Identification methodology

Following Fatas and Mihov (2001), Blanchard and Perotti (2002) or Perotti (2005), structural fiscal shocks are identified using a Structural VAR model. By ordering first public expenditure, one assumes that the government cannot react contemporaneously to changes in economic variables. First, I identify the SVAR with a Choleski decom-position. Then, I use the methodology introduced by Blanchard and Perotti (2002). If discretionary decisions taken by the government cannot occur within a quarter, changes in economic variables can automatically and contemporaneously impact the level of pub-lic expenditure and of tax revenues. In this sense, I use informations on elasticities of expenditure and tax revenues to the different economic variables to impose constraints in the SVAR.

Let us represent the following baseline VAR process:

X_t =A(L)X_t−1+U_t (1.43)

11I also run estimates with data detrended with the Hodrick-Prescott filter. Results are very close.

In the following, I consider the case of a public consumption shock and in which the real wage is introduced, such asXt ≡(C_t^g, Tt, Yt,Πt, Rt, Wt) defines the vector of variables, A(L) is a autoregressive lag polynomial and U_t ≡ [u^cg_t , u^t_t, u^y_t, u^π_t, u^r_t, u^w_t ] the vector of residuals associated with each variable. According to the LM tests and the Akaike and Schwarz information criteria, 4 lags are included in the VAR.

Choleski decomposition

First, I identify structural government spending shocks via a Choleski decomposition.

The AB model¹² can be defined as: AU_t = Be_t, with e_t ≡ [e^cg_t , e^t_t, e^y_t, e^π_t, e^r_t, e^w_t ] the vector of structural innovations. Applying a Cholesky decomposition yields the following constraints:

where A is a upper triangular matrix and B a diagonal matrix. The model is just-identified with a number of contraints equal to 2k² − ^k(k+1)₂ with k the number of variables.

12See L¨utkepohl (2007) for details about the SVAR modeling and the AB model.

The Blanchard-Perotti approach

The reduced-form residualsu^cg_t andu^t_t can be expressed as:

u^cg_t =acg,yu^y_t +acg,πu^π_t +acg,ru^r_t +acg,wu^w_t +βcg,cge^cg_t +βcg,te^t_t (1.46)

and

u^t_t =at,yu^y_t +at,πu^π_t +at,ru^r_t +at,wu^w_t +βt,te^t_t+βt,cge^cg_t (1.47) Similarly, residuals for the remaining variables can be expressed as:

u^y_t =b_y,cgu^cg_t +b_y,tu^t_t+β_y,ye^y_t (1.48)

u^π_t =bπ,cgu^cg_t +bπ,tu^t_t+bπ,yu^y_t +βπ,πe^π_t (1.49) u^r_t =br,cgu^cg_t +br,tu^t_t+br,yu^y_t +br,πu^π_t +βr,re^π_t (1.50) u^w_t =b_w,cgu^cg_t +b_w,tu^t_t+b_w,yu^y_t +b_w,πu^π_t +b_w,ru^r_t +β_w,we^w_t (1.51) In equation (1.46), and similarly foru^t_tin equation (1.47), reduced-form residual of pub-lic consumption is expressed as linear combination of the residuals of the other variables, the structural innovation of tax revenuese^t_t and its own structural innovation e^cg_t . The different parameters ”a” can capture two different effects: the automatic response of the public spending and taxes to the economic variables and the discretionary decisions of the government following changes in economic variables. By ordering first the fiscal variables, one makes the assumption that a government cannot react to changes on the economic variables within a quarter. Thereafter the parameters ”a” only capture the automatic response of the fiscal variables to the economic variables. These parameters are set thanks to institutional informations about elasticities of government expenditure and tax revenues to the different economic variables.

Elasticities of public expenditure This is commonly accepted that output elas-ticities of public consumption and public investmenta_cg,y anda_ig,y are set to 0. How-ever, it is likely that changes in prices affect contemporaneously public consumption

and investment. Following Perotti (2005), I set a_cg,π = a_ig,π = −0.5. Then, since our definition of public expenditure do not include interest payments, interest rate elasticities a_cg,r and a_ig,r are also set to 0. For real wage elasticities, this is un-likely than purchases of goods via public consumption or public investment react to changes in real wage, thereafter wage elasticities are also set to 0. Similarly, it is un-likely that public expenditure react to changes on other labor market variables, such as acg,n=aig,n =a_cg,l=a_ig,l=acg,u=aig,u= 0.

