Looking ahead at the effects of automation in an economy with matching frictions

We study the effects of an automation-augmenting shock in an economy with matching frictions and endogenous job destruction. In the model, tasks can be produced by workers or by machines but workers have a comparative advantage in producing advanced tasks. Firms choose the input at the time of entry. And according to the evolution of the workers’ comparative advantage, some ﬁrms using labor prefer to ﬁre the worker and automate the task. In our model, an automation-augmenting shock reduces the labor share, increases job creation, and increases job destruction. The effects on employment depend on how rapidly workers may lose their comparative advantage: an automation-augmenting shock increases employment in slow-changing environments but catastrophically reduces it in rapid-changing ones.


Introduction
In the last five decades, total hours worked and employment rose in developed countries, despite the ubiquitous fall in the labor share.This employment growth looks staggering as it coexisted with the emergence of new technologies that automate production and are supposed to displace labor.But a meticulous look at the effect of these new technologies -namely, automation -shows that they have actually favored employment growth: Autor and Salomons (2018) and Gregory, Salomons and Zierahn (2018) document that these new technologies have created more jobs than they have destroyed. 1In this paper, we ask: will automation always create more jobs than it destroys or can we expect a different future?
To answer this question, we build a theoretical model that satisfies two criteria.First, in order to be consistent with the past, an automation-augmenting shock -a shock that increases the productivity of all machines/robots -is able to reduce the labor share and simultaneously increase employment.And, second, in order to be insightful about how the future may differ from the past, the model is flexible enough to generate different outcomes from the same sort of shocks.In the literature, among the models that explain the fall in the labor share, none offers a qualitatively flexible response of employment.In these models, either employment always falls (Caballero and Hammour, 1998;Zeira, 1998;Hornstein, Krusell and Violante, 2007;Prettner and Strulik, 2017;Acemoglu and Restrepo, 2018) or employment always increases (Guimarães and Gil, 2019). 2 Our model borrows several features from these models to offer a framework that is consistent with the past and insightful about potential future scenarios.In our model, an automation-augmenting shock reduces the labor share but may both increase or catastrophically reduce employment.
The narrative and assumptions of our model broadly agree with those in Acemoglu and Restrepo (2018).In our model, labor has a comparative advantage in producing new and complex tasks and, thus, new firms tend to invest in, what we call, the manual technology and produce using only labor.Machines, however, tend to catch up with labor in producing tasks.Every period, some workers lose their comparative advantage, motivating their employers to fire them and automate the production of the tasks.In this case, firms move to, what we call, the automated technology and produce 1 Autor and Salomons (2018) study the effect of total factor productivity (TFP) shocks on employment using data on multiple industries for 18 OECD countries since 1970.Their results indicate that TFP shocks directly displace employment in the sectors in which it originates but this direct effect of TFP is more than outweighed by indirect employment gains in other sectors.Gregory, Salomons and Zierahn (2018), on the other hand, analyze the effects on employment of a more specific type of innovation: routine-replacing technological change (RRTC) in Europe from 1999 to 2010.Still, their findings are very similar to the ones by Autor and Salomons: the direct effect of RRTC has been to significantly reduce employment (about 1.6 million jobs) but these effects have been offset by the indirect effects of RRTC.They conclude that RRTC has increased employment by about 1.5 million jobs.
2 These models do not propose the same mechanism or shock to explain the fall in the labor share.But irrespective of the mechanism, they predict robust directions for employment after the shock that reduces the labor share.tion post-entry. 6ven though both flows increase after an automation-augmenting shock, their absolute and relative magnitudes crucially depend on the calibration of the model.In some calibrations, job creation increases more than job destruction, thereby raising employment.In other calibrations, the opposite occurs and employment falls.The relative magnitudes of the changes in the flows depend crucially on one parameter, which we interpret as a feature intrinsic to each task controlling for how rapidly workers may lose their comparative advantage in producing it.In slow-changing environments, in which the comparative advantage of labor in producing each task is relatively stable, job destruction barely shifts after the automation-augmenting shock.In these conditions, job creation increases more than job destruction.Nonetheless, in rapidchanging environments, an automation-augmenting shock leads to massive job destruction.This jump in job destruction is not followed by an equal jump in job creation because the increase in labor market tightness makes it more costly to find the right worker and allows workers to demand higher wages.In these scenarios, employment catastrophically drops.These results show how our model can both agree and disagree with the facts documented by Autor and Salomons (2018) and Gregory, Salomons and Zierahn (2018).Thus, our paper conveys an important message: if current and future jobs are made of tasks in which workers rapidly lose their comparative advantage, then automation-augmenting shocks may have dramatically different consequences in the future.
We also try to dissect the mechanism behind our results and we confirm that the increase in wages after the automation-augmenting shock plays a very important role.In tighter labor markets (as observed in our model after the shock), workers demand higher wages for two reasons.One is that the outside option of manual firms of looking for an alternative worker is more costly and another is that workers can easily find other jobs.When we counterfactually assume that wages are orthogonal to labor market tightness (and to the productivity of the automated technology), job creation is seriously magnified to the point that employment increases for a much wider range of calibrations.Employment does, however, still fall in quite rapid-changing environments because matching frictions also play their role.If job creation increases, it becomes harder to find a worker suitable for the job, which increases costs and discourages further job creation.Job destruction, on the other hand, is not much affected by matching frictions and increases significantly in quite rapid-changing environments, leading to the net fall in employment.
We consider two other variants of our model to further dissect the mechanism.In one variant, we deviate from the typical assumption in models with matching frictions that workers must stay nonemployed for at least a period after losing their jobs.This reduces the prevalence of matching frictions and increases the pool of available workers for firms investing in the manual technology.We find that relaxing this assumption does promote greater employment but we also find that it does not have much quantitative impact.
In another variant, we consider the implications of, what we call, human touch.Even though both workers and machines can execute the same task, consumers may deem tasks executed by humans and by machines differently due to the relevance of the human touch.A simple case is the one of sellers and vending machines.Both broadly sell (they perform the same task) but consumers do not necessarily find the same task performed by one or the other perfect substitutes.In the scenario in which they are imperfect substitutes, a widespread use of machines increases the price of the tasks produced by workers relative to the price of the tasks produced by machines, which largely reduces job destruction but barely changes job creation.Thus, if many of the tasks produced in the economy are directed to consumers and they find the differentiated human touch relevant, then an automation-augmenting shock is unlikely to catastrophically reduce employment.
Our paper also relates to Prettner and Strulik (2017), Basso and Jimeno (2018), Berg, Buffie and Zanna (2018), and Caselli and Manning (2019) (and again with Acemoglu and Restrepo, 2018) in that these papers also assess how automation-related shocks may affect either wages or employment in the future.Prettner and Strulik build a lifecycle model in which machines complement high-skill labor but substitute low-skill labor.They conclude that innovation asymptotically increases automation and inequality.And in an extension, they show that innovation always reduces low-skill employment due to greater automation and the high costs of acquiring skills for some workers.Basso and Jimeno assess the effect of demographical changes in a life-cycle model in which R&D investment may be directed to innovation (new tasks) or automation (of current tasks).They conclude that the demographic transition in the United States and Europe promoted higher wages in the beginning of 2000's but lower wages afterwards.Berg, Buffie and Zanna build a model with a nested CES (constant-elasticity of substitution) production function in which standard capital complements a composite of labor and robots; this composite assumes that labor and robots are substitutes.They conclude that robot-augmenting shocks can only benefit labor in the very long run.Caselli and Manning study how innovation affects real wages in economies with constant returns to scale, constant real interest rate, and multiple types of labor.They conclude that average wages increase as long as the price of capital falls more than that of consumption goods.Under this condition, they also conclude that all wages increase if the supply of labor types is perfectly elastic.But their model, as well as the models in Basso and Jimeno and Berg, Buffie and Zanna, abstracts from the impacts of shocks on employment as labor supply is assumed inelastic.More generally, our model differs from all these models because they assume perfectly competitive labor markets.
The remainder of this paper is organized as follows.We start by detailing our model in Section 2. In Section 3, we calibrate our model and study numerically the effects of automation-augmenting shocks.In Section 4, we dissect the mechanisms underlying our results, including the role of the human touch.In Section 5, we conclude.

