Daniel Koudijs 10217150
University of Amsterdam Master Economics
Monetary Policy, Banking and Regulation Thesis supervision: Dr. Marcelo Zouain Pedroni
Macroprudential Policy and Housing Sector Booms
Within a Monetary Union
Daniel Koudijs
In this thesis I look at the effectiveness of macroprudential policy in reducing volatility and limiting the accumulation of credit following a shock to the economy. I construct a monetary union DSGE model including a financial accelerator mechanism and a housing sector. A macroprudential instrument is modelled which directly affects the lending rate in response to steady state deviations in credit growth. The two economies in the model are calibrated to represent the Netherlands versus the collective of other EMU economies. I find that macroprudential policy is beneficial following housing sector and financial booms, but potentially damaging to the economy following productivity shocks. This leads to the conclusion that macroprudential policy should optimally be able to identify the source of the shock in the economy. Furthermore, I find that for a small open economy like the Netherlands, the macroprudential instrument is especially useful in reducing volatility following EMU-wide shocks and can thus function as a complement to monetary policy. Further research should aim at modelling a less abstract instrument in order to gain a better understanding of the dynamics between macroprudential and monetary policy.
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Statement of Originality
This document is written by Daniel Koudijs who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text
and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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Index
1. Introduction ... 4
2. A Model for Analysing House Price Booms In a Monetary Union ... 5
2.1 The Home Economy ... 6
2.1.1 Households ... 6
2.1.1.1 Savers ... 6
2.1.1.1.1 Optimal Allocation Across Varieties of Goods ... 7
2.1.1.1.2 Optimal Allocation Across Home and Foreign Consumption ... 8
2.1.1.1.3 Maximization of the Utility Function... 9
2.1.1.2 Borrowers ... 10
2.1.2 Financial Intermediaries ... 10
2.1.3 Producers ... 11
2.2 The Foreign Economy ... 13
2.3 The Monetary Union ... 13
2.4 Market Clearing Conditions ... 14
2.5 System of Dynamic Stochastic Equations ... 15
2.5.1 The Home economy ... 15
2.5.2 The Foreign Economy ... 17
2.5.3 The Monetary Union ... 19
3. Calibration ... 20
4. Simulation Results ... 24
4.1 Productivity Shocks ... 24
4.2 Housing Demand Shocks ... 25
4.3 Financial Shocks ... 26
5. Robustness of the Results ... 27
6. Conclusion ... 28
7. Bibliography... 29
8. Appendices ... 31
Appendix A: The First Stage Household Problem ... 31
Appendix B: The Household Maximization Problem ... 31
Appendix C: The Producer Problem ... 33
Appendix D: Derivation of the Log-linearized System ... 35
Appendix E: Data Sources ... 44
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1. Introduction
Household credit is a primary source of financial instability in advanced economies around the world. The build-up of household credit in tandem with a booming housing sector is known to amplify business cycles during both up- and downturns as is evidenced by IMF (2012) and Claessens, Kose and Terrones (2008). The extension of mortgages inflates housing prices during economics booms, through which it drives the swing of the financial cycle1. In addition to this destabilizing cyclicality of household credit,
the experience of recent years has also shown that high levels of household credit can contribute to a weak economic recovery in the wake of a recession (Crowe et al., 2013).
In order to limit both the build-up of these cyclical forces as well as the subsequent economic outfall, existing monetary policy has since the crisis been complemented with macroprudential policy. Macroprudential policies and its instruments are explicitly aimed at fostering financial stability throughout the financial cycle. These instruments are enforced in most countries by various authorities and cover a wide range of markets, institutions and areas of risk2. Mortgages and booming housing
sectors have been at the heart of many past financial crisis, and as a result limiting the expansion of household credit over the business cycle is defined as one of the primary targets of macroprudential policy (ESRB, 2014). Preliminary empirical research on these policies has found that they appear to be effective across a variety of advanced economies. Borrower-based macroprudential policies such as loan to value caps are found to coincide with reductions in credit growth and house prices (Cerutti et al., 2015).
Macroprudential policies of this kind are especially relevant within the framework of a monetary union such as the EMU. Following the financial crisis, the economies of the Eurozone suffered a period of anaemic economic recovery and instability in financial markets. Imbalances between countries have increased over recent years while fiscal policy across the union has been restrained. In light of these developments, the adoption of national macroprudential measures has been reasoned as a way to increase domestic financial stability as well as stability across the entire Economic and Monetary Union (Houben and Kakes, 2013).
Though empirical research thus suggest these policies are beneficial to union financial stability, relatively little research has been done into the effectiveness of these policies from a general equilibrium context. Relatively few studies have explicitly incorporated macroprudential policies in monetary union DSGE models, examples are Quint and Rabanal (2013) and Brzoza-Brzezina et al. (2015). Both papers find macroprudential polices improve welfare across the union and complement supra-national monetary policy in line with what had been suggested by empirical research. However, these studies explicitly model a core/periphery structure; they do not study a country like the Netherlands: a small, very open economy with an important housing sector and relatively high levels of household credit.
The Dutch economy is in this case of particular interest as loan to value ratios on mortgages are exceptionally high (+/- 100%) and thereby potentially damaging to financial stability (ECB, 2015). This was made evident in the wake of the financial crises as the housing market slumped and many households saw the value of their house fall beneath their mortgage. These “underwater” mortgages consequently became a prime concern for Dutch banks, financial authorities and politics as for example outlined in the Dutch Central Bank’s quarterly Financial Stability Report (DNB, 2014). Underwater mortgages are believed to have contributed to both financial instability and weak economic recovery in the Netherlands.
In light of these issues, macroprudential measures relating to household credit can potentially provide a significant benefit to the Dutch economy. There has already been a push by the Dutch government and financial authorities to lower the LTV ratio cap by 1% a year until it reaches 100% in
1 Moreover, arguments have been made (Caverzasi, 2014) placing mortgages within the framework of the Financial Instability Hypothesis of Minsky (1992).
5 2018. A further lowering of this cap to around 90% after 2018 has been recommended by the Dutch Central Bank and financial market authority AFM (DNB, 2015). Moreover, within the ESRB’s macroprudential framework, each member country including the Netherland adopted cyclical capital requirements (CCyB) to be controlled by the national financial authorities aimed at protecting banks from excessive credit growth. As credit demand peaks during an economic upturn, this regulation forces banks to hold more reserves, increasing bank resilience and making credit more expensive at the same time. This regulation will be implemented over the period 2016-19 and fits into the general framework of stricter, anti-cyclical prudential policy.
In this paper I analyse the effect of implementing a macroprudential instrument on volatility in the real economy and credit growth following an economic shock. I construct a two-country monetary union DSGE model with financial frictions and a housing (durable) good. One economy represents the Netherlands (Home) whereas the other represents the collective of other EMU countries (Foreign). The Dutch financial authorities do not control monetary policy but instead enforce a macroprudential instrument which responds to credit growth and directly impacts the lending rate. Furthermore, the LTV ratio plays a crucial role in the model as it functions as the primary financial accelerator in an economy with highly leveraged housing consumption. I estimate the shocks of the model to match data collected on the Dutch economy. The model contain three types of shocks: a productivity, housing demand and financial shock. Furthermore, these shocks hit either only the Home economy or EMU-wide (a common shock to both the Home and Foreign economy) for a total of six different shocks. This allows for an analysis of the benefits of macroprudential policy with respect to both domestic as well as monetary union-wide shocks.
The results of my simulation suggest the macroprudential instrument is beneficial depending on the type of shock. Following housing demand and financial shocks, the instrument reduces volatility in the real economy and limits the accumulation of credit. As the housing sector booms, the macroprudential instrument slows down the financial accelerator and consequently curbs spill-over effects to the consumption sector. Following a financial shocks, as lending rates are exogenously lowered, the instrument is able to reduce volatility in both sectors of the economy and curb credit growth. Even when, following union-wide shocks, monetary policy responds adequately to shocks, the instrument still proves to be beneficial. However, when the economy is hit by a productivity shock, the macroprudential instrument produces adverse effects. When the productivity shock is domestic, residential investment volatility and housing price inflation are both increased while credit growth is left unaffected. Following an EMU-wide productivity shock, the instruments has no real contribution in terms of stability. This leads to the conclusion that identifying between shocks is crucial to the success of macroprudential policy.
The thesis is organised as follows. Section 2 describes the model set-up and derives the system of equations necessary to analyse the model. Section 3 details the calibration of the model parameters. Section 4 analyses the impulse response functions obtained from the model. Section 5 provides several robustness checks of the model and section 6 concludes. The final two sections, 7 and 8 consist of the bibliography and the appendices.
2. A Model for Analysing House Price Booms In a Monetary Union
The model I use to analyse my research question is a dynamic stochastic general equilibrium model consisting of two economies within a monetary union, each made up of two good producing sectors and
6 two types of households. The model relates to the one used in Kannan et al. (2012) and Quint and Rabanal (2013) 3, and can best be thought of as hybrid of these two models.
The two countries in the model are of unequal size, with the smaller economy labelled Home and the larger Foreign. The economies are symmetric in households, production sectors and model assumptions. The Home economy represents the economy of the Netherlands, whereas the Foreign economy represents the collective of other Eurozone countries. The Home and Foreign economy together represent the complete Eurozone. Monetary policy operates at monetary union level, similar to the role played by the ECB. The model consequently consists of three blocks: the Home economy, the Foreign economy and the overall monetary union. Below I will describe the assumptions and equations relating to each these three blocks. As the Home and Foreign economy are symmetric, I will not discuss the Foreign economy in detail. The monetary union equations relate to the monetary policy rule and are followed by the market clearing conditions. The final part of this section contains the full set of log-linearized equations necessary to analyse shocks to the model.
2.1 The Home Economy
The Home economy represents an 𝑠 ∈ [0,1] share of the monetary union, with the remaining 1 − 𝑠 being represented by the Foreign economy. The Home economy is populated by a 𝑗 number of households made up of savers (𝑗 ∈ [0, 𝜆 ]) and borrowers (𝑗 ∈ [𝜆, 1]). Savers are more patient then borrowers, meaning their discount factor is higher ( 𝛽𝑆> 𝛽𝐵). As a result, they are in equilibrium willing to forego consumption and lend bonds to borrowers. This transferring of funds happens not directly from savers to borrowers but passes through domestic financial intermediaries who charge a spread on top of the deposit rate 𝑅𝑡. This spread is primarily dependent on the borrower’s loan to value ratio and functions as a financial accelerator mechanism in the spirit of Bernanke et al. (1998). The size of the spread is also affected by a financial shock term and the macro-prudential instrument 𝜍𝑡. Below I first detail the conditions for domestic savers and borrowers, followed by financial intermediaries and finally the producers.
