Pitfalls of DSGE Model Approach in Monetary Union

Households in each country are allowed to consume both home and foreign products. They are also the only supplier of labor in economy and have the discounted welfare function and utility function: (1)Eo{∑t=0∞βtut(cti,ct-1i,g˜t)}E_o \left\{ {\sum\limits_{t = 0}^\infty {\beta ^t u_t \left( {c_t^i ,c_{t - 1}^i ,\tilde g_t } \right)} } \right\}(2)ut(cti,ct-1i,g˜t)={[cti-hct-1i]1-σc-11-σc+ζg˜t1-σc-11-σc,σc>0,σc≠1log[cti-hct-1i]+ζ log g˜t,σc=1u_t \left( {c_t^i ,c_{t - 1}^i ,\tilde g_t } \right) = \left\{ {\matrix{ {{{\left[ {c_t^i - hc_{t - 1}^i } \right]^{1 - \sigma _c } - 1} \over {1 - \sigma _c }} + \zeta {{\tilde g_t^{1 - \sigma _c } - 1} \over {1 - \sigma _c }},} \hfill & {\sigma _c > 0,\sigma _c \ne 1} \hfill \cr {{\rm{log}}\left[ {c_t^i - hc_{t - 1}^i } \right] + \zeta\, {\rm{log}}\,\tilde g_t ,} \hfill & {\sigma _c = 1} \hfill \cr } } \right.

These functions are same for every type of household in economy marked by i. Variable ctic_t^i is consumption of final goods and g˜t\tilde g_t represents the government services given to households. The parameter σ_c is the coefficient of relative risk aversion, h is the degree of habit formation in consumption and finally ζ is the relative weight of services given by government. The distribution of home/foreign goods in consumption basket depends on size of home country ω and on the degree of home bias in consumption ψ where P_At, P_Bt are price indexes: (3)cAticBti=(ω+ψ1-ω-ψ)PBtPAt.{{c_{{At}}^i } \over {c_{{Bt}}^i }} = \left( {{{\omega + \psi } \over {1 - \omega - \psi }}} \right){{P_{{Bt}} } \over {P_{{At}} }}.

Following Galí (2008) only fraction (1 – μ) of households can optimize their consumption without restriction on liquidity. Optimizing Ricardian households have access to capital markets and are able to substitute and distribute their consumption in time. Households spend their income on consumption, investments, buying bonds and paying taxes (from consumption, wages, investments, bonds and lump-sum taxes). Their income consists of profits from owning a firm, returns on capital investments, home and foreign bonds. They also receive various subsidies, wages from private and public sector and finally benefit in unemployment. Assuming the law of motion for capital with investments adjustment costs: (4)kto=(1-δk)kt-1o1+[1-κI2(ItoIt-1o)2]Ito,k_t^o = \left( {1 - \delta ^k } \right)k_{t - 1}^o 1 + \left[ {1 - {{\kappa _I } \over 2}\left( {{{I_t^o } \over {I_{t - 1}^o }}} \right)^2 } \right]I_t^o , the budget constraint of Ricardian households is equal to: (5)(1+τtc)cto+Ito+Bto+DtoPt+Tt(1-μ)=ΠtPt+((1+τtk)rtk+τtkδtk)kt-1o++Rt-1Bt-1oPt+Rt-1ecbe-ψd(dt-1-d)/Yt-1Dt-1oPt-τtb(Rt-1-1)Bt-1oPt+Subt(1-μ)++(1-τtw)(wtpntp,o+wtgntg,o)+(1-ntp,o-ntg,o)κB\eqalign{ & \matrix{ {\left( {1 + \tau _t^c } \right)c_t^o + I_t^o + {{B_t^o + D_t^o } \over {P_t }} + {{T_t } \over {(1 - \mu )}} = {{\Pi _t } \over {P_t }} + \left( {(1 + \tau _t^k )r_t^k + \tau _t^k \delta _t^k } \right)k_{t - 1}^o + } \cr { + {{R_{t - 1} B_{t - 1}^o } \over {P_t }} + {{R_{t - 1}^{{ecb}} e^{ - \psi _d (d_{t - 1} - d)/Y_{t - 1} } D_{t - 1}^o } \over {P_t }} - \tau _t^b {{(R_{t - 1} - 1)B_{t - 1}^o } \over {P_t }} + {{{Sub}_t } \over {(1 - \mu )}} + } \cr { + (1 - \tau _t^w )\left( {w_t^p n_t^{p,o} + w_t^g n_t^{g,o} } \right) + \left( {1 - n_t^{p,o} - n_t^{g,o} } \right)\kappa ^B } }}

