R or Python for private sector economist/strategist Quick question (but complex answer) : R or Python ?

I work as an economist/Strategist in the finance industry. As I do a lot of presentations, notes-writing, data searching, my programming time is limited but we try to develop “small scale” models to answer economic/finance questions. So, I mainly do standard stuff such as PCA/factor models SVAR with sign restrictions, VECM…I usually use what tools is best suited for the job (if I find replication codes I can adapt for instance), so usually MATLAB for SVARs and factor analysis, Eviews for quick and dirty stuff…

Now, I am looking at Python and R (which I dabbled with a few years go). Python is broader and I could use it for other stuff (like automate boring stuff with a comp or an iPad) but it seems there are fewer pure econometrics packages than in R (did not find anything for SVAR with sign restrictions for instance). I am looking to extract data from the web as well, and although they both seem to be able to do that, Python, seems more suited right ?

I know there is always the possibility of calling one from the other (with like Rpy) but then you need to learn both languages.
Any advice ?

Thanks!

If you already know how to code in MATLAB then python is more similar to it than R so I would say you will have easier time to transitioning there.

Otherwise, both R and Python are programming languages so you will be able to do all those things in both of them as you can always program your own functions.

The strength of R is that the language has a large following in the research community, which then in turn means that people write a lot of packages that focus on exactly the models that are commonly used in research. For more than two decades academics and statisticians basically helped to develop R so you can now find library for anything there save for really the most cutting edge econometric techniques - and you can bet that the first place where those will get their packages will be R. For most of the things you describe in your post you will have some excellent libraries and they are relatively more easier to estimate with R than with Python.

Python is more of an general purpose programming language which strength is very intuitive syntax. Writing in Python can sometimes feel like writing in pseudo code - its very intuitive and natural. However, since its more general purpose language its not as tailored to statistical analysis as R. You will definitely be able to do all you want to do there but more routine statistical analysis will be a bit more time consuming to code.

I actually prefer using R for any standard statistical analysis and Python for numerical analysis & machine learning & mining data through web-scraping.


How would the risk premium and a simplified taylor rule change the MP curve? Ok so we're given a monetary policy rule where

$$R^{CB}_t-\bar r = \bar n \tilde Y \space  where \space \bar n>0  $$

and
$$R_t = R^{CB}_t+\bar p $$

Where $\bar p $ is risk premium $\bar n$ is a parameter and $R^{CB}_t$ is short run interest rate.

The IS curve is of course $ \tilde Y = \bar a - b (R_t - \bar r)$

is $\bar p = 0$ is assume the IS-MP looks the same graphically except the MP curve is now determined by $R_t = R^{CB}_t+\bar p $ so rather than just being the target interest rate of the central bank it's a sum of the target rate and risk premium so if $\bar p > 0$ it would distort monetary policy. As it would require higher targets to get the desire interest rate or inflation.

Also i thought by rearranging that $R_t - \bar r=\bar m (\pi_t - \bar \pi) =\bar n \tilde Y + \bar p  $

Which mean IS curve is  $\tilde Y = \bar a - b(\bar n \tilde Y + \bar p )$
With mp curve

I'm a bit confused

I know that the whole point of taylor rule is to counteract shock in the economy with with fiscal stimulus hence $\bar n \tilde Y $ the risk premium is solely a distortion of the MP curve so maybe i should have $\bar p $ in the is curve?

Oh yeah i haven't consider the fishing equation which i presume calculates the MP curve
$$i_t = R_t + \pi_t = r+\pi_t +m(\pi_t - \bar \pi) $$

Then if $R_t = R^{CB}_t+\bar p  $
$$i_t =R^{CB}_t+\bar p + \pi_t = r+\pi_t +m(\pi_t - \bar \pi) $$

But i want to make it look like this
$$i_t =R^{CB}_t+\bar p + \pi_t + \bar n \tilde Y \space \text{With an upward sloping demand curve} $$

I'M quite confused

Edit: So i got something like this but i'm not so sure i don't like that i have a $-\bar n \tilde Y$  it should be positive

I get it now

Under traditional monetary policy
MP Curve is set by the central bank and follow the fisher equation
$$i_t = R_t + \pi_t$$

But traditionally the taylor asks that when the central bank considers monetary policy that they consider short run output and inflationary gap.
$$i_t = R_t + \pi_t+\bar m(\pi_t-\bar \pi)+\bar n \tilde Y_t$$
Where the monetary policy rule is
$$R_t-\bar r = m(\pi_t-\bar \pi)+n \tilde Y_t  $$
Now
$$R^{CB}_t-\bar r = \bar n \tilde Y \space  where \space \bar n>0  $$

and
$$R_t = R^{CB}_t+\bar p $$

I assume that in the original taylor rule
$$R_t-\bar r = m(\pi_t-\bar \pi)+n \tilde Y_t  $$

Hence in the original taylor rule
$$i_t = R_t + \pi_t+\bar m(\pi_t-\bar \pi)+\bar n \tilde Y_t$$
$$i_t = R_t + \pi_t+R_t-\bar r$$

But in this simplified taylor rule $R^{CB}_t-\bar r=n $
$$R^{CB}_t-\bar r = \bar n \tilde Y  $$

To which i assume also that
$$R_t-\bar r = \bar n \tilde Y = m(\pi_t-\bar \pi) $$

Hence
$$i_t = R_t + \pi_t+R_t-\bar r$$
$$i_t = R_t + \pi_t+n \tilde Y $$

If $R_t = R^{CB}_t+\bar p$

$$i_t = R_t + \pi_t+n \tilde Y $$ $$i_t =R^{CB}_t+\bar p + \pi_t+n \tilde Y $$

Hence the $ n \tilde Y $ component of the simplified taylor rule makes the MP curve upward sloping.


Incomes of different professions Doctors average salary is around \$110,000 a year, whereas NBA stars salary may well cross \$5,000,000 a season.

Why do sports players and television stars make more than doctors and politicians?

NBA stars create more money (ticket prices, jersey sales, merchandising, branding). However, only few basketball players play in the NBA, the 99% of basketball players are amateurs. But all the doctors earn realitively well.


Practical examples of fair division algorithms being used Consider the problem of fairly sharing a homogeneous cake between two people. It is well-known that a fair division can be achieved through the divide and choose procedure: player 1 cuts the cake into two pieces and player 2 chooses a piece.

This problem can be generalized to non-homogeneous cake, more than two players, etc.

My question is: are there any concrete examples of people using the fair division procedures (such as divide and choose) that emerge as the solution to such problems in practical applications?

The easiest generalization, of envy free sharing of a heterogeneous cake between two cake eaters is quite common. My family growing up frequently used the you divide and I choose method for sharing a lone piece of dessert. Depending on what you'd accept for "concrete example", Abraham and Lot use this method to divide the land of Canaan.  A  two-stage fair division problem was used in the partitioning of Germany after World War II. The Talmud has examples of fair division rules, which though are only thought experiments, are thought to have been applied in the Jewish diaspora over inheritance matters.

I would also argue that the marriage / matching problems of Lloyd Shapley and Alvin Roth are a form of fair division, and one that scales to very large numbers of players and applies only to multiple, indivisible "cakes. Their methods have been used extensively in real world problems of school, job, and kidney assignment.


Adjusting GDP for Environmental and Resource Impacts It is widely recognised that GDP as conventionally measured does not reflect an economy’s impact on the environment and its consumption of natural resources.  There have been various attempts to develop broader measures of economic performance via adjustments to conventional GDP (some of which also address non-environmental limitations of conventional GDP), for example:

Measure of Economic Welfare (Nordhaus & Tobin 1972)
“True NNP inclusive of natural resource stock diminution” (Hartwick 1990)
Gross Sustainable Development Product (GSDP) (Global Community Assessment Centre)
Genuine Progress Indicator (GPI) (eg Anielski 2001)
Green GDP (a term whose precise content appears to be disputed (see eg Boyd 2006))

Is this just a proliferation of alternative measures, or is it possible to discern progress or convergence towards a best or most useful measure that adjusts GDP for environmental and resource impacts, or perhaps different best measures for different purposes?

A good place to start is a report by the U.S. National Academy of Science called Nature's Numbers. The upshot: There is a consensus among economists that it is possible to refine standard measures of GDP rigorously to incorporate adjustments for impacts on environment and natural resources. Implementation is in practice difficult due to data problems.

Most alternative indicies, e.g. GPI, are not consistent with national income accounting principles. But since there is a demand for such indicies, there is a supply response.


In the case of externalities, does the initial allocation of rights affect the final outcome from the perspective of each party? I think I understand the main implication of the Coase Theorem—that the outcome will be Pareto efficient regardless of the initial allocation of property rights, provided transaction costs are zero, but I am not sure whether the outcome is the same from the perspective of each party.
As far as I can see the initial allocation of property rights has a major impact on the costs to each party because it determines which party ends up bearing the costs—either of eliminating the cause of the externality or by compensating the victim for it.
I made a decision-tree to illustrate the point based on the historic case of Bryant v. Lefever that Coase described in The Problem of Social Cost (page 11):

Can someone confirm this?  In this sense, the deliberations of the judges in deciding rights are not inconsequential, even if they do not affect the optimum solution from a societal perspective.

Yes you're correct.
Stigler's "Coase Theorem" merely asserts that if transaction costs are zero, then the initial allocation of rights will not affect the total size of the economic pie, but may affect the distribution of the pie.
Two examples:
Example 1. Profit > Damage.
A producer $X$ producing widgets earns \$3 in profits but causes \$1 of pollution damage to a neighbor $Y$.

If $X$ has the right to pollute, then the widgets will be produced anyway, and $Y$ will simply suffer \$1 of damage (while $X$ earns \$3 in profits).
If $X$ has no right to pollute, then $X$ has to compensate $Y$ \$1, but the widgets will be produced anyway, and $Y$ suffers no damage, while $X$'s profits are reduced to \$2.

In either case, the widgets are produced, the pollution damage is done, and the size of the economic pie is the same. In particular, the net addition to the economic pie is \$3 - \$1 = \$2.
However, the distribution of the pie differs: In Case 1, $X$ enjoys +\$3 while $Y$ suffers -\$1. In Case 2, $X$ enjoys only +\$2 while $Y$ is not affected (+\$0).
Example 2. Profit < Damage.
The profits remain \$3, but now the pollution damage is $\color{red}{\\\$4}$.

