Fiscal policy, foresight and the trade balance in the U.S

Fiscal Policy, Foresight and the Trade Balance in the U.S. Luca Gambetti∗ Universitat Autonoma de Barcelona September 1, 2010 Abstract This paper investigates the effects of fiscal policy on the trade balance using a structural factor model. A fiscal policy shock worsens the trade balance and produces an appreciation of the domestic currency but the effects are quantitatively small. The findings match the theoretical predictions of the standard Mundell-Fleming model, although fiscal policy should not be considered one of the main causes of the large US external deficit. My conclusions differ from those reached using VAR models since the fiscal shock, possibly due to fiscal foresight, is nonfundamental for the variables typically used in open economy VARs. JEL classification: C32, E32, E62. Keywords: structural factor model, fiscal policy, twin deficits, trade deficit, current account, Mundell-Fleming. ∗I am grateful to Mario Forni for helpful discussions. The financial support from the Spanish Ministry of Science and Innovation through grant ECO2009-09847 and the Barcelona Graduate School Research Network is gratefully acknowledged. 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 Since the mid 1980s, the U.S. economy has been characterized by a large and growing trade deficit. Around the mid 1980s the deficit was about 3% of GDP while since 2000 has been on average about 5% of GDP. The phenomenon, given its magnitude, has attracted a great deal of attention devoted to assessing the possible causes. Expansionary fiscal policy is in the list. According to the standard textbook Mundell-Fleming model, a fiscal policy expansion worsens the trade balance through the appreciation of the domestic currency following the inflow of foreign capital attracted by a higher interest rate.1 Quite surprisingly however, little evidence about the effects of fiscal policy shocks on the trade deficit and the exchange rates is available.2Moroever existing empirical analyses based on VAR models yield contrasting results, none of which supporting the predictions of the standard Mundell-Fleming model. Kim and Roubini (2008) finds that an expansionary fiscal shock depreciates the real exchange rate and improves the current account balance. The finding can be rationalized by the presence of crowding out of private investment and Ricardian movements in private savings.3A similar result is obtained in Corsetti and Muller (2006). Monacelli and Perotti (2007), on the contrary, finds that an increase in government spending depreciates the real exchange rate and worsens the trade balance. This evidence has sparked an important research effort to better understand the mechanisms that propagate fiscal policy actions. Studying the effects of fiscal shocks using VAR techniques can be problematic though. A few recent works have convincingly argued that, because of the existence of legislative and implementation lags, private agents receive signals about future changes in taxes and government spending before these changes take actually place, the phenomenon called “fiscal foresight” (see e.g. Yang, 2007, Leeper, Walker and Yang, 2008, Mertens and Ravn, 2009). Leeper, Walker and Yang (2008) (LWY henceforth) shows theoretically that, under fiscal foresight, standard VAR techniques are likely to fail in correctly estimating the fiscal policy shock since a problem of non-fundamentalness emerges. Nonfundamentalness typically arises when agents have a larger information set than the econometrician4, a situation that can occur when a limited number of variables are con1A partial list of models where a fiscal expansion may generate a worsening of the trade balance includes Dornbusch (1976), Baxter, (1995) and Kollmann, (1998), Erceg, Gust and Guerrieri (2005). 2On the contrary, a lot of evidence is available on the effects of government spending shocks on domestic variables, see e.g. Blanchard and Perotti (2002) and Ramey and Shapiro (1988). 3An improvement of the current account balance after a permanent increase in government spending can be found in the model of Obstfeld and Rogoff (1995). 4see Hansen and Sargent (1980). 