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- Social distancing and supply disruptions in a pandemic - PMC
Individuals in Group 1 provide labor services inelastically to firms in Sector 1. Individuals in Group 2 provide labor services inelastically to firms in Sector 2.
Individuals in groups 3 and 4, the young and the old, are not in the labor force. Final goods are produced with inputs from the two intermediate sectors with a constant elasticity of substitution function.
These inputs are imperfect substitutes for each other. In Sector 1, labor inputs are subject to a minimum scale requirement. This scale requirement is a simple way to capture the specialized skills of different workers, all of which are necessary to produce a certain product. Larger labor shortfalls make it more likely that production will be impaired by the absence of essential members of a team.
We abstract from modeling the interaction of capital with the labor input in Sector 1. We have in mind production structures in which capital cannot easily compensate for shortfalls in the labor input.
For example, if doctors and nurses do not show up for work, it seems unlikely that adjustments could be made to compensate for their absence. By contrast, with Sector 2, we are attempting to capture production processes in which the utilization of capital services can be more easily adapted, and in which labor inputs are more readily substitutable for capital services.
Households maximize consumption and supply two types of labor, l 1 , t and l 2 , t inelastically. The utility function of households is. Households choose streams of consumption, investment, capital, and utilization to maximize utility subject to the budget constraint. Households' utility maximization is also subject to the law of motion for capital, given by. Moving to the description of the production sector, firms in Sector 1 use labor l 1 , t to produce the good v 1 , t and charge the price p 1 , t.
The production function is given by. The dynamics of the epidemiological and the macroeconomic models are interwoven. On the one hand, the virus and mitigation measures—both spontaneous and mandated—directly reduce economic activity: Symptomatic sick individuals may not work. The labor supply may also decline if healthy individuals decide not to work either because of workplace closures or because of their own choosing to reduce their exposure to the virus.
Similar considerations can also precipitate a contraction in consumption. On the other hand, individuals' ability and willingness to engage in economic activity has direct implications for the spread of the virus.
People who, for whichever reason, work from home or not at all have fewer relevant contacts that could result in an infection. Under this law, the rate at which infective and susceptible individuals meet is proportional to their spatial density. We specify a mapping from spatial density to economic variables, which accounts for the fact that not all reductions in spatial density translate necessarily into a reduction of economic activity. Epidemiologists have carefully studied people's social contact patterns to understand the spread of infectious diseases.
Importantly, contacts differ by location and age. The POLYMOD study, one influential study of social contacts, allows to derive matrices for the contacts between the members of different age groups in four location settings: home h , school s , work w , and other o. Absent contact restrictions, the average contact matrix aggregated over locations satisfies.
Spontaneous and mandatory restrictions reduce social contacts through lowering spatial density. Consistent with the law of mass action, we assume the quadratic form. Equation 14 foreshadows our calibration assumption that contacts at home between family members cannot be reduced by mitigation measures. Of course, the economic costs can differ across types of restrictions.
Viruses mutate and they can become more or less contagious. Appropriate hygiene, masks, and keeping proper physical distance seem to lower the transmission risk according to the Center for Disease Control and Prevention. The transmission also appears to be higher indoors than outdoors; increased outside activity during the warmer months of the year may thus lower temporarily the transmission risk. Absent direct quantitative evidence how these factors affect the transmission risk, we shy away from specifying a functional form that describes the evolution of the transmission risk over time.
A pandemic may cause economic costs and disruptions through different channels. Our focus is on how infections and contact restrictions impair the labor supply—a key driver of economic activity. Specifically, we link the evolution of the labor supply explicitly to infections and contact restrictions using data on mobility and the ability to work from home. As the disease starts spreading, we assume that sick and symptomatic individuals that are in the resolving state, R j , t , do not work.
In addition, the labor force of each sector is reduced by deaths. We have already shown how spontaneous and mandatory restrictions reduce contacts; see equation Consistent with our focus on potential supply disruptions from the disease, we posit that contact restrictions directly relate to economic activity only by affecting the supply of labor services.
As defined earlier, r j , t w denotes the share of individuals in group j , that stop going to the workplace per effects of contact restrictions.
Now, not all work restrictions imply a fall in labor services, since some jobs can be carried out from home. Assuming that contact restrictions apply to all individuals in a group regardless of their health status, then the labor supply in sector j is given by.
In equation 15 , the contraction in the supply of labor services in addition to deaths is accounted for by three terms. The second and third terms net out individuals who are sick and symptomatic.
We then discuss our solution method. Note : This table summarizes the parameterization of the baseline integrated assessment model. Hence, after 10 about days, an individual either is cured or deceased. Again, we assume the probability of death to be identical across groups. We then combine the information on contact matrices with estimates for the reproduction number to obtain estimates for the transmission rate.
