The cross-country comparison below shows that the GDP effects are roughly proportional to the funds received, when the financing of EU contributions is also taken into account: the largest recipients in terms of their baseline GDP, for example Latvia, Lithuania and Poland, show the largest increases in GDP. As argued in Sect.
5.3, EU11 countries spend roughly 70–80% of Cohesion Fund payments on infrastructure and human resource-related projects; therefore, the sum of these two spending categories in terms of baseline GDP dominate the differentiated country-specific long-run effects. In the following figures, the bars represent (net) cohesion spending received (as percentage of GDP) and the solid lines the simulated GDP impact (as percentage difference from baseline).
In this section, we describe in more detail the modelling of production, human capital and the government budget constraint, which constitute the key elements for modelling the Structural Funds interventions. For a more detailed description of the full model, see Roeger et al. (
2008) and Varga and in ’t Veld (
2011b). A detailed analysis of the country-level calibration can be found in D’Auria et al. (
2009).
^{5}
A share ε of households are liquidity-constrained (so-called rule-of-thumb consumers), who cannot trade in financial and physical assets and consume their disposable income each period. The other households are non-constrained and have full access to financial markets where they can buy and sell domestic and foreign assets (government bonds), accumulate physical capital which they rent out to the intermediate sector, and they also buy the patents of designs produced by the R&D sector and license them to the intermediate goods-producing firms. Each non-constrained household maximises an intertemporal utility function in consumption (
U(
C
_{t})) and leisure (
V(1 −
L
_{t})) subject to a budget constraint. These households make decisions about consumption, labour supply (
L
_{t}), investments into domestic and foreign financial assets (
B
_{t},
B
_{F, t}), the purchases of investment good (
J
_{t}) subject to adjustment costs (
Γ
_{J}(
J
_{t})), the renting of physical capital stock (
K
_{t}), the corresponding degree of capacity utilisation (
u
_{t}), the purchases of new patents from the R&D sector (
J
_{A, t}), and the licensing of existing patents (
A
_{t}), and receive wage income (
W
_{t}), unemployment benefits (
BEN
_{t}), transfer income from the government (
TR
_{t}) and interest income (
i
_{t}). All firms of the economy are owned by the non-constrained households who share the total profit of the final and intermediate sector firms (
\( P{R}_t^x,P{R}_t^Y\Big) \). All households pay wage income taxes (
t
_{w}) and capital income taxes (
t
_{K}) less tax credits (
τ
_{A}) and depreciation allowances
δ
_{K},
δ
_{A} after their earnings on physical capital and patents (
i
_{K},
i
_{A}). There is no perfect arbitrage between different types of assets. When taking a position in the international bond market, households face a financial intermediation premium, which depends on the economy-wide net holdings of internationally traded bonds (
rp
_{F, t}). Also, when investing into tangible and intangible capital households require risk premia
rp
_{K} and
rp
_{A} in order to cover the increased risk on the return related to these assets. Hence, non-liquidity constrained households face the following Lagrangian
$$ \underset{{\left\{\begin{array}{c}{C}_{i,t},{L}_{i,s,t},{B}_{i,t}\\ {}{J}_{i,t},{K}_{i,t}\\ {}{J}_{A,i,t},{A}_{i,t}\end{array}\right\}}_{t=0}^{\infty }}{\mathit{\max}}{V}_{i,0}={E}_0{\sum}_{t=0}^{\infty }{\beta}^t\left(U\left({C}_{i,t}\right)+{\sum}_{s\in \left\{L,M,H\right\}}V\left(1-{L}_{i,s,t}\right)\right) $$
