Abstract
This paper documents the theoretical structure and empirical properties of the latest version of the Global Macrofinancial Model (GFM). This dynamic stochastic general equilibrium model of the world economy, disaggregated into forty national economies, was developed to support multilaterally consistent macrofinancial policy, risk and spillover analysis. It features a range of nominal and real rigidities, extensive macrofinancial linkages, and diverse spillover transmission channels. These macrofinancial linkages encompass bank and capital market based financial intermediation, with financial accelerator mechanisms linked to the values of the housing and physical capital stocks. A variety of monetary policy analysis, fiscal policy analysis, macroprudential policy analysis, spillover analysis, and forecasting applications of the GFM are demonstrated. These include quantifying the monetary, fiscal and macroprudential policy transmission mechanisms, accounting for business cycle fluctuations, and generating relatively accurate forecasts of inflation and output growth.
I. Introduction
The Global Financial Crisis (GFC) highlighted the potency of macrofinancial linkages, both within and across economies. Much progress has since been made in incorporating macrofinancial linkages into structural macroeconometric models within economies, but less has been made across economies. The development of highly disaggregated structural macroeconometric models of the world economy featuring extensive macrofinancial linkages along both dimensions is prerequisite to the effective integration of multilateral and bilateral surveillance at the International Monetary Fund (IMF).
This paper documents the theoretical structure and empirical properties of the latest version of the Global Macrofinancial Model (GFM). This dynamic stochastic general equilibrium (DSGE) model of the world economy, disaggregated into forty national economies, was developed to support multilaterally consistent macrofinancial policy, risk and spillover analysis at the IMF. It features a range of nominal and real rigidities, extensive macrofinancial linkages, and diverse spillover transmission channels. These macrofinancial linkages encompass bank and capital market based financial intermediation, with financial accelerator mechanisms linked to the values of the housing and physical capital stocks. A variety of monetary policy analysis, fiscal policy analysis, macroprudential policy analysis, spillover analysis, and forecasting applications of the GFM are demonstrated. These include quantifying the monetary, fiscal and macroprudential policy transmission mechanisms, accounting for business cycle fluctuations, and generating relatively accurate forecasts of inflation and output growth.
The theoretical structure of the GFM builds on the canonical New Keynesian model of an open economy due to Galí and Monacelli (2005). In particular, following Smets and Wouters (2003) the GFM features short run nominal price and wage rigidities generated by monopolistic competition, staggered reoptimization, and partial indexation in the output and labor markets. Building on Christiano, Eichenbaum and Evans (2005), the resultant inertia in inflation and persistence in output is enhanced with other features such as habit persistence in consumption, adjustment costs in residential and business investment, and variable capital utilization. Following Galí (2011), the model incorporates involuntary unemployment though a reinterpretation of the labor market. Households are differentiated according to whether they are bank intermediated, capital market intermediated, or credit constrained. Bank intermediated households have access to domestic banks where they accumulate deposits, as well as to domestic property markets where they trade real estate, whereas capital market intermediated households have access to domestic and foreign capital markets where they trade money, bond and stock market securities. Motivated by Tobin (1969), these households solve portfolio balance problems, allocating their financial wealth across alternative assets which are imperfect substitutes. Firms are grouped into differentiated industries. The energy and nonenergy commodity industries produce internationally homogeneous goods for foreign absorption, while all other industries produce internationally heterogeneous goods for domestic and foreign absorption. Banks perform global financial intermediation subject to financial frictions and regulatory constraints. Building on Hülsewig, Mayer and Wollmershäuser (2009), they issue risky mortgage loans to domestic developers at infrequently adjusted predetermined mortgage loan rates, as well as risky domestic currency denominated corporate loans to domestic and foreign firms at infrequently adjusted predetermined corporate loan rates, given regulatory loan to value ratio limits. Also building on Gerali, Neri, Sessa and Signoretti (2010), they obtain funding from domestic bank intermediated households via deposits and from the domestic money market via loans, accumulating bank capital out of retained earnings given credit losses to satisfy a regulatory capital requirement. Motivated by Kiyotaki and Moore (1997), the GFM incorporates financial accelerator mechanisms linked to borrowing by developers and firms collateralized against the values of the housing and physical capital stocks, respectively. Finally, building on Monacelli (2005) the model accounts for short run incomplete exchange rate pass through with short run nominal price rigidities generated by monopolistic competition, staggered reoptimization, and partial indexation in the export and import markets.
The parameterization of the GFM is based on a mix of calibration and estimation. In particular, subsets of the parameters and variables of the GFM are jointly estimated by full information maximum likelihood, conditional on calibrated values of its other parameters and observed values of its other variables. To cope with the curse of dimensionality—which manifests through an explosion in the number of parameters as the numbers of economies and variables increase— behavioral and innovation standard deviation parameters are restricted to coincide across economies, occasionally within groups sharing a structural characteristic. In contrast, structural characteristics represented by great ratios and bilateral exposures implied by steady state equilibrium relationships are economy specific.
This paper is the latest in a series documenting the progressive development of the GFM. In response to the increasing multilateral and bilateral surveillance demands placed on the model at the IMF, it has been periodically extended and refined to enhance its macrofinancial policy, risk and spillover analysis capabilities. Previous versions of the GFM were used to simulate many global macrofinancial risk scenarios for the Global Financial Stability Report, as well as many banking sector solvency stress test scenarios for the Financial Sector Assessment Program. Relative to the previous version of the GFM documented in Vitek (2017), the version of the model documented in this paper primarily extends or refines its terms of trade dynamics, fiscal instrument set, and interbank market. This previous version of the GFM primarily added a housing sector to the version of the model documented in Vitek (2015), which in turn primarily added a banking sector to the version documented in Vitek (2014).
