Temporary and Persistent Fiscal Policy Shocks Sergio Sola The Graduate Institute of International and Development Studies (IHEID) First draft: June 2011 This draft: December 2011

Abstract This paper conducts an empirical investigation of the eects of temporary versus persistent scal policy shocks. Using data from the US I show that short lived scal expansions have a positive eect on output and consumption; while persistent scal shocks generate negative eects on output and consumption, and are associated with an increase in private savings. Consistently with consumption smoothing, short-lived scal expansions generate a temporary de cit in the current account, while persistent scal shocks leave the external balance unaected. I nd evidence of non linearity in the eects of temporary and persistent scal shocks according to (i) the level of public debt and (ii) the state of the business cycle. Persistent scal shocks have larger negative eects on consumption and output if they take place at high levels of public debt, possibly due to the expectations of tax increases. The state of the business cycle is also very relevant. Persistent scal shocks generate negative multipliers in times of economic boom, but these negative multipliers disappear in periods of recession. On the other hand, temporary scal shocks have positive eects both in times of expansion and in times of recession, but with the multipliers being way larger in the latter case. These asymmetric eects are not the results of an asymmetric response of the monetary policy rule. Keywords: Fiscal Policy; Public Debt; Business Cycle. JEL Classi cation Numbers: C10, E43, F42, F62, H68.

 Address:

Avenue de la Paix, 11a, Geneve, Switzerland. e-mail: [email protected]. The author would like to thank, without implicating, Charles Wyplosz, Cedric Tille, Alessandro Missale, Ugo Panizza, Domenico Giannone and Gianni Amisano for helpful comments and suggestions. All mistakes remain my own.

1

Temporary and Persistent Fiscal Policy Shocks

1 Introduction Facing the prospects of a dire and prolonged recession, during 2008 and 2009 many governments around the world have discussed and implemented several stimulus packages in the hope that this would serve to spur economic activity and absorb mounting unemployment. The size of the packages has been remarkable, ranging from around 2% of GDP in Europe to 13% of GDP in China. The political debate around the implementation of such important measures was re ected in the revival of the academic research on the eectiveness of scal policy interventions. Although the debate took place under unusual circumstances - i.e. the sharpest economic decline since the Great Depression - the arguments advanced by the opposing factions are hardly new. Concerns about scal sustainability have led some economists to insist on a relatively short-lived scal stimulus, while the rapid increase in unemployment caused by the free-falling private demand has induced others to support a more prolonged intervention. Economic research is not conclusive in supporting either view. The possibility that temporary and persistent scal expansions have dierent eects on the real economy has been contemplated in economic theory, but so far the empirical research has been lagging behind.1 Part of the problem is related to the fact that dierent studies employ dierent methodologies and identi cation strategies, which impair the comparison of the results. From the theoretical point of view, Keynesian arguments would suggest persistent scal policy shocks to be preferable, as the larger government's intervention the larger the economic expansion. According to standard Keynesian models if consumption is a function of disposable income alone, an increase in budget de cit is obliged to have a large eect on output. Budget de cits increase aggregate output one for one, and the increase in disposable income triggers a multiplier eect which raises output more than proportionally. Because there are no concerns about future sustainability or future taxes, de cit spending ensures \bang for the buck" and carries no side eects. This type of dynamics is embedded in theoretical models such as the one by Romer and Bernstein (2009). On the other hand, a \neoclassical" perspective would suggest short-lived scal policy to be preferable as persistent scal shocks can raise concerns about future scal sustainability and large increase in future tax liabilities. Neoclassical models show that because de cit spending is associated with larger burden of future taxes, it induces agents to reduce consumption therefore limiting the eect of the scal stimulus (Baxter and King 1993). The possibility of these perverse eects would therefore suggest that persistent scal policy shocks, because of the large accumulation of public debt they entail, might be associated with contraction in the real economy (Sutherland 1997, Bertola and Drazen 1993 and Berben and Brosen 2007). The possibility of a negative correlation between scal expansion and the real economy, which has long been referred to as the \German view of scal policy" has found some empirical support by a series of studies which analyzed scal consolidations (Giavazzi and Pagano 1990 and Alesina and Perotti 1997 among others). The literature not only suggests that the response of the real economy to scal policy shocks will depend on the 1 Some

recent empirical studies have analyzed the eects of spending shocks which are followed by expectations of future spending reversals: Corsetti et al. 2009 and Cimadomo et al. 2011. Of these, however, only the latter proposes a framework which allows to compare the eects of dierent types of scal shocks.

2

Temporary and Persistent Fiscal Policy Shocks nature of the shock but also provides good reasons to suspect that this reaction will not be linear and its magnitude will depend on the level of public debt and on the state of the business cycle. First, at high level of public debt consumers are more likely to question the sustainability of public nances. As a consequence they would more heavily discount the tax burden associated with persistent scal policy shocks. This might therefore cause a larger negative eect of persistent scal policy expansions. The reverse of the reasoning would also hold: persistent scal consolidations might trigger positive real eects as agents react to the news of lower future taxes - Bertola and Drazen 1993 and Perotti 1999. At low level of public debt, instead, consumers will be less worried about the tax bill associated with large scal expansions and therefore less likely to modify their consumption and savings decisions as a consequence of persistent scal policy shocks. Dierences in the eects of scal policy shocks might also be due to the dierent reaction of monetary authority. With high levels of public debt it is possible that the Central Bank will be \dominated" by the scal authority and therefore be forced to lower interest rates as a consequence of a large scal expansion (Davig and Leeper 2011). Second, recent empirical work has shown scal policy multipliers to be dierent in times of expansion and in times of recession (Tagkalakis 2008; Baldacci et al. 2010; Auerbach and Gorodnichenko 2010, 2011). From a theoretical point of view, this asymmetry is justi ed by the fact that during recessions, the proportion of credit constrained agents increases and therefore standard Keynesian eects are likely to dominate the negative wealth eect of the agents which can smooth consumption (Gali et al 2007). Alternatively, the presence of unutilized productive capacity might limit the occurrence of crowding out eects through increases of the interest rates (Buiter 2010). Finally, the stronger eect could be due to the change in the behavior of the Central Bank. During periods of economic contraction, in fact, low in ation or even de ation and mounting unemployment could make the monetary authorities more accommodative towards large scal expansions. Reacting by keeping low interest rates, they will therefore contribute to large scal policy multipliers (Christiano et al. 2009; Erceg and Linde 2010; Woodford 2010). In this paper I contribute to the debate by comparing the eects of persistent versus short-lived scal expansions in the US while taking into account the potential non-linearities. Using Vector Autoregressions I show that there exist marked dierences in the eects of short-lived and persistent scal policy shocks. Short-lived scal expansions generate positive eect on output, consumption and investments, while persistent de cit spending shocks are associated with negative multipliers. Consistently with the hypothesis that agents react to the higher burden of future taxes, persistent scal policy shocks are also associated with a signi cant increase in private savings. Because of the large negative wealth eect persistent scal policy shocks are not re ected in current account de cits, while temporary scal expansions induce a temporary worsening of the current account. I then add an interaction term to the VAR to assess whether the eects of these two types of scal shocks are dierent at dierent level of public debt and show that at high level of public debt persistent scal policy shocks indeed have a stronger negative eect on consumption and output. This is consistent with the idea that agents are more concerned with public debt 3

