References about leading, lagging, and coincident economic indicators

The Wooldridge texts are part of most graduate level econometric studies in the US. They are:

Introductory Econometrics: A Modern Approach, 6th Edition
Econometric Analysis of Cross Section and Panel Data, 2nd Edition

I would start with the first, unless you have a lot of formal training in statistics.

Hope this helps,

Justin

econometrics macroeconomics statistics r

UPDATED EXAMPLES: from INTRODUCTORY ECONOMETRICS by Jeffrey M. Wooldridge

While my suggested texts about Econometrics were downvoted, below is proof of how the text book referenced illustrates how Economists can use statistical methods to identify and measure leading, lagging, and coincident relationships among economic indicators.

The first examples are from chapter 16 on Simultaneous Equations. Examples 16.4 and 16.6 illustrate how to use Instrumental-variable regression by two-stage least squares for identifying and measuring coincident economic indicators. In this case, how annual inflation drops by about 1/3 of a percent for every 1 percent increase in the import share of GDP.

The second is an example 18.8 of the text and illustrate how autoregresive $AR(1)$ and vector autoregressive $VAR(1)$ time series methods can be used to identify and measure, intertemporal relationships between economic indicators, in an attempt to forecast the future unemployment rate using today's unemployment and inflation rates.

Example 16.4: INFLATION AND OPENNESS

  "Romer (1993) proposes theoretical models of inflation that imply that more "open" countries should have lower inflation rates. His empirical analysis explains average annual inflation rates (since 1973) in terms of the average share of imports in gross domestic product since 1973 - which is his measure of openness. In addition to estimating
  the key equation by OLS, he uses instrumental variables. While Romer does not specify
  both equations in a simultaneous system, he has in mind a two-equation system:"

$$inf = \beta_{10} + \alpha_1open + \beta_{11}log(pcinc) + \mu_1$$

$$open = \beta_{20} + \alpha_2inf + \beta_{21}log(pcinc) + \beta_{22}log(land) + \mu_2$$

  "where $pcinc$ is 1980 per capita income, in U.S. dollars, assumed to be exogenous, and
  $land$ is the land area of the country in square miles, also assumed to be exogenous. The first equation is the one of interest, with the hypothesis that $\alpha < 0$. More open
  economies have lower inflation rates."

  "The second equation reflects the fact that the degree of openness might depend on the average inflation rate, as well as other factors. The variable $log(pcinc)$ appears in both equations, but $log(land)$ is assumed to appear only in the second equation.
  The idea is that, ceteris paribus, a smaller country is likely to be more open, so $\beta_{22} < 0$."

  "Using the identification rule that was stated earlier, the first equation is identified, provided $\beta_{22} \ne 0$. The second equation is $not$ identified because it contains both exogenous variables. Be we are interested in the first equation.

Example 16.6: INFLATION AND OPENNESS

  "Before we estimate the first equation in 16.4 using the data in $openness$, we check to see whether $open$ has sufficient partial correlation with the proposed $IV$, $log(land)$. The reduced form regression is:"

$$\widehat{open} = \beta_0 + \beta_{1}log(pcinc) + \beta_{2}log(land)$$

open_model <-lm(open ~ lpcinc + lland, data = openness)
summary(open_model)
Coefficients:
        Estimate Std. Error t value Pr(>|t|)

(Intercept) 117.0845    15.8483   7.388 2.97e-11

lpcinc        0.5465     1.4932   0.366    0.715
lland        -7.5671     0.8142  -9.294 1.51e-15

  "The $t$ statistic on $log(land)$ is over nine in absolute value, which verifies Romer's assertion that smaller countries are more open. The fact that $log(pcinc)$ is so insignificant in this regression is irrelevant."

  "Estimating the first equation using $log(land)$ as an $IV$ for $open$ gives:"

$$\widehat{inf} = \beta_0 + \beta_{1}open + \beta_{2}log(pcinc)$$

library(AER)
inflation_IV <- ivreg(inf ~ open + lpcinc | lpcinc + lland, data = openness)
summary(inflation_IV)

Coefficients:
        Estimate Std. Error t value Pr(>|t|)

(Intercept)  26.8993    15.4012   1.747   0.0835 .

open         -0.3375     0.1441  -2.342   0.0210
lpcinc        0.3758     2.0151   0.187   0.8524

  "The coefficient on open is statistically significant at about the 1% level against a one sided alternative of $\alpha_1 < 0$. The effect is economically important as well: for every percentage point increase in the import share of GDP, annual inflation is about 1/3 of a percentage point lower. For comparison, the OLS estimate is -0.215, $se = 0.095$."

Example 18.8: FORECASTING THE U.S. UNEMPLOYMENT RATE

  "We use the $PHILLIPS$ DATA, but only for the years 1948 through 1996, to forecast
  the U.S. civilian unemployment rate for 1997. We use two models. The first is a simple
  AR(1) model for $unem$:"

$$\widehat{unemp_t} = \beta_0 + \beta_1unem_{t-1}$$

  "In a second model, we add inflation with a lag of one year:"

$$\widehat{unemp_t} = \beta_0 + \beta_1unem_{t-1} + \beta_2inf_{t-1}$$

library(dynlm)
phillips <- ts(phillips, start = 1948)
unem_AR1 <- dynlm(unem ~ unem_1, data = phillips, end = 1996)
unem_inf_VAR1 <- dynlm(unem ~ unem_1 + inf_1, data = phillips, end = 1996)

stargazer(unem_AR1, unem_inf_VAR1, keep.stat=c("n","adj.rsq","ser")
=================================================================
                                 Dependent variable:
                    ---------------------------------------------
                                        unem
                             (1)                    (2)
-----------------------------------------------------------------
unem_1                     0.732                  0.647
                           (0.097)                (0.084)

inf_1                                             0.184
                                                  (0.041)

Constant                   1.572                  1.304
                           (0.577)                (0.490)

-----------------------------------------------------------------
Observations                  48                     48
R2                          0.554                  0.691
Adjusted R2                 0.544                  0.677
Residual Std. Error    1.049 (df = 46)        0.883 (df = 45)
F Statistic         57.132   (df = 1; 46)  50.219   (df = 2; 45)

  "The lagged inflation rate is very significant in the second model $(t \approx 4.5)$, and the adjusted R-squared much higher than that from the first. Nevertheless, this does not necessarily mean that the second equation will produce a better forecast for 1997. All we can say so far is that, using the data up through 1996, a lag of inflation helps to explain variation in the unemployment rate."

  "To obtain the forecasts for 1997, we need to know $unemployment$ and $inflation$ in 1996. These are 5.4 and 3.0, respectively. Therefore, the forecast of $unem_{1997}$ from the first equation is $1.572 + .732(5.4)$, or about $5.52$. The forecast from the second equation is $1.304 + 0.647(5.4) + 0.184(3.0)$, or about $5.35$. The actual civilian unemployment rate for 1997 was $4.9$, so both equations over-predict the actual rate. The second equation does provide a somewhat better forecast."


Does risk aversion cause diminishing marginal utility, or vice versa?

I think I've found an answer to my question, in this excerpt from Nobel laureate John C. Harsanyi's 1994 paper "Normative validity and meaning of von neumann-morgenstern utilities", presented at the Ninth International Congress of Logic, Methodology and Philosophy of Science.  Harsanyi starts by proving the same lemma that Alecos proved in his answer, namely that if $u$ is a vNM utility function of an individual, then $u(10) - u(5) < u(5) - u(0)$ if and only if they would prefer a guaranteed 5 dollars compared to a 50% of 10 dollars and a 50% chance of 0 dollars.  In the comments section I said that was insufficient to demonstrate that the vNM utility function represented intensity of preferences, because what if the individual's actual pleasure and pain was accurately described by some other utility function $v$, which is a monotonic transformation but not an affine transformation of $u$?  In that case couldn't $v$ fail to satisfy the expected value property, and couldn't $v(10) - v(5) = v(5) - v(0)$?

Harsanyi has a clever argument dealing with this issue. Let $L_1$ be the lottery where you get 5 dollars guaranteed, let $L_2$ be the lottery where you have a 50% chance of 10 dollars and a 50% chance of 0 dollars, and let $L_3$ be the lottery where you have a 50% chance of 10 dollars and a 50% chance of 5 dollars.  Then obviously the person prefers $L_3$ to both $L_1$ and $L_2$.  And Harsanyi argues that $L_3$ is preferred to $L_1$ less strongly than $L_3$ is preferred to $L_2$ if and only if $v(10) - v(5) < v(5) - v(0)$.  That's because in the choice between, $L_3$ vs $L_1$, 50% of the time they get 5 dollars, and 50% of the time they have to make a choice between 10 and 5.  Similarly in the choice between $L_3$ and $L_2$, 50% of the time they get 10 dollars, and 50% of the time they have to make a choice between 5 and 0.

Now here comes the master stroke: $L_1$ is preferred to $L_2$ if and only if $L_3$ is preferred to $L_1$ less strongly than $L_3$ is preferred to $L_2$.  Therefore, $L_1$ is preferred to $L_2$ if and only if $v(10)-v(5) < v(5) -v(0)$.  And thus we reach the grand conclusion that $u(10) - u(5) < u(5) - u(0)$ if and only if $v(10)-v(5) < v(5) -v(0)$.

Thus Harasanyi reaches the conclusion that the vNM utility function represents preferences intensities.  So the answer to my question seems to be that diminishing marginal utility in the vNM utility function reflects genuine diminishing marginal utility when it comes to intensity of preferences, and thus (assuming the vNM axioms are true) diminishing marginal utility really is the cause of risk aversion.

By the way, on a side note I wonder whether we could identify the set of all functions $v$ that satisfy the constraint that $u(x) - u(y) < u(z) - u(w)$ if and only if $v(x)-v(y) < v(z) -v(w)$ (and similarly for greater than and equal to).  (EDIT: I asked about this on Mathematics.SE here.)


Fast way to write out the utility optimization problem for a Cobb-Douglas function?