The organization of this paper is as follows. The next section develops the nonlinear theoretical structure of the GFM, while the following section describes its corresponding approximate linear structure. The parameterization of the model is the subject of section four. Policy and spillover analysis within the framework of the GFM is conducted in section five, while forecasting is undertaken in section six. Finally, section seven offers conclusions and outlines future model development plans.
II. The Theoretical Framework
Consider a finite set of structurally isomorphic national economies indexed by i ϵ {1,…N} which constitutes the world economy. Each of these economies consists of households, developers, firms, banks, and a government. The government in turn consists of a monetary authority, a fiscal authority, and a macroprudential authority. Households, developers, firms and banks optimize intertemporally, interacting with governments in an uncertain environment to determine equilibrium prices and quantities under rational expectations in globally integrated output and financial markets. Economy i* issues the quotation currency for transactions in the foreign exchange market.
A. The Household Sector
There exists a continuum of households indexed by h ϵ [0,1]. Households are differentiated according to whether they are credit constrained, and according to how they save if they are credit unconstrained, but are otherwise identical. Credit unconstrained households of type Z = B and measure ϕB have access to domestic banks where they accumulate deposits, and to domestic property markets where they trade real estate, where 0 < ϕB < 1. In contrast, credit unconstrained households of type Z = A and measure ϕA have access to domestic and foreign capital markets where they trade financial assets, where 0 < ϕA < 1. Finally, credit constrained households of type Z = C and measure ϕC do not have access to banks or capital markets, where 0 < ϕC < 1 and ϕB + ϕA + ϕC = 1. All households are originally endowed with one share of each domestic developer, firm and bank.
In a reinterpretation of the labor market in the model of nominal wage rigidity proposed by Erceg, Henderson and Levin (2000) to incorporate involuntary unemployment along the lines of Galí (2011), each household consists of a continuum of members represented by the unit square and indexed by (f, g) ϵ [0,1] × [0,1]. There is full risk sharing among household members, who supply indivisible differentiated intermediate labor services indexed by f ϵ [0,1], incurring disutility from work determined by g ϵ [0,1] if they are employed and zero otherwise. Trade specific intermediate labor services supplied by bank intermediated, capital market intermediated, and credit constrained households are perfect substitutes.
Consumption and Saving
The representative infinitely lived household has preferences defined over consumption Ch,i,s, housing Hh,i,s, labor supply
where Et denotes the expectations operator conditional on information available in period t, and 0 < β < 1. The intratemporal utility function is additively separable and represents external habit formation preferences in consumption and labor supply,
where 0 ≤ αC < 1 and 0 ≤ αL < 1. Endogenous preference shifters
where ι > 0. The intratemporal utility function is strictly increasing with respect to consumption if and only if serially correlated consumption demand shock
The representative household enters period s in possession of previously accumulated property balances
According to this dynamic budget constraint, at the end of period s, the representative household holds property balances
The local currency denominated values of economy specific long term bond portfolios
Bank Intermediated Households
The representative bank intermediated household has a capitalist spirit motive for holding real property balances, independent of financing deferred consumption, motivated by Weber (1905). It also has a diversification motive over the allocation of real property balances across alternative assets which are imperfect substitutes, motivated by Tobin (1969). The set of assets under consideration consists of bank deposits and domestically traded real estate. Preferences over the real values of bank deposits
where serially correlated housing risk premium shock
In the limit as
In period t, the representative bank intermediated household chooses state contingent sequences for consumption
which equates the expected present value of the gross real property return to one. In addition, these solutions satisfy intratemporal optimality condition
which equates the marginal rate of substitution between housing and consumption to the real rental price of housing. Furthermore, these solutions satisfy intratemporal optimality condition
which equates the marginal rate of substitution between leisure and consumption for the marginal trade specific labor force participant to the corresponding after tax real wage. Abstracting from risk premium shocks, the expected present value of the gross real property return satisfies intratemporal optimality condition
which relates it to the expected present values of the gross real returns on bank deposits and real estate. Finally, abstracting from the portfolio diversification motive over the allocation of real property balances these solutions satisfy intratemporal optimality condition
which equates the expected present values of the gross real risk adjusted returns on bank deposits and real estate. Provided that the intertemporal utility function is bounded and strictly concave, together with other optimality conditions, and transversality conditions derived from necessary complementary slackness conditions associated with the terminal nonnegativity constraints, these optimality conditions are sufficient for the unique utility maximizing state contingent sequence of bank intermediated household allocations.