Temporary and Persistent Fiscal Policy Shocks sustainability. Finally, following Amisano et al. (2009) and Auerbach and Gorodnichenko (2010), I estimate a non linear model to allow the eects to dier according to the state of the business cycle. These estimates are obtained using a Smooth Transition VAR (ST-VAR) where the transition from one state to the other is modelled using a logistic function. Consistent with the theory, I show that persistent scal policy shocks have negative eects in times of economic boom and mildly positive eects during recessions. On the other hand, temporary scal shocks have positive eects both in times of expansion and in times of recession, but with the multiplier being about 10 times as large in the latter case. These dierences do not seem to be due to the reaction of the monetary authority. The paper is organized as follows: Section 2 presents the empirical framework and discusses the identi cation strategy; Section 3 brie y presents the data used; Section 4 discusses the main results and Section 5 concludes.

2 Methodology To analyze the eects of the scal policy shocks I employ VAR analysis and I use an identi cation procedure which allows me to distinguish between two dierent types of scal shocks: (i) short-lived scal expansions - which revert to zero relatively fast and (ii) persistent expansions - which revert to zero only slowly over time. The identi cation is obtained using data on the expected stock of future debt. In fact, if agents are rational and use all of their available information to form expectations about the future, it is very likely that a scal expansion which is accompanied by an increase in expected future debt will turn out to be persistent. On the other hand, temporary scal expansions will either cause the expected future debt to decline or leave it unaected. The baseline speci cation of the VAR includes a measure of budget de cit, forecasts for the level of public debt, output, consumption and the federal fund rate. As I will discuss in more details in the next section, the rst two variables are used to identify the scal policy shocks, while the federal fund rate is included to assess whether the reaction of the monetary policy changes depending on the type of shock. To check the robustness of the results and deepen the understanding of the transmission mechanisms of the two scal policy shocks, I then re-estimate the baseline speci cation including a set of control variables (Section 4.1.1). The same identi cation strategy is then embedded into non-linear estimation techniques to investigate whether the real eects of these scal policy shocks are \state-dependent". However, because with non-linear models the number of parameters to estimate becomes very large, I limit my analysis to the baseline speci cation.

2.1 Identi cation In general the literature on scal policy has followed three dierent paths to identify exogenous scal policy shocks. Some studies (Perotti 2005; Auerbach and Gorodnichenko 2010) have followed the Structural VAR methodology proposed by Blanchard and Perotti (2002). Using information about the size of tax elasticities, this approach isolates discretionary scal shocks by taking into account the automatic reaction of the budget de cit to the business cycle. 4

Temporary and Persistent Fiscal Policy Shocks Some others (Ramey and Shapiro 1998, Edelberg et al 1999, Romer and Romer 2010, Ramey 2011) have followed the so called \narrative approach", which consists of constructing a time series of discretionary scal shocks. Originally (Ramey and Shapiro 1998) it consisted simply of estimating the eects on output and consumption of war episodes, arguing that those were the only instances of strong exogenous increase in government outlays. This approach has been recently re ned by Ramey (2011) who constructed a series of \defense news shocks" using information about the changes in the defense budget taken from the press. A third strategy is to employ sign restrictions - or \shape restrictions" (Canova and Pappa 2007, Mountford and Uhlig 2009, Dungey and Fry 2009). In this case the identi cation of scal policy shocks is obtained by imposing some theory-driven restrictions on the responses of the variables. Exogeneity with respect to the business cycle is obtained by further identifying a business cycle shock which is by construction orthogonal to the scal policy shocks. Here I follow the third option and identify the scal policy shocks using sign restrictions. Fiscal policy shocks are identi ed as movements in the cyclically adjusted primary de cit which are orthogonal to a business cycle shock, de ned as a co-movement between output and consumption. Sign restrictions allow me to distinguish between temporary and persistent scal shocks. This distinction is in fact obtained by restricting the co-movement between the cyclically adjusted budget de cit and the 5 years ahead forecasts on the stock of government debt. Both the cyclically adjusted de cit and the projections on the Government Debt are published by the Congressional Budget Oce (CBO). Following Laubach (2009) I use the forecasts for the baseline scenario and I consider the 5 years ahead forecasts to minimize the possibility that they are driven by considerations on the state of the business cycle. The fact that the public debt is nothing else than the \stock side" of budget de cits means that scal policy shocks that are perceived as persistent will be characterized by an increase in the budget de cit and a contemporaneous increase in the forecasts on public debt. On the other hand, scal shocks that are perceived as temporary will leave the forecasts on public debt unaected, or at most will induce a reduction in expected future debt if the de cit shock is expected to be reabsorbed by future surpluses. In sum, the identi cation of the shocks is obtained imposing the following set of restrictions:

