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Surprise and Uncertainty Indexes: Real-Time Aggregation of Real-Activity Macro Surprises

Chiara Scotti1

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at http://www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/.

Abstract:

I construct two real-time, real activity indexes: (i) a surprise index that summarizes recent economic data surprises and measures optimism/pessimism about the state of the economy, and (ii) an uncertainty index that measures uncertainty related to the state of the economy. The indexes, on a given day, are weighted averages of the surprises or squared surprises from a set of macro releases, where the weights depend on the contribution of the associated real activity indicator to a business condition index à la Aruoba, Diebold, and Scotti (2009). I construct indexes for the United States, Euro Area, the United Kingdom, Canada, Japan. I show that the surprise index preserves the properties of the underlying series in affecting asset prices, with the advantage of being a parsimonious summary measure of real-activity surprises. For the United States, I present the real-activity uncertainty index in relation to other proxies commonly used to measure uncertainty and compare their macroeconomic impact. I find evidence that when uncertainty is strictly related to real activity it has a potentially milder impact on economic activity than when it also relates to the financial sector.

Keywords: Business cycle, dynamic factor model, state space model, forecasting weights

JEL classification: C38, E32


1  Introduction

This paper proposes a new methodology to construct two real-time, real activity indexes: (i) a surprise index that summarizes recent economic data surprises and measures deviation from consensus expectations and (ii) an uncertainty index that measures uncertainty related to the state of the economy. The indexes, on a given day, are weighted averages of the surprises or squared surprises from a set of releases, where the weights depend on the contribution of the associated real activity indicator to a business condition index à la Aruoba, Diebold, and Scotti (2009). The surprise index measures whether agents are more optimistic or pessimist about the real economy than indicated by actual data releases. A positive (negative) reading of the surprise index suggests that economic releases have on balance been higher (lower) than consensus, meaning that agents were more pessimistic (optimistic) about the economy. The uncertainty index measures how uncertain agents are about current real activity conditions. A greater (smaller) reading of the uncertainty index suggests that agents have on balance been more (less) uncertain about the state of the economy. I apply this methodology to construct indexes for the United States, Euro Area, the United Kingdom, Canada, Japan, and an aggregate of the five countries over the 2003-2012 period.

The Aruoba, Diebold, and Scotti (ADS) index maintained by the Federal Reserve Bank of Philadelphia has proven to be a successful economic indicator and as such it has been classified by the Wall Street Journal among the 50 economic indicators that really matter (Constable and Wright, 2011) and has been added by Bloomberg to the data that can be followed in real time through its platform (ADS BCI Index).2 The ADS index measures the state of the economy and serves as a summary statistics of the information market participants have received thus far about real activity. However, in efficient markets, asset prices react to new information. Thus it is important to measure the surprise component of the information that has just arrived and the uncertainty surrounding that information. To this end, the surprise index presented in this paper aggregates the information contained in the surprises to construct a summary measure of the deviation of the real economy from consensus expectations, and the uncertainty index quantifies economic uncertainty, which is otherwise challenging to measure. The indexes are not competitors but complements to the existing business condition indicators such as the ADS index and to existing uncertainty indexes.

This paper relates to several branches of the literature. First and foremost is the uncertainty literature, which has thrived in recent years. Because uncertainty is not observable, a number of proxies have been used to measure it, ranging from stock market realized and implied volatilities (Bloom, 2009), to the cross-sectional dispersion of survey-based forecasts (Bachmann, Elstner and Sims, 2013), the frequency of newspaper references to economic policy uncertainty (Baker, Bloom, and Davis, 2013), or the common variability in the purely unforecastable component of the future value of a big number of variables (Jurado, Ludvigson, and Ng, 2013). However, these measures tend to combine economic uncertainty with other notions. For example, stock return volatility combines information about stock market volatility with economic uncertainty, and forecast disagreement could measure divergence of opinions among forecasters rather than just the underlying uncertainty about the economy. My paper contributes to this literature by providing a daily macroeconomic information uncertainty measure which quantifies the part of uncertainty that specifically relates to the state of the real economy. It also contributes by helping to disentangle the impact of purely macro uncertainty versus more general uncertainty. Second, this paper relates to those papers that study the impact of news surprises on asset price such as Andersen, Bollerslev, Diebold and Vega (2003, 2007), and Gilbert, Scotti, Strasser and Vega (2012), and contributes to this literature by providing a parsimonious summary measure of real-activity macroeconomic surprises. The paper also relates to papers that use similar factors models to extract a business condition index or to nowcast GDP such as the seminal Stock and Watson paper (1989), Aruoba, Diebold, and Scotti (2009), and Banbura, Giannone, and Reichlin (2010) among others. It also employs the idea of forecasting weights developed in Koopman and Harvey (2003) and applied by Banbura and Rünstler (2010) and Camacho and Perez-Quiros (2010), among others, to study the impact of news releases on GDP forecast revisions.

In order to construct the surprise and uncertainty indexes, I first employ a dynamic factor model to estimate monthly business condition indexes for the aforementioned countries and compute the weights representing the contribution of the economic indicators to these business condition indexes. I then use those weights to average the surprises or squared surprises in order to construct the surprise and the uncertainty indexes, respectively. The weights depend on (i) the time elapsed since the release of the associated information and (ii) the unbalancedness pattern of the underlying releases. The former is a time decay feature that reduces the contribution of each surprise over time. The latter is a missing data characteristic that sets to zero the contributions of an indicator in months in which no data is available.

I find that, surprise indexes tend to be negative during the recession associated with the 2008 financial crisis, the so-called Great Recession, suggesting that agents were more optimistic about the real economy than it warranted.3 There appear to be other episodes when the indexes are negative. Of note are the most recent decline in the euro-area surprise index, the sharp drop in the Japanese surprise index after the March 2011 earthquake, and the prolonged low levels of the U.K. index in 2010 and 2011. On the other hand, there are also several instances where the surprise indexes are positive, especially coming out of the recession in the United States, the United Kingdom and Canada. I show that the surprise index preserves the properties of the underlying series in affecting asset prices, with the advantage of being a parsimonious summary measure of real-activity surprises. In light of this, Demiralp, King, and Scotti (2013) make use of it as a control variable when investigating the effects of political commentaries on policy rate decisions and policy expectations in the United States and the Euro Area, and find it to be significant determinant of policy expectations. Similarly, Brunetti, Buyuksahin, and Harris (2013) employ it as a control variable in studying the impact of speculation activity in the crude oil market.

The uncertainty indexes tend to be higher during recession periods. Interestingly, the euro-area uncertainty index reaches its highest values just before and after the 2008-2009 recession, suggesting that agents were more uncertain about the economy as the Euro Area was entering and exiting the recession. The daily U.S. uncertainty index is remarkably similar to the U.S. stock market implied volatility as measured by the VIX. Implied volatility, a forward-looking measure, is computed from option prices. The uncertainty index, a historical measure, is calculated from current and past macroeconomic news surprises. The former is a wider measure that combines information about risk aversion and future stock market volatility/uncertainty, and to the extent that these two move with news surprises, the VIX also contains information about current and future economic uncertainty. Although understanding the exact link between the two goes beyond the scope of this paper, it is nonetheless quite astonishing that macroeconomic uncertainty seems to be such an important component of the VIX during the period analyzed.4 The monthly version of the uncertainty index appears to be less correlated to other uncertainty proxies mentioned above.5

In a bivariate VAR exercise with employment and uncertainty proxies for the United States over the last decade, I find that, when uncertainty is strictly related to real activity as measured by real-activity uncertainty index, it has a potentially milder impact on economic activity. Just flipping the argument, when uncertainty is more generally related to economic and financial conditions as measured by the VIX, its impact on real-activity variables is stronger and more prolonged. This finding supports recent work by Caldara, Fuentes-Albero, Gilchrist and Zakrajsek (2013) which finds that the financial channel is key in the transmission of uncertainty shocks.

The surprise and uncertainty indexes tend to be negatively correlated, meaning that bad news increases volatility.6 This results is similar to the inverse relationship between first and second moments of asset returns found in the financial literature, phenomenon that Fostel and Geanakopoplos (2012) provide a theoretical explanation to, together with explaining a decrease in leverage.

The remainder of the paper is organized as follows: section 2 presents the data and the rationale behind using Bloomberg forecasts; section 3 presents the details of the dynamic factor model, the forecasting weights and the construction of the surprise and uncertainty indexes; section 4 covers the estimation details; section 5 presents the results; section 6 shows some applications; and section 7 concludes.


2  Data

Before getting into the model, this section presents information about the data used to construct the surprise and uncertainty indexes. I use two different types of data: the actual first release of the macroeconomic variable, say gross domestic product (GDP) or nonfarm payroll, and its forecast as measured by the Bloomberg median expectation. The actual releases of macroeconomic variables are used to estimate the underlying factor model from which I gather the weights. The difference between actual releases and Bloomberg expectations, also known as news surprise or forecast error, is then used together with the weights to construct the surprise and uncertainty indexes. In what follows, I describe the details of the data and study some of the properties of the news surprises.

The analysis covers five countries: the United States, the Euro Area, the United Kingdom, Canada, and Japan. I use five indicators for each country, except the United States for which I use six. Several considerations guide the choice of variables. First, I want to use those variables that are regarded as the main real activity indicators and as such followed by the business community, governments, and central banks as indication of the state of the economy. Second, I choose indicators for which analysts form expectations that are publicly available. Table 1 lists the indicators, together with their frequency, publication lags and transformations that I use to construct the real activity factor. The two rightmost columns list the source of the data series that I use to construct the factor, and the corresponding Bloomberg data series that I use to construct the surprise and uncertainty indexes.

The analysis for the surprise and uncertainty indexes covers the period from May 15, 2003 through September 30, 2012. However, a longer dataset is used to estimate the underlying business condition indexes: January 1980 to September 30, 2012, except for the Euro area where the sample starts in January 1985.

The first indicator is quarterly real GDP. For each country, the first GDP release for the corresponding quarter is used. The second indicator is industrial production (IP), which is a monthly indicator. The third indicator is employees on nonagricultural payrolls, when available, or the unemployment rate.7 The former tends to be more timely than the latter, but unfortunately it is not available for all countries.8 The fourth indicator is retail sales, which is another monthly variable. The fifth indicator is a survey measure of the manufacturing sector or the overall economy (composite) depending on the availability of the Bloomberg forecast. I use the ISM manufacturing index for the United States, the composite PMI for the Euro Area, the manufacturing PMI for the United Kingdom and Canada (Ivy survey), and the Tankan survey for Japan. The Tankan survey is a quarterly series, whereas the other surveys are all monthly.9 Although monthly series are generally preferred when available, the Tankan survey has the advantage of being very timely, as it is released on average four days before the end of the quarter it refers to.10 The average publication lag for the other series vary a lot as shown in table 1. Survey measures are the most timely of all: the euro-area Flash composite PMI is the first indicator to be released, followed by the Japanese Tankan survey, the U.S. ISM and the U.K. PMI. On the other hand, GDP and IP data tend to be the last information to be released.

The additional indicator for the United States is the Bureau of Economic Analysis (BEA) personal income. Household income or personal income are generally available for the other countries but because their expectation is not, I drop them from the dataset.

As already mentioned, while the announcement itself is used in constructing the real activity factor, the news surprise, that is the difference between announcement realizations $ (y_{t}^{i})\ $and their corresponding Bloomberg expectations $ (E[y_{t}^{i}\vert\mathcal{F}_{t}]) $, is used in constructing the surprise and uncertainty indexes. Because units of measurement vary across macroeconomic variables, I standardize the resulting surprises by dividing each of them by their sample standard deviation $ (\sigma ^{i})$. The standardized news surprise associated with the macroeconomic indicator $ y^{i} $ at time $ t$ is therefore computed as:

$\displaystyle s_{t}^{i}=\frac{y_{t}^{i}-E[y_{t}^{i}\vert\mathcal{F}_{t}]}{\sigma ^{i}}.$ (1)

Table 1. Summary Information of the Real Activity Indicators Used in the Paper to Construct the Surprise and Uncertainty Indexes for the United States, Euro Area, United Kingdom, Canada, and Japan

CountrySeries NameDescriptionFrequencyPublication Lag (days)Transformation for FactorSourceBloomberg Mnemonic
United StatesGDPReal GDP, levelQ29log diffBEAGDP CQQQ
United StatesIPIndex, levelM16log diffFRBIP CHNG
United StatesEmploymentLevelM5log diffBLSNFP TCH
United StatesRetail SalesLevelM13log diffISMRSTAMOM
United StatesISM ManufacturingIndexM2diffISMNAPMPMI
United StatesPersonal IncomeLevelM29log diffBEAPITLCHNG
Euro AreaGDPReal GDP, levelQ48log diffEUROSTATEUGNEMUQ
Euro AreaIPIndex, levelM46log diffEUROSTATEUITEMUM
Euro AreaUnemployment rateLevel, percentM32log diffEUROSTATUMRTEMU
Euro AreaRetail SalesLevelM41log diffEUROSTATRSSAEMUM
Euro AreaPMI Composite (Flash)IndexM-9diffMarkitECPMICOU
United KingdomGDPReal GDP, levelQ24log diffUK ONSUKGRABIQ
United KingdomIPIndex, levelM38log diffUK ONSUKIPMOM
United KingdomUnemployment rateLevel, percentM15log diffUK ONSUKUER
United KingdomRetail SalesLevelM20log diffUK ONSUKRVAMOM
United KingdomPMI ManufacturingIndexM2diffMarkitPMITMUK
CanadaGDPReal GDP, levelQ61log diffSTCACGE9ANN
CanadaIP (monthly GDP)Index, levelM60log diffSTCACAIPMOM
CanadaEmploymentLevelM7log diffSTCACANLNETJ
CanadaRetail SalesLevelM52log diffSTCACARSCHNG
CanadaIvey PMIIndexM6diffPMACIVEY
JapanGDPReal GDP, levelQ46log diffESRIJGDPAGDP
JapanIPIndex, levelM28log diffMETIJNIPMOM
JapanUnemployment rateLevel, percentM28log diffMICJNUE
JapanRetail SalesLevelM27log diffMETIJNRETMOM
JapanTankann SurveyIndexQ-4diffBoJJNTSMFG