2.1.1 Households
Below I illustrate the assumptions, preferences and problems to be solved for households in the Home economy.
2.1.1.1 Savers
The problem for savers, and analogously borrowers, follows three stages. In the first stage, they choose the optimal allocation across varieties of non-durable domestic, non-durable foreign and durable domestic goods. In the second stage they choose the optimal allocation of non-durable consumption over domestic and foreign producers. In the third stage the household maximizes his utility over non-durable consumption, non-durable consumption, investment and labour supply. The utility function of a representative saver is given by
𝐸0∑(𝛽𝑆)𝑡 ∞ 𝑡=0 [𝛾 log(𝐶𝑡𝑆,𝑗− 𝜖𝐶𝑡−1𝑆 ) + (1 − 𝛾)𝜁𝑡log(𝐷𝑡 𝑆,𝑗 ) −(𝐿𝑡 𝑆,𝑗 )1+𝜑 1 + 𝜑 ] Subject to the budget constraint
𝐶𝑡𝑆,𝑗+𝑃𝑡 𝐷 𝑃𝑡𝐶 𝐼𝑡𝑆,𝑗+𝐵𝑡 𝑆,𝑗 𝑃𝑡𝐶 ≤ 𝑅𝑡−1 𝐵𝑡−1𝑆,𝑗 𝑃𝑡𝐶 +𝑊𝑡 𝐶 𝑃𝑡𝐶 𝐿𝑆,𝐶,𝑗𝑡 +𝑊𝑡 𝐷 𝑃𝑡𝐶 𝐿𝑆,𝐷,𝑗𝑡
7 where variables denoted by 𝑆 refer to savers, 𝐶𝑡𝑆,𝑗 represents consumption of the non-durable good, 𝜁𝑡 is the durable preference shock following an AR(1) process in logs, 𝐷𝑡𝑆,𝑗 is the stock of the durable good, 𝐿𝑡𝑆,𝑗 is the labour supply index, 𝐼𝑡𝑆,𝑗 is investment in stock of the durable good, 𝐵𝑡𝑆,𝑗 are bonds deposited with financial intermediaries paying deposit rate 𝑅𝑡 and 𝑊𝑡𝑥 are the wages in each sector 𝑥 = {𝐶, 𝐷}.
The parameter 𝛽𝑆 is the relevant discount factor for the saver, 𝛾 is the share of the non-durable good in the utility function, 𝜖 is the habit formation parameter with respect to aggregate last period consumption and 𝜑 denotes the inverse Frisch elasticity of labour supply. Bonds function for the patient households as a saving vehicle carrying the monetary union-wide deposit rate 𝑅𝑡. The functional form of the household utility function is similar to the one proposed in DSGE models including durable goods such as Iacoviello and Neri (2010). I will first detail the optimality conditions of the first stage and second stage household problems before returning to the utility function.
2.1.1.1.1 Optimal Allocation Across Varieties of Goods
A variety ℎ ∈ [0, 𝑠] of durable goods is supplied by durable good producers where the elasticity of substitution between these goods is 𝜎𝐷. A similar variety ℎ of the non-durable good is produced by domestic non-durable producers and a variety 𝑓 ∈ [𝑠, 1] of non-durable goods by foreign producers; both subject to a similar elasticity of substitution 𝜎𝐶 = 𝜎𝐶∗. As such, optimal consumption of durable goods, domestic non-durable goods and foreign non-durable goods by household 𝑗 is defined as
𝐷𝑡𝑆𝑗 ≡ [(1 𝑠) 1 𝜎𝐷 ∫ 𝑌𝑡𝐷(ℎ) 𝜎𝐷−1 𝜎𝐷 𝑠 0 𝑑ℎ] 𝜎𝐷 𝜎𝐷−1 𝐶𝑡𝑆,𝐻,𝑗≡ [(1 𝑠) 1 𝜎𝐶 ∫ 𝑌𝑡𝐶(ℎ) 𝜎𝐶−1 𝜎𝐶 𝑠 0 𝑑ℎ] 𝜎𝐶 𝜎𝐶−1 𝐶𝑡𝑆,𝐹,𝑗≡ [( 1 1 − 𝑠) 1 𝜎𝐶 ∫ 𝑌𝑡𝐶∗(𝑓) 𝜎𝐶−1 𝜎𝐶 1 𝑠 𝑑𝑓] 𝜎𝐶 𝜎𝐶−1
Where the factors(1 𝑠) 1 𝜎𝐷, (1 𝑠) 1 𝜎𝐶 and ( 1 1−𝑠) 1 𝜎𝐶
adjust for the relative size of each economy. Minimizing costs across varieties, we obtain the optimal allocations for the representative household across the varieties of intermediate goods4
𝑌𝑡𝐷(ℎ) = ( 𝑃𝑡𝐷(ℎ) 𝑃𝑡𝐷 ) −𝜎𝐷 𝐷𝑡𝑆𝑗 𝑌𝑡𝐶(ℎ) = ( 𝑃𝑡𝐶,𝐻(ℎ) 𝑃𝑡𝐶,𝐻 ) −𝜎𝐶 𝐶𝑡𝑆,𝐻,𝑗 𝑌𝑡𝐶∗(𝑓) = (𝑃𝑡𝐶,𝐹(𝑓) 𝑃𝑡𝐶,𝐹 ) −𝜎𝐶 𝐶𝑡𝑆,𝐹,𝑗
8 Note that since these assumption are not dependent on the type of household, these functions have an analogous counterpart for borrowing households. In the demand functions above, the aggregate price levels of each good are given by
𝑃𝑡𝐷≡ ( 1 𝑠∫ (𝑃𝑡 𝐷(ℎ))1−𝜎 𝐷 𝑑ℎ 𝑠 0 ) 1 1−𝜎𝐷 𝑃𝑡𝐶,𝐻 ≡ (1 𝑠∫ (𝑃𝑡 𝐶,𝐻(ℎ))1−𝜎𝐶𝑑ℎ 𝑠 0 ) 1 1−𝜎𝐶 𝑃𝑡𝐶,𝐹 ≡ ( 1 1 − 𝑠∫ (𝑃𝑡 𝐶,𝐹(𝑓))1−𝜎𝐶𝑑𝑓 1 𝑠 ) 1 1−𝜎𝐶
2.1.1.1.2 Optimal Allocation Across Home and Foreign Consumption
As the economy is part of a monetary union, trade exists between the member countries. I assume trade is only possible for the non-durable good. This assumption is common in the literature5 and is meant to
reflect the role of the durable good as housing, an asset not commonly “consumed” cross-borders. A consequence of opening the economy up to trade is that households have to optimally allocate their non-durable consumption over Home and Foreign consumption. The non-non-durable consumption index is given by 𝐶𝑡𝑗= [(𝜏) 1 𝜂(𝐶 𝑡 𝐻,𝑗 ) 𝜂−1 𝜂 + (1 − 𝜏)1𝜂(𝐶 𝑡 𝐹,𝑗 ) 𝜂−1 𝜂 ] 𝜂 𝜂−1
where 𝐶𝑡𝐻,𝑗 and 𝐶𝑡𝐹,𝑗 represent non-durable consumption from respectively Home and Foreign producers and 𝜂 reflects costly re-allocation of consumption across countries. 𝜏 ∈ [0,1] measures the share of domestic produced goods in total non-durable consumption and functions as a proxy of the economy’s openness. Note that here I do not distinguish between variables for savers and borrowers. As the non-durable consumption index is identical for savers and borrowers, the optimal allocation is identical for both. I therefore derive domestic and foreign consumption demand as a function of total consumption 𝐶𝑡𝑇𝑂𝑇 instead of separately for savers and borrowers. Total non-durable consumption in the economy is defined as
𝐶𝑡𝑇𝑂𝑇 = 𝜆𝐶𝑡𝑆+ (1 − 𝜆)𝐶𝑡𝐵
solving for the optimal allocation across Foreign and Home consumption we obtain the two demand functions6 𝐶𝑡𝐻 = 𝜏 ( 𝑃𝑡𝐶,𝐻 𝑃𝑡𝐶 ) −𝜂 𝐶𝑡𝑇𝑂𝑇 𝐶𝑡𝐹 = (1 − 𝜏) ( 𝑃𝑡𝐶,𝐹 𝑃𝑡𝐶 ) −𝜂 𝐶𝑡𝑇𝑂𝑇 where the CPI for the non-durable good is defined as
𝑃𝑡𝐶 = [(𝜏)(𝑃𝑡𝐶,𝐻) 1−𝜂
+ (1 − 𝜏)(𝑃𝑡𝐶,𝐹)1−𝜂] 1 1−𝜂
this equation shows the wedge created by trade between domestic prices set by domestic producers and the CPI of non-durables households face in their consumption decision.
5 See for example Quint et al. (2013) and Aspachs-Bracon et al. (2011)
9
2.1.1.1.3 Maximization of the Utility Function
Having defined the optimal allocation across the three varieties of goods and the optimal allocation of non-durable consumption across domestic and foreign producers, I return to the maximization problem as defined by the utility function and budget constraint. Before solving the first order conditions of this problem, I first detail the assumptions with respect to the law of motion of the durable good and the labour supply index.
The durable good differs from the non-durable good in that it has residual value in the next period. Durable goods are purchased through investments 𝐼𝑡𝑆 which increase the stock 𝐷𝑡𝑆. The law of motion of the durable good is thereby given as
𝐷𝑡𝑆,𝑗 = (1 − 𝛿)𝐷𝑡−1𝑆,𝑗 + [1 − 𝑆 (𝐼𝑡 𝑆,𝑗 𝐼𝑡−1𝑆,𝑗 )] 𝐼𝑡
𝑆,𝑗
where 𝛿 represents the depreciation rate of the durable good and 𝑆(. ) is the adjustment costs function. Following the assumptions as put forward by Christiano, Eichenbaum and Evans (2005), 𝑆(. ) is a convex function which in the steady state 𝑆̅ exhibits 𝑆̅ = 𝑆̅′= 0 and 𝑆̅" = 𝛷 > 0. Adjustment costs are added to the law of motion in order to generate hump-shaped responses of investment to shocks. In general, including adjustment costs in the model ensures the response of investment to shocks becomes less volatile, similar to the effect of habit formation in consumption.
