Knowledge that Transforms

Abstract Bitcoin provides its users with transaction-processing services which are similar to those of traditional payment systems. This article models the novel economic structure implied by Bitcoin’s innovative decentralized design, which allows the payment system to be reliably operated by unrelated parties called miners. We find that this decentralized design protects users from monopoly pricing. Competition among service providers within the platform and free entry imply no entity can profitably affect the level of fees paid by users. Instead, a market for transaction-processing determines the fees users pay to gain priority and avoid transaction-processing delays. The article (i) derives closed-form formulas of the fees and waiting times and studies their properties, (ii) compares pricing under the Bitcoin Payment System to that under a traditional payment system operated by a profit-maximizing firm, and (iii) suggests protocol design modifications to enhance the platform’s efficiency. The Appendix describes and explains the main attributes of Bitcoin and the underlying blockchain technology.

Abstract We study the first-order asymptotic properties of a class of estimators of the structural parameters in dynamic discrete choice games. We consider K-stage policy iteration (PI) estimators, where K denotes the number of PIs employed in the estimation. This class nests several estimators proposed in the literature. By considering a “pseudo likelihood” criterion function, our estimator becomes the K-pseudo maximum likelihood (PML) estimator in Aguirregabiria and Mira (2002, 2007). By considering a “minimum distance” criterion function, it defines a new K-minimum distance (MD) estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) and Pakes et al. (2007). First, we establish that the K-PML estimator is consistent and asymptotically normal for any $K \in N$. This complements findings in Aguirregabiria and Mira (2007), who focus on K=1 and K large enough to induce convergence of the estimator. Furthermore, we show under certain conditions that the asymptotic variance of the K-PML estimator can exhibit arbitrary patterns as a function of K. Second, we establish that the K-MD estimator is consistent and asymptotically normal for any $K \in N$. For a specific weight matrix, the K-MD estimator has the same asymptotic distribution as the K-PML estimator. Our main result provides an optimal sequence of weight matrices for the K-MD estimator and shows that the optimally weighted K-MD estimator has an asymptotic distribution that is invariant to K. The invariance result is especially unexpected given the findings in Aguirregabiria and Mira (2007) for K-PML estimators. Our main result implies two new corollaries about the optimal 1-MD estimator (derived by Pesendorfer and Schmidt-Dengler (2008)). First, the optimal 1-MD estimator is efficient in the class of K-MD estimators for all $K \in N$. In other words, additional PIs do not provide first-order efficiency gains relative to the optimal 1-MD estimator. Second, the optimal 1-MD estimator is more or equally efficient than any K-PML estimator for all $K \in N$. Finally, the Appendix provides appropriate conditions under which the optimal 1-MD estimator is efficient among regular estimators.

Abstract We study default effects in the context of a residential electricity-pricing program. In the large-scale randomized controlled trial we analyse, one treatment group was given the option to opt-in to time-varying pricing while another was defaulted into the program but allowed to opt-out. We provide dramatic evidence of a default effect on program participation, consistent with previous research. A novel feature of our study is that we also observe how the default manipulation impacts customers’ subsequent electricity consumption. Passive consumers who did not opt-out but would not have opted in—comprising more than 70% of the sample—nonetheless reduce consumption in response to higher prices. Observing of this follow-on behaviour enables us to assess competing explanations for the default effect. We draw conclusions about the likely welfare effects of defaulting customers onto time-varying pricing.

Abstract The willingness to pay for insurance captures the value of insurance against only the risk that remains when choices are observed. This article develops tools to measure the ex ante expected utility impact of insurance subsidies and mandates when choices are observed after some insurable information is revealed. The approach retains the transparency of using reduced-form willingness to pay and cost curves, but it adds one additional sufficient statistic: the percentage difference in marginal utilities between insured and uninsured. I provide an approach to estimate this additional statistic that uses only the reduced-form willingness to pay curve, combined with a measure of risk aversion. I compare the approach to structural approaches that require fully specifying the choice environment and information sets of individuals. I apply the approach using existing willingness to pay and cost curve estimates from the low-income health insurance exchange in Massachusetts. Ex ante optimal insurance prices are roughly 30% lower than prices that maximize observed market surplus. While mandates reduce market surplus, the results suggest they would actually increase ex ante expected utility.

