Macroeconomic shocks and the business cycle : evidence from a structural factor model

Macroeconomic Shocks and the Business Cycle: Evidence from a Structural Factor Model Mario Forni∗ Universit`a di Modena e Reggio Emilia CEPR and RECent Luca Gambetti† Universitat Autonoma de Barcelona and RECent March 22, 2010 Abstract We use a dynamic factor model to provide a semi-structural representation for 101 quarterly US macroeconomic series. We find that (i) the US economy is well described by a number of structural shocks between two and six. Focusing on the four-shock specification, we identify, using sign restrictions, two non-policy shocks, demand and supply, and two policy shocks, monetary and fiscal. We obtain the following results. (ii) Both supply and demand shocks are important sources of fluctuations; supply prevails for GDP, while demand prevails for employment and inflation. (ii) Policy matters: Both monetary and fiscal policy shocks have sizeable effects on output and prices, with little evidence of crowding out; both monetary and fiscal authorities implement important systematic countercyclical policies reacting to demand shocks. (iii) Negative demand shocks have a large long-run positive effect on productivity, consistently with the Schumpeterian “cleansing” view of recessions. JEL classification: C32, E32, E52, F31. Keywords: structural factor model, sign restrictions, monetary policy, fiscal policy, demand, supply ∗Contact: Dipartimento di Economia Politica, via Berengario 51, 41100, Modena, Italy. Tel. +39 0592056851; e-mail: [email protected] †Contact: Office B3.174, Departament d’Economia i Historia Economica, Edifici B, Universitat Autonoma de Barcelona, Bellaterra 08193, Barcelona, Spain. Tel (+34) 935811289; e-mail: luca.gamb[email protected] 1 1 Introduction What and how many are the shocks that drive economic fluctuations? What is the relative importance of supply and demand disturbances? What are the effects of macroeconomic policies? These questions have been at the core of macroeconomic research for more than half a century, since the answer is key to assessing competing theories of the business cycle and the implied policy recommendations. Since Sims’ (1980) seminal paper, structural vector autoregressive models (SVAR) have been a major tool to address the questions above. Such models replaced large scale econometric models, their main advantage being that they do not require the imposition of “incredible” identifying restrictions. Over the last three decades, SVAR literature have substantially contributed to improve our knowledge of macroeconomic dynamics, providing evidence often used as a guideline by both policymakers and theorists. Nonetheless, we believe that SVAR models have an important limitation: the amount of information that they can handle is perforce small, owing to the so-called “curse of dimensionality”. The relevance of this information issue is stressed in several papers, including Quah (1990), Sims (1992), Lippi and Reichlin (1993, 1994), Bernanke and Boivin (1993), Bernanke et al. (2005). If, as plausible, both policy makers and private economic agents base their decisions on all of the available macroeconomic information, structural shocks should be innovations with respect to a large information set, perhaps larger than the one that can be included in a standard VAR. An alternative to SVAR models is given by a new generation of large dimensional models: the “generalized” or “approximate” dynamic factor models introduced by Forni et al. (2000), Forni and Lippi (2001), Stock and Watson (2002a, 2002b) and recently proposed for structural economic analysis (Stock and Watson, 2005, Forni et al., 2009). Such models have been successful in solving well known VAR puzzles (Bernanke et al., 2005, Forni and Gambetti, 2010). Their key advantage is that they combine a large number of macroeconomic variables with a reduced number of macroeconomic shocks. Two basic features distinguish large factor models from old-fashioned large scale models. First, identification can be reached in just the same way as in VAR models, without relying on “incredible” restrictions. Second, the forecasting performance is good (Stock and Watson 2002a, 2002b, Altissimo et al., 2010). 2 In this paper we use a large structural factor model to address the questions raised at the beginning of this introduction. Specifically, we apply the model and the estimation method of Forni et al. (2009) to 101 US quarterly series, covering the period 1959-I to 2007-IV. Following Uhlig (2005), we adopt an identification scheme based on inequality constraints. Such constraints are milder than the traditional zero restrictions commonly used in the VAR literature, in that only the sign of the impulse response functions at a few specific lags is imposed. Sign restrictions are particularly appropriate in our data-rich framework, since they can be imposed on a broad set of variables and this, in turn, is likely to deliver a better characterization of the shocks. As a first step in our analysis we answer the question: how many shocks are there in the macroeconomy? This question has largely been ignored in the empirical literature, probably because it is not meaningful within a VAR framework, where the number of economic shocks is determined by the number of variables included in the model. We find that the US economy can be well described by a number of shocks between 2 and 6, contrary to both theories relying on a single source of fluctuations, like early RBC models, and models with many macroeconomic shocks, like the one in Smets and Wouters (2007). We then focus on a four-shock specification and identify two non-policy shocks, demand and supply, and two policy