Fiscal Policy in a Floating Exchange Rate Regime with Consumption Home Bias

This paper presents New Open Economy Macroeconomics as the analytical framework in attempt to explore the long term effects of fiscal expenditure shocks on various macroeconomic variables (e.g. consumption, output, prices, exchange rate, terms of trade), and tries to explain the role that consumption home bias plays. With theoretical derivation and simulation analysis, we find that in the long-term, an increasing in fiscal spending will cause rise of domestic output, domestic price index and the exchange rate, but it will crowd out domestic private consumption, the relationship between fiscal spending and the terms of trade, which is depending on asymmetry of consumption bias behavior of consumers between countries.

policy on macro economy, especially that the effects of fiscal policy on macroeconomic variables (such as private consumption, private investment, real wages and employment) is not consistent.In the theoretical literature, the Real Business Cycle model proposed by Baxter and King (1993) assumed household with indefinite life, wherein its consumption decision is limited by intertemporal budget constraint equation.When government spending increases and incorporated with lump-sum taxes, the present value of after-tax income will be reduced, resulting in a negative wealth effect reducing consumption, and under a given wage level, labor supply increases.In equilibrium, the real wages fell, employment rose and output increased.If the employment continued to increase enough, it will raise the marginal productivity of capital, resulting in increased investment (see Galí et al., 2007).In contrast, the consumption of the household withtraditional IS-LM model is a function of current disposable income, instead of lifetime income function.Therefore, an increase in government spending will cause consumption to increase, and in the assumption that the money supply is fixed, a corresponding rise will occur in short-term nominal interest rates, thereby, private investment will fell.
From the foregoing statement, research made on the effects of fiscal policy on macro economy mostly focused in a closed economy (such as Barro, 1990;Futagami et al., 1993;Devereux & Love, 1995;Greiner, 1998;Greiner & Hanusch, 1998;Dasgupta, 1999 andXie et al., 1999, etc.), and the analysis in topic of the effects of fiscal policy in an open economy is relatively rare, until recently, with the rapid emerge of literature titled "NOEM", such as literatures of Corsetti and Pesenti (2001), Ganelli (2003) and Pitterle and Steffen (2004a;2004b), had made the topic of research on the effects of fiscal policy extend to open economy aspect.However, in the conventional NOEM model, the main reason causing exchange rate fluctuations is private consumption behavior, therefore, the subject triggering this paper to be attractive is, if we further assumed that consumer behavior also includes the consumption behavior of government, and no matter the consumption behavior of individual or government exists consumption home bias, what will be the result?So, the purpose of this paper is to explore the correlation among government expenditure, consumption home bias and macroeconomic variables.Tervala (2008) had ever analyzed the effects of fiscal policy at NOEM architecture, the findings demonstrated that the marginal rate of substitution behind individual and government consumption is the main reason that fiscal expenditure affecting the welfare effect, however, it ignored a hot topic recently discussed-consumption home bias.
Although Obstfeld and Rogoff (2000) have deemed "home bias in consumption puzzle" as one of six puzzles of international economics, (Note 1) under the NOEM framework, the role that asymmetry of "consumption home bias" plays is still lack of complete research analysis, which is the direction this paper further to seek breakthrough.The so-called consumption home bias puzzle means that consumers have tendency to prefer domestic goods in the real world, but, this phenomenon cannot be explained by researchers in real market.In the studies made on the topic of consumption home bias, they mostly focused on the early exploration of the causes of consumption home bias, such as trade costs (Obstfeld & Rogoff, 2000;Ried, 2009), country size and openness (Sutherland, 2005;De Paoli, 2009), non-traded goods (Stockman & Dellas, 1989;Pesenti & Van Wincoop, 2002) as well as trade in intermediate input factors (Hillberry & Hummels, 2002), all are main causes that scholars believe to constitute consumption home bias.More recent studies have focused on discussion on the effect of consumption home bias, such as Pierdzioch (2004) analyzed the effect of monetary shock on different home bias and the extent of capital mobility, Hau (2002), Pitterle and Steffen (2004a;2004b), Kollmann (2004), Sutherland (2005), Leith and Lewis (2006) and Cooke (2010) discussed the effect of home bias on exchange rate fluctuations, De Paoli (2009) discussed the welfare effects of home bias and monetary policy.In addition, it worth mentioning that the effect of home bias on the optimal monetary policy is quite a hot topic recently, which including research made by Faia and Monacelli (2006), Jondeau and Sahuc (2008), Galí and Monacelli (2008) and Wang (2010); obviously, the studies made in respect of consumption home bias were quite enthusiastic, but none of literature up to now can clearly explain the role of home bias on the effects of government expenditure shock.
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 makes the simulation analysis for exploration on the long-term effects of government spending on the macroeconomic variables and the role of consumption home bias; Section 4 includes conclusions and recommendations.