The POLYMOD study, funded by the European Union, aims to strengthen public health decision making in Europe through the development, standardization, and application of mathematical, risk assessment, and economic models of infectious diseases. Mossong et al. Prem, Cook, and Jit and Prem et al. Contacts in locations other than school, work, and home include contacts during commuting, shopping, and leisure activities. Other contacts account for an important fraction of total contacts only for the old.
To obtain an estimate of the transmission risk we use the contact matrices and estimates of the basic reproduction number. It is worth reiterating that the calibration of our SIRD model is daily. The relative sizes of the four groups are informed by the employment to population ratio, the age distribution of the U.
The employment shares reflect hours worked by industry in the productivity release of the BLS. The shares reported in the table are for , the latest year for which data are available at the time of writing. The unit of time for the economic model is set to 1 month. In line with the broad range in Altig et al. The Appendix discusses how our calibration of the scale parameters allows the model to match the observed collapse in economic activity when we feed into the model a series of labor supply shocks that replicates the reduction in labor inputs implied by the increase in unemployment from March through October , relative to the unemployment level in February In our model, the macroeconomic cost of inaction is driven by the reduction in the labor supply caused by the inability of symptomatic infective individuals to work until recovered.
To calculate the reduction in labor supply, we need to rely on an estimate of the asymptomatic infected individuals. A study of the passengers of the Diamond Princess cruise ship provides useful guidance. As reported in Russell et al. The asymptomatic share was also found to be different by age group. Given that labor supply is exogenous in our economic model, the fall in labor supply becomes more acute as the infective share increases.
When we study the effects of social distancing measures, we need to allow for the possibility that a fraction of the individuals subject to lockdown measures may still be able to work from home.
The survey also provides differential rates by industry. The solution method has three important characteristics: First, it allows for a solution of the SIRD model that is exact up to numerical precision; second, it conveys the expected path of the labor supply in each group to the economic model as a set of predetermined conditions, following the numerical approach detailed in the Appendix of Bodenstein, Guerrieri, and Gust ; and third, it resolves the complication of the occasionally binding constraints, implied by capital irreversibility, with a regime switching approach following Guerrieri and OccBin The modular solution approach has the advantage of allowing us to consider extensions of either module without complicating the solution of the other.
We are now ready to use our model. We carry out two main exercises. In a first exercise the next subsection , we show that labor supply disruption can go a long way to explain a contraction in output similar to the one experienced by the United States at the beginning of the pandemic.
To this end, we calibrate our model using mobility data and estimates of the share of workers that can work from home. In our second exercise, we repeat the analysis replacing the estimates of mobility with a lockdown, which we design drawing on the main lessons from our integrated model.
This is meant to highlight the potentially large economic consequences of the disease when its spread is unmitigated by any, spontaneous or mandatory, social distancing. We emphasize from the start that our main goal is assessing the economic consequences of potential supply disruptions from labor market shortages. However, a shock of the size and nature of a pandemic raises a unique set of questions concerning how the supply structure of an economy can continue to work when confronting an abrupt reduction in the scale of production.
This reduction is what our model is designed to capture. In this first set of simulations, our model tracks data on the observed reduction in mobility from the beginning of March through the end of October , together with labor market and occupational data.
Our goal is to bring our integrated model to bear on the estimated path of the reproduction rate over the same period. The figure also shows that the decline in workplace mobility was mirrored by an increase in the residential mobility measure from Google —basically proxying for the time spent at home. Note: The dips in workplace mobility at the end of May, beginning of July and end of September correspond to national holidays.
Their effects are prolonged by the moving average. Source: Google For our analysis, we need to map the decline in mobility into a reduction in contacts through the workplace and a reduction in labor inputs. Accordingly, we need to take a stand on the share of workers who continued to work from home. Overall, the evidence suggests that a large share of the workers who had the ability to work from home stayed at home.
In our simulations, we impose that the path of the reproduction rate implied by our simulations is close to realistic estimates of this rate. The panel clarifies that the mobility changes go a long way in capturing the empirically relevant reproduction rate. Dynamics in the SIRD model. Note: The paths shown are aggregates for the total population. The observed reproduction rate is used in the model simulations and to back out the paths in the bottom three panels.
The paths in the top panel are daily. All other panels show monthly averages of daily series. This assumption is buttressed by the reduction in nonwork mobility measures indicative of social distancing across different population groups. Moreover, in our simulations, we set school contacts to 0 from the beginning of April to the beginning of August, in line with the widespread school closures in the United States during this period.
