EC4342: Briefly Explain why Some Industries are More Reliant on Institutional Quality than Others: International Trade II Assignment, NUS, Singapore

(I.1) Briefly explain why some industries are more reliant on institutional quality than others.

(I.2) True or False? As there is little evidence of learning-by-exporting at the firm level, we shall not expect the industry-level productivity to be affected by international trade.

(I.3) True or False? In the Melitz model, higher fixed trade barriers (fX) protect the domestic firms from foreign competition by lowering the domestic productivity cut-off (ϕD). As a result, everything else being equal, higher fX leads to higher welfare in the trade equilibrium.

(I.4) True or False? In the Antras model of vertical integration, everything else being equal, higher bargaining power (δ) of the headquarter firm will always lead to a higher propensity to integrate with the suppliers.

(I.5) A researcher estimates the following equation: ln xic = αi + αc + β1ziQc + β2hiHc + β3kiKc + εic, where xi is the total export of country c in industry i. αi and αc controls for industry and country fixed effects. The researcher also controls for the skill intensity and endowment (hi and Hc) and capital intensity and endowment (ki and Kc). zi is institution-intensity, and Qc is a measure of rule-of-law.

The researcher wants to test the hypothesis that countries with better rules of law shall export more in institution-intensive industries. If the researcher estimates the above equation with OLS, will β1 be biased? Why?

II. A Melitz Model without Entry

Start from a standard two-country symmetric Melitz model as in the lecture, and use the notations from the slides and the lecture notes. We make the following changes to the model:

Instead of assuming free entry so that anyone can pay fe to draw productivity, we now assume that the mass of potential entrepreneurs, n, is exogenously fixed as a model parameter. The rest is the same as in the lecture: all the potential entrepreneurs draw productivity from G(ϕ). Those with productivity above the survival cutoff pay f and start to produce.

Note that without free entry, aggregate profit will no longer be zero. Assume
that all the profits will be equally distributed back to workers so that the
the following condition will be true in equilibrium:
Xi = wiLi + Πi
where Xi is the total income, wi the wage rate, Li the population, and Πi the total profit in country i.

Questions:
(II.1) (5 marks) Assuming autarky equilibrium, derive the expression of the domestic production cutoff, ϕ as a function of wi, Pi , Xi , and the model parameters.

(II.2) (10 marks) Assuming autarky equilibrium, note that the aggregate profit, Πi by definition, can be written as:

where πi(ϕ) is the profit of a firm with productivity ϕ. Prove that in autarky equilibrium, aggregate profit must be a fixed fraction of aggregate income. In other words, prove that Πi Xi must be a constant and find the expression of the constant as a function of model parameters.

(II.3) In the data, the sales distribution across firms is often estimated to be a Pareto distribution. In the Melitz model, the equilibrium firm-level sales, ri(ϕ) = pi(ϕ)qi(ϕ), also follows a Pareto distribution. In particular, one can show that:

where Pr(r > x) is the probability that firm sales r are greater than x, and C and ζ are constants. Derive the expression of ζ as a function of model parameters.

III. Organizational Mode Problem Consider a perfectly competitive firm that can sell an arbitrary amount of output at some exogenously given price p. The production function is given by

where h is “headquarter services” and x is intermediate inputs. Headquarter services are produced using only labor that earns a wage w. That is, h = l, where l is the employment of labor in the headquarter services. Intermediate supply x is in an exogenous and fixed supply somewhere in a foreign country. (We can think of x as the quantity of oil in a particular oil field, and of h as the engineering and logistics services to extract the oil and process it for consumption in the marketplace.)

Contracts are incomplete in a foreign country. That is, once the firm spent resources on producing a quantity h of headquarter services, the firm and the owners of x bargain over the division of the surplus, with the home firm receiving a share β of the surplus, and the x-owners the remaining 1 − β. Since both h and x are worth nothing outside of the relationship, the surplus is simply the total revenue. Note that as we have assumed x to be exogenous, you do not need to worry about the under-investment problem of the supplier.

Questions:

(III.1) Set up the firm’s profit maximization problem. Solve for the equilibrium investment in h. How does it depend on β?

(III.2)  How does the level of h above differ from the outcome under complete contracts? Write down the ratio of actual h to the level of the complete contract of h. How does this ratio depend on z? Interpret what your answer says about the impact of incomplete contracts.

(III.3)  Derive the profits of the firm. How do they depend on β?

(III.4) Imagine that there are two modes of dealing with the suppliers of x: integration, whereby the home firm (partly) owns the production facility of x, and outsourcing, in which the home firm purchases x from the foreign owner at arm’s length. Under integration, the contract friction is not fully solved, but the firm does have greater bargaining power: βO < βV < 1, where O refers to outsourcing, and V to vertical integration. Also, suppose that integration involves a fixed cost f, whereas outsourcing does not. If f = 0, which organizational form will the firm choose?

(III.5) In general, how do βO, βV, and f affect the organizational decision of the firm? For this part, qualitative answers will do. For example, your answers could be, “if βO is higher, the firm is more likely to choose outsourcing/integration because.