If the producer $X$ has the right to pollute, then the neighbor $Y$ will pay $X$ between \$3 and \$4 to not produce the widgets.
If $X$ has no right to pollute and must compensate for any damage, then $X$ will not produce the widgets.

In either case, the widgets are not produced, the pollution damage is not done, and the size of the economic pie is the same.
However, the distribution of the pie differs: In Case 1, $Y$ transfers to $X$ some amount between +\$3 and +\$4. In Case 2, no widgets are produced, no transfers are made, $Y$ suffers no damage, and $X$ fails to enjoy any profit.


How game theoretic models and analysis is different from ABM? "An agent-based model (ABM) is one of a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) with a view to assessing their effects on the system as a whole." Wiki

In game theoretic models, same thing is done- we model individuals and the process of interactions.

How game theoretic models and analysis is different from ABM? Is the simulation compulsory in ABM?

One of the key (and often criticized) assumptions of Game Theory is the rationality of the players/agents and common knowledge thereof. That is the agents will make the best decision for themselves given the information available.

This assumption basically says cognitive costs are negligable. E.g. I can easily tell wether it is optimal for me to buy luggage insurance. In reality I would probably need to look up statistics and make some basic calculations.

Agent-based modelling frequently uses heuristic behavioral rules instead of optimization. In some circumstances this rules are not optimal, but very close. A nice example is the gaze heuristic:

  The gaze heuristic is used by humans and animals for catching flying objects. It entails the fixation of one's gaze to the object and adjustment of the running speed so that the angle of the gaze remains constant while approaching the object (see the three decision rules in the table above). Empirical evidence shows that experienced ball-catchers use the gaze heuristic and similar heuristics, as do dogs when trying to catch Frisbees.

Similarly in the Solow model one assumes that consumers save a constant portion of their income, without any utility calculations.

By simulating models with different behavioral rules one may find a model which is a good approximation of reality or one may find a simple rule which would make near optimal decisions.

While ABM is more flexible, that flexibility is also a problem: There is a myriad of heuristics to chose from, and different heuristics frequently lead to wildly different outcomes.


Pay What You Want Pricing; Micro Foundations One of those things that makes intuitive sense to me, but not economic sense is the "pay what you want" (PWYW) scheme of pricing. When thinking of traditional micro theory, the effective price of a good under classical PWYW is zero, which creates infinite demand for the good and no equilibria. Yet in real life, consumers willingly pay a positive amount of money for these goods. I understand PYWY can eliminate some of the problems with adverse selection and it is used for market penetration, but I don't have any foundational idea for why this is the case or how you would model consumers in this pay scheme.

(I am aware of the existence of this question, but I feel like mine is different enough to warrant a separate one.)

It seems that some consumers get utility from paying for the good.  This isn't always true, and it does seem counter-intuitive at times.  In fact, it often seems that consumers get utility from getting a "great deal," and we often hear them brag about their amazing feats of 80% off.
In this case, however, for a few different reasons, some consumers get utility for paying.  It is the responsibility of the seller to try to maximize or enhance the utility for paying in order to increase revenue.  They have a few tools to do this, including making a big deal about how some of their proceeds may go to charity and by thanking "viewers like you" who choose to pay more than $0 for the good in question, and whose contributions allow the producer to continue operating.  They may also provide Internet Points in much the same way that that Stack Exchange and other sites do in order to help incentivize suppliers to provide quality content in exchange for zero dollars.

They can also be thought of as providing disutility, using some of the same tools, to those who don't pay.

And, as you mentioned, sellers often go with a PWYW scheme to improve market penetration, and this is often stressed.  Sellers who need market penetration can typically pass as "indie," and flaunting their indieness may again improve the utility the consumers get by choosing to "support" them, the "little guy" or underdog.  This brings to mind a couple of economic papers (which I can't seem to find at the moment) relating to horseracing and how it seems that people get utility from betting on the underdog to the point where it was once possible to have a positive expected value for betting on the favorite whenever the odds were above somewhere around 1:1 or 1:2.
Anyway, marketplaces for these goods tend to strongly emphasize this, doing whatever they can to promote their sellers as home-grown upstart startups, even putting it in their respective names, encouraging consumers who pay to think of themselves as supporters or patrons rather than consumers or even foolish rubes who paid for something that they could have gotten for the sum or $0.

To summarize, I think that those who choose to pay are actually purchasing the good in a bundle: the item being sold, along with some quantity of warm fuzzies.  At a certain point, consumers either get no additional fuzzies or start getting anti-fuzzies (cold stabbies?  Ice bricks?) for paying any more.  Some consumers get no fuzzies for paying, or their willingness to pay for fuzzies is low, so they pay zero dollars. Sellers know this, so they are responsible for maximizing the quantity of fuzzies (perhaps by influencing consumers) and gaging how many consumers they can expect to get fuzzies before deciding to use PWYW.  It's possible that the quality of the good being sold is related to the quantity of fuzzies that the buyer receives.  That is to say, consumers may enjoy paying parties who make "good" goods, and they will likely feel ripped off if they voluntarily pay for a "lemon."


Unbalanced panel data in prodest package in R I have a question regarding the usage of unbalanced panel data for TFP estimation by using the prodest package.
The dataset could be found here: https://drive.google.com/file/d/1W5pva05hRiruo1AMNc62ln0GNtcVr5p6/view?usp=sharing
As you can see from the dataset, there are a lot of firms that have not reported some values in specific years, ending up with unbalanced panel data.
The code is the following. BUT in case I do not filter the data with >0 values, I receive error messages coming from the estimation of TFP, saying that there are NaNs.
remove(list=ls())

library(plm)
library(dplyr)
library(ggplot2)
library(prodest)

pckg<-c("plm","readxl","dplyr","ggplot2","prodest")
#install.packages(c("plm","readxl","dplyr","ggplot2","prodest"))
lapply(pckg, require, character.only = TRUE)

# Set the working directory
setwd("C:/Users/vadya/Desktop/LT original currency")

# Downloading the survey data
Data <- read.csv("LToc.csv", header=TRUE, sep=",")
str(Data)

Data$ID<-as.numeric(as.factor(Data$ID))

summary(Data)

# Creating a panel data frame

DataA <- Data %>%
  #filter(NACE == 'A') %>%
  #filter(TURN > 0, TFA > 0, FA > 0, VA > 0, L > 0, M > 0) %>%
  mutate(ID = ID,
         Year = Year,
         turn = log(TURN),
         tfa = log(TFA),
         fa = log(FA),
         va = log(VA),
         cogs = log(COGS))
         #l = log(L),
         #m = log(M))
################################################################################################

mod2ACF <-  prodest::prodestACF(DataA$va, fX = DataA$cogs, sX = DataA$tfa, pX = DataA$cogs, idvar = DataA$ID, timevar = DataA$Year,
                                R = 100, cX = NULL, opt = 'optim', theta0 = NULL, cluster = NULL)

mod2ACF
omegaACF <- prodest::omega(mod2ACF)
summary(mod2ACF)
summary(omegaACF)

mod2W <-  prodest::prodestWRDG(DataA$turn, fX = DataA$cogs, sX = DataA$tfa, pX = DataA$cogs, idvar = DataA$ID, timevar = DataA$Year,
                               cX = NULL)
mod2W
omegaW <- prodest::omega(mod2W)
summary(mod2W)
summary(omegaW)

####################################################################################################################################

If I do not filter the dataframe, in the TFP estimation part (e.g., ACF method) I get the following error message.

Am I doing something wrong, and is there a way to make the prodest functions to work with unbalanced panel data?
Thanks in advance for the ideas! Would really much appreciate your concern!

A common technique we use in Python through Pandas is the introduction of means, medians and modes (depending on the structure of data) in the stead of these missing values.
Another great technique is introducing fitted values by a regression model, thus, predicting the missing values. In this case you'd want a command to drop your NaNs, estimate a model, and replace empty cells with their fitted value. Depending on your data's structure, you might encounter problems with this technique.
As a final comment, I'd suggest you use Python. Here's the pertinent website.


If there was world war 3, which stocks should I short? With the Trump administration, Turkish dictatorship, North Korean nuclear weapons, and general tension around the world, we might think that there is a likelihood of something like a world war happening soon. If this were the case, and someone wished to profit from such a situation, which stock or commodities would be the best short (or invest in)?

Gold is generally the best option for expected political and economic strife as it generally reacts inversely with the markets. Here's a good article on the connection between war and the value of gold.

Another thought would be to buy stock in companies involved in the defense industry. Raytheon, Boeing, Northorp Grumman all jump during wartime due to the anticipation for more demand for weapons production.

An even safer bet would be to buy stocks in metal production such as steel given that in a wartime economy demand for these goods spikes as production of ships and vehicles will increase for a period of time.


Profit Maximisation if MC is still falling after intersecting MR really basic one here, I am just in the process of re-covering old ground.

I understand that for any profit maximising firm
FOC: MC=MR
SOC: MR'< MC'

But suppose MC has a minimum beyond the point at which MR=0. So MR still intersects MC from above but MC is still falling (does this still satisfy SOC?).  In that case would the max difference between TR and TC be greatest at some Q higher than where MC=MR?

Also I am looking for sources/examples of where economic assumptions are really taken apart in an applied setting.  A lot of the Industrial Organisation I am looking at sticks to the same neat assumptions.

Thanks in advance.

Since the OP "recovers old-ground", let's turn the flashlight on some dark spots of this ground.

It is almost "automatic" to think that "marginal revenue" is the price at which the additional unit of output will be sold 9so that it is "the revenue that the additional unit brings in"), and that "marginal cost" is what this additional unit will cost. We should remember that this only holds when the firm is a price-taker, and its choices on output level does not affect the price of output, nor the prices to be paid for input factors. For if

$$TR(q) = pq \implies MR = p$$

but if

$$TR(q) = p(q)\cdot q \implies MR = p'(q)q + p < p$$

since $p'(q) <0$

The same goes for Total Cost, where denoting by $\mathbb w$ the prices commanded by input factors

$$TC(q) = C(\mathbb w, q) \implies MC = \frac {\partial C}{\partial q}$$

but if

$$TC(q) = C(\mathbb w(q), q) \implies MC = \frac {\partial C}{\partial \mathbb w}\cdot \frac {\partial \mathbb w}{\partial q}  + \frac {\partial C}{\partial q}$$
(I have avoided matrix-differentiation notation). Note that the effect of increased quantity on input prices is not clear-cut: in the usual monopsonistic setting, it will tend to decrease the unit cost of the inputs -but if the currently supplied quantity of input has reached a ceiling, it may push prices up (although that is considered more of a short-term effect).

