Is the market really a good teacher?

Abstract

This paper proposes to model market mechanisms as a collective learning process for firms in a complex adaptive system, namely Jamel, an agent-based, stock-flow consistent macroeconomic model. Inspired by Alchian’s (J Polit Econ: 5(3):211–221, 1950) “blanketing shotgun process” idea, our learning model is an ever-adapting process that puts a significant weight on exploration vis-à-vis exploitation. We show that decentralized market selection allows firms collectively to adapt their overall debt strategies to the changes in the macroeconomic environment so that the system sustains itself, but at the cost of recurrent deep downturns. We conclude that, in complex evolving economies, market processes do not lead to the selection of optimal behaviors, as the characterization of successful behaviors itself constantly evolves as a result of the market conditions that these behaviors contribute to shaping. Heterogeneity in behavior remains essential to adaptation. We come to an evolutionary characterization of a crisis, as the point where the evolution of the macroeconomic system becomes faster than the adaptation capabilities of the agents that populate it.

Appendices

Appendix A: Parameter values (baseline scenario)

Random draws are performed at each period and for each agent.

Table 4

Appendix B: Pseudo-code of Jamel

B.1 Initialization

Table 5

Equities (E_j,0) of each firm and of the bank are divided in ten equal shares, and given to randomly drawn households.

B.2 Execution

In each period t, t = 1,...,d^S:

• 1. (Interest rate adjustment:)

  $$ {i_{t}} = \max \left( {\phi_{\pi}} ({\pi_{t}} - {\pi^{T}}), 0 \right) $$

  (1)

  where π_t is the price inflation computed over past win periods, ϕ_π and π^T are parameters.

• 2. (Fixed capital stock depreciation:) Each machine m of each firm j is depreciated by $\frac {I_{j,m}}{{d^k}}$ where I_j,m, is the initial value of the machine paid by j and d^k the expected life time of the machine (in months, straight-line depreciation method).

• 3. (Payment of dividends:)

  Each firmj i) computes ${\tilde {F}_{j,t}}$, its average past net profits F_j over win periods, ii) computes the share of net profits to be distributed as $\frac {{E_{j,t}}}{{E^T_{j,t}}}$, and iii) distributes to its owners the amount${{FD}_{j,t}} = \min \left (\frac {{E_{j,t}}}{{E^T_{j,t}}} {\tilde {F}_{j,t}} , {\kappa _d} {E_{j,t}}\right )$, in proportion to their relative share holding.The bank distributes ${{FD}_{B,t}} = \max ({E_{B,t}}-{E^T_{B,t}},0)$

• 4. (Price:)

  $$ \begin{array}{ll} \text{if} \ ({s_{j,t-1}} > {s^T_{j,t-1}} \text{ and\ } {{in}_{j,t}} < {{in}^T_{j,t}}) & \left\{ \begin{array}{l} {\overline{P}_{j,t}} = {\overline{P}_{j,t-1}} (1 + {\delta^P}) \\ {\underline{P}_{j,t}} = {{P}_{j,t-1}} \\ {{P}_{j,t}} \hookrightarrow \mathcal{U}({\underline{P}_{j,t}}, {\overline{P}_{j,t}}) \end{array} \right.\\ \\ \text{else if} \ ({s_{j,t-1}} < {s^T_{j,t-1}} \text{ and} {{\ in}_{j,t}} > {{in}^T_{j,t}}) & \left\{ \begin{array}{l} {\overline{P}_{j,t}} = {{P}_{j,t-1}} \\ {\underline{P}_{j,t}} = {\underline{P}_{j,t-1}} (1 - {\delta^P}) \\ {{P}_{j,t}} \hookrightarrow \mathcal{U}({\underline{P}_{j,t}}, {\overline{P}_{j,t}}) \end{array} \right.\\ \\ \text{else} & \left\{ \begin{array}{l} {\overline{P}_{j,t}} = {\overline{P}_{j,t-1}} (1 + {\delta^P}) \\ {\underline{P}_{j,t}} = {\underline{P}_{j,t-1}} (1 - {\delta^P})\\ {{P}_{t,j} }= {{P}_{j,t-1}} \end{array} \right. \end{array} $$

  (2)

  with${\overline {P}_{j,t}}$, the ceiling price,${\underline {P}_{j,t}}$, the floor price.

• 5. (Wage offer:) Each firm j observes a random sample of g’ other firms. If the observed sample contains a firm k such that k_k,t > k_j,t, then:

  $$ \left\{ \begin{array}{l} {W_{j,t}} = {W_{k,t}}\\ {\overline{W}_{j,t}} = {W_{j,t}} (1 + {\delta^W}) \\ {\underline{W}_{j,t}} = {W_{j,t}} (1 - {\delta^W}) \end{array} \right. $$

