Global Macroeconomic Effects of Exiting from Unconventional Monetary Policy

Abstract

This paper evaluates the international macroeconomic effects of the Eurosystem’s expanded Asset Purchase Programme (APP) under alternative assumptions about (i) the unwinding of the asset positions accumulated under the APP and (ii) the normalization of the U.S. monetary policy stance. We simulate a five-region New Keynesian model of the euro area (EA) and the world economy (calibrated to the EA, US, China, Japan, and a residual region labelled “rest of the world”, RW). Our results suggest that an early exit from the APP, by severely dampening its effectiveness in stimulating the EA economy, dampens the EA aggregate demand and, therefore, EA imports. The expansionary international spillovers are, as such, reduced. Spillovers from the US to the EA are expansionary but always modest. This being the case, it becomes even more crucial to correctly identify the appropriate point in time to exit EA non-standard monetary policy measures.

Appendices

Appendix

Data Sources

We rely on several data sources in order to compute the different asset holdings that characterize the model. In particular, money balances held by households are computed as 2001–2012 averages using the variable “Currency in circulation” from the IMF’s International Financial Statistics database. Data on foreign private and official holdings of US government bonds is taken from the April 2013 issue on Foreign Portfolio Holdings of US Securities.¹⁴ The outstanding holdings refer to June 2012. We include both short- and long-term debt issued both by the Treasury and by the Government-sponsored Agencies. The latter have been taken over or placed into conservatorship by the U.S. Treasury in September 2008, and as such should command a liquidity premium equal or, at least, very close to that on U.S. Treasury bonds. As the information provided for China only refers to the aggregate holdings, with no distinction between private and official holdings being available, we assume that the entire holdings are official, except for a small part which we arbitrarily assume is being held by private households: alternatively, we would have needed to modify the model in order to set private Chinese household holdings of US bonds equal to zero, but this would have added some complications to our calibration procedure. Foreign holdings of euro denominated government bonds are computed from Tables A1 and A2 in The International Role of the Euro, July 2013, ECB. As we have no information on the different types of holders, we apply the same percentage shares used for US government bonds, taken from the aforementioned publication, to compute private versus official holdings of euro denominated government bonds. Finally, data on domestic holdings of government bonds are computed by combining the IMF’s Fiscal Monitor database and the information on the different types of holders (private vs. official) reported in Andritzky (2012).

The Model

In this Appendix we report a detailed description of the model except for fiscal and monetary policies and households’ optimization problems, which are reported in the main text.¹⁵

There are five blocs, Home, US ($^{*}$), CH (China, $^{**}$), JP (Japan, $^{***}$), and RW (rest of the world, $^{****}$). In what follows we illustrate the Home economy. The structure of each of the other four regions is similar and to save on space we do not report it.

1.1 Final Consumption and Investment Goods

There is a continuum of symmetric Home firms producing nontradable final consumption under perfect competition. Each firm producing the consumption good is indexed by $x\in (0,n]$, where the parameter $0<n<1$ measures the size of Home economy. Firms in the other regions are similarly indexed (the size of the world economy is normalized to 1, so $n+n^{*}+n^{**}+n^{***}+n^{****}=1$). The CES production technology used by the generic firm x is

$$\begin{aligned} A_{t}\left( x\right) \equiv \left( \begin{aligned}&a_{TA}^{\frac{1}{\phi _{A}}}\left( \begin{aligned}&a_{HA}^{\frac{1}{\rho _{A}}}Q_{HA,t}\left( x\right) ^{\frac{\rho _{A}-1}{ \rho _{A}}} \\&+\left( 1-a_{HA}\right) ^{\frac{1}{\rho _{A}}}\left( \sum _{i=1}^{C-1}a_{IMPA,i}^{\frac{1}{\rho _{IMP}}}Q_{IMPA,i,t}\left( x\right) ^{\frac{\rho _{IMP}-1}{\rho _{IMP}}}\right) ^{\frac{\rho _{IMP}}{ \rho _{IMP-1}}} \end{aligned} \right) ^{{\frac{\rho _{A}}{\rho _{A}-1}}{\frac{\phi _{A}-1}{\phi _{A}}}} \\&+\left( 1-a_{TA}\right) ^{\frac{1}{\phi _{A}}}Q_{NA,t}\left( x\right) ^{ \frac{\phi _{A}-1}{\phi _{A}}} \end{aligned} \right) ^{\frac{\phi _{A}}{\phi _{A}-1}} \end{aligned}$$