It is worth reiterating here that mobility and contacts, however important, are not the only factors affecting the spread of the disease. The number of infected individuals reaches a peak in the second quarter. Even at this peak, however, the reduction in labor supply attributable to the inability to work of symptomatic infected individuals was too small to have a significant effect on the overall labor supply.
While both models have qualitatively similar implications for the course of economic activity, there is a marked quantitative difference. Both models predict large contractions—a significant share of the observed decline in GDP in the United States in the second quarter of which clearly reflects a number of other forces.
The rationale for this assumption is that the share of work from home is different across the two sectors. If we applied the mobility data homogeneously across sectors, the reduction in labor inputs would be heavily skewed toward the essential sector. By keeping the reduction in value added balanced across the two sectors, our distribution of labor cuts actually minimizes the drop in aggregate output—as a way to reduce the risk of overstating the incidence of supply shortages in disrupting economic activity.
In this section, we discuss how the tradeoffs between health and economic outcomes can be improved by adopting mandated social distancing measures that recognize the need to protect the core sector of the economy. In simulations that follow, changes in the reproduction rate from the initial level of 2 come about exclusively from the reduction in contacts implied by mandated social distancing measures.
For comparison, we also bring forward a scenario under a constant reproduction rate, that is, conditional on no social distancing. Indeed, in the absence of a clear understanding of the factors that could influence the transmission of the disease, early debates were sometimes conducted under the assumption that, absent policy intervention, the reproduction rate would stay constant at its initial level. However, our analysis draws on key principles that are also building blocks in optimal policy exercises.
Specifically, we consider policy measures that are meant to internalize the infection externality from individual interactions, not efficiently accounted for by optimizing individuals on their own see, e. To minimize the supply disruption of a lockdown, the health measures we consider in our experiment target first and foremost workers who are able to continue supplying their labor services from home. In our work, we further stress the indirect, potentially significant costs from supply constraints on the economy that follows a large contraction of the core sector.
Comparing these scenarios, the importance of smoothing out the peak of the infection curve is apparent. Key to this result is that, while the social distancing policy compresses the trough for value added similarly in both sectors, Sector 1 remains more active relative to the scenario without intervention.
Another notable result in the figure is that, independently of mandated social distancing measures, the pandemic has persistent economic consequences. These consequences reflect both the death toll on the size of labor force, and the fact that a smaller labor force leads to a persistent reduction in the productivity of the essential sector, weighing on final output, consumption, and investment—not only in the aggregate but also in per capita terms.
In sum, the key takeaway from our exercise is that lockdowns can be structured to reduce the risks of large supply disruption in the economy. In particular, lockdown policies should be stricter on workers in the noncore sector and nonactive population, and targeted specifically at workers who could reasonably keep performing their occupational tasks from home.
Such combination of measures is successful to the extent that they address the infection externality where it has more economic bite, that is, they keep the infection rate among the workers in core industries low.
The rest of this section uses the model to address the costs of a long lockdown put in place in view of the availability of a vaccine, including some sensitivity analysis motivated by the considerable uncertainty surrounding the parameters of the model. They hire starting at age Yes they hire you with a work permit.
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Retail positions you can apply at Starbucks are Baristas and Shift Supervisors. Starbucks also offers few internships, and they offer them to existing employees before the general public. People here are treated fairly regardless of their sex. On average, the treated city has a 2. The probability to exit, shown in Column 3 , is positive and significant. The estimate suggests treated cities experienced a 4. Finally, the result in Column 4 suggests treated cities have a lower probability to continue exporting to a foreign market.
Summing up, we find a significant negative effect of lockdown on the city's extensive margin of exports. The findings suggest our baseline results are robust. One key assumption in the DID identification strategy is the assumption of parallel trends: without a lockdown policy, the export of treated cities would have evolved in the same way as that of untreated cities.
This specification enables us to treat the coefficient estimates relative to a base month before lockdowns were enforced. The coefficients of interest are those on the interaction before the lockdown.
If trends are similar, the coefficient is small in magnitude and statistically insignificant. Before the lockdown, the coefficients are small in magnitude and statistically insignificant, suggesting trends were similar in treated and untreated cities. It is comforting that the average negative effects of the lockdown are only significant during the first three months after lockdowns were introduced.
Furthermore, there is a sign of recovery in the third month, April Event study of the lockdown policy. The omitted month before the lockdown policy is the benchmark. Source: Authors' calculations from China's Customs data [Color figure can be viewed at wileyonlinelibrary.
To alleviate this concern, we include prelockdown city characteristics interacted with time dummies to control for prepolicy differences in our baseline regressions see Lu et al.
