Fiscal foresight and the effects of government spending

Fiscal Foresight and the Effects of Government Spending∗ Mario Forni† Universit`a di Modena e Reggio Emilia CEPR and RECent Luca Gambetti‡ Universitat Autonoma de Barcelona and RECent May 6, 2010 Abstract We study the effects of government spending by using a structural, large dimensional, dynamic factor model. We find that the government spending shock is non-fundamental for the variables commonly used in the structural VAR literature, so that its impulse response functions cannot be consistently estimated by means of a VAR. Government spending raises both consumption and investment, with no evidence of crowding out. The impact multiplier is 1.7 and the long run multiplier is 0.6. JEL classification: C32, E32, E62. Keywords: structural factor model, sign restrictions, fiscal policy, government spending shock, fundamentalness, non-fundamentalness. ∗We are grateful to Valerie Ramey for providing us with the dataset of the paper “Identifying government spending shocks: It’s all in the timing”. †Contact: Dipartimento di Economia Politica, via Berengario 51, 41100, Modena, Italy. Tel. +39 0592056851; e-mail: [email protected] ‡The financial support from the Spanish Ministry of Science and Innovation through grant ECO200909847 and the Barcelona Graduate School Research Network is gratefully acknowledged. Contact: Office B3.1130 Departament d’Economia i Historia Economica, Edifici B, Universitat Autonoma de Barcelona, Bellaterra 08193, Barcelona, Spain. Tel (+34) 935814569; e-mail: luca.gamb[email protected] 1 1 Introduction Understanding the effects of discretionary fiscal policy actions is key to assessing competing theories of the business cycle and providing guidance to policymakers. Recent developments in the conduct of fiscal policy in the US and other industrialized countries have sparked a renewed interest in the topic. Little consensus however has emerged over the last years: economists disagree about the sign of the response of private aggregate demand components, in particular consumption, and, as a consequence, the magnitude of the government spending multiplier. In their seminal paper, Blanchard and Perotti (2002) use a VAR model and identify a government spending shock by imposing that government spending is not affected on impact by the other shocks. The main finding is that government spending leads to a large increase in consumption. Similar results are obtained by Fatas and Mihov (2001), Gali, Lopez Salido, and Valles (2007), Mountford and Uhlig (2002), and Perotti (2002, 2007), which may be included in the so-called “government spending innovation approach”. On the contrary, Ramey and Shapiro (1998), using a dummy variables identification approach, find that consumption falls, implying a very small value for the government spending multiplier. Burnside, Eichenbaum, and Fisher (2004), Cavallo (2005), Edelberg, Eichenbaum, and Fisher (1999) and Eichenbaum and Fisher (2005) find similar results. Recently, a few works have convincingly argued that one of the intrinsic characteristic of fiscal policy actions is that they are anticipated (see e.g. Yang, 2007, Leeper, Walker and Yang, 2008, Mertens and Ravn, 2009). That is, private agents receive signals about future changes in taxes and government spending before these changes actually take place. The reason is the existence of legislative and implementation lags: it takes time for a policy action to be passed and implemented. The phenomenon is called “fiscal foresight”; empirical estimates of the lag range from a few months to a couple of years. Leeper, Walker and Yang (2008) show that fiscal foresight poses a formidable challenge to the econometrician. The authors consider a simple neoclassical growth model with two shocks, a technology and an anticipated tax shock. They show that the MA representation of any pair of variables among capital, taxes and technology, is nonfundamental; that is, the determinant of the MA matrix has roots smaller than one in modulus. The implication is that the variables do not have a VAR representation in the structural shocks, so that the true fiscal policy shock and the related impulse response functions cannot be found by estimating a VAR. The problem can be reformulated in terms of information sets. Typically, economic agents can see the structural shocks. By contrast, the econometrician can only observe the economic variables. Obviously, such variables convey information about the shocks, but if the impact effects are small and the delayed effects are large, such information 2 is not enough to recover the shocks (Lippi and Reichlin, 1993). Persuasive evidence that the information set used in the VAR fiscal policy literature is indeed too poor is provided in Ramey (2009). Ramey shows that the fiscal policy shock obtained by using a VAR similar to the one in Perotti (2007) is not an innovation with respect to available macroeconomic information, being Granger-caused by the forecast of government spending from the Survey of Professional Forecasters. In recent years a few works have tried to overcome the problem posed by fiscal foresight. Two different strategies have been adopted. On the one hand, Mertens and Ravn (2009) estimate the effects of government spending shocks using the methodology proposed by Lippi and Reichlin (1994), based on Blaschke matrices. On the other hand, some authors augment the VAR with variables presumably conveying better information about discretionary fiscal policy actions. Ramey (2009) constructs two series for exogenous government spending shocks: one is based on