COMPANION APPENDIX TO Fiscal Consolidation with Tax Evasion and Corruption (not intended for publication)

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1 COMPANION APPENDIX TO Fiscal Consolidation with Tax Evasion and Corruption (not intended for publication) Evi Pappa Rana Sajedi Eugenia Vella December, Corresponding author, European University Institute, European University Institute, Max Weber Programme, European University Institute,

2 A More extensions based on Blanchard and Leigh (3)

3 Table : Blanchard & Leigh (3) Regressions with Additional Controls - Components of GDP and Unemployment DEPENDENT VARIABLE: Forecast error of the growth of REGRESSORS Unemployment Rate Priv. Consumption Investment Exports Imports Planned Fiscal Consolidation.*** *** ** (.9) (.9) (.3) (.) (.773) High Tax Evasion.8** *** and Corruption Dummy (.) (.7) (3.3) (3.8) (3.8) Interaction ***. 3.3 (.39) (.33) (.37) (.8) (.) Constant -.787***..83.8*** 7.3*** (.3) (.) (.8) (.79) (.38) Observations R-squared Robust standard errors in parentheses p., p., p. 3

4 B Extensions of VAR Evidence B. Full IRFs for Baseline Regressions x x x x GDP 8 Govt Cons Expenditure 8 Govt Debt 8 Shadow Employment Empirical IRFs for Expenditure Cut - VAR with Output x x x x GDP 8 Direct Tax Rev enues 8 Gov t Debt 8 Shadow Employment Empirical IRFs for Tax Hike - VAR with Output

5 x x x x Unemployment Rate 8 Govt Cons Expenditure 8 Govt Debt 8 Shadow Employment Empirical IRFs for Expenditure Cut - VAR with Unemployment x x x x Unemployment Rate 8 Direct Tax Rev enues. 8 Gov t Debt 8 Shadow Employment Empirical IRFs for Tax Hike - VAR with Unemployment

6 B. Robustness Checks In order to verify the robustness of our baseline results to the identification strategy used, we present results from three alternative exercises aimed at ascertaining the effects of fiscal consolidations in Italy. To begin with, we use a different set of sign restrictions to identify the two fiscal consolidation shocks jointly in one VAR regression. In particular, we estimate a five variable VAR with GDP, government final consumption expenditures, tax revenues, the share of informal workers in total workers, and government debt, and identify uncorrelated government spending and tax shocks. To do so, we impose that debt falls with a lag following both shocks, and use zero restrictions that ensure that only one instrument is active in each case. In other words, to identify a consolidation through a spending cut we assume that taxes do not move on impact after the shock, while the opposite is assumed in the case of a consolidation through a tax hike. All other responses are left unrestricted. The sign restrictions used are summarised in Table. As before, we then run the same regressions replacing GDP with the unemployment rate. Table : Sign Restrictions - Five Variable VAR Variable: Govt Expenditure Tax Rate Debt-to-GDP Shock: t =, t =, t = Expenditure Cut Tax Hike + The resulting impulse response functions are shown in Figures -. As with the baseline regressions presented in the paper, we see that both types of consolidations are contractionary, both in terms of reducing output and increasing unemployment. Furthermore, in both the GDP and unemployment specifications of the VAR, we again see that shadow employment falls significantly after a spending cut, and rises significantly after a tax hike.