Our results, with or without these additional controls, are qualitatively the same and comparable in magnitude cf. Table 1. The parallel trend test also appears satisfied. Nonetheless, to formally address this concern, we implement a propensity score matching procedure here.
In particular, we match a treated city with four control cities. If multiple potential matches have the same propensity score, we randomly choose one. Before doing the matching, we observe differences between cities that faced a lockdown and those that did not, namely in temperature, population size, economic development, and industry structure.
Yet, cities with and without a lockdown appear comparable in other dimensions, such as precipitation, export size, and distance to a port see Online Appendix Table D4. The results in Table 6 suggest that matching balanced the distribution of covariates in the two groups. Note: The nearest neighbor matching approach is used to match the treated cities with four control cities, and the t test results indicate that there are no significant differences in covariate means after the matching.
Table 7 gives the DID estimates using the matched sample. The coefficient for the interaction term is similar to the baseline results in magnitude and statistical significance. In Columns 1 and 2 , matched cities appear only once. In Column 3 we allow cities to appear more than once—for example, if a control city is matched with two cities that implemented a lockdown—resulting in a larger number of observations.
Findings in Column 3 indicate the main result still holds. So far, we considered the lockdown in several cities as an exogenous shock. This is plausible, as the Chinese government did not implement a lockdown during the SARS epidemic.
To alleviate the concern, we employ a 2SLS estimator, where we use the city's distance to Wuhan as an instrumental variable. Online Appendix B reports the implementation of the IV estimator. The IV results suggest lockdowns are associated with a This suggests the OLS estimate is possibly biased upwards towards a less negative effect.
More importantly, the results suggest a causal relationship between the lockdown and a slowdown in the city's export growth. This section provides further robustness checks of the main results. One potential concern is that the findings are driven by chance. Online Appendix C presents three placebo tests. In one placebo test, we randomly allocated 23 out of the cities to the treatment group, assuming these cities imposed a lockdown in February This suggests it is the lockdown rather than other confounders that drive our main results.
Next, we consider alternative measures to proxy for the stringency of the lockdown. Column 1 of Table 8 shows results if we consider the number of monthly newly confirmed cases. The virus is transmitted from person to person. Hence, once there is an infected case, residents living in the same building or even the whole community face restrictions in their movement. Thus new cases imply a strengthening in control and prevention measures, which are likely to slow down recovery in trade.
The coefficient of the interaction term is negative and significant, suggesting that newly confirmed cases are negatively associated with the city's export growth. Alternatively, Column 2 uses the total cumulative case load, and the results are similar. In another robustness analysis, we consider cities with a full lockdown, while relegating cities with a partial lockdown to the control group. The coefficient for the interaction term in Column 3 is statistically significant as before, and more importantly, it is larger in magnitude.
We also consider sensitivity of the results to excluding observations for Yunnan province, which only reports aggregate export data for the first 2 months of About one percent of the observations for the whole sample is dropped. The results are similar, see Column 4. To address this concern, we use alternative measures of our dependent variable, as well as alternative estimation methods. To facilitate these examinations, we treat a destination country reporting a positive export over our sample period as a potential foreign market, filling the trade matrix with zeros whenever the export value is missing.
The coefficient for the interaction term in column 1 of Online Appendix Table D3 is statistically significant and similar in magnitude to the baseline results. Second, following Bricongne et al. In Column 2 , the magnitude of the coefficient for the interaction term is again similar to the baseline and statistically significant. It is worth noting that the estimator precludes us to take the log difference of the outcome variable of interest, as the difference may lead to negative values for the dependent variable.
The coefficient on the interaction term is not directly comparable with our earlier results, still the results shown in Colum 3 of Online Appendix Table D3 confirm the baseline finding. This section offers suggestive evidence on the disruption.
We examine the role of the lockdown in restricting people's movements. Following H. Because the data set has daily observations, it enables us to define the treatment and control group in a more flexible way. Our regression specification is as follows:. Lockdown it is a dummy variable, which takes the value 1 if the city imposed a lockdown on that date and 0 otherwise.
X it denotes the weather controls similar to Equation 1. Also, we include date fixed effects to account for nationwide shocks that are common to all cities, such as the Spring Festival holidays. Table 9 presents estimates for the relationship between lockdowns and human mobility.
The coefficients imply that cities in lockdown experienced a These measures concern population movements for various purposes, of which business travel is only one of the possible purposes. Nevertheless, it suggests the underlying mechanism is plausibly at work here. We also conduct an event study to check the dynamic effects of lockdowns on people's movements. To do so, we replace the lockdown dummy with a set of event dummies indicating the number of weeks before and after the lockdown.