Labour supply across sectors is given by the labour supply index, which aggregates the labour supplied to each sector and is defined as
𝐿𝑡𝑗= [(1 − 𝛼)−𝜈(𝐿 𝑡 𝐷,𝑗 )1+𝜈+ 𝛼−𝜈(𝐿 𝑡 𝐶,𝑗 )1+𝜈] 1 1+𝜈
where 𝐿𝑥,𝑗𝑡 represents labour supplied to each sector 𝑥 = {𝐶, 𝐷}, 𝛼 is the share of employment in the non-durable sector and 𝜈 is the parameter accounting for costly re-allocation of labour across sectors. Assuming costly re-allocation, 𝜈 ≠ 0, is important in explaining the co-movement of variables as will be discussed in section 4.
Following the assumptions as stated above regarding the law of motion of the durable good and the labour supply index, the Lagrangian for the saving household problem is defined as
𝐿 = 𝐸0∑∞𝑡=0(𝛽𝑆)𝑡 { 𝛾 log(𝐶𝑡𝑆,𝑗− 𝜖𝐶𝑡−1𝑆 ) + (1 − 𝛾)𝜁𝑡log(𝐷𝑡 𝑆,𝑗 ) − ([(1−𝛼)−𝜈(𝐿𝑆,𝐷,𝑗𝑡 )1+𝜈+𝛼−𝜈(𝐿𝑡𝑆,𝐶,𝑗)1+𝜈] 1 1+𝜈 ) 1+𝜑 1+𝜑 } −𝐸0∑∞𝑡=0(𝛽𝑆)𝑡𝜆𝑡𝑆[𝑃𝑡𝐶𝐶𝑡 𝑆,𝑗 + 𝑃𝑡𝐷𝐼𝑡 𝑆,𝑗 + 𝐵𝑡𝑆,𝑗− 𝑅𝑡−1𝐵𝑡−1 𝑆,𝑗 − 𝑊𝑡𝐶𝐿𝑡 𝑆,𝐶,𝑗 − 𝑊𝑡𝐷𝐿𝑡 𝑆,𝐷,𝑗 ] −𝐸0∑∞𝑡=0(𝛽𝑆)𝑡𝜇𝑡𝑆[𝐷𝑡 𝑆,𝑗 − (1 − 𝛿)𝐷𝑡−1𝑆,𝑗 − [1 − 𝑆 (𝐼𝑡𝑆,𝑗 𝐼𝑡−1𝑆,𝑗)] 𝐼𝑡 𝑆,𝑗 ] where 𝜆𝑡𝑆 and 𝜇
𝑡𝑆 are the Lagrange multipliers for respectively the budget constraint and the law of motion of the non-durable good. The first order conditions with respect to 𝐶𝑡𝑆, 𝐷𝑡𝑆, 𝐼𝑡𝑆, 𝐵𝑡𝑆, 𝐿𝑆,𝐶𝑡 , 𝐿𝑆,𝐷𝑡 are summarized by7 𝛽𝑆𝑅𝑡𝐸𝑡[( 𝐶𝑡𝑆− 𝜖𝐶𝑡−1𝑆 𝐶𝑡+1𝑆 − 𝜖𝐶𝑡𝑆) ( 𝑃𝑡𝐶 𝑃𝑡+1𝐶 )] = 1
10 (1 − 𝛾)𝜁𝑡 𝐷𝑡 = 𝜇𝑡𝑆+ 𝛽𝑆(1 − 𝛿)𝐸𝑡𝜇𝑡+1𝑆
(
𝛾
𝐶
𝑡𝑆− 𝜖𝐶
𝑡−1𝑆)
𝑃
𝑡𝐷𝑃
𝑡𝐶=
𝜇𝑡 𝑆(
1 − 𝑆(
𝐼𝑡 𝑆 𝐼𝑡−1𝑆)
− 𝐼𝑡 𝑆 𝐼𝑡−1𝑆 𝑆′(
𝐼𝑡 𝑆 𝐼𝑡−1𝑆))
+ 𝛽𝑆𝐸𝑡𝜇𝑡+1𝑆[
𝑆′(
𝐼𝑡𝑆 𝐼𝑡−1𝑆) (
𝐼𝑡+1 𝑆 𝐼𝑡𝑆)
2]
(𝐿𝑡𝑆)𝜑−𝜈(1 − 𝛼)−𝑣(𝐿 𝑡 𝑆,𝐷)𝜈= ( 𝛾 𝐶𝑡𝑆− 𝜖𝐶𝑡−1𝑆 ) (𝑊𝑡 𝐷 𝑃𝑡𝐶 ) (𝐿𝑆𝑡)𝜑−𝜈(𝛼)−𝑣(𝐿𝑡𝑆,𝐶) 𝜈 = ( 𝛾 𝐶𝑡𝑆− 𝜖𝐶𝑡−1𝑆 ) (𝑊𝑡 𝐶 𝑃𝑡𝐶 )Because these conditions are symmetric for all savers, the subscript 𝑗 is dropped. The first equation is the standard Euler equation with habit formation. The second equation describes the optimality condition for durable consumption. The third equation describes the optimal investment decision with non-zero investment adjustment costs. The final two equations define the optimal labour supply decision for both sectors.
2.1.1.2 Borrowers
Borrowers differ from savers on two main points. First, their discount factor 𝛽𝐵 is lower than those of savers. This makes this type of household “impatient” and consequently wanting to borrow in equilibrium. Secondly, the interest rate they pay on these borrowed funds is not the deposit rate but the lending rate 𝑅𝑡𝐿, which equals the deposit rate plus a spread. The representative borrower 𝑗 ∈ [𝜆, 1] has the utility function
𝐸0∑(𝛽𝐵)𝑡 ∞ 𝑡=0 {𝛾 log(𝐶𝑡𝐵,𝑗− 𝜖𝐶𝑡−1𝐵 ) + (1 − 𝛾) 𝜁𝑡log(𝐷𝑡 𝐵,𝑗 ) −(𝐿𝑡 𝐵,𝑗 )1+𝜑 1 + 𝜑 }
where variables with subscript 𝐵 are borrower specific and analogues to the saver’s denoted by 𝑆. The budget constraint of the borrower is given by
𝑃𝑡𝐶𝐶𝑡 𝐵,𝑗 + 𝑃𝑡𝐷𝐼𝑡 𝐵,𝑗 + 𝑅𝑡−1𝐿 𝐵𝑡−1 𝐵,𝑗 ≤ 𝐵𝑡𝐵,𝑗+ 𝑊𝑡𝐶𝐿𝑡 𝐶,𝐵,𝑗 + 𝑊𝑡𝐷𝐿𝑡 𝐷,𝐵,𝑗
The non-durable consumption index, the law of motion of the durable good and the labour supply index are all assumed to be symmetric to those defined for savers. As a consequence, optimal allocation across the varieties of goods, foreign/domestic demand and the first order conditions for borrower are all symmetric to those of savers, with the most notable difference being the lending rate 𝑅𝑡𝐿 taking the place of the deposit rate 𝑅
𝑡 in the Euler equation.
2.1.2 Financial Intermediaries
The financial intermediaries play a crucial role in the model as they provide the mechanism through which the loan to value ratio (LTV) feeds back into the lending rate faced by borrowers. Financial intermediaries represent the channel through which funds are transferred from savers to borrowers. The functional form of these intermediaries is not defined as a maximization or minimization problem but rather as a financial accelerator in the style of Bernanke et al. (1998).
Savers deposit their savings with financial intermediaries at deposit rate 𝑅𝑡. Borrowers borrow these funds at the lending rate 𝑅𝑡𝐿. The difference between these two rates is the spread which consists of three terms and, following Kannan et al. (2012), is defined as
𝑅𝑡𝐿= 𝑣𝑡𝐹 ( 𝐵𝑡𝐵 𝑃𝑡𝐷𝐷𝑡𝐵 ) 𝜍 (𝐵𝑡−1 𝐵𝑡−2 ) 𝑅𝑡
11 The first term 𝑣𝑡 represents a financial shock term which follows an AR(1) process in logs. Shocks to this term can be seen as exogenous shocks to the financial market that cause financial intermediaries to lower their spread. This can be due to lower market risk, increased competition or other factors.
The second term 𝐹(. ) is an increasing function of the borrower’s loan to value ratio 𝐵𝑡𝐵 𝑃 𝑡𝐷𝐷𝑡𝐵 ⁄ where 𝐹′( . ) = Γ > 0. There exists a steady state level of the borrower’s LTV ratio 𝜒 for which 𝐹(𝜒) = 1. This LTV ratio is not perfectly binding and allows for deviations around steady state, though at a premium. Through this mechanism, the loan to value ratio is not fixed within the model and the lending rate is allowed to fluctuate following changes in the borrower’s LTV ratio. As such 𝜒 can be seen as the LTV ratio recommended by the authorities. In this set-up the model differs to for example Iacoviello (2005), who constructs a model where the LTV ratio is fixed at its steady state level. The model could incorporate this assumption by setting 𝐹′( . ) = ∞, which makes any deviation from the steady state LTV infinitely costly and thus effectively fixes the model’s LTV ratio.
The final term 𝜍 is an increasing function of lagged credit growth and represents the macro-prudential instrument, the primary focus of this study. The functional form of this instrument is derived from the model by Kannan et al. (2012). This instrument is meant to be highly illustrative an representative of a great variety of macro-prudential measures. Essentially, any measure that forces financial intermediaries to increase their lending rate, either directly or indirectly, in response to credit growth can be represented by this term. Examples of such measures are cyclical capital requirements or specific loan provision. BIS (2010) describes in more detail how such measures impact the lending rate and margins set by financial institutions. When this instrument is implemented (𝜍 > 0), this term increases the lending rate in response to deviations in credit growth from its steady state level. This means that at the steady state level of credit growth ϒ, 𝜍(ϒ) = 1. Combined with our assumptions on the steady state level of 𝐹(𝜒) this implies that in the steady state the lending rate equals
𝑅̅𝑡𝐿= 𝑣̅𝑡𝑅̅𝑡
where 𝑣𝑡, is the mean of the financial shock term8, and equal to the steady state mark-up for financial intermediaries9. Furthermore, in the steady state both 𝑅
𝑡𝐿 and 𝑅𝑡 are equal to the inverse of their respective discount factors, 𝛽𝐵 and 𝛽𝑆. Together, these assumptions ensure a return to the steady state following a shock while still allowing for deviations in the loan to value ratio.
