency will be more highly valued than it would have been otherwise (lowered inflation). However, in the long run potential investors are presented with an incentive to lend in the currency, increasing the savings rate and lowering spending until their nominal interest rate (dependent on the amount of currency available and the spending rate) is low enough that the real interest rate is the same as it was before (assuming a constant level of expected future returns in the economy over this period).

This relies on investors only considering the real economy to be of significance in their long-run deliberations "Will future demand in this industry justify my investment and provide me with a good real rate of return down the line? If I think future inflation will be very low or negative it might just be more appropriate to hang onto my money." This is, like any model, a huge simplification, but in terms of a perfectly rational investment community (it's ok, you're allowed to laugh) it seems as though it should hold fairly well.

However, to bring this into the real world somewhat. Short-run levels of inflation and short-run levels of the spending and savings rates do not seem to be especially short run. Ordinary consumers who make up the majority of the economy take a long time to change their behaviour to bring these into an equilibrium, and shocks and government interventions and technology changes are sufficiently frequent that in effect everything stays more dynamic than monetarists would imply. Does this make the hypothesis useless? Not entirely, as an investor with no means of predicting the future accurately you could do worse than trusting it and just trying to keep your margins high in case of unpleasant surprises.

As a concise answer to your question: You're right in the short-run, the fisher hypothesis is supposed to apply to the long-run, but whether it does so accurately is virtually impossible to tease out of chaotic real world data.


Episodes of Housing Crashes and Never Recovering Looking at many housing markets in major cities around the world today it looks like most (London, New York, Sydney, Beijing, Toronto,...) have become totally detached from the earnings of the local market. This seems unsustainable but I can only think of one chart, see below, of Japanese property that goes into a boom, crashes and never recovers.

Are there any other episodes in recent history where the price of real estate crashes and never recovers in price?

Maybe the case of Germany before and after WWI could provide you an example. See here. The short story is that there was a big housing shortage before the WWI, which, after the war, which was no solved by the market, because of rent controls, profits controls, and other regulations.

The origin of housing shortage and rising prices:

  Germany's housing problem originated in the period of rapid industrialization,  population  growth,  and  urban  concentration  between  1870
  and  1914. Population mushroomed  from  41  million to  67 million,  and
  by   1910  twenty-six German  cities  boasted populations of  200,000.

This led to:

  high  real  estate  prices, heavy mortgage indebtedness, and high rents

State intervention begun:

  Systematic government  intervention  in the German housing  market
  began  during  World  War  I.

Some thought it would stop after the war:

  After  the war,  many  Germans  would  have  been satisfied  to  permit the wartime measures to  expire,  allowing the economy to  return  to  "normal." With  a return  to  normalcy,  private  enterprise would return to the housing market, eliminating the need for state intervention.

However, this did not happen:

  Plagued by inflation and  a severe capital shortage, the German housing
  industry  failed  to return to normal. The little capital that was available
  commanded exorbitant interest  rates;  until the credit crisis of June 1931
  first mortgage interest rates hovered between  8 and   10.8 %  per cent. ...  Predictably, there was practically no  demand  for new  housing,  and  thus very  little new construction. ...

The state capacity to build was also damaged:

  the war  effort  had exhausted  Germany's  capital supply, the loss of her colonies, merchant marine,   and  industrial  investments   in  Alsace-Lorraine  diminished  the nation's  capacity   for  new  capital formation,
    and   reparations  payments appeared to have first claim  on  any capital formation  the country might manage.

So, albeit not the exact narrative of a modern housing crises, it might be of help.


Why is Price Vector Orthogonal to Vector connecting two bundles on Budget Hyperplane Here is my revised version/understanding why price vector is orthogonal to any vector from a bundle on the budget hyperplane to another bundle on the hyperplane: (see below for original question)

  Want to show geometrically that budget hyperplane is the relative terms of exchange. This is a fancy way of saying it represents the 'ratio' of the prices between any two commodities. For simplicity sake, look at $L=2$. We have two options for a ratio: either $\frac{p_1}{p_2}$ or $\frac{p_2}{p_1}$. What would it be? The way the price vector is constructed is p$=(p_1,p_2)$, so when you draw this vector from any point on the budget line that is negatively sloped in the case of $L=2$, the vector is essentially the slope (e.g. rise over run) of $\frac{p_2}{p_1}$. So obviously, if the negatively sloped budget line is supposed to represent the price ratio, then it has to be the case $\frac{-p_1}{p_2}$. In fact, this is so from the Walrasian budget set definition where $w=x\cdot p$.

When we look at a typical Walrasian budget set in $\mathbb{R^+_2}$, why is the price vector orthogonal to the consumption vector (e.g. any two on the slope) on the budget hyperplane? This goes back to Chapter 2 of MWG.
 I understand the analytical explanation using dot product.

  $p\cdot x=p\cdot x'=w$ for $x,x'\in\{x\in\mathbb{R^+_2}:p\cdot x=w\}$.
   Hence, $p\cdot\Delta x=0$.

But I am having a tough time understanding two things:

  (Q) Why does this orthogonality between price and consumption vector on hyperplane relate back to the slope of the budget line determining the relative rate of exchange between two commodities? How do you make sense between intuition and geometric interpretation?

Thanks for your 2 cent!

Note that $p$ is not orthogonal to consumption vectors on the budget line, but it is orthogonal to a any vector $v$ that satisfies $x+v=x'$ with $x,x'$ in the budget line. MWG are drawing vectors starting from some $x$.

About the slope: In the budget line you can see that the slope for any $x$ is $D_x (p.x)=p$ (that is the line that is drawn from $x$). That line or vector can be represented with the function $x_2=(p_2/p_1)*x_1$ (note that if $x_1=p_1$, $x_2=p_2$). The slope is $p_2/p_1$.

On the other hand, all vectors on the budget line satisfy $x_2=(-p_1/p_2)*x_1+w/p_2$. The slope here is $(-p_1/p_2)$. This slope is the rate of exchange. Both slopes imply that the two functions (the vector $p$ and the budget line) are orthogonal. Or maybe it's better to say that the orthogonality between the budget line and the vector $p$ imply that $dx_2/dx_1=-p_1/p_2$, that is, the last term captures the rate of exchange.


What is a rational consumer? There is a lot of debate on whether or not consumers and investors are rational. Unfortunately, I haven't seen much qualification for what is called a rational consumer.  What are the requirements that must be met for us to consider a consumer to be rational?

In consumer theory, preferences are called rational if they are transitive and complete. Some nomenclature: An alternative A is weakly preferred to another alternative B, if you either like A more than B or you are indifferent between the two. Transitive means that whenever an alternative A is weakly preferred to alternative B, and B is weakly preferred to C, then A is weakly preferred to C. Complete means that for any two elements A and B of the set of possible alternatives, either A is weakly preferred to B, B is weakly preferred to A, or both. In short, preferences are rational when they are defined for all possible alternatives, and when they don't contradict each other in obvious ways.

Rational expectations are a different beast and are specific to different models. Agents in a model have rational expectations if they use the model to form expectations about the future. This means that expectations are consistent with the model/theory in question, and it also means that every rational expectations model has a different "theory" about how people form their expectations. Rational expectations are as much a concept to solve dynamic models as they are an assertion on people's behavior. They are commonly used because they make sure that people are not systematically wrong about their beliefs, and they keep models' properties from being driven by more arbitrary assumptions on how people form expectations.

I don't think there is a lot of thought going into alternatives to rational preferences and most people are content with making the assumption that preferences are rational. There is a big literature in macro and finance on relaxing rational expectations assumptions. A lot of people work with models of bounded rationality, in which agents use a simpler approximation to the true model to form expectations.


Calculating Time to Balanced Growth Path $\textbf{Model:}$
$$\underset{\{c_t,k_t\}}{max}\;\sum_{t=0}^\infty\beta^t\frac{c_t^{1-\gamma}}{1-\gamma}$$
$$s.t.\;c_t=Rk_{t-1}-k_t$$
$$c_t,k_t\geq0$$
At time $t$, $c_t$ is consumption and $k_{t-1}$ is the capital used in production. $0<\beta<1,\;\gamma>0,\;\gamma\neq1$

$\textbf{(a)}$ Compute a balanced growth path in which consumption and capital grow at constant rates.

Solving this using the Euler equation, we get
$$\frac{c_{t+1}}{c_t}=\big(\beta R\big)^{\frac{1}{\gamma}}$$
We know that capital must grow at the same rate as consumption in a balanced growth path, so
$$\frac{k_{t+1}}{k_t}=\big(\beta R\big)^{\frac{1}{\gamma}}$$
This means that:
$$c_t=\bigg(\frac{R}{(\beta R)^{\frac{1}{\gamma}}}-1\bigg)k_t$$
$\textbf{(b)}$ What restrictions are necessary for both capital and consumption to grow at a positive rate on the balanced growth path?

For this question, it seems like all we need is $R>1$

Now, my question is the following: How long will it take for consumption and capital to reach the balanced growth path? In general, how would one calculate time to balanced growth path? Or is it more based on economic intuition?

$\textbf{Edit:}$ According to another student, the professor said this will never reach a balanced growth path. However, the professor never stated why. Can someone give me a reasoning as to why this would never reach a balanced growth path?

a) Your calculations are correct, but in order for consumption to be positive, so for
$$
c_t=\bigg(\frac{R}{(\beta R)^{\frac{1}{\gamma}}}-1\bigg)k_t > 0,
$$
you will need to additional conditions. The first is the obvious $k_t > 0$. If there is nothing to gain interest on, there will be no growth and no consumption. The second is the more nuanced
$$
\frac{R}{(\beta R)^{\frac{1}{\gamma}}}-1 > 0.
$$
This is actually a necessary condition for the existence of an optimal solution.  The inequality may be reformulated as
$$
\beta \cdot R^{1 - \gamma} < 1.
$$
If this does not hold, then given any consumption path the consumer would gain by pushing off all consumption one period further. Since there is no infinitely distant timeperiod, no optimum exists.

b) On reaching the balanced consumption path:
Perhaps there is a trick with the indeces. $c_0$ seems ill defined unless there is a $k_{-1}$. If consumption only starts at $t = 1$, the above conditions are satisfied and the consumer is rational then
$$
\forall t: \ c_t=\bigg(\frac{R}{(\beta R)^{\frac{1}{\gamma}}}-1\bigg)k_t
$$
defines the optimal consumption path as I assume $k_0$ is given and
$$
\forall t: \ k_t = k_0 \cdot (\beta R)^{\frac{t}{\gamma}}.
$$
Hence
$$
\forall t: \ c_t=\bigg(\frac{R}{(\beta R)^{\frac{1}{\gamma}}}-1\bigg) \cdot k_0 \cdot (\beta R)^{\frac{t}{\gamma}}.
$$
It is straightforward to check that this path is feasible (if the conditions set out in a) are met) and balanced.

