Policy Exploration with Agent-Based, Economic Geography Methods of Regional Economic Integration in South Asia

Abstract

Parts of Asia continue to enjoy high economic growth—this rapid growth however does not extend to all regions of Asia, and within geographic regions growth disparities remain high. This paper features applied and complex models for regional economic development. In a pioneering approach that makes explicit the complex connections needed to spur growth in trade, this South Asia-focused study details a unique method to assess how Aid for Trade (AfT) investments interact with agents of economic change, such as consumers and producers and traders of intermediate and final goods and to evaluate their potential to reduce the cost of bringing more products to more markets. Furthermore, it presents a new tool for policy makers to foster regional economic integration and pursue the overarching development objective of more inclusive growth across a region. The paper shows how modeling restructuring across geographies can visualize policy choice hitherto unseen and unrecognized.

The models exhibit structural changes in the regional South Asia economy through the decreases in intra-regional trade transaction costs which are influenced by a set of investment based policy choices. The cost reduction pattern and the nature of non-linear and distributed interactions between the geographic elements of the agent-based system allow it to functionally restructure itself over time. When low growth sections of the regional economy are integrated into evolving regional and global trade networks and agent-based relationships, the benefits of high economic growth are extended to low growth sections of a regional economy, as is made visually apparent in Geographic Information System (GIS) map-based simulations. The paper will review representations of regional development models in terms of their assumptions (peeled away like an onion) and in terms of their level of complexity, very much in the tradition of Peter Allen’s classification system. Traditional mechanical models of regional economic development assume away structural change with the assumption of completeness of network connections among agents in the system, thereby imposing a simplifying homogeneity on economic agents that significantly reduces explanatory power.

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Appendix: Adjacency Network of Tile-Based Economies in~the~Model

To accurately measure benefits stemming from infrastructure investment projects, we need a model which is flexible enough to capture the effects that such investments have on the spatial distribution of economic activity. This requires an explicit representation of real space—a geography that can be matched along key dimensions with the actual geography of a region of interest. We model a number of markets that are located in this space. Each market is called a tile (which may be thought of as a local independent economy). The area of a tile is small enough for transportation costs within the tile to be assumed negligible. Production, consumption and trade can take place within tiles. Trade can also occur between tiles. However, costs of transportation must be taken into account for inter-tile trade. Infrastructure investments will then affect the spatial distribution of economic activity (i.e. the production and consumption of each good at the different locations) by changing the cost of transportation between tiles.

Our approach, which draws among others upon the model of Rossi-Hansberg (2005), will be first to specify the economy of a tile and identify relative prices in the absence of trade. For the tile economy, we assume Walrasian market-clearing. We then allow individuals in different tiles to trade taking into account price differences. In the context of trading behavior, we assume that heterogeneous, autonomous, and boundedly rational agents interact in explicit space and time, following rules that are sensible though not fully rational (as is characteristic of agent-based models). Each tile is populated with individuals who consume goods, and are also the owners of the firms that produce these goods. Although we can, in principle, allow for heterogeneity in incomes and preferences, due to data availability issues we assume identical Cobb-Douglas utilities, and take incomes within tiles to be equal (but allow for differences in incomes across tiles). Our model has an intermediate good (X _I ), and two goods that enter the utility function—the “final” good (X _F ) and leisure (L). There is a fixed total labor endowment for each person (A _L ) and Labor supplied can be computed from leisure choice as $N\equiv {A}_L-L$.

The demand function for final good in a given tile can be computed from the utility function. Once we aggregate across individuals we get the demand curve in Eq. (1).

$$ {X}_F={\alpha}_s{A}_X\frac{M}{P_F} $$

(1)

The parameter α _s is a population scale factor; M is the total income of households in the tile; ${A}_X$ captures relative preference for the final good (X _F ); and relative preference for leisure is captured by ($1-{A}_X$). Income (M) is the sum of wages and rents:

$$ M\equiv w{A}_L+\Pi {\omega}_i $$

(Π is the combined profits of all firms, and ω _i is the individual’s share—this will be taken to equal ${\omega}_i\equiv 1/{\alpha}_s$, but different ownership patterns are also feasible). Individual utility maximization also allows us to compute the total labor supply in the tile:

$$ N={\alpha}_s\left({A}_X{A}_L-\left(1-{A}_X\right)\raisebox{1ex}{$\Pi $}\!\left/ \!\raisebox{-1ex}{$w$}\right.\right) $$

(2)

Labor is assumed to be immobile across tiles but mobile across sectors.

There are two produced goods—the final good and the intermediate good. Both require land and labor for production. Additionally, the final good also requires the intermediate good. Since the intermediate good is tradable, the production of the final good can be spatially dispersed. The intermediate good could be produced in one tile, and then transported to another tile where it is used to produce the final good. We let θ _I denote the fraction of land in tile s used for the production of the intermediate good and θ _F the fraction used for the final good. Let S be the total area of the tile. We assume CES Production functions. Where values of key parameters (such as the elasticity of substitution) are unavailable, we make plausible assumptions. The final good output per unit of land is:

$$ {X}_F={\gamma}^F\left({N}^a+{C}^a\right),\kern1em \mathrm{where}\;a\in \left(0,1\right). $$

We compute the derived demand for labor and intermediate good (wage is w, the price of the final good is P _F , and the price of the intermediate good is P _I ). Standard calculations then yield, for the demand for labor and the intermediate good:

$$ {N}_F={\theta}_FS{ \left({\it aP}_F{\gamma}^F\right)}^{\frac{1}{1-a}}{w}^{\frac{-1}{1-a}} $$

(3)

$$ C={\theta}_FS{\left({\it aP}_F{\gamma}^F\right)}^{\frac{1}{1-a}}{P_I}^{\frac{-1}{1-a}} $$

