G. Natvik - Quantitative and Qualitative Analysis in Social Sciences ...

We start by evaluat**in**g the policy **in**efficiency hypothesis on U.S. data. Moreover,due to **in**ternational f**in**ancial **in**tegration, it is likely that U.S. stockmarket volatility **and** U.S. corporate spreads at least partially capture movements**in** global economic uncerta**in**ty. We therefore extend our analysis byestimat**in**g how these two uncerta**in**ty measures **in**teract with the transmissionof monetary policy **in** six small open economies: Australia, Canada, NewZeal**and**, Norway, Switzerl**and** **and** the United K**in**gdom. Beyond serv**in**g as arobustness check of our results from the United States, this extension has thebenefit that the U.S.-based uncerta**in**ty measures are likely to be exogenouswith respect to monetary policy **in** each of these countries.Our ma**in** f**in**d**in**g is that the policy **in**effectiveness hypothesis has bite at themacro level. Across the countries we study, the effects of monetary policyshocks tend to be considerably weaker when uncerta**in**ty is high. The patternis particularly stark for GDP **and** **in**vestment, **and** the effects are sizeable.In the United States, a monetary tighten**in**g has almost no effect when stockmarket volatility is **in** its upper decile, while the same impulse makes **in**vestment**and** GDP drop by approximately one percent when volatility is **in** itslower decile. The effect when volatility is **in** its lower decile is more than fivetimes larger than when it is **in** its upper decile, **and** we show these differencesto be statistically significant. When uncerta**in**ty is measured by the corporatespread, forecaster disagreement or the Google-**in**dex, the results are qualitativelysimilar, but quantitatively somewhat smaller. For these measures, thepolicy effect is approximately halved when uncerta**in**ty is **in** its upper ratherthan **in** its bottom decile. The differences **in** policy effects rema**in** statisticallysignificant. It is only economic policy uncerta**in**ty that does not seemto dampen the **in**fluence of monetary policy, which might reflect that policyactions directly **in**fluence policy uncerta**in**ty.For GDP **and** particularly **in**vestment, our f**in**d**in**gs from the six small openeconomies are qualitatively **in** l**in**e with the pattern for the United States.The **in**vestment responses to a monetary policy shock are approximatelyhalved when stock market volatility is **in** its bottom **in**stead of its top decile,**and** the response differences are statistically significant **in** all countries. Whenuncerta**in**ty is measured by the spread, **in**vestment responses are also weakerif uncerta**in**ty is high, **and** the 84% probability b**and**s for the response differencesexceed zero **in** 4 out of 6 countries. That the **in**teraction effects arequantitatively smaller here than **in** the United States, is hardly surpris**in**ggiven that the uncerta**in**ty measures are obta**in**ed from U.S. f**in**ancial markets.Our study is closely related to the recent literature **in**itiated by Bloom (2009),3

that uses SVARs to identify uncerta**in**ty shocks **and** how they affect themacroeconomy. Bloom (2009) showed that shocks to U.S. stock marketvolatility are followed by contractions **in** U.S. employment **and** **in**vestment.Bachmann et al. (2013) measure uncerta**in**ty by forecast disagreement **and**dispersion **in** forecast errors **in** bus**in**ess surveys from Germany **and** the U.S.,document that the two measures are correlated, **and** show how **in**novations**in** these **in**dexes are followed by economic contractions **in** the two countries.They also show that shocks to spreads, stock market volatility **and** theGoogle-**in**dex foreshadow similar contractions. Baker et al. (2012) construct**in**dexes of economic policy uncerta**in**ty **in** the United States, Canada **and**Europe **and** f**in**d similar effects. Alexopoulos **and** Cohen (2009) construct anuncerta**in**ty **in**dex reflect**in**g the frequency with which the news media refersto economic uncerta**in**ty, **and** also they f**in**d that **in**creased uncerta**in**ty is followedby reduced economic activity. Other studies **in** this ve**in** are Bachmann**and** Bayer (2011) **and** Knotek **and** Khan (2011). Notably, the recent str**and**of macroeconomic empirical research has focused exclusively on the questionof how movements **in** uncerta**in**ty affect economic activity, while no attentionhas been directed to the policy-effectiveness hypothesis which we address.The evidence that exists on policy-effectiveness **and** uncerta**in**ty is obta**in**edeither through micro-data (e.g. Bloom et al. (2007)), or through structuralmodels where the implication of policy **in**effectiveness is largely imposed bytheory (e.g. Bloom (2009), Bloom et al. (2007)). A particularly relevantpaper is Bloom et al. (2012), who build **and** calibrate a dynamic stochasticgeneral equilibrium model with non-convex adjustment costs, **and** study howthe **in**fluence of expansive policy depends on uncerta**in**ty. Our contributionis to empirically evaluate with macroeconomic data if the effect of monetarypolicy **in**teracts with the level of uncerta**in**ty **in** the economy. This relates ourpaper to the vast empirical literature on the transmission of monetary policyshocks, summarized at one stage by Christiano et al. (1999). 3 With**in** thisfield, several studies explore how the monetary transmission mechanism hasevolved over time, such as Boiv**in** et al. (2010), Canova **and** Gambetti (2009),Boiv**in** **and** Giannoni (2006) **and** Kuttner **and** Mosser (2002). However, toour knowledge, this literature has not previously addressed how uncerta**in**tymight alter the effectiveness of monetary policy.The rema**in**der of our paper is organized as follows. Section 2 gives a theoreticalmotivation for our empirical **in**vestigation, based on a stylized modelof an irreversible **in**vestment decision. Section 3 describes our data **and** the3 See, for example, Sims (1992), Bernanke **and** Mihov (1998), Romer **and** Romer (2004) **and**Bernanke et al. (2005).4

