A9.6 References
Bernard, A. B. and J. B. Jensen (1999). ”Exceptional Exporter Performance: Cause, Effect or Both?” Journal of International Economics, Vol. 47 (1), 1-25.
Bussolo, M., F. de Nicola, U. Panizza, and R. Varghese (2022). Politically connected firms and privileged access to credit: Evidence from Central and Eastern Europe. European Journal of Political Economy, Volume 71.
Callado-Muñoz, F. J., J. Hromcová, M. Sanso-Navarro, N. Utrero-González, and M. Vera-Cabello (2022). Firm Performance in Regulated Markets: The Case of Spanish Defence Industry.
De Loecker, J. (2007). Do Exports Generate Higher Productivity? Evidence from Slovenia. Journal of International Economics, 73, 69-98.
De Loecker, J. and F. Warzynski (2012). “Markups and Firm-Level Export Status“, American Economic Review, 102 (6), 2437-2471.
Fons-Rosen, C., Ş. Kalemli-Ozcan, B. E. Sorensen, C. Villegas-Sanchez, and V. Volosovych (2017). Foreign investment and domestic productivity: Identifying knowledge spillovers and competition effects. NBER Working Paper, No. 23643
Giacomello, G. and O. Preka (2023). Sources of strength: mapping the defence sector in Europe. Defence Studies.
Hall, B. H., F. Lotti, and J. Mairesse (2013). Evidence on the impact of R&D and ICT investments on innovation and productivity in Italian firms. Economics of Innovation and New Technology, 22(3), 300–328.
Javorcik, B. S. (2004). Does Foreign Direct Investment Increase the Productivity of Domestic Firms? In Search of Spillovers through Backward Linkages. American Economic Review, 94 (3), 605-627.
Kalemli-Özcan, Ş., B. Sorensen, C. Villegas-Sanchez, V. Volosovych, and S. Yesiltas (2015). ‘‘How to Construct Nationally Representative Firm Level Data from the Orbis Global Database: New Facts and Aggregate Implications.’’ NBER Working Paper, No. 21558.
Kalemli-Özcan, Ş., B. Sorensen, C. Villegas-Sanchez, V. Volosovych, and S. Yesiltas (2024). How to Construct Nationally Representative Firm-Level Data from the Orbis Global Database: New Facts on SMEs and Aggregate Implications for Industry Concentration. American Economic Journal: Macroeconomics, vol. 16, no. 2, 353–74.
Lauwers, A. R. (2022). In the Right Hands? Capital Inflows and Allocation of Credit Across Firms: Evidence from Emerging Europe. Working Paper.
Vaze, P., C. Thol, A. Fraser, J. Derbyshire, and M. Savic (2017). Exploring the Value of Defence Jobs in the UK. Department for Business, Energy and Industrial Strategy, UK.
Wolff, G.B., A. Burilkov, K. Bushnell, I. Kharitonov, J. Mejino-López, and T. Morgan (2025). Kiel Military Procurement Tracker - second release, Kiel Institute for the World Economy.
A10 Model structure and simulations
This annex documents the macroeconomic model used in Chapter 2, formally defines the notion of self-financing, and outlines the simulation exercises. The framework is a quarterly, medium-scale New Keynesian dynamic stochastic general equilibrium model featuring nominal rigidities, sectoral production, capital accumulation, and an explicit fiscal-monetary block. Its disaggregation into civilian and defence sectors allows for the characterisation of relative prices and defence-specific investment dynamics. This structure provides a realistic representation of the European defence industry’s size and facilitates the integration of micro-level empirical evidence into the macroeconomic calibration. The model is used to analyse defence spending shocks and their transmission to aggregate demand, prices, public finances, and productivity. A key feature of the framework is its overlapping generation structure, which breaks Ricardian equivalence: households with finite planning horizons do not fully offset government borrowing with additional saving. As a result, the way defence spending is financed – whether through deficit or taxes – has real economic implications.
A10.1 Model
We study an overlapping generations economy in the tradition of the Blanchard-Yaari perpetual youth model (Yaari, 1965; Blanchard, 1985). The overlapping-generations structure introduces non-Ricardian equivalence and can be interpreted as a reduced-form representation of richer incomplete-market environments in the Heterogeneous Agent New Keynesian literature (Farhi and Werning, 2019). The overlapping generations structure closely follows Rachel and Ravn (2025), to which we refer for further details.
