A Theoretical Analysis of Financial Agglomeration in China Based on Information Asymmetry

1 Introduction

The development of modern information technology has brought about a lot of changes to the microstructure and pattern of financial markets. The transmission of goods, capital and information can be realized among different areas efficiently and in low cost. Accordingly some scholars believe that with sophisticated networks of electronic communications and electronic money the circulation of capital is no longer obstructed by distance for financial industry. Despite the fact that electronic transmission of information has substantially reduced the friction of distance, the financial sector has its high degree of spatial agglomeration in particular locations. Many financial institutions are focused on a particular city or region around the globe. These cities are often political, economic, culture, transportation and business centers for a country. Even with higher operating costs than other cities, these cities have attracted a large number of financial institutions being gathered here. Well, what is the reason for this phenomenon? Why is there spatial agglomeration of financial activities? This paper attempts to answer this question.

A financial center is conventionally regarded as a place with an agglomeration of financial institutions providing all banking and financial services, nationally or internationally. The development of financial centers can offer a good example to illustrate the continuous significance of geography in the location choice of businesses. [1, 2] explore that international financial centers have a particular set of location determinants by exemplifying the case of London. He also argues that the advantages of a given location as a financial center can be defined by the local characteristics and localized information jointly. [3, 4] suggest that the agglomeration process of financial services can be understood by assessing the importance of information hinterland and asymmetric information. [5] summarizes the state of arts of geography of money and finance, emphasizing the political economic approach in understanding the formation of geographies of money and finance. He agrees that, to a great extent, a wide range of social factors might contribute to the survival and success of international financial centers in particular places. [6] finds that financial services rely on information as an input and produce it as an output. Information is both the process and the product of financial services. [7, 8] assert that the friction of information flows across physical distance affects the location of financial activities, as information collection and verification are particularly crucial for financial business to play safe games.

[9, 10] argue that information problems have created the need for geographic agglomeration of financial activities based on the source of information. This is true even in an era when financial markets work through sophisticated telecommunication networks. Based on a survey of the actual location of multinational corporation (MNC) regional headquarters, and through investigation of reasons for the agglomeration of these headquarters, they anticipate that Beijing, as the prime source of policy information, is more likely than other Chinese cities to be the national pre-eminent financial center when the Chinese financial markets become more open to foreign firms in the near future. [11] finds significant agglomeration forces between financial intermediaries (downstream industry) on the one hand and business services and computer industry (upstream industries) on the other using macro data of Luxembourg services industry.

As the financial services industry is quite different from other industries, the traditional model of industrial agglomeration is not applicable for investigating finance agglomeration. This paper regards the financial services industry as a special kind of industry, and establishes a multi-region model, which reflects the characteristics of financial services industry.

The paper is organized as follows. The next section represents the basic multi-region model. Section 3 discusses a few numerical examples and considers the equilibrium of financial agglomeration. Section 4 investigates and explains the reasons and forces which determine the agglomeration by examining whether the equilibrium of financial agglomeration is sustainable. Conclusions are presented in Section 5.

2 The multi-region model

A lot of researches have been done about the economics of trade and agglomeration. [12] presents a simple formal analysis which incorporates some important elements, such as economies of scale, the positive of product differentiation, and imperfect competition, and shows how it can be used to shed some light on these issues which cannot be handled in more conventional models. His model is derived from Dixit-Stiglitz’s model[13] of monopolistic competition. These issues include, in particular, the causes of trade between economies with similar factor endowments, and the role of a large domestic market in encouraging exports. He examines the effect of transportation costs, and shows that countries with larger domestic markets will, other things equal, have higher wage rates. He finds that countries will tend to export those goods for which they have relatively large domestic markets.

[14] develops a simple model that shows how a country can endogenously become differentiated into an industrialized “core” and an agricultural “periphery”. In order to realize scale economies while minimizing transport costs, manufacturing firms tend to locate in the region with larger demand, but the location of demand itself depends on the distribution of manufacturing. Emergence of a core-periphery pattern depends on transportation costs, economies of scale, and the share of manufacturing in national income. [15] adopts an impressive number of simplifying assumptions in order to focus tightly on agglomeration forces created by pecuniary externalities.