2.1  News Surprises

Market participants watch, and react to, scheduled macroeconomic announcements because these announcements potentially contain new information that was not previously incorporated into market participants' expectations about the state of the economy. Several studies have looked into the forecast efficiency, or rationality, of market expectations. Under rationality, the surprise component, measured as difference between the actual release and its forecast, should truly represent "news," meaning that market agents optimally use available information in forming their forecasts, and therefore the forecast error should be orthogonal to information available when the forecast is produced. This is equivalent to testing whether the error term $ \varepsilon^{i} _{t}$ is orthogonal to the forecast $ y_{t}^{i,f} = E[y_{t}^{i}\vert\mathcal{F}_{t}] $ in the equation

$\displaystyle y^{i,f}_{t} = y_{t} +\varepsilon^{i} _{t}.$ (2)

In particular, testing for forecast efficiency boils down to testing that $ \alpha^{i} = \beta^{i} = 0$ in the regression

$\displaystyle s^{i}_{t} = \alpha^{i} +\beta^{i} y_{t}^{i,f} + u^{i}_{t}$ (3)

where $ s^{i}_{t} = y^{i}_{t} - y_{t}^{i,f}$ is the forecast error, a.k.a news surprise. This is sometimes known as the Mincer$ -$Zarnowitz test (Mincer and Zarnowitz 1969). Several earlier papers have applied these tests mainly using data revisions (among others, see Croushore and Stark (2001) and Faust, Rogers and Wright (2005)). Table 2 reports evidence from the baseline tests of forecast rationality $ -$ tests of the hypothesis that $ \alpha^{i} = \beta^{i} = 0$ in equation (3). As can be seen in the middle columns, $ \alpha^{i}$ and $ \beta^{i}$ are very often significantly different from zero and the F test fails to reject the null hypothesis that $ \alpha^{i} = \beta^{i} = 0$ only in 1/3 of the cases.

But given that Bloomberg median forecasts are not efficient, why are they so important? Why do I use them rather than using efficient forecasts that I could construct within the factor model? The answer is simple: financial markets react neither to my own private forecast nor yours; financial markets react to Bloomberg forecasts, which are public and everyone can see.

A wide literature has documented the asset price response to macroeconomic news announcements. Andersen, Bollerslev, Diebold and Vega (2003, 2007) and Gilbert, Scotti, Strasser and Vega (2012) among others have looked into this question. Table 3 displays the results of univariate regressions of foreign exchange returns on the individual macro announcement surprises over the sample period 2003-2012. These results do not necessarily correspond to what reported in the existing literature because of the different samples used. However, they clearly state the point that Bloomberg forecasts (and surprises) are important because financial markets react to them.

Table 2. Forecast Efficiency Regression Results

CountrySeries Name $ \mathbf{\alpha }$ $ \mathbf{ \beta }$Fpvalue
United StatesGDP-0.02-0.040.710.50
United StatesIP

-0.12***

0.27***6.620.00
United StatesEmployment

-12.94**

-0.06*4.000.02
United StatesRetail Sales-0.020.080.520.59
United StatesISM1.40-0.021.250.29
United StatesPersonal Income0.05-0.011.100.34
Euro areaGDP-0.010.11**2.760.08
Euro areaIP-0.06-0.16***4.490.01
Euro areaUnemployment0.040.000.210.81
Euro areaRetail Sales-0.12**-0.26*4.650.01
Euro areaPMI1.27-0.030.410.66
United KingdomGDP-0.15***0.27***6.130.01
United KingdomIP-0.23***-0.027.320.00
United KingdomUnemployment0.04-0.01**3.120.05
United KingdomRetail Sales0.20***-0.043.560.03
United KingdomPMI2.89-0.051.160.32
CanadaGDP0.05-0.010.110.90
CanadaIP-0.07***0.066.560.00
CanadaEmployment5.700.122.520.09
CanadaRetail Sales-0.060.26**2.660.07
CanadaIvey Survey15.95***-0.27***4.060.02
JapanGDP0.12-0.011.790.18
JapanIP-0.44***0.0610.410.00
JapanUnemployment0.29**-0.07**4.440.01
JapanRetail Sales0.130.25***3.800.03
JapanTankann0.170.010.220.80

* 10 percent significance, ** 5 percent significance, and *** 1 percent significance

Table 3. Results of Univariate Regressions in Which Exchange Rate Returns are Regressed on Each Individual Macroeconomic News Announcement Surpise (July 2003-Sept 2012), $ dlog(FX_{t})=\alpha +\beta \ast s_{t}^{i}+\varepsilon _{t}$

  Euro/$: Beta Euro/$: R2 GBP/$: Beta GBP/$: R2 CAD/$: Beta CAD/$: R2 JPY/$: Beta JPY/$: R2
US: IP 0.058 0.007 0.022 0.001 0.046** 0.005 -0.053 0.005
US: Employment 0.258*** 0.091 0.186*** 0.094 -0.058 0.008 0.377*** 0.210
US: Retail sales 0.033 0.003 0.091* 0.026 -0.097** 0.024 0.215*** 0.117
US: Personal income 0.013 0.000 -0.019 0.001 0.036 0.003 -0.057 0.010
US: PMI 0.021 0.001 0.010 0.000 -0.029 0.002 0.091** 0.022
US: GDP 0.139* 0.043 -0.106* 0.030 0.054* 0.006 0.025 0.002
Foreign: IP -0.107*** 0.033 -0.131*** 0.066 -0.029 0.002 0.114 0.021
Foreign: Employment/unemployment 0.133*** 0.035 -0.037 0.002 -0.260*** -0.124 0.023 0.002
Foreign: Retail sales -0.190*** 0.079 -0.131*** 0.044 -0.215*** 0.094 -0.067** 0.001
Foreign: PMI/Ivey/Tankann 0.014 0.000 -0.250*** 0.092 -0.120*** 0.025 -0.099* 0.029
Foreign: GDP -0.107 0.034 -0.394*** 0.295 -0.108 0.035 0.049 0.013

* 10 percent, ** 5 percent, and *** 1 percent significance with Newey-West standard errors.
Employment is used for US and CA, unemployment for EA, UK, and JA. IP, empl, rtsales, and pers.income have around 104-110 observations depending on the country. GDP has 35-36 observations. PMI observations vary the most: 110 (US), 64 (EA), 78 (UK), 102 (CA), 37 (JA, quarterly).


3  The Model

I use a standard dynamic factor model at a monthly frequency which explicitly accounts for missing data and temporal aggregation.

3.1  The Dynamic Factor Model

I model the unobserved factor as a VAR process of order $ p$:

$\displaystyle x_{t+1}$ $\displaystyle =$ $\displaystyle \Lambda x_{t}+\eta _{t},$ (4)
$\displaystyle \eta _{t}$ $\displaystyle \thicksim$ $\displaystyle i.i.d.N(0,\sigma _{\eta }).$ (5)

The model includes both monthly and quarterly variables. The monthly variables $ y_{t}^{M}$ follow a single factor model representation of the type:

$\displaystyle y_{t}^{M}$ $\displaystyle =$ $\displaystyle \mu ^{M}+Z^{M}x_{t}+\varepsilon _{t}^{M}$ (6)
$\displaystyle \varepsilon _{t}^{M}$ $\displaystyle =$ $\displaystyle \alpha \varepsilon _{t-1}^{M}+e_{t}^{M}$ (7)

where $ x_{t}$ represents the underlying real activity factor, $ \varepsilon _{t}$ is a vector of idiosyncratic components, and $ Z^{M}$ represent the factor loadings for the monthly variables. $ \varepsilon _{t}$ follows an $ AR(1)$ process, as shown in equation (7), and $ e_{t}^{M}\thicksim i.i.d.N(0,\Sigma _{e}^{M})$.

The quarterly variables $ y_{t}^{Q}$ follow a similar factor model representation:

$\displaystyle y_{t}^{Q}$ $\displaystyle =$ $\displaystyle \mu ^{Q}+Z^{Q}x_{t}+\varepsilon _{t}^{Q}$ (8)
$\displaystyle \varepsilon _{t}^{Q}$ $\displaystyle =$ $\displaystyle \rho \varepsilon _{t-1}^{Q}+e_{t}^{Q}$ (9)

with $ e_{t}^{Q}\thicksim i.i.d.N(0,\Sigma _{e}^{Q})$. Quarterly variables in the model are GDPs for all countries and the Japanese Tankan survey. I follow Mariano and Murasawa (2003) in the way I incorporate quarterly GDP into the monthly factor model. I define $ Y_{t}^{Q}=100\log (GDP)$, then

$\displaystyle y_{t}^{Q}=\left\{ \begin{array}{cl} Y_{t}^{Q}-Y_{t-3}^{Q} & \text{if }{t=3,6,9,12} \\ NA & \text{otherwise,} \end{array} \right.$ (10)

and using the Mariano and Murasawa (2003) approximation I get that for $ { t=3,6,9,12}$

$\displaystyle Y_{t}^{Q}-Y_{t-3}^{Q}\approx (Y_{t}^{M}+Y_{t-1}^{M}+Y_{t-2}^{M})-(Y_{t-3}^{M}+Y_{t-4}^{M}+Y_{t-5}^{M})=y_{t}+2y_{t-1}+3y_{t-2}+2y_{t-3}+y_{t-4}.$ (11)

Based on this I can link the quarterly variables to the monthly factor as

$\displaystyle y_{t}^{Q}$ $\displaystyle =$ $\displaystyle \mu ^{Q}+Z_{t}^{Q}x_{t}+2Z_{t}^{Q}x_{t-1}+3Z_{t}^{Q}x_{t-2}+2Z_{t}^{Q}x_{t-3}+Z_{t}^{Q}x_{t-4}$ (12)
    $\displaystyle +\varepsilon _{t}^{Q}+2\varepsilon _{t-1}^{Q}+3\varepsilon _{t-2}^{Q}+2\varepsilon _{t-3}^{Q}+\varepsilon _{t-4}^{Q} \notag$  

A similar treatment can be applied to any other quarterly series in the dataset.11

Stacking monthly and quarterly variables, this model can be easily cast in a state space representation:12

$\displaystyle y_{t}$ $\displaystyle =$ $\displaystyle \mu +Z\alpha _{t}$ (13)
$\displaystyle \alpha _{t}$ $\displaystyle =$ $\displaystyle T\alpha _{t-1}+u_{t},$  $\displaystyle u_{t}\thicksim i.i.d.N(0,\Sigma )$ (14)

where $ y_{t}=(y_{t}^{M},y_{t}^{Q})^{\prime },$ $ \mu =(\mu ^{M},\mu ^{Q})^{\prime }$ and the state vector includes both the common factor and the idiosyncratic components:

$\displaystyle \alpha _{t}=\left( x_{t},x_{t-1},x_{t-2},x_{t-3},x_{t-4},\varepsilon _{t}^{M},\varepsilon _{t}^{Q},\varepsilon _{t-1}^{Q},\varepsilon _{t-2}^{Q},\varepsilon _{t-3}^{Q},\varepsilon _{t-4}^{Q}\right) ^{\prime }$ (15)

We define the total number of indicators as $ n^{MQ}$. Of course, the model could be extended to a multiple factor model.

3.2  Forecast Weights

With the dynamic factor model approach described above, each of the real activity variables is used to extract information about the common (unobserved) factor. The contribution of each series to the determination of the factor represents the weight applied to construct the surprise index. As shown in Koopman and Harvey (2003), the weights $ w_{j}(\alpha_{t\vert t})$ are used to calculate the estimator of the state vector based on information available as of time $ t$ and can therefore be used to compute the contribution of variable $ y_{j}^{i}$ in forecasting the factor $ x~$at time $ t $:

$\displaystyle x_{t\vert t}=\sum_{j=1}^{t-1}w_{j}(\alpha_{t\vert t})y_{j}.$ (16)

As in the previous section, $ y_{t}$ can contain vectors of monthly or quarterly series $ (y_{t}^{M},y_{t}^{Q}).$ Each series is indicated by $ y^{i}. $

I consider the real-time release schedule of each real activity series $ y^{i} $. For example, if I want to calculate the factor for the month of March 2012, information about that month will be released gradually. In the United States, the ISM index will be the first series to be released, most likely followed by employment, retail sales, industrial production, and personal income. The advance reading of GDP for the first quarter (i.e. the one which includes January) will be released with an average delay of 29 days from the end of the quarter. Based on this real-time schedule, I can recursively compute the underlying unobserved factor at time $ t$ based on the data availability until day $ t$, that is $ x_{t\vert t}$. Equation (16) displays the factor at time $ t$ as a weighted average of the data $ y$ released between day $ 1$ and $ t.\ $The weights implicitly display a time decay feature with more recent data exhibiting higher importance in determining the factor.