  (3)

  else:

  $$ \begin{array}{ll} \text{if\ } ({\rho_{j,t-1}} > {\rho^T}) &\left\{ \begin{array}{l} {\overline{W}_{j,t}} = {\overline{W}_{j,t-1}} (1 + {\delta^W}) \\ {\underline{W}_{j,t}} = {W_{j,t-1}} \end{array} \right.\\ \\ \text{else} &\left\{ \begin{array}{l} {\overline{W}_{j,t}} = {W_{j,t-1}} \\ {\underline{W}_{j,t}} = {\underline{W}_{j,t-1}} (1 - {\delta^W}) \end{array} \right.\\ \\ \text{and then} &{W_{j,t}} \hookrightarrow \mathcal{U}({\underline{W}_{j,t}}, {\overline{W}_{j,t}}) \end{array} $$

  (4)

  with:

  • ${\rho _{j,t-1}} = \frac {{n^T_{j,t-1}}-{n_{i,t-1}}}{{n^T_{j,t-1}}}$, the vacancy rate previously observed by the firm,

  • ${\overline {W}_{j,t}}$, the ceiling wage,

  • ${\underline {W}_{j,t}}$, the floor wage.

• 6. (Labor demand:)${n^T_{j,t}}$ (within the lower bound 0 and the upper bound k_j,t):

  $$ {n^T_{j,t}} = (1+\delta_{j,t}^{h}) {n^T_{j,t-1}} $$

  (5)

  where${n^T_{j,t-1}}$ is the labor demand of the firm in period t − 1, and δ_j,t is the size of the adjustment, computed as:

  $$ \delta_{j,t}^{h} = \left\{\begin{array}{ll} \alpha_{j,t} {\nu_{F}} & \text{if\ } 0 \leq \alpha_{j,t} \beta_{j,t} < \frac{{{in}^T_{j,t}} - {{in}_{j,t}}}{{{in}^T_{j,t}}} ,\\ -\alpha_{j,t} {\nu_{F}} & \text{if} \ 0 \leq \alpha_{j,t} \beta_{j,t} < \frac{{{in}_{j,t}} - {{in}^T_{j,t}}}{{{in}^T_{j,t}}} ,\\ 0 & \text{else.} \end{array}\right. $$

  (6)

  with α_j,t, $\beta _{j,t} \hookrightarrow \mathcal {U}(0,1)$ and ν_F > 0.

  $$ \left\{ \begin{array}{ll} \text{if\ } {n_{j,t}}>{n^T_{j,t}} &\text{fires\ } {n_{j,t}}-{n^T_{j,t}} \text{ (on a last-hired-first-fired basis)} \\ \text{else} &\text{posts\ } {n^T_{j,t}}-{n_{j,t}} \text{ job offers.} \end{array} \right. $$

  (7)

• 7. (Financing of current assets): according to the existing job contracts, the workforce target ${n^T_{j,t}}$, and the new wage rate offered on the labor market W_j,t:

  • computes the anticipated wage bill ${{WB}^T_{j,t}}$;

  • borrows $\max ({{WB}^T_{j,t}}-{M_{j,t}}, 0)$ (non-amortized short-term loan).

• 8. (Reservation wages:)

  Each household i updates his reservation wage ${W^r_{i,t}}$.

  • If i is unemployed:

    $$ {W^r_{i,t}} = {W^r_{i,t-1}} (1 - \delta^w_{i,t}) $$

    (8)

    where$\delta ^w_{i,t} \geq 0$ is the size of the downward adjustment, and is computed as:

    $$ \delta_{i,t}^{w}= \left\{\begin{array}{ll} \beta_{i,t} \cdot {\eta_{H}} & \text{if\ } \alpha_{i,t} < \frac{{d^{u}_{i,t}}}{{d^r}} \\ 0 & \text{ else.} \end{array}\right. $$

    (9)

    where α_i,t, β_i,t are $\mathcal {U}(0,1)$, and η_H > 0 and d^w ≥ 1 are parameters.

  • Else:

    $$ {W^r_{i,t}} = {W_{i,t-1}} $$

    (10)

    where W_i,t− 1 is the wage earned by household i at the previous period t − 1.

• 9. (Labor market:) Each unemployed household i) consults a random sample of g job offers; ii) selects the job offer with the highest offered wage, denoted by W_j,t; iii) if ${W_{j,t}}>={W^r_{i,t}}$, accepts the job for a duration of d^w months, else, remains unemployed for the period t.

• 10. (Production): Each firm distributes uniformly the hired workers on its machines (one per machine). Once a production process of a machine is completed (after d^p iterations by a worker), it adds pr^k goods to the firm’s inventories in_j,t, the value of which is then incremented by the production costs of pr^k goods.

  This process updates i) firms’ wage bills and vacancy rates, ii) production levels, and iii) households’ cash-on-hand M_i,t = W_i,t + FD_i,t + M_i,t− 1 (where W_i,t + FD_i,t represents its income flow, made of FD_i,t, the dividends that household i may receive if it owns shares in the bank or a firm, see Step 1., and W_i,t its labor income, and M_i,t− 1 is its cash-on-hand transferred from t − 1).

• 11. (Goods supply:) Each firm j puts ${s^T_{j,t}}$ goods in the goods market:

  $$ {s^T_{j,t}} = \max({\mu_F} \cdot {{in}_{j,t}}, {d^{m}}\cdot{{pr}^k}\cdot{k_{j,t}}) $$

  (11)

• 12. (Individual experimentation:) With a probability pb_BSP, for each firm j, $\ell _{j,t + 1} \hookrightarrow \mathcal {N}(0, {\sigma _{{BSP}}})$, else ℓ_j,t,+ 1 = ℓ_j,t.