Information is both the process and the product of financial services. As the potential opportunity and profitability of the financial sector depend much on the accessibility and reliability of information, the sizes as well as the features of information hinterland are key aspects that are attractive to the financial firms. Financial businesses need to collect, disseminate and interpret huge amounts of information. High-level financial firms, therefore, seek to locate within the information hinterland of an international city where information can be easily accessed and verified at lower costs.

By examining various forces behind the formation of a financial center, we argue that information problems have created the necessity of the geographic agglomeration of financial activities in the source of information even in the era when financial markets have worked through sophisticated telecommunication networks. So we assume that there will be opportunity costs caused by information asymmetry. That is to say, there will be costs caused by friction of information flows across physical distance. We consider an economy with two sectors, financial sector and real sector. There are two kinds of goods, financial products and real economy products. There are two kinds of resources, labor and capital.

3 Numerical examples

In order to focus on the analysis of financial sector, we use the wage rate of the real sector as the numeraire and assume that real sector workers have the same wage rate in all regions. So we can get w1I=w2IandG1I=G2I=1. The real wage equations (33) and (34) become

The income equations (41) and (42) become

So the model’s simplified instantaneous equilibrium can be thought of as determined by the simultaneous solution of the equations (29), (30), (31), (32), (43) and (44).

It is very helpful to look first at some numerical examples. The workers will move toward regions that offer high real wages and away from regions that offer below-average real wages. We can ask whether ω₂ is greater or less than ω₁to judge the migration choices of workers. If ω₂ ≤ ω₁ satisfies, then financial workers will not move out of region 1; if ω₂ > ω₁satisfies, then financial workers will move out of region 1. So panel (a), (b) and (c) of figure 1 plot ω₁ – ω₂, the difference between the two regions’ real wage rates in financial sector, against x, the region 1 share of financial activities. We can get considerable insight by examining an obvious special case: that of a two-region economy in which real sector is evenly divided between regions. So we get λ = 1/2. All three figures are calculated for σ = 5, μ = 0.3. However, the opportunity costs caused by information asymmetry is different in each: panel (a) of figure 1 shows a high opportunity costs case, τ₁ = τ₂ = 1.5, panel (b) of figure 1 a low case, τ₁ = τ₂ = 1.4, and panel (c) of figure 1 an intermediate case, τ₁ = τ₂ = 1.45.

Figure 1

Real wage differences

In panel (a) of Figure 1, the wage difference is positive if x is less than 0.5, negative if x is greater than 0.5. This means that if a region has more than half the financial labor force, it is less attractive to workers than the other region. Clearly, in this case the economy converges to a long-run symmetric equilibrium in which financial firms is equally divided between the two regions.

In panel (b) of Figure 1, by contrast, the wage difference slopes strictly upward in x: the higher the share of financial firms in either region, the more attractive the region becomes. Other things equal, a larger financial labor force makes a region more attractive both because the larger local market leads to higher nominal wages and because the larger variety of locally produced goods lowers the price index. The important point here is that although an equal division of financial activities between the two regions is still an equilibrium, it is now unstable: if one region should have even a slightly larger financial sector, that sector would tend to grow over time while the other region’s financial sector shrank, leading eventually to a pattern with all financial activities concentrated in one region.

Finally, panel (c) of Figure 1, for an intermediate level of opportunity costs caused by information asymmetry shows a more complicated picture. The symmetric equilibrium is now locally stable, as in panel (a) of Figure 1. However, two unstable equilibriums now flank it: if x starts from either a sufficiently high or a sufficiently low initial value, the economy converges not to the symmetric equilibrium but to a pattern with all financial activities in only one region. This picture then has five equilibriums: three unstable (the symmetric equilibrium and financial activities concentration in either region) and two unstable.

From these three cases it is straightforward to understand how the types of equilibriums vary with opportunity costs caused by information asymmetry. At sufficiently high opportunity costs, there is a unique stable equilibrium in which financial activities are evenly divided between the regions. When opportunity costs caused by information asymmetry fall below some critical level, new stable equilibrium emerge in which all financial activity is concentrated in one region. When they fall below a second critical level, the symmetric equilibrium becomes unstable.

