On high frequency trading

I have complained to my coworker a few times about how I don't think high frequency trading is socially efficient. The coworker didn't really empathize as he saw the benefit of additional liquidity and I didn't really have a strong rationale behind my complaints. I have been thinking more about this issue lately and I think now I have some arguments to support my feeling.

The inefficiency is that trading firms spend millions of dollars to reduce latency at the unit of milliseconds. This is a natural consequence of the nature of high frequency trading competition, just as price competition is a natural consequence of free market. When a supplier in free market reduces the price of its products, its loss from the competition transfers directly to the consumers and in fact the perfect competition that drives the price down to the marginal cost exhausts all mutually beneficial trades to reach a Pareto optimum. On the other hand, the cost incurred from latency competition does not benefit anyone, except for very marginal increase in liquidity (the real social benefit of HFT is liquidity in terms of ask-bid spread, not in latency). In short, all those millions of dollars spent by trading firms to cut down the latency is deadweight loss to the society. And since the latency can never reach a true zero, the arms race can continue on and on. My guess is that at this very moment highly scarce human capital is spent on researching for reducing the trade latency.

I should mention that this is the same kind of social cost incurred by education signalling that I commented on last year. More precisely, it is a social cost of type of competition that has no counter party benefiting from the cost of competition. This type of competition is of course nothing but a form of Prisoner's dilemma, where the player reaps a huge benefit as long as he spends a little more than everyone else. The unique Nash equilibrium in this case would be that everyone spends as much as the benefit which is the worst social outcome.

I can't think of any way to solve this problem. Setting some minimum latency would be an obvious solution but the cost of enforcing it would well exceed the benefit. An easier rule to enforce is no high frequency trading at all. Not to say that HFT is without its benefits, but perhaps it deserves a cost-benefit analysis.

On patent

The recent court battle between Apple and Samsung has stirred the economics community a little to discuss about the efficiency of patent law. Becker and Posner both show concern that the current patent system is excessive. Becker cites Arnold Plant (1934) who advocated the elimination of patent system, agreeing that Plant erred in the right direction. Still, Becker finds patent system still necessary, writing: Although ending the patent system is a clean solution to all the problems induced by modern patenting, it clearly is not desirable given the importance of industries like the pharmaceutical industry. Since this industry spends on average hundreds of millions of dollars bringing to market a successful drug, pharmaceutical companies would not invest such large sums without the protection of patents (or without other benefits).

And today, I came across an article by Jordan Weissman that cites a working paper by Boldrin and Levine that argues for abolishing the patent system entirely: the best solution is to abolish patents entirely through strong constitutional measures and to find other legislative instruments, less open to lobbying and rent-seeking, to foster innovation whenever there is clear evidence that laissez-faire under-supplies it. The base of the bold argument is that, although well-designed patent system would indeed spur innovations, such system cannot occur with the current political structure. This part of the argument (part 3) feels rather weak at the moment, but that is not unexpected from a working paper.

The paper reminded me of an article by Steven Johnson in Wired magazine (October 2012, "Inventors' Gold"). Focusing primarily on pharmaceutical industry, Johnson argues that the government should offer lump-sum payouts instead of granting patents. The benefit of this alternative is that it eliminates the externality of patent monopoly while still providing incentive for innovation (the lump-sum payment, or the prize, would constitute the "other benefits" Becker mentions). It further solves Plant's concern that, as Becker summarizes, patents distort innovations in favor of goods and processes that can be patented and away from innovations that cannot be patented. In similar vein, Johnson argues that the current patent system does not allow innovations in some of the most needed drugs, such as those for tropical disease.

The last point, of course, is arguable and is in fact one down side of lump sum prize compared to patent. The burden of measuring the value of innovation lies on the government with the lump sum prize, while it lies on the innovators with patent system. As we know, government has less incentive to make accurate estimate. Furthermore, the cost of wrong estimation transfers from the innovator to the taxpayers with the lump sum prize, which may be socially undesirable. Still, I find the alternative of lump sum prize quite attractive over the current patent system.

Homogeneous production and average cost

I have discussed before that constant returns to scale (CRS) function with a single factor is of the form F(x) = cx where c is a constant. In this post, I wanted to show that if the two−factor production function has CRS, then the average cost is independent of the output level. Then I decided that such a result is too boring to deserve a post, so I am going to discuss the relationship between homogeneity of production function and average cost in full generality, following Sandmo (1970).

