SFC models

Stock-flow consistent ecological macro models

(NOTE: This section is around 40% complete.)

Duration: 2013-present

What are Stock-flow consistent model?

All countries record economic activities in the National System of Accounts (NSA) where the rules are defined by the XXX. These accounts are central to keep track of domestic activity and its iteractions with the rest of the world (RoW). These accounts also give us the well know identity:

\[Y = C + I + G + (X - M)\]

where \(Y\) equals total output or GDP, \(C\) is domestic consumption, \(I\) is domestic investment, \(G\) is government expenditure, \(X\) are export and \(M\) are imports. This economic acitivity is generated by different economic sectors which are households, financial firms (including banks), non-financial firms (or the production sector), the government, and the central bank. The activity of these sectors is recorded for each year by the central banks or statistical institutions. At the end of each financial year, a sector-level balance sheet is produced, while the flows in between years are recorded in a transition flow matrix, or its variant, the structural accounting matrix. This whole accounting system work with the core principle of a quadruple entry system, that is, each activity generates four entries: a debit and a credit either within two balance sheet items of a sector, or balance sheet items of two different sectors. Therefore, by construction, the flows have to be a zero-sum game. These constraints are built into the SFC models and can help identify indirect consequences of policies. The second advantage of SFCs comes from the economic setup. They are come from a long tradition of post-Keynesian thinking which in the past few decades, has worked a lot on topics of effective demand, adaptive expectations, role of distributions, market frictions, and institutional structures especially public investment. Therefore they have a completely different closure as compared to neo-classical models which are supply-side driven and assume perfect forsight.

How are SFC models set up?

While the behavior of the sectors is determined through mostly post-Keynesian literature. Some key differences between SFC and neo-classical model are functional forms of consumption which also depends on wealth, price which is defined by cost structures and markup and demand is determined in the next step. Capital stock buildup is defined by a capacity utilization rate where some capital stock is kept slack to accommodate fluctuations in demand. This in turn affects investment decisions. Firms can self-finance investment or borrow money from banks. Since money plays an important role in the model, banks are introduced as more than passive entities that take deposit and give out loans. In contrast, they make active profit-making decisions, endogenously adjustment interest rates, targeting debt-to-equity ratios, and full-filling other conditions, for example, those introduced by the Basel accords. Similarly the government is an active player in the economy, making consumption and investment decision, employing households. The government can formulate cyclical or counter-cyclical policies, and can have deficit targets (e.g. the Maastricht Treaty in the EU). The central bank issues (exogenous or endogenous) money, sets the interest rates, and supports with monetary policies.

SFC models, in terms of complexity, are somewhere between few equation analytical models and large agent-based models. These meso models are complex enough to incorporate different institutional structure but simple enough to still have analytical solutions. This is highly useful to understand multiplier effects of certain policies and how they pan out across the different state variables.

In my own work with colleagues, SFCs have now been expanded into dealing with input-output structures, forward-looking expectations, and multi-region models. This page will be updated to showcase the set up of each of these frameworks.

Where does the ecological part come into play here?

Here were start with the standard assumption that in order to produce goods, one needs labor (\(L\)) and capital (\(K\)). And on top of this, one also needs energy (\(E\)) and materials (\(M\)). All together, the production function of an economy is defined as \(Y = f(K,L,E,M)\). If anyone of these inputs is missing, output cannot be produced. Each input can also be assumed to have a productivity level. Over time, as technologies develop, or more R&D-type resources are diverted towards a certain inputs become more efficient. Whether we assume these technologies to be exogenous or endogenous (following the logic from Acemoglu’s directed technological change paper), we can safely assume that technology functions are competing with each other. For example, investing in labor-saving technology will reduce the demand for labor, similarly, higher green R&D expenditure will make green energy more feasible. Can we deal with four inputs with a standard CES-like production function? Maybe through nested function but unlike IAMs or other climate models, SFC are not used for infinite horizon forecasts. They tend to take a 50-100 year time framework and therefore start with a baseline share of complementary inputs based using actual data, where their respective productivity levels can be made endogenous through endogenous. But how do firms decide between inputs? For example between green and brown energy? Here we go back to Tobin’s portfolio choice setup. Each energy-type has a baseline demand calibrated from data. In addition to this, we assume that input demand can deviate from the baseline based on various signals like prices, changes in expectations, elasticity of demand etc. This choice matrix has to be zero-sum. An increase in demand for one input needs to be fully counter-balanced by a decline in demand of another input. Therefore by manipulating the signals, one can change the direction of the demand.

The next part is the the environment part. Economic activity results in emissions or \(Emm = f(Y)=f(f(K,L,E,M))\). The source of emissions and how they are generated can be expanded to include a host of factors, but the core assumption is that there is an emmission intensity parameter (equivalent to productivity) that also evolves over time. In such a framework, one can study the impact of climate policies on emission reductions in levels or intensity terms or go in the direction of DICE-like models to conduction a cost-benefit analysis with damage functions (following from Nordhaus’ DICE logic), where output is endogenous to emissions. For example, emission levels can impact capital stock through higher depreciation, or labor stock through lower productivity.

Expanding the models

  • SFC-IOs: SFC models can be expanded to include input-output (I-O) structures. Within this framework policies can have non-trivial consequences through the intermediate demand input-output matrix and the final demand. This goes a step further than classic I-O models where parameters are assumed fixed, and for example, do not accomodate endogenous changes in demand levels resulting from policy-led supply or price shocks.

  • Two-region or multi-region models: Multi-region models, combined with I-O structures can provide a rich and tractable framework for value chain analysis. For example, in an upcoming paper we explore the role of unilaterial climate policies inside the EU on trade and emissions outside the EU.

  • Forward-looking expectations: A key issue of post-Keynesian models, when dealing with climate topics is that they usually assume adaptive expectations (or past behavior informs current decisions and some forward looking expectations). This can be constraining especially when analyzing policies that will be implemented in the future. For this we need to assume that some agents will adapt and change their behavior now in anticipation of future policies. For example banks might change lending behavior to brown firms if they know that brown firms will be taxed higher in the future resulting in lower profitability. These “forward-looking” climate sentiments have been explored in Dunz et. al. 2021 (JFS), where we model and discuss the orderly versus disorderly transitions in the banking sector.

Selected papers and reports

Dunz, N., Naqvi, A., Monasterolo, I. (2021). Climate Transition Risk, Climate Sentiments, and Financial Stability in a Stock-Flow Consistent approach. Journal of Financial Stability. DOI: https://doi.org/10.1016/j.jfs.2021.100872.

Naqvi, A., Stockhammer, E. (2018). Directed Technological Change in a Post‑Keynesian Ecological Macromodel. Ecological Economics 154 (164–188). DOI: https://doi.org/10.1016/j.ecolecon.2018.07.008

Brüning, L., Naqvi, A. (2018). Automation in an aging EU society: Effects of demographic and technological change on pensions in a Stock-Flow Consistent Framework. Draft.

Jackson, T., Victor, P., Naqvi, A. (2015). Towards a Stock-Flow Consistent Ecological Macroeconomics, ESRC Passage Working paper Series 15-02.

Naqvi, A. (2015). Modeling Growth, Distributions and the Environment in a Stock‑flow consistent Framework. WWWforEurope Policy Paper 18.