shocks, monetary and fiscal. All shocks are normalized as expansionary by imposing positive effects on output (GDP and industrial production). We further impose that supply reduce prices, whereas the other three shocks raise prices (CPI and GDP deflator). Moreover, we impose that expansionary monetary policy reduces the federal fund rate and expansionary fiscal policy raises federal deficit. Our main findings are the following. First, both supply and demand shocks explain a considerable fraction of the fluctuations in real variables. However, their relative importance depends on the specific variable considered. Supply shocks explain most of GDP volatility, while demand shocks prevail for employment and other labor market variables. Demand shocks are less persistent than supply shocks and their long-run effect on GDP is not significant. Concerning inflation, both supply and demand have relevant effects; but demand shocks prevail, particularly in the long-run. Second, policy is important. Discretionary monetary policy shocks have sizeable effects on output and prices and are responsible for the early 80s recession and disinflation. Dis3 cretionary fiscal policy shocks have sizeable effects on GDP and do not have important crowding-out effects on private consumption and investment, with the sole exception of residential investment. As for systematic policy, there is evidence of a strong countercyclical response of both monetary and fiscal authorities to demand and, to a lesser extent, supply shocks. Finally, negative demand shocks have a persistent positive effect on labor productivity. This finding, while being at odds with most of the business cycle literature, is consistent with a stream of empirical and theoretical work concerning the interactions between growth and cycle and the Schumpeterian view of recessions as providing a cleansing mechanism for reducing organizational inefficiencies and resource misallocations. The remainder of the paper is organized as follows. Section 2 presents the model. Section 3 shows results concerning the number of shocks and presents in detail the definition of the shocks and the identification scheme. Section 4 presents the main results. Section 5 concludes. 2 Theory 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. 2.1 The factor model We assume that each variable xit of our macroeconomic data set is the sum of two mutually orthogonal unobservable components, the common component χit and the idiosyncratic component ξit: xit =χit +ξit.(2.1) 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 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 4 say “microeconomic” fluctuations); for strictly macroeconomic variables, like GDP, investment or consumption, the idiosyncratic component must be interpreted essentially as a measurement error. 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 =aif f ft.(2.2) The dynamic relations between the macroeconomic variables arise from the fact that the vector f f ftof the common factors follows the VAR relation f f ft=D1f f ft−1+· · · +Dpf f ft−p+  t   t=Ru u ut, (2.3) where Ris a r×qmatrix and u u ut= (u1tu2t· · · uqt)0is a q-dimensional vector of orthonormal white noises, with q≤r. Such white noises are the “common” or “primitive” shocks or “dynamic factors” (whereas the entries of f f ftare the “static factors”). 1 From equations (2.1) to (2.3) it is seen that the model can be written in the dynamic form xit =bi(L)u u ut+ξit,(2.4) where bi(L) = ai(I−D1L− · · · − DpLp)−1R. (2.5) The dynamic factors u u utand bi(L) are “structural” macroeconomic shocks and impulseresponse functions respectively.2 1Observe that, if q < r, the residuals of the above VAR relation have a singular variance covariance matrix. Equations (2.1) to (2.3) 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. 2Unlike the dynamic factors, the static factors do not have a structural economic interpretation; rather, they are a statistical tool which is useful to model the dynamics of the system. Loosely speaking, given the number of primitive shocks q, the number of “static factors” rgoverns the “degree of heterogeneity” of the impulse-response functions. For instance, in the simple case q= 1, if r= 1 all the impulse-response functions are proportional. On the other hand, if ris larger, different variables can load the shock with 5 2.2 Identification Representation (2.4) is not unique, since the impulse-response functions and the related primitive shocks are not identified. In particular, if His any orthogonal q×qmatrix, then Ru u utin (2.3) is equal to Sv v vt, where S=RH0and v v vt=Hu u ut, so that χ χ χit =ci(L)v v vt, with ci(L) = bi(L)H0=ai(I−D1L− · · · − DpLp)−1S. However, assuming mutually orthogonal structural shocks, post-multiplication by H0is the only admissible transformation, i.e. the impulse-response functions are unique up to orthogonal transformations, just like in structural VAR models (FGLR, Proposition 2). As a consequence, structural analysis in factor models can be carried on along lines very similar to those of standard SVAR analysis. To be precise, let us assume that economic theory implies a set of restrictions on the impulse-response functions of some variables, the first m≤nwith no loss of generality. Let us write such functions in matrix notation as Bm(L) = (b1(L)0b2(L)0· · · bm(L)0)0. Given any non-structural representation χ χ χmt =Cm(L)v v vt,(2.6) along with the relation Bm(L) = Cm(L)H, (2.7) if theory-based restrictions on Bm(L) are sufficient to obtain H, then bi(L) is uniquely determined for any i(just identification). In the present paper however we do not identify uniquely the shocks and the impulseresponse functions; rather, following Uhlig (2005), we identify a distribution of shocks and related impulse-response functions by imposing a set of sign restrictions on the impulseresponse functions themselves. Formally, let bik be the coefficient of the term of degree k of bi(L). We impose bik >0 for i∈ I,k∈ K and bjh <0 for j∈ J ,h∈ H, where I,K, Jand Hare sets of integers. The precise set of restrictions that we impose in the present paper is discussed below. A quite natural parameterization of the orthogonal matrices His given by the hyperspherical coordinates of the unit sphere Swof dimension w= (q2−q)/2, i.e. H=H(θ), θ being a w-dimensional vector of angles such that 0 ≤θj< π,j= 1, . . . , w −1, 0 ≤θw<2π. different delays, so that we may have leading, coincident and lagging variables. If ris large enough, any (finite order) MA dynamics can be written in the form (2.1)-(2.3) (FGLR, Section 2). 