methodology we use. Section 4 **and** 5 presents our results for the UnitedStates **and** the six small open economies, respectively. F**in**ally, we makesome conclud**in**g remarks **in** Section 6.2 Theoretical MotivationIn this section we use a simple theoretical model to show how uncerta**in**ty**in**fluences a decision that can be postponed. The model is highly stylized,**in** order to allow an analytical expression of the hypothesis we want to test.The same qualitative prediction is obta**in**ed numerically **in** the more detailedmodels with non-convex adjustment costs used by for **in**stance Bloom et al.(2012), Bloom et al. (2007) **and** Bloom (2007). The classic textbook expositionof these effects is given **in** Dixit **and** P**in**dyck (1994).There are 3 periods, 0, 1 **and** 2. In period 0, a cont**in**uum of entrepreneurs**in**dexed by i face the opportunity to **in**vest **in** a project. The cost of undertak**in**gthis **in**vestment is γ i , which is uniformly distributed across **in**vestors withdensity 1/α. If **in**vested **in**, the project pays off y **in** periods 1 **and** 2, wherey is stochastic. With probability p, y = y h , while y = y l with probability1 − p. The distance between y h **and** y l captures the degree of uncerta**in**ty **in**this economy, **and** is denoted σ. Uncerta**in**ty about y is realized **in** period 1,**and** after observ**in**g this level, an entrepreneur who did not **in**vest previouslymay choose whether or not to **in**vest for period 2. We assume that after y isrealized, the resale price of capital does not exceed y, **and** hence projects arenever term**in**ated **in** period 1. The alternative to **in**vest**in**g **in** the project isto spend γ i on a risk-free asset yield**in**g the gross **in**terest rate R.To make the **in**vestment decision **in**terest**in**g, we assume that the project isunprofitable if the state with low productivity materializes: γ i > y l /R +y l /R 2 for all **in**vestors i. On the other h**and**, if the high-productivity statematerializes, the project is profitable even if it operates for one period only:γ i ≤ y h /R.The net present value from **in**vest**in**g the amount γ i **in** period 0 is givenby E ( )πi,0**in**v = E (y) /R + E (y) /R 2 − γ i , while the net present valuefrom postpon**in**g the **in**vestment decision until period 1 is E ( )π no−**in**vi,0 =(1 − p) γ i +p/R [ ] 2 y h + (R − 1) γ i −γi . The latter expression reflects that bydelay**in**g the **in**vestment decision, the **in**vestor ga**in**s the option to **in**vest **in** therisk-free asset rather than a project that has turned out to be unprofitable.Naturally, the **in**vestment will be made **in** period 0 if **and** only if E ( π **in**vi,05)−

E ( )π no−**in**vi,0 ≥ 0. From the two profit expressions, we can therefore expressthe **in**dividual **in**vestment decision **in** terms of the fixed **in**vestment cost.Entrepreneur i will choose to **in**vest if γ i ≤ γ, whereγ =RE (y) + (1 − p) ylR 2 (1 − p) + (R − 1)pAggregate **in**vestment **in** period zero, I 0 , is then given by the mass of **in**vestorswith γ i ≤ γ. Hence, I 0 = 1/2 + [γ − E (γ)] /α.We can now answer how uncerta**in**ty affects **in**vestment. 4 First, the effect ofa mean-preserv**in**g **in**crease **in** uncerta**in**ty is: 5∂I 0∂σ | E(y) =− (1 − p) p[R 2 (1 − p) + (R − 1) p] α < 0.We see that higher uncerta**in**ty leads to lower **in**vestment. This is the “delay”effect of higher uncerta**in**ty. The effect follows from equation (1), as themean preserv**in**g **in**crease **in** uncerta**in**ty by def**in**ition reduces y l , **and** therebytightens the condition for **in**vestors to take action. Intuitively, a wider distributionof potential payoffs **in**creases the cost of mak**in**g a wrong decision **and**therefore raises the value of postpon**in**g the **in**vestment decision **in** order toga**in** further **in**formation. As consequence, the **in**vestment cost that triggersdelay falls, **and** fewer **in**vest. This delay effect has been scrut**in**ized **in** thegrow**in**g literature on uncerta**in**ty shocks referred to **in** the **in**troduction.Second, higher uncerta**in**ty **in**fluences how strongly movements **in** the **in**terestrate R, affects the motive to **in**vest:(1)∂ 2 I 0∂R∂σ | E(y) =(1 − p) p [2R (1 − p) + p][R 2 (1 − p) + (R − 1) p] 2 α > 0.As the partial effect of a higher **in**terest rate on **in**vestment, ∂I 0 /∂R, is negative,it follows that higher uncerta**in**ty reduces the **in**fluence of monetarypolicy. This reflects the “caution effect” that uncerta**in**ty creates. Whenuncerta**in**ty goes up, there is more at stake when decid**in**g whether to **in**vestor not, **and** hence a marg**in**al change **in** **in**vestment **in**centives, as **in**duced bya change **in** R, has a smaller impact. In terms of equation (1), the effect can4 Notably, the key assumption beh**in**d the uncerta**in**ty effects here is that projects cannot beliquidated at a price that exceeds their productivity. This assumption makes **in**vestmentirreversible **in** this model. If projects could be term**in**ated **and** sold at prices that exceededy, the option value of postpon**in**g **in**vestments would not be **in**creased by higher uncerta**in**ty.5 Here we have utilized that dyldσ | E(y) = −p.6