For each data series included in $ y$, say $ y^{i}$, there exist a time series of weights $ w_{j}^{i}$, so that cumulative forecast weights can be computed as in Banbura and Rünstler (2010)

$\displaystyle w_{cum}^{i}=\sum_{j=1}^{t}w_{j}^{i}.$ (17)

Forecast weights do not depend on time $ t$, but depend on the forecast horizon and the real-time release pattern of the data. In this paper, I abstract from data revisions.

An alternative to using the forecast weights as outlined above, would be to use the weights as described in Banbura and Modugno (2010). In this case, the weights would have a different interpretation, as they would represent the contribution of the news releases to the factor revision from period $ t$ to $ t+1$. The Banbura and Modugno (2010) weights are represented by the $ b_{\nu+1,j}$ in:

$\displaystyle E[x_{t}^{i}\vert\Omega_{\nu+1}]-E[x_{t}^{i}\vert\Omega_{\nu}] = \sum_{j=1}^{J_{\nu+1}}b_{\nu+1,j} (y_t - E[y_{t}^{i}\vert\Omega_{\nu}])$ (18)

where $ E[x_{t}^{i}\vert\Omega_{\nu+1}]-E[x_{t}^{i}\vert\Omega_{\nu}]$ represents the revision to the factor implied by the new data release, $ (y_t - E[y_{t}^{i}\vert\Omega_{\nu}])$ is the news surprise, and $ \Omega_{\nu}$ and $ \Omega_{\nu+1}$ are two consecutive data vintages with $ \Omega_{\nu} \subset \Omega_{\nu+1}$. In the Banbura and Modugno (2010) framework, $ E[y_{t}^{i}\vert\Omega_{\nu}]$ is the model implied expectation of the variable $ y$, while in my framework $ E[y_{t}^{i}\vert\Omega_{\nu}]$ would be the Bloomberg expectation for the macro variable $ y$. The advantage of their set-up is that the weights represents the impact of the news release of a variable $ y$ on the underlying factor forecast, rather than the importance of the underlying series $ y$ in determining the factor. The drawback, however, is that the weight $ b$ is practically the Kalman gain and as such, this set-up does not provide me with a time series of the weights similar to what I have in my framework. A way to overcome this issue could be to apply some arbitrary time decay feature similar to what applied by Citigroup to construct the so-called "Citigroup Economic Surprise Indexes." These indexes are defined as weighted historical standard deviations of data surprises where the weights of economic indicators are derived from the announcement's impact that these data surprises have on foreign exchange markets to which a subjective decay function is applied.

3.3  The Surprise Index

I construct the surprise index starting from equation (16). With the idea that forecast weights represent the importance of the series in determining the underlying unobservable factor, I use those same weights to combine the standardized surprises so that the surprise index $ \mathcal{S} $ at time $ t$ is:

$\displaystyle \mathcal{S}_{t}=\sum_{j=1}^{t}w_{j}s_{j}$ (19)

where $ s_{j}=(s_{t}^{M},s_{t}^{Q})^{\prime }$ contains the vectors of the standardized surprise $ s^{i}$ corresponding to each data series $ y^{i}.$ In the application, I construct the underlying series that feed into the factor so that a higher (lower) number means that the economy is doing better (worse). Likewise, I construct each surprise such that a positive surprise means good (bad) news for the economy. This implies that the weights should be positive.

3.4  The Uncertainty Index

The uncertainty index is computed starting from equation (16) and averaging squared surprises

$\displaystyle \mathcal{U}_{t}=\sqrt{\sum_{j=1}^{t}w_{j}s_{j}^{2}}.$ (20)

The link with realized volatility is straightforward. Just like realized volatility is computed as the square root of the average of squared returns, $ RV_n=\sqrt{\frac{1}{n}\sum_{t=1}^{n}ret_{t}^{2}},$ the uncertainty index is computed as the square root of the weighted average of the squared surprises.13 The weights are not simply $ 1/n$ but are time varying. Moreover, unlike the volatility which is computed on one instrument at a time using the history from $ t=1,\ldots ,n$, the uncertainty index is computed across different instruments/surprises as well as across time.


4  Estimation

The construction of the indexes requires three steps:

(i)  estimation of the state space model of equations (13) and (14),

(ii)  determination of the weights $ w_{j}$ as defined in equation (16) and

(iii)  construction of the indexes as for equations (19) and (20).

For step (i), the estimation of the model in equations (13) and (14) requires estimation of the parameters $ \theta =\{\mu ,Z,T,\Sigma \}$. The missing data pattern complicates the estimation of the model. Missing data occur both because the data are at different frequencies and because indicators are released at different times after the end of the reference period (ragged edge). A number of papers have dealt with different frequencies and missing observations either within a Kalman filter framework (see among others Aruoba, Diebold, and Scotti (2009), Giannone, Reichlin and Small (2008), and Banbura and Modugno (2010)) or within a mixed data sampling (MIDAS) regression framework (Andreou, Kourtellos, and Ghysels (2011)). I estimate the parameters by maximum likelihood implemented by the Expectation Maximization (EM) algorithm as proposed by Doz, Giannone, and Reichlin (2012) and extended by Banbura and Modugno (2010) to deal with missing observations and idiosyncratic dynamics.14 The EM algorithm iterates over two steps: in the expectation step, the log-likelihood conditional on the data is calculated using the estimated parameters from the previous iteration; in the maximization step, the parameters are re-estimated by maximizing the expected log-likelihood with respect to $ \theta .\ $Following Doz, Giannone, and Reichlin (2011, 2012), the initial parameters $ \theta (0)$ are obtained through principal components and the iteration between the two steps is stopped when the increase in likelihood between two steps is small.

In step (ii), once the parameters $ \theta \ $are estimated, the weights can be computed by running the algorithm defined in Koopman and Harvey (2003) to get the smoothed weights. The history of weights $ w_{j}(\alpha _{t\vert t})~$for $ j=1,...,t$ is computed in real time for any $ t$ based on the information available up until that time.

Finally, in step (iii), the surprise and uncertainty indexes are computed based on (19) and (20).

Each country is estimated separately. The estimation of the underlying business condition index is based on the longest common sample across countries (1980-2012), except for the euro area for which not enough indicators are available before 1985. The Kalman filter is then run based on the estimated parameters in a real time framework (i.e. based on data that are released sequentially), and steps (ii) and (iii) are repeated to get the smoothed weight matrix and the real-time surprise and uncertainty indexes for each day from May 15, 2003 to September 30, 2012.15 Step (i) is run over the entire sample, unlike steps (ii) and (iii), because for countries in which data series become available later in the sample estimates are not accurate at first.16 For the United States, where there are no issues of data availability, there are no significant differences in the surprise indexes constructed according to the two methodologies. 17


5  Results

Here I discuss the results following the steps described in the estimation section.

5.1  Real Activity Indexes

The real activity indexes that I estimate based on the indicators listed in table 1 are displayed in figure 1. As mentioned, I use a longer history for the estimation of these factors in order to have more reliable estimates. The figure shows the latest factors, which include information as of September 30, 2012, for the United States, the Euro Area, the United Kingdom, Canada, Japan, and an aggregate of the five countries.

The average value of each index is zero by construction. Therefore, a value of zero is interpreted as average economic activity for that country, whereas progressively bigger positive values indicate progressively better-than-average conditions and progressively more negative values indicate progressively worse-than-average conditions. Importantly, average conditions differ across countries. For example, a value of zero for Japan corresponds to a number akin to 0.7 percent annual real GDP growth while a value of zero in the United States corresponds to around 2.5 percent annual real GDP growth. The shaded areas in the panels represent official recessions as defined by the NBER, CEPR, and ECRI. The indexes fall sharply during recessions and tend to reach relatively high values during good times, for example the late 1990s. As expected, the U.S. business condition index is very similar to the Aruoba, Diebold, and Scotti (ADS) index maintained by the Federal Reserve Bank of Philadelphia, with the difference that the ADS index is daily and also includes weekly data such as initial jobless claims. Because the other countries do not have relevant weekly data, I opted here for a monthly frequency. The last panel shows the aggregate business condition index, which is created by aggregating the other indexes weighing them by each country's GDP.

Table 4. Average cumulative weights for each indicator used to construct the surprise index. For comparability across countries, weights are standardized so that the sum of all weights in each country is equal to 1. The average is computed over the last five years of the sample when all the indicators are available.

  United States Euro area United Kingdom Canada Japan
GDP 0.04 0.06 0.13 0.00 0.01
IP 0.35 0.31 0.39 0.02 0.57
Employment/Unemployment 0.30 0.40 0.30 0.92 0.17
Retail Sales 0.14 0.15 0.11 0.01 0.13
PMI 0.12 0.09 0.08 0.04 0.12
Personal Income 0.05        

5.2  Weights

To gauge the importance of the various indicators in constructing the surprise and uncertainty indexes, I consider two different standpoints in analyzing the weights: (i) I construct the cumulative weights as in equation (17) and (ii) I analyze, at each time $ t,$ the vector of $ t\times 1$ weights, $ w_{t}^{j}$, that are multiplied by the announcements to get the time $ t$ surprise index based on equation (19).

To be clear, for $ t=\widetilde{t}$, the variable $ w$ that represents the weights in equation (19) is a matrix of dimension $ \widetilde{t}\times MQ$ which contains those weights applied to all the announcements available up to time $ \widetilde{t}$ that are used in the construction of the index. The sum of these weights over time represents the cumulative weight for indicator $ i$ at time $ \widetilde{t}$, that is $ w_{cum}^{i}=\sum_{j=1}^{\widetilde{t}}w_{j}^{i}$.

The average cumulative weights are reported in table 4. 18 The weights are averages because I calculate the mean of $ w^{cum}$ over the last five years of the sample. The choice of the five years is arbitrary to some extent and is linked to the availability of PMI data in the euro area and in the United Kingdom.19 Based on this measure, employment (or unemployment) and industrial production have the highest weight in the United States, the Euro Area, and in the United Kingdom. In Canada, most of the weight (92 percent) is concentrated on employment. In Japan, industrial production is the most important series followed by unemployment and retail sales.

Cumulative weights, however, are not constant over time and therefore looking at their mean is not enough. They are affected by the pattern of missing observations due to the different release schedule of the underlying indicators (ragged edge). Figure 2 shows the evolution of the cumulative forecast weights $ w_{cum}^{i}\ $for each indicator over the first quarter of 2012. Each panel in the figure displays the weights for a specific country. A clear pattern stands out: as soon as new information about an indicator becomes available, the contribution of that particular indicator increases. So, for example, the weight of the U.S. nonfarm payroll series (NFP), represented by the green line in the top leftmost panel, increases on January 6, February 3, and March 9 (solid vertical lines) when the December, January and February figures are announced. Until the IP numbers are released (dotted vertical lines), nonfarm payroll has the biggest weight. With the release of the IP figures, the weight for IP (red line) increases and becomes the highest of all. However, as additional information about real activity in the United States is released, nonfarm payroll and IP weights start to decline gradually. A similar pattern can be observed in the other countries: as the more timely information becomes available, its weight jumps up and it declines as other indicators are subsequently released. In the euro area (the top rightmost panel), unemployment tends to have the highest weight overall, but when IP numbers are released, IP weights become slightly bigger than those of the unemployment data. In the United Kingdom, IP weights are always bigger than any other weight. In Canada unemployment is consistently and by far the highest weight. Finally, in Japan, the Tankan survey has the highest weight at the beginning of the quarter when it represents the only available information for that quarter, but its weight is immediately overtaken as other information become available and, in particular, as IP numbers are released.

Turning to (ii), figure 3 shows the weights $ w$ when computed on March 31, 2012 for the six months prior to that day.20 The weights in all the countries display a time decay feature. For the United States, nonfarm payroll and IP (the green and red bars) have the highest weight for the month of February based on information as of March 31, 2012. Interestingly, IP weights are more persistent than the others, suggesting that past IP information continues to be important whereas the nonfarm payroll information value is limited to the latest available month. Because no data about March are released as of March 31, all the weights are zero for the month of March. Weights are close to zero for all indicators after about six months. Of note, the time decay feature implies that an increase in the index might be due to a smaller weight given to an old negative surprise or to a new positive surprise.

The Euro Area represents an interesting case because as of March 31, 2012, flash euro-area PMI numbers for February and March are available, whereas any other real activity information refers to January. While past PMI numbers have a very small weight, the February and March PMI figures have a relatively high weight. Once more, the weights for IP are the slowest to decline and the last available unemployment data displays the highest weight.

The United Kingdom seems to have the slowest time decay in its weights compared to the other countries. In Canada, the employment weights dominate every other weight. Japan displays the quickest time decay with weights reaching practically zero already after only four months. Unlike the other countries, unemployment does not have the highest weight.

These weights are computed based on the available information as of March 31, 2012. Of course, the pattern would be different if the weights were to be computed on another day when different information was available.

5.3  Surprise Indexes

The news surprise indexes for the United States, the Euro area, the United Kingdom, Canada, Japan, and the aggregate of the five countries are displayed in figure 4 (solid lines).21 A positive (negative) reading of the surprise index suggests that economic releases have on balance been higher (lower) than consensus, meaning that agents were more pessimistic (optimistic) about the economy. A positive number does not mean the economy is doing well on any ordinary measure, but merely that economic forecasts were overly pessimistic. The surprise index reaches its lowest value during the global financial crisis of 2008-2009 in all the countries. This suggests that, as the crisis was unfolding, agents were less pessimistic about its possible outcome and its impact on the real economy, while the actual data turned out to depict a grimmer picture of the stance of economic activity around the globe.