6 Given the non-structural representation Cn(L)v v vt, the sign restrictions above define an admissible region Θ on the unit sphere, such that for θ∈ΘBn(L) = Cn(L)H(θ) satisfies such inequalities. Following Uhlig (2005), we assume that the true shocks and impulse-response functions are associated with a point θwith uniform probability density in the region Θ. This in turn implies upper and lower bounds and a probability density for each coefficient of the impulse-response functions Bn(L). 2.3 Estimation As for estimation, we proceed as follows. First, starting with an estimate ˆrof the number of static factors, we estimate the static factors themselves by means of the first ˆrordinary principal components of the variables in the data set, and the factor loadings by means of the associated eigenvectors. Precisely, let ˆ Γxbe the sample variance-covariance matrix of the data: our estimated loading matrix ˆ An= (ˆa0 1ˆa0 2· · · ˆa0 n)0is the n×rmatrix having on the columns the normalized eigenvectors corresponding to the first largest ˆreigenvalues of ˆ Γx, and our estimated factors are f f ft=ˆ A0 n(x1tx2t· · · xnt)0. Second, we set a number of lags ˆpand run a VAR(ˆp) with f f ftto get estimates of D(L) and the residuals   t, say ˆ D(L) and ˆ   t. Now, let ˆ Γbe the sample variance-covariance matrix of ˆ   t. As the third step, having an estimate ˆqof the number of dynamic factors, we obtain an estimate of a non-structural representation of the common components by using the spectral decomposition of ˆ Γ. Precisely, let ˆµ j,j= 1,...,ˆq, be the j-th eigenvalue of ˆ Γ, in decreasing order, ˆ Mthe q×qdiagonal matrix with qˆµ jas its (j, j) entry, ˆ Kthe r×qmatrix with the corresponding normalized eigenvectors on the columns. Setting ˆ S=ˆ Kˆ M, our estimated matrix of non-structural impulse response functions is ˆ Cn(L) = ˆ Anˆ D(L)−1ˆ S. (2.8) Consistency of the above estimation procedure (as both the cross-sectional and the time dimension go to infinity) is proven in FGLR. To account for estimation uncertainty, we adopt the following standard non-overlapping block bootstrap technique. Let X= [xit] be the T×nmatrix of data. Such matrix is partitioned into Ssub-matrices Xs(blocks), s= 1, . . . , S, of dimension τ×n,τbeing the 7 integer part of T/S.3An integer hsbetween 1 and Sis drawn randomly with reintroduction Stimes to obtain the sequence h1, . . . , hS. A new artificial sample of dimension τS×nis then generated as X∗=hX0 h1X0 h2· · · X0 hSi0and the corresponding impulse-response functions are estimated. A set of non-structural impulse-response functions is obtained by repeating drawing and estimation. Finally, we obtain a distribution of impulse-response functions by imposing our sign identification restrictions. Precisely, we proceed as follows. For each artificial sample X∗ we compute the corresponding non-structural impulse response functions ˆ Cn(L). Then we draw Ntimes a vector of angles θwith dimension w= (q2−q)/2 from a uniform distribution in the range 0 ≤θj< π,j= 1, . . . , w −1, 0 ≤θw<2πand retain the related ˆ Bn(L) = Cn(L)H(θ) as long as they satisfy the sign restrictions. This gives a distribution of estimated ˆ Bn(L)’s. We get a point estimate and the related confidence bands by retaining the mean along with the relevant percentiles of such a distribution.4 2.4 Discussion FGLR is a special case of the generalized dynamic factor model proposed by Forni, et al. (2000, 2004, 2005) and Forni and Lippi (2001, 2008). This model differs from the traditional dynamic factor model of Sargent and Sims (1977) and Geweke (1977) in that the number of cross-sectional variables is infinite and the idiosyncratic components are allowed to be mutually correlated to some extent, along the lines of Chamberlain (1983), Chamberlain and Rothschild (1983) and Connor and Korajczyk (1988). Closely related models have been studied by Forni and Reichlin (1998), Stock and Watson (2002a, 2002b, 2005), Bai and Ng (2002, 2007), Bai (2003) and Bernanke et al. (2005). Large statistical factor models are compatible with a variety of economic models, including both neo-classical and neo-keynesian DSGE models, augmented with measurement errors (see Sargent and Sims, 1977, Sargent, 1989; Altug, 1989; Ireland, 2004, Giannone et al., 2006 and the literature mentioned therein). However, in the present work we do not 3Note that τhas to be large enough to retain relevant lagged autoand cross-covariances In the present paper we set τ= 19. 4Here we impose an upper bound (10) to the number of impulse-response functions to retain for each step of the bootstrap procedure in order to avoid that a single bootstrap provide a disproportionately large number of functions. 