2.1.3 Producers
Both consumption goods (durable and non-durable) are produced by firms who are monopolist in the supply of their variety of good. All firms hire homogenous labour supplied by the households to produce these goods. Domestic producers in each of the two sectors use this labour to produce a variety ℎ ∈ [0, 𝑠] of intermediate goods. Each period they demand a cost minimizing amount of labour and set their optimal price according to Calvo-pricing and indexation behaviour assumptions. As stated above, non-durable goods are tradeable, which implies foreign produced non-non-durable goods also enter the domestic market and vice versa. Durable goods on the other hand can only be bought from domestic producers. Finally, labour movement between the Home and Foreign economy is restricted, which implies that producers can only hire workers from domestic labour supply.
In the first stage, taken a fixed level of output, producers demand a cost minimizing level of labour. In the second stage, producers set the optimal prize for their good given assumptions on pricing behaviour. The first stage problem follows from the production functions defined as
8 As in the steady state all shocks are equal to their defined mean. 9 Following the steady state values of 𝑅̅
𝑡𝐿 and 𝑅̅𝑡, the discount factors of the households imply the financial
12 𝑌𝑡𝐷(ℎ) = 𝐿𝐷𝑡(ℎ) 𝑓𝑜𝑟 𝑎𝑙𝑙 ℎ ∈ [0, 𝑠]
𝑌𝑡𝐶(ℎ) = 𝐴𝐶𝑡𝐿𝐶𝑡(ℎ) 𝑓𝑜𝑟 𝑎𝑙𝑙 ℎ ∈ [0, 𝑠]
where in the non-durable sector, the production function is subject to a productivity shock (TFP) which follows an AR(1) process in logs. Cost minimization in each sector implies that the real marginal cost of production equals the real wage
𝑀𝐶𝑡𝐶 = 𝑊𝑡𝐶⁄𝑃𝑡𝐶 𝐴𝑡𝐶 𝑀𝐶𝑡𝐷= 𝑊𝑡𝐷 𝑃𝑡𝐷
The pricing decision involves a more complex problem. Producers in each sector face a Calvo-type restriction on their price setting, also known as “staggered pricing” (Calvo, 1983). This restriction implies that for each sector 𝑥 = {𝐶, 𝐷} only a portion 𝜃𝑥 of producers get to adjust (re-optimize) their prices each period. The remaining 1 − 𝜃𝑥 is not allowed to adjust their prices. Furthermore, of those not allowed to re-optimize, a portion 𝜙𝑥 sets their prices equal to last period’s inflation rate. Taking into account these assumptions, the optimal pricing problem for durable producers is defined as
max 𝑃𝑡𝐷(ℎ)𝐸𝑡∑(𝜃 𝐷𝛽)𝑘𝜆𝑡+𝑘 𝜆𝑡 ∞ 𝑘=0 {[𝑃𝑡 𝐷(ℎ) 𝑃𝑡+𝑘𝐷 ( 𝑃𝑡+𝑘−1𝐷 𝑃𝑡−1𝐷 ) 𝜙𝐷 − 𝑀𝐶𝑡+𝑘𝐷 ] 𝑌𝑡+𝑘𝐷 (ℎ)}
subject to future demand given by
𝑌𝑡+𝑘𝐷 (ℎ) = [𝑃𝑡 𝐷(ℎ) 𝑃𝑡+𝑘𝐷 ( 𝑃𝑡+𝑘−1𝐷 𝑃𝑡−1𝐷 ) 𝜙𝐷 ] −𝜎𝐷 𝑌𝑡+𝑘𝐷
The producer sets his price 𝑃𝑡𝐷(ℎ) in order to maximize his expected future profits, which equal his price minus marginal costs 𝑀𝐶𝐷 times demand. As the market is in perfect competition and the good produced is homogenous in all characteristics aside from price, the only factor that drives demand for the producer’s variety is his price, as shown in the future demand constraint. The terms (. )𝜙𝐷 represent the additional effect of indexation to the last periods inflation. Maximizing this problem with respect to 𝑃𝑡𝐷(ℎ) gives the optimal pricing decision10
𝑃̂𝑡𝐷 𝑃𝑡𝐷= ( 𝜎𝐷 𝜎𝐷− 1) 𝐸𝑡∑ (𝜃𝐷)𝑘Δ 𝑘,𝑡+𝑘(∑ (Π𝑡+𝑠−1 𝐷 )𝜙𝐷 Π𝑡+𝑠𝐷 𝑘 𝑠=1 ) −𝜎𝐷 𝑀𝐶𝑡+𝑘𝐷 𝐷𝑡+𝑘 (𝜃𝐷)𝑘Δ 𝑘,𝑡+𝑘(∑ (Π𝑡+𝑠−1 𝐷 )𝜙𝐷 Π𝑡+𝑠𝐷 𝑘 𝑠=1 ) 1−𝜎𝐷 𝐷𝑡+𝑘 ∞ 𝑘=0
where 𝑃̂𝑡𝐷 is the optimal price level, Δ𝑘,𝑡+𝑘= (𝛽𝑆)𝑘 𝜆𝑡+𝑘 𝑆
𝜆𝑡𝑆 is the real stochastic discount factor and inflation is defined as Π𝑡𝐷=
𝑃𝑡𝐷
𝑃𝑡−1𝐷 . Following the assumptions as outlined above, the aggregate price level is defined as 𝑃𝑡𝐷= {𝜃𝐷[𝑃𝑡−1𝐷 (Π𝑡−1D ) 𝜙𝐷 ] 1−𝜎𝐷 + (1 − 𝜃𝐷)[𝑃̂𝑡𝐷]1−𝜎𝐷} 1 1−𝜎𝐷
The pricing problem in the non-durable sector is equivalent and leads to a similar result, taking into account the appropriate changes of notation. In the non-durable sector it is important to distinguish
13 between the price set for the non-durable good by domestic intermediate good producers (𝑃𝑡𝐶,𝐻) and the price consumers face (𝑃𝑡𝐶). In this model the two are not equal because of the existence of foreign intermediate good producers who also supply the domestic economy. More specifically, 𝑃𝑡𝐶,𝐻 is defined as 𝑃𝑡𝐶,𝐻 = [𝜃𝐶(𝑃𝑡−1 𝐶,𝐻 (Π𝑡−1𝐶,𝐻)𝜙 𝐶 ) 1−𝜎𝐶 + (1 − 𝜃𝐶)[𝑃̂𝑡𝐶,𝐻]1−𝜎 𝐶 ] 1 1−𝜎𝐶
where 𝑃̂𝑡𝐶,𝐻 is the price level resulting from the optimal pricing decision for non-durable producers similar to the one demonstrated above. The CPI price level of the non-durable good 𝑃𝑡𝐶 is given by
𝑃𝑡𝐶 = [(𝜏)(𝑃𝑡𝐶,𝐻) 1−𝜂
+ (1 − 𝜏)(𝑃𝑡𝐶,𝐹)1−𝜂] 1 1−𝜂
were we to isolate the economy from the EMU (𝜏 = 1), we halt trade and effectively close this wedge so that 𝑃𝑡𝐶,𝐻= 𝑃𝑡𝐶.
2.2 The Foreign Economy
The Foreign economy is of size 1 − 𝑠 and analogous to the Home economy. The Foreign economy consists of savers, borrowers, two good producing sectors and financial intermediaries. Because the optimal behaviour for these parties is identical to that of the Home economy I do not present these conditions here but include them in the full system of log-linearized equations below.
Furthermore, most parameters related to household preferences are assumed to be identical between the two economies. Exceptions are the pricing parameters (𝜃𝐶∗, 𝜃𝐷∗, 𝜙𝐶∗, 𝜙𝐷∗), investment adjustment costs (𝛷∗), the share of domestic non-durable consumption (𝜏∗), the steady state level of the LTV ratio (𝜒∗) and the macroprudential instrument (𝜍∗). All of these parameters are allowed to differ between the Home and Foreign economy as will be discussed in more detail in the section on calibration.
2.3 The Monetary Union
The primary function conducted at the level of the monetary union is monetary policy. Equivalent to the Eurozone and the European Central Bank monetary policy in this model is exercised by taking into account aggregate monetary union variables. Prices, inflation and output in the monetary union are defined as 𝑃𝑡𝐶,𝐸𝑀𝑈= (𝑃𝑡𝐶)𝑠(𝑃𝑡𝐶∗)1−𝑠 Π𝑡𝐶,𝐸𝑀𝑈 =𝑃𝑡 𝐶,𝐸𝑀𝑈 𝑃𝑡−1𝐶,𝐸𝑀𝑈 𝑌𝑡𝐸𝑀𝑈= 𝑠𝑌𝑡+ (1 − 𝑠)𝑌𝑡∗
Where monetary union aggregates are weighted by the share of their respective economy in the union. As in Quint et al. (2013) and Aspachs-Bracon et al. (2011), prices of the non-durable goods are left out of the aggregate EMU price level as both are set and consumed solely on a national level. The monetary policy rule, following a standard Taylor rule is given by
𝑅𝑡 = (𝑅𝑡−1)𝛾𝑅[( Π𝑡𝐶,𝐸𝑀𝑈 Π̅𝐶,𝐸𝑀𝑈) 𝛾𝜋 (𝑌𝑡 𝐸𝑀𝑈 𝑌𝑡−1𝐸𝑀𝑈) 𝛾𝑌 𝑅̅] 1−𝛾𝑅
14 The functional form of the monetary policy rule follows from Kannan et al. (2012) and is similar to the common Taylor rule. The ECB’s preference towards last period’s interest rate (interest rate inertia) is given by 𝛾𝑅, the inflation parameter is given by 𝛾𝜋 and the output parameter by 𝛾𝑌. The variables topped with a bar represent the steady state level of these variables.