A note on reaching the balanced consumption path: This concept usually exists when there is some conflict between balancedness and optimality or when the consumer is boundedly rational. (E.g. Solow model.) Here this does not seem to be the case. However when such conflicts arise there is usually a never-ending (Is this the correct spelling of this word? Please correct if wrong.) convergence towards the balanced path. The distance decreases in every period but never becomes 0.


Sequential vs. trembling hand perfect equilibrium For any game, trembling hand perfect equilibria are a subset of sequential equilibria.
What is a simple example where a sequential equilibrium is not a trembling hand perfect equilibrium?
Is it possible to create a normal form example?

Links:

Kreps-Wilson: Sequential Equilibria

Selten: Reexamination of the Perfectness Concept for
Equilibrium Points in Extensive Games

Yes. In a normal form game, every Nash equilibrium is also a sequential equilibrium. But not every Nash equilibrium is trembling hand perfect. Consider the game in which each of two players has two strategies, A and B. Both players get payoff 0 except in one case: they achieve positive payoffs if they both choose A. Then (A,A) and (B,B) are two Nash equilibria of this game. Both are therefore also sequential equilibria. However, (B,B) is not trembling hand perfect. If there is even the smallest tremble in player 2's choice, player 1 has a strict preference for A. Only (A,A) is trembling hand perfect. The generalization of this is that Nash equilibria in which some players play weakly dominated strategies are not trembling hand perfect.


Is Marx considered an important classical economist? In a post on the politics stack exchange, I came across the following description of how Marxism fits into the history of economic thought:

  Most professional economists consider Marx' work on economic theory to be a substantial part of economic theory. Marx and Engels are included in the list of great classical economists, along with Adam Smith, Jeremy Bentham, David Ricardo, and Thomas Malthus. Marx pointed out that the long-term equilibrium for the "standard of living" is what a class insists upon before having, raising, and equipping enough children to replace itself. Several key concepts of economics (including "Cobb-Douglas production functions" and "value added") are designed to explain Marx' observations about the fraction of a factory's revenue that is not paid out for materials or proletarian labor.

The idea that "the long-term equilibrium for the 'standard of living' is what a class insists upon before having, raising, and equipping enough children to replace itself." seems foreign to me as an idea in economics and I am curious about the accuracy of the claims about Cobb Douglass and Value added, since they were not supported with references.

Is Marx commonly considered to be an influential classical economist, and if so, what is an example of an idea he added to economics as a discipline?

Among economic historians, Marx is often considered the most important economist of the 19th century.  His attempts to provide a systematic explanation of the functioning of capitalism  was on a far grander scale than anyone who preceded him, and in that sense, he reset the bar very high for what would henceforth be considered comprehensive economic theory, even if parts of it were fundamentally flawed. Refer to Mark Blaug's classic text Economic Theory in Retrospect (Chapter 7) for a nice attempt to parse out Marx's economic theory from the rest of his ideas.  This is a standard and authoritative text in the history of economic theory.

Blaug says of Marx "Marx the economist is alive and relevant today in a way none of the writers we have thus far considered." Those considered were Smith, Malthus, Say, Ricardo, & Mill.

In terms of his understanding of the dynamic long run evolution of economic systems, the nature of technical change, business cycles, and volume of employment, his insights were often brilliant, transformative and unparalleled in any writers that preceded him, and remain deeply influential.  (I'm paraphrasing Blaug here)

[It's worth mentioning that Blaug did his Ph.D at Columbian under George Stigler, who was a key leader in the Chicago School. So Blaug was hardly a lightweight, nor a "pinko" ;) ]


What was economics like as a field before Adam Smith, the father of *modern* economics? Adam Smith is called the "father of modern economics" and his book The Weath of Nations, a fundamental work in the field of economics, is considered the first modern book on economics.  In addition, economics first became a study in 1776 when The Wealth of Nations was published.

Why is the word "modern" used in both descriptions?  I know that individuals throughout the centuries and even Aristotle have dabbled with some economic theories, but I do not recall anyone making any significant contributions to economics before Adam Smith.

Were there important contributions to economics made before 1776?
If not, then why do we use the term "modern" even if there was no one in the study previously?

There exists the... "Adam Smith of the Arabs": Ibn Khaldun. He lived during the 14th century. The work of his that focuses on Economics is Muqaddimah translated in English in 1958 as "The Muqaddimah: An Introduction to History".

He advocated less involvement of the state in production and trade activities, which should focus instead on stabilization policy. He also argued in favor of a reduction in military expenses, in order to invest more on education and technology. He also pointed to the increased efficiency that comes from specialization of labor.

Don't all these sound eerily familiar? (400 years before Adam Smith). For a summary of his economic theories, see here.


Marginal buyer/seller as determinant of price In competitive markets without frictions, the marginal buyer/seller determine the price. To what extent is this argument true in markets where a fraction of the sellers are constrained?

Think about the labor market. Some workers are optimally supplying labor given their marginal rate of substitution and the wage rate. Some workers are borrowing-constrained such that they have to supply their full labor endowment.

Assume perfect competition on the labor demand side. Under which conditions can we determine the wage rate using first-order condition of the firms and the first type of workers?

If I have understood correctly, the question asks what should we know so that we can determine the wage using only information on the unconstrained workers. Here is a toy static model:

Let's say we have $N_u$ unconstrained workers and $N_c$ constrained workers. Each has a total labor endowment $t$. Worker population is denoted $N_c+N_u = N$.
The unconstrained workers will solve a utility maximization problem

$$\max u(c,\ell_u)\;\; \text{s.t.}\;\; c_u = w\ell_u,\;\; u_c>0, u_l<0$$
Subscripts in functions denote derivatives.
The above will give

$$\ell_u^s: wu_c+u_l = 0 \Rightarrow \ell_u^s = h(c,w)$$

The constrained workers will supply each $t$. So total labor supply will be

$$L^s = N_ct + N_uh(c,w) = (N-N_u)t + N_uh(c,w),\;\; h_w>0$$

(note that some simple utility function forms lead to the supply of labor being independent of the wage. We assume this is not the case here. Also, $h_w>0$ assumes away backward-bending of the individual supply curve).

Since we assume perfect competition (and price taking behavior) on the labor demand side, the firms do not explore possible benefits from the existence of two types of workers. They just go on and equate the marginal product of labor to the market wage

$$\ell^d: MP_L = w \Rightarrow \ell^d = g(w, k_j,T), \;\; g_w <0$$

where $k_j$ is firms capital, and $T$ is technology.
If there are $m$ firms we will have the equilibrium condition

$$L^s = L^d \Rightarrow (N-N_u)t + N_uh(c,w)= mg(w, k_j,T)$$

or writing $n_u = N_u/N$

$$(1-n_u)t + n_uh(c,w)= \left(\frac mN\right)g(w, k_j,T) \tag{1}$$

So if we know the proportion of unconstrained workers, and the total worker population, we can determine the wage from $(1)$, using the first-order conditions related to labor demand, and conditions related to the unconstrained workers.

If we further assume a Cobb-Douglas production function (constant returns to scale) for the firms, then labor demand will be linear in capital, and so $g(w, X) = \xi(w,T)k_j$. Then $(1)$ becomes

$$(1-n_u)t + n_uh(c,w)= \xi(w,T)\frac {K}{N} \tag{2}$$

Here we need to know only the proportion of unconstrained workers, and the capital per worker.

Is this what the question asked?


Are there some nice properties for a finite two-player game having an increasing differences utility and a decreasing differences utility? Nice properties of the set of Nash equilibria can be shown for supermodular games(see here). But for a two-player game in which

Strategy spaces for two player, $S_1$ and $S_2$ are finite, and both of them are subsets of $\mathbb R$.
$u_1$ exhibits increasing differences while $u_2$ exhibits decreasing differences.

What can we say about it?

There is a recent paper which may help you:
Games with strategic complements and substitutes (Monaco and Sabarwal (2015))


Interpretation of Nash equilibrium as a potential stable point of a dynamic process I'm reading an article called "The Nash equilibrium: A perspective" by Holt and Roth, and the below paragraph caught my attention.

When the goal is prediction rather than prescription, a Nash
equilibrium can also be interpreted as a potential stable point of a
dynamic adjustment process in which individuals adjust their behavior
to that of the other players in the game, searching for strategy
choices that will give them better results.

Is this paragraph referring to repeated games, or can this view of the Nash equilibrium be thought to apply to single-shot games as well? It mentions "game" (i.e. singular). However, I don't see how you can adjust strategies in a single game. On the other hand, if it is saying that a single-shot game is equivalent to a hypothetical series of steps that are taken, then that would be a very interesting take on what constitutes a "game", and one which I would love to know more about.

I am not a big fan of any "dynamic adjustment" ideas in static games to justify Nash equilibrium, but for some people it is helpful. I would see it more as an inner monologue with many "what if"-questions.
As an example, consider Cournot competition. Supposse, two firms compete in quantities. The figure below (also from the wikipedia page) depicts the reaction functions (or best-response functions). If firm 2 sets quantity $q_2$, the best response by firm 1 is to set $q_1= R1(q_2)$. We have a Nash equilibrium where these two functions intersect, i.e., when all firms play a best response against each other. The NE is at $(q1,q2)$ in the figure.

