## Appendix A: Timeline of the Industry Evolution

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---

### I. Introduction — research focus and key empirical puzzles
- Research focus: life cycle of the U.S. automated teller machine (ATM) and debit card industry; study interaction of product innovation (debit function) and banking deregulation in producing an industry shakeout.
- Empirical stylized facts motivating analysis:
  - Number of shared ATM networks grew rapidly to a peak in the mid-1980s and declined sharply afterward despite continued growth in ATM transaction volumes (Figure 1).
  - Two major shocks identified at the outset of the shakeout: a product innovation (debit card function introduction) and banking deregulation.
- Key questions:
  - How did the debit innovation and banking deregulation interact to produce the observed shakeout?
  - What are the quantitative contributions of each factor to industry evolution and welfare?
- Methodology:
  - Dynamic structural model of a competitive industry with forward-looking networks calibrated to a dataset on network entry, exit, size, and product offerings.
  - Counterfactual analyses to disentangle roles of innovation and deregulation.

### II. Industry background — institutional details and measured facts
- Organization and data:
  - Shared ATM networks emerged in the early 1970s; networks connect ATMs of multiple financial institutions and charge fees to participating banks.
  - Two organizational forms: proprietary networks with franchisees; joint-venture shared networks. Third-party data processors sometimes hold interests.
  - Primary data source: EFT Data Book annual lists of regional ATM networks between 1984 and 2006.
  - Sample: 144 networks existed during the period; exclude 12 networks serving exclusively credit unions and/or savings and loan banks → sample of 132 networks.
  - Collected number of cards in circulation and ATM transactions up to year 2000 for networks in sample.
- Key measured facts (preserved descriptions):
  - Total network numbers peaked around 120 in the mid-1980s; half of networks exited by mid-1990s; less than 30 networks survived to 2006 (Figure 1).
  - ATM-only networks declined monotonically; ATM-debit networks initially rose and later fell (Figure 3).
  - Entry: short wave on and after 1984; entry essentially stopped after 1987 (Figure 4A).
  - Exit: similar annual exit rates across network types; ATM-only exit rates more volatile (Figure 4B).
  - Debit adoption rate stayed positive until 1994 and fell to zero afterward (Figure 4C).
  - Network size: ATM-debit networks saw dramatic size increases over time; ATM-only network size relatively stable (Figure 4D).
  - Size ratio (ATM-debit / ATM-only) rose over time by cards and transactions (Figure 4E).
  - Market share of ATM-debit cards exceeded 95 percent after the mid-1990s (Figure 4F).
  - Banking sector: commercial bank exit rate jumped from about 1 percent pre-mid-1980s to about 6 percent after mid-1980s (Figure 2B; FDIC data).
  - Legal change: Supreme Court/Marine Midland case (1984/1985) allowed national banks’ use of shared ATM networks; states gradually relaxed restrictions enabling geographic expansion.

### III. Theory — model structure and mechanisms
- Model scope and main assumptions:
  - Discrete time, infinite horizon competitive market for ATM and debit card services.
  - Two product generations: ATM-only (quality !a) and ATM-debit (quality !d) with !d > !a > 0.
  - Networks charge per-card fee P_i for i ∈ {a,d}, incur sunk cost K, convex variable cost C(q).
  - Banks: continuum of mass one; each bank normalized to serve one customer; bank heterogeneity θ ∼ G; net revenue per card R(θ; !i; P_i) = !i θ − P_i.
  - Entry: potential entrants pay sunk cost K; outside option payoff π_.
  - Exogenous exit shock: incumbent exit probability pre before deregulation; increased to ρ after deregulation (ρ > pre).
  - Debit adoption: incumbent ATM-only network can invest adoption cost I_t with success probability s; I_t increases over time; ATM-debit cost-efficiency improves via g_t with ∂g_t/∂t < 0.
- Representative value-function expressions (as reported):
  - U__t = π_ + max{β U__{t+1}, β U_a_{t+1} − K}.
  - U_a_t = max{π_ + β U__{t+1}, π_a_t + pre β U__{t+1} + (1 − pre) β U_a_{t+1}}.
  - After shocks at time T:
    - V__t = π_ + max{β V__{t+1}, β V_a_{t+1} − K}.
    - V_a_t = max{π_ + β V__{t+1}, π_a_t + ρ β V__{t+1} + (1 − ρ) max[β V_a_{t+1}, β(s V_d_{t+1} + (1 − s) V_a_{t+1}) − I_t]}.
    - V_d_t = max{π_ + β V__{t+1}, π_d_t + ρ β V__{t+1} + (1 − ρ) β V_d_{t+1}}.
- Industry dynamics insights:
  - Entry wave occurs at T if K justified by future profits; many entrants enter as ATM-only at T and may attempt adoption later.
  - Adoption occurs while Δ_t = β(s V_d_{t+1} + (1 − s) V_a_{t+1}) − I_t − β V_a_{t+1} > 0.
  - As adoption spreads and ATM-debit technology improves (g_t declines), P_a_t and P_d_t fall; rising I_t and falling Δ_t stop adoption at T_0.
  - Continued progress can push P_a_t down to a critical P̄_a at T_{00}, triggering voluntary exits of ATM-only networks.
  - Long-run possibilities:
    - (a) Gradual voluntary exit of ATM-only networks with coexistence for a period (n_a_t satisfies equilibrium equations 15–21).
    - (b) Complete elimination of ATM-only networks by T_{00}, leaving only ATM-debit networks thereafter if profits exceed π_.