Non-Ricardian households, remaining μ part, are not allowed to save or borrow money in time, therefore they can spend on consumption only their actual income from wages and unemployment benefit. (6)(1+τtc)ctr=(1-τtw)(wtpntp,r+wtgntg,o)+(1-ntp,r-ntg,r)κB(1 + \tau _t^c )c_t^r = (1 - \tau _t^w )\left( {w_t^p n_t^{p,r} + w_t^g n_t^{g,o} } \right) + \left( {1 - n_t^{p,r} - n_t^{g,r} } \right)\kappa ^B

Production process in economy is divided into three sectors of retail, intermediate goods and labor firms that produce homogenous labor. Retailers buy the intermediate goods and create the final products that is sold under perfect competition. The maximization problem of representative firm: (7)max{y˜t(j):j∈[0,ω]}PAt(∫0ω(1ω)1εy˜t(j)ε-1εdj)εε-1-∫0ωPAt(j)y˜t(j)dj, ε>1\mathop {\max }\limits_{\{ \tilde y_t (j):j \in [0,\omega ] \}} P_{{At}} \left( {\int_0^\omega {\left( {{1 \over \omega }} \right)^{{1 \over \varepsilon }} \tilde y_t (j)^{{{\varepsilon - 1} \over \varepsilon }} {dj}} } \right)^{{\varepsilon \over {\varepsilon - 1}}} - \int_0^\omega {P_{{At}} (j)\tilde y_t (j){dj},\,\,\,\varepsilon > 1} results in total demand for each intermediate input. (8)ωy˜t(j)=yt(j)=(PAt(j)PAt)-εYt.\omega\, \tilde y_t (j) = y_t (j) = \left( {{{P_{{At}} (j)} \over {P_{{At}} }}} \right)^{ - \varepsilon } Y_t .

The sector of intermediate goods is characterized by following technology depending on total factor productivity ɛ^a, public stock capital determined by government kt-1gk_{t - 1}^g , demand for capital services k˜t\tilde k_t (j) and for labor services l_t ( j). (9)yt(j)=εa(kt-1g)η(k˜t(j))α(lt(j))1-αy_t (j) = \varepsilon ^a \left( {k_{t - 1}^g } \right)^\eta \left( {\tilde k_t (j)} \right)^\alpha (l_t (j))^{1 - \alpha }

According to Calvo pricing every period there is a randomly chosen fraction θ_p of firms that cannot re-optimize their prices, remaining part choose the price PAt˜\widetilde{P_{{At}} } in order to maximize their profit. As a result, the law of motion of the price level is given by: (10)PAt=[θp(PAt-1)1-ε+(1-θp)(PAt˜)1-ε]1/(1-ε)P_{{At}} = \left[ {\theta _p (P_{{At} - 1} )^{1 - \varepsilon } + \left( {1 - \theta _p } \right)\left( {\widetilde{P_{{At}} }} \right)^{1 - \varepsilon } } \right]^{1/(1 - \varepsilon )}

The labor market is the most complicated sector in production, the details are not presented here and can be found in original work of Stähler and Thomas (2012). The process of matching employers with employees is present in the sector and so that wage bargaining. Similar to previous optimizations, every period only fraction of firms is allowed to renegotiate the wages and the law of motion of for public (g) or private (p) sector is: (11)Ntf=(1-sf)Nt-1f+pfU˜t, f=p,g.N_t^f = \left( {1 - s^f } \right)N_{t - 1}^f + p^f {\widetilde{U_t}} ,f = p,g.

Today’s employment is given by employment that has survived from last period and plus the new matches from unemployed population.

Fiscal policy is performed by government and therefore its debt b_t plays an important role. Debt accumulation can be expressed as: (12)bt=Rt-1πtbt-1-PDt,b_t = {{R_{t - 1} } \over {\pi _t }}b_{t - 1} - PD_t , where primary deficit PD_t is defined as the difference of fiscal expenditures (government purchases, investments and employees, payments for unemployment benefits and subsidies) and revenues (social contributions, taxes from wages, bonds, consumption, investments and lump-sum taxes. (13)PDt=[Ctg+Itg+[(1+τtsc)wtgNtg]pBt1-ω-ψpBt1-ω-ψ+κBUt+Subt]-[(τtw+τtsc)(wtpNtp+wtgNtg)+τtbRt-1-1πtbt-1+τtCCt+τtk(rtk-δk)kt-1+Tt)]\eqalign{ & \matrix{ {{PD}_t = \left[ {{{C_t^g + I_t^g + \left[ {(1 + \tau _t^{{sc}} )\,w_t^g N_t^g } \right]p_{{Bt}}^{1 - \omega - \psi } } \over {p_{Bt}^{1 - \omega - \psi } }} + \kappa ^B U_t + {Sub}_t } \right] - } \cr {\left[ {(\tau _t^w + \tau _t^{{sc}} )\left( {w_t^p N_t^p + w_t^g N_t^g } \right) + \tau _t^b {{R_{t - 1} - 1} \over {\pi _t }}b_{t - 1} + \tau _t^C C_t + \tau _t^k \left( {r_t^k - \delta ^k } \right)k_{t - 1} + T_t )} \right]} }}