A function F: Rⁿ → R is homogeneous of degree k if a^kF(x) = F(ax) for all a > 0 and x in Rⁿ. A production function has constant returns to scale if it is homogeneous of degree 1. It has increasing returns to scale if homogeneous of degree k > 1, and decreasing returns to scale if homogeneous of degree k < 1. These properties can be defined locally (that is, find k as a function of x) by taking the derivative of the identity equation above with respect to a and then solving for k (assuming F is differentiable): ka^k−1F(x) = Σ F_ix_i and since a^k−1F(x) = F(ax)/a, we get k = aΣ (F_ix_i/F(ax)). Evaluating at a = 1, k = Σ (F_ix_i/F(x)).

Assume perfect competition in factor markets so that the factor prices are exogenously determined. Let r_i be the price of factor i and let r be the vector of prices. The total cost is then Σ r_ix_i. For fixed output level Q, the firm is cost minimizing with regard to x subject to its production function F(x) = Q. The Lagrangian is L = Σ r_ix_i − λ(F(x) − Q) and the first order conditions are r_i − λF_i = 0 for i = 1,..., n and F(x) − Q = 0. These n+1 equations yield the optimal x* as a function of r and Q and we can find the optimal cost C as a function of r and Q: C(r,Q) = Σ r_ix_i*.

While we are talking about cost function, let's mention that the Lagrange multiplier in cost minimization problem can be interpreted as the marginal cost. The derivative of this minimum cost function with regard to Q then is the marginal cost: dC/dQ = Σ r_i(dx_i*/dQ). By the first order conditions, r_i = λF_i. Totally differentiating F(x) = Q condition, we get Σ F_i(dx_i*/dQ) = 1. Thus, λ = dC/dQ.

Going back to the average cost problem, let A(r,Q) = C(r,Q)/Q be the average cost. To show the behavior of average cost as Q varies, take dA/dQ = Q⁻²(dC/dQ × Q − C). Thus the direction of average cost in Q depends on the sign of dC/dQ × Q − C or dC/dQ − C/Q. We showed C = Σ r_ix_i = λΣ F_ix_i and λ = dC/dQ. By the constraint, Q = F(x). Thus dC/dQ − C/Q = λ(1 − Σ (F_ix_i/F(x))). But we have also shown that k = Σ (F_ix_i/F(x)). Therefore, the average cost is increasing in Q if k > 1 (decreasing returns to scale), decreasing in Q if k < 1 (increasing returns to scale), and constant in Q if k = 1 (CRS).

The Basic Ricardian Model

Given that Ricardian insight of comparative advantage is introduced in the very introductory economics classes and that the model is introduced quite early in the intro microeconomics, one would expect that I should know at least the simple Ricardian model inside out. Well, sadly this is not the case; I find going over the model in detail surprisingly nontrivial. In this post I am going to outline the basic Ricardian trade model.

Set Up

In the simple Ricardian model, there are two countries, home and foreign. It seems a literature tradition to postfix foreign variables with ^* so I will follow the tradition. There are two goods, 1 and 2, and single production factor, labor (L). The total labor endowments, L and L^*, are exogenously fixed (immobile across countries). Within each country, labor is perfectly mobile between the industries for good 1 and 2 (L₁ + L₂ = L).

The production function has constant returns to scale with marginal product of labor equal to a_i at home and a_i^* for i = 1, 2. In other words, to produce one unit of good 1 at home, it takes 1/a₁ units of labor, etc. As discussed earlier, CRS with single factor implies that the production function is linear: Q_i(L) = a_iL.

At this point we can find the production-possibility frontier: {(Q₁, Q₂) s.t. Q₁ = a₁L₁, Q₂ = a₂L₂, and L₁ + L₂ = L} = {(Q₁, Q₂) s.t. Q₁/a₁ + Q₂/a₂ = L}. Graphed on Q1-Q2 plane, the PPF is a straight line with slope -a₂/a₁.

Autarky Equilibrium

Let's consider the autarky equilibrium. Let p_i denote price in each industry and let p = p₁/p₂ be the relative price (of good 1). The model assumes perfect competition, so each industry makes zero profit: Π_i = p_iQ_i - w_iL_i = 0, where w_i denotes the wage for industry i. Solving for the wage, we get w_i = p_iQ_i/L_i = p_ia_i.

Suppose consumer preference is such that at any price both goods are demanded. For both goods to be produced, we require w₁ = w₂, implying p = a₂/a₁. We cannot determine the exact autarky equilibrium without a specific demand function, but we know it lies on some interior point of the PPF found above.