Identi caton

Budget Expected De cit

Debt

Business Cycle Shock Temporary Fiscal Shock > 0

0

Peristent Fiscal Shock

>0

>0

Y

C

>0

>0

Ffr

It is important to note that because I use the cyclically adjusted budget de cit in the VAR it is in theory not necessary to identify also the business cycle shock. In fact, repeating the analysis identifying only the two scal policy shocks does not aect the results. In the spirit of this study, the responses of output and consumption to the scal shocks are left completely unre5

Temporary and Persistent Fiscal Policy Shocks stricted. Also the response of the federal fund rate is left unrestricted. This will yield important insight on the conduct of monetary policy when facing scal shocks with dierent temporal pro les.2

2.2 Non-Linear Eects Following the literature on the non linear eects of scal policy, I investigate whether short-lived and persistent scal policy shocks have dierent eects depending on: (i) the level of public debt; (ii) the state of the business cycle. From a theoretical point of view, the level of public debt can in uence the eects of scal policy shocks through two main channels. First, the level of debt determines the likelihood of a scal consolidation after a scal shock. In fact, at high levels of debt, it is more likely that a scal shock jeopardizes scal sustainability making consolidation inevitable. If this is incorporated by private agents, it might translate into large negative responses of consumption and output. Because persistent scal shocks are associated by de nition with higher future level of debt, they will more likely generate larger negative multipliers. Second, the level of public debt can in uence the reaction function of the Central Bank. In fact, if a scal expansion leads to a violation of the government budget constraint, the monetary authority can decide to step in and monetize the de cit, therefore ensuring solvency. The injection of liquidity will cause interest rates to fall and - everything else being equal - an expansion in real activity. Non-linearities with respect to the state of the business cycle are also likely to be important. As pointed out by Gali et al. (2007), in recessions the share of credit constrained agents increases. Hence there will be relatively more agents that react to scal shocks in a standard Keynesian fashion given that, without access to capital markets, their consumption depends only on disposable income. As a consequence, both types of scal shocks will display larger multipliers in recession than in expansions. However, because even in recessions there is a fraction of agents that is not credit constrained, the multipliers generated by temporary scal shocks will always be larger than those generated by persistent scal shocks. The reaction of the monetary authority can be a further source of asymmetries between the scal shocks. In a recession, in fact, the monetary authority is less concerned with the in ationary consequences of a scal policy expansion and is therefore less likely to react to the increase in budget de cit. This would further increase the scal policy multipliers in periods of recessions but generate dierences in the eects of persistent and temporary shocks in case the reaction of the central bank is not exactly similar in the two cases. So far the investigation of the non-linear eects of scal policy shocks has been mainly conducted using standard panel techniques (Giavazzi, Jappelli and Pagano 2005, Tagkalakis 2008, Beber and Brosens 2007 among others). Here I follow some more recent literature and estimate non linear VARs. In particular, to assess the eect of the level of public debt I borrow from the framework proposed by Sa et al. (2011) and Towbin and Weber (2011) 2 Following Canova and Pappa (2007) and Jarocinski (2010) the restrictions are obtained by rotating the orthogonalized shocks using an othonormal rotation matrix R which is such that RR = I .

6

Temporary and Persistent Fiscal Policy Shocks and include an interaction term in an otherwise standard VAR. Instead, to gauge the asymmetric eects over the business cycle I adapt the Smooth Transition VAR (ST-VAR) originally by Amisano et al. (2009) and then further developed by Auerbach and Gorodnichenko (2010).

2.2.1 VAR with Interaction term To allow the eects of scal policy shocks to vary with the level of public debt I re-estimate the baseline speci cation of the VAR introducing an interaction term. The VAR takes the form: Yt = A (L) Yt

1

+ B (L) Y

t

1

Xt

1

+E

t

where the variable X contains the log of the debt to GDP ratio. This formulation can in theory allow all the elements of the vector Y to be interacted with the variable X in each equation of the VAR. However, for parsimony, in each equation of the VAR I allow an interaction term only with the lags of the structurally adjusted budget de cit and of the federal fund rate. In practice this is equivalent to assuming that the non linear eects of public debt derive from the reaction functions of the government and of the central bank. In particular, level of primary de cit and of public debt will jointly determine the central bank's decision on the interest rate and the level of the interest rate and the level of public debt will determine the decision of the government about the budget de cit.

\ \

Because the equations of the VAR still have the same elements, consistent estimates can be obtained by standard OLS equation by equation. Once we have the matrices of the estimated coecients A (L) and B (L) we can assign a value to the variable X and, after having identi ed the shocks of interest, we can study the responses of the t

variables in Y at low and high levels of the variable X . I take value of the variable X which correspond to the top t

and bottom quartile of the debt to GDP ratio, which in the sample is equivalent to 34% and 45% respectively. The low debt regime roughly corresponds to the rst years at the beginning of the sample and the years 2000 to 2003 after the president Clinton's scal consolidation. Periods of very high public debt, instead correspond to the last years of the sample and to the years between 1991 and 1995, the last years of the G. H. W. Bush administration and the rst years of the Clinton's administration.

2.2.2 ST-VAR To study the asymmetric eects of the shocks over the business cycle, I follow Amisano et al. (2009) and Auerbach and Gorodnichenko (2010) and use of a Smooth Transition VAR (ST-VAR). The model is speci ed by the following set of equations:

7

Temporary and Persistent Fiscal Policy Shocks

Yt = (1



F (zt 1 )) A (L) Yt

1

= (1 F (z 1 ))  + F (z exp ( z ) F (z ) = 1 + exp ( z ) t

E

t

+ F (z

t

t

1

1

) B (L) Y

t

1

+E

(1)

t

)

(2)

