Measurement Error in Macroeconomic Data and Economics Research: Data Revisions, Gross Domestic Product, and Gross Domestic Income

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Measurement Error in Macroeconomic Data and Economics Research: Data Revisions, Gross Domestic Product, and Gross Domestic Income Andrew C. Chang and Phillip Li 2015-102 Please cite this paper as: Chang, Andrew C. and Phillip Li (2015). “Measurement Error in Macroeconomic Data and Economics Research: Data Revisions, Gross Domestic Product, and Gross Domestic Income,” Finance and Economics Discussion Series 2015-102. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2015.102. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Measurement Error in Macroeconomic Data and Economics Research: Data Revisions, Gross Domestic Product, and Gross Domestic Income Andrew C. Chang∗and Phillip Li† October 30, 2015 Abstract We analyze the effect of measurement error in macroeconomic data on economics researchusingtwofeaturesoftheestimatesoflatentUSoutputproducedbytheBureau of Economic Analysis (BEA). First, we use the fact that the BEA publishes two theoretically identical estimates of latent US output that only differ due to measurement error: the more well-known gross domestic product (GDP), which the BEA constructs using expenditure data, and gross domestic income (GDI), which the BEA constructs using income data. Second, we use BEA revisions to previously published releases of GDP and GDI. Using a sample of 23 published economics papers from top economics journalsthatutilizeGDPasakeycomponentofanestimatedmodel, weassesswhether using either revised GDP or GDI instead of GDP in the published paper would change reported results. We find that estimating models using revised GDP generates the same qualitative result as the original paper in all 23 cases. Estimating models using GDI, both with the GDI data originally available to the authors and with revised GDI, instead of GDP generates larger differences in results than those obtained with revisedGDP.For3of23papers(13%), theresultsweobtainwithGDIarequalitatively different than the original published results. ∗Chang: Board of Governors of the Federal Reserve System. 20th St. NW and Constitution Ave., Washington DC 20551 USA. +1 (657) 464-3286. a.christopher.chang@gmail.com. https://sites.google.com/site/andrewchristopherchang/ †Li: Office of the Comptroller of the Currency. phillip.li@occ.treas.gov. ‡The views and opinions expressed here are those of the authors and are not necessarily those of the Board of Governors of the Federal Reserve System, the Department of the Treasury, or the Office of the Comptroller of the Currency. We thank Stephanie Aaronson, Jeremy J. Nalewaik, Christopher J. Nekarda, Bo Sun, Kurt von Tish, and seminar participants at OCC, OFR, and UC - Irvine for helpful comments. We thank Tyler J. Hanson, Erik Larsson, Kim T. Mai, Anthony Marcozzi, Shawn M. Martin, Tyler Radler, Adam Scherling, and John Stromme for research assistance. We also thank Felix Galbis-Reig and Spencer C. Li for technical assistance. Any errors are ours. 1

JEL Codes: C80; C82; E01 Keywords: Data Revisions; Data Vintages; Gross Domestic Product; GDP; Gross Domestic Income; GDI; Latent Output; Measurement Error; National Statistics; National Income and Product Accounts; NIPA; Real-Time Data 1 Introduction Low unemployment. Modest inflation. High output growth. Economists have devoted a substantial amount of effort to understanding how these three goals are simultaneously achieved in the real economy. Unfortunately, the unemployment rate, the inflation rate, and the output growth rate of an economy are all unobserved variables. Econometricians rely on estimates of these unobserved variables from national statistical agencies. For example, to estimate the unobserved output growth rate of the US economy, the Bureau of Economic Analysis (BEA) publishes US gross domestic product (GDP). However, because this statistic is based on finite samples and imperfect source data, published GDP contains measurement error. This paper analyzes the potential effect that the measurement error in US GDP has on economics research. In addition to the more well-known data revision dimension, where the BEA revises previously released statistics to incorporate better methodologies or source data, we exploit the fact that the BEA also publishes two theoretically identical measures of unobserved US output. First, the BEA publishes the more familiar GDP measure of unobserved output that estimates it based on total expenditures. Second, the BEA publishes the less familiar gross domestic income (GDI) measure that estimates it based on total income. As total expenditures must necessarily equal total income, GDP and GDI are theoretically identical. However, because of measurement error the BEA’s published GDP and GDI statistics differ. Our analysis of the potential effect of measurement error in GDP on economics research proceeds in three steps. First, we acquire a sample of 67 published economics papers that use US GDP to estimate a key result, and we replicate 29 of these published papers (Chang 2

and Li, 2015). Second, using the original replication data files we identify which vintage (publication date by the BEA) of GDP the published papers use in their estimation by comparing the data files to historical vintages of GDP. We successfully identify the original data vintage for 23 papers. Third, we reestimate these 23 papers by replacing the original vintage of GDP the authors use with the original vintage of GDI, the revised current-vintage GDP, and the revised current-vintage GDI. Comparingthekeyresultsofthe23publishedpaperstotheresultswefindusingthethree alternative estimates of unobserved output (current-vintage GDP, original-vintage GDI, and current-vintage GDI), we find that current-vintage GDP gives the same qualitative result as the original article in all 23 cases. However, when we estimate models with either originalvintage GDI or current-vintage GDI, the results we obtain exhibit greater quantitative differences from the published results compared with when we estimate the models with current-vintage GDP. For three papers, the results we obtain when using GDI (either with original-vintage GDI or current-vintage GDI) are qualitatively different than the original articles. This paper has two main contributions to the growing body of literature on measurement error of national statistics.1 For our first contribution, we analyze the effect of measurement error on 23 papers sampled from 11 top economics journals, a larger and more comprehensive set of economics papers than the literature has used. Previous studies that look at the effect of measurement error on economics research typically select a single paper or use a selected small sample of papers to highlight their claims.2 Our use of a broad sample mitigates 1ExamplesofstudiesthatlookintomeasurementerrorofnationalstatisticsincludeMankiwandShapiro (1986);Orphanides(2001);OrphanidesandvanNorden(2002);Koenig,Dolmas,andPiger(2003);Nalewaik (2010); Ponomareva and Katayama (2010); Wolff, Chong, and Auffhammer (2011); Feng and Hu (2013); Zucman (2013) and Nalewaik (2014). 2For example, Ponomareva and Katayama (2010) use Ramey and Ramey (1995) as an example of how revisions to the Penn World Tables may influence results. Wolff, Chong, and Auffhammer (2011) use Noorbakhsh (2006) as an example of how results change due to measurement error in the human development index released by the United Nations Development Programme. Croushore and Stark (2002, 2003) examine theeffectofdatarevisionsonthequalitativeresultsofHall(1978);BlanchardandQuah(1989)andKydland andPrescott(1990). Faust,Rogers, andWright(2003)usemanydatavintagestoanalyzetheexchangerate forecasting model of Mark (1995). 3

selection bias concerns. For our second contribution, we contrast the effects of measurement error across both revisions to the same estimate of unobserved output (GDP) and also against a theoretically identical estimate of unobserved output based on completely different source data (GDI). To our knowledge, our paper is the first to investigate the effects of measurement error in a national statistic where a second, theoretically identical measure of the same quantity of interest is available. Under normal circumstances where two estimates of the same quantity of interest are available, the estimates use different data definitions or have different coverage schemes. For example, to estimate total US employment a researcher can use either the data from the current employment statistics (CES) or the current population survey (CPS). However, the two surveys have different definitions of what constitutes employment.3 Therefore, total employment measured with the CES will necessarily differ from total employment derived from the CPS because of data definitions, not just measurement error. Economic models generally abstract from different data definitions or coverage schemes. In our case, GDP and GDI only differ because of measurement error as both GDP and GDI are estimates of the same quantity: unobserved output. As far as we are aware, the existing literature on the effect of measurement error of national statistics on economic research focuses only on revisions to the same statistic or survey dataset.4 The purpose of this paper is to document whattheeffectoneconomicresearchwouldbewhenusingdifferentmeasuresoflatentoutput in estimated models. This paper does not investigate whether GDP or GDI is a better measure of latent output nor do we analyze what qualities of GDP or GDI lead models to give different results. 3TheCESmeasureofjobgainsuseschangesinprivatepayrollemployment,whereeachnewjobisfromthe establishment-sideperspective. IntheCESindividualswithmultiplejobsarecountedateachestablishment the individual is employed at. The CPS measures job gains by household-level employment where each new employed individual counts as a new job. Therefore, in the CPS individuals with multiple jobs count as one employed person. 4Forexample,CroushoreandStark(2003);Koenig,Dolmas,andPiger(2003);PonomarevaandKatayama (2010)andWolff,Chong,andAuffhammer(2011). Forareviewofresearchintoreal-timedata,seeCroushore (2011). 4

2 Description of BEA’s Data Release Schedule, GDP, and GDI We provide a brief description of the BEA’s data release schedule, GDP, and GDI. Interested readers can see Fixler and Grimm (2008) or Landefeld, Seskin, and Fraumeni (2008) for additional details on the BEA’s construction of GDP and GDI, and the appendices to Nalewaik (2010) for information on the source data behind GDP and GDI. The BEA publishes its first release of GDP for the previous quarter, called the advance release, approximately one month after the quarter ends. The BEA then publishes a oncerevised release for the previous quarter, called the second release, in the next month and a twice-revised release for the previous quarter, called the third release, another month thereafter. For example, the advance release of Q4 GDP would appear in January, the second release would appear in February, and the third release would appear in March. The third release is then unrevised until the summer, when the BEA conducts an annual revision and revises its published statistics for the last three calendar years. In addition, once approximately every five years, the BEA conducts a comprehensive revision where all of its previously published statistics are potentially revised.5 Figure 1 plots the net revision to the level of nominal GDP between the September 26th, 2013vintageofGDPandtheSeptember26th, 2008vintageofGDP.6 Figure1showsthatthe level of GDP published in the September 26th, 2008 vintage was eventually revised upwards. In addition, revisions to GDP enacted from 2008 to 2013 extended back to published GDP estimates of the 1940s. Because GDP is nonstationary and economic models generally take nonstationarity into account, a more informative version of Figure 1 may be a comparison of vintages of a 5The last three comprehensive revision estimates were released on December 10th, 2003; July 31, 2009; and July 31, 2013. 6Because of chain aggregation and differences in the GDP deflator, comparisons of real GDP across BEA vintages are not meaningful. See Whelan (2002) for a discussion. We choose an arbitrary difference of five years to illustrate the statistical discrepancy. 5

