Nicolas Himounet
email: nicolas.himounet@univ-paris13.fr

Francisco Serranito
email: francisco.serranito@parisnanterre.fr

Julien Vauday
email: julien.vauday@univ-paris13.fr

Uncertainty is bad for Business. Really?

Keywords: Uncertainty, local projection methods, economic activity. JEL Codes: C32, C38, E32

We investigate the impact of uncertainty shocks according to their nature applying local projection methods in a nonlinear framework. More precisely, we investigate the impact of uncertainty shocks according to their nature (nonfinancial and financial) in different regimes of general uncertainty: high, moderate and low. We get a positive and significant effect of the nonfinancial uncertainty shocks when the general level of uncertainty is high or moderate.

Introduction

The common wisdom about uncertainty is that it is negative. The last financial crisis and the following surge of papers in the literature that study the effects of uncertainty were perceived as empirical validations of this consensus. However, since the middle of the last decade some papers have started to consider the possibility that some forms of uncertainty may instead have a positive impact on the economy. This recent and still rare literature has started with a paper by [START_REF] Segal | Good and bad uncertainty: Macroeconomic and financial market implications[END_REF] that states uncertainty may also be about positive growth perspectives. For instance one may think to recent developments on Artificial Intelligence (AI). Despite forecasting what will be the industrial achievements due to AI in ten years is highly uncertain, predicting that these achievements will generate very large profits is a safe bet. Some authors refer to this theory as the ''growth option'' theory. [START_REF] Segal | Good and bad uncertainty: Macroeconomic and financial market implications[END_REF] postulate that uncertainty may be good or bad, they develop a theoretical model in which they introduce good and bad shocks and study the effect of uncertainty surrounding those shocks. They show theoretically that good uncertainty may have a positive effect on various variables when there is a channel through which uncertainty influences future growth. They then confirm this empirically.

Another paper that highlights a positive effect of uncertainty is [START_REF] Ludvigson | Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response?[END_REF].

They use an index of macroeconomic uncertainty (developed in a previous paper, [START_REF] Jurado | Measuring Uncertainty[END_REF] and an index of financial uncertainty which is newly built for this work. They have various results but focusing on a possible positive effect of uncertainty, they find that a shock on the macroeconomic uncertainty generally has a positive effect on industrial production on the short term that turns negative in the long-run. They argue that the positive effect they identify confirms the ''growth option'' theory. [START_REF] Forni | Downside and Upside Uncertainty Shocks[END_REF], rely on the work by [START_REF] Adrian | The Term Structure of Growth-at-Risk[END_REF] to estimate quantiles of predicted growth to also distinguish good and bad uncertainty. They show that despite the main effect on real economic activity of uncertainty is related to its bad component, it is possible that its positive one may have a positive effect. They explain that the reason why they, as well as the other papers of this literature, mostly find a negative effect of uncertainty is due to the predominance of its negative components in the data. [START_REF] Larsen | Components of Uncertainty[END_REF] uses machine learning techniques that autonomously identify some types of uncertainty by analyzing many Norwegian business press articles. Then the author introduces these various types in SVARs and it appears that some of them, especially those related to business (e.g. Mergers & acquisitions), have a positive effect.

One last paper that finds a short run positive effect of uncertainty is [START_REF] Ferrara | Commodity price uncertainty comovement: Does it matter for global economic growth? CAMA Working Papers 2022-08[END_REF].

They show that an energy-specific uncertainty shock may have a short run positive effect on economic activity. This result being especially true for countries that produce energy. This paper is in line with this very recent literature in that it is about finding under which conditions uncertainty may have a positive effect. Despite very rare, previous empirical results highlight that positive uncertainty may come from industrial prospects or be more broadly macroeconomic. Arguably, industrial perspectives are a subset of the macroeconomic context.

To the contrary, uncertainty is not positive when it is about finance. The three papers above as well as the other works analyzing the effects of uncertainty starting with the seminal paper of [START_REF] Bloom | The Impact of Uncertainty Shocks[END_REF] do all conclude that uncertainty related to financial variables has a clear negative impact. So we first propose a mean to empirically distinguish endogenously financial uncertainty from non financial one. Second, we show that non financial uncertainty may have a positive effect under some conditions. Contrary to previous works that find a positive effect of uncertainty, we provide a more general approach that allows to identify a positive effect of uncertainty.