$$ -{E}_0{\sum}_{t=0}^{\infty }{\lambda}_{i.t}\frac{\beta^t}{P_t}\left(\begin{array}{c}\left(1+{t}_{C,t}\right){P}_{C,t}{C}_{i,t}+{B}_{i,t}+{B}_{F,i,t}+{P}_{I,t}\left({J}_{i,t}+{\varGamma}_J\left({J}_{i,t}\right)\right)+{P}_{A,t}{J}_{A,i,t}\\ {}-\left(1+{i}_{t-1}\right){B}_{i,t-1}-\left(1+{i}_{F,t-1}+{rp}_{F,t}\right){B}_{F,i,t-1}\\ {}-\sum \limits_s\left(\left(1-{t}_{w,s,t}\right){W}_{s,t}{L}_{i,s,t}-b{W}_{s,t}\left(1- NPAR{T}_{i,s,t}-{L}_{i,s,t}\right)\right)\\ {}-\left(1-{t}_K\right)\left({i}_{K,t-1}-r{p}_K\right){P}_{I,t-1}{K}_{i,t-1}-{t}_K{\delta}_K{P}_{I,t-1}{K}_{i,t-1}\\ {}-\left(1-{t}_K\right)\left({i}_{A,t-1}-r{p}_A\right){P}_{A,t-1}{A}_{i,t-1}-{t}_K{\delta}_A{P}_{A,t-1}{A}_{i,t-1}-{\tau}_A{P}_{A,t-1}{J}_{A,i,t}\\ {}-T{R}_{i,t}-P{R}_t^x-P{R}_t^Y\end{array}\right) $$
(A.1)
$$ -{E}_0\sum \limits_{t=0}^{\infty }{\lambda}_{i,t}{\xi}_{i,t}{\beta}^t\left({K}_{i,t}-{J}_{i,t}-\left(1-{\delta}_K\right){K}_{i,t-1}\right) $$
$$ -{E}_0\sum \limits_{t=0}^{\infty }{\psi}_{A,i,t}{\beta}^t\left({A}_{i,t}-{J}_{A,i,t}-\left(1-{\delta}_A\right){A}_{i,t-1}\right) $$
The budget constraints are written in real terms with the price for consumption, investment and patents (
P
_{C, t},
P
_{I, t},
P
_{A, t}) and wages (
W
_{t}) divided by GDP deflator (
P
_{t}).
We account for the productivity-enhancing effect of infrastructure investment via the following aggregate final goods production function:
$$ {Y}_{jt}={\left({L}_{Yjt}\right)}^{\alpha }{\left(\underset{0}{\overset{A_t}{\int }}{\left({x^i}_{jt}\right)}^{\theta } di\right)}^{\left(1-\alpha \right)/\theta }{\left({K}_t^G\right)}^{\alpha_G}-F{C}_Y,\mathrm{where}\;\underset{0}{\overset{A_t}{\int }}{x^i}_{jt} di={K}_t $$
(A.2)
The final good sector uses a labour aggregate (
L
_{Yjt}) and intermediate goods (
x
^{i}
_{jt}) using a Cobb-Douglas technology, subject to a fixed cost
FC
_{Y}. Our formulation assumes that investment in public capital stock (
\( {K}_t^G \)) increases total factor productivity with an exponent of
α
_{G} set to 0.10.
Public infrastructure investment (
\( {I}_t^G \)) accumulates into the public capital stock
\( {K}_t^G \) according to
$$ {K}_t^G=\left(1-{\delta}_G\right){K}_{t-1}^G+{I}_t^G $$
(A.3)
where
δ
_{G}, the depreciation rate of public capital is set at 4%. Infrastructure investment is assumed to be proportional to output
$$ {I}_t^G=\left( IG{S}_t+{\varepsilon}_t^{IG}\right){Y}_t $$
(A.4)
where
\( {\varepsilon}_t^{IG} \) is an exogenous shock to the share of government investment (
IGS
_{t}). It is through this shock that we simulate the increase in infrastructure investment.
The intermediate sector consists of monopolistically competitive firms that have entered the market by buying licenses for design from domestic households and by making an initial payment
FC
_{A} to overcome administrative entry barriers. Capital inputs are also rented from the household sector for a rental rate of
i
_{K}. Firms that have acquired a design can transform each unit of capital into a single unit of an intermediate input. Intermediate goods-producing firms sell their products to domestic final good producers. In symmetric equilibrium the inverse demand function of domestic final good producers is given as
$$ p{x}_{it}={\eta}_t\left(1-\alpha \right)\left({Y}_{jt}+F{C}_Y\right){\left(\underset{0}{\overset{A_t}{\int }}{\left({x^i}_{jt}\right)}^{\theta } di\right)}^{-1}{\left({x^i}_{jt}\right)}^{\theta -1}, $$
(A.5)
where
η
_{t} is the inverse gross mark-up of the final goods sector.