Well all Cobb-Douglas have an structure, it is the utility that makes shares constants as budget shares independent of prices
$p_{l}x^{CD}_{l}(p,w)/w=\alpha_{l}$ with $u^{CD}(x)=\sum_{l}\alpha_{l}log(x_{l})$ and $\sum_{l}\alpha_{l}=1$.
then you can go back and compute $x_l(p,w)$, with this the indirect utility, then invert to obtain the expenditure and then derive to get the hicksian.
Not sure if this is what you want but some utility functions have a defining property, the same with the leontief or CES.


In the expenditure measure of GDP $$Y = C + I + G + (X – M)$$

imports $M$ appear to reduce GDP.  However, this only offsets the consumption $C$ met by imports; if instead the money had not been spent on a Ferrari but had instead just been saved (and possibly lent abroad so it has no other effect on GDP) then GDP would have the same.

There is a slight effect on GDP if a Ferrari dealership in the US was involved in the transaction: its margin (the final sale price minus the import cost) would count as value added in GDP and would appear in the expenditure measure since the consumption amount would exceed the import amount.


Is information technology going to turn most "common goods" into private goods?

Many obstacles to converting common goods into private goods are legal or normative rather than technological. For example, the technology necessary for congestion pricing of traffic is long established and indeed in use since the 1970's in Singapore. The existence of electronic transmitters or plate readers (London) may make for finer gradations of pricing and simpler administration but haven't made for widespread adoption. In fact, many notably congested larger cities like New York and Hong Kong have had failed congestion charge proposals. Or take a crowded national park. If ticket prices at Yellowstone were \$115 per person like Disney World instead of the nominal \$30 per car they actually charge it wouldn't be nearly as crowded. Prices are well below the market clearing rate as a matter of public policy, not because there is a technological obstacle to charging more.


Would a major wealth redistribution cause a major inflation?

Inflation is only inflation if supply can't keep up, and if the money supply increases without growing the economy.

Massive wealth distribution (edit: on a long time scale) would be a huge boost to the economy. Why? All the purchases of consumer goods will increase production of all those goods, which will move through the entire economy causing expansion. Of course there will likely be some inflationary effects but as long as the wealth distribution didn't happen overnight whatever mechanism of distribution is probably going to redistribute slower than what the economy can handle anyway.

If you wanted to estimate potential inflationary effects you'd have to figure out the stickiness of production schedules of a basket of consumer goods that the poor would be likely to buy compared to the speed of redistribution.

Also, it's worth pointing out that a lot of money in equity is 'virtual money'. It doesn't actually exist (or rather, it exists, as long as you don't use too much of it at once). What I mean is, if for example Bill Gates wanted to liquidate half his stock, he would sell the stock at a massive loss to the current market rate and would get a lot less than you would think. The same applies to sales of any equity or land... In theory those assets have the value on paper but you can't just redistribute that form of wealth, it would end up destroying the paper wealth since the buyers wouldn't be able to afford it, and would require the seller to sell at a 'loss'... Forced distribution on a short timescale of large amounts of wealth would result in that wealth being destroyed without any real advantage, because the wealth isn't in actual money. So you could also argue that there would be some deflationary effects due to wealth distribution too!


Why do externalities lead to a Pareto-inefficient outcome?

If you allow side payments then the issue you identify goes away in a Coase sense.

The citizens being polluted could pay for production to be reduced by one unit.  This amount would have to be between the benefit of the reduced pollution and the loss to the pharmaceutical firm from the reduced production. But this last figure is small: at the competitive equilibrium the firm is matching its marginal revenue with its marginal cost so its profit from the final unit of production is very small, while presumably the pollution effect is larger (if not then the competitive equilibrium is already efficient).

So the position with the side payment dominates the position without it in a Pareto sense, as both the citizens and the pharmaceutical firm are better off.  Possibly further side payments and production reductions would be even more efficient, at least until the marginal profit loss exceeds the value of reduced pollution; that point is then Pareto optimal and the starting point was not.

You may have to extend this slightly as the reduction in production also affects the customers of the pharmaceutical firm, who see a reduction in consumer surplus from the lower production. But again, side payments from the citizens to the customers can move to a Pareto optimal position, until the marginal value of the reduced pollution equals the combined marginal losses of the pharmaceutical firm and its customers.

Advocates of the "polluter pays principle" would describe this as unfair, but Pareto optimality does not judge fairness.  Another practical issue would be creating a mechanism which avoids free-riding and leads to an efficient agreement, a frequent issue with Coasian bargaining.


How does one calculate an optimal consumption bundle if the MRS only contains one variable?

I wanted to add this as a reply to denesp's comment, but I do not have enough reps.

MRS and a binding BC gives a system of two equations from which we can solve the optimum bundle. In case of income  = 10, these two equations have positive solutions, in case of income = 1, these two equations do not have positive solutions. See this:

Income = 1 just makes the choice set small enough that there is no MRS = price ratio, hence the corner solution.

I completely agree that income =1 is really the more fun question.


heteroskedasticity variance estimator bias direction

I think the problem is that you are mixing up terminology. The statment about an estimator being BLUE states given the Gauss-Markov assumption, OLS is the best linear unbiased estimator. But as your model is heteroskedastic the Gauss-Markov assumptions no longer hold and the proof of OLS being BLUE is no longer true.

Unfortunalty there is no general result that shows whether a estimater is the "best" in the case of hetroskedacity. In theory if you know the exact functional form of the heteroskedascity you can perfectly correct for the hetroskadicity and you WLS is just as effective as OLS when the Gauss-Markov assumptions hold. But in reality this is never the case, and unless you have a small sample or a very strong argument of why you know the functional form of the hetroskedacity then you are better of using Whites robust standart errors.


Data Set of Bourguignon and Morrison 2002 AER

The wayback machine has snapshots: https://web.archive.org/web/20120217010359/http://www.delta.ens.fr/XIX/


Blackwell order of information structures

Its for all priors and all utility matrices. Its possible for $p_1,u_1$ and $p_2,u_2$ to rank $S$ and $S'$ different.


Useful software for notes and graphs in economics?

I've been trying to find a solution for this same question.  As mentioned by others, most of the solutions are a bit too time consuming to do on the spot if you're taking notes, so I still think it's easier to draw out the graphs by hand on the spot.

There's a good post referencing some of the different software options, along with how to do this with R and ggplot if you're interested on Andrew Heist's blog

Also, see Create simple graphs without functional forms

Among these options, I'm trying to learn to do everything with TiKZ, but it's a work in progess...


fixed an marginal cost calculation issue

The marginal cost is 3. Marginal costs do not depend on the fixed cost, and when your variable costs are constant, then the marginal cost and the variable cost are the same. Note that your total cost is $C=FC+3q$ and the marginal cost is always the derivative of your total cost, in this case, $3$.

As for the fixed costs, 4000 is definitely part of it, but maybe also the forgone profits from selling the goods in the various stores at sub-optimal prices, as pointed out by another response. Other's have pointed out that if you calculate the variable profits for each price, 9 gives the largest profits, so in all the other stores that you made less profits, the lost profits should probably be added to the fixed cost.


It is your second answer. From MWG:

  $$\frac{\partial u(x^*)/\partial x_\ell}{\partial u(x^*)/\partial_k}=\frac{p_\ell}{p_k}\tag{3.D.5}$$
  The expression on the left of $\text{(3.D.5)}$ is the marginal rate of substitution of good $\ell$ for good $k$ at $x^*$, $MRS_{\ell k}(x^*)$; it tells us the amount of good $k$ that the consumer must be given to compensate her for a one-unit marginal reduction in her consumption of good $\ell$.


What is the statistical program used in the Worldwide Governance Indicators?

This isn't a matter of statistical packages as much as it is a matter of how to write a program to maximize/minimize a function. You can do this readily in Stata, Matlab, R, Python, etc. No matter what language you use, though, the process is basically the same. You write a function that specifies the functional form your trying to, say, minimize, set the parameters you're optimizing over as the function arguments, then call some built-in minimization routine on that function. Here is a primer for doing this in Stata and here is an introduction for R. Matlab and Python will both be very similar to R, with the primary exception being that you will have to declare the function in a different .m file for Matlab.


Is there autocorrelation in stock prices?

Stock prices follow a random walk process, usually we include a drift term to account for the somewhat prolonged upward/downward drifts. This is basically an AR(p) process, p being the lag order. For instance AR(1) with drift is $X_t=\delta+\beta X_{t-1}+u_t$ where $\beta = 1$. Try testing this model for unit root using ADF test in stata. One lag is enough. You should fail to reject the unit root for an evidence of autocorrelation in the prices. Stock returns are not autocorrelated, they usually follow a stationary process if you take sufficiently long sample.


If I make an international purchase with a card which contains domestic currency, is this currency converted to the currency of the seller?

Generally the receiver bank / payment-gateway makes the conversion - except for currency accounts where the transaction is made directly into the account or if the sender chooses to make the conversion.

You can lookup the cutoff times for currency transactions on the different banks.


Self-selection bias during the course of experiments

Apparently this is called attrition bias. It's very similar to survivorship bias. This paper suggest correcting for it using Heckman correction. Propensity score matching may also help somewhat. My experience with both has been mixed, but they are commonly used. You should figure out what exact approach is most appropriate for your setting.

One last edit: These two papers, which talk about bounding the average treatment effect, may also be of use to you.


Why can the job offer have a negative relationship between salary and quantity of work?

Sure it is! Look up Borjas, Labor Economics, in the Labor Supply chapter.
In the following graph you notice that the supply curve is upwards sloping until wage $W = 20$, but for any greater level of compensation, the worker does not need to work as hard anymore, and starts reducing their hours of labor.

For an example, you might want to imagine a young music performer. If their earnings from concerts are, say, $ W = \\\$800 $ a month, they might have to gig a lot. As their music becomes known, their earnings from concerts might exceed $ W=\\\$8000 $, at which point, they may decide to work less, thus, reducing their number of concerts.