The usual setting, and the one indicated by the OP, is to assume price-taking behavior in the markets for inputs (in which case the non-constancy of marginal cost stems purely from technological factors), while assuming some monopolistic power in the product market, i.e. a downward sloping demand curve.

So it is more general to think "marginal revenue is the increase in total revenue if we increase quantity by one unit", and "marginal cost is the increase in cost if we increase quantity by one unit", disassociating the concepts from the revenues and the costs of the "additional unit" itself.

Having cleared this, the OP asks

  But suppose MC has a minimum beyond the point at which MR=0. So MR
  still intersects MC from above but MC is still falling (does this
  still satisfy SOC?)

This is something like

which looks pretty standard. As to whether Second-order conditions hold, in this post one can find a mnemonic about slopes, since the SOC is phrased in terms of derivatives of the curves shown in the above graph.

  In that case would the max difference between TR and TC be greatest at
  some Q higher than where MC=MR?

Since at $MR=MC$ the marginal revenue curve is assumed to cross the marginal cost curve from above, it follows that for higher quantities, marginal cost will be higher than marginal revenue. Given the previous suggestion as to how it is best to think about Marginal Revenue and Marginal Cost, I believe the answer to the question is easy.


2 Player All-Pay Auction Consider a 2 player all-pay auction, bidding for $1.

Each submits a bid that is a real number, thus $S_i=[0,\infty)$. The player with a higher bid wins $1, but both players must pay the submitted bid.

Player $i$'s payoff function is:

$v_i(s_i,s_{j})=$

$-s_i$ if $s_i<s_{j}$

($\frac{1}{2}-s_i$) if $s_i=s_{j}$

($1-s_i$) if $s_i>s_j$.

Suppose player $j$ plays a mixed strategy in which she is uniformly choosing a bid between 0 and 1.

I am only interested in the expected payoff from player $i$'s bidding less than 1, because if $s_i$>1, he would win, but also incur a negative payoff.

My question:

Why is Pr$(s_i=s_j)$=0 for any $s_i\in[0,1]$ if player $j$'s mixed strategy is U[0,1]?

My confusion is: the PDF of player $j$ is 1 for any $s_j\in(0,1)$. So if I only consider $s_i<1$ and Pr$(s_i=s_j)$, how do I justify it becomes $0$?

This seems like a basic issue about probability calculus/theory.

The intuition behind the uniform distribution over $[a,b]$ is that all outcomes between and $a$ and $b$ are equally likely. Because of this, one can get an intuitive grasp about the probability that the outcome $x$ falls in a subinterval $[a_1,b_1] \subset [a,b]$. As the ratio of their length is
$$
\frac{b_1 - a_1}{b - a},
$$
the subinterval $[a_1,b_1]$ contains $(b_1 - a_1)/(b-a)$ share of all the points in $[a,b]$. Each point is an equally likely outcome, therefore
$$
P\left(x \in [a_1,b_1]\right) = \frac{b_1 - a_1}{b - a}.
$$
A problem arises if the subinterval is in fact a single point, $a_1$. What is
$P\left(x \in \left\{a_1\right\}\right)$?
 By the above intuitive reasoning
$$
P\left(x \in [a_1,a_1]\right) = \frac{a_1 - a_1}{b - a} = 0.
$$
A more rigorous approach:
 Let us denote this probability $P\left(x \in \left\{a_1\right\}\right)$ by $\alpha$. As the distribution is uniform, all points are equally likely outcomes and hence for any $a_i \in [a,b]$ we have
$$
P\left(x \in \left\{a_i\right\}\right) = \alpha.
$$
There are infinitely many (disjoint) points in $[a,b]$. Let $A$ be an arbitrary set of infinitely many such points, that is
$$
A = \bigcup_i^{\infty} a_i.
$$
Then as probability is sigma additive over disjoint sets
$$
P\left(x \in A \right) = P\left(x \in \bigcup_i^{\infty} a_i \right)
= \sum_i^{\infty} P\left(x \in \left\{a_i\right\}\right)
= \sum_i^{\infty} \alpha.
$$
However as $A \subseteq [a,b]$, $P\left(x \in A \right) \leq 1$. But for any $\alpha > 0$ the sum $\sum_i^{\infty} \alpha$ would be infinite. Therefore $\alpha$ cannot be positive, it is zero.


What are the units of utility? I'm trying to show a result that involves utility and money (the latter is in dollars). I would like to know if it is safe to assume that the units of utility is dollars? After all, in auction scenarios, we seem to deduct the bid, which is in dollars from the total utility for the item, and maximize that difference.

Therefore, am I doing the right thing in saying that a utility gain of 10 units can be equated to a gain of 10 dollars?

No, you can not really say that. Here is the reason:

Utility is generally used to describe preferences. Let's say my happiness is described by this utility of chocolates: $Y(X) = X$. So, two chocolates will give me two units of happiness. However, by definition of preferences, I am allowed to apply monotone transformations to them. Hence, you can just transform that function to $Y(X) = X^2$. Now two chocolates will give me 4 units of happiness.

Again, by definition, this is a completely valid transformation. However, now I am getting 4 dollars instead of $2 because I simply transformed the function. For obvious reasons, you can not do that.

Hence, utility is unitless.


Can a spending freeze solve the problem of the Italian enormous government debt? In view of the upcoming Italian general election, I've been reading the program of a party (please let me know in the comments whether I can/should mention its name), and in a section of it they propose a freeze of the public spending for the next 5 years in order to face the gigantic public debt. Not having a solid understanding of Economics, I thought of asking about it here.
Here's the translation of the relevant passage:

The Italian government debt, stabilised over the last few years around 132% of GDP, has become an unsustainable weight for the country's economy.
Interest expenditure, equal to 66 billion euros (around 8% of the total expenditure), is a huge weight on the national budget that determines a displacement of resources in the economy. Besides, the high stock of debt is a threat to the stability of the whole euro area and one of the major obstacles to the process of integrating budgetary policies at European level.
To face the problem we propose a freeze of the public expenditure in nominal terms for the duration of the next parliamentary term, as well as a redesign of taxation with cuts to the tax rates on income of people and companies, and a reduction of fiscal expenditure: thus there would be a redistribution of resources from the public to the private, from income to productive economy.
To freeze nominal expenditure means to establish an insurmountable limit for five years, which entails a reduction of public spending as a share of GDP if inflation and economic growth are positive. It is therefore necessary to reduce current outlay and tax benefits in order to compensate for the inertial increase of pension costs, by acting on current expenditure on the basis of the guidelines set by the former commissioners for the spending review.

I have seen critics to this strategy: according to Dr Domenico Moro, a lecturer in Economics at Birmingham Business School, debt growth does not depend on public primary expenditure. Indeed he states that in Italy it was below the European average in 2016, whereas the problem is interest expenditure (4% in Italy vs 1.8% in the EMU). He also points at wrong choices made by the Treasury Department over the last few years.
But in fact he adds that reducing public spending wouldn't be only useless, but even counterproductive: in a context of weak recovery and most of the new workers having a temporary contract and being underemployed, it would result in a drop of aggregate demand. This notoriously has a downward effect on GDP growth, and in turn an upward effect on public debt - since it is calculated as a percentage of GDP.
He then concludes the other proposal, i.e. the reduction of the company tax rate accompanied by the VAT increase, would make it worse: prices would rise and workers' income would drop proportionally; this would yield a further decrease of aggregate demand, especially of consumer goods rather than luxury ones, and consequently a decrease of GDP.
Question: is Moro's analysis completely sound? Did he really demolish the economic agenda of this political party?

This question is somewhat political, and runs into the area of “opinion-based,” which this site has to avoid. I am only going to attempt to discuss part of it. There’s some long-running economic debates involved, so I will try to describe the debates. I obviously have my own opinions.

One side issue: it is unclear in what sense is an “enormous” debt a “problem”, other than the technical issue of the European treaties? But since those treaties exist, I will put that aside.

As background information, we normally think about the size of the government as a percentage of GDP. So if nominal GDP is growing in steady state, so would government spending. Therefore, a “freeze” in euro terms, although that might be interpreted as unchanged, would be thought of as shrinking government spending relative to trend. In commonly used terms, it would be viewed by many as a mild austerity policy.

This leads us to the debate about expansionary austerity. Alberto Alesina is the economist most associated with the revival of this policy. I am not familiar with the more recent literature, but this paper by the IMF was critical of idea of expansionary austerity - IMF paper link. I would summarise the conclusions that there was a mild depressing effect on growth (“contractionary” versus “expansionary”), but one may note that this is just reducing the growth rate of an already growing economy.

I am not going to claim to give the “correct” answer, but the debate is this: will the cut in spending reduce growth, so that the effect on the denominator of the debt/GDP ratio of reduced spending is cancelled out? Realistically, it probably depends on the state of the cycle. Cutting spending right after a crisis when confidence is low may have a more dampending effect than when the economy is starting to grow more rapidly. In Italy’s case, one would need to do a detailed forecasting exercise to see how large the margin of safety is.

However, freezing spending would only reduce the deficit if the tax take rises along with nominal GDP. The suggested policy is to cut tax rates. That enters into another bitter debate in economics, the supply side effect of tax cuts.

(As an immdiate disclaimer, it is possible to redesign the tax system so that a lower tax rate will imply a higher tax take; for example, eliminate a popular deduction. It does not sound like that is the case here.)

The original supply side debate was very strong in the era of Ronald Reagan, the “Laffer Curve” (an idea of economist Art Laffer) was that very high tax rates were counter-productive. Cutting taxes would raise incomes through growth, and so revenues would increase. In 2018, I do not know of anyone who would argue that this would happen right now in the short term (one or two years, say). I believe the consensus is that the improved growth will appear on a longer horizon. In the United States, there is a debate about “dynamic scoring” that discusses this. There are plenty of resources for dynamic scoring on the internet, this is a recent presentation by the CBO - link to CBO presentation.

So one could expect that such a policy might result in a higher deficit in the short term (1-2 years), but will the tax cut lead stimulate enouh new activity on a longer horizon - that leads to a falling debt-to-GDP ratio? That question would either require analysis by experts on the Italian economy, or it would be largely opinion-based.