stationary transformation of GDP. Figure 2 plots the net revision to nominal GDP between thesametwovintagesshowninFigure1, exceptexpressedasannualpercentchangestomake the GDP series stationary. Figure 2 shows that the revisions to the annual percent changes of GDP tend to be larger for more recent data. However, even for data that have already undergone a comprehensive revision, subsequent revisions can have meaningful changes in publishedestimates. Forexample,publishedestimatesofGDPgrowthofthe1990swereoften revised by ±0.5% due to revisions that occurred between 2008 and 2013, approximately ten years after the initial GDP estimates were published. The magnitude of the average revision that took place from 2008 to 2013 of GDP for 1947 to 2008 is 0.30 percentage point.7 GDP is an estimate of unobserved output, as defined as the total value of goods and services produces in the economy, that the BEA produces using data on expenditures. At a high level, this approach corresponds to using data on consumption, investment, government expenditures, and net exports (Landefeld, Seskin, and Fraumeni, 2008). We emphasize that the BEA’s published GDP is an estimate of the total value of goods and services produced in the economy based on expenditure-side data. Published GDP is generally not the actual total value of goods and services produced in the economy, which is generally the unobserved output variable of interest to economists. The release schedule for GDI is similar to the schedule for GDP, although the data the BEA uses to construct GDI are less timely than the data for GDP.8 The BEA publishes its first release of GDI approximately two months after the quarter ends, except in the case of the fourth quarter, when it publishes its first GDI statistic three months after the quarter ends. For the first through third quarters, the BEA revises its initial GDI release a month afterpublication. TheBEA’sGDIreleasesaresubjecttothesameannualandcomprehensive 7ForGDPsince1990themagnitudeoftheaveragerevisionis0.59percentagepoint. ForGDPsince2000 themagnitudeoftheaveragerevisionis0.82percentagepoint. ThemagnitudeofrevisionstoGDPinNBER expansions since 1947 Q1 (0.29 percentage points) is about the same as in NBER recessions since 1947 Q1 (0.33 percentage points), although since 1990 Q1 the revisions in recessions have been larger on average. 8The timeliness of the source data is one reason the BEA prefers GDP to GDI (Landefeld, Seskin, and Fraumeni, 2008). Another reason why the BEA may prefer GDP to GDI is because the BEA publishes deflators for detailed components of GDP, but does not publish such deflators for GDI (Nalewaik, 2012). 6

revision schedule as GDP. GDI is an estimate of unobserved output the BEA produces using data on income, specifically compensation, rental income, profits and proprietor’s income, taxes less subsidies, interest, miscellaneous payments, and depreciation (Landefeld, Seskin, and Fraumeni, 2008). LikeGDP,theBEA’spublishedGDIisanestimateofunobservedoutput, nottheunobserved output variable of interest to economists. In theory, GDP and GDI should be identical. Both GDP and GDI are estimates of the same quantity: unobserved output. However, because the data the BEA uses to construct GDP and GDI are imperfect and largely independent, the published estimates of GDP and GDI differ from each other and contain measurement error. The BEA refers to the difference between GDP and GDI as the statistical discrepancy. Figure 3 plots the statistical discrepancy using annualized seasonally adjusted quarterly data of the September 26th, 2013 vintage of BEA data. This data vintage was shortly after a BEA comprehensive revision, so all of the data points were subject to at least one round of revisions by the BEA. Figure 3 reveals persistent differences between real GDP and real GDI even after the BEA revises its previously published estimates. The BEA’s GDP figures are generally greater than its GDI figures until the mid-1990s, with real GDP exceeding real GDI by $250 billion (2009 chain-weighted dollars) in the first quarter of 1993. After the mid- 1990s, GDI generally exceeds GDP up to a maximum of $259 billion (2009 chain-weighted dollars) in the third quarter of 2006. The quarter-to-quarter variance of the statistical discrepancy has been widening over time, which may reflect the nonstationarity of real GDP and real GDI. Figure 4 plots the implied annual percent changes of the statistical discrepancy. To reemphasize, the data in Figure 4 have been subject to at least one BEA comprehensive revision, with older data points undergoing multiple comprehensive revisions. From Figure 4, we can see considerable persistent differences in the quarter-to-quarter movements of GDP and GDI. From the 264 quarterly observations from the first quarter of 1947 to the second quarter of 2013, 58% 7

have a statistical discrepancy of at least ± 1 percentage point, and 29% have a statistical discrepancy of at least ± 2 percentage points, with the mean magnitude of the discrepancy at 1.49 percentage points.9 3 Methodology To analyze the effect of measurement error in US GDP on economic research, we start with a sample of 29 papers for which we were able to replicate the key published results using author-provided data and code files (Chang and Li, 2015). We identify the key result for each paper in our sample prior to running our replications to avoid pretesting within our study. These papers come from well-regarded, peer-reviewed economics journals: American Economic Journal: Economic Policy, American Economic Journal: Macroeconomics, American Economic Review, Canadian Journal of Economics, Econometrica, Economic Journal, Journal of Applied Econometrics, Journal of Political Economy, Review of Economic Dynamics, Review of Economic Studies, Review of Economics and Statistics, and the Quarterly Journal of Economics. AllpapersinoursamplecontainUSGDPasakeycomponentoftheir estimated models.10,11 Because these papers are from well-regarded, peer-reviewed journals, and because authors provide data and code files to run their models (either from journal replication archives, their personal websites, or directly to us through emails), we believe the quality and robustness of the research findings of these papers are very high. After replicating published results, we identify the original vintage of GDP that the published papers use by comparing the author-provided data files to historical BEA vintages of GDP. We also check the papers to see whether authors identify the original vintage of data 9The mean implied annual percent changes of real GDP and real GDI from the first quarter of 1947 to the second quarter of 2013 are both about 3.2%, again calculated with the September 26th, 2013 vintage of BEA data. 10Our sampling frame also includes papers that use GDI as a key component of estimated models, but we were unable to locate any paper that uses GDI instead of GDP to estimate models. The dearth of papers that use GDI is probably in part because the BEA features GDP more prominently than GDI in its press releases (Nalewaik, 2010). We do not take sides on whether GDP or GDI is a better indicator of unobserved output. 11Chang and Li (2015) provide a full description of the replication procedure. 8

they use. If these two procedures leave us unable to identify the original vintage and we have not contacted the authors requesting assistance with replication, then we email the authors about the original vintage of GDP they use, following the method in Chang and Li (2015). In most cases, we precisely match the original vintage with this three-step procedure.12 In some cases, a historical BEA vintage closely approximates the original vintage in the authorprovided data files, but we do not find an exact match. For 3 of the 29 papers in our sample, we are unable to identify the original vintage of GDP used in the paper and hence exclude them from our analysis (Krishnamurthy and Vissing-Jorgensen, 2012; Mertens and Raven, 2011; Heutel, 2012).13 We exclude two papers where we do not possess code to reestimate the models with alternative data (Schmitt-Grohé and Uribe, 2011, 2012).14 We also exclude Clark and McCracken (2010) because the paper relies completely on real-time data that encompass many vintages of GDP, so we are unable to change a single original vintage for a current-vintage series.15 Section 4 and the web appendix detail the original vintages we identify for each paper in our sample.16 For our remaining sample of 23 papers, we reestimate the models but replace the original vintageofGDPwiththeoriginalvintageofGDI,thecurrentvintageofGDP,andthecurrent 12Because of different sample periods and the BEA’s data revision schedule, on occasion we can match multiple vintages to the author’s vintage. For example, suppose a paper estimates a model with data from 1984 Q1 to 2005 Q4 using the January 2007 vintage of GDP. Because the BEA only revises GDP more than one quarter back during an annual or comprehensive revision, the January 2007, February 2007, and March 2007 GDP vintages for 1984 Q1 to 2005 Q4 are all identical, as only 2006 Q4 GDP is different between these three vintages. When we are able to match more than one vintage, we use and report one of the observationally equivalent vintages in the web appendix available on Chang’s website, https://sites.google.com/site/andrewchristopherchang/research. 13The most common cause of our inability to identify data vintages is because the author-provided data files, only the transformed series used in the analysis. For example, if GDP appears in the model as the debt-to-GDP ratio and the authors only include the debt-to-GDP ratio in the data file, then we cannot identify the GDP vintage. 14In this scenario, the original author-provided code files have parameter estimates hard-coded, which enables replication of the original tables and figures but does not allow for reestimation. When the original replication files lack code for reestimation, we email the authors requesting additional code to reestimate their models. 15Anissuewedonotinvestigateistheeffectofusingreal-timevintagesagainstend-of-samplevintages. Usingreal-timevintagesinsteadofend-of-samplevintagesmayhaveimplicationsforforecastaccuracy(Koenig, Dolmas, and Piger, 2003; Chang and Hanson, 2015). The data we use in this paper are end-of-sample vintages. 16ThewebappendixisavailableonChang’swebsite,https://sites.google.com/site/andrewchristopherchang /research. 9

vintage of GDI, where current vintage is the fully revised data as of September 26th, 2013. When original-vintage GDP appears more than once in the estimated models, we replace original-vintage GDP wherever it appears.17 For example, if a paper estimates a VAR with GDP and net exports where net exports is scaled by GDP, then we replace both the GDP variable and the denominator of the scaled net exports variable. If the GDP deflator also appears in the estimated models, then when we reestimate the models using current-vintage data we also replace the original-vintage GDP deflator with the current-vintage GDP deflator. The BEA deflates GDP and GDI using the same GDP deflator, so our specifications with both current-vintage GDP and current-vintage GDI use the same vintage of the GDP deflator. We do not update the vintage of data other than the GDP deflator and GDP.18 Table 1 lists the papers in our analysis.19 We defined the entire methodology in this section prior to executing any analysis. Defining our methodology prior to the analysis carries three benefits: (1) we set a uniform standard for analyzing the results of models; (2) we avoid hindsight bias in model selection and analysis; and (3) we avoid pretesting our results. 4 Results We find that using current-vintage GDP produces the same qualitative result as the original article for all 23 of our papers. For 3 of 23 papers, using either original-vintage GDI or current-vintage GDI instead of original-vintage GDP produces qualitatively different results than the original article. We focus on whether the qualitative conclusions change when 17TheBureauofEconomicAnalysis(BEA)maintainsquarterlyUSGDPdatasince1947andannualGDP data since 1929. If the paper uses a combination of pre-1947 and post-1947 quarterly GDP data, then we replace only data since 1947. Similarly, we only replace annual data since 1929. 18Following this definition, we similarly do not update the vintage of other price deflators. For example, when papers deflate data with the core personal consumption expenditures price deflator, we do not update the vintage of this deflator. 19A researcher could characterize this study as the “scientific replication” of 23 papers, following the terminology of Hamermesh (2007). 10

estimating the original models with other measures of output for three reasons: (1) it is difficult to justify comparing quantitative differences across papers due to different models as papers report fundamentally different results, so quantitative comparisons are tenuous at best; (2) the policy recommendation of a paper would only substantively change when the fundamental qualitative conclusion of a paper is different; and (3) focusing on qualitative results also allows us to give a lower bound on the effect of measurement error of GDP on economic research, as we classify many quantitative differences as no qualitative change. Togivethereaderanideaofhowweclassifyresults,thissectionfirstdetailsapaperwhere wefindresultsqualitativelysimilartotheoriginalpaperbutwhereourquantitativeestimates are different. This section then explains each of the papers where we find qualitatively different results after estimating the models using the other measures of unobserved output. The web appendix gives the results for the remaining papers, where we believe the results with the other measures of unobserved output are all qualitatively similar to the published results. 4.1 Auerbach and Gorodnichenko (2012, 2013) We use Table 1 from Auerbach and Gorodnichenko (2012), as corrected in Auerbach and Gorodnichenko (2013) as an example of finding quantitatively different yet qualitatively similar results using our other measures of unobserved output. The web appendix shows our analysis of the other key figures from Auerbach and Gorodnichenko (2012). Table 2 shows the published estimates of Table 1 from Auerbach and Gorodnichenko (2012)andTable3showsourreplicationresults. Mostofourreplicationestimatesarewithin 10% of their reported values, although we find slightly higher defense spending multiplier in recessions (max multiplier of 4.27) than the authors do (max multiplier of 3.56). Our replication supports two of the main results of Auerbach and Gorodnichenko (2012): (1) higher fiscal multipliers in recessions than expansions and (2) particularly large defense spending multipliers in recessions. 11