7 x 8 8 GDP x 8 Govt Cons Expenditure x 8 Tax Rates x x 8 Debt to GDP 8 8 Shadow Employment (%) Figure : Empirical IRFs for Expenditure Cut - Five Variable VAR with Output x x x 8 GDP x 3 x 8 Govt Cons Expenditure 3 8 Tax Rates 8 Debt to GDP 8 Shadow Employment (%) Figure : Empirical IRFs for Tax Hike - Five Variable VAR with Output 7

8 x x x 8 Unemployment Rate 8 Govt Cons Expenditure 8 Tax Rates x 3 x 8 Debt to GDP 8 Shadow Employment (%) Figure 3: Empirical IRFs for Expenditure Cut - Five Variable VAR with Unemployment x x... 8 Unemployment Rate 8 Debt to GDP 3 x 8 8 Govt Cons Expenditure x 8 Shadow Employment (%) x 8 Tax Rates Figure : Empirical IRFs for Tax Hike - Five Variable VAR with Unemployment 8

9 As a further exercise, we leave behind the sign restriction methodology and instead use simple Cholesky decompositions to identify the shocks. We again separate the analysis into two VARs for spending and tax based consolidations respectively. In each case, we order the endogenous variables as follows: {Inst, GDP, Debt, ShadowEmployment}, where Inst is either government spending or tax revenues. Again, we repeat the exercise using the unemployment rate in place of GDP. The results are shown in Figures and. Finally, we attempt to use the narrative fiscal consolidation episodes identified by Devries et al. () to identify the effects of consolidation on shadow employment. We use the methodology of Guajardo et al. (), who incorporate these episodes in a VAR to identify the effects of both tax based and spending based fiscal consolidations. We replicate their exercise, restricting to the case of Italy and adding the informal employment series. We then repeat the same exercise, replacing GDP with unemployment. It should be noted that, since we are looking at only one country, these estimates are based on relatively few consolidation episodes, making it diffi cult to obtain significant results. Nonetheless, Figures 7 and 8 show that the median response using the fiscal consolidation episodes confirms the previous result: informal employment falls after a spending based consolidation and rises after a tax based consolidation. 9

10 Figure : Empirical IRFs - VAR with Output - Cholesky Decomposition x x x x Govt Cons Expenditure (% GDP) 8 GDP 8 Shadow Employment (% Total) 8 Govt Debt (% GDP) Expenditure Cut x x x x Direct Tax Revenues (% GDP). 8 GDP 8 Shadow Employment (% Total) 8 Govt Debt (% GDP) Tax Hike

11 Figure : Empirical IRFs - VAR with Unemployment Rate - Cholesky Decomposition x x x x Gov t Cons Expenditure (% GDP) 8 Unemployment Rate. 8 Shadow Employment (% Total) 8 8 Gov t Debt (% GDP) Expenditure Cut x x 8 x x Direct Tax Rev enues (% GDP) 8 Unemployment Rate 8 Shadow Employment (% Total) 8 Gov t Debt (% GDP) Tax Hike

12 percent percent percent percent SHADOW EMPLOYMENT GDP Tax based Spending based Spending based Tax based 3 3 Figure 7: Empirical IRFs - Narrative Fiscal Consolidation Episodes - with Output SHADOW EMPLOYMENT UNEMPLOYMENT RATE Spending based Spending based Tax based Tax based 3 3 Figure 8: Empirical IRFs - Narrative Fiscal Consolidation Episodes - with Unemployment Rate

13 Table 3: Anticipated Shocks Dependent Variable: VAR Expenditure Shocks REGRESSOR Raw Professional. Forecast Errors (.) Purified Professional -. Forecast Errors (.) Constant.. (.) (.) R-squared.9. Robust standard errors in parentheses p., p., p. B.3 Anticipated Shocks An important problem that may arise when using sign restrictions to identify shocks is the issue of anticipated shocks. This problem is particularly pertinent to fiscal shocks due to the way in which fiscal policy is carried out, with news about future policy changes released to the public ahead of time, and lags between policy decisions and their implementation. As discussed in Perotti () and Ramey (), this can have significant implications for the results of VAR estimation. Dealing comprehensively with this issue is not straightforward, and is beyond the scope of this paper. As a first pass at ascertaining whether the shocks we have identified are truly unanticipated, we follow Perotti () and regress the spending shocks on professional forecasts of government expenditure, taken from the ECB s survey of professional forecasts. We also repeat the exercise first regressing the forecast errors on the lag of the variables in the VAR, and then regressing the VAR shocks on these purified forecast errors. The results of these regressions are shown in Table 3. We see that the forecasts are uncorrelated to our shocks, suggesting that VAR shocks are not predictable. 3

