What does economics tell us about replaceability?

Introduction

‘Replaceability’ has become a core concept in discussions of career choice among Effective Altruists (EAs) – put simply, people should not simply consider the ‘direct impact’ from doing a job, but instead the difference in outcomes resulting from taking that job, relative to not taking it. Ben Todd and Seb Farquhar have both written blogs introducing this concept, and the importance of counterfactual reasoning in general (read these first if you’re not familiar with replaceability!); Paul Christiano and Ben Kuhn (among others) have written blogs further exploring the concept, and its various representations and applications. Some Effective Altruists (EAs) have noted that representations of replaceability have varied in their sophistication, and Will MacAskill summarises this nicely as the ‘simple view’, ‘simplistic replaceability’ and ‘correct replaceability’.

‘Correct replaceability’ is particularly nuanced and complicated, and comprises taking into account the full set of counterfactual outcomes not only in your (potential) job, but in any other jobs affected by the employment decision, through knock-on and labour market effects. Given this, and that ‘replaceability’ varies significantly across different industries and jobs, Will MacAskill and Ben Todd asked me to think about what Economics has to tell us about the concept. For clarity, rather than think about the ethical considerations of ‘replaceability’ as a whole, they asked me to answer a sub-question, namely: “according to mainstream economics, if I add myself to the labour pool for job type X (being a doctor, or an aid worker, or a banker), then how many more type X jobs come into being (on average)?”. Although these issues have been discussed before, this blog post is a first attempt at providing a thorough analysis of this question.

Summary

  • I set out the classical, Econ 101 supply and demand model and discuss the assumptions it makes. I argue that this is a useful framework for considering our question, then show how the answer depends crucially on the elasticities of labour supply and demand. Unfortunately, empirical economic research cannot tell us much about these elasticities for individual industries.

  • There is no ‘one-size-fits-all’ answer to our question – it will vary considerably across different industries and we must try to understand how each industry functions in order to make an informed estimate.
    I believe that the supply and demand framework, or some variant of it, is useful for analysing our question for most jobs and industries, particularly those that are not highly specialised.

  • I discuss how (and whether) this framework should be applied in a few industries, most of which are seen as viable EA career paths. This framework can lead us to some (tentative) conclusions:

    • Entrance into industries with a quantity restriction (e.g. through a limited number of occupational licences) is likely to have (close to) zero impact on the number of jobs in that industry. This may apply to medical school and licensed professional industries (e.g. becoming a barrister in the UK).
    • Entrance into (narrowly defined) industries which require relatively transferable skills is likely to result in less than 0.5 additional jobs in this industry, as (potential) workers can easily substitute into other industries (labour supply is elastic). This may apply to banking and consultancy.
    • Entrance into industries in which (potential) workers have a strong preference to work is likely to result in more additional jobs (perhaps between 0.5 and 1), as workers will not substitute into other industries at such a high rate (labour supply is inelastic). This may apply to jobs in the charity sector.
    • In highly specialised industries/jobs, applying this framework may not be appropriate, as the hiring process will not resemble a competitive market. This may apply, for example, to taking a job with Givewell, who likely follow a process more akin to ‘threshold hiring’.In this case, it seems likely that taking this job may increase the number of overall jobs by close to 1.
  • This post only discusses one aspect of replaceability, and does not consider other issues related to the (direct) impact of a job, effects on the quality of employees, or long term effects of a job, such as creating social value.

1. Econ 101: Classical Supply and Demand analysis

I set out the classical Econ 101 supply and demand model as a useful framework to answering our question, and explore under which conditions its conclusions vary, and under which assumptions it is valid. Let’s start by assuming that you are (potentially) entering a distinct labour market with a large number of hiring firms and a large number of (potential) workers, who have (roughly) the same skill level1, but have different reservation wages (wages at which they are willing to work in this labour market). in this case, simple textbook economics says that if you add your labour to industry x, you are increasing the supply of labour in that market. as shown in diagram 1, at any given wage there is now one extra person willing to work at that wage2. The supply curve shifts out, which reduces wages (w) and increases the number of people hired in that industry (Q).