### IV. Model calibration — parameterization, targets, and fit
- Functional forms and calibrated parameter values (Table 1 reported values preserved):
  - Cost: C(q_a_t) = c_0 (q_a_t)^{c_1} with c_0 = 3; c_1 = 2.
  - ATM-debit cost: c_0 q_{d_t}^{c_1} / g_t with g_0 = 0.7; g_1 = 0.11.
  - Qualities: !a = 1; !d = 1.6.
  - Bank heterogeneity: Pareto G(θ) = 1 − d_0 θ^{−d_1} with d_0 = 1500; d_1 = 3.
  - Adoption cost path: I_t = I_0 (1 + I_1)^{t−T} with I_0 = 3.12; I_1 = 0.13.
  - Adoption success: s = 0.07.
  - Exogenous exit rates: pre = 0.01; ρ = 0.08.
  - Outside option: π_ = 0.1.
  - Sunk cost: K = 10.
  - Discount factor: β = 0.95.
- Calibration targets:
  - Pre-shock steady state (1983): number of networks and cards per network.
  - Post-shock path (since 1984): annual numbers of ATM-only and ATM-debit networks; number of new entrants each year; annual network debit adoption rate; annual output ratio between ATM-debit and ATM-only networks.
- Calibration outcomes (reported):
  - Pre-shock steady state in 1983: 118 networks; each network had 0.5 million cards in circulation (reported as a half million).
  - Twin shocks dated to 1983; first production use of debit technology in 1984.
  - Calibration reproduces observed time series (Figures 5A–5F) for network numbers by type, new entrants, exit rates, debit adoption rate, size ratio, and card market shares.
- Numerical solution notes:
  - Equilibrium solved via backward induction; technical details in Appendix B.
  - For stationarity, g_t and I_t assumed to reach constant levels after 150 periods.

### Model fit and baseline calibration — key quantitative matches and implied moments
- Targeted and matched outcomes:
  - Calibrated number of ATM-only networks declines monotonically; ATM-debit networks initially rise then fall.
  - Model generates 21 new entrants in 1984, equaling the total number of new entrants that occurred between 1984–1987 in the data.
  - Sample period 1984–2006 corresponds to t < T00 in model; exogenous network exit rate of 8 percent matches data average.
  - Calibration endogenously determines an 11-year debit adoption window ending in 1994, matching the data.
  - Model’s annual debit adoption rate before 1994 is 7 percent, matching the data average.
  - Rising output ratio between ATM-debit and ATM-only networks reproduced; magnitudes consistent when measured by cards or ATM transactions.
  - Evolution of card market shares closely matches data.
- Untargeted (model-implied) moments:
  - Along equilibrium, both P_a_t and P_d_t decrease.
  - Profit of ATM-only networks falls; profit of ATM-debit networks rises due to technological progress dominating price decline.
  - After shocks, V_d increases over time while V_a decreases; explains single-period entry wave after twin shocks.
  - Baseline calibration yields T00 = T + 115; all remaining ATM-only networks exit at T00.

### Counterfactual analysis — experiments and insights
- Purpose: evaluate separate roles of debit innovation and banking deregulation.

A. No Debit Innovation (deregulation present, no debit product)
- Setup specifics:
  - Deregulation raises exogenous exit risk to ρ = 0.08 from ρpre = 0.01; no debit product and no technological progress.
- Outcomes:
  - Deregulation with fixed ATM-only technology reduces number of firms at new steady state.
  - Prices must be higher to compensate firms for elevated exit risk; higher ATM-only card prices lead to higher output per firm but lower industry output → welfare reduction.
  - Industry reaches new steady state in the year 1999 (simulation).
  - Transition: price rises because incumbents exit at ρ = 0.08 while entry waits until price approaches new steady-state level.