R

(3)

t

t

t

where Y is the vector of endogenous variables variables and A (L) and B (L) are coecients in the lag operator t

and F (z ) are weights between zero and one, which are modelled to be the result of a logistic function in z . The t

t

variable z is de ned to be the seven quarter moving average of output growth. Hence F (z ) will take values t

t

close to 1 whenever the economy is in a state of recession, while it will take values close to zero for situations of economic expansion. Therefore the coecients A (L) and B (L) can be used to construct impulse response functions for the two states of the economy. As already discussed in Auerbach and Gorodnichenko (2010), modelling the recession/expansion states of the economy using a logistic function presents some major advantages. First of all it makes use of all the observations in the sample to estimate the coecients A (L) and B (L), which is particularly useful when there are not so many observations in one of the two states. Moreover, it allows the transition between the expansion and the recession states to happen gradually. In particular, the speed of transition between the two states is governed by the parameter : For values of  ! 1 the transition takes place with an instantaneous jump, similar to that obtained by using a simple dummy variable instead of the logistic weights F (z ). For values t

of  ! 0, instead, the transition takes place gradually. It is important to notice that the equation (1) would be linear in the parameters A (L) and B (L) if the coecient  was known. However, estimating (1) by OLS conditional on an appropriate value of  would not allow the variance covariance matrix of the error term to be time varying. Here, following Auerbach and Gorodnichenko (2010) I assume the variance covariance matrix to be a time varying function of two matrices  and  which are respectively the variance covariance matrices of the error terms in E

R

times of economic expansions and recessions. The time variation in the variance covariance matrix  is given by t

the logistic weights F (z

t

1

) and (1 F (z

t

1

)). Having this time varying error structure, although more realistic,

introduces some complications in terms of the estimation of the model. In fact, the matrices  and  are E

R

unobservable and therefore their estimation requires a Maximum Likelihood method. In theory, conditional on 

the set of parameters fA (L) ; B (L)g the likelihood function can be maximized for  ;  E

R



thus providing some

consistent estimates for the two variance covariance matrices. Then, conditional on the Maximum Likelihood n

b ; b estimates  E

R

o

ML

, the parameters fA (L) ; B (L)g can be re-estimated through Weighted OLS. Here I use

a multiple step estimation, iterating the maximization of the likelihood and the weighted OLS estimation until the likelihood function reaches convergence. Moreover, dierently from Amisano et al. (2009) and Auerbach and Gorodnichenko (2010) I do not calibrate the parameter  a priori, but I estimate it together with the two variance covariance matrices. More details on the estimation procedure are provided in Appendix A. 8

Temporary and Persistent Fiscal Policy Shocks Once the parameters of the model are estimated I can derive impulse response functions for the two extreme states of the economy; in particular impulse response functions for states of recessions are obtained as the limit for F (zt 1 ) ! 1 and impulse response functions for states of expansions are obtained as the limit for F (zt 1 ) ! 0.

The identi cation of the temporary and persistent scal shocks in the two regimes is obtained implementing the same set of restrictions presented in the previous section. The con dence bands are then obtained by Monte Carlo simulation.

3 Data The estimation is performed for the US for the period 1981Q4 to 2008Q4. The length of the sample and the choice of the country are dictated by the availability of data. In fact, the Congressional Budget Oce is the only institution that publishes regular forecasts for the government's budget over a long time horizon. As pointed out by Leeper (2009), the main advantage of using CBO forecasts is that they are widely known to the public. Hence they should be a good proxy of agents' expectations about the future path of scal policy. In general the CBO forecasts are released only twice a year, and therefore the data were interpolated to obtain forecasts at a quarterly frequency. The forecasts are then transformed to real terms using the CBO's forecasts for core in ation over the same horizon. The CBO is also the source for the data on the structural de cit. This is computed by eliminating the impact of automatic stabilizers from the primary de cit. Output and consumption are taken from the NIPA tables. Following Mountford and Uhlig (2009), I measure investments using \Private Non-Residential Investment". This is constructed from the NIPA tables subtracting \Private Residential Investments" - NIPA Table I.1, row 11 from \Nominal Gross Private Domestic Investments" - NIPA Table I.1, row 6. Savings and current account balance are taken from the FRED database and they correspond respectively to the voices: \Gross Private Savings" and \Balance on the Current Account". All the variables are converted to real terms using the GDP de ator. The federal fund rate is taken from the historical series published by the New York Fed. Following Mountford and Uhlig (2009) I convert all the series to logs, so that the magnitude of the responses can be interpreted as elasticities,3 while the interest rate is left expressed in percentage points.

4 Results The discussion of the results is divided into two sections. Section 5.1 presents the results of the linear speci cation, while Section 5.2 discusses the results coming from the non-linear estimations. 3 For the cyclically adjusted de cit and the current account balance, because they have negative values, the adjustment to logs is done following Levy Yeyati, Panizza and Stein (2007). The adjusted variable is therefore de ned as: et = sign(Xt ) log (1 + jXt j) X

9

Temporary and Persistent Fiscal Policy Shocks

4.1 Linear VAR The baseline model consists of estimating a linear VAR which contains: the structurally adjusted de cit, the 5 years ahead forecasts on public debt, output, consumption and the federal fund rate. The VAR is estimated in levels with a constant term and two lags of the endogenous variables, as suggested by the Schwarz and the Hannan and Quinn information criteria (Table 1). The shape restrictions are imposed for 1 quarter for the structural de cit and for 4 consecutive quarters for expected debt. The business cycle shock is instead identi ed as a co-movement between output and consumption for 4 consecutive quarters. The choice of the timing of the restrictions is driven by the scope of the exercise: I want to isolate scal shocks with dierent future path, therefore I do not restrict the de cit to be positive for more than one quarter, while at the same time I constrain the path of expected future debt to move in one direction or another for a longer period of time. This should allow me to capture both persistent scal shocks and scal shocks that die out within a couple of quarters. The identi cation strategy indeed isolates two scal policy shocks with a very distinct time path (Figure 1): the temporary shock reverts back to zero after around 4 quarters, before becoming slightly negative; the persistent shock instead declines more slowly reverting to zero only after about 16 quarters. For ease of comparison the impulse responses are normalized so that they both represent the responses to a unitary shock. As embedded in the identifying restrictions, the path of the expected debt is a re ection of the pro le of the scal shocks. When the scal policy shock is persistent, the response of the expected debt is hump shaped: it responds positively on impact, then it increases for about four quarters before converging back to zero. The shape of this response indicates that the presence of a budget de cit increases the stock of future debt up to the point where agents start expecting a scal stabilization. On the other hand when the scal shock is temporary, the response of expected future debt is mildly negative, showing that the scal expansion is expected to be short lived. Note, however, that the path of the expected future debt represents what agents expect about the future scal policy, and therefore a priori it needs not to be entirely consistent with the path of the scal shocks. However, the results show that in general agents' expectations are consistent with the actual behaviour of the budget de cit. More importantly, the responses of the real variables are markedly dierent across the two types of scal shocks Figure 1). While temporary shocks have a standard Keynesian eect, persistent shocks display negative output

