







We study the distributions of money in a simple closed economic system for different types of monetary transactions. We know that for arbitrary and random sharing with locally conserving money transactions, the money distribution goes to the Gibb's distribution of statistical mechanics. We then consider the effects of savings, etc. and see how the distribution changes. We also propose a new model where the agents invest equal amounts of money in each transaction. We find that for short time-period, the money distribution obeys a power-law with an exponent very close to unity, and has an exponential tail; after a very long time, this distribution collapses and the entire amount of money goes to a tiny fraction of the population.
Credit Crises, Precautionary Savings, and the Liquidity Trap*
Abstract We study the effects of a credit crunch on consumer spending in a heterogeneous-agent incomplete-market model. After an unexpected permanent tightening in consumers’ borrowing capacity, constrained consumers are forced to repay their debt, and unconstrained consumers increase their precautionary savings. This depresses interest rates, especially in the short run, and generates an output drop, even with flexible prices. The output drop is larger with sticky prices, if the zero lower bound prevents the interest rate from adjusting downward. Adding durable goods to the model, households take larger debt positions and the output response can be larger.

A Debt Puzzle
Over 60% of US households with credit cards are currently borrowing – i.e., paying interest – on those cards. We attempt to reconcile the high rate of credit card borrowing with observed levels of life cycle wealth accumulation. We simulate a lifecycle model with five properties that create demand for credit card borrowing. First, the calibrated labor income path slopes upward early in life. Second, income has transitory shocks. Third, consumers invest actively in an illiquid asset, which is sufficiently illiquid that it can not be used to smooth transitory income shocks. Fourth, consumers may declare bankruptcy, reducing the effective cost of credit card borrowing. Fifth, households have relatively more dependents early in the life-cycle. Our calibrated model predicts that 20% of the population will borrow on their credit card at any point in time, far less than the observed rate of over 60%. We identify a resolution to this puzzle: hyperbolic time preferences. Simulated hyperbolic consumers borrow actively in the revolving credit card market and accumulate relatively large stocks of illiquid wealth, matching observed data.

Ergodicity Economics – Formal economics without parallel universes
Does the way we look at a problem – over time or across an ensemble – change what we see? The main insight from Ergodicity Economics is that when ergodicity […]
A Theory of the Consumption Function, with and without Liquidity Constraints
This paper argues that the modern stochastic consumption model, in which impatient consumers face uninsurable labor income risk, matches Milton Friedman's (1957) original description of the Permanent Income Hypothesis much better than the perfect foresight or certainty equivalent models did. The model can explain the high marginal propensity to consume, the high discount rate on future income, and the important role for precautionary behavior that were all part of Friedman's original framework. The paper also explains the relationship of these questions to the Euler equation literature, and argues that the effects of precautionary saving and liquidity constraints are often virtually indistinguishable.
Demand for emergency savings is higher for low-income households, but so is the cost of shocks
This paper examines how the precautionary motive varies with income. I first develop a theoretical benchmark of how we would expect precaution to vary with income starting from a basic version of the buffer-stock model. Emergency savings provide a way for households to smooth over shocks and so give insight into the precautionary motive. Using data from the Survey of Consumer Finances in the USA, I show that as income declines, the desired emergency savings relative to income increase, suggesting that low-income households are more precautionary. Observable differences, such as income uncertainty, do not explain the rise. Instead, I propose and estimate a model with a minimum subsistence level and unexpected expenses. The model implies that low-income households are increasingly exposed to shocks, explaining the increase in precaution. Supporting the approach, I show that expenses on repairs are a larger fraction of the spending of low-income households.
Why the super rich are inevitable
Why some mathematicians argue the economy is designed to create a few super rich people – unless we stop it.