Are white collar workers the blue collar workers of the future? Edward Luttwak published an essay in 1994, titled Why Facism is the Wave of the Future; he wrote in this essay:

  Partly because with generational change even senior managers can now themselves work those machines if they want to, thereby allowing them to understand their uses, abuses and non-uses; partly because more junior managers are increasingly compelled to use those machines in place of clerical help and clerical companionship;

then

  and partly because computer networks allow managers at the next level up literally to oversee, right on their own screens, the work that their underlings are doing or not doing, thereby giving it the same transparency as assembly-line work, with the same immediate visibility of inefficient procedures, inefficient habits and inefficient employees – for all these reasons the long-awaited, long-delayed increase in the efficiency of office-work has finally arrived, exposing hitherto more secure white-collar workers to the work-place dislocations, mass firings or at least diminishing employment prospects that have long been the lot of blue-collar industrial workers in mature economies.

I've heard the term 'precariat' banded about a bit in the UK for the past few years, which sort of tallies with this projection; but can firmer figures be put on this phenomenon?

the long-awaited, long-delayed increase in the efficiency of
  office-work has finally arrived

Actually, so far opposite has turn out to be true. The article was written in nineties, in time of boom of productivity. Contrary to expectations, technological advances did not bring higher efficiency of work. As a matter of fact, the productivity has stagnated, as shown in the data below (note that the chart presents all nonfarm labour, including services, office support, admin., etc.).

Source: U.S. Bureau of Labor Statistics, United States Nonfarm Labour Productivity, 1988-2018

Not only software did not boost the office productivity, it is also one of the major factors of the stagnation - after all there are more distractions than ever in today’s workplace (social media, online games, etc.).

It seems that software designed to monitor employee productivity is not widely used. There are lots of time management apps (like TimeDoctor or WorkIQ, to name the few), budgeting apps, workflow apps, but it cannot be said that they expose
'white-collar workers to the work-place dislocations, mass firings or at least diminishing employment prospects'.

With that being said, there are plenty of white-collar occupations that can be completely automated (for example bank tellers, bookkeepers, basically all the white collar jobs that include collecting and processing data), but that’s another issue. This is one of the main factors why employment in services in US, understood as % of total employment, never went back to the levels prior to the crisis of 2008.

Source: World Bank, Employment in services (% of total employment) in US, 1991-2017

Precariat is something different, but related to the loss of job and overall lack of security in life. It was highly used in public debate amids of the crisis in eurozone (you can read one viewpoint from Guy Standing, who popularized the term).

** As a side note, I used U.S. data, since USA is deemed to be pioneer in technological advances in services, but Japan would be another interesting example.


Rising Marginal Costs: where is the empirical evidence? I was trying to find some kind of survey of the empirical literature on the evidence of firms operating under rising marginal costs. Recently I was in contact with Alan Blinder's 1998 book Asking About Prices: A new Approach to Understand Price Stickeness and the book shows a research on firms mentioning that they operate mostly under falling or constant marginal costs (in USA, almost 90% of them).

While I can raise some issues regarding the research, such as being the product of answers from the firms or that marginal costs are often not observed and must be estimated, I could not find a survey of the literature confirming this assumption (the evidence for behavior under rising marginal costs). Would anyone know where to begin?

Based on data/work with consultants/business school discussions with executives: A good example of a set of industries where marginal costs are rising is commodity production (metals, agricultural products, and energy such as oil). In such industries, companies own many plants (Glencore, BHP Billiton) and they tend to switch on production in a plant when the price is above the marginal cost of that plant. So it makes sense to order plants in increasing order of their marginal cost, and assume that the lowest-marginal-cost plant will be the last one to be shut down. Of course if the firm acquires a plant that has a lower marginal cost than the lowest-marginal-cost plant, it will shift that firm's marginal cost curve. Look for Carmin Nappi's slides online on the aluminum industry, plenty of that analysis going on.

Some of the slides are in here, see slide 11. http://www.riotinto.com/documents/Media-Speeches/Rio_Tinto_Alcan_Carmine_Nappi_11_June_2008.pdf

Now this is a similar framework adopted by Pindyck, for instance in http://www.jstor.org/stable/41322920?seq=1#page_scan_tab_contents.


Can econometrics test for correlation or causality between prices and corruption? This week there was news that some prices are rising. I heard that in some countries where corruption is high the prices are also higher. I wonder if there is causaility or just both at same. It would be interesting to find some material to support if the claim is true. Is there some study e.g. comparing prices levels for energy and testing whether corruption levels in an economy (bribing, black market, unregulated markets) influences prices?

Some related studies:

Al-Marhubi, F. A. (2000). Corruption and inflation. Economics Letters, 66(2), 199-202.
The analysis is based on cross-country data consisting of 41 countries from Asia and Latin America for which data is available on four alternative indices of corruption (two from Transparency International, one is the Business International index, and the fourth from another economics study). Note that numerically, these are essentially non-corruption indicators -they range from $0=$ maximum corruption to $10=$  no corruption. The panel covers the period 1980-1995. Four alternative OLS regressions were run (each with one corruption indicator present), with heteroskedasticity-robust standard errors. In all cases a statistically significant positive correlation between corruption and inflation was found.

How large a correlation (to judge its economic significance also)?  The dependent variable was the logarithm of inflation. The value of the coefficient on the corruption variable was on average $-0.22$. Given how the indicators are defined, the minus sign says that  less corruption = less inflation. The actual value roughly says that $1/5$ of inflation was associated with corruption. So if the inflation was, say $10$%, 2 percentage points can be attributed to corruption. Not small.

Braun, M. & Di Tella R., (2004). Inflation, inflation variability, and corruption. Economics & Politics, 16(1), 77-100.
They examine the reverse relationship: inflation facilitates corruption. They present a theoretical model, and also empirical evidence. For the theoretical model they write:

  "(...)high variability of inflation can make over-invoicing by
  procurement officers and under-invoicing by salespersons easier
  because it makes auditing more expensive to the principal".

So here there is a causative theoretical argument as to why unstable prices increase corruption.

Their data relates to 75 countries and for the period 1980-1994:

  Algeria, Argentina, Austria, Bahamas, Bahrain, Bangladesh, Belgium,
  Bolivia, Botswana, Burkina Faso, Cameroon, Canada, Chile, Colombia,
  Costa Rica, Cote d’Ivoire, Cyprus, Denmark, Dominican Republic,
  Ecuador, Egypt, El Salvador, Ethiopia, Finland, France, Gambia,
  Germany, Ghana, Greece, Guatemala, Haiti, Honduras, Hungary, India,
  Indonesia, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Korea
  (South), Luxembourg, Madagascar, Malaysia, Malta, Mexico, Morocco,
  Myanmar, Netherlands, Niger, Nigeria,Norway, Pakistan, Paraguay, Peru,
  Philippines, Portugal, Senegal, Singapore, South Africa, Spain, Sri
  Lanka, Suriname, Sweden, Switzerland, Thailand, Togo, Trinidad and
  Tobago, Turkey, United Kingdom, USA, Uruguay, Venezuela, Zimbabwe.

Here the dependent variable is the corruption index. They use the International Country
Risk Guide (ICRG), that ranges from $0$ to $6$. Here too, a higher score means less corruption. They regress it (among various controls), on inflation variance (since what they want to test is whether an unstable price system introduces noise into transactions that facilitates corruption). They find statistically significant regression coefficients with values around $0.5$. They even find that inflation variability correlates more strongly with corruption, than inflation itself. Lots of references.

Dreher, A., & Herzfeld, T. (2005). The economic costs of corruption: A survey and new evidence. Public Economics, 506001.
A more general study on the costs of corruption, looking also at inflation. For their empirical study (71 countries, 1975-2001), they also use the ICRG index. They regress the level of inflation on this index, and they find a positive sign on the coefficient. Since the index is as described above, a non-corruption index, higher values mean less corruption. So what they find is that less corruption is correlated with higher inflation. Irrespective of whether this can stand reason, their findings are also incredibly large: if you move up the ladder by one point in the ICRG scale (less corruption), the corresponding inflation will be 10 percentage points higher(i.e. if it was, say, 5%, it will become 15%). This is too large to be believable even if the direction of association is to be accepted. Despite this, this is a survey, so lots of references.

Blackburn, K., & Powell, J. (2011). Corruption, inflation and growth. Economics Letters, 113(3), 225-227.
This is a theoretical model. as the authors write:

  "We present a model in which the embezzlement of tax revenues by public
  officials leads the government to rely more on seigniorage to finance
  its expenditures. This raises inflation which depresses investment and
  growth via a cash-in-advance constraint."

So here we have a causative theoretical argument about why increased corruption causes increased inflation.

Bittencourt, M. (2012). Inflation and economic growth in Latin America: some panel time-series evidence. Economic Modelling, 29(2), 333-340.
Four Latin American countries (Argentina, Bolivia, Brazil, Peru) for the period 1970-2007. As the authors note, these four countries account for $\approx 70$% of total GDP and population in South America (for 2009). The dependent variable on their regressions is the growth rate, while both inflation and a composite "political situation" variable are included as regressors. The "political situation" variable again increases with increased transparency and controls on power, and so it can be expected to correlate negatively with corruption (i.e. the higher its value, the less corruption). For our purpose we need to look not at the regression results but at the correlation matrix of the regressors: there we see that the political situation variable is negatively correlated with inflation, with correlation coefficient $-0.142$ (so again, more corruption is associated with more inflation).

Overall, it appears that scholars have empirically detected a positive correlation between the level of corruption and the level of inflation, and also offered theoretical insights on how this can come about, although one theoretical model argues in favor of a causal effect from inflation to corruption, while the other from corruption to inflation. Since both arguments seem reasonable, one could think that it may be the case of a vicious feedback spiral.


When is self-selection a problem? Mincer equation I need help understanding this selection bias problem. I am estimating a mincer equation for a final year project and I was told I need to worry about self-selection bias IN OCCUPATIONS.

My lecturer said that, because wages vary between occupations, and individuals select occupations as a choice, the sample is selected. In that sense, I need to correct this problem. We were taught the Heckman selection model in the context of people deciding whether to work or not. I understand this case, but not the case of occupations. I mean, all is a choice, isn't? In my model I also have hours of work, public or private sector, full time or part time, region, industry, and other common variables. Why do we worry about occupations but not about everything else? I just cannot get my head around this.

Occupations are low, middle and high skill. I'm estimating the returns to education for Australian workers.

I think one thing is important, which is if the variable is included or not in the regression. For example, normally you cannot include a variable
of employment or inactive, because inactive have no wage. This is why, as I understood from the lecture, we need to test for selection. But choice variables that are included, are they a concern?

