Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty

This paper describes the first model considered in the computational suite project that compares different numerical algorithms. It is an incomplete markets economy with a continuum of agents and an inequality (borrowing) constraint.     

Assessing the accuracy of the aggregate law of motion in models with heterogeneous agents

This paper shows that the R² and the standard error have fatal flaws and are inadequate accuracy tests. Using data from a Krusell–Smith economy, I show that approximations for the law of motion of aggregate capital, for which the true standard deviation of aggregate capital is up to 14% (119%) higher than the implied value and which are thus clearly inaccurate, can have an R² as high as 0.9999 (0.99). Key in generating a more powerful test is that predictions of the aggregate law of motion are not updated with the aggregated simulated individual data.     

Multi-country real business cycle models: Accuracy tests and test bench

This paper describes the methodology used to compare the results of different solution algorithms for a multi-country real business cycle model. It covers in detail the structure of the model, the choice of values for the parameters, the accuracy tests used in the comparison, and the computer program specifically developed for performing the tests.     

Comparison of solutions to the multi-country Real Business Cycle model

We compare the performance of perturbation, projection, and stochastic simulation algorithms for solving the multi-country RBC model described in Den Haan et al. (this issue). The main challenge of solving this model comes from its large number of continuous-valued state variables, ranging between four and 20 in the specifications we consider. The algorithms differ substantially in terms of speed and accuracy, and a clear trade-off exists between the two. Perturbation methods are very fast but invoke large approximation errors except at points close to the steady state; the projection methods considered are accurate on a large area of the state space but are very slow for specifications with many state variables; stochastic simulation methods have lower accuracy than projection methods, but their computational cost increases only moderately with the state-space dimension. Simulated series generated by different methods can differ noticeably, but only small differences are found in unconditional moments of simulated variables. On the basis of our comparison, we identify the factors that account for differences in accuracy and speed across methods, and we suggest directions for further improvement of some approaches.     

Comparison of solutions to the incomplete markets model with aggregate uncertainty

This paper compares numerical solutions to the model of Krusell and Smith [1998. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy 106, 867–896] generated by different algorithms. The algorithms have very similar implications for the correlations between different variables. Larger differences are observed for (i) the unconditional means and standard deviations of individual variables, (ii) the behavior of individual agents during particularly bad times, (iii) the volatility of the per capita capital stock, and (iv) the behavior of the higher-order moments of the cross-sectional distribution. For example, the two algorithms that differ the most from each other generate individual consumption series that have an average (maximum) difference of 1.63% (11.4%).     

Approximate dynamic programming with post-decision states as a solution method for dynamic economic models

I introduce and evaluate a new stochastic simulation method for dynamic economic models. It is based on recent work in the operations research and engineering literatures (Van Roy et al., 1997, Powell, 2007, Bertsekas, 2011), but also had an early application in economics (Wright and Williams, 1982, Wright and Williams, 1984). The baseline method involves rewriting the household׳s dynamic program in terms of post-decision states. This makes it possible to choose controls optimally without computing an expectation. I add a subroutine to the original algorithm that updates the values of states not visited frequently on the simulation path; and adopt a stochastic stepsize that efficiently weights information. Finally, I modify the algorithm to exploit GPU computing.     

Asset prices in affine real business cycle models

I describe a tractable way to study macroeconomic quantities and asset prices in a large class of dynamic stochastic general equilibrium models. The proposed approximate solution is analytical, log-linear, and adjusted for risk. Therefore, it is well suited to investigate economic mechanisms, describe the time series properties or estimate the model, and deal with stochastic volatility. I explain the pitfalls encountered by previous attempts to use simple approximation techniques, in particular with models featuring recursive preferences. Finally, I show the theoretical relationship between my solution and higher-order perturbation methods.     

Solving the incomplete markets model with aggregate uncertainty using parameterized cross-sectional distributions

This note describes how the incomplete markets model with aggregate uncertainty in Den Haan et al. [Comparison of solutions to the incomplete markets model with aggregate uncertainty. Journal of Economic Dynamics and Control, this issue] is solved using standard quadrature and projection methods. This is made possible by linking the aggregate state variables to a parameterized density that describes the cross-sectional distribution. A simulation procedure is used to find the best shape of the density within the class of approximating densities considered. This note compares several simulation procedures in which there is—as in the model—no cross-sectional sampling variation.     

Solving the multi-country real business cycle model using ergodic set methods

We use the stochastic simulation algorithm, described in Judd et al. (2009), and the cluster-grid algorithm, developed in Judd et al. (2010a), to solve a collection of multi-country real business cycle models. The following ingredients help us reduce the cost in high-dimensional problems: an endogenous grid enclosing the ergodic set, linear approximation methods, fixed-point iteration and efficient integration methods, such as non-product monomial rules and Monte Carlo integration combined with regression. We show that high accuracy in intratemporal choice is crucial for the overall accuracy of solutions and offer two approaches, precomputation and iteration-on-allocation, that can solve for intratemporal choice both accurately and quickly. We also implement a hybrid solution algorithm that combines the perturbation and accurate intratemporal-choice methods.     

What do interest rates reveal about the functioning of real business cycle models?

This paper begins by documenting the extent to which the predictions of standard Real Business Cycle (RBC) models are incompatible with observed movements in real interest rates. The main finding of the paper is that extending the baseline model to include habit persistence in consumption and adjustment costs to capital significantly improves the model's empirical performance. In our evaluation of the model's performance, we take special care of estimating and testing predictions of the model using both moments drawn directly from the data and moments calculated after identifying shocks to the stochastic trend.     