Elasticities of general government tax revenues. It is common practice to rep-resent output and price elasticities of tax revenue as the sum of the elasticities of its different components such as, fora_ty:

aty=^Ø

i

ξTi,BiξBi,yTi

T (1.52)

withT_ithe different tax components,ξ_Ti,Bi the elasticity of the tax componentT_ito its tax base andξ_Bi,y the elasticity of the tax base i to output. Giorno (1995) splits total tax revenue in 4 components: revenues from personal income tax, corporate income tax, indirect tax and social security contribution. The tax base for both personal income tax and social security contribution are compensations to employees. For the corporate income tax, the tax base is the gross operating surplus and for indirect tax the tax base is private consumption.

Following Burriel and al. (2010),¹³ output elasticity is set toa_t,y = 1,54 and price elasticity is set to a_t,π = 1,14. For interest rate elasticity, similarly to public expendi-ture, I setat,r = 0.

In contrary to public expenditure, changes on labor market variables can impact most likely tax revenues. First, changes in the unemployment rate can alter the EA general government tax revenue. For instance, according to the different tax compo-nents highlighted above, personal income tax and social security contribution could fall

13The authors estimate the effects of fiscal policy using a SVAR for the Euro Area following also Blanchard and Perotti (2002).

following a rise in unemployment. To compute the unemployment elasticity of general government total tax revenue, I use the following formula:

a_t,u=ξ_t,yξ_y,u= ξt,y

ξ_u,y (1.53)

To set ξu,y, the output elasticity of unemployment, I use computations found in Girouard and Andr´e (2005). The authors estimate the elasticities for a set of OECD countries including the 12 former EA members. I compute an elasticity for the Euro-Area as a whole by averaging the elasticities of individual members weighted by the share of each member state GDP in total Euro-Area GDP. I find an elasticity of un-employment to output equal to ξ_u,y = −4,26.¹⁴ With ξ_t,y = 1,54 as defined previ-ously, the unemployment elasticity of EA general government total tax revenue is set toa_t,u=−0,36.

Similarly to the unemployment elasticity, the employment elasticity of total tax rev-enue can be expressed as:

at,n = ξt,y

ξ_n,y (1.54)

The output elasticity of labor is set toξ_n,y = _α¹ withαthe labor elasticity of output as it can be found in a Cobb-Douglas production function. According to different esti-mates and in line with European Commission (2010),ξn,y is set to 1,53. I thus compute a_t,n = 1.

Compensations to employees affect at least directly two tax components: the per-sonal income tax revenue and the social security contribution. Price, Dang and Guille-mette (2014) produce new estimates for these two tax components to earnings for OECD countries. I compute an average for the Euro Area and I obtain an elasticity of personal income tax to earnings equal to 1,89 and an elasticity of social security contribution to

14Price, Dang and Guillemette (2014) compute new estimates for the output elasticity of unem-ployment for OECD countries. An average for the Euro Area according to these estimates yields ξu,y=−3,67. In this caseat,u=−0,43. Results with this value are however very close.

earnings equal to 0.91.¹⁵ Furthermore, I assume that the corporate income tax revenue and the indirect tax revenue are not influenced by compensations to employees. Finally, using equation (1.52) yieldsa_t,w = 0.68.

The last elasticity to set is at,lwhich defines the automatic response of the EA gen-eral government revenue to a change in the labor force participation. I seta_t,l= 0 since this is unlikely that a rise or a drop in the labor force participation affects the different tax components. On the expenditure side it could affect transfers and unemployment benefits, however I do not consider these public expenditure in this chapter.

With the help of these estimates, the cyclically-adjusted reduced form tax and spend-ing residuals can be expressed as:

¯

u^cg_t =u^cg_t −acg,yu^y_t −acg,πu^π_t −acg,ru^r_t −acg,wu^w_t =βcg,cge^cg_t +βcg,te^t_t (1.55)

and

¯

u^t_t=u^t_t−at,yu^y_t −at,πu^π_t −at,ru^r_t −at,wu^w_t =βt,te^t_t+βt,cge^cg_t (1.56) Finally, I setβcg,t= 0 andβt,cg Ó= 0, which means that the government decides the level of public expenditure first and that taxes respond to changes in public expenditure.¹⁶

¯

u^cg_t and ¯u^t_t can then be used to estimate the ”b” parameters by OLS.

All the previous constraints yield the followingAandBmatrix for the baseline case,

15Van den Noord (2000) and Bouthevillain (2001) find close estimates: an elasticity of personal income tax equals to 2 and an elasticity of social security contribution equals to 1.

16The opposite case whereβcg,tÓ= 0 andβt,cg= 0 is also tested and it provides very close results.

so thatX_t≡(C_t^g, T_t, Y_t,Π_t, R_t, W_t):

TheAandBmatrix contain 51 constraints, that makes the SVAR model just-identified.