The euro-area surprise index dropped sharply in March 2012. As agents became more optimistic on a resolution of the European debt crisis with the bond exchange taking place in Greece, real activity indicators for 2012 that were released in March were disappointing. The January unemployment rate, released on March 1, was 10.70 percent versus an expectation of 10.40 percent. The February and March euro-area PMIs released on February 22 and March 22 were 49.70 and 48.70 respectively, versus expected values of 50.50 and 49.60, respectively. Finally, based on data released on March 14, euro-area industrial production increased 0.2 percent from December 2011 to January 2012 versus an expectation of a 0.5 increase.

Interestingly, the U.K. index dropped sharply on January 25, 2011 when a very disappointing Q4 GDP for 2010 was released (-0.5 percent versus an expectation of +0.5 percent). Although subsequent data helped the index to move higher, it continued to be depressed until the second half of 2011. Agents reportedly attributed the slowdown to a series of temporary factors (such as bad weather, the Japanese earthquake, and the royal wedding) that were believed to be short-lived. The transitory nature of these events most probably made agents mark up their economic outlook, but as a series of temporary factors occurred, these expectation were always disappointed.

The Japanese surprise index dropped sharply on April 27, 2011 as the actual number for IP turned out to be a lot lower than expected following the March 2011 earthquake: IP decreased 15.30 percent between February and March versus the expectation of a 10.60 percent decrease.

On the other hand, there are also several instances where the surprise indexes are positive, especially coming out of the recession in the United States, the United Kingdom, and Canada.

For comparison, the dotted lines in figure 4 show the Citi Economic Surprise Indexes (CESI). Although CESIs also measure economic news, they are constructed based on a different methodology. CESIs are defined as weighted historical standard deviations of data surprises (actual releases versus Bloomberg median survey) and are calculated daily in a rolling three-month window. The weights of the economic indicators are derived from relative high-frequency spot foreign exchange impacts of 1 standard deviation data surprises adjusted to include a time decay feature so as to replicate the limited memory of markets. Because the index constructed in this paper does not rely on the impact that macroeconomic surprises have on asset prices, it represents a more objective measure of deviation from consensus expectations. Although the two indexes follow very similar patterns for all the countries, they also present some differences because both the set of indicators and the weights are different. For example, the euro-area surprise index tends to lag the CESI especially during the shaded area which represents the 2008-2009 recession.

5.4  Uncertainty Indexes

The uncertainty indexes for the United States, the Euro area, the United Kingdom, Canada, Japan and the aggregate of the five countries are displayed in figure 5 (solid lines). These indexes measure how uncertain agents are about current real activity conditions. A greater (smaller) reading of the uncertainty index suggests that agents have on balance been more (less) uncertain about the state of the economy. The indexes tend to be elevated during recessions, although there are other episodes when the indexes spike up. In the United States, economic uncertainty was also relatively high in 2004 and a big jump was observed at the end of 2005. The euro-area uncertainty index reaches its highest values just before and after the 2008-2009 recession, suggesting that agents were more uncertain about the economy as the euro-zone was entering and exiting the recession. Increased macro uncertainty characterized also the beginning of 2010 when the Greece "problem" started to be in prime time and the period between the end of 2011 and the start of 2012. Uncertainty in the United Kingdom has been particularly elevated since early 2009, when compared to its value in the first part of the sample. Canada has experienced several episodes of elevated economic uncertainty, whereas in Japan, the period after the March 2011 earthquake was by far the one with the highest uncertainty regarding the state of the Japanese economy.
The dotted lines in the panels show stock market implied volatilities in the United States, Euro Area, United Kingdom, Canada, and Japan as represented by the VIX, VSTOXX, VTFSE, VIXC and VXJ. The dashed lines display the stock market realized volatilities for the respective countries. Notably, especially in the latter part of the sample, the uncertainty index and the VIX are very similar, whereas the uncertainty index of the euro area differs somewhat from the VSTOXX. The two measures (implied volatility and uncertainty index) are constructed in completely independent ways. Implied volatility, a forward-looking measure, is computed from option prices. The uncertainty index, a historical measure, is calculated from current and past macroeconomic news surprises. The former is a wider measure that combines information about risk aversion and future stock market volatility, and to the extent that these two move with news surprises, the VIX also contains information about current and future economic uncertainty. On the other hand, the uncertainty index presented here is a clean measure of agents' uncertainty about the current state of the economy.


6  Applications

In this section, I present a couple applications for the surprise and uncertainty indexes. In the first application, the surprise index is shown to preserve the properties of the underlying macro series in affecting asset prices in replicating the regressions shown in table 3. Combining several macro series into one, the surprise index has the advantage of being potentially easier to use and very parsimonious. In light of this, Demiralp, King, and Scotti (2013) make use of it as a control variable when investigating the effects of political commentaries on policy rate decisions and policy expectations in the United States and the Euro Area, and find it to be significant determinant of policy expectations. Similarly, Brunetti, Buyuksahin, and Harris (2013) employ it as a control variable in studying the impact of speculation activity in the crude oil market.

In the second application, the U.S. uncertainty index is compared to other uncertainty measures commonly used in the literature. The uncertainty index has a negative impact on real-activity series. Papers like Bloom (2009), Baker, Bloom, and Davis (2013), and Bachmann, Elstner, and Sims (2013) have documented a similar analysis with different measures of uncertainty. I find that, in the United States over the last decade, when uncertainty is strictly related to the state of the economy as measured by real activity, it has a potentially milder impact on macro activity than when the uncertainty is related to both the macro and the financial sectors as measured by the VIX.

Table 5. Results of univariate regressions in which exchange rate returns are regressed on the surprise index (July 2003 - Sept 2012): $ dlog(FX_{t})=\alpha +\beta \ast d(\mathcal{S} _{t})+\varepsilon _{t}$

 

Euro/$: $ \mathbf{\beta }$
Euro/$: R2

GBP/$: $ \mathbf{\beta }$

GBP/$: R2
CAD/$: $ \mathbf{\beta }$
CAD/$: R2
JPY/$: $ \mathbf{\beta }$
JPY/$: R2
US surprise index 0.362*** 0.022 0.263*** 0.014 -0.096 0.002 0.418*** 0.031
Foreign surprise index -0.332*** 0.013 -0.140 0.007 -0.691*** 0.042 0.128 0.002

* 10 percent, ** 5 percent, and *** 1 percent significance with Newey-West standard errors.

6.1  Surprise Indexes and News Impact on Foreign Exchanges

As shown in section 2, macroeconomic news announcement affect asset prices. The surprise index presented in this paper represents a nice summary measure that can be used to parsimoniously control for news announcement surprises in more general models.

Table 5 presents the results of a set of regression where the euro/$, GBP/$, CAD/$, and JPY/$ exchange rate returns are regressed on the U.S. surprise index and the respective foreign surprise index, i.e. the euro/$ return is regressed on the U.S surprise index and the euro-area surprise index, the GBP/$ return is regressed on the U.S surprise index and the U.K. surprise index, etc. I cover approximately the sample period for which the surprise indexes are available (July 2003 to Sept. 2012).22 As shown in the table, the surprise indexes tend to have the right sign and be significant: a positive change in the U.S. surprise index (i.e. the U.S. economy doing better than expected) appreciates the U.S. dollar versus the foreign currency, whereas a positive change in the foreign surprise index depreciated the U.S. dollar.

6.2  Uncertainty Measures and the Business Cycle

A "true" measure of economic uncertainty does not exist and stock market realized and implied volatilities have been commonly used as proxies for uncertainty. Bloom (2009), for example, uses the Chicago Board of Option Exchange VXO index as a proxy for uncertainty.23 More recently, a growing literature has focused on finding new measures of macroeconomic uncertainty. Bachmann, Elstner and Sims (2012) use survey expectation data to construct time-varying business-level uncertainty. For Germany and the United States, they construct a measure of uncertainty with forecast disagreement from the IFO Business Climate Survey and the Business Outlook Survey, respectively. Baker, Bloom, and Davis (2013) create an economic policy uncertainty (EPU) measure based on the frequency of newspaper references to economic policy uncertainty, the number and size of the federal tax code provisions set to expire in future years, and the disagreement among economic forecasters about policy relevant variables. Leduc and Liu (2012) use a measure of perceived uncertainty of consumers and businesses from the Thomson Reuters/University of Michigan Surveys of Consumers in the United States and the Confederation of British Industry (CBI) Industrial Trends Survey in the United Kingdom. Jurado, Ludvigson, and Ng (2013) define uncertainty as the variability in the purely unforecastable component of the future value of a variable and measure macro uncertainty as the uncertainty factors common to individual measures of uncertainty across a large number of series. Similarly to Jurado et al. (2013), my measure uses forecast errors, which however are not the objective and efficient forecast errors from a model. Instead they are market based forecast errors and as such my uncertainty index measures the perceived uncertainty about the state of the economy. Agents base decisions on their perceived uncertainty rather than an objective uncertainty that they do not observe.

Figure 6 compares the real-activity uncertainty index developed here against some of the available other measures of uncertainty for the United States. All measures are de-meaned and standardized for comparison; they are all countercyclical, rising during economic downturns. Their pairwise correlations range from about 20-25 percent between the uncertainty index and Baker, Bloom, and Davis or Bachmann, Elstner, and Sims to over 50 percent between the uncertainty index and the VIX.24 The uncertainty index exceeds 1.65 standard deviations above its mean only three times but the peaks do not always correspond with the peaks of the other series suggesting that these uncertainty measures might indeed carry slightly different information.

A growing literature has also focused on analyzing the relationship between real activity and uncertainty, and the latter has been generally found to have a significant role in firms' hiring decisions (employment) and output. To estimate such effects, I estimate a bivariate VAR with log employment and each one of the uncertainty proxies from figure 6, separately. Because of the short data set (monthly data from May 2003 to September 2012), the bivariate VAR represents a parsimonious way to model the joint dynamics between these variables. As shown in Bachmann, Elstner and Sims (2013), the results are robust to estimating a larger VAR similar to Bloom (2009).25 Each VAR is estimated selecting the lag length based on the Schwarz Information Criterion; employment enters in log levels, while uncertainty measures in levels.

Figure 7 shows the recursive impulse responses of employment to a one-standard-deviation uncertainty shock as measured by the different proxies, where uncertainty is ordered first. The shaded region is the +/- one standard error confidence interval for the real-activity uncertainty shock. Employment decreases after an uncertainty shock between 0.9 and 1.2 percent on average at its trough, with the exception of the Baker, Bloom and Davis EPU measure which shows a lower impact over this period. As shown in figure 8 by the confidence intervals for the real-activity uncertainty index and the VIX, when uncertainty is strictly related to real activity, it has potentially milder impact on economic activity. Just flipping the argument, when uncertainty is more generally related to economic as well as financial conditions as measured by the VIX, its impact on real-activity variables appears to be stronger and more prolonged. This finding supports recent work by Caldara, Fuentes-Albero, Gilchrist and Zakrajsek (2013) which finds that the financial channel is key in the transmission of uncertainty shocks. Although I do not explicitly introduce a financial channel, using the real-activity uncertainty index and the VIX allows me to distinguish between purely macro versus the more general macro and financial uncertainty.

For robustness, some alternative specifications are considered. The result just described holds true with other measures of real activity, such as industrial production or unemployment rate. Although a similar comparison is not shown for the other countries, the negative impact of an uncertainty shock on employment is generally significant across countries. A part of the uncertainty literature, considers uncertainty as a consequence of depressed economic activity, rather than a cause. In this case, the recursive identification scheme implemented above should be inverted. As a robustness check, I estimate generalized impulse responses from Pesaran and Shin (1998) which do not depend on the ordering of the variables and the results actually remain quite consistent across uncertainty proxies and variables.


7  Summary and Concluding Remarks

The goal of this paper is to construct measures of (i) real-time economic news and their deviation from consensus expectations and (ii) real-time uncertainty about the state of the economy. I view this paper as a "complement" to the Aruoba, Diebold and Scotti (2009) business condition index updated on a daily basis by the Federal Reserve Bank of Philadelphia. While the ADS index is a real time measurement of the state of the economy, the surprise index presented in this paper measures agents' optimism or pessimism about the economy by combining macroeconomic news surprises, and the uncertainty index measures agents' uncertainty about the current state of the economy. This paper is also a "complement" to other papers that develop uncertainty measures in that it only measures perceived uncertainty about the state of the economy and as such is mostly linked to Bachmann, Elstner, and Sims (2013).

