Solving incomplete markets models by derivative aggregation

This article presents a novel computational approach to solving models with both uninsurable idiosyncratic and aggregate risk that uses projection methods, simulation and perturbation. The approach is shown to be both as efficient and as accurate as existing methods on a model based on Krusell and Smith (1998), for which prior solutions exist. The approach has the advantage of extending straightforwardly, and with reasonable computational cost, to models with a greater range of diversity between agents, which is demonstrated by solving both a model with heterogeneity in discount-rates and a lifecycle model with incomplete markets

The economic impact of demographic structure in OECD countries

We examine the impact of demographic structure, the proportion of the population in each age group, on growth, savings, investment, hours, interest rates and inflation using a panel VAR estimated from data for 20 OECD economies, mainly for the period 1970-2007. This flexible dynamic structure with interactions among the main macroeconomic variables allows us to estimate long-run effects of demographic structure on the individual countries. Our estimates confirm the importance of these effects

The art of the possible : tools and methods for solving models with substantial heterogeneity

Macroeconomic models with rational, heterogeneous agents offer the opportunity to study both individual and aggregate economic outcomes, and the interaction between the two. Solving such models is diffcult: the non-trivial problem of solving a maximisation problem in the presence of uncertainty is complicated by the need to determine model-consistent expectations in an economy with a non-degenerate distribution of agents over states. This thesis provides both technical and mathematical tools which aid the economist in working with such models. Chapter 1 provides an introduction to the topic and discusses the literature. Chapter 2 presents software libraries which automate some of the steps, for example calculating expectations from policy functions. The economist can focus on the code which implements the model-specific solution to the optimisation problem. The libraries are shown to solve models far more efficiently than a comparable solution coded in Matlab. Chapter 3 introduces a new algorithm for calculating model-consistent expectations which relies on straightforward mathematics and a guess for the distribution of agents over states. The initial guess, the distribution obtained under constant aggregate conditions, yields good results. Multiple approaches for further improvement in the forecasting function are discussed. All solutions are computed using the libraries from chapter 2, and the algorithm is also implemented as part of those libraries for use in other models. Chapter 4 discusses a model of the labour market with matching and large, heterogeneous forms. The forms experience idiosyncratic demand shocks and adjust their size in response. Steady state solutions are computed for different values of the exogenous tax rate and the transition path demonstrates that, in contrast to the canonical matching model, employment does not adjust instantaneously to changes in market conditions. Chapter 5 discusses some avenues for potential future research

The art of the possible : tools and methods for solving models with substantial heterogeneity

Macroeconomic models with rational, heterogeneous agents offer the opportunity to study both individual and aggregate economic outcomes, and the interaction between the two. Solving such models is diffcult: the non-trivial problem of solving a maximisation problem in the presence of uncertainty is complicated by the need to determine model-consistent expectations in an economy with a non-degenerate distribution of agents over states. This thesis provides both technical and mathematical tools which aid the economist in working with such models. Chapter 1 provides an introduction to the topic and discusses the literature. Chapter 2 presents software libraries which automate some of the steps, for example calculating expectations from policy functions. The economist can focus on the code which implements the model-specific solution to the optimisation problem. The libraries are shown to solve models far more efficiently than a comparable solution coded in Matlab. Chapter 3 introduces a new algorithm for calculating model-consistent expectations which relies on straightforward mathematics and a guess for the distribution of agents over states. The initial guess, the distribution obtained under constant aggregate conditions, yields good results. Multiple approaches for further improvement in the forecasting function are discussed. All solutions are computed using the libraries from chapter 2, and the algorithm is also implemented as part of those libraries for use in other models. Chapter 4 discusses a model of the labour market with matching and large, heterogeneous forms. The forms experience idiosyncratic demand shocks and adjust their size in response. Steady state solutions are computed for different values of the exogenous tax rate and the transition path demonstrates that, in contrast to the canonical matching model, employment does not adjust instantaneously to changes in market conditions. Chapter 5 discusses some avenues for potential future research

Demographic structure and macroeconomic trends

We analyse both empirically and theoretically the effects of changes in demographic structure on the macroeconomy, looking particular at their impact to medium-term trends. Our empirical exercise examines the impact of the proportion of the population in each age group, on growth, savings, investment, hours, interest rates and inflation using a panel VAR estimated from data for 20 OECD economies for the period 1970-2007. This flexible dynamic structure with interactions among the main variables allows us to estimate both the direct impact of demographic structure and their feedback effects. Our estimates confirm the importance of age structure, with young and old dependants having a negative impact on most macroeconomic variables while workers contribute positively. Our theoretical framework incorporates demographic heterogeneity and endogenous productivity, allowing us to study the medium-term interaction of demographic changes and savings, investment, and innovation decisions. Theoretical simulations incorporating the changes in demographic structure experienced by many OECD countries in the past decades replicate well our empirical findings. The current trend of population aging and reduced fertility, expected to continue in the next decades, is found to be a strong force in reducing output growth and real interest rates across OECD countries

Demographic structure and macroeconomic trends

We estimate the effect of changes in demographic structure on long term trends of key macroeconomic variables using a Panel VAR for 21 OECD economies from 1970-2014. The panel data variation assists the identification of demographic effects, while the dynamic structure, incorporating multiple channels of influence, uncovers long-term effects. We propose a theoretical model, relating demographics, innovation and growth, whose simulations match our empirical findings. The current trend of population ageing and low fertility is projected to reduce output growth, investment and real interest rates across OECD countries

Demographic structure and the macroeconomy

The disappointing recovery after the crisis has sparked renewed interest in the medium-run outlook of advanced economies. Lower population growth and its impact on labour supply gained widespread prominence. This column takes a more general view identifying the impact of the evolution of demographic structure, or the entire age profile, on the macroeconomy. Age profile changes have significant implications for savings, investment and growth but also affect innovation activities. The population aging predicted for the next decades is found to be a significant factor in reducing output growth and real interest rates across OECD countries