Model Setting
This paper follows NOEM model proposed by Obstfeld and Rogoff (1995) as the theoretical basis, the main assumptions are as follows: 1) There are two countries in the world: "home country" and "foreign country".Hereunder, all the foreign economic variables are marked with "*".
2) The population in the world is distributed between intervals of [0,1], where domestic individuals are distribution in [0, n ), and foreign individuals are distributed in [ n , 1].
3) Each individual is both consumer and producer, operating a monopoly competitor factory and using labor for production.
4) Consumption home bias exists in the economy system and fiscal policy is the only one exogenous shock.

Household
Assuming that all individuals have the same preferences, utility (U ) and consumption ( C ) and real money balances ( P M / ) are in positive proportional, and is inversely proportional to the output ( y ), wherein, the lifetime utility function is set as follows: Where β is the discount factor ( 1 0    ),  is the elasticity of marginal utility of real money balances, (Note 2) χ and  represent the degree of significance of real money balances and output on the utility function, z refers to a particular product.
In Eq. ( 1), define the consumption index of consumer as the function of constant elasticity of substitution (CES): Where ) (z c h is the consumption of domestic consumers for domestic specific products Z, ) (z c f is the consumption of domestic consumers for foreign specific product Z ,  is the consumption home bias parameters to measure the degree of domestic consumers preferring domestic goods, and  is the elasticity of substitution of goods between two countries. Based on Eq. (2), domestic price index ( P ) can be derived under the problem of expenditure minimization as: Likewise, the foreign price index ( * P ) is as follows: In the above two equations, Where E represents the exchange rate.
From Eqs. ( 2) and (3), we can respectively derive consumption of domestic representative consumer on domestic and foreign specific commodities as follows: Likewise, the consumption that foreign representative consumer on domestic and foreign specific commodity as follows:

Government
Suppose that government uses seignorage and lump-sum tax revenue to finance expenditure, hence the government budget constraint is: Where the left hand side of equation refers to real government expenditure, while the first item on the right of the equation refers to real tax revenue and the second item on the right of the equation is real seigniorage revenue.
Suppose that government and private sectors have the same preferences, the function of government expenditure shall be also CES, that is: represents the consumption of domestic government sector on domestic specific goods z , ) (z g f represents domestic government's consumption on foreign specific goods z .

Asset Market
Suppose that there is an integrated international capital markets between two countries, and each individual can trade real bonds ( B ) in this international capital market, and the relationship between real interest rate ( r ) and nominal interest rate ( i ) of maturing bonds is as shown in Fisher In the equation, consumer's source of income in period t includes: the balance of the money in period  7) and ( 9), demand on the goods that domestic manufacturers face can be expressed as: Where * G refers to the consumption of foreign government sector.Likewise, Eqs. ( 8) and ( 10), demand on the goods that foreign manufacturers face can be expressed as:

First Order Conditions
Under the budget constraint (Eq.( 14)), the first-order conditions of utility (Eq.( 1)) maximization is expressed as: Where Eq. ( 17) is Euler equation of consumption, which describes intertemporal consumption behavior, Eq. ( 18) is money demand equation for indicating the substitution relationship between real money demand and consumption, Eq. ( 19) refers to the labor supply equation, which gives the alternative relationship between labor supply and consumption, in the equation, W  C represents world private consumption,