Capital Market Intermediated Households
The representative capital market intermediated household has a capitalist spirit motive for holding real portfolio balances, independent of financing deferred consumption, motivated by Weber (1905). It also has a diversification motive over the allocation of real portfolio balances across alternative financial assets which are imperfect substitutes, motivated by Tobin (1969). The set of financial assets under consideration consists of internationally traded and local currency denominated short term bonds, long term bonds, and stocks. Short term bonds are discount bonds, while long term bonds are perpetual bonds with coupon payments that decay exponentially at rate ωB where 0 < ωB < 1, following Woodford (2001). Preferences over the real values of internationally diversified short term bond
where internationally and serially correlated duration risk premium shock
where serially correlated currency risk premium shocks
where
In period t, the representative capital market intermediated household chooses state contingent sequences for consumption
which equates the expected present value of the gross real portfolio return to one. In addition, these solutions satisfy intratemporal optimality condition
which equates the marginal rate of substitution between housing and consumption to the real rental price of housing. Furthermore, these solutions satisfy intratemporal optimality condition
which equates the marginal rate of substitution between leisure and consumption for the marginal trade specific labor force participant to the corresponding after tax real wage. Abstracting from risk premium shocks, the expected present value of the gross real portfolio return satisfies intratemporal optimality condition
which relates it to the expected present values of the gross real returns on domestic and foreign short term bonds, long term bonds, and stocks. In addition, abstracting from the portfolio diversification motive over the allocation of real portfolio balances these solutions satisfy intratemporal optimality condition
which equates the expected present values of the gross real risk adjusted returns on domestic and foreign short term bonds. Furthermore, abstracting from the portfolio diversification motive over the allocation of real portfolio balances these solutions satisfy intratemporal optimality condition
which equates the expected present values of the gross real risk adjusted returns on domestic short and long term bonds. Finally, abstracting from the portfolio diversification motive over the allocation of real portfolio balances these solutions satisfy intratemporal optimality condition
which equates the expected present values of the gross real risk adjusted returns on domestic short term bonds and stocks. Provided that the intertemporal utility function is bounded and strictly concave, together with other optimality conditions, and transversality conditions derived from necessary complementary slackness conditions associated with the terminal nonnegativity constraints, these optimality conditions are sufficient for the unique utility maximizing state contingent sequence of capital market intermediated household allocations.
Credit Constrained Households
In period t, the representative credit constrained household chooses state contingent sequences for consumption
which equates the sum of consumption and housing expenditures to the sum of profit and disposable labor income net of transfer payments, where profit income Πi,t satisfies
which equates the marginal rate of substitution between housing and consumption to the real rental price of housing. Finally, these solutions satisfy intratemporal optimality condition
which equates the marginal rate of substitution between leisure and consumption for the marginal trade specific labor force participant to the corresponding after tax real wage. Provided that the intertemporal utility function is bounded and strictly concave, these optimality conditions are sufficient for the unique utility maximizing state contingent sequence of credit constrained household allocations.
Labor Supply
The unemployment rate
There exist a large number of perfectly competitive firms which combine differentiated intermediate labor services Lf,i,t supplied by trade unions of workers to produce final labor service Li,t according to constant elasticity of substitution production function
where serially uncorrelated wage markup shock
Since the production function exhibits constant returns to scale, in equilibrium the representative final labor service firm generates zero profit, implying aggregate wage index:
As the wage elasticity of demand for intermediate labor services
In an extension of the model of nominal wage rigidity proposed by Erceg, Henderson and Levin (2000) along the lines of Smets and Wouters (2003), each period a randomly selected fraction 1 − ωL of trade unions adjust their wage optimally, where 0 ≤ ωL < 1. The remaining fraction ωL of trade unions adjust their wage to account for past consumption price inflation and trend productivity growth according to partial indexation rule
where 0 ≤ γL < 1. Under this specification, although trade unions adjust their wage every period, they infrequently do so optimally, and the interval between optimal wage adjustments is a random variable.
If the representative trade union can adjust its wage optimally in period t, then it does so to maximize intertemporal utility function (1) subject to dynamic budget constraint (7), intermediate labor service demand function (32), and the assumed form of nominal wage rigidity. Since all trade unions that adjust their wage optimally in period t solve an identical utility maximization problem, in equilibrium they all choose a common wage
This necessary first order condition equates the expected present value of the marginal utility of consumption gained from labor supply to the expected present value of the marginal utility cost incurred from leisure foregone. Aggregate wage index (33) equals an average of the wage set by the fraction 1 − ωL of trade unions that adjust their wage optimally in period t, and the average of the wages set by the remaining fraction of trade unions that adjust their wage according to partial indexation rule (34):
Since those trade unions able to adjust their wage optimally in period t are selected randomly from among all trade unions, the average wage set by the remaining trade unions equals the value of the aggregate wage index that prevailed during period t − 1, rescaled to account for past consumption price inflation and trend productivity growth.
B. The Construction Sector
The construction sector supplies housing services to domestic households. In doing so, developers obtain mortgage loans from domestic banks and accumulate the housing stock through residential investment.
Housing Demand
There exist a large number of perfectly competitive developers which combine differentiated intermediate housing services Hi,e,t supplied by intermediate developers to produce final housing service Hi,t according to constant elasticity of substitution production function
where endogenous rental price of housing markup shifter
Since the production function exhibits constant returns to scale, in equilibrium the representative final developer generates zero profit, implying aggregate rental price of housing index:
As the price elasticity of demand for intermediate housing services
Residential Investment
There exist continuums of monopolistically competitive intermediate developers indexed by e ∈ [0,1]. Intermediate developers supply differentiated intermediate housing services, but are otherwise identical. We rule out entry into and exit out of the monopolistically competitive intermediate construction sector.
The representative intermediate developer sells shares to domestic bank intermediated households at price
where
Shares entitle households to dividend payments equal to profits
Earnings are defined as revenues derived from sales of differentiated intermediate housing service Hi,e,s at rental price
Motivated by the collateralized borrowing variant of the financial accelerator mechanism due to Kiyotaki and Moore (1997), the financial policy of the representative intermediate developer is to maintain debt equal to a fraction of the value of the housing stock,
given by regulatory mortgage loan to value ratio limit
The representative intermediate developer enters period s in possession of previously accumulated housing stock Hi,e,s, which subsequently evolves according to accumulation function
where 0 ≤ δH ≤ 1. Effective residential investment function
where serially correlated residential investment demand shock
In period t, the representative intermediate developer chooses state contingent sequences for residential investment
which equates the expected present value of an additional unit of residential investment to its price, where
which equates it to the expected present value of the sum of the future marginal revenue product of housing, and the future shadow price of housing net of depreciation, less the product of the loan to value ratio with the spread of the effective cost of bank over capital market funding. Provided that the pre-dividend stock market value is bounded and strictly concave, together with other necessary first order conditions, and a transversality condition derived from the necessary complementary slackness condition associated with the terminal nonnegativity constraint, these necessary first order conditions are sufficient for the unique value maximizing state contingent sequence of intermediate developer allocations.