B. No Deregulation (debit innovation present, ρ = ρpre = 0.01)
- Setup specifics:
  - Low exogenous exit risk ρ = ρpre = 0.01; technological progress of ATM-debit networks slower than baseline.
- Scenario 1 example:
  - Set g1 = 0:05 (nearly half of baseline).
  - Lower exit risk encourages entry; slower technological progress discourages entry.
  - In example, lower exit risk effect dominates → number of entrants larger than baseline.
  - Prices lower for both card types; larger entrants + slower technological progress → earlier cessation of adoption and smaller ATM-debit market share than baseline.
- Scenario 2 example:
  - Set g1 = 0:035 (about a third of baseline).
  - Number of entrants smaller than baseline; prices higher.
  - Deregulation enhances industry performance in this scenario.
  - Slower technological progress again leads to earlier cessation of debit adoption and smaller ATM-debit market share than Scenario 1.
- Overall insight:
  - Whether deregulation enhances or undermines industry performance depends on how much it facilitates technological progress relative to the additional disturbances it introduces.

### Additional discussions
A. Anticipated shocks
- Baseline assumes unexpected arrival of debit innovation and deregulation due to lack of expectation data.
- Formal extension introduces probability  that shocks arrive in any period; modifies pre-shock value functions (Eqs (23) and (24)).
- Implications:
  - Anticipation raises option value of entering as ATM-only → larger pre-shock number of networks → lower pre-shock price and higher industry output.
  - Post-shock path with anticipation yields lower prices and higher industry outputs than baseline because incumbents can attempt adoption one period ahead of new entrants.
- Appendix C provides technical details for solving pre-shock equilibrium with anticipated shocks.

B. Firm heterogeneity
- Baseline: firms identical conditional on technology; empirical checks split networks into “large ATM-only” (top one-third by cards in 1984) and “small ATM-only” (rest).
- Empirical findings:
  - Large and small ATM-only networks that had not adopted debit had similar exit rates in most periods (Figure 10A).
  - Large ATM-only networks had a higher annual debit adoption rate than small ones (Figure 10B).
  - Both large and small networks experienced faster size growth only after adopting debit; otherwise similar low growth rates (Figures 10C–10D).
- Interpretation:
  - Some firm-size advantages in adoption probability (network effects), but debit innovation is primary driver of growth.
  - Model extension to include heterogeneous initial sizes and higher adoption success for large networks is possible but judged to add complexity with limited gain.

### Concluding remarks and suggested future research
- Contribution summary:
  - Dynamic equilibrium model calibrated to novel dataset explains interaction of debit innovation and banking deregulation in producing industry shakeout.
  - Counterfactuals indicate:
    - Absent technological innovation, deregulation can reduce firm count, raise prices, and lower industry output.
    - Absent deregulation, innovation may progress with slower technological improvement.
    - Net effect of deregulation depends on how much it facilitates technological progress relative to added disturbances.
- Suggested future research directions:
  - Explore entry cohorts and vintage capital/cohort effects.
  - Study different exit modes: about 35 percent of networks exited through merger or acquisition in dataset.
  - Introduce external adjustment costs to reconcile model-implied rapid pre-shakeout buildup with observed slow network number growth.
  - Incorporate richer measures of network differentiation (horizontal competition, local ATM proximity) if richer data become available.

### Appendix B: Model solution and numerical procedure (solution algorithm) — key steps and primitives
- Model primitives listed: (β; d0; d1; c0; c1; ϕe; K; ωa; ωd; I0; Ig; g0; g1; τ; ρpre; ρ).
- Endogenous variables solved: N e (entrants at time T); T0 (final time of debit adoption); T00 (start of voluntary exit); sequences (P_a_t; P_d_t); outputs per network (q_a_t; q_d_t); profits (π_a_t; π_d_t); network numbers (n_a_t; n_d_t); value functions (V_a_t; V_d_t); voluntary exits x_a_t.
- Solution strategy (two-dimensional grid search over (N e, T0) + backward induction):
  - Step 1: Discretize control space of N e and T0; initial guess N e.
  - Step 2: Given N e and guess of T0, characterize dynamics for ranges T to T0; T0 to T00; T00 onward. Determine T00 from condition profits of ATM-only equal outside option ϕe. Solve full paths and apply backward induction over 400 periods to get V_a_t and V_d_t from Eqs (8)–(10).
  - Step 3: Check condition (12): ζ_t ≥ 0 for t ≤ T0 and ζ_t < 0 for t > T0. If violated, update T0 and repeat Step 2.
  - Step 4: Verify entrant condition (11) for N e; iterate until conditions satisfied within tolerance 1e-5.