and consumption multipliers. This suggests that as long as scal sustainability is not put in jeopardy by an unsustainable increase in public debt, agents react by increasing consumption and output. If however, the scal expansion is accompanied by an excessive accumulation of debt, the negative wealth eect of the future tax burden induces agents to compress consumption and hence income. The accumulation of public debt can also increase agents' uncertainty about the timing of the scal consolidation. However, because the size of scal consolidations increases as these are postponed in the future, this uncertainty might induce households and rms to increase their precautionary savings. Increase in savings will therefore drag down consumption and output (Minsky 1986). The next section will show that indeed private savings react consistently with this hypothesis. 10

Temporary and Persistent Fiscal Policy Shocks Negative output and consumption multipliers, however, can be possible only with a suciently large share of \Ricardian agents". If in fact credit market imperfections restricted consumption and investments to the disposable income and cash ow, agents would not optimize over their lifetime wealth and therefore would respond positively to any type of scal policy shock (Gali et al. 2007). However, as pointed out among others by Biilbie et al. (2008), nancial innovation and nancial market deepening are likely to have greatly reduced the incidence of credit constraints in the US over the last 20-30 years. Section 4.2 will show that indeed, during recessions as the share of credit constrained agents increases, the negative multipliers disappear. The size of the multipliers is however relatively small. With an average de cit to GDP ratio of around 2% over the sample, an elasticity of 0.005 translates into a multiplier of about 0:25, which is very close to that obtained by Biilbie et al. (2008). The reaction of the monetary authority (bottom panel ofFigure 1) is consistent with a standard Taylor rule. The Central Bank, in fact, increases the interest rates when output and consumption increase and cuts them in the other case. Figure 2 shows the impulse response functions to the business cycle shock. As imposed by the restrictions, con-

sumption and output increase and this induces the monetary authority to increase interest rates to prevent an overheating of the economy. Interestingly, also the cyclically adjusted budget de cit reacts indicating that probably not all the cyclical components of the de cit are adequately taken care of by the CBO's adjustment. Repeating the analysis by eliminating the restrictions for the business cycle shock does not alter the results.

4.1.1 Robustness Checks To validate these empirical results, the rst issue to tackle is the possibility that the identi ed scal policy shocks are anticipated by economic agents. Because of the implementation lags typical of scal policy decisions, in fact, it is possible that agents anticipate with their actions the actual increase in the budget de cit, reacting to the scal policy shock when this is still discussed by the government. The literature on scal policy refers to this issue with the term of \Fiscal Foresight". From an empirical point of view the presence of anticipation eects imply that the residuals of a standard VAR are not unanticipated shocks and mapping the reaction of variables to those residuals will give a biased view about the true eects of scal policy. Leeper et al. 2008 show that when scal policy shocks are anticipated, it is impossible to recover structural shocks from the moving average representation of the VAR and the identi ed shocks will be a combination of anticipated and unanticipated innovations. In theory, however, this problem can be solved if the information set spanned by the variables included in the VAR contained also the \news" about future scal policy. Hence, I re-estimate the linear VAR including the one year ahead forecasts on budget de cit published by the CBO among the variables. As for the forecasts on future debt, also these data are released only semi-annually and therefore I had to interpolate the missing observation to obtain quarterly frequency. The results from this speci cation are reported in Figure 3. The pro les of the scal shocks look very similar to 11

Temporary and Persistent Fiscal Policy Shocks the baseline case, and the responses of the other variables are qualitatively and quantitatively very similar. As a second step I re-estimate the baseline speci cation adding a set of control variables. To avoid running out of degrees of freedom, however, I include them one at the time following the approach in Ramey (2011). This exercise not only serves the purpose of validating the results, but allows us to investigate more closely the possible channels of transmission of the two scal shocks. As mentioned in the previous section, one important channel through which persistent scal shocks can determine a negative reaction of output and consumption is the increase in private savings. Figure 4 shows that indeed persistent scal expansions are accompanied by a signi cant increase in private savings. On the other hand, the response of private savings to temporary scal shocks oscillates around zero and it is never statistically signi cant. This evidence supports the claim according to which persistent scal policy shocks, because they are accompanied by a large increase in public debt, induce households to depress consumption in the attempt of increasing their precautionary savings. The increase in private savings can also take place at the expense of private investments. Figure 5 shows that in fact as a response to persistent scal policy shocks private non residential investments fall,

while they react positively - albeit just marginally signi cant - to temporary scal expansions. Finally, I introduce the current account balance. Short-lived scal expansions generate a temporary current account de cit, while persistent scal policy shocks have no impact on the current account. This is consistent with the idea that consumers want to smooth consumption over time. In presence of a scal expansion which is thought to be temporary, agents will not cut on consumption and therefore the budget de cit will have to be nanced by borrowing from abroad.4 On the other hand, if the scal policy shock is assumed to be persistent (or permanent), then the negative wealth eect will induce agents to increase savings and cut consumption therefore leaving the external balance unaected. The baseline results seem therefore to be robust and internally consistent. Temporary scal shocks generate an increase in output, consumption and - to a certain extent - investments. Private savings do not react making it more likely for the budget de cit to be nanced by a temporary current account de cit. On the other hand, as a consequence of a persistent scal shock private agents respond by increasing savings and decreasing investments. In the spirit of the \Ricardian Equivalence" this reaction osets the increase in Government's de cit leaving the current account balance unaected. The combination of higher savings and lower investments can then explain the negative eects on aggregate output.5

4 Obstfeld and Rogo 1995. 5 As a further robustness check

I performed the estimation of the baseline VAR by Bayesian method using a Litterman Prior. This allowed me to obtain results more robust with respect to the relatively small sample size. These results (available upon request) con rm what I obtained by simple OLS.