(4)

The output of intermediate good output per unit of land is given by the production function:

$$ C={\gamma}^I\left({N}^d\right),\kern1em \mathrm{where}\;d\in \left(0,1\right) $$

Derived demand for labor is:

$$ {N}_I={\theta}_IS{\left({\it dP}_I{\gamma}^I\right)}^{\frac{1}{1-d}}{w}^{\frac{-1}{1-d}} $$

And total demand for labor is ${D}_L={N}_F+{N}_I.$ Given the technology above we can determine the supply functions of intermediate and final goods:

$$ C={\theta}_IS{\left(\frac{w}{d}\right)}^{\frac{-d}{1-d}}{\left({\gamma}^I\right)}^{\frac{1}{1-d}}{\left({P}_I\right)}^{\frac{d}{1-d}} $$

(5)

$$ {X}_F={\theta}_FS{\left(\frac{1}{a}\right)}^{\frac{-a}{1-a}}{\left({\gamma}^F\right)}^{\frac{1}{1-a}}\left({P_I}^{\frac{a}{1-a}}+{w}^{\frac{a}{1-a}}\right){P_F}^{\frac{a}{1-a}} $$

(6)

Rental income for each unit of land is calculated as the profit per unit of land for the type of firm that occupies the land. Profits for final and intermediate good firms (at equilibrium values of prices and quantities) ${\pi}_F={\theta}_FS\left({P}_F{\gamma}^F\left({N_F}^a+{C}^a\right)-w{N}_F-{P}_IC\right)$ and ${\pi}_I={\theta}_IS\left({P}_I{\gamma}^I\left({N_I}^d\right)-w{N}_I\right)$.

Since that demand and supply for each good has been characterized, we can compute market clearing prices within a tile (P _F , P _I , and w). We use a zero finding algorithm, which searches for prices that make all excess demands zero, to compute equilibrium (relative) prices.

Inter-tile differences in prices induce trade. This will definitely be the case if transportation costs are zero—but trade will also occur if the advantages of a lower price outweigh the costs of transportation. We illustrate our methodology using a two tile model. Our key assumption is that costs follow the iceberg model (i.e. some fraction of goods are lost in transportation, and this fraction increases with distance and transportation time). The costs can depend upon the nature of the good as well. As we may imagine, perishable goods are more likely to be sensitive to transportation time. As goods proceed through the value chain they are transported, and processing can change the costs (by changing the characteristics of the good—e.g. by making a good non-perishable). New infrastructure has the effect of changing costs. Clearly, a bridge across a river will reduce transportation costs by changing distance as well as time spent in moving goods between points on two sides of the river. Similarly, refrigeration facilities will change the rate at which perishables depreciate. Such investments have an effect on the geographical distribution of production and consumption through their effects on transportation costs.

Suppose P _F is higher in Tile 1. Then some people in Tile 1 will buy from Tile 2, where prices are lower. Our assumption is that these people shift their market participation to another market. Costs act like a tax—some units of the good are taken away (but unlike a genuine tax, are destroyed). We will move the entire demand curve of an individual in Tile 1, and shift the total demand curves in Tile 1 and Tile 2 by appropriate amounts. This individual’s purchases in Tile 2 are subject to a tax, whereas there is no tax in Tile 1. Any market price in Tile 2 buys the agent a fraction r less. This fact needs to factor into the decision regarding which market to participate in. An individual can buy at price P ¹ _F in Tile 1, or P ² _F in Tile 2. At the lower price, the agent could buy more, pay the tax, and still come out ahead. The effects can be computed using the following logic. View the inverse demand function $-{P}_F={A}_X\frac{M}{X_F}$—as the maximum willingness to pay for the last unit (X _F ) purchased. Then for any unit, the agent would be willing to pay only a little less. If he is willing to pay $100 for the last unit in Tile 1, he is willing to pay only $100(1−r) in Tile 2, because he is only getting (1−r) units to consume. ${X}_F=\left(1-r\right){A}_X\frac{M}{P_F}$ is the individual’s demand when buying from Tile 2, and this needs to be added to the total demand in Tile 2. ${X}_F={A}_X\frac{M}{P_F}$ is the individual’s demand in Tile 1, which needs to be subtracted from the total demand there. We continue to shift individuals until the price differential is such that, accounting for the tax, it is no longer worthwhile to buy in the cheaper market. The easiest approach would be to compare buying one unit at price P ¹ _F versus (1−r) units at price P ² _F . The effective price per unit in Tile 2 is ${P}_F^2/\left(1-r\right)$. We also allow for inter-tile trade in the intermediate good. In both cases, trade will erase price differentials, although prices will differ in equilibrium because of transportation costs.

The graphs in Fig. 5 depict the results of a simulation with two tiles that differ only in the population scale parameter. Note the convergence in prices at equilibrium. The remaining differences are a result of the cost (5 % of goods are lost in transit). The two-tile model generates a number of useful qualitative results, such as (1) the pattern of trade (exports and imports) between the two tiles, (2) the pattern of production and consumption in each tile, (3) comparisons between inter-tile trade and autarky (especially, effect on income and consumption), (4) shifts in patterns due to production externality, and (5) the impact of infrastructure changes that shift transportation costs. Generalization to multiple tiles and calibration with real data is both important and complicated. However, the two tile model illustrates all the key conceptual principles involved.

Fig. 5

Convergence of prices in the two tile model

GIS Map 1

District-income income growth above baseline S1, due to S2 investments

GIS Map 2

District-income income growth above S2 due to S3 investments

GIS Map 3

District-income income growth above baseline from full AfT investment package [Source: ADB (2011)]