Concerning the theoretical mechanisms that may explain a positive effect of uncertainty. [START_REF] Segal | Good and bad uncertainty: Macroeconomic and financial market implications[END_REF] proposes a model based on the intuition that when it concerns industrial prospects, uncertainty may be good. [START_REF] Ludvigson | Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response?[END_REF] refer to this mechanism as the ''growth option'' theory and connect it to several old papers [START_REF] Oi | The Desirability of Price Instability Under Perfect Competition[END_REF][START_REF] Hartman | The effects of price and cost uncertainty on investment[END_REF]Tisdell, 1978;[START_REF] Abel | Optimal Investment under Uncertainty[END_REF]) that in fact are not really directly about growth [START_REF] Larsen | Components of Uncertainty[END_REF], does a distinction). They rather show that because firms are not risk averse, they may prefer price instability because the best uncertain issues generate very large profits. Nevertheless, they all relate to industry inasmuch firms are at the center of these mechanisms. In this paper, we add to these possible mechanisms another one that is inferred from recent works by [START_REF] Papers | A Sparsity-Based Model of Bounded Rationality[END_REF][START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF] on behavioral new Keynesian models. Simply put, the idea is as follows. The second article shows that agents, because they are partly myopic, fail to perfectly anticipate future taxes after a stimulus is enacted. This implies that Ricardian equivalence does not hold. The first article as for it models how agents decide what degree of attention to bring to each existing information in order to process an action aimed at optimizing their utility. We develop what we may call an intuitive demonstration, despite not a formal proof, that conditions under which increased uncertainty may lead to a reduced mean attention do exist. As a consequence, by increasing agent's myopia, uncertainty may lead stimuli to have a stronger (positive) effect. This leads us to posit that uncertainty may have a positive effect not only when it concerns industrial aspects but more generally when it is non-financial.

Come back to the empirics of uncertainty. This is an unobservable phenomenon and measuring it is clearly a challenge. In recent years, a booming economic research has emerged to take up this challenge and to propose how to quantify uncertainty. [START_REF] Ferrara | Uncertainty Fluctuations: Measures, Effects and Macroeconomic Policy Challenges[END_REF] review all the different methodologies to measure uncertainty and their impact on macroeconomic variables. In this paper, we contribute to this growing empirical literature and we propose three new improvements. Firstly, using a new measure of general uncertainty (See [START_REF] Himounet | Searching the nature of uncertainty: Macroeconomic and financial risks VS geopolitical and pandemic risks[END_REF], we provide an empirical analysis in order to identify not only changes in the overall level of uncertainty in the US but also the determinants of an uncertainty shock (financial, macroeconomic policy, news index, geopolitical risks, ...). Secondly, we identify the conditions under which uncertainty could have a positive effect on the economy by testing an intuition derived from Gabaix? results in a linear VAR model. Thirdly, we validate this intuition using a non linear VAR model hence empirically proving that conditions which for uncertainty has a positive effect on the economy do exist.

As in [START_REF] Himounet | Searching the nature of uncertainty: Macroeconomic and financial risks VS geopolitical and pandemic risks[END_REF], we apply a principal component analysis (PCA) in order to build up a global measure of uncertainty for the US using new measures recently developed in the literature. The novelty of our approach is to interpret and use both the first and the second factors of the PCA. In particular, if as expected the first factor can be interpreted as a measure of the general level of uncertainty, the second one of this PCA is more about the nature of uncertainty. This second factor is high when uncertainty is industrial/macroeconomic, hereafter we will write non-financial, and low when it is financial. We use these factors to study the impact of uncertainty shocks using local projection methods [START_REF] Jordá | Estimation and Inference of Impulse Responses by Local Projections[END_REF] on US data on the period 1990-2019.

Our US global uncertainty variable (Factor 1) is shown to have a negative and significant effect on all the macroeconomic variables used in the estimations as the literature generally finds.