There is no fundamental difference between the choice of occupation and say region. In fact,  there exists a large literature in migration that builds on Roy's model, starting with Borjas (1987).  I'd argue that ideally you'd like to correct for self- selection/ sorting in all choice dimension. In practice this can be hard/ cumbersome/ impossible to do.

Why do we tend to worry about self- selection more in the context of occupations than regions? I suppose it boils down to the fact that everyone had to actively choose an occupation at some point,  whereas we are all born in some region. But,  again,  there is no fundamental difference.


What are some examples of indirect mechanisms that are not auctions? I'd like to know if there are any examples of indirect mechanisms that are not auctions. Auctions seem like a very controlled environment. I'd like to see some examples of indirect mechanisms "out in the wild".

Voting mechanisms would seem to be a good example.  So are matching mechanisms such as those used to assign students to public schools.


How is the "value added" of firms distributed While it can be justified that the sales (or revenues) of firms in an industry follow a Pareto-distribution, I wonder how the value added (sales minus input costs minus taxes, excluding depreciation) can be summarized by a parametric distribution. Pareto seems not to work, since negative values are possible.

Is there an econometric theory that gives ground for a specific class of distributions? My dataset suggest something like Gumbel.

Interesting question.

Indeed, it's somewhat difficult to model value added because in many models firms don't make profits all the time.  But therein lies your answer I think. Model VA as $Z$ in a distribution $g$ with two dimensions $(Z,Y)$, where Y is the size of the firm, Pareto distributed,  and then for any given $Y$, $Z$ is distributed as $Z \sim Y \cdot (1+ X)$ with $X$ a normal variable or something like that, so that $Z$ can be negative, but it is still on average proportional to $Y$. You can maybe then solve for $f_Z=\int g(Z,Y)dY$ analytically or numerically otherwise.


Pareto Optimality of Endowments Consider a $2*2$ exchange economy where individual $1$ has an endowment $(4,5)$ and individual 2 has an endowment $(6,5)$.
The utility functions of individuals are represented by $U({x}_i{y}_i)$=${x}_i{y}_i$ where $i$ refers to individual $1$ or $2$.
I know that the allocations which equate $MRS$ for both individuals would be the Pareto Optimal allocations. However, I seem to be very confused regarding the endowments. I cannot find an allocation that is Pareto Superior to the endowments. Also, the endowment (if it is, in fact, Pareto Optimal) does not satisfy the equality of $MRS$ condition.
Is it the case that equality of $MRS$ is not a necessary condition for pareto optimality? I can think of examples, such as Lexicographic Preferences which yield Pareto Efficient points without the condition of ${MRS}_i=$${MRS}_j$.
I think I'm missing out on something.
My concepts seem quite shaky so please bear with me.

Given the endowments
Individual 1 : $(4,5); U(4,5) = 20$ and Individual 2 : $(6,5); U(6,5)=30$

Given that there is no more than and 10 units of Good X and 10 units of Good Y in the economy. If I allocate Individual 1 one with $X$ units of Good X and $Y$ units of Good Y then Individual 2 has $(10-X)$ units of Good X ($10-Y$) units of Good Y.

Now the set of Pareto superior allocations to the given endowments, if they exist will satisfy these two simultaneous non linear inequalities.

$ XY \geq 20$ Red region

$ (10-X)(10-Y) \geq 30$ Blue region

Graphically plotting these inequalities we observe: The small common region which you see between red and blue areas is actually the infinite set of all Pareto superior allocations to the given endowment.

Now our job is to find out that allocation which is Pareto optimal, that is that convex lens shaped common region should not be present.

This point could be achieved where both curves are tangent to each other.

Which are required Pareto optimal efficient/superior allocations.


Why did the US credit rating downgrade in 2011 decrease US government bond yields? I'm not sure how bond yields were decreased by the  US credit rating downgrade in 2011. Since the credit rating is down, shouldn't the yields increase since the US government wants to attract more bond buyers?

My guess is this is a coincidence. That is, the effect of the credit rating agencies was either approximately zero, or if it was substantial and negative, that this was swamped out by other factors.
If bond ratings have a causal effect on yields, that effect is usually for smaller issues and smaller issuers where the market depends on the rating agencies for critical information. For the big issuers the banks are well informed on the issuer and need the rating agency less.
For example, consider the paper The relationship between credit default swap spreads, bond yields, and credit rating announcements (JBF 2004). When they look at CDS spreads, which are mostly for bigger issuers, they find:

By pooling all observations we find a significant (at the 1% level)
increase in the CDS spread well in advance of a downgrade event. In
the case of reviews for downgrade and negative outlooks there is a
significant (at the 1% level) increase in the CDS spread during the 30
days preceding the event. CDS spreads increase by approximately 38 bps
in the 90 days before a downgrade, by 24 bps before a review for
downgrade, and by 29 basis points before a negative outlook. When
observations are pooled there are no significant changes in CDS spread
during the 10 business days after any type of negative event.

I interpret this as saying that bond markets seem to react to the information on these larger issuers that the credit rating agencies are also using to change their ratings and at the same time they are considering those changes. However, the actual rating change, the information in that rating, and the reasoning behind it doesn't matter much. What holds for large corporate issuers is going to be even more true for a large issuer like the US government.
However, there is alternative evidence from the sovereign market in Europe. Credit rating agency downgrades and the Eurozone sovereign debt crises (JFS 2016):

This paper studies the reaction of the Euro's value against major
currencies to sovereign rating announcements from Moody's, S&P and
Fitch CRAs during the Eurozone debt crisis in 2010–2012 based on event
study methodology combined with GARCH models. We also analyze how the
yields of French, Italian, German and Spanish government long-term
bonds were affected by CRA announcements. Our results reveal that CRA
downgrades, watchlist and outlook announcements had no impact on the
value of the Euro currency but increased exchange rate volatility.
At the same time, downgrades as well as negative outlook
announcements increased the yields of French, Italian, and Spanish
bonds and even affected the German bond's yields. This shows that
the monetary union has led to a breakdown of the consequences of the
rating shocks between currency value and sovereign bond yields. The
reason is that part of the rating shock is absorbed by an internal
repricing of sovereign bonds.


How can all the bitcoin in the world be worth more than McDonald's Corporation? What makes bitcoin so valuable?  It has already surpassed the value of almost all publicly traded companies.  I understand it can be used to buy things like digital money but why does the price go up?  Can't people buy things with a more steady price of bitcoin?  It seems like a steady price would be better for using it to buy things.

Have people missed this rally or does the current price grossly undervalue bitcoin?

Bitcoin doesn't have a value. It doesn't create wealth - it destroys it. It therefore has no yield.

It does, however, have a price. It's designed to have tightly-constrained supply, so that those people who got bitcoins early, can get rich by luring more people into buying bitcoin. And demand is just as large as the number of gullible people who can be fooled into buying it. That combination of extremely inelastic supply, and very malleable demand, creates very volatile pricing.

This extreme volatility makes it very impracticable as a currency, as does its extremely inflexible supply.


Why does allocative efficiency occur when P=MC rather than MB=MC I understand that allocative efficiency is where the demand curve and supply curve intersect, i.e. where MB=MC as demand and supply can be interpreted as marginal benefit and cost respectively; however, where do we get P=MC from?

Question: If I set a price of $p$, which consumers will buy the good?

Answer: a consumer will buy the good if and only if his benefit from consuming it is bigger than his cost, $p$, of buying it. This means that the last (i.e. marginal) consumer who buys will be the one for whom the benefit is just equal to the cost. In other words, for any price, $\text{MB}=p$ must hold.

For efficiency, we know that we need $\text{MB}=\text{MC}$.

Putting these two equations together yields $\text{MB}=\text{MC}=p$.

What is going on here? We know (as you pointed out) that  we need $\text{MB}=\text{MC}$ for allocative efficiency. But we can't just go out and tell consumers whether to buy or not. We have to give them the incentive to make the efficient choice on their own. The way this is achieved is by setting the price such that only consumers for whom purchasing is efficient will be willing to buy.


Why don't we count incomes of the government from taxation when calculating GDP using the income approach? According to the income approach GDP is equal to wages + rent + interest + profit, income from taxes isn't included.

The government provides people and organizations with public goods (like roads and the national defence). It can provide said public goods because it taxes its population. It seems for me that government receiving taxes can be viewed as transfer of money for public goods from population to the government. So it seems quite strange that incomes of government from taxation aren't included, despite its goods being an important part of the economy.

Or maybe we don't count government incomes from taxes because we adopt different perspective on it?
Maybe we view it as a parasite that just sucks money out of the economy, without giving anything in return? If yes, then why do we ignore public goods that the government provides?

Actually you could use taxes because GDP formula using income approach can be also expressed as value added at basic prices + taxes less subsidies. However, you can’t do it at the same time when using the approach in your question as you would be double counting.

Using:

$$GDP= w+i + r+ \pi + o$$

Where $w$ are wages $i$ interest income $r$ return on capital $\pi$ profits and $o$ something you forgot in your question adjustments for things like net foreign factor income, capital consumption and revenue from some gov enterprise (not tax revenue) etc.

You would be double counting if you would include taxes, because taxes are subtracted from these. If you earn 100e and government taxes 10e then economy does not suddenly have 110e. The 10e is just transfer.

If government invests the money in some productive way it will show up as an gov revenue from those productive activities.

The value of public goods like army is already reflected in the income approach as soldiers earn wages, military contractors profits etc. The same holds for any other public good. Let’s say you build a road there are wages to be paid, contractors get profit etc.

Also, when government engages in pure transfers - for example redistribution this can’t show up on national accounts as it does not create more output in the economy, it’s just juggling output around.

However, this is not because government is viewed as parasitical. If you are Ralwsian or Utilitarian transfers from rich to poor are moral imperative. But economics is not moral philosophy it’s a science and GDP is a measure of output that is grounded in real production and fact of the matter is that transfers don’t create any additional output by themselves.


If all indifference curves are parallel lines, then preference has linear representation Given a continuous preference relation $\succeq$ over $X=\mathbb{R}^2_{+}$ where all sets:
$$
I_x\equiv\{y\in X:y\sim x\}
$$
are lines on $X,\forall x\in X$, and are parallel to $I_y,\forall y\notin I_x$.

How can I show that $\succeq$ has a linear representation?

It seems intuitive that if every indifference curve is a line, then the utility itself must be a line, but I'm not sure how to go back to it. Would someone be willing to help me?