BETTER THAN FREE | Edge.org
This super-distribution system has become the foundation of our economy and wealth. The instant reduplication of data, ideas, and media underpins all the major economic sectors in our economy, particularly those involved with exports — that is, those industries where the US has a competitive advantage. Our wealth sits upon a very large device that copies promiscuously and constantly.
Exponential Economist Meets Finite Physicist | Do the Math
[An updated treatment of some of this material appears in Chapter 2 of the Energy and Human Ambitions on a Finite Planet (free) textbook, also mirrors a 2022 article in Nature Physics..]
Exponential Growth Bias and Household Finance
ABSTRACT Exponential growth bias is the pervasive tendency to linearize exponential functions when assessing them intuitively. We show that exponential growth bias can explain two stylized facts in household finance: the tendency to underestimate an interest rate given other loan terms, and the tendency to underestimate a future value given other investment terms. Bias matters empirically: More‐biased households borrow more, save less, favor shorter maturities, and use and benefit more from financial advice, conditional on a rich set of household characteristics. There is little evidence that our measure of exponential growth bias merely proxies for broader financial sophistication.

The Future of Money: How the Digital Revolution Is Tran…
A cutting-edge look at how accelerating financial chang…

Anomalies: Saving, Fungibility, and Mental Accounts
Last New Year's day, after a long evening of rooting the right team to victory in the Orange Bowl, I was lucky enough to win $300 in a college football betting pool. I then turned to the important matter of splurging the proceeds wisely. Would a case of champagne be better than dinner and a play in New York? At this point my son Greg came in and congratulated me. He said, "Gee Dad, you should be pretty happy. With that win you can increase your lifetime consumption by $20 a year!" Greg, it seems, had studied the life-cycle theory of savings. The theory is simple, elegant, and rational—qualities valued by economists. Unfortunately, as Courant, Gramlich, and Laitner observe "for all its elegance and rationality, the life-cycle model has not tested out very well." In this column, however, I focus on an assumption of the life-cycle model that has not received very much attention, but which, if modified, can allow the theory to explain many of the savings anomalies that have been observed. The key assumption is fungibility. This column will review a small portion of the empirical savings literature, with the objective of showing how violations of fungibility, and more generally the role of self-control, strongly influences saving behavior.
The Self-Constrained Hand-to-Mouth
Abstract Many studies have shown that consumption responds to the arrival of predictable income (excess sensitivity). This paper uses a buffer stock model of consumption to understand what causes excess sensitivity and to test which parameterization is consistent with empirical excess sensitivity estimates. Using high-frequency granular data from a personal finance app, I find that while liquidity constraints are a proximate cause, preferences are the ultimate cause of excess sensitivity. Furthermore, it finds that for feasible parameters, a quasi-hyperbolic version of the model is more consistent with the level of excess sensitivity relative to a standard exponential model.

Asymmetric Consumption Smoothing
Analyzing account-level data from an account aggregator, we find that households increase consumption when they receive expected tax refunds, as if they face liquidity constraints. However, these same households smooth consumption when making payments in other years, primarily by transferring funds among liquid accounts. Even households carrying credit card debt smooth consumption when making payments, and even highly liquid households spend out of refunds. This behavior is inconsistent with pure liquidity constraints or hand-to-mouth behavior and is most consistent with a mental accounting life-cycle model.
Fungibility and Consumer Choice: Evidence from Commodity Price Shocks*
Abstract We formulate a test of the fungibility of money based on parallel shifts in the prices of different quality grades of a commodity. We embed the test in a discrete-choice model of product quality choice and estimate the model using panel microdata on gasoline purchases. We find that when gasoline prices rise, consumers substitute to lower octane gasoline, to an extent that cannot be explained by income effects. Across a wide range of specifications, we consistently reject the null hypothesis that households treat “gas money” as fungible with other income. We compare the empirical fit of three psychological models of decision making. A simple model of category budgeting fits the data well, with models of loss aversion and salience both capturing important features of the time series.

Monetary incentives, what are they good for?
This paper is a critical reflection on the use of monetary incentives in economic experiments. The argument is that incentives have their effect through their influence on one or more of three fact...

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