e observed by not**in**g that an **in**terest rate hike reduces **in**vestment **in**centivesby rais**in**g the discount**in**g of E (y) **and** y l . The higher is uncerta**in**ty,the lower is y l , **and** hence the smaller is the effect of R on the **in**dividual**in**vestment decision as captured by γ. This “caution effect” is what we willexplore **in** this paper.3 Data **and** Empirical StrategyWe aim to estimate how economic uncerta**in**ty **in**fluences the transmission ofmonetary policy shocks. We perform our analysis first for the United States,**and** thereafter for six small economies. These are Canada, Australia, NewZeal**and**, Switzerl**and**, Norway **and** the United K**in**gdom. 6We use quarterly data throughout. For the US, we cover the period 1970Q1to 2011Q3. 7 For all the other countries we use data from 1978Q4 to 2011Q3,s**in**ce this is the longest period over which we have consistent macroeconomicseries.3.1 Measur**in**g Economic Uncerta**in**tyAs our ma**in** measure of uncerta**in**ty, we will use the series for volatility **in** theUS stock market constructed by Bloom (2009), extended to cover the periodfrom 2008 to 2011. From 1986 **and** onward, these data are taken from theChicago Board Options Exchange VXO **in**dex of implied volatility. For theperiod before 1986, the implied volatility **in**dex is unavailable, **and** realizedvolatility, calculated as quarterly st**and**ard deviation of the daily S&P500,is used **in**stead. We will refer to the stock market volatility **in**dex as theVXO-**in**dex throughout.6 We do not **in**clude Euro area countries **in** the analysis as it complicates the identificationof monetary policy shocks **and** requires us to tackle the issue of the **in**troduction of a s**in**glecurrency.7 We start **in** 1970 because our longest series for uncerta**in**ty is the US stock market volatility**in**dex from Bloom (2009), which trends upward from a low level until 1970. The volatilitylevel is therefore unlikely to treat periods of uncerta**in**ty **in** a symmetric way before **and**after 1970. For **in**stance, the Cuban missile crisis **in** 1962 leads to a spike **in** the volatility**in**dex that lies below its average over the entire period. Us**in**g dummies to capture uncerta**in**tyspikes, as **in** Bloom (2009), does not suffer from this problem, but this approach isnot compatible with the **in**teraction VAR strategy that we will apply.7

While f**in**ancial market volatility is a natural start**in**g po**in**t for measur**in**guncerta**in**ty, **in** the recent literature on uncerta**in**ty shocks several alternativemeasures have been proposed. We therefore consider a host of these.First, we use the alternative measures provided **in** Bachmann et al. (2013),namely the corporate bond spread, forecast disagreement, **and** the Google**in**dex. The corporate bond spread is the spread of the 30-year Baa-ratedcorporate bond yield **in**dex over the 30-year treasury bond yield, where the20-year treasury bond has been used when the 30-year bond was miss**in**g. Theforecast disagreement measure stems from the the Federal Reserve Bank ofPhiladelphia’s Bus**in**ess Outlook Survey, where large manufactur**in**g firms **in**the Third Fed district are asked to give their own “evaluation of the generalbus**in**ess activity six months from now.” 8 Disagreement is measured as thecross-sectional dispersion **in** these po**in**t forecasts. The Google **in**dex is thenumber of articles **in** a given month that refer to “uncerta**in**ty” **and** phrasesrelated to the economy, divided by the number of articles conta**in****in**g the word“today” **in** order to control for the overall **in**creas**in**g news volume. Note thatthis variable is only available from 1985Q1.Second, we use the economic policy uncerta**in**ty (EPU) **in**dex constructed byBaker et al. (2012). The EPU **in**dex is built on the follow**in**g components:the frequency of newspaper references to economic policy uncerta**in**ty, thenumber of federal tax code provisions set to expire, **and** the extent of forecasterdisagreement over future **in**flation **and** government purchases. As forthe Google **in**dex, this variable is only available from 1985.The uncerta**in**ty measures are plotted **in** Figures 1 **and** 2.3.2 Macroeconomic variablesFor each country we **in**clude the follow**in**g macroeconomic variables: the CPI**in**flation rate, GDP, **in**vestments, private consumption, the short term **in**terestrate. In addition we **in**clude the real effective exchange rate for the sixsmall open economies. Inflation is computed as the annual growth rate of theCPI **in**dex **and** is expressed **in** percentage terms. GDP, **in**vestment **and** privateconsumption are **in**stead expressed **in** real terms **and** transformed us**in**gnatural logarithms. 98 More precisely, accord**in**g to Bachmann et al. (2013), the survey is sent to firms **in**Delaware, the southern half of New Jersey, **and** the eastern two-thirds of Pennsylvania,with voluntary participation, **and** monthly responses from executives **in** 100-125 firms.9 For Norway we exclude the oil sector **and** use GDP **and** **in**vestments for the ma**in**l**and**-Norway only. This is important because the oil sector is relatively large **in** Norway, **and**8

To construct **in**vestment series which are both comparable across countries**and** consistent with the theoretical model, we use “gross fixed capital formation”of the private sector. These series are taken from Datastream wherethe orig**in**al sources are the national statistical offices. For all countries, theshort term **in**terest rate is the **in**terest rate on 3 months government bonds.It is expressed **in** percentage terms **and** is considered as an **in**dicator of themonetary policy stance. Our measure of the real exchange rate is the “CPIreal effective exchange rate” published **in** the International F**in**ancial Statisticsof the IMF. It is a trade weighted measure of real exchange rate, **and** itis constructed so that an **in**crease means an appreciation of the currency.3.3 Empirical modelTo study how time-vary**in**g uncerta**in**ty affects the transmission of monetarypolicy, we estimate an **in**teracted structural VAR model. By **in**teract**in**g themacroeconomic variables with the uncerta**in**ty **in**dex, we allow the impact ofmonetary policy to change with the degree of uncerta**in**ty. The model buildson the **in**teracted panel VAR model developed by Towb**in** **and** Weber (2013)**and** Sa et al. (2013). However, it differs **in** two aspects. First, while the twomentioned papers use a panel approach, we apply a separate model to eachof the economies we study. Second, the **in**teraction term we use differs fromthe two mentioned papers. Notably, with this approach time-variation **in**the effect of policy is directly l**in**ked to a specific determ**in**ant, uncerta**in**ty,**in** contrast to the studies that use VARs with stochastically time-vary**in**gcoefficients, such as Canova **and** Gambetti (2009) **and** Primiceri (2005).We consider the follow**in**g **in**teracted VAR model:Y t = A 0 + B 0 X t +L∑l=1(Al Y t−1 + B l Y SMt−1 X t)+ CZt + E t (2)where E t is a vector of reduced form residuals at time t. The vector Y tconta**in**s CPI **in**flation, GDP, private consumption, private **in**vestments, **and**the short term **in**terest rate. For the small open economies we also **in**cludethe real exchange rate. Furthermore, the model allows the variables **in** Y t to**in**teract with X t . X t is also **in**cluded as an additional regressor. 10largely driven by other forces than the rest of the Norwegian economy.10 This is the multivariate analog to a st**and**ard **in**teraction term, **in** which the effects of Y t−lon Y t is a l**in**ear function of X t .9