12

Temporary and Persistent Fiscal Policy Shocks

4.2 Non-linear Speci cations I now turn to the results from the non-linear speci cations. As mentioned in Section 2.2 I analyze whether there exist dierences in the propagation of temporary and persistent shocks depending on the level of public debt and on the state of the business cycle. To preserve degrees of freedom I re-estimate only the baseline speci cation (Section 4.1) and I identify the two types of shocks using exactly the same sign restrictions as before. Figure 7 and Figure 8 report the results obtained from the VAR with the interaction term. With respect to the

standard linear speci cation, we can see that when public debt is within the lower 25% of its distribution temporary scal policy shocks have a slightly larger positive eects, while persistent scal shocks have smaller negative eects which - on top of that - are almost never statistically signi cant. On the other hand, when the level of public debt is included in the highest quartile of its distribution, persistent scal policy shocks have larger negative eects, while the eect of temporary scal shocks hardly changes. This evidence indicates that the accumulation of public debt associated with persistent scal policy expansions becomes a major cause of concern for private agents when public debt is above a given threshold. The Ricardian behaviour of households and rms, however, does not disappear at low levels of debt, but it is not so pronounced to generate negative multipliers. Comparing the reactions of the monetary policy authority in the two cases (bottom left panel of Figure 7 and Figure 8) is also instructive. If persistent scal policy shocks take place at low levels of public debt, the central

bank lowers the federal fund rate for about three quarters to counterbalance the small contraction in output. If instead persistent scal policy shocks take place at high levels of public debt, the central bank lowers interest rates for a longer period of time. This accommodating behaviour, however, can not be fully interpreted as an instance of \Fiscal Dominance" given that the cut of the interest rates seems to be relatively low compared with the large contraction in economic activity. The ST-VAR framework is instead employed to investigate asymmetries over the business cycle. The transition function F (z ) (Figure 9) shows that the estimation method eectively captures recession episodes which correspond t

roughly to the NBER recession dates, and the estimates show that the transition from expansions recessions happens very fast. The analysis of the impulse response functions points towards some important asymmetries in the propagation of temporary and persistent scal policy shocks in recessions and expansions. From comparing Figure 10 Figure 11 we can notice that persistent scal expansions have a negative eect on output and consumption only

when the economy is booming. During recessions, instead, the reaction of consumption and output to persistent scal expansions is basically zero. This can be explained by the fact that, during recessions, due to the higher incidence of credit constraints the fraction of agents that can respond with higher savings to a persistent scal policy shock decreases, therefore eliminating the negative scal multipliers. The opposite is true when the economy is in expansion. Temporary scal policy shocks, instead, have positive eects on output and consumption both in expansions and in recessions. In the latter case, however, the eect is about 10 to 20 times stronger with a multiplier of about 4, very similar to that calibrated by Christiano et al. (2009). The reaction of the federal fund rate shows 13

Temporary and Persistent Fiscal Policy Shocks that during expansions the central bank reacts to persistent scal policy shocks by tightening the monetary policy stance, while it is accommodating for transitory scal shocks. During periods of recessions, instead, it slightly lowers interest rates after persistent scal expansions, wile considerably tightening them when scal policy shocks are short-lived. This result, although counter-intuitive, can be explained by the large expansionary eects of the scal shock.

5 Concluding remarks Since the onset of the \Great Recession", economists have been ercely arguing on columns of blogs and in academic publications about the pros and cons of government intervention. Concerns about scal sustainability and about the possibility of \Ricardian" reactions of the private sector have led some to insist on a \short lived-if any" scal intervention. Others, instead, decisively support a more prolonged involvement of the Governments, arguing that standard Keynesian eects are likely to prevail over sustainability concerns: and the more so the larger the share of credit constrained agents or the larger slack in aggregate demand. This paper contributes to this lively debate by introducing an empirical framework that allows to compare the real eects of temporary versus persistent scal expansions. I estimate a VAR using US data and, by means of sign restrictions, I identify two dierent scal policy shocks which dier by their temporal path. I show that scal expansions which are short-lived - and therefore not accompanied by large build-ups of public debt - have a positive eect on output and consumption. On the other hand, persistent scal shocks have negative eects, and generate an increase in private savings. As conjectured by \ scal hawks ", the negative eects of persistent scal expansions increase with the level of public debt. Moreover, despite the fact that these negative multipliers disappear in periods of economic downturns, way larger \bang for the buck" is obtained by implementing temporary scal expansions. These results provide some guidelines for the design of a successful stimulus package. They suggest that persistent scal policy shocks, because they are accompanied by a large increase in expected future debt, fail to stimulate the economy. Temporary scal expansions, instead, have positive eects as they do not trigger any \Ricardian" reaction. These positive eects are particularly pronounced in times of recession, when the share of credit constrained agents increases. It is however possible, as pointed out by De Grauwe (2009), that there are some \abnormal recessions" where the combination of private sector de-leveraging and de ationary spirals ensures that persistent scal policy shocks have large and long lasting real eects. The size of the multipliers of scal shocks in \balance sheet" recessions is an issue that I leave for future research.

