Entry decision, the option to delay entry, and business cycles

Layer 1: Overview

Research question and motivation. US cohorts of establishments born in recessions persistently employ fewer workers at entry and over their life cycle, yet are on average more productive than expansionary cohorts; the number of entrants is procyclical and roughly four times as volatile as aggregate employment. Standard firm-dynamics models cannot reproduce this strong, persistent selection of entrants without generating excessive variation in aggregate variables, because the expected lifetime value of entry is relatively insensitive to aggregate shocks of reasonable magnitude. The paper asks what makes initial aggregate conditions matter so much for the selection of entrants, and answers: potential entrants’ ability to delay entry, a margin missing from existing frameworks.

Model setup. The author builds a discrete-time, infinite-horizon firm-dynamics model with endogenous entry and exit, building on Moreira (2015) in the style of Hopenhayn (1992). The only aggregate shock is an exogenous AR(1) aggregate demand shock z. Heterogeneous incumbents differ in idiosyncratic productivity s (AR(1)) and customer capital b (accumulated from past sales, depreciating at rate δ), operate under monopolistic competition, draw a random fixed operating cost each period, and may exit endogenously or via a random exit shock γ. A constant mass of potential entrants holds heterogeneous signals q about post-entry productivity, drawn from a time-invariant Pareto distribution W(q). The key deviation: entrants may keep their signal and delay, observing a new z next period (probability τ of retaining the signal; τ=0 nests the standard model, τ=1 is the baseline). This creates a non-negative option value of delay V^w(q,z) that rises with q and with z.

Main findings (with magnitudes). The option to delay generates a countercyclical opportunity cost of entry: for reasonable parameters, entrants postpone until the present value of entry is up to twice the fixed entry cost. The threshold signal is countercyclical, so recessionary cohorts are fewer but more productive. Expected delay duration ranges from zero to six periods (years), negatively correlated with q. Calibrated to BDS establishment data 1977-2015 (a period is a year), with ρz=0.57, σz=0.0022, and τ=1 (an alternative identification gives τ=0.965, with nearly identical dynamics). The mechanism raises the variance of the number of entrants, for a given shock process, by about seven times. Recessionary (expansionary) cohorts employ 5.7% fewer (5.0% more) workers than the average cohort, persisting beyond 15 years; shutting down delay (τ=0) collapses this to ~1%, so ~80% of cohort-employment variation comes from delayers. Average recessionary productivity is ~3% higher under τ=1 vs only 0.4% under τ=0. The full model explains more than three-fourths of the persistence and variance of aggregate employment (model autocorrelation 0.57 vs data 0.61; std 0.012 vs 0.015). Empirically, cohort-level employment differences are driven by the composition (high-productivity/high-growth share), not the number, of entrants; the persistent customer-capital process plays a minor role (<7%).

Implications. Validating against the Great Recession: cohorts entering 2008-2016 account for ~45% of the depth (of an 8.9% drop in 2012) and ~85% of the slow recovery by 2016 in the data; the model reproduces ~39% of the 2012 depth and ~75% by 2016, with most of it coming from the entry margin. A standard model without delay, calibrated to the same facts, requires σz ~7x larger, yields aggregate-employment variance 1.7x the data, and predicts a Great-Recession employment drop twice as large as observed. Matching aggregate employment instead requires aggregate-demand-shock autocorrelation 1.40x and variance 25x higher. Ignoring the option to delay therefore yields misleading predictions about entrants’ responses to permanent, temporary, and anticipated (news) policy shocks.

Layer 2: Deep Dive

What is the core mechanism that amplifies the effect of initial aggregate conditions on entrant selection?

The option to delay entry. Because entering today and entering tomorrow are mutually exclusive, waiting carries a non-negative option value V^w(q,z) that rises with the signal q and with aggregate demand z. With this intertemporal choice, a firm enters only if its gross value of entry exceeds the total opportunity cost = fixed entry cost ce + option value of delay. This total cost is countercyclical (up to twice ce in recessions), so the threshold signal q*(z) becomes much more elastic to z. Even a small change in the relative benefit of entering today vs tomorrow shifts selection substantially, whereas without delay (τ=0) entry follows a neoclassical rule — enter if net lifetime benefits are non-negative — and the threshold barely moves with z.

Why does a firm ever find it optimal to delay, given it forgoes period profits?

The decision hinges on the net value of waiting, V^w(q,z) − (V^gross(q,z) − ce). The aggregate demand level at entry affects not only first-period profits but also the expected post-entry survival rate (1−γ)G(c*_f), which is procyclical: in recessions the expected long-run value is lower, raising the risk of premature post-entry failure. This procyclical ‘discount factor’ makes entry during expansions more valuable. Medium-productivity firms wait until the expected survival rate is high enough to compensate for low early-life demand. The author stresses that without irreversible and endogenous exit, the benefits of waiting would always be negative — endogenous exit risk is essential to the mechanism.

