Optimal lockdown in altruistic economies

The recent COVID-19 crisis has revealed the urgent need to study the impact of an infectious disease on market economies and provide adequate policy recommendations. The present paper studies the optimal lockdown policy in a dynamic general equilibrium model where households are altruistic and they care about the share of infected individuals. The spread of the disease is modeled here using SIS dynamics, which implies that recovery does not confer immunity. To avoid non-convexity issues, we assume that the lockdown is constant in time. This strong assumption allows us to provide analytical solutions. We find that the zero lockdown is efficient when agents do not care about the share of infected, while a positive lockdown is recommended beyond a critical level of altruism. Moreover, the lockdown intensity increases in the degree of altruism. Our robust analytical results are illustrated by numerical simulations, which show, in particular, that the optimal lockdown never trespasses 60% and that eradication is not always optimal.     

Optimal investment with vintage capital: Equilibrium distributions

The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distribution, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.     

Moral hazard,debt overhang and capital structure

This paper investigates the impact of managerial moral hazard on the debt overhang of a firm by constructing a contingent claims model in which the manager faces costly effort. Using a calibrated capital structure model, we show that the costs of debt overhang become more serious in the presence of managerial moral hazard. Such costs even account for more than half of the total agency costs at a high level of cash flow. Moreover, in contrast to the results of Hackbarth and Mauer (2012), our model predicts a U-shaped relationship between the leverage ratio and investment opportunities of a firm, which is caused by managers’ moral hazard. Finally, by considering this moral hazard, we also show the coexistence of low leverage ratios and high credit spreads, which explains the phenomenon of “low debt levels and high credit spreads” observed in practice.     

A two-generation new product model by considering forward-looking customers: Dynamic pricing and advertising optimization

Nowadays, one of the challenges of the firm managing multi-generation products is the forward-looking behavior of customers. Anticipating the introduction of a newer generation affects the demand and sales volume of the current generation and next generation. In this research, we investigated how to efficiently structure the pricing and advertising strategies of a firm that launches a two-generation new product to a market populated by forward-looking customers. Two thresholds were determined on the advertising expenditure of Generations 1 and 2. Our analysis proposed that the optimal pricing path of Generation 1 was monotonically decreasing or increasing and, then, decreasing. The optimal pricing of Generation 2 followed a concave curve. A heuristic solution method was proposed to solve the numerical examples. Findings revealed that, with increasing the customers' forward-looking behavior, the firm's profit would decrease. In the presence of forward-looking customers, it is beneficial for the firm to reduce the price of Generation 1 and allocate more budget to advertise Generation 2. Among other results, the advertising expenditure was shown to be positively affected by the number of potential customers and advertising effectiveness. Also, the length of the planning horizon had a negative effect on the advertising expenditure. A higher discount rate could lead to lower price, while higher advertising effectiveness and length of the planning horizon would result in higher price. Further, the results showed that, with increasing the word-of-mouth advertising effectiveness, the firm should increase the advertising expenditure and decrease the price firstly and, afterwards, decrease the advertising effort and increase the price.     

Equity premium prediction and optimal portfolio decision with Bagging

We propose using the statistical method of Bagging to forecast the equity premium out-of-sample for multivariate regression models. Bagging allows for the flexible and efficient extraction of valuable informational content from a large set of predictors, leading to statistically and economically significant gains relative to not only the historical mean, but also other soft-threshold methods such as forecast combinations and shrinkage estimators in our empirical results. Furthermore, we find that the source of economic gains for Bagging primarily comes from the fact that it encourages the investor to actively manage portfolio by flexibly utilizing short selling or leveraging to better time the market following correctly prognosticated trends. However, other strategies such as forecast combinations keep the equity shares nearly fixed regardless of the predicted market prospect.     

Government size,composition of public spending and economic growth in Brazil

The performance of the fiscal policy is largely affected by the relationship between government size, composition of public spending and economic growth. We use a theoretical framework to find optimal relations among these variables and confront them with a panel data for the Brazilian states. Private capital and government spending are substitute inputs in production as the Brazilian states require provision of public spending to fill gaps in the underdeveloped private sector. Public investment and current government expenditures are combined in fixed ratios in the overall government spending due to strong rigidity of the public budget. The optimal share of public investment is considerably lower than current expenditures, as occurs in developing countries characterized by low economic dynamism. Finally, the average tax burden from the data is below the estimated optimal level, meaning that there is space for increasing tax rate without harming economic growth for some Brazilian states.     

Optimal allocation of direct and embodied arable land associated to urban economy: Understanding the options deriving from economic globalization

Land resources do not flow directly but can be allocated as “embodied land” in goods and services during economic globalization. The term “embodied arable land” can help link local land allocation strategies to the global and national supply chains and trade activities, and suggest new lens in optimizing arable land allocation. China is facing a serious arable land shortage, especially in municipal administrative areas. Based on the nested input-output analysis (Nested IOA), this work takes Shanghai as an example, exploring the allocation of direct and embodied arable land of an urban economy within the process of economic globalization. The amount of embodied arable land associated with Shanghai economy is 6.09 Mha, broken down into local arable land use (0.20 Mha), domestic inflows (3.20 Mha) and foreign inflows (2.69 Mha). This area supports local final demand (4.32 Mha), domestic outflows (1.24 Mha) and foreign outflows (0.53 Mha). Land-related imbalances emerge in the study, namely the economy’s demand versus the city’s size, the arable land demand versus supply, and embodied arable land inflows versus outflows. Regarding the role of the urban economy in allocation of global arable land under economic globalization, on the one hand, Shanghai has intensively involved with a large amount of embodied foreign arable land resources, and has been heavy dependent on foreign embodied arable land; On the other hand, there is still large potential for Shanghai to take the opportunity of economic globalization for an optimal allocation of direct and embodied arable land. Policy suggestions on taking the opportunity of economic globalization for an optimal allocation of direct and embodied arable land are put forward.     

General existence of competitive equilibrium in the growth model with an endogenous labor–leisure choice

We prove the existence of competitive equilibrium in the canonical optimal growth model with elastic labor supply under general conditions. In this model, strong conditions to rule out corner solutions are often not well justified. We show using a separation argument that there exist Lagrange multipliers that can be viewed as a system of competitive prices. Neither Inada conditions, nor strict concavity, nor homogeneity, nor differentiability are required for existence of a competitive equilibrium. Thus, we cover important specifications used in the macroeconomics literature for which existence of a competitive equilibrium is not well understood. We give examples to illustrate the violation of the conditions used in earlier existence results but where a competitive equilibrium can be shown to exist following the approach in this paper.