Each domestic intermediate firm solves the following profit-maximisation problem:
$$ P{R}_{i,t}^x=\underset{{x^i}_t}{\max}\left\{p{x}_{it}{x^i}_t-{i}_K{P}_{I,t}{k}_{i,t}-{i}_{A,t}{P}_{A,t}-F{C}_A\right\} $$
(A.6)
subject to a linear technology which allows to transform one unit of effective capital (
u
_{t}
k
_{t}) into one unit of an intermediate good.
The no-arbitrage condition requires that entry into the intermediate goods-producing sector takes place until
$$ P{R}_{i,t}^x=P{R}_t^x={i}_{A,t}{P}_{A,t}+\left({i}_{A,t}+{\pi}_{A,t+1}\right)F{C}_A,{\pi}_t^A=\frac{P_{A,t}}{P_{A,t-1}}-1 $$
(A.7)
For an intermediate producer, entry costs consist of a licensing fee
i
_{A, t}
P
_{A, t} for the design or patent, which is a prerequisite of production of innovative intermediate goods, and a fixed entry cost
FC
_{A}.
Innovation corresponds to the discovery of a new variety of producer durables that provides an alternative way of producing the final good. The R&D sector hires high-skilled labour
L
_{A, t} and generates new designs according to the following knowledge production function:
$$ \Delta {A}_t=\nu {A_{t-1}^{\ast}}^{\omega }{A}_{t-1}^{\varphi }{L}_{A,t}^{\lambda }. $$
(A.8)
In this framework we allow for international R&D spillovers following Bottazzi and Peri (
2007). Parameters
ω and
φ measure the foreign and domestic spillover effects from the aggregate international and domestic stock of knowledge (
A
^{∗} and
A) respectively. Negative value for these parameters can be interpreted as the “fishing out” effect, that is when innovation decreases with the level of knowledge, while positive values refer to the “standing on shoulders” effect and imply positive research spillovers. Note that
φ = 1 would give back the strong scale effect feature of fully endogenous growth models with respect to the domestic level of knowledge. Parameter
ν can be interpreted as total factor efficiency of R&D production, while
λ measures the elasticity of R&D production on the number of researchers (
L
_{A}). The international stock of knowledge is taken into account as the weighted average of all foreign stock of knowledge. We assume that the R&D sector is operated by a research institute which employs high-skilled labour at their market wage,
W
^{H}. We also assume that the research institute faces an adjustment cost of hiring new employees and maximises the following discounted profit-stream:
$$ \underset{L_{A,t}}{\max}\sum \limits_{t=0}^{\infty }{d}_t\left({P}_t^A\Delta {A}_t-{W}_t^H{L}_{A,t}-\frac{\gamma_A}{2}{W}_t^H\Delta {L}_{A,t}^2\right) $$
(A.9)
The labour aggregate
L
_{Y, t} is composed of three skill types of labour force:
$$ {L}_{Yjt}={\left({s}_L^{1/{\sigma}_L}{\left({h}_{L,t}{L}_{Ljt}\right)}^{\left(1-{\sigma}_L\right)/{\sigma}_L}+{s}_M^{1/{\sigma}_L}{\left({h}_{M,t}{L}_{Mjt}\right)}^{\left(1-{\sigma}_L\right)/{\sigma}_L}+{s}_{HY}^{1/{\sigma}_L}{\left({h}_{HY,t}{L}_{HY jt}\right)}^{\left(1-{\sigma}_L\right)/{\sigma}_L}\right)}^{\sigma_L/\left(1-{\sigma}_L\right)} $$
(A.10)
Parameter
s
_{s} is the population share of the labour force in subgroup
s (low, medium and high skilled),
L
_{s} denotes the employment rate of population
s,
h
_{s} is the corresponding accumulated human capital (efficiency unit) and
σ
_{L} is the elasticity of substitution between different labour types.