The Model
In the model, the aggregate output is the sum of the production of a number of tasks, which can be produced by one of two technologies: an automated technology and a manual technology.At the time of entry, a firm must first create a task, which amounts to an entry cost denoted by Ω.If the firm produces the task using the automated technology, it must pay an additional κ K , which can be interpreted as a robot investment.If the firm produces the task using the manual technology, it must pay an additional κ L µ(θ) to match with a worker and it must bargain wages with the worker. 7ntering firms that choose the manual technology must search for workers in the labor market.A Cobb-Douglas matching function determines the number of matches between these firms and the workers that were nonemployed at the beginning of the period. 8This matching function has constant returns to scale, has as argument labor market tightness, θ, is scaled by matching efficiency, χ > 0, and has an elasticity with respect to nonemployed workers of 0 < η < 1.Thus, we write the job-filling probability and the job-finding probability as, respectively, µ(θ) ≡ χθ −η and f (θ) ≡ χθ 1−η .
Each task has a stochastic idiosyncratic productivity, z, in the interval [z min , z] according to a probability distribution function G(z).Acemoglu and Restrepo (2018) assume that workers have a comparative advantage in producing more productive (higherindexed) tasks.We borrow this assumption and assume that the manual technology produces z L z units of the task, while (as a normalization) the automated technology produces z K units of the task.Thus, z represents the comparative advantage of workers in producing the respective task, so that highly-productive tasks (high z) tend to be produced by the manual technology and less-productive tasks with the automated technology.
Firms' technological choice depends on the task's idiosyncratic productivity, z.In Figure 1, we summarize the timeline of how z affects the distribution of firms between the technologies.In Acemoglu and Restrepo (2018), labor has the highest comparative advantage in producing new tasks because newly created tasks have the highest index.We assume a more general environment.Of the number of new tasks created each period, a proportion 1 − λ e has the highest productivity, z, and, thus, workers have the maximum comparative advantage.In this case and in equilibrium, firms choose the manual technology and produce z L z units of the task.Conversely, a proportion λ e of new tasks have their productivity drawn from the distribution G(z) of productivity levels over the interval [z min , z] and firms choose technology according to the presentdiscounted values of the technologies.Producing tasks with higher z is more profitable if the firm uses the manual technology to take advantage of the higher workers' comparative advantage.As a result, there is an idiosyncratic productivity cutoff, denoted by z * e , above which firms prefer the manual technology and below which firms prefer the automated technology at the time of entry.
Firms that start production using the manual technology can move to the automated technology in later periods.Their technological choice depends on how the task's idiosyncratic productivity, z, evolves over time.If it becomes too low, manual firms prefer to destroy the job and automate the production of the task.This line of events further echoes the setting in Acemoglu and Restrepo (2018).In their model, tasks previously performed by labor can be automated as the tasks' (relative) productivity falls due to the expansion of the technological frontier over time and the implied gradual obsolescence of existing manual tasks.We also find a similar mechanism in the model of Hornstein, Krusell and Violante (2007).They build a model in which a unit of vintage capital is matched with a worker.As technology evolves, firms that use the oldest vintage of capital prefer to scrap their capital and, as in our model, destroy the job.Yet, in the models of both Acemoglu and Restrepo and Hornstein, Krusell and Violante, the fall in the task's idiosyncratic productivity (relative to the technology frontier) is deterministic while, in our model, we assume it to be stochastic. 9To model the evolution of z, we build on Mortensen and Pissarides (1994).After production takes place, a proportion 1 − λ n of manual firms sees no change in their tasks' idiosyncratic productivity and, thus, in their position relative to the technology frontier, z.But a proportion λ n of manual firms redraws the task's idiosyncratic productivity from the same distribution G(z) of productivity levels.If the new idiosyncratic productivity, z, is too low -below the cutoff, which we denote by z * -the manual firm fires the worker and shifts from the manual to the automated technology. 10As a result, λ n controls for how rapidly workers lose their comparative advantage, which directly affects job destruction.
These assumptions imply that shocks to the economy can change the employment rate by affecting both job creation and job destruction.Thus, this setting allows for a rich environment to study how automation-augmenting (rise in z K ) shocks affect the employment rate.
In writing the equations below, we omit the time subscripts as we are only interested in steady-states.Yet, within a period, there is an order of events that we must further clarify before laying out the equations.1) New firms pay Ω to create a task and enter the market until a free-entry condition is satisfied.2) A proportion λ e of new firms and a proportion λ n of manual firms (re)draw the task's idiosyncratic productivity, z. 3) Depending on the productivity draw, z, and anticipating wage bargaining, firms decide which technology to use in the following period.If an incumbent manual firm decides to automate the production of the task, it must fire the worker, pay κ K , and wait a period to resume production.4) Production takes place and manual firms bargain wages with their workers.5) A proportion δ L of the tasks produced by active (producing within the period) manual firms and a proportion δ K of the tasks produced by active automated firms are exogenously destroyed.