Building on the work of Antonova et al. (2025), we consider a stylised two-sector economy. We study the interaction between a specialised defence industry and the rest of the economy that we refer to as the civilian sector. The defence industry produces military equipment and related services for the government, which acts as a monopsonist in the demand for defence output. We consider a closed-economy setting and calibrate the military sector to match empirical evidence on the domestic absorption of defence production. Our empirical findings at the micro-level are used to discipline the spillovers from defence-related investment to aggregate productivity.
Households
Households are of two types: optimising (Ricardian) and hand-to-mouth. Ricardian households smooth consumption intertemporally and accumulate both government bonds and physical capital, while hand-to-mouth households consume their current disposable income. Each period, a new cohort of households of mass 1-q is born; each household has survival probability q between periods. Preferences are given by
\[ U_{s,t} = \sum_{h=0}^{\infty} (\beta q)^h \left( \log c_{s,t+h} - \frac{\psi}{1+\kappa} n_{s,t+h}^{\,1+\kappa} \right), \]
where \[ U_{s,t} \] denotes expected lifetime utility of a cohort born at time s≤t. The effective discount factor is βq<1 due to survival risk. Households derive utility from consumption \[ c_{s,t} \] and disutility from labour supply \[ n_{s,t} \], with \[ 1/\kappa \] denoting the Frisch elasticity and ψ>0 a scaling parameter.
We introduce a competitive life-insurance sector. At the end of each period, households deposit their assets with an insurance intermediary, which intermediates capital and bond holdings. In the event of survival, households receive actuarially fair payouts; in the event of death, assets are redistributed within the insurance sector. Free entry implies actuarially fair pricing, so that the effective return on assets of surviving households includes a mortality premium of 1-q/q.
Households earn labour income, capital and bond income, firm profits, lump-sum transfers, and pay taxes. The flow budget constraint is
\[ P_{t,c} c_{s,t} + P^{K}_{c,t} K_{c,s,t} + P^{K}_{d,t} K_{d,s,t} + P^{n}_{t} B^{n}_{s,t} = \sum_{i \in \{c,d\}} \left[ \frac{ P^{K}_{i,t}\left(1-\delta_i(u_{i,t})\right) + R^{K}_{i,t} u_{i,t} }{q} \right] K_{i,s,t-1} + (1-\tau_{l,t}) W_t n_{s,t} + \frac{1-\xi + \xi P^{n}_{t}}{q} B^{n}_{s,t-1} + P^{n}_{t} d_{s,t} - T_{s,t} + \Phi_{s,t}. \]
Pt,c is the civilian good price (numeraire), Ki,s,t represents sectoral capital holdings, while ui,t is the utilisation rate, which affects both depreciation 𝛿i and the return on capital \[ R^K_{i,t}, B^n_{s,t} \] denotes nominal government bonds. The term 1/q reflects the insurance-adjusted return. \[ T_{s,t} \] are government transfers, while \[ \Phi_{s,t} \] are nominal profits from firms holding. As in (Sterk and Tenreyro, 2018) we allow for a social fund. The social fund runs a balanced budget and makes real transfers to newborn agents \[ d_{s,t} \] financed by taxing "old" households. This ensures that at the initial steady state the real interest rate is equal to 1/β.
Aggregating over cohorts yields the behaviour of Ricardian households (Farmer et al., 2011). Aggregate consumption satisfies:
\[ C_{t+1} + \rho \left(\frac{V_t}{q} - \frac{V^{SS}}{q}\right) = \beta \frac{R_t}{\Pi_{t+1}} C_t \]
Where \[ q = \frac{(1-q)(1-\beta q)}{q(1+rk)} \]. Aggregate wealth is given by
\[ V_t = \sum_{i \in (c,d)} \left[ P_{i,t}^K \left(1 - o_i(u_{i,t}) + R_{i,t}^K u_{i,t} \right) K_{i,t-1} + (1 - \xi + \xi P_t^n) B_{t-1}^n \right]. \]
The overlapping-generations structure implies that each period a fraction q of households dies with average wealth Vt, and is replaced by a new cohort. This generational turnover introduces a wedge in the aggregate Euler equation: aggregate consumption dynamics depend not only on the real interest rate but also on aggregate wealth. Higher wealth slows consumption growth as richer cohorts are replaced by poorer entrants. A key implication is that government bond issuance is perceived as net wealth by households, raising consumption and putting upward pressure on equilibrium interest rates. All else equal, this amplifies the crowding-out of investment compared to an infinite horizon economy.