Suppose firm 1 thinks: "I believe firm 2 sets quantity $q'_2<q2$. Hence, I will respond with $q'_1=R1(q'_2)$." Next firm 1 would think: "But wait, if I set $q'_1$, then firm 2 would not set $q'_2$, but $q''_2=R2(q'_1)$. This means I should set $q''_1=R1(q''_2)$." Next: "But wait, then firm 2 would set $q'''_2=R2(q''_1)$..." and so on. This though process converges to the NE $(q1,q2)$. Similarly, we arrive at the same NE when starting with $q'_2>q2$. If you want to, you can also think about the firms actually setting these quantities in repeated interactions, making only one of the steps of the thought experiment, and thereby they would also arrive at the NE and stay there.
In this sense,  "a Nash equilibrium can also be interpreted as a potential stable point of a dynamic adjustment process in which individuals adjust their behavior to that of the other players in the game, searching for strategy choices that will give them better results."


GDP calculation on selling house at a profit This question may appear to be naive, however, since I am having problems understanding it, I had to resort to ask it here.

How will the sale of an old house at a profit affect the GDP?
Let us say I bought a house in 2010 for $ \$100,000$. Depreciation per year was $ \$10,000$, hence in the year 2015, the house should have been worth $ \$50,000$. However, in the same year (2015), I sold the house at a price of $ \$80,000$  (thus a profit of $ \$30k$). Certainly the $ \$50k$ won't be added into the GDP of the year 2015 because it is nothing but just a sharing of the expenses, but, what's bothering me is the profit of $ \$30k$.
Since this is a kind of "value added", how do I incorporate it in the expenditure and income models of the GDP? Should I consider it as an investment made by the business?

Revised:
The sale of the old house is not counted toward GDP as GDP is intended to measure the value of currently produced goods and services in the economy. Used goods are not currently produced, and were already counted the year they were newly produced.

However, the services provided this year by real estate agents are in the current year, so the market value of those services, measured by real estate agent commissions are included in GDP.

http://www.sextonmacro2e.nelson.com/student/section/ch06.html

If the house was new it would fall under the expenditure approach the purchase of a house sold at 80 K would fall under Residential Investment (part of I investment).

Using the Income Approach (http://www.econport.org/content/handbook/NatIncAccount/CalculatingGDP/Examples.html#incomeexample )

Depreciation -50 K
business profits - 30 K

Depreciation and business profits would be added together toward National Income.


Meaning of «intertemporal substitution effect dominates the income effect» Assume a household intertemporal optimisation problem, where they only either consume or labour, and one of the equilibrium conditions states that labour will be a positive function of productivity, when « the intertemporal substitution effect dominates the income effect».
The real wage is also a positive function of productivity, regardless of the above effects interaction.
How would one interpret the meaning of « the intertemporal substitution effect dominates the income effect», when there's a positive productivity shock?
My take on this is:

The intertemporal substitution effect refers to how easily the household substitutes consuming tomorrow for consuming today.
The income effect refers to how consumption by household will change, given a change in income. Income rises, and the household will want to consume more and work less.

Therefore, I would interpret the sentence «the intertemporal substitution effect dominates the income effect» as the household choses to work more today to consume more tomorrow, instead of consuming more today.
Am I correct?

I suppose the right approach is to start with the statement: "Real wage is also a positive function of productivity".
Let's start with the income effect: If both goods, free time and consumption are normal goods (This is the standard case; normal good simply means: if you are richer you want to consume more of them), then the individual wants to increase both consumption and free time simply because he got richer and can afford it now. More free time translates into less working hours.
The substitution effect: As real wages increase the individual would miss one hour of higher salary after the wage increase. This makes free time relative to consumption more cost full than before. The substitution effect induces the individual to work more.
As long as the second (substituion) effect is greater than the first (income) effect labor demand will increase as productivity increases.

So far, the pretty standard interpretation for a change in relative prices. Regarding the intertemporal component of the substitution effect i found in Mankiw, Rotemberg and Summers 1982, p.8:

The intertemporal substitution hypothesis implies that labor supply should depend on the relative return from working in period t and from working in period t+1.This depends on the real wage in period t relative to the discounted real wage in period t+1.

I suggest this implies that as long as the productivity shock has a relative higher impact on real wages in $t$ than in $t+1$ the intertemporal substitution effect has a positive impact on labor supply in $t$. With all of this in mind you should be able to understand the proposition « labour will be a positive function of productivity, when  the intertemporal substitution effect dominates the income effect»


Is there an index, parameter, ecuation, or anything to compare the tax pressure exercised by a country in relation to others countries? In my country we are told often that the tax pressure over the companies and people is huge, making it unbearable and being a reason bankrupting the Economy, and one of the largests in the world. We are told that each product price is more than 50% of taxes and each company has to pay more than 50% in taxes for each employee they have. But when I take a look at the overall amount of money collected by taxes in a year, this seems to be over 100 times smaller than United States, a supposed very capitalist country which opposes heavy taxation. Of course we have to take in consideration other parameters, such how large are the economies of each country, but if I compare the amount of money collected with taxes in relation with the GDP of each country, it would seem my country pays half of the taxes of United States (100 times less taxes with 50 times less GDP than US) . I thought that may be I should compare people's wages with the amount of taxes divided the amount of people, but it still seems that United States is paying over twice the taxes that we pay here.

Then, because of all of this, my question is,

Is there an index, parameter, ecuation, or anything to compare the tax pressure exercised by a country to its own Economy in relation to the pressure exercised by others countries?

I am not sure how you calculated the tax revenue in relation to GDP, but one measure would be tax revenue as % of GDP. This is quite common measure of how heavy the taxation is because it tells you what percentage of total output produced by country is collected by government. OECD provides data on this measure here.

However, it can always happen that even a country with high tax rate collects less taxes than country with lower tax rate. First, you have classic Laffer curve - if you set taxes to 100% you collect zero tax revenue because nobody will work for fee so you collect the same tax as at 0 tax rate - hence having higher tax rates does not necessarily mean higher tax revenue. This being said empirically most real life countries don’t have taxes so high as to be over the peak of the Laffer curve so this will probably not apply to your case. Another, issue is tax avoidance. In some countries it’s child’s play to avoid VAT or many people can work in informal sector to avoid income tax. If government does not have good institutions that prevent this then again even government with 50% tax rate can collect less tax revenue than government with 10% tax rate if in second country tax authorities are efficient in preventing tax avoidance but in first country not.

Another possible measure could be looking at average or marginal tax rate across the economy and compare these between two countries. However, this is just crude comparison of how high taxes are.

If you would care about comparing the burdens the tax systems in the two countries create then a good measure is the marginal cost of public funds or marginal excess burden of taxation. This is a measure of by how much government must reduce economic activity (by its distortionary taxes) to extract 1 euro (or local currency). For example marginal marginal excess burden of  0.5 would imply that to raise 1e in tax revenue output on margin contracts by additional 0.5e so in total government has to take “out” of the economy 1.5e to get 1e. This gives you some idea of distortionary effect of taxes (in case of no distortions the marginal excess burden should be 0e).

You can also calculate average excess burden which is the same measure but it gives you information about average burden instead of burden at the margin (i.e. the last euro collected). I don’t know of any dataset that just gives you this measure though because it has to be estimated and based on different estimation techniques or assumptions behind the model used you can get little bit different values, but you can try to search for it in google scholar. For US there are many papers trying to estimate the excess burden of almost any tax you can think of, but if you come from small country research might be not available on this.


Misspecified autoregressive models I want to know the impact of misspecifying lag levels in AR models. Say the true model is AR(P), while in estimation AR(P-1) is estimated and used for forecast.

What will be the impact of estimating AR(P-1) on the estimated coefficients of $\phi_1 - \phi_{p-1}$, can they be consistently estimated. What about the forecast error.

Just think your true model is:
$$y_t = \phi_0 + \phi_1 y_{t-1} + \phi_2 y_{t-2} + u_t \tag{1}$$

So, under your true model, $u_t$ is uncorrelated with all explanatory variables.

So, instead of using AR(2), use selected AR(1) model as:
$$y_t = \phi_0 + \phi_1 y_{t-1} + \epsilon_t \tag{2}$$
So, now, $\epsilon_t = \phi_2 y_{t-2} + u_t$; therefore, $y_{t-1}$ will no longer will be uncorrelated with $\epsilon_t$ (due to correlation between $y_{t-1}$ & $y_{t-2}$). In simple words, this lead to the problem of endogeneity. And we know, OLS estimators are not consistent when residuals are correlated with any of the explanatory variables.


What was the US monetary policy like in the 70s? Today the US inflation target is roughly 2%.
However in 1974 the inflation rate was 11% and in 1980 it was 13.5%.
What monetary policy did they follow at that time that allowed the inflation to rise to these levels?

Looking at the U.S. National Unemployment Rate:

we see that it had a local minima of 4.6% in october 1973 and another one at 5.7% in June 1979.

In the 70s U.S. Fed policy was in disarray and Fed was not following consistent monetary policy (at least not by present day standards). Generally monetary scholars characterize the Fed monetary policy in the 70s as "go-stop" policy. As argued by Goodfriend (2007):

At the heart of the disarray in monetary policy practice in the 1970s was the
tendency for a central bank like the Federal Reserve to pursue “go-stop” monetary
policy. Go-stop policy was a consequence of a central bank’s inclination to be
responsive to the shifting balance of public concerns between inflation and unemployment. The central bank would stimulate employment in the “go” phase of the
cycle until the public became concerned about rising inflation. Then aggressive
interest rate policy initiated the “stop” phase of the policy cycle to bring inflation
down, while unemployment rates moved higher with a lag. Public support for  interest rate increases evaporated once the unemployment rate began to rise, so it
was politically difficult to reverse a higher inflation rate.

