K+S Schumpeter-Keynes Growth ABM Model

Standard growth theory treats technological change as either exogenous (Solow 1956) or as a smooth aggregate process (Romer 1990, Aghion-Howitt 1992). The K+S model family rejects both simplifications. Productivity growth emerges bottom-up from heterogeneous capital-goods firms investing in R&D, occasionally discovering better production techniques, and diffusing those techniques through the economy via machine purchases by consumption-goods firms. Nelson and Winter (1982) laid the evolutionary foundation: firms follow routines, innovate stochastically, and are selected by the market. Dosi, Fagiolo, and Roventini (2010) built the first full K+S model by marrying this Schumpeterian supply side with a Keynesian demand side where aggregate demand fluctuations generate recessions, hysteresis, and coordination failures that purely supply-driven models miss entirely.

The core mechanism has two legs. On the supply side, capital-goods firms allocate a fraction of revenue to R&D. Each R&D draw is a stochastic search over a technology space: with some probability the firm discovers a machine embodying higher labor productivity, and with some probability it successfully imitates a competitor's technology. These innovations propagate to consumption-goods firms when they purchase new capital vintages. On the demand side, consumption-goods firms set prices, hire labor, produce output, and face an uncertain demand signal. When aggregate demand is insufficient - because wages are too low, credit is too tight, or expectations are too pessimistic - firms cut production and fire workers, which reduces income and demand further. The interaction between these two legs is the model's distinctive contribution: a productivity-enhancing innovation wave can be choked off by a demand contraction, and a demand boom can pull forward the adoption of better technologies that would otherwise sit unused.

The K+S line has been developed largely at the Sant'Anna School of Advanced Studies in Pisa, and it has reached European policy debate mainly through EU-funded research consortia (for example the H2020 ISIGrowth project on innovation-fuelled, sustainable and inclusive growth) and through publication in policy-facing outlets. Claims that a particular statistical agency or Commission service has adopted a K+S model operationally circulate widely but are not documented in the model papers themselves; check them against the institution's own publications before repeating them. Within the academic line, the model has been extended to credit and fiscal policy (Dosi et al. 2013), fiscal and monetary policy with an endogenous banking sector (Dosi et al. 2015), labor market regulation (Dosi et al. 2017), inequality (Dosi et al. 2018), climate transition (Lamperti, Dosi, Napoletano, Roventini and Sapio 2018), and trade. It is one of the most cited macro ABM families in the literature, with the 2010 paper alone exceeding 1,000 citations.

The model has evolved through several generations. The original K+S (Dosi et al. 2010) had two industrial sectors, no government and no bank. Dosi et al. (2013) added the credit market, a government running fiscal policy with automatic stabilizers, and the income-distribution block linking firm markups to household incomes. Dosi et al. (2015) added an explicit banking sector with endogenous credit creation and a central bank following a Taylor-type rule - that is where monetary policy enters the family, not in 2013. Dosi et al. (2017) added a labor market with search-and-matching frictions and wage bargaining, and Dosi et al. (2018) sharpened the inequality channel. The frontier includes a climate extension with carbon taxes and directed technical change (Lamperti, Dosi, Napoletano, Roventini and Sapio 2018), an international trade version with two-country dynamics, and experiments with alternative expectation formation rules including machine-learning-based heuristics.

The economy is built from two industrial sectors plus supporting institutional agents. Sector 1 contains F1 capital-goods firms (typically 50 in calibrated runs, 10-20 in toy models). Each capital-goods firm invests in R&D, searches for innovations and imitations, and sells machines embodying specific labor productivity levels to consumption-goods firms. Sector 2 contains F2 consumption-goods firms (typically 200 in calibrated runs, 30-50 in toy models). Each consumption-goods firm buys machines from Sector 1, hires workers, produces a homogeneous consumption good, sets prices via a markup rule, and competes for market share based on price and unfilled demand. A population of L workers (typically 1,000-5,000) supplies labor to both sectors, earns wages, and consumes. A banking sector provides credit to both firm types subject to capital adequacy constraints. A government collects taxes, pays unemployment benefits, and may run fiscal policy. A central bank sets the policy rate.