Table 4 shows our results from replacing original-vintage GDP with original-vintage GDI. With original-vintage GDI, we find a much higher defense spending multiplier in recessions (max multiplier of 6.15) and a defense spending multiplier for expansions that is always negative (max multiplier of -0.49). The estimate of the nondefense multiplier for expansions is also smaller (max multiplier of 0.51) than the published estimate (max multiplier of 1.12). In addition, the estimate of the government investment spending multiplier is almost zero for recessions (max multiplier of -0.08), whereas the published estimate is expansionary (max multiplier of 2.85). However, we continue to estimate higher fiscal multipliers in recessions than expansions for government consumption spending and total government spending, with government defense spending still having the highest multiplier. Therefore, we classify the results with original-vintage GDI as consistent with the published results. The web appendix showsouranalysisofAuerbachandGorodnichenko(2012)Table1withcurrent-vintageGDP and current-vintage GDI, both of which give the same qualitative result as the published estimates. We now turn to results where an alternative output measure gives different qualitative results than the published paper. 4.2 Corsetti, Meier, and Müller (2012) Corsetti, Meier, and Müller (2012) explain their key empirical result as follows: an “increase in government spending causes a substantial rise in aggregate output... a positive spending shock triggers a sizable buildup of public debt, followed over time by a decline of government spending below trend” (pg. 878). The authors show these results from the impulse responses from vector autoregressions (VARs) in their Figures 1 and 2. Corsetti, Meier, and Müller (2012)’s Figure 1 identifies the VAR using the Blanchard and Perotti (2002) method, while Corsetti, Meier, and Müller (2012)’s Figure 2 identifies the VAR following Ramey (2011). Their measure of debt is the US debt-to-GDP ratio, so GDP appears twice in their baseline 12

VARs.20 Our replication of these two figures, using data and code from the files posted at the Review of Economics and Statistics, match the published paper exactly (Chang and Li, 2015).21 Figure 5 plots the impulse responses from the Corsetti, Meier, and Müller (2012) Figure 1 VAR using current-vintage GDP instead of original-vintage GDP as the measure of output. Figure 5 shows a statistically significant effect of government spending on output, with a multiplier of approximately 1. Debt-to-GDP continues to rise and subsequently decrease. Figure 6 plots the impulse responses from the Corsetti, Meier, and Müller (2012) Figure 2 VAR using current-vintage GDP. As in Figure 5, output rises immediately following the government spending shock, and the increase in output is statistically significant. The multiplier at the time of the government spending shock is, again, approximately 1. Debt-to-GDP rises and immediately falls. Taken together, the evidence from Figures 5 and 6 are qualitatively consistent with the findings of Corsetti, Meier, and Müller (2012). Hence, we conclude that revisions to GDP have no qualitative effect on their results. Figure 7 plots the impulse responses from the Corsetti, Meier, and Müller (2012) Figure 1 VARusingoriginal-vintageGDIasthemeasureofunobservedoutput. Figure7showssimilar debt-to-GDI dynamics as Corsetti, Meier, and Müller (2012), but the impulse response of GDI differs considerably from Corsetti, Meier, and Müller (2012). The effect of government spending on GDI immediately following the shock is no longer statistically significant and the point estimate of the multiplier is approximately zero. Further out, the effect of the government spending shock on GDI is negative and statistically significant approximately eight quarters following the shock. Figure 8 plots the impulse responses from the Corsetti, Meier, and Müller (2012) Figure 2 VAR using original-vintage GDI. The figure continues to indicate that the government 20The Corsetti, Meier, and Müller (2012) specifications with net exports are also scaled by GDP so GDP appears three times in these VAR specifications, but their baseline VAR does not have net exports as a variable. 21We identify the Corsetti, Meier, and Müller (2012) GDP vintage as March 2010. 13

spending shock has no effect on GDI. Figures 9 and 10 plot the Corsetti, Meier, and Müller (2012) impulse responses using current-vintage GDI. The results are similar to using original-vintage GDI: a government spending shock has a zero to negative effect on GDI. Because using current-vintage GDP gives similar results to the original paper (a significant and positive government spending multiplier on output) and because both originalvintage GDI and current-vintage GDI indicate a zero or negative effect of government spending on output, we conclude that data revisions to the same measure of output have no qualitative effect on these results, but switching from GDP and GDI does qualitatively influence the results for this paper. 4.3 Inoue and Rossi (2011) From the abstract of Inoue and Rossi (2011): “This paper investigates the sources of the substantial decrease in output growth volatility in the mid-1980s by identifying which of the structural parameters in a representative New Keynesian and structural VAR models changed.” As highlighted in their introduction, Inoue and Rossi (2011) “focus on a representative New Keynesian model, although our main results are robust to standard VAR estimation as well as larger-scale DSGE model estimation” (pg. 1187).22 The authors display their key results in their Tables 1 and 3. Inoue and Rossi (2011) Table 1 displays p-values for the hypothesis test of time-varying structural parameters in their representative New Keynesian model. Their null hypothesis is that the parameters are time-invariant, and they use the estimate of the set of stable parameters (ESS) procedure. Inoue and Rossi (2011) Table 3 lists the contributions to the variance of output, inflation, and the interest rate in their representative New Keynesian model, where each parameter is allowed to change from its estimated value during the Great Moderation to its estimated value pre-Great Moderation. 22We found the estimation results for Inoue and Rossi (2011) were slightly different between different versions of Matlab, but our qualitative conclusions for the effects of using different measures of output are robust to the version of Matlab we use. 14

Table 5 shows our replication of Inoue and Rossi (2011) Table 1. We continue to identify the volatility of the technology shock, σ , as the only parameter in their model that is z constant over time. From Table 6, which shows our replication of Inoue and Rossi (2011)’s Table 3, the contributions to the change in implied volatility of output, inflation, and the interest rate from progressively letting parameters move from their Great Moderation values to their pre-Great Moderation values are all similar to their reported estimates.23 Table 7 shows Inoue and Rossi (2011)’s Table 1 reestimated with current-vintage GDP. The results show that the ESS procedure identifies the standard deviation of the cost-push shock, σ , as time-invariant in addition to σ . Table 8 shows Inoue and Rossi (2011)’s e z Table 3 reestimated with current-vintage GDP. While the contributions to the change in the implied volatility of output, inflation, and the interest rate are all a bit different from the published estimates and our replication results, the qualitative results continue to hold. The results from Table 8 indicate that progressively allowing parameters in the Inoue and Rossi (2011) New Keynesian model to be time-varying, according to the p-values of the Andrews (1993) Quandt Likelihood Ratio (QLR) stability test, implies that a time-varying standard deviation of the persistent monetary policy shock, σ , and a time-varying persistence of the ν preference shock, ρ , would both significantly increase the volatility of output, inflation, and a the interest rate. Similarly, allowing the standard deviation of the preference shock, σ , and a the degree of inflation aversion of the Federal Reserve, ρ , to be time-varying would have π offsetting effects on volatility. Table 9 shows Inoue and Rossi (2011) Table 1 reestimated with original-vintage GDI. The Inoue and Rossi (2011) ESS procedure now identifies two additional parameters, α and ψ, as time-invariant. Table 10 shows Inoue and Rossi (2011) Table 3 reestimated with original-vintage GDI. The results of the table are qualitatively different than both the published results and the results estimated with current-vintage GDP. Focusing on the set of stable parameters, Table 23We find the Inoue and Rossi (2011) original GDP vintage is from August 2004. 15

10showsthatallowingσ tobetime-varyingwoulddampenoutputvolatilityintheestimated z model as opposed to increasing output volatility as in Inoue and Rossi (2011). In addition, the reestimated contribution of σ to the volatility of inflation is over twice that of the z published results. As far as the unstable parameters of the Inoue and Rossi (2011) model, the majority of the contributions to the volatilities of output, inflation, and the interest rate are much larger in magnitude and are frequently of opposite signs to the published results. For example, using original-vintage GDI causes us to estimate σ as dampening the a volatilities of output and the interest rate by more than ten times the published estimates. The results with original GDI also show that σ has the effect of increasing the volatility a of inflation, whereas the published estimate has σ as a slightly negative contributor to the a volatility of inflation. Tables 11 and 12 show Inoue and Rossi (2011)’s Tables 1 and 3 reestimated with currentvintage GDI. The results are largely similar to the results with original-vintage GDI: the parameters have larger contributions, in magnitude, to the volatilities of output, inflation, and the interest rate that are frequency of the opposite sign as published estimates. 4.4 Morley and Piger (2012) From the Morley and Piger (2012) abstract, the authors cite their key result as “...we construct a model-averaged measure of the business cycle. This measure also displays an asymmetric shape...”, which is also consistent with the title of their paper, “The Asymmetric Business Cycle.” The authors further elaborate on this result when they show their modelaveraged measure of the business cycle in their Figure 3: “Perhaps the most striking feature of this [model-averaged] measure [of the business cycle] is its asymmetric shape, which it inherits from the bounceback models. In particular, the variation in the cycle is substantially larger during recessions than it is in expansions” (pg. 218). Our replication of this figure matches the result published in Morley and Piger (2012) and is shown in Figure 11.24 24We match the Morley and Piger (2012) GDP vintage to March 2007. 16