8 propose a fully developed economic model characterized by “deep” parameters. Rather, our approach is very much in the spirit of the “structural” VAR literature. Our impulse response functions can indeed be labeled as “semi-structural”, rather than “structural”: while not being reduced form coefficients, they are still a mixture of behavioral and policy parameters, so that we cannot tell, say, what would happen in absence of systematic fiscal or monetary policy. The results of the present paper should then be interpreted essentially as stylized facts, conditional on the identified shocks. Why use a structural factor model rather than a structural VAR? Factor models impose a considerable amount of structure on the data, implying restricted VAR relations among variables (see Stock and Watson, 2005 for a comprehensive analysis). In this sense, they are less general than VAR models. On the other hand, factor models have a few advantages which may be important in the present context. First, within a factor model we can study how many shocks there are in the macro economy, an interesting question which does not even make sense within the statistical VAR framework, where the number of shocks is necessarily equal to the number of variables that the econometrician chooses to include in the data set. Determining the number of shocks is important since it can provide useful guidelines for building macroeconomic models. Second, being much more parsimonious in terms of parameters, factor models can handle a much larger amount of information. The data set used here, for instance, includes about one hundred variables. A VAR model with the same number of series would have too many parameters to estimate, given the number of observations available in the time dimension. Having a large data set is important for three reasons. First, we can study the impulse response functions of virtually all relevant macro variables within a unified framework. We exploit this opportunity here by showing results for 23 key macro variables. Second, it enables us to impose identifying restrictions on several variables, reducing the region of admissible impulse response functions and causing the confidence bands to shrink. For instance, we identify an expansive demand shock by imposing positive effects on output and prices; as output series we use both GDP and the industrial production index, while prices are measured by both the GDP deflator and the CPI. Last, but not least, large information is likely to produce better results. The relevance of the information issue is stressed in several influential papers, including Quah (1990), 9 Concerning the supply shock, Figure 3 shows that both the producer price index of crude materials and the unit labor cost immediately and significantly fall, indicating that the supply shocks are partly made up of unexpected changes in some key production costs. Moreover, Figure 9 shows a large and significant positive impact on labor productivity, in line with the consensus view that supply shocks include an important technological component. An expansionary monetary policy shock increases monetary aggregates, as predicted by the theory of the liquidity effect (the response function of M2 is shown in Figure 1). Moreover, the impact effects on output and prices are small and not significant, consistently with the zero identifying restrictions often imposed in the SVAR literature (Fig. 4). Finally, the fiscal policy shock immediately and significantly increases federal government expenditures (Fig. 2). Note also the different reaction of current receipts to fiscal policy and private demand shocks. While both shocks significantly affect GDP on impact and the size of the effects are similar (Fig. 4), non-policy demand significantly raises federal receipts, whereas fiscal policy does not, suggesting the presence of a tax reduction component compensating for the increase in GDP. 4.2 The relative importance of supply and demand shocks Table 2 shows the variance decomposition of (the stationary transformation of) some selected series. Columns 2 to 6 report the percentages of variance explained by the monetary policy shock (MP), the fiscal shock (FS), the supply shock (S), the non-policy demand shock (D) and the two policy shocks jointly (MP+FS). Supply shocks explain around 55% of the variance of GDP growth, being slightly more important for consumption than for investment. Such result is in line with King et al. (1991). Policy shocks account for about 26% of the variance, while non-policy demand shocks explain only 18%. The picture however changes substantially when other variables are considered. Regarding industrial production, for instance, the contribution of supply reduces to 37%, as against 39% of non-policy demand. This is consistent with the fact that, as already noted, private-demand shocks primarily concern investment and exports, which mainly involve goods, rather than services. The importance of demand is even larger for labor market variables, such as employment, hours worked or the unemployment rate. 16 Focusing on employment, for instance, the percentage of variance accounted for by supply shocks reduces to 35%, while the one accounted for by non-policy demand shocks is raised up to 42%. Such a large difference between employment and GDP variance decompositions is probably due to the technology component of supply shocks. While demand affects output mainly through employment changes, supply largely affects GDP through the important impact on productivity already noted above. Tables 3a-3c display the decomposition of the forecast error variance at different horizons. The previous results are confirmed. In particular, supply shocks explain most of GDP variance, while demand shocks prevail as far as employment is concerned. On impact (k= 0) such dichotomy is particularly pronounced: supply shocks explain 63% of output as against 11% of employment, whereas non-policy