I look forward to a variety of variations and extensions of this basic theme, including but not limited to:

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Appendix - The State Space Representation

We report below the details of the state space representation as specified by equations (13) and (14) when the only quarterly variable is GDP:

$\displaystyle \underset{y_{t}}{\underbrace{\left[ \begin{array}{c} {\small y}_{t}^{M} \\ {\small y}_{t}^{Q} \end{array} \right] }}=\underset{Z}{\underbrace{\left[ \begin{array}{c} {\small\mu }^{M} \\ {\small\mu }^{Q} \end{array} \right] +\left[ \begin{array}{ccccccccccc} {\small Z}^{M} & {\small0} & {\small0} & {\small0} & {\small0} & {\small I}_{n^{M}} & {\small0} & {\small0} & {\small0} & {\small0} & {\small0} \\ {\small Z}^{Q} & {\small 2Z}^{Q} & {\small 3Z}^{Q} & {\small 2Z}^{Q} & {\small Z}^{Q} & {\small0} & {\small 1} & {\small 2} & {\small 3} & {\small 2} & {\small 1} \end{array} \right] }}\underset{\alpha _{t}}{\underbrace{\left[ \begin{array}{c} {\small x}_{t} \\ {\small x}_{t-1} \\ {\small x}_{t-2} \\ {\small x}_{t-3} \\ {\small x}_{t-4} \\ {\small\varepsilon }_{t}^{M} \\ {\small\varepsilon }_{t}^{Q} \\ {\small\varepsilon }_{t-1}^{Q} \\ {\small\varepsilon }_{t-2}^{Q} \\ {\small\varepsilon }_{t-3}^{Q} \\ {\small\varepsilon }_{t-4}^{Q} \end{array} \right] }}$
$\displaystyle \left[ \begin{array}{c} {\small x}_{t} \\ {\small x}_{t-1} \\ {\s... ...^{Q} \\ {\small0} \\ {\small0} \\ {\small0} \\ {\small0} \end{array} \right] }}$

with $ n^{M}$and $ n^{Q}$ representing the number of monthly and quarterly variables, $ \varepsilon _{t}^{M}=\left( \varepsilon _{t}^{1^{M}},...,\varepsilon _{t}^{n^{M}}\right) ^{\prime }, e_{t}^{M}=\left( e_{t}^{1^{M}},...,e_{t}^{n^{M}}\right) ^{\prime },$ $ \varepsilon _{t}^{Q}=\left( \varepsilon _{t}^{1^{Q}},...,\varepsilon _{t}^{n^{Q}}\right) ^{\prime }$ and $ e_{t}^{Q}=\left( e_{t}^{1^{Q}},...,e_{t}^{n^{Q}}\right) ^{\prime }$ . Because we are considering the case of only one quarterly variable, $ \varepsilon _{t}^{Q}=\left( \varepsilon _{t}^{1^{Q}}\right) $ and $ e_{t}^{Q}=\left( e_{t}^{1^{Q}}\right) .~$Also $ Z^{M}=\left( Z^{1^{M}},...,Z^{n^{M}}\right) $ and

$\displaystyle Var(u_{t})=\Sigma =\left( \begin{array}{ccccc} {\small\sigma }_{\eta } & & {\small\cdots } & & {\small0} \\ & {\small0} & & & \\ {\small\vdots } & & {\small\Sigma }_{e}^{M} & & {\small\vdots } \\ & & & {\small\sigma }_{e}^{Q} & \\ {\small0} & & {\small\cdots } & & {\small0} \end{array} \right)$     with % latex2html id marker 5428 $\displaystyle \Sigma _{e^{M}}=\left( \begin{array}{ccc} {\small\sigma }_{e^{1^{M}}} & {\small0} & {\small0} \\ {\small0} & {\small\ddots } & {\small0} \\ {\small0} & {\small0} & {\small\sigma }_{e^{n^{M}}} \end{array} \right) .\footnote{ We use the notation $\Sigma $\ to indicate a variance-covariance matrix and $ \sigma $\ to indicate its elements. \ }$   26 

The parameters to be estimate are

$ \theta =\left\{ {\small\mu } ^{M}{\small ,\mu }^{Q}{\small ,Z}^{M}{\small ,Z}^{Q}{\small ,\Lambda ,\alpha }_{1}{\small ,...,\alpha }_{n^{M}}{\small ,\alpha }_{Q}{\small ,\sigma } _{\eta }{\small ,\sigma }_{e^{1}}^{M}{\small ,...,\sigma }_{e^{n^{M}}}^{M} {\small ,\sigma }_{e}^{Q}\right\} .$

Figure 1: Real activity indexes (factors) for the United States, Euro Area, United Kingdom, Canada, Japan, and aggregate of the five countries.

Figure 1: Data for Figure 1 immediately follows.

