The Econometrics of Fiscal Policy

Transcription

1 The Econometrics of Fiscal Policy Carlo Favero, F.Giavazzi, M.Karamisheva Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 1 / 33

2 Papers This presentation is based on the following three papers: Alesina A., C.Favero and F.Giavazzi (forthcoming) "The Output E ect of Fiscal Adjustment Plans", Journal of International Economics Alesina A., Barbiero O., CA Favero, F.Giavazzi and M.Paradisi(2014) "Austerity in " Favero CA, M. Karamisheva (2015) "The Measurement of the Output E ect of Fiscal Adjustment" Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 2 / 33

3 Roadmap SVAR and Shocks The problem: Fiscal Foresight The solution: Narrative Identi cation From shocks to plans How this can be done What happens if you do not do it Empirical Results Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 3 / 33

4 SVAR and Shocks Empirical macro models (often SVARs) are used in the literature to establish empirical facts to be matched by theoretical models VARs can be interpreted as (approximations to) reduced form of DSGE models shocks are the "correct" experiment because the e ect of shocks is measured without changing any parameter in simulation When analyzing the e ect of economic policy VAR are reduced form approximation modelling jointly the structure of the economy and economic policy rules Exogenous deviations (obtained via appropriate rotations of the VAR innovations) from the rule are the interesting experiments to learn about the response of the macroeconomic variables to economic policy. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 4 / 33

5 SVAR and Fiscal Policy Fiscal policy is conducted through rare decisions and it is implemented through multi-year plans. The very nature of scal policy and scal foresight prevent the application of standard identi cation techniques to construct the interesting experiments. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 5 / 33

6 Fiscal Foresight Fiscal foresight happens when agents receive signals on the taxes they will face in the future. Consider the simplest RBC model, adapted from Leeper(2008). The equilibrium conditions are the following: 1 1 Y t+1 = αβe t (1 τ t+1 ) C t C t+1 K t C t + K t = Y t = A t Kt α 1 τ t = τ exp et τ p,t A t = exp et A This reduces (after log-linearization) to a bivariate model for capital and technology θe t k t+1 (1 + αθ) k t + αk t 1 = ρe t τ t+1 e A,t θ = αβ (1 τ), ρ = τ 1 θ 1 τ Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 6 / 33

7 After solving the model we obtain the following representation: k t = αk t 1 + e A t ρ i=0 θ i E t e τ t+1+i p,t+1+i a t = e A t Consider now estimating a bivariate VAR in a t, k t and retrieving the two shocks from the VAR innovations. As the equilibrium looks di erent for di erent degrees of scal foresight, the outcome of this procedure would clearly be a ected by it. In the case of no scal foresight the (q = 0) the equilibrium is k t = αk t 1 + e A t a t = e A t and a VAR in a t, k t would feature stochastic singularity, as only one shock will drive the two variables. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 7 / 33

8 In the case of one-period scal foresight, q = 1, the equilibrium is a t = e A t k t = αk t 1 + e A t ρe τ t,t+1 and a Choleski identi cation for the innovations in the VAR in a t, k t would allow to correctly identify the structural shocks of interest. In the case of two-periods scal foresight, q = 2, the equilibrium is a t = et A k t = αk t 1 + et A ρ et τ 1,t+1 + θet,t+2 τ and it would not be possible to identify the structural shocks of interest from the VAR innovations. In fact, for any q = 2 we have non-invertibility of the moving average component of the time series of k t (see Hansen and Sargent, 1991, Lippi and Reichlin, 1994). Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 8 / 33

9 The R&R "narrative" approach A time-series of exogenous shifts in taxes is constructed using o cial documentation, such as congressional reports, etc.to identify the size, timing, and principal motivation for all major postwar tax policy actions legislated tax changes are classi ed into endogenous (induced by short-run countercyclical concerns) and exogenous, taken to deal with an inherited budget de cit, or driven by concerns about long-run economic growth or politically motivayed: ε RR t i ε RR t i measure the impact of a tax change at the time it was implemented (t i) on tax liabilities at time t. the e ect of ε RR t i on output is estimated using quarterly data and OLS in a single equation, a truncated (M=12) MA y t = a + M j=0 b i et RR j + v t For M=12. Note that this equation is a truncated MA. Impulse responses Carlo are Favero, read F.Giavazzi, directly M.Karamisheva o the() b i coe The Econometrics cients. of Fiscal Policy 9 / 33