14 C Derivations C. Household s maximisation problem We can write in full the Lagrangean for the representative household s maximisation problem. Firstly, we can incorporate the composition of the household, as well as the definition of the total effective consumption bundle, directly into the utility function of the household. Then, we can plug the definition of the matches m j t = ψ hj t u j t into the law of motion of employment in each sector, and also replace i t in the budget constraint using the law of motion of private capital. Then we are left with 3 constraints, and the following Lagrangean: L = E t= { β t [α (c t ) α + ( α )(g t ) α ] η α η λ ct [ ( + τ c t)c t + k t+ ( δ)k t + ω + Φ [ ut n F t n I t ] ϕ ϕ ( ) kt+ k t + B t+π t+ k t R t ] ( τ n t )wt F n F t wt I n I t ϖ( s t )u t B t Π p t + T t [ ] λ n F t n F t+ ( σ F )n F t ψ hf t ( s t )u t r t k t [ ] } λ n I t n I t+ ( ρ σ I )n I t ψ hi t s t u t () The controls are c t, k t+, B t+, n F t+, ni t+, u t and s t. The first order conditions are: [wrt c t ] cc ( η α ) t α c (α ) t λ ct ( + τ c t) = () [wrt k t+ ] [wrt B t+ ] [wrt n F t+ ] ( )] [ kt+ λ ct [ + ω βe t λ ct+ δ + r t+ + ω k t ( (kt+ k t+ ) )] = (3) λ ct R t + βe t λ ct+ π t+ = () [ ] λ n F t βe t Φl ϕ t+ λ ct+( τ n t+)wt+ F λ n F t+( σ F ) = ()

15 [wrt n I t+ ] λ n I t βe t [Φl ϕ t+ λ ct+w I t+ λ n I t+( ρ σ I )] = () [wrt u t ] Φl ϕ t + λ ct ϖ + λ n F tψ hf t ( s t ) + λ n I tψ hi t s t = (7) [wrt s t ] λ n F tψ hf t u t + λ n I tψ hi t u t λ ct ϖ = (8) Equations ()-() are the arbitrage conditions for the returns to consumption, private capital and bonds. Equations () and () relate the expected marginal value from being employed in the each sector to the wage, accounting for the income tax in the regular sector, the utility loss from the reduction in leisure, and the continuation value, which depends on the separation probability. Equation (7) states that the value of being unemployed (rather than enjoying leisure), λ ct ϖ, should equal the marginal utility from leisure minus the expected marginal values of being employed in each sector, weighted by the respective job finding probabilities and shares of jobseekers. Equation (8) is an arbitrage condition according to which the choice of the share, s t, is such that the expected marginal values of being employed, weighted by the job finding probabilities, are equal across the two sectors. We can define the marginal value to the household of having an additional member employed in the two sectors, as follows: V h n F t L n F t = λ ct w F t ( τ n t ) Φl ϕ t + ( σ F )λ n F t (9) = λ ct w F t ( τ n t ) Φl ϕ t + ( σ F )βe t (V h n F t+ ) V h n I t L n I t = λ ct w I t Φl ϕ t + ( ρ σ I )λ n I t () = λ ct w I t Φl ϕ t + ( ρ σ I )βe t (V h n I t+ ) where the second equalities come from equations () and () respectively. C. Derivation of the resource constraint Consider the household s budget constraint: ( + τ c t)c t + i t + B t+π t+ R t r t k t + ( τ n t )w F t n F t + w I t n I t + ϖu F t + B t + Π p t T t ()