Data for Figure 1

DATES      F1B_US     F1B_EU     F1B_UK     F1B_CA     F1B_JA     SCOTTI.RTI.M.AE2
Jan-80-2.830-3.46-0.090.09-0.96
Feb-80-2.30-3.06-0.040.65-0.78
Mar-80-2.640-2.62-0.12-0.2-0.89
Apr-80-3.550-2.35-0.1-0.2-1.21
May-80-3.80-2.07-0.37-0.17-1.3
Jun-80-2.590-1.850.09-0.12-0.81
Jul-80-1.330-1.810.31-0.51-0.45
Aug-800.680-1.880.87-0.710.15
Sep-801.490-1.811.360.120.45
Oct-802.250-1.661.21-0.20.69
Nov-802.010-1.521.11-0.490.58
Dec-801.130-1.261.1-0.050.32
Jan-810.270-0.971.4700.07
Feb-81-0.170-0.781.37-0.29-0.09
Mar-81-0.250-0.580.72-0.04-0.11
Apr-81-0.520-0.490.57-0.03-0.12
May-81-0.220-0.260.39-0.23-0.06
Jun-810.400.01-0.040.40.13
Jul-810.3600.14-0.650.40.13
Aug-81-0.3900.05-0.750.26-0.19
Sep-81-1.4200.01-1.090.19-0.54
Oct-81-2.070-0.09-1.310.24-0.72
Nov-81-2.550-0.32-1.420.07-0.88
Dec-81-2.690-0.28-1.73-0.08-0.88
Jan-82-2.480-0.2-1.76-0.18-0.86
Feb-82-0.9300.08-1.85-0.15-0.39
Mar-82-1.1900.21-2.03-0.15-0.5
Apr-82-1.400.22-2.45-0.31-0.58
May-82-1.1800.09-2.66-0.29-0.56
Jun-82-1.580-0.11-2.76-0.2-0.6
Jul-82-1.740-0.18-2.48-0.18-0.68
Aug-82-1.530-0.15-2.220.01-0.56
Sep-82-1.410-0.15-1.79-0.31-0.48
Oct-82-1.420-0.13-1.39-0.47-0.42
Nov-82-0.8400-0.950.24-0.24
Dec-82-0.2200.28-0.28-0.320
Jan-830.7300.450.27-0.540.31
Feb-830.4400.460.65-0.090.23
Mar-831.2600.31.110.40.51
Apr-831.700.321.240.220.66
May-831.8100.361.180.40.7
Jun-831.9700.311.440.70.77
Jul-832.1300.441.430.20.8
Aug-831.0200.461.210.320.48
Sep-833.2300.420.720.641.19
Oct-832.0100.420.010.340.74
Nov-831.8900.36-0.170.430.69
Dec-831.9800.26-0.10.580.74
Jan-842.1600.23-0.170.570.81
Feb-841.880-0.260.060.720.7
Mar-841.340-0.580.010.280.51
Apr-841.470-0.650.150.240.52
May-841.160-0.610.730.510.42
Jun-841.050-0.3810.260.43
Jul-840.610-0.250.640.310.33
Aug-840.3500.040.170.460.21
Sep-840.4100.290.180.10.24
Oct-840.3700.440.20.270.19
Nov-840.600.520.270.30.25
Dec-840.1900.730.610.290.16
Jan-850.260.410.860.780.470.65
Feb-850.160.410.870.650.020.52
Mar-850.380.460.920.650.010.53
Apr-850.180.510.790.770.410.46
May-850.280.530.60.740.190.45
Jun-850.080.520.280.62-0.240.3
Jul-850.110.47-0.070.750.220.29
Aug-850.440.34-0.040.64-0.20.36
Sep-850.520.150.030.55-0.510.38
Oct-850.17-0.100.81-0.040.19
Nov-850.4-0.520.071.06-0.210.18
Dec-850.53-0.420.110.9-0.190.12
Jan-860.13-0.30.360.63-0.07-0.04
Feb-86-0.340.080.490.34-0.12-0.03
Mar-86-0.390.530.440.38-0.40.18
Apr-86-0.10.850.440.57-0.360.42
May-86-0.020.840.240.06-0.050.41
Jun-86-0.340.640.270.07-0.090.16
Jul-860.430.360.28-0.1-0.460.32
Aug-860.310.090.45-0.17-0.270.17
Sep-860.62-0.170.68-0.110.30.18
Oct-860.11-0.410.660.02-0.15-0.07
Nov-860.23-0.620.490.08-0.42-0.1
Dec-860.34-0.880.430.110.06-0.12
Jan-870.03-0.530.40.41-0.11-0.22
Feb-870.69-0.080.550.690.210.24
Mar-870.770.420.60.930.350.59
Apr-870.870.820.591-0.030.71
May-870.810.950.851.01-0.150.73
Jun-870.770.950.950.830.890.76
Jul-871.070.890.960.730.860.86
Aug-870.960.860.860.790.670.73
Sep-870.950.860.70.991.040.59
Oct-871.511.010.731.121.080.5
Nov-8710.680.771.010.780.47
Dec-870.860.540.790.980.640.52
Jan-880.20.650.820.70.60.34
Feb-880.720.430.70.540.710.68
Mar-880.550.450.60.280.440.48
Apr-880.490.560.580.050.760.53
May-880.330.720.61-0.070.330.53
Jun-880.521.060.74-0.030.340.78
Jul-880.260.910.79-0.030.180.69
Aug-880.130.90.72-0.010.340.56
Sep-880.411.110.580.150.770.69
Oct-880.691.060.410.430.30.71
Nov-880.770.810.40.670.50.74
Dec-880.720.830.320.930.450.81
Jan-890.451.080.250.940.380.7
Feb-890.080.830.280.560.20.5
Mar-8900.780.220.280.420.41
Apr-89-0.130.940.31-0.190.080.29
May-89-0.450.650.12-0.250.250.22
Jun-89-0.370.740.14-0.140.290.13
Jul-89-0.420.450.23-0.07-0.240.15
Aug-89-0.120.530.290.110.160.2
Sep-89-0.060.920.2-0.10.090.25
Oct-89-0.240.880.11-0.150.130.19
Nov-890.171.20.21-0.020.280.48
Dec-890.151.040.20.050.150.43
Jan-900.421.20.170.21-0.390.34
Feb-900.460.80.140.090.20.35
Mar-900.250.470.18-0.280.780.23
Apr-90-0.220.520.13-0.50.21-0.09
May-90-0.220.16-0.18-0.740.220.09
Jun-90-0.410.14-0.52-0.590.16-0.05
Jul-90-0.70.31-0.76-0.840.57-0.23
Aug-90-1.120.38-0.91-1.050.37-0.7
Sep-90-1.310.39-0.99-1.3-0.21-0.74
Oct-90-1.910.5-0.93-1.74-0.06-0.73
Nov-90-2.090.24-1.03-1.990.23-0.8
Dec-90-1.90.51-1.07-20.06-0.74
Jan-91-1.850.57-1.08-1.870.15-0.71
Feb-91-1.560.06-1.14-1.65-0.05-0.61
Mar-91-0.9-0.32-1.18-1.08-0.44-0.52
Apr-91-0.43-0.58-0.98-0.270.19-0.36
May-910.02-0.3-0.8-0.070-0.07
Jun-910.32-0.29-0.75-0.33-0.5-0.1
Jul-91-0.25-0.79-0.76-0.61-0.22-0.34
Aug-91-0.25-0.37-0.67-0.71-0.2-0.3
Sep-91-0.18-0.17-0.48-0.85-0.31-0.13
Oct-91-0.510.39-0.27-0.91-0.24-0.06
Nov-91-0.590.36-0.24-1.14-0.5-0.06
Dec-91-0.370.57-0.26-1.13-0.640.05
Jan-92-0.070.51-0.25-1.13-0.560.1
Feb-920.27-0.18-0.28-1.14-0.40.07
Mar-920.52-0.63-0.26-1.12-0.77-0.22
Apr-920.62-1.26-0.28-0.94-0.6-0.34
May-920.51-1.49-0.26-0.76-0.57-0.29
Jun-920.24-1.58-0.04-0.74-0.07-0.53
Jul-920.26-1.470.06-0.68-0.46-0.52
Aug-920.15-1.280.09-0.83-0.74-0.52
Sep-920.11-1.270.12-0.60.1-0.52
Oct-920.55-1.280.05-0.42-0.6-0.37
Nov-920.54-1.590-0.37-0.82-0.35
Dec-920.45-1.960-0.14-0.32-0.27
Jan-93-0.3-2.010.150.010.09-0.3
Feb-93-0.33-1.690.2-0.1-0.17-0.33
Mar-93-0.4-1.420.16-0.27-0.38-0.5
Apr-930.48-1.030.17-0.510.2-0.21
May-930.28-0.990.25-0.34-0.1-0.17
Jun-930.07-0.710.26-0.13-0.4-0.18
Jul-930.32-0.490.38-0.12-0.350.11
Aug-930.19-0.240.38-0.02-0.360.14
Sep-930.53-0.270.410.01-0.410.14
Oct-930.91-0.490.5-0.12-0.420.28
Nov-931.05-0.060.57-0.01-0.210.36
Dec-931.14-0.020.62-0.26-0.350.61
Jan-940.320.190.64-0.07-0.180.41
Feb-940.450.510.720.280.20.38
Mar-941.240.350.750.450.390.69
Apr-941.190.50.770.530.410.65
May-940.990.380.710.870.290.38
Jun-940.780.390.590.870.580.41
Jul-940.680.550.560.870.570.53
Aug-940.710.430.540.680.270.55
Sep-940.880.520.490.6300.54
Oct-940.820.580.380.410.050.59
Nov-940.880.550.290.580.280.56
Dec-940.570.440.260.120.10.34
Jan-950.270.420.2-0.05-0.120.18
Feb-95-0.210.40.09-0.220.320.08
Mar-95-0.210.210.19-0.280.40.09
Apr-95-0.230.320.22-0.550.280.04
May-95-0.270.160.17-0.52-0.15-0.01
Jun-950.220.010.24-0.36-0.350.11
Jul-950.16-0.170.26-0.26-0.40.04
Aug-950.58-0.40.29-0.07-0.20.19
Sep-950.44-0.290.230.04-0.050.08
Oct-950.09-0.410.09-0.160.23-0.08
Nov-950.16-0.340.23-0.370.060.11
Dec-950.13-0.190.22-0.080.030.09
Jan-960-0.430.17-0.06-0.37-0.1
Feb-961.13-0.510.21-0.160.250.26
Mar-960.94-0.210.12-0.330.430.33
Apr-960.98-0.030.08-0.120.340.42
May-961.150.160.08-0.110.280.5
Jun-960.970.120.19-0.26-0.050.44
Jul-960.480.060.29-0.18-0.230.23
Aug-960.550.180.41-0.360.080.31
Sep-960.590.010.49-0.660.280.38
Oct-960.53-0.20.51-0.380.330.31
Nov-960.73-0.090.70.080.490.49
Dec-960.640.010.560.390.440.39
Jan-970.690.20.710.590.560.56
Feb-9710.290.550.330.160.72
Mar-970.950.840.430.260.050.7
Apr-970.720.610.510.38-0.260.6
May-970.830.740.450.81-0.010.64
Jun-970.960.710.550.9600.78
Jul-971.160.740.40.97-0.20.79
Aug-970.90.60.370.82-0.290.4
Sep-971.270.550.440.42-0.430.72
Oct-971.020.660.520.22-0.60.58
Nov-970.940.520.560.15-0.740.49
Dec-970.810.780.340.05-0.750.56
Jan-980.730.750.34-0.06-0.820.47
Feb-980.490.430.40.36-1.20.39
Mar-980.430.440.310.4-1.310.24
Apr-980.630.030.10.24-0.680.33
May-980.730.3600.08-0.470.36
Jun-980.310.34-0.020.16-0.280.14
Jul-980.340.19-0.040.49-0.480.15
Aug-981.10.1-0.040.62-0.790.17
Sep-980.830.170.090.55-0.080.18
Oct-980.840.030.030.43-0.210.34
Nov-980.710.240.040.42-0.390.34
Dec-980.660.360.080.41-0.040.33
Jan-990.420.60.190.530.10.39
Feb-990.630.550.140.190.090.35
Mar-990.210.410.180.180.150.25
Apr-990.490.620.310.41-0.050.32
May-990.530.820.420.490.320.33
Jun-990.581.050.60.560.220.55
Jul-990.761.010.810.680.480.64
Aug-990.740.750.850.510.520.6
Sep-990.741.080.670.460.350.66
Oct-991.31.290.610.560.071.1
Nov-991.231.10.420.740.211.01
Dec-991.10.730.410.870.130.94
Jan-000.70.940.330.70.240.66
Feb-000.561.170.40.40.150.75
Mar-000.881.160.480.320.610.86
Apr-000.611.130.420.170.630.66
May-000.280.80.250.070.460.27
Jun-00-0.180.230.14-0.020.30.05
Jul-00-0.190.470.13-0.020.130.01
Aug-00-0.440.520.020.120.18-0.11
Sep-00-0.280.340.090.24-0.21-0.11
Oct-00-0.70.680.030.20.26-0.17
Nov-00-0.60.880.110.220.14-0.15
Dec-00-0.830.810.160.09-0.35-0.29
1-Jan-1.030.30.29-0.37-1.03-0.55
1-Feb-0.950.050.23-0.4-0.46-0.7
1-Mar-0.980.010.03-0.26-0.59-0.79
1-Apr-1.27-0.34-0.06-0.2-0.59-0.89
1-May-1.25-0.3-0.06-0.26-0.91-0.94
1-Jun-1.37-0.340.06-0.57-1.03-0.97
1-Jul-1.29-0.44-0.06-0.59-1.15-1.01
1-Aug-1.15-0.27-0.08-0.44-1.05-0.99
1-Sep-1.16-0.64-0.18-0.4-0.84-1.11
1-Oct-1.1-0.98-0.22-0.31-0.28-0.93
1-Nov-1.07-0.45-0.15-0.23-0.38-0.66
1-Dec-0.7-0.42-0.07-0.03-0.25-0.4
2-Jan-0.3-0.1400.57-0.21-0.26
2-Feb-0.230.050.080.730.170
2-Mar00.160.230.920.620.2
2-Apr-0.07-0.17-0.030.990.970.04
2-May-0.02-0.280.060.951.040.05
2-Jun0-0.13-0.180.920.1-0.09
2-Jul-0.54-0.41-0.050.8-0.13-0.33
2-Aug-0.58-0.410.30.850.08-0.25
2-Sep-0.75-0.350.160.420.33-0.55
2-Oct-0.56-0.380.070.280.28-0.23
2-Nov-0.45-0.730.010.380.12-0.33
2-Dec-0.59-0.87-0.020.48-0.31-0.54
3-Jan-0.24-0.57-0.030.39-0.17-0.28
3-Feb-0.54-0.380.070.220.05-0.39
3-Mar-0.58-0.660.12-0.31-0.05-0.45
3-Apr-0.39-0.40.18-0.690-0.2
3-May-0.01-0.410.26-0.460.39-0.07
3-Jun0.16-0.170.360.060.10.11
3-Jul0.270.140.40.220.120.25
3-Aug0.180.10.380.070.210.23
3-Sep0.320.310.390.320.680.37
3-Oct0.420.550.490.460.650.58
3-Nov0.30.270.310.40.140.35
3-Dec0.08-0.110.30.240.370.28
4-Jan0.03-0.060.34-0.010.420.21
4-Feb-0.040.30.18-0.040.140.11
4-Mar0.21-0.090.150.140.290.17
4-Apr0.260.190.040.310.390.2
4-May0.360.140.090.170.290.23
4-Jun-0.180.02-0.1300.19-0.02
4-Jul0.1-0.15-0.1-0.110.07-0.01
4-Aug0.25-0.57-0.19-0.1-0.06-0.03
4-Sep0.36-0.08-0.080.020.050.18
4-Oct0.720.030.02-0.08-0.230.41
4-Nov0.5-0.180.03-0.19-0.130.29
4-Dec0.75-0.24-0.05-0.29-0.270.41
5-Jan0.030.18-0.08-0.280.040.12
5-Feb0.070-0.02-0.21-0.150.1
5-Mar-0.090.130.01-0.260.220.09
5-Apr0.180.250.100.460.22
5-May0.150.24-0.070.080.140.22
5-Jun0.380.59-0.020.340.110.36
5-Jul0.220.4-0.10.4-0.280.3
5-Aug-0.410.21-0.110.20.05-0.07
5-Sep-0.70.4-0.01-0.040.19-0.07
5-Oct0.170.58-0.050.12-0.050.27
5-Nov0.890.50.140.080.220.64
5-Dec0.790.730.12-0.240.260.6
6-Jan0.830.810.03-0.240.140.59
6-Feb0.560.72-0.060.30.20.47
6-Mar0.30.99-0.240.480.190.33
6-Apr0.041.07-0.160.480.280.14
6-May-0.411.14-0.150.46-0.04-0.01
6-Jun-0.310.93-0.120.080.080
6-Jul-0.180.59-0.09-0.110.220.01
6-Aug-0.20.390.01-0.310.170.04
6-Sep-0.210.410.1-0.210.060.09
6-Oct-0.240.820.1600.190.12
6-Nov0.051.090.210.330.270.31
6-Dec0.181.060.250.690.060.32
7-Jan-0.010.750.430.65-0.10.12
7-Feb0.180.80.350.690.030.25
7-Mar0.220.690.460.52-0.010.24
7-Apr0.130.430.320.140.160.14
7-May-0.010.360.350.180.220.08
7-Jun-0.20.60.40.270.20
7-Jul-0.260.10.190.080.06-0.11
7-Aug-0.230.470.090.140.24-0.12
7-Sep-0.140.08-0.020.28-0.26-0.19
7-Oct-0.390.36-0.080.370.05-0.21
7-Nov-0.340.040.020.230-0.32
7-Dec-0.530.12-0.20.03-0.09-0.38
8-Jan-0.760.39-0.170.21-0.18-0.63
8-Feb-1.02-0.08-0.470.29-0.27-0.68
8-Mar-1.15-0.61-0.740.04-0.29-0.89
8-Apr-1.49-1.09-0.95-0.11-0.39-1
8-May-1.62-1.56-1.33-0.18-0.24-1.22
8-Jun-1.86-1.57-1.56-0.35-0.65-1.5
8-Jul-2.42-1.29-1.69-0.4-0.61-1.75
8-Aug-3.35-1.49-1.8-0.35-0.99-2.31
8-Sep-4.3-2.44-2.05-0.31-0.86-3.22
8-Oct-3.91-3.51-2.45-1.13-1.62-3.45
8-Nov-4.43-4.83-2.56-2.13-3.24-3.9
8-Dec-4.76-4.93-2.5-2.53-4.14-4.11
9-Jan-4.59-5.18-2.14-2.74-3.76-4.13
9-Feb-3.88-4.25-1.95-2.31-2.87-3.42
9-Mar-3.53-2.93-1.36-1.72-0.37-2.41
9-Apr-2.68-1.35-0.99-1.261.32-1.4
9-May-1.83-0.44-0.71-1.051.41-0.8
9-Jun-1.38-0.19-0.53-0.850.84-0.57
9-Jul-0.59-0.04-0.38-0.550.5-0.05
9-Aug-0.140.03-0.35-0.10.820.18
9-Sep-0.250-0.260.170.810.2
9-Oct-0.17-0.12-0.060.160.810.18
9-Nov0.140.04-0.010.290.830.27
9-Dec0.160.210.1-0.031.060.21
10-Jan0.350.190.090.121.240.29
10-Feb0.290.480.40.220.940.3
10-Mar0.690.790.490.290.510.74
10-Apr0.780.630.420.40.510.67
10-May1.050.720.260.390.250.68
10-Jun0.020.570.240.290.080.23
10-Jul0.060.160.18-0.040.260.17
10-Aug-0.020.03-0.03-0.16-0.050.06
10-Sep-0.090.01-0.17-0.29-0.63-0.02
10-Oct0.130.18-0.25-0.05-0.680.12
10-Nov0.230.33-0.250.150.250.21
10-Dec0.470.47-0.230.30.760.23
11-Jan0.40.33-0.310.310.690.11
11-Feb0.160.41-0.33-0.02-0.96-0.1
11-Mar0.1-0.04-0.39-0.14-3.91-0.42
11-Apr-0.1-0.14-0.43-0.07-0.93-0.24
11-May-0.29-0.32-0.47-0.081.52-0.19
11-Jun-0.06-0.58-0.45-0.041.550.04
11-Jul0.02-0.5-0.45-0.121.040.03
11-Aug0.02-0.74-0.44-0.150.56-0.12
11-Sep0.23-1.32-0.57-0.19-0.12-0.13
11-Oct0.29-1.56-0.58-0.61-0.35-0.04
11-Nov0.28-1.23-0.53-0.54-0.37-0.02
11-Dec0.5-1.08-0.44-0.310.230.14
12-Jan0.57-0.75-0.41-0.30.370.33
12-Feb0.31-0.72-0.38-0.120.180.1
12-Mar-0.11-0.87-0.390.340.2-0.22
12-Apr-0.15-1.16-0.380.28-0.12-0.36
12-May-0.24-0.65-0.26-0.11-0.38-0.39
12-Jun-0.37-0.46-0.16-0.38-0.23-0.32
12-Jul-0.32-0.160.1-0.47-0.3-0.28
12-Aug-0.66-0.10.04-0.240.03-0.42
12-Sep-0.5-0.080.04-0.21-0.03-0.51

Figure 2: Average cumulative weights for the United States, Euro Area, United Kingdom, Canada, and Japan over the first quarter of 2012.

Figure 2: Data for Figure 2 immediately follows.