2.4 Market Clearing Conditions
Finally, to close the model we need market clearing conditions equating supply and demand in both Home and Foreign markets. Labour supply in each sector and each country must equal labour demand, which gives four separate labour conditions
∫ 𝐿𝐶𝑡(𝑗)𝑑𝑗 𝑠 0 = 𝜆 ∫ 𝐿𝐶,𝑆,𝑗𝑡 (𝑗)𝑑𝑗 𝑠 0 + (1 − 𝜆) ∫ 𝐿𝐶,𝐵,𝑗𝑡 (𝑗)𝑑𝑗 𝑠 0 ∫ 𝐿𝐷𝑡(𝑗)𝑑𝑗 𝑠 0 = 𝜆 ∫ 𝐿𝑡𝐷,𝑆,𝑗(𝑗)𝑑𝑗 𝑠 0 + (1 − 𝜆) ∫ 𝐿𝐷,𝐵,𝑗𝑡 (𝑗)𝑑𝑗 𝑠 0 ∫ 𝐿𝑡𝐶∗(𝑗)𝑑𝑗 1 𝑠 = 𝜆∗∫ 𝐿𝐶,𝑆,𝑗∗𝑡 (𝑗)𝑑𝑗 1 𝑠 + (1 − 𝜆∗) ∫ 𝐿𝐶,𝐵,𝑗∗𝑡 (𝑗)𝑑𝑗 1 𝑠 ∫ 𝐿𝐷∗𝑡 (𝑗)𝑑𝑗 1 𝑠 = 𝜆∗∫ 𝐿𝐷,𝑆,𝑗∗𝑡 (𝑗)𝑑𝑗 1 𝑠 + (1 − 𝜆∗) ∫ 𝐿𝐷,𝐵,𝑗∗𝑡 (𝑗)𝑑𝑗 1 𝑠 Durable goods are produced and consumed solely on a national level
𝑌𝐷= 𝜆𝐼𝑡𝑆+ (1 − 𝜆)𝐼𝑡𝐵 𝑌𝐷∗= 𝜆∗𝐼
𝑡𝑆∗+ (1 − 𝜆∗)𝐼𝑡𝐵∗
Non-durable goods are traded between countries and as such we have to take into account foreign (domestic) consumption of domestically (foreign) produced goods and the respective size of each country, which implies that
𝑠𝑌𝑡𝐶 = 𝑠[𝜆𝐶𝑡 𝐻,𝑆
+ (1 − 𝜆)𝐶𝑡𝐻,𝐵] + (1 − 𝑠)[𝜆∗𝐶𝑡𝐻,𝑆∗+ (1 − 𝜆∗)𝐶𝑡𝐻,𝐵∗] (1 − 𝑠)𝑌𝑡𝐶∗= (1 − 𝑠)[𝜆∗𝐶
𝑡𝐹,𝑆∗+ (1 − 𝜆∗)𝐶𝑡𝐹,𝐵∗] + 𝑠[𝜆𝐶𝑡𝐹,𝑆+ (1 − 𝜆)𝐶𝑡𝐹,𝐵] Aggregate production in the Home and Foreign economy is given by
𝑌𝑡 = 𝛼𝑌𝑡𝐶+ (1 − 𝛼)𝑌𝑡𝐷 𝑌𝑡∗= 𝛼∗𝑌𝑡𝐶∗+ (1 − 𝛼∗)𝑌𝑡𝐷∗
In the bond market the funds of saving household can be transferred across the monetary union as they essentially are the same asset, carrying deposit rate 𝑅𝑡11. However, borrowers can only borrow from domestic financial intermediaries. As such the balance sheet of Home and Foreign financial intermediaries is
𝑠𝜆(𝐵 + 𝑀) + 𝑠(1 − 𝜆)(𝐵𝐵) = 0
(1 − 𝑠)𝜆∗(𝐵∗+ 𝑀∗) + (1 − 𝑠)(1 − 𝜆∗)(𝐵𝐵∗) = 0
11Essentially this is identical to assuming international financial intermediaries who trade uncontingent assets between the two economies with the market clearing for international transfers as their balance sheet.
15 where 𝑀 are the international transfers of funds to the Home economy and 𝑀∗ are the equivalent transfers to the Foreign economy. The transfers between the two economies must satisfy
𝑠𝜆𝑀 + (1 − 𝑠)𝜆∗𝑀∗= 0
The law of motion of these international transfers follows from aggregation imports, exports and capital transfers and is given by
𝑠𝜆𝑀𝑡 = 𝑠𝜆𝑅𝑡−1𝑀𝑡−1+ (1 − 𝑠)𝑃𝑡𝐶,𝐻𝐶𝑡𝐻∗− 𝑠𝑃𝑡𝐶,𝐹𝐶𝑡𝐹
𝑠𝜆𝑀𝑡= 𝑠𝜆𝑅𝑡−1𝑀𝑡−1+ (1 − 𝑠)𝑃𝑡𝐶,𝐻[𝜆∗𝐶𝑡𝐻,𝑆∗+ (1 − 𝜆∗)𝐶𝑡𝐻,𝐵∗] − 𝑠𝑃𝑡𝐶,𝐹[𝜆𝐶𝑡𝐹,𝑆+ (1 − 𝜆)𝐶𝑡𝐹,𝐵]
2.5 System of Dynamic Stochastic Equations
In order to analyse the response of the model to shocks I derive the corresponding system of log-linearized equations that describe movements of the variables around the equilibrium steady state. The log-linearized equations are obtained by replacing each endogenous variable 𝑋𝑡 by 𝑋̅𝑒𝑥𝑡 where 𝑥𝑡 is the log-deviation of the variable around the steady state defined as 𝑥𝑡 = ln (
𝑋
𝑋̅) with 𝑋̅ being the steady state value of the variable. Subsequently a first order Taylor approximation is applied, resulting in the approximation 𝑋̅𝑒𝑥𝑡≈ (1 + 𝑥
𝑡)𝑋̅. The complete system of log-linearized equations consists of three blocks: conditions for the Home (Dutch) economy, an equivalent set conditions for the Foreign (EMU) economy and market clearing conditions, the monetary policy rule and specific shock processes. Additionally, I define the following
For every variable 𝑥, Δ𝑥 = 𝑥𝑡− 𝑥𝑡−1. In the case of prices I write Δ𝑝𝑡 as 𝜋𝑡, the common symbol for inflation.
The price of the durable good relative to the non-durable good is defined as 𝑄𝑡 = 𝑃𝑡𝐷⁄𝑃𝑡𝐶. The terms of trade 𝑇𝑡 are defined as 𝑇𝑡 = 𝑃𝑡𝐶,𝐹⁄𝑃𝑡𝐶,𝐻.
𝑏𝑡𝐵, is defined as the deviation of the real value of credit in non-durable consumption units from its steady state value: 𝐵𝑡𝐵/𝑃𝑡𝐶. This implies that non-durable consumption prices also appear in the log-linearized LTV-ratio (𝑏𝑡𝐵− 𝑑
𝑡𝐵− 𝑝𝑡𝐷+ 𝑝𝑡𝐶). 𝜔𝑡𝑖,𝑗
is defined as deviations from 𝑊𝑡𝑖,𝑗⁄𝑃𝑡𝐶,𝑗, for each country 𝑗 = {𝐻, 𝐹} and each sector 𝑖 = {𝐶, 𝐷} where the wages in each sector are thus divided by the non-durable CPI price level. The full derivation of the log-linearized system is found in Appendix D.
2.5.1 The Home economy
The Home economy consists of saving and borrowing households, final and intermediate good firms and financial intermediaries. Conditions for the representative saver are given by
𝜖Δ𝑐𝑡𝑆= 𝐸𝑡[Δ𝑐𝑡+1𝑆 ] − (1 − 𝜖)(𝑟𝑡− 𝐸𝑡[𝜋𝑡+1𝐶 ]) [1 − 𝛽𝑆(1 − 𝛿)](𝜁 𝑡− 𝑑𝑡𝑆) = 𝜇𝑡𝑆− 𝛽𝑆(1 − 𝛿)𝐸𝑡[𝜇𝑡+1𝑆 ] 𝑞 −𝑐𝑡 𝑆− 𝜖𝑐 𝑡−1𝑆 1 − 𝜖 + 𝛷(𝑖𝑡 𝑆− 𝑖 𝑡−1𝑆 ) = 𝜇𝑡𝑆+ 𝛽𝑆𝛷(𝐸𝑡[𝑖𝑡+1𝑆 ] − 𝑖𝑡𝑆) 𝑐𝑡𝑆− 𝜖𝑐𝑡−1𝑆 1 − 𝜖 + [(𝜑 − 𝜈)𝛼 + 𝜈]𝑙𝑡 𝑆,𝐶+ (𝜑 − 𝜈)(1 − 𝛼)𝑙 𝑡𝑆,𝐷= 𝜔𝑡𝐶 𝑐𝑡𝑆− 𝜖𝑐 𝑡−1𝑆 1 − 𝜖 + [(𝜑 − 𝜈)(1 − 𝛼) + 𝜈]𝑙𝑡 𝑆,𝐷+ (𝜑 − 𝜈)𝛼𝑙 𝑡𝑆,𝐶 = 𝜔𝑡𝐷
16 where the first equation is the standard Euler equation with habit formation, the second equation defines the optimal level of non-durable good holding, the third equation relates to the optimal level of investment (where 𝛷 = 𝑆"(. ) ) and the last two equations define labour supply for each sector. The analogous equations for domestic borrowers are:
𝜖Δ𝑐𝑡𝐵 = 𝐸𝑡[Δ𝑐𝑡+1𝐵 ] − (1 − 𝜖)(𝑟𝑡𝐿− 𝐸𝑡[𝜋𝑡+1𝐶 ]) [1 − 𝛽𝐵(1 − 𝛿)](𝜁 𝑡− 𝑑𝑡𝐵) = 𝜇𝑡𝐵− 𝛽𝐵(1 − 𝛿)𝐸𝑡[𝜇𝑡+1𝐵 ] 𝑞 −𝑐𝑡 𝐵− 𝜖𝑐 𝑡−1𝐵 1 − 𝜖 + 𝛷(𝑖𝑡 𝐵− 𝑖 𝑡−1 𝐵 ) = 𝜇 𝑡𝐵+ 𝛽𝐵𝛷(𝐸𝑡[𝑖𝑡+1𝐵 ] − 𝑖𝑡𝐵) 𝑐𝑡𝐵− 𝜖𝑐𝑡−1𝐵 1 − 𝜖 + [(𝜑 − 𝜈)𝛼 + 𝜈]𝑙𝑡 𝐵,𝐶+ (𝜑 − 𝜈)(1 − 𝛼)𝑙 𝑡𝐵,𝐷 = 𝜔𝑡𝐶 𝑐𝑡𝐵− 𝜖𝑐𝑡−1𝐵 1 − 𝜖 + [(𝜑 − 𝜈)(1 − 𝛼) + 𝜈]𝑙𝑡 𝐵,𝐷 + (𝜑 − 𝜈)𝛼𝑙𝑡𝐵,𝐶 = 𝜔𝑡𝐷
where, aside from the added 𝐵 subscript the only noticeable exception is the lending rate borrowers face. The budget constraint of the borrowing household is
𝐶̅𝐵𝐶
𝑡𝐵+ 𝐼̅𝐵(𝑞𝑡+ 𝑖𝑡𝐵) + 𝑅̅𝑡𝐿𝐵̅𝐵(𝑟𝑡−1𝐿 + 𝑏𝑡−1𝐵 − 𝜋𝑡𝐶) = 𝐵̅𝐵𝑏
𝑡𝐵+ 𝛼𝑊̅ 𝐿̅𝐵(𝜔𝑡𝐶+ 𝑙𝐶,𝐵𝑡 ) + (1 − 𝛼)𝑊̅ 𝐿̅𝐵(𝜔𝑡𝐷+ 𝑙𝑡𝐷,𝐵) The lending rate is set by financial intermediaries according to
𝑟𝑡𝐿= 𝑟𝑡+ Γ(𝑏𝑡𝐵− 𝑑𝑡𝐵− 𝑞𝑡) + 𝑣𝑡+ 𝜍(𝑏𝑡−1𝐵 − 𝑏𝑡−2𝐵 + 𝜋𝑡−1𝐶 )
Where Γ = 𝐹′(χ) is the premium borrowers are charged when their LTV-ratio deviates from its steady state level.
