Non-equilibrium dynamic models and impacts Patrice Dumas (CIRED,CIRAD) Stéphane Hallegatte (World Bank) Michael Ghil (ENS, Paris, & UCLA) Workshop on Coupled Climate-Economics Modelling and Data Analysis November 2012 ENS, Paris

Outline Endogenous business cycles Dynamics of reconstruction and extreme events economic consequences

Endogenous business cycles

A tale of two theories: the "real" cycle and the endogenous cycle theories In the real cycle theory, fluctuations from exogenous "real" (i.e. not monetary) shocks (changes in productivity or in energy prices, fiscal shock). Aside from exogenous shocks, the economic system is stable: – all markets are at equilibrium, no involuntary unemployment – Deviation from equilibrium are damped more or less rapidly – Acting on the economy (recovery policy), is not usefull In endogenous business cycle (EBC) models, cyclical behavior originates from endogenous instabilities in the economic system Several instabilities have been proposed: · profitability-investment instability · delays in investment · income distribution Acting on the economy can have positive effects, stabilizing it or shifting its mean state.

NEDyM (Non-equilibrium Dynamic Model) Represents an economy with one producer, one consumer, one goods that is used both to consume and invest. Based on the Solow (1956) model, in which all equilibrium constraints are replaced by dynamic relationships that involve adjustment delays. The NEDyM equilibrium is neo-classical and identical to that in the original Solow model. If the parameters are changing slowly, NEDyM has the same trajectories as the Solow model. Because of market adjustment delays, NEDyM model dynamics exhibits Keynesian features, with transient trajectory segments, in response to shocks. NEDyM possesses endogenous business cycles! Hallegatte, Ghil, Dumas & Hourcade (J. Econ. Behavior & Org., 2008)

Hopf bifurcation: from stable equilibrium, to limit cycle, to chaotic behavior

 inv = 1.7 (purely periodic)  inv = 2.5 transition to chaos (irregular behavior)

 inv = 10 irregular orbit (kinky torus)  inv = 20 very asymmetric business cycle (relaxation oscillation)

Endogenous dynamics: an alternative explanation for business cycles

Interpretation of the instability Business cycles originate from the profit-investment relationship (oscillations with a 5.5-year period) higher profits > more investment > larger demand > higher profits Business cycles are limited in amplitude by three processes: Increase in labor costs when employment is high Constraints in production and the consequent inflation in goods prices when demand increases too rapidly Financial constraints on investment

Main flaw in the model business cycle: the amplitude of price oscillations

Correction: accounting for quantities in behavioral equations

Calibration of NEDyM Need to calibrate the endogenous business cycle Kalman filter shows good result on « identical twins » experiments But much harder on real data => start from a representative cycle?

Economic consequences of extreme events

Direct vs indirect losses Direct losses: Casualties and injuries Direct economic losses (i.e., value of what has been destroyed or damaged) Indirect losses: –(1) Business interruption, supply-chain disruption, and propagations –(2) Lost production during reconstruction –(3) Demand surge and increased reconstruction costs –(4) A macro-economic feedback? –(5) Long-term consequences on economic growth Other costs: Emergency costs (Katrina: $8 billion) Political destabilization Psychological trauma and social network disruption Long-term impact on specific sectors (e.g., tourism)

Business interruption and propagation data from the Northridge earthquake in 1994 From Tierney (1997) Survey by the Disaster Research Center, at the University of Delaware. Conducted with a representative, randomly-selected sample of businesses (1100) in the cities of Los Angeles and Santa Monica, two jurisdictions that were particularly hard-hit by the earthquake Businesses with no damages had to close because of propagations, making the total cost larger. Data on the Northridge earthquake

Demand surge and reconstruction costs from the 2004 and 2005 hurricane seasons Definition: “a temporary increase in repair costs above the standard level of costs due to the lack of qualified workers or materials” Data from XActimate and Risk Management Solutions

A macroeconomic feedback ? Supported by (rough) data on demand surge The demand surge remained limited after Andrew (20%). This might be explained by the pre-existing economic situation:

How to model extreme events consequences? Natural disasters are a series of shocks that destroy capital, leading to a disequilibrium Preexisting disequilibrium may be important Using a classical production function is problematic as there are no decreasing returns on capital hit by a disaster Accounting for financial and technical constraints on the reconstruction pace is necessary to reproduce the observed response to past disasters over the short term

Extreme event economic consequences modelling From Hallegatte et al. (2007, Ecological Economics) The total cost of an event depends on the reconstruction capacity of the economy.

Interaction between intrinsic dynamics and shocks (1) From Hallegatte and Ghil (2007)

Interaction between intrinsic dynamics and shocks (2) From Hallegatte and Ghil (2007) Limited losses if the disaster affects an economy in recession

Interaction between intrinsic dynamics and shocks (3) From Hallegatte and Ghil (2007) Large losses if the disaster affects an economy in expansion A vulnerability paradox: growing economies are more vulnerable !

Consequences of extreme events Here also, the average loss depends on the event characteristics and on reconstruction capacity

Natural disasters and bifurcation in losses The impact of a series of events is not the sum of the event impacts. Index of disaster frequency and intensity Index of reconstruction capacity

Positive feedbacks and poverty traps Limited economic development Limited reconstruction capacity Large cost of natural disasters Impossibility to increase the infrastructure and capital stocks Long reconstruction period after each disaster « Positive » feedback Possibility of poverty trap Disasters can be a significant obstacle to economic growth and development

Reconstruction and endogenous technical change Accounting for endogenous technical change changes the consequences of disasters: If reconstruction uses the best available technologies (EN), endogenous technical change reduces the negative consequences of disasters. But if reconstruction only replace the capital, using identical technologies (IM), then endogenous technical change amplifies the negative consequences of disasters

Technical change and a series of disasters If reconstruction uses the best available technologies (EN), the mean GDP losses due to a series of disasters are cancelled out. Otherwise (identical reconstruction, IM), mean GDP losses are increased.

Indirect costs in an input output approach Production changes in 15 sectors in Louisiana, in the Katrina’s aftermath, using the ARIO (Adaptive Regional Input-Output) Model. An input-output model of the local economy, with 15 sectors that interact with each other. We investigate the interplay of: (1)the decrease in production capacity due to damages; (1)the increase in demand due to reconstruction needs Direct losses: $107b Total losses: $135b Decrease in production capacity Boom in the construction sector

Nonlinear relationship between direct and indirect costs The boom in the reconstruction sector is limited by economic and technical constraints, and by damages, leading to a nonlinearity. In Louisiana, this nonlinearity appears when direct losses exceed $50 billion.

Sectoral results Employment losses per sector, data and model Underestimation in sectors with small businesses

Conclusion Non equilibrium economic model allows to represent some stylised facts on business cycles, but there is a need for calibration Constraints on reconstruction leads to realistic dynamics Smaller scales allow to understand the constraints