The government therefore has six instruments on the revenue side and five instruments on the expenditure side that can be used to affect the economy. Every group is characterized by rule.

Revenue side, for every instrument X ∈ {τ^w, τ^sc, τ^b, τ^c, τ^k} and its target X¯\bar X it holds: (14)Xt=X¯+ρX(Xt-1-X¯)+(1+ρX)ΦXexaux(bt-1Yt-1totpBt1-ω-ψ-ωb)+εtXX_t = \bar X + \rho _X (X_{t - 1} - \bar X) + (1 + \rho _X )\Phi _X e_x^{{aux}} \left( {{{b_{t - 1} } \over {Y_{t - 1}^{{tot}} }}p_{{Bt}}^{1 - \omega - \psi } - \omega ^b } \right) + \varepsilon _t^X

Expenditure side, for every instrument X ∈ {C^g, I^g, w^g, N^g, Sub,T} and its target X¯\bar X it holds: (15)XtX¯=(Xt-1X¯)ρx(bt-1ωbYt-1totpBt1-ω-ψ-ωb)(1-ρx)Φxexp(εtX),{{X_t } \over {\bar X}} = \left( {{{X_{t - 1} } \over {\bar X}}} \right)^{\rho _x } \left( {{{b_{t - 1} } \over {\omega ^b Y_{t - 1}^{{tot}} }}p_{Bt}^{1 - \omega - \psi } - \omega ^b } \right)^{(1 - \rho _x )\Phi _x } \exp \left( {\varepsilon _t^X } \right), where an εtX~IID\varepsilon _t^X \sim IID is shock and exauxe_x^{{aux}} is exogenous auxiliary variable for simulation purposes.

Monetary policy is controlled by one central bank for whole union with nominal interest rate RtecbR_t^{{ecb}} and long-run targets on inflation and GDP growth. The responds are given by simple Taylor rule (exponent * marks the all other members of union). (16)RtecbR¯ecb=(Rt-1ecbR¯ecb)ρR{[(πtτCπ¯τC)ω(πtτC,*π¯τC,*)1-ω]Φπ[(YttotYt-1tot)ω(Yttot,*Yt-1tot,*)1-ω]Φy}(1-ρR){{R_t^{{ecb}} } \over {\bar R^{{ecb}} }} = \left( {{{R_{t - 1}^{{ecb}} } \over {\bar R^{{ecb}} }}} \right)^{\rho _R } \left\{ {\left[ {\left( {{{\pi _t^{\tau ^C } } \over {\bar \pi ^{\tau ^C } }}} \right)^\omega \left( {{{\pi _t^{\tau ^C ,*} } \over {\bar \pi ^{\tau ^C ,*} }}} \right)^{1 - \omega } } \right]^{\Phi _\pi } \left[ {\left( {{{Y_t^{{tot}} } \over {Y_{t - 1}^{{tot}} }}} \right)^\omega \left( {{{Y_t^{{tot},*} } \over {Y_{t - 1}^{tot,*} }}} \right)^{1 - \omega } } \right]^{\Phi _y } } \right\}^{(1 - \rho _R )}

The final part of models are the international linkages between members of union which are given by trade of goods, services and international bonds. Net foreign asset position of home country changes according to: (17)dt=Rt-1ecbe-ψd(dt-1-d)/Yt-1πAtdt-1+1-ωω(CAt*+IAt*)-pBt(CBt+IBt),d_t = {{R_{t - 1}^{{ecb}} e^{ - \psi _d (d_{t - 1} - d)/Y_{t - 1} } } \over {\pi _{{At}} }}d_{t - 1} + {{1 - \omega } \over \omega }\left( {C_{{At}}^* + I_{{At}}^* } \right) - p_{{Bt}} (C_{{Bt}} + I_{{Bt}} ), where the last difference of real exports and imports is trade balance TB_t. Zero net supply of international bonds holds: (18)ωdt+(1-ω)pBtdt*=0.\omega d_t + (1 - \omega )p_{{Bt}} d_t^* = 0.