Wage and price setters learned to take advantage of tight labor and product
markets in the “go” phase of the policy cycle to make increasingly inflationary
demands, which neutralized the monetary stimulus. As a result, central banks
became ever more expansionary in the pursuit of low unemployment. Lenders
demanded ever-higher inflation premia in bond rates which moved higher and
fluctuated widely. By pursuing low unemployment and fighting inflation only when
it became the predominant public concern, central banks then increased the
volatility of both inflation and output.

Other factors contributed to the disarray in monetary policy in the 1970s. In
the 1960s, the widespread belief in a long-run Phillips curve trade-off between
inflation and unemployment inclined central banks to allow inflation to drift
upward in the hope of achieving a permanently lower level of unemployment. Also,
the productivity growth slowdown of the 1970s caused central banks like the
Federal Reserve to overestimate noninflationary potential output (Orphanides,
2003). Oil price shocks that occurred in 1973 and 1979 – 80 worsened the inflation
problem, although neither of the oil price shocks produced the 3 percentage point
increase in U.S. inflation that occurred in the 18 months prior to Paul Volcker
becoming Fed chairman in August 1979.

Consequently, the Fed was pursuing generally quite erratic loose monetary policy with occasional abrupt tightening.


Is falling inflation in India one of the reasons for the Nifty crossing the 10,000 points mark? Recently the Nifty crossed the 10,000 mark for the first time. At the same time inflation in India is falling. My question is whether the fall in inflation in India one of the reasons for the Indian stock market doing well?

Back to economy basic 101:
Inflation is due to excessive cash chasing limited goods.

So to relieve monetary inflation, an institution can only do either or all of this:

Slow down money printing
Find ways to produces goods/needs/services that absorb the money
Enact policies to make people stash the excess cash, e.g. high-interest long term bonds, tax incentive on saving.

Other claims just typical media noise.

So "Is falling inflation in India one of the reasons for the Nifty crossing the 10,000 points mark?"

The answer is No.

No government can uplift market speculation by reducing money. The good news is, India stock market cross the 10k mark is because more hot money(inflated money) is entering the stock market.  When excessive cash is snapped up in the stock market, there is little room for the cash to "chase" for the factors that cause goods price hikes, e.g. rents, raw material.

Thus, in a country with poor institutional control, stock rallies are extremely dangerous. Once the speculator cash out their profits from stock market, they may switch attention to other more profitable speculation, e.g. real estate.

Unless the country production sustains continuous growth (rule no 2) to absorb the overflow cash, otherwise you will see a repetition of 1997 Asia financial crisis.

Perhaps OP should ask, can Nifty dodge the fake of (East) Asia financial crisis and take the path of China (which thousands billions export surplus offset the inflation).

(update)
As in economics study, one must be very careful to distinguish between noise and facts. IMHO, all market analytical tools are noise, not facts.  That's why real investor like Warren Buffet simply ignore "market analytical tools" and went straight to costly and time-consuming facts digging.

To learn the bubble is outside the scope of the question. But just a hint, IMHO, index stocks are the best anchor to check against bubbles.


Optimize by MR = MC vs TR = TC I know that I should optimize production by solving $MR = MC$ with respect to $Q$.

But if $TR > TC$, I am making a profit. Why is not enough to just solve $TR = TC$ with respect to $Q$?

Let $TR(Q), TC(Q): [0, \infty) \to [0, \infty)$ be continuous and twice differentiable functions w/ resp derivatives $MR(Q), MC(Q)$.

It is not always the case that

$$TR(Q) > TC(Q) \ \forall Q$$

If it were, we would have

$$\{Q | TR(Q) = TC(Q)\} = \emptyset$$

Even if we had

$$TR(Q) > (or \ge) \ TC(Q) \ \forall Q$$

meaning our profit is positive for any quantity Q:

$$\pi(Q) := TR(Q) - TC(Q) > 0$$

we still want to find $Q^{*}$ s.t. $\pi(Q^{*}) = TR(Q^{*}) - TC(Q^{*})$ is maximised.

Analogy: $e^x > x \ \forall x \in \mathbb R$, but $f(x) := |e^x - x|$ is not constant. Some values of $x$ give greater distances between $e^x$ and $x$ than others

This is not done by solving

$$TR(Q) = TC(Q)$$

which merely gives the quantities that give us zero profit ie

$$\pi(Q) := TR(Q) - TC(Q) = 0$$

We want to maximise $\pi(Q)$ so we get the first derivative and set it to zero:

$$0 = \frac{d}{dQ} \pi(Q) = MR(Q) - MC(Q)$$

Btw, solving

$$0 = MR(Q) - MC(Q)$$

gives us some value $Q_0$, but this is not necessarily give $Q^{*}$. We must check the value of $\pi''(Q_0)$


Understanding a multi-player Tragedy of the Commons game In the formulation of the Tragedy of the Commons below, what does $n$ exactly represent? Is a threshold? The text is from plato.stanford.edu website on Kuhn's Prisoner's dilemma.

Also, it says that $\bf D$ strongly dominates $\bf C$ for all players, and so rational players would choose $\bf D$ and achieve $0$, while preferring that everyone would choose $\bf C$ and obtain $C+B$.

I don't understand the last part. The reason $\bf D$ dominates $\bf C$ is because either the player gets $B$ or $0$ which are better from $C+B$ or $C$. Why would rational players prefer everybody to cooperate?

what does  exactly represent? Is a threshold?

Yes, $n$ is the threshold above which the benefit $B$ realizes. Think of this as a situation where a public good with benefit $B$ is provided only if more than half of the population votes for it. $C$ is the cost of voting, and $n=\lceil\frac12N\rceil$ is the smallest integer greater than half of the population size ($N$).

  Why would rational players prefer everybody to cooperate?

While a rational player would choose $\mathbf{D}$ regardless of what others would choose, he/she would still prefer the outcome with benefit $B$ to the outcome with $0$ benefit. Hence, he/she would prefer everyone else chooses $\mathbf{C}$, i.e. bearing the cost of providing benefit $B$, while he/she enjoys $B$ without incurring any cost by choosing $\mathbf{D}$.

Additionally, suppose there are $N$ players, and that $n<N-1$. Then with all the other $N-1$ players playing $\mathbf{C}$, it doesn't really matter if the remaining player chooses $\mathbf{C}$ or $\mathbf{D}$. So arguably it's less morally objectionable for the last player to choose $\mathbf{D}$.


Are Trade Blocs regionalism rather than Globalisation While studying globalisation, The subject of Trade Blocs was brought up, with hindsight, I wondered, aren't Trade Blocs fostering regionalism (as in devotion to the interests of one's own region) as opposed to globalisation? Trade blocs are anti-free-trade since they are essentially barriers to trade from nations outside of the bloc. Since Globalisation is "developed" through free trade as opposed to "regionalisation" of Trade, then are Trade Blocs regionalism and thus anti-Globalisation?

This is an important question in the trade literature. The regionalization of trade is of serious concern to many international economists who view multilateralism as far superior to regionalism for improving welfare.

In a nice paper, Caroline Freund and Richard Baldwin survey the available theoretical and empirical evidence on the relationship between regionalism and multilateralism, with the aim of discerning whether the spread of regionalism is likely to be a threat to, or an opportunity for, broader trade liberalization. I summarize here their main insights:

Two main related concerns raised by the "multilateralists":

The first is trade diversion: preferential trade agreements, by diverting trade away from the most efficient global producers in favor of regional partners, may prove welfare reducing.
Regionalism may hinder multilateralism, leading to a bad equilibrium in which several regional trade blocs maintain high external trade barriers. Regionalism can also undermine multilateralism simply by diverting limited government resources from multilateral negotiations.

However the "regionalists" argue that

it is precisely because the trade diversion is costly to bloc members that there is an incentive to reduce external tariffs. As tariffs fall, trade diversion disappears, and regionalism becomes a force for general liberalization.

Although the verdict is not yet in, the evidence indicates that regionalism is broadly liberalizing. So regionalism does not go against globalization.


Are White's Robust standard errors robust to clustered errors? I want to ask about OLS White's 1980 "robust" standard errors.
The key assumption, is that regression errors $u_i$ have distinct variances $σ_i^2$. Then the variance matrix is: $$\Sigma = \operatorname{diag}(\sigma_1^2, \ldots, \sigma_n^2)$$ with its White's estimator: $$\hat\sigma_i^2 = \hat u_i^2$$ This is the HCE (heteroscedasticity-consistent estimator).
 Is the White's robust variance of $\hat{\beta}$ estimated by OLS assuming  independence? For example, assume that there is some $i,j$ such that $$Cov(u_i,u_j)\neq0$$ Because $i,j$ are part of a cluster. In that case $\Sigma$ is not diagonal but has the same diagonal as before. Will the White estimator converge to the diagonal of the true $\Sigma$?

No. White's robust errors are only robust to errors that vary linearly based on X(t).  If you have a type of serial correlation or clustering you will want to use Hansen method to adjust standard errors.


How to determine the Steady State of this model? Consider the system of two equations: $$y_t=\beta\mathbb{E}_t[y_{t+1}+\gamma\cdot z_{t+1}]$$ $$x_t=\rho x_{t+1}+y_t$$ $$z_t=(z_0-Z_t)e^{-at}+z_T$$
  Determine the steady state.

The solution manual says: $$y=\frac{\beta\gamma z}{1-\beta}$$ $$x=\frac{\beta\gamma z}{(1-\beta)(1-\rho)}$$
Now I have no idea how to derive these values. The lecture sheets don't mention anything, except that the steady state is solved when we have the value of the shock $z_t$ (intial and terminal). Could anyone explain me the mathematical derivation of the steady state?

In general, a steady state in discrete time is that the first difference is zero at some $t=t_0$, and that it remains so: $$y_t-y_{t-1}=x_t-x_{t-1}=0$$ for all $t\geq t_0$.

Hence, in a steady state, $y_t$ and $x_t$ are constant at some values $y$ and $x$. Thus, $y=\beta(y+\gamma z)$, which implies $$y=\frac{\beta\gamma z}{1-\beta},$$ and $x=\rho x+y$, which implies $$x=\frac{y}{1-\rho}=\frac{\beta\gamma z}{(1-\rho)(1-\beta)}.$$


Calculating the Net Domestic Product This should be fairly simple but I think I am missing something here.