### Appendix C: Anticipated shocks — pre-shock steady-state characterization (key equations)
- Free-entry and entrant relationships with anticipation probability :
  - U =  +U ⇒ U =  1 ; (26)
  - U =  +[V_a + (1)U_a] ¦ K: (27)
  - Implied condition:  1 = [V_a + (1)U_a] ¦ K : (28)
- Incumbent value with anticipation:
  - [1(1)(1 pre )]U_a = a + pre U +(1 pre )V_a : (30)
- Steady-state market clearing and profit relations:
  - 1G(P_a !a) = N_a q_a(P_a ); (31)
  - Network profit functional form and equilibrium conditions given in Eqs (32) and (33).
- Pre-shock steady state pinned down by Eqs (28), (30), (32), and (33). V_a(N_a) solved numerically via algorithm in Appendix B.

*Content summarized from the provided PDF excerpt (_wp15192 - Appendix A, Appendices B–C, and related sections).*

### Appendix A: Timeline of the Industry Evolution ........................................................................3

### Appendix A: Timeline of the Industry Evolution ........................................................................36

### Available entries in the supplied excerpt
- Appendix A: Timeline of the Industry Evolution ........................................................................36
- Appendix B: Model Solution .......................................................................................................36
- Appendix C: Anticipated Shocks .................................................................................................38

*Source: _wp15192 - Appendix A: Timeline of the Industry Evolution; source PDF filename: _wp15192 - Appendix A: Timeline of the Industry Evolution ........................................................................3*

### References .............................................................................................................

### _wp15192 - References .............................................................................................................

### I. Introduction — research focus and key empirical puzzles
- Studied life cycle of a financial service industry: the U.S. automated teller machine (ATM) and debit card industry.
- Empirical stylized facts motivating the analysis:
  - Number of shared ATM networks grew rapidly to a peak in the mid-1980s and declined sharply afterward despite continued growth in ATM transaction volumes (Figure 1).
  - Two major shocks identified at the outset of the shakeout: a product innovation (debit card function introduction) and banking deregulation.
- Key questions:
  - How did the debit innovation and banking deregulation interact to produce the observed shakeout?
  - What are the quantitative contributions of each factor to industry evolution and welfare?
- Conceptual links to existing literature:
  - Industry life-cycle patterns (Gort and Klepper, 1982; Klepper and Graddy, 1990; Agarwal and Gort, 1996).
  - Role of technological innovations and shakeouts (Hopenhayn, 1994; Jovanovic and MacDonald, 1994; Klepper, 1996; Wang, 2008).
  - Deregulation effects on market structure (Winston, 1998).
- Main methodological approach:
  - Construct a dynamic structural model (competitive industry, forward-looking networks) calibrated to a novel dataset on network entry, exit, size, and product offerings.
  - Conduct counterfactual analyses to disentangle roles of innovation and deregulation.

### II. Industry background — institutional details and measured facts
- Industry organization and operations:
  - Shared ATM networks emerged in the early 1970s; networks connect ATMs of multiple financial institutions and charge fees to participating banks, which pass charges to customers.
  - Two organizational forms: proprietary networks with franchisees; joint-venture shared networks. Third-party data processors sometimes hold interests.
- Data construction:
  - Primary data source: EFT Data Book annual lists of regional ATM networks between 1984 and 2006.
  - Sample: 144 networks existed during the period; exclude 12 networks serving exclusively credit unions and/or savings and loan banks → sample of 132 networks.
  - Collected number of cards in circulation and ATM transactions up to year 2000 for networks in sample.
- Empirical facts summarized (Figures 1–4):
  - Total network numbers peaked around 120 in the mid-1980s; half of networks exited by mid-1990s; less than 30 networks survived to 2006 (Figure 1).
  - Distinct dynamic patterns by network type:
    - ATM-only networks declined monotonically.
    - ATM-debit networks initially rose and later fell (Figure 3).
  - Entry and exit dynamics:
    - Short entry wave on and after 1984; entry essentially stopped after 1987 (Figure 4A).
    - Similar annual exit rates across network types; ATM-only exit rates more volatile (Figure 4B).
    - Debit adoption rate stayed positive until 1994 and fell to zero afterward (Figure 4C).
  - Size and market share dynamics:
    - ATM-debit networks saw dramatic size increases over time (measured by cards in circulation and ATM transaction volumes); ATM-only network size relatively stable (Figure 4D).
    - Size ratio (ATM-debit / ATM-only) rose over time measured by both cards and transactions (Figure 4E).
    - Market share of ATM-debit cards exceeded 95 percent after the mid-1990s (Figure 4F).
  - Banking sector context:
    - Commercial bank exit rate jumped from about 1 percent pre-mid-1980s to about 6 percent after mid-1980s (Figure 2B; data source: FDIC).
    - Legal development: Supreme Court/Marine Midland case (1984/1985) allowed national banks’ use of shared ATM networks without violating federal branching restrictions; states gradually relaxed restrictions facilitating network geographic expansion.