Thanks! Any helpful tips are appreciated! :D

The indifference curves are constructed by viewing the utility function as an equation (for a fixed utility index value per curve).  So from

$$U = U(x_1,x_2)$$

where the left side is just a symbol, we move to

$$\bar U = U(x_1,x_2)$$
where now the left side is a specific number.

Take the total differential on both sides to obtain

$$0 = U_1dx_1 + U_2dx_2 \implies \frac {dx_2}{dx_1} = -\frac {U_1}{U_2}$$

Any straight line in the two-dimensional plane has a constant slope so also

$$\frac {dx_2}{dx_1} =c$$

Same for $y$-bundle. Etc.


Expenses as a function of Income I am wondering if any one has attempted to describe household expenses as a function of income. I have an idea that the curve should look something like a natural log over a root function. It creates a curve with a hump at the left side and a dip in the middle on to an ever growing tail. Does anyone know of a model that describes such behavior?

Take an individual's maximization problem:

$$\max_{x_i} = U(x_1,...,x_n) \quad \text{s.t.} \ \vec{p} \cdot \vec{x} = w$$

Where one of the goods $j$ is a riskless savings good (savings account, government bond, mattress, whatever).

You can then use the Slutsky decomposition to measure how a change in income will change the consumption of good $j$, which you can then adjust to be relative to income, $w$.

More relevant (though harder) would to set up the problem as a dynamic programming problem, where the consumer wishes to consumption smooth over their lifetime.


Is there an economic term for decreased demand due to expected decrease in price due to a product's value lasting for a finite amount of time So, at work we are doing a charity bake sale.

Lunch hour is long gone. An email was sent out offering everything at half price.

I imagine decreased demand as everyone knows they have to get rid of it all by the end of the day, therefor everyone will expect the price to decrease further, therefor people will not buy due to the expectation of lower prices when an item is only of value for a finite amount of time.

Is there an economic term to describe this situation?

You are describing a market where a "non-storable" (or "perishable") good is traded. This is the (in terms of historical precedent) model of a market, since in the old days, most goods were agricultural, and many amongst them were "non-storable".

The argument behind "market clearing", i.e. that prices will adjust so that all quantity available will be sold, owes a lot to the goods being non-storable. You can observe this today in the so-called "farmer's markets", where if you monitor a day of trading, you will observe that prices go down as the day nears to an end, as suppliers attempt to sell all their quantity.

Why some consumers nevertheless buy early on and so at higher prices, even though they know that later on prices will go down, has to do with

a) constraints imposed on the consumer schedule (say, he has to buy early because he has to prepare lunch), and/or

b) quality considerations: early on the suppliers may give you more room to "pick and choose" item per item, or  they themselves will offer the better quality, to justify the higher price. It may be the case that some consumers have a lexicographic preference over a certain threshold of quality, which they expect it won't be around at the end of the day when prices will fall.

On the other hand, some consumers will hold on, given their constraints/preferences. As you can see, the phenomenon of all consumers waiting till "the last minute" presuposes a situation were the consumers are perfectly "flexible", and the quality of the good does not deteriorate with time, but the good looses all its "good-properties", instantly, at the end of its "useful life". In reality quality erodes gradually, in almost all cases.


Why isn't the "annihilator" matrix a zero matrix? I am struggling to understand why M is not null since:
$$\mathbf M=I−X(X′X){^-}^1X′=I−XX{^-}^1X'{^-}^1X′=I-I=[0] $$
What's wrong with that reasonning?

This is more a related thought than anything else, but I thought it might be useful for people looking at this question in the future. Herr K. should write a short answer and have it marked as accepted.

Let $X$ be an $n \times k$ matrix with linearly independent columns. Let $S \equiv \text{span}(X)$.

Regression can be thought of as the following problem: Given an n-dimensional vector $y \in \mathcal{R}^n$, find the vector in $\hat{y} \in S$ that is closest to $y$ -- i.e.
$$\hat{y} = \arg\min_{z \in \mathcal{R}^n} ||y - z||$$
It can be shown that the solution to this problem is given by
$$\hat{y} = Py = X (X' X)^{-1} X' y$$
where we refer to the matrix $P = X (X' X)^{-1} X'$ as the "projector matrix." Then the matrix $M = (I - P)$ allows you to get the residuals of your regression by $\hat{u} = (I - P)y = y - \hat{y}$. As you said, if $X$ is square then $P$ reduces to the identity and the residuals are 0. This is insightful for several reasons.

Geometrically, if $X$ is square and has $n$ linearly independent columns then $\text{span}(X)$ is all of $\mathcal{R}^n$. Then the projection problem reduces to picking the vector in $\hat{y} \in \mathcal{R}^n$ that is closest to some vector in $y \in \mathcal{R}^n$. Obviously, if your vector is coming from the span of the set, the minimum distance choice would be the vector itself. We see this because as you showed $P = I$ in this case. Then $M = (I - P) = 0$ which means you have 0 residuals and you have a perfect fit of your data.
Additionally, this is why empirical economists are careful about "throwing in the kitchen sink" in terms of how many variables are included. If you have as many linearly independent variables as observations then you can get a perfect match whether your exogenous variables are related to your endogenous variables or not.


The verification of my solution Farmer Smith's cattle wander into Farmer Jones' land once a month and cause $\$3,000$ of damage. If Smith reduced the size of his herd by half it would reduce the damage by half but it would also reduce his profits from $\$7,500$ to $\$3,500$. If Smith left the cattle business entirely, he would lose the entire $\$7,500$. If the two parties could negotiate at zero transactions cost, what would be the resulting size of the herd? If there are large transactions costs, Jones hires a lawyer and sues Smith for damages. You are the local judge. Should you allow Jones to collect damages from Smith? If so how much would you award?

I have this question. And I give the following answer. But I am not sure whether this following answer is enough or there are some mistakes.

If there are no transaction costs, then smith pays jones $3000 as compensation since it is profitale for him to do so. Notice that if he cuts his herd to hald, he loses 3500 and earns 4000 but if he pays up for the damages i.e. 3000 dollars he earns 7500-3000=4500 , i.e. he still earns 500 more in this situation.

Now the transaction cots are high. Yes I would allow jones to collect for the damages from smith since that way I am maximizing the society's payoff i.e. I am making Smith internalise the cost of damages that he has caused. I would tell smith to give $3500 to jones because

a. compensation to the damages

b. pay up the transaction costs

c. make him indifferent between cutting his herd to half and keeping the whole herd since this will mean no profit no loss situation which maximizes surplus of the society.

What do you think? Please share with me. thank you.

Zero transaction cost:

It is correct that the resulting herd will be $\$7,500$, but the transfer from Smith to Jones is not necessarily $\$3,000.$  For instance, the negotiation may result in the transfer amount of $\$4,000$, in which case Smith will be indifferent between producing the ``full-size'' herd and cutting it down by half as $\$7.500 - \$4,000 = \$3,500$. The resulting transfer depends on the negotiation powers of the parties and can be anything between $\$3,000$ and $\$4,000$.

  High transaction cost:

Notice that your decision as a judge should depend on the value of the transaction cost.  Suppose the transaction cost is $\$4,000$, then what would be your decision? Can (or should) you make Smith indifferent in this case? Hope this will help you with the solution.


Why does the Brexit cause a fall in crude oil prices? Oil prices have also fallen sharply in the wake of the referendum
  outcome, with Brent crude down 5.2%. The price of Brent crude fell by
  \$2.68 to \$48.24 a barrel, its biggest fall since February. At the same
  time, US crude was down 5.4%, or \$2.69, to \$47.52 a barrel.

From http://www.bbc.com/news/business-36611512

But why does this happen?

I'd like to extend Lasse's excellent answer.

Fear and uncertainty are driving markets - but they can drive prices in either direction of course.

Specifically what's happening here is that the oil markets are pricing in at least two effects.

Firstly, the UK is an oil producer, and Sterling's slide means that its oil just got cheaper for other countries. This is a small effect, but relevant, as UK short-run marginal extraction costs are close to current prices, so some UK fields are marginal producers and thus price-setters.

Much more importantly, the markets are now pricing in the possibility of a further slump in oil demand, as a result of poor general economic performance. That would be driven not only by a soon-to-be-declining UK economy, but also driven by a (much larger) destabilised European economy; and also driven by the possibility that this vote will mark the turning point, where globally we move away from a consensus on the value of tariff-free international trade, and back towards protectionism and isolationism, which would leave the global economy worse off, as well as leaving most participants individually worse off too.


Stock pricing with cross ownership Cross-ownership is a phenomenon where companies own parts of other companies they do business with. An example:

  Two companies are now involved in the diamond operation, the mining group Anglo-American, and De Beers. The two are umbilically linked, making them impregnable to corporate raids. Some reshuffling has gone on of late but not much has changed: De Beers owns 42 per cent of Anglo- American and a similar share of its capital is owned by the mining group.

Source

Assume that asset prices are the net present value of all future dividends, i.e. they contain no bubbles. (Incredible assumption, I know.)
Suppose Anglo-American changes a minor operating procedure and as a result will save a small amount of money each year, hence the net present value of its profits increase by \$1. This should increase the company value (and hence stock price) of Anglo-American, but since De Beers owns parts of the company it will share the increased cashflow and its company value (and hence stock price) should increase as well, increasing the company value of Anglo-American again, etc.

If I wanted to calculate the exact change in company value would I be correct in assuming I would have to create some sort of ownership matrix:
$$
M =
\begin{bmatrix}
58\% & 42\% \\
42\% & 58\%
\end{bmatrix}
$$
and take the Leontief inverse of this?
$$
\begin{bmatrix}
\Delta p_{AA} \\
\Delta p_{DB}
\end{bmatrix}
= (E-M)^{-1} \begin{bmatrix}
1 \\
0
\end{bmatrix}
$$

What if the Leontief inverse of the ownership matrix does not exist? E.g. both companies own half of the other. Is there any way to proceed in this case? (Note: I am not sure if it was possible to price companies with such an ownership structure to begin with.)

