Abstract
This paper estimates the cost of the lockdown of some sectors of the world economy in the wake of COVID-19. We develop a multi sector disequilibrium model with buyer-seller relations between agents located in different countries. The production network model allows us to study not only the direct cost of the lockdown but also indirect costs which emerge from the reductions in the availability of intermediate inputs. Agents determine the quantity of output and the proportions in which to combine inputs using prices that emerge from local interactions. The model is calibrated to the world economy using input-output data on 56 industries in 44 countries including all major economies. Within our model, the lockdowns are implemented as partial reductions in the output of some sectors using data on sectoral decomposition of capacity reductions. We use computational experiments to replicate the temporal sequence of the lockdowns implemented in different countries. World output falls by 7% at the early stage of the crisis when only China is under lockdown and by 23% at the peak of the crisis when many countries are under a lockdown. These direct impacts are amplified as the shock propagates through the world economy because of the buyer-seller relations. Supply-chain spillovers are capable of amplifying the direct impact by more than two folds. Naturally, the substitutability between intermediate inputs is a major determinant of the amplification. We also study the process of economic recovery following the end of the lockdowns. Price flexibility and minor technological adaptations help in reducing the time it takes for the economy to recover. The world economy takes about one quarter to move towards the new equilibrium in the optimistic and unlikely scenario of the end of all lockdowns. Recovery time is likely to be significantly greater if partial lockdowns persist.
Introduction
In February-March 2020 the world economy entered uncharted territory. Never before has an economy as interlinked as the present system been subject to shocks as large as the lockdowns in the wake of COVID-19. Already in March with the lockdown of China alone, Indian pharmaceutical companies began to struggle as they procure more than 70% of active pharmaceutical ingredients from sellers located within the geographical boundries of China (Chatterjee 2020). Matters are not very different in the US and other parts of the world. In a recent survey conducted by the US based Institute for Supply Management, nearly three quarters of the respondents said they had experienced supply chain disruptions (Zeiger 2020). Similarly, Hassan et al. (2020) in a study of the earning calls of more than 12,000 publicly listed companies based in more than 70 countries find that supply chain disruption has become one of the primary concerns of firms around the world. Interestingly enough the stock markets have responded more to COVID-19 than to the Spanish Flu which killed rough 2% of the world population (Barro et al. 2020). Baker et al. (2020), among others, have argued that the sizeably greater response of stock markets to COVID-19 may have something to do with the greater interlinkage of the global economy coupled with the supply-chain disruption caused by the lockdowns. In this paper, we use an agent-based model of out-of-equilibrium economic dynamics to analyze the propagation of the lockdown shocks through input-output linkages. And on this basis assess the short-term costs of the COVID lockdowns.
Our model builds on Gualdi and Mandel’s (2016) agent-based extension of Acemoglu et al.’s (2012) equilibrium production network model. We study the out-of-equilibrium dynamics of the system by unbundling a sequence of decisions which are assumed to occur contemporaneously in equilibrium models. This out-of-equilibrium approach allows us to characterise relative price deviations, spill over of excess demands from one market to another, and non-linear paths of sectoral and aggregate recovery after an exogenous shock. Note that within such a general disequilibrium setting, prices at each time step are not generated by a Walrasian auctioneer who considers the inter-relations between all markets. Rather prices emerge from the interactions between agents who act as buyers in their input market and sellers in their output market. These decentralized interactions mean that the system can be out-of-equilibrium for a substantial period of time. Furthermore, the spill over of excess demands from one market to another is a major source of the disruption of the economic system and therefore an important determinant of the cost the lockdown. Within our setting, the propagation of the lockdown shock through the system generates miscoordination as firms no longer combine inputs in proportions determined by equilibrium prices. The economy suffers not only from the shortage of intermediate inputs but also because inputs are not combined in equilibrium proportions. This is not because firms do not minimise costs, they do, but because firms face disequilibrium prices using which they minimize costs. The propagation of disequilibrium prices and the miscoordination it generates are an important determinant of the cost of the lockdown. It is likely therefore that equilibrium models which ignore such dynamics understate the cost of the supply-chain disruptions.