Gross Investments:    46
Exports:  9
Disposable
Income:  190
Personal Savings: 10
Purchases:    84
Net Foreign Factor Income:    10
Consumption of Fixed Capital: 52
Dividends:  13
Imports of the U.S.:  12
Taxes on Production and Imports:  22
Personal Taxes:   38
SS   Contributions:   23
Statistical Discrepancy:  0

What is the net domestic product?

I am calculating 265 but being told it is 255. Am I suppose to subtract savings afterwards?

This is how I am calculating it:

Investments + Purchases + Disposable Income + Exports - Imports - Depreciation(Consumption of Fixed Capital)

46 + 84 + 190 + 9-12 - 52 = 265 then apply - 10 from Personal Savings?

After you get 265 you should take out -10 from Net Foreign Factor Income. This is in there implicity through disposable income etc, but was not produced in the country. Since you want domestic production you must take that out.


A differentiation step in a economic growth model I started studying Olivier Blanchard and Stanley Fischer's Lectures on Macroeconomics, but I couldn't follow the reasoning behind a differentiation step (at least I think it is something involving differentiation) in the chapter 2 (Consumption and Investment: Basic Infinite Horizon Models), page 38.
There, it is exposed by a simple production function the idea that output is either consumed or invested:
(1) $Y_t = F(K_t, N_t) = C_t + \frac{K_t}{dt}$
Then, as one of this production function's properties is homogeneity of degree one, everything is divided by $N_t$ for us to get the per capita form of this production function:
(2) $f(k_t) = c_t + \frac{dk_t}{dt} + nk_t$
And that is my question: I suppose that the $nk_t$ term is originated by the $N_t$ division of equation 2, since $\frac{d\frac{K_t}{N_t}}{dt}$ can be determinated as a multivariate chain rule, since both $K_t$ and $N_t$ are functions of $t$. But when I proceed like that, I always end up with:
(3) $f(k_t) = c_t + \frac{dk_t}{dt} - nk_t$ instead of a positive $nk_t$.
After some hours of trying to figure it out, I realized that my approach might not even be appropriated, since when we divide equation 1 by $N_t$, it makes more sense that equation 1 gets a form:
(4) $\frac{Y_t}{N_t} = \frac{C_t}{N_t} + \frac{\frac{dK_t}{d_t}}{N_t}$
Instead of what I originally thought:
(5) $\frac{Y_t}{N_t} = \frac{C_t}{N_t} + \frac{d\frac{K_t}{N_t}}{dt}$
And then I am kinda stuck. It is a basic question, but if someone could shed some light on it, I would be really, really grateful.

You have most of this; it seems like you might have a miscalculation when differentiating the fraction:
$$
\begin{align*}
\frac{dk_t}{dt} = \frac{d\frac{K_t}{N_t}}{dt} & = \frac{\frac{dK_t}{dt}N_t - \frac{dN_t}{dt}K_t}{N_t^2} \\
& = \frac{\frac{dK_t}{dt}}{N_t} - nk_t
\end{align*}
$$
thus
$$
\frac{\frac{dK_t}{dt}}{N_t} = \frac{dk_t}{dt} + nk_t,
$$
and you can plug this into your equation (4).


Debt-to-GDP ratio in connection to inflation On this segment of the Tucker Carlson show, interviewing Robert Hockett, as an advisor to Rep. Octavio-Cortez on the proposed Green New Deal, the following interchange ensues:

Tucker: "On the low end, this will be the most expensive thing the US has ever undertaken, including rural electrification, the Second World War,... And I'm just kind of wondering in a country that has more debt than GDP, how would we pay for that?"
RH: "Here's the key, [...], here is the take away - I want you to remember this; I hope everybody will remember this - inflation is a relation, right? It's the relation between the quantity of money and the quantity of goods. Now, if the money that you're spending is resulting in the production of a great many more goods, you have no inflation problem: more production absorbs more expenditure. The problem with the $7 trillion dollars that we spent during the Bush years, and of course, in the last tax cut is that it wasn't actually productive, but note that even that didn't bring about inflation."

Clearly, Robert Hockett seems to imply that in the absence of inflation, the high debt-to-GDP ratio is not an issue.
The question is:

Can inflation (or absence thereof) be used as a sole indicator that the debt-to-GDP ratio is (not) having deleterious consequences?

In fact it would seem as though inflation would help repay the debt by making it cheaper, and that the real problem would come in the absence of inflation, having to service the interest on the debt  through tax increases, or more debt...
Note the following passage in this answer by Brian Romanchuk:

...it is reasonably safe to argue that greater interest payments will squeeze out other spending if we want to keep inflation around a target level.

So interest on the debt would crowd out spending in other areas if inflation is to be contained. Naturally, there is the big distorting effect of the \$US acting as a haven investment strategy, potentially nullifing any linear relationship between debt and inflation. In fact it makes sense to consider the US as an aside case given that the $US is the reserve currency.
With all these caveats, inflation could act as an indirect indicator that the debt-to-GDP ratio is hard to manage.
That being said, it seems like a specious argument to claim that the stability of inflation following the last two rounds of tax cuts should be reassuring when two thirds of the US Budget go to non-discretionary spending as it is, and the projected cost of servicing the debt is about to surpass military spending, according to the NY Times:

But this is a comment more directed to the argument in this case than to the actual question about the value of inflation as a metric of too-high a ratio.

The premise that a high debt-to-GDP ratio will imply higher inflation is questionable. If we look at the data for the United States, there appears to be a negative correlation: the ratio was lowest in the high inflation period of the 1970s to early 1980s.

link to FRED graph

As hinted by your question, growing the denominator (nominal GDP) lowers the ratio.

Unless one believes in the Fiscal Theory of the Price Level (described in other questions), there is no obvious link between the debt ratio and inflation.

If we drop the focus on the ratio and look at government spending, we arrive at the theory of Functional Finance: the constraint on government spending is inflation. That is, we need to look at the size of the deficit, what the government is purchasing now, etc.; the debt ratio just tells us about historical spending.

Link to Kelton article on Functional Finance.

It looks like your question is really about the validity of Functional Finance, but you have written it up as being about the debt-to-GDP ratio.


What impact did monetary policy actions taken during the Great Recession (2007-09) have on U.S. economic performance? What impact did monetary policy actions taken during the Great Recession (2007-09) have on U.S. economic performance?

Quantitative easing and unconventional policy actions such as asset purchases and "forward guidance". I think I'm missing some things.

The consensus appears to be that the effect was large and positive. The IGM Forum asked a panel of economists to assess the statement

"Informed postmortems of Ben Bernanke’s Fed chairmanship will judge favorably the Fed's creative and aggressive policy initiatives from autumn 2008 through early 2009."

Not one disagreed. Weighted by their confidence, 90% of those polled agreed or strongly agreed with the statement.

http://www.igmchicago.org/igm-economic-experts-panel/poll-results?SurveyID=SV_1GF6NyHSVWhEtN3


Urn balls and probabilities Think of the following balls as individuals of populations.

Say I have $U$ urns, and some balls. Both numbers are really large. So large, that authors like Blanchard and Diamond have approximated the binomial operations that follow with Poisson probabilities.

The balls are either red ($R$) or green ($G$). At the beginning of the period, every ball is (randomly, iid) tossed into an urn. There is no miss chance (i.e. every ball is in some urn). Some urns will have more than one ball, some might have none.

There are two exercises I want to do in this setup, and I'm not sure to what extent they're overlapping (i.e. helping me understand one would help me understand the other one as well), so I will post both.

My issue is kind of that I have a binomial thinking going on, and you can see that from the structure that I have imposed onto solving the following probabilities. Should I switch to Poisson probabilities instead? What is the neatest way to solve the following setups?

Red Ball Solo

I would like to compute the ex-ante probability of a red ball (from the perspective of a red ball) of being tossed into an urn where there is no other red ball.

So far, I was thinking about doing

$$
Prob(\text{sole red ball}) = \sum_{x = 1}^{R + G} Prob(\text{Urn has $x$ balls}) \cdot \sum_{y=0}^{x-1}Prob(\text{No other red ball }  | x \text{ balls})
$$

Red Ball Super Ball

Out of each urn, one red ball becomes a super ball. This probability is uniform. I would like to compute the probability of a red ball becoming a super ball.

My abstract idea was again similar:

$$
Prob(\text{red ball becomes super ball}) = \sum_{x = 1}^{R + G} Prob(\text{Urn has $x$ balls}) \cdot \sum_{y=0}^{x-1}Prob(\text{$y$ other red balls | $x$ total balls }) \frac{1}{1+y}
$$

(If urns are vacancies and balls are unemployed, what distinction between unemployed workers does the Red/Green dichotomy reflects?)

Each ball has in front of it an identical box, each with the exact same lottery tickets, its ticket has a number on it, and each number corresponds to an urn.

We say "Go!" and each ball draws "randomly" (i.e. with equal probability) a ticket from the box in front of it. Note that the requirement that the probabilities are Uniform, impose the condition that, if we want to have proper distributions, the number of urns must be finite (not even countably infinite -see this post in statistics.se) Then:

RED BALL SOLO
From the point of view of a single Red ball, what is the probability that it will draw a number that no other Red ball draws?

Since each ball draws independently from the others, it is clear that we don't care at all about the existence of Green balls, to the degree that no upper limit of "number of balls in an urn" exists (if it existed the draws would not be independent). So Green balls (their number and what they draw from their boxes) can be kept out of the picture.