narrative evidence for defense spending, the second is based on the Survey of Professional Forecasters. Fisher and Peters (2009) identify government spending shocks with statistical innovations to the accumulated excess returns of large US military contractors. Both approaches have shortcomings. The former requires many restrictions, some of them relying on the correct specification of the theoretical model; moreover, the structural shocks cannot be estimated consistently. As for the latter, it is hard to judge whether the additional variables included in the VAR are fully successful in capturing the relevant information. In this paper we depart from the VAR approach and use instead a large structural factor model. The motivation is that, as argued in Forni, Giannone, Lippi and Reichlin (2009), large factor models are not affected by the non-fundamentalness problem. The basic intuition is that these models typically use most of the available macroeconomic information and this helps in closing the gap between the information set of the econometrician and that of economic agents. To better understand how non-fundamentalness arises and how the factor model can avoid the problem, let us start from a vector MA representation, obtained from a DSGE model. Typically the number of variables is larger than the number of shocks, so that we have a rectangular, “tall” MA system. As we shall show, for such systems, observing the variables is equivalent to observing the shocks, and the non-fundamentalness problem is not there. In the model of Leeper, Walker and Yang (2008), for instance, the tall system made up by the three state variables and the two shocks is fundamental (see Section 2). Unfortunately, a rectangular system cannot be estimated by using standard VAR techniques. This is because observed series do not have reduced dynamic rank: by estimating a VAR with nvariables, we end up with nlinearly independent residuals and find too many structural shocks. In order to estimate a VAR we have to ignore 3 some variables and “cut” the tall system to get a square one. But in such a way we open the door to non-fundamentalness. The factor model follows an alternative strategy to handle the reduced rank problem. It retains all of the variables and adds measurement errors. Since the number of variables is very large, and the errors are poorly correlated across section, we can get rid of them by taking suitable linear combinations of the variables (the principal components). In such a way we end up with a fundamental, rectangular system which can be estimated consistently by means of a reduced rank VAR technique. Let us now summarize our main findings. To begin, we find that the government spending shock is non-fundamental for the variables commonly used in the structural VAR literature. Precisely, we select a few square sub-matrices of our tall impulse-response matrix, corresponding to standard VAR specifications. Then we compute the smallest root of the determinant and find that in most cases it is smaller than one in modulus. Then we identify a government spending shock by using sign restrictions (Uhlig, 2005). More specifically, an expansionary government spending shock is defined as a shock having a positive effect on government expenditure, output, prices, the prime rate, the government primary deficit and tax receipts (the last inequality is imposed to distinguish the government spending shock from a tax shock). All restrictions are imposed only on responses delayed by six months (the third coefficient of the impulse response functions), so that the impact effect on all variables, and in particular government expenditure, is left unrestricted to avoid the fiscal-foresight criticism. The main results are the following. First, our estimated shock, unlike the VAR shock, passes Ramey’s Granger-causation test, i.e. it is not caused by the forecast of government spending from the Survey of Professional Forecasters. Second, the shape of the impulse response functions suggests that actually there is a great deal of anticipation. After an immediate and significant increase, government spending gradually rises and reaches its maximum, which is about two times larger than the initial effect, after a couple of years. By contrast, the effect on consumption is transitory and reaches its maximum on impact. Finally, there is no evidence of crowding-out. Consumption reacts positively to the fiscal shock. More surprisingly, the reaction of total investment is positive and significant on impact and becomes negative only in the long-run. Our estimated multiplier is 1.7 on impact, reaches its maximum, 2.2, after 3 quarters and then declines towards its long-run value, about 0.6. The remainder of the paper is organized as follows: Section 2 discusses non-fundamentalness; Section 3 presents the factor model; Section 4 shows results; Section 5 concludes. 