demand accounts for 58% of employment but only 13% of output. From Tables 3a-3c it also emerges clearly that, in the long run, the effects of non-policy demand on all real variables reduce, while the effects of supply increase, consistently with the consensus view that supply shocks are more persistent. Considering prices, the bulk of fluctuations in the GDP deflator is accounted for by the three demand shocks, which, taken together, account for about 70% of the variance of the two series. The result is confirmed by Tables 3a-3c: demand shocks account for about 68%, 75% and 84% at horizons 0, 4 and 24 quarters, respectively. Figure 4 plots the impulse response functions of GDP and the GDP deflator to the four shocks. Several interesting features emerge. First, all of the shocks except monetary policy affect significantly output on impact. The effect is particularly large for supply shocks. Second, both fiscal policy and non-policy demand shocks have temporary effects on output, whereas the supply shock has large and significant permanent effects. Long-run neutrality of demand on output is consistent with mainstream theory and is adopted as an identifying assumption in the SVAR literature, starting with the seminal work of Blanchard and Quah (1989). Third, despite this, demand is not long-run neutral on all real variables, persistency being particularly pronounced for employment. We will come back to this point below. Fourth, the GDP deflator significantly increases at all horizons for the three demand shocks and reduces significantly at all horizons for the supply shock. To get some additional insights about the relative importance of structural shocks, Figure 5 and 6 plot the historical decomposition of output growth and inflation. The dotted 17 lines refer to the original series, while the solid line refers to the series of inflation generated using the particular component specified in the title of each panel.10 As noted above, both demand and supply shocks have an important role in shaping economic fluctuations. However, their relative importance is not constant over time. In the 70s supply shocks seem to have a primary role. Actually, they are responsible for the two recessions of 1971 and 1974. Supply appears to be very important also in the last part of the sample, from the early 90s onward. The 1991 recession, in particular, is mainly attributable to the supply component. These results are consistent with the narrative literature attributing to supply factors such as increases in commodity prices the two recessions of the 70s and the recession of 1991. On the other hand, demand shocks play a relevant role during the 80s. In particular the recession of the early 80s is attributable to both policy and non-policy demand factors. As discussed above, demand shocks are by far the primary source of fluctuations in prices. The last row of Figure 6 shows that demand shocks very well track the series of inflation, with the exception of the two peaks in inflation dated 1975 and 1979, which correspond to the two oil shocks and are driven by supply. The left panel of the last row plots the component of inflation changes obtained using only the fiscal policy and non-policy demand components. In the first half of the 80s this series lies always above the actual series, whereas the two series almost exactly overlap when also the monetary policy component is added (right panel). The monetary policy shock correctly captures the Volcker disinflation episode, where a strongly anti-inflationary monetary policy stance was adopted to fight inflation. In summary, both supply and demand shocks are important sources of macroeconomic fluctuations, but the relative importance differs substantially for different variables. Supply prevails for GDP, whereas demand prevails for labor market variables, industrial production and prices. Demand shocks are less persistent than supply shocks for all real variables. While being long-run neutral for output, neutrality does not hold for employment. Finally, policy shocks have sizeable effects on output and prices. In particular the former seems to be 10This component is computed as follows. First, we estimate a non-structural orthogonal representation for the original data as explained in Section 2. Then we draw randomly the candidate rotation matrices and retain the impulse response functions satisfying our sign restriction along with the corresponding shocks (we got about 2000 admissible impulse response functions). Finally we filter each shock with the corresponding response function to get the component and average across components. 18 responsible for the early 80s recession and disinflation. This picture is more complex than the one emerging from the VAR literature, where the limited dimension makes it difficult to compare all of the relevant series. 4.3 Macroeconomic policies This sub-section addresses three key policy questions. First, what and how big are the effects of monetary and fiscal discretionary policies on GDP and prices? Second, are consumption and investment crowded out by discretionary fiscal policy? Third, do monetary and fiscal authorities react systematically to macroeconomic shocks? Monetary policy and fiscal shocks account for about 9% and 17% of the fluctuations in GDP, respectively (see Table 2). Fiscal policy shocks are more important in the short run (25% at k= 0 and 5% at k= 24), while monetary policy shocks produce bigger effects at long horizons (3% at k= 0 and 9% at k= 24). This is due to the different shape of the impulse response functions (Fig. 4). On the one hand, the response of GDP to a monetary policy shock is persistent but has a nearly zero impact effect. On the other hand, the response to