Trade Equilibrium

Allow the countries to trade with each other. Assume the foreign country has a comparative advantage in good 2. That is, a₂/a₁ < a₂^*/a₁^*, implying that home autarky relative price of good 1 is lower than the foreign's: p_a < p_a^*. To find the equilibrium price with trade, we consider the supply and demand as usual.

The world relative supply (of good 1) is 0 when both countries specialize in good 2. This occurs when the world relative price p is less than both the home and foreign autarky relative prices. On the other hand, both countries specialize in good 1 when p is greater than both of the autarky prices. If the world price lies strictly in between the autarky prices, so that p_a < p < p_a^*, then home specializes in good 1 while the foreign country specializes in good 2. The relative supply in this region is then (La₁)/(L^*a₂^*).

There are end points to consider. When p = p_a, the home country may produce both goods while the foreign country specializes in good 2, so that the world relative supply is less than or equal to (La₁)/(L^*a₂^*). When p = p_a^*, the foreign country may produce both goods while the home country specializes in good 1, so that the supply is greater than or equal to (La₁)/(L^*a₂^*).

Assuming identical and homothetic tastes across the countries so that the relative demand is decreasing in the relative price p, there are three possible cases. The equilibrium price may equal to the home autarky price or the foreign autarky price, or it my lie in between. Let's focus on the last case in which both countries specialize. Consider the new PPF of the home country. Since it specializes in good 1, it has total income of p₁a₁L. So the new PPF is {(Q₁, Q₂) s.t. p₁Q₁ + p₂Q₂ = p₁a₁L} = {(Q₁, Q₂) s.t. Q₁/a₁ + (1/p)Q₂/a₁ = L}. Since 1/p < 1/p_a = a₁/a₂, it follows that the old PPF is a proper subset of the new subset (and since we assumed the preference is such that both goods are demanded, the home country is strictly better off). Graphically, the PPF pivots outward centered at (La₁, 0) since the slope of the curve is now p > p_a. Similarly, for the foreign country which specializes in good 2, the PPF includes the end point (0, L^*a₂^*) but now has the slope of p < p_a^* so again it pivots outward.

So in the trade equilibrium, both countries are better off than in autarky. The Econ 101 punchline of the Ricardian model: mutually beneficial trade occurs when there exists a comparative advantage and the direction of the comparative advantage determines the specialization and direction of the trade. In particular, even if a country has no absolute advantage in either good, mutually beneficial trade occurs. For example, even if a₁ < a₁^* and a₂ < a₂^*, comparative advantage can lead to a trade (of course, if one country has a comparative advantage in one good, the other country has the advantage in the other good; if there is no comparative advantage, then autarky prices of both countries are the same, so there will be no gain from trading). How can the home country export when it has lower MPL for both goods?

The answer is that the wages are adjusting to the productivity. In the home country (specializing in good 1), the wage level is w = p₁a₁ and in the foreign country, it is w^* = p₂a₂^* > p₁a₁^* since p = p₁/p₂ < a₂^*/a₁^* = p_a^*. So a₁ < a₁^* implies w < w^*.

It is tempting to close the model with such an optimistic and insightful conclusion, but we have not finished examining the model since we have skipped the end point cases. The only thing to note here is that in the case both countries specialize, we can determine the relative output (La₁)/(L^*a₂^*) and use this to determine the equilibrium price given the demand (without demand specified, we can only put a bound). In the case only one country fully specializes, we know the price (the autarky price of the other country) but we have to determine the quantity from a specific demand function from the price. The point is, the model is analytically rather cumbersome even at the basic setting.

Thus the post-Ricardian models have focused on expanding the model to allow multiple countries and factors for empirical studies. Indeed, many international trade models seem to be characterized by three parameters: the number of countries, the number of industries, and the number of factors. Other than those, the most important part of Ricardian model would be the technological difference across countries, which allows gain from trade.

The Envelope Theorem

I learned in school the Kuhn-Tucker conditions and the envelope theorem but I always felt I didn't have a complete understanding of them. One thing confusing about the envelope theorem is that there are different varieties of it, depending on the flavor of the optimization problem. I decided to review envelope theorem today and keep the notes in the blog.

Consider a constrained optimization problem on the function f(x,a) with regard to x subject to a g(x,a) = 0, where x is an n-vector and a is a scalar. Let M(a) be the solution to the problem; that is,

M(a) = max_x f(x,a) s.t. g(x,a) = 0.