The central bank that issues the currency won; they can now issue an additional $100 without increasing the price level. This is similar to seignorage rents due to overseas circulation— in fact, to a central bank, the two are indistinguishable, as the central bank would be unaware that your note had been destroyed.


Time costs and the St. Petersburg paradox

Consider the version of the paradox from Wikipedia:

  A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The pot starts at 2 dollars and is doubled every time a head appears. The first time a tail appears, the game ends and the player wins whatever is in the pot. Thus the player wins 2 dollars if a tail appears on the first toss, 4 dollars if a head appears on the first toss and a tail on the second, 8 dollars if a head appears on the first two tosses and a tail on the third, 16 dollars if a head appears on the first three tosses and a tail on the fourth, and so on. In short, the player wins 2k dollars, where k equals number of tosses. What would be a fair price to pay the casino for entering the game?

If there is a finite fixed per-period time cost, $c$, of playing the game then the paradox would not be resolved. The payoff from the lottery would then be
$$-c+\sum_{t=1}^\infty \left[\frac{1}{2^t}\left(2^t-c\right)\right]=\sum_{t=1}^\infty \frac{1}{2^t}2^t-\sum_{t=0}^\infty \frac{c}{2^t}=-2c+1+1+1+\ldots=\infty$$

Thus, as in the original paradox, the value of the lottery is infinite.

An alternative might be to suppose that the marginal cost of time spent is not constant (e.g. it is increasing). However, it is hard to see how one would justify an increasing cost of time without invoking some idea of the dis-utility of time (but the whole purpose of this exercise is to get away from invoking a utility function).

Two solutions that are related (in the sense that they involve a time dimension) and that might be more appealing are:

(1) discounting. Even if your utility of wealth is linear, you might put a low weight on future payments because you have to forego some return during the period between now and when the payment occurs. If the future is discounted at rate $\delta<1$ then the lottery would have value
$$\sum_{t=1}^\infty\delta^{t-1}\frac{1}{2^t}2^t=\frac{1}{1-\delta}.$$
Thus, the value of the lottery is finite for any $\delta<1$ and the lottery is more valuable to more patient people (i.e. people with larger $\delta$).

(2) finite lifespan. This is formally equivalent to discounting, but conceptually different. Now the idea is that the player is not going to live forever so there is a chance that they 'die' before having the opportunity to collect the lottery's payoff. In particular, suppose that the player dies at the end of each period with probability $\lambda$ and that the payoff is zero if s/he dies before the end of the lottery. The value of the lottery is therefore
$$\sum_{t=1}^\infty\lambda^{t-1}\frac{1}{2^t}2^t=\frac{1}{1-\lambda}.$$
Thus, players who expect to live a long time have a higher willingness to pay for the lottery, but the value of the lottery is finite for anyone who does not expect to live forever.


What does efficient and inefficient innovators mean?

My understanding of this chart is based on the Global Innovation Index 2015 report. Definitions are not explicit however.

They compute an Innovation Efficiency Ratio as the ratio of the "Output Sub-Index" score  over the "Input Sub-Index" score (definitions of these scores are presented in Figure 1). It is designed to assess the effectiveness of innovation systems and policies. In other words, this ratio shows how much innovation output a given country is getting for its inputs. Based on Table 1, all the countries with a ratio over the median (.71) appear to be considered as "efficient innovators".

For instance, Angola and Côte d'Ivoire do not show significant innovation input and  output  results,  yet  their  efficiency ratios appear high because their outputs outweigh their inputs on a low level.


Some areas of economics have more consensus and predictive power than others. Most economists would agree on the effects of trade barriers, could fairly accurately forecast the effects of a price change given a good demand estimate, would come to the same conclusion about the effects of allowing a merger between two large competing firms, know how asset prices will react to a change in interest rates, etc.

The effect of a fiscal stimulus is one of the most complicated questions in economics because you are asking about the effect of stimulating a system with millions of moving parts (people and firms) and many dimensions (consumption/saving, employment/work, trade, investment, innovation, ...). This is a long way from the simple, closed systems for which natural science is able to give sharp predictions. In fact, when you look at parts of the natural sciences that deal with similar levels of systemic complexity, the overall (lack of) predictive power looks similar to that in economics:

although principles of ecology are well understood, it is almost impossible to accurately predict what the final effect of, say, introducing a new species into an ecosystem will be
the theory of evolution is probably one of the greatest scientific theories of all time, but can only be used to make the vaguest predictions about the future
medics cannot accurately predict the onset of a wide range of diseases—only diagnose them ex post
models of future global temperature increases have wide error bars
weather forecasts more than one or two days into the future have wide error bars

The other thing to note is that fiscal stimulus is a highly politicised topic and economists often do a (frustratingly) poor job of keeping politics out of the debate. If you read the economic literature, you will find a story similar to that for your car crash: any outcome is possible but some look more likely, depending on the exact circumstances. Given this ambiguity, politicians of different persuasions have no difficulty finding an economist willing to ignore this nuance and take a politically expedient position (just as conservative politicians can always find scientists willing to play down anthropogenic global warming). But that is less a failing with economics than with economists.


Proof that EV = CV when there is no income effect

This is because when the Marshallian demand $x_i(p,w)$ is constant in $w$ (i.e. no income effect), the Hicksian demand $h_i(p,u)$ is constant in $u$. To see this, we only need to apply the relation
$$h_i(p,u)=x_i(p,e(p,u)).$$
For $u^0\neq u^1$, we have
$$h_i(p,u^0)=x_i(p,e(p,u^0))=x_i(p,e(p,u^1))=h_i(p,u^1).$$

Therefore,
$$\int_{p^0_1}^{p^1_1} \! h_i(p,u^0) \mathop{dp_1} = \int_{p^0_1}^{p^1_1} \! h_i(p,u^1) \, \mathop{dp_1}.$$


You're correct it is graph A. Regressive tax means that the lower income you have the higher %tax you have. If you imagine at the lowest level of income, you still have a flat tax(The intercept).

Since the slope is constant the %tax component is the same for all income levels.

Therefore this flat tax component is the part you need to look at. The flat tax represents a larger proportion for lower income earners. As a whole (%tax + Flat tax) the tax is then a higher % for lower income earners, hence regressive taxation.


Heteroskedasticity assumption in fGLS into linear form?

I'm using the 4th edition, but the content should be the same.  It sounds like you are asking how he got from

$$
Var(u|\boldsymbol{x}) = \sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)
$$

to

$$
u^2=\sigma^2exp(\delta_0 +\delta_1x_1+\delta_2x_2+...+\delta_kx_k)v
$$

As you correctly noted, $Var(u|\boldsymbol{x}) = E(u^2|\boldsymbol{x})$ under the zero conditional mean expectation assumption ($E(u|\boldsymbol{x}) = 0$).  So that allows us to replace the left-hand side of the equation, as Wooldridge did.  $E(u^2|\boldsymbol{x})$ turned into $u^2$ because $u^2 = E(u^2|\boldsymbol{x}) + \epsilon$, where $\epsilon$ is the component of $u^2$ that's uncorrelated with any function of $\boldsymbol{x}$.  That component could have been left in at this stage, but it can be removed because later on it would turn into a part of the error term anyway that does not affect the fitted values from the regression of $log(u^2)$ on $\boldsymbol{x}$ (i.e., part of $e$ in the next equation in the book).

On the right-hand side of the equation, Wooldridge adds $v$, which has a mean equal to unity, conditional on $\boldsymbol{x} = (x_1, x_2, ..., x_k)$.  That means that given some set of values for $\boldsymbol{x}$, $v$ is expected to have a multiplicative factor effect of $1$ on $u^2$ (in other words, no effect).  By introducing this term to the equation (and assuming that it is independent of $\boldsymbol{x}$), we can then convert it into the error term $e$ in the subsequent equation:

$$
log(u^2) = \alpha_0 + \delta_1x_1+\delta_2x_2+...+\delta_kx_k+e
$$

because taking a log of a variable that has a mean of $1$ will give us a variable that has a mean of $0$ plus some constant (equal to the negative of the mean of the log values of the original variable $v$).  That constant is moved to the constant term (that's why this last equation has $\alpha_0$ instead of $\delta_0$) and we are left with an equation that can be estimated using OLS.

P.S. The $v$ in this book is not the same $v$ that you found in Assumption 6 in the linked paper.  There it is a function, not a variable.


Why is macroeconomics about general equilibrium?

Not sure what you mean by formally proven in this case, but it’s just true by definition.

Macroeconomics is by definition branch of economics that studies the behavior of economy as a whole as opposed to individual markets or actors separately which is studied by Microeconomics.

General equilibrium is by definition an equilibrium of whole economy or several markets.

Hence it just follows from definition of both general equilibrium and macroeconomics. Most of the economics is devoted to study of equilibria for better or worse so if you study macroeconomics you almost always study general equilibrium in one way or another. It’s equivalent to say that microbiology is about small organisms. It’s true just by definition.


The Corruption Perceptions Index of Transparency International could work for you. Chavez was in power from 14 April 2002 – 5 March 2013 and the index is available from 1995-2015 and includes Venezuela. In addition to the cross-country data, there is a more detailed Venezuela page produced by Transparency International.


Why did large denomiations exist in the early 20th century?

There were plenty of relatively large purchases that were regular enough to buy with large amounts of cash. If you wanted to buy a Model T in 1909 you'd need \$825-\$1000. A typical house could easily cost a few thousand dollars in an age when mortgage finance was much less common. So there were plenty of expensive things to need significant cash for, at least occasionally.

But why cash? The most important part of the answer is bounced checks. If you need to pay someone a lot of money by check you have problem. If Abby gives Betty a check and Abby walks off with the goods and the check bounces, Betty will have a problem. If Abby pays Betty but doesn't give Abby the goods until the check clears, Abby may have a problem if Betty never shows up with the goods after the check clears. You can do escrow, but that's expensive and complicated. Cash allows instantaneous settlement.

