The Effects of Tariff Policy under the Fixed Exchange Rate Regime

In this paper, New Open Economy Macroeconomics with micro-foundation was served as an analytical framework to explore the long-term effects of tariffs on various macroeconomic variables (e.g. consumption, output, price and terms of trade, and so on) while a country adopts a fixed exchange rate regime and with the presence of consumption home bias behavior. Through theoretical derivation and simulation analysis, we discovered that the correlation of domestic tariff rate with single variables for the long-term does not have monotonic nature, which shall depend on home (foreign) consumers’ consumptive preferences on imports and exports.


Introduction
Tariff policy has been allowed by World Trade Organization (WTO) and is one of the most important macroeconomic means that many countries have taken. It reflects an effective rate of protection and trade liberalization level throughout the country to some extent which plays an important modulation role on a country's economy. Exchange rate represents relative price of domestic and foreign currency assets, which is in charge of an important task, connecting domestic and international economy, regulating internal and external balance of economy. Reviewing the existing literature, the effects of tariffs under a floating exchange rate regime has been explicitly discussed (e.g. Batra andRamachandean, 1980, Fender andYip, 2000), however, when a country adopted a fixed exchange rate regime and the exchange rate cannot afford transmission function in the economic system, how was the effect of tariff policy on the macroeconomic variables has not yet been discussed completely. Furthermore, consumption home bias is a phenomenon that exists commonly in the real world, indicating that in an economic system, consumers often have a tendency to prefer domestic commodities. Herewith, this paper intended to discuss consumption home bias with the effects of tariff policy, and to analyze macroeconomic effects of tariff policy and the role of consumption home bias under the fixed exchange rate regime. effects of tariff shocks from a view of dynamic analysis began to emerge, such as a series of literatures displayed by Eichengreen (1981), Razin and Svensson (1983), Van Wijnbergen (1987), Edwards and Van Wijnbergen (1987) and Roldos (1991), but these literature all used perfectly competitive market structure as the basis of analysis in order to simplify the analysis, therefore, they also faced a situation that model assumptions did not match with the reality, resulting in problems of lack of credibility of theoretical analysis. So further, Rama (1993), Fender and Yip (1994), Bettendorf and Heijdra (1999), Devadoss and Lanclos (2000) and Sen (2001) turned the settings of market structure into a more realistic assumption with imperfectly competitive market to analyze the effects of the tariff shocks. At the same time, micro-foundation also was the trend of research. Razin and Svensson (1983) used two-period model with micro-foundation as the analysis base, and found that the impact of tariffs on the current account was related to the intertemporal elasticity of substitution, Roldos (1991) used specific factors model to discuss the impact of tariff changes on current accounts, he found that the effects depend on the accumulation speed of capital stock, Brock and Turnovsky (1993) established special factors model with two departments and three factors to analyze the effects of different types of tariffs (consumption tax and investment tax) on capital accumulation, Osang and Pereira (1996) discussed correlation among tariff structure, welfare and economic growth rate according to endogenous growth model in a small open economy, Bettendorf and Heijdra (2001) used dynamic overlapping-generations model to analyze tariff issue under imperfect competition of commodity markets, they found that an increase of the tariff would reduce real output and employment level in a long-term equilibrium, thereby improving the terms of trade, Ikeda (2003) found that the effect of tariff on current accounts shall be depending on the preference with imports and exports of agents, and subsequent researchers also continued to seek a more suitable theoretical model as base of analysis.
Recently, NOEM literature rise up rapidly, the model provided a complete framework on a clear micro-foundation and dynamic analysis under imperfectly competitive market structure. Therefore, relevant scholars were urged to re-examine a variety of macroeconomic issue from NOEM perspective, and the analysis on the effects of tariff policy was one of NOEM topics. Fender and Yip (2000) have ever analyzed the effects of protection policy (tariffs) on domestic (foreign) output and welfare according to NOEM model proposed by Obstfeld and Rogoff (1995). Their findings found that the increase in temporary tariff will result in decrease of domestic output, while it has uncertain effect on foreign output in the short-term, the conclusion made for the effect of tariff policy in the long-term is the same as that for short-term effect. On the other hand, for welfare, an increase of tariff will improve domestic welfare, while it gave impact on foreign welfare negative, thus the increase of import tariffs will have effect of "beggar-thy-neighbor". However, the part that aroused more attention is that although Obstfeld and Rogoff (2000) have considered "home bias in consumption puzzle" as one of six puzzles in international economics, (Note 1) the phenomenon of "home bias in consumption" has yet integrated with the research of the effects of tariff under NOEM architecture, hence, this paper further sought for breakthrough.
The so-called consumption home bias puzzle refers to a tendency of consumers on domestic goods in real world. But, this phenomenon occurred to the goods market cannot be explained by researchers. The study with topic in respect of consumption home bias has mostly focused on discussion of the causes, such as trade costs (Obstfeld and Rogoff, 2000;Ried, 2009), country size and the extent of openness (Sutherland, 2005;De Paoli, 2009), non-traded goods (Stockman and Dellas, 1989;Pesenti and Wincoop, 2002) and trade in intermediate input factor (Hillberry and Hummels, 2002), which are all main causes that scholars believed for consumption home bias. More recent studies have focused on discussion of the effect of home bias, such as Pierdzioch (2004) analyzed the effects of monetary policy on different extent of home bias and the capital mobility, Hau (2002), Pitterle and Steffen (2004), Kollmann (2004), Sutherland (2005), Leith and Lewis (2006) and Cooke (2010) discussed the effect of home bias on the exchange rate fluctuation, while De Paoli (2009) discussed the welfare effects of home bias and monetary policy. In addition, it is worthy to mention that the effect of home bias on the optimal monetary policy is also a quite hot topic, where it includes works by Faia and Monacelli (2006), Jondeau and Sahuc (2008), Galí and Monacelli (2008) and Wang (2010). Obviously, researches on the topic in respect of home bias was quite hot, however, there is no literature may clearly account for the role of home bias on the effects of tariff shocks under fixed exchange rate regime, thus inducing the motivation of this paper. This paper divided into four sections. Except for the introduction, the other sections are arranged as follows: Section 2 constructs a theoretical model; Section 3 depicts simulation analysis to discuss the long-term effects of tariff on macroeconomic variables in a fixed exchange rate regime, and explain the role that consumption home bias plays; Section 4 includes conclusions and recommendations.