The Lagrangian is then L = f(x,a) − λg(x,a), giving n+1 first-order conditions (or, n first-order conditions and m complementary slackness conditions for more general constrained optimization problem with m inequality constraints). These conditions yield the optimizing argument x*(a) and the solution M(a) = f(x*(a), a).

The envelope theorem states that if x*(a) is a C¹ function and the usual constraint qualification is satisfied (∇g(x*(a))≠0), then M'(a) = ∂L(x,a)/∂a evaluated at x = x*(a). To put crudely, to differentiate the solution with regard to a parameter (say for comparative statics), one only needs to differentiate the Lagrangian with respect to the parameter and then "plug in" the solution x* rather than explicitly find M(a) and then differentiate it.

The proof for this version of envelope theorem is a straight-forward calculation. Since M(a) = f(x*(a), a), it follows

M'(a) = Σ(∂f/∂x_i)(∂x_i/∂a) + ∂f/∂a

for i = 1,..., n.

By the first order conditions, ∂f/∂x_i = λ∂g/∂x_i for each i. It follows

M'(a) = λ Σ(∂g/∂x_i)(∂x_i/∂a) + ∂f/∂a

Identically, it must be that g(x*(a), a) = 0. Differentiating this equality with respect to a yields Σ(∂g/∂x_i)(∂x_i/∂a) + ∂g/∂a = 0. So we get

M'(a) = -λ∂g/∂a + ∂f/∂a evaluated at x = x*(a).

But of course, -λ∂g/∂a + ∂f/∂a = ∂L/∂a

The more general case with m inequality constraints have a similar flavor of proof: differentiate the maximum function with respect to the parameter, collect the terms, and then use the first order conditions and complementary slackness conditions to cancel out the terms. The theorem can be further generalized into the case in which the parameter is a k-vector rather than a scalar.

CRS function with single factor

An assumption of Ricardian model is constant returns to scale production function with single production factor (labor). Therefore, the marginal product of labor (or, in the usual manner of presentation, its inverse, the units of labor required to produce one unit of good) completely describes the production function. This was so intuitively clear that I never bothered to check.

A production function F(x): Rⁿ → R has constant returns to scale if F(ax) = aF(x) for all a > 0, where x is a n-vector and a is a scalar. In other words, it's economists' way of saying degree 1 homogeneous.

The claim is that if n = 1, then F(x) = cx for some real number c. The proof is simple. Suppose F has constant returns to scale, and denote F(1) = c. Then ac = aF(1) = F(a) for all a > 0. F(0) = 0 follows from the observation that F(0) = aF(0) for all a > 0. Finally, since F(1) = -F(-1), it follows -ac = aF(-1) = F(-a) for all a > 0.

Of course, I could have used Euler's theorem which states that F(x) is homogeneous of degree k iff nF(x) = Σ_ix_iF_i where F_i is partial derivative of F regard to x_i. Thus, single factor CRS function satisfies F(x) = xF'(x). Solving differential equation yields F(x) = cx.

On donations

It's the season of charity and donations and I am going to write against donations. Well, not exactly, but I do have some bad things to say about humanity.

The problem with donation is of information. When you buy a product, you own that product. Then you can assess how good the product is and perhaps even share your assessment. Eventually, consumers gain knowledge of the value of these products and companies that fail to produce quality products at competitive price will be driven out of the market.

On the other hand, when someone donates money the benefit is given to whomever the donor wants to help. The donor rarely gets any information to assess the value of his donation; if you give $1000 to UNICEF, what exactly does it do? The answer to such a simple question is rather difficult to have and consequently choosing a charity to make donation is difficult. If you want to improve the well-beings of African children, should you donate to UNICEF, Save the Children, Invisible Children, the Gates Foundation, or Amnesty International? Most likely, same amount of money given to each of these organizations will lead to different results, some improving the life quality of the children more than the others. Yet there is no way for a person to gain this information. Compare this to, for example, buying a TV. The potential buyer will present himself with different options, consider the pros and cons of each of them, and then make the final decision based on the cost-benefit analysis. This process is largely omitted when someone decides to donate to charity as the information is simply unavailable.

I am claiming that this problem arises as the buyers (donors) differ from the consumers (beneficiaries of the charity) but let me go little further. The task of measuring the value of charity program is a difficult one; much more difficult than measuring the value of say a TV. Suppose a charity has fund to spend on helping people in Ethiopia. It can buy lots of food with the money and give it out to people. It can try to assist building infrastructure. It can lend out money to farmers hoping the investment will increase the output. It can raise the awareness as to increase the future fund to help them. It can run a campaign to reduce the US and EU tariffs on sugar, among other agricultural products that Ethiopia produces. Measuring the benefits of these programs is difficult but nonetheless important, since some actions, no matter how well-intended, can do more harms than goods. It is by now well known that foreign aid in simple form of giving out foods foods can hurt the local economy and foster long-term dependency.