4 2 Fundamentalness, structural VARs and fiscal foresight 2.1 Fundamentalness in square and tall systems Let us consider the statistical MA representation χt=B(L)ut,(1) where χt= (χ1t· · · χnt)0is an n-vector of weakly stationary variables, B(L)isa(n×q) matrix of rational functions in the lag operator L, with n≥q, and ut= (u1t· · · uqt)0is aq-dimensional white-noise normalized to have identity variance-covariance matrix. By equation (1), χtlies in the space spanned by present and past values of ut, i.e. χt∈Hu t= span(u,j= 1, . . . , q, τ ≤t). However, the converse does not necessarily hold. If it does, i.e. ut∈Hχ t, we say that representation (1) is fundamental and utis fundamental for χt. In such a case, observing χtis equivalent to observing ut, in the sense that Hu t=Hχ t. Moreover, by the uniqueness of the orthogonal decomposition, (B(L)−B(0))utis the projection of χtonto its own past Hχ t−1and B(0)utis the residual, i.e. the innovation of the information set Hχ t.1A fundamental white noise is not unique, but it is easily seen that if vtis also fundamental, then it is a linear transformation of ut. By contrast, non-fundamental white-noise vectors can be obtained from utby applying linear filters that involve the future of utand the so-called Blaschke matrices (see e.g. Lippi and Reichlin, 1994). If B(z) is rational, as assumed above, we can characterize fundamentalness in terms of its rank: representation (1) is fundamental if, and only if, the rank of B(z) is qfor all zsuch that |z|<1 (see e.g. Rozanov, 1967, Ch. 1, Section 10, and Ch. 2, p. 76). In the particular case n=q, such condition reduces to the requirement that det B(z) does not vanish within the unit circle in the complex plane.2 Our main point here is that, as argued in Forni, Giannone, Lippi and Reichlin (2009), there is a substantial difference between the case n=q, on one hand, and n>q, on the other hand. In the former case, the determinant is a rational function, which generally vanishes somewhere and may well vanish within the unit circle. In the latter case, B(z) is a “tall”, rectangular matrix; its rank is less than qfor some z only if all of the (q×q) sub-matrices of B(z) are singular. Hence in general B(z) is “zeroless”, i.e. has rank qfor all z, and non-fundamentalness is very unlikely. More precisely, letting pbe the l-vector whose entries are the parameters of B(L) and Π ∈Rl the set of all possible p, in the case n > q fundamentalness holds generically (i.e. the subset of Π where fundamentalness does not hold is meagre), whereas in the case n=q fundamentalness is not generic. 1Conversely, if B(0)utis the innovation of Hχ t,utis fundamental for χt. 2Observe that invertibility implies fundamentalness, but the converse does not hold, because if the rank falls for some unit modulus z, we do not have invertibility. 5 Consider for instance the simple case n= 2, q= 1, χ1t=ut+b1ut−1,χ2t= ut+b2ut−1. Now consider the square subsystem made up by the first equation: ut is non-fundamental for χ1tif and only if |b1|>1. In this case, the fundamental representation is χ1t=ηt+b−1 1ηt−1,ηt=(1 + b1L)/(b1+L−1)ut.3Similarly utis non-fundamental for χ2tif and only if |b2|>1. However, the tall system made up by both equation is non-fundamental if and only if b1=b2and |b1|>1. Observe that ut is generally fundamental for χteven if it is non-fundamental for both χ1tand χ2t. 2.2 Fundamentalness and VAR models Now let us assume that (1) is derived as the solution of a DSGE model, so that the variables in χtare the macroeconomic variables of interest, the entries of utare structural shocks and B(L) is a matrix of impulse-response functions (whose coefficients are functions of the deep parameters of the model). The number of variables nis typically larger than the number of shocks q, so that B(L) is a tall matrix and χtis dynamically singular (i.e. its spectral density matrix has reduced rank q). utis the innovation of the information set of economic agents. This is quite reasonable even if utis not directly observable, because, as noted above, utwill be fundamental for χt, except for negligible cases, implying that B(0)utis the residual of the projection of χt, which we assume observable, onto its own past Hχ t−1. At this stage the economist passes on the baton to the econometrician. The aim is to estimate B(L) and ut, starting from the information in Hχ t. Unfortunately, macroeconomic series are not dynamically singular, perhaps because χtis observed with error. By estimating an n-dimensional VAR we would end up with nlinearly independent shocks, in conflict with the theory. The standard strategy is then the following: (i) selecting a square, q-dimensional subsystem, say χ∗ t=B∗(L)ut; (2) (ii) estimating the VAR A(L)χ1t=tto find out the innovations t=B∗(0)utand the MA filter A(L)−1=B∗(L)B∗(0)−1; (iii) identifying B∗(0), and therefore representation (2), by imposing the normalization B∗(0)B∗(0)−1= Σalong with identifying restrictions derived from theoretical considerations. However, as argued above, the square subsystem could be non-fundamental, or, equivalently, the reduced information space used by the econometrician, Hχ∗ t, could be smaller than the one of the agents, Hu t. In such a case, utis not a linear transformation of t, so that step (ii) is wrong and the VAR cannot produce the correct result, whatever be the identification scheme adopted in (iii). Obviously, the choice of the subsystem in 3Observe that the Blaschke factor b(L) = (1 + b1L)/(b1+L−1)is such that b(z)b(z−1) = 1, so that the spectral density of ηtis constant and ηtis white noise. 6 step (i) may be relevant, but, as shown in the example below, a fundamental subsystem does not necessarily exist. 2.3 A fiscal foresight example Leeper, Walker and Yang (2008) show that fiscal shock non-fundamentalness in VAR models naturally arises in an economy with fiscal foresight.4Starting with a standard growth model with log preferences and inelastic labor supply, the authors obtain the equilibrium capital accumulation equation kt=λ1kt−1−λ−1 2 ∞ X i=0 θiEt(ν0at+i+1 −ν1at+i+ψτt+i+1) (3) where kt,atand τtdenote the log of capital, the log of technology and the tax rate, respectively, in deviation from the steady state. The parameters appearing in the above equation are functions of the deep parameters of the model; from the theory we know that |θ|<1 (θis a discount rate). Technology and taxes follow the exogenous law of motions at=uA,t τt=uτ,t−2 where uτ,t and uA,t are i.i.d. shocks that economic agents can observe. The second equation says that the effect of fiscal policy on taxes is delayed by two periods. Solving for ktwe get5    at kt τt   =   0 1 −λ−1 2ψ(L+θ) 1−λ1L λ−1 2ν1 1−λ1L L20    uτ,t uA,t!