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IMPACT OF GLOBAL LOW INTEREST RATES TO THE CAPITAL FLOWS AND FINANCIAL VULNERABILITY OF SMALL OPEN ECONOMIES

Article History Received: 20 January 2020 Revised: 24 February 2020 Accepted: 26 March 2020 Published: 14 April 2020

returns, and many economies have been with secular stagnation for quite a long time ( (Bernanke, 2005;Caballero, 2018;Summers, 2014)) both the nominal and real interest rates are at historical lows across advanced economies (Del Negro, Giannone, Giannoni, & Tambalotti, 2019). Countries elsewhere were faced by spillovers from extremely easy global liquidity conditions and attendant volatile capital flows and financial stability risks 2 in a world with increasingly integrated financial markets. The spillover impacts of global low interest rates have raised serious concerns for countries elsewhere. The ensuing cross-border large and volatile capital inflows and its resulting financial vulnerability have created challenges to policy makers. Analysis of the impact of global low interest rates on the capital flows and financial vulnerability will be helpful for giving advice to policy makers to manage volatile capital flow movements and develop precautionary instruments to guarantee financial stability. This paper is relative to several strands of literature. Global interest rates, mainly refer to interest rates of large advanced economies (especially the US), have long been a key factor leading to extreme capital flow movements and risks. The relationship between interest rates of advanced economies and capital flow movements of countries elsewhere, have been well studied in the empirical literature (Forbes & Warnock, 2012;Ghosh, Qureshi, Kim, & Zalduendo, 2014;Yang, Shi, Wang, & Jing, 2019). The interest rates of advanced economies usually have a significant negative relationship with capital inflows to EMEs. In contrast to existing extensive empirical literature, This paper is also related to open economy DSGE analysis, which is widely used in analyzing the impact of exogenous shocks and policy analysis. After the GFC, researchers started to introduce financial frictions into financial intermediaries to make previous DSGE models more reality (Gertler & Kiyotaki, 2010). In this paper, we develop a small open economy model with financial frictions based on the models proposed by Gertler and Kiyotaki (2010) and Kitano and Takaku (2017). Existence of financial frictions means that bankers have incentives to divert assets and it is easier for bankers to divert foreign borrowing compared to domestic deposits. Another contribution of this paper is that, via introducing a variant of the banking sector, we refine the DSGE models to capture some form of financial fragility to foreign or global economy shocks (Adrian & Shin, 2009;Ghilardi & Peiris, 2016): the fraction of divertible assets by bankers is time varying, and related to the changes in the exogenous global interest rate.
Another related strand of literature focuses on capital controls and macroprudential policies. Many countries have implemented various capital control and macroprudential instruments to deal with the extreme capital flow movements, economic fluctuations and financial vulnerability risks from external shocks 3 . Different kinds of instruments and their effectiveness have been well studied in previous literature (De Paoli & Lipinska, 2013;Farhi & Werning, 2014;Liu & Spiegel, 2015;Ostry, Ghosh, & Korinek, 2012;Schmitt-Grohé & Uribe, 2016). This paper examines the effectiveness of macroprudential policies in dealing with exogenous global low-interest-rate shocks and compares two different instruments. The two macroprudential policy instruments considered in this paper include a liability-side macroprudential policy instrument depending on bank's foreign debt leverage 4 , and an assetside instrument depending on bank's total asset expansion. More specifically, the liability-side macroprudential policy instrument depends on the proportion of bank's foreign debt in total asset, and the asset-side one depends on the bank's asset expansion. The results show that macroprudential policies are effective in limiting the world interest rate shock and the foreign-liability-related macroprudential policy is more effective than the other one for the net capital inflows, domestic business cycle amplification and financial leverage are much smaller during the scenario.
The remainder of this paper is arranged as follows. In Section 2, we present a small open economy DSGE model with macroprudential policies, and we calibrate the parameters. In Section 3, we present the main results of this paper. Specifically, we examine the shocks of global low interest rates to the small open economies with and without macroprudential policies. Then we examine the validity of the results using the real data from small open economies in Section4. Section 5 concludes this paper.