2 sidered like in VAR models5. But in presence of fiscal foresight non-fundamentalness becomes a very likely scenario. The intuition is that fiscal variables like taxes or government spending, typically used to identify fiscal policy shocks, are affected only with a delay by fiscal policy actions so that their current and past values do not convey enough information about the current shock. Forni and Gambetti (2010) provides evidence that government spending shocks are actually non-fundamental for the variables usually considered in standard closedeconomy specifications. The finding confirms the result obtained in Ramey (2009) that the fiscal policy shock estimated with a VAR as in Perotti (2007) is Granger-caused by the forecast of government spending from the Survey of Professional Forecasters. Although the specifications considered by the authors do not include open economy variables, the results cast some doubt on the reliability of the findings obtained with structural VARs and motivate the analysis conducted here. In this paper I depart from the VAR approach and study the effects of fiscal shocks on the trade balance using a large structural factor model. The main motivation is that, as argued in Forni, Giannone, Lippi and Reichlin (2009), in this class of models structural shocks are always fundamental. The factor model uses a large number of variables driven by a much smaller number of economic shocks. Rich information helps per se in mitigating the problem of non-fundamentalness since reduces the gap between the information sets of economic agents and the econometrician. But most importantly, having less shocks than variables implies that macroeconomic dynamics are represented by a rectangular, “tall” MA system where, as I shall show, shocks are fundamental. The model is estimated using US quarterly data for 115 US macroeconomic time series. The shock is identified using sign restrictions. An expansionary fiscal shock is defined as a shock having (i) a positive effect on output (GDP and industrial production), prices (GDP deflator and CPI) and the short term interest rate (the prime rate) at an horizon of three quarters, and (ii) a positive effect on government primary deficit at horizons three to eight quarters. The main findings are the following. The fiscal shock is non fundamental for the variables typically used in open economy fiscal VAR models, so that its impulse response functions cannot be consistently estimated by means of a VAR. A fiscal policy shock worsens the trade balance and produces an appreciation of the domestic currency but the effects are quantitatively small, the shock accounting for about 14% of the volatility of the trade and current account balance and the exchange rate. The results broadly match the theoretical predictions of the standard Mundell-Fleming model, although fiscal policy cannot be considered the main cause of the large US external deficit. The remainder of the paper is organized as follows. Section 2 presents the factor 5see Lippi and Reichilin (1994). 3 model; Section 3 discusses the model specification and presents the main results; Section 4 concludes. 2 The structural factor model In the present section I provide a presentation of the model and estimation procedure. For additional details see Forni, Giannone, Lippi and Reichlin (2009), FGLR from now on.6 2.1 Representation Each macroeconomic variable is the sum of two mutually orthogonal unobservable components, the common component χit and the idiosyncratic component ξit: xit =χit +ξit.(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. For variables related to particular sectors, like industrial production indexes or production prices, the idiosyncratic component may reflect sector specific variations; for strictly macroeconomic variables, like GDP, investment or consumption, the idiosyncratic component must be interpreted essentially as 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.(2) The dynamic relations between the macroeconomic variables arise from the fact that the vector ftfollows the relation ft=N(L)ut,(3) 6FGLR is a special case of the generalized dynamic factor model proposed by Forni, et al. (2000, 2004, 2005) and Forni and Lippi (2001, 2010). 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). 7Altug, (1989), Sargent, (1989), and Ireland (2004) show that the model can be interpreted as the linear solution of a DSGE model with measurement error. 4 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, as it will be clear from the discussion in subsection 2.4 , the rank of N(z) is qfor any z, which implies fundamentalness. This ensures that fthas the finite order VAR representation (Anderson and Deistler, 2008) D(L)ft=t=Rut,(4) where D(L) is a r×rmatrix of polynomials such that D(L)−1R=N(L) and R=N(0). From equations (??) to (??) it is seen that the model can be written in the dynamic form xit =bi(L)ut+ξit,(5) where bi(L) = aiN(L) = aiD(L)−1R. (6) The entries of the q-dimensional vector bi(L) are the impulse response functions. Observe that, under appropriate regularity conditions on the factor loadings ai,9 the linear space spanned by the χ’s includes the factors, so that utis fundamental for the χ’s. Moreover, since the idiosyncratic components are poorly correlated across sections and the x’s are infinite in number, by taking appropriate averages of the x’s the idiosyncratic components can be eliminated and the factor without error can be obtained. This can be restated by saying that utis fundamental for the x’s. 2.2 Identification Representation (??) 