Figure 12 plots the Morley and Piger (2012) model-averaged measure of the business cycle estimated with current-vintage GDP, shown in their Figure 3. Figure 12is qualitatively consistent with Morley and Piger (2012). The figure displays large dips in output during National Bureau of Economic Research (NBER) recessions, with a gradual run-up in output after the initial bounceback during NBER expansions. Figure13plotstheMorleyandPiger(2012)model-averagedmeasureofthebusinesscycle estimated with original-vintage GDI. This model-averaged measure displays much shallower recessions and larger run-ups in output just prior to a recession than the same measure estimated with either vintage of GDP. For example, during the tech bubble leading up to the2001recession, theMorleyandPiger(2012)model-averagedmeasureofthebusinesscycle estimated with original-vintage GDI more than doubles the measures estimated on either original-vintage GDP or current-vintage GDP. Similarly, in the years leading up to the 1990 recession, the model-averaged measure of the business cycle estimated with original-vintage GDI exhibits much more volatility and a larger run-up prior to the 1990 recession than when the measure is estimated using either original-vintage GDP or current-vintage GDP. Figure14plotstheMorleyandPiger(2012)model-averagedmeasureofthebusinesscycle estimated with current-vintage GDI. The results are largely similar to when the measure is estimated with original-vintage GDI: larger run-ups in output prior to a recession and shallower recessions than when the measure is estimated with GDP. Table 13 formally tests the differences in the model-averaged measures of the business cycle. The table shows variances in NBER expansions and NBER recessions for the modelaveraged measure estimated across original-vintage GDP, current-vintage GDP, originalvintage GDI, and current-vintage GDI, and the p-values from the F-test of equality of variance between expansions and recessions for each output estimate. For the two measures of the business cycle estimated with GDP, the variance of output in recessions is about twice that in expansions and the F-test rejects equality of variance between expansions and recessions at the 1% level, consistent with the findings of Morley and Piger (2012). For the 17

model-averaged measure using original-vintage GDI, the variance of output in recessions is about 50% larger than the variance in expansions. The F-test for equality of variances is only marginally significant (p = 0.069). For the model-averaged measure using current-vintage GDI, the variance of output in recessions is only about 30% larger than the variance in expansions and the F-test is unable to reject equality of variances at standard levels (p = 0.199). We take this table as additional evidence that GDI may differ systematically from GDPduetomeasurementerrorandthatthedifferencesbetweenGDPandGDIcaninfluence published results. 5 Conclusion We investigate the effect that measurement error in latent US output has on economic research using two approaches. First, we use data revisions to GDP, which is the BEA’s estimate of latent US output based on expenditure data. Second, we use GDI, a theoretically identical estimate of latent US output that the BEA creates with income data. To our knowledge, this paper is the first study that uses the fact that a national statistical agency produces two theoretically identical estimates of the same unobserved variable to look at the effect that measurement error has on economic research. Existing studies that look at this effect only use data revisions. Using a sample of 23 published economics articles from well-regarded peer-reviewed journals, we find that revisions to GDP have no qualitative effect on published results. However, for 3 of 23 articles, estimating models with GDI changes the qualitative conclusions of the papers. Our result that revisions to GDP have no effect on published research is at odds with the literature that we are aware of, which generally concludes that data revisions do have an effect. For example, Croushore and Stark (2002, 2003) find that using revised data qualitatively alters the results of Hall (1978) and Blanchard and Quah (1989), although they 18

find no effect of data revisions on Kydland and Prescott (1990). Ponomareva and Katayama (2010) compare using different vintages of the Penn World Tables (PWT) on the conclusions of Ramey and Ramey (1995) and find that newer versions of the PWT alter the original results. Faust, Rogers, and Wright (2003) re-run the model of Mark (1995) using successive data vintages up to October 2000 and find that newer data vintages generate results that are at odds with Mark (1995). We outline two reasons why we believe our finding that revisions to data have no effect on published results may be different than the literature. The first reason is that the time dimension of our data revisions is a bit shorter than the literature. The median paper in our sample uses a GDP vintage from July 2008. Therefore, the median time gap from original vintage to current vintage is 5 years and 2 months. Croushore and Stark (2002, 2003) update the original vintage of Hall (1978) (original-vintage May 1977) and Blanchard and Quah (1989) (original-vintage February 1988) to a current vintage of February 1998. Ramey and Ramey (1995) originally use PWT 5.0 (May 1991), and Ponomareva and Katayama (2010) compare that version to PWT 6.1 (October 2002). Faust, Rogers, and Wright (2003) use successive vintages from Mark (1995)’s original vintage of April 1992 up to October 2000, although they find that data vintages a mere two years away from Mark (1995)’s original vintage generate qualitatively different conclusions.25 The second reason why we find a different effect of data revisions than the literature does may be that existing studies select either a single paper or select a small sample of papers to illustrate their claims. Because of the potential editorial preference for significant results, it is possible that the papers we are aware of (and cite in this article) are biased toward finding significant results, which would be an illustration of the Rosenthal (1979) filedrawer problem. Because our sample of papers spans multiple journals across topic areas in 25Apotentialsuggestionthataneditororrefereemaymaketousinthefutureistoreestimatethemodels in our sample using even newer data, as our current vintage of data is from September 26th, 2013. We are strongly against this idea. We (and the editor or referee who would make this suggestion) have already observed the results using the September 26th, 2013 vintage of data and, should we reestimate the models using newer data, the estimation would have been conditioned on observing the results with the September 26th, 2013 vintage of data and would therefore be pretested. 19

macroeconomics, we feel our result that data revisions do not qualitatively affect economics research is less likely to suffer from the file-drawer problem. Our finding that results from models estimated with current-vintage GDP can differ from models estimated with current-vintage GDI supports the hypothesis that measurement error in the National Income and Product Accounts (NIPAs) does not revise away with multiple data revisions. Because the difference between original-vintage and current-vintage always spansatleastoneBEAcomprehensiverevision, wefindthatmeasurementerrorintheNIPAs does not revise away even after a BEA comprehensive revision, consistent with research by Nalewaik (2010, 2014). We assert that measurement error in macroeconomic data can have meaningful consequences on research because we find that estimating models using GDI instead of GDP can change published results. In general, we recommend that economic models should take into account when data are the estimates of the true quantities of interest, although we have no panacea on how to implement this recommendation. For the specific context of models estimated with GDP, we suggest that estimation should be robust to using either GDP or GDI as an author’s estimate of latent output. An assumption behind our assertion is that latent output is the object of interest behind the papers in our sample. This assumption could fail if authors use models that explicitly take into account the measurement error that is specific to GDP and is not present in GDI. We are not aware of any research into the GDP or GDI statistics that is able to differentiate the measurement error in the two statistics to such a fine degree. Nalewaik (2010, 2014)’s research into the GDP and GDI statistics concludes that there is both classical measurement error and a loss of signal measurement error in both GDP and GDI, but it does not isolate a source or form of measurement error that is specific to GDP and not to GDI. We also do not believe the papers in our study differentiate the measurement error specific to GDP that is not present in GDI. Most papers in our sample ignore measurement error. Another reason why latent output may not be the object of interest is if authors conduct 20

research into the national statistics themselves instead of the objects the statistics estimate, suchasbylookingintotheeffectsofmacroeconomicdataannouncementsonthestockmarket or foreign exchange rates (e.g., Faust, Rogers, Wang, and Wright, 2007; Rangel, 2011). From our reading of the papers where we find significantly different results than the authors using GDI, we believe the object of interest of the papers is latent output, not the GDP statistic.26 Overall, we view our results as a lower bound on the potential effect that measurement error in macroeconomic data has on economic research because of two factors that contribute to positive selection. First, we draw our sample of papers only from published research in well-regarded journals. These papers all survived intense peer review, which includes a barrage of reported robustness checks and, presumably, another barrage of unreported robustness checks that confirm the published findings.27 Second, in our exercise we only affect the GDP series used in the original paper by updating the vintage to current vintage, switching GDP to GDI, or both. In models that use multiple data series, we leave the remainder of the data the same as in the published work. If we were to modify all variables included in multivariate models, then the potential effectofmeasurementerroracrossallvariablescouldbegreaterthansimplythemeasurement error in GDP. 26For Corsetti, Meier, and Müller (2012), the authors describe their result as follows: an “increase in government spending causes a substantial rise in aggregate output... a positive spending shock triggers a sizable buildup of public debt, followed over time by a decline of government spending below trend” (pg. 878). Corsetti, Meier, and Müller (2012) do not reference GDP until section 2. According to its abstract, Inoue and Rossi (2011) “investigates the sources of the substantial decrease in output growth volatility in the mid-1980s” − instead of, perhaps, investigating the source of the substantial decrease in the volatility of the GDP statistic in the mid-1980s. Their results are also framed in terms of output, not GDP. In addition, Inoue and Rossi (2011) do not mention GDP until the third section (methodology). Similarly, Morley and Piger (2012), in their analysis of the asymmetric business cycle, argue that “the model averaged measure of the business cyclecaptures a meaningfulmacroeconomic phenomenon and shedsmore light on thenature of fluctuations in aggregate economic activity than simply looking at the level or the growth rates of real GDP” (pg. 208-209, emphasis added). That is, Morley and Piger (2012) are interested in general real business cycle patterns, not the pattern of the GDP statistic, and their academic contribution is to improve on just looking at GDP. 27Aresearchercouldimagineascenariowhereunpublishedworkingpapershaverelativelymorerobustresultsthanpublishedpapers,butthatscenariowouldbeparticularlydiscouragingformaintainingpublication as an outlet for scholarly communication. 21

A limitation of our analysis is that we do not discern which measure of output, GDP or GDI, is closer to true unobserved output.28 The purpose of this paper is to show that measurement error in national statistics could affect economics research and we have provided a broad scope of examples to this effect. Our intent is to expand the literature on measurement error, not to single out or criticize any particular author, journal, ideology, or methodology. 28For a discussion on this issue, see Nalewaik (2010, 2014) who asserts that GDI is superior to GDP. See also comments on Nalewaik (2010) by Diebold (2010) and Landefeld (2010), as well as work by Fleischman and Roberts (2011). 22

Table 1: Papers Under Study Paper Auerbach and Gorodnichenko (2012, 2013) Barro and Redlick (2011) Baumeister and Peersman (2013) Canova and Gambetti (2010) Carey and Shore (2013) Chen, Curdia, and Ferrero (2012) Corsetti, Meier, and Müller (2012) D’Agostino and Surico (2012) Den Haan and Sterk (2011) Favero and Giavazzi (2012) Gabaix (2011) Hansen, Lunde, and Nason (2011) Inoue and Rossi (2011) Ireland (2009) Kilian (2009) Kormilitsina (2011) Mavroeidis (2010) Mertens and Ravn (2013) Morley and Piger (2012) Nakov and Pescatori (2010) Ramey (2011) Reis and Watson (2010) Romer and Romer (2010) 23

Table 2: Auerbach and Gorodnichenko (2012) Table 1, Top Panel Published Results Max Standard Cumulative Standard Point Estimate Error Point Estimate Error Total Spending Linear 1.00 0.32 0.57 0.25 Expansion 0.57 0.12 -0.33 0.2 Recession 2.48 0.28 2.24 0.24 Defense Spending Linear 1.16 0.52 -0.21 0.27 Expansion 0.8 0.22 -0.43 0.24 Recession 3.56 0.74 1.67 0.72 Nondefense Spending Linear 1.17 0.19 1.58 0.18 Expansion 1.26 0.14 1.03 0.15 Recession 1.12 0.27 1.09 0.31 Consumption Spending Linear 1.21 0.27 1.2 0.31 Expansion 0.17 0.13 -0.25 0.1 Recession 2.11 0.54 1.47 0.31 Investment Spending Linear 2.12 0.68 2.39 0.67 Expansion 3.02 0.25 2.27 0.15 Recession 2.85 0.36 3.42 0.38 Corrected results from Auerbach and Gorodnichenko (2013). Table shows output multipliers for a $1 increase in government spending. 24