Now, the charity organization could spend some of its fund to figure out what would be optimal choice. There is some effort to do this, but we know remarkably little about how effective and efficient various measures of aids are. We need to learn the economy, people, their needs, what works and not, what is sustainable. And before we have learned this, we need to be more careful and avoid doing things that we think will do good. Lives are lost due to this inefficiency.

Let me trace back a little. I don't want to just argue that there is inefficiency in the charity market. I want to argue that this inefficiency is inherent. So let me go back to my old point: the existence of a charity organization does not depend on how successful it provides its intended aid but on how successfully it collects donations. As pointed out earlier, this problem arises because the buyers and consumers are different. But why is this really a problem, if the donors actually care about the well-being of those who are receiving the aid?

To give a dismal answer, this shouldn't be. If we really cared, then we would demand more information. We would demand to see the proofs that they are doing what they claim to be doing and that those actions are theoretically sound and empirically supported. We would demand that charities regularly provide reports on how well or poorly they are doing in terms of meeting their aims. We would demand to see a third party organization that tries to objectively measure the performance of different charity organizations, so that donors can make more informed decision.

Yet we do not, because what we care about is not other people, but our own moral satisfaction. It is disturbing to know that somewhere in the world there are children dying because they don't have food and fresh water. We feel guilty knowing that there are people dying of diseases that can be cured relatively easily with modern medical technology. We are uncomfortable with inequality and being on the better side without trying to help the other side. So the charity organizations provide satisfaction our moral needs by allowing us to donate money for humane purpose. The act of donating itself, rather than the improvement in the well-being of others, satisfies our moral need.

I am getting little too heated, so let me cool down and finish the post. I have argued that the charity market is inefficient, in the sense that the money collected from the donors by the organizations is not used in the optimal way to improve the life quality of the intended beneficiaries. This inefficiency arises because unlike other markets, those who pay for the product differ from those who consume the product. I argued, although admittedly without much evidence, that this problem will at least partially solved if the donors cared more about the actual well-being of the people who they intend to help. I believe that this will lead to organizations that evaluate different charity organizations in an unbiased way and make the information easily accessible. This would provide incentives for the charity organizations to minimize its current inefficiencies.

Edit (15 September 2012): Here is an interesting WSJ article that is somewhat relevant. I don't quite agree with every argument of the article, but I value the insight in the article that observed how charity market is fundamentally different from most other ones and how its efficiency can be improved.

On grade inflation

Has the US been experiencing a grade inflation? It is a fact that the average grade a student receives has been increasing over the past decades. Yet, this does not suffice to claim that there is a grade 'inflation' since to do so we must assume that the student ability has not changed over time.

First, we must agree on whether grade should be measured relatively or absolutely. In many cases, grades are measured relatively; a student grade often reflects how many standard deviations he is away from the median student of the class. In this case, grade inflation translates to a higher GPA number assigned to the median student. Yet, we would at least like to measure grades absolutely. In other words, grade should reflect the degree to which the student has achieved the course objectives. The relative measure is merely one way to overcome the difficulty of objective absolute grading.

If grades are measured absolutely, then the grade inflation must look not only at the time trend of the average grade, but also at the change in average student achievement. If students are on average learning more efficiently and therefore meet the course objectives to greater degree, then the average grade should increase. It is difficult to find empirical data on the degree student achievement since it is most commonly measured by GPA. There are, however, good reasons to believe that students on average learn better than they did before. The argument comes from two sides.

One side is that the college has become increasingly competitive. A fact: the average acceptance rate to universities is decreasing. There would be many reasons for this: increasing population, increasing returns to education, and decreasing transportation cost which increases the candidate pools by bringing international students. No matter what the reason is, it is undeniable that the selection to the university is becoming increasingly competitive, and therefore, if we believe that admission committee does its job and selects more able students from the candidate pool, then we should believe that the average ability of students is increasing.

On the other side, teaching become more efficient over the past decades. Students today have access to better textbooks, greater resources (much thanks to the Internet), and hopefully better teaching methods (due to slow but existing pedagogical progress), compared to students in the past. We would at very least hope that these improvements help students to learn, in which case an average student would achieve more learning objectives now than in the past.