Firms
An active firm using the manual technology to produce a task with idiosyncratic productivity z has the following present-discounted value J L (z): where we assume a discount factor of β.This firm produces z L z units of the task (and, thus, of the output) and pays the wage w(z) to its worker.There is a probability 1 − δ L that it will keep producing in the following period.And if it does produce, its value remains unchanged with a probability 1 − λ n and changes due to the redraw of the idiosyncratic productivity, z, with a probability λ n .Those that draw a productivity below z * prefer to fire the worker and change to the automated technology; in this not demand us to keep track of how far or close a task is from being automated.The other, and more important, is that tasks may differ on the speed at which they are automated; thus, we find it more realistic to assume that the transition from manual to automated is random rather than deterministic. 10Naturally, some firms also draw a higher z.We can interpret this as a form of technological catching up of the task.In any case, the most relevant aspect for the mechanism of the model is that these firms remain manual.case, because they already paid Ω and it takes one period to shift technologies, their value equals the discounted value of the automated technology, βJ K , reduced of the technology-specific cost κ K .If they draw a productivity above z * , they choose to maintain the manual technology; in this case, their value equals the unconditional expected value of the manual technology between z * and z.This intuitively implies that z * is determined by the following indifference condition: (2) The present-discounted value of the automated technology, J K , is much simpler as its productivity is constant: (3) At the time of entry, all firms pay Ω to create a new task.A proportion λ e of the new firms draws the task's idiosyncratic productivity; the other firms start with the manual technology with idiosyncratic productivity z.Among the firms that draw idiosyncratic productivity, a proportion G(z * e ) chooses the automated technology and the remaining firms choose the manual technology.These assumptions allow us to write the freeentry condition in our model: ) where the present-discounted values, J K and J L (z), are discounted by β because it takes one period for firms to start production.New firms that draw productivity are only indifferent between either technology if their values net of the technology-specific entry cost are equal.This occurs when the task's idiosyncratic productivity equals z * e : (5)

Workers
In our model, there is a unit measure of risk-neutral workers who are either employed or nonemployed.The lifetime income of an employed worker is given by E(z): (6) E(z) increases with the wage w(z), which varies with the idiosyncratic productivity of the task the worker is producing at the firm.E(z) falls with the probability that the job is exogenously destroyed and the worker is back to nonemployment.In this case, the lifetime income is given by U .E(z) also changes with the future productivity draw of the firm: if the new productivity draw is low -below z * -, the firm fires the worker and the lifetime income returns to U ; if the new productivity draw exceeds z * , then wages change, shifting the lifetime income of employment.
If nonemployed, a worker enjoys income b ≥ 0 and finds a job with a probability f (θ).In equilibrium, nonemployed workers only match with new firms to produce new tasks.But new tasks vary in idiosyncratic productivity.A proportion 1 − λ e of new tasks start with idiosyncratic productivity z and, thus, are produced by labor.On the other hand, a proportion λ e of new tasks have their idiosyncratic productivity drawn from G(z) and the firms producing the tasks only hire a worker if the draw exceeds z * e .As a result, we write the lifetime income of a nonemployed worker as

Wage Bargaining
Workers and firms bargain over wages such that the bargained wage maximizes the Nash product: where the parameter 0 < φ < 1 measures the worker's bargaining power.A firm that employs a worker has two outside options.It may fire the worker and look for a new one, which generates a value of βJ L (z) − κ L µ(θ) .11Alternatively, it may fire the worker and adopt the automated technology, which generates a value of βJ K − κ K .We infer that there is an idiosyncratic productivity cutoff that makes the manual firm indifferent between the two outside options, which turns out to be the same as the entry cutoff, z * e , in Eq. ( 5).Thus, we summarize the solution to Nash bargaining as In both cases, workers retain a proportion φ of the surplus, which is an increasing function of the idiosyncratic productivity, z, only due to J L (z).As a result, wages increase with z but less than proportionately.Eq. ( 9), for example, implies that wages increase in proportion This confirms our anticipation that greater idiosyncratic productivity implies greater profits, guaranteeing that only the least productive firms in using the manual technology prefer to use the automated technology.
Given Nash bargaining, job destruction only occurs when the surplus of the match is negative; thus, both workers and firms deem it optimal to destroy the job.The surplus of the match is only negative if it is less profitable for the firm to stay in the manual technology than to move to the automated technology, which occurs when J L (z) < βJ K − κ K .In other words, all firms that draw the task's idiosyncratic productivity below the cutoff z * , fire the worker and move to the automated technology.Simultaneously, when the task's idiosyncratic productivity is too low, workers prefer to move to nonemployment than to stay employed and earn a low wage because E(z) < U .Thus, the cutoff z * satisfies E(z * ) = U or, equivalently, Eq. (2).

Equilibrium
The equilibrium of the model is defined at the aggregate level of the economy and is characterized by the vector (θ, z * , z * e , w(z)), which satisfies the free-entry condition, Eq. ( 4), and the two indifference conditions, Eqs. ( 2) and ( 5), and solves Nash bargaining.

Employment Rate and Number of Firms
We define employment as the number of workers employed at the time of production.As usual, in equilibrium, employment is determined by the balance between the flows from employment to nonemployment and the flows from nonemployment to employment.Using n to denote the employment rate, the flows from nonemployment to employment sum up to f (θ)(1− n): a proportion f (θ) of the nonemployed workers, (1− n), find jobs every period.The flows from employment to nonemployment take two forms because workers may lose their jobs exogenously and endogenously.There is a probability δ L that employed workers lose their jobs for exogenous reasons.From those that do not lose their jobs for exogenous reasons, there is a probability λ n that the productivity of the task changes.And there is a probability G(z * ) that the new productivity is below the cutoff z * , leading the firm to move to the automated technology and fire the worker.Thus, after some algebra, we get an equilibrium employment rate of Because every manual firm employs one worker, n also represents the number of manual firms.But the number of firms that use the automated technology is more intricate: some firms immediately choose the automated technology; others start with the manual technology and then move to the automated technology.We start by measuring the former.First, only a proportion λ e of new firms can choose technologies.Second, if the firms can choose technology, they only choose the automated technology if the idiosyncratic productivity is below the cutoff z * e ; this occurs with a probability G(z * e ).Third, the proportion of those that enter and choose the manual technology is λ e (1 − G(z * e )) + 1 − λ e , which corresponds to the number of firms choosing the manual technology: f (θ)(1 − n).Thus, every period, there is that start production immediately using the automated technology.Now we measure the other source of automated firms: those that start with the manual technology and change technology.To measure this, we must determine the number of firms that endogenously fire their workers every period.Given that there are n manual firms, there is a probability δ L that the job is exogenously destroyed, there is a probability λ n that the productivity of the task changes, and there is a probability G(z * ) that a firm that redraws productivity moves to the automated technology, then the number of firms that automate the production of their respective tasks is Additionally, denoting n K as the stock of automated firms, there are δ K n K automated firms destroyed every period.Thus, there are automated firms.