=B(L)ut Let us consider the square subsystem given by the first two rows (technology and capital): the determinant λ−1 2ψ(z+θ) 1−λ1zvanishes for z=−θ, which is less than 1 in modulus. Similarly, the determinant of the submatrix given by the first and the last rows of B(z) (technology and taxes) is z2, which vanishes for z= 0. Finally, the determinant of the subsystem formed by the second and the last row (capital and taxes) also vanishes for z= 0. In conclusion, ut= (uτ,tuA,t)0is non-fundamental for any pair of variables on the left-hand side, implying that standard VAR techniques are unable to correctly estimate the fiscal shock. To better appreciate the role of anticipation, observe that with 4Simple examples of non-fundamentalness in economic models can also be found in Lippi and Reichlin (1993) and Fern´andez-Villaverde, Rubio-Ramirez, Sargent and Watson (2006). 5Strictly speaking the system is just a block of the model since for simplicity we abstract from consumption. However the implications discussed later remain unchanged. 7 no implementation delay (τt=uτ,t), utwould be fundamental for all of the subsystems, whereas, with a one-period delay (τt=uτ,t−1), fundamentalness would still hold for the subsystem with taxes and capital. Intuitively, the variables convey information about the current values of the fiscal shock, as long as they are contemporaneously affected by such shock. In presence of implementation delay, taxes are not affected on impact, and therefore do not provide useful information. Capital is more helpful; however, if the delay is larger than one period, its contribution is not sufficient to recover the shock. Let us now consider the whole system. utis fundamental for χt, since B(z) is zeroless, i.e. has rank 2 everywhere in the complex plane. In fact, it is easily seen that χthas the reduced rank VAR representation6     1 0 0 λ−1 2ψL 1−λ1L0 ν1(L−θ)L2 ψθ2 (L−θ)(1−λ1L)L2 λ−1 2ψθ21−L2 θ2       at kt ˆτt   =   0 1 −λ−1 2ψθ λ−1 2ν1 0 0    uτ,t uA,t!. Put differently, present and past values of the three variables, capital, taxes and technology, are sufficient to estimate the two shocks. Unfortunately, standard VAR techniques cannot be used to this end. In the next section we present a structural factor model, whose core is a tall system like the one above. Such a system can be consistently estimated through appropriate procedures. 3 The large factor model 3.1 Representation In the present section we provide a presentation of our model and estimation procedure. For additional details see Forni, Giannone, Lippi and Reichlin (2009), FGLR from now on. A convenient assumption, which is standard in the large factor model literature, is that there are infinitely many variables xit,i∈N. The econometrician observes the first nof them, and consistency results are obtained for both nand T(the number of time observation) going to infinity. Each macroeconomic variable is the sum of two mutually orthogonal unobservable components, the common component χit and the idiosyncratic component ξit: xit =χit +ξit.(4) The idiosyncratic components are poorly correlated in the cross-sectional dimension (see FGLR, Assumption 5 for a precise statement). They arise from shocks or sources 6Notice that the VAR representation has finite order. Existence of a finite VAR representation is a general property for zeroless tall rational systems (Anderson and Deistler 2008). 8 of variation which considerably affect only a single variable or a small group of variables; in this sense, we could say that they are not “macroeconomic” shocks. For variables related to particular sectors, like industrial production indexes or production prices, the idiosyncratic component may reflect sector-specific variations (with a slight abuse of language we could say “microeconomic” fluctuations); for strictly macroeconomic variables, like GDP, investment or consumption, the idiosyncratic component must be interpreted essentially as a measurement error. With equation (1) in mind it is easily seen that the factor model can be interpreted as the log-linear solution of a DSGE model augmented with a measurement error.7 The common components are responsible for the main bulk of the co-movements between macroeconomic variables, being linear combinations of a relatively small number rof factors f1t, f2t,· · · , frt, not depending on i: χit =a1if1t+a2if2t+· · · +arifrt =aift.(5) Such factors can be interpreted as the state variables of the economic system. The dynamic relations between the macroeconomic variables arise from the fact that the vector ftfollows the relation ft=N(L)ut,(6) where N(L) is a r×qmatrix of rational functions in the lag operator Land ut= (u1tu2t· · · uqt)0is a q-dimensional vector of orthonormal white noises, with q < r. Such white noises are the structural macroeconomic shocks.8 Since N(L) is tall, the discussion in the previous section motivate the assumption that N(z) is zeroless, i.e. rankN(z) = qfor any z, which implies fundamentalness. This ensure that fthas the finite order VAR representation (Anderson and Deistler, 2008) D(L)ft=t=Rut,(7) where D(L) is a r×rmatrix of polynomials such that D(L)−1R=N(L) and R=N(0). From equations (4) to (7) it is seen that the model can be written in the dynamic form xit =bi(L)ut+ξit,(8) 7See also Altug, 1989, Sargent, 1989, and Ireland 2004 for the link between factor models and DSGE models. 