This argument counters a claim that grade inflation causes students to be more lazy. To the contrary, it is an increase in learning efficiency that causes the seeming grade inflation. The only concern with the inflation is then that GPA may lose its signal value, but then again, that might not be a bad thing.

On school grades

Surely any teacher would be offended by the signaling theory of education. If people who go to school don’t come out any better, what does that imply about teachers? The theory seems to suggest that their only function is to make it costly for low ability students to go to school. I believe that most teachers strive quite the opposite. They would want to see improvements especially among the low ability students.

So why do schools assign grades to students? Grading serves as a mechanism to distinguish high ability students from low ability ones, so that the school can reward the high grade students and/or punish the low grade students psychologically, financially, or even physically.

If a school’s interest is to improve students’ abilities rather than to make itself a signaling mechanism, then it should abandon the grading system altogether. One could argue that grades can be used as incentives for students to work harder, but if this were to be true, then grades need to be based on marginal improvement. In reality, grades are based on comparison with others’ performances rather than with one’s own past performance. There is reasons to think that this form of grading can provide disincentives to put effort for low ability students.

By signaling mechanisms, schools that are harsher to low ability students are more popular, since attending such schools signal that students have high ability. If a grade-free school was introduced, such school would be less costly for low ability students, attendance to such schools will give bad signals, and thus the school will be driven out of the market.

What should we do, then? Make a collective effort to make schools grade-free. Schools, with the aim of improving students' abilities, can function without giving grades. On the other hand, grading system leads to early sorting processes potentially resulting in discrimination against low-income students (holding abilities constant, students from high-income families can more easily earn higher grade, earning potentially life-long advantage through signaling). Further, valuable resources are being wasted on grading in the sense that those resources can be put into better improving students’ abilities. Students want teachers, not graders.

On taste-based vs. statistical discrimination

Since in both labor and experimental economics class we are discussing about discrimination, I have been thinking on this topic for a little while.

It seems there is a general sentiment that taste-based discrimination is morally unacceptable, while statistical discrimination to some degree is permissible. A person who offers  lower wage to minority out of his dislike of the minority is contemptible, but who can blame an insurance company that charges different premium based on gender, age, race, etc.?

As usual, I find myself having controversial thoughts. I find taste-based discrimination to be at least in some cases more permissible than statistical one. Why is it wrong to hate, say, women, but acceptable to hate those who hate women? If an employer strongly believe that racism is morally unacceptable and offers lower wages to racists, is he wrong to do so? Surely one is entitled to have opinions and like or dislike certain type of people, whether that taste is based on “truth” or not.

Besides, there is a sense of reciprocity in taste-based discrimination in that the discriminators pay in order to discriminate. On one hand this reveals how discriminatory a person is, but on the other hand it seems more acceptable than essentially selfish behavior of profit-maximizing even when it involves discrimination. The former foregoes his own earnings in order to discriminate; the latter foregoes non-discriminatory behavior in order to earn more.

Furthermore, taste-based discrimination can be mutual in the sense discrimination can occur from either supply or demand side; a white employer can offer lower wage to black employee, but a black employee could demand higher wage from white employer. This mutuality disappears in statistical discrimination since this discrimination arises from asymmetry of information.

The main reason I find statistical discrimination so disturbing is that it seems potentially self-fulfilling in some cases. As a crude example, I think it is plausible to think as follows. Possibly originating from taste-based discrimination, minorities are less productive and thus the status of minority sends a signal to the employers. Statistically discriminating employers will offer lower wage to the minorities. Given lower income level, the minorities cannot invest as much on their children, and thus the second-generation minorities are less productive as well. The signal is thus confirmed and Bayesian-updating employers continue to discriminate.

Taste-based discrimination can disappear with the flow of time, but statistical discrimination will form a cycle if the discriminatory behavior has an averse effect on the relevant characteristics of the discriminated people. I find this kind of discrimination to be the worst.

On costly monitoring model

What I found to be the most interesting model we studied in macroecon was Williamson’s model of costly monitoring. In the model, some entrepreneurs with high auditing cost do not receive credit from the bank, resulting in a failure of Pareto optimality. Could the government resolve this information problem?

What the government can do that the bank assumedly cannot is that it can “punish” the entrepreneur for lying. The bank in any contract can at most take all the money that the entrepreneur has (and the entrepreneur begins with no capital), while the government can impose additional cost to the entrepreneurs through imprisonment, etc. This allows the government to use mixed strategy; if the additional cost is high enough, the government can select a few random entrepreneurs to audit and still make the expected cost high enough for entrepreneurs to always tell the truth. In this case, the bank can make contract with all entrepreneurs without loss.