Output and the Labor Share
To quantify output, we only need to sum the output produced by manual and automated firms because we assume that tasks are perfect substitutes.The output of automated firms is z K n K as all these firms produce z K .But it is not as simple to determine the output of manual firms because they are not distributed according to G(z) from z * to z.To measure output, we need to distinguish between three groups of manual firms: we need to calculate how many manual firms produce tasks with productivity (i) z from the moment they were created and have not redrawn productivity afterwards, (ii) above z * e (by means of draws or redraws of z), and (iii) between z * and z * e (by means of redraws of z).We denote the latter two as n * e and n * , respectively.And we obtain the number of firms producing tasks with productivity z from inception as the residual: n − n * e − n * .
There are two ways in which a manual firm may produce a task with idiosyncratic productivity above z * e and belong to n * e : either the productivity of the task was drawn at the time of entry or it was later redrawn in the interval [z * e , z].The number of manual firms that draw productivity at the time of entry is This follows from two factors.First, every period, f (θ)(1 − n) new manual firms are created.Second, these firms split between those that do not draw productivity (in proportion 1 − λ e of all new firms) and those that draw productivity and prefer the manual technology (in proportion λ e (1−G(z * e )) of all new firms).Furthermore, the number of manual firms that redraw productivity and obtain z above given that a proportion 1 − δ L of manual firms survive exogenous shocks and a proportion λ n redraw productivity.But some of these firms were already included in n * e ; thus, the net inflow of firms by redrawing productivity into n * e is only There are also two ways in which a manual firm leaves n * e : either the firm ends exogenously or it draws productivity below z * e .These exit flows sum to δ Combining the flows into and out of n * e implies after a few derivations: We can apply a similar logic to find the firms that produce tasks with idiosyncratic productivity between z * and z * e .Making the necessary adjustments and taking into account that no firm starts in the manual technology with productivity between z * and z * e , we obtain Having established the number of firms, we quantify output as ) in which we multiply the number of firms in each group by its respective average output.The labor share then is ratio of the number of workers in each group of manual firms (recall that every manual firm employs one worker) multiplied by its respective average wage relative to output: (16)

Calibration
We calibrate the model to monthly US data and summarize our benchmark calibration in Table 1.We set β = 0.996, which implies an annual discount rate of 4.91%.We follow Petrongolo and Pissarides (2001) and set η = 0.5.We also set φ = 0.5.In our model, firms draw the task's idiosyncratic productivity from a uniform distribution, i.e., G(z) = z−z min z−z min , in which z = 0.25 and z min = 0.15.12To calibrate b, we assume it is 70% of the productivity of the firm that draws z = z min + z+z min 2 .This is similar to what we find in many studies in the literature (including Hall and Milgrom (2008), Pissarides (2009), and Coles and Kelishomi (2018)) that assume that b ≈ 0.7z L in models with homogeneous firms.To calibrate the exogenous probability of manual firm destruction, δ L , we impose that the steady-state probability that a firm-worker match breaks equals the average job destruction rate in the US from 1948 to 2010 (Shimer, 2012) For the automated technology, we assume it is δ K = 0.01.We do not impose any particular value for λ e and λ n ; instead we analyze how different values of these two parameters change our results.To increase the range of λ e and λ n , we set κ K = 0.01.We also arbitrarily set κ L = 0.01 and χ = 0.1, but run sensitivity analysis.
Finally, we set z L , z K , and Ω such that our steady-state matches three targets.We target the prime-age (aged 25-54) workers' employment rate and the labor share in the US from 1977 until 2018;13 this implies that n = 0.78 and LS = 0.61.We also target G(z * e ) = 0.5 such that half of the productivity draws exceed the entry cutoff.But, since this target is arbitrarily set, we run sensitivity analysis on this target.

Employment: Is the Future like the Past?
Looking into the last four decades, recent empirical studies on the effects of TFP and routine-replacing technological shocks point to a net increase in employment (e.g., Autor and Salomons, 2018;Gregory, Salomons and Zierahn, 2018).These studies document that the direct labor-displacing (job destruction) effect has been outweighed by indirect effects that ultimately lead to job creation.But do these results hold under all circumstances?In other words, can the future be different?To answer this question, we assess the effects of an automation-augmenting shock under various calibrations of our model.We conclude that our results are highly dependent on the calibration: employment may both increase or dramatically fall. of 1% in the productivity of the automated technology, z K , changes employment, n, when all firms draw productivity at the time of entry (λ e = 1) and under different values of λ n .Clearly, the probability that workers lose their comparative advantage and are endogenously fired -controlled by λ n -affects the response of employment to an automation-augmenting shock (rise in z K ).In the case of (very) low λ n , our model in this paper is very close to the model we used in Guimarães and Gil (2019).Consequently, the results are quite similar in the two models: when λ n is close to zero, manual firms rarely automate the production of the tasks, and a rise in z K slightly increases employment.If, however, we assume larger values of λ n , an automation-augmenting shock may lead to sizable losses in employment: if λ n = 0.15,14 manual firms are more likely to automate the production of the tasks after the shock, and employment falls 2.5%, that is, two and a half times the magnitude of the shock to z K .
Shocks in the economy affect employment through changes in both job creation and job destruction.Thus, to shed more light on the mechanisms in our model, we decompose the two effects of an automation-augmenting shock of 1% on employment on the right-hand side of Figure 2. In particular, we show how the job-finding probability, f (θ), (which indicates job creation) and the job-destruction probability, JD ≡ δ L +(1−δ L )λ n G(z * ), react to the automation-augmenting shock (also as a function of λ n and in the case of λ e = 1).To understand how a rise in z K affects employment, let's first consider the extreme case of λ n = 0.This case implies that tasks that start as manual are never automated: tasks have constant idiosyncratic productivity, z, meaning that workers never lose their comparative advantage; thus, firms have no incentive to shift from the manual to the automated technology in equilibrium.As a result, λ n = 0 also implies that job destruction is constant and unaffected by the automation-augmenting shock.The same is not true for job creation.A rise in z K increases the value of the automated technology, leading to a reallocation effect: some entering firms steer away from the manual technology and invest instead in the automated technology (z * e increases); for a given number of entering firms, job creation shrinks.But an automation-augmenting shock also increases the expected value of a firm, which incentivizes firm entry. 15The free-entry condition, Eq. ( 4), is only satisfied if the value of the manual technology drops, which occurs in our model through higher wages and, most importantly, greater labor market tightness.A tighter labor market is synonym of greater job-finding probability and, necessarily, higher job creation.Therefore, if λ e = 1, the aggregate effect of greater firm entry exceeds the reallocation effect implied by the increase in z * e and, thus, an automation-augmenting shock increases job creation. 16This, together with the constant job destruction (λ n = 0), increases employment.
If λ n > 0, a rise in z K affects both job-finding and job-destruction probabilities.As before, the job-finding probability increases because a rise in z K boosts entry more than it boosts reallocation at the time of entry.Because firms are forward-looking, they have an even higher incentive to create jobs and invest in the manual technology (when λ n > 0 than when λ n = 0) in anticipation of the greater profits when they automate production.But the job-destruction probability also increases: as machines are more productive, firms that use the manual technology are motivated to shift to the automated one.This translates into a higher z * , reducing the average time of a worker-firm match.Because λ n is the probability that the firm redraws the productivity of the task, a higher λ n increases the number of manual firms drawing low productivity (for a given z * ), leading to even greater job destruction.If λ n is large enough, then the increase in job destruction surpasses the increase in job creation, implying less employment. 17  The rise in z K may lead to greater employment even if we mute the channel in Guimarães and Gil (2019) and set λ e = 0.The bottom three lines of Table 2 show the effects of higher z K on the employment, job-finding probability, and job-destruction probability (besides output and the labor share) when λ e = 0 and λ n equals 0.01, 0.05, or 0.15.To allow for a direct comparison, the top four lines of Table 2 show the same experiments when λ e = 1 (and we include the case of λ n = 0 for completeness).If λ e = 0, all tasks demand labor when created, as in Acemoglu and Restrepo (2018), and 15 The expected value of a firm (prior to entry) surges because a higher zK directly increases the expected value of the automated firms and, ceteris paribus, indirectly increases the expected value of manual firms.The latter occurs because the productivity of the tasks produced with manual technology is heterogeneous and the firms drawing the least productive of these tasks prefer the automated technology when zK increases (z * e increases). 16The same mechanism can be found in Guimarães and Gil (2019) and relies on the assumption of an undirected-technological search process as in Benhabib, Perla and Tonetti (2017). 17The increase in z * exacerbates the rise on the left-hand side of Eq. ( 4) as firms only destroy jobs if it is more profitable for them (JL(z) increases for all z; see Eq. ( 1)).Thus, a higher increase in job destruction must be accompanied by an even tighter labor market.But, as we will show in Section 4.1, λn affects job destruction by more than job creation because the automation-augmenting shock increases wages and the prevalence of matching frictions.firms may only take advantage of the increased productivity if they automate the production of the task.Thus, it is remarkable that an increase in z K -the productivity of a technology that can only be used after a job is destroyed -is still capable of leading to greater employment under a slightly positive λ n (see the line regarding λ e = 0 and λ n = 0.01 in Table 2).Indeed, in the case of λ e = 0, an increase in z K continues to affect both job creation and job destruction.First, it continues to promote greater firm entry and job creation because of the increase in the value of the automated technology, as an outside option of the firms using the manual technology.But different from the case of λ e > 0, if λ e = 0, workers only benefit from larger firm entry because all firms start as manual and must hire a worker.Second, an automation-augmenting shock implies that firms have a higher opportunity cost of employing the worker and, thus, prefer to shift earlier to the automated technology (z * increases).This increases job destruction.If λ n is low, the job-creation effect dominates; but if λ n is large, the job-destruction effect dominates. 18  Our results show how our model may both agree and disagree with the empirical findings in Autor and Salomons (2018) and Gregory, Salomons and Zierahn (2018).Under some calibrations, job creation increases more than job destruction, agreeing with their findings that employment increased after productivity enhancements in the past.But under other calibrations, job destruction increases more than job creation and employment may significantly fall.Thus, this suggests that the future of employment may differ from the past.Our model calls the attention specifically to λ n , which we interpret as a feature intrinsic to tasks that characterizes how rapidly workers lose their comparative advantage.In an economy in which workers rapidly lose their comparative advantage (rapid-changing environments) and with matching frictions, employment falls after an automation-augmenting shock.In this economy, jobs last for less periods and the increase in labor market tightness makes it more costly to hire the right worker for the task and allows workers to enjoy greater wages.These effects prevent job creation from keeping pace with job destruction.Therefore, if the nature of the new and current 18 It is not possible to pin down analytically why this result obtains in the case of λe = 0.But there are two aspects that offer a hint on why it happens.First, when λn is low, the weight of endogenous job destruction on total job destruction, JD, is very low: a change in z * barely alters JD if λn is low.Yet, λn does not change the elasticity of f (θ) with respect to θ.Second, if we use Eqs.( 1) and ( 6) both measured at z and z * together with the firing cutoff equation, Eq. ( 2), and free-entry condition, Eq. ( 4), we obtain To properly assess assess how z * and θ affect each other, we need another equation relating them.But the equation above shows that the labor market becomes tighter when the productivity of the automated technology goes up (JK increases).This is a direct effect that takes into account that without a change in z * , the increase in zK directly increases the value of the firm in the cases in which the task is already automated.This naturally increases the value of a job and, thus, job creation.This equation also shows that a rise in z * reduces θ (because jobs last for less periods) and that the elasticity of θ with respect to z * increases with λn (we confirm this numerically given that zL and δL are used to reach our steady-state targets).Thus, for a given change in θ, if λn is low, z * cannot change much to satisfy this equation.Furthermore, any change in z * has a minor effect on JD.But if λn is higher, z * has to fluctuate more to satisfy this equation and has a larger impact on JD, shifting the ranking of the forces at play.jobs is different from the past -particularly, if tasks feature a higher λ n in the future than in the past and, thus, tasks rapidly become liable to be automated -the same productivity shock of the past may have dramatically different consequences in the future.

