2018. vol. 22. No. 3

In this paper, we consider the classical problem of maximizing discounted utility, provided that the moment of the next purchase and receipt of a loan is random (Poisson). The purpose of the study is to take into account the uncertain waiting period for receipt of a credit in consumption decision-making. The model is formulated as the problem of optimal stochastic control. The consumer at random moments buys the product at a non-random price and at the same random moments can take and return indefinite loans. For loans, the agent continuously pays interest. He constantly receives dividends in the form of external receipt of money into the account and can accumulate non-interest non-cash money. The optimality conditions are obtained using the Lagrange multiplier method. Sufficient optimality conditions reduce to partial differential equations with variable and unknown delay. They can only be solved by using a combinations of analytic expansions with respect to a small parameter. A special difficulty is the regularization («softening») of the conditions of complementary slackness. As a result, functions were obtained that determine the optimal control of consumption purchases and the size of the loan. One can see how the consumption expenditures change as the end of the planning period approaches. First, consumption depends on money and debt not separately, but on their difference – own means of the consumer. Secondly, far from the planning horizon, consumption is small and grows as the final point in time approaches. This model can be used as part of the description of the consumer agent in dynamic stochastic general equilibrium models.

In this paper a real sector model of Russian economy is presented based on multiproduct decomposition of macroeconomic statistic. Model allows to reproduce statistic accurately in constant and current prices which is not possible in many other macroeconomic models.

Model economy consists of agent-traders with the help of which GDP and its components are decomposed into unobservable products, agent-producer and agent-consumer. Traders are described by CES-functions. Analytical solution of trader problem gives ratios that are used for GDP decomposition.

Producer has specific production function in which are considered two types of investments – investments that support fixed assets and investments that help to build up fixed assets. In addition, labor demand is described using an original scheme. Moreover, stock formation is described in producer model which is usually omitted in standard macroeconomic models.

Aggregate consumer model reproduces optimal trajectories for consumption, labor and consumer deposits. Specific form of utility function gives opportunity to include labor as endogenous variable in the model which is not usually made in standard macroeconomic models. Considering economically active population and modifying calibration function it is possible to receive high accuracy in reproducing consumption, labor and deposits trajectories even in crisis periods.

In this paper models are analytically solved and calibrated on real data without linearization procedure.

The study analyzes the topology of the interbank network in the agent-based model of the banking system with detailed description of the protocols and stylized one of the external (with respect to the banking system) economy. It is shown that the main incentive for the inter­bank market creation originates from liquidity gaps resulting from maturities mismatch bet­ween deposits and credits. The impact of this effect on the dynamics of total capital and cash in the case of increasing term structure of the yield curve generating credit and deposit’s maturities mismatch as a result of banks optimizing behavior, is illustrated. Different properties of this graph are compared to those of the real interbank networks. It is shown that the model in which banks are represented by agents-automata can reproduce various topological properties of the real interbank networks. These properties are: significant size of the giant strongly connected component, fat‑tailed nature of the distributions of In- and Out-degrees, fat-tailed nature of the distribution of allocated funds, disassortativity, nonuniformity of the distribution of clustering coefficient over the vertices. The properties which can be reproduced only in the model with a more detailed description of agents’ behavior were also marked out. These properties are the following: absence of the oriented cycles in the networks with low aggregation of the data, low fraction of the banks not participating in the interbank market and of the net-creditor banks, absence of fat tails in the distribution over the borrowed funds, low clustering coefficient. The reasons for such a difference between the properties of model networks and the real ones are noted. The changes of the model needed to reproduce such properties of real networks are discussed.

The paper describes the new version of the model of the Russian banking system, which successfully reproduces a wide set of parameters characterizing its performance: loans and deposits of firms and households, liquidity nominated both in rubles and in foreign currency, mandatory reserves. We describe the technique of derivation of model relations, which includes the statement of the problem of macroeconomic agent “bank”. This problem is based on the maxi­mization of discounted flow of profit subject to budget constraint, balance of loans and deposits, liquidity constraints and reserve sufficiency requirements. The paper contains the system of equations which describes the solution of the problem. We provide a detailed description of transition of continuous to discrete time and the new approach to the relaxation of complementary slackness conditions based on the assumption that the model exhibits a turnpike property.

Apart from the standard approach to the parameter estimation for this class of models, we apply a method of multi-step forecasting. We show that the standard method of estimations allows to closely reproduce the historic series but leads to the poor quality of forecasts. The method of multi-step forecasting, on the other hand, successfully reproduces historic series and also leads to rather accurate forecasts. We compared it with standard econometric techniques and show that the model with parameters obtained via multi-step forecast method provides somewhat better forecasts than ARIXAM and much better ones than AR, ARIMA, VAR and VARX. We also show that then we use multi-step forecasting method, optimal values of parameters are about the same for different intervals of estimation and different lengths of forecasts (from one to six months). Such a stability of parameters makes us think that the model reproduces long-term relations of variables and can be used for forecasting and scenario analysis.

The model can be used for the evaluation of reaction of the banking system on the monetary policy, external constraints of different kind and the general condition of the economy. The model can be used as a block of a bigger general equilibrium model of the Russian economy.

The most computations with DSGE models are use linear approximation with perturbation method. It is rare when higher order approximations are used, but linear approximation is necessary step for computation of higher order approximations. However, conventional approximation techniques can be inaccurate. It is related to properties of QZ-decomposition code, which is used for finding linear approximation. This problem was discovered recently with small-scale DSGE model example. This paper investigate how large numerical errors for different DSGE-models. Simple measure is suggested for estimation of corresponding inaccuracy. One version of measure is likelihood based. Alternative versions are moments based. Various 8 DSGE-models are analyzed. They are small scale and medium-large scale models; conventional DSGE- models and models with unconventional structure; models that are focused on nonlinear properties and models that do not pay attention to nonlinear properties. This problem is important only for minority of the models. However, the errors are large for few models (small-scale). Known approach against numerical inaccuracy (that is based on special matrix balancing) decreases errors, but such decreases are not large enough for problem solving. Thus, it is important to recognize whether numerical errors of DSGE models linear approximation are large or no what can be done with suggested measure.

We investigate the consequences of excessive international debt overhang as they relate to both debtor and creditor countries. In particular, we assess the impact of monetary policy on financial stability and how it can be used to smooth borrowers, as well as creditors, consumption over the business cycle. Based on [Goodhart, Peiris, Tsomocos, 2018], we establish that an independent countercyclical monetary policy, that contracts liquidity whenever debt grows whereas it expands it when default rises, reduces volatility of consumption. In effect, monetary policy provides an extra degree of freedom to the policymaker. We implement our approach to the Czech and Eurozone area economies during the 1990s.

In our model, we introduce endogenous default ά la [Shubik, Wilson, 1977], whereby debtors incur a welfare cost in renegotiating their contractual debt obligations that is commensurate to the level of default. However, this cost depends explicitly on the business cycle and it should be countercyclical. Hence, contractionary monetary policy reduces the volume of trade and efficiency, thus increasing default. This occurs as the default cost increases the associated default accelerator channel engenders higher default rates. On the other hand, lower interest rates increase trade efficiency and, consequently, reduce the amplitude of the business cycle and benefit financial stability.

In sum, the appropriate design of monetary policy complements financial stability policy. The modelling of endogenous default allows us to study the interaction of monetary and macroprudential policy.