This paper implements a model with a population of heterogeneous macro forecasters. Their objectives are to forecast output and inflation, both inputs in standard New Keynesian macro models. The model is implemented by first calibrating the agents to professional forecasters at the micro level. Model runs then try to replicate both the dynamics, bias and cross sectional heterogeneity of forecasts and the economy. These are done both in a model with static forecasters, and one where the forecasters are learning from each other in a social fashion. We find that expectations about the inflation process which conjecture near random walk behavior can be self-fulfilling, yielding inflation volatility and persistence on the order of magnitude of U.S. macro data. However, our forecasting populations often fall short of the heterogeneity of predictions from survey data. In some cases, monetary policy can be used to shift the model from its volatile/persistent equilibrium over to a more stable, strongly mean reverting inflation rate.

There has been a revival of interest among theorists in nonlinear models of growth and fluctuations . In contrast with the earlier work by Goodwin (1951), Hicks (1950), and others, the new models explicitly incorporate maximizing agents, competitive behavior, and rational expectations. An example of the latest type of model is implicit in Boldrin and Montrucchio (1986). There they show that, for any twice continuously differentiable function /( ) that maps a compact set into itself, there exists a neoclassical growth model that possesses for its solution a capital stock sequence k1 that solves an equation kt+ ,; f(k1) . Because such a neoclassical growth model gives exactly the same solution as a dynamic competitive-equilibrium model with perfect foresight, the Boldrin-Montrucchio theorem can be used to establish the theoretical possibility that even a rather simple deterministic setup can give rise to a time path that is as if generated by an arbitrary deterministic dynamics. These and other examples (e.g., Grandmont, 1985) seem to put the nonlinear deterministic models of fluctuations on a theoretical footing that equals that of the stable systems buffe1ed by exogenous shocks that constitute the underpinning of linearreally log·linear macroeconometric models. From an empirical point of view, matters are quite different . It seems unlikely that a low--order deterministic system accounts for ob· served economic data even if one allows fo r measurement error. On the other hand, both types of models are particular cases of one, such as

This paper presents new empirical methods for both estimating and validating agent-based financial models. The key issue is the estimation of learning gradients, or the objective surface on which adaptive agents move as they adapt their behavior. These surfaces are estimated using a new data set that allows for the construction of very long volatility time series which are used to assess optimal trading strategies. It is shown that strategies relying on relatively short half-lives thrive, and dominate longer, slower to adjust, strategies. These features are then used to estimate the intensity of choice parameter in an agent-based financial market setting. This novel estimation strategy uses the gradient surface to generate a hypothetical agent population which can then be used to test a simulated model, or update the intensity of choice in an iterative fashion. The paper shows both that this is a useful technical tool for assessing agent-based models, and also emphasizes the importance of short memory behavior in explaining the key dynamic properties of financial markets.

Models with small numbers of agents have recently been simplified for direct empirical estimation. Parameters are estimated at the macro level to get a best fit to the data. However, little analysis is done at the micro level to examine the choices made by agents for forecasting rules. This paper explores one of these recent models from the standpoint of micro agent behavior. It is shown that at the fitted forecasting rules, agents would prefer deviating to other nearby rules. The simple two type model is then compared with several multi-type models allowing for agents to use a broader set of rules. This can impact the dynamics of the generated time series, but it also may not if one takes the parameter estimates of the original model as an exogenous restriction on a reasonable support for the forecasting rules. This result emphasizes that these models may be imposing some hidden micro assumptions about agent behavior.

This paper explores a common machine learning tool, the kernel ridge regression, as applied to financial volatility forecasting. It is shown that kernel ridge provides reliable forecast improvements to both a linear specification, and a fitted nonlinear specification which represents well known empirical features from volatility modeling. Therefore, the kernel ridge specification is still finding some nonlinear improvements that are not part of the usual volatility modeling toolkit. Various diagnostics show it to be a reliable and useful tool. Finally, the results are applied in a dynamic volatility control trading strategy. The kernel ridge results again show improvements over linear modeling tools when applied to building a dynamic strategy.

Several unique data sets are brought together to build approximate daily realized volatility estimates back to the early 1930's. Estimators are tested extensively on modern data to see how well they line up with common estimators using high frequency pricing information. Estimators are also shown to pass several diagnostic tests from the early samples as well. Finally, well known qualitative features are tested for their stability across subsamples. This includes empirical volatility term structures which give reasonable estimates for perceived persistence to volatility shocks. Recommendations are made as to best practice for estimating long horizon realized volatility.