Who delays, and who does not?

Delay has no effect on high- and low-productivity potential entrants; only medium-range-signal firms (q in [q*{τ=0}(z), q*{τ=1}(z)]) find it profitable to wait for better aggregate demand. The lower the aggregate demand, the wider this range. At the business-cycle peak, nobody delays, so selection coincides with and without the option.

What is the empirical identification strategy and its main threat?

Using the Business Formation Statistics (BFS), based on IRS EIN/SS-4 applications matched to BDS new employer businesses, the author separates applications that form a business within the first four quarters (First 4Q) from the second four quarters (Second 4Q), 2004Q3-2016Q4. The ‘wait-and-see’ channel is identified from the share of late start-ups = Second4Q/(First4Q+Second8Q), which is significantly countercyclical (Fact 2). The main confound (Fact 3’s threat): bad aggregate conditions could lengthen the time required to build a business (e.g., harder credit access in recessions) rather than reflecting deliberate waiting. The author controls for this using the average duration of business formation within the first four quarters and the total number of formations within eight quarters; the countercyclical share of late start-ups survives (Table 2, coefficient -0.304*** on HP real-GDP cycle). A separate caveat: the author cannot evaluate the economic magnitude of the channel from data, because entrants who delay AND delay applying for EINs, or who apply but never return, are unobserved — hence the quantitative role is assessed via the structural model.

What is the testable implication that distinguishes the mechanism, and is it borne out in data?

The model predicts that recessionary cohorts have, on average, HIGHER long-run survival rates than expansionary cohorts (countercyclical survival), because firms wait until expected survival is high enough. Without the option (τ=0) the model produces acyclical survival rates. In BDS data 1979-2015, cohort survival rates at ages g=1..5 are persistently negatively correlated with aggregate conditions at entry (e.g., for S3, corr with HP real-GDP cycle = -0.38, p=0.02; corr with Ihp = -0.46, p=0.00), robust across HP, linear-trend, unemployment, and NBER indicators, and across firm- vs establishment-level units. Note two counteracting forces: low demand directly lowers survival (higher failure) but raises it via selection; the net countercyclicality supports the selection channel.

How is the model calibrated?

17 parameters; a period = a year, unit = establishment. β=0.96 (4% riskless rate). Demand/customer-capital/productivity parameters from Foster et al. (2008, 2016): ρs=0.814, price elasticity ρ=1.622, demand-to-customer-capital elasticity η=0.919, depreciation δ=0.188. Entrant-distribution, selection, survival, size, and growth parameters (q, ξ, ce, μf, σf, γ, b0, σ_s, σ_e, α) jointly matched to BDS cohort moments (average entry rate ~12.1%, entrant employment share, size and survival to 30 years, employment share to age 5). The aggregate demand process (ρz=0.57, σz=0.0022) is calibrated to the autocorrelation (0.25) and std (0.06) of the HP-filtered (smoothing 100) entry rate. τ set to 1; an alternative strategy using the aggregate-employment time series identifies τ=0.965.

How does the paper decompose the source of persistent cohort-employment differences?

Counterfactuals (Table 6) hold the variation in the number of entrants fixed while varying composition. ‘Adjust lowest s’ (number variation from low-productivity firms) yields small, transient cohort-employment effects; ‘adjust highest s’ yields large, persistent effects. The baseline lies between them: medium-productivity firms that delay amplify the procyclical variation in high-productivity entrants, raising persistence. This matches Decker et al. (2014) and Pugsley-Sedlacek-Sterk: a small share of high-growth firms drives cohort contributions, and ex-ante entrant types explain most post-entry performance. The ‘only selection’ counterfactual (shutting demand effects on post-entry firms) shows the customer-capital process contributes less than 7% to cohort-employment persistence.

How does the impulse-response analysis illustrate propagation?

A one-time negative demand shock sized to cut entrants by 25% (the Great-Recession magnitude): the baseline economy takes 3 years to recover half the employment decline and another 12 years to recover an additional 25%. An economy where the shock does not affect the entry margin recovers three-fourths of the decline in only 2 years, even when the shock is enlarged to match the baseline’s initial employment drop. Persistent entry-margin shocks accumulate, substantially deepening and prolonging the downturn (Table 9).

What are the policy implications and their scope conditions?