Figure 1

Table_1

1.1. Does the classical model apply for small changes?

The immediate, and to economists perhaps obvious, question is whether this is actually a useful framework to use for analysing such a tiny change in a market with a large number of firms and workers. Usually, the answer is no – economists typically care about the overall effects on a market, and small changes such as an outward shift in supply by one person give negligible changes to wages and quantities and so are usually ignored by economists. But our question is not really usual – we are interested in the effect of your labour supply decision on the (expectation of the) number of people employed in a given industry, a change which (as we will see) is likely to be between zero and one – miniscule in relation to most economic applications, but potentially of significant interest to the ethically-minded job seeker.

To expand on this point, imagine that you add yourself to labour market X, which is perfectly competitive and has no frictions, causing a decrease in market wages from $15.01 to $15.00. If there is a probability of 0.5 that there is someone who is willing to work for $15 or more, but on the margin is not offered a job at $15.01 but is at $15.00, then the expected increase in the number of jobs in that industry as a result of you entering it is 0.5.

You may (quite reasonably) protest that this is not actually how the market functions, and that while the market would respond to a shift in supply of say 1000 workers, no firm or worker will respond to an additional one worker, even if (strictly) a response is optimal. This may be due to, for example, costs of adjustment, or costs of gaining information about such tiny changes – these are optimisation frictions. In a framework proposed by Chetty (2012), we might think that economic agents’ behaviour is determined by ‘satisficing’ – they will not readjust their actions unless the status quo is costing them more than (say) 1% of their utility. So if a firm is at their optimal point, and you add yourself to the market then that firm will not readjust as not doing so is not very costly. But if a firm has not had to re-optimise through previous additions of workers, it may be at the margin, and your addition causes it to reoptimise – your action does have an effect, in expectation at least. A related intuition is that if 1 extra worker has no effect on the market, but 1000 extra workers do, then in expectation you have 1/1000th the impact of 1000 workers.

1.2. The elasticities of labour supply and demand are important

So, under certain assumptions – that our labour market of interest is competitive and has a large number of firms and workers – it seems that classical supply and demand may be a fruitful way of answering our question: how many jobs come into being in industry X as a result of adding yourself to that industry? The number depends crucially on the slopes of the supply and demand curves in a neighbourhood around the existing market equilibrium3. we can think of these supply and demand curves as being ‘inelastic’ or ‘elastic’, where inelastic means that there is very little (or no) quantity response to a change in price (the curve is more vertical) and elastic means there is a large quantity response to a change in price (the curve is more horizontal)4. As shown in Figure 2, when labour demand is very elastic (i.e. firms’ hiring decisions are very sensitive to changes in market wages), by adding yourself to the labour market in industry X, the number of people hired in industry X is likely to increase by a large amount. If firms’ hiring decisions are inelastic, there will be a small change in the number of people hired. Conversely, if labour supply is elastic, other potential workers are able to respond to your addition to the market (for example by substituting into other labour markets) and so your overall effect is small, while if labour supply is inelastic, they are less able to respond, so the increase in the number of jobs will be greater.

Figure 2

Table_2

Figure 2: Note that, for all slopes in this framework, by adding one person to the labour market (an outwards horizontal shift in supply of magnitude 1) the number of additional jobs that come into existence (the change in Q) is between zero and one (zero if demand is perfectly inelastic (vertical), one if it is perfectly elastic(horizontal)). If both slopes (and thus elasticities) are equal at the equilibrium, then adding yourself to this labour market will result in 0.5 new jobs. If supply is more elastic (flatter) than demand, the number of jobs increases by less than 0.5 – the intuition here is that if supply is more elastic than demand, then workers are able to exit the market more easily than firms are able to create jobs in response to lower wages induced by your entry. If supply is less elastic than demand the number of jobs increases by more than 0.5 as firms create jobs more easily than workers are able to exit the market in response to lower wages.