10 The R&R "narrative" approach Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 10 / 33

11 Devries et al (2011, D&al) and used in Guajardo et al (forthcoming). These episodes cover 17 OECD countries between 1978 and Among all stabilization episodes these authors have selected those that were designed to reduce a budget de cit and to put the public debt on a sustainable path Cloyne(2012) does R&R for the UK Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 11 / 33

12 Fiscal Policy occurs through plans not shocks Narrative identi cation can be naturally used to study the response of output (and of other variables) to multi-year scal consolidation plans which is di erent from simulating the impact of individual shifts in tax revenue or in spending When scal policy is conducted through multi year plans, scal adjustments in each year say year t consist of three components: unexpected shifts in scal variables (announced upon implementation at time t) shifts implemented at time t but announced in previous years future announced corrections (announced at time t for implementation in some future year). unanticipated and anticipated shifts and corrections in T and G are correlated Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 12 / 33

13 Pooling Fiscal plans are rare: pool episodes from di erent countries pooling is dangerous in the presence of heterogeneity (Favero, Giavazzi, Perego 2012) AFG (2014) pool the data from di erent countries by allowing for two sources of heterogeneity within country heterogeneity with respect to the type of scal adjustments: TB or EB between country heterogeneity in the way scal policy is conducted, e.g. persistence Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 13 / 33

14 Step 1: Reconstructing plans Considering, for the sake of illustration, a forward horizon of 1 year, a narrative adjustments e t can be described as follows: e t = e u t + e a t,0 + e a t,1 e a t,1 = ϕ 1 e u t + v t,1 e a t,0 = e a t 1,1 Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 14 / 33

15 Step 1: The traditional approach In the traditional approach a truncated MA representation is adopted : z i,t = α + B(L)e i,t + λ i + χ t + u i,t Two possible representation a truncated in nite MA from a VAR a speci cation to estimate an Average Treatment E ect Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 15 / 33

16 Step 2: A model to estimate and simulate plans without heterogeneity Direct estimation of the MA representation: z i,t = α + B 1 (L)e u i,t + B 2 (L)e a i,t,0 + +γ 1 e a i,t,1 + λ i + χ t + u i,t e a i,t,1 = ϕ i,1 e u i,t + v 1,i,t e a t,0 = e a t 1,1 to be estimated on a panel of countries i for the variable of interest z i,t. The standard MA representation is modi ed to allow exibility in the e ect of plans upon announcement and implementation. No distributed lag for the e ect of future announced plans is introduced because the e ect in time of announced adjustment is followed through the plan. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 16 / 33

17 Step 3: A model to estimate and simulate plans with heterogeneity But countries are di erent and plans are di erent so we propose: z i,t = α + B 1 (L)ei,t u TB i,t + B 2 (L)ei,t,0 a TB i,t + C 1 (L)ei,t u EB i,t + C 2 (L)ei,t,0 a EB i,t + +γ 1 ei,t,1 a EB i,t + δ 1 ei,t,1 a TB i,t + λ i + χ t + u i,t ei,t,1 a = ϕ i,1 ei,t u + v i,t,1 ei,t,0 a = ei,t a 1,1 ei,t u = τ u i,t + gi,t u ei,t,0 a = τ a i,t,0 + gi,t,0 a if τ u t + τ a t,0 + τ a t,1 > gt u + gt,0 a + gt,1 a =) TBt = 1, EB t = 1 TB t Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 17 / 33

18 Step 4: Putting the model at work Simulate, within sample, the output e ect of scal adjustment plans (i.e. compute impulse responses) Simulate, out of sample, the e ect of a speci c plan (Austerity in ) auxiliary system non-necessary but useful to check that the simulated sample is not too di erent from the estimation sample Not a full econometric model, so out-of sample simulation does not produce a forecast of output conditioning upon a full information set, but rather conditioning upon a speci c scal adjustment (that, if correctly identi ed, should be orthogonal to omitted info) Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 18 / 33

19 What are the consequences of collapsing plans into shocks? e IMF t = e u t + e a t,0 1 Restrictions are imposed on the general model that allows for plans: z i,t = α + B 1 (L)e u i,t + B 2 (L)e a i,t,0 + +γ 1 e a i,t,1 + λ i + χ t + u i,t e a i,t,1 = ϕ i,1 e u i,t + v 1,i,t e a i,t,0 = e a i,t 1,1 B 1 (L) = B 2 (L), γ 1 = 0,(this is why the uncertainty surrounding our estimates is much smaller than that surrounding the IMF estimates). Auxiliary system for the style of plans not estimated.simulated corrections might be very di erent from those observed in the sample used to estimate parameters. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 19 / 33

