Analytical framework

4.3.1. Capital accumulation under credit constraints

We illustrate the demand for capital under perfect capital markets in Figure 1.

The role of social capital in alleviating credit constraints: A study of entrepreneurs in Sri Lanka 65

Figure 1: Capital stock under perfect capital markets

Source: Authors’ own illustration.

The horizontal axis measures the quantity of capital (K) and the vertical axis represents the cost of capital (r). The demand curve (D) slopes down; an increase in the cost of capital reduces the firm’s desired capital stock. The supply of capital (S) is a function of:

Ki=g(W, B, F) (1)

where the subscript i indexes the entrepreneur and W is the entrepreneur’s wealth or savings⁸, B represents access to bank loans and F access to informal loans, e.g. from the (extended) family. The amount of capital invested in the firm then depends on both the demand for capital and its supply. Under the standard perfect capital market assumption, firms face a horizontal supply curve of capital at a single fixed interest rate. In this case, the first-best capital stock, K0, is determined by the intersection of the demand and supply curve at the interest rate r0. At point K0, the marginal return to capital equals the market interest rate. This is depicted by the concave curve MPK representing the marginal product of capital, f(K). The marginal return to capital will be the same for all firms and will not depend on the characteristics of the entrepreneur or his/her household. The location of the demand curve is determined by the cost of capital and its expected future profitability. If, for instance, ability and capital are complements the expected future profitability of capital will be higher for high-ability entrepreneurs and they will desire to invest more capital. Under perfect capital markets, internal and external financing are perfect

8Wealth or savings may include business profits that are reinvested in the enterprise. Fazzari et al. (1988) develop a framework where reinvestment of cash flow allows a credit-constrained firm to adjust towards its optimal capital stock over time. This suggests that firm age will affect the level of investment. The business cycle might affect investment levels as well through its impact on cash flows.

Capital stock (K) Interest rate (r)

r₀

K₀

Figure 1: Capital stock under perfect capital markets MPK

D

66 The role of social capital in alleviating credit constraints: A study of entrepreneurs in Sri Lanka

substitutes and changes in net worth or cash flow variables (e.g. profits) should be irrelevant for the investment decision.

We now abandon the assumption of perfect capital markets. Problems of asymmetric information between borrowers and lenders and the resulting risk of moral hazard or adverse selection lead to credit rationing and result in a wedge between the costs of external and internal financing (Hubbard, 1998). This has two implications. First, a firm faces different interest rates depending on the source of credit. Second, the costs of capital from each source may vary between entrepreneurs, e.g. due to different capacities to provide collateral. This results in a step (or linear upward sloping) capital supply curve as depicted in Figure 2. The slope of the supply curve reflects the information costs related to external financing. In the case represented here, we assume that the firm uses KW units of internal wealth at the interest rate rw. It borrows additional capital from the bank at the higher interest rate rB. A firm is credit-constrained if the total amount of capital invested by the firm is less than the amount it would want to invest given the highest interest rate it is currently paying. In Figure 2, the firm would like to invest the amount KB where the marginal product of capital equals the interest rate. However, as credit constraints bind the firm, it can only borrow a maximum amount of K1 and thus operates with suboptimal levels of capital. It is now easy to see that under credit constraints an increase in the entrepreneur’s wealth and/or cash flow will expand his/her use of capital.

Figure 2: Capital stock under imperfect capital markets

Source: Authors’ own illustration.

Capital stock (K) Interest rate (r)

r_W

KW K1

rB

KB

rF

KF

D MPK

The role of social capital in alleviating credit constraints: A study of entrepreneurs in Sri Lanka 67

In our example, the entrepreneur cannot only access internal finance and (limited) bank credit but can also borrow capital from the kin at the interest rate rF. Given that the family usually has more information about the creditor than formal banking institutions and that for them monitoring may be less costly, there is reason to believe that rF ≤ rB. However, it is also possible that social norms, etc. result in higher interest rates for family credit. Access to family finance may not only change the capital costs for the entrepreneur but also alleviate credit constraints if a formally credit-constrained entrepreneur can obtain the desired amount of capital from the kin. If rF ≤ rB, the entrepreneur would like to invest even more than KB. In either case, we expect access to family finance to be positively correlated with the capital stock of the firm.

We expect credit-constrained firms to increase their capital stock over time by investing retained profits. Capital stocks would then be increasing with firm age and should increase faster if profits are high. To sum up, we describe the current level of capital stock as a function of the optimal “steady-state” capital (denoted K*), enterprise profits, wealth, ability, firm age and access to family finance. We further hypothesize that profits, wealth and access to family finance only matter for determining the capital stock of formally credit-constrained entrepreneurs.

K=g[K*(W [+]), ability [+], W [+], profits [+], family finance [+], firm age [+]] (2)

4.3.2. Choosing a production technology under credit constraints

In the last section, we have shown that formally credit-constrained entrepreneurs may face different costs of capital, which in turn causes some firms to operate with suboptimal levels of capital. Alternatively, the capital-constrained entrepreneur may choose to invest in different technologies (Banerjee & Duflo, 2005). Therefore, we expect that credit constraints and access to alternative sources of capital will also influence the capital-output - and the capital-labour ratio. The capital-labour ratio is determined by the costs of capital (r) and labour (w) as well as the output elasticities of the two input factors. Assuming a Cobb-Douglas production function

𝑌_𝑖= 𝐴_𝑖𝐾_𝑖^𝛼𝐿^1−𝛼_𝑖 where Ai is firm-level total factor productivity, Ki is capital and Li is labour input, the capital-labour ratio is given by

𝐾_𝑖

𝐿_𝑖 = 𝛼 1 − 𝛼

𝑤 𝑟

(3) Ceteris paribus, as the cost of one input increases it will be used less in the production process.

Due to imperfect capital markets, we must add a shadow price to the factor price of capital. If we assume that own wealth and access to family finance reduce the cost of capital (or expand its use) we expect to find a positive correlation between these variables and the capital-labour

68 The role of social capital in alleviating credit constraints: A study of entrepreneurs in Sri Lanka

ratio. Similarly, the use of more family labour lowers labour costs (because contributing family members are typically not paid) and results in a decreasing capital-labour ratio.