Working papers results

2022 - n° 682 06/06/2022
We revisit the role of temporary layoffs in the business cycle, motivated by their unprecedented surge during the pandemic recession.We first measure the contribution of temporary layoffs to unemployment dynamics over the period 1979 to the present. While many have emphasized a stabilizing effect due to recall hiring, we quantify an important destabilizing effect due to "loss-of-recall", whereby workers in temporary-layoff unemployment lose their job permanently and do so at higher rates in recessions. We then develop a quantitative model that allows for endogenous flows of workers across employment and both temporary-layoff and jobless unemployment. The model captures well pre-pandemic unemployment dynamics and shows how loss-of-recall enhances the recessionary contribution of temporary layoffs. We also show that with some modification the model can capture the pandemic recession. We then use our structural model to show that the Paycheck Protection program generated significant employment gains. It did so in part by significantly reducing loss-of-recall.

Mark Gertler, Christopher Huckfeldt, Antonella Trigari
2022 - n° 681 03/03/2022
We study strategic reasoning in a signaling game where players have common belief in an outcome distribution and in the event that the receiver believes that the sender's first-order beliefs are independent of her payoff-type. We characterize the behavioral implications of these epistemic hypotheses through a rationalizability procedure with second-order belief restrictions. Our solution concept is related to, but weaker than Divine Equilibrium (Banks and Sobel, 1987). First, we do not obtain sequential equilibrium, but just Perfect Bayesian Equilibrium with heterogeneous off-path beliefs (Fudenberg and He, 2018). Second, when we model how the receiver may rationalize a particular deviation, we take into account that some types could have preferred a different deviation, and we show this is natural and relevant via an economic example.

Pierpaolo Battigalli, Emiliano Catonini
2022 - n° 680 14/02/2022
A start-up and an incumbent negotiate over an acquisition price under asymmetric information about the start-up's ability to succeed in the market. The acquisition may result in the shelving of the start-up's project or the development of a project that would otherwise never reach the market because of financial constraints. Despite this possible pro-competitive effect, the optimal merger policy commits to standards of review that prohibit high-price takeovers, even if they may be welfare-beneficial ex post. Ex ante this pushes the incumbent to acquire startups lacking the financial resources to develop independently, and increases expected welfare.

Chiara Fumagalli, Massimo Motta, Emanuele Tarantino
Keywords: Optimal merger policy, selection effect, nascent competitors
2021 - n° 679 22/12/2021
A central aspect of strategic reasoning in sequential games consists in anticipating how co-players would react to information about past play, which in turn depends on how co-players update and revise their beliefs. Several notions of belief system have been used to model how players' beliefs change as they obtain new information, some imposing considerably more discipline than others on how beliefs at different information sets are related. We highlight the differences between these notions of belief system in terms of introspection about one's own conditional beliefs, but we also show that such differences do not affect the essential aspects of rational planning and the behavioral implications of strategic reasoning, as captured by rationalizability.

Pierpaolo BATTIGALLI, Emiliano CATONINI, Julien MANILI
Keywords: Sequential games, chain rule, partial introspection, rational planning, rationalizability
2021 - n° 678 22/12/2021

We propose that the mathematical representation of situations of strategic interactions, i.e., of games, should separate the description of the rules of the game from the description of players’ personal traits. Yet, we note that the standard extensive-form partitional representation of information in sequential games does not comply with this separation principle. We offer an alternative representation that extends to all (finite) sequential games the approach adopted in the theory of repeated games with imperfect monitoring, that is, we describe the flow of information accruing to players rather than the stock of information retained by players, as encoded in information partitions. Mnemonic abilities can be represented independently of games. Assuming that players have perfect memory, our flow representation gives rise to information partitions satisfying perfect recall. Different combinations of rules about information flows and of players mnemonic abilities may give rise to the same information partition . All extensive-form representations with information partitions, including those featuring absentmindedness, can be generated by some such combinations. 

Pierpaolo Battigalli, Nicolò Generoso
2021 - n° 677 12/07/2021

Macroeconomic  outcomes depend on the distribution of markups across firms and over time, making firm-level markup estimates key for macroeconomic analysis. Methods to obtain these estimates require data on the prices that firms charge. Firm-level data with wide coverage, however,  primarily comes from financial statements, which lack information on  prices. We use an analytical framework to show that trends in markups or the dispersion of markups across firms can still be well-measured with such data. Finding the average level of the markup does require pricing data, and we propose a consistent estimator for such settings. We validate the analytical results with simulations of a quantitative macroeconomic model and firm-level administrative production and pricing data. Our analysis supports the use of financial data to measure trends in aggregate markups.

Maarten De Ridder, Basile Grassi, Giovanni Morzenti
Keywords: Macroeconomics, Production Functions, Markups, Competition
2021 - n° 676 22/02/2021
We investigate the effects of the Federal Reserve's quantitative easing and maturity extension programs on the yields of US dollar-denominated corporate bonds using a multiple-regime heteroskedasticity-based VAR identification approach. Impulse response functions suggest that a traditional, rate-based expansionary policy may lead to an increase in yields while quantitative easing is linked to a general and persistent decrease in yields, particularly for long-term bonds. The responses generated by the maturity extension program are significant and of larger magnitude. A decomposition shows that the unconventional programs reduce the cost of private debt primarily through a reduction in risk premia that cannot be entirely accounted for by a reduction in corporate default risk.

Massimo Guidolin, Valentina Massagli, Manuela Pedio
Keywords: unconventional monetary policy; transmission channels; heteroskedasticity; vector autoregressions; identification; corporate bond yields
2021 - n° 675 15/02/2021
We determine optimal market access pricing for an exchange or Social Planner. Exchanges optimally use rebate-based pricing (vs. strictly positive fees) when ex ante gains-from-trade and trading activity are low (high). Exchange rebate-based pricing increases (decreases) welfare when investor valuation dispersion and trading activity are low (high). A Social Planner increases welfare using rebate-based pricing. High-frequency traders strengthen exchange incentives for rebate-based pricing; a new explanation for widespread Maker-Taker and Taker-Maker pricing. With HFTs, rebate-based pricing improves total welfare, but Pareto transfers are needed to improve investor welfare. Sequential bargaining games between competing exchanges setting fees have pure-strategy equilibria.

Roberto Riccó, Barbara Rindi, Duane J. Seppi
Keywords: Market access fees, make-take, limit order markets, liquidity, market microstructure
2021 - n° 674 09/02/2021
We show that rational but inattentive agents can become polarized, even in expectation. This is driven by agents' choice of not only how much information to acquire, but also what type of information. We present how optimal information acquisition, and subsequent belief formation, depends crucially on the agent-specific status quo valuation. Beliefs can systematically update away from the realized truth and even agents with the same initial beliefs might become polarized. We design a laboratory experiment to test the model's predictions; the results confirm our predictions about the mechanism (rational information acquisition) and its effect on beliefs (systematic polarization).

Vladimir Novak, Andrei Matveenko, Silvio Ravaioli
Keywords: polarization, beliefs updating, rational inattention, status quo, experiment
2020 - n° 673 22/10/2020
During the 2020 Corona virus crisis in Lombardy -a stranger time- the Game Design Workshop at Bocconi University studied the implementation of the algorithms proposed by Maccheroni (2020, SSRN paper 3622663) for digital play using only six-sided dice. Swords & Wizardry by Finch (2011, Frog God Games) is a popular restatement of the Original Dungeons & Dragons Game by Gygax and Arneson (1974, Tactical Studies Rules). A case study, the present paper presents an implementation of the aforementioned algorithms for this game.
Alberto Maccheroni and Fabio Maccheroni