Table 3: Auerbach and Gorodnichenko (2012) Table 1, Top Panel With Original-Vintage GDP (Replication) Max Standard Cumulative Standard Point Estimate Error Point Estimate Error Total Spending Linear 0.89 0.29 0.60 0.23 Expansion 0.49 0.13 -0.80 0.16 Recession 2.12 0.18 2.17 0.19 Defense Spending Linear 1.53 0.56 0.39 0.22 Expansion 0.76 0.21 -0.94 0.26 Recession 4.27 0.93 2.18 0.78 Nondefense Spending Linear 1.69 0.08 2.09 0.15 Expansion 1.20 0.16 1.16 0.15 Recession 1.06 0.30 1.10 0.32 Consumption Spending Linear 0.83 0.28 0.90 0.29 Expansion 0.10 0.12 -0.16 0.12 Recession 2.16 0.65 1.33 0.36 Investment Spending Linear 2.06 0.60 2.75 0.60 Expansion 2.86 0.27 2.03 0.17 Recession 2.79 0.53 4.18 0.46 Replication of Table 1 of Auerbach and Gorodnichenko (2012) as corrected in Auerbach and Gorodnichenko (2013). Source: Chang and Li (2015). Table shows output multipliers for a $1 increase in government spending. 25

Table 4: Auerbach and Gorodnichenko (2012) Table 1, Top Panel With Original-Vintage GDI Max Standard Cumulative Standard Point Estimate Error Point Estimate Error Total Spending Linear 0.14 0.22 -0.03 0.24 Expansion 0.10 0.15 -1.68 0.20 Recession 1.18 0.16 1.38 0.17 Defense Spending Linear 0.42 0.23 -0.09 0.26 Expansion -0.49 0.24 -3.05 0.37 Recession 6.15 0.84 2.20 0.65 Nondefense Spending Linear 1.86 0.08 2.03 0.17 Expansion 1.13 0.22 0.82 0.19 Recession 0.51 0.26 0.46 0.27 Consumption Spending Linear 0.54 0.25 0.36 0.28 Expansion -0.06 0.13 -0.75 0.16 Recession 3.06 0.69 1.91 0.42 Investment Spending Linear 0.94 0.52 0.62 0.59 Expansion 3.11 0.29 3.02 0.24 Recession -0.08 0.84 -1.95 0.55 Table shows output multipliers for a $1 increase in government spending. 26

Table 5: Inoue and Rossi (2011) Table 1 With Original-Vintage GDP (Replication) Model Parameters Individual p-Value ESS p-Value ρ 0 0 e σ 0 0 ν α 0 0 σ 0 0 a σ 0 0 π ρ 0 0 a γ 0 0 ψ 0 0.01 ρ 0 0 gy σ 0 0 e ρ 0 0 υ ρ 0 0 π σ 1 1 z OriginalGDPvintageisAugust27, 2004. Setofstableparameters(90%probabilitylevel): S = {σ }. This table reports p-values of the QLR stability test (Andrews, 1993) on individual z parameters, labeled “Individualp-value,” and the p-values ofeach stepof the Inoueand Rossi (2011) ESS procedure, labeled “ESS p-value.” Source: Chang and Li (2015). 27

Table 6: Inoue and Rossi (2011) Table 3 With Original-Vintage GDP (Replication) Parameter: Output Inflation Interest Rate No change: (actual S.D.) 0.89 0.48 0.30 Unstable Parameters: % Contribution to Change ρ 7% 10% -1% e σ 71% 35% 40% ν α -2% 12% 1% σ -22% -4% -104% a σ 4% 15% 35% π ρ 25% 2% 94% a γ 20% 0% 18% ψ 0% 0% 0% ρ -43% 1% 24% gy σ -2% -5% -1% e ρ 6% 5% -15% υ ρ -13% -23% 5% π Stable Parameters: σ 49% 53% 3% z All change: (actual S.D.) 1.45 0.92 0.39 Original GDP vintage is August 27, 2004. Set of stable parameters (90% probability level): S = {σ }. This table shows the percentage contribution to the increase or decrease in the z volatilitiesofoutput, inflation, andtheinterestratebyprogressivelyallowingeachparameter to be time-varying, ordered according to the p-values of the QLR stability test (Andrews, 1993). Source: Chang and Li (2015). 28

Table 7: Inoue and Rossi (2011) Table 1 With Current-Vintage GDP Model Parameters Individual p-Value ESS p-Value ρ 0 0 e σ 0 0 ν α 0 0 σ 0 0 a σ 0 0 π ρ 0 0 a γ 0 0 ψ 0 0 ρ 0 0 gy σ 1 1 e ρ 0 0 υ ρ 0 0 π σ 1 1 z Set of stable parameters (90% probability level): S = {σ ,σ }. This table reports p-values e z of the QLR stability test (Andrews, 1993) on individual parameters, labeled “Individual pvalue,” and the p-values of each step of the Inoue and Rossi (2011) ESS procedure, labeled “ESS p-value.” Table 8: Inoue and Rossi (2011) Table 3 With Current-Vintage GDP Parameter: Output Inflation Interest Rate No change: (actual S.D.) 0.92 0.49 0.30 Unstable Parameters: % Contribution to Change ρ 5% 7% 0% e σ 98% 48% 94% ν α -2% 9% 2% σ -33% -6% -96% a σ 4% 10% 17% π ρ 23% 2% 67% a γ 34% 1% 1% ψ 0 0 0 ρ -72% 4% 19% gy ρ 8% 5% -11% υ ρ -15% -29% 6% π Stable Parameters: σ -1% -1% 0% e σ 50% 50% 1% z All change: (actual S.D.) 1.38 0.90 0.38 Set of stable parameters (90% probability level): S = {σ ,σ }. This table shows the percente z age contribution to the increase or decrease in the volatilities of output, inflation, and the interest rate by progressively allowing each parameter to be time-varying, ordered according to the p-values of the QLR stability test (Andrews, 1993). 29

Table 9: Inoue and Rossi (2011) Table 1 With Original-Vintage GDI Model Parameters Individual p-Value ESS p-Value ρ 0 0 e σ 0 0 ν α 1 1 σ 0 0 a σ 0.02 0 π ρ 0 0 a γ 0 0 ψ 0.09 0.19 ρ 0 0 gy σ 1 1 e ρ 0 0 υ ρ 0 0 π σ 1 1 z Original GDI vintage is August 27, 2004. Set of stable parameters (90% probability level): S = {α,σ ,σ ,ψ}. This table reports p-values of the QLR stability test (Andrews, 1993) e z on individual parameters, labeled “Individual p-value,” and the p-values of each step of the Inoue and Rossi (2011) ESS procedure, labeled “ESS p-value.” 30

Table 10: Inoue and Rossi (2011) Table 3 With Original-Vintage GDI Parameter: Output Inflation Interest Rate No change: (actual S.D.) 0.98 0.93 0.35 Unstable Parameters: % Contribution to Change ρ 2% -19% 0% e σ 50% -192% 40% ν σ -346% 78% -1663% a σ 1% -16% 17% π ρ -52% 3% -292% a γ 690% -189% 988% ρ -193% -355% 964% gy ρ 5% -13% -27% υ ρ -12% 681% 75% π Stable Parameters: α 0% 0% 0% σ 0% -3% 0% e σ -45% 126% -2% z ψ 0% 0% 0% All change: (actual S.D.) 1.31 0.84 0.39 Original GDI vintage is August 27, 2004. Set of stable parameters (90% probability level): S = {α,σ ,σ ,ψ}. This table shows the percentage contribution to the increase or decrease e z in the volatilities of output, inflation, and the interest rate by progressively allowing each parameter to be time-varying, ordered according to the p-values of the QLR stability test (Andrews, 1993). 31

Table 11: Inoue and Rossi (2011) Table 1 With Current-Vintage GDI Model Parameters Individual p-Value ESS p-Value ρ 0 0 e σ 0 0 ν α 0 0 σ 0 0 a σ 0 0 π ρ 0 0 a γ 0 0 ψ 0 0 ρ 1 1 gy σ 0.19 0.07 e ρ 0 0 υ ρ 0.04 0 π σ 0.71 0.75 z Set of stable parameters (90% probability level): S = {ρ ,σ }. This table reports p-values gy z of the QLR stability test (Andrews, 1993) on individual parameters, labeled “Individual pvalue,” and the p-values of each step of the Inoue and Rossi (2011) ESS procedure, labeled “ESS p-value.” Table 12: Inoue and Rossi (2011) Table 3 With Current-Vintage GDI Parameter: Output Inflation Interest Rate No change: (actual S.D.) 0.89 0.51 0.29 Unstable Parameters: % Contribution to Change ρ 2% 5% 0% e σ 2% 7% 22% ν α 0% 5% 0% σ -47% -3% -93% a σ 0% 6% 3% π ρ 173% 5% 332% a γ -97% -3% -140% ψ 0% 0% 0% σ 0% -1% 0% e ρ 1% 3% -9% υ ρ 1% 11% -11% π Stable Parameters: ρ 2% -3% -5% gy σ 64% 67% 1% z All change: (actual S.D.) 1.49 1.14 0.39 Setofstableparameters(90%probabilitylevel): S={ρ ,σ }. Thistableshowsthepercentgy z age contribution to the increase or decrease in the volatilities of output, inflation, and the interest rate by progressively allowing each parameter to be time-varying, ordered according to the p-values of the QLR stability test (Andrews, 1993). 32

Table 13: Morley and Piger (2012) Model-Averaged Measure Variances Models Estimated With: Original- Current- Original- Current- Vintage GDP Vintage GDP Vintage GDI Vintage GDI (Replication) Variance of NBER 0.340 0.337 0.310 0.314 Expansions Variance of NBER 0.631 0.642 0.463 0.417 Recessions F-test 0.005 0.003 0.069 0.199 (p-value) We calculate variances based on Morley and Piger (2012)’s model-averaged measure of the business cycle. The replication and original-vintage GDI columns use revised data as of March 30, 2007. Current-vintage data columns use revised data as of September 26th, 2013. F-tests for the equality of variances between National Bureau of Economic Research (NBER) expansions and NBER recessions for each model-averaged measure, H : variances are equal, 0 H : variances are different. A 33

Figure 1: GDP Revisions from September 2008 to September 2013 - Nominal Levels 800 700 600 500 GDP Revisions 400 (nominal billions) 300 200 100 0 -100 1950 1960 1970 1980 1990 2000 2010 Year Figure plots annualized, seasonally adjusted, quarterly nominal GDP from the September 26th, 2013 vintage minus annualized, seasonally adjusted, quarterly nominal GDP from the September 26th, 2008 vintage. 34

Figure2: GDPRevisionsfromSeptember2008toSeptember2013-AnnualPercentChanges 2 1 0 GDP Revisions (annual -1 % change) -2 -3 -4 1950 1960 1970 1980 1990 2000 2010 Year Figure plots annual percent changes of seasonally adjusted quarterly nominal GDP from the September 26th, 2013 vintage minus annual percent changes of seasonally adjusted quarterly nominal GDP from the September 26th, 2008 vintage. 35