1.3. What do we know about these elasticities in the overall labour market?

Assuming for now that the assumptions of this model are correct (I will come onto this more later), what do economists know about the slopes of supply and demand curves around the market equilibrium? To estimate the demand curve, the econometrician needs a number of ‘exogenous’ shifts in supply so that they can trace out the demand curve using the various equilibrium points. It is key that the change is exogenous – that it only affects the market equilibrium by shifting the supply curve, and everything else must remain the same. Unfortunately, such shifts are empirically quite hard to come up with – one example might be a change in the legal minimum age of employment as a shift in the supply of low skilled workers, though you might think of ways this may also affect demand in this market (employers in low wage industries may face changes in demand due to income changes, and this may reduce their demand for low skilled labour) and you are reliant on everything else in this labour market staying the same before and after the policy change for this analysis to be valid.

There are studies that attempt to do this for the macroeconomy – for example Hall (1991) argues that the labour demand schedule is likely to be flat (elastic) in the macroeconomy as well as in individual industries. The intuition is that as labour is just one factor of production, firms are easily able to substitute away from labour if prices go up. In the aggregate labour market workers are less inclined to substitute away from employment to unemployment, and so we may think their labour supply is less elastic, though this may be less true for individual industries where they are more inclined to move to another labour market (more on the definition of a labour market below). By its nature, it is hard to estimate the system of supply and demand, and studies attempting to do this are relatively few.

Instead of attempting to estimate the whole underlying structural system of supply and demand, economists often focus instead on estimating labour market elasticities – how much employment in a labour market changes in response to a change in prices5. Perhaps the largest, and best known, literature in this vein is estimating how the number of people employed in the aggregate labour market responds to an (exogenous) change in labour prices (wages), typically given by reforms to the tax and welfare system. Although these studies use the language of ‘labour supply elasticities’, they are typically capturing the whole market response to a change in tax rates – as noted by Saez, Slemrod and Giertz (2012), ‘taxes trigger a host of behavioural responses’. Chetty table 2 gives an overview of the most well known papers, which estimate this overall market response elasticity to be quite small, somewhere between 0.13 and 0.456.

1.4. What do we know about the elasticities in specific industries?

What can we learn from estimates of the aggregate labour market elasticities, in relation to our question for specific industries? Unfortunately, not that much, other than at the macroeconomic level, these elasticities seem to be quite low, indicating that the overall labour market does not respond much to changes in prices. However, it is important to note that elasticities are different for different populations under study – for example women are generally found to have a higher labour force participation elasticity than men, and the responses will vary in different labour markets, in different industries, at different income levels and at different points in time if an industry’s equilibrium has shifted. Further, an unemployment vs. employment decision for which many of these elasticities are calculated, is very different to an employment in industry Y vs employment in industry X decision, where we might think that the options are closer substitutes, and the elasticity therefore higher (more below).

The key message of this post therefore, is that there is no ‘one-size-fits-all’ number of jobs that your entry to a market will result in, and in fact the number may be VERY different in different labour markets or industries. There is some research on elasticities and labour supply and demand curves in specific labour markets, for example Nelson (1971) outlines how one might estimate supply and demand in the labour market faced by an individual firm, Falch (2010) estimates a supply elasticity for Norwegian teachers at an individual school of 1.4, and Sullivan (1989) and Staiger et al (2010) look at the labour supply elasticity of nurses to individual hospitals, though their results are very different7. However, such studies require excellent data (and often some sort of ‘natural experiment’ and strong assumptions) and lots of hard work, so it is implausible that there will exist an empirical study on a labour market potentially being faced by a job seeker at a given point in time! The rest of this post will explore how we should make a best guess to answer our question of interest – in particular how and whether we should apply the classical supply-demand model in different circumstances.