8In the large dynamic factor model literature they are sometimes called the “common” or “primitive” shocks or “dynamic factors” (whereas the entries of ftare the “static factors”). Equations (4) to (6) need further qualification to ensure that all of the factors are loaded, so to speak, by enough variables with large enough loadings (see FGLR, Assumption 4); this “pervasiveness” condition is necessary to have uniqueness of the common and the idiosyncratic components, as well as the number of static factors rand dynamic factors q. 9 prices (CPI and the GDP deflator), the prime rate, the government primary deficit and tax receipts. The positive effect on output and prices is imposed to distinguish the shock from a systematic spending reaction to a recessionary shock stemming from the private sector. An increasing deficit is imposed to exclude expenditures entirely financed with additional receipts. The last inequality is imposed to distinguish the government spending shock from a tax shock. All of the restrictions are imposed only on the responses delayed by six months (the third coefficient of the impulse response functions), so that the impact effect on all variables, and in particular government spending, is left unrestricted to avoid the fiscal-foresight criticism. Having defined the relevant sign restrictions, we proceeded as explained at the end of Section 3.2 to get a set of admissible impulse response functions (satisfying the restrictions) and a set of corresponding fiscal shock series. We obtained 350 admissible shock series out of 20,000 drawings of the rotation parameters. We took the simple average of such series as our estimate of the fiscal shock. Finally we performed the bootstrapping procedure explained at the end of Section 3.3 to get a posterior density distribution for the impulse response functions. We generated 300 artificial samples X∗and for each one of them we drew 1,000 rotation vectors H1. We retained 1,029 admissible sets of impulse response functions. In the pictures below we show the average along with the 16th and the 84th percentiles of the related distribution. 4.4 Granger causation and anticipation Having obtained our estimate of the government spending shock we verify whether such shock passes Ramey’s Granger-causation test. As already noted, Ramey (2008) shows that the government spending shock obtained with a VAR similar to that of Perotti (2007) is Granger-caused by the government spending forecast from the Survey of Professional Forecasters. Here we perform a similar exercise using our estimated shock. Specifically, we regress the government spending shock on four lags of the shock itself and four lags of the government spending forecast. Table 4 shows the results. None of the parameters is statistically significant. The F-statistic obtained under the null hypothesis that the parameters of the lags of the forecast variable are jointly zero is 1.862, which is very much smaller than the 10% critical value. In conclusion, our government spending shock is not Granger-caused by the government spending forecast series. Let us now go deeper into the analysis of government spending anticipation by examining the estimated impulse response functions. Figures 1-3 depict the reaction profile of several variables of interest to a government spending shock which raises government spending by one percent of GDP as the maximum effect (horizon 8). Consistently with 16 the existence of implementation lags, government spending increases slowly, reaching the maximal level after two years. About one half of the total spending takes place immediately, half is delayed by one quarter or more. By contrast, consumption and investment reach their maximal level either on impact (consumption), or 1-2 quarters after the shock (GDP and investment). Hence, the spending is spread over time, whereas economic agents react immediately. This seems to fit the story that agents receive signals about changes in taxes and government spending, and react to them, before these changes are fully in place. 4.5 Crowding-out and the multiplier Now let us look at the reaction of GDP and its components. GDP reacts immediately, increasing by 2%. The response stays at that level for about one year and starts decreasing afterward, the effects being no longer significant after 6 quarters. Given the normalization imposed, the impulse response function represents the government spending multiplier. The estimated multiplier is 1.7 on impact, reaches its maximum, 2.2, after 3 quarters and then declines towards its long-run value, about 0.6. Confidence bands show that the multiplier is significantly above one at horizon 2, while is not different from zero in the long run. The size and shape of the multiplier can be explained by looking at the response of private consumption and investment. Both consumption and investment immediately and significantly increase by about 1% and 3% respectively. The response of consumption is very short-lived, declining and becoming not significant after the second quarter. On the contrary, the response of investment appears to be more persistent, the effect vanishing only after about six quarters. In the long run, the point estimate of the response of both variables is negative, although not significant. By inspecting the disaggregated components (Fig. 2), it is clear that the response of aggregate investment is mainly driven by non-residential investment while residential investment is crowded out after the nearly zero