Derivation of Steady-State
The following sections discussed the effects of fiscal policy on every macroeconomic variables.Firstly, given that the economic system does not exist consumption home bias behavior and fiscal expenditure shock was not served in the initial state (0 steady state) as a baseline, then to seek a long-term steady state of economy system.
The following symbols, the subscript "t" represents the macroeconomic variables in the long-term steady state, and the subscript "0" represents the macroeconomic variables in the initial state.For example: Long-term steady state describes that the entire economic system reaches the convergence state after going through exogenous shocks.In the long-term steady state, all variables are fixed, and . Therefore, when we apply the government's budget constraint (Eq.( 11)) into private sector's budget constraints (Eq.( 14)), we can get: Likewise, for foreign aspect, we have:

Log-Linearization
In order to obtain a closed-form solution, this paper uses approach proposed by Uhlig (1995).Firstly, we put model in log-linearization, then to assign values to the parameters of the model to perform simulation analysis.(Note 3) Below we will put all variables in the vicinity of the initial state into log-linearization to obtain the degree of each variable fluctuates.In this paper, the superscript "  " means the variable carrying out log-linearization.
For example: If t X ˆ is the result of the variable t X , performing log-linearization in the initial state ( 0 X ), then:

Log-linearization of Price Index
Apply Eqs ( 5) and (6) into Eq.( 3) and (4), and put into log-linearization to obtain: Subtract Eq. ( 23) from Eq. ( 22) to obtain difference between fluctuations of price indices of two countries: 2.3.2Log-Linearization of the Law of One Price Give Eqs. ( 5) and ( 6) the process of log-linearization, and get the following equations:

Log-Linearization of World Budget Constraint
Based on Eqs. ( 20) and ( 21), the world budget constraint is obtained as follows: Put Eq. ( 27) into log-linearization and use Eqs.( 25) and ( 26) to get:

Log-Linearization of Demand Function
Put domestic and foreign demand functions (Eqs.( 15) and ( 16)) into log-linearization to get: 2.3.5 Log-Linearization of Labor Supply Function Give Eq. ( 19) the log-linearization process to obtain the following equation: Similarly, for foreign country, we have:

Log-Linearization of Money Demand Function
Give Eq. ( 18) the log-linearization process to obtain the following equation: Likewise, for foreign country, we have: Subtract Eq. (34) from Eq. ( 33) and put it into log-linearization, also use Eq. ( 24) to get the following relationship equation:

Log-Linearization of Terms of Trade
Define the terms of trade (TOT) as the ratio of export price to import price of the commodity, namely:

Steady-State Solution
The Eqs ( 20) and ( 21) are given the log-linearization process to obtain the following equations: We will seek solution of a total of 13 simultaneous equations, including the price index after log-linearization (Eqs.( 22) and ( 23)), law of one price after log-linearization (Eqs.( 25) and ( 26)), the world consumption equation after log-linearization (Eq.( 28)), domestic and foreign demand function after log-linearization (Eqs.( 29) and ( 30)), domestic and foreign labor supply function after log-linearization (Eqs.( 31) and ( 32)), domestic and foreign currency demand function subtraction equation after log-linearization (Eq.( 35)), the terms of trade after log-linearization (Eq.( 36)) and domestic and foreign private budget constraints equation after log-linearization (Eqs.( 37) and ( 38) ) to get correlation equation between 13 endogenous and exogenous variables, the 13 endogenous includes domestic consumption ( ), foreign prices of particular product domestically ( ), foreign prices of particular product in a foreign country ( )), the exchange rate ( t E ˆ), domestic price index ( t P ˆ), foreign price index ( * ˆt P ) and the terms of trade ( T O T ˆ).