2. Applying the supply and demand framework to specific industries

2.1 Defining the labour market – how specialised and distinct is it, and how do its agents make decisions?

The first thing one must do is define the labour market that they are considering entering. This is more difficult than simply defining it as ‘industry X’, as people can and do move between industries, sometimes with little cost. For example, we could define our labour market as ‘the investment banking industry’ but we should note that a job in investment banking is relatively substitutable with a job elsewhere in finance, and perhaps to a lesser extent in accounting or consulting. The degree to which a job is ‘substitutable’ for those in other industries will affect the elasticity of supply in that labour market – more specialised industries (or more distinct labour markets) are likely to have more inelastic labour supply curves if workers have preferences specific to that industry and so are less inclined to seek jobs in another industry. Similarly, industries with very specialised skills/requirements, such as computer programming or EA organisations, will have more inelastic labour demand, as firms will find it less easy to replace workers, all else being equal8. In the extreme, if we define our labour market as a single firm in a perfectly competitive market (homogenous firms and workers), then it faces an infinitely elastic (horizontal) labour supply curve as the job it offers is perfectly substitutable for a job in any other firm, and so it must pay exactly the market wage if it is to attract any workers.

A further, EA-relevant example to highlight the implications of how agents within a specific labour market make decisions is given by the charity sector. In this case, it seems that the skills required to work in the charity sector are not particularly specialised, relative to computer programming for example, but that the preferences of potential workers for working in this sector might be quite strong. This relates to Paul Christiano’s point that workers do not choose jobs/industries entirely based upon monetary compensation, but might also consider their (direct) altruistic impact among other considerations. In such industries, it seems likely that labour supply is fairly inelastic with respect to wage changes at the market equilibrium; charities still maximise some objective with respect to a budget constraint however, and so should still be fairly responsive with respect to prices. Therefore, in this case, it seems likely that labour demand is more elastic than labour supply, and the number of jobs created by adding yourself to this labour market is more than half9. The intuition for this is that if you enter the charity sector, there is a (small) downwards effect in wages, but because other (potential) workers in this sector have a strong preference to work in this sector, they do not substitute out of this industry at the same rate as those in industries in which workers have a weaker preference to work.

2.2 Are there a ‘large’ number of firms and (potential) workers?

The second consideration when applying this framework, is whether the assumption of a large number of workers and firms is reasonable. For most industries and jobs, it seems reasonable to think that there are a large number of (potential) workers. An exception might be for extremely specialised jobs, where this assumption breaks down, and the supply and demand analysis should be discarded. An example of this might be Givewell, who have openly admitted that they find it hard to find employees who match their very specific criteria, and Jane Street (as pointed out by Ben Kuhn) – in this case it seems that their demand for more employees is not being met, and the market is incomplete. We may reasonably conclude that by taking a job at Givewell, you are increasing their number of employees by close to one.

On the labour demand side, we should also ask whether the assumption that there are a large number of firms in an industry is reasonable. If it is not, then firms may have market power and may not set a competitive wage – if so, we should employ a model of monopsony or oligopsony. Similar to a monopoly model, a monopsonist will set employment so that the marginal cost of labour is equal to the marginal revenue product of labour, as explained in this simple overview. In this case, our analysis does not fundamentally change (the increase in people employed in industry X is still between zero and one, and still depends on relevant slopes) though we should expect the change in the number of people employed to be slightly larger all else equal. As shown in Figure 3, the appropriate slope is now the marginal cost of labour (MCL), rather than the labour supply (average cost of labour), which will be steeper, and so the overall response of adding yourself to the market is larger, though the difference is not very large.

Table_3

2.3. Market distortions – regulated prices and quantities

A more fundamental distortion to the market that affects our analysis is regulation that prevents the market equilibrium from being reached. For example, if you are considering entering into an industry in which wages are kept artificially high, by unions, a minimum wage or efficiency wages, then your entry may have no effect on the number of workers in that industry, as the market does not clear and there is no equilibrium response. Take the asian garments industry for example, where there are many employers and many workers, but where the minimum wage is binding. As shown in Figure 4, while in a competitive equilibrium the number of employed workers would shift from Q* to Q*’, with a binding minimum wage (NMW) the number of workers in this industry is stuck at Qd, despite the increased supply. There is simply an increased disparity between the number of people willing to work at the minimum wage and the number of jobs available.