THE RBC-DSGE MODEL WITH MACROPRUDENTIAL POLICIES FOR SMALL OPEN ECONOMIES
To explore the impact of global low interest rates, we build a real business cycle dynamic stochastic general equilibrium model (RBC-DSGE model) of a small open economy, with the world interest rate as an exogenous variable. The framework of our model is presented as follows Figure 1.
The model consists of households, banks, non-financial firms (goods producers and capital producers), and the government. This is a model with infinite periods and only intra-temporal trade. We assume there is a representative household, who consumes domestic and foreign goods, and provides labor to goods producers and deposits to banks. Banks raise funds from domestic households and foreign borrowing, and provide loans to domestic capital producers. Capital producers raise funds from banks to buy domestic goods (from goods producers) and foreign goods as inputs, producing new capitals and sell them to goods producers. Each goods producer produces output using an identical constant return to scale (CRS) Cobb-Douglas production function with capital and labor as inputs. Goods producers buy the capital from capital producers and pay wages to the labor provided by households. We assume that the capital, which could be viewed as intermediate goods for producing final goods, is not mobile, but labor is perfectly mobile across firms and countries. To deal with foreign shocks from global low interest rates, the government imposes macroprudential policies by imposing taxes on the banks' excessive asset and foreign debt.

Households
Following Kitano and Takaku (2017) there is an infinite lived representative household with GHH utility preference 5 . the households maximize the following expected lifetime utility: © 2020 AESS Publications. All Rights Reserved. (1) where is the expectation operator conditional on date information, is the discount factor for household's utility, is a composite consumption index, is the labor supply, is the relative utility weight of labor to consumption, is the inverse of intertemporal elasticity of substitution, and is the inverse Frisch elasticity of labor supply. The composite consumption index is defined by: ( 2) where is the elasticity of substitution between domestic and imported goods, and is the degree of trade openness (i.e., inverse degree of home bias). Given the consumption index , the optimal expenditure allocation between domestic and imported goods is: ( where is consumption allocation on domestic goods, is consumption allocation on imported goods, is the domestic price level, is the import price level, and is the consumer price index (CPI) defined by: Let denote the real wage rate, lump-sum taxes, the quantity of bank deposits made by households on date , the gross return on the deposits from to , and net distributions from nonfinancial firms to households. Then the households will choose consumption, labor supply, and bank deposit to maximize his/her expected lifetime utility (1) subject to the flow of funds constraints: The first-order optimality conditions with respect to consumption, labor supply and deposit are given by (6) © 2020 AESS Publications. All Rights Reserved.
where is the Lagrangian multiplier associated to the constraint (5), and is the household's stochastic discount factor from to .

Banks
In order to finance lending in each period, banks raise funds in both domestic and international markets.
We assume that, at the beginning of each period, banks accept deposits from domestic households and borrow money from foreign investors, and then lend to final goods producers. For each bank, the flow-of-funds constraint is given by: where is the market price of the bank's claim at date , is the volume of loans (banks' claim) to goods producers, is the net worth, is the stock of deposits from domestic households, is the real exchange rate, and is the quantity of foreign debt.
Let be the gross return on domestic deposit from date to date . Similarly, let be the gross return on foreign debt in terms of domestic currency from date to date , gross return on assets from date to , and the tax rate imposed by government on banks' assets or foreign debts in terms of domestic currency from date to date . Then, the bank's net worth at date is given by: We also assume that the bank could bankrupt with probability ( ), and the bank maximizes the present value of future net worth discounted by the factors , . Thus, the value of bank at date is given by: Similar to Gertler and Kiyotaki (2010) the bankers have incentives to divert a fraction of their assets.
Divertible assets consist of total gross asset net a fraction of domestic deposit for some .
Different from previous studies, we assume that the fraction of divertible assets depends on the world gross interest rate : where measures the degree of home bias in banker's finance, and is the steady-state value of . As Adrian and Shin (2009)  or divert more funds when the gross interest rate is low. Thus, a sudden increase in due to a decline in can be thought of capturing some form of one country's financial fragility to foreign or global economy shocks.
Because the fund suppliers recognize the bank's incentive to divert funds, they will not lend to the banks unless banks satisfy the following incentive constraint: With , the bank is unable to divert any deposit from households. In this case, the domestic financing market operates frictionlessly. In contrast, with , domestic depositors are exactly like the foreign investors.
Therefore, can be thought of as a degree of frictions in the financial market.
In the next, we will derive the aggregate relation of , and . Here, we follow the same approach proposed by Kitano and Takaku (2017). Let denote the maximum value of defined in (11) given and . The Bellman equation for the bank's optimization problem at date is given by (14) In order to solve this dynamic programming problem, we guess (and then verify) that function is linear in and such that: where , and are time-varying parameters that will be verified later. Note that these parameters are independent of individual bank's structure, and are supposed to be positive.
Let be the Lagrangian multiplier for the incentive constraint (13). Then, according to the conjectured form of , the first-order optimality conditions for , and are given by: Since the parameters is independent of individual bank's structure, we can aggregate Equation 23 across banks: where capital letters indicate corresponding aggregate variables. Using aggregate version of Equations 9 gives us (32) Following from (24), we have (33) When there are some bankers go bankruptcy and become households, we assume that the same number of households become bankers so that the portion of bankers in the economy is constant over time. This will simplify our model and we do not need to keep track of the distributions of household and banking sector. When the households become bankers, they obtain a fraction of fund from exiting bankers. And the evolution of is given by:

Goods Producers
The final goods producers operate in a fully competitive market and produces domestic goods using capital and labor according to the CRS Cobb-Douglas function: where is total output, is the capital, and is the labor. Since we assume that labor supply is perfectly mobile, the first-order optimality condition for labor supply leads to: It follows that the gross profit per unit of capital is then given by: In a fully competitive market, the firms earn zero profits. Then the gross return on the capital from date to must satisfy: where is the depreciation rate of the capital.

Capital Producers
Capital producers acquire new capitals from final domestic and foreign goods, and subject to adjustment costs.
Similar to , we define new capitals by: Then, the optimal capital acquirements on domestic and foreign goods are given by 1.
respectively. The optimization problem of a capital producer is to choose , , such that the present value of future profits is maximized: where is the adjustment cost function satisfying , and so that the aggregate output of the capital producers is decreasing returns to scale in the short run and is constant returns to scale in the long run, and is the inverse elasticity of net investment to the price of capital. The first-order optimality condition for then gives us: As we have assumed in Section 2.1, the profits, if there is any, are redistributed to households in lump sum.

Government
Government imposes taxes on the foreign debt and households, and spend on domestic and foreign goods. The government's budget constraint is given by: where is the government composite consumption index, is the government spending on domestic goods and is the government spending on foreign goods. Similar to , the optimal government spending allocation is given by (44) We assume that is fixed at its steady-state level . Therefore the government spending on domestic and foreign goods are constants for every period. The reason we make this assumption is that the purpose of this paper is to study the effects of external shocks on a small open economy's capital flows, such as foreign debt. Thus, fixing at a constant level is helpful in making such effects distinguishing.
We first consider a simple rule for liability-side macroprudential policy related to excessive foreign debt, given by: where is the steady-state value of , and is the parameter for tax level. This rule indicates that the government raises (reduces) tax rate on foreign borrowing when the fraction of foreign borrowing in assets increases (decreases). The purpose of this rule is to discourage the banks relying heavily on the foreign borrowing.
This could effectively reduce the likelihood of a surge in capital inflows when the foreign rate is low and a sudden stop when is high, and could also limit the related real exchange fluctuations.
We also consider another rule for an asset-side macroprudential policy given by Aoki, Benigno, and Kiyotaki where is the steady-state value of . Here, the tax rate on banks is an increasing function of the percentage deviation of bank's asset from non-stochastic stationary steady state. Thus, government raises the tax rate when banks excessively expand its asset quantity, which leads to accelerated credit growth.