Model Setting
This paper follows NOEM proposed by Obstfeld and Rogoff (1995) as a theoretical basis; the main assumptions are stated as follows: (1). There are two countries in the world, "home country" and "foreign country", all of the following foreign economic variables are marked as "*" for identification.
(2). World population is distributed in the interval [0,1], where individuals of home country are distributed between [0, n ) and foreign individuals are distributed between [ n ,1].
(3). Each individual is both consumer and producer, and he operates a monopoly competitor factory using labor for production.
(4). Consumption home bias exists in economic system, and tariff is the only one exogenous shock.

Household
Assuming that all individuals have the same preferences, utility (U ) is a function to the consumption ( C ), real money balances ( P M / ) and output level ( y ), the lifetime utility function is set as follows: ,  is the elasticity of marginal utility of real money balances, (Note 2)  and  represent the importance that real money balances and output level in the utility function, and z refers to a particular product .
In Eq. (1), the consumption index of the representative consumer is defined as the function of constant elasticity of substitution (CES): is the consumption that domestic consumers on domestic specific product z , ) (z c f is the consumption that domestic consumers on foreign specific product z ,  is the parameters of consumption home bias to measure the degree of preference that domestic consumers on domestic goods,  is the elasticity of substitution of products between countries. We can deduce domestic price index ( P ) from the definition of consumption index (Eq. (2)) by the problem of expenditure minimization as follows: Likewise, the foreign price index ( * P ) is as follows: In above two equations, ) ( z p h represents the price of home commodity z expressed in domestic currency, ) (z p f represents domestic currency price of foreign goods z , ) ( * z p h represents the foreign currency price of domestic goods z , ) ( * z p f represents foreign currency price of foreign goods z , * that foreign consumer prefer foreign commodity. In addition, in this economic system with the presence of tariffs, domestic and foreign tariff rates are  and *  respectively, and the change in tariff is a permanent shock, that is, For any kind of goods, the law of one price is held as follows: Where E represents the exchange rate. From Eqs. (2) and (3), we can deduce the consumption of domestic representative consumer for specific home/foreign commodities as follows: Likewise, the consumption that foreign representative consumer for domestic specific commodity and foreign specific commodities as follows: In both formulas as above, is the consumption of foreign consumer for specific domestic products z , ) ( * z c f is the consumption of foreign consumer for specific foreign products z .

Government
To focus on the exploration of effects of tariffs, assuming that government sectors have no expenditure and the government returns seigniorage revenue and tariff revenue to the agent by lump-sum fashion, the budget constraint of government is: Where the first item at left side of equation is real seigniorage revenue, while the second item at left side of equation is real tariff revenue, and the right side of equation is government transfer payments.