### III. Theory — model structure and mechanisms
- Model scope and assumptions:
  - Discrete time, infinite horizon, competitive market for ATM and debit card services.
  - Two product generations: ATM-only cards and ATM-debit (ATM + point-of-sale) cards; ATM-debit quality denoted !d and ATM-only quality denoted !a with !d > !a > 0.
  - Supply: networks provide card services, charge per-card fee Pi for i ∈ {a,d}, incur initial fixed cost and convex variable cost C(q).
  - Demand: continuum of banks of mass one; each bank normalized to serve one customer; bank-specific preference parameter θ distributed by G; net revenue per card for a bank R(θ; !i; Pi) = !i θ − Pi.
  - Entry: potential entrants (measure ∞) pay sunk cost K to set up ATM network (takes one period). Outside option payoff denoted π_e (π_ in text).
  - Exogenous exit shock: incumbent network exit probability pre before deregulation; increased to ρ after deregulation (ρ > pre).
  - Debit adoption: incumbent ATM-only network can invest adoption cost I_t to attempt upgrade; success probability s; I_t increases over time; ATM-debit networks enjoy process improvements captured by a cost-efficiency term g_t with ∂g_t/∂t < 0 (g_t falling over time).
- Value function structure (representative expressions reproduced from the model):
  - U__t = π_ + max{β U__{t+1}, β U_a_{t+1} − K}.
  - U_a_t = max{π_ + β U__{t+1}, π_a_t + pre β U__{t+1} + (1 − pre) β U_a_{t+1}}.
  - After shocks at time T:
    - V__t = π_ + max{β V__{t+1}, β V_a_{t+1} − K}.
    - V_a_t = max{π_ + β V__{t+1}, π_a_t + ρ β V__{t+1} + (1 − ρ) max[β V_a_{t+1}, β(s V_d_{t+1} + (1 − s) V_a_{t+1}) − I_t]}.
    - V_d_t = max{π_ + β V__{t+1}, π_d_t + ρ β V__{t+1} + (1 − ρ) β V_d_{t+1}}.
- Industry dynamics and scenarios:
  - Entry wave at T if K justified by future profits; many entrants enter as ATM-only networks at T and attempt adoption subsequently.
  - Adoption attempts occur while value of adoption Δ_t = β(s V_d_{t+1} + (1 − s) V_a_{t+1}) − I_t − β V_a_{t+1} > 0.
  - As adoption spreads and ATM-debit technology improves (g_t declines), prices P_a_t and P_d_t fall; increasing adoption costs I_t and falling Δ_t eventually stop adoption at T_0.
  - After T_0, continued technological progress for ATM-debit networks can push P_a_t down to a critical level P̄_a at time T_{00}, at which voluntary exits of ATM-only networks begin.
  - Two possible long-run outcomes depending on parameters:
    - (a) Gradual voluntary exit of ATM-only networks with both types coexisting for a period (with n_a_t satisfying equilibrium equations 15–21 in the text).
    - (b) Complete elimination of ATM-only networks by T_{00}, leaving only ATM-debit cards thereafter; ATM-debit networks remain if profits exceed the outside option π_.