16 Recall the government s budget constraint: B t+ π t+ R t B t = DF t Plugging this into (): ( + τ c t)c t + i t + DF t r t k t + ( τ n t )w F t n F t + w I t n I t + ϖu F t + Π p t T t () Recall also the definition of the deficit: DF t = g t + ϖu F t ( ξ T R ) [ (τ n t + τ s t)w F t n F t + τ c tc t + T t ] ργp x t x t Plugging this directly into equation (): ( + τ c t)c t + i t + g t + ϖu F t ( ξ T R ) [ τ c tc t + (τ n t + τ s t)w F t n F t + T t ] ργp x t x t = r t k t + ( τ n t )w F t n F t + w I t n I t + ϖu F t + Π p t T t Cancelling out the taxes and unemployment benefits, we have: c t +i t +g t ργp x t x t = r t k t +(+( ξ T R )τ s t ξ T R τ n t )w F t n F t ξ T R (τ c tc t + T t )+w I t n I t +Π p t (3) Recall now that (i) the price of the final good is normalised to, (ii) the retail firms turn x t units of the intermediate good into y t units of the final good, and (iii) the differentiated retail goods are costlessly aggregated into the final consumption good. Then by definition, the profit from the retail firm can be written as: Π p t = y t p x t x t () Substituting this into equation (3), we obtain: c t +i t +g t = r t k t +(+( ξ T R )τ s t ξ T R τ n t )w F t n F t ξ T R (τ c tc t + T t )+w I t n I t +y t ( ργ)p x t x t () The price of the intermediate good, p x t, is determined by the zero-profit condition of the intermediate goods producing firm. That is, it satisfies: ( ργ) p x t x }{{ t [ ( + τ s } t)wt F n F t + wt I n I t + r t k t + κ F υ F t + κ I υ I ] t = }{{} Revenue of intermediate firms Costs of intermediate firms

17 Plugging this into equation (): c t + i t + g t = r t k t + ( + ( ξ T R )τ s t ξ T R τ n t )wt F n F t ξ T R (τ c tc t + T t ) +wt I n I t + y t [ ( + τ s t)wt F n F t + wt I n I t + r t k t + κ F υ F t + κ I υ I ] t () Cancelling terms we have: c t + i t + g t = y t ( κ F υ F t + κ I υ I ) t ξ T R ( τ c tc t + T t + (τ s t + τ n t ) wt F n F ) t (7) Rearranging terms we get the final expression: y t = c t + i t + g t + κ F υ F t + κ I υ I t + ξ T R T R t C.3 Derivation of the wages For each sector j = F, I the Nash bargaining problem is to maximize the weighted sum of log surpluses: { } max ( ϑ j ) ln V h w j n j t + ϑj ln V f n j t t where V h n j t and V f n j t are defined as: V h n F t = λ ctw F t ( τ n t ) Φl ϕ t + ( σ F )λ n F t (8) V h n I t = λ ctw I t Φl ϕ t + ( ρ σ I )λ n I t (9) V f n F t Q n F t V f n I t Q n I t = ( ργ) p x t ( α F ) xf t n F t = ( ργ) p x t ( α I ) xi t n I t ( + τ s t)w F t w I t + ( ρ σi )κ I ψ fi t The first order conditions of these optimization problems are: + ( σf )κ F ψ ff t () () ϑ F ( + τ s t)v h n F t = ( ϑf )λ ct ( τ n t )V f n F t () ϑ I V h n I t = ( ϑi )λ ct V f n I t (3) Plugging the expressions for the value functions into these FOCs, we can rearrange to find expressions for w F t w F t = ( ϑf ) ( + τ s t ) and w I t. Using (8), () and (), we can solve for w F t, which yields: ( ( ργ) p x t ( α F ) xf t n F t + ( σf )κ F ψ ff t ) ϑ F ( + λ ct ( τ n t ) Φl ϕ t ( σ F )λ n F t ) 7

