Abstract
The paper derives “targeting rules” for optimal policy in a simple two-country model in which financial markets are incomplete and policy is noncooperative. The optimal rules are compared with the cooperative case. Although the model is simple, it is complex enough so that the distortion introduced by incomplete financial markets matters. The complete markets case serves as a benchmark. Under complete markets, it is shown that the policy response in one state of the world influences outcomes in all other states through the effect on asset prices. It is noted that monetary policy cannot replicate an optimal tariff, so that the absence of a tariff instrument is a distortion even in the complete-markets economy. We show that optimal policy, even under complete markets and cooperation, does not try to minimize spillovers.
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Notes
That is, undistorted assuming that there was an appropriate constant subsidy to output to alleviate the underproduction that arises in the model from the monopoly power of producers.
This wedge corresponds to the labor market wedge in the macroeconomics literature. See, for example, Hall (1997), Gali and others (2007), or Chari and others (2007).
The numeraire for state contingent claims is irrelevant. We express things in nominal terms here so that the model can be easily generalized to the sticky nominal price case.
See Senay and Sutherland (2007, 2013) for a comparison of optimal policy in models with asset trade, in the cases of commitment vs. discretionary policy (policy chosen after portfolios have been set).
The Appendix derives the solution to the model under balanced trade and complete markets, in terms of productivity shocks and the employment subsidy.
Hereinafter, we omit the state subscript j when there is no possibility of confusion.
See Engel and Matsumoto (2009) and Heathcote and Perri (2013) for examples of similar models where there is substantial home bias in equity holdings when nonstate-contingent bonds are also traded.
These derivations and results correspond to those in Corsetti, Dedola, and Leduc (2011a).
In order to take these differences, it is important that the log linearizations in both cases of incomplete and complete markets are around the same steady state.
See Corsetti, Dedola, and Leduc (2011b), Engel (2014) and Bhattarai, Lee, and Park (2015) for examples of dynamic two-country New Keynesian models with incomplete markets, where policymaking under cooperation is considered.
These steps draw on the Appendix of Devereux and Engel (2003).
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Additional information
*This paper was prepared for the Jacques Pollak Annual Research Conference, International Monetary Fund, Washington, DC, November 13–14, 2014. The author acknowledges research support from NSF grant # 1226007. He thanks Mick Devereux, Pierre-Olivier Gourinchas, Linda Tesar, Anton Korinek, reviewers for the IMF Economic Review, and participants at the conference at the IMF and seminars at Wisconsin and Johns Hopkins for helpful comments. Charles Engel is the Hester Professor of Economics at the University of Wisconsin.
Appendix
Appendix
Derivation of Equilibrium under Complete Markets
Here, we solve for the ratio of Lagrange multipliers, λ/λ*, in Equation (10).Footnote 11 From the zero profit condition under free entry in competitive markets and the budget constraint (equation (4)), using the definition of profits (equation (7)), we have:
Then using the equilibrium condition (equation (12)) and the demand equations (2) and (3), we can write this equation as:
Multiply by the price of contingent claims, sum up over states, and recall ∑ Z j D j =0, to get:
Then use the first-order conditions (equations (5) and (6)) to write
Substituting into the previous expression, we find:
Solution to Model in Terms of Productivity Shocks and Labor Subsidies
The equivalent equation to Equation (11) for the Foreign country is given by:
Using this equation and Equation (11), we find:
Then using Equation (18), the trade-balance equation, we can derive:
Substitute this equation back into Equation (11) and we find:
Analogously, for the Foreign country, we have:
Under complete markets, we can combine Equation (A.3) with the condition for equilibrium (equation (16)) to find:
We can use this to derive:
Also, using Equations (11), (A.2), and (A.7) and (A.8), we find:
From these expressions, we can solve:
This expression can be substituted into Equations (A.8), (A.9) and (A.10) to complete the characterization of the solution.
As noted in the text, there are two well-known cases in which the balanced-trade and complete-markets solution are the same. The first is when σ=1, in which case we find
The second case is when ν=1, in which case we find
