key: cord-0148533-cncb5vhe
authors: Czaller, L'aszl'o; T'oth, GergHo; Lengyel, Bal'azs
title: Vaccine allocation to blue-collar workers
date: 2021-04-09
journal: nan
DOI: nan
sha: e06bd59d27a6a5c533da69bf2946a02faa5798c0
doc_id: 148533
cord_uid: cncb5vhe

Vaccination may be the solution to the pandemic-induced health crisis, but the allocation of vaccines is a complex task in which economic and social considerations can be important. The central problem is to use the limited number of vaccines in a country to reduce the risk of infection and mitigate economic uncertainty at the same time. In this paper, we propose a simple economic model for vaccine allocation across two types of workers: white-collars can work from home; while blue-collars must work on site. These worker types are complementary to each other, thus a negative shock to the supply of either one decreases the demand for the other that leads to unemployment. Using parameters of blue and white-collar labor supply, their infection risks, productivity losses at home office during lock-down, and available vaccines, we express the optimal share of vaccines allocated to blue-collars. The model points to the dominance of blue-collar vaccination, especially during waves when their relative infection risks increase and when the number of available vaccines is limited. Taking labor supply data from 28 European countries, we quantify blue-collar vaccine allocation that minimizes unemployment across levels of blue- and white-collar infection risks. The model favours blue-collar vaccination identically across European countries in case of vaccine scarcity. As more vaccines become available, economies that host large-shares of employees in home-office shall increasingly immunize them in case blue-collar infection risks can be kept down. Our results highlight that vaccination plans should include workers and rank them by type of occupation. We propose that prioritizing blue-collar workers during infection waves and early vaccination can also favour economy besides helping the most vulnerable who can transmit more infection.

Humanity has learned in the COVID-19 pandemic that restricting the mobility of individuals and social distancing can slow down virus diffusion 1, 2 but also comes with enormous economic consequences 3 . Unprecedented fall of demand 4 has led to many job losses 5, 6 and uncertainties in production chains propagate these shocks across countries, sectors, and firms 7, 8 .

To balance the mitigation of infection risks with saving economic activity, commuting to work has been a general exception of mobility restrictions even during the most severe quarantines. However, infection risks at work have been found considerable in early outbreak 9 and remained comparable with other forms of social mixing such as commuting or even nightclubs at later stages 10 . Although home-office became the new normal for high-skill and high-income white-collar employees 11, 12 , tasks of lower educated workers tend to require physical presence, thus blue-collar workers face higher risks of infection in order to keep their jobs 13, 14 . Higher exposure of certain occupations has been observed through infection tests 15 , excess deaths 16 , and documented COVID-related deaths 17 . Partly because income tends to sort white and blue-collar workers to separate neighborhoods, higher exposure is reflected in higher infection rates in densely populated low-income neighborhoods 18, 19 where the likelihood of within-household infection is also high 20 and where lock-down strategies are less effective [21] [22] [23] .

Vaccine availability has created a new situation and the question governments must quickly answer is how to locate the limited number of early vaccines to be able to ease restrictions in their country. The consensus is that vaccine allocation arXiv:2104.04639v1 [econ.GN] 9 Apr 2021 must be optimized to save lives and must favor the endangered population 24, 25 . However, some argue that certain working groups should be included early in order to speed up vaccination 26 and immunize those groups that have more contacts and carry more infections [27] [28] [29] [30] . Despite their obvious importance 31 , economic rationals are almost completely ignored in this discussion. One exception is Cakmakli et al. 32 who illustrate that an ethical distribution of vaccines across countries 33 can pay off in functioning global production and supply chains. Yet, the notion that local economies combine white-collar and blue-collar workers differently is still missing from this discourse and differences across workers are left out from vaccination strategies of most countries.

In this paper, we build on a fundamental economic argument on complementary tasks of blue-and white-collar workers (also termed routine/non-routine 34 and low/high-skill tasks 35 ) in production on the short-term. This enables us to demonstrate that blue-collar workers should follow the high-risk population in vaccine allocation. Such strategies can favour economies by saving most jobs, besides helping the most vulnerable employees 13 and mitigating infection transmission 15 .

We propose a short-run economic model in which technology is fixed. The model consists of two worker types:

white-collars work from home with some productivity losses; while blue-collars work on site. These worker types are used in a fixed combination, thus a negative shock to the supply of either one decreases the demand for the other, leading to unemployment. This model can be used to express the optimal share of vaccines allocated to blue-collars with parameters of labor supply of blue and white-collars, their different infection risks, productivity losses at home office, and the volume of available vaccines. Model results suggest that blue-collars should be prioritized against white-collars during infection waves when the relative infection risks of blue-collars depart from the infection risks of white-collars. This regime of priority is even more pronounced when available vaccines can cover only a small fraction of workers.