Housing Supply
In period t, the representative intermediate developer adjusts its rental price of housing to maximize pre-dividend stock market value (40) subject to housing accumulation function (43) and intermediate housing service demand function (38). We consider a symmetric equilibrium under which all developer specific endogenous state variables are restricted to equal their aggregate counterparts. It follows that all intermediate developers solve an identical value maximization problem, which implies that they all choose a common rental price of housing
This necessary first order condition equates the marginal revenue gained from housing supply to the marginal cost incurred from construction. Aggregate rental price of housing index (39) satisfies
C. The Production Sector
The production sector supplies output goods for domestic and foreign absorption. In doing so, firms demand labor services from domestic households, obtain corporate loans from domestic and foreign banks, and accumulate the private physical capital stock through business investment.
The production sector consists of a finite set of industries indexed by k ∈ {1,…, M}, of which the first M* produce nonrenewable commodities. In particular, the energy commodity industry labeled k = 1 and the nonenergy commodity industry labeled k = 2 produce internationally homogeneous output goods for foreign absorption, while all other industries produce internationally heterogeneous output goods for domestic and foreign absorption.
Output Demand
There exist a large number of perfectly competitive firms which combine industry specific final output goods
where
Since the production function exhibits constant returns to scale, in equilibrium the representative final output good firm generates zero profit, implying aggregate output price index
where
There exist a large number of perfectly competitive firms which combine industry specific differentiated intermediate output goods Yi,k,l,t supplied by industry specific intermediate output good firms to produce industry specific final output good Yi,k,t according to constant elasticity of substitution production function
where serially uncorrelated output price markup shock
Since the production function exhibits constant returns to scale, in equilibrium the representative industry specific final output good firm generates zero profit, implying industry specific aggregate output price index:
As the price elasticity of demand for industry specific intermediate output goods
Labor Demand and Business Investment
There exist continuums of monopolistically competitive industry specific intermediate output good firms indexed by l ∈ [0,1]. Intermediate output good firms supply industry specific differentiated intermediate output goods, but are otherwise identical. We rule out entry into and exit out of the monopolistically competitive industry specific intermediate output good sectors.
The representative industry specific intermediate output good firm sells shares to domestic and foreign capital market intermediated households at price
where
Shares entitle households to dividend payments equal to net profits
where
Motivated by the collateralized borrowing variant of the financial accelerator mechanism due to Kiyotaki and Moore (1997), the financial policy of the representative industry specific intermediate output good firm is to maintain debt equal to a fraction of the value of the private physical capital stock,
given by regulatory corporate loan to value ratio limit
The representative industry specific intermediate output good firm utilizes private physical capital Ki,k,l,s at rate
This production function exhibits constant returns to scale, with
where internationally and serially correlated productivity shock
In utilizing private physical capital to produce output, the representative industry specific intermediate output good firm incurs a cost
where industry specific fixed cost
where
The representative industry specific intermediate output good firm enters period s in possession of previously accumulated private physical capital stock Ki,k,l,s, which subsequently evolves according to accumulation function
where 0 ≤ δK ≤ 1. Following Christiano, Eichenbaum and Evans (2005), effective business investment function
where serially correlated business investment demand shock
In period t, the representative industry specific intermediate output good firm chooses state contingent sequences for employment
where
which equates the marginal revenue product of utilized private physical capital to its marginal cost. In equilibrium, demand for the final business investment good satisfies necessary first order condition
which equates the expected present value of an additional unit of business investment to its price, where
which equates it to the expected present value of the sum of the future marginal revenue product of private physical capital net of its marginal utilization cost, and the future shadow price of private physical capital net of depreciation, less the product of the loan to value ratio with the spread of the effective cost of bank over capital market funding. Provided that the pre-dividend stock market value is bounded and strictly concave, together with other necessary first order conditions, and a transversality condition derived from the necessary complementary slackness condition associated with the terminal nonnegativity constraint, these necessary first order conditions are sufficient for the unique value maximizing state contingent sequence of industry specific intermediate output good firm allocations.
Output Supply
In an extension of the model of nominal output price rigidity proposed by Calvo (1983) along the lines of Smets and Wouters (2003), each period a randomly selected fraction
where
If the representative industry specific intermediate output good firm can adjust its price optimally in period t, then it does so to maximize pre-dividend stock market value (54) subject to production function (57), industry specific intermediate output good demand function (52), and the assumed form of nominal output price rigidity. We consider a symmetric equilibrium under which all industry and firm specific endogenous state variables are restricted to equal their industry specific aggregate counterparts. It follows that all intermediate output good firms that adjust their price optimally in period t solve an identical value maximization problem, which implies that they all choose a common price
This necessary first order condition equates the expected present value of the after tax marginal revenue gained from output supply to the expected present value of the marginal cost incurred from production. Aggregate output price index (53) equals an average of the price set by the fraction
Since those intermediate output good firms able to adjust their price optimally in period t are selected randomly from among all intermediate output good firms, the average price set by the remaining intermediate output good firms equals the value of the industry specific aggregate output price index that prevailed during period t − 1, rescaled to account for past industry specific output price inflation.