Sensitivity Analysis
In this section, we assess how different calibrations of our model change the outcomes of an automation-augmenting shock of 1%.We consider eight experiments, and in each experiment we recalibrate one parameter (or target) of the model.We conclude that none of the experiments changes the qualitative predictions of our model.In all cases, both job creation and job destruction increase after an automation-augmenting shock (except in the case of λ n = 0, in which case the job-destruction probability is constant by assumption).And the change in the job-destruction probability is still more sensitive to λ n than the change in the job-finding probability.This implies a negative relation between the change in employment after the rise in z K and λ n : if λ n is low, employment increases; on the contrary, if λ n is high, employment falls.
Our experiments do, however, change the results quantitatively.And among our eight experiments, two have particularly large quantitative effects that we show in Panels B and C of Table 3.These two panels show how a rise in z K affects employment, job-finding probability, and job-destruction probability in economies with z = 0.225 (instead of z = 0.25) and with a Pareto distribution of productivity draws (instead of a uniform distribution), respectively.As in Table 2, we consider various combinations of λ n and λ e .And to ease comparability with the results of our model using the baseline calibration (reported in Table 2), we reproduce those results in Panel A of Table 3.
Economies with a tighter range of productivity draws (low z or high z min ) experience larger changes in the flows after the rise in z K and also tend to experience larger changes in employment than in our baseline economy.We also find a similar result in the case of the Pareto distribution.If the cumulative distribution of productivity draws is of the form G(z) = 1 − z min z ξ , a higher ξ (which concentrates productivity draws near the minimum) increases the effects of the shock. 19The intuition is simple.If we reduce z or increase ξ, the distribution of productivity draws becomes more concentrated and, thus, the same change in z * and z * e alters the optimal decision of a larger proportion of firms.In these circumstances, the same rise in z K amplifies the required change in labor market tightness, θ, to balance the free-entry condition, Eq. ( 4), andmost importantly -motivates a much larger proportion of manual firms to destroy jobs and automate the production of the tasks.Therefore, these experiments paint an even bleaker picture than our baseline: depending on the calibration, the fall in employment after the shock can be as catastrophic as 6.5-fold the magnitude of the shock.
In Panel D of Table 3, we consider the case of a smaller matching function elasticity, η = 0.4 (instead of η = 0.5).We consider this case as it reduces the elasticity of the hiring costs, κ L µ(θ) = κ L θ η χ , relative to labor market tightness, θ.As a result, we would expect greater flows in the labor market, particularly for job creation, to balance the free-entry condition, Eq. ( 4).We show that this does occur but the final impact of reducing η on employment is whimsy because it also magnifies job destruction. 20Finally, we consider the cases of a higher cost of capital, κ K , lower workers' bargaining power, φ, lower proportion of firms that draw productivity below the entry cutoff, G(z * e ), higher jobfilling costs, κ L , and higher matching efficiency, χ.The results of these experiments are detailed in Tables A1 and A2, which we relegate to the Appendix A as they barely affect the results of our model.