The **in**teraction term X t is the uncerta**in**ty measure, assumed to be exogenous**in** our model. We use a four quarter mov**in**g average to account for a laggedreaction of consumers **and** **in**vestors to the level of uncerta**in**ty. Note that**in** our exercise we want to quantify the extent to which the response of theendogenous variables to the **in**terest rate changes with the level of uncerta**in**ty.Therefore, **in** each equation we **in**teract X t only with the lags of the **in**terestrate.The vector Z t conta**in**s additional exogenous variables. For all countrieswe **in**clude a l**in**ear trend **in** Z t , **and** for the small open economies we also**in**clude the U.S. **in**terest rate. We have also considered specifications wherewe **in**clude commodity prices or oil prices **in** Z t , both because their **in**clusionhas been proposed as important to identify monetary policy shocks withoutgenerat**in**g a “price puzzle”, **and** because several of the small open economieswe consider are commodity producers. Our results are robust to **in**clud**in**gcommodity prices or oil prices **in** the model.A 0 is a vector of constant terms, while B 0 , A l , B l **and** C, are parametervectors for the **in**teracted variable (X t ), the endogenous variables (Y t ), the**in**teraction term (Y t−1 X t ) **and** the exogenous variables (Z t ), respectively.F**in**ally, several of the countries we study have changed monetary policyregime **and** adopted **in**flation target**in**g over our sample period. In Z t wetherefore **in**clude a dummy variable which takes the value 1 for the periodafter the regime change. 11To study the effect of policy effectiveness **in** our econometric model, we needto identify monetary policy shocks. Our identification strategy is expla**in**edbelow.3.4 Estimation **and** IdentificationFor the U.S. analysis, we identify monetary policy shocks by impos**in**g recursiveshort-run restrictions, allow**in**g the **in**terest rate to respond with**in** thesame quarter to all the macroeconomic variables, but not vice versa. Hence,macroeconomic variables react with a lag to monetary policy shocks. Thisrecursive structure **in** the identification of monetary policy is the most con-11 For Norway we also follow Bjørnl**and** **and** Jacobsen (2010) **and** **in**clude three dummyvariables for 1992Q3, 1992Q4 **and** 1993Q1 to account for episodes of extreme turbulence**in** the **in**terest rate **and** exchange rate due to the breakdown of the fixed exchange rateregime.10

ventional one **in** the established SVAR literature, see for **in**stance (see Stock**and** Watson (2001) **and** Christiano et al. (1999)).For the small open economies, we deal with the simultaneity between theexchange rate **and** the **in**terest rate by employ**in**g a mixture of sign **and**contemporaneous zero restrictions. We allow both the **in**terest rate **and** theexchange rate to respond with**in** the same quarter to all other macroeconomicvariables **in**cluded **in** the VAR, but not vice versa. In addition, we allowthe **in**terest rate **and** the exchange rate to react contemporaneously to eachother. In order to to separate a monetary policy shock **and** an exchange rateshock we impose two additional sign restrictions. We follow Jaroc**in**ski (2010)**and** impose that a positive monetary policy shock is associated with a jo**in**t**in**crease **in** the **in**terest rate **and** an appreciation of the exchange rate, whilean exchange rate shock is associated with a decrease **in** the **in**terest rate **and**an appreciation of the exchange rate. 12 The sign restrictions are imposed tohold for two quarters.As with st**and**ard **in**teraction terms, the effect of the identified shock canthen be graphed for different levels of the variable X t . We choose to focuson the bottom decile **and** on the top decile of the uncerta**in**ty **in**dicators.We estimate our model us**in**g Bayesian techniques. Follow**in**g Sims **and** Zha(1999), Uhlig (2005) **and** Sa et al. (2013) we impose that the priors, **and**hence also the posterior density, of the regression coefficients **and** the covariancematrix belongs to the Normal-Wishart family. We use un**in**formativepriors, **and** draw all parameters jo**in**tly from the posterior (**in**clud**in**g the coefficientson the **in**teraction terms). 13 The priors **and** the implementation ofthe Bayesian estimation are discussed **in** more detail **in** appendix A. Oncewe have estimated the parameters of the VAR **in** equation (2) we identifystructural shocks with the strategies expla**in**ed above. When impos**in**g signrestrictions for the small open economies we follow Rubio-Ramirez et al.(2010). For each posterior draw of the covariance matrix we compute thematrix R, obta**in**ed by orthogonaliz**in**g the variance covariance matrix 14 **and**multiply**in**g it by an orthonormal matrix Q. The matrix Q is constructedexactly as **in** Jaroc**in**ski (2010): it is an identity matrix with a lower blockobta**in**ed via a QR decomposition of a 2 × 2 r**and**om matrix drawn from an12 See Bjørnl**and** (2009) for an alternative way to separate exchange rate shocks **and** monetarypolicy shocks us**in**g long-run restrictions.13 We start with 22,000 draws, discard the first 2,000 of them, **and** thereafter select onlyevery tenth draw to avoid correlation. Consequentially, we are left with 2,000 draws of theparameters.14 We here use a st**and**ard Choleski factorization.11