impact effect. As far as consumption is concerned, the three components react positively and significantly on impact. Government spending crowds-in, in the short run, private components of aggregate demand. Results for consumption stand in sharp contrast with the standard prediction of RBC models, where government spending shock generate negative wealth effect that depresses consumption. They are consistent with the evidence in Blanchard and Perotti (2002), with the remarkable difference that here the response is temporary and shortlived, with the maximal effects observed on impact. The response of investment contradicts the standard textbook crowding-out effect triggered by the increase in the interest rate. A positive response of investment, however, is the outcome predicted in Baxter and King (1993) after a permanent gov17 ernment spending shock. There, the increase in investment is caused by an increase in the marginal productivity of capital following a sharp increase in employment which is also found here (see Fig. 3).17 4.6 Variance decomposition Table 2 shows the variance decomposition for several variables of interest. Columns 2-5 report the percentage of forecast error variance of the variables listed in column 1, accounted for by the shock at various horizons. Column 6 reports the percentage of the variance of the series, transformed to reach stationarity (e.g. inflation instead of prices), accounted for by the shock. The shock accounts for about 25% of the variance of government spending (both federal and total) and about 10% of the variance of deficit and taxes. At a first sight, these numbers could seem small but recall that (i) we are ruling out tax shocks; (ii) we are ruling out spending not increasing current deficit; and (iii) this is discretionary policy, in that it excludes systematic reactions to shocks stemming from the private sector. The shock accounts for about 16%, 13% and 16% of the variance of GDP, investment and consumption, respectively. Interestingly, the shock is more important in the very short run (on impact it explains 21% 14% and 20% of the three variables, respectively) than at longer horizons (at horizon 20 percentages are 9%, 8% and 9%, respectively. 4.7 Robustness This subsection studies the robustness of the results to changes in model specification. First let us compare the results of our benchmark specification (r= 13, q= 6) with five alternative specifications: 1) r= 10, q= 6; 2)r= 16, q= 6; 3)r= 10, q= 4; 4)r= 13, q= 4; 5)r= 16, q= 4. Figure 4 displays the impulse response functions of consumption and investment for the six different specifications. The first column depicts the responses for the 4 dynamic shock specification, the second those for the 6 dynamic shock specification. Overall the results are remarkably similar both from a qualitative and from a quantitative point of view. The only minor difference is that the effects tend to be slightly larger in the 10 static factor specification and slightly smaller in the 16 factor specification than in our benchmark. We also made several other checks listed below. 1) We used the federal funds rate and the 10 year bond rate instead of the prime rate to identify the shock. 2) We used federal government spending instead of and together with total government 17However, unlike Baxter and King (1993), here the persistent increase in labor cannot be caused by a negative wealth effect, given that consumption increases. 18 spending to identify the shock. 3) We did not restrict the interest rate. 4) We used two instead of three lags in the VAR for the factors. 5) We imposed the identifying restriction for periods 4 or/and 5. 6) We used the second (instead of first) differences of the log of prices and other nominal variables. 7) We used the estimation procedure proposed by Forni and Lippi (2010). In all these experiments we found the same results obtained in the benchmark model. Overall results seem to be robust to changes in model specification. 5 Conclusions This paper studied the effects of government spending shocks in the US using a structural, large dimensional, dynamic factor model. The main motivation is that in this model, unlike in VARs, the shocks are fundamental even in presence of fiscal foresight. We find that the government spending shock is non-fundamental for the variables commonly used in the structural VAR literature, so that its impulse response functions cannot be consistently estimated by means of a VAR. Government spending raises both consumption and investment, with no evidence of crowding out. The impact multiplier is 1.7 and the long run multiplier is 0.6. 19 Appendix: Data Transformations: 1=levels, 2= first differences of the original series, 5= first differences of logs of the original series, 5= second differences of logs of the original series. no.series Transf. Mnemonic Long Label 1 5 GDPC1 Real Gross Domestic Product, 1 Decimal 2 5 GNPC96 Real Gross National Product 3 5 NICUR/GDPDEF National Income/GDPDEF 4 5 DPIC96 Real Disposable Personal Income 5 5 OUTNFB Nonfarm Business Sector: Output 6 5 FINSLC1 Real Final Sales of Domestic Product, 1 Decimal 7 5 FPIC1 Real Private Fixed Investment, 1 Decimal 8 5 PRFIC1 Real Private Residential Fixed Investment, 1 Decimal 9 5 PNFIC1 Real Private Nonresidential Fixed Investment, 1 Decimal 10 5 GPDIC1 Real Gross Private Domestic Investment, 1 Decimal 11 5 PCECC96 Real Personal Consumption Expenditures 12 5 PCNDGC96 Real Personal Consumption Expenditures: Nondurable Goods 13 5 PCDGCC96 Real Personal Consumption Expenditures: Durable Goods 14 5 PCESVC96 Real Personal Consumption