With the option to delay, entrant responses depend on the relative benefit of entering today vs tomorrow, so policy effects vary with type, magnitude, timing, and duration. (1) A temporary cut in fixed entry cost raises the number of entrants more than a permanent cut during recessions, with equal effect in expansions; marginal entrants are high-productivity firms in recessions, low-productivity in expansions. Without the option, the response is invariant to policy duration. (2) News of a future entry-cost cut (after T periods) weakly raises the threshold signal in all states — i.e., reduces entry today — and for small T this indirect, entry-deterring effect can dominate the eventual entry boost; standard models would only transmit such news through general-equilibrium channels. Scope: results derive from a partial-equilibrium reduced form; the author argues (Appendix A.3) that in general equilibrium the option value stays non-negative, so the entry threshold is weakly higher than in models without persistent signals, though procyclical wages partly offset the procyclical-discount-factor force.

How does the paper relate to and differ from prior work?

It addresses the Samaniego (2008) result that entry/exit are insensitive to reasonable productivity shocks and the Lee-Mukoyama (2018) ‘puzzle’ of generating strong entrant selection. Rather than imposing cyclical entry costs (Lee-Mukoyama 2018), an entry function (Sedlacek-Sterk 2019), or exogenous entry-specific shocks (Clementi-Palazzo 2016; Sedlacek-Sterk 2017), it derives amplified selection endogenously from the option to delay. It complements ‘missing generation’ (Gourio-Messer-Siemer) and demand-side (Sedlacek-Sterk; Moreira) explanations of procyclical cohort employment, extends the real-options literature (Bernanke 1993; Dixit-Pindyck 1994; Pindyck 2009; Bloom 2009) to the entry margin, and reinforces Sedlacek-Sterk’s finding that entry-stage selection, not post-entry choices, drives cohort contributions to aggregate fluctuations.

What extensions and robustness checks are provided?

(1) A two-stage entry phase (Appendix A.1) micro-founds the constant mass of potential entrants by adding an ‘aspiring start-up’ free-entry stage, calibrated so only ~13% of aspiring start-ups (cq=0.022) become actual entrants, reconciling the low BFS application-to-employer-business transition rate (~14% over two years). (2) Allowing accumulation of delayed potential entrants (Appendix A.2) amplifies cyclical differences across cohorts and increases procyclical entry-rate variation. (3) A general-equilibrium version (Appendix A.3) shows the model performs at least as well as standard models. Empirical results are robust to alternative cycle definitions (HP, linear trend, unemployment deviations, NBER), to firm- vs establishment-level units, to annual vs quarterly BFS data, and to ten-year pre-crisis cohort averages in the Great-Recession exercise.

What caveats does the author flag?

The model generates a countercyclical average entrant size (consistent with Lee-Mukoyama 2015 for manufacturing plants) but at odds with Sedlacek-Sterk’s finding of procyclical entrant size in BDS; the author conjectures that allowing procyclical initial customer capital would only widen cyclical cohort-employment differences. The economic magnitude of the wait-and-see channel cannot be measured directly because key delaying groups are unobserved in BFS. Other Great-Recession forces (credit crunch, structural change in entrants) are not modeled and could also explain the 2008-2016 cohort employment drop. Explaining whether delayed entrants actually return to the market is left for future research.

Key Concepts

Option value of delay (V^w(q,z)): The present value a potential entrant forgoes by entering today instead of retaining its productivity signal and entering in a future period. It is non-negative everywhere, weakly increases in the signal q and in aggregate demand z, and exists only because exit is irreversible and endogenous (otherwise waiting would never pay).

Countercyclical opportunity cost of entry: The total cost of entering — fixed entry cost ce plus the option value of delay — which rises in recessions (up to twice ce). It endogenously raises the elasticity of entry to aggregate demand and creates a group of firms that stay out despite positive expected net profits.

Threshold signal q_τ(z)*: The minimum productivity signal at which a potential entrant chooses to enter at aggregate state z. It is countercyclical; under τ=1 it equals the signal at which gross entry value equals the total opportunity cost, and it is far more elastic to z than the τ=0 (no-delay) threshold.

Signal q and probability of recalling the signal τ: q is a potential entrant’s heterogeneous, time-invariant signal about its initial post-entry productivity (drawn from Pareto W(q)). τ is the probability a delaying entrant keeps that signal next period; τ=0 collapses the model to a standard framework, τ=1 is the baseline (calibrated; identified value τ=0.965).

Customer capital (b): A demand-side stock tied to a firm’s past sales, depreciating at rate δ, that shifts demand for its differentiated good. Because it accumulates from prior sales, it slows firms’ demand adjustment and creates persistence in production and employment, distinct from productivity differences (per Foster et al. 2016).

Wait-and-see channel: The empirical counterpart of the option-to-delay mechanism: a bad aggregate state at entry induces some potential entrants to postpone forming a business, raising the (countercyclical) share of late start-ups in BFS data, distinct from recessions merely lengthening the time required to build a business.

Recessionary vs expansionary cohorts: Cohorts of establishments that begin operating when aggregate demand is below (z<1) vs above (z>1) the stochastic steady state. Recessionary cohorts are fewer, more productive, higher-survival, and persistently smaller in employment.