**in**dependent st**and**ard normal. We keep the posterior draw if the matrix Rgenerates impulse responses that satisfy the sign restrictions for both shocks.For a given parameter draw, we keep 100 impulse responses which satisfy ourrestrictions.To draw the impulse responses to a given shock we must specify values of the**in**teraction variable X t at which to evaluate the effect of the shock. This isaga**in** the multivariate analog to a st**and**ard **in**teraction term. As for st**and**ardl**in**ear regressions like y t = β 0 + β 1 z t + β 2 x t + β 3 x t z t + ε t , the presence of∂ythe **in**teraction term implies that: t∂x t= β 2 + β 3 z t . This means that theeffect of a change **in** x t is a l**in**ear function of the value of the variable z t .To quantitatively evaluate the importance of the **in**teraction effect we mustchoose two values of the variable z t , which we denote “z hight ” **and** “ztlow ”, **and**compute impulse responses under each of them. In our exercise we use thevalues of the uncerta**in**ty measures correspond**in**g to the top 10% **and** to thebottom 10% of their distribution. From the Figures 1 **and** 2 it is evident thatthe episodes of highest uncerta**in**ty **in** our sample correspond to the periodsaround the “Black Monday” stock market crash, the 9/11 terror attack, thecollapse of the dot-com bubble, **and** f**in**ally the onset of the sub-prime crisis.After hav**in**g assigned values to the variable X t the estimated VAR reducesto:Y hightY lowt= ̂Dhigh ∑ Lhigh0 + (̂D l Yt−l ) + ĈZ t + Êtl=1= ̂Dlow ∑ Llow0 + (̂D l Yt−l ) + ĈZ t + Êtl=1where ̂D 0high= Â 0 + ̂B 0 X high **and** ̂D 0low= Â 0 + ̂B 0 X low . Similarly, ̂D lhigh=Â l + ̂B l X high **and** ̂D llow= Â l + ̂B l X low . These are st**and**ard reduced formVAR-models, **and** there is therefore no further complication associated withus**in**g the restrictions discussed above to identify a monetary policy shock**and** analyze its effects at high **and** low levels of uncerta**in**ty on the variables**in**cluded **in** Y t . F**in**ally, for the small open economies where a sign restrictionis employed, we compute the impulse responses apply**in**g the “median targetmethod” proposed by Fry **and** Pagan (2011).12

3.5 A Test Statistic for the Interaction EffectBecause there exists correlation between impulse responses for low **and** highlevels of uncerta**in**ty, the confidence b**and**s around each response alone yieldsa distorted impression about the statistical significance of their difference.Hence, to assess the difference more formally, we perform a test us**in**g theimpulse responses based on draws of the posterior parameters. For eachof the 2,000 saved draws we compute the differences between the responseof the variables to a monetary policy shock under high **and** low uncerta**in**ty,respectively. This provides us with an empirical distribution of the differencebetween the responses, which we can then use to compute a probability b**and**.The two impulse responses can be considered statistically different from eachother if the **in**terval between the probability b**and**s lie above or below zero.We will report these probability b**and**s **in** figures. Each figure will displaythe distribution of the the difference between the impulse response underhigh **and** low uncerta**in**ty. For example, a positive value for **in**vestment willmean that a monetary tighten**in**g causes a greater drop **in** **in**vestment whenuncerta**in**ty is low than when uncerta**in**ty is high. For each variable, we willreport 84% **and** the 95% probability b**and**s, respectively.4 Uncerta**in**ty **and** the Effect of MonetaryPolicy Shocks **in** the USWe first estimate how uncerta**in**ty affects the transmission of monetary policyshocks **in** the United States.4.1 Interaction with Stock Market VolatilityOur start**in**g po**in**t is to estimate the effects of monetary policy shocks us**in**gstock market volatility as our measure of uncerta**in**ty. Figure 3 displays theeffects of a one percentage po**in**t unanticipated **in**crease **in** the policy rate.The impulse responses with circles are estimated for the case where volatilityis **in** its upper decile, while the curves with marks give the estimated responseswhen volatility is **in** its lower decile. The figure plots responses for the first20 quarters after the shock.We see that for GDP, **in**vestment **and** consumption, responses are sizeable,**and** **in** l**in**e with conventional monetary theory, when volatility is low. In13

contrast, when stock market volatility is high, the same variables respondnegligibly. Investment falls by less than 0.2 % when volatility is **in** its upperdecile, while it falls by more than 1 % when volatility is low. This differenceis consistent with the cautiousness effect expla**in**ed above. Consumptiondisplays a similar pattern, **and** it falls by a maximum of almost 3 percentagepo**in**ts when volatility is low, which is about ten times more than whenuncerta**in**ty is high. The GDP response is consistent with the **in**vestment**and** consumption movements, **and** it falls by at most 1 percentage po**in**twhich is about five to ten times the response when volatility is high.For **in**flation, we see that **in** both the high **and** low volatility scenarios, thereis a “price puzzle” as **in**flation **in**itially **in**creases **in** response to the monetarytighten**in**g. This puzzle is a well-known by-product of us**in**g a structural VARwith recursive order**in**g to identify monetary policy shocks, see for **in**stanceSims (1992) **and** Christiano et al. (1999). More **in**terest**in**gly, we see that this**in**itially positive **in**flation response is practically **in**sensitive to the level ofstock market volatility. Moreover, once the **in**itial **in**crease has tapered off,the response under high uncerta**in**ty settles at zero, while the low-uncerta**in**tyresponse becomes negative after about 10 quarters.The test statistic for each difference **in** impulse response is reported **in** Figure4. As we would expect from the large effects discussed above, we see that forthe real variables, the 95% probability b**and**s all lie above zero. For **in**flationthe difference between responses becomes significant at the 84% level after14 quarters, but the 95% b**and**s always conta**in** zero.4.2 Interaction with Alternative Uncerta**in**ty MeasuresThe first alternative uncerta**in**ty measure we consider is the corporate bondspread. Figures 5 **and** 6 report impulse responses **and** the test statistic,respectively. **Qualitative**ly, the pattern is very similar to what we obta**in**edus**in**g stock market volatility, but quantitatively the effects are weaker. GDP,**in**vestment **and** consumption all fall about twice as much when uncerta**in**ty islow. The test statistic shows that these differences are statistically significant.For **in**flation, there is now no difference **in** responses.Next, we use forecaster disagreement. Figure 7 shows that the effect of amonetary tighten**in**g on the three real variables is approximately halved whenforecaster disagreement is **in** its upper decile rather than its lower decile. Thetest statistics **in** Figure 8 show that these differences are significant at the14

