We coin the term *Protocols for Loanable Funds (PLFs)* to refer to protocols which establish distributed ledger-based markets for loanable funds. PLFs are emerging as one of the main applications within Decentralized Finance (DeFi), and use smart contract code to facilitate the intermediation of loanable funds. In doing so, these protocols allow agents to borrow and save programmatically. Within these protocols, interest rate mechanisms seek to equilibrate the supply and demand for funds. In this paper, we review the methodologies used to set interest rates on three prominent DeFi PLFs, namely Compound, Aave and dYdX. We provide an empirical examination of how these interest rate rules have behaved since their inception in response to differing degrees of liquidity. We then investigate the market efficiency and inter-connectedness between multiple protocols, examining first whether Uncovered Interest Parity holds within a particular protocol and second whether the interest rates for a particular token market show dependence across protocols, developing a Vector Error Correction Model for the dynamics.

We study a general family of economic geography models that features endogenous agglomeration. In many-region settings, the spatial scale---"global" or "local"---of the dispersion force(s) in a model plays a key role in determining the resulting endogenous spatial patterns and comparative statics. A global dispersion force accrues from competition between different locations and leads to the formation of multiple economic clusters (or cities). A local dispersion force is caused by crowding effects within each location and induces the flattening of each city. By distinguishing local and global dispersion forces, we can define three prototypical classes, namely, models that have only global, only local, and both local and global dispersion forces. The three model classes engender qualitatively different spatial patterns. Multiple cities are formed only when a global dispersion force is at work; otherwise, only a unimodal distribution can be formed. A city can have its spatial extent only when a local dispersion force is at work. A wide variety of extant models are reduced into the three prototypical classes. Our framework adds consistent interpretations to the empirical literature and also provides general \Red{insights into} treatment effects in structural economic geography models.

A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium} respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous-time Markov chain and the discount function is log sub-additive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence.

Since March 25, 2020, India had been under a nation-wide lockdown announced as a response to the spread of SARS-CoV-2 and COVID-19 and has resorted to a process of 'unlocking' the lockdown over the past couple of months. This work attempts to examine the effect of novel coronavirus 2019 (COVID-19) and its resulting disease, the COVID-19, on the foreign exchange rates and stock market performances of India using secondary data over a span of 112 days spanning between March 11 and June 30, 2020. The study explores whether the causal relationships and directions among the growth rate of confirmed cases (GROWTHC), exchange rate (GEX) and SENSEX value (GSENSEX) are remaining the same across different pre and post-lockdown phases, attempting to capture any potential changes over time via the vector autoregressive (VAR) models. A positive correlation is found between the growth rate of confirmed cases and the growth rate of exchange rate, and a negative correlation between the growth rate of confirmed cases and the growth rate of SENSEX value. However, on applying a vector autoregressive (VAR) model, it is observed that an increase in the confirmed COVID-19 cases causes no significant change in the values of the exchange rate and SENSEX index. The result varies if the analysis is split across different time periods - before lockdown, the four phases of lockdown, and the first phase of unlock. Nuanced and sensible interpretations of the numeric results indicate significant variability across time in terms of the relation between the variables of interest. The detailed knowledge about the varying patterns of dependence could potentially help the policy makers and investors of India in order to develop their strategies to cope up with the situation.

This paper is a study of the history of the transplant of mathematical tools using negative feedback for macroeconomic stabilization policy from 1948 to 1975 and the subsequent break of the use of control for stabilization policy which occurred from 1975 to 1993. New-classical macroeconomists selected a subset of the tools of control that favored their support of rules against discretionary stabilization policy. The Lucas critique and Kydland and Prescott's time-inconsistency were over-statements that led to the "dark ages" of the prevalence of the stabilization-policy-ineffectiveness idea. These over-statements were later revised following the success of the Taylor rule.

It is empirically established that order flow in the financial markets is positively auto-correlated and can serve as an example of a social system with long-range memory. Nevertheless, widely used long-range memory estimators give varying values of the Hurst exponent. We propose the burst and inter-burst duration statistical analysis as one more test of long-range memory and implement it with the limit order book data comparing it with other widely used estimators. This method gives a more reliable evaluation of the Hurst exponent independent of the stock in consideration or time definition used. Results strengthen the expectation that burst and inter-burst duration analysis can serve as a better method to investigate the property of long-range memory.

In the face of a pandemic, urban protests, and an affordability crisis, is the desirability of dense urban settings at a turning point? Assessing cities' long term trends remains challenging. The first part of this chapter describes the short-run dynamics of the housing market in 2020. Evidence from prices and price-to-rent ratios suggests expectations of resilience. Zip-level evidence suggests a short-run trend towards suburbanization, and some impacts of urban protests on house prices. The second part of the chapter analyzes the long-run dynamics of urban growth between 1970 and 2010. It analyzes what, in such urban growth, is explained by short-run shocks as opposed to fundamentals such as education, industrial specialization, industrial diversification, urban segregation, and housing supply elasticity. This chapter's original results as well as a large established body of literature suggest that fundamentals are the key drivers of growth, and that the shocks considered in this paper have not had historically a measurable long-term impact on metropolitan population growth. The chapter illustrates this finding with two case studies: the New York City housing market after September 11, 2001; and the San Francisco Bay Area in the aftermath of the 1989 Loma Prieta earthquake. Both areas rebounded strongly after these shocks, suggesting the resilience of the urban metropolis.

Research on infodemics, i.e., the rapid spread of (mis)information related to a hazardous event, such as the COVID-19 pandemic, requires the integration of a multiplicity of scientific disciplines. The dynamics emerging from infodemics have the potential to generate complex behavioral patterns. In order to react appropriately, it is of ultimate importance for the fields of Business and Economics to understand the dynamics emerging from it. In the short run, dynamics might lead to an adaptation in household spending or to a shift in buying behavior towards online providers. In the long run, changes in investments, consumer behavior, and markets are to be expected. We argue that the dynamics emerge from complex interactions among multiple factors, such as information and misinformation accessible for individuals and the formation and revision of beliefs. (Mis)information accessible to individuals is, amongst others, affected by algorithms specifically designed to provide personalized information, while automated fact-checking algorithms can help reduce the amount of circulating misinformation. The formation and revision of individual (and probably false) beliefs and individual fact-checking and interpretation of information are heavily affected by linguistic patterns inherent to information during pandemics and infodemics and further factors, such as affect, intuition and motives. We argue that, in order to get a deep(er) understanding of the dynamics emerging from infodemics, the fields of Business and Economics should integrate the perspectives of Computer Science and Information Systems, (Computational) Linguistics, and Cognitive Science into the wider context of economic systems (e.g., organizations, markets or industries) and propose a way to do so.

We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, e.g., in non-linear option pricing problems or in probabilistic discretization schemes for fully non-linear parabolic partial differential equations. Our algorithm can be generically applied when the underlying dynamics stem from an Euler approximation to a stochastic differential equation. A built-in variance reduction ensures that the convergence in the number of samples to the true regression function takes place at an arbitrarily fast polynomial rate, if the problem under consideration is smooth enough.