20 What are the consequences of collapsing plans into shocks? 1 "Shocks" become predictable (Jordà and Taylor, 2013) Cov e IMF t, et IMF 1 = Cov et u + et,0 a, e u t 1 + et a 1,0 = Cov et u + et a 1,1, e u t 1 + et a 1,0 = ϕ 1 Var (et u 1) 2 Similar consideration apply to R&R for which we have: ei,t RR = ei,t u + ei,t,1 a z i,t = α + B(L)ei,t RR + λ i + χ t + u i,t imposes the restrictions that (i) shocks annouced now for the future have the same e ect of shocks announced now and implemented now (ii) annouced shocks have no e ect upon implementation Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 20 / 33

21 Exogeneity and Predictability Predictability of et IMF by their own past does not necessarily imply violation of the relevant exogeneity concepts. Consider, for the sake of illustration, this simple representation u1t y t = β 0 + β 1 et IMF t = ρet IMF 1 + u 2t e IMF u 2t s N 0 0, + u 1t σ11 σ 12 σ 12 σ 22 The condition required for et IMF to be weakly exogenous for the estimation of β 1 is σ 12 = 0, and it is independent of ρ. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 21 / 33

22 Tax-based and spending-based plans: an example Stabilization plans in Italy: year τ u t τ a t,0 τ a t,1 τ a t,2 τ a t,3 gt u gt,0 a gt,1 a gt,2 a gt,3 a TB EB Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 22 / 33

23 The Econometric Speci cation z i,t = α + B 1 (L)e u i,t TB i,t + B 2 (L)e a i,t,0 TB i,t + (1) C 1 (L)e u i,t EB i,t + C 2 (L)e a i,t,0 EB i,t j=1 γ j e a i,t,j EB i,t + e a i,t,1 = ϕ 1,i e u i,t + v 1,i,t e a i,t,2 = ϕ 2,i e u i,t + v 2,i,t e a i,t,3 = ϕ 3,i e u i,t + v 3,i,t 3 j=1 e a t,0 = e a t 1,1 e a t,j = e a t 1,j+1 + e a t,j e a t 1,j+1 j > 1 δ j e a i,t,j TB i,t + λ i + χ t + u i,t the model is estimated with SUR simultaneously for all 14 countries. It is a quasi-panel: cross-country restrictions on B i, C i, not on correlation between e a i,t,j and eu i,t,j : we allow for heterogeneity in the style of scal plans z: (Y, C, I Business Con dence, Consuner Con dence, 3-mo Rate, Term spread) one at a time Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 23 / 33

24 Model Restrictions z i,t = α + B 1 (L)τ u i,t + B 2 (L)τ a i,t,0 + C 1 (L)gi,t u + C 2 (L)gi,t,0 a j=1 γ a j τa i,t,j + τ a i,t,t+1 = ϕ 1,i τ u i,t + v 1,i,t τ a i,t,t+2 = ϕ 2,i τ u i,t + v 2,i,t τ a i,t,t+3 = ϕ 3,i τ u i,t + v 3,i,t gi,t,t+1 a = ϕ 4,i gi,t u + v 4,i,t g a i,t,t+2 = ϕ 5,i g u i,t + v 5,i,t g a i,t,t+3 = ϕ 6,i g u i,t + v 6,i,t g u i,t = ϕ 13,i τ u i,t + v 13,i,t 3 j=1 δ j gi,t,j a + λ i + χ t + u i,t τ a i,t,t+1 = ϕ 7,i g u i,t + v 7,i,t τ a i,t,t+2 = ϕ 8,i g u i,t + v 8,i,t τ a i,t,t+3 = ϕ 9,i g u i,t + v 9,i,t g a i,t,t+1 = ϕ 10,i τ u i,t + v 10,i,t g a i,t,t+2 = ϕ 11,i τ u i,t + v 11,i,t g a i,t,t+3 = ϕ 12,i τ u i,t + v 12,i,t we estimate three ϕ 0 s parameters instead of thirteen and then distinguish between tax-based and expenditure based adjustments. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 24 / 33