International Market
Because we are considering a small open economy, the home country will not affect the price level in the foreign countries. Therefore, we can assume that , where is the price index in the foreign country in terms of the domestic currency. The terms of trade is then defined by: Following from the definition of in (4), we further define by: Combining the above definition for and Equations 3, 40 and 44, we have: and (51) The real exchange rate is then given by (52)

Market Clearing
In order to close the model, we require market clearing in goods, capital and labor.
First, aggregate output is divided between household consumption , investment expenditures , government domestic spending and exogenous demand for exports as follows (53) where is the adjustment cost.
The trade balance in terms of CPI is given by: .
And the evolution of foreign debt in terms of foreign currency is given by (55) where is the bank's foreign borrowing rate from date to date . Then the current account is given by (56) and the relation between and is given by (57) We assume that the bank's gross foreign borrowing rate is the sum of an exogenous world gross interest rate and a country premium as follows (58) where is the steady-state value of , and is the parameter for country-specific interest rate premium.
Note that the country premium increases with the fraction of foreign debt. This is adopted to guarantee the stationary of foreign debt. In addition, we assume that the logarithm of exogenous world gross interest rate follows the AR(1) process: where is the expected value of and is the independent and identical shock following normal distribution with zero mean and standard deviation .
The funds for final goods producers to purchase capitals are financed from banks as follows (60) The capital accumulation is given by: Finally, the condition that labor supply equals labor demand requires that In all, follows an exogenous stochastic process. Five prices and nine quantities together with four shadow prices are determined as a function of the state variables by the sequence of eighteen equations: the first-order optimality conditions for households, banks and nonfinancial firms (8,20,21,28,29,30,31,34,35,38,42,55), and the market clearing conditions for goods, capital, exchange rate and labor (32, 53, 57, 60, 61, 62).

Calibration
We choose the parameters based on existing literatures and calibration. The values of parameters are summarized in Table 1. For the parameters for households, we set the discount factor to 0.98 and the inverse intertemporal elasticity of substitution to 2 as in Aguiar and Gopinath (2007). The curvature on labor is 1.455 as in Mendoza (1991). The relative utility weight of labor is set to 3.092 such that the labor supply is 0.2 in the steady state.
For the parameters for banks, we follow the methods used by Gertler. and Karadi (2011). is set to make the bank's life to be eight years, the index for financial friction is set to 0.25 in the benchmark case, and the parameters and are set to 0.606 and 8.258 , respectively, such that the spread between and is 100 basis point per year and the leverage ratio is 4 in the steady state.
The parameters for non-financial producers are set according to Gertler and Kiyotaki (2010). The effective capital share , the capital depreciation and the inverse elasticity of net investment to the price of capital are set to 0.330, 0.0025 and 1.5, respectively.
For the parameters related to government and open economy, the steady-state level of fraction of government expenditure is set to 0.2 (Kitano & Takaku, 2017) and the steady-state value of portion of foreign debt to output is set to 0.4 (Devereux, Lane, & Xu, 2006). The tax level related to macroprudential policies(or we may call capital control level) is set to 0.05 for the benchmark case. The elasticity of substitution between domestic and imported goods is set to 1.5 according to Ravenna and Natalucci (2008). Following Cook (2004) the degree of openness is set to 0.28. The parameter for country-specific risk premium is set to 0.03, that lies between 0.0075 in Unsal (2011) and 0.05 in Akinci and Queralto (2014). The persistence and the standard deviation of the foreign interest rate shock, and , are set to 0.98 and 0.0025, respectively.

SIMULATION RESULTS OF THE IMPACT OF GLOBAL LOW INTEREST RATES
In interest rate, which matches the current predictions that the US will probably reduce the interest rate of total 100 basis points through this year to fight the world economic contraction 7 . As shown in Figure 2, an exogenous decline in the world interest rate decreases the foreign borrowing cost of small open economies, and this leads to a deteriorate of the current account, which means increasing net capital inflows to small open economies. As a result, the foreign debt of small open economies accumulates and the real exchange rate appreciates. The increasing foreign debt leads to an increase in bank's asset and producer's capital . The increase in capital raises up the output and investment , which causes the capital price increases. However, the bank's net worth does not change significantly, which implies that the bank's leverage ratio increases due to the surge in capital inflows. Therefore, exogenous decline in foreign interest rates amplified the domestic business cycle ( , and ) through bank's higher leverage ratio, and the financial vulnerability accumulates.