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 χit =ci(L)vt where ci(L) = bi(L)H0and vt=Hut. 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). 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 (??) to (??) 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. 9see FGLR, Assumption 4. 5 As a consequence, structural analysis in factor models can be carried on along lines very similar to those of standard SVAR analysis. Specifically q(q−1)/2 restrictions have to be imposed on the matrix of impulse response functions Bn(L) = (b1(L)0b2(L)0· · · bn(L)0)0, where nis the number of variables in the dataset, to pin down all the elements of H. If the researcher is interested in identifying just a single shock (partial identification), the target is to determine the entries of a single column of the matrix H, say H1, which is enough to obtain the first column of Bn(L), say Bn1(L). In the present paper the shock and the impulse response functions are not uniquely identified; rather, following Uhlig (2005), a distribution of shocks and related impulse response functions is identified by imposing a set of sign restrictions on the impulse response functions themselves.10 The first column H1of the matrix His a point on the unit sphere Sq−1. Given the non-structural representation Cn(L)vt, the sign restrictions that are imposed on Bn1(L) define an admissible region Θ on the unit sphere, such that for H1∈ΘBn1(L) = Cn(L)H1satisfies such inequalities. Following Uhlig (2005), a uniform a priori probability density in the region Θ is assumed. This in turn implies a density and the associated confidence bounds for each coefficient of the impulse response functions. 2.3 Estimation Estimation proceeds through the following steps. 1. Starting with an estimate ˆr, the static factors are estimated by means of the first ˆrprincipal components of the variables in the dataset, and the factor loadings by means of the associated eigenvectors. Precisely, let ˆ Γxbe the sample variancecovariance matrix of the data: the estimated loading matrix ˆ An= (ˆa0 1ˆa0 2· · · ˆa0 n)0 is the n×rmatrix having on the columns the normalized eigenvectors corresponding to the first largest ˆreigenvalues of ˆ Γx, and the estimated factors are ˆ ft=ˆ A0 n(x1tx2t· · · xnt)0.11 2. ˆ D(L) and ˆtare obtained by running a VAR(ˆp) with ˆ ftwhere the number of lags ˆpis chosen according to some criterion. 3. Let ˆ Γbe the sample variance-covariance matrix of ˆt. Having an estimate ˆqof the number of dynamic factors, an estimate of a non-structural representation of the common components is obtained 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, 10The precise set of restrictions imposed is discussed below. 11The factors are identified only up to linear transformations. What is estimated is a basis of the factor space. 6 ˆ Mthe q×qdiagonal matrix with qˆµ jas its (j, j) entry, and ˆ Kthe r×qmatrix with the corresponding normalized eigenvectors on the columns. The estimated matrix of non-structural impulse response functions is ˆ Cn(L) = ˆ Anˆ D(L)−1ˆ Kˆ M.(7) To account for estimation uncertainty, the following non-overlapping block bootstrap technique is adopted. 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 integer part of T/S.12 An 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 hSi0 and the corresponding impulse response functions, ˆ Cn(L), are estimated. A vector H1is generated N times by drawing its qentries from a standard normal distribution and normalized by its Euclidean norm. For each of the Nvectors the impulse response functions ˆ Bn1(L) = ˆ Cn(L)H1are computed. Those satisfying the sign restrictions are kept.13 A set of non-structural impulse response functions is obtained by repeating drawing, estimation and identification. 2.4 Discussion Here I discuss in detail why in the factor model the shocks are fundamental. Let us consider the statistical MA representation χt=Bn(L)ut,(8) where χt= (χ1t· · · χnt)0is an n-vector of weakly stationary variables, Bn(L) is a (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. Under what conditions the shocks utare fundamental for χt, i.e. present and past values of χtare sufficient to recover ut? Representation (??) is fundamental if and only if the rank of Bn(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 the determinant of Bn(z) does not vanish within the unit circle in the complex plane. If this condition holds, then the shock utcan be found using a VAR for χtand the related standard identification techniques. In general, however, there is no guarantee that the q 12Note that τhas to be large enough to retain relevant lagged autoand cross-covariances. 