The supply side
The supply side follows a standard New Keynesian structure with two production sectors: civilian (C) and defence (D). Final output in each sector is produced under perfect competition using differentiated intermediate goods. Capital is sector-specific, while labour is perfectly mobile across sectors. Defence production uses civilian goods as intermediate inputs, capturing supply-chain linkages.
Final goods
In each sector S ∈ {C,D}, final output is produced by aggregating a continuum of intermediate varieties j ∈ [0,1]:
\[ Y_{S,t} = \left( \int_0^1 Y_{S,j,t}^{\frac{\varepsilon - 1}{\varepsilon}} \, dj \right)^{\frac{\varepsilon}{\varepsilon - 1}}, \quad \varepsilon > 1. \]
Cost minimisation implies the sectoral price index: \[ P_{S,t} = \left( \int_0^1 P_{S,j,t}^{1-\varepsilon} \, dj \right)^{\frac{1}{1-\varepsilon}}. \]
Final goods are allocated as follows. Civilian output is used for household consumption, the production of investment goods for civilian and defence capital – denoted \[ I_{CC,t} \], and \[ I_{DCt} \], respectively, government consumption \[ G_{C,t} \], and as intermediate inputs in defence production \[ X_{C,t} \]:
\[ Y_{c,t} = C_t + I_{CC,t} + I_{DC,t} + X_{C,t} + G_{c,t}. \]
Defence output is used for government purchases of defence goods \[ G_{D,t} \] and for the production of investment goods in the defence sector:
\[ Y_{D,t}=I_{DD,t}+G_{D,t^.} \]
Intermediate goods
In each sector S ∈ {C,D}, a continuum of monopolistically competitive firms produces differentiated varieties used in final goods production. Civilian firms produce according to
\[ Y_{Cj,t} = A_C \left( u_{Cj,t} K_{Cj,t-1} \right)^{\alpha} N_{Cj,t}^{1-\alpha} \]
while defence firms combine sector-specific production with civilian intermediate inputs:
\[ Y_{Dj,t} = \left( A_D \left( u_{Dj,t} K_{Dj,t-1} \right)^{\alpha} N_{Dj,t}^{1-\alpha} \right)^{\omega} X_{Cj,t}^{1-\omega} \]
Firms hire labour at wage Wt and rent capital at rate \[ R^K_{S,t} \]. Cost minimisation implies sector-specific marginal costs \[ MC_{S,t} \], which are identical across firms within each sector.
Price setting
Firms face quadratic price adjustment costs à la Rotemberg (1982). Each firm chooses price PSj,t+s to maximise
\[ \mathbb{E}_t \sum_{s=0}^{\infty} \beta^s \frac{\Lambda_{t+s}}{\Lambda_t} \left[ P_{Sj,t+s} Y_{Sj,t+s} - MC_{S,t+s} Y_{Sj,t+s} - \frac{\kappa_P}{2} \left( \Pi_{Sj,t+s} - 1 \right)^2 P_{S,t+s} Y_{S,t+s} \right], \]
subject to demand:
\[ Y_{Sj,t} = \left( \frac{P_{Sj,t}}{P_{S,t}} \right)^{-\varepsilon} Y_{S,t}, \qquad \varepsilon > 1. \]
In symmetric equilibrium, aggregation across firms delivers sector-specific inflation dynamics that reduce to a nonlinear Phillips-type relationship linking inflation, marginal costs, and price adjustment costs.
