We explore alternative approaches to numerical solutions of large rational-expectations models. We discuss and compare several current alternatives, focusing on the trade-offs in accuracy, space, and speed. The models range from representative-agent models with many goods and capital stocks, to models of heterogeneous agents with complete or incomplete asset markets. The methods include perturbation and projection methods. We show that these methods are capable of analyzing moderately large models even when we use only elementary, general-purpose numerical methods.

There is now a substantial theoretical literature arguing that inflation impedes financial deepening. Furthermore, it has been hypothesized that the relationship is a nonlinear one, in that there is a threshold level of inflation below which inflation has a positive effect on financial depth, but above which the effect turns negative. Using a large cross-country sample, empirical support is found for the existence of such a threshold. The estimates indicate that the threshold level of inflation is generally about 3–6 percent per annum, depending on the specific measure of financial depth that is utilized.

We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature to derive the Pontryagin conditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic system gives rise to an ill-posed problem in the sense of Hadamard. We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly different from those of the nonspatial linear Ramsey model due to the spatial dynamics induced by capital mobility.

Different theories of expectation formation and learning usually yield different outcomes for realized market prices in dynamic models. The purpose of this paper is to investigate expectation formation and learning in a controlled experimental environment. Subjects are asked to predict the next period's aggregate price in a dynamic commodity market model with feedback from individual expectations. Subjects have no information about underlying market equilibrium equations, but can learn by observing past price realizations and predictions. We conduct a stable, an unstable, and a strongly unstable treatment. In the stable treatment, rational expectations (RE) yield a good description of observed aggregate price fluctuations: prices remain close to the RE steady state. In the unstable treatments, prices exhibit large fluctuations around the RE steady state. Although the sample mean of realized prices is close to the RE steady state, the amplitude of the price fluctuations as measured by the variance is significantly larger than the amplitude under RE, implying persistent excess volatility. However, agents' forecasts are boundedly rational in the sense that fluctuations in aggregate prices are unpredictable and exhibit no forecastable structure that could easily be exploited.

Different theories of expectation formation and learning usually yield different outcomes for realized market prices in dynamic models. The purpose of this paper is to investigate expectation formation and learning in a controlled experimental environment. Subjects are asked to predict the next period's aggregate price in a dynamic commodity market model with feedback from individual expectations. Subjects have no information about underlying market equilibrium equations, but can learn by observing past price realizations and predictions. We conduct a stable, an unstable, and a strongly unstable treatment. In the stable treatment, rational expectations (RE) yield a good description of observed aggregate price fluctuations: prices remain close to the RE steady state. In the unstable treatments, prices exhibit large fluctuations around the RE steady state. Although the sample mean of realized prices is close to the RE steady state, the amplitude of the price fluctuations as measured by the variance is significantly larger than the amplitude under RE, implying persistent excess volatility. However, agents' forecasts are boundedly rational in the sense that fluctuations in aggregate prices are unpredictable and exhibit no forecastable structure that could easily be exploited.

Building on Kilian and Park's (2009) structural VAR analysis of the effects of oil demand and supply shocks on the U.S. stock market, this paper focuses on the differences and commonalities of stock price responses in oil exporting and importing economies in 1974–2011. Structural oil price shocks add to our understanding of the 2008 stock market crash. I find that unexpected reductions in world oil supply do not affect stock returns in any of six OECD countries. Although an increase in global aggregate demand consistently raises oil prices and cumulative real stock returns, the effect is more persistent for oil exporters. Other, e.g., precautionary oil demand shocks have a detrimental impact on stock markets in oil-importing countries, a statistically insignificant effect for Canada, and a significantly positive effect for Norway. Oil price shocks account for a larger share of the variation in aggregate international stock returns than in national stock returns.

We analyze the role of intrafirm bargaining in the large-firm matching model and underline the conditions under which the Pissarides equivalence between this model and the “single-worker” firm's model holds.

This paper applies a factor-augmented vector autoregressive model to U.S. data with the aim of analyzing monetary transmission via private sector balance sheets, credit risk spreads, and house prices and of exploring the role of monetary policy in the housing and credit boom prior to the global financial crisis. We find that monetary policy shocks have a persistent effect on house prices, real estate wealth, and private sector debt and a strong short-lived effect on risk spreads in money and mortgage markets. Moreover, the results suggest that monetary policy contributed considerably to the unsustainable precrisis developments in housing and credit markets. Although monetary policy shocks contributed discernibly at a late stage of the boom, feedback effects of other (macroeconomic and financial) shocks via lower policy rates kicked in earlier and appear to have been considerable.

We present a model of a dynamic and complex economy in which the creation and the destruction of money result from interactions between multiple and heterogeneous agents. In the baseline scenario, we observe the stabilization of the income distribution between wages and profits. We then alter the model by increasing the flexibility of wages. This change leads to the formation of a deflationary spiral. Aggregate activity decreases and unemployment increases. The macroeconomic stability of the model is affected and eventually a systemic crisis arises. Finally, we show that the introduction of a minimum wage would have made it possible to boost the aggregate demand and to avoid this crisis.