84% level, but not at the 95% level. For **in**flation, the **in**itial **in**crease isnow more pronounced when uncerta**in**ty is high. After 5 quarters forecasterdisagreement is irrelevant.The results us**in**g the Google-**in**dex are given **in** Figures 9 **and** 10. Note thatthe sample beh**in**d these results is considerably shorter, as the Google-**in**dexgoes back only to 1985. Once aga**in** we see lower effects of policy on real activitywhen uncerta**in**ty is high. **Quantitative**ly, the **in**fluence of uncerta**in**tyis similar to what we found us**in**g the credit spread **and** forecaster disagreement:the responses of real variables are roughly halved when uncerta**in**ty is**in** its upper rather than **in** its lower decile. The 84% b**and**s consistently lieabove zero, whereas the 95 % b**and**s at some po**in**t exceed zero for all threereal variables. For **in**flation, the **in**fluence of uncerta**in**ty is negligible.F**in**ally, we consider the EPU-**in**dex, which also starts **in** 1985. Figures 11 **and**12 shows that this uncerta**in**ty measure pa**in**ts a very different picture thanthe other four. The **in**itial effect of the monetary policy shock on the realeconomy is greater when the EPU-**in**dex is high, the direct opposite effectof what we have seen before. Moreover, the **in**terest rate dynamics nowdiffer a great deal with the uncerta**in**ty measure, with far higher persistencewhen uncerta**in**ty is low. Inflation responds positively **and** persistently whenuncerta**in**ty is low, **and** negligibly when uncerta**in**ty is high. A potentialreason why the EPU-**in**dex gives such different results could be that theevents it captures are related to uncerta**in**ty about future monetary policy.In a period of high policy uncerta**in**ty, expansive policy might stimulate theeconomy by reduc**in**g the policy uncerta**in**ty itself, which would expla**in** thereal effects **in** Figure 11. In a nutshell, our practice of treat**in**g the uncerta**in**ty**in**dexes as exogenous is likely to be particularly severe when we consider theEPU-**in**dex.5 Uncerta**in**ty **and** the Effect of MonetaryPolicy Shocks **in** Small Open EconomiesIn this section we extend our analysis to a set of six small open economies.We will study the **in**teraction effects between monetary policy shocks **and** thesame U.S.-based uncerta**in**ty measures as we utilized above. Partly, this canbe seen as a robustness check, to see if our **in**sights from the United Stateshold more generally. More importantly though, by study**in**g how small openeconomies are affected by uncerta**in**ty measured **in** the United States, our15

esults are less prone to any potential biases from treat**in**g uncerta**in**ty asexogenous. For some of these countries, such as New Zeal**and** **and** Norway,it is highly unlikely that their macroeconomic development is **in**fluenc**in**g theUS-based uncerta**in**ty measures to any noteworthy extent. For others, suchas the United K**in**gdom, this might be more likely. We therefore displayresults for each country separately.Us**in**g U.S. stock market volatility to measure uncerta**in**ty, our results for thesix countries are displayed **in** Figures 13 to 24. In general, the responses to aone st**and**ard deviation **in**crease **in** the **in**terest rate are as expected: **in**flation,output, **in**vestments **and** private consumption decrease, while the exchangerate appreciates **in** all countries except Australia.The starkest pattern from this analysis is that for **in**vestment, the effect ofuncerta**in**ty is highly similar to what we found for the United States: Whenuncerta**in**ty is high, the **in**itial **in**vestment responses are dampened **in** allcountries. In Australia, Switzerl**and** **and** New Zeal**and** the response of private**in**vestments is negative **and** statistically significant only when uncerta**in**ty islow, while it is small **and** statistically **in**significant otherwise. For the UK,Norway **and** Canada the response of **in**vestments is statistically significantboth with low **and** high levels of uncerta**in**ty, but the magnitude of the responseis about three times larger **in** a low-uncerta**in**ty environment. In fiveof six cases the 95% probability b**and**s of the response differences exceed zeroat some horizon after the shock. **Quantitative**ly, the **in**vestment responsesare about two (New Zeal**and** **and** the UK) to five (Australia) times higherwhen stock market volatility is **in** the bottom decile than when it is **in** thetop decile.For GDP, the response to a monetary policy shock is weaker under highuncerta**in**ty **in** four out of six countries, while **in** the last two (Norway **and**Switzerl**and**) the difference is negligible. The pattern of consumption responsesis what differs the most from our previous f**in**d**in**gs from the UnitedStates, **and** the effects vary considerably across countries. For Norway, consumptiondecl**in**es more when uncerta**in**ty is high, while **in** the UK, NewZeal**and** **and** Switzerl**and**, its response is generally more muted **and** it is negative**and** statistically significant only when the level of uncerta**in**ty is low.In Australia **and** Canada the response of consumption is negative **and** statisticallysignificant irrespective of the level of uncerta**in**ty. In four out of thesix countries we study there is a price puzzle. It is smaller for these smallopen economies than what we observed for the US.As we did for the United States, we have also extended our analysis of thesmall open economies by consider**in**g alternative uncerta**in**ty measures. With16