Capital goods and investment
Capital is produced by competitive capital producers subject to adjustment costs and accumulates according to
\[ K_{S,t} = \left(1 - \delta_{S,t}\right) K_{S,t-1} + I_{S,t}. \]
Adjustment costs imply a standard investment Euler equation linking the shadow value of capital \[ P^K_{S,t} \] (Tobin’s q) to investment dynamics:
\[ P_{S,t}^K = P_{S,t}^I \left[ 1 - \kappa_I \left( \frac{I_{S,t}}{I_{S,t-1}} - 1 \right) - \frac{\kappa_I}{2} \left( \frac{I_{S,t}}{I_{S,t-1}} - 1 \right)^2 \right] + \beta \mathbb{E}_t \frac{\Lambda_{t+1}}{\Lambda_t} \kappa_I \left( \frac{I_{S,t+1}}{I_{S,t}} - 1 \right) \left( \frac{I_{S,t+1}}{I_{S,t}} \right) P_{S,t+1}^I. \]
Investment \[ I_{S,t} \] is a CES composite of civilian and defence goods:
\[ I_{S,t} = \prod_{J \in C,D} I_{SJ,t}^{\lambda_{SJ}}, \qquad \sum_J \lambda_{SJ} = 1. \]
Cost minimisation yields
\[ P_{J,t} I_{SJ,t} = \lambda_{SJ} P_{S,t}^I I_{S,t}, \qquad P_{S,t}^I = \prod_{J \in C,D} \left( \frac{P_{J,t}}{\lambda_{SJ}} \right)^{\lambda_{SJ}}. \]
We assume 𝜆cc=1 and 𝜆cd=0, so civilian investment uses only civilian goods, while defence investment uses both inputs.
Capital utilisation uS,t raises effective capital services but increases depreciation (Christiano et al. 2005):
\[ \delta_{S,t} = \delta_{0S} + \delta_1 u_{S,t}^{1+\varphi}. \]
Labour market
Labour services are differentiated across a continuum of unions, each of which supplies a distinct type of labour and sets its own nominal wage. Competitive labour aggregators combine these differentiated labour varieties into a homogeneous aggregate labour input used by firms. Because labour types are imperfect substitutes, each union has some monopoly power in wage setting.
Unions are subject to Calvo-style nominal wage rigidities. In each period, only a fraction 1-𝜃w of unions can re-optimise their wage, while the remaining unions adjust wages according to past inflation. Aggregate wages dynamics satisfy
\[ W_t = \left[ \theta_w \left( W_{t-1} \Pi_{t-1}^{\gamma_w} \Pi^{1-\gamma_w} \right)^{1-\varepsilon_w} + (1-\theta_w)(W_t^*)^{1-\varepsilon_w} \right]^{\frac{1}{1-\varepsilon_w}}, \]
where Wt* denotes the newly reset wage, 𝜀w is the elasticity of substitution across labour types, and 𝛾w governs the degree of wage indexation to past inflation. Union optimisation yields a Philips curve-type relationship for nominal wage inflation.
Spillovers from defence capital to civilian productivity
To capture productivity spillovers from defence to the civilian sector, civilian total factor productivity(TFP) is assumed to depend on the stock of defence capital. This implies that sustained increases in defence investment raise the level of productivity, without generating endogenous trend growth. Civilian TFP therefore evolves according to
\[ \log A_{C,t} = \log A_C + \phi_d \left( \frac{K_{D,t-1}}{K_D} - 1 \right), \]
where KD denotes the steady-state level of defence capital and 𝜙d measures the elasticity of civilian productivity with respect to defence capital.
This specification provides a tractable mapping between empirical estimates based on investment flows at the single firm level and a transmission mechanism based on aggregate investment. The parameter 𝜙d is calibrated using our microeconomic estimates based on firm-level data, implying that a 1% increase in defence-related investment raises civilian TFP by approximately 0.008%. A sustained expansion of the defence sector - for example, doubling defence capital - implies an increase in civilian TFP of about 0.8% under the baseline calibration.
Fiscal policy and government debt
The government purchases civilian goods GC,t, defence goods GD,t, and provides lump-sum transfers Tt to households. Expenditures are financed through capital and labour taxes and the issuance of long-term government debt.
The real government budget constraint (in units of civilian goods) is:
\[ P_t^B b_t = \frac{(1-\xi) + \xi P_t^B}{\Pi_t} b_{t-1} + G_{C,t} + p_{D,t} G_{D,t} + p_{D,t} \mu_{D,t}^I I_{D,t} + T_t - \mathcal{R}_t, \]
where bt denotes real public debt, \[ P^B_t \] the price of long-term bonds, and Πt gross inflation. The parameter ξ ∈ (0,1) governs debt duration. The relative price of defence goods is pD,t ≡PD,t/PC,t, and Rt denotes total tax revenues.