a fiscal fiscal policy shock reaches the maximal level on impact and is relatively short lived. As far as inflation is concerned, monetary and fiscal policy shocks explain around 27% and 7% of the volatility of the growth rates of the GDP deflator, respectively. Percentages are similar at all horizons. In conclusion, both fiscal and monetary policy have non-negligible effects on output and prices; fiscal policy seems to be more relevant for output fluctuations, while monetary policy is dominant for fluctuations in prices. Figure 7, line 2, plots the impulse response functions of investment, residential investment and nonresidential investment to a unit variance fiscal policy shock. The responses of nonresidential and residential investment differ substantially. The former increases significantly for the first year (in the long run the point estimate is positive but not significant). The latter, after a nearly zero initial effect, reduces significantly in the long run. The difference could be attributable to a different sensitivity of the two types of investment to the interest rate, which permanently and significantly increases (see below). On aggregate, investment increases significantly on impact and for the first quarter after the shock, despite the increase of interest rates. 19 Figure 8, line 2, plots the impulse response functions of consumption, durable consumption and nondurable consumption to a unit variance fiscal policy shock. The three responses have similar shapes, with a positive impact effect, followed by a reduction. The impact effect is much larger for durables (0.3% as against 0.06%). On aggregate the impact effect is small (0.1% as compared to 0.3% of investment). All effects are (borderline) significant only on impact. All of the three responses are very similar, both quantitatively and qualitatively, to the corresponding ones of non-policy demand. Such picture is different to that of Blanchard and Perotti (2002), where consumption is found to considerably increase, but is also different to those of Ramey and Shapiro (1998) and Ramey (2009), where consumption is found to significantly fall. The small reaction of nondurable consumption (and hence aggregate consumption) to both the fiscal policy and the non-policy demand shocks seems in line with standard permanent income theory, provided that, at least in part, consumers correctly perceive the increase of income as transitory. The positive sign of the response is in contrast with theoretical predictions from standard RBC models. Overall, there is little evidence of crowding-out of private expenditure after a fiscal policy shock, with the relevant exception of residential investment. Let us now study whether there is evidence of a systematic monetary and fiscal policy reacting to our structural shocks. Let us consider first monetary policy. After both a non-policy demand and a fiscal policy shock the federal funds rate immediately and permanently increases (Fig. 1). The effect is significant in both cases, although, from a quantitative point of view, the effect of the non-policy demand shock is about two times larger than that of fiscal policy. As for money aggregates, a significant reduction of M2 is found in both cases, the reduction being particularly large for the non-policy demand shock (Fig. 1). This suggests a very active countercyclical behavior of monetary policy, which is consistent with standard Taylor rules implying systematic policy reaction to increases in prices and output. On the contrary, the federal funds rate responds negatively to the supply shock on impact, although the effect is not significant. However, the effect becomes positive and significant after about one year, converging to 0.4% in the long run. Taking as benchmark a standard Taylor rule, the result indicates that while in the very short run the opposite effects of output and inflation offset each other, in the long run the effects on inflation 20 reduce and the federal funds rate seems to follow the pattern of output. Let us now come to systematic fiscal policy (Fig. 2). Government spending essentially does not react to monetary policy and supply shocks, the effect of such shocks being not significant at any horizon. On the contrary, the non-policy demand shock induces a strong countercyclical behavior of fiscal authorities. Government spending reduces significantly at all horizons by about 0.4%. We can get some idea of the effects of such policy by looking at Table 2. The fraction of variance of GDP growth explained by the non-policy demand shock (18%) is sizeably smaller than the one of its components: investment (35%), consumption (19%), and government expenditure (27%). This is attributable to the negative comovement of private demand components and government spending. There is little evidence, however, of an active behavior of fiscal authorities on the receipt side, since current receipts essentially follow GDP changes. Both supply and demand bring about a significant positive and permanent increase in current receipts which reduces government deficit. In summary, the evidence suggests a strong countercyclical systematic response of both monetary and fiscal authorities to demand shocks. Given that discretionary policy has sizeable effects on both output and prices, systematic policy could be effective in controlling inflation and reducing output fluctuations arising from non-policy demand. As a consequence, output fluctuations originated by non-policy demand, which, as documented above, are fairly small in comparison with supply-driven variations, could be much larger if systematic policy where not in place. Unfortunately, with the present model we cannot proceed to evaluate the quantitative importance of stabilization policies, nor we can say whether the corresponding variance reduction over-compensates for discretionary policies, which, as we have seen, are non-negligible sources of additional fluctuations. 