### IV. Model calibration — parameterization, targets, and fit
- Functional forms and key model parameter definitions:
  - Cost function for ATM-only: C(q_a_t) = c_0 (q_a_t)^{c_1} with c_0 > 0 and c_1 > 1.
  - ATM-debit cost: c_0 q_{d_t}^{c_1} / g_t (text notation indicates cost efficiency g_t multiplicative).
  - Bank heterogeneity θ distributed Pareto: G(θ) = 1 − d_0 θ^{−d_1} with d_0 > 0, d_1 > 1.
  - Adoption cost path: I_t = I_0 (1 + I_1)^{t−T} with I_0 > 0, 1 > I_1 > 0 (I_t increasing over time).
  - Debit technological progress: g_t = g_0 (1 − g_1)^{t−T} with 0 < g_1 < 1 (g_t falling over time).
  - Exogenous exit rate pre before shocks; ρ after deregulation.
  - Adoption success rate s (denoted  in text).
- Calibration targets:
  - Pre-shock steady state (1983): (1) number of networks, (2) number of cards in circulation per network.
  - Post-shock path since 1984: (1) annual numbers of ATM-only and ATM-debit networks, (2) number of new entrants each year, (3) annual network debit adoption rate, (4) annual output ratio between ATM-debit and ATM-only networks.
- Calibrated parameter values (as reported in Table 1):
  - Cost function: c_0 = 3; c_1 = 2.
  - Demand function / qualities: !a = 1; !d = 1.6.
  - Debit technology: g_0 = 0.7; g_1 = 0.11.
  - Demand scale parameters: d_0 = 1500; d_1 = 3.
  - Adoption cost: I_0 = 3.12; I_1 = 0.13.
  - Exogenous exit rates: pre = 0.01; ρ = 0.08.
  - Outside option: π_ = 0.1.
  - Adoption success: s = 0.07.
  - Sunk cost: K = 10.
  - Discount factor: β = 0.95.
- Pre-shock calibration outcomes:
  - Calibrated pre-shock steady state in 1983: 118 networks; each network had 0.5 million cards in circulation (reported as a half million in text).
  - Pre-shock exogenous annual exit rate set to 0.01 matches commercial bank exit behavior before mid-1980s (Figure 2B).
- Post-shock calibration outcomes:
  - Twin shocks dated to 1983 with first production use of debit technology in 1984 (text statement: twin shocks arrived in 1983 and debit technology first used in production in 1984).
  - Model reproduces observed patterns shown in Figures 5A–5F:
    - Time series fit for network numbers by type, number of new entrants, exit rates by type, debit adoption rate, network size ratio, and market shares of cards match empirical moments well (figures referenced in text).
- Numerical solution notes:
  - Equilibrium solved via backward induction; technical solution details in Appendix B.
  - For stationarity in numerical exercises, g_t and I_t assumed to reach constant levels after 150 periods (text assumption).

_Italics: Content summarized from the provided PDF text (pages and figures referenced in the original source)._

### 1. Our model Öts well with the total number of networks over time. Also, the cal-

### _wp15192 - 1. Our model Öts well with the total number of networks over time. Also, the cal-

### Model fit and baseline calibration
- The calibrated model reproduces the total number of networks over time and key dynamics of product adoption and exit.
- Specific calibrated/fit outcomes:
  - The calibrated number of ATM-only networks declines monotonically.
  - The number of ATM-debit networks initially rises before it later falls.
  - The calibrated model generates 21 new entrants in 1984, which equals the total number of new entrants that occurred between 1984-1987 in the data.
  - The calibrated sample period 1984-2006 falls into the time range t < T00, so the model has an exogenous network exit rate of 8 percent, which matches the average of the data.
  - The calibration endogenously determines an 11-year window of debit adoption ending in 1994, the same as the data.
  - The model’s annual debit adoption rate before 1994 is 7 percent, which matches the average of the data.
  - The calibration generates a rising output ratio over time between an ATM-debit network and an ATM-only network; the magnitude is consistent with data measured either by cards in circulation or ATM transaction volumes.
  - The evolution of market shares of different cards generated by calibration closely matches the data.

- Untargeted (model-implied) moments:
  - Along the equilibrium time path, both prices of ATM-only and ATM-debit cards decrease.
  - As a result, profit of an ATM-only network falls, but profit of an ATM-debit network rises because technological progress dominates the price decline.
  - After the arrival of shocks, the value function of an ATM-debit network increases over time, but that of an ATM-only network decreases; this explains why entry can only occur for one period right after the arrival of the twin shocks.
  - Baseline calibration yields T00 = T + 115; and all the remaining ATM-only networks exit at T00.

### Counterfactual analysis: overview and experiments
- Purpose: Evaluate the separate contributions of debit innovation and banking deregulation by running counterfactual simulations.