Expenditures: Services 15 5 GPSAVE/GDPDEF Gross Private Saving/GDP Deflator 16 5 FGCEC1 Real Federal Consumption Expenditures & Gross Investment, 1 Decimal 17 5 FGEXPND/GDPDEF Federal Government: Current Expenditures/ GDP deflator 18 5 FGRECPT/GDPDEF Federal Government Current Receipts/ GDP deflator 19 2 FGDEF Federal Real Expend-Real Receipts 20 1 CBIC1 Real Change in Private Inventories, 1 Decimal 21 5 EXPGSC1 Real Exports of Goods & Services, 1 Decimal 22 5 IMPGSC1 Real Imports of Goods & Services, 1 Decimal 23 5 CP/GDPDEF Corporate Profits After Tax/GDP deflator 24 5 NFCPATAX/GDPDEF Nonfinancial Corporate Business: Profits After Tax/GDP deflator 25 5 CNCF/GDPDEF Corporate Net Cash Flow/GDP deflator 26 5 DIVIDEND/GDPDEF Net Corporate Dividends/GDP deflator 27 5 HOANBS Nonfarm Business Sector: Hours of All Persons 28 5 OPHNFB Nonfarm Business Sector: Output Per Hour of All Persons 29 5 UNLPNBS Nonfarm Business Sector: Unit Nonlabor Payments 30 5 ULCNFB Nonfarm Business Sector: Unit Labor Cost 31 5 WASCUR/CPI Compensation of Employees: Wages & Salary Accruals/CPI 32 5 COMPNFB Nonfarm Business Sector: Compensation Per Hour 33 5 COMPRNFB Nonfarm Business Sector: Real Compensation Per Hour 20 no.series Transf. Mnemonic Long Label 34 5 GDPCTPI Gross Domestic Product: Chain-type Price Index 35 5 GNPCTPI Gross National Product: Chain-type Price Index 36 5 GDPDEF Gross Domestic Product: Implicit Price Deflator 37 5 GNPDEF Gross National Product: Implicit Price Deflator 38 5 INDPRO Industrial Production Index 39 5 IPBUSEQ Industrial Production: Business Equipment 40 5 IPCONGD Industrial Production: Consumer Goods 41 5 IPDCONGD Industrial Production: Durable Consumer Goods 42 5 IPFINAL Industrial Production: Final Products (Market Group) 43 5 IPMAT Industrial Production: Materials 44 5 IPNCONGD Industrial Production: Nondurable Consumer Goods 45 2 AWHMAN Average Weekly Hours: Manufacturing 46 2 AWOTMAN Average Weekly Hours: Overtime: Manufacturing 47 2 CIVPART Civilian Participation Rate 48 5 CLF16OV Civilian Labor Force 49 5 CE16OV Civilian Employment 50 5 USPRIV All Employees: Total Private Industries 51 5 USGOOD All Employees: Goods-Producing Industries 52 5 SRVPRD All Employees: Service-Providing Industries 53 5 UNEMPLOY Unemployed 54 5 UEMPMEAN Average (Mean) Duration of Unemployment 55 2 UNRATE Civilian Unemployment Rate 56 5 HOUST Housing Starts: Total: New Privately Owned Housing Units Started 57 2 FEDFUNDS Effective Federal Funds Rate 58 2 TB3MS 3-Month Treasury Bill: Secondary Market Rate 59 2 GS1 1-Year Treasury Constant Maturity Rate 60 2 GS10 10-Year Treasury Constant Maturity Rate 61 2 AAA Moody’s Seasoned Aaa Corporate Bond Yield 62 2 BAA Moody’s Seasoned Baa Corporate Bond Yield 63 2 MPRIME Bank Prime Loan Rate 64 5 BOGNONBR Non-Borrowed Reserves of Depository Institutions 65 5 TRARR Board of Governors Total Reserves, Adjusted for Changes in Reserve 66 5 BOGAMBSL Board of Governors Monetary Base, Adjusted for Changes in Reserve 67 5 M1SL M1 Money Stock 68 5 M2MSL M2 Minus 69 5 M2SL M2 Money Stock 21 no.series Transf. Mnemonic Long Label 70 5 BUSLOANS Commercial and Industrial Loans at All Commercial Banks 71 5 CONSUMER Consumer (Individual) Loans at All Commercial Banks 72 5 LOANINV Total Loans and Investments at All Commercial Banks 73 5 REALLN Real Estate Loans at All Commercial Banks 74 5 TOTALSL Total Consumer Credit Outstanding 75 5 CPIAUCSL Consumer Price Index For All Urban Consumers: All Items 76 5 CPIULFSL Consumer Price Index for All Urban Consumers: All Items Less Food 77 5 CPILEGSL Consumer Price Index for All Urban Consumers: All Items Less Energy 78 5 CPILFESL Consumer Price Index for All Urban Consumers: All Items Less Food & Energy 79 5 CPIENGSL Consumer Price Index for All Urban Consumers: Energy 80 5 CPIUFDSL Consumer Price Index for All Urban Consumers: Food 81 5 PPICPE Producer Price Index Finished Goods: Capital Equipment 82 5 PPICRM Producer Price Index: Crude Materials for Further Processing 83 5 PPIFCG Producer Price Index: Finished Consumer Goods 84 5 PPIFGS Producer Price Index: Finished Goods 85 5 OILPRICE Spot Oil Price: West Texas Intermediate 86 5 USSHRPRCF US Dow Jones Industrials Share Price Index (EP) NADJ 87 5 US500STK US Standard & Poor’s Index if 500 Common Stocks 88 5 USI62...F US Share Price Index NADJ 89 5 USNOIDN.D US Manufacturers New Orders for Non Defense Capital Goods (BCI 27) 90 5 USCNORCGD US New Orders of Consumer Goods & Materials (BCI 8) CONA 91 1 USNAPMNO US ISM Manufacturers Survey: New Orders Index SADJ 92 5 USVACTOTO US Index of Help Wanted Advertising VOLA 93 5 USCYLEAD US The Conference Board Leading Economic Indicators Index SADJ 94 5 USECRIWLH US Economic Cycle Research Institute Weekly Leading Index 95 2 GS10-FEDFUNDS 96 2 GS1-FEDFUNDS 97 2 BAA-FEDFUNDS 98 5 GEXPND/GDPDEF Government Current Expenditures/ GDP deflator 99 5 GRECPT/GDPDEF Government Current Receipts/ GDP deflator 100 2 GDEF Governnent Real Expend-Real Receipts 101 5 GCEC1 Real Government Cons. Expenditures & Gross Investment, 1 Decimal 102 5 Real Federal Cons. Expenditures & Gross Investment National Defense 103 2 Federal primary deficit 104 5 Real Federal Current Tax Revenues 105 5 Real Government Current Tax Revenues 106 2 Government primary deficit 22 References [1] Altug, S. (1989). Time-to-Build and Aggregate Fluctuations: Some New Evidence, International Economic Review 30, 889-920. [2] Amengual, D. and M.W. Watson (2007). Consistent Estimation of the Number of Dynamic Factors in a Large N and T Panel, Journal of Business and Economic Statistics 25, 91-96. [3] Bai, J. (2003). Inferential Theory for Factor Models