where $Q_{HA}$, $Q_{IMPA}$, and $Q_{NA}$ are bundles of respectively tradable intermediate goods produced in the Home country, tradable intermediate goods produced in one among the other four regions and imported by Home, and nontradable intermediate goods produced in the Home country. The parameter $\rho _{A}>0$ is the elasticity of substitution between tradable goods and $\phi _{A}>0$ is the elasticity of substitution between tradable and nontradable goods. The parameter $a_{HA}$ ($0<a_{HA}<1$) is the weight of the Home tradable, the parameter $a_{IMP,i}$ ($0<a_{IMP,i}<1$, $\sum _{i=1}^{C-1}a_{IMPA,i}$) the weight of the generic imported tradable from country i, and the parameter $a_{TA}$ ($0<a_{TA}<1$) the weight of tradable goods.

The production of investment good is similar. There are symmetric Home firms under perfect competition indexed by $y\in (0,n]$. Output of the generic Home firm y is

$$\begin{aligned} E_{t}\left( x\right) \equiv \left( \begin{aligned}&a_{TE}^{\frac{1}{\phi _{A}}}\left( \begin{aligned}&a_{HE}^{\frac{1}{\rho _{E}}}Q_{HE,t}\left( x\right) ^{\frac{\rho _{E}-1}{ \rho _{E}}} \\&+\left( 1-a_{HE}\right) ^{\frac{1}{\rho _{E}}}\left( \sum _{i=1}^{C-1}a_{IMPE,i}^{\frac{1}{\rho _{IMP}}}Q_{IMPE,t}\left( x\right) ^{\frac{\rho _{IMP}-1}{\rho _{IMP}}}\right) ^{\frac{\rho _{IMP}}{\rho _{IMP-1}}} \end{aligned} \right) ^{{\frac{\rho _{E}}{\rho _{E}-1}}{\frac{\phi _{E}-1}{\phi _{E}}}} \\&+\left( 1-a_{TE}\right) ^{\frac{1}{\phi _{E}}}Q_{NE,t}\left( x\right) ^{ \frac{\phi _{E}-1}{\phi _{E}}} \end{aligned} \right) ^{\frac{\phi _{E}}{\phi _{E}-1}}. \end{aligned}$$

Finally, we assume that public expenditure $C^{g}$ is composed by nontradable intermediate goods only.

1.2 Intermediate Goods

1.2.1 Demand

Bundles used to produce the final consumption goods are CES indexes of differentiated intermediate goods, each produced by a single firm under conditions of monopolistic competition:

$$\begin{aligned} Q_{HA}\left( x\right)\equiv & {} \left[ \left( \frac{1}{n}\right) ^{\theta _{T}}\int _{0}^{n}Q\left( h,x\right) ^{\frac{\theta _{T}-1}{\theta _{T}}}dh \right] ^{\frac{\theta _{T}}{\theta _{T}-1}}, \end{aligned}$$

(24)

$$\begin{aligned} Q_{NA}\left( x\right)\equiv & {} \left[ \left( \frac{1}{n}\right) ^{\theta _{N}}\int _{0}^{n}Q\left( i,x\right) ^{\frac{\theta _{N}-1}{\theta _{N}}}di \right] ^{\frac{\theta _{N}}{\theta _{T}-1}}, \end{aligned}$$

(25)

$$\begin{aligned} Q_{IMPA,US,t}\left( x\right)\equiv & {} \left[ \left( \frac{1}{n^{*}} \right) ^{\theta _{T}}\int _{n}^{n+n^{*}}Q\left( g,x\right) ^{\frac{ \theta _{T}-1}{\theta _{T}}}dg\right] ^{\frac{\theta _{T}}{\theta _{T}-1}}, \end{aligned}$$

(26)

where firms in the Home tradable and nontradable sectors are respectively indexed by $h\in (0,n]$ and $x\in (0,n]$, while Home firms in the sector importing US goods are indexed by g. A similar indexation holds for firms in sectors importing from CH, JP, RW. Parameters $\theta _{T}$, $\theta _{N}>1$ are respectively the elasticity of substitution across brands in the tradable and nontradable sectors. The prices of the nontradable intermediate goods are denoted p(i). Each firm x takes these prices as given when minimizing production costs of the final good. The resulting demand for nontradable intermediate input i is

$$\begin{aligned} Q_{A,t}\left( i,x\right) =\left( \frac{1}{n}\right) \left( \frac{P_{t}\left( i\right) }{P_{N,t}}\right) ^{-\theta _{N}}Q_{NA,t}\left( x\right) , \end{aligned}$$