D. The Banking Sector
The banking sector supplies global financial intermediation services subject to financial frictions and regulatory constraints. In particular, banks issue risky mortgage loans to domestic developers at infrequently adjusted predetermined mortgage loan rates, as well as risky domestic currency denominated corporate loans to domestic and foreign firms at infrequently adjusted predetermined corporate loan rates, given regulatory loan to value ratio limits. They obtain funding from domestic bank intermediated households via deposits and from the domestic interbank market via loans, accumulating bank capital out of retained earnings given credit losses to satisfy a regulatory capital requirement.
Credit Demand
There exist a large number of perfectly competitive banks which combine economy specific local currency denominated final corporate loans
where
Since the portfolio aggregator exhibits constant returns to scale, in equilibrium the representative global final bank generates zero profit, implying aggregate effective gross corporate loan rate index:
This aggregate effective gross corporate loan rate index equals the minimum cost of producing one unit of the domestic currency denominated final corporate loan, given the rates on economy specific local currency denominated final corporate loans.
There exist a large number of perfectly competitive banks which combine differentiated intermediate mortgage or corporate loans
where Z ∈ {D, F}, while serially uncorrelated mortgage or corporate loan rate markup shock
where f(D) = M and f(F) = C. Since the portfolio aggregator exhibits constant returns to scale, in equilibrium the representative domestic final bank generates zero profit, implying aggregate gross mortgage or corporate loan rate index:
As the rate elasticity of demand for intermediate mortgage or corporate loans
Funding Demand and Bank Capital Accumulation
There exists a continuum of monopolistically competitive intermediate banks indexed by m ∈ [0,1]. Intermediate banks supply differentiated intermediate mortgage and corporate loans, but are otherwise identical. We rule out entry into and exit out of the monopolistically competitive intermediate banking sector.
The representative intermediate bank sells shares to domestic bank intermediated households at price
The derivation of this result imposes a transversality condition that rules out self-fulfilling speculative asset price bubbles.
Shares entitle households to dividend payments
Profits are defined as the sum of the increase in deposits
The representative intermediate bank transforms deposit and money market funding into risky differentiated intermediate mortgage and corporate loans according to balance sheet identity:
The bank credit stock
In transforming deposit and money market funding into risky mortgage and corporate loans, the representative intermediate bank incurs a cost of satisfying the regulatory capital requirement,
where fixed cost
given regulatory capital requirement
The financial policy of the representative intermediate bank is to smooth retained earnings intertemporally, given credit losses. It enters period s in possession of previously accumulated bank capital stock
where bank capital destruction rate
where χB > 0. In steady state equilibrium, these adjustment costs equal zero, and effective retained earnings equals actual retained earnings.
In period t, the representative intermediate bank chooses state contingent sequences for deposit funding
which equates the deposit rate to the interbank loans rate. In equilibrium, retained earnings satisfies necessary first order condition
which equates the expected present value of an additional unit of retained earnings to its marginal cost, where
which equates it to the expected present value of the future shadow price of bank capital net of destruction, less the sum of the marginal utilization cost of bank capital and the spread of the cost of deposit over interbank market funding. The evaluation of this result abstracts from risk premium shocks. Provided that the pre-dividend stock market value is bounded and strictly concave, together with other necessary first order conditions, and transversality conditions derived from the necessary complementary slackness conditions associated with the terminal nonnegativity constraints, these necessary first order conditions are sufficient for the unique value maximizing state contingent sequence of intermediate bank allocations.
Credit Supply
In an adaptation of the model of nominal output price rigidity proposed by Calvo (1983) to the banking sector along the lines of Hülsewig, Mayer and Wollmershäuser (2009), each period a randomly selected fraction 1 − ωC of intermediate banks adjust their gross mortgage and corporate loan rates optimally, where 0 ≤ ωC < 1. The remaining fraction ωC of intermediate banks do not adjust their loan rates,
where Z ∈ {D, F}, while f (D) = M and f (F) = C. Under this financial friction, intermediate banks infrequently adjust their loan rates, mimicking the effect of maturity transformation on the spreads between the loan and deposit rates.
If the representative intermediate bank can adjust its gross mortgage and corporate loan rates in period t, then it does so to maximize pre-dividend stock market value (76) subject to balance sheet identity (78), intermediate loan demand function (74), and the assumed financial friction. We consider a symmetric equilibrium under which all bank specific endogenous state variables are restricted to equal their aggregate counterparts. It follows that all intermediate banks that adjust their loan rates in period t solve an identical value maximization problem, which implies that they all choose common loan rates
where g(D) = M and g(F) = C, E, while h(D) = 1 and h(F) = 2. These necessary first order conditions equate the expected present value of the marginal revenue gained from mortgage or corporate loan supply to the expected present value of the marginal cost incurred from intermediation. Aggregate gross mortgage or corporate loan rate index (75) equals an average of the gross mortgage or corporate loan rate set by the fraction 1 − ωC of intermediate banks that adjust their loan rates in period t, and the average of the gross mortgage or corporate loan rates set by the remaining fraction ωC of intermediate banks that do not adjust their loan rates:
Since those intermediate banks able to adjust their loan rates in period t are selected randomly from among all intermediate banks, the average gross mortgage or corporate loan rate set by the remaining intermediate banks equals the value of the aggregate gross mortgage or corporate loan rate index that prevailed during period t − 1.
