Overconfidence is among the most well studied behavioral biases. When graphing confidence, many have found it to be too flat, downward sloping, or even hump-shaped. In surveys, as many as 90 percent of respondents may report that they believe they are ``above average" at a given skill/topic and even above the median. This paper characterizes all confidence-knowledge graphs and what fraction of the population can believe they are above the average in the presence of unknown unknowns. When learning any topic, one does not initially know how information there is on the topic to potentially learn. The unknown unknowns are the things you do not know that you do not know. I find, that in a world with unknown unknowns, there is no restriction on what confidence-knowledge graphs can be generated by fully rational Bayesian agents or what fraction of these agents can think they are above average, even when they are not. This result forces us to question if any studies documenting overconfidence are actually evidence of a behavioral bias.
An agent is engaged in a sequential search problem. Rather than the options arriving randomly the order is chosen by another player. The agent must use the information that the order in which options are presented is being chosen strategically by someone with potentially conflicting preferences. The model is built off the framework of the classic secretary problem for tractability. In equilibrium, either a low-ball option is presented first followed by increasingly attractive options for an unknown amount of time, the best option is presented first followed by each option getting successively worse, or the ordering is a mix of the two. It is also shown that the agent is sometimes made better off by giving up their decision power and letting the other player chose for them. Applications include recommender systems, bargaining, and countless other economic situations where an agent must choose an ordering of objects.
Changes in the price of a financial asset represent learning as the market updates its expectation about fundamentals. In this paper I characterize what price dynamics are possible when the information is being released strategically by a profit maximizing trader. I study how information is incorporated into prices over time in model with general trading strategies that allow for the spread of false information and price manipulation. Every period an informed trader reveals their information by buying or selling an asset. After observing the trade, beliefs and prices are updated. The informed trader’s preferred equilibrium is characterized with and without commitment leading to starkly different results. Regardless of how beliefs impact prices, the optimal strategy for the informed trader is to release their information gradually mixed with a nearly equal amount of misinformation. This strategy leads to volatile price paths that bounce back and forth each period. In the continuous time limit, the price process converges to a Brownian motion. Moving prices back and forth in this way hinges critically on the informed traders ability to commit ex ante to their strategy. Without such commitment power, the optimal strategy is to release nearly all information suddenly at randomized times. The optimum resembles a pump-and-dump price manipulation scheme and can lead to sudden crashes or spikes in the price of the asset. In the limit, the price converges to a Poisson process. This paper gives a micro-foundation to price processes commonly assumed in the literature.
Holding fixed the total amount of information, which is preferred, a market where one trader has more private information, or a market where two traders each have less private information? Using a Kyle model, I show an equivalence between two informed traders with independent pieces of information and a single informed trader with both pieces of information. However, the equivalence fails when comparing two traders with the opportunity to acquire costly pieces of independent information and a single trader with the opportunity to acquire both pieces of information. Liquidity is a public good that is reduced by the presence of private information. Multiple traders will over acquire information ignoring the negative externalities on other traders through liquidity effects. Hence, a more dispersed distribution of information acquisition opportunities leads to lower liquidity, harming traders, but greater informativeness of prices. These results are exactly opposite to most intuition on insider trading and its regulation.
Through gerrymandering, a state drawing congressional districts can have a large effect on who gets elected. This in turn affects the policy chosen by elected representatives. This paper studies the optimal gerrymandering in an equilibrium of the fifty states electing members of the United States House of Representatives. First I find the optimal districting strategy when a party seeks to maximize the expected number of seats they win. This strategy always employs “cracking” (splitting up the opponent’s base to spread them out in many districts) and it sometimes employs “packing” (cramming one district full of exclusively the opponent’s base.) The optimal strategy can be found using techniques from information design. When the district drawer seeks to maximize the welfare of the state’s citizens the care not just about the average seats won by each party, but the entire seat-vote curve. A seat-vote curve is a graph of the fraction of seats in congress that go to a political party against the fraction of votes obtained by that party. The national social optimal is for each state to have a seat-vote curve that is less responsive (flatter) than proportional (45 degree line). However, each state has an incentive individually to choose a highly responsive seat-vote curve to disproportionately swing policy in their favor. In equilibrium each state chooses an extreme seat-vote curve close to a winner-take-all election. This is a prisoner’s dilemma situation where every state is worse off in equilibrium, but it is the dominant strategy of each state to choose a highly responsive seat-vote curve. I then empirically estimate the seat-vote curve for each state and observe a few motivating facts. First, seat-vote curves are highly responsive. Every state’s seat-vote curve has a slope much steeper than one (the ”proportional” seat-vote curve). Second, the size of the state is predictive of the responsiveness. Smaller states have steeper curves.
I present a model of universities to explain patterns of grade inflation that have been observed. I model the university as an information designer hired to evaluate students for employment purposes. I find both pooling and separating equilibria. I show how the university’s desire to build or maintain their own reputation interacts with their desire for the success of their students in forming the optimal grading scheme. In every equilibrium grade inflation is concentrated at the high quality universities as observed in the data. I also show how the observed patterns of grade inflation are not likely to be driven by heterogeneous students selecting into quality universities.
This paper uses a large scale overlapping generations model with heterogeneity across the life cycle and over lifetime income groups to evaluate the distributional effects of tax policy. The model is calibrated to the U.S. economy and includes realistic demographics, mortality risk, and progressive income taxes. The model generates distributions of hours worked, earnings, and wealth that are consistent with those observed in the U.S. We consider the effects of two policies that have the same steady-state revenue effect: (i) a progressive wealth tax and (ii) a progressive increase in income tax rates. We find that the wealth tax is extremely effective at reducing inequality relative to an increase in the progressivity of the income tax with the same steady-state tax revenue. The costs of reducing inequality using the wealth tax are primarily borne by the top 10 percent of wage earners and by individuals over the age of 60. The reductions in wealth and consumption from the income tax are concentrated among the top 20 percent of wage earners and among middle-aged individuals between the ages of 40 and 70.