A. No Debit Innovation
- Setup: Banking deregulation present but no debit innovation. Deregulation raises the exogenous exit risk for ATM networks to ρ = 0.08 compared with ρpre = 0.01; no new debit product and no technological progress.
- Simulation outcomes and interpretation:
  - Deregulation with fixed ATM-only technology reduces the number of firms at the new steady state.
  - Prices must be higher to compensate firms for elevated exit risk; higher ATM-only card prices lead to higher output per firm but lower industry output, implying a welfare reduction.
  - In the simulation, the industry reaches the new steady state in the year 1999.
  - During transition, price rises because incumbents exit at exogenous rate ρ = 0.08 while no new firm enters until price approaches the new steady-state level; entry starts later and then balances exit in long run.

B. No Deregulation
- Setup: Debit innovation present but no banking deregulation. All networks have low exogenous exit risk ρ = ρpre = 0.01; technological progress of ATM-debit networks is slower than baseline.
- Scenario 1 (illustration): set post-shock technological progress rate g1 = 0:05 (nearly half of baseline).
  - Absence of deregulation → lower exogenous exit risk encourages entry.
  - Slower technological progress → discourages entry.
  - In this example, the lower exit risk effect dominates → number of entrants larger than baseline.
  - Along equilibrium path, prices are lower for both ATM-debit and ATM-only cards; deregulation would undermine industry performance in this comparison.
  - Larger entrants + slower technological progress → networks stop adopting debit earlier and ATM-debit market share becomes smaller than baseline.

- Scenario 2: set g1 = 0:035 (about a third of baseline).
  - Number of entrants is smaller than baseline; prices of cards become higher.
  - Therefore, deregulation enhances industry performance in this scenario.
  - Slower technological progress again leads to earlier cessation of debit adoption and smaller ATM-debit market share compared with Scenario 1.

- Overall insight: Whether deregulation enhances or undermines industry performance depends on how much it facilitates technological progress relative to the additional disturbances it introduces.

### Additional discussions
A. Anticipated shocks
- Baseline assumption: debit innovation and banking deregulation arrived as unexpected shocks due to lack of data on expectations.
- Formal extension: let  denote the probability that shocks will arrive in any period; pre-shock value functions can be rewritten to incorporate  (Eqs (23) and (24) in the source).
- Implications of anticipated shocks:
  - Anticipation increases the option value of entering as an ATM-only network → larger number of ATM networks in pre-shock equilibrium → lower price and higher industry output in pre-shock equilibrium.
  - Along the post-shock path, anticipation leads to lower prices and higher industry outputs than baseline because incumbents can try debit adoption one period ahead of new entrants.
- Appendix C in source provides technical details for solving the pre-shock equilibrium with anticipated shocks.

B. Firm heterogeneity
- Baseline model assumption: firms identical conditional on technology; real-world firms may be heterogeneous.
- Empirical grouping and findings (Figures 10A-10D):
  - Networks ranked in top one-third by cards in circulation in 1984 labeled “large ATM-only networks”; the rest labeled “small ATM-only networks.”
  - Figure 10A: large and small ATM-only networks that had not adopted debit had similar exit rates in most periods.
  - Figure 10B: large ATM-only networks had a higher annual debit adoption rate than small ones.
  - Figures 10C–10D: both large and small networks experienced faster size growth only after adopting debit; otherwise both had similar low growth rates.
- Interpretation:
  - Figure 10B suggests some firm-size advantages (e.g., network effects: large networks better able to convince merchants to accept debit due to larger cardholder base and infrastructure).
  - Figures 10C–10D suggest debit innovation was the driving force behind network growth; regardless of initial size, networks expanded fast only after adopting debit, helping rule out spurious causality that pre-existing large-network advantages alone drove growth.
- Model extension possibility: incorporate heterogeneous initial network sizes and allow large ATM-only networks a higher success rate adopting debit; but authors note limited gain vs complexity because baseline model already explains data well.

### Concluding remarks and suggested future research
- Summary of contribution:
  - Constructed a dynamic equilibrium model to study interaction of a major product innovation (debit function) and banking deregulation in driving industry shakeout.
  - Calibration to novel dataset on network entry, exit, size, and offerings shows the theory fits quantitative industry patterns.
  - Counterfactuals indicate:
    - Absent technological innovation, deregulation may introduce disturbances leading to fewer firms, higher prices, and lower industry output.
    - Absent deregulation, innovation may proceed with slower technological progress.
    - Net effect of deregulation on industry performance depends on its facilitation of technological progress relative to additional disturbances.