We provide industry-level estimates of the elasticity of substitution (σ) between capital and labor in the United States. We also estimate rates of factor augmentation. Aggregate estimates are produced. Our empirical model comes from the first-order conditions associated with a constant–elasticity of substitution production function. Our data represent 35 industries at roughly the 2-digit SIC level, 1960–2005. We find that aggregate U.S. σ is likely less than 0.620. σ is likely less than unity for a large majority of individual industries. Evidence also suggests that aggregate σ is less than the value-added share-weighted average of industry σ's. Aggregate technical change appears to be net labor–augmenting. This also appears to be true for the large majority of individual industries, but several industries may be characterized by net capital augmentation. When industry-level elasticity estimates are mapped to model sectors, the manufacturing sector σ is lower than that of services; the investment sector σ is lower than that of consumption.

This paper compares the forecasting performance of some leading models of inflation for G-7 countries. We show that bivariate and trivariate models suggested by economic theory or statistical analysis are not much better than univariate ones. Phillips curve specifications fit well into this class. Improvements in both the MSE of the forecasts and turning point prediction are obtained with time-varying coefficients models, which exploit international interdependencies. The performance of the latter class of models is stable throughout the 1990s.

We introduce automation into a standard model of capital accumulation and show that (i) there is the possibility of perpetual growth, even in the absence of technological progress; (ii) the long-run economic growth rate declines with population growth, which is consistent with the available empirical evidence; (iii) there is a unique share of savings diverted to automation that maximizes long-run growth; and (iv) automation explains around 14% of the observed decline of the labor share over the last decades in the United States.

Many oil industry analysts believe that there is predictive power in the product spread, defined as the difference between suitably weighted refined product market prices and the price of crude oil. We derive a number of alternative forecasting model specifications based on product spreads and compare the implied forecasts to the no-change forecast of the real price of oil. We show that not all product spread models are useful for out-of-sample forecasting, but some models are, even at horizons between one and two years. The most accurate model is a time-varying parameter model of gasoline and heating oil spot price spreads that allows for structural change in product markets. We document mean-squared prediction error reductions as high as 20% and directional accuracy as high as 63% at the two-year horizon, making product spread models a good complement to forecasting models based on economic fundamentals, which work best at short horizons.

Business cycle models with sticky prices and endogenous firm entry make novel predictions on the transmission of shocks through the extensive margin of investment. I test some of these predictions using a VAR with model-based sign restrictions. I find a positive and significant response of firm entry to expansionary shocks to productivity, aggregate spending, monetary policy, and entry costs. The estimated response to a monetary expansion does not support the monetary policy transmission mechanism proposed by the model. Insofar as firm startups require labor services, wage stickiness is needed to make the signs of the model responses consistent with the estimated ones. The shapes of the empirical responses suggest that congestion effects in entry make it harder for new firms to survive when the number of startups rises.

This paper provides long-run evidence on the dynamic effects of supply and demand shocks on commodity prices. I assemble and analyze a new data set of price and production levels of copper, lead, tin, and zinc from 1840 to 2014. Using a novel approach to identification, I show that price fluctuations are primarily driven by demand, rather than supply shocks. Demand shocks affect the price for up to 15 years, whereas the effect of mineral supply shocks persists for up to 5 years. Price surges caused by rapid industrialization are a recurrent phenomenon throughout history. Mineral commodity prices return to their declining or stable trends in the long run.

Previous research shows that volatility in oil prices has tended to depress output, as measured by nonresidential investment and GDP. This is interpreted as evidence in support of the theory of real options in capital budgeting decisions, which predicts that uncertainty about, for example, commodity prices will cause firms to delay production and investment. We continue that investigation by analyzing the effect of oil price uncertainty on monthly measures of U.S. firm production related to industries in mining, manufacturing, and utilities. We use a more general specification, an updated sample that includes the increased oil price volatility since 2008, and we control for other nonlinear measures of oil prices. We find additional empirical evidence in support of the predictions of real options theory, and our results indicate that the extreme volatility in oil prices observed in 2008 and 2009 contributed to the severity of the decline in manufacturing activity.

Recent empirical findings suggest that macroeconomic variables are seldom normally distributed. For example, the distributions of aggregate output growth-rate time series of many OECD countries are well approximated by symmetric exponential-power (EP) densities with Laplace fat tails. In this work, we assess whether real business cycle (RBC) and standard medium-scale New Keynesian (NK) models are able to replicate this statistical regularity. We simulate both models, drawing Gaussian- vs Laplace-distributed shocks, and we explore the statistical properties of simulated time series. Our results cast doubts on whether RBC and NK models are able to provide a satisfactory representation of the transmission mechanisms linking exogenous shocks to macroeconomic dynamics.

We study the impact of oil price shocks on the U.S. stock market volatility. We jointly analyze three different structural oil market shocks (i.e., aggregate demand, oil supply, and oil-specific demand shocks) and stock market volatility using a structural vector autoregressive model. Identification is achieved by assuming that the price of crude oil reacts to stock market volatility only with delay. This implies that innovations to the price of crude oil are not strictly exogenous, but predetermined with respect to the stock market. We show that volatility responds significantly to oil price shocks caused by unexpected changes in aggregate and oil-specific demand, whereas the impact of supply-side shocks is negligible.

The rational expectations hypothesis swept through macroeconomics during the 1970s and permanently altered the landscape. It remains the prevailing paradigm in macroeconomics, and rational expectations is routinely used as the standard solution concept in both theoretical and applied macroeconomic modelling. The rational expectations hypothesis was initially formulated by John F. Muth Jr. in the early 1960s. Together with Robert Lucas Jr., Thomas (Tom) Sargent pioneered the rational expectations revolution in macroeconomics in the 1970s.