Data for Figure 2

dateus_ipus_nonfarmus_rtsalesus_pincomeus_ismus_gdpeu_ipeu_rtsaleseu_pmieu_unempeu_gdpuk_ipuk_rtsalesuk_pmiuk_unempuk_gdpca_gdp_mca_employca_rtsalesca_pmica_gdpja_ipja_rtsalesja_unempja_gdpja_tankan
1-Jan-120.5495350.3410120.206170.2848230.0539250.0256810.3456130.1407110.117190.3415890.0533830.3953340.0600050.0747170.3273520.0969680.0614910.60650.0270060.0627050.0107620.0951120.0203370.0324130.0024330.102902
2-Jan-120.5495350.3410120.206170.2848230.0539250.0256810.3456130.1407110.117190.3415890.0533830.3953340.0600050.0747170.3273520.0969680.0614910.60650.0270060.0627050.0107620.0951120.0203370.0324130.0024330.102902
3-Jan-120.4581780.284320.1718950.2374730.1099850.0214110.3456130.1407110.117190.3415890.0533830.346690.0526220.0991430.2870730.0850360.0614910.60650.0270060.0627050.0107620.0951120.0203370.0324130.0024330.102902
4-Jan-120.4581780.284320.1718950.2374730.1099850.0214110.3456130.1407110.117190.3415890.0533830.346690.0526220.0991430.2870730.0850360.0614910.60650.0270060.0627050.0107620.0951120.0203370.0324130.0024330.102902
5-Jan-120.4581780.284320.1718950.2374730.1099850.0214110.3456130.1407110.117190.3415890.0533830.346690.0526220.0991430.2870730.0850360.051660.5095340.0226880.1048640.0090410.0951120.0203370.0324130.0024330.102902
6-Jan-120.3756850.5263840.1409460.1947170.083960.0175570.2445630.2123220.0905690.5080320.0377750.346690.0526220.0991430.2870730.0850360.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
7-Jan-120.3756850.5263840.1409460.1947170.083960.0175570.2445630.2123220.0905690.5080320.0377750.346690.0526220.0991430.2870730.0850360.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
8-Jan-120.3756850.5263840.1409460.1947170.083960.0175570.2445630.2123220.0905690.5080320.0377750.346690.0526220.0991430.2870730.0850360.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
9-Jan-120.3756850.5263840.1409460.1947170.083960.0175570.2445630.2123220.0905690.5080320.0377750.346690.0526220.0991430.2870730.0850360.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
10-Jan-120.3756850.5263840.1409460.1947170.083960.0175570.2445630.2123220.0905690.5080320.0377750.346690.0526220.0991430.2870730.0850360.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
11-Jan-120.3756850.5263840.1409460.1947170.083960.0175570.2445630.2123220.0905690.5080320.0377750.346690.0526220.0991430.2870730.0850360.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
12-Jan-120.3485320.4930020.3032870.1806440.0785540.0162880.4229260.1726170.0799550.4156410.030070.4604220.0443840.0862610.2445430.0717240.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
13-Jan-120.3485320.4930020.3032870.1806440.0785540.0162880.4229260.1726170.0799550.4156410.030070.4604220.0443840.0862610.2445430.0717240.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
14-Jan-120.3485320.4930020.3032870.1806440.0785540.0162880.4229260.1726170.0799550.4156410.030070.4604220.0443840.0862610.2445430.0717240.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
15-Jan-120.3485320.4930020.3032870.1806440.0785540.0162880.4229260.1726170.0799550.4156410.030070.4604220.0443840.0862610.2445430.0717240.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
16-Jan-120.3485320.4930020.3032870.1806440.0785540.0162880.4229260.1726170.0799550.4156410.030070.4604220.0443840.0862610.2445430.0717240.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
17-Jan-120.3485320.4930020.3032870.1806440.0785540.0162880.4229260.1726170.0799550.4156410.030070.4604220.0443840.0862610.2445430.0717240.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
18-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.4229260.1726170.0799550.4156410.030070.4211630.0405990.0782090.3406360.0656080.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
19-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.4229260.1726170.0799550.4156410.030070.4211630.0405990.0782090.3406360.0656080.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
20-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.4229260.1726170.0799550.4156410.030070.4198920.060570.0779610.3395360.0654180.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
21-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.4229260.1726170.0799550.4156410.030070.4198920.060570.0779610.3395360.0654180.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
22-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.4229260.1726170.0799550.4156410.030070.4198920.060570.0779610.3395360.0654180.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
23-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.4229260.1726170.0799550.4156410.030070.4198920.060570.0779610.3395360.0654180.0310580.6736090.013640.0599240.0054360.0951120.0203370.0324130.0024330.102902
24-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.3627930.1480740.1184830.3565430.0257940.4198920.060570.0779610.3395360.0654180.030940.6719990.0322770.0597690.0054150.0951120.0203370.0324130.0024330.102902
25-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.3627930.1480740.1184830.3565430.0257940.3256110.0489030.0637840.2830.2077590.030940.6719990.0322770.0597690.0054150.0951120.0203370.0324130.0024330.102902
26-Jan-120.6133050.3774930.2303120.1336720.0599310.0120530.3627930.1480740.1184830.3565430.0257940.3256110.0489030.0637840.2830.2077590.030940.6719990.0322770.0597690.0054150.0880330.1254720.0300810.0023060.097695
27-Jan-120.5293940.3375940.1979720.0979760.0526850.1574950.3627930.1480740.1184830.3565430.0257940.3256110.0489030.0637840.2830.2077590.030940.6719990.0322770.0597690.0054150.0880330.1254720.0300810.0023060.097695
28-Jan-120.5293940.3375940.1979720.0979760.0526850.1574950.3627930.1480740.1184830.3565430.0257940.3256110.0489030.0637840.2830.2077590.030940.6719990.0322770.0597690.0054150.0880330.1254720.0300810.0023060.097695
29-Jan-120.5293940.3375940.1979720.0979760.0526850.1574950.3627930.1480740.1184830.3565430.0257940.3256110.0489030.0637840.2830.2077590.030940.6719990.0322770.0597690.0054150.0880330.1254720.0300810.0023060.097695
30-Jan-120.4840210.3097530.1809280.250530.0482590.1433320.3627930.1480740.1184830.3565430.0257940.3256110.0489030.0637840.2830.2077590.030940.6719990.0322770.0597690.0054150.3030960.0650960.0948740.0011040.048212
31-Jan-120.4840210.3097530.1809280.250530.0482590.1433320.2669810.1089680.0934540.5372750.0189820.3256110.0489030.0637840.2830.2077590.0712320.6626950.0316050.0588320.00530.3030960.0650960.0948740.0011040.048212
1-Feb-120.4036050.258290.1508680.2089070.10460.1195190.2669810.1089680.0934540.5372750.0189820.285630.0428980.0875740.2482510.1822490.0712320.6626950.0316050.0588320.00530.3030960.0650960.0948740.0011040.048212
2-Feb-120.4036050.258290.1508680.2089070.10460.1195190.2669810.1089680.0934540.5372750.0189820.285630.0428980.0875740.2482510.1822490.0712320.6626950.0316050.0588320.00530.3030960.0650960.0948740.0011040.048212
3-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.285630.0428980.0875740.2482510.1822490.0247840.7307690.0109970.020470.0018440.3030960.0650960.0948740.0011040.048212
4-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.285630.0428980.0875740.2482510.1822490.0247840.7307690.0109970.020470.0018440.3030960.0650960.0948740.0011040.048212
5-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.285630.0428980.0875740.2482510.1822490.0247840.7307690.0109970.020470.0018440.3030960.0650960.0948740.0011040.048212
6-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.285630.0428980.0875740.2482510.1822490.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
7-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.285630.0428980.0875740.2482510.1822490.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
8-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.285630.0428980.0875740.2482510.1822490.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
9-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.3979580.0370250.0773960.2147360.1566510.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
10-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.3979580.0370250.0773960.2147360.1566510.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
11-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.3979580.0370250.0773960.2147360.1566510.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
12-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.3979580.0370250.0773960.2147360.1566510.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
13-Feb-120.3313920.5034990.1238750.1715290.0797020.0981350.2564220.2178710.0914090.519020.0182320.3979580.0370250.0773960.2147360.1566510.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
14-Feb-120.3077280.4721510.2854840.1592810.0746650.0911270.4328860.1769130.0805910.4241080.0145020.3979580.0370250.0773960.2147360.1566510.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
15-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3635220.1474010.0752010.3643650.1272850.3651210.033970.0703360.3101840.1437250.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
16-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3635220.1474010.0752010.3643650.1272850.3651210.033970.0703360.3101840.1437250.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
17-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3635220.1474010.0752010.3643650.1272850.362340.0794470.0698260.3079770.142630.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
18-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3635220.1474010.0752010.3643650.1272850.362340.0794470.0698260.3079770.142630.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
19-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3635220.1474010.0752010.3643650.1272850.362340.0794470.0698260.3079770.142630.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
20-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3635220.1474010.0752010.3643650.1272850.362340.0794470.0698260.3079770.142630.0247180.7291670.0109670.0415320.0018390.3030960.0650960.0948740.0011040.048212
21-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3635220.1474010.0752010.3643650.1272850.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.3030960.0650960.0948740.0011040.048212
22-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3118630.1264550.1139790.3125860.1091970.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.3030960.0650960.0948740.0011040.048212
23-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3118630.1264550.1139790.3125860.1091970.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.3030960.0650960.0948740.0011040.048212
24-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3118630.1264550.1139790.3125860.1091970.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.3030960.0650960.0948740.0011040.048212
25-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3118630.1264550.1139790.3125860.1091970.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.3030960.0650960.0948740.0011040.048212
26-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3118630.1264550.1139790.3125860.1091970.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.3030960.0650960.0948740.0011040.048212
27-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3118630.1264550.1139790.3125860.1091970.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.1495020.1475420.0467970.0005440.02378
28-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3118630.1264550.1139790.3125860.1091970.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.3790190.0815170.0190980.0002220.009705
29-Feb-120.5807920.3629910.2177140.1182130.0572010.0676320.3118630.1264550.1139790.3125860.1091970.362340.0794470.0698260.3079770.142630.0246430.7282090.0213370.0414610.0018340.3790190.0815170.0190980.0002220.009705
1-Mar-120.4413830.2767860.165390.2286650.108470.0507190.2307020.0935450.0904870.5021220.0807790.317790.0696790.0941220.2701110.1250940.0246430.7282090.0213370.0414610.0018340.3437050.0739140.1054130.0001950.008537
2-Mar-120.4413830.2767860.165390.2286650.108470.0507190.2307020.0935450.0904870.5021220.0807790.317790.0696790.0941220.2701110.1250940.0441010.7064610.0198350.0397860.0238660.3437050.0739140.1054130.0001950.008537
3-Mar-120.4413830.2767860.165390.2286650.108470.0507190.2307020.0935450.0904870.5021220.0807790.317790.0696790.0941220.2701110.1250940.0441010.7064610.0198350.0397860.0238660.3437050.0739140.1054130.0001950.008537
4-Mar-120.4413830.2767860.165390.2286650.108470.0507190.2307020.0935450.0904870.5021220.0807790.317790.0696790.0941220.2701110.1250940.0441010.7064610.0198350.0397860.0238660.3437050.0739140.1054130.0001950.008537
5-Mar-120.4413830.2767860.165390.2286650.108470.0507190.2217740.2007090.0886010.4856190.0776530.317790.0696790.0941220.2701110.1250940.0441010.7064610.0198350.0397860.0238660.3437050.0739140.1054130.0001950.008537
6-Mar-120.4413830.2767860.165390.2286650.108470.0507190.2217740.2007090.0886010.4856190.0776530.317790.0696790.0941220.2701110.1250940.0441010.7064610.0198350.0397860.0238660.3437050.0739140.1054130.0001950.008537
7-Mar-120.4413830.2767860.165390.2286650.108470.0507190.2217740.2007090.0886010.4856190.0776530.317790.0696790.0941220.2701110.1250940.0441010.7064610.0198350.0397860.0238660.3416040.0734570.104850.0037020.00797
8-Mar-120.4413830.2767860.165390.2286650.108470.0507190.2217740.2007090.0886010.4856190.0776530.317790.0696790.0941220.2701110.1250940.0441010.7064610.0198350.0397860.0238660.3416040.0734570.104850.0037020.00797
9-Mar-120.3619890.5199750.1356410.1875340.0827430.0415970.2217740.2007090.0886010.4856190.0776530.4322250.0596970.0824050.2314850.1061230.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
10-Mar-120.3619890.5199750.1356410.1875340.0827430.0415970.2217740.2007090.0886010.4856190.0776530.4322250.0596970.0824050.2314850.1061230.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
11-Mar-120.3619890.5199750.1356410.1875340.0827430.0415970.2217740.2007090.0886010.4856190.0776530.4322250.0596970.0824050.2314850.1061230.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
12-Mar-120.3619890.5199750.1356410.1875340.0827430.0415970.2217740.2007090.0886010.4856190.0776530.4322250.0596970.0824050.2314850.1061230.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
13-Mar-120.3358740.4871160.2980680.1740040.0774350.0385960.2217740.2007090.0886010.4856190.0776530.4322250.0596970.0824050.2314850.1061230.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
14-Mar-120.3358740.4871160.2980680.1740040.0774350.0385960.4024650.1638460.0785180.3989130.0620150.3958030.0546660.0747730.3275510.0971810.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
15-Mar-120.3358740.4871160.2980680.1740040.0774350.0385960.4024650.1638460.0785180.3989130.0620150.3958030.0546660.0747730.3275510.0971810.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
16-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.4024650.1638460.0785180.3989130.0620150.3958030.0546660.0747730.3275510.0971810.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
17-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.4024650.1638460.0785180.3989130.0620150.3958030.0546660.0747730.3275510.0971810.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
18-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.4024650.1638460.0785180.3989130.0620150.3958030.0546660.0747730.3275510.0971810.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
19-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.4024650.1638460.0785180.3989130.0620150.3958030.0546660.0747730.3275510.0971810.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
20-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.4024650.1638460.0785180.3989130.0620150.3958030.0546660.0747730.3275510.0971810.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
21-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.4024650.1638460.0785180.3989130.0620150.3958030.0546660.0747730.3275510.0971810.0165690.7376670.0074520.0149480.0089670.3416040.0734570.104850.0037020.00797
22-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0165260.7368990.0156490.0149150.0089440.3416040.0734570.104850.0037020.00797
23-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0165260.7368990.0156490.0149150.0089440.3416040.0734570.104850.0037020.00797
24-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0165260.7368990.0156490.0149150.0089440.3416040.0734570.104850.0037020.00797
25-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0165260.7368990.0156490.0149150.0089440.3416040.0734570.104850.0037020.00797
26-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0165260.7368990.0156490.0149150.0089440.3416040.0734570.104850.0037020.00797
27-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0165260.7368990.0156490.0149150.0089440.3416040.0734570.104850.0037020.00797
28-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0165260.7368990.0156490.0149150.0089440.1684270.1523050.0516960.0018250.003929
29-Mar-120.6035960.3732830.2265420.1288170.0591260.0285730.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0165260.7368990.0156490.0149150.0089440.3508870.0754780.1072170.0006530.001406
30-Mar-120.5495350.3410120.206170.2848230.0539250.0256810.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0345980.7323130.015460.0147350.0088290.3508870.0754780.1072170.0006530.001406
31-Mar-120.5495350.3410120.206170.2848230.0539250.0256810.398320.1621590.1351810.3948050.0613760.3926890.1014680.0742110.3251350.0964160.0345980.7323130.015460.0147350.0088290.3508870.0754780.1072170.0006530.001406

Figure 3: Time Series of weights for each indicator based on the information available as of March 31, 2012.