- Suggested directions for future research:
  - Explore role of entry cohorts and possible first-mover or vintage capital effects (cohort effects not detected significantly in this industry).
  - Study different firm exit modes: about 35 percent of networks exited through merger or acquisition in dataset; investigating M&A cases could reveal exits not equivalent to failure.
  - Consider external adjustment costs to address discrepancy between model-implied rapid pre-shakeout steady state and observed slow buildup of network numbers.
  - Incorporate richer measures of network differentiation (horizontal competition, local ATM proximity) if richer data become available.

### Appendix B: Model solution and numerical procedure (solution algorithm)
- Model primitives (exogenous parameters): (β; d0; d1; c0; c1; ϕe; K; ωa; ωd; I0; Ig; g0; g1; τ; ρpre; ρ).
- Endogenous variables: number of new entrants N e at time T; final time of debit adoption T0; starting time of voluntary exit T00; sequences (Pa t; Pd t); outputs per network (qa t; qd t); profits (πa t; πd t); network numbers (na t; nd t); value functions (Va t; Vd t); voluntary exits xa t.
- Solution strategy: two-dimensional grid search over control space (N e and T0) and backward induction; key steps:
  - Step 1: Discretize control space of entrants N e and endogenous time T0; make initial guess of N e.
  - Step 2: Given N e and a guess of T0, characterize dynamics for three time ranges (T to T0; T0 to T00; T00 onward). Derive sequences of prices, outputs per network, profits, network numbers, voluntary exits until T0. Determine T00 (> T0) from condition that profits of ATM-only networks equal outside option value ϕe. With T00 known, solve full paths (Pa t; Pd t; qa t; qd t; πa t; πd t; na t; nd t; xa t). Apply backward induction over 400 periods to derive value functions (Va t; Vd t) from Eqs (8)–(10).
  - Step 3: Verify condition (12): ζt ≥ 0 for all t ≤ T0 and ζt < 0 for t > T0. If not satisfied, update guess of T0 and repeat Step 2 until consistent T0 and other variables obtained for given N e.
  - Step 4: Verify entrant condition (11) for N e with derived T0. If discrepancy above tolerance (set to 1e-5), iterate Steps 2–3 until both equations (11) and (12) satisfied within tolerance. Solve dynamics of all endogenous variables.

*Source: Excerpt from _wp15192 (PDF chapter/section)._

### Appendix C: Anticipated Shocks

### Appendix C: Anticipated Shocks

### Pre-shock steady-state equilibrium: purpose and setup
- Provides details for solving the pre-shock steady-state equilibrium with anticipated shocks.
- Uses the free entry condition and incumbent optimization to derive equilibrium relationships.
- Key equations referenced: (25), (26), (27), (28), (29), (30), (31), (32), (33).

### Free entry and entrant value relationships
- Under the free entry condition, Eq (23) is rewritten as:
  - U = + max{U ;[V_a + (1)U_a] ¦ Kg: (25)
- This implies:
  - U = +U =)U = 1 ; (26)
  - and U = +[V_a + (1)U_a] ¦ K: (27)
- Therefore:
  -  1 = [V_a + (1)U_a] ¦ K : (28)

### Incumbent network value and sunk cost implication
- Because of the sunk cost paid, an incumbent network would strictly prefer staying in the industry.
- Incumbent value rewritten (from Eq (24)):
  - U_a =a +[ pre V + (1 pre )V_a ] +(29)
  - +(1)[ pre U + (1 pre )U_a ]g;
- Which implies:
  - [1(1)(1 pre )]U_a =a + pre U +(1 pre )V_a : (30)

### Steady-state market clearing and profit functions
- At the steady state:
  - 1G(P_a !a) = N_a q_a(P_a ); (31)
- The network profit a is determined by P_a (N_a).
- Under the parameterization given:
  - a_t(P_a) = (c11)c c1 1c1 1 c1 1c1 0 P_a 
 c1 c11 ; (32)
  - d0  P_a !a  d1 = N_a  P_a c0 c1  1 c1 1 : (33)

### Solution characterization and numerical approach
- The pre-shock steady-state equilibrium is pinned down by Eqs (28), (30), (32), and (33).
- Note: V_a is the value function of being an ATM-only network in the period when the shocks indeed arrive and the number of existing networks is N_a.
- V_a(N_a) can be numerically solved using the algorithm described in Appendix B.

*Source: Appendix C: Anticipated Shocks, _wp15192 - Appendix C: Anticipated Shocks*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15192.pdf_