Other options existing in this era have other problems. Cashier's and certified checks, as well as money orders may serve in some cases, but don't easily allow negotiation because they denomination is fixed at the time of issuance. Wire transfers have existed since the age of the telegraph but like today remain an expensive technology for everyday use.

Hundred dollar bills are the (update: second) most common denomination today, which may surprise you:

Source: New estimates of U.S. currency abroad, the domestic money supply and the unreported Economy

This is mostly because the dollar is used internationally for business transactions.


Microeconomics, deriving demand equations from utility unction

You're right in that $\frac{1+y}{p_x}=\frac{x}{p_y}$. This implies that $yp_y=xp_x-p_y$, and using this in the budget constraint $I=xp_x+yp_y$ yields
$ I =xp_x+xp_x-p_y=2xp_x-p_y$ or

$$x=\frac{I+p_y}{2p_x}.$$

In order to determine whether these goods are gross substitutes (or complements), you need to compute $\frac{\partial x}{\partial p_y}$ and observe that this is

$$\frac{\partial x}{\partial p_y}=\frac{1}{2p_x}>0.$$

This means that increases in the price of $y$ are associated with increases in the consumption of $x$, a behaviour that corresponds to gross substitutes.

As for whether $x$ is a normal good, you need to determine if increases in income are associated with increases or decreases in its consumption, so we calculate

$$\frac{\partial x}{\partial I}=\frac{1}{2p_x}>0.$$

As consumption of $x$ increases with $I$, we say that $x$ is a normal good (has positive income elasticity).


Why is trade openness positively correlated with economic prosperity?

In short: Yes and due to comparative advantage.

The level of GDP growth gained with opening trade does vary by country and time. I'd suggest Wacziarg & Welch (2008). Trade Liberalization and Growth: New Evidence, World Bank Economic Review, vol. 22(2) for a relatively new study on the subject.


Cryptocurrency is never a good medium of trade exchange compare to printed notes.

Anyone follows the history and trend of cryptocurrency can tell you that, cryptocurrency has become speculative medium than a currency itself. The best scenario to describe the speculation is various Initial coin offering(ICO) that went boom and bust.

A cryptocurrency such as Petro coins does not fair better than others, even Venezuela government say it is "backing" with something like oil. Because the logistics are too complicated and costly. Thus, Petro coin is anything but just yet another ICO to attract speculators to pay it in dollars(or any foreign currency that Venezuela needs).

In short, something like Petro is not going to replace the currency, but as a tool or "virtual commodity honeypot" used by Venezuela to get foreign currency without any sound production.


Why do some researchers include oil price in a VAR model?

Output and oil price can be endogenous even for relatively small and open country if the country is oil producer. Actually, in international trade whether economy is small depends on whether in particular case country can affect world price by varying its output. For example Kuwait is generally small open economy, but when it comes to oil production they are (at the time of writing) ranked 10th in the world so in oil market they are not small economy. For Kuwait there would be definitely an endogeneity between oil prices and output.
Ghana (at the time of writing) it is ranked 49th in world oil production which is somewhere in the middle between being significant and trivial so I can imagine someone arguing that there could be some endogeneity between oil prices and output. I suppose it is possible that if Ghana would shut down its oil production world price would move slightly.

VAR model actually does not require for all variables to be endogenous. It is completely fine to estimate VAR model where there are also exogenous control variables. Doing so does not violate any assumption of VAR. VAR allows for endogeneity to be present, it does not require it. However, if you are completely sure those variables are exogenous, and you are only using two variables, running VAR would be equivalent to just running two ARDL models where one of those ARDL models will be superfluous. It would not be the most efficient modeling choice but I also can't think of reason why it would introduce bias.


Is the use/consumption of natural resources considered an externality per se?

Use or consumption of natural resources is not in mainstream economics considered as an externality per se.

First of all the quote from Mankiw is probably from undergraduate textbook and taken out of context as it is incomplete.

For example according to Economics by Mankiw and Taylor (2014) 3rd ed the externality is defined as:

  the cost or benefit of one person's decision on the well-being of a bystander (a third party) which the decision maker does not take into account in making the decision.

Moreover, if you consider the above definition somehow 'tainted' because it is not just Mankiw but Mankiw and Taylor then consider the following quote from Mankiw (2018) Principles of Microeconomics 8th edition:

  An externality arises when a person engages in an activity
  that influences the well-being of a bystander but neither pays nor receives
  compensation for that effect. If the impact on the bystander is adverse, it is called
  a negative externality. If it is beneficial, it is called a positive externality. In the
  presence of externalities, society’s interest in a market outcome extends beyond
  the well-being of buyers and sellers who participate in the market to include the
  well-being of bystanders who are affected indirectly. Because buyers and sellers
  neglect the external effects of their actions when deciding how much to demand
  or supply, the market equilibrium is not efficient when there are externalities. That
  is, the equilibrium fails to maximize the total benefit to society as a whole.

These more complete quotes bring necessary context into the discussion. First as is clear from the both first and second quote, not any decision that has effect on third party causes externality. As both of the quotes above clearly state for the third party effect to qualify as an externality the third party's well being and cost for the third party must not be taken into an account.

However, assuming perfect market the cost that is created by the fact that if rivalrous good is consumed other person cannot enjoy it is taken into account through supply and demand interactions. Consider the following simplistic model:

We have single buyer offering some commodity, lets use an egg sandwich as example - clearly rivalrous good - also if we would replace the egg sandwich by wood or stone or iron the result would not change. Now lets assume there are two people Aria and Ceresi. Aria values sandwich at \$50 and Ceresi at \$40. Also for the sake of simplicity lets assume that the sandwitch was produced at no cost to seller (its purely simplification assumption to make the problem easier to solve) - it was just an endowment. Also I will assume for simplification total informational symmetry so we dont need to go through some game theory to solve the problem. In such situation there will be a bidding war between Aria and Ceresi, and since Ceresi values the sandwich at \$40 but Aria which values the sandwich more will bid \$40.01 and gets the sandwich. Now it is true that this can be considered as a negative effect to Ceresi as now she missed opportunity to consume sandwich that would give her utility equal to \$40 dollars, but is this an externality? No! Why? Because the fact that Ceresi is not going to enjoy the sandwich is already captured in the market price that Aria payed for the sandwich! Hence here we cannot say that the condition that the effect on the third party was not taken into account applies.

In order to create negative externality in this case, the egg sandwich would have to make Aria fart which would create additional disutility to Ceresi which was not captured in the market transaction because if Ceresi would knew that the sandwich would create fart she might be willing to bid the price more in order to avoid that disutility but this was not captured by market.

Now replace egg sandwich with a natural resource - oil - and you get the same effect. If the oil is bought just to be consumed as a part of some art installation there would be no externality, the fact that the oil is consumed and so other people cant enjoy it is already reflected in the market through supply and demand interaction. However, if the oil is burned which creates pollution which then harms people, and this harm is no longer captured by the market interactions we get the negative externality.

This is also clearly expressed by Mankiw in his principles of economics where he says:

  In the
  presence of externalities, society’s interest in a market outcome extends beyond
  the well-being of buyers and sellers who participate in the market

However, the condition for an externality is even stricter because to truly satisfy the condition that the well-being of the bystander is not taken into account there cannot be any other market effect that would result in internalizing the effect on a bystander.

For example, consider a factory that processes oil and during the production process spills some oil waste on a nearby ground where some rancher herds his cattle. If the rancher has no property rights over the land this would create externality as the well being of the rancher would not be taken into an account. However, if the rancher owns the land and the oil refinery creates a damage to it through the oil waste he can sue for the damages which forces the factory to internalize the externality and making it disappear.

Consequently, the rivalrous property does not cause in itself externality. In fact most often the externalities have nothing to do with whether the good is rivalrous or non-rivalrous but with whether the good is excludable or non-excludable. Most often externalities arise due to the fact that some good is non-excludable.

Furthermore, Mankiw is an excellent economist but he writes textbooks for undergraduates. Any undergraduate text will have to sacrifice some precision in order to make the text more accessible. According to the more advance texts, like for example MWG - the bible of microeconomics, the externality is defined as a situation where as a result of makret failure the joint surplus of actors is not maximized. For example in our Aria - Ceresi example I gave above the joint surplus is maximized even though Ceresi did not received anything as Ceresi's surplus was zero while Arias's surplus was \$9.99, the 'producer surplus is \$40,01 and hence total surplus is \$50. Moreover, it is easy to see that given that no other allocation of sandwich would increase the total surplus, if the sandwich is not sold everyone gets zero, if Ceresi gets sandwich maximum total surplus would be \$40 in this situation.

Hence even though I personally consider Mankiw's textbook superb and I use them when I teach microeconomics to undergraduates as a TA, you have to keep in mind that undergraduate books always have to sacrifice some accuracy for the sake of accessibility. Even I had to do that here, the full formal mathematical description of externality in MWG is more nuanced still but I hope that all of the above already provided enough clarity that I don't need to present it here.

In response to @KennyLJ,  it is true that in the past the definition of externality was quite vague. Moreover, it is also true that there might not be consensus on what externality is between different schools of economic though. However, I dont know of any textbook or mainstream paper that works on externalities that would define externality in a broad term as any rivalous good as @KennyLJ using the definition:

"A decision's effects are called external if they fall on someone other than the decision-maker(s). A positive (negative) external effect is called an external benefit (cost)."

Here is the list of different definitions given in different widely used textbooks:

Mankiw and Taylor (2014) Economics 3rd ed:

the cost or benefit of one person's decision on the well-being of a bystander (a third party) which the decision maker does not take into account in making the decision.

concept more narrow then what @KennyLJ claims

Mankiw (2018) Principles of economics. 8ed.

