The universal shape of economic recession and recovery after a shock

📝 Abstract

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect large and small shocks, including those which do not lead to a recession; we also discuss its predictive power. Finally, a two-sector toy model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy.

💡 Analysis

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect large and small shocks, including those which do not lead to a recession; we also discuss its predictive power. Finally, a two-sector toy model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy.

📄 Content

arXiv:0802.2004v5 [q-fin.GN] 22 Aug 2009 The universal shape of economic recession and recovery after a shock∗ Damien Challet1,2, Sorin Solomon3,2 and Gur Yaari3,2 1 D´epartement de Physique, Universit´e de Fribourg, P´erolles, 1700 Fribourg, Switzerland 2 Institute for Scientific Interchange, via S. Severo 65, 10113 Turin, Italy 3 The Racah Institute of Physics, Hebrew University, Jerusalem, 91905, Israel October 22, 2018 Abstract We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect large and small shocks, including those which do not lead to a recession; we also discuss its predictive power. Finally, a two-sector toy model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy. keywords: Economic growth, GDP, shocks, response function, modelling, predic- tion, optimal policy JEL: C32, O23, O41 ∗We thank Vladimir Popov and Paul Ormerod for their public comments, and David Br´ee for his critical reading of the first version of this manuscript. This work has been supported in part by the EU projects DAPHNet (ICT grant 018474-2) and CO3 (NEST grant :12410) 1 1 Introduction Explaining growth and recessions has been central to Economics ever since its begin- ning (Quesnay 1888; Smith 2000; Ricardo 2004; Keynes 2007; Solow 2000; Schumpeter 1980; Romer 1990; Robbins 2000). Since recessions and subsequent recoveries are usually split into distinct episodes in economic analysis, the factors of decline and growth have been investigated separately (e.g. Popov (2006); Kolodko (2000); Cernat (2002)) and little attention has been devoted to the intrinsic relationship between reces- sion and recovery. Here we argue that

1. recessions and their subsequent recoveries can be fitted rather well by a single 3-parameter function that contains both the recession and the recovery parts. It assumes that during recession-recovery periods, at any time a fraction of the economy is shrinking exponentially while the rest is growing exponentially. As a consequence the two parts of the GDP curve are intrinsically linked and cannot be considered as separate events. In particular, we show why this yields much better estimates of the decaying and expansion rates.
2. The shape of this function is the simplest one that respects the underlying eco- nomic process: economic activity grows and shrinks exponentially. A more complex superposition of exponentials or non-constant parameters is of course possible, as discussed below.
3. It is valid as long as no other shock occurs, thus can be used a contrario to sepa- rate a GDP time series into episodes of economic growth, providing a factinating new way of reading the fluctuations of GDP time series, even outside times of recessions. This leads to the conclusion that this model is in fact the response function of the economy as a whole to rare negative shocks, both exo- and endo- geneous. In section 2, we consider the yearly evolution of countries having experienced last- ing recessions others than those due to wars, which include many of the former com- munist block economies following their liberalisation. We find that our “universal recession-recovery shape” fits all of them well between shocks and that each additional shock brings a new episode fitted by our equation. Its accuracy, and in particular, the smooth shape of GDP evolution between shocks it implies, is confirmed to a high de- gree by quarterly data for Finland and the United Kingdom. We illustrate how this equation can be used to detect additional shocks automatically. In section 3, as a theoretical exercise, we introduce a simple two-sector model of growth with economic transfer. We also discuss why a simple two sector model is able to reproduce faithfully the typical global dynamics of recession-recovery. Then we exploit this understanding in order to find an effective transfer rate that minimises the depth and duration of the recession, and maximises both the GDP value and the final growth rate. We finally propose a means to differentiate static from dynamical effective policies in historical data. 2 Data analysis The economic activity of many countries shows dramatic and sudden decreases fol- lowed by a slow road to recovery, a pattern commonly known in Economics as L, U or 2 1990 2000 80 100 120 140 160 Albania GDP 1990 1994 1998 95 100 105 110 115 120 Bahamas 1995 2005 80 100 120 140 Belarus 1985 1995 90 100 110 120 130 140 Bolivia 1985 1995 80 100 120 140 160 180 200 220 Chile 1990 2000 80 100 120 140 Estonia GDP 1990 2000 90 100 110 120 130 140 Finland 1990 2000 80 90 100 110 120 130 Hungary 1990 2000 60 70 80 90 100 110 120 K

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