The term \[ p_{D,t}\mu^I_{D,t}I_{D,t} \] captures government support to defence investment. By lowering the effective cost of capital through a subsidy \[ \mu^I_{D,t} \], this policy encourages capital deepening in the defence sector and amplifies productivity spillovers to the civilian economy.
Long-term debt gives rise to valuation effects: increases in interest rates reduce the market price of outstanding debt, generating capital losses for households and partially offsetting higher debt servicing costs for the government. Valuation effects also arise as a consequence of unexpected inflation.
Fiscal rule
Fiscal policy ensures debt sustainability through a feedback rule on lump-sum transfers:
\[ T_t = T - \phi_b \log\left(\frac{b_t/Y_t}{(b/Y)^{ss}}\right) - \phi_y \log\left(\frac{Y_t}{\bar{Y}}\right) + \varepsilon_{T,t}. \]
Higher debt levels reduce transfers (increase net revenues), stabilising the debt-to- gross domestic product (GDP) ratio over time. The parameter 𝜙b measures the strength of fiscal adjustment to deviations of the debt ratio from its steady state, while 𝜙y measures the response of automatic stabilisers to fluctuations in economic activity. The coefficient T governs the degree of policy inertia. Distortionary taxes follow exogenous persistent processes and play a secondary role in fiscal adjustment in the baseline calibration.
Monetary policy
Monetary policy is conducted through a Taylor-type interest rate rule:
\[ \frac{R_t}{\bar{R}} = \left(\frac{R_{t-1}}{\bar{R}}\right)^{\rho_R} \left(\frac{\Pi_t}{\bar{\Pi}}\right)^{\phi_\pi(1-\rho_R)} e^{\varepsilon_{m,t}}, \]
where \[ \bar{R} \] denotes the steady-state nominal interest rate, \[ \bar{\Pi} \] the inflation target, 𝜌R∈[0,1) captures interest rate smoothing, and \[ \phi_\pi>1 \] governs the policy response to inflation deviations from target. The term 𝜀m,t represents a monetary policy shock.
A10.2 Self-financing
We define self-financing as the extent to which an increase in defence-related fiscal spending is offset by endogenous general equilibrium responses. These adjustments operate through three main channels: (i) expansions in tax bases, (ii) valuation effects on outstanding government debt, and (iii) changes in relative prices. Self-financing is evaluated holding fiscal instruments fixed, so that all adjustments arise from macroeconomic responses rather than discretionary policy.
Counterfactual fiscal policy
The government budget constraint can be expressed in a compact form as:
\[ P^B_tb_t=((1-\xi)+\xi P_t^B)\frac{b_{t-1}}{\Pi_t}+F_t-\tilde{R_t}, \]
where \[ \tilde{R}_t \equiv \mathcal{R}_t - T_t \]
denotes net fiscal revenues, and total fiscal expenditure is:
\[ F_t \equiv G_{C,t} + p_{D,t} G_{D,t} + \mu_{I,t} p_{D,t} I_{D,t}. \]
To isolate endogenous fiscal responses, we define a counterfactual in which fiscal instruments are held fixed at their steady-state values:
\[ \tau_{l,t} = \tau_l, \qquad \tau_{k,t} = \tau_k, \qquad T_t^* = T - \phi_y \log\left(\frac{Y_t}{\bar{Y}}\right). \]
Counterfactual net revenues are therefore given by \[ \tilde{R}_t^* \equiv \mathcal{R}_t(\tau_l, \tau_k; \text{tax base}) - T_t^*. \]
Under this definition, \[ \tilde{R}_t^* \] varies only through endogenous movements in tax bases. Let Qt denote the stochastic discount factor. Iterating the budget constraint forward and isolating the contribution from \[ \tilde{R}_t^* \] gives the present discounted value budget constraint
\[ \sum_{t=0}^{\infty} Q_t \Delta F_t = \sum_{t=0}^{\infty} Q_t \Delta \tilde{R}_t^* + \sum_{t=0}^{\infty} Q_t \left( \Delta R_t - \Delta \tilde{R}_t^* \right) - V_0 \]
where \[ V_0 \equiv \left(1 - \xi + \xi P_0^B\right) \frac{b_{-1}}{\Pi_0} \] is the initial real value of government debt.
