Macroeconomic Implications of the Trade Protection Policy under Local-Currency Pricing
3. Flexible prices
Since the purchasing power parity does not necessarily hold in our model, this condition implies that consumptions may not generally equal across countries.
. Following the monetary policies adopted in Obstfeld (2006), the interest rate rules in these two countries are as follows:5
( )
, *,ln 1+it = +i
ω
pt+φ ε
H a t+φ ε
F a t (10a)(
*)
* * , * *,ln 1+it = +i ωpt +φ εH a t +φ εF a t (10b) The monetary authority in each country adjusts the nominal interest rate in reaction to the domestic price levels and shocks from both countries.
φ
H andφ
F are the home monetary policy parameters determining how the home monetary authority reacts to shocks. The foreign monetary policy follows an analogous form.63. Flexible prices
To understand how sticky prices would affect the economy, we have to know how the economy works under flexible nominal prices. Assume that the central bank does not respond to productivity shocks so that the nominal interest rate rule is simplified as 1+ = +it i
ω
pt in the flexible-price case.The tradeoff between the labor supply and consumption is:
*
Substituting this equation back into Eq. (9), we can see that . In a monopolistic competition market, firms will set the price as a fixed markup over the marginal cost for the home and foreign countries;
*
t t t
W =ξW
5 Amato and Laubach (2004) find that a simple interest rate rule can nearly lead to the optimal allocation for any degree of habit formation. They adopt an inertial interest rate rule where the interest rate reacts to the past interest rate, the inflation rate and the output. The optimal monetary policy suggests a super-inertia interest rate rule that, in which the current interest rate reacts more than one hundred percent to its past value. The coefficient incorporating the nominal interest rate’s reaction to the inflation rate is 2.37 when there is no habit formation. Both of these two responses of the interest rate decrease with the degree of habit formation.
6 Following Obstfeld (2006), we assume there is no nominal shock to the interest rate rule. This case can be extended easily.
that is, ,
− respectively. Therefore, combined with the relative wage, relative price is simply the relative productivity across countries:
* *
The combination of Eq. (11) and the composite price index yields the consumptions in these two countries respectively:
Eq. (12) shows that shocks are shared across countries. The home consumption increases with positive home and foreign shocks because higher productivity lowers both the domestic and foreign good prices. On the contrary, higher tariff increases the domestic import price level and thus reduces the consumption. However, the imposition of the tariff affects the consumption in the domestic economy only. The share of the tradable goods in the overall consumption determines the magnitude of these effects.
Because all the variables follow lognormal distribution, take logarithms for the Euler equation Eq. (8) under flexible prices. Substitute the interest rate rule and solve the price level recursively, then we can write the price level in terms of expected future consumption growth and variances of endogenous variables, which are assumed constant over time:
All lower cases denote the logarithm of the variables. Substitute consumption functions Eq. (12) into Eq. (13), we will see that the price level can be written as:
Same as consumption, the home aggregate price level is influenced by the domestic tariff only. However, the
impact of the tariff on the price level, , involves not only current tariff rate but also the expected future
tariff policy changes. While current tariff shock causes higher price level, expected tariff increase lowers the aggregate price level. It is because lower consumption is caused by higher price level in the future, forcing the monopolistic firms to reduce prices.
, FP
Λp t
The moment terms in the parenthesis are primarily associated with variances of consumption and the covariance between consumption and price and are assumed to be identical across countries. Because the tariff affects consumption, its variation would also impact the level of price and other macroeconomic variables.
However, throughout the paper we neglect the effects caused by the policy fluctuations because the trade protection policy is not subject to frequent adjustments.
The trade policy also drives exchange rate movements. Substitute the consumption and price level, Eq. (12) and (14), into the risk-sharing condition Eq. (10), we can derive the nominal exchange rate:
(
1) (
*)
,This equation holds because . Both relative productivity shock current and future
relative tariff rates cause the nominal exchange rate movements. Higher home productivity reduces home prices relative to foreign and thus the nominal exchange rate depreciates in reaction to the relative productivity movements. On the other hand, greater home tariff leads to the nominal exchange rate depreciation to diminish the magnitude of the domestic demand shift from import to the home goods due to the tariff.
*
1 , 1 ,
FP FP
t c t t c t
E−Λ =E−Λ
Following past studies, we are interested in whether the tariff policy is contractionary or expansionary. In the monopolistic competition market, because the productions of each country consist of the goods sold to the domestic and foreign markets, the home production can be obtained from the world demand for home goods, Eq. (7), combined with relative prices:
( )
Becauseρ>1, we can see that current home tariff is expansionary, but the foreign tariff is contractionary for the home production. While the current home tariff has a direct negative effect on the aggregate consumption by raising up the aggregate price level, it also causes the home demand to shift toward the home produced goods due to the improvement of the home terms of trade. The substitution effect in the latter dominates and thus the overall home production benefits from the protection policy. On the other hand, the foreign tariff reduces the foreign aggregate consumption as well as the import from home firms to the foreign market, and thus leads to lower home export. Note that, the future tariff plan does not influence the production. In Section 5, we will propose three trade policies and examine the impacts of different tariff structures on the economy.