4.4 Demand shocks and labor productivity As shown above, the non-policy demand shock does not have permanent effects on GDP. This however does not mean that demand is long-run neutral, since the private demand shock has permanent effects on several real variables. In particular, an expansionary shock increases employment and hours worked and reduces unemployment and the unemployment rate (the effect on employment is reported in Figure 9). Since output does not increase in 21 the long run, labor productivity (non-farm business sector, output per hour of all persons) significantly decreases (Figure 9). Such an effect is quantitatively important. A unitvariance shock, increasing GDP by 0.2 per cent on impact, reduces labor productivity by almost 0.4% in a couple of years: a change which, in absolute value, is even larger than that of the supply shock. Table 3c confirms such ranking: private demand explains about 45% of the forecast error variance at a six-year horizon, as against the 35% explained by the supply shock. Moreover, the wage rate (nonfarm business sector, real compensation per hour) decreases substantially as far as the point estimate is concerned, even though the effect is not significant, owing to the large confidence bands (not shown). The findings above, while being at odds with most of the business cycle literature, are consistent with a stream of empirical and theoretical work concerning the interactions between growth and cycle. Empirical evidence of a long-run negative effect of a positive demand shock on productivity is reported in Bean (1990), Saint-Paul (1993) and Galı´and Hammour (1991), where an impulse response function almost identical to the one obtained here is found by using a structural VAR approach. Possible explanations are provided by theoretical works which, in various ways, revive the Schumpeterian view of recessions as providing a cleansing mechanism for reducing organizational inefficiencies and resource misallocations. During recessions, less efficient firms become unprofitable and shut down, thus improving average productivity (Caballero and Hammour, 1993). Moreover, the opportunity cost of undertaking productivity-enhancing activities are lower, so that recessions are the right time to reorganize production, and/or improve the matching between workers and firms, implement new technologies, invest in human capital (Davis and Haltiwanger, 1992, Hall, 1991, Aghion and Saint-Paul, 1991). Such efficiency effects are long-lasting.11 Let us highlight two relevant implications of the above findings. The first one is related to empirical economic research. A widespread practice in structural VAR literature is to identify technology shocks as the only ones having long-run effects on productivity (Galı´ , 1999, Christiano et al., 2003). But if demand also affects productivity, this identification assumption may produce a mixture of true positive technology shocks and negative demand 11According to the above explanations, productivity is related to the business cycle, rather than demand per se). This is consistent with our estimated response of productivity to supply shocks, which reaches its maximum after about one year and then declines sharply, dissipating about one half of the impact effect in the following six quarters (see Figure 9). 22 shocks, leading to incorrect conclusions. For instance, the finding that technology reduces hours worked (Galı´ , 1999) could be due to the negative demand component. Indeed, our supply shock have a significant positive impact on hours worked (not shown). Moreover, the puzzling finding that technology has little effect on investment (Christiano et al., 2003) may result from positive technology effects canceling out with negative demand effects. Actually with our identification procedure supply shocks account for about 72% of fluctuations in investment at the 4-year horizon (see Table 3c). The second implication is a policy one. Systematic counter-cyclical policies, if successful in reducing fluctuation, may have long-run ’side effects’. Specifically, expansive measures following negative demand shocks, while not hurting GDP growth, may permanently support employment on one hand, and reduce per-capita GDP and real wages, on the other hand. On balance, such effects are not necessarily undesirable. But policy makers should be fully aware of the efficiency issues related to public support for employment and shaky companies, in order to design intervention properly. 5 Conclusions This paper studies the sources of the business cycle and the role of macroeconomic policies using a structural factor model. Our main results are the following. First, theories based on the existence of a single source of fluctuations as well as theories relying on a large number of shocks are inconsistent with our evidence. The US economy can be well described by a number of shocks between 2 and 6. Second, by specifying a four-shock model we find that both demand and supply components are important to explain fluctuations in real macroeconomic variables, although the relative importance varies, depending on the specific variable considered. Supply explains most of GDP volatility while demand prevails for employment and other labor market variables. Fluctuations in prices are mostly explained by demand shocks. Third, policy is important. Discretionary policies produce sizeable effects on output and prices, with little evidence of crowding out effects of public expenditure. Both fiscal and monetary authorities follow systematic policy rules reacting mainly to private demand shocks. Such stabilization policies could in principle be very effective in reducing demanddriven fluctuations. 