Abstract In this article, we quantify the effects of nurses on health care delivery and patient health in the context of an unintended and policy-induced nurse shortage. Our empirical strategy takes advantage of a parental-leave program in Denmark, which offered any parent the opportunity to take up to one year’s absence per child aged 0–8. Combining the policy variation with administrative employer–employee match data, we document substantial program take-up among nurses, who could not be replaced on net despite public education and immigration expansion efforts to mitigate the employment effects. We find that the parental leave program reduced hospital and nursing home nurse employment by 15% and 10%, respectively. Using detailed patient health records, we find detrimental effects on hospital-care delivery as indicated by a large increase in 30-day readmission rates among acute myocardial infarction patients. We find no evidence for an increase in hospital mortality. In nursing homes, we estimate a large increase in mortality.

Abstract Unlike in standard models, decision makers often narrowly bracket and make each decision in isolation. I develop a new approach, which I term narrow thinking, to systematically model narrow bracketing. The definition of narrow thinking is that different decisions are based on different, non-nested, information. As a result, the narrow thinker makes each decision with imperfect knowledge of other decisions and faces difficulties coordinating her multiple decisions. The narrow thinker effectively cares less about her other decisions when making each decision. The main application of narrow thinking is to provide a smooth model of mental accounting without requiring the decision maker to have explicit budgets. My approach generates unique predictions about how the degree of mental accounting depends on expenditure shares and cognitive limitations. It also illustrates how narrow bracketing and mental accounting can be explained by the same underlying friction.

Abstract Macroeconomists traditionally ignore temporary price markdowns (“sales”) under the assumption that they are unrelated to aggregate phenomena. We revisit this view. First, we provide robust evidence from the U.K. and U.S. CPI micro data that the frequency of sales is strongly countercyclical, as much as doubling during the Great Recession. Second, we build a general equilibrium model in which cyclical sales arise endogenously as retailers try to attract bargain hunters. The calibrated model fits well the business cycle co-movement of sales with consumption and hours worked, and the strong substitution between market work and shopping time documented in the time-use literature. The model predicts that after a monetary contraction, the heightened use of discounts by firms amplifies the fall in the aggregate price level, attenuating by a third the one-year response of real consumption.

Abstract In order to share risk, protection buyers trade derivatives with protection sellers. Protection sellers’ actions affect the riskiness of their assets, which can create counterparty risk. Because these actions are unobservable, moral hazard limits risk sharing. To mitigate this problem, privately optimal derivative contracts involve variation margins. When margins are called, protection sellers must liquidate some assets, depressing asset prices. This tightens the incentive constraints of other protection sellers and reduces their ability to provide insurance. Despite this fire-sale externality, equilibrium is information-constrained efficient. Investors, who benefit from buying assets at fire-sale prices, optimally supply insurance against the risk of fire sales.

Abstract We provide new time-varying estimates of the housing wealth effect back to the 1980s. We use three identification strategies: ordinary least squares with a rich set of controls, the Saiz housing supply elasticity instrument, and a new instrument that exploits systematic differences in city-level exposure to regional house price cycles. All three identification strategies indicate that housing wealth elasticities were if anything slightly smaller in the 2000s than in earlier time periods. This implies that the important role housing played in the boom and bust of the 2000s was due to larger price movements rather than an increase in the sensitivity of consumption to house prices. Full-sample estimates based on our new instrument are smaller than recent estimates, though they remain economically important. We find no significant evidence of a boom–bust asymmetry in the housing wealth elasticity. We show that these empirical results are consistent with the behaviour of the housing wealth elasticity in a standard life-cycle model with borrowing constraints, uninsurable income risk, illiquid housing, and long-term mortgages. In our model, the housing wealth elasticity is relatively insensitive to changes in the distribution of loan-to-value (LTV) for two reasons: first, low-leverage homeowners account for a substantial and stable part of the aggregate housing wealth elasticity; second, a rightward shift in the LTV distribution increases not only the number of highly sensitive constrained agents but also the number of underwater agents whose consumption is insensitive to house prices.

Abstract What is the role of monetary policy in a bubbly world? To address this question, we study an economy in which financial frictions limit the supply of assets. The ensuing scarcity generates a demand for “unbacked” assets, i.e., assets that are backed only by the expectation of their future value. We consider two types of unbacked assets: bubbles, which are created by the private sector, and money, which is created by the central bank. Bubbles and money share many features, but they also differ in two crucial respects. First, while the rents from the creation of bubbles accrue to entrepreneurs and foster investment, the rents from money creation accrue to the central bank. Second, while bubbles are driven by market psychology, and can rise and fall according to the whims of the market, money is under the control of the central bank. We characterize the optimal monetary policy and show that, through its ability to supply assets, monetary policy plays a key role in the bubbly world. The model sheds light on the recent expansion of central bank liabilities in response to the bursting of bubbles.