of Large Dimensions, Econometrica 71, 135-171. [4] Bai, J., and S. Ng (2002). Determining the number of factors in approximate factor models, Econometrica 70, 191-221. [5] Bai, J., and S. Ng (2007). Determining the Number of Primitive Shocks in Factor Models, Journal of Business and Economic Statistics 25, 52-60. [6] Baxter, M. and R. King (1993). Fiscal Policy in General Equilibrium. American Economic Review 83(3), 315-34. [7] Bernanke, B. S., J. Boivin and P. Eliasz (2005). Measuring Monetary Policy: A Factor Augmented Autoregressive (FAVAR) Approach, The Quarterly Journal of Economics 120, 387-422. [8] Blanchard, O.J. and R. Perotti (2002). An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output, The Quarterly Journal of Economics: 1329-1368. [9] Burnside, C., M. Eichenbaum, and J. D. Fisher (2004). Fiscal Shocks and Their Consequences. Journal of Economic Theory 115, 89-117. [10] Cavallo, M. (2005). Government Employment Expenditure and the Effects of Fiscal Policy Shocks. Federal Reserve Bank of Chicago Working Paper 2005-16. [11] Chamberlain, G. (1983). Funds, factors, and diversification in arbitrage pricing models, Econometrica 51, 1281-1304. [12] Chamberlain, G., and M. Rothschild (1983). Arbitrage, factor structure and mean variance analysis in large asset markets, Econometrica 51, 1305-1324. [13] Connor, G., Korajczyk, R.A., 1988. Risk and return in an equilibrium APT. Application of a new test methodology. Journal of Financial Economics 21, 255-89. 23 [14] Edelberg, W., M. Eichenbaum, and J. D. Fisher (1999). Understanding the Effects of a Shock to Government Purchases. Review of Economic Dynamics 2 (1), 166206. [15] Eichenbaum, M. and J. D. Fisher (2005). Fiscal Policy in the Aftermath of 9/11. Journal of Money, Credit and Banking 37 (1), 1-22. [16] Fatas, A. and I. Mihov (2001). The Effects of Fiscal Policy on Consumption and Employment: Theory and Evidence. CEPR Discussion Paper No. 2760. [17] Fernndez-Villaverde J., J.F. Rubio-Ramrez, T.J. Sargent and M.W. Watson (2007). ABCs (and Ds) of Understanding VARs. American Economic Review, American Economic Association, 97(3):1021-1026. [18] Forni, M., L. Gambetti (2010) The dynamic effects of monetary policy: A structural factor model approach, Journal of Monetary Economics, forthcoming. [19] Forni, M., D. Giannone, M. Lippi and L. Reichlin (2009). Opening the Black Box: Structural Factor Models with Large Cross-Sections, Econometric Theory 25, 1319-1347. [20] Forni, M., M. Hallin, M. Lippi and L. Reichlin (2000). The generalized dynamic factor model: identification and estimation, The Review of Economics and Statistics 82, 540-554. [21] Forni, M., M. Hallin, M. Lippi and L. Reichlin (2005). The generalized factor model: one-sided estimation and forecasting. Journal of the American Statistical Association 100, 830-840. [22] Forni, M. and M. Lippi (2001). The generalized dynamic factor model: representation theory, Econometric Theory 17, 1113-1141. [23] Forni, M., Lippi, M. (2010). The unrestricted dynamic factor model. Representation results. Forthcoming in Journal of Econometrics. [24] Forni, M. and L. Reichlin (1998). Let’s get real: a factor analytical approach to disaggregated business cycle dynamics, Review of Economic Studies 65, 453-473. [25] Gali, J., D. Lopez Salido, and J. Valles (2007). Understanding the Effects of Government Spending on Consumption. Journal of the European Economic Association 5, 227-270. [26] Geweke, J. (1977). The dynamic factor analysis of economic time series, in D.J. Aigner and A.S. Goldberger, Eds., Latent Variables in Socio-Economic Models, North Holland, Amsterdam. 24 [27] Hallin M. and R. Liska (2007). Determining the number of factors in the general dynamic factor model, Journal of the American Statistical Association 102, 603617. [28] Ireland, P.N. (2004). A method for taking models to the data, Journal of Economic Dynamics and Control 28, 1205-1226. [29] Leeper, E.M., Walker, T.B. and S.S. Yang (2008). Fiscal Foresight: Analytics and Econometrics, NBER Working Paper No. 14028. [30] Leeper, E.M., Walker, T.B. (2009). Information Flows and News Driven Business Cycles, mimeo Indiana University [31] Lippi, M. and L. Reichlin (1993). The Dynamic Effects of Aggregate Demand and Supply Disturbances: Comment, American Economic Review 83, 644-652. [32] Lippi, M. and L. Reichlin (1994). VAR analysis, non fundamental representation, Blaschke matrices, Journal of Econometrics 63, 307-325. [33] Mountford, A. and H. Uhlig (2002). What Are the Effects of Fiscal Policy Shocks. CEPR Discussion Paper No. 3380. [34] Onatski, A. (2009). Testing Hypotheses About the Number of Factors in Large Factor Models, Econometrica 77, 1447-1479. [35] Pappa, E. (2009). The effects of fiscal shock on employment and the real wage, International Economic Review 50:217-244. [36] Perotti, R. (2002). Estimating the Effects of Fiscal Policy in OECD Countries. CEPR Discussion Paper No. 3380. [37] Perotti, R. (2007). In Search of the Transmission Mechanism of Fiscal Policy. NBER Macroeconomics Annual. [38] Ramey, V.A. (2009). Identifying Government Spending Shocks: It’s All in the Timing, NBER Working Papers no. 15464. [39] Ramey, V.A. and M. Shapiro (1998). Costly Capital Reallocation and the Effects of Government Spending. Carnegie Rochester Conference on Public Policy 48, 145-194. [40] Ravn, M. O. and K. Mertens (2009). Anticipation of Fiscal policy. University of Southampton manuscript. 25 Figure 2: Impulse response functions. 32 Figure 3: Impulse response functions. 33 Figure 4: Robustness: 13 factors (solid line), 10 factors (dotted line), 16 factors (dashed line). 34