Time to Build in Agent-Based Models: Emerging Business Cycle Trends Through Time-Sensitive Production Processes

Abstract

Traditional macroeconomic models often abstract from the temporal structure of production, treating the transformation of inputs into outputs as instantaneous, and largely overlooking micro-level production frictions. We develop an agent-based model that explicitly incorporates time-to-build constraints, heterogeneous production durations, and the possibility of production failures to investigate how the temporal organization of production shapes the interaction between supply and demand. The model features a central-planner-like mechanism that generates production orders and allocates investment goods, allowing us to examine how mismatches between firms’ orders and production capabilities propagate through the economy. We show that temporal rigidities and resource constraints can become endogenous drivers of aggregate dynamics and, ultimately, of distinct patterns of macroeconomic stability. By moving beyond static production functions and equilibrium assumptions, the framework highlights how production time, firm heterogeneity, and supply-side frictions interact to shape the stability properties of the economy.

Appendix A: Control Scenarios

As a preliminary study, we introduce a set of experiments to test and describe the behavior of the model. The first three cases are just control tests to check the functioning of the model: cases A.0.1, A.0.2 and A.0.3, whether the planner assigns zero, the total quantity or a random fraction of the investment goods required by the firms (step 5 in the operation sequence reported in Sect. 3). In the second and third cases, the planner operates regardless of the quantity of investment goods collected in step 7 of the same figure in the previous cycle.

1.1 A.0.1: Planner Zero

We start with a control run to verify the model’s behavior under stress.

Fig. 8

Central planner behavior and national accounts under the planner zero hypothesis

In Fig. 8, the planner behavior plot shows what happens when the latter assigns zero to the investment goods that the firms require: as they do not receive any of their requests, the amount of what they desire (grossInvExpected (value)) experiences, after an initial boost, a constant growth at a slower but still sustained pace.

The other series that we introduce here also for the successive cases are:

• inv goods bought, as investment goods bought by the planner (step 5 n the operation sequence reported in Sect. 3); in the case of the planner zero they go rapidly to zero as, missing the substitutions due to planner’s action, the production of investment goods declines;

• inv goods inventories are the inventories of investment goods left after the central planner’s previous step; they can be bought in successive time units;

• grossInvQ is the gross investment of the firms, deriving from the action of the planner always in step 5, in quantity;

• grossinvQ*price, the same in value.

The national accounts graph captures the long-run effects of missing investments on production: all the measures describing the economic behavior decline, rather unsurprisingly, towards zero.

1.2 A.0.2: Planner Total

We continue with a second control run, always to verify the model’s behavior under stress. The planner accommodates all requests for capital goods from enterprises, regardless of availability; in reality, it should import them.

Fig. 9

Central planner behavior and national accounts under the planner total hypothesis

In Fig. 9, the planner behavior plot displays a jump in its early phase as in the previous experiment. The event coincides with a considerable excess of what firms receive (red line) compared with the investment goods that the planner buys (blue line): to overcome this situation, the planner would have to collect imports of capital goods. After this warming-up phase, the model balances expected and assigned investment goods and reaches its stationary state. The same stationary state emerges from the national accounts plot, where all the values are constant over time. It is interesting to notice here that the size of consumption is valuably larger than that of investments: this depends on the structure of the firm population, which presents many more firms producing consumption goods than durable, productive goods.

Ça va sans dire, in all the cases, the sum of investments, consumption and inventories variation returns the total added value of the economy.

1.3 A.0.3: Planner Random

With this third control run, always to verify the model’s behavior under stress, we introduce a planner reacting to the firms’ requests randomly, from 0 to 100%.

Fig. 10

Central planner behavior and national accounts under the planner random hypothesis

Figure 10 shows what happens when the planner distributes only a share of the investment goods that firms require. Moreover, this share is randomly extracted. At the beginning of the simulation, we observe the same initial boost that we saw in the previous cases, which highlights a considerable excess of requests concerning the quantity existing internally in the economy. In this case, we again observe a stable trend in the firms’ expectations of investment goods.

It is worth noticing that the national accounts plot, reporting the national accounts, presents insignificant differences with the previous case, meaning that the economy is not sensitive to changes in the share of investment goods distributed to the firms. This situation depends on the fact that—being production orders exogenously generated—the productive capacity is still sufficient to fulfill them despite the reduced assignment of investment goods.