13At each step of the bootstrap procedure we collect at most 10 impulse response functions in order to avoid that a single bootstrap provides a disproportionately large number of functions. 7 variables are sufficient to recover the shocks (see Fern´andez-Villaverde, Rubio-Ramirez, Sargent and Watson, 2007). In particular, Leeper, Walker and Yang (2008) shows that under fiscal foresight the condition is violated and the shocks are non-fundamental. Now consider the case n > q. Notice that in this case (??) coincides with the vector of the common components of the factor model. In this situation, Bn(z) is a “tall”, rectangular matrix and its rank is less than qfor some z, i.e. the shock is nonfundamental, only if all of the (q×q) sub-matrices of Bn(z) are singular. Clearly this is a very special case since it requires n q!−1 equalities to be satisfied. Therefore, in general, when n > q B(z) has rank qfor all zand the shocks can be assumed to be fundamental. Intuitively fundamentalness is ensured if the generating processes of χjt, j=q+ 1, . . . , n, have impulse response functions which are sufficiently heterogeneous, with respect to the first q, to prevent the rank reduction. Finally let us stress again that, as already argued in Section 2, the q-dimensional square submatrices of N(z) = D(z)−1Rappearing in equation (??) can be singular for values of zwithin the unit circle, without hurting consistency of estimation. Similarly, considering a q-dimensional vector of integers I, such that Ii≤n,i= 1, . . . , q,ut can be non-fundamental for the subvector (χI1t· · · χIqt)0=BI(L)ut=AIN(L)utand det BI(z) can vanish within the unit circle. This is interesting because the smallest root of some selected square subsystems can be estimated and it can be verified whether the corresponding impulse response functions are indeed non-fundamental, implying a problem for VAR estimation. 3 Empirics We now discuss the model specification and present the main results. 3.1 Data and parameter specification The data set contains 115 quarterly macroeconomic time series spanning from 1973:I to 2007:IV. It includes fiscal policy variables, GDP and components, industrial production indexes, labor market variables, stock market variables, surveys, leading indicators, price indexes and deflators, money and credit aggregates, long and short term interest rates, and several open economy variables like the trade and current account balance, the real and nominal exchange rate and the terms of trade. The data are transformed to reach stationarity, as required by the model. The full list of variables along with the corresponding transformations is reported in the Appendix. All series are taken from FRED Database, Federal Reserve Bank of St. Louis. First of all the number of static factor, ˆr, the number of shocks, ˆq, and the number 8 of lags, ˆphave to be specified. To determine ˆrI rely on the ICp2criterion of Bai and Ng (2002), which gives ˆr= 10. I set ˆp= 3. The number of shocks is determined by a few consistent information criteria. Here I use three groups of criteria, proposed by Amengual and Watson (2007), Bai and Ng (2007) and Hallin and Liska (2007). The criterion ˆ BNICP (ˆyA) by Amengual and Watson gives 5 primitive factors in the ICp1version and 3 primitive factors in the ICp2 version (with ˆr= 10 and p= 3). The four criteria of Bai and Ng (2007), namely q1, q2, q3 and q4, give 6, 5, 5 and 3 shocks respectively (with ˆr= 10 and p= 3).14 Finally, the log criterion proposed by Hallin and Liska gives 3 shocks for all of the proposed penalty functions (independently of the initial random permutation). In summary, information criteria do not provide a unique result, the number of shocks being between 3 and 6. Here I conclude in favor of a five-shock specification. Below several robustness checks about the number of factors are made. Finally the length of the block, τ, is set equal to 16. 