  An externality arises when a person engages in an activity that influences the well-being of a bystander but neither pays nor receives compensation for that effect. If the impact on the bystander is adverse, it is called a negative externality. If it is beneficial, it is called a positive externality. In the presence of externalities, society’s interest in a market outcome extends beyond the well-being of buyers and sellers who participate in the market to include the well-being of bystanders who are affected indirectly.

which is again much more narrow than what KennyJL claims and also it disproves the claim of KennyJL that "My guess is that Mankiw would agree that his quoted definition is the same as the above." - Clearly Mankiw does not agree with KennyJL definition - to the extend that his own textbook shows.

Mas-Colell Whinston Green (1995) Microeconomic theory states:

  "Definition "11.B.1 An externality is present whenever the well-being of a consumer or the production possibilities of a firm are directly affected by the actions of another agent in the economy." .... "When we say 'directly,' we mean to exclude any effects that are mediated by prices.

Again inconsistent with what KennyJL claims to be the "standard" definition.

Varian Microeconomic Analysis 3rd edition:

  When the actions of one agent directly affect the enviroment of another agent, we will sa that there is an externality.  ... the first theorem of welfare economics does not hold in the presence of externalities. The reason is that there are things that people care about that are not priced.

Hence again even Varain's definition which is arguably less precise is clarified by Varian's statement that the reason why externalities exist is that "The reason is that there are things that peoole care about that are not priced."

Moreover, all examples given in Varian on chapter on externalities indicate that his definition is basically consistent with previous sources.

Varian distinguishes between consumption externalities and production externalities and gives examples such as smoking tobacco or having loud music or smoke affecting a production of clean laundry. None of the examples he gives an no fair reading of the chapter suggest he means that any external effect qualifies.

Cowen \& Tabarok Modern Principles of Economics 3rd ed:

  Externalities: external costs or external benefits. External cost: a cost borne by people other than the consumers or the producers trading in the market. External benefit: a benefit recieved by the people other than the consumers or producer trading in the market.

Hence yet again this definition is more narrow as it specifically mentions it has to occur outside the market.

Hence, I cant understand how @KennyJL can claim his interpretation is standard. Of course nobody can prove negative, but all this points to the fact that such interpretation is not standard.

Moreover, I think that @KennyJL grossly misrepresented his quotes that I would like to point out:

  Scitovsky (1954):

The concept of external economies is one of the most elusive in economic literature. … full clarity has never been achieved. Definitions of external economies are few and unsatisfactory.

yes but the same source also says this:

  It is
  agreed that they mean services (and disservices) rendered free (without compensation) by one producer to another;
  but there is no agreement on the nature
  and form of these services or on the
  reasons for their being free. It is also
  agreed that external economies are a
  cause for divergence between private
  profit and social benefit and thus for the
  failure of perfect competition to lead to
  an optimum situation

It is true that Buchanan and Stubblebine (1962) say:

  Externality has been, and is, central to the neo-classical critique of market organisation. … Despite this importance and emphasis, rigorous definitions of the concept itself are not readily available in the literature.

but the same paper also says:

  "Pigovian discussion concerning the divergence between marginal social cost (product) and marginal private cost (product). By saying that such a divergence exists, we are, in the terms of this paper, saying that a marginal externality exists

Hence again the authors here do not even claim that anything goes or that the broad definition of KennyJL would be valid. In fact the paper itself suggests that externality is something that happens outside price system.

I did not double checked books as due to current coronavirus with my university proxy I can only check papers and not books but the two above sources are clearly misrepresented.


Solow Model, Growth rate of K/L and Y/L in steady state

If $Y = C \cdot X$ where $C$ is constant and $\frac{\dot{X}}{X} = g$ then we can solve for $\frac{\dot{Y}}{Y}$ as follows:
$$ \frac{d}{dt} Y = \frac{d}{dt} C \cdot X = C \cdot \frac{dX}{dt} = C \cdot \dot{X} \Rightarrow$$
$$ \frac{\dot{Y}}{Y} = \frac{C \cdot \dot{X}}{ C \cdot X} = \frac{\dot{X}}{X} = g$$

Therefore, as you concluded, they both grow at rate $g$.


Is there a way to eliminate shilling, spiting, and overbidding in second price auctions?

Overbidding

The second price auction has an equilibrium in which player 1 bids a very large amount and all other players bid zero. None of the losing bidders have a profitable deviation because they would have to pay more than their value to win. People usually ignore this equilibrium because not bidding is weakly dominated. But we should acknowledge that it is indeed an equilibrium because it is relevant for some practical applications. A big challenge, for example, in spectrum auctions is convincing new entrants to show up to bid when everyone expects the big incumbents will win all of the licenses.

One way to eliminate this equilibrium is to make it strictly dominant for players to submit a bid. This can be done, for example, by modifying the auction in the following way:

  1) run a second price auction as normal.

  2) with probability $1-\epsilon$, determine the allocation and payments as usual. With probability $\epsilon$, ignore the bid of the highest bidder and give the item to the second highest bidder (who pays the third highest bid).

Even very small $\epsilon$ will suffice to make is strictly dominant for everyone to bid. Thus, the efficiency loss from this scheme can be kept relatively small.


What makes statistics economical reports so varied and different?

Regarding the general question in the title, the reasons why "the same" variable vary across sources depends very much on the particular variable you are talking about. Personally, one of my first shocks when I started working after my undergraduate was the high number of ways the same conceptual variable studied theoretically (e.g. inflation) could be measured in practice. These alternative definitions might refer to slightly different phenomena, or might reflect different set of assumptions by those computing the statistics. Depending on your ontological position when it comes to economic concepts (e.g. is there such a thing as "inflation" out there?), you can argue that some assumptions are better than others. But this does not deny the fact that there are potentially many ways to measure the same variable, and different institutions/individual might prefer one over the other.

Focusing in the case of GDP for Iran in particular, there is the "original" GDP (as coming from official or primary sources) in local currency (notice there are several definitions of GDP too, and in the case of Iran, one with and without oil production). For international comparison purposes, this metric needs to be transformed into e.g. current US\$ or PPP US\$, process which involves some assumptions (e.g. which exchange rate to use?). Again, different institutions might use different metrics and prefer different assumptions. As said below, for data coming from countries using the Islamic calendar, there are further complications when translating to the Gregorian calendar.

Let us dig deeper in the case of Iran's GDP. First, you need to start with the official data (or primary source), available in the website of the Statistical Center of Iran. If you select the file for GDP at current prices (this file), you get the quarterly data for GDP in current Iranian currency. Notice however, that this data corresponds to the Islamic year, which is different from the Gregorian calendar used in most of the world (and used in the websites you mention). The former starts around the 21st of March of the latter. This is not exactly the end of the first quarter of the Gregorian calendar. Since quarterly data is the minimum frequency of the Iranian GDP, there is no exact way to convert quarterly Islamic-based GDP into annual Gregorian-based GDP. This tells you immediately that the translation exercise is by definition an approximation.

One reasonable approximation is to use the last quarter of an Iranian year and the first three quarters of the next Iranian year to produce a metric of the Gregorian-based year GDP. For 2015, this is:

Quarter     GDP
-----------------
1393_4    439,687
1394_1    432,264
1394_2    450,158
1394_3    433,799

Which add up to 1,755,908 billion Rials (this includes Oil production).

To translate this into $USD, which is the metric of the World Bank data, you would need to assume something about the exchange rate. Do you use the average over the quarter? Over the year?

For example, the same official statistics website above offer a measure of GDP in USD for the Gregorian calendar (see here):

Unfortunately, they do not mention which exchange rate conversion was used.

Meanwhile, the World Bank offers a slightly different one:

The notes for the latter states:

  Dollar figures for GDP are converted from domestic currencies using single year official exchange rates.

Did they use a different conversion rate? It's very likely.

Regarding the IMF data, which is reported in the Wikipedia article (particularly in the graph here), this is measured in PPP terms (and the data is highly consistent with World Bank data of GDP in PPP; see here). PPP adjusts GDP figures not only by the exchange rate but also by a measure of the relative cost of living of Iran with respect to the US. This inflates the GDP of Iran (see PPP rates here).

There are plenty of questions in this site about PPP. For example, see here and here.


Sequential Price Competition for Perfect Complements

Just looking at the setup, everything is symmetric. This means that if they were to move simultaneously then we should have $p_1 = p_2$, and the payoffs for the two firms the same.

According to your calculation, $(p^*_1,p^*_2)=(\frac{a}{2},\frac{a}{4})$. Since $Q_1 = Q_2 \Rightarrow \pi_1 > \pi_2$. So it's quite clear that in this case, the first mover has the advantage.

Intuitively, you can figure out which mover has the advantage by simply asking, would the first mover get higher payoff if he/she moves second?

Mathematically, if strategies are strategic substitute, then you can show that the first mover will have the advantage. Reference here.

Added later: one interesting way (I think) to look at this is this is just like Cournot competition, just with price and quantity switched.


From the buyer's point of view, the "best" supplier is the one who offers them the highest utility. Using the utility function for scoring suppliers seems quite natural then. (In this paper the utility function is assumed to be quasilinear in money, which is just for simplicity.)


Does the Prospect Theory value curve change according to reference wealth size?

You are certainly right that Kahneman and Tversky neglect the importance of levels in their model (even though they do acknowledge the importance of levels informally, as in the quote you reference). However, this situation has now been rectified by Kosegi and Rabin, who include both 'levels' utility (i.e.'consumption utility') and 'gain/loss' utility (they also generalise Prospect Theory to handle many goods, and endogenise the reference point).

As I understand it, the point of the Anna/Ben story is that marginal utility is a decreasing function of wealth. I would think that this is adequately captured by Kosegi and Rabin, assuming that we specify that levels utility is a strictly concave function of consumption, as is standard.

Of course, a different route would be to allow the curvature of the Prospect Theory value function to depend on wealth (as you propose). However, I'm not sure what this would buy us above and beyond the Kosegi and Rabin approach. Moreover, the theory would still be missing the rather obvious fact that people do care about absolute levels of wealth, at least to some extent.


tl;dr No, it is not possible to have a negative Gini coefficient.