18 () Similarly using (9), () and (3), we can solve for w I t, which yields: w I t = ( ϑ I ) ( ( ργ) p x t ( α I ) xi t n I t ) + ( ρ σi )κ I ( ) ψ fi + ϑi Φl ϕ t ( ρ σ I )λ λ n I t t ct () D Calibration strategy We calibrate the model using annual data on the Italian economy over the period 98-. D. Formal Labor market We calibrate the labor-force participation and the unemployment rates that are related to the formal market to match the observed average values from the data. We set lf n F + u F = % and uf lf = %. Then using definitions we can get: u F = uf lf lf n F = lf u F We fix the separation rate, σ F, equal to.7 and we can derive: m F = σ F n F and ψ hf = mf u F Since there is no exact estimate for the value of the formal vacancy-filling probability, ψ ff, in the literature, we use what is considered as standard by setting it equal to.9. Hence, we can also derive: υ F = mf ψ ff We set the matching elasticity with respect to vacancies, µ, equal to.7, close to the estimate for Italy in Peracchi and Viviano (). Then the matching effi ciency parameter for the formal sector can be set to satisfy: µ F = m F (υ F ) µ (u F ) µ 8

19 D. Formal Production We set the capital depreciation rate, δ, equal to.88. Then we derive i k : i k = δ Following the literature, we set the discount factor, β, equal to.9. Next, we get R: R = β and r = R + δ The elasticity of demand for intermediate goods, ɛ, is set such that the gross steady-state markup, ɛ ɛ, is equal to., and the price of the final good is normalized to one. Then px is determined by: p x = ɛ ɛ We set the TFP parameter in this sector A F = and the capital share α F =.3. We set the probability of audit and the fraction of total profits paid as a fine in the event of an audit as follows: ρ =., which is close to the value used in Boeri and Garibaldi (7), and γ =.3. Then we can obtain from the firms FOC with respect to capital: y F k = r ( ργ) p x α F From the production function in the regular sector we have: n F k = A F ( y F k ) α F Using definitions we can then obtain: k = n F ( n F k ), y F = yf k k, i = i k k We set the vacancy costs in the formal sector κ F =. and the payroll tax rate τ s =. close to the value used in Orsi et al. (). Then we have: w F = ] [( ργ) p x ( α F ) yf n F (R + σf ) κf ψ ff /( + τ s ) 9

20 D.3 Informal Production We set the TFP in the informal sector A I =. and α I =.. Using Istat data we set ni n =.3 and we can derive: n I = n I n n F ni n Then by definition we have: y I = (A I n I ) αi, y = y F + y I D. Informal Labor Market We set the exogenous job destruction rate in the informal sector σ I =.. We denote by σ I the total steady state separation rate in the underground sector, that is: σ I σ I + ρ Then we have m I = σ I n I Then we set ψ fi =. and get: υ I = mi ψ fi We set the vacancy cost in the informal sector κ I =.3 and derive w I = ( ργ) p x ( α I ) yi n I (R + σi ) κi ψ fi D. Fiscal Variables Next, we set the replacement rate, ϖ w F, equal to.3 close to the estimates in Martin (99), also used by Fugazza and Jacques (). Then by definition: ϖ = ϖ w F wf We set government spending and the tax rates as follows: g y = %, τ n =., in line with Orsi et al. (), and τ c =.8. Then by definition: g = g y y

21 We set the steady state debt-to-gdp ratio from the data, b = 3% and using the law of motion of debt-to-gdp we derive DF y = (β )b and by definition DF = DF y y We set the corruption parameter ξ T R =.. Then using the definition of the deficit we derive T R = g + ϖuf ργp x y DF ξ T R Then using the resource constraint we have: c = y i g κ F υ F κ I υ I ξ T R T R and from the definition of tax revenues we have T = T R (τ n + τ s ) w F n F τ c c D. Household We set the intertemporal elasticity of substitution, η, equal to. and the weight of private consumption in effective consumption, α = for the case of wasteful government spending. For the case of utility-enhancing spending we set α =.8 and α =., so that private and public spending are complements. This gives us the consumption bundle by definition: cc = [α (c) α + ( α )(g) α ] α and also: λ c = cc( η α ) α c (α ) + τ c We then use the following three equations: [ ] [ β( σ F ) + βψ hf ]λ n F = βλ c ( τ n )w F uf u F + u I ϖ ] [ β( σ I ) + β mi u I ]λ n I = βλ c [w I uf u F + u I ϖ

