Chapter 3 Macroeconomic Effects of Asset Purchase Programmes in a Monetary Union
3.3 Analytical analyses of the yield spread and transmission mechanisms
3.3.2 Transmission mechanisms
3.3.2 Transmission mechanisms
As pointed out by Chen et al. (2012), the unconventional monetary policy will affect consumption and investment, and hence GDP. Similarly, in this model, through its effects on the long-term yield and term premium, the asset purchase program will influence consumption and investment.
3.3.2.1 The effect of the asset purchase program on consumption
Following Andrés et al. (2004), we proceed to log-linearize Eqs. (3.4), (3.5) and (3.9) and combine these equations with the population size of the restricted and unrestricted households as the weight to obtain the aggregate consumption in country H . We apply the analogous process to the households’ first-order conditions in country F . The Euler equation of the aggregate consumption in country H and F can be shown as follows: the inflation rates. Eqs. (3.50) and (3.51) differ from the conventional Euler conditions in the term premiums. As shown above, the lower term premium caused by the asset purchase program can lead to greater consumption due to the intertemporal substitution effect. This effect mainly falls on the restricted households, but not the unrestricted ones, and thus the share of restricted households in the overall population ωr can influence the magnitude of the policy’s effects on consumption.
Moreover, since the monetary expansion may lead to higher inflation across the union, the common monetary authority may raise the short-term interest rate Rt in response. The higher short-term real rate may counteract the effects of the asset purchase program on consumption. In
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most cases, as shown by the simulation results in Section 3.5, the decline in the term premium dominates and thus the asset purchase program will result in greater consumption in both countries.
The aggregate consumption of the monetary union CtMU can be derived from the sum of Eqs.
(3.50) and (3.51):
Similar to the previous two equations, the intervention of the central bank of the monetary union on the long-term bonds can bring about greater union-wide consumption.
3.3.2.2 The effect of the asset purchase program on investment
The investment demand of the capital production depends on the rental rate of capital, which can be closely related to the long-term yield. Thus, the asset purchase program may indirectly affect the investment demand through its effect on the long-term yield and term premium.
By log-linearizing and combining the first-order conditions of the capital producer, Eqs. (3.15) and (3.17), and the households’ Euler condition, Eqs. (3.4), (3.5) and (3.9), we derive the relation for the real return on capital and the long-term yield as
{
1 1 ,}
1 , term premium and the return on capital. Thus, the asset purchase program which results in the decline in H ,tξ~ will lower the rental rate of capital
r and lead to a greater demand for capital
k investment. The expansionary effects of the asset purchase program on consumption and investment will help stimulate output.‧ 國
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3.4 Calibration
In general, there is no analytical solution for this model. We use numerical method to solve the model by log-linearizing around the steady state, thereby studying numerically the macroeconomic effect under an unconventional monetary policy in the Euro area. To characterize the status quo of the Euro area where the fiscal situation of Germany and France perform better than Italy and Spain which may lead to different effects of asset purchase programs, we use a model with asymmetric fiscal situations as the benchmark and calibrate for the data of these four Euro countries, where Germany and France represent the low-debt countries and Italy and Spain represent the high-debt countries. The numerical analyses will evaluate alternative asset purchase programs’ effects under asymmetric fiscal situation.
In our model, structural parameters are divided into two groups. Each parameter in the first group is calibrated to match the quarterly data of the Euro countries which is asymmetric in country H and F . As stated above, to emphasize the asymmetric fiscal situation of member states, the key feature of the study is the unequal discount factors of the countries H and F which characterize the different long-term premiums for these two countries in the steady state before the asset purchase program is implemented. According to the first group of parameters, we calibrate the parameters of country H for the weighted average of the data for Germany and France (indicated by GF) as the low-debt economies, and those of country F for the weighted average of the data for Italy and Spain (indicated by IS) as the high-debt economies. We use the period between 2000Q1 and 2009Q4 as the pre-crisis period, and that between 2010Q1 and 2014Q4 as the period during the crisis, before the asset purchase program was launched at the beginning of 2015.