^{6} An individual’s human capital is produced by participating in education and Λ
_{s, t} represents the amount of time an individual spends accumulating human capital:
$$ {h}_{s,t}={h}_s{e}^{\psi {\Lambda}_{s,t}},\psi >0 $$
(A.11)
The exponential formulation used here adapts Jones (
2002) into a disaggregated skill structure by incorporating human capital in a way that is consistent with the substantial growth accounting literature with adjustments for education.
^{7} The
ψ parameter has been studied in a wealth of microeconomic research. Interpreting Λ
_{s, t} as years of schooling, the parameter corresponds to the return to schooling estimated by Mincer (1974). The labour-market literature suggests that a reasonable value for
ψ is 0.07, which we apply here. Investments in human capital can then be modelled by increasing the years of schooling (Λ
_{s, t}) for the respective skill groups.
For the government sector various expenditure and revenue categories are separately modelled. On the expenditure side we assume that government consumption (
G
_{t}), government transfers (
TR
_{t}) and government investment (
\( {I}_t^G \)) are proportional to GDP and unemployment benefits (
BEN
_{t}) are indexed to wages. The government provides subsidies (
S
_{t}) on physical capital and R&D investments in the form of a tax-credit and depreciation allowances, which are exogenous in the model.
Government revenues (
\( {R}_t^G \)) consist of taxes on consumption as well as capital and labour income. Fiscal transfers received from the EU are denoted by
COH
_{t} (which is negative for the net contributors). Labour taxes gradually adjust to stabilise the debt to GDP ratio in the long run according to the following rule
$$ \Delta {t}_t^L={\tau}^B\left(\frac{B_{t-1}}{Y_{t-1}}-{b}^T\right)+{\tau}^{DEF}\Delta \left(\frac{B_t}{Y_t}\right) $$
(A.12)
where
b
^{T} is the government debt target,
τ
^{B} and
τ
^{DEF} are coefficients. Therefore, government debt (
B
_{t}) evolves according to
$$ {B}_t=\left(1+{r}_t\right){B}_{t-1}+{G}_t+I{G}_t+T{R}_t+ BE{N}_t+{S}_t-{R}_t^G- CO{H}_t\cdot $$
(A.13)
We assume that donor countries finance their contributions to the EU budget (COH<0) through increases in labour taxes.
Cohesion policy programmes are subject to the condition of additionality and co-financing. Additionality requires that Structural Funds are additional to domestically financed expenditure and are not used as a substitute for it. The co-financing principle means the EU provides only matching funds to individual projects that are part of the operational programmes and that the EU funds are matched to a certain extent by domestic expenditure. The problem with defining a proper benchmark means that in practice the principle of additionality is hard to verify and is thus not always binding. Member states are not required to create new budgetary expenditure to co-finance cohesion policy support. Existing national resources that were used to finance similar areas of interventions (and are thus concerned by the additionality requirement) can be ‘earmarked’ to co-finance Structural Fund transfers. Total spending increases only by the amount of Structural Fund transfers.
More formally, assume a cofinancing rate of
c, that is the EU transfer
COH
_{t} has to be matched by domestically financed expenditure,
c·COH. The additionality and co-financing principles can be expressed as the following condition for total government spending in a beneficiary country:
$$ TOTEX{P}_t= CO{H}_t+\max \left( EX{P}_0,c\cdot CO{H}_t\right) $$
(A.14)
where
TOTEXP
_{t} is total expenditure,
COH
_{t} is the fiscal transfer received from the EU Cohesion Funds,
EXP
_{0} is the domestically financed expenditure in the counterfactual situation (without Structural and Cohesion Funds) and
c is the co-financing rate. Examining past additionality tables of member states, it seems that most national public expenditure concerned by additionality exceeded the co-financing needs by far. In this case
EXP
_{0}>
c ⋅
COH
_{t}, and total expenditure is given by
$$ TOTEX{P}_t= CO{H}_t+ EX{P}_0 $$
(A.15)
As spending on infrastructure and education is already high in the new member states, the standard procedure in model-based evaluations has been to take domestically financed expenditure
EXP
_{0} in the counterfactual situation (without Structural and Cohesion Funds) as the benchmark and only examine the impact of the fiscal transfer
COH
_{t} received from the EU Cohesion Funds (Varga and in ’t Veld 2011b).