Figure 3: The Statistical Discrepancy - Real Levels 300 200 100 GDP Minus GDI (chained 0 2009 billions) -100 -200 -300 1950 1960 1970 1980 1990 2000 2010 Year Figure plots annualized, seasonally adjusted, quarterly real GDP minus annualized, seasonally adjusted, quarterly real GDI using the September 26th, 2013 vintage of BEA data. 36

Figure 4: The Statistical Discrepancy - Real Annual Percent Changes 8 6 4 2 GDP Minus GDI (annual 0 % change) -2 -4 -6 -8 1950 1960 1970 1980 1990 2000 2010 Year Figure plots annual percent changes of seasonally adjusted quarterly real GDP minus annual percent changes of seasonally adjusted quarterly real GDI using the September 26th, 2013 vintage of BEA data. 37

Figure 5: Corsetti, Meier, and Müller (2012) Figure 1 With Current-Vintage GDP Government Spending GGoDvPer Cnmurernetn St Vpienntadgineg GGoDvePCr nComnuserrunemtn Spt tpVioeinnntdaigneg GDPC Conusrruemntp Vtioinntage Consumption 1 21 0. 1 5 12 0. 2 5 1 0.5 1 0 00 00 0 00 0 -1 0 5 10 15 20 --21 0 0 5 5 1 1 0 0 1 1 5 5 2 2 0 0 -0 - -. 1 52 00 0 55 5 11 100 0 11 155 5 22 200 0 -0 - . 2 5 00 55 1100 1155 2200 -0.5 0 5 10 15 20 Government Spending GGGooDvveePrr nnCmmuerernnettn SSt pVpeeinnntdadiignnegg GGGoDDvePPr InCCnmvuuererrrsneettnmn Stte VpVneiitnnnttdaaiggneeg GDPCI NnCoteenutrs reEruesxmntp tpRo Vtraitoistnentage ReaCIln oEtenxrsceuhsmat nRpgtaieot enRate DeRbte/GalD EPx cChuarnregnet RVaintetage Debt/GDP Current Vintage Interest Rate Real Exchange Rate Debt/GDP Current Vintage 0 1 . . 5 5 0 1 0 1 . . 0 1 5 5 0 1 0 2 0 0 - . . 0 1 0 2 2 4 00 2 1 0 1 0 0 0 0 - . . . . 0 2 5 0 1 5 0 1 5 02 4 0 0 0 0 - 2 1 . . . - 2 4 0 5 0 1 05 0 0 -11 2 -5 0 00 0 1 2 0 0 -0.5 0 5 10 15 20 -0 - . -1 5 2 0 00 5 55 1 110 00 1 115 55 2 220 00 - - 0 0 - - -- - . . 1 2 4 2 23 2 00 00 55 55 11 1100 00 11 1155 55 22 2200 00 - - - - - -0 0 0 0 1 1 - . . . . 2 5 5 5 0 4 2 00 00 55 55 11 1100 00 11 1155 55 22 2200 00 - -- 0 00 - 1 1 . .. 4 250 0 5 000 555 111000 111555 222000 -150 00 55 1100 1155 2200 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Interest Rate ReaI Iln n Et t e exr rce ehs sat t nR Rga aet t e eRate DeRbRte e/Ga a Il lDn E E tPex x rc cCeh h sua a tr n nrReg g ane e tt e R RVa aint tte eage D D e e bR b t t e/ / G G alD D EP P Ixn cC C fhlau u atr r inr r oe e gnn n et t RV V ai i n n tet t a a g g e e Debt/GDPIn Cflautriroennt Vintage Inflation 0.4 0.4 0.4 0.40 00 0.05 0.5 0.2 0 0 . .- 2 0 25 002. - - .2 0 5 5 5 0 22 -5 00 20 0 0 -1100 -111000 0 100 -0.2 -0-1.20 -0-1.200 -0.4 0 5 10 15 20 - - 0 0 -1. . 4 2 5 0 0 0 5 5 5 1 1 10 0 0 1 1 15 5 5 2 2 20 0 0 - - 0 - - 0 1 1 . . 4 5 5 5 0 00 0 0 55 5 5 11 1 100 0 0 11 1 155 5 5 22 2 200 0 0 - - 0 1 . 5005 00 0 0 55 5 5 11 1 100 0 0 11 1 155 5 5 22 2 200 0 0 -0.5 0 00 55 1100 1155 2200 0 5 10 15 20 Inflation I I n n f f l l a a t t i i o o n n Impulse res I p n o fl n a s ti e o s n from a vector autoregression identified with the Blanchard and Perotti 0.6 0.5 (02.5002) method. Solid blue lines indicate the point estimate. Grey area indicates the 90% 0.4 0.6 0.2 0.4 confidence interval. Horizontal axis indicates quarters. Vertical axes denotes deviations from 0 0 0 0.2 trendinpercentpointsoftrendoutput(inthecaseofquantities); percentagedeviationsfrom -0.2 0 -0.4 --00..52 -t0h.5e preshock level (real exchange rate); and deviations from the preshock level in terms of 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 quarterly percentage points (real interest rate and inflation). 38

News Government Spending GDP Current Vintage 20 2 2 1 0 0 0 Figure 6: Corsetti, Meier, and Müller (2012) Figure 2 With Current-Vintage GDP -2 -20 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 News Government Spending GDP Current Vintage Consumption Interest Rate Real Exchange Rate NNeewwss GGoovveerrnnmmNNeeeennwwtts sSSppeennddiinngg GGGGooDDvveePPrr nnCCmmuNueerrerrnneewttn n sSStt ppVVeeiinnnnttddaaiigngnegeg GGGoDDvPePr CnCmuurerrrneetnn tSt VpVieinnnttadagigneeg GDP Current Vintage 20 2 2 0.5 10 2200 2 2 0 0 22 2 1 2 . 02 5 22 2 24 2 1 1011 1 11 0 12 0 0 0 -20 - 0 1 0 0 -1- 0 0 0 0 2 0 - 0 0- . . 0 0 1 - 0 - 5 5 0 2 0 2 0 -0 - - . - 5 1 2 0 0 2 0 - - 2 1 - 0 0 2 0 0 5 10 15 20 --22000 5 10 15 20 -2-0-110 5 10 15 20 -2-010 5 10 15 20 -10 5 10 15 20 0 5 10 15 20 00 55 1100 1155 2200 0000 5555 11110000 11115555 22220000 00000 55555 1111100000 1111155555 2222200000 000 555 111000 111555 222000 0 5 10 15 20 Consumption Interest Rate Real Exchange Rate Debt/GDP Current Vintage Inflation News Government Spending GDPC IConnvuserrusemtmnpte tVinoitnntage CIINnnotetneetsr rEeeussmxtpt poRRtriaaotsttnee RReeaaCIInlnl otEEtenexxrsrceceuhhssmatat npnRRgtgaiaeoette n eRRaattee RReeaaIlln EEtexxrccehhsaatn nRggaeet eRRaattee Real Exchange Rate 2 0.5 10 20 0.5 20 2 25 002..55 01.22500 01.05 10 2 1 0.5 10 1 0 0 0 0 1 1 00 1 000 1 0 0 0 0 0 000 0 0 0 -0. 0 5 -- - 00 1 -0.. 15 0 5 -0-1.050 - -- 0 0 -11. . 5 05 0 -10 -0.5 -2 -20 -1 -1 -20 -20 -1 -20 -10 5 10 15 20 --150 5 10 15 20 --1-110 5 10 15 20 ----2211000 5 10 15 20 -2-010 5 10 15 20 -20 0 5 10 15 20 0 5 10 15 20 000 555 111000 111555 222000 0000 5555 11110000 11115555 22220000 00000 55555 1111100000 1111155555 2222200000 000 555 111000 111555 222000 0 5 10 15 20 Debt/GDP Current Vintage Inflation Consumption Interest Rate DDeebRbtte//GGalDD EPPx cCChuuarrnrreegnnett RVVaiinnttetaaggee DDeebbtt//GGDDPPII n nCCfflluauartrtirriooeennnntt VViinnttaaggee Debt/GDPIInn Cffllaauttriioroennnt Vintage Inflation 20 0.5 2 0.5 212000 2010.051 02.051 0.5 0 0 1 0 0 0 0 0 0 -0. 0 5 - - 0 1 .05 0 0 - - - 0 2 1 0 . 0 0 5 0 -0. 0 5 0 -0.5 -30 -1 0 5 10 15 20 -2 - 0 10 0 5 5 1 1 0 0 1 1 5 5 2 2 0 0 -- - 22 2- 0 1 0 0 0 0 0 0 5 55 5 1 1 1 1 0 0 0 0 1 1 1 1 5 5 5 5 2 2 2 2 0 0 0 0 -2-0- 1 1 000 0 555 5 111 1000 0 111 1555 5 222 2000 0 -2-- 011 000 555 111000 111555 222000 -1 0 5 10 15 20 Debt/GDP Current Vintage Inflation Impulse responses from a vector autoregression identified with the Ramey (2011) method. 20 0.5 Solid blue lines indicate the point estimate. Grey area indicates the 90% confidence interval. 0 0 Horizontal axis indicates quarters. Vertical axes denotes deviations from trend in percent -0.5 points of trend output (in the case of quantities); percentage deviations from the preshock -20 -1 level (real exchange rate); and deviations from the preshock level in terms of quarterly 0 5 10 15 20 0 5 10 15 20 percentage points (real interest rate and inflation). 39

