Drozd & Nozal(2012) (Understanding International Prices: Customers as Capital)

This paper builds a model that treats consumers as a form of non-productive capital in an attempt to resolve a few outstanding puzzles in the international macro literature.

Puzzles

The puzzles are:

1. In the standard theory (like BKK), the price of exported goods co-moves negatively with the price of imported goods. In their sample o2 12 OECD countries, the authors find that the correlation is always positive and covers a range from 0.57 to 0.94, with a median of 0.87.
2. Standard theory predicts that the volatility of the terms of trade (ratio of import to export price) and the real exchange rate is exactly the same. In their data sample, the ratio of these volatilities range from 0.21 to 0.83.
3. Finally, there is a lot of empirical evidence of pricing to market – an apparent violation of the law of one price (LOP). Standard theory suggests that the LOP always holds.

Model

Environment:

• Discrete time, infinite horizon
• Two ex-ante identical, symmetric countries called home and foreign
• The only source of uncertainty is country-specific productivity shocks
• Tradable goods are country specific and are produced using a CRS technology in capital and labor, subject to a productivity that is AR(1) in logs
• Producers sell their goods to retailers in each country, then retailers sell the goods to final consumers

Households:

• In each country there is a unit mass of identical households
• Each period they choose the level of consumption, investment physical capital, labor supply, purchase of tradable goods from domestic and foreign sources, and a portfolio from a complete set of one period state-contingent bonds to maximize the expected discounted lifetime utility from consumption and leisure.
• Domestic and foreign goods are combined with a CES technology with home bias. The aggregate is then allocated across consumption and investment.

Producers:

• The novel part of this model is that producers must make costly matches with retailers in each country in order to sell their goods.
• To do this the authors introduce two additional variables into an otherwise standard firm problem: marketing capital and a customer list – both are market specific.
  • Marketing capital is non-productive, but is required for matching with new retailers
  • The customer list is the total number of matches a producer has made in that market. It is assumed that the producer can sell one unit of their output to each retailer in their customer list.
• The customer list depreciates at a constant rate and is increased each period by the measure of searching retailers times this producer’s share of the marketing capital in the destination market.
• The marketing capital depreciates at a constant rate, and is increased each period by direct marketing input less a fixed cost of adjusting.
• The firm takes as given his productivity state, level marketing capital and customer list in each market and chooses capital, labor, and marketing input to maximize the expected discounted value of profit streams.

Retailers:

• In each country there is an atomless retailers that purchase goods from producers and resell them to consumers in a destination-specific competitive market.
• They face a cost of entry and dynamics are governed by a free entry condition
• When a retailer meets a producer, they bargain over the total surplus from a potential match. The surplus is split with a Nash bargaining solution with continuous renegotiation. The solution is a constant share of the surplus going to producers and retailers each period.

Results

This model is able to resolve all three puzzles simultaneously.

The main result is that in this model, deviations from the law of one price are driven by movement in the real exchange rate. Here’s the main mechanism.

The real exchange rate moves when firms get a productivity shock relative to its competitors. In this case they will find it optimal to add new buyers when the surplus from trading is higher in one market than the other (they want to equate these). But, because there are adjustment costs, firms don’t equate these in one period, so there is a sustained short and medium run price differential. Along this transition the real exchange rate is moving.

To understand the intuition behind these responses, consider the sequence of the events that follows the productivity shock. From panel A, observe that the domestic production cost v falls, which, ceteris paribus, must raise the surplus from trading the domestic good in matches. Second, due to home-bias in trade, relative to the foreign country retailers, the domestic country retailers have an advantage in meeting the domestic country producers. Not surprisingly, this creates a gap in the relative search intensity, which leads to the real exchange rate depreciation (this last implication follows from risk sharing condition). The price differential created by that feeds into prices at which producers sell to retailers and creates an incentive for the domestic country producers to expand their market share abroad more than at home. However, as implied by Lemma 1, in the short- and medium- run the adjustment of market shares will not close the initial price gap completely due to increasing cost of matching. As a result, the equilibrium response of prices features persistent deviations from LOP in our model.