(27)

where $P_{N,t}$ is the cost-minimizing price of one basket of local intermediates:

$$\begin{aligned} P_{N,t}=\left[ \int _{0}^{n}P_{t}\left( i\right) ^{1-\theta _{N}}di\right] ^{ \frac{1}{1-\theta _{N}}}. \end{aligned}$$

(28)

We can derive $Q_{A}(h,x)$, $Q_{A}(f,x)$, $C_{A}^{g}(h,x)$, $C_{A}^{g}(f,x)$ in a similar way. Firms y producing the final investment goods have similar demand curves. Aggregating over x and y, it can be shown that total demand for nontradable intermediate good i is

$$\begin{aligned}&\int _{0}^{n}Q_{A,t}\left( i,x\right) dx+\int _{0}^{n}Q_{E,t}\left( i,y\right) dy+\int _{0}^{n}C_{t}^{g}\left( i,x\right) dx \\= & {} \left( \frac{P_{t}\left( i\right) }{P_{N,t}}\right) ^{-\theta _{N}}\left( Q_{NA,t}+Q_{NE,t}+C_{N,t}^{g}\right) , \end{aligned}$$

where $C_{N}^{g}$ is public sector consumption. Home demands for (intermediate) domestic and imported tradable goods can be derived in a similar way.

1.2.2 Supply

The supply of each Home nontradable intermediate good i is denoted by $N^{S}(i)$:

$$\begin{aligned} N_{t}^{S}\left( i\right) =\left( \left( 1-\alpha _{N}\right) ^{\frac{1}{\xi _{N}}}L_{N,t}\left( i\right) ^{\frac{\xi _{N}-1}{\xi _{N}}}+\alpha ^{\frac{1 }{\xi _{N}}}K_{N,t}\left( i\right) ^{\frac{\xi _{N}-1}{\xi _{N}}}\right) ^{ \frac{\xi _{N}}{\xi _{N}-1}}. \end{aligned}$$

(29)

Firm i uses labor $L_{N,t}^{p}(i)$ and capital $K_{N,t}(i)$ with constant elasticity of input substitution $\xi _{N}>0$ and capital weight $0<\alpha _{N}<1$. Firms producing intermediate goods take the prices of labor inputs and capital as given. Denoting $W_{t}$ the nominal wage index and $R_{t}^{K}$ the nominal rental price of capital, cost minimization implies that

$$\begin{aligned} L_{N,t}\left( i\right) =\left( 1-\alpha _{N}\right) \left( \frac{W_{t}}{ MC_{N,t}\left( i\right) }\right) ^{-\xi _{N}}N_{t}^{S}\left( i\right) \end{aligned}$$

(30)

and

$$\begin{aligned} K_{N,t}\left( i\right) =\alpha \left( \frac{R_{t}^{K}}{MC_{N,t}\left( i\right) }\right) ^{-\xi _{N}}N_{t}^{S}\left( i\right) \end{aligned}$$

where $MC_{N,t}(n)$ is the nominal marginal cost:

$$\begin{aligned} MC_{N,t}\left( i\right) =\left( \left( 1-\alpha \right) W_{t}^{1-\xi _{N}}+\alpha \left( R_{t}^{K}\right) ^{1-\xi _{N}}\right) ^{\frac{1}{1-\xi _{N}}}. \end{aligned}$$

(31)

The productions of each Home tradable good, $T^{S}(h)$, is similarly characterized.

1.2.3 Price Setting in the Intermediate Sector

Consider now profit maximization in the Home nontradable intermediate sector. Each firm i sets the price $p_{t}(i)$ by maximizing the present discounted value of profits subject to the demand constraint and the quadratic adjustment costs,

$$\begin{aligned} AC_{N,t}^{p}\left( i\right) \equiv \frac{\kappa _{N}^{p}}{2}\left( \frac{ P_{t}\left( i\right) }{P_{t-1}\left( i\right) }-1\right) ^{2}Q_{N,t}, \end{aligned}$$

which is paid in unit of sectorial product $Q_{N,t}$ and where $\kappa _{N}^{p} \ge 0$ measures the degree of price stickiness. The resulting first-order condition, expressed in terms of domestic consumption, is

$$\begin{aligned} p_{t}\left( i\right) =\frac{\theta _{N}}{\theta _{N}-1}mc_{t}\left( i\right) -\frac{A_{t}\left( i\right) }{\theta _{N}-1}, \end{aligned}$$