Figure 4

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A similar restriction, is a quantity restriction on the number of jobs available. This is how a number of (often self regulated) professional industries operate – for example in the UK there are (close to) a fixed number of barrister and doctor training positions available each year. Indeed, Kleiner and Krueger (2010) find that in 2006, 29% of the US workforce was required to hold an occupational licence from a government agency, yielding a 15% premium in wages (after adjusting for skill differences), suggesting that these licences do restrict the quantity of jobs available, on average. In this case, supply of labour at the prevailing wages (Qs) is again higher than demand (Qd), as the market is not able to clear, and so adding yourself to this market and shifting supply will have no overall effect on the number of doctors or barristers who qualify, which is again stuck at Qd.

Table_5

2.4. Level of seniority of entry position

The effect your entry to a given industry has can depend upon what level of seniority you enter/exit that industry at. For example, I have just argued that if you enter into medical school then you are having no overall effect on the number of places available, as these are fixed below the market equilibrium, with a surplus of qualified candidates. However, if you complete medical school, you are facing a very different labour market. In the UK my impression is that, for many types of doctors, regulation of wages and quantities of doctors employed by primary care trusts, hospitals and the newly created Clinical Commissioning Groups has been gradually phased out over the last 20 years and so a newly qualified doctor in the UK faces a labour market similar to the classical one given in Figure 1. As such, while adding yourself to the doctor training market has no effect on the total number of doctors, adding (or not removing) yourself from the market once qualified will increase the number of doctors in the UK, depending on the slopes of the supply and demand curves, as discussed by gregory lewis in his excellent post on the subject. given that doctors are highly skilled, and can only be substituted out for nurses and other healthcare inputs to a limited extent, i suspect that labour demand is fairly inelastic. however, given the lengthy training process, it seems that most qualified doctors have demonstrated a strong preference for becoming a doctor, and so labour supply in this market is also likely fairly inelastic. if both supply and demand elasticities are equal at the market equilibrium, then the number of jobs created by adding yourself to the market is 0.510, and so gregory’s estimation of 0.6 looks very reasonable.11

2.5 When not to think in terms of supply and demand

Finally, there may be cases in which our supply-demand framework should not be applied at all, such as Givewell and Jane Street’s difficulty in hiring discussed in section 2.2 – in these cases supply may not be able to meet demand and so firms’ behaviour is more akin to threshold hiring’ than within a competitive market, as proposed by Ben Kuhn. I believe that these cases will be relatively rare for relatively junior positions, particularly for most entry level jobs, and will only apply for highly specialised positions or industries. As your career progresses, and you gain more specialised skills, this scenario will become more plausible, but at entry level the supply-demand framework (potentially with quantity restrictions) should be relevant in most cases.

3. Conclusion

I believe that the supply and demand framework is a useful way of thinking about the number of jobs that come into being as a result of you entering a specific industry for all but very specialised jobs and industries. However, one should be careful when applying this analysis, and proceed on a case-by-case basis, considering whether the labour market is competitive, if there are any restrictions or regulations on it and what the relative slopes of the supply and demand curves are likely to be. As pointed out by Paul Christiano, for most narrowly-defined industries (and particularly at entry level) labour supply is relatively elastic as workers have transferable skills and can easily transfer to other industries if prices change. In these industries, it seems likely that supply is more elastic than demand and so the number of jobs that come into being by you joining the industry is less than half (see figure 2). Other industries have a restriction or cap on the number of entrants, for example due to occupational licensing, such that adding yourself to that labour market has no effect on the number of jobs in that industry. However, in some cases labour demand is more elastic than supply and so adding yourself to this industry will likely increase the number of jobs in that industry by more than half (see figure 2). Such jobs seem most likely to be in industries in which labour supply decisions are not very responsive to wages, such as the charity sector (see section 2.1). Finally, for some highly specialised positions, the market framework is not appropriate as supply may not be able to meet demand, and firms’ hiring decisions follow some other process, such as threshold hiring.