22 m I λ n I u I = λ n F ψhf + λ c ϖ to solve for the three unknowns λ n F, λ n I and u I. This gives us, by defintion: ψ hi = mi u I l = lf n I u I u = u F + u I s = ui u µ I = m I (υ I ) µ (u I ) µ We set the value of leisure in the utility function, ϕ, equal to. Then we can derive Φ to satisfy: Φ = ( λ c ϖ + λ n F ψ hf ) l ϕ We set the bargaining power parameters in the two sectors to satisfy: ϑ F = ΩF wf Ω F ΩF ϑ I = ΩI wi Ω I ΩI where Ω F [ ( ργ) p x ( α F ) yf n F ] [ ] + ( σf )κ F /(+τ s ), Ω I ψ ff ( ργ) p x ( α I ) yi ni + ( σi )κ I, ψ fi Ω F [ Φl ϕ ( σ F )λ n F ] / (λc ( τ n )), Ω I [ Φl ϕ ( σ I )λ n I ] /λc. D.7 Other Parameters The steady state debt-to-gdp target is set equal to the actual debt-to-gdp ratio, b = b = 3%. In order to achieve a % drop in the debt-to-gdp target periods after a shock, we set ρ =.8 and ρ =.. We set the inflation targeting parameter in the Taylor rule, ζ π =., the capital adjustment costs ω =. and the price-stickiness parameter χ =.. Finally, we set the parameters of the fiscal policy rule in each case to ensure that we meet the target after periods. E Additional Figures

23 .. Figure 9: Comparison of Benchmark and Full Model - Expenditure Cut PARTICIPATION RATE CONSUMPTION INVESTMENT GROSS REAL INTEREST RATE CAPITAL FORMAL VACANCIES 8 FORMAL JOBSEEKERS FORMAL EMPLOYMENT FORMAL W AGE FORMAL OUTPUT 8 ACTIVE INSTRUMENT BENCHMARK MODEL FULL MODEL TAX REVENUE 8 8 DEFICIT TO GDP RATIO 8 DEBT TO GDP RATIO 8 OFFICIAL UNEMPLOYMENT RATE.. 8 3

24 .. Figure : Comparison of Benchmark and Full Model - Labor Tax Hike PARTICIPATION RATE CONSUMPTION INVESTMENT GROSS REAL INTEREST RATE CAPITAL FORMAL VACANCIES 8 FORMAL JOBSEEKERS 8... FORMAL EMPLOYMENT 8... FORMAL W AGE 8.. FORMAL OUTPUT 8 ACTIVE INSTRUMENT TAX REVENUE 3 DEFICIT TO GDP RATIO DEBT TO GDP RATIO OFFICIAL UNEMPLOYMENT RATE 8 8 BENCHMARK MODEL FULL MODEL

25 ... Figure : Comparison of Benchmark and Full Model - Mixed Consolidation PARTICIPATION RATE CONSUMPTION INVESTMENT... GROSS REAL INTEREST RATE.. CAPITAL FORMAL VACANCIES 8 FORMAL JOBSEEKERS 8... FORMAL EMPLOYMENT FORMAL W AGE 8.. FORMAL OUTPUT 8 POLICY INSTRUMENTS g τ n TAX REVENUE.. DEFICIT TO GDP RATIO DEBT TO GDP RATIO OFFICIAL UNEMPLOYMENT RATE. 8 BENCHMARK MODEL FULL MODEL