Limited participation in international business cycle models: A formal evaluation

In this paper, we argue that limited asset market participation (LAMP) plays an important role in explaining international business cycles. We show that when LAMP is introduced into an otherwise standard model of international business cycles, the performance of the model improves significantly, especially in matching cross-country correlations. To perform formal evaluation of the models we develop a novel statistical procedure that adapts the statistical framework of Vuong (1989) to DSGE models. Using this methodology, we show that the improvements brought out by LAMP are statistically significant, leading a model with LAMP to outperform a representative agent model. Furthermore, when LAMP is introduced, a model with complete markets is found to do as well as a model with no trade in financial assets – a well-known favorite in the literature. Our results remain robust to the inclusion of investment specific technology shocks.     

Solving the incomplete markets model with aggregate uncertainty using the Krusell–Smith algorithm

This paper studies the properties of the solution to the heterogeneous agents model in Den Haan et al. [2009. Computational suite of models with heterogeneous agents: incomplete markets and aggregate uncertainty. Journal of Economic Dynamics and Control, this issue]. To solve for the individual policy rules, we use an Euler-equation method iterating on a grid of pre-specified points. To compute the aggregate law of motion, we use the stochastic-simulation approach of Krusell and Smith [1998. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy 106, 868–896]. We also compare the stochastic- and non-stochastic-simulation versions of the Krusell–Smith algorithm, and we find that the two versions are similar in terms of their speed and accuracy.     

Forecasting with vector autoregressive (VAR) models subject to business cycle restrictions

In the last decade VAR models have become a widely-used tool for forecasting macroeconomic time series. To improve the out-of-sample forecasting accuracy of these models, Bayesian random-walk prior restrictions are often imposed on VAR model parameters. This paper focuses on whether placing an alternative type of restriction on the parameters of unrestricted VAR models improves the out-of-sample forecasting performance of these models. The type of restriction analyzed here is based on the business cycle characteristics of U.S. macroeconomic data, and in particular, requires that the dynamic behavior of the restricted VAR model mimic the business cycle characteristics of historical data. The question posed in this paper is: would a VAR model, estimated subject to the restriction that the cyclical characteristics of simulated data from the model “match up” with the business cycle characteristics of U.S. data, generate more accurate out-of-sample forecasts than unrestricted or Bayesian VAR models?     

Integration of family-owned business succession with turnover and life cycle models: Development of a successor retention process model

Family-owned businesses face a unique obstacle: continuation of the business through intergenerational transfer. Most family-owned businesses cease when the next generation does not enter the business. This paper develops parallels between failed intergenerational transfer and voluntary turnover. Based on past research, we develop a taxonomy of characteristics hypothesized to influence intergenerational transfer in family-owned businesses. We, then, integrate these dimensions with prominent turnover and socialization theories to propose a successor retention process model. Implications for research are described.     

VARs,common factors and the empirical validation of equilibrium business cycle models

Equilibrium business cycle models have typically less shocks than variables. As pointed out by Altug (1989) International Economic Review 30 (4) 889–920 and Sargent (1989) The Journal of Political Economy 97 (2) 251–287, if variables are measured with error, this characteristic implies that the model solution for measured variables has a factor structure. This paper compares estimation performance for the impulse response coefficients based on a VAR approximation to this class of models and an estimation method that explicitly takes into account the restrictions implied by the factor structure. Bias and mean-squared error for both factor- and VAR-based estimates of impulse response functions are quantified using, as data-generating process, a calibrated standard equilibrium business cycle model. We show that, at short horizons, VAR estimates of impulse response functions are less accurate than factor estimates while the two methods perform similarly at medium and long run horizons.     

Emotional intelligence,job insecurity,and psychological strain among real estate agents: a test of mediation and moderation models

We develop two models of the relationships between emotional intelligence (EI), job insecurity, and psychological strain. The moderation model suggests that EI reduces psychological strain by helping individuals cope with job insecurity when it arises. The mediation model suggests that EI reduces psychological strain by enabling individuals to conserve resources, thereby reducing their experience of job insecurity. Our results, based on a sample of 232 real estate agents, show that job insecurity mediates the relationship between EI and psychological strain. Contrary to what the moderation model suggested, the positive relationship between job insecurity and psychological strain was found to be stronger when EI was higher. Overall, the results provide more nuanced insights into the role of EI in psychological strain.     

Monetary policy and bank performance: The role of business models

This paper examines the relationship between monetary policy and bank performance in a multiple-instrument environment, particularly highlighting the conditioning role of bank business models. Employing a unique dataset of Vietnamese commercial banks from 2007 to 2019, we display that banks react to monetary policy changes, either when the central bank increases policy rates or injects money into the economy through open market operations, by decreasing overall returns and increasing financial instability. Additionally, we document that the accumulation of foreign exchange reserves benefits bank outcomes, contrasting to open market operations, albeit the central bank uses both of these policy instruments to alter money supply in the economy. Our key analysis of interest reveals that business models considerably matter in the effects of monetary policy on bank performance. Collectively, our findings demonstrate that banks’ business models that yield more non-interest income or diversify more into different income sources may mitigate the pass-through of monetary policy to bank performance. This finding holds across all interest- and quantitative-based monetary policy indicators and across all the functions of risk-taking behavior, earning-profit capacity, and financial stability. Furthermore, while plotting the marginal effects of monetary policy, we realize that they are insignificant for banks whose business models heavily rely on non-traditional segments.     

The number of banking relationships and the business cycle: New evidence from Colombia

We study the determinants of multiple bank–firm relationships using a uniquely rich data set comprised of information on individual loans of a large number of firms in Colombia. We control for firm-specific variables and find that the business cycle exerts important influence on the number of bank relationships sustained by firms. Our evidence suggests that the number of bank relationships is counter-cyclical, decreasing during macroeconomic expansions and increasing during contractions. However, this effect is stronger for large firms which have more access to alternative sources of funding.