Stock-and-flow-consistent macroeconomic model for South Africa

1 Introduction

This paper presents a financial-real stock-and-flow-consistent model of the South African economy. The model dynamics build on the simple computable general equilibrium (CGE) model developed by Devarajan and Go (1998) and incorporate elements of dynamic stochastic general equilibrium (DSGE) models and stock-and-flow models in the tradition of Backus et al. (1980) and Godley and Lavoie (2012). The model also incorporates elements of the theoretical models developed by Borio and Zhu (2012) and Woodford (2010).

In recent decades DSGE models have been widely adopted by central banks, finance ministries, and policy analysts; however, they have been subject to extensive criticism, particularly with respect to financial sector dynamics (see Sims 2006; Caballero 2010; Blanchard 2016). In response to these criticisms, there have been significant efforts to incorporate financial dynamics in DSGE models, including the incorporation of financial accelerator mechanisms derived from Bernanke et al. (1999). In these models, a fall in firms’ net worth is accompanied by greater reliance on external financing. The mechanism creates a feedback loop between higher lending premiums, associated with the higher agency costs involved in external finance, and falling net worth. The approach is employed by FernándezVillaverde (2010), Carrillo and Poilly (2010), and Kollmann et al. (2013) to study the impact of fiscal policy. A second modification introducing finance into DSGE models assumes that lenders can force borrowers to repay their loans only in the presence of some durable asset serving as collateral (Kiyotaki and Moore 1997); Ottonello (2013) and Fornaro (2015) study the impact of sudden stops in capital flows with such a model. In the models of Gertler and Karadi (2011) and Ellison and Tischbirek (2014) the ability of a representative bank to borrow from other financial institutions is limited by its balance sheet. The mechanism aims to capture how unconventional monetary policy interventions can reduce balance sheet constraints and increase lending. A different bank lending constraint is used by Gerali et al. (2010), in which the ability of banks to extend loans is limited by the holding of deposits and a capital requirements ratio imposed by the macro prudential authorities.

The inclusion of such financial sector elements in DSGE models creates several problems. The models are linear and thus cannot capture the boom-and-bust dynamics that characterize the financial sector and do not capture heterogeneous and systemic risk, which are important drivers of financial sector dynamics. The inclusion of a financial accelerator mechanism increases the persistence of shocks rather than creating boom-and-bust dynamics (Borio and Zhu 2012; Duca and Muellbauer 2014). Balance sheet dynamics are either not represented at all or considered only for the balance sheet of a representative bank (Gerali et al. (2010) Gertler and Karadi 2011). But, as Calvo et al. (2004), Eggertsson and Krugman (2012), and Borio and Zhu (2012) argue, disaggregated balance sheet dynamics are important for studying the impacts of sudden stops, fiscal policy, and general risk behaviour of agents in the economy.

To address some of these criticisms, we develop a model that is stock-and-flow-consistent. This implies that we have several financial instruments, rates of return, and institutional balance sheets. We model equities, bonds, loans, and cash and deposits as financial instruments; their returns; and the balance sheets of the Central Bank, the household sector, the financial sector, government, the non-financial sector, and the foreign sector. This is a significantly richer representation than the financial representation of institutions and financial instruments in DSGE models. The stock and flow consistency implies that there are strict budget constraints. Changes to the balance sheet of one institution must be matched by changes to the balance sheets of other institutions. These changes reflect that some institutions save more than they invest in physical capital and thus increase their net financial assets. At the same time, those institutions that record higher investment in physical capital than their savings see an increase in their net financial liabilities. The changes to the balance sheets also reflect changes to the prices of assets and liabilities. What is a particularly striking difference between stock-and-flow-consistent models and other models is that cyclical flow changes affect the long-term real and financial behaviour of institutions through their impact on the respective institutional assets and liabilities stocks (Backus et al. 1980).

Recent analyses using stock-and-flow-consistent models include Barwell and Burrows’ (2014) study of the evolution of the UK economy in the years leading up to the financial crisis of 2008, in which balance sheet linkages enable financial fragilities to be identified. In their stock-and-flow-consistent model, Caiani et al. (2014) analyse the monetary dynamics that emerge from a Schumpeterian structural change in the economy driven by innovation. Burgess et al. (2016) develop a stock-and-flow-consistent model for the United Kingdom and use it to study the impact of house price changes, shocks to the risk-weighted capital ratio, government consumption shocks, and sudden-stop shocks. They also highlight some of the problems associated with stock-and-flow-consistent models as compared with DSGE models. These problems include model equations which are not based on the optimization problem of individual agents (making the model parameters subject to the Lucas Critique), high levels of complexity due to the requirement for stock and flow consistency, and large data requirements.

While our model is similar in terms of its stock and flow consistency to those recent models, it is different in terms of the behavioural specification for the different agents. Consumption and production behaviour are micro-founded in agents’ inter-temporal optimization, allowing us to capture how changes in preferences, technology, and resource constraints affect outcomes. Prices exhibit a degree of stickiness, and there is a monetary policy reaction function based on a Taylor Rule. These features make it similar to new Keynesian DSGE models, but unlike DSGE models ours is not stochastic.

There are two features of our model that make it different to both the traditional-stock-andflow-consistent models and DSGE models. These features provide better representation of financial sector dynamics. First, our analysis of financial sector behaviour is based on modern theories of financial transmission mechanisms developed in the wake of the 2008 global financial crash (Woodford 2010; Borio and Zhu 2012), with modifications appropriate for application to South Africa. Second, we specify a dynamic adjustment model of household expectations with properties that differ radically from the way expectations are formed in both stock-and-flow-consistent and DSGE models.