Since Red balls are indistinguishable, let's take $R_1$ as our hero. If it draws the number $1$ (i.e. conditional on) we want the probability

$$\Pr(R_j \neq 1 \mid R_1 =1)\;\;  j=2,...N_R$$
But draws are independent so we want simply

$$\Pr(R_j \neq 1) = \prod_{j=2}^{N_R}[1-\Pr(R_j = 1)] =  (1-1/N_U)^{N_R-1}$$

But $R_1$ can draw not just $"1"$, but any number, and each with probability $1/N_U$. So the probability of the event that we want, denote it $\Pr(\text{RBS})$ is (Law of Total Probability)

$$ \Pr(\text{RBS}) = \sum_{i=1}^{N_U}\left(\frac {1}{N_U}\right)\cdot \Pr(R_j \neq i \mid R_1 =i) = \left(\frac {1}{N_U}\right)\sum_{i=1}^{N_U}(1-1/N_U)^{N_R-1}$$

$$\implies \Pr(\text{RBS}) = \left(\frac {1}{N_U}\right) \cdot N_U \cdot (1-1/N_U)^{N_R-1} = (1-1/N_U)^{N_R-1}$$

...again.

This is intuitive: the greater the number of urns, the higher the probability. The greater the number of Red balls, the lower the probability.

Now, define job market tightness as usual by
$$\theta = N_U/N_R \implies N_R = \frac 1 {\theta} N_U$$

(here "U" denotes "urns" so vacancies). Then

$$\Pr(\text{RBS}) = \left(1-\frac 1{N_U}\right)^{\frac 1 {\theta}  N_U-1}$$

If $N_U$ grows "large" then the above is well approximated by

$$\Pr(\text{RBS}) \approx e^{-\frac 1 {\theta} }$$

The higher job market tightness, the higher the probability that an unemployed will be matched solo to a vacancy (again, ignoring what the Greens represent).


A question about Fixed effects estimation I have a fixed effects model as follows:

$Y = x_1, x_2, x_3$, (fixed effect), (error term)

Is there any way I can check whether Cov($x_1$, (fixed effect)) is larger or smaller than 0?

The panel data I have consists of 7858 individuals and 5 years.

Thanks!

Having read up on your question it seems the fixed effect is fixed. If this is indeed the case it will have zero variance and hence zero covariance with any variable.


Simple closed economy problem Consider a simple closed economy model where Y = C + I + G, consumption is given by the function C = 100 + 0.5 (Y - T), investment is I = 50, government purchases are G = 20, and the government’s
budget is balanced.

How do I work out what tax is, to work out the amount of autonomous spending? Is there something obvious I'm missing?

Given your equations, you can find

$$Y = C + 50 + 20 \implies Y = C + 70$$

You can then substitute $Y$ for its equal into your other equation

$$C = 100 + 0.5(C + 70 - T)$$

Finally, given a balanced buget, you know that $G = T$, which should be enough for you to solve for $C$.


Doesnt fractional reserve systems limit collapse of the money supply? For example the black death occurred in basically a full reserve system. Because there was no m2 to destroy, the fall in output was inflationary. The same money existed chasing fewer goods.
Doesnt the same paradigm apply to fractional reserve? If the monetary base is around 10% of the supply then wouldn't a 90% collapse in output eventually become inflationary?
Money velocity is one way deflation could still happen. But even then arent there also fairly high floors to velocity, for example rental yields tend to increase in recessions therefore this would raise velocity anyway?

Without a historical reference, I have doubts about the Black Death reference. Scholarship around the Black Death has changed.
The premise behind this question is that the velocity of money is constant. Since we can see that it is not - link to FRED M2 velocity - we need to ask what else drives the price level.
The obvious concern is that there is no explanation of how output falls 90%. Is it because of out-of-control bankruptcies causing business failures, while the government does nothing? That’s a deflationary environment. Was there a war or pandemic that destroyed industrial capacity? Probably inflationary.
If we step away from the text of the question, and just look at the title - does fractional reserve banking limit the shrinkage of the money supply - the answer is technically no. For the few remaining countries with reserve requirements, if deposits fall, so do required reserves. If the central bank keeps excess reserves at zero, then reserves will shrink along with deposits. As for currency in circulation, it is determined by the desire of the private sector to hold it. If holdings depend on incomes, holdings will fall in line with incomes.
What might keep the monetary base from shrinking is a deliberate policy choice of the central bank.


Numerical analysis in economics Recently, I have become interested in numerical analysis withinin macroeconomics. In particular, I have been trying to learn algorithms such as "backwards iteration", the "shooting method" etc, in order to numerically solve an optimal control model, more specifically a growth model.

Could you give me some references for introductory and intermediate numerical analysis textbooks ?

You can also find Kenneth Judd's book on numerical analysis here. It is one of the very known and notorious books in that field.


In law of DMU statement what is meant by "keeping other commodities"? Law of Diminishing Marginal Utility states that marginal utility from consuming each additional unit of a commodity declines as its consumption increases, while keeping consumption of other commodities constant. Here my doubt is that "keeping consumption of other commodities constant" means what? Here "other commodities" means which are those? Please clarify this with an example.

You have a beer. The beer is great. You have a second one. It's equally good, but it adds less to your utility (decreasing marginal returns). You have a third beer, which makes you also feel better, but the effect is relatively small. Since you're drinking only for a while, you become hungry and you order a spicy pizza. The pizza makes you thirsty and you have, you name it, another beer. This fourth one is likely to be better than the third one, as it kills the spices.

In this example, the pizza is the 'other commodity'. The term "keeping consumption of other commodities constant" is just a typical economics way of saying "I look at beer consumption in isolation, but I am aware that things are usually more complicated". The law of diminishing marginal utility is just not valid anymore if you consume lots of commodities because of complementarities in consumption.


Intermediate demand vs. Intermediate consumption I am trying to understand what's the difference between intermediate consumption and intermediate demand. The context is the European System of Accounts, which says that intermediate demand is the same as intermediate consumption for the total economy, but not whithin sectors. I think the difference may be related to trade margins or transport, but I can't find it.
Thank you so much

Intermediate consumption

total intermediate consumption is the difference between gross output (sales or receipts, which can include sales to final users in the economy or sales to other industries (intermediate inputs) and Value added GDP (total market value of all final goods and services produced).

This difference would be called intermediate inputs which are goods and services that are used in the production process of other goods and services and are not sold as final goods.

They are consumed or used up as inputs in production process by businesses, they are typically subcategorized as raw materials, energy, and purchased business services (which include various other operating expenses).

Intermediate demand

intermediate demand which is called Intrasector transactions or Intrasectoral transactions.  I will go with the name intrasectoral transactions (they all mean the same thing).  It is the value of production sold to other industries( i.e. NAICS 481, 482  ) within the same sector (NAICS 48).

To avoid double counting with the economic measurement within a sector intrasectoral transactions(the value of certain inputs produced within the same industry/sector) are removed.

The sectoral measures remain the only estimate that is useful at both the detailed industry level and the aggregate sector economy level.

When measuring the total economy one would use intermediate input in order to construct gross output  but when you are measuring sector level data and you are using the same intermediate inputs that are produced by industries within the same sector then those values need to be removed in order to prevent double counting.


Derive the growth rate of an equation I have the following equation:

$$\mu =\left [s_{\pi }-v(s_{\pi }-s_{W})+\zeta   \right ]$$

And I have to derive its growth rate, which is:

$$\dot \mu =-\frac{v}{\mu } (s_{\pi }-s_{W})\dot v$$

Do you have any idea about the approach to follow? Thank you so much :)

First, note that the growth rate of $\mu$ is defined as $\dot\mu = \frac{ d\mu }{ \mu }$. Therefore, you will have to

take the total differential of the equation; and
divide by $\mu$.

For the first step, as in your previous question, simply use the rules of total differentials, specifically the product rule that states that for variables $X$ and $Y$, the total differential of $XY$ is given by

$$d(XY) = Y \, dX + X \, dY$$

Assuming that $s_\pi$, $s_W$ and $\zeta$ are (constant) parameters (so that by the constant rule, $ds_\pi = ds_W = d\zeta = 0$), we can apply this to your equation:

$$\begin{align}
d\mu & = d \left[ s_\pi - v (s_\pi - s_W) + \zeta \right] \\
& = ds_\pi - d \left[ v (s_\pi - s_W) \right] + d\zeta \\
& = -\left[ (s_\pi - s_W) \, dv + v \, d(s_\pi - s_W) \right] \\
& = -(s_\pi - s_W) \, dv
\end{align}$$

Now divide both sides by $\mu$, noting that since $\dot v = \frac{ dv }v$, we also have $dv = v \dot v$:

$$\begin{align}
\dot\mu = \frac{ d\mu }\mu & = -\frac{ dv }\mu (s_\pi - s_W) \\
& = -\frac v\mu (s_\pi - s_W) \dot v
\end{align}$$

which is the desired result. As before, see  chapter 8 of Chiang and Wainwright, Fundamental Methods of Mathematical Economics, 4th ed., McGraw-Hill 2005, for more on total differentials. Alternatively, see this Q&A post of mine explaining the rules of total differentials and showing another example of how to apply them to an equation.


What analysis has been done to predict the next big financial crash? There has been a lot of talk about a big pending financial crash due to the slowing global economy, low interest rates, rising debt levels, etc.  Now I'm wondering:

Has anyone done any analysis to predict exactly when the next big crash / credit crunch will be?

Specifically, what indicators have analysts been tracking to predict when the next crash will happen?  Has anyone agreed or suggested what will be the critical thresholds, and/or likely trigger(s)?

Ideally I am looking for some measure of systemic risk which effectively gauges how unsustainable a system is, or rather, how long an economic system can be sustained before it is likely to collapse.

I have made my own analysis and prediction based on long-term trends in slowing growth vs rising debt, but has anyone done this kind of analysis before?

Slowing growth: http://bit.ly/1IbPZam

Rising debt: http://bit.ly/1N94886

A useful principle to have in mind here is the so called 'volatility paradox´ oft-cited by Marcus Brunnermier (Princeton prof):

The idea is as follows: a) financial institutions are in the business of taking reasonable risks; b) when the financial system is deemed very stable, then it makes sense for financial institutions to engage in risky activities, because, if the system is stable those risky bets are manageable, reasonable bet; c) when all financial institutions jointly engage in risky activities, the system becomes unstable. In other words, safety engenders individual risk-taking, which creates aggregate risk. This works the other way too: riskiness engenders risk averse attitudes, which lead to a stable system.