Taking labor supply data from 28 European countries, we quantify blue-collar vaccine allocation that minimizes unemployment across levels of blue-and white-collar infection risks. In case of vaccine availability to only 20% of all employees, our model minimizes unemployment by allocating 66% of vaccines to blue-collar workers in 70-80% of all infection risk scenarios and across all European countries. As more vaccines become available, those European economies that host large-shares of employees in home-office shall increasingly immunize them in case blue-collar infection risks can be kept down. However, economies where blue-collar work dominates, can benefit from continued blue-collar vaccination as more and more vaccines are available, regardless of infection risks.

Consider an economy, where each firm produces a single good by combining two types of tasks: teleworkable tasks (t) can be performed from home, and non-teleworkable tasks (n) require the physical presence of workers 3, 12 . Suppose that workers are able to perform both tasks with unit productivity but once they are trained for one of the tasks, they cannot switch to the other. We assume that the technology combining these tasks is Leontief, that captures short-term production without long-term adjustments to shocks 35 , so that the aggregate production function is

where L w is the amount of white-collar (w) labor performing t tasks and and L b is the amount of blue-collar (b) labor performing n tasks, α w and α b are unit input requirements and y is aggregate output. Taking labor supply and unit input requirements as given, firms optimize L w and L b in order to maximize profit which implies that:

The epidemic starts after firms have optimized labor such that L w and L b are fixed. The government obligates firms to send white-collars to home-office. As a consequence, the probability of becoming infected will be lower for white-collars while the exposure of blue-collar workers performing non-teleworkable tasks will remain unaffected. Formally, let β i be the probability of infection for workers in task i such that β w ≤ β b . Opportunities for remote work, however, come with a price.

Although working from home benefits employees by eliminating their daily commutes it might decrease their productivity by making negotiation, instructing and monitoring more cumbersome, and by increasing reaction time in complex decision situations 3, 36 . Thus, we assume that the productivity of white-collars decreases to γ ∈ (0, 1) as long as they work from home.

Production decreases during the pandemic because effective labor in both tasks deviate negatively from optimal amounts.

Without available vaccines the supply of effective labor is reduced tō

In the logic of Equation 2, reduction of effective labor in one task decreases labor demand in the other task and workers become unemployed. Suppose that β b > 1 − (1 − β w )γ holds, so β b reduces the supply of blue-collar labor to a greater extent than β w and γ decreases white-collar labor. In this situation,

L w healthy white-collar workers will be unnecessary for production.

L w blue-collar workers will become redundant.

Now suppose that a social planner distributes V amount of vaccines across L workers such that V < L. The vaccination has two effects: 1. it immunizes workers and increases effective labor, and 2. it makes social distancing among vaccinated workers unnecessary. After getting the vaccine, white-collar workers performing teleworkable tasks restore their full productivity because they are allowed to go back to the office. Vaccines are scarce and not all workers can be immunized.

Therefore, the social planner aims to distribute the vaccines among workers to minimize job losses of healthy workers due to complementary teleworkable and non-teleworkable tasks. i

We quantify the share of vaccines that should be allocated to a certain type of worker. Let v i be the number of immunized workers i ∈ {b, w}. Assuming that all vaccines are used, ∑ i∈(b,w) v i = V and every worker accepts the vaccine, labor supplies can be written using v b only as:

The social planner's problem is to minimize the job losses arising from complementary tasks and can be formalized by the objective function

The global minimum of the objective function is zero which can be found at

Hence, the solution of the social planner's problem is 

which means that there is no unemployment among healthy workers. Finally, if v b ≥ V all vaccines should be given to blue-collar workers in non-teleworkable tasks.

, Solutions are depicted in Figure 1 . If v n ≤ 0, we get the corner solution of v * b = 0, which means that all available vaccines should be given to white-collar workers. In such cases, the effective white-collar labor determines output and the total amount of blue-collar work:

Substituting v * b = 0 into (Equation 3), and then subtractingL b gives the number of unemployed blue-collar workers:

Note that, although this vaccine allocation cannot maintain full employment among healthy blue-collar workers, it still reduces their unemployment due to complementary tasks by

If v b lies within the interval (0,V ), the social planner is able to find a vaccination plan that provides the optimal proportion of white-collar and blue-collar workers. This implies that nobody drops out of work due to the reduction of work capacity in complementary tasks, soL i =L i , ∀i ∈ (b, w).

Finally, if v b ≥ V , all vaccines should be given to blue-collar workers, v * b = V , in order to minimize unemployment of white-collar workers. When blue-collar workers are a bottleneck of production, white-collar employment becomes

which implies

unemployed white-collar workers. Compared to the baseline case, this vaccine allocation scheme reduces unemployment in teleworkable tasks by

The optimal allocation of vaccines depends on blue-collar and white-collar labor supplies (L b and L w ), the parameters describing the structure of the economy (α b , α w , and γ), the number of vaccines available (V ) and the task-specific probabilities of infection (β b and β w ). It follows that there is no uniform recipe for the distribution of vaccines which derives solely from the characteristics of the economy. By differentiating equation (5) with respect to β b we obtain

hence if the probability of infection for blue-collar workers performing non-teleworkable tasks increases (e.g. safety regulations are not followed by employees at the workplace), more vaccines should be given to them not just to avoid workplace infection but also to minimize redundancy of white-collar labor. Clearly, if all blue-collar workers are vaccinated, v b = L b , β b has no further effects on v b .