The CPI price level of the non-durable good is given by 𝜋𝐶 = 𝜏𝜋
𝑡𝐶,𝐻+ (1 − 𝜏)𝜋𝑡𝐶,𝐹
Since borrowers and savers have the same preferences for Home and Foreign consumption, I define import and export demand as a function of total non-durable consumption
𝑐𝑡𝐻= (1 − 𝜏)𝜂𝑡𝑡+ 𝑐𝑡𝑇𝑂𝑇 𝑐𝑡𝐹= −𝜏𝜂𝑡 𝑡+ 𝑐𝑡𝑇𝑂𝑇 Where 𝑐𝑡𝑇𝑂𝑇 is defined as 𝑐𝑡𝑇𝑂𝑇= 𝜆𝐶𝑆𝑐𝑡𝑆+ (1 − 𝜆)𝐶𝐵𝑐𝑡𝐵 𝜆𝐶𝑆+ (1 − 𝜆)𝐶𝐵 And the evolution of the terms of trade is given by
𝑡𝑡 = 𝑡𝑡−1+ 𝜋𝑡𝐶,𝐹− 𝜋𝑡𝐶,𝐻
For both household, the relative price of the non-durable good, and the law of motion for non-durable good stock evolve according to
𝑞 = 𝑞𝑡−1+ 𝜋𝑡𝐷− 𝜋𝑡𝐶 𝑑𝑡𝑆= (1 − 𝛿)𝑑𝑡−1𝑆 + 𝛿𝑖𝑡𝑆 𝑑𝑡𝐵 = (1 − 𝛿)𝑑𝑡−1𝐵 + 𝛿𝑖𝑡𝐵
17 The production functions of the firms are given by
𝑦𝑡𝐶 = 𝑎𝑡𝐶+ 𝑙𝑡𝐶,𝑇𝑂𝑇 𝑦𝑡𝐷 = 𝑙𝑡𝐷,𝑇𝑂𝑇
The pricing equations in both sectors follow Calvo-pricing and indexation behaviour assumptions and are given by 𝜋𝑡𝐶,𝐻− 𝜙𝐶𝜋𝑡−1𝐶,𝐻 = 𝛽𝑆𝐸𝑡[𝜋𝑡+1𝐶,𝐻− 𝜙𝐶𝜋𝑡𝐶,𝐻] + 𝜅𝐶[𝜔𝐶− 𝑎𝑡𝐶 + (1 − 𝜏)𝑡𝑡] 𝜋𝑡𝐷− 𝜙𝐷𝜋𝑡−1𝐷 = 𝛽𝑆𝐸𝑡[𝜋𝑡+1𝐷 − 𝜙𝐷𝜋𝑡𝐷] + 𝜅𝐷[𝜔𝐷− 𝑞𝑡] where 𝜅𝐶 =(1−𝜃𝐶)(1−𝛽𝑆𝜃𝐶) 𝜃𝐶 and 𝜅𝐶 = (1−𝜃𝐷)(1−𝛽𝑆𝜃𝐷)
𝜃𝐷 . The domestic terms of trade enter the price equation of the non-durable good essentially as a new kind of “cost-push shock” in the same spirit as the real wage and TFP.
The log-linearized market clearing conditions for hours worked in each sector are 𝑙𝑡𝐶,𝑇𝑂𝑇 =𝜆𝐿 𝑆,𝐶𝑙 𝑡𝑆,𝐶 + (1 − 𝜆)𝐿𝐵,𝐶𝑙𝑡𝐵,𝐶 𝜆𝐿𝑆,𝐶+ (1 − 𝜆)𝐿𝐵,𝐶 𝑙𝑡𝐷,𝑇𝑂𝑇=𝜆𝐿 𝑆,𝐷𝑙 𝑡𝑆,𝐷+ (1 − 𝜆)𝐿𝐵,𝐷𝑙𝑡𝐵,𝐷 𝜆𝐿𝑆,𝐷+ (1 − 𝜆)𝐿𝐵,𝐷 Market clearing in the domestic bonds market is given by
𝑠𝜆(𝑏𝑡+ 𝑚𝑡) + 𝑠(1 − 𝜆)𝑏𝑡𝐵 = 0
where 𝑚𝑡 represent transfers of savings between the two economies and 𝑏𝑡 are domestic savings and 𝑏𝑡𝐵 are domestic borrowings.
Market clearing in both goods markets is given by 𝑦𝑡𝐶 = 𝜏𝑐𝑡𝐻+ (1 − 𝑠)(1 − 𝜏∗) 𝑠 𝑐𝑡 𝐻∗ 𝑦𝑡𝐷= 𝜆𝛿𝐷𝑆𝑖𝑡𝑆+ (1 − 𝜆)𝛿𝐷𝐵𝑖𝑡𝐵 𝜆𝛿𝐷𝑆+ (1 − 𝜆)𝛿𝐷𝐵
Finally, aggregate output and inflation for the domestic country are given by 𝑦𝑡 = 𝛼𝑦𝑡𝐶+ (1 − 𝛼)𝑦𝑡𝐷
𝜋𝑡 = 𝛾𝜋𝑡𝐶+ (1 − 𝛾)𝜋𝑡𝐷
2.5.2 The Foreign Economy
The second block consists of the foreign, or EMU economy, which is symmetric to the domestic economy 𝜖∗Δ𝑐 𝑡𝑆∗ = 𝐸𝑡[Δ𝑐𝑡+1𝑆∗ ] − (1 − 𝜖∗)(𝑟𝑡− 𝐸𝑡[𝜋𝑡+1𝐶∗ ]) [1 − 𝛽𝑆(1 − 𝛿)](𝜁 𝑡∗− 𝑑𝑡𝑆∗) = 𝜇𝑡𝑆∗− 𝛽𝑆(1 − 𝛿)𝐸𝑡[𝜇𝑡+1𝑆∗ ] 𝑞∗−𝑐𝑡 𝑆∗− 𝜖∗𝑐 𝑡−1𝑆∗ 1 − 𝜖∗ + Φ∗(𝑖𝑡 𝑆∗− 𝑖 𝑡−1𝑆∗ ) = 𝜇𝑡𝑆∗+ 𝛽𝑆Φ∗(𝐸𝑡[𝑖𝑡+1𝑆∗ ] − 𝑖𝑡𝑆∗)
18 𝑐𝑡𝑆∗− 𝜖∗𝑐𝑡−1𝑆∗ 1 − 𝜖∗ + [(𝜑 ∗− 𝜈∗)𝛼∗+ 𝜈∗]𝑙 𝑡𝑆,𝐶∗+ (𝜑∗− 𝜈∗)(1 − 𝛼∗)𝑙𝑡𝑆,𝐷∗= 𝜔𝑡𝐶∗ 𝑐𝑡𝑆∗− 𝜖∗𝑐𝑡−1𝑆∗ 1 − 𝜖∗ + [(𝜑∗− 𝜈∗)(1 − 𝛼∗) + 𝜈]𝑙𝑡𝑆,𝐷∗+ (𝜑∗− 𝜈∗)𝛼∗𝑙𝑡𝑆,𝐶∗= 𝜔𝑡𝐷∗ 𝜖∗Δ𝑐𝑡𝐵∗ = 𝐸𝑡[Δ𝑐𝑡+1𝐵∗ ] − (1 − 𝜖∗)(𝑟𝑡𝐿∗− 𝐸𝑡[𝜋𝑡+1𝐶∗ ]) [1 − 𝛽𝐵(1 − 𝛿)](𝜁 𝑡∗− 𝑑𝑡𝐵∗) = 𝜇𝑡𝐵∗− 𝛽𝐵(1 − 𝛿)𝐸𝑡[𝜇𝑡+1𝐵∗ ] 𝑞∗−𝑐𝑡 𝐵∗− 𝜖∗𝑐 𝑡−1𝐵∗ 1 − 𝜖∗ + Φ∗(𝑖𝑡𝐵∗− 𝑖𝑡−1𝐵∗ ) = 𝜇𝑡𝐵∗+ 𝛽𝐵Φ∗(𝐸𝑡[𝑖𝑡+1𝐵∗ ] − 𝑖𝑡𝐵∗) 𝑐𝑡𝐵∗− 𝜖∗𝑐𝑡−1𝐵∗ 1 − 𝜖∗ + [(𝜑∗− 𝜈∗)𝛼∗+ 𝜈∗]𝑙𝑡𝐵,𝐶∗+ (𝜑∗− 𝜈∗)(1 − 𝛼∗)𝑙𝑡𝐵,𝐷∗ = 𝜔𝑡𝐶∗ 𝑐𝑡𝐵∗− 𝜖𝑐𝑡−1𝐵∗ 1 − 𝜖∗ + [(𝜑∗− 𝜈∗)(1 − 𝛼∗) + 𝜈∗]𝑙𝐵,𝐷∗𝑡 + (𝜑∗− 𝜈∗)𝛼∗𝑙𝑡𝐵,𝐶∗ = 𝜔𝑡𝐷∗ 𝐶̅𝐵∗𝐶𝑡𝐵∗+ 𝐼̅𝐵∗(𝑞𝑡∗+ 𝑖𝑡𝐵∗) + 𝑅̅𝑡𝐿∗𝐵̅𝐵∗(𝑟𝑡−1𝐿∗ + 𝑏𝑡−1𝐵∗ − 𝜋𝑡𝐶∗) = 𝐵̅𝐵∗𝑏 𝑡𝐵∗+ 𝛼∗𝑊̅∗𝐿̅𝐵∗(𝜔𝑡𝐶∗+ 𝑙𝐶,𝐵∗𝑡 ) + (1 − 𝛼∗)𝑊̅∗𝐿̅𝐵∗(𝜔𝑡𝐷∗+ 𝑙𝑡𝐷,𝐵∗) 𝑟𝑡𝐿∗= 𝑟𝑡+ Γ∗(𝑏𝑡𝐵∗− 𝑑𝑡𝐵∗− 𝑞𝑡∗) + 𝑣𝑡∗+ 𝜍∗(𝑏𝑡−1𝐵∗ − 𝑏𝑡−2𝐵∗ + 𝜋𝑡−1𝐶∗ ) 𝜋𝐶∗= (1 − 𝜏∗)𝜋𝑡𝐶,𝐻+ 𝜏∗𝜋𝑡𝐶,𝐹 𝑐𝑡𝐻∗= 𝜏∗𝜂𝑡𝑡+ 𝑐𝑡𝑇𝑂𝑇∗ 𝑐𝑡𝐹∗= −(1 − 𝜏∗)𝜂𝑡𝑡+ 𝑐𝑡𝑇𝑂𝑇∗ 𝑐𝑡𝑇𝑂𝑇∗ = 𝜆∗𝐶𝑆∗𝑐 𝑡𝑆∗+ (1 − 𝜆∗)𝐶𝐵∗𝑐𝑡𝐵∗ 𝜆∗𝐶𝑆∗+ (1 − 𝜆∗)𝐶𝐵∗ 𝑞∗= 𝑞𝑡−1∗ + 𝜋𝑡𝐷∗− 𝜋𝑡𝐶∗ 𝑑𝑡𝑆∗= (1 − 𝛿)𝑑𝑡−1𝑆∗ + 𝛿𝑖𝑡𝑆∗ 𝑑𝑡𝐵∗= (1 − 𝛿)𝑑 𝑡−1 𝐵∗ + 𝛿𝑖 𝑡𝐵∗ 𝑦𝑡𝐶∗= 𝑎𝑡𝐶∗+ 𝑙𝑡 𝐶,𝑇𝑂𝑇∗ 𝑦𝑡𝐷∗= 𝑙𝑡𝐷,𝑇𝑂𝑇∗ 𝜋𝑡𝐶,𝐹− 𝜙𝐶∗𝜋 𝑡−1𝐶,𝐹 = 𝛽𝑆𝐸𝑡[𝜋𝑡+1𝐶,𝐹 − 𝜙𝐶∗𝜋𝑡𝐶,𝐹] + 𝜅𝐶∗[𝜔𝐶∗− 𝑎𝑡𝐶∗− (1 − 𝜏∗)𝑡𝑡] 𝜋𝑡𝐷∗− 𝜙𝐷∗𝜋 𝑡−1𝐷∗ = 𝛽𝑆𝐸𝑡[𝜋𝑡+1𝐷∗ − 𝜙𝐷∗𝜋𝑡𝐷∗] + 𝜅𝐷∗[𝜔𝐷∗− 𝑞𝑡∗]
