Search and matching under the AI pooling equilibrium

How the use of AI in job hunting affects the labour market: a search-theoretic approach

When AI is used to write cover letters, it maximises textual alignment with job postings. Presumably, the same mechanism applies for CVs too¹. However, employers respond via ascribing less weight to these documents in the hiring process. In other words, CVs are downgraded as a signal of ability. Anecdotally, I also notice that “first-stage” phone calls, once somewhat of a novelty outside a few industries, have now become almost ubiquitous. Now, verification of whether the applicant is actually a human being is an essential feature of the process.

So how do we square these findings with the fact that, as noted in the paper, greater time spent editing AI drafts is associated with increased hiring success? Or that probably over 30% of candidates use LLMs for their applications? Likewise, if AI use is associated with substantial gains in the worker’s productivity, then a clear sign of competency in using AI should be a positive signal of ability?

I believe that this data is indicative of the emergence of a pooling equilibrium. Yes, whilst AI is easy to detect in writing, editing can easily obfuscate this. Why else would so many media companies adopt blatant use of LLMs, meaning that once editing is accounted for, the above figures for prevalence of AI in media writing is likely to be a large underestimate? Therefore, we have an initial minority of applicants that use LLMs to form an initial draft of their CVs or cover letters, which optimises for matching with the relevant vacancy, then edits to signal authenticity². This combination maximises the applicant's probability of being hired. Over time, applicants that do not use AI in drafting their documents will discover their disadvantage, as they are increasingly ignored for vacancies that they are otherwise qualified for. Hence, edited AI drafts will become a majority strategy, so a pooling equilibrium will form. However, to the extent that these CVs and cover letters are written for alignment with the vacancy, as opposed to alignment with the candidate’s history or skill-set, this equilibrium is suboptimal. The applicant knows their true ability, however ex-ante an employer does not until the applicant is hired. This AI pooling equilibrium increases the information frictions, so amplifies adverse selection, and reduces the efficiency of matching.

What are the broader implications for the labour market? Consider a simple DMP-like model. I will first stimulate such for aggregate employment trends, then analyse the special case of AI-exposed entry-level jobs. I argue that this AI pooling equilibrium, by amplifying information frictions, is a more inefficient matching process, so vacancies increase relative to the counterfactual, albeit the effect on unemployment is uncertain.

Let m=μM(u,v) be our matching function, with μ taking any real value. The probability of an unemployed individual finding a job is given by:

Φ(θ) = m/u = μM(1,θ)

with θ=v/u denoting labour-market tightness, and Φ’(.)>0. The Beveridge curve is then defined as³:

u = s/(s+Φ(θ))

for s being the separation rate.

Upon a successful match, an employee receives surplus ω-β, where β gives the value of the outside option. The employer receives y-ω-(-kyθ), for y being the employee’s output and -kyθ being the opportunity cost of hiring said employee relative to continued searching⁴, with 0<k<1. Total surplus then follows, and is y-β+kyθ. If total surplus is positive, then the vacancy will be filled, at a given wage ω* that satisfies both parties.

Wages are set to split total surplus under Nash bargaining. Let ω-β = γ(y-β+kyθ), where 0<γ<1 represents the bargaining power of the employee. Then the wage curve is given by:

ω = (1-γ)β + γ(y+kyθ)

Therefore wages are a weighted average of the worker’s outside option and their value to the firm, weighted according to their bargaining power. There exists a positive reduced-form relationship between wages and labour market tightness.

A vacancy is created when it is expected to boost firm profitability. The surplus the employer receives upon creating the vacancy is given by (y-ω)/(r+s) - ky/q(θ), which is the present value of the returns from filling a vacancy⁵ minus the expected opportunity cost, ky weighted by the expected time the vacancy remains open as a function of tightness, 1/q(θ). q(θ) gives the vacancy filling rate:

q(θ) = m/v = μM(1/θ,1)

with q’(.)<0.

In expectation, the employer’s surplus is zero, given a competitive goods market. A vacancy will henceforth be created under the following condition:

(y-ω)/(r+s) = ky/q(θ)

A negative relationship between wages and labour market tightness arises. Higher wages reduce the expected returns from filling a vacancy, which leads to lower vacancy creation. However that raises tightness so reduces the expected time a vacancy remains open, hence reduces the expected cost of creating the vacancy.

Wages and labour market tightness are hence determined in equilibrium by the wage creation curve and the job creation curve. The wage creation curve is upward-sloping in wages and tightness, and the job creation curve is downward-sloping in both those variables. Given ω* and θ*, we can also plot our point on the Beveridge curve to obtain v* and u*.

Let us now simulate the effects of AI on the overall labour market. If AI is complementary to the skills of some workers, then this will increase y. AI also increases the discount rate via higher real interest rates, with the effect on separations being ambiguous so assumed to be constant. So in aggregate, we would expect AI to increase wages and labour market tightness, as both the total surplus from the match and the returns from creating the vacancy increase.

However, when we introduce heterogeneity in skills and job roles, we can see that for AI-exposed entry-level jobs, which are perhaps most at risk of being replaced by AI, k falls. Instead, y is held constant. The more AI becomes a viable substitute, the less costly it is for the employee to keep the vacancy open, which reduces both total surplus and the costs of creating the vacancy. As I have noted before, “whether AI is a complement or substitute to labour as a factor of production depends on the employee and the task at hand”, so I am assuming that the overall effect is ambiguous. However, there is tentative evidence that AI may be substitutes for some entry-level positions. For those professions, this will dampen any gains to wages and vacancy rates, so the total effect on wages and vacancies for those groups is uncertain.

However, labour market tightness only represents vacancies relative to unemployment, and not the total number of vacancies and unemployed. For a given θ*, there exists multiple equilibria for v and u, selected by the parameter for matching efficiency, μ. As matching has become less efficient, the Beveridge curve shifts outward.

This AI pooling equilibrium will increase vacancies and unemployment for any given level of tightness. However, overall tightness will also increase. Hence vacancies will be higher relative to the counterfactual, with the effect on unemployment being uncertain. AI-exposed entry level jobs are most at risk. Nonetheless, labour markets are currently cooling, with a growing divergence between stockmarket indicators and vacancies. Yet it is obvious from this model that AI cannot fully explain these trends.

1. I forget that most of my audience is American, so forgive my use of “CV” over “resumé”.

2. Mechanism design 101 of course is that private traits =/= public signals, unless you specifically incentivise such under a VCG. Gibbard-Satterthwaite anyone? So there is no contradiction here.

3. Ut+1 - Ut = s(L-Ut)-fUt for f=Φ(θ) being the job finding rate, so in equilibrium where Ut+1=Ut=U*, U*=(s/(s+f))L. As convention dictates, I use lowercase for rates, so dividing by L gives u*=s/(s+f).

4. Intuitively, a tighter labour market means it's harder to find qualified candidates, so it's more costly to continue searching relative to taking the first applicant available. k here represents the cost of delaying output by keeping the vacancy open.

5. Discounted by the real rate of interest, plus the probability of separation.