Definition of self-financing
Let ΔXt ≡Xt-X denote level deviations from steady state. Taking deviations and rearranging yields:
\[ \sum_{t=0}^{\infty} Q_t \Delta F_t = \sum_{t=0}^{\infty} Q_t \Delta \tilde{R}_t^* + \sum_{t=0}^{\infty} Q_t \left( \Delta R_t - \Delta \tilde{R}_t^* \right) + \sum_{t=0}^{\infty} \Delta Q_t \left( R_t - F_t \right) - \Delta V_0 \]
The next to last term captures the effect of time variation in the stochastic discount factor on the present value of fiscal flows. Intuitively, changes in real interest rates reweight the entire stream of steady-state fiscal obligations and therefore affect fiscal capacity. The last term captures the time-0 valuation effect of changes in bond prices and inflation on the outstanding stock of nominal debt. The change in total fiscal expenditure ΔFt can be further decomposed in
\[ \Delta F_t = \Delta G_{C,t} + p_D \Delta G_{D,t} + p_D I_D \Delta \mu_{I,t} + X_D \Delta p_{D,t}, \]
where XD≡GD+μIID. The last term captures changes in the fiscal cost of defence expenditure induced by movements in relative prices.
By defining \[ \Delta\tilde{F}_t \equiv\Delta G_{C,t}+p_D \Delta G_{D,t}+ p_DI_D \Delta \mu_{I,t} \],we can express the self-financing ratio as the fraction of the fiscal expansion that is offset by endogenous fiscal adjustments, valuation effects, and relative price effects:
\[ \mathcal{SF} = \frac{\sum_{t=0}^{\infty} \Delta\left(Q_t \tilde{R}_t^*\right) - \Delta V_0 - \sum_{t=0}^{\infty} X_D \,\Delta p_{D,t}}{\sum_{t=0}^{\infty} \Delta\left(Q_t \tilde{F}_t\right)}. \]
A10.3 Calibration
The model is calibrated at quarterly frequency to a euro area aggregate composed of France, Germany, Italy, and Spain. Table A10.1 reports the calibrated parameters. Preferences, technology, and nominal rigidities follow Coenen et al. (2013) and Albonico et al. (2019). The share of hand-to-mouth households and the survival probability are chosen to target an average marginal propensity to consume of 0.3, consistent with Carroll et al. (2017). Steady-state public debt is set to 95.8% of GDP, corresponding to the 2024 average, while the debt-decay parameter targets an average maturity of 7.5 years.
Government expenditure-to-GDP ratios are calibrated to weighted averages over 2002–2024, implying steady-state labour and capital tax rates of 42.6% and 16.4%, respectively; the profit tax rate is set to 30%. Fiscal adjustment is assumed to operate through lump-sum transfers, which stabilise temporary deviations of the debt-to-GDP ratio, while tax rates adjust only to permanent shifts in expenditure. The fiscal rule is calibrated to return debt to steady state within 20 years. Monetary policy parameters follow Coenen et al. (2013) and Albonico et al. (2019), with an inflation response of 1.57 and an interest‑rate smoothing parameter of 0.88.
We model the defence sector as the recipient of government demand for both defence-related intermediate consumption and defence investment. The latter comprises expenditures on military equipment, ammunition, and research and development, while the former includes maintenance, repair, and other service inputs. Based on the United Nations’ Classification of the Functions of Government data, steady-state defence consumption and investment are set to 0.6% and 0.3% of GDP, respectively, implying total defence demand of 0.9% of GDP. Military personnel expenditures are excluded and classified as civilian government consumption. This calibration yields a defence-sector output of about 1% of GDP, consistent with European Union (EU)-level industry turnover data.
We abstract from modelling defence exports and imports, as these are of similar magnitude and broadly offset each other in aggregate. What matters for our purposes is to match the size of the domestic military sector, as this determines the scale of spillovers and the proportional response of investment to defence demand shocks.