Impulse Responses of Main Variables to Negative Shocks on Global Interest Rates with Macroprudential Policies
Based on the simulation results of the DSGE model with macroprudential policies, we examine the effectiveness of macroprudential policies and compare two different instruments. The impulse responses of main variables to a decrease in global interest rates with and without macroprudential policies are shown in Figure 3.
The black solid, red dash and blue dotted lines in Figure 3 are the cases with the liability-side macroprudential policy with a focus on foreign borrowing (45), the asset-side macroprudential policy, (46) and no macroprudential policy with , respectively. Figure-2. Impulse responses to negative world interest rate shock without macroprudential policies.
Source: Authors' calculation in MATLAB. Figure-3. Impulse responses to negative world interest rate shock. Controls 1 and 2 correspond to the liability-side macroprudential policy limiting excessive foreign borrowing(45) and the asset-side macroprudential policy with a focus on domestic bank's asset expansion (46), respectively.
Now we commence to compare the cases with and without macroprudential policies in Figure 3. We can see that the effects of an exogenous decrease in foreign interest rates on , , , , , and are larger when there are no macroprudential policies. Moreover, the economy with the liability-related macroprudential policy limiting excessive foreign debt (45) experiences smaller movements in real exchange rate, capital inflows, foreign debt and financial leverage than the economy with the asset-side macroprudential policy (46). Therefore, we can conclude that the liability-side macroprudential policy with a focus on foreign debt is more effective than the asset-side macroprudential policy with a focus on domestic asset expansion(this could also be viewed as credit growth) in avoiding large fluctuation caused by the sudden decline in the world interest rate of small open economies.

Impulse Responses of Main Variables under Larger Shocks
In this subsection, we examine the effects of different macroprudential policies under larger negative shocks on world interest rates. Specifically, we set the standard deviation twice as in the benchmark case. The impulse responses of main variables with and without macroprudential policies are summarized in Figure 4. In Figure 4, we can see that the patterns of responses of main variables to the larger exogenous shocks are the same as those of benchmark case in Figure 3, except that the sizes of fluctuations are further amplified. For example, shocks, which means the larger capital inflows under large global interest rate shock. Moreover, it is worth to pay attention to the large difference of foreign debt with and without macroprudential policies in Figure 4. The foreign debt increases 15% after eighteen periods under the large shocks if no macroprudential policy is applied, while the largest increase in is less than 7% with the liability-side macroprudential policy (45). This result strongly supports the validity of the macroprudential policies adopted by EMEs in order to protect their financial system from risks of capital inflow surges and financial vulnerability accumulation due to global low interest rates.     conditions improved since the negative world interest rate shock and deteriorated sharply since 2014. This is possibly because the main factors affecting the capital inflows to these areas are commodity prices. The capital inflows to these areas declined with most of the commodity prices started to decline, and reversed for many commodity prices started to go up since 2016.

MODEL VALIDATION IN REAL WORLD
As for advanced economies, Euro Zone and other developed economies experienced capital outflows during the global low interest rate period since the external negative world interest rate shock, and the capital outflows continued to increase before 2013. This implies that capital flowed from Euro Zone and other developed economies to elsewhere during the global low interest rate period, and one possible explanation is that the interest rates in these economies are highly related to the US. While things are quite different for Canada, for Canada experienced continuous large net capital inflows during the global low interest rate period since the external negative world interest rate shock during 2007-2010.

CONCLUSIONS
In this paper, we have developed a RBC-DSGE model with financial frictions and different macroprudential policies for small open economies. The financial frictions are characterized by the time-varying divertible proportion of banks' assets and differences in divertibility of bankers in domestic and foreign debt. We then explore how the exogenous low world interest rate shocks affect the small open economies and study the effectiveness of two macroprudential policies for protecting the external sector and financial system from the global low interest rate shocks. It turns out that the foreign debt, capital, output and financial leverage of small open economies increase while the current account to output ration deteriorates (which means capital inflow surges) when the world interest rate experiences a negative shock. The sizes of economic fluctuations exaggerate under larger shocks on the world interest rate. We find that the liability-side macroprudential policy limiting excessive foreign borrowing is effective in smoothing the responses of economy variables but the asset-side one with a focus on banks' total assets expansion works in a less effective way. The real data of small open economies illustrates that the EMEs and advanced economies both experienced capital inflow surges when there was a negative world interest rate shock to ultra-low levels, which is consistent with the conclusion of the model. However, for the regional data, it is not always consistent with the model's conclusion.
Funding: This research is supported by National Natural Science Foundation of China (NSFC Grant Numbers: 71532013). Competing Interests: The authors declare that they have no competing interests.