Output and Labor Share
Although our focus in this paper is on the effects of automation-augmenting shocks on employment, we can use our model to gather insights about the effect of these shocks on output and the labor share.Table 2 shows that an automation-augmenting shock increases output and reduces the labor share and that λ n amplifies both changes.Thus, the scenarios in which employment falls coincide with an even larger increase in output and fall in the labor share.We find that these results follow from mainly four factors.First, the automation-augmenting shock directly increases output and directly reduces the relative contribution of labor for output.Second, firm entry is amplified by λ n : higher λ n increases the probability that the firm will take advantage of the higher productivity in the automated technology, increasing the incentives for firm entry, which markedly increases output.Third, this increased entry is more concentrated on firms that use the automated technology, lowering the labor share.And fourth, a higher λ n incentivizes firms to fire workers and destroy jobs, also dropping the labor share.
The fact that our model is able to simultaneously reduce the labor share and increase employment is particularly important as this is the pattern observed in most developed countries.Using data for these countries, Autor and Salomons (2018) document that TFP shocks have been employment-augmenting but labor-share displacing.In the literature, most of the models that are able to explain the fall in the labor share predict lower employment (e.g., Caballero and Hammour, 1998;Zeira, 1998;Hornstein, Krusell and Violante, 2007;Prettner and Strulik (2017); Acemoglu and Restrepo, 2018).To the best of our knowledge, until now, only our previous model in Guimarães and Gil (2019) was able to account for the two patterns (lower labor share and increased employment) simultaneously after only one shock.Yet, our previous model robustly predicts an increase in employment after an automation-augmenting shock, which prevents it from giving insights about how the future may differ from the past.Our model in Section 2 is also consistent with the documented patterns in Autor and Salomons but is flexible enough to provide scenarios in which different outcomes may arise from the same sort of shocks.

Ad hoc Function for Wages
Our baseline model shows that after an automation-augmenting shock, employment increases if λ n is low and falls if λ n is large.We find that both job creation and job destruction increase after a rise in z K (unless λ n = 0, in which case the job destruction rate is fixed).But, the change in the job-destruction rate increases much more with λ n than the change in the job-finding rate.One factor that may explain this behavior is the wage response.In all our calibrations, wages increase due to the rise in the job-finding probability and in the value of the manual firm (which increases namely due to a better outside option to move to the automated technology).Yet, the worker's productivity remains unchanged, implying that the rise in z K squeezes the operational profits in the manual technology.So we ask: if wages were only a function of the task's productivity, how would the job-creation and job-destruction margins react to an increase in z K ?
To answer this question, we build a new version of the model in which we replace Nash bargaining with an ad hoc functional form for wages: Wages are the weighted sum of a constant term and the tasks' productivity.In this case, the improvement in the worker's and firm's outside option have no effect on the wage.Importantly, a rise in z K has no effect on wages.
Panel B of Table 4 shows how employment, job-finding probability (indicator of job creation), and job-destruction probability change after an automation-augmenting shock of 1% under various combinations of λ e and λ n .21For convenience, Panel A of the same table reproduces the results for the same experiments using our baseline model of Section 2. The main takeaway from Panel B is that employment increases for all the combinations we consider of λ e and λ n , which is in stark contrast with the results reported in Panel A. By further contrasting Panels A and B, we see that the job-finding rate increases much more while the job-destruction rate increases less in this version of the model than in the baseline one.Thus, if wages are orthogonal to z K and θ, firms have a much greater incentive to hire a worker as their operational profits remain unchanged.Furthermore, and by the same token, firms have less incentives to fire the worker and move to the automated technology.Note: This table shows the effects of an automation-augmenting shock under various combinations of the probability that the task's productivity is drawn at the time of entry, λe, and the probability that it is redrawn afterwards, λn.The first two columns show the calibration of these two probabilities.The next columns, divided in four panels, show the percentage change in the employment, job-finding probability, and job-destruction probability.In each panel, we use a different version of our model.The shock to zK is of 1%.
Panel B of Table 4 also shows that the change in the job-destruction rate continues to increase much more with λ n than the change in the job-finding rate.The net effect is that the change in employment tends to be negatively related with λ n , which suggests that for sufficiently high λ n , employment may still drop after an automationaugmenting shock.We confirm this in parallel experiments: employment falls if λ e = 1 and λ n ≥ 0.26, as well as if λ e = 0 and λ n ≥ 0.23, because job destruction increases more than job creation after the rise in z K .It is natural that the job destruction rate increases with λ n as this rate becomes more sensitive to endogenous factors.Yet, at first sight, it is unclear why the job-finding probability increases less than the job-destruction probability given that there are also greater incentives to create new tasks and jobs if λ n is high.
We conjecture that matching frictions are behind this pattern.As the labor market tightness, θ, increases, the costs of a firm to match with a worker also increase, reducing incentives for job creation.We can test this conjecture by checking how our results change with different calibrations of the matching function elasticity, η.If η is low, then the costs of a firm to match with a worker are less sensitive to the labor market tightness ( κ L µ(θ) = κ L θ η χ ).Thus, matching frictions are less relevant for job creation and we should observe greater job creation after an automation-augmenting shock.Using our baseline model, in Section 3.3, we concluded that η barely affects how employment reacts to the increase in z K .Yet, Figure 3 shows a different result if we use our model with the ad hoc wage equation; in fact, it confirms our conjecture that matching frictions prevent a greater increase in employment.This figure plots how the job-finding and job-destruction rates change after the automation-augmenting shock for a range of values of λ n and using our model with the ad hoc wage equation.On both panels, λ e = 1.The difference between the panels lies only in the value of η: the left-panel assumes η = 0.4; the right-panel assumes η = 0.5.Confirming our conjecture, job creation increases much more after the rise in z K if η = 0.4 than if η = 0.5.Interestingly, η barely affects the change in job destruction.Thus, employment reacts more after an automation-augmenting shock if η = 0.4.But why are the results so different when we use Nash bargaining and when we use our ad hoc equation?The reason seems to lie in the outside option of workers, U .If the job-filling probability, µ(θ) = χθ −η , is less sensitive to changes in labor market tightness, θ, then the job-finding probability, f (θ) = χθ 1−η , is more sensitive.Thus, given that U and f (θ) are positively related (see Eq. 7), ceteris paribus a lower η increases the elasticity of U relative to θ, allowing all workers to demand greater wages.Our ad hoc wage, however, prevents the operational profit of manual firms to be affected by U , leading to the different results.
Our experiments with the model assuming the ad hoc equation work as counterfactuals to understand the dynamics in our original model.But these experiments do not seem to be a good account of how an automation-augmenting shock is likely to unfold in the future.Unless the historical positive relationship between labor market tightness and wage increments definitely breaks in the future, the automation-augmenting shock will increase wages, which may promote the sizable negative employment effects that we obtain using our baseline model.Note: This figure shows the effects of an automation-augmenting shock using our model with the ad hoc wage equation.In both panels, we assume that all firms draw the tasks' productivity at the time of entry, λe = 1, and different probabilities that this productivity is redrawn afterwards, λn.Both panels show the percentage change in the job-finding probability and in the job-destruction probability.In Panel A, η = 0.4; in panel B, η = 0.5.The shock to zK is of 1%.