If the two regions have different amount of financial information, there will exist an information hinterland. So we suppose τ₁ < τ₂, then region 1 is the information hinterland.

We can get considerable insight by examining an obvious special case: there are no costs required to collect and verify the information from region 1. That is to say, the relevant price of a financial variety produced in location 1 at consumption location 2 will remain the same. So we can get τ₁ = 1. Panel (d) of Figure 1 shows a high opportunity costs of region 2 case, τ₂ = 10, panel (e) of Figure 1 a lower case, τ₂ = 7, and panel (f) of Figure 1 an intermediate case, τ₂ = 5, panel (g) of Figure 1 a low case, τ₂ = 3, panel (h) of Figure 1 a lower case, τ₂ = 2. These figures show that ω₁ – ω₂ is always positive, and so the equilibrium of a core-periphery pattern with all financial activities concentrated in region 1 is stable.

4 Equilibrium and sustainability of finance agglomeration

Suppose we start with all financial firms concentrated in one region, say region 1. To determine whether this is a stable equilibrium, we ask whether a small group of workers moving from region 1 to region 2 would receive a higher real wage than that received by the workers remaining behind. If so, a core-periphery pattern is not a stable equilibrium: financial firms will shift over time to the peripheral region. If not, a core-periphery pattern is a stable equilibrium. The concentration of financial activities will be self-sustaining. In fact, finance agglomeration and real sector industry agglomeration will influence each other. In order to capture these characteristic, we suppose all real sector firms concentrated in one region, say region 2.

In short, to assess whether a core-periphery pattern is sustainable, we need to posit a situation in which x = 1; λ = 0, and ask whether in that case ω₂ is greater or less than ω₁. If we can get ω₂ ≤ ω₁, then the core-periphery pattern is sustainable, because financial workers will not move out of region 1.

Suppose we set x = 1; λ = 0. Simply guess that w1=1,w2I=1;η=1,τ2=ατ1; in that case, we can get

And notice that the financial price index is higher in 2 than in 1, because location 2 has to import all its financial products. The real sector price index is higher in 1 than in 2, because location 1 has to import all its real sector products. Notice that whether the income is higher in location 1 than in location 2 depends on the share of the financial activities in the economy.

Because w1=1,G1=1,G1I=τ satisfies, it then follows that ω1=w1G1−μ(G1I)−(1−μ)=τμ−1 as well. So we all need to do is determine ω₂, and see whether it is more or less than τ^μ–1. That is to say, determine whether ω2τ1−μis more or less than 1. Substituting into the nominal and real wage equations (32) and (34), we have ω2τ1−μ=τ1−μτ1−μ[μτ21−σ+(1−μ)τ1σ−1]1/σ.

It is helpful to rewrite it, in the form

where σ > 1, τ₁ > 1, τ > 1,0 < μ < 1.

Proposition 6

There is a critical point τ*, if τ₁ < τ*, the financial agglomeration is sustainable; if τ₁ > τ*, the financial agglomeration is not sustainable.

When ρ > μ, we can get

limτ1→0+J(τ1)=+∞,limτ1→+∞J(τ1)=+∞.

So figure 2 shows the curve of J(τ₁). There is a minimum point of J(τ₁).

Figure 2

Sustain point of financial agglomeration

When τ₁ = 1, using equation (52) we can get

dJdτ1=μα1−σ(1−σ−σμ)τσ(1−μ)+(1−μ)(σ−1−σμ)τσ(1−μ).

When τ₂ = 1, α = 1, we get

dJdτ1=−τσ(1−μ)σμ+τσ(1−μ)(1−σ)(2μ−1).

If |σμ|<|(1 – σ)(2μ–1)| satisfies, we know that

dJdτ1>0.

So τ₀ lies on the left side of τ₁ = 1. So we can get a critical point τ₁ = τ*. When τ₁ < τ*, we get ω2τ1−μ<1 and when τ₁ > τ*, we get ω2τ1−μ>1.