14

Temporary and Persistent Fiscal Policy Shocks

References Alesina A. and R. Perotti (1997), \Fiscal Adjustments in OECD Countries: Composition and Macroeconomic Eects", IMF Working Paper 96/70. Amisano G., Giammarioli N., Stracca L. (2009), "EMU and the adjustment to asymmetric shocks: the case of Italy," Working Paper Series 1128, European Central Bank. Auerbach A., and Gorodnichenko Y. (2011), \Fiscal Multipliers in Recession and Expansion", NBER Working Paper N. 17447 Auerbach A., and Gorodnichenko Y. (2010), \Measuring the Output Responses to Fiscal Policy", NBER Working Papers 16311, forthcoming in American Economic Journal { Economic Policy. Baldacci E., Gupta S., Mulas-Granados C. (2009), \How Eective is Fiscal Policy Response in Systemic Banking Crises?", IMF Working Paper, WP N. 09/160. Baxter, M., and R. G. King (1993), \Fiscal Policy in General Equilibrium", American Economic Review, 83, 315{334. Berben R. P., Brosens T. (2007), \The Impact of Government Debt on Private Consumption in OECD Countries", Economic Letters 94, pp. 220 { 225. Bertola G., Drazen A. (1993), \Trigger Points and Budget Cuts: Explaining the Eects of Fiscal Austrerity", American Economic Review, 83(1), pp. 11 { 26. Bilbiie F. O., Meier A. and G. J. Muller (2008), \What Accounts for the Changes in U.S. Fiscal Policy Transmission?", Journal of Money Credit and Banking, Blackwell Publishing, vol. 40(7) October, pp. 1439-1470. Blanchard O. and Perotti R. (2002), \An Empirical Characterization of the Dynamic Eects of Changes in Government Spending and Taxes on Output", Quarterly Journal of Economics, Vol. 117, N. 4 (Nov. 2002), pp. 1329 { 1368. Buiter W. (2010), \The Limits to Fiscal Stimulus", Oxford Review of Economic Policy, Vol. 26, N. 1-2010, pp. 48-70. Canova F. and Pappa E. (2007), \Price dierential in Monetary Unions: The role of scal shocks", Economic Journal, 117, 713-737 Christiano L. J., Eichembaum M., Rebelo S. (2009), \When is the Government Spending Multiplier Large?", NBER Working Paper 15394, October 2009.

15

Temporary and Persistent Fiscal Policy Shocks Cimadomo J., Hauptmeier S., Sola S. (2011), \Identifying the Eects of Government Spending Shocks with and without Expected Reversal: an Approach Based on U.S. Real-Time Data", IHEID Working Papers 07-2011, Economics Section, The Graduate Institute of International Studies. Corsetti G., Meier A., Muller G. J. (2009), \Fiscal Stimulus with Spending Reversals", April 2009, IMF Working Paper N. 09106. De Grauwe P. (2009), \Keynes' Savings Paradox, Fisher's Debt De ation and the Banking Crisis", MIMEO. Davig T., Leeper E. (2011), \Monetary{Fiscal Policy Interactions and Fiscal Stimulus", European Economic Review 55 (2011) 211{227 Dungey M., Fry R. (2009) \The identi cation of scal and monetary policy in a structural VAR,", Economic Modelling, vol. 26(6), pp 1147-1160, November. Edelberg W., Eichembaum M., Fisher J. D. M. (1999), \Understanding the Eects of a Shock to Government Purchases", Review of Economic Dynamics, Vol. 2, January, pp. 166-206. Erceg C., Linde J. (2010), \Is There a Fiscal Free Lunch in a Liquidity Trap?" CEPR Discussion Papers 7624, C.E.P.R. Discussion Papers. Gali J., Lopez Salido J. D., Valles J. (2007), \Undesrstanding the Eects of Government Spending on Consumption", Journal of the European Economic Association, March 2007, 5(1), pp. 227 { 270. Giavazzi F. and M. Pagano (1990) \Can Severe Fiscal Contractions be Expansionary? Tales of two small European Countries", in NBER Macroeconomic Annuals, ed. by Olivier Blancharnd and Stanley Fischer, Cambridge Massachusetts, MIT Press. Giavazzi F., Jappelli T., M. Pagano (2005), \Searching for Non-Monotonic Eects of Fiscal Policy: New Evidence", NBER Working Paper N. 11593 Jarocinski M. (2010), "Responses to monetary policy shocks in the east and the west of Europe: a comparison," Journal of Applied Econometrics, vol. 25(5), pp 833-868. Laubach T., (2009), \New Evidence on the Interest Rate Eects of Budget De cits and Debt", Journal of the European Economic Association 2009 7:4, 858-885. Leeper E. (2009), \Anchoring Fiscal Expectations", Reserve Bank of New Zealand Bulletin, Reserve Bank of New Zealand, vol. 72, pp. 17-42, September. Leeper E., Walker T. B., Yang S. C. (2008), \Fiscal Foresight: Analytics and Econometrics", NBER Working Paper N. 14028.

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Temporary and Persistent Fiscal Policy Shocks Levy Yeyti E., Panizza U., Stein E. (2007), \The Cyclical Nature of North-South FDI", Journal of International Money and Finance 26 (2007), pp. 104-130. Mountford A. and H. Uhlig (2009), \What are the Eects of Fiscal Policy Shocks?", Journal of Applied Econometrics, 24(6), pp. 960 { 992. Minsky H. (1986), \Stabilizing an Unstable Economy", McGraw-Hill Professional. Obstfeld M., Rogo K. (1995), \Foundations of International Macroeconomics", MIT Press. Perotti R. (1999) \Fiscal Policy in Good Times and Bad", Quarterly Journal of Economics, 114(4), pp. 1399-1346. Perotti R. (2005), \Estimating the Eects of Fiscal Policy in OECD countries", CEPR Discussion Paper N. 4842. Ramey V., Shapiro M. D. (1998), \Costly Capital Reallocation and the Eects of Government Spending" , CarnegieRochester Conference Series on Public Policy. Vol. 48, June 1998, pp. 145 { 194. Ramey V. (2011), \Identifying Government Spending Shocks: it's all in the Timing", Quarterly Journal of Economics, 126(1), pp. 1-50. Romer C. and Bernstein J. (2009), \The Job Impact of the American Recovery and Reinvestment Plan", January 8, 2009. Romer D. H., Romer C. D. (2010), \The Macroeconomic Eects of Tax Changes: Estimates Based on a new Measure of Fiscal Shocks" , American Economic Review 100, June 2010, pp. 763 { 801. a F., Towbin P., Wieladek T. (2011), \Low interest rates and housing booms: the role of capital in ows, monetary policy and nancial innovation", Globalization and Monetary Policy Institute Working Paper 79, Federal Reserve Bank of Dallas. Sutherland A. (1997), \Fiscal crises and aggregate demand: can high public debt reverse the eects of scal policy?", Journal of Public Economics, Vol. 65, Issue 2, August 1997, pp. 147-162. Tagkalakis A. (2008), \The Eects of Fiscal Policy on Consumption in Recessions and Expansions" , Journal of Public Economics, 93 (2008), pp. 1486 { 1508. Towbin P., Weber S. (2011). \Limits of Floating Exchange Rates: the Role of Foreign Currency Debt and Import Structure", IMF Working Papers 11/42, International Monetary Fund. Woodford M. (2010), \Simple analytics of the government expenditure multiplier", NBER Working paper N 15714.