23 Finally, non-policy demand shocks, while being long run neutral on GDP, have a large and permanent negative effect on productivity. Such a result is consistent with the Schumpeterian view of crises as providing a “cleansing” device for reducing inefficiencies and resource misallocations. 24 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 6 COMPNFB Nonfarm Business Sector: Compensation Per Hour 33 5 COMPRNFB Nonfarm Business Sector: Real Compensation Per Hour 25 [46] Sims, C.A. (1980). Macroeconomics and Reality, Econometrica 48, 1-48. [47] Sims, C.A., 1992. Interpreting the Macroeconomic Time Series Facts, The Effects of Monetary Policy. European Economic Review 36, 975-1011. [48] Smets, F. and R. Wouters (2007). Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach, American Economic Review 97, 586-606. [49] Stock, J.H. and M.W. Watson (2002a). Macroeconomic Forecasting Using Diffusion Indexes, Journal of Business and Economic Statistics 20, 147-162. [50] Stock, J.H. and M.W. Watson (2002b). Forecasting Using Principal Components from a Large Number of Predictors, Journal of the American Statistical Association 97, 1167-1179. [51] Stock, J.H. and M.W. Watson (2005). Implications of Dynamic Factor Models for VAR Analysis, NBER Working Papers no. 11467. [52] Uhlig, H. (2005). What are the effects of monetary policy on output? Results from an agnostic identification procedure. Journal of Monetary Economics 52, 381-419. 32 Tables Table 1: 0 1 2 3 4 5 6 7 0 0.001 0.002 0.003 0.003 0.004 0.005 0.006 1 0.012 0.021 0.028 0.036 0.042 0.05 2 0.927 0.107 0.147 0.183 0.215 3 0.06 0.107 0.147 0.183 4 0.852 0.982 0.746 5 0.746 0.595 6 0.336 33 Table 2: Explained variances MP FP S D MP+FP Variable % var std % var std % var std % var std % var GDP 8.95 5.78 17.25 9.28 55.81 13.45 17.98 10.63 26.21 Investment 7.75 6.10 9.76 6.52 47.96 14.71 34.54 13.22 17.50 Consumption 10.80 7.38 11.34 7.67 58.56 13.08 19.30 9.73 22.14 Gov. Exp.&Inv. 17.91 17.23 37.77 19.95 17.07 14.38 27.26 18.48 55.68 Deficit 16.40 12.17 19.88 12.19 17.19 9.10 46.53 14.21 36.28 Industrial Production 8.32 6.32 14.98 9.98 37.68 11.74 39.01 12.99 23.30 Employment 11.10 7.57 11.02 8.23 35.23 13.82 42.64 14.51 22.13 Unemployment Rate 7.25 6.22 10.87 6.77 42.20 13.20 39.68 12.95 18.12 Labor Productivity 11.39 8.47 22.05 12.43 51.37 13.52 15.18 5.62 33.44 GDP Deflator 26.80 18.76 7.02 8.56 29.65 16.27 36.53 18.92 33.82 PPI 19.65 13.81 34.68 17.23 29.77 13.92 15.90 12.27 54.33 Federal Funds Rate 18.97 11.70 17.43 10.96 18.73 8.90 44.86 12.05 36.40 New Orders 11.09 7.51 12.12 6.74 32.10 9.75 44.69 11.34 23.22 34 Table 3a: Explained forecast error variances at horizon k= 0 MP FP S D MP+FP Variable % var std % var std % var std % var std % var GDP 3.23 6.01 19.96 13.84 62.87 18.47 13.93 14.83 23.20 Investment 2.29 4.11 8.71 9.89 41.36 20.93 47.63 22.73 11.01 Consumption 6.91 8.49 9.06 12.01 63.94 20.52 20.09 19.12 15.98 Gov. Exp.&Inv. 16.08 21.18 39.26 25.55 15.53 18.04 29.13 22.21 55.34 Deficit 15.38 16.76 18.71 16.11 7.38 10.98 58.53 20.45 34.10 Industrial Production 4.59 7.50 18.99 16.00 28.11 17.17 48.31 20.73 23.58 Employment 14.88 18.73 15.27 17.54 11.16 12.01 58.69 25.95 30.16 Unemployment Rate 2.24 3.80 13.15 11.45 28.43 16.47 56.18 19.68 15.39 Labor Productivity 7.26 11.45 22.53 16.92 64.90 18.15 5.30 6.08 29.80 GDP Deflator 30.80 23.28 5.77 9.86 32.70 18.04 30.74 21.79 36.57 PPI 16.60 16.21 35.88 22.45 35.53 17.67 12.00 15.24 52.48 Federal Funds Rate 26.93 16.92 19.95 18.70 8.72 10.41 44.40 22.31 46.88 New Orders 7.84 8.89 10.97 12.12 10.22 12.02 70.96 21.43 18.81 35 Table 3b: Explained forecast error variances at horizon k= 4 MP FP S D MP+FP Variable % var std % var std % var std % var std % var GDP 6.89 7.48 7.39 8.26 73.55 16.81 12.16 13.35 14.28 Investment 7.00 7.88 3.96 4.99 64.97 20.35 24.07 18.18 10.96 Consumption 11.10 10.19 5.29 5.93 76.03 14.52 7.58 8.48 16.39 Gov. Exp.&Inv. 13.17 17.13 41.92 25.29 14.63 15.37 30.29 23.50 55.09 Deficit 10.59 10.69 9.80 9.57 18.36 15.27 61.25 18.95 20.38 Industrial Production 6.18 6.22 7.19 7.76 54.03 18.67 32.60 17.93 13.37 Employment 7.68 7.41 6.68 8.03 38.12 20.57 47.52 21.26 14.36 Unemployment Rate 4.86 5.97 5.35 6.42 54.25 19.89 35.54 19.01 10.21 Labor Productivity 9.52 11.02 11.14 10.97 58.08 16.85 21.26 12.97 20.66 GDP Deflator 27.36 22.22 4.86 8.53 25.70 17.49 42.09 21.33 32.21 PPI 29.26 23.46 34.03 25.49 23.87 18.96 12.84 15.12 63.29 Federal Funds Rate 7.10 6.31 16.27 12.47 10.39 7.69 66.24 14.90 23.37 New Orders 5.65 6.58 4.96 5.40 44.10 20.91 45.29 20.79 10.61 36 Table 3c: Explained forecast error variances at horizon k= 24 MP FP S D MP+FP Variable % var std % var std % var std % var std % var GDP 8.82 9.64 4.97 6.98 78.61 14.70 7.60 9.03 13.79 Investment 9.34 10.43 5.19 5.77 72.03 18.95 13.44 14.19 14.53 Consumption 12.00 11.44 6.34 7.14 72.15 15.16 9.51 9.37 18.34 Gov. Exp.&Inv. 12.37 17.10 41.08 27.13 19.19 19.82 27.36 24.77 53.45 Deficit 11.85 12.93 15.46 12.94 28.60 20.51 44.08 23.07 27.32 Industrial Production 8.87 8.92 4.77 6.54 67.77 18.72 18.59 16.11 13.64 Employment 9.80 9.72 4.75 5.98 54.82 23.37 30.63 21.38 14.56 Unemployment Rate 7.56 8.95 4.06 5.37 68.82 20.43 19.56 17.26 11.62 Labor Productivity 10.17 12.34 10.49 12.27 34.67 18.61 44.67 19.52 20.66 GDP Deflator 31.30 24.72 4.59 8.86 16.26 17.19 47.85 22.78 35.89 PPI 30.05 25.88 26.47 25.95 31.20 26.60 12.28 13.18 56.52 Federal Funds Rate 5.29 5.61 10.53 10.71 25.37 16.56 58.82 17.95 15.82 New Orders 7.42 9.57 5.60 5.49 60.18 22.28 26.81 20.66 13.02 37 Figures Figure 1 38 Figure 2 39 Figure 3 40 Figure 4 41