If |σμ| > |(1 – σ)(2μ – 1)| satisfies, we know that

dJdτ1<0.

So τ₀ lies on the right side of τ₁ = 1. So we can get a critical point τ₁ = τ*. When τ₁ < τ*, we get ω2τ1−μ<1 and when τ₁ > τ*, we get ω2τ1−μ>1.

If |σμ| = |(1 – σ)(2μ – 1)| satisfies, we know that

dJdτ1=0.

So τ₁ = 1 is the minimum point of J(τ₁). So we can get a critical point τ₁ = τ*. When τ₁ < τ*, we get ω2τ1−μ<1 and when τ₁ > ω2τ1−μ>1.

When τ₂ > 1, α > 1 satisfies, we can get the following results:

If

α1−σ>(μ−1)(σ−1−σμ)μ(1−σ−σμ)

satisfies, we know that

dJdτ1<0.

So τ₀ lies on the right side of τ₁ = 1. So we can get a critical point τ₁ = τ*. When τ₁ < τ*, we get ω2τ1−μ<1 and when τ₁> τ*, we get ω2τ1−μ>1.

If

α1−σ=(μ−1)(σ−1−σμ)μ(1−σ−σμ)

satisfies, we know that

dJdτ1=0.

So τ₁ = 1 is the minimum point of J(τ₁). So we can get a critical point τ₁ = τ*. When τ₁ < τ*, we get ω2τ1−μ<1 and when τ₁> τ*, we get ω2τ1−μ>1.

If

α1−σ=(μ−1)(σ−1−σμ)μ(1−σ−σμ)

satisfies, we know that

dJdτ1>0.

So τ₀ lies on the left side of τ₁ = 1. So we can get a critical point τ₁ = τ*. When τ₁ < τ*, we get ω2τ1−μ<1 and when τ₁>τ*, we get ω2τ1−μ>1.

To sum up, we can get the conclusion of Proposition 6. The conclusion of Proposition 6 is the same with the results of numerical examples. This explains why there isn’t one specific financial center throughout the world. Because there is a sustain point for the financial agglomeration. If the costs caused by the space are too high, the financial activities will find a new place to locate.

Proposition 8

If the share of financial goods is large, the financial agglomeration is sustainable.

When τ = 1 and regard J as a function of μ, we can get

(54)dJdμ=(τ21−στ1−σμ−τ1σ−1−σμ)−σ[μτ21−στ1−σμ+(1−μ)τ1σ−1−σμ]ln⁡τ1

After a few calculations, we can get dJdμ<0. When μ = 0, we can get ω2=(τ1σ−1)1/σ>1 because of τ₁ > 1. When μ = 1, we can get ω2=(τ21−στ1−σ)1/σ<1 The curve of ω₂ is shown by Figure 3.

Figure 3

Curve of ω₁

5 Conclusions

Through this analytical model, this paper discusses the formation mechanism and equilibrium of finance agglomeration. Our findings suggest that emergence of a core-periphery pattern of finance agglomeration depends on opportunity costs caused by information asymmetry, economies of scale, the share of financial services industry in the economy and the amount of financial information. And the agglomeration of real sector industry will enhance the agglomeration of finance. Finally, this paper puts forward a ratio, which is related with the opportunity costs, could be regarded as a measure of whether the central area is an information center.

Currently, China has prioritized Shanghai to be the top financial center in the country. Many incentive policies have been introduced to promote the financial sector there. Shanghai has achieved remarkable social and economic transformation in the past decade. We suggest that Shanghai should improve the sophistication in information technologies, so that standardized information can be obtained over greater distances without much cost. In this way, there will be less opportunity costs for the periphery locations to consume the financial products in Shanghai. However, at the same time Shanghai should be the source of information and the information hinterland. There should be more innovations in financial sector of Shanghai, so there will be much non-standardized financial information in Shanghai. Such advantages could create cumulative causation effects and make Shanghai be the most important financial service hub of China. The effect of information asymmetry would push financial firms closer to an information source in order to find and interpret non-standardized information that a financial firm can use to make profit.