(32)

where $mc_{t}(i)$ is the real marginal cost and $A_t(i)$ contains terms related to the presence of price adjustment costs:

$$\begin{aligned} A_{t}\left( i\right)\approx & {} \kappa _{N}^{p}\frac{P_{t}\left( i\right) }{ P_{t-1}\left( i\right) }\left( \frac{P_{t}\left( i\right) }{P_{t-1}\left( i\right) }-1\right) \\&-\beta \kappa _{N}^{p}\frac{P_{t+1}\left( i\right) }{P_{t}\left( i\right) } \left( \frac{P_{t+1}\left( i\right) }{P_{t}\left( i\right) }-1\right) \frac{ Q_{N,t+1}}{Q_{N,t}}. \end{aligned}$$

The above equations clarify the link between imperfect competition and nominal rigidities. When the elasticity of substitution $\theta _{N}$ is very large and hence the competition in the sector is high, prices closely follow marginal costs, even though adjustment costs are large. To the contrary, it may be optimal to maintain stable prices and accommodate changes in demand through supply adjustments when the average markup over marginal costs is relatively high. If prices were flexible, optimal pricing would collapse to the standard pricing rule of constant markup over marginal costs (expressed in units of domestic consumption):

$$\begin{aligned} p_{t}\left( i\right) =\frac{\theta _{N}}{\theta _{N}-1}mc_{N,t}\left( i\right) . \end{aligned}$$

(33)

Firms operating in the intermediate tradable sector solve a similar problem. We assume that there is market segmentation. Hence the firm producing the brand h chooses ${p}_{t}(h)$ in the Home market, and a price in each of the other 4 regions (${p}_{t}^{*}(h)$ ${p}_{t}^{**}\left( h\right)$, ${p}_{t}^{***}\left( h\right)$, ${p}_{t}^{****}\left( h\right)$) to maximize the expected flow of profits (in terms of domestic consumption units),

$$\begin{aligned} E_{t}\sum _{\tau =t}^{\infty }\Lambda _{t,\tau }\left[ \begin{array}{c} p_{\tau }\left( h\right) y_{\tau }\left( h\right) +\frac{p_{\tau }^{*}\left( h\right) }{rer^{*}} y_{\tau }^{*}\left( h\right) +\frac{p_{\tau }^{**}}{rer^{**}}\left( h\right) y_{\tau }^{**}\left( h\right) \\ +\frac{p_{\tau }^{***}}{rer^{***}}\left( h\right) y_{\tau }^{***}\left( h\right) +\frac{p_{\tau }^{****}}{rer^{****}}\left( h\right) y_{\tau }^{****}\left( h\right) \\ -mc_{H,\tau }\left( h\right) \left( y_{\tau }\left( h\right) +y_{\tau }^{*}\left( h\right) +y_{\tau }^{**}\left( h\right) y_{\tau }^{***}\left( h\right) y_{\tau }^{****}\left( h\right) \right) \end{array} \right] , \end{aligned}$$

subject to quadratic price adjustment costs similar to those considered for nontradable goods and standard demand constraints. Each term “rer” represents bilateral exchange rate between Home currency and the currency of the considered importing country. The term $E_{t}$ denotes the expectation operator conditional on the information set at time t, $\Lambda _{t,\tau }$ is the appropriate discount rate, and $mc_{H,t}(h)$ is the real marginal cost. The first order conditions with respect to ${p}_{t}(h)$, ${p}_{t}^{*}(h)$, ${p}_{t}^{**}(h)$, ${p}_{t}^{***}(h)$, and ${p}_{t}^{****}(h)$ are

$$\begin{aligned} p_{t}\left( h\right)= & {} \frac{\theta _{T}}{\theta _{T}-1}mc_{t}\left( h\right) -\frac{A_{t}\left( h\right) }{\theta _{T}-1}, \end{aligned}$$

(34)

$$\begin{aligned} p_{t}^{*}\left( h\right)= & {} \frac{\theta _{T}}{\theta _{T}-1} \frac{mc_{t}}{rer^{*}}\left( h\right) -\frac{{A_{t}^{*}}\left( h\right) }{\theta _{T}-1}, \end{aligned}$$

(35)

$$\begin{aligned} p_{t}^{**}\left( h\right)= & {} \frac{\theta _{T}}{\theta _{T}-1} \frac{mc_{t}}{rer^{**}}\left( h\right) -\frac{{A_{t}^{**}}\left( h\right) }{\theta _{T}-1}, \end{aligned}$$

