_{1}

Constructing a stochastic international trade model where exporting firm faces uncertain trade policy expressed by geometric Brownian motion, we examine the effect of an increase in the trade policy uncertainty on the optimal start time of export. It is revealed that when the trade policy is less uncertain than a threshold level, an increase in the trade policy uncertainty accelerates the optimal exporting timing of export, which is in sharp contrast to the standard result that an increase in the uncertainty postpones the optimal timing. It is also revealed that such a stochastic version of the backfiring effect reduces the world welfare if demand for exported products is low, starting export is costly or future is not important.

Studies on trade policy, which progressed by paying attention to strategic interaction between governments and firms (Brander and Krugman (1983) [

Structure of this paper is as follows. After constructing a basic model to derive the equilibrium profit of exporting firm in Section 2, section 3 formulates the objective function of the exporting firm. Based on these analyses, in section 4 we demonstrate the relationship between the trade policy uncertainty and the start time of export, followed by the welfare implication of the backfiring effect in Section 5. Concluding remarks are made in section 6.

Let us consider an inter temporal economy where time passes continuously with importance of the future diminishing with discount rate ρ. The economy consists of two countries, i.e., domestic and foreign ones, each of which is assumed to have one firm that takes prices as given.

We assume that

with initial value

We specify the domestic firm’s average revenue from exporting decreases to

with initial value

We assume that the domestic firm incurs a fixed cost of K when starting the export, followed by variable costs of ^{*}, as well as the amount of the export in each period. As for the foreign firm, for the simplicity of the analysis, we assume that the foreign firm supplies

Since the domestic firm’s profit in period t,

order condition for the profit maximization as

From Equation (3), we have its first derivative and second derivative with respect to

where

By making use of this stochastic process of the domestic firm’s profit, let us express the domestic firm’s objective function to maximize in period 0, ^{*}, the level of φ in

period t^{*}. For this purpose, if we let ^{*} (i.e., the expected value of

where γ_{1} < 0 and γ_{2} > 0 are solutions to the characteristic equation^{*} is the domestic firm’s profit in period t^{*}, it follows that α = 0 and

Thus, we can calculate the domestic firm’s objective function to maximize in period 0 as

by substituting

Now, we are ready to determine the domestic firm’s optimal start time of the export.

Since the model of the present paper is stochastic, the optimal timing is expressed by the cut off level of φ^{*}. Therefore, by differentiating Equation (7) with respect to φ^{*} and setting it to zero, we have the domestic firm’s optimal cut off level of φ^{*} as

If ε < 1, graph of φ^{*} is depicted as a hump-shaped trajectory on s-φ^{*} space with φ^{*}-intercept being ^{*} decreases monotonically as s increases.

Since large s means an increase in the uncertainty of the trade policy and small (large) φ^{*} means postponement (acceleration) of starting of the export, we have the following proposition.

Proposition 1: 1) If the trade policy is less uncertain than a threshold level, an increase in the trade policy uncertainty accelerates the domestic firm’s start time of the export; 2) if the trade policy is more uncertain than a threshold level, however, an increase in the trade policy uncertainty postpones the domestic firm’s start time of the export.

In the present model, as Equation (3) shows, an increase in the trade policy uncertainty pulls up the growth rate of the domestic firm’s profit, to accelerate the start time of the export. If this accelerating effect surpasses the standard postponing effect caused by the value of waiting, overall effect accelerates the start time of the export, which we define here as a stochastic version of the backfiring effect that was shown by Ishikawa and Lee (1997) [

If^{*} is depicted as a decreasing graph on s-φ^{*} space as in

We can derive the welfare implication of the stochastic version of the backfiring effect, i.e., how the export triggered by the trade policy uncertainty makes effect on the world welfare which we define as sum of the surpluses of the two countries.

For this purpose, let us first assume that firms’ costs are payment for the labor and capital the households provide, so that they are canceled out in calculating the welfare. Since the tariff revenue is also canceled out, the world welfare in period t without exporting,

When the domestic firm exports, on the other hand, the world welfare in period t,

By comparing (9) and (10), we have

Since the φ^{*}-intercept in

Proposition 2: Backfiring effect reduces the world welfare if

This proposition demonstrates that the stochastic version of the backfiring effect reduces the world welfare if the demand for the exported products are low (A is small), starting the export is costly (K is large) or the future is not important (ρ is large) and so on.

We began this research wishing to invent anew framework that combines the optimal stopping theory with the standard microeconomics-based trade theory. Our result was more surprising than we had expected: if the trade policy is less uncertain than a threshold level, an increase in the trade policy uncertainty accelerates the domestic firm’s optimal start time of the export, which was missed in the previous studies that did not formulate the demand structures explicitly. We also revealed that such a stochastic version of the backfiring effect reduces the world welfare if the demand for the exported products is low, starting the export is costly or the future is not important.

We truly hope this research note, which sheds new light on the problem of the optimal start time of the export, will contribute to the progress of studies on international economics.

Yasunori Fujita, (2016) Backfiring Effect of Uncertain Trade Policy. Modern Economy,07,613-618. doi: 10.4236/me.2016.75067