In particular, we put seven days into a bin to avoid the noise caused by fluctuations of daily measures. The benchmark week is 1 week before the introduction of lockdown.
We plot the coefficients on the event dummies in Online Appendix Figure D1. Clearly, at the time of writing, the pandemic has a major ongoing impact on health and mortality. Policy responses to prevent the virus from spreading create a supply shock that reduces trade and economic growth.
In our baseline analysis, we find that cities implementing a lockdown experienced a ceteris paribus 34 percentage point lower export growth rate compared to cities that did not. This effect translates to a 3 million US dollar additional decline in trade for cities in lockdown, implying a substantial welfare loss. The findings are similar to our baseline results. In addition, estimates using the city's distance to Wuhan as an instrument for the likelihood of a lockdown also indicate that our results are robust.
Our findings show substantial heterogeneity in the relationship between export growth and lockdowns. Coastal cities, cities with better ICT infrastructure, and cities with a larger share of potential teleworkers tend to be more resilient to supply disruptions caused by lockdown measures, whereas no significant effect for the share of processing trade is observed.
Furthermore, considering global supply chains and their concomitant flow of intermediate inputs, we find that sectors relying more on imported domestic intermediates suffer a sharper flatter slowdown in export growth. Hence, it appears that supply disruptions have come to an end.
More generally, examining the various socioeconomic outcomes due to lockdown policies will be helpful for understanding the impact it has and guide future policymaking during pandemics. We thank Jiayu Zhang for excellent research assistance.
Pei, J. Journal of Regional Science , 62 , — As the authors acknowledge, these regions are not completely comparable, not only in terms of population size, but also geographically.
In any case, lockdown policies appear effective in these places; while economic costs may differ see e. Due to data constraints, prefectures of Yunnan province are not included. Yunnan accounted for only 0. In the customs data set with trade statistics by province, January and February are not reported separately but combined.
There are two reasons: i we use monthly weather data rather than daily data and the number of weather stations we obtained is , which is fewer than what S. This forest district hardly reports trade. It has only 14 recorded transactions between and of which one in and zero in It is not included in the analysis. We did not include these cities into our treatment group.
There are two main reasons for doing so. First, only a small proportion of companies were targeted in the partial lockdown measures. Second, local governments took effective measures to quickly contain the spread of the virus and have done so arguably successfully.
The correlation coefficients between the variables used to split cities in two groups are lower than 0. The low correlation coefficients suggest different cities are considered depending on the variable used to split the sample. The data are from China's Input—Output table, which is the latest benchmark table available, with imported and domestically produced intermediate inputs distinguished.
If the exit dummy is 1, it implies all firms registered in the city did not export to a specific destination, which could be a rare event. In particular, we first match the treated cities with comparable control cities using the observable city characteristics, which are measured before the lockdown policy, that is, the year of We appreciate the suggestion by the editor and the anonymous referees to implement a propensity score matching procedure.
In this regard, the cooperative nature of different agents should be taken into account when designing lockdown policies see e. They find that lockdowns led to improvements in air quality, although PM 2. Gaaitzen de Vries, Email: ln. Meng Zhang, Email: moc. J Reg Sci. Published online Aug Author information Article notes Copyright and License information Disclaimer.
Corresponding author. Email: ln. Received Jun 15; Accepted Aug 2. Associated Data Supplementary Materials Supporting information. Open in a separate window. Figure 1. Figure 2. Figure 3. Figure 4. Table 1 Baseline results. Table 2 Heterogeneous treatment effects: City characteristics. Heterogeneous effects for the location of the city Many local governments enforced travel restrictions, such as partially shutting down highway entrances or canceling trains to prevent the outbreak of the coronavirus, especially in cities adjacent to Hubei province.
Heterogeneous effects in the share of potential teleworkers To contain the spread of the virus, firms are required to implement strict policies and practices such as social distancing in the workplace. Heterogeneous effects depending on the share of processing trade Processing trade played an important role in China's merchandise exports during the s. Heterogeneous effects by product and sector characteristics The trade data for cities does not allow us to examine effects conditional on product characteristics and neither to disentangle quantity and prices.
Table 3 Heterogeneous treatment effects: Product or sector characteristics. Disruption to global supply chains This section aims to examine the effects of supply disruptions at the sector level, taking into account international supply chain relations.
Table 4 Disruptions conditional on global supply chain participation: Sectoral evidence. Table 5 Results for adjustments in the intensive and extensive margin.
Figure 5. Table 6 Balancing test for propensity score matching. Mean t test Variables Treated Matched t statistic p value Temperature Table 7 Results for propensity score matching.
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