The Gini coefficient is the area between the line of equality and the Lorentz curve, and this area cannot be negative. Let the area of equality as in the link be denoted by $A$, and the area under the Lorentz curve be denoted by $B$, then the Gini coefficient is given by

$$ G = \frac{A-B}{B}$$

If negative income (or whatever you are measuring) is not permitted, the maximum inequality is $1$. If negative income is permitted, it can potentially be larger than $1$. In any case, the minimum for the Gini coefficient is $0$, which corresponds to total equality.


What is the mechanism for when the fed purchases a gov't or corporate bond from a non bank?

When the Fed buys a bond as part of a Quantitative easing program, they execute with Primary Dealers through a website interface.  Hedge funds do not execute directly with the Fed, although they could execute with a Primary dealer who executes with the Fed.
When the Fed executes with a primary dealer, it credits the account of the primary dealer using newly created funds.  The dealer deposits the fund in a bank account, which increases bank reserves in the system.


Why there is no supply on monopoly markets?

The argument is that the monopolist's decision is based on the demand curve (in effect matching marginal total revenue to marginal cost) so is not independent of the demand curve, and in that sense there is not a corresponding supply curve with price and quantity in equilibrium where the two curves cross; the monopolist equilibrium point is likely to be at a lower quantity and higher price.
The conventional demand curve illustrates the price against quantity.  If instead the demand curve illustrated marginal total spending against quantity, then where it crossed the supplier's marginal cost curve would give the monopolist equilibrium quantity (though not the equilibrium price), and in that sense the monopolist's marginal cost curve could the be seen as the supply curve.


Objective criteria and judgement of models

This is a good question with a complex answer. Different models are created with different purposes in mind. As an example, there are qualitative and quantitative models. Qualitative models sacrifice some realism to demonstrate a particular phenomenon in the clearest way possible. Quantitative models sacrifice this clarity to create something more empirically relevant.
I once came across this sentence in a paper and I like the way they phrased it:
It's from "Optimal Environmental Taxation in the presence of other taxes: General-equilibrium analyses" by Bovenberg and Goulder:

  The use of a numerical model enables us to employ a realistic
  specification of taxes and adopt a fairly detailed representation of
  production and demand. Our paper thus combines the strength of
  analytical and numerical approaches: a stylized analytical model
  uncovers the major mechanisms at play, while a numerical model
  explores the empirical significance of these mechanisms in a more
  realistic setting. Despite considerable differences in the complexity
  of the analytical an numerical models, we find a strong coherence
  between the two model's results.

Also,
there are some models that are purely statistical.
There are also some models that are built solely for prediction. In short, there are many more types of models with different purposes. A model should be judged on its purpose.

Also, as for uncovering "the truth." You might consider reading more about causal inference. This is one of the most important parts of econometrics. For starters, read about the method of Instrumental Variables. There are several other questions and answers on this website that deal with this.


The Laffer Curve is a theoretical argument that feels strongly true the moment one hears about it. The complexities around it once one wants to have a closer look are many (just for a taste the wikipedia article can be consulted).

Even in the simplest econometric study, one has to make sure that what one does is consistent with the theory one wants to test (or the one on which one relies), otherwise it won't be an econometric study but an exercise in pure mathematical approximation devoid of economic content (after all any bounded continuous function can be approximated by polynomials as per Stone-Weierstrass theorem).

So what does the Laffer Curve (very) basic theory (and in its strongest form) asserts?
1) That output is a negative function of the tax rate.
2) That a tax rate of $100\%=1$ should result in zero output, and so zero tax revenue.
3) Moreover, logic says that if the tax rate is zero, tax revenues should be zero.
it appears then that we can start by an assumption that somewhere in between there is a point of maximum tax revenues (although one of the complexities mentioned earlier is that the curve may not be unimodal, i.e. it may also have a local maximum).

Let's see which conditions should the simplest "quadratic regression" satisfy in order to be consistent with the theory. We have

$$T(\tau, Y(\tau)) = \beta_0 + \beta_1\tau + \beta_2\tau^2 + u$$

where $Y$ is output (or sales), $\tau$ is the tax rate, $T(\tau, Y(\tau))$ is Total tax revenues, and $u$ is an error term, to account from deviations from the mean-value.

We can deduce the following:
A) In order to satisfy point 3) above on average, $T(0, Y(0)) = 0$, it must be the case that $\beta_0 =0$.

B) This equation, in deterministic terms has derivatives

$$\frac {{\rm d}T(\tau)}{{\rm d} \tau} = \beta_1 + 2\beta_2\tau, \;\; \frac {{\rm d^2}T(\tau)}{{\rm d} \tau^2} = 2\beta_2$$

and so it will have a maximum at the point
$\tau^* = -\frac {\beta_1}{2\beta_2}$ if and only if $\beta_2 < 0$.

C) Finally, in order for the equation to satisfy point 2) above, $T(1, Y(1)) = 0$, it must be the case that $\beta_1 = -\beta_2$.

But then we also obtain that the maximizer will be $\tau^* = 0.5$. This last consequence is not good: our tool (a specific mathematical functional form that appears convenient for our purposes), forces on us a very specific conclusion that is not predicted by the theory, something that should be left for the data to decide, even in the case were the data do indeed exhibit "Laffer-curve" properties. In other words, the quadratic regression postulates not "general Laffer curve properties", but a very specific Laffer curve (this essentially comes from the fact that the independent variable $\tau$ is restricted to lie in $[0,1]$).

But run the regression we must: so we found that for this specific "quadratic regression specification" to be valid, theory imposes three restrictions on the parameters,

$$\beta_0 =0,\;\;\; \beta_2 < 0,\;\; \beta_1 = -\beta_2$$

Since one of the restrictions is an inequality, one could use Inequality-Constrained Least-squares which requires an iterated algorithm, but I won't go there.

Otherwise, one should first run a regression with the coefficients unconstrained, and see whether at least, $\hat \beta_2 <0$.  Then run the regression imposing the two equality constraints, hope that in this restricted regression $\hat \beta_2$ remains negative, and conduct an $F$-test on the two specifications to determine which fits the data better.

Now assume that the restricted model does have a $\hat \beta_2 <0$ and that it outperforms the unrestricted model: one can then argue that this data set behaves like the Laffer-curve theory would predict, but also, that the tax revenue maximizer is around the value $0.5$. One cannot escape this last conclusion, if the restricted model prevails.

If it does not prevail, other aspects of Laffer-curve theory are not supported by the data, so to mechanically calculate a tax revenue maximizer based on the estimates from the unrestricted model will be rather shaky.

And there are also important statistical misspecification issues:
1) Can we argue that the sales and the tax rates of the various states come from the same distribution, and are independent? (this would be needed to have the "i.i.d. sample" framework)

and especially (which I believe is what @FooBar 's answer focused upon)
2) Is the tax rate uncorrelated with the error term, or is it endogenous? Are there factors that affect directly output/sales and are also correlated with the tax rate (e.g.: if a productivity or other mid-term range shock affects output, is there pressure to change the tax rates also, and do they adjust?)

In light of the above, I would say that the $R^2$ "fit criterion" is not the first thing to check, nor the primary method, in order to judge the quality of such a regression estimation.


OLS, Frisch-Waugh-Lovell Theorem and few observations

We know that $M_X\mathbf{u}= \mathbf{\hat u}$, where $\mathbf{y}=\mathbf{x\beta}+\mathbf{u}$. So even if the error terms are independent, the residuals will not be independent of the other residuals. This is makes the usual assumption of no autocorrelation invalid.

Of course, if we use a HAC estimator then we can circumvent the existence of autocorrelation. However, the HAC estimators that I know of are just of asymptotic behaviour. So, it wouldn't be useful for a small sample size.


Actual availability of regressors may be an issue here, but if all four mentioned variables are available, the situation is as @Michael mentioned in a comment:

Since $X_2$ is correlated with $Y$, it should be included in the regression specification as a "control".

$$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + u$$

This is intuitive, but it also takes care of the technical aspect.
Then since $X_2$ is endogenous, i.e we have ${\rm Cov}(X_2,u) \neq 0$, but we have an instrument that is not correlated with the error term $u$ since $X_2$ has been included in the specification, we end up with

$$Y=\beta_0 + \beta_1Z + \beta_2X_2 + u$$

for which the OLS estimator will be asymptotically consistent, since (writing $\mathbf W = [1:Z:X_2]$)

$$ \hat \beta = \beta + \left (\mathbf W'\mathbf W\right)^{-1}\mathbf W' \mathbf u$$

and its consistency will depend on the following probability limit being zero

$${\rm plim}\mathbf W' \mathbf u ={\rm plim} \left[\begin{matrix}
\frac 1n\sum u_i\\
\frac 1n\sum Z_iu_i\\
\frac 1n\sum X_{2i}u_i\\
\end{matrix}\right] \rightarrow  {\rm plim} \left[\begin{matrix}
\frac 1n\sum E(u_i)\\
\frac 1n\sum E(Z_iu_i)\\
\frac 1n\sum E(X_{2i}u_i)\\
\end{matrix}\right]= \left[\begin{matrix}
0\\
0\\
0\\
\end{matrix}\right]$$

holds because both $Z$ and $X_2$ are orthogonal/uncorrelated to the error term $u$.

In other words, the fact that the regressors $X_2$ and $Z$ are correlated with each other does not create any problem (as long as of course the co-linearity between them is not near-perfect), on the contrary it more generally justifies including both in the regression specification, making it "multiple regression" -it exists exactly for such cases.


Why would the rich care about the poor's overinvestment in riskier investments?

How does the poor's larger investment in riskier investments, affect
  wealthier investors' appraisal of what makes a share's price
  affordable?

It does not. The author purportedly (and mistakenly) thinks that tolerance to risk is governed solely by the investor's wealth.

Your question mistakenly conveys that a wealthy investor's method of valuation of share's price consists of merely reading (or as your question portrays, is "affect[ed]" by) the non-wealthy investor's assessment. But that reading significantly differs from what the author wrote.