Where 𝜅𝐶∗=(1−𝜃𝐶∗)(1−𝛽𝜃𝐶∗ 𝑆𝜃𝐶∗) and 𝜅𝐶∗=(1−𝜃𝐷∗)(1−𝛽𝜃𝐷∗ 𝑆𝜃𝐷∗) . Market clearing conditions in the Foreign economy are 𝑙𝑡𝐶,𝑇𝑂𝑇∗=𝜆 ∗𝐿𝑆,𝐶∗𝑙 𝑡𝑆,𝐶∗+ (1 − 𝜆∗)𝐿𝐵,𝐶∗𝑙𝑡𝐵,𝐶∗ 𝜆∗𝐿𝑆,𝐶∗+ (1 − 𝜆∗)𝐿𝐵,𝐶∗ 𝑙𝑡𝐷,𝑇𝑂𝑇∗=𝜆 ∗𝐿𝑆,𝐷∗𝑙 𝑡𝑆,𝐷∗+ (1 − 𝜆∗)𝐿𝐵,𝐷∗𝑙𝑡𝐵,𝐷∗ 𝜆∗𝐿𝑆,𝐷∗+ (1 − 𝜆∗)𝐿𝐵,𝐷∗ (1 − 𝑠)𝜆∗(𝑏 𝑡∗+ 𝑚𝑡∗) + (1 − 𝑠)(1 − 𝜆∗)𝑏𝑡𝐵∗= 0
19 𝑦𝑡𝐶∗= 𝜏∗𝑐 𝑡𝐹+ 𝑠(1 − 𝜏) 1 − 𝑠 𝑐𝑡 𝐹 𝑦𝑡𝐷∗= 𝜆∗𝛿𝐷𝑆∗𝑖𝑡𝑆∗+ (1 − 𝜆∗)𝛿𝐷𝐵∗𝑖𝑡𝐵∗ 𝜆∗𝛿𝐷𝑆∗+ (1 − 𝜆∗)𝛿𝐷𝐵∗ Aggregate output and inflation in the Foreign economy are given by
𝑦𝑡∗= 𝛼∗𝑦𝑡𝐶∗+ (1 − 𝛼∗)(𝑦𝑡𝐷∗+ 𝑞∗) 𝜋𝑡∗= 𝛾∗𝜋
𝑡𝐶∗+ (1 − 𝛾∗)𝜋𝑡𝐷∗
where I have made use of 𝑡𝑡∗= −𝑡𝑡 and the assumption that the parameters 𝛽𝑆, 𝛽𝐵, 𝛿, 𝜎𝐷, 𝜎𝐶 and 𝜂 are identical in the Home and Foreign economy.
2.5.3 The Monetary Union
On the aggregate monetary union level we have the equations relating to monetary policy, its objectives and the evolution of the current account. Monetary policy, as conducted by the ECB, is given by
𝑟𝑡 = 𝛾𝑅(𝑟𝑡−1) + (1 − 𝛾𝑅)[𝛾π𝜋𝑡𝐶,𝐸𝑀𝑈+ 𝛾𝑌(𝑌𝐸𝑀𝑈− 𝑌𝑡−1𝐸𝑀𝑈)] where
𝜋𝑡𝐶,𝐸𝑀𝑈= 𝑠𝜋𝑡𝐶+ (1 − 𝑠)𝜋𝑡𝐶,∗ 𝑦𝐸𝑀𝑈= 𝑠𝑦 + (1 − 𝑠)𝑦∗ Market clearing in the international transfer of bonds is given by
𝑠𝜆𝑚𝑡+ (1 − 𝑠)𝜆𝑚𝑡∗= 0 where the evolution of these transfers is given by
𝜆𝑚𝑡 = 𝜆 1 𝛽𝑆𝑚𝑡−1+ (1 − 𝑠)(1 − 𝜏∗) 𝑠 (𝑐𝑡 𝐻− 𝑡 𝑡) − (1 − 𝜏)𝑐𝑡𝐹 Finally, we have the following shock processes in the model
𝑎𝑡𝐶 = 𝜌𝑎𝑎𝑡−1𝐶 + 𝜀𝑡𝑎+ 𝜀𝑡𝑎,𝐸𝑀𝑈 𝜁𝑡 = 𝜌𝜁𝜁𝑡−1+ 𝜀𝑡𝜁+ 𝜀𝑡𝜁,𝐸𝑀𝑈 𝑣𝑡 = 𝜌𝑣𝑣𝑡−1+ 𝜀𝑡𝑣+ 𝜀𝑡𝑣,𝐸𝑀𝑈 𝑎𝑡𝐶∗= 𝜌𝑎∗𝑎𝑡−1𝐶∗ + 𝜀𝑡𝑎∗+ 𝜀𝑡 𝑎,𝐸𝑀𝑈 𝜁𝑡∗= 𝜌𝜁∗𝜁𝑡−1∗ + 𝜀𝑡 𝜁∗ + 𝜀𝑡𝜁,𝐸𝑀𝑈 𝑣𝑡∗= 𝜌𝑣∗𝑣𝑡−1∗ + 𝜀𝑡𝑣∗+ 𝜀𝑡𝑣,𝐸𝑀𝑈
where the shocks common to both economies carry the label 𝐸𝑀𝑈. In my analysis, I will ignore the shocks specific to the Foreign economy as these represent the unlikely event of an economic shock affecting the entire EMU except for the Netherlands. In the following simulations I instead focus on EMU-wide and Home economy shocks. I first discuss the calibration of the model parameters.
20
3. Calibration
The parameters of the model follow primarily from the original version of the model by Kannan et al. (2012) and from Quint et al (2013). Where the parameters used by the first are calibrated to match U.S. data, the latter provides estimates of most parameters for the EMU area which are thus preferable. I estimate the standard deviations and AR(1) coefficients of the Home and common EMU-wide shocks in order to match the model on the data. Below, I first detail the calibrated parameters, followed by the results of the estimations.
The calibrated parameters are summarized in Table 1. The parameters 𝑠, 𝜏 and 𝜏∗(respectively: the share of the Home (Dutch) economy in the monetary union, the share of domestic non-durable consumption in total non-durable consumption in the Home economy and in the Foreign economy) are new to the model and are set according to aggregate GDP and import/export data12 following methods
similar to those used by Aspachs-Bracon et al. (2013) and Quint et al. (2013).