E. The Trade Sector
The nominal effective exchange rate εi,t measures the trade weighted average price of foreign currency in terms of domestic currency, while the real effective exchange rate
where the real bilateral exchange rate
where the internal terms of trade
where
The Export Sector
There exist a large number of perfectly competitive firms which combine industry specific final export goods
where Xi,k,t = Yi,k,t for 1 ≤ k ≤ M*, while
Since the production function exhibits constant returns to scale, in equilibrium the representative final export good firm generates zero profit, implying aggregate export price index
where
Export Demand
There exist a large number of perfectly competitive firms which combine industry specific differentiated intermediate export goods Xi,k,n,t supplied by industry specific intermediate export good firms to produce industry specific final export good Xi,k,t according to constant elasticity of substitution production function
for 1 ≤ k ≤ M*, where serially uncorrelated export price markup shock
Since the production function exhibits constant returns to scale, in equilibrium the representative industry specific final export good firm generates zero profit, implying industry specific aggregate export price index:
As the price elasticity of demand for industry specific intermediate export goods
Export Supply
There exist continuums of monopolistically competitive industry specific intermediate export good firms indexed by n ∈ [0,1]. Intermediate export good firms supply industry specific differentiated intermediate export goods, but are otherwise identical. We rule out entry into and exit out of the monopolistically competitive industry specific intermediate export good sectors.
The representative industry specific intermediate export good firm sells shares to domestic capital market intermediated households at price
The derivation of this result imposes a transversality condition that rules out self-fulfilling speculative asset price bubbles.
Shares entitle households to dividend payments equal to profits
Earnings are defined as revenues derived from sales of industry specific differentiated intermediate export good Xi,k,n,s at price
In an adaptation of the model of nominal import price rigidity proposed by Monacelli (2005) to the export sector, each period a randomly selected fraction 1 − ωX of industry specific intermediate export good firms adjust their price optimally, where 0 ≤ ωX ≤ 1. The remaining fraction ωX of intermediate export good firms adjust their price to account for past industry specific export price inflation, as well as the contemporaneous change in the domestic currency denominated price of energy or nonenergy commodities, according to partial indexation rule
where 0 ≤ γX ≤ 1 and μX ≥ 0. Under this specification, the probability that an intermediate export good firm has adjusted its price optimally is time dependent but state independent.
If the representative industry specific intermediate export good firm can adjust its price optimally in period t, then it does so to maximize pre-dividend stock market value (113) subject to industry specific intermediate export good demand function (111), and the assumed form of nominal export price rigidity. Since all intermediate export good firms that adjust their price optimally in period t solve an identical value maximization problem, in equilibrium they all choose a common price
This necessary first order condition equates the expected present value of the marginal revenue gained from export supply to the expected present value of the marginal cost incurred from production. Aggregate export price index (112) equals an average of the price set by the fraction 1 − ωX of intermediate export good firms that adjust their price optimally in period t, and the average of the prices set by the remaining fraction ωX of intermediate export good firms that adjust their price according to partial indexation rule (115):
Since those intermediate export good firms able to adjust their price optimally in period t are selected randomly from among all intermediate export good firms, the average price set by the remaining intermediate export good firms equals the value of the industry specific aggregate export price index that prevailed during period t − 1, rescaled to account for past industry specific export price inflation, as well as the contemporaneous change in the domestic currency denominated price of energy or nonenergy commodities.
The Import Sector
There exist a large number of perfectly competitive firms which combine the final noncommodity output good
where serially correlated import demand shock
Since the production function exhibits constant returns to scale, in equilibrium the representative final absorption good firm generates zero profit, implying aggregate private consumption, residential investment, business investment, public consumption or public investment price index:
Combination of this aggregate private consumption, residential investment, business investment, public consumption or public investment price index with final noncommodity output and import good demand functions (104) yields:
These demand functions for the final noncommodity output and import goods are directly proportional to final private consumption, residential investment, business investment, public consumption or public investment good demand, with a proportionality coefficient that varies with the external terms of trade. The derivation of these results selectively abstracts from import demand shocks.
Import Demand
There exist a large number of perfectly competitive firms which combine economy specific final import goods
where serially correlated export demand shock
Since the production function exhibits constant returns to scale, in equilibrium the representative final import good firm generates zero profit, implying aggregate import price index:
This aggregate import price index equals the minimum cost of producing one unit of the final import good, given the prices of economy specific final import goods. The derivation of these results selectively abstracts from export demand shocks.
There exist a large number of perfectly competitive firms which combine economy specific differentiated intermediate import goods Mi,j,n,t supplied by economy specific intermediate import good firms to produce economy specific final import good Mi,j,t according to constant elasticity of substitution production function
where serially uncorrelated import price markup shock
Since the production function exhibits constant returns to scale, in equilibrium the representative economy specific final import good firm generates zero profit, implying economy specific aggregate import price index:
As the price elasticity of demand for economy specific intermediate import goods
Import Supply
There exist continuums of monopolistically competitive economy specific intermediate import good firms indexed by n ∈ [0,1]. Intermediate import good firms supply economy specific differentiated intermediate import goods, but are otherwise identical. We rule out entry into and exit out of the monopolistically competitive economy specific intermediate import good sectors.
The representative economy specific intermediate import good firm sells shares to domestic capital market intermediated households at price
The derivation of this result imposes a transversality condition that rules out self-fulfilling speculative asset price bubbles.
