The dynamics of the leverage cycle

We present a simple agent-based model of a financial system composed of leveraged investors such as banks that invest in stocks and manage their risk using a Value-at-Risk constraint, based on historical observations of asset prices. The Value-at-Risk constraint implies that when perceived risk is low, leverage is high and vice versa, a phenomenon that has been dubbed pro-cyclical leverage. We show that this leads to endogenous irregular oscillations, in which gradual increases in stock prices and leverage are followed by drastic market collapses, i.e. a leverage cycle. This phenomenon is studied using simplified models that give a deeper understanding of the dynamics and the nature of the feedback loops and instabilities underlying the leverage cycle. We introduce a flexible leverage regulation policy in which it is possible to continuously tune from pro-cyclical to countercyclical leverage. When the policy is sufficiently countercyclical and bank risk is sufficiently low the endogenous oscillation disappears and prices go to a fixed point. While there is always a leverage ceiling above which the dynamics are unstable, countercyclical leverage can be used to raise the ceiling. We also study the impact on leverage cycles of direct, temporal control of the bank's riskiness via the bank's required Value-at-Risk quantile. Under such a rule the regulator relaxes the Value-at-Risk quantile following a negative stock price shock and tightens it following a positive shock. While such a policy rule can reduce the amplitude of leverage cycles, its effectiveness is highly dependent on the choice of parameters. Finally, we investigate fixed limits on leverage and show how they can control the leverage cycle.Comment: 35 pages, 9 figure

Comparative Economic Cycles

The income cycles that have been experienced by six OECD countries over the past 24 years are analysed. The amplitude of the cycles relative to the level of aggregate income varies amongst the countries, as does the degree of the damping that affects the cycles. The study aims to reveal both of these characteristics. It also seeks to determine whether there exists a clear relationship between the degree of damping and the length of the cycles. In order to estimate the parameters of the cycles, the data have been subjected to the processes of detrending, anti-alias filtering and subsampling.Business cycles, Autoregressive models

A comparison of bearing life in new and refurbished railway axle boxes

A simple linear dynamical model shows that at normal running speeds of freight wagons, forced oscillations due to periodic track compliance are transferred to the overlying unsprung mass and significantly amplified. Due to these oscillations, a small gap opens and closes between the collar of a journal bearing and the axle box many times every second. The forces between these components reach peaks of over 10 tonnes. This is an environment in which wear of the soft spherical graphite iron of the axle box will eventually take place. Due to repeated unloadings of the weight on the bearing during oscillations, the bearing collar may slowly slip against the axle box wall. Although our calculations show that abrasive wear due to this slippage is negligible, the calculation raises general principles that apply to other possible wear mechanisms. If lifetime is proportional to hardness, we can estimate relative lifetimes of refurbished and new boxes. Although the resleeve material is softer than the original, the cost to lifetime ratio would favour refurbishment under this assumption. Important unanswered questions are identified and a specific integrated program of field, laboratory, and theoretical study is suggested

The effects of interbank networks on efficiency and stability in a macroeconomic agent-based model

We develop a macroeconomic agent-based model that consists of firms, banks, unions and households who interact on labour, goods, credit and interbank markets. The model endogenises pricing decisions by firms, wage setting by unions and interest rate setting by banks on both firm and interbank lending. Banks also set leverage targets and precautionary liquidity buffers on the basis of internal risk models. Our model produces endogenous fluctuations driven by the pricing behaviour of firms and the wage setting behaviour of unions. Fluctuations lead to loan defaults which are exacerbated as lenders reduce lending and charge higher interest rates, inducing a credit crunch. We also study how making the inter-banking network more connected affects the key outcomes of the economy and find that while the flow of funds from surplus banks to firms can be increased, the latter effect is soon dominated by increasing instability in the real sector as firms default at higher rates. While the banking sector experiences fewer defaults as a whole, losses on the interbank market increase as a source of bank defaults

Investigating Economic Trends And Cycles

Methods are described for extracting the trend from an economic data sequence and for isolating the cycles that surround it. The latter often consist of a business cycle of variable duration and a perennial seasonal cycle. There is no evident point in the frequency spectrum where the trend ends and the business cycle begins. Therefore, unless it can be represented by a simple analytic function, such as an exponential growth path, there is bound to be a degree of arbitrariness in the definition of the trend. The business cycle, however defined, is liable to have an upper limit to its frequency range that falls short of the Nyquist frequency, which is the maximum observable frequency in sampled data. This must be taken into account in fitting an ARMA model to the detrended data.

Making Mountains of Debt Out of Molehills: The Pro-Cyclical Implications of Tax and Expenditure Limitations

This paper presents evidence that property tax limits have detrimental effects on state and local revenues during recessions. Property tax limits cause states to rely on income–elastic revenue sources, such as the income tax or charges and fees. Greater reliance on these revenue sources results in greater revenue declines during economic downturns. We present analysis of time–series, cross–sectional data for the U.S. states for each of these conclusions. Our results suggest that states would have fewer and more modest financial problems during economic downturns if they did not enact property tax limitations

Good speciation and endogenous business cycles in a constraint satisfaction macroeconomic model

We introduce a prototype agent-based model of the macroeconomy, with budgetary constraints at its core. The model is related to a class of constraint satisfaction problems (CSPs), which has been thoroughly investigated in computer science. The CSP paradigm allows us to propose an alternative price-setting mechanism: given agents' preferences and budgets, what set of prices satisfies the maximum number of agents? Such an approach permits the coupling of production and output within the economy to the allowed level of debt in a simplified framework. Within our model, we identify three different regimes upon varying the amount of debt that each agent can accumulate before defaulting. In presence of a very loose constraint on debt, endogenous crises leading to waves of synchronized bankruptcies are present. In the opposite regime of very tight debt constraining, the bankruptcy rate is extremely high and the economy remains structure-less. In an intermediate regime, the economy is stable with very low bankruptcy rate and no aggregate-level crises. This third regime displays a rich phenomenology:the system spontaneously and dynamically self-organizes in a set of cheap and expensive goods (i.e. some kind of "speciation"), with switches triggered by random fluctuations and feedback loops. Our analysis confirms the central role that debt levels play in the stability of the economy. More generally, our model shows that constraints at the individual scale can generate highly complex patterns at the aggregate level.Comment: 14 Pages, 11 Figures. Updated Journal Referenc