If you believe this story then you get some insight into why its difficult to predict crises: they happen when risks build up during periods of safety and stability...


Maximisation problem in a multiproduct firm I am currently reading the book "Microeconomics: Principles and Analysis" by Cowell on my own. I'm interested in the section of the multiproduct firm, but i'm confused with the use of the profit function. Specifically, about how to pose the target for the maximization problem. Here an example with two goods $x$ and $y$, two factor $k$ and $l$ and two Cobb-Douglas production functions.

\begin{equation}
\begin{array}{l}
\text{Max}\quad \pi=p_{x}q_{x}+p_{y}q_{y}-w(l_{x}+l_{y})-v(k_{x}+k_{y}) \\
\text{subject to:} \\
 q_{x}\leq k_{x}^{\alpha}l_{x}^{\beta} \\
q_{y}\leq k_{y}^{\gamma}l_{y}^{\delta} \\
L=l_{x}+l_{y} \\
K=k_{x}+l_{y}
\end{array}
\end{equation}

Am I posing the question well? How are the first order conditions?

The question "how are the first order conditions" seems very unclear to me, and I am providing a set-up for finding and writing them out, while explaining the Kuhn-Tucker conditions that are easy to struggle with.

Though we try to avoid giving away basic study question answers, it's a positively voted question without an answer, and I still think these questions have value for future users. Enough time has also passed where there's no risk of helping someone get through a class, if that was the intention.

Usually in cost minimization problems where the production function is a constraint, there is a set quantity to be produced that then leads to minimizing cost with respect to that. Here in this profit maximization problem, you have a minimum amount of production required of both goods, which I find interesting.

We can note the objective function (profit) is linear, and therefore concave and differentiable. The constraints are more interesting because the Cobb-Douglas form is not necessarily concave, namely when the exponents sum to more than 1. So you can ask yourself when the constraints will be convex (they are certainly differentiable). These ideas are related to the sufficient conditions for an optimum. A solution exists by the Weierstrass Theorem (constraint is compact and the objective function is continuous).

To look at the first order necessary conditions, we can omit your last two equalities since they don't add anything. We take:

\begin{equation}
\begin{array}{l}
\max_{q_{x}, q_{y}, l_{x}, l_{y}, k_{x}, l_{x}} \quad p_{x}q_{x}+p_{y}q_{y}-w(l_{x}+l_{y})-v(k_{x}+k_{y}) \\
\text{s.t.} \\
q_{x} - k_{x}^{\alpha}l_{x}^{\beta} \leq 0 \\
q_{y} - k_{y}^{\gamma}l_{y}^{\delta} \leq 0 \\
\end{array}
\end{equation}

Form the Lagrangean:

$$\max \quad \mathscr{L} = p_{x}q_{x}+p_{y}q_{y}-w(l_{x}+l_{y})-v(k_{x}+k_{y}) - \mu_x (q_{x} - k_{x}^{\alpha}l_{x}^{\beta}) - \mu_y (q_{y} - k_{y}^{\gamma}l_{y}^{\delta})$$

(note the signs in front of the Lagrangean multipliers)

Then, in place of the derivative with respect to the multipliers, we have our constraints with complementary slackness conditions. We take the other constraints as well.

$$\frac{\partial \mathscr{L}}{\partial \ ( \cdot )} \leq 0 \quad ; \quad ( \cdot ) \geq 0 \quad \forall ( \cdot )$$
$$\text{constraint} \quad ; \quad \mu_{(\cdot)} \geq 0$$

And from there you can move on to solve the system, but you may find yourself in a weird spot because we haven't been able to establish uniqueness.


Finding "own" price elasticity of demand Only two groups buy the Dripfix, abbreviated as good $D$. Group 1's demand function for the Dripfix is $f_1 (p_D)=300-p_D$, where $p_D$ is the price of Dripfix. Group 2's demand function is $f_2(p_D)=120-p_D$.

What is each group's "own" price elasticity of demand?
What is the equation for the market demand?
At what price $p_D$ is the market elasticity $-1$?

Here is my work so far:

Group 1's price elasticity is $\epsilon_1=-\frac{p_D}{300-p_D}$. Group 2's is $\epsilon_2=-\frac{p_D}{120-p_D}$.
The market demand is $420-2p_D$ for $p_D \leq 120$ and $300-p_D$ for $p_D > 120$.

Are these two parts correct so far? If so, how do go about determining the market elasticity when the market demand is made up of two components?

Your work for 1 and 2 is correct.

For 3, look at each segment individually. There are two points which have an elasticity of $-1$, one on each segment.


Transfer payments and IS multiplier Where do transfer payments (unemployment subsidies, etc.) enter in the multiplier formula for the IS curve?

The usual multiplier is of the form $\frac{1}{1-c(1-t)-m}$, where $c$ is the marginal propensity(m.p.) to consume, $m$ is m.p. to import, and $t$ is the tax rate. I've tried to see $t$ instead as net transfers rate, i.e. transfer payments minus taxes. But I'm not sure if it's the right way to think about this...

Any help would be appreciated.

Notice that you only  consume out of your disposable income, that is, adding transfers and removing taxes. Thus, from that formula of the multiplier, yes, it should be there, in the $(1-t)$.

As (assuming) $C=cY^D=c(1-t)Y$ and thus, $MPC=\partial C/\partial Y = c (1-t)$, then $Y-Y^D=tY=\text{Taxes}-\text{Transfers}$, with $t$ "condensing" all the information.


Why do we model that higher government involvement increases output? I have just read about the "real intertemporal" model of a macroeconomy in Macroeconomics by Stephen Williamson. I am concerned about how it says any increase in government spending, even if it is equal to an increase in taxes, increases the output of the economy. This is because taxes don't reduce private consumption spending as much as government spending increases demand. But, if I extend this idea to the extreme, where government involvement is exceedingly high, I don't understand why people will carry on spending more than they earn, with high taxes and no way to pay off their debt. It seems like the autonomous component of private spending is problematic when thinking about tax (as opposed to an equilibrium), because this theoretically causes people to overspend in comparison to their income.

The deduction is that, with any positive multiplier (not just one greater than 1 as mentioned in the textbook), the more the government intervenes in the economy, the higher the GDP will be, ad infinitum, so that this model encourages higher and higher government involvement. In reality, socialist countries such as Russia have had lower output than free-market countries such as the United States, and it is well known that government bureaucracies are more inefficient than the private sector. What I'm checking here is where the theory leads. I assume this must be a Keynesian-type model, because it encourages government involvement, and that other models give a different story (neoclassical perhaps?).

As a public administration student as well, I don't like it how government spending is treated so differently to private spending, and this separation here seems to be problematic (as assuming that government departments are efficient in comparison to the private sector).

The book is talking about the short term effect. And yes, such a policy would be thought as Keynesian.

In the long run, excessive government spending will cause inflation (if unfunded) or reduce both private production and demand (due to excessive taxation).


Change in price and income using the Slutsky equation Quantity bought is given by
$$
q(m,p) = 0.02 m - 2 p
$$
where $q$ is number of bottles bought, $m$ is income and $p$ is price per bottle.

If income is $m = 7500$ and price is $p = 30$, the number of bottles is
$$
q(7500,30) = 0.02 \cdot 7500 - 2 \cdot 30 = 75 \cdot 2 - 60 = 90
$$

Now if price rose to $p = 40$, how much income would I need in order to buy the same amount as before the price change?

I would just solve $q(m,40) = 90$ with respect to $m$, i.e.
$$
q(m,40) = 0.02 \cdot m - 2 \cdot 40 = 90 \Leftrightarrow m = \frac{90 + 2 \cdot 40}{0.02} = 8500
$$

But apparently, I should have used the Slutsky equation, so the answer is something like
$$
\Delta m = q \Delta p = 90 \cdot (40-30) = 900
$$
so the new income is $7500 + 900 = 8400$.

But with an income of $m = 8400$ and price $p = 40$, I cannot afford 90 bottles since $q(8400,40) = 0.02 \times 8400 - 2 \times 40 = 88$, So why is this solution correct?

Why is my solution incorrect and how is $\Delta m = q \Delta p$ related to the Slutsky equation?

The question is not asking what you solved. You literally gave how much income would be needed by buy $90$ bottles at the new price. What the question is asking is basically "calculate the income effect, and add it to the original income, in order to cancel it out".

That is, you solved for what he would have bought if there was no income or substitution effect, but the answer wants to know what he would have bought if there was no income but still a substitution effect.

How the slutsky equation comes into play? That formula you gave is the income effect. The difference of two bottles is the substitution effect.

From here on is an attempt at providing intuition that may be wrong in some aspect. I would not read it unless the above paragraphs did not make sense.

At original prices and income you want to buy $90$ bottles. At the new price and income you want to buy
$$
.02 \cdot 7500 - 2\cdot 40 = 70\text{ bottles}
$$
you the quantity demanded has changed by $20$. That is,
$$\frac{d x}{dp} = 20
$$
(counting a ten dollar price change as small, which is probably not the best assumption).

The slutsky equation says that we can decompose this change in quantity demanded into an income and substitution effect. That is,
\begin{align}
\Delta x \text{ price change } = \Delta x \text{ substitution effect} + \Delta x \text{ income effect}
\end{align}
Our income has decreased by the number of bottles we were buying times the change in price (This is important to understand, IMO). Think about it, if you were buying $90$ bottles, and the price went up by $\$10$, now you are paying $90\cdot 10 = 900$ dollars more. Therefore, after the price change it is like we are facing prices of $\$30$ and income of $7500-900=\$6600$, if we are discussing the income effect. That is, if we are discussing the idea/thought/alternate reality where, instead of prices changing, we had prices be the same but instead our income decreased by $900$ dollars, we would demand
$$
6600\cdot .02 - 2\cdot 30 = 72
$$
Which means that we have a substitution effect of $2$ and an income effect of $18$. So to cancel the income effect, we would need enough original income to buy $70 +18$ bottles, which is $8400$ dollars.