We calibrate our model to the world economy using the World Input-Output Table with 56 sectors in 44 countries (Timmer et al. 2015). We initialise the world economy by setting all variables to their equilibrium values corresponding to the primitives defined by the input-output relations, the exponents of the production functions, and other parameters. We then shock the equilibrated system with the temporal sequence of the lockdowns observed in the real world using publicly available information on the start and end dates of the lockdown. We therefore have two distinct lockdown periods. The first of which extends from February 1 to March 15 and the second of which begins on 15 March. Most world economies enforced a lockdown within the first 10 days of the second period, with the lockdown duration ranging from 40 to 60 days. Note that the lockdown policies were not homogeneous in their sectoral composition. Many countries distinguished between essential and non-essential services, allowing some sectors to operate at reduced capacity, while others were completely shutdown. We shock the equilibrium world economy using a sectoral decomposition of lockdown provide by the IFO-Institute (2020). We then study the geographical and sectoral propagation of the lockdown shocks using computational experiments on our calibrated model economy. We compute not only the direct cost of the lockdown but also the indirect costs which emerge from supply-chain disruptions. Our estimates suggest that the indirect costs can be roughly equivalent to the direct costs, with the relation between two being mediated by the degree of substitutability between intermediate inputs. An economy with high complementarity between intermediate inputs will suffer more from supply-chain disruptions than an economy with high substitutability.
The role of price flexibility is limited because the major hurdle faced by firms is sizeable reductions in the availablity of inputs, with few input producers being in a position to respond to the price changes by producing more. Our estimates suggest that the lockdown reduces global output by about 33% at the peak of the lockdown, with the yearly impact being more than 9% of annual GDP.
The remaining of the paper is organized as follows. Section “Related Literature” reviews the related literature. Section “The Model” introduces the model. Section “Shock Propagation in the Global Economy” presents the results of our analysis of the COVID lockdowns. Section “Concluding Remarks” concludes the paper.
Related Literature
The Literature On The Economics of COVID
The sheer size of market responses to the pandemic itself and the lockdowns in its wake has motivated a growing literature on the economic impact of the lockdowns (Gormsen and Koijen 2020; Alfaro et al. 2020). The models used in the literature can be divide into three classes. The first class of models study the direct impact of COVID and related lockdowns, but ignore indirect effects that emanate from supply-chain relations. The second class of models study the direct and indirect impact within an equilibrium framework. They do not consider temporary relative prices effects and overshooting of some sectors in the disequilibrium dynamics that are likely to follow the lockdown. The third class of models study the direct and indirect effect within a framework general enough to incorporate disequilibrium dynamics. Each class of models can be further subdivided into those calibrated to national economies and those which consider world input-output relations. They can also be subdivided based on whether they are solely economic models or economic models embedded within an epidemiological model. Needless to say, not all models fit neatly into one of the three classes.
Several economists have developed models that fall roughly within the first class. They are not high dimensional in terms of the sectors they consider but attempt to present a rough but useful estimate of the direct cost of the lockdown. Bodenstein et al. (2020), for instance, combine an epidemiological model with a two sector model of the US economy. Similarly, Toda (2020) combines an SIR model with a standard asset pricing model to predict the decline in stock prices. Bayer et al. (2020) use a model with a handful of different kinds of firms to study the multiplier associated with the fiscal spending by various governments in response to the COVID slowdown. Fornaro and Wolf (2020) study the effectiveness of macroeconomic policy using a New Keynesian model which represents the global economy as a single production unit. And del Rio-Chanona et al. (2020) study the direct impact of the lockdowns without analysing supply-chain disruptions.
The second class of models, i.e. those that study indirect network effects, have fewer inhabitants than the first. Walmsley et al. (2020) use a computable general equilibrium model to estimate the cost of the lockdowns for the US economy. They consider the supply chain within the US but ignore international buyer-seller relations. The World Bank (2020) too uses a computable general equilibrium model to study the impact on Africa. Barrot et al. (2020) study the fall in GDP because of social distancing policies by considering direct and indirect impacts. They calibrate their model to granular data on France and more coarse data on Europe. These equilibrium production network models are closely related to recent work on the role of buyer-seller linkages in amplifying supply shocks (Carvalho et al. 2014; Barrot and Sauvagnat 2016; Boehm et al. 2019).