25 ATE based on Local Projection Method Consider rst the case in which the narrative identi ed shocks satisfy the exogeneity property (selection on observables). In this case the average policy e ect is E [(y t,h (d j ) y t ) (y t,h (d 0 ) y t ) j w t ] = θ h can be calculated by the LPM (which is based again on a simpli ed MA representation) y t+h y t = α h + θ h e IMF t + γ h0 w t + v t+h Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 25 / 33

26 What is LPM? consider the following simple VAR, augmented with the observable, narratively identi ed, et IMF shocks Y t = AY t 1 + β 1 e IMF t The MA if the VAR truncated at lag h is + ɛ t Y t+h = A h+1 Y t 1 + A h β 1 et IMF + v t+i v t+i = β 1 et+h IMF +...A h 1 β 1 et+1 IMF + A h β 1 et IMF + +ɛ t+h + Aɛ t+h A i ɛ t The impulse response E Y t+h p et IMF = 1, I t E Y t+h p e IMF t can be obtained by a series of regressions y t+h = π 0 h Y t 1 + θ h e IMF t = 0, I t + v t+i = Y t+h e IMF t = A i β 1 Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 26 / 33

27 What is LPM? in practice the conditioning set Y t 1 can be augmented in LPM as LPM is based on a single equation estimation (after the identi cation of the shocks) and more degrees of freedom are available: y t+h = γ h0 w t + θ h e IMF t + v t+i LPM regressions omit et+h IMF,..., eimf t+1.this omitted variables problem would not lead to inconsistent estimates of the parameters of A i β 1 (p lim h ^ i = A i β 1 ) only if et IMF were orthogonal to all omitted variables. Unfortunately, this orthogonality is lost when scal policy is implemented through plans because, as shown above, the very nature of plans generates a correlation in et IMF. The hope for the LPM method is that w t captures the relevant variation in all omitted variables. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 27 / 33

28 ATE based on Local Projection Method and IPW If the IMF shocks can be predicted by controls and controls are correlated with output there is an allocation bias problem. Moving from plans to shocks is our route to solve this problem Jordà and Taylor (2013) proceed in a di erent way and try to apply the LPM after having purged the shocks from predictability : (i) rede ne et IMF innovations as a 0/1 dummy variable, (ii) estimate a propensity score deriving the probability with which a correction is expected by regressing it on its own past and predictors, (iii) use the propensity score to derive an Average Treatment E ect based on Inverse Probability Weighting. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 28 / 33

29 ATE based on Local Projection Method and IPW Denote the policy propensity score p j (w, ψ) for j = 1, 0 (the predicted values from a probit projections of the policy indicator on the set of predictors w). θ h = E [(y t,h (d 1 ) y t ) (y t,h (d 0 ) y t ) j w t ] 1 fdt = d 1 g 1 fd t = d 0 g = E (y t,h y t ) p 1 (w, ψ) 1 p 1 (w, ψ) j w t ^ h θ = 1 T (y t,h y t ) ^ δ t ^ δ t = 1 fd t = d 1 g ^ p 1 (w, ψ) 1 fd t = d 0 g 1 ^ p 1 (w, ψ) Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 29 / 33

30 ATE based on Local Projection Method and IPW In the LP framework ATE can be combined with LP in the following estimator LP-IWPRA estimator ^ h θ = 1 T (y t,h y t ) ^ δ t ^ φ t = 1 fd t = d 1 g ^ p 1 (w, ψ) ^ p 1 (w, ψ) ^φt m w t, γ h 1 fd t = d 0 g 1 1 ^ p 1 (w, ψ) ^ p 1 (w, ψ) where m w t, γ h is the mean of (y t,h y t ) predicted by the LP Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 30 / 33

31 Comments on Jorda-Taylor Replacing et IMF innovations with a 0/1 dummy variable gives up relevant information on the intensity and the nature of the adjustment. The links between the announced and the implemented part of a stabilization plan are lost. the di erent e ect of anticipated and unanticipated corrections depends only on the propensity score. Third, the presence of the forward looking component which is omitted from the speci cation might introduce a bias in the impulse response computed via local-projections whenever there is a systematic relation between the forward looking component and the unexpected component of the adjustment, as in the case in the D&al episodes. Fiscal plans are di erent across countries because the style of scal adjustments di ers across countries: thus they cannot be assimilated to an identical common treatment administered to many patients. Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 31 / 33

32 Empirical Results use the narrative shocks by allowing for error-in-variables. not applicable to plans Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 32 / 33

33 Conclusions lots of work needed Carlo Favero, F.Giavazzi, M.Karamisheva () The Econometrics of Fiscal Policy 33 / 33