The way I would think of this is as follows. Let us write the value
of the first company as $V_{A}$and the second as $V_{B}.$ Given
your definition, let me know if you agree with the following argument:
$$
V_{A}=s_{AA}\sum_{t=0}^{\infty}\pi_{tA}+s_{AB}\sum_{t=0}^{\infty}\pi_{tB}
$$
 Where $s_{AA}$ denotes the time invariant share of company A that
comapny A owns and $s_{BA}$ denotes the share of the company B that
A owns. Moreover, $\pi_{t}=A_{t}-L_{t}$ or the equity of each company.
By a symmetric argument, we have that :
$$
V_{B}=(1-s_{AA})\sum_{t=0}^{\infty}\pi_{tA}+(1-s_{AB})\sum_{t=0}^{\infty}\pi_{tB}
$$

Now, consider company $A.$ Taking differentials:
$$
dV_{A}=s_{AA}\sum_{t=0}^{\infty}d\pi_{tA}+s_{AB}\sum_{t=0}^{\infty}d\pi_{tB}
$$
Ceteris Paribus,you claim that $\sum_{t=0}^{\infty}d\pi_{tA}=1$
and the other term equals 0. So what you have then is:
$$
dV_{A}=s_{AA}\times1
$$
and
$$
dV_{B}=(1-s_{AA})\times1
$$
The answer is fairly intuitive- the change in value of each firm is
the change in profits that one of the firms has experienced times
the share of the profitable firm owned by either.
If each firm owned half, then the change in the value of each firm for an increase in $1 would be half, since each firm would have half the claim on the firm whose profit has increased by a half.


Why is Indian rupee is stable against the USD even though most other currencies weakening? The Indian Rupee (INR) seems fairly stable against the USD (1 USD = 62-64 INR) in the recent times even though most other currencies have weakened against USD, some by 20-30%. Apparently, INR is responsive to most other currencies these days except the USA. Is it related to the strength of the Indian economy, or that INR has already fallen to its lowest point well before other currencies?

That is because India maintains strong economic relations with the United States. In addition, India might be looking at maintaining a fixed currency with the US. In exchange, India would have to give up Monetary Autonomy, or Free Flow of Capital.

As far as I know, India does not restrict the flow of capital to and from the country, so I assume that most policies are more government related when it comes to the US (although the new bilateral agreement is to work to reduce that). Overall, India's strong economic relations with the United States and a tied trade allows them to maintain growth.

In fact, recently with numerous trade agreements, I wouldn't say India has reached it's lowest point (that would be a few years ago), but is rather trying to secure a very high peak for the next 5-10 years.


Difference between Sequential and Weak Sequential (Weak Perfect Bayesian) Equilibria? This is in reference to the Game theoretic concepts as Nash equilibrium refinements. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. Whereas Weak Sequential Equilibria (sometimes referred to as Weak Perfect Bayesian) also necessitates sequential rationality, but has a weaker consistency requirement,which is my main source of confusion. Moreover, SE and WSE(WPBE) are often coincide as sets of solutions which really only adds to the frustration of trying to differentiate these almost identical concepts. My main question is, how would I go about checking the consistency requirement for a given extensive form game?

Let's review the definitions of the two concepts. Let $\sigma$ be a profile of strategies and $\mu$ a system of beliefs.

  A pair $(\sigma,\mu)$ is a weak perfect Bayesian equilibrium (WPBE)
  if

  $\sigma$ is sequentially rational given $\mu$, and
  $\mu$ is derived from $\sigma$ using Bayes rule whenever applicable.

and

  A pair $(\sigma,\mu)$ is a sequential equilibrium (SE) if

  $\sigma$ is sequentially rational given $\mu$, and
  $\mu$ and $\sigma$ are consistent in the following sense:   There exists a sequence of completely mixed strategies $\sigma^k\to\sigma$
  as $k\to\infty$ such that, for each $k$, $\mu^k$ is derived from
  $\sigma^k$ using Bayes rule (which is always applicable), and that
  $\mu$ is the limit of $\{\mu^k\}_k$.

From the definitions, we can see that the two concepts differ in their restrictions of beliefs: WPBE requires beliefs to be consistent with Bayes rule whenever it is applicable, and places no restriction on cases where Bayes rule does not apply (as when an information set is reached with probability zero). In contrast, the consistency requirement imposed by SE forces Bayes rule to apply everywhere in the tree by demanding that the SE-belief is the limit of a sequence of beliefs derived from a profile of completely mixed strategies.

To illustrate, consider the following example of market entry game. The entrant first decides to enter ($I$) or stay out ($O$), and if entered, the entrant (E) and the resident (R) simultaneously choose whether to fight ($F$) or abstain ($A$).

The equilibrium where entrant chooses $(O,\text{$A$ if $I$})$ and the resident chooses $F$, together with the resident believing that the entrant will choose $F$ when entered constitute a WPBE. Clearly the resident's belief is wrong, but that is allowed in WPBE because the information set at which the resident makes his decision is reached with probability zero. Thus Bayes rule does not apply, and he is free to have any belief.

SE will not allow this to happen, because as soon as $I$ is played with a positive (albeit tiny) probability, Bayes rule applies at the resident's information set, and given the entrant's strategy, the only consistent belief is to assign probability $1$ to the node after $A$. Thus the strategy profile $((O,\text{$A$ if $I$}),F)$ is not a SE.

Therefore we have the following theorem relating SE and SPE (subgame perfect equilibrium):

  If $(\sigma,\mu)$ is a SE, then $\sigma$ is a SPE.


applications of the slutsky equation Calculate the substitution and income effects for the following utility function:

$$ u(x,y)=\frac{x^a}{a}+\frac{y^a}{a}$$

I know that we are supposed to use the Slutsky equation which accounts for the substitution effect minus the income effect however I am not quite sure how to solve it. The only thing which I know how to do is derive the $x$ and I will get $x^{a-1}$ but after I am not sure what to do.

Solve the "consumer's problem":

$\max U(x,y)$ subject to $I=p_xx+p_yy$

Then you will have $x=x(p_x,p_y,I)$ so x is some function of the parameters. The same goes for y.

Then determine the Hicksian demand functions, either by using some duality result or solving the dual problem:

$\min p_xx+p_yy$ subject to $U(x,y)=\bar u$ and you'll have both x and y in terms of prices and $\bar u$. We denote these demands as $h_x$ and $h_y$.

Now Slutsky's equation for x with respect to $p_x$:
$\displaystyle\frac{\partial x}{\partial p_x}=\displaystyle\frac{\partial h_x}{\partial p_x}-\displaystyle\frac{\partial x}{\partial I}x(p_x,p_y,I)$

The substitution effect is the first term on the RHS, and the income effect is the third term.

The general formula for all cases is here https://en.wikipedia.org/wiki/Slutsky_equation


Why is infinite recursion on the common knowledge assumption necessary? If something is common knowledge in a game, that means that every player knows it, and every player knows that every player knows it, and so on. Are there cases where only one such level of knowing that others know is necessary?

What happens if such 'knowledge of knowing' stops at a certain level? What breaks down if at some level, the 'knowledge of knowing' doesn't hold? E.g., I know that you know, but you don't know that I know that you know.

On the same note, I'd like to understand how this infinite recursion (for lack of a better term...) of knowledge figures mathematically into say, equilibrium concepts.

Thanks in advance!

Ariel Rubinstein has a fabulous paper in which he illustrates that Common Knowledge and Almost Common Knowledge are very different!

http://www.cs.cornell.edu/courses/cs6764/2018fa/The_Electronic_Mail_Game.pdf


Would capitalism without banks work? According to Merriam-Webster's dictionary, capitalism is "an economic system characterized by private or corporate ownership of capital goods, by investments that are determined by private decision, and by prices, production, and the distribution of goods that are determined mainly by competition in a free market."

One could argue that banks are the engine which drive capitalism in today's world, since they are the institution which actually creates money through the lending of money at a rate of interest. However, there is nothing in the above definition of capitalism which indicates that banks are necessary for capitalism to thrive.

My question is what would happen if every country in the world were to make a law that would make it illegal to lend money at a positive rate of interest? Then of course, traditional banks would cease to exist. But would capitalism also cease to thrive? In other words, would people lose their incentive or ability to produce?

Under most capitalism-like systems, companies are funded in two ways.  One is debt with positive interest, the other is by selling equity to shareholders.  If you could effectively prohibit debt, then companies could conceivably adapt by switching to a 100% equity model, in which individuals would shift all of their interest-bearing savings into shares.  This would create various inefficiencies (and create a lot of problems for consumers who would be unable to obtain mortgages), but wouldn't fundamentally destroy the incentive to produce.


Monetary policy: increasing interest rate What happens to the quantity of treasury bonds when central bank sells short-term bonds?

The overall question for the assignment is: Suppose that the central bank of a country decides to increase the short-term interest rate. Discuss the transmission of this decision via financial markets. Your discussion should include the transmission to the money market, longer bond markets, wider borrowing rates, common stock prices, and the exchange rate.

However, I already got stuck at the first part...

I would highly appreciate any help with this assignment as I am very lost and I do not know if I can just apply the opposite results as when the central bank would lower the interest rate.

so admittedly the question as a whole seems slightly confusing. BUT taking the first part: When the Federal Reserve wants to increase the inter-bank lending rates (The "Fed Funds" rate) -- it SELLS its own Treasury Bills through something called "Open Market Operations." By selling its T-bills, it takes money OUT of the system. Less money in the "system" means the inter-bank lending rate will go up. By selling its securities, it is taking money OUT of the system. Decent video here.

I'm not sure why your teacher asked about common stocks, or longer-term bonds, etc. The Fed lowers/raises the Fed Funds Rate only through buying & selling short-term Treasury Bonds.


Do I need to log transform these two kinds of variables? Before regression (like fixed-effects, random-effects), for these two kinds of variables:

1) Price levels (e.g. price level of capital formation)
They are usually ratios like 0.987, 1.022..., based on USA 2010=1

2) % of GDP (e.g. broad money as % of GDP)
They are also ratios (%) like 80.5, 99.7 (or in decimal form 0.805, 0.997)

Do I need to log transform them, and how can I log transform them?

You don't need to log transform these variables. Consider the following model

  $\log y = \beta x.$

Then, you can interpret $\beta$ as a semi-elasticity, i.e., the percentage change in $y$ when $x$ increases by 1 unit.

To see this you can transform the previous equation as:
$y = \exp(\beta x),$ in which case $dy/dx = \beta \exp(\beta x)$. Thus, the percentage change in $y$ when $x$ changes is $\frac{dy/dx}{y} = \frac{\beta\exp(\beta x)}{\exp(\beta x)} = \beta$.

Note also that

  $\Delta \log y = \beta \Delta x$ so $100.\Delta \log y = (100.\beta) \Delta x$

It follows that

  $\% \Delta y \approx (100.\beta) \Delta x$


Can the supply curve shift while the PPF does not shift? Can the supply curve shift left while the PPF remains unchanged? For example, if I am a blue berry farmer and I injure my leg, I can no longer pick as many blue berries. So in the blue berry market, the supply curve for any price would shift to the left.