And then there are a handful of models which fall between the second and the third class. Inoue and Todo (2020) presents one such model. They extend and calibrate Hallegatte’s (2008) input-output model to study the impact of the shutdown of Tokyo on the Japanese economy. Inoue and Todo’s (2020) simulations suggest that though Tokyo accounts for roughly one fifth of the national output, its lockdown would generate a four fifths reduction in Japanese output. Inoue and Todo’s (2020) approach is similar to that of the Asian Development Bank (2020), which studied the supply-chain impact of COVID lockdowns using their Multi Regional Input-Output Table (MIROT) model. These models do not assume equilibrium but neither do they explicitly characterise the out-of-equilibrium dynamics which emerge from inter-related microeconomic decisions in response to exogenous shocks.
Out-of-Equilibrium Equilibrium Models
From a theoretical and technical point of view our paper is closely related to older work on disequilibrium multi market models which study the dynamic properties of input-output systems (Jorgenson 1961). Barro and Grossman’s (1971) pioneering paper on general disequilibrium sparked a whole literature on understanding the dynamic properties of adjustments within a network economy. Some of these contributions are worth mentioning in the light of their significance in analyzing COVID dynamics. Benassy (1975) developed a model with decentralized trades in a money using economy with arbitrary many markets. He intended to develop something comparable to the Arrow-Debreu system in its generality. Green and Laffont (1980) developed a model of disequilibrium inventory dynamics with a single storable output, money, and labor. Other important contributions include those by Rosen and Nadiri (1974), Sharp and Perkins (1977), and Muellbauer and Portes (1978). These contributions study how excess demand spills over from market to another. Overall, this literature generalized Leontief’s (1941) classic treatment of the structure of the American economy. Our model in essence is yet another step towards realizing the goal of developing a general disequilibrium model which in its treatment of prices, quantities, input combinations, and ultimately the network structure itself is able to complement equilibrium analysis on an equal footing.
Our contribution also related to recent work that uses agent-based models to analyze economic dynamics out-of-equilibrium. Numerous economists have used agent-based models to investigated the propagation of shocks in stylized models of the economic system (Gatti et al. 2005; Weisbuch and Battiston 2007; Battiston et al. 2007). Economists before us have also developed empirically grounded agent-based models to analyse middle to long term impacts of policy on economic growth (Dosi et al. 2013; Dawid et al. 2014). And more recently, agent-based models have been used to analyze potential economic impacts of climate change (Lamperti et al. 2019). Our paper adds to this literature by providing an agent-based analysis of the short-term impact of economic shocks in a fully calibrated model at a higher level of granularity.
Ultimately, the question of equilibrium versus disequilibrium models must be settled empirically. In so far as the economic system is sufficiently close to equilibrium, there are good reasons to use equilibrium models not the least of which is their analytical tractability, and the consistency between micro decisions and macro states. In certain circumstances however the economy may be far from equilibrium at least for short periods of time, in which case general disequilibrium models are more suitable. Symptomatic evidence suggests the world economy has been jolted away from equilibrium by the COVID lockdown shocks. Financial markets have exhibited aberrant and volatile behaviour with the VIX index close to historic highs (Gormsen and Koijen 2020). And reported unemployment in the US and Europe have witnessed an unprecedented jump (Bernstein et al. 2020). These indicators suggest we are not in normal times. While there are no econometric studies yet to sort between equilibrium and disequilibrium models of the COVID lockdown, an older generation of econometric studies suggest several parts of an economy can remain out-of-equilibrium for more than a quarter in response to exogenous shocks (Boschen and Grossman 1982; Rudebusch 1989), including credit markets (Takatoshi and Ueda 1981), labor markets (Rosen and Quandt 1978), housing markets (Fair and Jaffee 1972; Riddel 2004), and the market for industrial output (Seiichi et al. 1982). None of this is to suggest that it is trivial to econometrically distinguish between equilibrium and disequilibrium states (Quandt 1978; Ito 1980; Gourieroux and Monfort 1980), but that there are sufficiently good reasons to attempt to do so.
The Model
General Equilibrium Framework
We represent the world economy as a network of input-output relationships embedded in a general equilibrium model as in Acemoglu et al. (2012). The economy consists of K countries, each comprising of the same L industries. The model is calibrated to the world economy using the world input-output database (Timmer et al. 2015), which provides input-output relationships between L = 56 industries in K = 44 countries. The data set includes all major economies and a composite country representing the rest of the world. Within our model, each industry of each country is represented as one monopolistically competitive firm. Each of the K countries also has two representative households, which are differentiated by the source of their revenues. The workers’ representative household receives the labor share of value-added from each domestic sector, while the capitalists’ receives the capital share.