Asset Market
Suppose that there is an integrated international capital markets between two countries, each individual can trade real bonds ( B ) in this international capital market, the correlation between real interest rate ( r ) and nominal interest rate ( i ) of maturing bonds is as shown in Fisher equation, namely: The holding condition of bonds reflects the lending relationship between the residents of two countries, thus satisfying Where B is the amount of bond that domestic representative individual is holding, while * B is the amount of bonds held by foreign representative individual.

Budget Constraint
Representative Individual's budget constraint is set as follows: Where the income source of consumer in period t includes: money balances in period 1  t ) and government transfer income ( t t T P ), consumers may use this income to hold currency ( t M ), consumption ( t t C P ) and purchase bonds ) ( t t B P in period t .

Aggregate Demand
Based on the equation of consumption of home country specific products by domestic consumer (Eq. (7)) and the equation of consumption of home country specific products by foreign consumer (Eq. (9)), it can be inferred that the demand function faced by the home manufacturers is: Similarly, from on the equation of consumption of foreign specific products by domestic consumer (Eq. (8)) and the equation of consumption of foreign specific products by foreign consumers (Eq. (10)), it can be inferred that the demand function faced by the foreign manufacturers is:

First Order Conditions
When consumer is under the restriction of budget constraint (Eq. (14)), the first-order conditions for the maximization of the utility (Eq. (1)) are: Where Eq. (17) is Euler equation of consumption for describing intertemporal consumption behavior; Eq. (18) refers to a money demand equation for indicating that the substitution relationship between real money demand and consumption, and Eq. (19) is the labor supply equation for giving the alternative relation between labor supply and consumption, in which W C represents world consumption,

Derivation of Steady-State
The effects of tariff shocks on macroeconomic variables in the long-term are explored below. Firstly, given that economic system does not exist consumption home bias and tariff shock in the initial state (0 steady state) as a baseline in comparison, and then to deduce a long-term steady state of economy system. Among the following symbols, the subscript " t " represents each economic variable under long-term steady state, and the subscript " 0 " represents each economic variable under the initial state. For example: t C and 0 C represent the consumption under long-term steady state and initial state respectively.
Long-term steady state describes that after going through the exogenous shock, the whole economic system reaches the convergence state. In the long-term steady state, all variables are fixed, and . Therefore, applying the government sector's budget constraint (Eq. (11)) into private sector's budget constraints (Eq. (14)), we can get: Likewise, for foreign country, we have:

Log-linearization
In order to obtain a closed-form solution, this paper uses Uhlig (1995)'s approach. Firstly, put the model in log-linearization, followed by granting values to the parameters in the model to perform simulation analysis. We put each variable in the vicinity of the initial state into log-linearization for acquiring the degree of each variable fluctuating in the steady state. In this paper, the superscript "  " indicates the value of each variable being put into log-linearization.
For example: If t X means the result of variable t X being put into log-linearization in the vicinity of initial state ( 0 X ), then:

Log-linearization of Price Index
Apply Eqs. (5) and (6) into Eqs. (3) and (4), and perform log-linearization, then to use the feature that the exchange rate will not change under fixed exchange rate regime ( 0  t E ), we have: Subtract Eq. (23) from Eq. (22), we can acquire the difference of change on the price index between two countries as follows:

Log-linearization of the Law of One Price
If we put Eqs. (5) and (6)

Log-linearization of World Budget Constraint
We can also acquire world budget constraints equation from Eqs. (20) and (21): Log-linearize Eq. (27) and use Eqs. (25) and (26), the following can be obtained:

Log-linearization of Demand Function
Put domestic and foreign demand function (Eqs. (15) and (16)) into log-linearization, we can acquire:

Log-linearization of Labor Supply Function
Log-linearize domestic labor supply function (Eq. (19)) and the following can be obtained: Likewise, for foreign country, we have:

Log-linearization of Money Demand Function
Put domestic money demand function (Eq. (18)) into log-linearization to acquire: Similarly, for foreign country, we have:

.3.7. Log-linearization of Terms of Trade
Define the terms of trade (TOT) as the ratio of the export price of commodity relative to imported one, namely:

The Effects of Tariff Shocks on Macroeconomic Variables
To capture the changes of the parameters of consumption home bias on the effects of tariff, we conduct a simulation analysis.