Table 1: Calibrated Parameters
Parameter Description Value
𝑠 Share of Home economy in MU 0.07
1 − 𝜏 Share of domestic imported non-durable consumption 0.09 1 − 𝜏∗ Share of foreign imported non-durable consumption 0.01
𝛽𝑠 Discount factor savers 0.99
𝛽𝐵 Discount factor borrowers 0.98
𝜆 Share of savers 0.5
𝛼 Share of non-durable production in GDP 0.9
𝜖 Habit formation parameter 0.3
𝛿 Depreciation of durable good 0.025
𝜑 Inverse elasticity of labour supply 1
𝜈 Costly readjustment of labour supply 1
𝛾 Share of non-durable consumption in utility function 0.79
𝜂 Cross country readjustment cost of consumption 1
𝜎 𝜎 − 1⁄ Average mark-up 1.1
𝛷 Investment adjustment costs 0.65
𝛷∗ Investment adjustment costs 1.75
𝜒 Steady state LTV ratio in the Home economy 1
𝜒∗ Steady state LTV ratio in the Foreign economy 0.8
Γ Elasticity of lending rate spread to LTV ratio in the Home economy 0.04
21 Γ∗ Elasticity of lending rate spread to LTV ratio in the Home economy 0.04
𝜃𝐶 Calvo Lottery Non-durable 0.70
𝜃𝐷 Calvo Lottery Durable 0.70
𝜃𝐶∗ Calvo Lottery Non-durable 0.70
𝜃𝐷∗ Calvo Lottery Durable 0.70
𝜙𝐶 Indexation Non-durable 0.30
𝜙𝐷 Indexation Durable 0.30
𝜙𝐶∗ Indexation Non-durable 0.30
𝜙𝐷∗ Indexation Durable 0.30
𝛾𝑅 Monetary parameter on interest rate 0.7
𝛾𝜋 Monetary parameter on inflation 1.25
𝛾𝑌 Monetary parameter on output deviations 0.2
𝜍 Macroprudential instrument in Home economy 0.3
𝜍∗ Macroprudential instrument in Foreign economy 0.3
𝜌𝑎∗ AR(1) Coefficient Foreign non-durable TFP shock 0.79
𝜌𝜁∗ AR(1) Coefficient Foreign durable preference shock 0.98
𝜌𝑣∗ AR(1) Coefficient Foreign financial shock 0.85
𝜎𝐶∗ Standard deviation Foreign non-durable TFP shock (in %) 0.83 𝜎𝜁∗ Standard deviation Foreign durable preference shock (in %) 1.46 𝜎𝑣∗ Standard deviation Foreign financial shock (in %) 0.23
The parameters concerning the share of savers, household preferences, depreciation rate and share of non-durables in GDP are all set according to the original model and are all well within the ranges of values commonly used in two-country, two-sector DSGE models13. These parameters are
assumed to be identical in the two economies; a common assumption in two country models.
Notable exceptions to this are the habit formation parameter 𝜖 and the investment adjustment cost 𝛷, 𝛷∗. In the original model the habit formation parameter is calibrated exceptionally high at 𝜖 = 0.8. I opt instead for a lower value of 𝜖 = 0.3, below the EMU estimates by Quint et al. (2013). Moving below their average of about 0.5 allows the model to explain better the volatility in consumption growth found in the data. The U.S. data used to calibrate the original model deviates the strongest from the data on the Dutch economy in the area of consumption growth, which is significantly more volatile over the sample period. This parameter is assumed to be identical cross-country.
The EMU investment adjustment cost is set according to EMU estimates by Quint (𝛷∗= 1.75). Its Home economy counterpart is calibrated at a lower level in order to better explain the investment
13 The parameter 𝛾, the share of non-durable consumption in the utility function, cannot be calibrated separately but is a function of 𝜆, 𝜖, 𝛽𝑆,𝛽𝐵,𝛼, 𝛿 and 𝜑 as detailed in appendix
22 volatility found in the data (𝛷 = .65). The standard deviation of investment growth found in the Dutch data is similar to the one found in the original U.S. data.
The steady state LTV ratio (𝜒) and the elasticity of the lending rate spread to the LTV ratio (Γ) are both parameters essential to the model’s financial accelerator mechanism. The first is relevant as it defines the steady state level of borrowings 𝐵𝐵 in each economy. As described in section 1, the Netherlands has a relatively high LTV ratio of around 100%. This implies that in the steady state of the model, domestic impatient households fully fund their durable good (housing) consumption by borrowing. Though this ratio is being guided down, the current economy is still characterised by this high LTV ratio and I thus calibrate 𝜒 = 1. For the EMU I calibrate a lower, more common, steady state LTV ratio similar to the level proposed by Kannan et al. (𝜒∗= 0.8). This level of the LTV ratio is further supported by European mortgage surveys (ECB, 2009).
The elasticity of the spread to the LTV ratio is a crucial parameter to the model mechanics but difficult to define. Rough estimates are found in the work of Ambrose et al. (2006), who studies a large dataset of individual loans from a selection of countries. Filtering for borrower characteristics, he finds the elasticity of the LTV ratio to the lending rate to be between 0.02 and 0.06. In the original model, Kannan et al. calibrate this value to 0.02 (the equivalent parameter of Γ in their model is 𝜅), which is thus on the lower end of the estimates found by Ambrose et al. (2006). As such I calibrate both the Home and Foreign elasticity at a slightly higher level, without differentiating between the two economies (Γ = Γ∗= 0.04). As this parameter captures one of the essential mechanisms of the model, I test the sensitivity of the results to its calibration in section 5.
The parameters relating to pricing in the Home and Foreign economy are all set according to EMU estimates by Quint et al. (2013). The values he estimates differ from those in similar studies such as Smets and Wouters (2003). However, I prefer those estimates over other studies as the model they employ is similar to the one I use and a data sample period similar to mine. I deviate here from Kannan, who in the original model set indexation to 𝜙𝐶 = 𝜙𝐷= 1, which is both unrealistic as well as incompatible with my data.
As the parameters in the monetary policy rule concern the aggregate EMU, I take their estimates directly from Quint et al (2013). Moreover, these estimates do not differ greatly from those used in the original model. The macroprudential instrument is taken from Kannan; primarily since this parameter is non-existent in the Quint model and its function is largely demonstrative14.
The shocks to the Foreign economy are set according to the EMU estimates by Quint whereas the Home and common EMU-wide shocks are estimated to match data on the Netherlands. The data set I target consists of three observables: (non-durable) consumption growth, investment growth and CPI inflation. The data is collected on a quarterly basis and ranges from1995Q1 to 2015Q4. The data has been demeaned and transformed in a similar fashion to the original model data15. In order to match the
model variables with the data I construct two additional observable variables, defined as Δ𝑐𝑡𝑇𝑂𝑇 = 𝑐𝑡𝑇𝑂𝑇− 𝑐𝑡−1𝑇𝑂𝑇 Δ𝑖𝑡𝑇𝑂𝑇= 𝑖𝑡𝑇𝑂𝑇− 𝑖𝑡−1𝑇𝑂𝑇 where 𝑖𝑡𝑇𝑂𝑇=𝜆𝛿𝐷̅ 𝑆𝑖 𝑡 𝑆+ (1 − 𝜆)𝛿𝐷̅𝐵𝑖 𝑡 𝐵 𝜆𝛿𝐷̅𝑆+ (1 − 𝜆)𝛿𝐷̅𝐵
14 Kannan et al report difficulties in adequately estimating this parameter when optimizing monetary policy as it is always optimal for the monetary authority to set 𝜍 at an infinitely high value to supress any credit growth. 15 The data sources and manipulations can be found in appendix E.
23 and 𝑐𝑡𝑇𝑂𝑇 has been previously defined in the model. CPI inflation doesn’t require additional
observation equations as this already has a perfect equivalent in the model (𝜋). I use Bayesian estimation techniques and prior distributions by Quint et al. (2003) to obtain the posterior modes reported in table 2. All estimates are rounded to two digits.
Table 2: Prior Distributions and Posterior modes of shock processes
Parameter Prior distribution Posterior mode
AR(1) coefficients
𝜌𝑎 Non-durable TFP shock 𝛣(0.8; 0.1) 0.79
𝜌𝜁 Durable preference shock 𝛣(0.8; 0.1) 0.96
𝜌𝑣 Financial shock 𝛣(0.8; 0.1) 0.95
Std. Dev. Shocks (in percent)
𝜎𝐶 Home non-durable TFP shock 𝐼𝐺(0.7; 0.1) 0.51
𝜎𝜁 Home durable preference shock 𝐼𝐺(0.7; 0.1) 3.56
𝜎𝑣 Home financial shock 𝐼𝐺(0.4; 0.1) 0.92
𝜎𝐶,𝐸𝑀𝑈 EMU non-durable TFP shock 𝐼𝐺(0.7; 0.1) 0.58
𝜎𝜁,𝐸𝑀𝑈 EMU durable preference shock 𝐼𝐺(0.7; 0.1) 0.60
𝜎𝑣,𝐸𝑀𝑈 EMU financial shock 𝐼𝐺(0.4; 0.1) 0.22
As both in the estimation by Quint and in the original model the AR(1) coefficients of the shocks are set at relatively high levels, I chose to set high, informative (small 𝜎) prior distributions. The estimated persistence of the non-durable productivity shocks differs the most from the original paper. This is the result of opening up of the economy to trade in non-durables: as non-durables are now imported and exported within the monetary union, shocks in domestic productivity fade out quicker and have a less significant impact on the overall economy. As the other two shocks centre on fully domestic markets (durables and borrowing), their persistence in the economy is markedly higher and similar to the values reported in Kannan et al. (2012).
Prior distributions of the standard deviations follow inverse gamma distributions with uninformative priors in order to allow the shocks to match the model. As in the original version of the model, the durable good preference shock is found to be the most important. The technology shock in the non-durable sector is found to be relatively less important while the financial shock takes a far more prominent role compared to the original model.
Following these estimations, and the calibrated parameters as described, the standard deviations of the model and the data as well as the variance decomposition are provided in table 3. The model succeeds relatively well in explaining the volatility of investment growth, and consumption growth though it overstates the volatility of CPI inflation. This can argued to be the result of trade. As non-durables are traded and make up a significant share of CPI inflation, prices are volatile to productivity shocks in the Foreign economy too.