Of course, if the government is credibly committed, then the cost of punishment is irrelevant, since all entrepreneurs will be telling the truth and thus the government would not need to actually punish anyone.

How should the government collect its tax to pay for the auditing? I guess the answer is not so obvious since now the bank may use a different contract. This will be for later.

The Classroom Game

For those who do not subscribe to Mankiw’s blog, here is a blog post by a Canadian economics professor.

The professor asks a math question in the class, and gives two possible answers. Students who believe the first answer is correct raise their hands. Then students who believe the second answer is correct raise theirs. To the professor’s disappointment, about 75% of the students choose the wrong answer, while only about 10% choose the right one.

In the way the response is measured, however, it may not be that 75% of students are wrong, 10% right, and 5% uncertain. A similar voting result could have been achieved when 40% are wrong, 30% are right, and the remaining 30% are uncertain.

For the simplicity of the argument, let’s suppose that all students choose to respond. A student has an incentive to choose the right answer since his answer signals his intelligence. His signal, however, depends also on how other students have answered. It doesn’t feel good to be wrong, but at least you aren’t so embarrassed if most students are wrong as well.

We can think of a game in which students first make decision based on what they believe is the right answer, and then change the decision after seeing the initial response (there might be a strategic reason why students tend to avoid the first row). A student believes that the chance that the first answer is correct is p and the chance that the second answer is correct is 1-p. His initial response will be to choose the first answer if p > 1-p and to choose the second answer if p < 1-p (if p =.5, then the student chooses either one).

Once every student made the initial response, each student will decide whether to change his response or not based on his payoff:

	The majority of other students
A student		Right Answer	Wrong answer
	Right answer	a	b
	Wrong answer	c	d

The best case is that the student chose the right answer while the majority of the other students chose the wrong answer. The second best is to choose the right answer while others did too. The worst case is to choose the wrong answer while others chose the right one. So for all students: b > a > d > c.

The key insight is that for most students, the loss of being in the wrong minority is greater than the gain of being in the right minority. Being in the minority attracts greater attention, and thus the signal effect is magnified. To be the wrong minority, therefore, gives a strong signal of lacking intelligence. On the other hand, being in the right minority can give a strong signal of intelligence, but this signal has a negative effect of getting enmity from other students, especially in a class where grade is curved.

Let’s have an example. Peter thinks that the second answer is right, but he isn’t completely sure. For Peter, p = 0.2 and 1-p = 0.8. His payoff is as follows:

	The majority of other students
Peter		Right Answer	Wrong answer
	Right answer	4	6
	Wrong answer	-11	0

Initially, he does not raise his hand for the first answer since 0.8 > 0.2. It happens, however, that most students have raised their hands. If he remains firm, then there is a 0.2 chance that the majority is right while he is wrong and 0.8 chance that the majority is wrong while he is right, so his expected payoff is (0.3)(-11) + (0.7)(6) = 0.9. If changes his response, then his expected payoff is (0.3)(4) + (0.7)(0) = 1.2, so he changes his mind and raises his hand for the first answer, although he doesn’t think it is correct.

The result of this is an exaggeration in the voting. A student may vote for the first answer, even if he thinks the second answer is more likely to be correct, when more than half of the class vote for the first. Conversely, a student who thinks that the first answer is correct may not vote for it if only a few other students have voted for it.

When 40% are wrong, 30% are right, and 30% are uncertain, we could expect around 55% of students to initially choose the wrong answer. This will attract more students to choose the wrong answer, especially the remaining 15% uncertain students. Depending on the level of certainty and individual payoffs, even those who are right may choose to vote for he wrong answer or hesitate to vote for the right answer. Thus, this situation can easily end up with 75% voting for the wrong answer and 10% for the right.

On Nudge

If I have a high expectation of a book due to hearing many praises of the book, would I end up liking the book more or less? The authors of Nudge may suggest that due to our tendency to conform to what other people do, I would value the book more highly for reasons involving the information conveyed by other people’s judgments and the peer pressure. Well, I don’t have peer pressure in the context I am in now, so that’s maybe why I was somewhat disappointed.

The book is easy to read and yet by no means shallow. I strongly agree with the authors on many points, especially on marriage and education. The book presents a strong justification of what the authors call liberal paternalism. Many applications of Nudge seem appealing.