Figure 3: Data for Figure 3 immediately follows.

Data for Figure 3

dateus_ip3us_nonfarm3us_rtsales3us_pincome3us_ism3us_gdp3eu_ip3eu_rtsales3eu_pmi3eu_unemp3eu_gdp3uk_ip3uk_rtsales3uk_pmi3uk_unemp3uk_gdp3ca_ip3ca_emp3ca_rtsales3ca_ivey3ca_gdp3ja_ip3ja_rtsales3ja_unemp3ja_gdp3ja_tankan3
2011m80.0003-0.00060.00010.0002000.00290.0013-0.00010.001400.01500.00170.004500.00030.00410.00020.00020-0.00010000
2011m90.0024-0.00080.0010.00130.00010.00260.00810.0037-0.00020.0041-0.00620.02420.00420.00270.0070.00020.00080.01040.00050.0005-0.0061-0.0004-0.0001-0.00010-0.001
2011m100.0093-0.00050.00370.00490.000500.0230.0103-0.00020.013300.04030.0040.00450.011800.00230.01190.00120.00120-0.00010-0.000100
2011m110.0270.0020.01080.01430.001700.05780.02570.00060.037300.066700.00760.021400.00500.00250.002400.00280.00060.000500
2011m120.06880.00710.02750.03650.00440.0250.13030.05780.00210.08640.06640.10670.01840.01210.03540.09060.00880.09040.00460.00460.01340.01910.00420.00380.00070.0021
2012m10.16640.01840.06640.08830.010700.17270.06170.00580.249800.11380.03570.01880.057600.0170.24770.00640.005800.10980.02420.022200
2012m20.2750.31530.09650.13910.03650000.02920000.03450.02380.1792000.36420000.21940.04650.080800
2012m3000000000.09800000000000000000

Figure 4: The solid lines show the surprise indexes for the United States, Euro Area, United Kingdom, Canada, Japan, and the aggregate of the five countries. The dotted lines show the Citigroup Economic Surprise Indexes for the corresponding country (left axis).

Figure 4: The solid lines show the surprise indexes for the United States, Euro Area, United Kingdom, Canada, Japan, and the aggregate of the five countries. The dotted lines show the Citigroup Economic Surprise Indexes for the corresponding country (left axis).

Figure 5: The solid lines show the uncertainty indexes for the United States, Euro Area, United Kingdom, Canada, Japan, and the aggregate of teh five countries. The dotted and dashed lines show stock market implied and realized volatilities respectively (left axis).

Figure 5: The solid lines show the uncertainty indexes for the United States, Euro Area, United Kingdom, Canada, Japan, and the aggregate of teh five countries. The dotted and dashed lines show stock market implied and realized volatilities respectively (left axis).

Figure 6: The solid line represent the uncertainty index withich is compared against other common proxies for uncertainty, namely the Baker, Bloom and Davis measure, the Bachmann, Elstner and Sims measure, and the VIX. All series are demeaned and standardized. The horizontal ine represents the 1.65 standard deviation limit.

Figure 6: Figure 6 plots the Uncertainty Index along with other common proxies for uncertainty, namely the Baker, Bloom and Davis measure; the Bachmann, Elsner and Sims measure; and the VIX. The horizontal axis plots the date on a quarterly basis. It ranges from the start of 2003 to the end of 2012. The vertical axis plots standard deviations and ranges from -4 to 5. All series plotted are demeaned and standardized. The standard deviation limit of 1.65 is given as a horizontal line to be used as a reference. Around late 2005, and early 2009, the Uncertainty Index is above the 1.65 standard deviation limit while the other common uncertainty proxies are not. During early 2008 the Bachman, Elstner and Sims measure is above the 1.65 standard deviation limit while the others are not. During late 2008, only the Baker, Bloom and Davis measure is not above the 1.65 standard deviation limit. During the middle of 2011 the Uncertainty Index is the only series not above the 1.65 standard deviation limit.

Figure 7: Employment response to a 1 standard deviation shock in the different uncertainty proxies. The shaded area represents the +/- one standard error confidence intreval for the uncertainty index.

Figure 7: Figure 7 plots the employment response to a one standard deviation shock in the different uncertainty proxies and also provides a shaded area that represents the +/- one standard error confidence interval for the Uncertainty Index. The proxies included are the VIX; the Bachmann, Elstner and Sims measure; the Real-Activity Uncertainty Index; and the Baker, Bloom and Davis measure. The horizontal axis represents different horizons and ranges from 0 to 60 months. The vertical axis ranges from -1.6 to 0.4 and displays the percentage change in employment due to a one-standard deviation shock in the uncertainty proxies. All impulse responses are within the given Uncertainty Index confidence interval at all points other than the Baker, Bloom and Davis measure which is plotted slightly above the confidence interval for the horizons between 0 and 25 months. After 25 months the Baker, Bloom and Davis measure remains within the Uncertainty Index confidence interval. All series plotted follow the same shape: all decrease to around a horizon of 15 months, slightly increase for the rest of the horizons and are always below 0 percent. The ordering of the impulse responses from smaller to bigger is: Baker, Bloom and Davis; Uncertainty Index; Bachmann, Elsner and Sims; and VIX. Only two measures cross: near the horizon of 50 months, the impulse response for the Baker, Bloom and Davis measure drops beneath the impulse response of the Uncertainty Index.

Figure 8: +/- one standard error confidence intreval for the real-activity uncertainty shock and the VIX.

Figure 8: Figure 8 plots the +/- one standard error confidence intervals for the Real-activity Uncertainty Index and the VIX. The horizontal axis displays the different horizons and ranges from 0 to 60 months. The vertical axis ranges from -1.6 to 0.4 and displays the percentage change in employment due to a one-standard deviation shock in the uncertainty proxies. The confidence intervals of both uncertainty proxies have the same shape: the upper limits of both decrease until between horizons of 10 and 15 months and increase for all horizons afterwards while the lower limits decrease until between 20 and 25 months and increase for all months afterwards. During the decreasing stage, the upper and lower limit of the Uncertainty Index decrease at slower paces than the respective limits of the VIX confidence interval. During the increasing stage, the upper limits of both uncertainty proxies increase at the same rate while the lower limit of the Uncertainty Index increases at a faster rate than the VIX. The lower limit of the Uncertainty Index is always within plotted confidence interval of the VIX and the upper limit of the Uncertainty Index is always greater than the upper limit of the VIX. Both intervals are completely negative until around a horizon of 50 when the upper limit of the Uncertainty Index confidence interval turns positive. The upper limit of the VIX confidence interval turns positive after about 55 months.

Footnotes

1.   I would like to thank for their useful comments Boragan Aruoba, David Bowman, Celso Brunetti, Domenico Giannone, Raffaella Giacomini, Rob Martin, Andrew Patton, Barbara Rossi, Jonathan Wright, Clara Vega as well as various participants of conferences and seminars: 2012 Computing in Economics and Finance; 2012 European Meeting of the Econometric Society; 2012 Conference on Real-Time Data Analysis, Methods, and Applications at the Philadelphia Fed; 2012 NBER-NSF Time Series Conference; Third IFO conference on Macroeconomics and Survey Data; 2013 Econometric Society Australasian Meeting; Boston College; and Board of Governors of the Federal Reserve System. For outstanding research assistance I thank Rebecca DeSimone, Eric English, and Olivia Kim. The views expressed in this paper are solely the responsibility of the author and should not be interpreted as reflecting the view of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. Correspondence to [email protected] Return to text

2.   http://www.philadelphiafed.org/research-and-data/real-time-center/business-conditions-index/  Return to text

3.   Unfortunately, we are not able to see whether this is a characteristic of all recessions because the surprise indexes only start in 2003 and hence only cover one recession episode. Expectation data are available from Bloomberg for all countries since 2003. Return to text

4.   The correlation between the daily U.S. uncertainty index and the VIX is 53 percent over the sample period analyzed. Return to text

5.   The correlation is 14 and 26 percent with the Baker, Bloom and Davis (2013) and the Bachmann, Elstner and Sims (2013) measures, respectively. Return to text

6.   The correlation ranges between -0.26 to -0.45 for the United States, Euro Area, the United Kingdom and Japan, whereas it is positive in Canada over the sample period analyzed in the paper. Return to text

7.   Employment data and expectations are available only for the United States and Canada. For the other countries we use the unemployment rate. Return to text

8.   To avoid confusion, because for all the indicators a higher number means that the economy is doing good, I feed the negative of the unemployment rate into the model. Return to text

9.   For Canada, Bloomberg used to provide expectations for the non-seasonally-adjusted IVY index, but as of March 2011, it started to provide expectations for the seasonally adjusted series. I splice the two series together being aware of the break point. Return to text

10.   The Tankan survey has an average publication lag of -4 days, but only Q4 numbers are released before the end of the quarter (around mid-December). Other releases occur at the beginning of the following quarter. Return to text

11.   The other quarterly series in the dataset is the Japanese Tankan survey. Because it is an index, I do not compute the $ log$ difference (growth rate) as for GDP. By defining $ Y_{t}^{Q}=$ $ Tankann_{t}$ and $ y_{t}^{Q}=Y_{t}^{Q}-Y_{t-3}^{Q}=Tankann_{t}-Tankann_{t-3},$ the same argument goes through and equation (11) holds exactly. Return to text

12.   Details about the state space representation can be found in the appendix. Return to text

13.   Realized volatility is more precisely defined as $ vol=\sqrt{\frac{1}{n}\sum ret_{i}^{2}-\left( \frac{1}{n}\sum ret_{i}\right) ^{2}}$ but because the second term, the average return, tends to be zero it is frequently dropped. Similarly, we abstract from using the second term, $ \left( \sum_{j=1}^{t}w_{j}s_{j}\right) ^{2}$ in the definition of the uncertainty index. In practice, this term is very close to zero. Return to text

14.   I thank Banbura, Giannone and Reichlin for sharing their EM codes. Return to text

15.   The surprise index is computed on a shorter sample due to the limited availability of expectation data for all the countries. Return to text

16.   The underlying real activity factor is estimated on the full sample to avoid parameter instability problems due to the fact that, for some of the countries, some macroeconomic releases become available later in the sample (namely retail sales and pmi series). Return to text

17.   That means, running (i), (ii) and (iii) in real time versus running (i)over the entire sample, and (ii) and (iii) in real time does not give significant differences for the United States. Return to text

18.   For comparability across countries, the table shows standardized weights so that the sum of all weights in each country is equal to 1. Return to text

19.   Euro-area flash PMI becomes available in June 2007 and U.K. PMI becomes available in March 2006. Return to text

20.   The idea is that $ w_{j}^{i}$ represents the bars in figure 3, while $ w_{cum}^{i}$ represent the lines in figure 2. Return to text

21.   The indexes continue to be updated daily and are available from the author upon request. Return to text

22.   For comparison with the exercise in table 3, I run the regression only on days in which there are news releases. This implies that I will have 556, 423, 443, 417, and 298 observations for the U.S., euro-area, U.K., Canadian and Japanese news, respectively. Return to text

23.   The VXO is equivalent to the VIX series that I use. The VIX was launched in 1993. In 2003, its formula was modified substantially. Data from the new 2003 VIX formula, also used to reconstruct historical data going back to 1990, is known as the VIX. The data associated with the original and revised VIX formulae is known as VXO. In my sub-sample VIX and VXO coincide. Return to text

24.   The smallest correlation is between Bachmann, Elstner, and Sims and Baker, Bloom, and Davis measures (about 10 percent). The highest correlation is between Baker, Bloom, and Davis EPU measure and the VIX (over 70 percent). Return to text

25.   Given the short dataset, I only estimate the bivariate VAR. Return to text

26.  We use the notation Σ to indicate a variance-covariance matrix and σ to indicate its elements.  Return to text

This version is optimized for use by screen readers. Descriptions for all mathematical expressions are provided in LaTex format. A printable pdf version is available. Return to text

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