Parameterisation
In order to simplify the analysis in this paper, on NOEM basis, we set two economic systems with equivalent size as the analysis objects, hence, on the aspect of selecting the parameter values, we try to introduce empirical data on the United States and countries with similar scale (such as OECD, the European Union) to analyze the effects of tariff shock between the United States and nations with similar size. First, we follow the setting mode proposed by Bergin et al. (2007) to set the elasticity of substitution of product between countries (  ) to 5, besides, we follow the practices of Mankiw and Summers (1986) and Schmidt (2006) to set the elasticity of marginal utility of real money balances (  ) to 1, then, we use the setting of consumption home bias parameter value ( 85 . 0   ) proposed by Wang (2010), and simulate the cases in absence of consumption home bias ( 5 . 0   ) and bias to foreign goods ( 15 . 0   ), the settings of parameter of consumption bias in foreign country is identical to the consumption home bias parameter values in home country, as for exogenous variables other than the rate of change in domestic tariff rates of (ˆ), such as the rate of change in domestic money supply ( M ), the rate of change in foreign money supply ( * M ), the rate of change in foreign tariff ( *  ), since they were not our focus of discussion in this paper, let us

Simulation and Comparative Static Analysis
In this section, we conduct the simulation analysis which parameter values that were set in the previous section to discuss the effects of tariff shock on consumption, prices, output and terms of trade and other macroeconomic variables. The simulation and detailed comparative static analysis results are shown in Table 2. , and bilateral exchange rates maintaining fixed, an increase in domestic tariff rates will increase the cost of production and trade, also suppress the production will, however, due to reason that the tariff income is transferred to the agent in a lump-sum fashion, the level of consumption will increase, thereby driving the price level to rise and terms of trade to improve. But, if consumer bias behavior between two countries is in asymmetry, the foregoing conclusion will change. Wherein, on the effect of tariffs on the domestic consumption, when the "consumers in both countries do not exist consumption bias phenomenon", "foreign consumers do not have consumption bias behavior, but domestic consumers have consumption bias behavior on domestic products", "domestic consumers have no consumption bias behavior, but foreign consumers have consumption bias behavior on foreign products", and "domestic consumers have consumption bias behavior on domestic products, foreign consumers have consumption bias behavior on foreign products" are established, the rise of domestic tariff rate will result in the decline of domestic consumption. Wherein, on the effect of tariffs on domestic output, when the "consumption bias act does not exist among foreigner, but domestic consumers have consumption bias on domestic products", "domestic consumers do not have consumption bias behavior, but foreigner have consumption bias on foreign products", and "domestic consumers have consumption bias behavior on domestic products, foreign consumers have consumption bias behavior on foreign products" are established, the rise of domestic tariff rate will result in the rise of domestic output. On the aspect of the effect of tariffs on domestic price index, under the above three cases mentioned in the foregoing output aspects, the rise of domestic tariff rate will result in decline of domestic prices level, and finally, on the effect of tariffs on the terms of trade, if "consumers in both countries have consumption bias behavior on products produced by the competitor country" and "domestic consumers have consumption bias behavior on domestic products, foreign consumers have consumption bias behavior on foreign products", the rise of domestic tariff rate will cause deterioration of terms of trade.

Conclusion and Suggestions
There has been more than 20 years since NOEM established, however, compared to the popularity of the researches made on the effects of monetary and fiscal policy, the researches made on the effects on trade policy (such as tariffs) were relatively rare, based on the above reasons, this paper use NOEM proposed by Obstfeld and Rogoff (1995) as the theoretical framework for integrating the consumption home bias behavior into a model to explore a situation that when a country adopts a fixed exchange rate regime, what is the role of consumption home bias plays in the process of the tariff affect macroeconomic variables, we also hope that the findings herein can be provided to the relevant authorities as a reference for policy-makers.
This study contributes to the existing literature by providing a detailed account of how tariff change on macroeconomic variables in an open economy with the introduction of consumption home bias under the fixed exchange rate regime. With the findings of theoretical derivation and simulation analysis, we find out that the relationship among domestic tariff rates and macroeconomic variables (such as consumption, output, price index and terms of trade) is depending on the asymmetry degree in consumption bias on the exported and imported goods by the consumers in both countries, when the consumption bias behavior of domestic and foreign consumers is in asymmetry, the relationship that tariff shock on consumption, output, price index and the terms of trade would exist reversal possibility.
Finally, we shall give a special note that, in order to simplify the analysis, this paper only focuses on the long-term analysis, therefore, the dynamic adjustment process in the economic system was not highlighted, which was one of the limitation herein. Furthermore, although the theoretical framework of NOEM plays full of significance in each economic topic, in fact, in order to obtain closed-form solution, it is usually established under a lot of assumptions, if we try to release one of assumptions or setting (such as the type of utility function, etc.), the results obtained may differ, and such deficiency will also be included in the restriction suffered in this paper.