Now how/why these decompositions work I am still trying to better understand myself, so my reasoning may be off or wrong somewhere. There are also different ways to consider/define the income/substitution effects, which is something to take into consideration.


How to calculate marginal utility with two goods? I'm just getting started as an amateur into microeconomics and I really can't understand this thing about marginal utility when more than one good is involved:

Let's say I have the utility function U = x(y+1).

Now, from what I've studied, I  think that the marginal utilities for x and y should be:

MUx = y+1
MUy = x

I just don't get how to arrive there "mathematically", and I fear I wouldn't be able to find the marginal utilities of a more complex function, for example U = x(x+y)

Could you help me?
Thank you!

This is quite simple to answer given you know a bit of multivariable differential calculus. You're looking for partial derivatives of the utility function.

So, given $$U(x,y) = x(y+1)$$ we have $$\frac{\partial U}{\partial x} = y+1$$ and $$\frac{\partial U}{\partial y} = x$$.

These are the goods' marginal utilities.


What assurances are there that the Federal Reserve does not give money to banks? My understanding of the operation of the United States Federal Reserve Bank is that it invents dollars by a unilateral, unbalanced credit to its own account and then it loans this money to member banks. In some cases this money is loaned to non-bank institutions of the Federal Reserves choosing and that all of these loans, whether to member banks or non-member institutions are secret.

What assurance is there that the Federal Reserve is not giving the money to the various recipients as opposed to lending it?

For example, let's imagine the Federal Reserve "loans" $400 billion to JP Morgan Chase. What is to prevent them from "forgiving" this loan, meaning to allow the recipient to never pay it back? Or, in a similar vein, simply making the terms of the loan essentially infinite, for example making it a zero coupon loan for 5000 years, which is effectively a gift.

What assurance do members of the public have that this is not occurring?

According to this official link

Does the Federal Reserve ever get audited?

  Yes, the Board of Governors, the 12 Federal Reserve Banks, and the
  Federal Reserve System as a whole are all subject to several levels of
  audit and review:
      The Government Accountability Office (GAO) conducts numerous reviews of Federal Reserve activities.
      The Board's financial statements, and its compliance with laws and regulations affecting those statements, are audited annually by an
  outside auditor retained by the Office of Inspector General (OIG).
      The Board's OIG audits and investigates Board programs and operations as well as those Board functions delegated to the Reserve
  Banks. Completed and active GAO reviews and completed OIG audits,
  reviews, and assessments are listed in the Board's Annual Report.
  (Before 2002, the reviews were listed in the Board's Annual Report:
  Budget Review.)
      The financial statements of the Reserve Banks are also audited annually by an independent outside auditor.
      Each week, the Federal Reserve publishes its balance sheet and charts of recent balance sheet trends, as well as provides an
  interactive guide to the Fed's balance sheet. The balance sheet is
  included in the Federal Reserve's H.4.1 statistical release, "Factors
  Affecting Reserve Balances of Depository Institutions and Condition
  Statement of Federal Reserve Banks."
  In addition, the Reserve Banks
  are subject to annual examination by the Board. The Board's financial
  statements and the combined financial statements for the Reserve Banks
  are published in the Board's Annual Report.
  See our audit page for
  more information on all of the above audits and more information on
  the accounting, financial reporting, and internal controls of the
  Federal Reserve Board and Federal Reserve Banks.


Stylized Facts: Price Dispersion I'm looking for as many empirical "stylized facts" about price dispersion (in products markets) in the idea of Burdett and Judd (1983) as possible.

For example,

how high is the variance of price dispersion over different markets?
Is there a time trend in price dispersion?
How does price dispersion vary over the business cycle?

For the last question, I only found Cornia et al (2011), who show that it is very pro-cyclical for airlines - probably not the most generalizable result.

A little empirical evidence for your first point can be found in

Erik Brynjolfsson & Michael D. Smith (2000): "Frictionless Commerce?
A Comparison of Internet and Conventional Retailers", Management
Science, 46(4), 563–585.

They look at the markets for books and for CDs both online and offline and estimate the price distributions. Whilst they look at price changes, they do not present data on the change in price distributions over time.


GDP per Capita in Panel Data: Must the base year be the same for all cross-sections? I'm trying to run a small project using time series in panel data. One of the variables used is the GDP per capita for a few countries (the countries are the cross-sections). Is there a problem if the base year for a few countries is different? Say for example, Spain's series has 2005 as base year while Germany's series 2010 as base year. Does this cause any sort of problems?
Thank you in advance.

Base rates account for the change in value of a currency that happens overtime because of inflation.
Not only do the base rates need to be the same, but if you are including all of these in the same panel, then the currencies need to be in the same unit as well, otherwise, the different country GDP's are not comparable.
Fortunately, most of the big international databases with GDP time series usually have multiple versions, with different base years, and converted to common currencies (usually USD) that you can use to assemble what you need.  Just a few places to start you off:
FRED
World Bank WDI
OECD Data
Note: for GDP data, these sites often present data from the same sources


Growth regressions over 3-year periods; regressors in average or year values? Say that I want to estimate a growth regression basically similar to the Augmented Solow Model one, except my dependent variable is not Y/L, but it's the average GDP growth over a 3-year period. As my independent variables, I'd take GDP at the beginning of the period and then average values of savings rate, human capital, etc... over the period. However, I've seen it done taking savings rate and such values for the last year of the period. So, it turns out something lie:

Avg Growth 2010-2012 = GDP 2010 + Sav Rate 2012 + Hum K 2012 etc...

When I estimate it, the coefficients are correct and significant, however I cannot understand if it's right. I'd understand taking all independent variables in first year values, or taking the rates as averages over the period, but I can't see why it would be correct to base the growth of the period over the last year's value.

Can somebody shed some light on this please? Could it just be a mistake?

I have never seen any "serious" (i.e. peer-reviewed) study defining independent variables as the end of the period under consideration (if you could provide some link to the ones you are referring to, it would be helpful). Normally, they are used as the average over the period or at the initial year. For instance, in the big field of finance and growth, that is the common approach. Thorsten Beck - among the most renown researchers in this field - says it himself (bottom half of page 2). There are many examples of this in other fields too. For instance, when estimating inequality on growth (top of page 282), or the famous paper by Xala-i-Martin, where he run 4 million growth regressions. Look in page 7 and 8, in sections "Data" and "Choosing the Fixed Variables".

Now, why not to use final period variables? Because of reverse causality concerns. An economy which grows fast over a given period might end up with a higher savings rate and human capital level at the end of the period. As such, the order of causality is in fact the opposite at the one your equation is assuming (even though the sign coming from estimations might be the same!), leading to endogeneity and therefore to inconsistent estimates.

Even the use of average period variables is subject to some controversy. As Xala-i-Martin puts it in the aforementioned paper (page 8):

  I reluctantly use some variables of this sort (the average savings or investment rate and the DeLong and Summers measures of equipment and non-equipment investment are examples in this category). The reason for being reluctant to the inclusion of such variables is that these may be “more endogenous” than the variables measured at the beginning of the period.

To conclude, using end of period variables is a very risky practice, and in my view very hard to justify theoretically and empirically. Even more, it seems unnecessary. Why not use beginning of period? Or average?


Are my conclusions correct in context of these examples of forceful extraction of money? There are two examples, one for a bandit, the another one is for the government.

Suppose we have a simple economy, a bandit and a teacher.
The teacher can teach the bandit, but the bandit can't offer anything of value to the teacher.

Suppose at the start the bandit has \$100, while the teacher has \$0. The bandit pays for lessons $100 and the teacher consequently teaches them. Now the teacher has all the money and the bandit has nothing but their gun. If we will stop here GDP will be \$100 because Consumption=\$100, while everything else is zero.

But our bandit being bandit uses their gun to take all money from the teacher. Here we go again, the bandit has \$100, while the teacher has zero. And again, our bandit pays \$100 for lessons. If we will stop here our GDP will increase by \$100, totaling to \$200. Conclusion #1: We will be able to increase our GDP with these robbing-spending cycles, each cycle increasing GDP by \$100.

Now let's replace our bandit with the government. Our bandit declares themselves to be the Sovereign over these lands, with God given divine right to take people's money by force, (i.e. to tax them). The teacher recognizes them as their Sovereign. We replace our robbing-spending cycle with taxing-spending cycle. The Sovereign pays for lessons, the teacher enjoys sitting on the money for a while and then they get taxed of all of their money. This time Consumption=0, but Government Expenditures increase by \$100 for each iteration of the cycle ("The State is me", as our Sovereign would say). Conclusion #2:  We will be able to increase our GDP with these taxing-spending cycles, each cycle increasing GDP by \$100.

Well this is trivially true because GDP measures output. Here the only producer in the whole economy is the teacher, if the bandit or government can make teacher work more then of course GDP increases.

Note the GDP increase here because the teacher actually produces 200\$ worth of services not because money ‘circulate’. You can calculate GDP even for barter economy where there is no money. What matters is that this bandit or government managed to ‘convince’ the teacher to produce 200\$ of services.

Even in a totalitarian society where everyone is forced to do things at the end of the barrel of a gun GDP won’t be necessary zero.

However, this being said it is not realistic to assume that if government set taxes to 100% people will still provide goods and services assuming government can’t use forced labor.


How is Turkish economy handling the pressure of so much defense purchase? How did Turkey manage to create a springboard for its defense industry so fast?

TFX program costs USD 10bn
S-400 purchase costs USD 2.5bn
Turkey targets 30% hike in military spending next year

How is Turkish economy handling the pressure of so much defense purchase?

Turkey had an estimated military spending of $14.8 billion in 2016.

A 30% increase would be a $4.5 billion increase. That's 0.5% of GDP. Turkey's government budget deficit was 1.1% in 2016. All else equals, the budget deficit would rise to 1.6% with that kind of increase in spending. Either that or they cut spending elsewhere.