The Effects of Government Spending Shocks on Macroeconomic Variables
In order to capture the effects of parameter change in consumption home bias on fiscal expenditure shocks, this paper conducted 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 subjects of analysis, so, on the selection of the parameter, we try best to introduce empirical data on the United States and countries with similar scale (such as OECD nations, the European Union) to analyze the effects of fiscal expenditure shock between the United States or other countries with similar size.Firstly, we follow setting mode of Bergin et al (2007) to set the elasticity of substitution of goods between countries (  ) to 5, besides, we follow practices of related literature submitted by Mankiw and Summers (1986) and Schmidt (2006) and set the elasticity of marginal utility of real money balance (  ) to 1, then adopt the consumption home bias parameter set by Wang (2010)  ), the parameter of bias degree that foreign country has on domestic and foreign goods is also the same as that of consumption bias parameter in the home country.Due to other domestic (foreign) exogenous variables other than the domestic fiscal expenditure shock ( G ˆ), such as domestic money supply ( M ˆ), foreign money supply ( * M ), and foreign fiscal expenditure shock ( * Ĝ ), were not the focus of discussion in this paper, let's assume that its change rate is 0, and parameter settings are sorted out as shown in Table 1.

Simulation and Comparative Static Analysis
In this section, parameter settings of the preceding section were used in the simulation to discuss the effects of fiscal policy on the exchange rate, prices, consumption, output and the terms of trade, wherein, the simulation results are set out in Table 2. Known by Table 2 (a) to (m), in the long-term, government expenditure and domestic output, domestic price index and the exchange rate exists a positive relationship, while existing negative relationship with domestic consumption; the relationship with the terms of trade will depend on the asymmetric consumption bias behavior of individual between two countries.When the cases of "consumers of both countries have consumption bias on the products produced by competitor country", "domestic consumers have no consumption bias behavior of consumption, but consumers in the foreign country have consumption bias behavior on domestically produced products", and "foreigner does not have consumption bias behavior, but domestic consumers have one on foreign products" are true, government expenditure and the terms of trade are in positive correlation, in the remaining cases, government expenditure and terms of trade are in negative correlation.
The intuition on economy behind the foregoing conclusions can be explained as follows: increase of government expenditure will rise up demand for domestic goods, leading to rise of domestic output and price level, but, due to the "crowding out effect", it results in a decline of private consumption, and reduction of the demand for money, leading to the depreciation of domestic currency (rise of exchange rate), as for the relationship between government expenditure and the terms of trade, it generates uncertain effect by mutual exclusivity of both effects of the rise in prices and exchange rates and it will depend on the asymmetry of consumption bias behavior in both countries.

Conclusion and Suggestions
Up to now, NOEM has elapsed more than 20 years for development, however, compared to the popularity in the study of effects of monetary shock, those in topic of fiscal shock are rare, in view of the above reasons, this paper takes NOEM model proposed by Obstfeld and Rogoff (1995) as a theoretical framework to integrate consumption home bias into the original model to explore a long-term effects of consumption home bias on macroeconomic variables in the face of fiscal expenditure shock, we also hope that the findings herein can be provided to the relevant authorities as reference for policy-makers.
With the findings of theoretical derivation and simulation analysis, we find that the increased government expenditure will trigger the rise of domestic output, domestic price index and the exchange rate, however, it will drop down the domestic consumption and the relationship between fiscal expenditure and the terms of trade is uncertain, which is depending on the asymmetric behavior of consumers in both countries on the consumption of commodity, when the cases of "consumers of both countries have consumption bias on the products produced by competitor country simultaneously", "domestic consumers have no bias behavior of consumption, but consumers in the foreign country have consumption bias behavior on domestically produced products", and "foreign consumers do not have bias behavior of consumption, but domestic consumers have one on foreign products" are true, the rise of government expenditure will improve the terms of trade.
Finally, it shall be specially noted that, in order to simplify the analysis, this paper only focuses on the long-term analysis, therefore, we did not highlight the dynamic adjustment process of economy, which is one of the limits set herein.Furthermore, NOEM theoretical framework, although has played its significance among each economic issue, in fact, it usually needs to build under a number of assumptions to seek solution easily.If we try to relax one of assumptions or settings (such as the setting of utility function), the results obtained may differ and this deficiency will also be included in the restrictions suffered herein.
foreign currency price of foreign commodity z , *  represents the degree of foreign consumers preferring foreign goods.

)
that foreign consumers for foreign specific product.
in the long-term steady state and initial state respectively.

Table 1 .
Selection of parameters *

Table 2 .
The long-term effects of fiscal policy on the macroeconomic variables (a) Long-term effect of fiscal policy on domestic consumption (