Yet I had a difficult time finishing the book. Some examples and concepts, although very interesting and even inspiring, appeared to be too stretched to make connections with the book’s main points. I felt that the book was jumping here and there, sometimes digressing to wilderness and sometimes coming back to the same point over and over. The flow of the book was less than ideal.

I was also little concerned with the recurring dichotomy of Humans and Econs, the irrational and rational aspects of an individual. I don’t think even the classical economists necessarily assume that individuals always behave rationally, that they make complex mathematical calculations to behave optimally. Rather, they would claim that people’s economic (and other) behaviors can be explained through rational and mathematical models. I thought that many of the cases in which people fail to behave optimally were due to lack of information rather than due to irrational aspects of human nature.

With all that, I do think that the principles of Nudge presents a great possibility for improvements in all kinds of things as the authors claim. I think one of the bonus nudges, discouraging college students from using trays in cafeteria, can be easily employed in UChicago.

On Freakonomics

It is slightly embarrassing to confess that I have not read Freakonomics until recently, but on the other hand I am somewhat glad that I delayed reading until I had at least some exposure to economics. I believe having some knowledge in economics allowed me to appreciate the book more than I would have otherwise. Many thoughts came to my mind while reading the book, and I’ve been intending to scribble those thoughts down for quite a few days now (Why did I not do immediately after finishing the book, when my thoughts were more vivid? Ask a behavioral economist).

The Q&A section of the book suggests that the chapter on abortion and crime rate was the most controversial one, so I’ll start with that. The gist of the argument in that chapter is that legalizing abortion causes crime rate to go down. The argument does not imply that abortion should be legalized (abortion might be categorically impermissible and even if you believe in consequentialism, you could argue that human life is worth more than reduced crime rate), but one can see why this argument faces unfriendly reaction.

Nevertheless, I think there is more than just the sensitivity of the subject matter that makes the argument controversial. Even if you think abortion should be legalized and are comfortable with the idea of quantifying the value of human life (the authors provide 100 fetuses to 1 new born ratio as an example of relative value of human lives to measure the efficiency of trade-off between abortion and crime rate), the argument is disturbing. Consider the secondary causes of crime rate reduction that the authors suggest, namely the increased number of prisons and police (essentially greater incentive to not commit crime). As authors themselves write, these factors do not “address the root causes of crime.” It almost seems that the only way to get rid of crime is to get rid of criminals before they are literally born. Of course this is not necessarily true since there can be other plausible solutions, but the authors at least suggest that the end we achieved (reduced crime rate) is not the result of the means we wanted. I think this has a significant implication on politics and more specifically liberal ideology, but I will not venture to discuss those here. Economics alone is sufficiently dismal.

What I personally find little more troublesome is the chapter on parenting. The main argument of the chapter is that “it isn’t so much a matter of what you do as a parent; it’s who you are.” This claim, however, comes with a lot of ‘but’s. To start off, it does matter what you do if you are doing bad: “Clearly, bad parenting matters a great deal” (Otherwise it would be difficult to explain why legalizing abortion reduces crime rate). So if you are beating up your children, your children will be affected, but if you are intending to do good, then those actions have no influence.

But there is another catch. The ELCS data show that what you do as a parent doesn’t affect your child’s school performance, not necessarily your child’s whole life. Authors write: “since most parents would agree that education lies at the core of a child’s formation, it would make sense to begin by examining a telling set of school data.” Fair enough, but the story not only begins at the school performance, but it also ends there. So I am convinced that having lots of books in the house or having Mozart music playing all the time won’t improve the child’s school performance, but I am not fully convinced that they don’t matter. The smartness of a child, measured by IQ, probably is the main determining factor of a child’s school performance especially in the early years, and I am willing admit that better neighborhood or museum trips won’t improve the child’s IQ. But as the authors state, school performance is “a useful but fairly narrow measurement… poor testing in early childhood isn’t necessarily a great harbinger of future earnings, creativity, or happiness.” And then the chapter ends with a brief mention of Sacerdote’s research that shows “the influence of the adoptive parents … made the difference [on children’s higher education and career].”

As I believe I exaggerated a little here, the whole chapter on the parenting doesn’t seem to have a strong message. What you do as a parent doesn’t affect your children’s IQs, but it could affect their future careers. I can agree that reading to your children won’t affect their school performances, but I am not convinced it doesn’t matter.

This was all in all a fun and interesting book to read, and I am excited to read Superfreakonomics, but coming up next is Nudge.