3.2 The smallest root of some selected sub-systems In this subsection I investigate whether the fiscal shock is fundamental for the variables which are typically used in open economy fiscal VARs. I consider six different variables specifications (listed in Table 1a) corresponding to six different choices of I(see Section 2.4), denoted Ijj= 1, ..., 6. The specifications are quite standard, in particular the fifth is the one considered in Kim and Roubini (2008). They all include the real GDP, the fiscal deficit to GDP ratio, the current account deficit to GDP ratio, and the real exchange rate. They differ each other because of the fifth variable included. For each specification the smallest root of the determinant of the corresponding impulse response functions BIj(L) is computed. If the root is smaller than one in modulus, the shock is non-fundamental for the variables defined in Ij. The roots are computed for all the bootstrap repetitions so that the entire distribution is available. Table 1b shows the point estimate, the mean, the median, several percentiles of the distribution of the modulus of the smallest root for the six specifications and the associated probability of being smaller than one. The point estimate, the mean, the median and the 68th percentile of the distribution is smaller than one for all the specifications. With probability ranging from 0.74 to 0.89 the shock is non-fundamental for the variables considered in the six specifications. The result implies that standard structural VAR techniques with the variables considered in the six specifications are likely to fail in recovering the fiscal shock correctly. 14The Bai and Ng criteria have two parameters. I set δ=.1 for all criteria and m(q1) = 1.1, m(q2) = 1.9, m(q3) = 1.8, m(q4) = 4. 9 no.series Transf. Mnemonic Long Label 34 6 GDPCTPI Gross Domestic Product: Chain-type Price Index 35 6 GNPCTPI Gross National Product: Chain-type Price Index 36 6 GDPDEF Gross Domestic Product: Implicit Price Deflator 37 6 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 6 BOGNONBR Non-Borrowed Reserves of Depository Institutions 65 6 TRARR Board of Governors Total Reserves, Adjusted for Changes in Reserve 66 6 BOGAMBSL Board of Governors Monetary Base, Adjusted for Changes in Reserve 67 6 M1SL M1 Money Stock 68 6 M2MSL M2 Minus 69 6 M2SL M2 Money Stock 16 no.series Transf. Mnemonic Long Label 70 6 BUSLOANS Commercial and Industrial Loans at All Commercial Banks 71 6 CONSUMER Consumer (Individual) Loans at All Commercial Banks 72 6 LOANINV Total Loans and Investments at All Commercial Banks 73 6 REALLN Real Estate Loans at All Commercial Banks 74 6 TOTALSL Total Consumer Credit Outstanding 75 6 CPIAUCSL Consumer Price Index For All Urban Consumers: All Items 76 6 CPIULFSL Consumer Price Index for All Urban Consumers: All Items Less Food 77 6 CPILEGSL Consumer Price Index for All Urban Consumers: All Items Less Energy 78 6 CPILFESL Consumer Price Index for All Urban Consumers: All Items Less Food & Energy 79 6 CPIENGSL Consumer Price Index for All Urban Consumers: Energy 80 6 CPIUFDSL Consumer Price Index for All Urban Consumers: Food 81 6 PPICPE Producer Price Index Finished Goods: Capital Equipment 82 6 PPICRM Producer Price Index: Crude Materials for Further Processing 83 6 PPIFCG Producer Price Index: Finished Consumer Goods 84 6 PPIFGS Producer Price Index: Finished Goods 85 6 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 Consumption Expenditures & Gross Investment, 1 Decimal 102 5 Real Federal Cons. 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Journal of Monetary Economics 52, 381-419. 21 Tables j Variables(*) 1 GDP(1), Deficit(111), CUR(112), RER(107), Gov. Cons. & Inv. (101) 2 GDP(1), Deficit(111), CUR(112), RER(107), Cons.(11) 3 GDP(1), Deficit(111), CUR(112), RER(107), Inv. (7) 4 GDP(1), Deficit(111), CUR(112), RER(107), CPI(75) 5 GDP(1), Deficit(111), CUR(112), RER(107), Int. rate(58) 6 GDP(1), Deficit(111), CUR(112), RER(107), Stock Prices(87) (*) The numbers correspond to those in the Appendix. Table 1a: Variables j Point Est Mean Median 68% 84% 90% 95% prob. 1 0.5891 0.6377 0.6902 0.8438 0.9534 1.0014 1.0388 0.8990 2 0.2529 0.7142 0.7713 0.9207 1.0223 1.0503 1.0782 0.8030 3 0.1345 0.7229 0.7900 0.9089 1.0011 1.0347 1.0630 0.8390 4 0.3219 0.6846 0.7533 0.8917 1.0029 1.0300 1.0540 0.8370 5 0.8705 0.6733 0.7203 0.8959 1.0059 1.0430 1.0693 0.8180 6 0.8563 0.7378 0.8325 0.9653 1.0347 1.0608 1.0838 0.7430 Table 1b: Modulus of the smallest root. 22 iˆ βiˆγi 1 0.0199 (0.1062) 0.1317 (0.2707) 2 0.0209 (0.1050) 0.0318 (0.2709) 3 -0.0015 (0.1047) 0.1430 (0.2761) 4 -0.0146 (0.1068) 0.0077 (-0.0795) F-test H0:γi= 0, i = 1, ..., 4 F=0.021 Table 2: Granger causality. The regression is shockt=α+P4 i=1 βishockt−i+P4 i=1 γispft−i+εt. Standard errors in parenthesis. Variables 0 4 8 20 Total 111 13.4831 4.7675 5.3842 7.9807 13.9665 112 17.9564 16.6256 13.5680 11.2501 14.1853 113 12.2453 14.8414 12.6473 10.9221 11.8825 107 11.6440 11.4998 11.3543 11.3894 11.3894 109 16.7146 15.2427 14.9971 14.7958 14.7958 110 7.0172 6.0647 6.0690 6.0358 6.0358 1 16.1968 5.0842 4.0832 4.2564 13.6802 11 6.5370 5.0644 6.8215 9.4937 9.8759 7 9.6978 2.7724 3.1201 4.8522 9.1006 Table 3: Variance decomposition 23 Figures Figure 1: Impulse response functions to an expansionary fiscal policy shock. 24 Figure 2: Robustness: 13 factors (solid line), 10 factors (dotted line), 16 factors (dashed line). 25