Figure 7: Corsetti, Meier, and Müller (2012) Figure 1 With Original-Vintage GDI Government Spending GDI Original Vintage Consumption Government Spending GDI Original Vintage Consumption Government Spending GDI Original Vintage Consumption 1 1 1 1 01 1 0 0 0 0 -200 - 0 2 0 -2 -1 - - 1 40 5 10 15 20 -- - 41 10 5 10 15 20 - - 1 40 5 10 15 20 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Government Spending GGoDveI rOnmrigeinnat lS Vpienntadgineg GDIIC nOoternirgseiusnmta Rlp Vtaiiotnentage ReaCl Eoxncshuamnpgteio Rnate Debt/GDI Original Vintage Government Spending GGoDveI rOnmrigeinnat lS Vpienntadgineg GDI OInrvigeisntaml eVninttage Net Exports Interest Rate Real Exchange Rate Debt/GDI Original Vintage Interest Rate Real Exchange Rate Debt/GDI Original Vintage 0.41 1 - 0 1 0 . . . 5 5 5 0 1 0 5 10 15 20 - -- - 1 0 1 1 0 1 4 2 0 0 00 5 55 1 110 00 1 115 55 2 220 00 - 0 0 0 . . . -- - - - - - - 2 4 2 0 1 0 1 4 2 0 3 2 1 0 1 4 2 0 0000 5555 1111 0000 1111 5555 222 2 000 0 - - 0 0 - - 0 0 1 1 . . - -- - . . 2 2 05 0 5 0 5 1 0 5 0 1 4 2 0 00 0 0 5 5 55 1 1 110 0 00 1 1 115 5 55 2 2 220 0 00 -- - 0 0 01 1 1 2 3 -. . .- 5 0 5 0 2 4 2 0 0 0 0 0 1 0 0 0 0 5 5 5 1 1 10 0 0 1 1 15 5 5 2 2 20 0 0 - - 1 2 3 1 1 - 0 0 0 0 5 0 5 0 0 0 5 5 1 1 0 0 1 1 5 5 2 2 0 0 1 2 3 0 0 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Interest Rate ReaI Iln n Et t e exr rce ehs sat t nR Rga aet t e eRate DeR Rbte e/Ga a Il l nD E E tIex xOrc c eh hrsia agt n niRng gaae elt eVR Ria ant tte eage D D e e R b b t te / / G Gal D D EI I In x O Ocflha r r i iat g gino i i n ngn a ae l l V VR i ia n nt t te a a g g e e Debt/GDI I n O fl r a ig tio in n al Vintage Inflation 0 0 . . 2 4 0 0 0 0 0 . . . . - 2 4 0 2 4 5 0 0 00 0 2 3 . . - - . . 2 42 4 0 5 0 0 0 5 0 0 0 2 3 2 3 . . -2 4 0 0 0 0 5 0 0 0 2 3 . . 2 4 0 0 -100 -1100 -11000 10 -0.2 0 5 10 15 20 --00 -1 ..22 5 00 55 1100 1155 2200 - - 0 - - - 0 1 1 1 . . 2 02 50 5 0 000 555 111000 111555 222000 -0- 1 1.2 0 0 0 5 000 555 111000 111555 222000 -0.2 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Inflation Inflation Inflation Inflation 0.6 Original vintage is March 2010. Impulse responses from a vector autoregression identified 0.6 0.4 0.4 w 0. i 4 th the Blanchard and Perotti (2002) method. Solid blue lines indicate the point estimate. 0.4 0.2 0.2 0.2 0.2 Grey area indicates the 90% confidence interval. Horizontal axis indicates quarters. Vertical 0 0 0 -0.2 0 axes denotes deviations from trend in percent points of trend output (in the case of quanti- -0.2 -0.2 -0.2 0 5 10 15 20 0 5 10 15 20 ties0); pe5rcen1t0age d15evia2t0ions from the preshock level (real exchange rate); and deviations from 0 5 10 15 20 the preshock level in terms of quarterly percentage points (real interest rate and inflation). 40

News Government Spending GDI Original Vintage 20 1 2 0 0 0 Figure 8: Corsetti, Meier, and Müller (2012) Figure 2 With Original-Vintage GDI -2 -20 -1 News Government Spending 0 G5DI O1rNi0geiwnas1l 5Vinta20ge 0 Gov5ernm10ent S15pend2i0ng 0 GD5I Ori1g0inal 1V5inta2g0e News GovernNmNeeewnwst sSpending GGoGovDveerIn rOnmmreigeninnt taS Slp Vpeiennndtadingingeg GGDDI IO Orirgigininaal lV Vinintataggee News 20 Government Spending GDI Original Vintage 20 Consumption Interest Rate Real Exchange Rate 20 20 1 2 1 2 0 0 01 21 11 1 .5 1 2 4 0.1 25 4 6 1 2 0 0 002 0 0 0 0 0 0 00 0 0 00 - .5 0 2 0 000 0 2 -2 0 -20 -1 - -0 1 2 - - 2 0 0 .-52 -0 - -. 1 25 -2 -10 -200 5 10 15 20 -20-10 5 10 15 20 -100 55 1100 1155 2200 0 5 10 15 20 0 5 10 15 20 -20 -10 5 10 15 20 -0400 555 110100 115155 220200 -1000 555 101100 115155 220200 -100 55 1010 1155 2200 -20 News 0 Gov 5 ernm 1 e 0 nt S 1 p 5 end 2 i 0 ng 0 GD 5 CI Oonr 1 isg 0 uinmapl 1 tV 5 ioinnta 2 g 0 e 0 5 Inte 1 r 0 est R 15 ate 20 0 R5eCalo En1xs0cuhmapn1t5gioen R2a0te 0 5Inte1r0est R15ate 20 0 Re5al Ex1c0han1g5e Ra2t0e Investment CIoNnnetest ruEemsxptp otRioratnste ReIanIlnt eEterxerceshsta tR nRagateet eRate RReeaal lE Exxcchhaannggee R Raatete 20 Consumption 1 Interest Rate 0.5 Real Exchange Rate 11D0ebt/GDI Original Vintage 0.5 Inflation 10 4 01.5 0.510 10 11 0.52 110 200.5 0.5 0 0 100 0 2 00 0 0 0 000 0 00 0 0 0 00 0 -0-. 0 52 -0 -1- . 1 5 0 -0 - - 0 .- 1 051 .5 0 0 - - - 0 0 1- . . 1 5 0 5 0 -10 -20 0 5 10 15 20 -1 0 5 10 15 20 - - 1 200 55 1100 1155 2200 --01 - . 1 50 5 10 15 20 -- -- 12 120 0 00 55 1100 1155 2200 -2 --21 00 0 5 10 15 20 -20 0 5 10 15 20 -1 0 5 10 15 20 -10 0 5 5 1 10 0 1 1 5 5 2 2 0 0 -2000 0 0 55 5 5 11 1 010 0 0 11 1 515 5 5 22 2 020 0 0 -20000 555 101100 115155 220200 -100 55 1010 1155 2200 1 Consumption 0 2 .5 0 Debt/G In D t I e O re r s ig t i R na a l t e Vintage 0 211 . 00 5 0 DDeebbRtt/e/GGaDlD EII I x n OOc f r l hr a iigag ti ini o nng n aaell VVRiinantttaeaggee 2 0 0 . D 51 Deebbt/tG/GDDI I I OI nn Or ffl ir la ga ig t itn ii i oo na nn al lV Vinintataggee 0 2 . 0 5 0Debt/5GDI I n 1 I O n 0 fl r fal i a g tit i o n i 1 on a5 n l Vin2t0age 0.5 0 5 In10flatio1n5 20 0 00 00 0.5 0 0 -100 0 0 0 0 -0.50 -10 --02 0 .05 0 -0.5 --02.05 -0 -0 .5 .5 -1 0 5 10 15 20 -2 -1 00 5 10 15 20 ---232 - 00 1 0 000 555 111000 111555 222000 -2-40 --011 00 55 1100 1155 2200 -2 - 0 10 5 10 15 20 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 00 55 1100 1155 2200 00 55 1010 1155 2200 Debt/GDI Original Vintage Inflation Original vintage is March 2010. Impulse responses from a vector autoregression identified 20 0.5 with the Ramey (2011) method. Solid blue lines indicate the point estimate. Grey area 0 indicates the 90% confidence interval. Horizontal axis indicates quarters. Vertical axes 0 denotes deviations from trend in percent points of trend output (in the case of quantities); -0.5 percentage deviations from the preshock level (real exchange rate); and deviations from the -20 -1 0 5 10 15 20 0 5 10 15 20 preshock level in terms of quarterly percentage points (real interest rate and inflation). 41

Figure 9: Corsetti, Meier, and Müller (2012) Figure 1 With Current-Vintage GDI Government Spending G G o D ve I r C n u m r e re n n t t S V p in e t n a d g in e g GGoDveI C rCnomu n r ser u enm nt t pS V tpio ien nntadgineg GDIC Counrsruemntp Vtiionntage Consumption 1 0 1 0.510 0.5 0 0.5 0 -2 0 -0. - 5 0 02 -0 - .5 0 2 -0.5 0 -1 --41 -- - 11 4 --14 -1 0 5 10 15 20 0 0 5 5 1 1 0 0 1 1 5 5 2 2 0 0 000 555 111 000 111 555 222 000 00 55 1100 1155 2200 0 5 10 15 20 Government Spending GGGooDvveeI rrCnnmumreerennntt tSS Vppieennntaddgiinnegg GGGoDDveIII n rCICnnte umuvr rree rereses ntnnt tm ttR S eVVp aniine tnte tntaadggineeg R G e D a CII l nN Co E teenu xtrs c r erEu h esm axntpn tpR og Vtrai e otints ne R ta a g te e De R bt e /G aCIl Dn EotIen x Crcsehu usam rtr n eRpg n taei t o t VenR in a t t a e ge DeRbte/GalD EIx Cchuarrnegnet VRiantteage Debt/GDI Current Vintage 0 1 . . 5 5 0 1 - 0 1 0 1 2 0 0 0 - . . -- 2 0 2 4 0 0 1 1 0 1 2 0 - 0 0 - 0 0 0 1 1 . . - - . . . . 5 5 05 0 0 2 4 5 5 2 0 0 0 1 - 0 0 0 0- 2 4 1 . . . . - 0 0 5 2 4 5 0 0 5 0 0 - 2 4 1 -0 0 5 0 0 2 4 0 0 -0.5 - - -1 1 4 -0-.- - - - 421 3 2 4 - -- 0 01 --. .1 5 2 5 4 -0-1-. 0 215 -105 0 0 5 10 15 20 0 00 5 55 1 110 00 1 115 55 2 220 00 0 0 000 5 5 555 1 1 111 0 0 000 1 1 111 5 5 555 2 2 222 0 0 000 0 0 00 0 5 5 55 5 1 1 11 1 0 0 00 0 1 1 1 1 15 5 5 5 5 2 2 2 2 20 0 0 0 0 0 000 5 555 1 111 0 000 1 111 5 555 2 222 0 000 00 55 1100 1155 2200 0 5 10 15 20 Interest Rate ReaI Iln n Et t e exr rce ehs sat t nR Rga aet t e eRate DeR Rbete/aGa Il l n D E E tII ex xnCrc cf eh lhua sa art tri n noeRg gnnae ett eRVRia ant tte eage D D e e bR b t t e/ / G G alD D EI I I x nC C cfluh u ara r tr r ineo e gnn n et t V V Ri i na n tt t ae a g g e e Debt/GDII nCfluartrioennt Vintage 0.4 0 0 0 . . . 2 4 40 0 0 0 03 . . . . 0 4 6 2 40 0 0 04 3. .0 4 6 0 0 0 04 . . 4 60 - - 0 0 0 . . . 2 4 2 0 - - 0 - - 0 01 1 . -. . 2 0 2 2 0 5 5 0 - - - - 0 0 0 - - 1 1 1 2 1 1 - . . . - 5 5 0 2 2 02 0 0 0 0 5 5 0 -- - 0 0 2 1 1 1 2 - . . 0 0 2 2 5 5 00 0 0 - 0 0 2. . 2 2 0 0 0 0 5 10 15 20 -0.400 55 1100 1155 2200 0 0 00 5 5 55 1 1 110 0 00 1 1 115 5 55 2 2 220 0 00 0000 555 111000 111555 222000 00 55 1100 1155 2200 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Inflation Inflation Inflation Inflation 0.6 0.6 0.6 Impulse responses from a vector autoregression identified with the Blanchard and Perotti 00..46 0.4 0.4 0.2 00..24 (200.202) method. Solid blue lines indicate the point estimate. Grey area indicates the 90% 0 0.02 con0fidence interval. Horizontal axis indicates quarters. Vertical axes denotes deviations from -0.2 -0.20 -0.2 0 5 10 15 20 -0.20 5 10 15 20 tren 0 din 5 perce 1 n 0 tp 1 o 5 ints 2 o 0 ftrendoutput(inthecaseofquantities); percentagedeviationsfrom 0 5 10 15 20 the preshock level (real exchange rate); and deviations from the preshock level in terms of quarterly percentage points (real interest rate and inflation). 42