In contrast, by differentiating v b with respect to β w we find that an infinitesimal change in the infection risk of white-collar workers decreases the optimal number of vaccinated blue-collar workers (v b ),

as long as v w < L w .

We illustrate the results of our model with numerical simulations. We relate our theoretical results to pre-Covid-19 observational data to examine the extent to which v * b varies across economies of different structures and various epidemiological scenarios represented by different combinations of theoretical infection risks β b and β w that range from 0 (no risk of infection) to 1 (infection is certain). We collect employment data from the EU Labor Force Survey ii for countries of the European Economic Area (EEA). To calculate L w and L b for each country, we use the country-level estimates of Dingel and Neiman on the share of jobs that can be done at home. 12 We calibrate unit input requirements to match model equations to employment data. First, α w is normalized to unity and α b is estimated by substituting L w and L b into Equation 2. Finally, remote work productivity γ is set to 0.8 following the results of a recent survey. 36 is relatively high, improving vaccine availability designates high v b /V ratios at any given β n infection risk. For example, in Romania, where the share of non-teleworkable jobs is higher than in Sweden, more vaccines should be given to blue-collar workers who can not work from home. Otherwise, the over-vaccination of white-collar workers would result in redundant blue-collar labor.

So far, we have analysed the relationship between v b /V and β b at given β w infection probabilities. Now, we proceed by calculating the share of vaccines given to blue-collar workers for all possible combinations of β w and β b . Figure   3 organizes v b /V ratios into matrices for Sweden (low L b /L) , Germany (medium L b /L), and Romania (high L b /L) at different levels of vaccine scarcity. Perhaps the most conspicuous pattern of this figure is that in countries where the rate of remote work is high (e.g. Sweden and Germany), more epidemic scenarios can be found where optimal vaccine allocations favor individuals performing teleworkable tasks. However, in countries where remote work is less common (see e.g. Romania) high v b /V ratios can be observed even in cases where β w exceeds β b . If we consider only those parameter combinations where β b > β w (above the matrix diagonal), differences between countries are blurred, especially when vaccines are widely available. Taken together, these results suggest that blue-collar vaccination should exceed white-collar vaccination regardless of infection risks and vaccine availability. Figure 4 shows the ratio of those β b > β w combinations where v b /V > 0.66. In case of serious vaccine shortage (V /L = 0.2), unemployment can be minimized by allocating at least 66% of vaccines to blue-collar workers in 70-80% of the considered epidemic scenarios in most European countries. As more vaccines become available, countries where remote work is more prevalent (e.g. Luxembourg, Switzerland and Sweden) shall start to vaccinate teleworkers in larger proportions to ensure full employment among healthy workers. These countries should aim for a more balanced vaccine allocation unless β b is too high compared to β w (see the Swedish case in Figure 3 .) However, in several countries where the share of teleworkable jobs is low (e.g. Romania, Bulgaria, Slovakia), mass vaccination of blue-collars remains necessary even if vaccines become widely available.

Clearly, the lower v th b the less variation can be observed across countries. This is due to the general notion illustrated in Figure 3 that when β b > β w blue-collar workers should almost always get more vaccines. For example, if v th b is set to 0.5 80-90% of the relevant risk combinations satisfy the condition v b /V > v th b in all countries except Luxembourg (illustrated in Supporting Figure 1) . However, the convergent v b /V nature of increasing vaccine availability illustrated in Figure 2 implies that countries of low L b /L (eg. Sweden) can allocate vaccines to white-collars earlier than countries of high L b /L (eg. Romania).

Vaccinating those who must go out to work even during the most sever phases of the pandemic can save lives. Only very few European countries, like Ireland and to some extent Spain 30 , differentiate occupations in their vaccination plans, but this practice remains exception and it is certainly not the rule yet. Our paper shows that immunization of blue-collar workers who can't work at home can save jobs as well. This is done in an abstract model by assuming that teleworkable and non-teleworkable tasks are complements in the production on the short run. Thus, prioritizing blue-collars in the vaccination strategies can be beneficial for white-collar jobs as well.

We quantify optimal shares of vaccines allocated to blue-collars by minimizing the unemployment arising from infection risks and productivity losses at home office. Our model suggests that European countries should allocate majority of the early vaccines for workers to blue-collars. As more vaccines become available, more advanced should increasingly immunize white-collars working in home-office in case blue-collar infection risks can be kept down. However, in less developed economies where blue-collar work dominates, should focus more on blue-collar vaccination.

Further work is needed to overcome the limitations of the model presented here. We are assuming that economic agents are not adjusting themselves to the dynamically changing circumstances over the pandemic job losses. Home office productivity losses are assumed to be identical across countries, which is probably not true given the technological and cultural differences that might influence the efficiency of working at home. Epidemic scenarios are completely ignored in this framework and infection risks are only considered in a very abstract manner. Finally, production only considers labor while other inputs and demand are ignored.

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