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Temporary and Persistent Fiscal Policy Shocks

6 APPENDIX A 6.1 Estimation of the ST-VAR The version of the ST-VAR presented in this paper closely follows that presented by Auerbach and Gorodnichenko (2010). The structural model: Yt = (1



F (zt 1 )) A (L) Yt

= (1 F (z 1 ))  + F (z exp ( z ) F (z ) = 1 + exp ( z ) t

E

t

+ F (z

1

t

1

t

1

) B (L) Y

1

t

+E

t

)

R

t

t

t

can be estimated by iterating a maximum likelihood estimation and weighted least squares. Let's rst rewrite the VAR in compact notation, stacking the coecients A (L) and B (L) into a matrix ;and let's call X the matrx t

that contains the regressors weighted by the transition function F (z

1

t

2

Xt = 6 4

(1 F (z

t

1

)) Y

1

t

(1 F (z

F (zt 1 ) Yt

1

1

t

)) Y

t

2

):

::: (1

F (zt 1 )) Yt p ;

F (zt 1 ) Yt 2 :::F (zt 1 ) Yt

3 7 5

p

The VAR model can therefore be written in compact form as: Yt = Xt + Et

So that the log likelihood function of the regression model can be writen as: X L =c 12 log (j j) 12 (Y T

t

Xt )0 t 1 (Yt

t

Xt )

t=1

which can then be rewritten in terms of trace:  L =c 21 log (j j) 21 tr (Y t



t

Xt ) (Yt

 Xt )0 t 1



Now, because  is a function of  ;  ;  , we can rewrite the likelihood making this demendence explicit: t

E

R

L =c 12 log   ;  E

R





;

t

1 h tr (Y 2

Xt ) (Yt

t


1 Xt )0  E ; R ;  t 

i

(4)



hence, conditional on estimates of , the likelihood can be maximized for  ;  ;  ;given some starting values





E (0)



n

o

b bE;  b R;  ; R(0) ; (0) : Then, given the ML estimates 

ML

E

R

the parameters in of the VAR can be ecientily 



b = 1 F z estimated by weighted least squares with the weight given by  t

18

t

1

  bE b 



+F z

t



1

b R . In b 

Temporary and Persistent Fiscal Policy Shocks particular, the expression for the parameters in   vec b

=

" T  X

is given by:

b 

t

1



0

X X t

#

1

T X

vec

t

t=1

!

0

b X t Yt  t

1

(5)

t=1

Then the maximization can iterate between (4) and (5) until the likelihood converges. In particular, for the estimation, I adopted a stopping criterion for the likelihood function de ned as:



L( ) L( 1) < 1e 4 L( 1) j

j

j; j

where L( ) is the log likelihood function at iteration (j ) and L( j

j; j

"Numerical Recipes" (2007), p. 423.

19

1)

=

jL +L (j )

2

(j

1)

j : The stopping criterion is from

Temporary and Persistent Fiscal Policy Shocks

7 APPENDIX B - Linear VAR Figure 1: Temporary and Persistent Fiscal Shocks - Baseline

Figure 2: Business Cycle Shock - Baseline shock.png

20

Temporary and Persistent Fiscal Policy Shocks Figure 3: Temporary and Persistent Fiscal Shocks - Exp Def

Figure 4: Temporary and Persistent Fiscal Shocks - Savings

21

Temporary and Persistent Fiscal Policy Shocks Figure 5: Temporary and Persistent Fiscal Shocks - Investments

Figure 6: Temporary and Persistent Fiscal Shocks - CA

22

Temporary and Persistent Fiscal Policy Shocks

8 APPENDIX C - Non Linear Eects Figure 7: Temporary and Persistent Fiscal Shocks - Low Public Debt

Figure 8: Temporary and Persistent Fiscal Shocks - High Public Debt

23

Temporary and Persistent Fiscal Policy Shocks Figure 9: Transition Function - F (z ; ) t

Figure 10: Temporary and Persistent Fiscal Shocks in Expansions

24

Temporary and Persistent Fiscal Policy Shocks

Figure 11: Temporary and Persistent Fiscal Shocks in Recessions

9 APPENDIX D - Tables Lag LR 0 NA 1 1280.537 2 111.0955 3 52.54637 4 26.93522 5 54.15123 6 38.41337 7 26.72927 8 40.97493 9 25.93799 10 44.80562*

Table 1: Lag Selection AIC SC HQ -0.820825 -0.688939 -0.76748 -14.22951 -13.43819 -13.90943 -14.99626 -13.54551* -14.40946* -15.12687 -13.01669 -14.27334 -14.96647 -12.19686 -13.84622 -15.20837 -11.77933 -13.82139 -15.2715 -11.18303 -13.61779 -15.19241 -10.44451 -13.27198 -15.40106 -9.993734 -13.21391 -15.38967 -9.322907 -12.93579 -15.83277* -9.106583 -13.11217

 indicates lag order selected by the criterion at 5% level LR: sequential modi ed LR test statistic; AIC: Akaike information criterion; SC: Schwarz information criterion; HQ: Hannan-Quinn information criterion

25