• 13. (Investment decision):

  • (a) selects a random sample of g suppliers (other firms);

  • (b) if (k_j,t = 0) buys m = 1 new machine, for a value I_j,t;

  • (c) else if (${E^T_{j,t}} > {E_{j,t}}$):

    • i. computes the vector of the prices of each investment project I_m (m the number of new machines to be bought), with m = 0, 1, 2,...;

    • ii. computes ${\tilde {s}_{j,t}}$, average of the sales s_j over the past window periods;

    • iii. computes ${s^e_{j,t}} = {\beta } \cdot {\tilde {s}_{j,t}}$, its sales expansion objective;

    • iv. given its sales expansion objective ${s^e_{j,t}}$, the expected life time of a machine d^k, the current price P_j,t, the current wage W_j,t, the discount factor $r=i_{t} - \tilde {\pi }_{t}$ ($\tilde {\pi }_{t}$ is the average past inflation computed over the window last periods), and the price I_m of each investment project m, computes the net present value NPV_m of each investment project m:

      $$ {NPV}_{m} \equiv \frac{{CF}_{m}}{{{r}_{t}}} \left( 1 - \frac{1}{{{r}_{t}}(1+{{r}_{t}})^{{d^k}}} \right) - I_{m} $$

      where CF_m is the expected cash-flow of the project:

      $$ {CF}_{m} = \min({s^e_{j,t}},m \cdot {{pr}^k})\cdot{{P}_{j,t}} - m\cdot{W_{j,t}} $$

      where the min term ensures that the future sales cannot exceed the maximum market capacity of the firms.

    • v. chooses the project m for which NPV_m+ 1 <NPV_m, for a value I_j,t.

    • vi. adds $\frac {I_{m}}{m}$ per new machine to its assets.

• 14. (Financing of fixed assets):

  • (a) borrows (amortized long-run loan) the amount: ${\ell ^T_{j,t}} {I_{j,t}}$;

  • (b) borrows (amortized short-run loan) the amount: $\max ((1-{\ell ^T_{j,t}}) {I_{j,t}} -{M_{j,t}}, 0)$;

• 15. (Saving/consumption plan:)

  Each household computes

  • (a) his average monthly income flow over the last window periods, denoted by ${\tilde {Y}_{i,t}}$;

  • (b) his cash-on-hand target ${M^T_{i,t}} ={\kappa _{S}} \cdot {\tilde {Y}_{i,t}}$;

  • (c) is targeted consumption expenditures as:

    $$ {C^T_{i,t}}= \left\{\begin{array}{ll} (1-{\kappa_{S}}) {\tilde{Y}_{i,t}} & \text{if} {\ M_{i,t}} \leq {M^T_{i,t}} \\ {\tilde{Y}_{i,t}} +{\mu_H}({M_{i,t}} - {M^T_{i,t}} ) & \text{ else.} \end{array}\right. $$

    (12)

    where μ_H ≥ 0 is a parameter. The budget constraint always gives ${C_{i,t}} \leq \min ({C^T_{i,t}}, {M_{i,t}})$.

• 16. (Goods market:)

  • (a) matches first the firms’ demand, then the households’ demand with the firms’ supply;

  • (b) goods bought by firms are transformed into new machines, while goods bought by households are consumed.

• 17. (Loans:) The firms pay back part of their loans and the interests to the bank. Interest is due at each period. For an amortized loan, principal is repaid by equal fractions at each period, while for a non-amortized loan, the total principal is due the term. If the cash-on-hand M_j,t of a firm j cannot fully cover the debt repayments, it benefits of an overdraft facility, ie a new short term loan at an higher rate including the risk premium of the bank (i_t + rp).

• 18. (Foreclosure:) If a firm has become insolvent (A_j,t < L_j,t), the bank starts the foreclosure procedure, a new ${\ell ^T_{j,t}}$ is copied from a surviving firm ($+\mathcal {N}(0, {\sigma _{{BSP}}})$), the firm is recapitalized up to E_j,t = κ_sA_j,t, and new households become owners as follows: all households that have at least 20% of E_j,t as cash-on-hand are solicited for at most 50% of their wealth, and the firm’s shares are distributed in proportion to their contribution. If the collected cash-on-hand is lower than E_j,t, the selection threshold is decreased to 10% of E_j,t. If the cash-on-hand on the solicited households is still not enough, the threshold is decreased to 4%, and then 2%. If this is still not enough to buy all the shares of the firm, the price of the shares is decreased by 10% until enough cash-on-hand can be collected. In case of more than 10 decreases, the simulation would stop.

• 19. This process starts all over again for a given length of d^S periods.

Appendix C: Stock-flow consistency

C.1 Stocks

Table 6

C.2 Balance sheet matrix

Table 7

C.3 Flows

Table 8

C.4 Transaction-flows matrix

Table 9

C.5 Full-integration matrix

Table 10