For the pre-crisis period, the long-term debt-to-GDP ratios of countries H and F, μB0HL and μB0LF*, are specified as being 43.63% and 62.09%, which are obtained from the data for countries GF and IS. For the crisis period, the long-term debt-to-GDP ratios of countries H and F are specified as being 56.72% and 78.51%, which is consistent with the debt-to-GDP ratios of countries GF and IS between 2010Q1 and 2014Q4.
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The steady-state long-term premium discrepancy between the countries H and F is calibrated for the premium between GF and IS before the asset purchase program started in 2015. The discount factor of unrestricted households in each country, βu
( )
βu* , is calibrated to be 0.998, which implies that the annual short-term real rate is equal to 0.80%. The discount factor for restricted households in country H, βr is calibrated to be 0.9945, which implies a 2.20% annual long-term yield in the steady state, which is consistent with the averaged long-term yield of countries GF and IS during the crisis period, between 2010Q1 and 2014Q4. The discount factor for restricted households in country F, βr*, is calibrated to be 0.9889, which implies a 4.48% annual long-term yield in the steady state, in line with the averaged long-term yield of country IS in the same period.The above expression implies that the annual (quarterly) term premium on long-term bonds in the countries H and F during the crisis are 1.38% (0.35%) and 3.66% (0.92%), respectively. The duration of the long-term bonds in the countries H and F (DL) is set to 40, implying that the duration of the long-term bonds is 10 years. Given the values of the discount factors and the duration of the long-term bonds, we can obtain that the coupon rates of the countries H and F, ιH and ιF are equal to 0.9804 and 0.9859 from the definition of DL. Equipped with Eq. (3.49), the powers of the transaction costs of long-term bonds, ϕξH and ϕξF, are 2.7827 and 2.5965, respectively. Table 3.3 lists the parameters of bonds and long-term yields.
[Insert Table 3.3 here]
Each parameter in the second group is tied to a commonly used value and is symmetric for both country H and F. First, we follow the estimation of Poutineau and Vermandel (2015) and set the coefficient of relative risk aversion
σ
to be 2. The shares of the home tradable goods in the home and foreign consumption bundles,γ
and γ*, are set to 0.57 and 0.43, respectively, to capture the home bias in consumption, which is consistent with Eggertsson et al. (2014). The elasticity of substitution between domestic and imported goodsθ
is set to 4.3, which is consistent with Poutineau and Vermandel (2015). Moreover, following the estimation of Smets and Wouters (2003), the inverse of the labor supply elasticityϕ
is set to 2.503. These two countries have‧ 國
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identical country size (
n
=0.5). Using demographic data in the Euro area, aged 50 years or younger, the share of unrestricted householdsω
u is set to 0.7.As for the firm sector, we establish that the probability of holding the price fixed in each period ΘH(ΘF) is equal to 0.66, which implies an average frequency of price changes of 3 quarters. This value is consistent with the calibration of Eggertsson et al. (2014). The elasticity of substitution
ν
across regions is set to 11, implying a steady-state markup of 1.1. The share of capital is set to 0.3, which implies a steady-state share of capital return in total output of 30. The depreciation rate,δ
, is set to 0.025. The shares of the home tradable goods in the home and foreign final goods bundles,a
and a*, are assumed to be 0.76 and 0.24, which is consistent with Chari et al. (2002).The elasticity of substitution between domestic and imported traded goods
μ
is set to 1.5, which is consistent with Duarte and Wolman (2008). To sum up the above, each parameter in the second group of parameters is identical in both countries for all cases. Table 3.4 lists the parameters of households and firms.[Insert Table 3.4 here]
We assume that the unconventional monetary policy shock follows an AR (1) process.
Throughout the analysis, we assume that the policy shock of the bond purchases is 1% with the AR(1) coefficient ρBL being equal to 0.9. The share of government expenditure in GDP is set to 0.2, as in Rabanal (2009). In addition, following Chen et al. (2012), the fiscal surplus shock follows a feedback rule and the coefficient of the fiscal surplus shock φT is set to 1.4448.
Following Duarte and Wolman (2008), the parameters of the nominal interest rate rule φ , Π φY and