The excerpts you reproduce reflect the author's cluelessness about basic concepts in finance. The end of the first excerpt seems to be inaccurately transcribed: The poor grammar in "The first arises directly from the fact are supposed to like the idea of a thriving" do not allow us to grasp the point the author is trying to make. More important, the second excerpt is nonsense.

The author wrote:

  less-well-off investors might invest in higher-risk investments than
  would wealthier ones, because they have less non-invested assets to
  lose.

Causation as purported by the author is wrong. It is true that some non-affluent investors might be more tolerant to risk, but that tolerance is not solely determined by their non-affluence. Their expertise (or lack thereof, as you later point out), and/or their ambitions (meaning a person's legitimate sake of wealth) influence the levels of risk each individual investor is willing to incur.

As a counterexample to refute the author's point, Nathan Rothschild and James de Rothschild continued getting into high-risk investments even after they had made fortunes, and much to the dismay of the next generation in the family.

Next, the author alleges that:

  Wealthier investors would then have a different appraisal of what
  makes a share's price affordable than their less wealthy comrades
  would.

If a share's price is affordable to a non-affluent investor, then it obviously is affordable to the wealthier investor as well. The author might have meant a more appropriate term such as risk-worthiness as a function of expected profit, which brings us back to my previous comment on being more (or less) risk-tolerant than other investors.

An investor buys stock because he has the expectation that the share price will go up. The fact that different investors have different appraisals on the future price of a stock has little or nothing to do with each investor's wealth. Of course, there is a phenomenon known as herd mentality where a multitude of agents are influenced by a contagious and/or blind belief that a share price will continue certain trend. That leads to price bubbles or collapse, accordingly, but that mechanism of affecting each investor's appraisals is unrelated to what the author and your question portray.

Unpredictability and difference of appraisals are precisely what allow the price of some stocks to fulfill some investors' expectations of profit. If everybody were able to predict the future value of an asset, for instance \$90 per share (for simplicity, assume a risk-free interest rate of 0%), nobody would be willing to sell his share for less than \$90, and nobody would be willing to buy a share for more than \$90. Consequently, the share price would stay at \$90, thereby failing every shareholder's expectation of profit.

The author does not substantiate, at least in those excerpts, why the assumption that "robust stock markets are a plus for the economy" is highly contestable.

  I understand how hedge fund managers with PhDs in Finance (who serve
  only the rich) can help the rich to appraise share prices differently
  (e.g. more accurately)

That is unsubstantiated, highly debatable, and very opinion-based. But I don't vote down questions (or answers) merely for a difference of opinions.

Edited on July 5, 2018, to address OP's follow-up comment, and to add last paragraph

(1) Edited, although see "the fact are supposed to like" in the excerpt. I assume the author meant to type something like "the fact that people|investors are supposed to like the idea of a thriving market". But the whole sentence is still unclear: Is it a fact that they like the idea of a thriving market? or are they supposed to like that idea? Saying "the fact that something is supposed" is rather meaningless for his argumentation.

More important, the author's inaccuracies and gaps reflect he does not handle some financial concepts well, and yet he tries to premise on those flawed arguments his proposition about a limited liability schema. I am not knowledgeable enough to support or criticize the author's conclusion(s) about LLCs/LLPs, but he should definitely rework his arguments away from engendering unwarranted confusion & controversy about "classes".

(2) You ask whether the following would change the sense of my answer:

  I know that the rich are more likely to be able to afford investment
  advisors who can help them appraise share prices differently (e.g.
  more accurately), and who don't cater to the poor.

There are two reasons why it wouldn't lead to a different answer. First: Paying an expensive financial advisor does not guarantee that the investor will obtain competent --let alone accurate-- advice. An advisor's certifications or designations certainly, and only, signal that he has demonstrated (typically via exams) standard knowledge of some prerequisite syllabi. However, the advisor remains subject to the aforementioned unpredictability of markets, and to internal policy at his employer agency.

Second: An advisor might recommend the same to wealthy and poor investors, yet the wealthy respond with "I hear you, advisor, but I still want you to do xyz with my funds" based on that investor's risk profile, scrutiny, fiscal planning, expertise, or moral/religious considerations.

I should have added yesterday that, even if the wealthy investor cared about the appraisals made by the poor investor, such reading of appraisals is impossible in today's stock markets because these involve so many buyers and sellers. The author "highly contests" (albeit without substantiating why) that "robust stock markets are a plus for the economy", but it is precisely that inability (in today's markets) to cross-read investments what strikes the author's insinuation that appraisals vary by "class".


Is saying that the demand is elastic or inelastic too oversimplified?

From your Q I am not sure if you are asking solely for linear demand functions or demand functions in general.
When it comes to demand functions just in general  actually, we do not a priori know that "elasticity varies from infinity to zero as we move along a linear demand curve"  there is a class of constant elasticity demand functions for which price elasticity of demand is always the same. For example:
$$P  = Q^{1/\epsilon}\implies Q= P^\epsilon$$
will have constant price elasticity. Since price elasticity is given as:
$$e_p= \frac{dQ}{dP} \frac{P}{Q}$$
In the above case the elasticity would be simply equal to $\epsilon$, as:
$$\frac{dQ}{dP} \frac{P}{Q} = \epsilon P^{\epsilon-1}\frac{P}{P^{\epsilon}}= \epsilon$$
The constant price elasticity functions are relatively popular in the literature and for these functions it clearly makes sense to label them as elastic or inelastic based on value of $\epsilon$.
However, even for a linear demand functions where price elasticity of demand changes along the function it would be reasonable to say that one demand curve is more inelastic relatively to some other demand curve, respectively being more or less elastic over some range. In such situations however the terminology might often be abused and demand function simply termed 'inelastic' - this happens especially in many undergraduate texts and I suppose you could call it an 'oversimplification'.


General model of economics, economics as mathematical structure

You may be interested in reading "Economic Models as Analogies", a 2014 article by Itzhak Gilboa, Andrew Postlewaite, Larry Samuelson and David Schmeidler, four well regarded economic theorists. They argue, somewhat contrary to your view of economic theorizing, that economic models are better viewed as "theoretical cases" rather than general rules akin to the laws of physics. Predictions are made by drawing analogies between the world in which the models live and reality. In Section 4 of the paper, they do propose a "model of economic models" that formalizes their argument. Although this model is probably not the one you were looking for, it may help clarify your (mis)perception of the methodology in theoretical economics.

The paper's abstract is as follows:

  People often wonder why economists analyse models whose assumptions are known to be false,
  while economists feel that they learn a lot from such exercises. We suggest that part of the
  knowledge generated by academic economists is case-based rather than rule-based. That is, instead
  of offering general rules or theories that should be contrasted with data, economists often analyse
  models that are ‘theoretical cases’, which help understand economic problems by drawing
  analogies between the model and the problem. Thus, economic models, empirical data,
  experimental results and other sources of knowledge are all on equal footing, that is, they all
  provide cases to which a given problem can be compared. We offer complexity arguments that
  explain why case-based reasoning may sometimes be the method of choice and why economists
  prefer simple cases.


Finance vs. financial economics (terminology)

Virtually same question was already addressed at quantitative finance stack by user Matthew Gunn.  The answer there can be summed as:

Financial economics is what economics calls finance. Finance is what finance calls finance.
Less flippantly though, there's a long debate on whether finance is a subfield of economics, ... Prof. Milton Friedman famously opposed awarding Markowitz a PhD in economics from the University of Chicago for his portfolio theory because while Markowitz's work was brilliant, Friedman didn't consider it to be economics. ... Myron Scholes also express views that finance is to some extent distinct from economics.

By many economists finance is not considered to be part of economics but rather to be a separate discipline. For example, according to Journal of Economic Literature (JEL) classification (which is authoritative source for classification in economics), there is no sub-field of finance in economics. There is only subfield of financial economics. This classification has a following guideline:

Guideline: Covers studies about issues related to various sub-fields in financial economics: general financial markets (both domestic and international) dealing with securities (stocks, bonds, and commodity and other futures); financial institutions and services; and corporate finance and governance.

This is something that probably most people who are in finance would recognize as subject matter of their field.
However, I would argue there is a subtle difference. People who study finance often do that in more practical way  with larger emphasis placed on analysis from the investors/financial firm point of view and applying concepts to some particular cases. While financial economics focuses much more on generalization and studying financial markets from much wider perspective than would be necessary for practical operation of financial firms. I will use a crude analogy but I think it is at least partially correct, many economists would consider economics to have similar relationship with finance as physics and engineering or biology and medicine.  This is admittedly a crude analogy as I think when it comes to finance/financial economics the distinction is more subtle and less obvious but that is the best analogy I can think of.


Which parts of health care can be considered market failures?

The most common one I have considered is health insurance as a private market. It becomes a case of the "market for lemons", where in this case the `lemons' are the people seeking insurance. https://personal.utdallas.edu/~nina.baranchuk/Fin7310/papers/Akerlof1970.pdf
The simplified narrative goes something like this:
Assumptions: Say insurance companies sell to everyone who wants insurance at some fair rate, and we cannot discriminate based on pre-existing conditions. Some people are very sick, and cost a lot to insure (lowers profits for the insurer) and others are healthy (profitable for the insurer.)

As sick people, who frequently utilize the insurance buy into the market, the average rates go up.

Healthy individuals, who don't need it at much, leave the market in response to the increasing prices, which only serves to continue increasing the price.

This process of healthy people leaving and sick people joining continues until the market collapses, nearly only sick people are insured.


Why is Land not considered as a fixed capital?

The distinction between land and physical capital is based on some of their economic properties, particularly relating to investment: whether it can be reproduced or not; whether it has a finite lifetime (compared to the human lifetime).

Almost all land is not reproducible, and does not have a finite lifetime.

Physical capital is reproducible, and does have a finite lifetime.

Hence, almost all land is not physical capital.