Lower Frictions
Our baseline model suggests that, as λ n increases, it becomes easier to fire a worker than to hire a worker due to matching frictions, because the latter increase wages and the costs to find a suitable worker.Matching frictions in our model come from the matching function but also come from our assumption that workers who lose jobs stay unemployed for at least a period (month).Although this is a typical assumption in models with matching frictions and finds support in the evidence (Hall and Kudlyak, 2019), we can argue that in an economy that experiences a surge in labor market flows, this assumption may be too restrictive.In such an economy, it is likely that workers find jobs even within a month from losing them and start production immediately. 22 Relaxing this assumption may be important in our model: in an economy that experiences a surge in job destruction, the pool of available workers to match with firms may become too narrow, raising the relevance of matching frictions.Thus, we ask: what are the predictions of our model if workers can look for jobs and start production immediately after losing their jobs?
Panel C of Table 4 answers this question and, by contrasting the results in this panel with those in Panel A, confirms our prediction.In an economy that experiences an automation-augmenting shock and in which workers who lose jobs can look for other jobs and restart production immediately, matching frictions become less relevant and 22 Christiano, Eichenbaum and Trabandt (2016) make a similar assumption.They build a model with matching frictions but calibrate each period as a quarter, whereas tipically these models are calibrated with monthly data.Because in US data many workers find jobs and start production within a quarter, it would be too restrictive to assume that workers who lose jobs need to wait for the quarter to end to restart production.In our case, the probability to find jobs may increase so much that it can be equally restrictive.
the job-finding probability increases more with λ n .The implication of this is that employment becomes less negatively correlated with λ n ; yet, and even though this model also generates a smaller increase in the job destruction rate than the baseline, the change in employment continues to fall significantly with λ n .
The lack of firepower of this experiment is not completely surprising.First, our sensitivity analysis with η in Section 3.3 shows that our results are not much sensitive to the calibration of the matching function.This suggests that the degree of matching frictions are not much quantitatively relevant in our model. 23Second, the change in the pool of nonemployed workers imposed by the rise in the job-destruction rate is not so great.Even in the case of λ e = 1 and λ n = 0.15, the rise in the job-destruction rate displaces only an additional 0.0037 proportion of the workforce per period.Given our steady-state target of nonemployment of 1 − n = 0.22, the number of workers looking for jobs is not much affected.

CES Aggregator
In our baseline model, we assume that the tasks produced by workers and by machines are perfect substitutes.In this section, we instead build a model assuming that -from the perspective of consumers -they are imperfect substitutes.Our motivation for this setup is to take into account that consumers may deem differently a task produced by a machine or by a worker, a factor that we call human touch.For example, both a vending machine and a seller sell goods and, thus, they broadly perform the same task.Nonetheless, consumers may value the task differently on the basis of who is performing it.The worker (seller) can offer a more personal (human touch) to the task whereas the machine (vending machine) offers an impersonal service.This naturally renders machine and worker imperfect substitutes, from the perspective of the consumer.An ubiquitous use of the automated technology may, then, change the relative price of the tasks produced by machines and workers as consumers look for the differentiated offer of the manual technology.Our goal, then, is to assess how the presence of the human touch (imperfect substitutability) affects the wrestle between the job-finding and job-destruction margins in determining how an automation-augmenting shock affects employment.In particular, can this setup reverse our prediction that economies with high λ n experience lower employment after an automation-augmenting shock?Or are there any relevant quantitative implications?
We implement this model by assuming a CES aggregator of the outputs of the tasks produced by automated and manual technologies, where y is an index of final consumption (i.e., a bundle of goods and services demanded by consumers).In this setup, the elasticity of substitution is ǫ, and this model nests our baseline model if ǫ = ∞.In particular, the CES takes the following form: where y K and y L are the sum of the outputs produced using each type of technology: Assuming competitive markets in the intermediate goods y K and y L and a profit-maximizing final-good producer, we get: Thus, a rise in z K leads to an increase in y K , which reduces the price of the tasks produced using the automated technology.Furthermore, it also leads to a rise in y, which converts into a higher price of the tasks produced using the manual technology.These two effects clearly affect the motivation to create jobs as well as to fire workers and automate the production of tasks (destroy jobs).
Panel D of Table 4 shows the effects of an automation-augmenting shock in the model with the CES assuming ǫ = 5 and under the various combinations of λ e and λ n .Assuming that the outputs of the two technologies are imperfect substitutes does not change our results qualitatively.In economies with high λ n , employment still falls.Yet, our setup with a CES affects the results quantitatively: it reduces the elasticities in the model because the total impact of the shock, p K z K , is lower reflecting the fall in the price of the automated good, p K , after the rise in z K .
One interesting outcome reported in Panel D of Table 4 is that our setup with the CES constrains job destruction much more than job creation.To shed light on this, on the left panel of Figure 4, we plot how the job-destruction probability, JD, and jobfinding probability, f (θ), change with the elasticity of substitution, ǫ, under the case of λ e = 1 and λ n = 0.15.On the right-hand side of the same figure, we plot the prices of the tasks produced by each type of technology also as a function of ǫ.The shock is, as usual, an automation-augmenting shock of 1%.Undoubtedly, the job-destruction margin is much more affected by the elasticity of substitution to the point that the shift of the two margins almost converges if ǫ = 2. (Recall that in the baseline, ǫ = ∞, the job-finding probability increases 1.32% and the job-destruction probability increases 13.11%).There are two aspects that can explain this.First, an automation-augmenting shock reduces p K and, thus, curbs down the increase in machines' productivity, p K z K .This naturally reduces the incentives to destroy jobs and automate tasks after the rise Note: This figure shows the effects of an automation-augmenting shock using our model with the CES aggregator.To produce these results, we assume that all firms draw the tasks' productivity at the time of entry, λe = 1, and that on average about every six months this productivity is redrawn afterwards, λn = 0.15.The left-panel shows the percentage change in the job-finding probability and in the jobdestruction probability.The right-panel shows the percentage change in the price of tasks produced using the manual technology and in the price of the tasks produced using the automated technology.The shock to zK is of 1%. in z K .It also reduces the incentives to create jobs as the shock has a lower impact on the value of firms.Yet, the same automation-augmenting shock increases p L and, thus, increases workers' productivity, p L z L z.This balances the effect (of lower p K z K ) on job creation but further reduces the motivation to destroy jobs and automate tasks.As we increase ǫ, the fall in p K and the rise in p L become smaller; thus, the incentives to automate and destroy jobs increase significantly while job creation changes much less as the effects of the two prices tend to almost balance out.
These mechanisms help explain why in calibrations with high λ n (keeping ǫ fixed), the assumption of imperfect-substitutability between the two outputs, y K and y L , (results reported in Panel D of Table 4) affects job-destruction much more than job creation.Economies with high λ n experience greater reallocation from the manual to the automated technology after an automation-augmenting shock.Greater reallocation then implies a greater rise in the number of firms using the automated technology, n K , and, thus, in the output produced using the automated technology, y K .In this setup with the CES, the greater rise in y K further drops p K and further increases p L , leading to lower incentives to fire workers and, thus, a greater drop in job destruction when contrasted with the baseline results.The two effects of p K and p L tend to balance the change in job creation, leading to the smaller relative drop in job creation when compared with the baseline.
These experiments with the CES aggregator show that consumers have an important role in determining the effects of automation-augmenting shocks on employment.If a large proportion of the tasks are directed to consumers, their preference for the hu-man touch may severely reduce the negative effects of automation-augmenting shocks on employment.