Agent-based financial markets have been extremely successful at matching features of financial markets at relatively short horizons, but they are often silent about long range features that cross into the area of macro/financial models. This is an area where they are often criticized by many in mainstream macroeconomics. This paper takes a relatively simple market which is capable of matching all the usual short horizon facts, and examines comovements in consumption and asset returns at longer horizons. This is done through the perspective of traditional intertemporal preferences. The key test is to see how close the simple ad hoc (but myopically optimizing) rules come to more traditional models for macroeconomic consumers. It is calibrated to exogenous inputs of both dividend and labor income. When generating high frequency data the model is relatively consistent with intertemporal optimization. However, at longer horizons it fails to hit the theoretical optimization values, but it fails in ways that are very close to the failures of representative agent consumption based models.

This short note draws some connections between Mandelbrot‗s empirical legacy, and the interdisciplinary work that followed in finance. Much of this work is now labeled econophysics, but some has always been more in the realm of economics than physics. In a few areas the overlap is even becoming quite complete as in market microstructure. I will also give some ideas about the various successes and failures in this area, and some directions for the future of agent- based modeling in particular.

This paper presents empirical evidence on the feasibility and value of various simple volatility forecasts in the construction of dynamic portfolio rules. Rules using limited past data are compared with rules using longer series in risk estimation. It is shown that in terms of performance, a utility based objective across these rules favors short memory/high gain forecasting rules. This empirical result is connected to recent work in agent-based finance which suggests that short memory volatility sensitive traders may be very important to the dynamics of long swings in asset prices around fundamentals.

This paper estimates the probability of a “lost decade,” where equity investments lose value over a 10-year period. The findings are a reminder that equity investments are risky even over longer time periods, and investors should take this into consideration when making portfolio choices. It also introduces a simple method to allow the reader to combine beliefs about long-run stock returns along with computer simulated return distributions. Finally, the results for the U.S. are augmented with international data which strengthen the case for large long horizon risk.

Heterogeneous agent models for financial markets have provided explanations for many empirical regularities of relatively high frequency (hourly/daily) financial time series. They have been much quieter when it comes to longer range features. This paper examines a simplified computational heterogeneous agent model in the context of various longer range time series properties for equity returns. The model is compared to a specially created long range data set, and is found to perform well in terms of replicating features, and even revealing some aspects of the data that have not been well quantified to date. By matching empirical properties at both short and long horizons this sets a higher standard in terms of validation which this model is able to match.

This paper explores the importance of heterogeneous gain levels in generating realistic time series mimicking well known time series features. The methodology takes a very strong stand on learning and evolution. Most forecasting rules involve dynamically adaptive parameters adjusted using a standard recursive least squares framework. Also, agents forecast both expected returns and risk as inputs to their portfolio choices. A population of agents using multiple gain levels in their learning are converged to a single “representative gain” for a small set of heterogeneous forecast strategies. Simulation results show that this dramatically alters the time series outcomes away from the realistic features generated in the heterogeneous gain model. It is therefore an early suggestion that in this class of models heterogeneity in gain levels is necessary for realistic time series replication.

In this paper we look at the relationship between daily realized volatility estimates using intraday data and range based estimates using daily high/low price range information. Several classical range based volatility estimators are compared with nonlinear functional forms in mapping range based information onto realized volatility measures. We find that the older range based estimators can be improved by using more generalized nonlinear functions of the high/low range information. We show that these nonlinearities form an important piece of information for understanding the dynamics of prices at high frequencies. We also show that these improved volatility estimates can be used in forecasting future variances and risk measures, and improve on the typical range estimators.

Many authors have contributed to the idea that financial markets are dynamically unstable. Much of this line of thinking suggests that bubbles and crashes will be a generic feature of most any speculative market, and that removing them would be difficult, if not impossible. Hyman Minsky is probably the one of the earlier contributors to this area, and recently his work has been looked at with new respect. This paper shows that some of his basic thinking about risk and extreme portfolio positions hold in agent-based financial markets in a way that appears close to his thinking. The advantage of this is that it presents a fully operational computer generated model with testable Minsky like effects which can be used to connect our understanding of Minsky to more modern, and rigorous approaches to macroeconomics.

This paper estimates the probability of a 'lost decade'' where equity investments lose value over a ten year period. The findings are a reminder that equity investments are risky even over longer time periods, and investors should take this into consideration when making portfolio choices. It also introduces a simple method to allow the reader to combine beliefs about long run stock returns along with computer simulated return distributions. Finally, the results for the U.S. are augmented with international data which strengthen the case for large long horizon risk.

The rosenberg Institute of Global Finance seeks to analyze and anticipate major trends in global financial markets, institutions, and regulations, and to develop the information and ideas required to solve emerging problems. It focuses on the policy implications of economic globalization. To this end, it sponsors informal exchanges among scholars and practitioners, conducts research and policy analyses, and participates in the School’s teaching programs. The Institute, founded in 2002, is named for Barbara C. Rosenberg ’54 and Richard M. Rosenberg.