Interaction runs through five channels. The technology channel connects Sector 1 to Sector 2: when a capital-goods firm innovates, it offers a better machine vintage; when a consumption-goods firm invests, it replaces old machines with new ones, raising its plant-level productivity. The demand channel connects household income to firm revenue: aggregate consumption depends on the wage bill plus transfers minus saving, and each firm's revenue depends on its market share. The credit channel connects bank balance sheets to firm investment: firms with insufficient internal funds borrow from banks, and banks ration credit based on firm leverage and their own capital position. The labor market channel connects firm production decisions to employment and income: firms hire when expanding and fire when contracting, and the wage adjusts to labor market tightness. The selection channel connects firm profitability to market structure: unprofitable firms shrink and eventually exit, replaced by entrants drawing from the current frontier technology.

State variables update each period in a fixed sequence. Capital-goods firms perform R&D and update their machine catalog. Consumption-goods firms form demand expectations, plan production, determine labor and investment demand, and place machine orders. The credit market clears: banks evaluate loan applications and allocate credit. The labor market clears: firms hire or fire workers, and wages adjust. Production occurs. The goods market clears: output is sold, revenues are realized, and market shares are updated based on competitiveness. Profits are computed, loans are serviced, taxes are paid, and government transfers flow. Entry and exit occur for firms below a viability threshold. Aggregate statistics are recorded. This fixed ordering is essential: it determines the propagation sequence from an innovation shock through the technology channel, demand channel, and selection channel to the aggregate growth path.

Dosi et al. (2015) used the K+S model with a fiscal policy extension to evaluate the impact of austerity versus stimulus during recessions. The model showed that fiscal consolidation during a demand downturn amplifies the recession by reducing household income, cutting aggregate demand, suppressing investment, and slowing the adoption of new machine vintages - creating a negative feedback loop between demand and productivity growth. Fiscal stimulus, by contrast, sustained demand during the trough, preserved investment spending, and allowed the economy to resume its innovation-driven growth path faster. The K+S result here is directional rather than numerical: the multiplier is larger in slumps than in booms. That sign pattern lines up with the state-dependent multiplier evidence in Auerbach and Gorodnichenko (2012), whose econometric estimates put the recession multiplier well above one and the expansion multiplier near or below one-half. Those magnitudes are the empirical estimates, not K+S output - the model was not calibrated to reproduce them, and quoting them as K+S results misattributes the source.

The K+S model has been applied to labor market policy (Dosi et al. 2017), comparing the effects of different firing-cost regimes, minimum wage levels, and unemployment benefit generosities on growth, unemployment, and inequality simultaneously. The key finding is that moderate labor market protections can improve long-run growth by stabilizing demand during downturns and sustaining the wage-consumption channel, while excessive flexibility increases precarity, suppresses demand, and paradoxically reduces the innovation adoption rate. This challenges the orthodox view that labor market deregulation unambiguously improves growth. Lamperti, Dosi, Napoletano, Roventini and Sapio (2018) extended the model into a climate-economy integrated assessment model (the Dystopian Schumpeter meeting Keynes, or DSK, model) to study green transition policy: carbon taxes combined with directed R&D subsidies toward clean technologies produce a faster transition than carbon pricing alone, because the subsidy accelerates the Schumpeterian search process in the clean-technology space.

The model breaks down in several identifiable situations. Pure supply-side growth questions where demand is always sufficient (e.g., long-run convergence dynamics across countries) are handled more transparently by Solow or endogenous-growth models because the K+S demand side adds complexity without changing the answer when demand is not the binding constraint. Short-run forecasting is not a strength: the model produces distributional predictions (probability of recession, range of growth outcomes) rather than point forecasts, and its calibration procedure targets long-run moments rather than quarter-ahead accuracy. Micro-level firm dynamics (entry/exit rates, size distributions, patent citation networks) are better handled by purpose-built IO models because the K+S firm sector, while heterogeneous, is still relatively coarse compared to models designed specifically for firm-dynamics questions.