Concluding Remarks
In this paper, we build a model to assess how an automation-augmenting shock -a generalized increase in the productivity of machines/robots -affects employment.This model relies on multiple previous contributions (Mortensen and Pissarides, 1994;Hornstein, Krusell and Violante, 2007;Acemoglu and Restrepo, 2018;and Guimarães and Gil, 2019) to satisfy two criteria.First, it is consistent with the past documented by Autor and Salomons (2018) and Gregory, Salomons and Zierahn (2018): an automationaugmenting shock can simultaneously reduce the labor share and increase employment.Second, our model is flexible enough to offer insights on how the future may differ from the past: depending on the calibration, an automation-augmenting shock may increase or decrease employment.
In our model, an automation-augmenting shock enlarges labor market flows.On the one hand, it promotes greater job destruction because the automated technology (that only uses robots) becomes more attractive than the manual technology (that only uses labor).On the other hand, due to either a sort of complementarity at the time of entry (as in Guimarães and Gil, 2019) or because hiring a worker is a crucial first step in starting the production of a task (as in Acemoglu and Restrepo, 2018), firm entry and job creation also increase.Yet, this robust increase in labor market flows predicted by our model contrasts with US data showing a downward trend in flows for the last decades (Davis and Haltiwanger, 2014).This documented trend is even more relevant given that the fall in labor market flows occurred in a period of increased automation and investment in robots (Prettner and Strulik, 2017;Acemoglu andRestrepo, 2019, Guimarães andGil, 2019).But a closer look into the changes in labor market flows across US sectors reveals that, even though labor market flows fell in all sectors, they fell unevenly across them.Particularly, Decker et al. (2014) document that labor market flows fell much more in retail and services sectors than in finance and manufacturing sectors -the sectors that arguably were more susceptible to automation.We can interpret these patterns in light of two trends: a general trend reducing labor market flows in all sectors (e.g., demographics as argued by Engbom, 2019) and a trend increasing labor market flows in some sectors (with greater pervasiveness of automation).Our model abstracts from the general trend and only takes into account the positive contribution of automation-augmenting shocks to labor market flows.
Using our model, we sort the cases in which employment increases after an automationaugmenting shock and those in which it falls.In environments in which the comparative advantage of workers in producing a task is relatively stable -slow-changing environments -the increase in job creation dominates the increase in job destruction.Therefore, in slow-changing environments, employment increases.On the contrary, in environments in which the comparative advantage of workers changes frequently -rapid-changing environments -an automation-augmenting shock leads to massive job destruction that clearly offsets the increase in job creation.In these environments, employment catastrophically falls.
We also find that the fall in employment in rapid-changing environments crucially depends on the relevance and prevalence of what we call human touch.Human touch refers to a consumers' preference for diversity in the producer/provider of the task itself: in a world with widespread usage of machines to offer multiple services to consumers, they may value the differentiated service of a human.If that is the case, an automation-augmenting shock (and ensuing spread of usage of machines/robots) increases the price of the tasks produced by workers relative to those produced by the machines/robots.This curtails job destruction, reducing the fall in employment.
Our paper then clarifies how the future may differ from the past.If the comparative advantage of workers in producing new tasks starts to vanish more rapidly than in the past, then automation-augmenting shocks will curb down employment rather than increase it.The extent of this fall will naturally depend on demand and, particularly, consumers' preferences.If many of the tasks produced in an economy are sold directly to consumers and they have a preference for the human touch, then the fall in employment will unlikely be catastrophic.But if most of the tasks are part of a vast value chain to produce a final good or if consumers have no preference for the human touch, then the fall in employment in the future may be catastrophic.Note: This table shows the effects of an automation-augmenting shock under various combinations of the probability that the task's productivity is drawn at the time of entry, λe, and the probability that it is redrawn afterwards, λn.The first two columns show the calibration of these two probabilities.The next columns show the percentage change in the employment, job-finding probability, and job-destruction probability under a slightly different calibration in each panel.The shock to zK is of 1%.Panel A presents the baseline results; Panel B presents the results assuming a higher cost of capital/robot; Panel C presents the results assuming a lower workers' bargaining power; Panel D presents the results assuming a lower proportion of productivity draws below the entry cutoff.Note: This table shows the effects of an automation-augmenting shock under various combinations of the probability that the task's productivity is drawn at the time of entry, λe, and the probability that it is redrawn afterwards, λn.The first two columns show the calibration of these two probabilities.The next columns show the percentage change in the employment, job-finding probability, and jobdestruction probability under a slightly different calibration in each panel.The shock to zK is of 1%.

A Further robustness checks
Panel A presents the baseline results; Panel B presents the results assuming higher job-filling costs; Panel C presents the results assuming a higher matching efficiency.

Figure 2
Figure 2 summarizes our main results.On the left, this figure plots how an increase

Figure 3 :
Figure 3: The effect of higher z K under λ e = 1 and different values of λ n and η

Figure 4 :
Figure 4: The effect of higher z K under λ e = 1, λ n = 0.15, and different values of ǫ

Table 2 :
The effect of an increase of 1% in z K This table shows the effects of an automation-augmenting shock under various combinations of the probability that the task's productivity is drawn at the time of entry, λe, and the probability that it is redrawn afterwards, λn.The first two columns show the calibration of these two probabilities.The next five columns show the percentage change in the output, labor share, employment, job-finding probability, and job-destruction probability.The shock to zK is of 1%.

Table 3 :
The effect of an increase of 1% in z K -Sensitivity Analysis This table shows the effects of an automation-augmenting shock under various combinations of the probability that the task's productivity is drawn at the time of entry, λe, and the probability that it is redrawn afterwards, λn.The first two columns show the calibration of these two probabilities.The next columns show the percentage change in the employment, job-finding probability, and jobdestruction probability under a slightly different calibration in each panel.The shock to zK is of 1%.Panel A presents the baseline results; Panel B presents the results assuming a lower maximum productivity draw; Panel C presents the results assuming a Pareto distribution of productivity draws; Panel D presents the results assuming a lower elasticity of the matching function.

Table 4 :
The effect of an increase of 1% in z K -Model comparison

Table A1 :
The effect of an increase of 1% in z K -Sensitivity Analysis

Table A2 :
The effect of an increase of 1% in z K -Sensitivity Analysis