News Government Spending GDI Current Vintage 4 20 1 2 0 0 0 -2 Figure 10: Corsetti, Meier, and Müller (2012) Figure 2 Wi-t2h0 Current-Vintage GDI -1 -4 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 NNeewwss GGoovveerrnnmmN Neee ennw wtt s SSsppeennddiinngg G GGGo oDDv v e IIe r CCr n n m uumrrNe rreeenennntw ttt S sSVVp piie nne n ttnaad dggin ieen g g GG GoD DvIe I C rCnu umr r rer e enn ntt tSV Vpin ineta tna gdg eineg GDI Current Vintage News Government Spending GDI Current Vintage Consumption Interest Rate Real Exchange Rate 20 2200 12 2.0 4 5 11 0 1. 2 5 1 4 6 2 4 1 0 1 0 4 6 . 2 45 1 102 4 -20 0 - - 2 2 - 0 0 1 0 1 0 0 00 55 1100 1155 2200 - - 0 0 2-2 - - - . . 0 0 4 2 0 2 5 5 0 1 0 0 0 0000 5555 11110000 11115555 22220000 - 0 0 - . . -2- - - 5 5 0 - 2 0 2 4 2 0 1 0 0 0 1 0 00000 55555 1111100000 1111155555 2222200000 -0-2 0 2 - - - . 4 2 0 5 0 1 0 000 555 111000 111555 222000 - - 2 1 - - 0 0 0 4 2 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 News Government Spending GDIC IConunversrsuetmnmtp eVtniiontntage IICNnntoteeentrr seEeussxmttp RoRprtaatisotteen RReeaaIlClIn nEEtotexexnrccresehhsusaatmt nn RRpggateeaito teRRenaattee RReeaalI lnE Etxexcrchehasantn gRgeae tR eRaatete Real Exchange Rate Consumption Interest Rate Real Exchange Rate Debt/GDI Current Vintage Inflation -2 2 0 0 0 - 0 1 1 0 1 - 0 0 -- . .- - 2 0 2 4 5 5 0 1 0 1 4 2 0 2 4 - - - 0 0 0 0 1 1 - . . . .1 0 1 - 0 0 0 5 5 0 5 5 0 1 0 1 - 0 0 - - - - - - 0 0 2 1 1 2 1 1 . . 2 25 5 0 - . . 0 0 0 0 0 0 0 0 0 0 0 5 5 1 0 1 0 - - -- 2 1 1 - - 0 0 0 0 2 1 1 0 0 0 0 - . . . . 0 0 0 0 5 5 1 0 5 5 0 - - 2 1 1 0 0 0 0 0 5 10 15 20 -10 5 10 15 20 000 555 111000 111555 222000 -200000 5555 11110000 11115555 22220000 00000 55555 1111100000 1111155555 2222200000 000 555 111000 111555 222000 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Consumption Interest Rate DDeeRbbtte//GGalDD EII xCCchuuarrrrneegnnett VVRiiannttteaaggee DDeebbtt//GGDDIIII nn CCfflu laaurttrriireooennnntt VVininttaaggee Debt/GD I IIn nC flfaluat rtio rioe nnnt Vintage Inflation Debt/GDI Current Vintage Inflation 1 0.5 1 21 0 00 02.50 0 21 .5 0 0.5 0 -0 2 . 0 0 5 0 - - - 0 0 -2 1 1 . . 0 0 0 5 5 00 0 0 - -- 0 0 02 . . .0 0 5 5 0 5 0 0 -0 0 .5 00 -0.5 0 -1 0 5 10 15 20 -20 0 5 10 15 20 -- - 32 2 - 0 1 0 0 000 555 111000 111555 222000 -4 -2 - - 01 10 000 555 111000 111555 222000 - - 2 1 - 0 1 00 55 1100 1155 2200 -1 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Debt/GDI Current Vintage Inflation Impulse responses from a vector autoregression identified with the Ramey (2011) method. 20 0.5 Solid blue lines indicate the point estimate. Grey area indicates the 90% confidence interval. 0 0 Horizontal axis indicates quarters. Vertical axes denotes deviations from trend in percent -0.5 -20 -1 points of trend output (in the case of quantities); percentage deviations from the preshock 0 5 10 15 20 0 5 10 15 20 level (real exchange rate); and deviations from the preshock level in terms of quarterly percentage points (real interest rate and inflation). 43

Figure 3. - Model-Averaged Measure of the U.S. Business Cycle Model Average (Original GDP) Model Average (Original GDI) Figure 11: Morley and Piger (2012) Figure 3 Replication 2.4 2.4 2.4 2.4 2.0 2.0 2.0 2.0 1.6 1.6 1.6 1.6 1.2 1.2 1.2 1.2 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.4 -0.8 -0.8 -0.8 -0.8 -1.2 -1.2 -1.2 -1.2 -1.6 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -2.0 -2.4 -2.4 -2.4 -2.4 -2.8 -2.8 -2.8 -2.8 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 1990 2000 Note. NBER recessions are shaded. Note. NBER recessions are shaded. Figure plots the Morley and Piger (2012) model-averaged measure of the business cycle, whichMisocodnsterulc tAedvuesinrgaBgayees ia(nUMpoddelaAtveerdag inGg oDvePr 3)3 univariate models. Source: Model Average (Updated GDI) Chang and Li (2015). 2.4 2.4 2.4 2.4 2.0 2.0 2.0 2.0 1.6 1.6 1.6 1.6 1.2 1.2 1.2 1.2 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.4 -0.8 -0.8 -0.8 -0.8 -1.2 -1.2 -1.2 -1.2 -1.6 44 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -2.0 -2.4 -2.4 -2.4 -2.4 -2.8 -2.8 -2.8 -2.8 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 1990 2000 Note. NBER recessions are shaded. Note. NBER recessions are shaded.

Figure 3. - Model-Averaged Measure of the U.S. Business Cycle Model Average (Original GDP) Model Average (Original GDI) 2.4 2.4 2.4 2.4 2.0 2.0 2.0 2.0 1.6 1.6 1.6 1.6 1.2 1.2 1.2 1.2 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.4 -0.8 -0.8 -0.8 -0.8 -1.2 -1.2 -1.2 -1.2 -1.6 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -2.0 -2.4 -2.4 -2.4 -2.4 -2.8 -2.8 -2.8 -2.8 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 1990 2000 Note. NBER recessions are shaded. Note. NBER recessions are shaded. Model Average (Updated GDP) Model Average (Updated GDI) Figure 12: Morley and Piger (2012) Figure 3 With Current-Vintage GDP 2.4 2.4 2.4 2.4 2.0 2.0 2.0 2.0 1.6 1.6 1.6 1.6 1.2 1.2 1.2 1.2 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.4 -0.8 -0.8 -0.8 -0.8 -1.2 -1.2 -1.2 -1.2 -1.6 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -2.0 -2.4 -2.4 -2.4 -2.4 -2.8 -2.8 -2.8 -2.8 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 1990 2000 Note. NBER recessions are shaded. Note. NBER recessions are shaded. Figure plots the Morley and Piger (2012) model-averaged measure of the business cycle, which is constructed using Bayesian Model Averaging over 33 univariate models. 45

Figure 3. - Model-Averaged Measure of the U.S. Business Cycle Model Average (Original GDP) Model Average (Original GDI) Figure 13: Morley and Piger (2012) Figure 3 With Original-Vintage GDI 2.4 2.4 2.4 2.4 2.0 2.0 2.0 2.0 1.6 1.6 1.6 1.6 1.2 1.2 1.2 1.2 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.4 -0.8 -0.8 -0.8 -0.8 -1.2 -1.2 -1.2 -1.2 -1.6 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -2.0 -2.4 -2.4 -2.4 -2.4 -2.8 -2.8 -2.8 -2.8 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 1990 2000 Note. NBER recessions are shaded. Note. NBER recessions are shaded. Figure plots the Morley and Piger (2012) model-averaged measure of the business cycle, which is constructed using Bayesian Model Averaging over 33 univariate models. Model Average (Updated GDP) Model Average (Updated GDI) 2.4 2.4 2.4 2.4 2.0 2.0 2.0 2.0 1.6 1.6 1.6 1.6 1.2 1.2 1.2 1.2 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.4 -0.8 -0.8 -0.8 -0.8 46 -1.2 -1.2 -1.2 -1.2 -1.6 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -2.0 -2.4 -2.4 -2.4 -2.4 -2.8 -2.8 -2.8 -2.8 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 1990 2000 Note. NBER recessions are shaded. Note. NBER recessions are shaded.

Figure 3. - Model-Averaged Measure of the U.S. Business Cycle Model Average (Original GDP) Model Average (Original GDI) 2.4 2.4 2.4 2.4 2.0 2.0 2.0 2.0 1.6 1.6 1.6 1.6 1.2 1.2 1.2 1.2 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.4 -0.8 -0.8 -0.8 -0.8 -1.2 -1.2 -1.2 -1.2 -1.6 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -2.0 -2.4 -2.4 -2.4 -2.4 -2.8 -2.8 -2.8 -2.8 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 1990 2000 Note. NBER recessions are shaded. Note. NBER recessions are shaded. Model Average (Updated GDP) Model Average (Updated GDI) Figure 14: Morley and Piger (2012) Figure 3 With Current-Vintage GDI 2.4 2.4 2.4 2.4 2.0 2.0 2.0 2.0 1.6 1.6 1.6 1.6 1.2 1.2 1.2 1.2 0.8 0.8 0.8 0.8 0.4 0.4 0.4 0.4 0.0 0.0 0.0 0.0 -0.4 -0.4 -0.4 -0.4 -0.8 -0.8 -0.8 -0.8 -1.2 -1.2 -1.2 -1.2 -1.6 -1.6 -1.6 -1.6 -2.0 -2.0 -2.0 -2.0 -2.4 -2.4 -2.4 -2.4 -2.8 -2.8 -2.8 -2.8 1950 1960 1970 1980 1990 2000 1950 1960 1970 1980 1990 2000 Note. NBER recessions are shaded. Note. NBER recessions are shaded. Figure plots the Morley and Piger (2012) model-averaged measure of the business cycle, which is constructed using Bayesian Model Averaging over 33 univariate models. References Andrews, Donald W.K., “Tests for Parameter Instability and Structural Change with Unknown Change Point,” Econometrica 61:4 (1993), 821-856. Auerbach, Alan J., and Yuriy Gorodnichenko, “Measuring the Output Responses to Fiscal 47

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