Before the model is estimated it is needed to introduce available information from data. Baseline parameters of the model are calibrated based on results stated in economic literature. The main purpose of our work is to analyse the changes in estimation for different sizes of country represented by parameter ω, therefore all other baseline parameters are remained the same as in Stähler and Thomas (2012) and can be found in Table A in Appendix. Targeted steady state values can be estimated by Bayesian techniques or calculated as means of respective variables for some periods of time. For the matter of our analysis, exact values are not important as they do not affect the final stability of equilibrium and are assigned based on Stähler and Thomas (2012).

First of all, neither economic policy, nor models are able to reflect all processes and relations in economy. It is also not expected that they perfectly would, but the omission of important fact can result in incorrect conclusions. The FiMod model (and so that a lot of other models of the monetary union) omits the close fiscal relations of union’s members that can spend at each other’s expense and wage “Fiscal Wars” between each other. Those relations are very special in case the countries are already joint in any other union as it is a case of EMU and was discussed previously.

Another real problem is that both, economic policy and models, fail in estimation of current expectations of economic subjects and therefore they are not able to predict the true direction of reactions on politic decisions. The theoretical transmission mechanism of political decisions is in general considered valid and also confirmed by observations, but only if the real expectations of subjects are in line with theoretical framework. The expectations are mainly influenced by the level of credibility, that is hardly introduced to models. Once the institution lost the credibility in the eye of economic subjects, it is pretty hard to gain it back. In case of lack confidence in economy then any intervention need not to result in desired output. It is more common that it would end completely different as it was planned. Let’s take a quick look on case of Eurozone and Greece.

Worldwide financial crisis exhausted the economies and they had started to face the problems with their public debts. The debts were cumulated from years of prosperity and mismanagement of government and were highly increased in years of crisis when the governments had tried to start up the economic growth. After revelations of Greece’s fake statistics, the credibility of Greek government and European institutions was severely compromised. The public did not firstly believe in rescue plans and interventions made by ECB (lowering the interest rates, buying of Greek bonds, printing of money) has not started up the consumption and investment yet. In a result after few years there is still deflation risk, the consumption is quite low, and the interest rates have almost reached the zero-low bound.

It seems that traditional tools are out of date and it is needed to come with something unconventional, new and unexpected, but first work hard to gain the trust back. The governments have to be deliberate in decisions and consolidate the national budgets. In 2012, almost all members of EU (25 of 28) signed the Treaty on Stability, Coordination and Governance in the Economic and Monetary Union (Fiscal Stability Treaty) in order to reinforce the coordination of economic policies between the members and to forego the crisis caused by mismanagement of public finances. This treaty undermines the position and strength of countries in their “Fiscal Wars”, but also reduces the state sovereignty. It was the concern of The Czech Republic and The United Kingdom and the main reason they refused to sign the Treaty.

Secondly, the problem of modelling is how we formally categorize the size of economy and its position in union. The standard way is to use the simple ratio of population size, as it is used in FiMod model introduced in previous parts. Can population size measure the size of economy and its impact on union correctly? The answer is not so obvious. We can think about the shares of GDP (economic power) or GDP per capita (economic level), but the methods of calculations for these statistics are frequently criticized. They are also already affected by all economic variables especially debts of economies and therefore they are not completely exogenous and suitable.

Economy can have small population, relatively quite small economic power, but its economic level might be very high and therefore can affect the rest of union. Just consider as an example group of four members, e.g. Spain, Greece, Luxemburg and Slovakia. Luxemburg is the smallest country by population and by economic power, but it is the biggest country by economic level. Slovakia is the smallest by economic power, Spain is the biggest by population and economic power. Greece is the second biggest by population and economic power and the second smallest by economic level. It is hard to say which of these countries can affect the union the most and therefore it is hard to decide which of the presented measures is the most suitable.

Third problem is the way in which the models and their results are used and explained. The current models consist of dozens of equations, parameters, are difficult to be understood and their complexity requires more and more computing capacity (which is not a case anymore in age of computers). On the contrary, as much as possible theoretic generalization is introduced in order to quickly estimate the model and to retain the acceptable level of interpretability. Too complicated model is not a tool that would be preferred by politics to make decisions. The exceptions are considered to be negligible without significant impact on results. Following this trend, functional models are taken over with only small adjustments from country to country and it can easily result in incorrect conclusions.