There are corner cases, where land is reproducible, and may appear and then disappear again in less than a handful of human lifetimes: in those very rare cases, that particular land behaves more like physical capital rather than how land generally behaves, and so could be classed as such.


I don't really see why you would price an ETF at fair value and not at last market price, given that those funds are very liquid. But in either cases you need to have two distinct securities in your portfolio, as the two classes of shares that you own in the ETF bear different risks, and will yield different performances, due to the xrate.


Why does the inflation not follow the money supply?

This is because classical economic theory absolutely does not say that:

inflation occurs when the money supply is increased faster than the economic growth.

Even in most basic 101 models inflation depends on variety of factors. Inflation is determined by changes in price level which in turn depends on what the money market equilibrium is. This is given by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY \implies \ln P = \ln M + \ln V− \ln Y$$
Where M is the money supply, V velocity of money, P price level and Y output. In the log-linearized version the effects of right hand side variables can be interpreted as % changes.
Even in this most simplest model your statement "inflation occurs when the money supply is increased faster than the economic growth" would only hold if velocity of money would be constant but in real life it is not. As you can plainly see from the data provided by Fed the velocity of money dropped drastically since the 90s which offests most of the increase in money supply during that period.

Lastly, the model above is still just the most simplistic 101 textbook money market model. In more realistic and complex models there are more variables that matter. For example, inflation expectations are absolutely crucial. Inflation will not move drastically if inflation expectations are well anchored (e.g. see Castelnuovo et al 2004; Kose et al 2019 or Lejsgaard & Grothe 2014 and sources cited therein for more info on the concept).
In addition, as famously shown by Krugman (1998) what matters is not just the actual change in money supply or other quantities but what are peoples expectations about changes in money supply and so on. An increase of money supply that is not credible to be permanent and expected to be quickly reversed will have no effect on inflation as if it would never even happen. Furthermore, Krugman also showed that when nominal interest rates are at zero lower bound (ZLB)  even large monetary expansion won't necessary be inflationary. The reason for that is that if you would want to go significantly below ZLB the peoples will strictly prefer to hold cash and any increase in money supply will be completely offset by drop in velocity of money.
There are also further nuances to this but full overview of modern scholarship on this topic would be well beyond scope of SE answer. I recommend you to have look at Monetary Theory and Policy by Walsh or Woodford Interest and Prices and sources cited therein for state of the art models and more information on the matter.


Jan Philipp Dapprich did something like this in his PhD-Thesis. For an introductory read, his blog might be a little more accessible, this article is a good start. His research, in short, is based on the assumption that the drastic increase in computational power during the last decades can be harnessed to fix some of the flaws of the planning performed in systems like the soviet union.
For a short description of the model I provide the following quote from the article:

An agent-based model that was developed for the purpose of the simulation is used to model the behaviour of consumers. In a real socialist economy this would not be necessary, as there would be actual consumers. In the simulation it is, however, necessary in order to determine the consumer demand for various product. Consumers are given a set amount of credits and will then semi-randomly decide how they will spend those credits. From this the overall demand for the various products is derived. What’s crucial about the consumer model is that demand is sensitive to credit prices. Consumers are less likely to buy a product if it has a higher price. Based on a comparison of demand and the supply of consumer products given by the optimized production plan “market clearing prices” can be approximated. This is done by successively adjusting the price of products depending on the difference between supply and demand until supply and demand match. The previous plan target is now adjusted through a comparison of prices and values (MDVs). The MDVs are scaled in order to make them comparable to prices. Should prices of a product exceed MDVs, this suggests that consumers are sufficiently interested in the product to justify further production. Therefore, the target entry for the product is increased. Should prices be below MDVs, this suggests that consumers are not interested enough in the product to justify the current emphasis on the product and the target entry is consequently lowered. By adjusting the plan target this way we make sure that in the next plan period the proportions at which products are produced more closely resemble what consumers actually need. This process also takes into account the cost of producing a product in the form of the MDVs. Should there be a significant limitation on the amount of greenhouse gas emissions that are allowed for, this would result in higher MDVs for products whose production involves higher amount of emissions. In this case the targets for those products will be lowered and a greater emphasis will be put on producing more environmentally friendly products. A central hypothesis that I wish to confirm using the simulation is that this shift towards environmentally friendly products distinguishes the effect of my model from the labour value model of Cockshott and Cottrell, as labour values don’t take emissions into account.

This excerpt is not sufficient to explain his whole methodology since it is quite complex. For the sake of readability I decided to just scratch the surface here and refer to the blog post series for deeper insight.


what is the most comprehensive History of Economic Thought book for an undergrad?

My suggestion is not necessarily the most comprehensive, but "The Worldly Philosophers" by Robert Heilbroner is very enjoyable.


Interpretation of multinominal logit regression (Stata)

You have that:
$$
\begin{align*}
\ln\left(\frac{\Pr(D|X = 1)}{Pr(A|X = 1)}\right) &= \ln\left(\frac{\Pr(D|X = 0)}{\Pr(A|X= 0)}\right) -1.264 + 0.627,\\
&\le \ln\left(\frac{\Pr(D|X = 0)}{\Pr(A|X= 0)}\right)
\end{align*}
$$
So taking exponents, we have that:
$$
\frac{\Pr(D|X = 1)}{\Pr(D| X = 0)} \le \frac{\Pr(A|X = 1)}{\Pr(A|X = 0)}.
$$
What you find is that:
$$
|\Pr(A|X=1)- \Pr(A|X = 0)| > |\Pr(D|X = 1) -\Pr(D|X = 0)|
$$
These two are not necessarily in conflict.
For example:
$$
\Pr(D|X= 1) = 0.1\\
\Pr(D|X = 0) = 0.3\\
\Pr(A|X = 1) = 0.4\\
\Pr(A|X = 0) = 0.677
$$


Is it possible to reconstitute a labor theory of value?

It would be helpful if your question were a little more honed in. This is a very broad set of questions about an entire theory, but a few thoughts that come to mind.

The labor-theory of value naturally predicts that profits will be higher in labor-intensive industries, as opposed to capital-intensive industries, and that's simply not what we see in the data. A firm needs a good balance between both capital and labor. Also note that in developing countries, labor is plentiful compared to capital, so wages are lower and capital is expensive. As welfare and the capital stock increases, labor becomes more sparse since there is more to do with leisure, so wages rise and the price of capital falls (we are better at producing capital.) So in some vague way, the price of a good depends more and more on labor as the development of a country increases, but not because of the intrinsic value of labor, but because of the marginal cost of labor for firms that increases.

When you ask,

  But is there any inherent reason why a labor-based system of value and pricing adequate to a modern market economy cannot work?

you assume that there is a system like this that is "adequate". It's not that labor has no place in production or determining the price of a good, but we have models that are better because they realize there's more than just labor that goes into production. Labor does not exist in a vacuum. Today we take into account both the value of labor as well as the value of capital, amongst other factors of production. Why would we want a model that ignores these things for the sake of saying the price of something should only depend on the amount of labor put into it.

A final note: in industries where worker labor is overwhelmingly the major part of production, the wages paid out are essentially the value of effort put into the product. The worker maximizes

See the second part of my answer to this question to see the mathematical set-up for that result.


Risk neutral probability for each of 3 states

I cannot really follow your formulas, what is the logic behind them?

Seems to me there is no way to divine three state risk-neutral probabilities from 1 financial instrument's prices. The equation
$$
p_1 288 + p_2 180 + (1 - p_1 - p_2) 120 = 180
$$
is underdetermined, there are infinitely many solutions to it. Now if you solved the equation system
$$
\begin{align*}
p_1 288 + p_2 180 + (1 - p_1 - p_2) 120 & = 180 \\
p_1 94 + p_2 134 + (1 - p_1 - p_2) 54 & = 100
\end{align*}
$$
there you have two unknowns and two equations, so usually this would admit exactly one solution.

P.s.: The numbers in my example are not corrected for intertemporal differences, there has been no discounting.


How can China shield its public from the effects of a trade war?

Barry Naughton is an authority on the Chinese economy. He offers evidence on China's government control over the economy in a nice paper called "Is China Socialist?"

China's government controls an unusually large proportion of national income flows. He argues that these income streams have grown dramatically as a share of GDP since the mid-1990s. He shows how the Chinese  government steers  the  economy  because it sees a strong economic performance as a core part of its political legitimacy. China's government has some tools to "shield the public from job cuts or factory closings" because of American tariffs.

Beyond the tools of funding direct government programs and ownership, the Chinese system has two distinctive mechanisms through which it attempts to foster development:

a set of bureaucratic incentives that reward officials for growth (of GDP and revenue);
planning that is centered on the national-level Five-Year Plans that propose a certain trajectory for growth.

Chinese Government's Control over National Income

The above Figure illustrates an expanded concept of government revenues that includes four main components:

budgetary revenues (not including social security);
social insurance  premiums;
land  revenues;
net  income from  state-owned enterprises.

These four components help Naughton providing an index of government control of resources, which tripled as a share of GDP between 1996 and 2013. This index gives an indication of the overall size of the Chinese government. For instance, all land in China is publicly owned: urban land is owned by the state, and housing is "privately owned" only in the sense that households hold long-term leases, typically of 50–70 years. The  financial system  in  particular is overwhelmingly dominated by the state-owned banks, which generate substantial profits.

Summing all four components, the Chinese government had direct or indirect control  of  38%  of  GDP  in  2015.  Overall,  the  Chinese  government  is  large,  well-resourced,  and  potentially  highly  intrusive.  This  is  both a  distinctive  feature  of the Chinese economy in comparative context, and a dramatic change from the China of 20 years ago.


Proof of Choice Coherence in Kreps (2013)

If there is no $z \in A$ such that
$u(z) > u(y)$ (perhaps because no other $z$ exists, perhaps for other reasons)
then by definition of $c_u$ we know that $y \in c_u(A)$. This would contradict the assumption of the third sentence, that $y \notin c_u(A)$.

  If, moreover, $y \notin c_u(A)$...