4. Directions for further analysis

This blog post only considers one aspect of what is commonly considered in discussions of ‘replaceability’ – the number of additional jobs in an industry that come into being as a result of you adding yourself to that labour market. It does not consider the direct (marginal) impact of those jobs, or the skill difference effects of taking a job for which you are ‘overqualified’ according to the market (i.e. accepting a lower wage than your market value) – the supply and demand analysis assumes that all workers in the market for a specific job in a given industry are similarly skilled (roughly homogenous). On workers’ skill heterogeneity, I also have not considered the effects of imperfect information, in particular noisy signals of ability available to employers – my gut feeling is that hiring mistakes roughly cancel out, and the market ‘gets it right’ on average. I also have not considered spillovers from taking a job in an industry – my analysis is static, but we may reasonably think that expanding certain industries may create more jobs or social value than others in the long run. Similarly, I have not considered ethical considerations related to changes in shares of surplus between firms and workers as a result of your addition to a given industry’s labour market. Finally, I again note that the question answered in this blog is narrow with respect to the impact of taking a job in a certain industry – ultimately it seems that we should care about the ‘output’ of an industry, which may produce social good or harm, not the number of people it employs. Whilst the former may be a decent proxy for the latter, it does not tell the full story – for example, in response to lower wages in an industry, firms may increase the hours worked of existing employees (an intensive margin response) as well as the number of people employed (an extensive margin response). Each of these caveats might provide a fruitful area for extending this analysis.



  1. In economics terms, by assuming roughly the same skill level among workers, we are treating their labour as a ‘homogenous good’. 

  2. Strictly there is one extra person willing to work for any wage at or above your reservation wage; for the overall question to be relevant, let’s assume from now on that you are willing to work in this labour market, and so your reservation wage is below the market equilibrium wage. 

  3. Although supply and demand curves are typically not linear, because we are looking at such small changes, we can continue to think of these as approximately or locally linear, as outlined here

  4. The slope of a curve is not equal to its elasticity, though the two are related – see this blog for a clear explanation. 

  5. For the purposes of this post I will focus only on ‘extensive’ marginal elasticities – that is effects of price changes on binary employment (someone is either employed or they are not). In reality, we may also care about ‘intensive’ elasticities – how much people work (e.g. in hours) in response to a change in price – and more generally how your decision to enter an industry changes output in that industry, but this complicates an already complicated analysis. For completeness, I am also focussing on Hicksian elasticities, which are calculated in the steady state equilibrium, rather than Frisch elasticities, which look at intertemporal substitution. 

  6. These estimates imply that, at the market equilibrium, a 1% decrease in wages will result in a 0.13% – 0.45% increase in the number of people employed. The effect of adding yourself to the labour market is empirically harder to estimate, as it requires estimation of the underlying structure of supply and demand, as discussed in the previous paragraph. The point here is that the estimated labour elasticity for the macroeconomy is typically estimated to be low. 

  7. Sullivan estimates a supply elasticity to an individual hospital of 1.3-3.8, though Staiger et al revise this down to 0.1. 

  8. Intuitively, and more generally, it seems that labour demand will likely be fairly inelastic in any knowledge-based industry, in which human capital is the main factor of production, as it is not easy to substitute away to non-labour inputs. 

  9. Note that there may be a direct impact of adding yourself to a labour market for a position for which you are overqualified and receive less than your market wage, as you may do the job far better than the next best candidate at the market wage. However, such considerations are beyond the scope of this post as I am focussing purely on the number of jobs that come into being in this market as a result of your addition, and this will not be affected by whether or not you are overqualified (unless there are employment spillovers generated by how you do your job, which I do not discuss here and leave for further analysis – see section 4). 

  10. If both elasticities’ absolute values are equal at the market equilibrium, then the absolute values of the slopes must also be equal at this point, as the equilibrium q and p are fixed – see here. The result can now be seen graphically, by simply drawing supply and demand with equal slopes, and shifting the supply curve outwards horizontally by one unit. 

  11. The market for qualified doctors in the USA is likely similar to the UK case, though there is the added complication of the residency matching process, which I do not know enough about to know whether this will change our analysis significantly. 

Author: Rossa O'Keeffe-O'Donovan

Rossa is a PhD candidate in Economics at the University of Philadelphia and a member of 80,000 Hours.