the U.S. credit spread as **in**teract**in**g variable, the results are qualitativelysimilar to what we found before. In all countries the **in**vestment response issmaller when uncerta**in**ty is high, **and** **in** all countries except Australia, the84% probability b**and**s lie above zero over an extended period. In contrast,when uncerta**in**ty is measured by forecaster disagreement, the Google **in**dexor the EPU **in**dex, no clear pattern arises.Overall, it seems that the two uncerta**in**ty measures based on U.S. f**in**ancialmarkets yield considerable **in**teraction effects for **in**vestments, while the nonf**in**ancial**in**dicators do not. A likely reason for this dichotomy is that whereasf**in**ancial markets are **in**ternationally **in**tegrated, **and** therefore tend to reflectaspects of the economic environment that are relevant across countries, thenon-f**in**ancial measures are more specific to the United States, **and** of lessrelevance for the small open economies.6 ConclusionOver the last years economic uncerta**in**ty has been given much attention,both by policymakers **and** **in** the academic literature, as a potential driverof bus**in**ess cycle fluctuations. Much of the debate has been motivated bythe fear that heightened uncerta**in**ty will motivate firms **and** households todelay decisions that are costly to reverse. This paper contributes here. Ourempirical f**in**d**in**gs **in**dicate that monetary policy is less effective when uncerta**in**tyis high. In the U.S.-data, both consumption **and** **in**vestment responsesto a monetary policy shock are approximately halved when uncerta**in**ty ishigh rather than low, **and** for **in**vestment the pattern holds across a set of sixsmall open economies. Taken at face value, this implies that **in** the face ofhigh uncerta**in**ty, monetary policymakers may face a trade-off between act**in**gdecisively **and** act**in**g correctly, as policy must be more aggressive thanotherwise **in** order to stabilize economic activity.Our results are consistent with the “cautiousness” effects suggested by economictheory about **in**dividuals who face non-convex adjustment costs. However,two of our f**in**d**in**gs may imply that alternative mechanisms are also atplay. First, non-convexities should be more important for **in**vestment thanconsumption, which conflicts somewhat with the f**in**d**in**g that **in** the UnitedStates uncerta**in**ty dampens consumption responses as much as **in**vestmentresponses. Second, the pattern of reduced policy effect is particularly stark,**and** the effects particulary large, when uncerta**in**ty measures from f**in**ancialmarkets are utilized. Further research on the exact mechanism beh**in**d the17

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AppendicesAppendix ABayesian estimation **and** priorsWe use an un**in**formative version of the natural conjugate priors described **in**Kadiyala **and** Karlsson (1997) **and** Koop et al. (2007). For simplicity, assumewe can rewrite equation 2 **in** the follow**in**g form:Y = Xβ + ɛ (3)where X now **in**cludes all regressors **in** equation 2, i.e. lagged endogenous,exogenous **and** **in**teracted variables, **and** ɛ has a variance-covariance matrixΣ.We apply the general Matricvariate Normal - Wishart priors for β **and** Σ −1 .where**and**p(β, Σ −1 ) = p(β)p(Σ −1 ), (4)(β|Σ) ∼ MN (β, V ) (5)(Σ −1 ) ∼ W(H, ν) (6)Non**in**formativeness is then achieved by impos**in**g that ν = 0 **and** H −1 = 0×I.By us**in**g the prior, we can derive the follow**in**g conditional posteriors forp(β|Y, Σ −1 )(beta|Y, Σ −1 ) ∼ MN (β, V ) (7)where**and****and** likewise for p(Σ −1 |Y, β)V = (V −1 +β = V (V −1 +T∑X ′ Σ −1 X) −1 (8)t=1T∑X ′ Σ −1 Y ) (9)t=1(Σ −1 |Y, β) ∼ W(H, ν) (10)whereν = T + ν (11)21

**and**H = [H −1 +T∑X ′ Σ −1 (Y − Xβ)(y − xβ) ′ ] −1 (12)t=1We then use the Gibbs sampler to sequentially draw from the normalp(β|Y, Σ −1 ) **and** the wishart p(Σ −1 |Y, β).22

Appendix BFiguresFigure 1: Uncerta**in**ty Measures S**in**ce 1970Note: The quarterly average of the stock market volatility **in**dex constructed as **in** Bloom(2009), a corporate bond spread **and** the forecast disagreement measure used **in** Bachmannet al. (2013) for the period 1970Q1-2011Q3. Each series has been demeaned **and** st**and**ardizedby its st**and**ard deviation.Figure 2: Uncerta**in**ty Measures S**in**ce 1985Note: The quarterly average of the policy uncerta**in**ty **in**dex **in** Baker et al. (2012) **and**the Google **in**dex used **in** Bachmann et al. (2013). Each series has been demeaned **and**st**and**ardized by its st**and**ard deviation.23

Figure 3: Monetary Policy Shock - USA - Stock Market VolatilityNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the stock market volatility **in**dex. Low uncerta**in**ty depicts responses whenstock market volatility is **in** its lower decile. High uncerta**in**ty depicts responses when stockmarket volatility is **in** its upper decile.Figure 4: Test - USA - VXO24Note: The distribution of the difference between the impulse responses under high **and** lowlevels of stock market volatility as described **in** section 3.5. The shaded areas represent the84% **and** the 95% probability b**and**s, respectively

Figure 5: Monetary Policy Shock - USA - Credit SpreadNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the credit spread. Low uncerta**in**ty depicts responses when the creditspread is **in** its lower decile. High uncerta**in**ty depicts responses when the credit spread is**in** its upper decile.Figure 6: Test - USA - Credit Spread25Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the credit spread as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively

Figure 7: Monetary Policy Shock - USA - Forecaster DisagreementNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the forecaster disagreement **in**dex. Low uncerta**in**ty depicts responseswhen the uncerta**in**ty measure is **in** its lower decile. High uncerta**in**ty depicts responseswhen the uncerta**in**ty measure is **in** its upper decile.Figure 8: Test - USA - Forecaster Disagreement26Note: The distribution of the difference between the impulse responses under high **and** lowlevels of forecaster disagreement, as described **in** section 3.5. The shaded areas representthe 84% **and** the 95% probability b**and**s, respectively