Shares entitle households to dividend payments equal to profits
Earnings are defined as revenues derived from sales of economy specific differentiated intermediate import good Mi,j,n,s at price
In an extension of the model of nominal import price rigidity proposed by Monacelli (2005), each period a randomly selected fraction 1 − ωM of economy specific intermediate import good firms adjust their price optimally, where 0 ≤ ωM < 1. The remaining fraction ωM of intermediate import good firms adjust their price to account for past economy specific import price inflation, as well as contemporaneous changes in the domestic currency denominated prices of energy and nonenergy commodities, according to partial indexation rule
where 0 ≤ γM ≤ 1, while
If the representative economy specific intermediate import good firm can adjust its price optimally in period, then it does so to maximize pre-dividend stock market value (113) subject to economy specific intermediate import good demand function (111), and the assumed form of nominal import price rigidity. Since all intermediate import good firms that adjust their price optimally in period t solve an identical value maximization problem, in equilibrium they all choose a common price
This necessary first order condition equates the expected present value of the marginal revenue gained from import supply to the expected present value of the marginal cost incurred from production. Aggregate import price index (112) equals an average of the price set by the fraction 1 − ωM of intermediate import good firms that adjust their price optimally in period t, and the average of the prices set by the remaining fraction ωM of intermediate import good firms that adjust their price according to partial indexation rule (115):
Since those intermediate import good firms able to adjust their price optimally in period t are selected randomly from among all intermediate import good firms, the average price set by the remaining intermediate import good firms equals the value of the economy specific aggregate import price index that prevailed during period t − 1, rescaled to account for past economy specific import price inflation, as well as contemporaneous changes in the domestic currency denominated prices of energy and nonenergy commodities.
F. Monetary, Fiscal, and Macroprudential Policy
The government consists of a monetary authority, a fiscal authority, and a macroprudential authority. The monetary authority conducts monetary policy, while the fiscal authority conducts fiscal policy, and the macroprudential authority conducts macroprudential policy.
The Monetary Authority
The monetary authority implements monetary policy through control of the nominal policy interest rate. We differentiate between flexible inflation targeting, managed exchange rate, and fixed exchange rate regimes. Under a monetary union, the leader economy follows a modified flexible inflation targeting regime, while all other union members follow fixed exchange rate regimes.
Under a flexible inflation targeting or managed exchange rate regime, the nominal policy interest rate satisfies a monetary policy rule exhibiting partial adjustment dynamics of the form
where 0 ≤ ρi < 1, ξπ > 1, ξY > 0 and
Under a fixed exchange rate regime, the nominal policy interest rate instead satisfies a monetary policy rule exhibiting feedback of the form
where ξεk > 1. As specified, the deviation of the nominal policy interest rate from its steady state equilibrium value tracks the contemporaneous deviation of the nominal policy interest rate of the leader economy from its steady state equilibrium value one for one, and is increasing in the contemporaneous deviation of the change in the corresponding nominal bilateral exchange rate from its target value.
The Fiscal Authority
The fiscal authority implements fiscal policy through control of public consumption and investment, as well as the tax rates applicable to corporate earnings and household labor income. It also operates a budget neutral nondiscretionary lump sum transfer program that redistributes national financial wealth from capital market intermediated households to credit constrained households while equalizing steady state equilibrium consumption across households, as well as a discretionary lump sum transfer program that provides income support to credit constrained households. The fiscal authority can transfer its budgetary resources intertemporally through transactions in the domestic money and bond markets. Considered jointly, the rules prescribing the conduct of this distortionary fiscal policy are countercyclical, representing automatic fiscal stabilizers, and are consistent with achieving public and national financial wealth stabilization objectives.
Public consumption and investment satisfy countercyclical fiscal expenditure rules exhibiting partial adjustment dynamics of the form
where Z ∈ {C,I}, while 0 ≤ ρG < 1. As specified, the deviation of public consumption or investment from its steady state equilibrium value depends on a weighted average of its past deviation and its desired deviation, which in turn tracks the contemporaneous deviation of potential output from its steady state equilibrium value one for one. Deviations from these fiscal expenditure rules are captured by mean zero and serially correlated public consumption or investment shock
The tax rates applicable to corporate earnings and household labor income satisfy acyclical fiscal revenue rules of the form
where Z ∈ {K,L}, while 0 < τi < 1 and 0 ≤ ρτ < 1. As specified, the deviations of these tax rates from their steady state equilibrium value depend on their past deviations. Deviations from these fiscal revenue rules are captured by mean zero and serially correlated corporate or labor income tax rate shock
The ratio of nondiscretionary lump sum transfer payments to nominal output satisfies a nondiscretionary transfer payment rule that stabilizes national financial wealth of the form
where
where
The gross yield to maturity on short term bonds depends on the contemporaneous gross nominal policy interest rate according to money market relationship:
Deviations from this money market relationship are captured by internationally and serially correlated credit risk premium shock
Deviations from this interbank market relationship are captured by internationally and serially correlated liquidity risk premium shock
The fiscal authority enters period t in possession of previously accumulated financial wealth
According to this dynamic budget constraint, at the end of period t, the fiscal authority holds financial wealth
The Macroprudential Authority
The macroprudential authority implements macroprudential policy through control of a regulatory capital requirement and loan to value ratio limits. It imposes the regulatory capital requirement on lending by domestic banks, and the regulatory loan to value ratio limits on borrowing by domestic developers and firms.