(36)

$$\begin{aligned} p_{t}^{***}\left( h\right)= & {} \frac{\theta _{T}}{\theta _{T}-1} \frac{mc_{t}}{rer^{***}}\left( h\right) -\frac{{A_{t}^{***}}\left( h\right) }{\theta _{T}-1}, \end{aligned}$$

(37)

$$\begin{aligned} p_{t}^{****}\left( h\right)= & {} \frac{\theta _{T}}{\theta _{T}-1} \frac{mc_{t}}{rer^{****}}\left( h\right) -\frac{{A_{t}^{****}}\left( h\right) }{\theta _{T}-1}, \end{aligned}$$

(38)

where $\theta _{T}$ is the elasticity of substitution of intermediate tradable goods, while A(h) and $A^{*}(h)$ involve terms related to the presence of price adjustment costs:

$$\begin{aligned} A_{t}\left( h\right)\approx & {} {\theta _{T}}-1+\kappa _{H}^{p}\frac{P_{t}\left( h\right) }{ P_{t-1}\left( h\right) }\left( \frac{P_{t}\left( h\right) }{P_{t-1}\left( h\right) }-1\right) \\&-\beta \kappa _{H}^{p}\frac{P_{t+1}\left( h\right) }{P_{t}\left( h\right) } \left( \frac{P_{t+1}\left( h\right) }{P_{t}\left( h\right) }-1\right) \frac{ Q_{H,t+1}}{Q_{H,t}}, \\ {A_{t}^{*}}\left( h\right)\approx & {} {\theta _{T}}-1+{{\kappa _{H}^{p*}}} \frac{{P_{t}^{*}\left( h\right) }}{{P_{t-1}^{*}\left( h\right) }} \left( \frac{{P_{t}^{*}\left( h\right) }}{{P_{t-1}^{*}\left( h\right) }}-1\right) \\&-\beta {{\kappa _{H}^{p*}}}\frac{{P_{t+1}^{*}}\left( h\right) }{{ P_{t}^{*}\left( h\right) }}\left( \frac{{P_{t+1}^{*}\left( h\right) } }{{P_{t}^{*}\left( h\right) }}-1\right) \frac{{Q_{H,t+1}^{*}}}{{ Q_{H,t}^{*}}}, \end{aligned}$$

where ${{\kappa _{H}^{p}}}$, ${{\kappa _{H}^{p*}}}$ respectively measure the degree of Home tradable nominal price rigidity in the Home country and in the US. Similar equations hold for CH, JP, RW.

1.3 Labor Market

In the case of firms in the nontradable intermediate sector, the labor input $L_{N}(i)$ is a CES combination of differentiated labor inputs supplied by domestic agents and defined over a continuum of mass equal to the country size ($j \in \left[ 0,n\right]$):

$$\begin{aligned} L_{N,t}\left( i\right) \equiv \left( \frac{1}{n}\right) ^{\frac{1}{\psi }} \left[ \int _{0}^{n}L_{t}\left( i,j\right) ^{\frac{\psi -1}{\psi }}dj\right] ^{\frac{\psi }{\psi -1}}, \end{aligned}$$

(39)

where $L\left( i,j\right)$ is the demand of the labor input of type j by the producer of good i and $\psi >1$ is the elasticity of substitution among labor inputs. Cost minimization implies that

$$\begin{aligned} L_{t}\left( i,j\right) =\left( \frac{1}{n}\right) \left( \frac{W_{t}\left( j\right) }{W_{t}}\right) ^{-\psi }L_{N,t}\left( j\right) , \end{aligned}$$

(40)

where W(j) is the nominal wage of labor input j and the wage index W is

$$\begin{aligned} W_{t}=\left[ \left( \frac{1}{n}\right) \int _{0}^{n}W_{t}\left( h\right) ^{1-\psi }dj\right] ^{\frac{1}{1-\psi }}. \end{aligned}$$

(41)

Similar equations hold for firms producing intermediate tradable goods. Each household is the monopolistic supplier of a labor input j and sets the nominal wage facing a downward-sloping demand obtained by aggregating demand across Home firms. The wage adjustment is sluggish because of quadratic costs paid in terms of the total wage bill,

$$\begin{aligned} AC_{t}^{W}=\frac{\kappa _{W}}{2}\left( \frac{W_{t}}{W_{t-1}}-1\right) ^{2}W_{t}L_{t}, \end{aligned}$$

(42)

where the parameter $\kappa _{W}>0$ measures the degree of nominal wage rigidity and $L_{t}$ is the total amount of labor in the Home economy.