Figure 9: Monetary Policy Shock - USA - GoogleNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the Google-**in**dex. Low uncerta**in**ty depicts responses when the the Google**in**dexis **in** its lower decile. High uncerta**in**ty depicts responses when the the Google-**in**dexis **in** its upper decile.Figure 10: Test - USA - Google27Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the Google-**in**dex, as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively

Figure 11: Monetary Policy Shock - USA - Economic Policy Uncerta**in**tyNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the EPU-**in**dex. Low uncerta**in**ty depicts responses when the EPU-**in**dexis **in** its lower decile. High uncerta**in**ty depicts responses when the EPU-**in**dex is **in** itsupper decile.Figure 12: Test - USA - Economic Policy Uncerta**in**ty28Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the EPU-**in**dex, as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively

Figure 13: Monetary Policy Shock - AUS - Stock Market VolatilityNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the stock market volatility **in**dex. Low uncerta**in**ty depicts responses whenstock market volatility is **in** its lower decile. High uncerta**in**ty depicts responses when stockmarket volatility is **in** its upper decile.Figure 14: Test - AUS - Stock Market Volatility29Note: The distribution of the difference between the impulse responses under high **and** lowlevels of stock market volatility as described **in** section 3.5. The shaded areas represent the84% **and** the 95% probability b**and**s, respectively

Figure 15: Monetary Policy Shock - CAN - Stock Market VolatilityNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the stock market volatility **in**dex. Low uncerta**in**ty depicts responses whenstock market volatility is **in** its lower decile. High uncerta**in**ty depicts responses when stockmarket volatility is **in** its upper decile.Figure 16: Test - CAN - Stock Market Volatility30Note: The distribution of the difference between the impulse responses under high **and** lowlevels of stock market volatility as described **in** section 3.5. The shaded areas represent the84% **and** the 95% probability b**and**s, respectively

Figure 17: Monetary Policy Shock - CHE - Stock Market VolatilityNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the stock market volatility **in**dex. Low uncerta**in**ty depicts responses whenstock market volatility is **in** its lower decile. High uncerta**in**ty depicts responses when stockmarket volatility is **in** its upper decile.Figure 18: Test - CHE - Stock Market Volatility31Note: The distribution of the difference between the impulse responses under high **and** lowlevels of stock market volatility as described **in** section 3.5. The shaded areas represent the84% **and** the 95% probability b**and**s, respectively

Figure 19: Monetary Policy Shock - NOR - Stock Market VolatilityNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the stock market volatility **in**dex. Low uncerta**in**ty depicts responses whenstock market volatility is **in** its lower decile. High uncerta**in**ty depicts responses when stockmarket volatility is **in** its upper decile.Figure 20: Test - NOR - Stock Market Volatility32Note: The distribution of the difference between the impulse responses under high **and** lowlevels of stock market volatility as described **in** section 3.5. The shaded areas represent the84% **and** the 95% probability b**and**s, respectively

Figure 21: Monetary Policy Shock - NZL - Stock Market VolatilityNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the stock market volatility **in**dex. Low uncerta**in**ty depicts responses whenstock market volatility is **in** its lower decile. High uncerta**in**ty depicts responses when stockmarket volatility is **in** its upper decile.Figure 22: Test - NZL - Stock Market Volatility33Note: The distribution of the difference between the impulse responses under high **and** lowlevels of stock market volatility as described **in** section 3.5. The shaded areas represent the84% **and** the 95% probability b**and**s, respectively

Figure 23: Monetary Policy Shock - UK - Stock Market VolatilityNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the stock market volatility **in**dex. Low uncerta**in**ty depicts responses whenstock market volatility is **in** its lower decile. High uncerta**in**ty depicts responses when stockmarket volatility is **in** its upper decile.Figure 24: Test - UK - Stock Market Volatility34Note: The distribution of the difference between the impulse responses under high **and** lowlevels of stock market volatility as described **in** section 3.5. The shaded areas represent the84% **and** the 95% probability b**and**s, respectively

Figure 25: Monetary Policy Shock - AUS - SpreadNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the credit spread. Low uncerta**in**ty depicts responses when the creditspread is **in** its lower decile. High uncerta**in**ty depicts responses when the credit spread is**in** its upper decile.Figure 26: Test - AUS - Spread35Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the credit spread as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively

Figure 27: Monetary Policy Shock - CAN - SpreadNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the credit spread. Low uncerta**in**ty depicts responses when the creditspread is **in** its lower decile. High uncerta**in**ty depicts responses when the credit spread is**in** its upper decile.Figure 28: Test - CAN - Spread36Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the credit spread as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively

Figure 29: Monetary Policy Shock - CHE - SpreadNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the credit spread. Low uncerta**in**ty depicts responses when the creditspread is **in** its lower decile. High uncerta**in**ty depicts responses when the credit spread is**in** its upper decile.Figure 30: Test - CHE - Spread37Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the credit spread as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively

Figure 31: Monetary Policy Shock - NOR - SpreadNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the credit spread. Low uncerta**in**ty depicts responses when the creditspread is **in** its lower decile. High uncerta**in**ty depicts responses when the credit spread is**in** its upper decile.Figure 32: Test - NOR - Spread38Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the credit spread as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively

Figure 33: Monetary Policy Shock - NZL - SpreadNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the credit spread. Low uncerta**in**ty depicts responses when the creditspread is **in** its lower decile. High uncerta**in**ty depicts responses when the credit spread is**in** its upper decile.Figure 34: Test - NZL - Spread39Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the credit spread as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively

Figure 35: Monetary Policy Shock - UK - SpreadNote: Impulse responses to a one percentage po**in**t **in**crease **in** the **in**terest rate, for twodifferent levels of the credit spread. Low uncerta**in**ty depicts responses when the creditspread is **in** its lower decile. High uncerta**in**ty depicts responses when the credit spread is**in** its upper decile.Figure 36: Test - UK - Spread40Note: The distribution of the difference between the impulse responses under high **and** lowlevels of the credit spread as described **in** section 3.5. The shaded areas represent the 84%**and** the 95% probability b**and**s, respectively