The regulatory capital ratio requirement applicable to lending by domestic banks to domestic and foreign developers and firms satisfies a countercyclical capital buffer rule exhibiting partial adjustment dynamics of the form
where 0 < κR < 1, 0 < ρκ < 1, ζκ, B > 0, ζκ, VH > 0 and ζκ, VS > 0. As specified, the deviation of the regulatory capital ratio requirement from its steady state equilibrium value depends on a weighted average of its past deviation and its desired deviation. This desired deviation is increasing in the contemporaneous deviation of bank credit growth from its steady state equilibrium value, as well as the contemporaneous deviations of the changes in the prices of housing and equity from their steady state equilibrium values. Deviations from this countercyclical capital buffer rule are captured by mean zero and serially correlated capital requirement shock
The regulatory loan to value ratio limits applicable to borrowing by domestic developers and firms from domestic and foreign banks satisfy loan to value limit rules exhibiting partial adjustment dynamics of the form
where Z ∈ {D, F}, while f (D) = H and f (F) = S. As specified, the deviations of the regulatory loan to value ratio limits from their steady state equilibrium values depend on a weighted average of their past deviations and their desired deviations, where 0 < ϕZ < 1, 0 < ρϕZ < 1, ζϕZ, B > 0 and ζϕZ, V > 0. These desired deviations are decreasing in the contemporaneous deviation of mortgage or nonfinancial corporate debt growth from its steady state equilibrium value, as well as the contemporaneous deviation of the change in the price of housing or equity from its steady state equilibrium value, respectively. Deviations from these loan to value limit rules are captured by mean zero and serially uncorrelated mortgage or corporate loan to value limit shock
The loan default rates applicable to borrowing by domestic developers and firms from domestic and foreign banks satisfy default rate relationships exhibiting partial adjustment dynamics of the form
where Z ∈ {M, C}, while f (M) = H and f (C) = S. As specified, the deviations of the mortgage or corporate loan default rates from their steady state equilibrium value depend on a weighted average of their past deviations and their attractor deviations, where 0 < δ < 1, 0 ≤ ρδ < 1, ζδz, Y > 0 and ζδz, V > 0. These attractor deviations are decreasing in the contemporaneous deviations of output from its potential value and the change in the price of housing or equity from its steady state equilibrium value, which affect the probability of default and loss given default, respectively. Deviations from these default rate relationships are captured by mean zero and serially uncorrelated mortgage or corporate loan default shock
G. Market Clearing Conditions
A rational expectations equilibrium in this DSGE model of the world economy consists of state contingent sequences of allocations for the households, developers, firms and banks of all economies that solve their constrained optimization problems given prices and policies, together with state contingent sequences of allocations for the governments of all economies that satisfy their policy rules and constraints given prices, with supporting prices such that all markets clear.
Clearing of the final output good market requires that exports Xi,t equal production of the domestic final output good less the total demand of domestic households, developers, firms and the government,
where
In equilibrium, combination of these final output and import good market clearing conditions yields output expenditure decomposition,
where the price of investment satisfies
Clearing of the final bank loan markets requires that mortgage loan supply equals the total demand of domestic developers, that is
where
The derivation of this result equates the principal and interest receipts of the banking sector to the total domestic currency denominated principal and interest payments of domestic and foreign firms.
Let At+1 denote the net foreign asset position, which equals the sum of the financial wealth of households
where
where
The derivation of this result abstracts from international financial intermediation except via the money markets and imposes restriction
III. The Empirical Framework
Estimation, inference and forecasting are based on a linear state space representation of an approximate multivariate linear rational expectations representation of this DSGE model of the world economy, henceforth referred to as the GFM. This multivariate linear rational expectations representation is derived by analytically linearizing the equilibrium conditions of the DSGE model around its stationary deterministic steady state equilibrium, and consolidating them by substituting out intermediate variables assuming small capital utilization costs and abstracting from the global terms of trade shifter. The response coefficients of these consolidated approximate linear equilibrium conditions are functions of behavioral parameters that have been restricted to coincide across economies—occasionally within groups sharing a structural characteristic—and economy specific structural characteristics implied by steady state equilibrium relationships. Except where stated otherwise, this steady state equilibrium features zero inflation, productivity and labor force growth, as well as public and national financial wealth.2
In what follows,
A. Endogenous Variables
Core inflation depends on a linear combination of its past and expected future values driven by contemporaneous real unit labor cost according to Phillips curve
which determines the core price level
Output price inflation
Consumption price inflation
Output
Domestic demand
Investment
Public domestic demand
The response coefficients of these relationships vary across economies with the composition of their domestic demand or their trade openness.
Consumption
Reflecting the existence of credit constraints, consumption also depends on contemporaneous, past and expected future credit constrained consumption, where polynomial in the lag operator
where economy specific auxiliary parameters
Residential investment
Reflecting the existence of a financial accelerator mechanism, the relative shadow price of housing depends on its expected future value, as well as the contemporaneous real property return and mortgage loan rate, according to residential investment Euler equation
which determines the shadow price of housing
which determines the rental price of housing
Business investment
Reflecting the existence of a financial accelerator mechanism, the relative shadow price of private physical capital depends on its expected future value, as well as the contemporaneous real portfolio return and effective corporate loan rate, according to business investment Euler equation
which determines the shadow price of private physical capital
The private physical capital stock
Exports
Imports
The response coefficients of the former relationship vary across economies with their trade pattern.
The nominal property return
Reflecting the existence of a portfolio balance mechanism, the nominal property return also depends on the contemporaneous housing risk premium. The real property return
The nominal interbank loans rate
The real interbank loans rate
The price of housing
Developer profits
where economy specific auxiliary parameter
The nominal portfolio return
Reflecting the existence of a portfolio balance mechanism, the nominal portfolio return also depends on contemporaneous domestic and foreign duration and equity risk premia. The response coefficients of this relationship vary across economies with their domestic and foreign bond and stock market exposures. The real portfolio return
The nominal short term bond yield
The real short term bond yield