The number of blue berries I have available to pick hasn't changed, therefore the PPF NOT shift but instead I wouldn't be producing along the PPF but inside the PPF. So, the supply curve has shifted left, and my position on the PPF is on the inside of the curve, but the PPF itself hasn't shifted. Is that correct?

If so, my follow up question of the same topic is: is it true that the PPF does NOT concern itself with the method of using resources, just the resources themselves? E.g. if a factory burns down but the stock of resources that goes through the factory remains unaffected, the supply curve would shift and the PPF would remain unchanged. Correct?

Edited.

PPF is the maximum potential output that a country could produce using its resources and technology. No, the PPF should shrink due to the loss of labour (from leg injury).

No, factory is a stock of capital, thus, ppf should shrink due to loss of capacity. It is also affected by the technology of production i.e. methods of production. It moves outwards due to technological progress.


Is it possible to pay the internal debt of the country and to cover the budget deficit by increasing taxes? Say for example the US govt. is putting an extra tax of 10% on the incomes of the people earning more than the average income. To make it easier, only tax the people earning more than 110% of the medium wage.

Say for example that the US govt. is also putting an extra tax of 10% on the wealth of the rich - the individuals and families that own more than 300.000 $US

Gather all those money in two separate accounts so everyone can see how much money are collected.

And then use all the collected money to pay a part of the internal debt of the country (the internal debt is a part of the public debt, which is actually the debt of the country).

This looks like something that might actually work but I'm asking because there are a lot of complicated and sophisticated intricacies in the field of economics, or at least that's how the experts in economy make it look like.

So I'm asking if it's possible to pay a part of the debt of the country by increasing the taxes.

The people that sit on the top-half of the food chain might be affected by an extra 10% tax but for sure they will be affected much less than the poor people who would have to pay an extra 10% tax because without that 10%, the poor people might not even have the money to buy enough food for the family.

And the companies won't be affected at all. This tax is for private persons only. No extra taxes for the companies.

Those 10% money are spent at this moment by the top-half of the food chain and that creates jobs for sure. But giving it to the government and then paying the financial markets to cover the debt means the money get to the financial markets and they will also spend it or they will invest it, and that also generates pretty much the same amount of jobs.

In the end, by paying the debt, the money get back into the pockets of the rich who own the financial markets so they should not be affected at all. By the contrary - they should be happy for getting their money back - plus some nice profit.

Now let's imagine another situation - say the internal debt is insignificant but the country made a huge budget deficit this year. Is it possible to cover that budget deficit (or a part of it) using such a tax?

It looks like something that might actually work but there might be some flaws in that construction, so I'm asking if it is actually possible for the govt. to do something like this.

At the time of writing, the question is far too long.

From a simplified accounting perspective:

The government fiscal deficit = all expenditures - taxes.

The change in debt in a year is equal to the fiscal deficit (under simplifying assumptions).

So if the government can raise taxes without affecting anything else, the deficit becomes smaller, or turns into a surplus, in which case the debt falls.

The reason why this is not normally done is that raising taxes reduces growth. The exact effect of tax increases is an object of academic and political debate. If you search for “austerity policies” you ahould be able to find a lot of information.


Why is the total wealth of the world not a conserved quantity? I have read that the GDP of the world is growing. I do not understand how this is possible. If I make profits out of a commodity or a service, somebody pays me for it. Hence, their wealth has to drop. So, shouldn't wealth only get redistributed? If so, how is it possible for the world GDP to grow?

There's no such thing as a law of conservation of wealth. Wealth is created and destroyed in many ways. It is created when society produces goods and saves them. It is destroyed in disasters, or consumed when we use up our savings.It is created when we create knowledge, software, etc.

In a toy example: when a society starts out without any saved food, it produces food, eats half and saves half, then it is richer at the end. The accumulated food is an asset.

There's all kinds of wealth in a society: patents, ideas, buildings, roads, cars, computers, education, etc.

What does not get created or destroyed are nominal claims that we have against each other: if I give you a paper promising to pay you 10, that makes you 10 richer and it makes me 10 poorer but that's it. This means that its pretty had to figure out what is a society's total wealth, because there's all kinds of claims, explicit or implicit that are hard to value.


Should I construct balanced data with only necessary variables or unbalanced data with many potentially usable variables? When I construct panel data from large household surveys (say, World Bank's Living Standard Measurement Surveys), I try to construct data set with as many potentially usable variables as possible. This creates a large unbalanced dataset and I don't know how many balanced data left until I run a regression.

I personally have not encountered any problems with this, but I wonder what other people think when they have to use dataset I construct.
I have not worked with others so far, but I wonder how I should construct a good dataset to work on if I need to work with professors.
Should I construct balanced dataset? Or unbalanced dataset with many variables with many missing values?

I would construct and maintain only the full (unbalanced) data set with many variables with many missing values. Why? We can always extract balanced panel data sets from the full one; we can't go the other way around. When a balanced set is needed (in order to reduce the file size or send it to others), I would use Stata or R and never do it manually. To err is human.


Financing U.S. government budget deficits, and their impact on interest rates I have two questions. The first is about how exactly the U.S. government finances a budget deficit. The second is about the effects of budget deficits on financial markets and interest rates.

Q1. We say that deficits are financed by the sale of government bonds. But I don't understand exactly what this means. Government bonds are always available for purchase, regardless of whether Congress passes a balanced budget in a particular fiscal year -- right? So it is not that the government issues bonds only in years that run a deficit. So what exactly do we mean when we say deficits are financed by the sale of government bonds? A priori, I could make several guesses. It could mean that if Congress passes a budget deficit in a certain fiscal year, the Treasury issues more attractive securities that fiscal year -- e.g. with higher interest rates -- to incentivize more bond sales that year. (This doesn't seem like it could be true for all Treasury securities, because, e.g. I-bond fixed rates have been virtually zero in recent years despite the huge deficits the last eight years.) Alternatively, it could simply mean that funds accrued from the sale of bonds in earlier fiscal years, stored in some Treasury account, are withdrawn to cover the deficit. I know these are naive questions, and I suspect both are too simple to tell the whole truth, if there's any truth to them. But I'd like to have a better idea of what exactly we mean when we say deficits are financed by the sale of bonds, partly because the answer to this question could matter for the second question.
Q2. In macro 101 we are taught the following toy model. The bond sales used to finance a budget deficit crowd out private investment, since funds spent on government bonds are no longer available for loan to private institutions. This reduction in the supply of loanable funds, in turn, is supposed to drive up interest rates, as financial institutions try to incentivize more investment. But we haven't seen an increase in interest rates in the U.S. despite big deficits over the last several years. Why? What does the toy model get wrong? Is the point that the upward pressure on interest rates predicted by the toy theory can be mitigated by low Fed rates?

If it's easier to point me to an intermediate reference on this material rather than provide an answer, please do so. I'm looking for much more detail than can be found in mainstream elementary macroeconomics books (e.g. Mankiw).

The treasury can issue more bonds and the central bank buys it up, prints more currency and gives it to the government. This is called monetizing the deficit.
Although this practice may be challenged by the central bank itself depending upon the situation.
The treasury can sell new bonds to commercial banks and other financial institutions. Commercial banks use these to be kept as statutory reserve requirements with the central bank and also as safe assets because these are, of course, most highly rated securities. The demand could be more or less but there is always a demand for safe assets. Think of a countries like China and Japan which invest heavily in U.S treasury bonds and other assets. Theoretically speaking, government can finance any amount of deficits via the central bank route.

Crowding out will happen when the government is borrowing huge loans from the commercial banks and dries up the sources of funds for the private investors. It also depends on the purpose and timing of the spending. Whether the government is spending on non-productive programs or productive programs which are in turn helping the overall health and investment environment of the nation and whether it is spending counter-cyclically or cyclically. Also, if there is an upward pressure on the interest rates due to possible crowding out, we can expect central bank to make necessary adjustments.
Moreover, the mechanism is not so simple. It is complex as hell. The flow of savings in the economy is not fixed and hence the pressure may or may not build up. It largely depends on the investor sentiments and expectations also.


Continuous time optimization with two laws of motion (the Hamiltonian with two laws of motion) How would we deal with a continuous time optimal control problem with two laws of motion? Suppose we have the following RCK like environment with human capital investment.
$$\max_{c(t),k(t),h(t)}\int_{t=0}^\infty e^{-\rho t} u(c(t)) dt$$
subject to:
$$\dot{k}(t)=Ak(t)^\alpha h(t)^{1-\alpha}-\delta_k k(t)-h(t)-c(t)$$
$$\dot{h}(t)=Ak(t)^\alpha h(t)^{1-\alpha}-\delta_h h(t)-k(t)-c(t)$$
$$Ak(t)^\alpha h(t)^{1-\alpha}=c(t)+k(t)+h(t)$$
$$u(c(t))=\frac{c(t)^{1-\theta}}{1-\theta}$$
If the logic extends over from an environment with a Lagrangian I'd check the optimal of maximizing over each constraint separately and then verify the solution with it with the other constraint. for example if we were discussing utility maximization with calorie and budget constraints we would conciser only one constraint at a time. In this context however we are looking at laws of motion.
Does the logic change?

In this case you have two state variables, so as you say, you have to check the FOC ($J$ is the Hamiltonian) for $\frac{\partial J}{\partial K}=-\dot\lambda_1$ and $\frac{\partial J}{\partial H}=-\dot\lambda_2$ (besides the FOC for control variables). In this sense the logic is the same as Lagrangian (in static context), there are as many lagrangians, as there are constraints (dynamics/laws of movement in this context). Hope this helps!


Will price increase as demand increase? I know the law of demand which states that

  if price of a product increases then the demand will decrease

In this, I think we assume that price is a function of demand. But I feel otherwise i.e.

  if demand increases then the price of the good will increases

My reasoning:

If demand increases then the producers will capitalize on this fact and to increase their profits, will increase the price of the goods.

Where am I wrong?

Note: I have taken an introductory course on microeconomics as a minor and therefore know just the basic concepts only.

The law of demand is a microeconomic law that states, all other factors being equal, as the price of a good or service increases, consumer demand for the good or service will decrease, and vice versa.

Now, when you say that "if demand increases then the price of the good will increase"", you aren't changing the price and based on the change in demand you are now predicting that the price would rise which is clearly against the law of demand as your "increase" in demand is obviously due to more user engagement, advertising, or some other external factors.