Then, we conduct the same analysis using the factor that discriminates between financial and non-financial uncertainty (Factor 2) and find no significant effect. Strikingly, using a nonlinear framework, we obtain a positive and significant effect of this second dimension of uncertainty on industrial production and a negative one on the unemployment when the general level of uncertainty is high. Several robustness checks confirm this result.

The rest of this paper is organized as follows. In section 2, we present a brief literature review on the positive effect of uncertainty and develop our intuitive demonstration from Gabaix' works. In section 3, we use local projection methods to investigate the dynamics between uncertainty and economic activity in a linear and a non linear framework. In section 4, we present robustness checks. The last section presents our conclusions and directions for future research.

Positive effect of uncertainty: Literature review and theoretical discussion

A recent literature has emerged proposing different measures of uncertainty based on various methodologies making the task of establishing a consensus on how to measure uncertainty very hard, if not impossible. This section presents the papers that have put forward a positive effect of uncertainty and then discusses the possible theoretical arguments for this positive effect. For those interested, [START_REF] Himounet | Searching the nature of uncertainty: Macroeconomic and financial risks VS geopolitical and pandemic risks[END_REF] proposes a very detailed literature review of all the papers that develops some measures of uncertainty with the aim of improving the [START_REF] Ferrara | Uncertainty Fluctuations: Measures, Effects and Macroeconomic Policy Challenges[END_REF]'s classification and uncertainty approximation with new measures and approaches.

2.1 Positive effect in the data [START_REF] Segal | Good and bad uncertainty: Macroeconomic and financial market implications[END_REF] is the first paper to break the consensus about the negative effect of uncertainty. They start from a conjecture: uncertainty may be good for business activities when considering future industrial perspectives. They give the example of the high tech revolution of the 1990s during which it was hard to guess what would be the concrete achievements for the business. However, many business analysts and specialists were almost certain that many firms would benefit from these new technologies. Arguably, it was true. Then, they first develop a theoretical model in which both kind of uncertainty shocks exist, negative and positive. These downside uncertainty and upside uncertainty. Downside uncertainty is considered as uncertainty on the future decrease of growth while upside uncertainty is considered as uncertainty on the future increase of growth.1 As expected, the authors get a negative effect of downside uncertainty and a slightly positive effect of upside uncertainty. Their results seem to underline that the negative component of uncertainty dominates the positive component in uncertainty data explaining the fact that most studies have got a negative effect. [START_REF] Ludvigson | Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response?[END_REF] have decomposed uncertainty between macroeconomic uncertainty and financial uncertainty. According to them, financial uncertainty could be very linked to recessions, both as a cause and as a propagating mechanism. Macroeconomic uncertainty and financial uncertainty are computed using [START_REF] Jurado | Measuring Uncertainty[END_REF]'s methodology. [START_REF] Jurado | Measuring Uncertainty[END_REF] have constructed a measure of macroeconomic uncertainty using a panel of macroeconomic and financial time series (industrial production, real income, hours, unemployment, prices, stock market indexes, ...).They argue that volatility measures are partly predictable. So, in order to get a ''true'' measure of uncertainty, the predictable component of each series must be removed.

Using this methodology, [START_REF] Ludvigson | Uncertainty and Business Cycles: Exogenous Impulse or Endogenous Response?[END_REF] have developed a financial uncertainty index from a panel of 148 monthly financial indicators (Treasury bill yields, price-earnings ratio, risk factors of [START_REF] Fama | The Cross-Section of Expected Stock Returns[END_REF], ...).

Then, they propose a new method to estimate a SVAR model with several event constraints.

One of their side result, this was not the objective of their paper to show this, is to find a positive effect of uncertainty. [START_REF] Himounet | A Positive Effect of Uncertainty Shocks on the Economy: Is the Chase Over ? The World Economy[END_REF] have showed that this result is at best to be considered very carefully. Indeed, it appears that the positive effect of uncertainty is fully explained by one constraint. This constraint is supposedly related to the end of Bretton-Woods but we show that it is also related to the end of a one year recession. Hence the positive effect of uncertainty would be in fact the surge of growth that followed the recession. [START_REF] Larsen | Components of Uncertainty[END_REF] relies on a different approach to measure uncertainty since he uses machine learning techniques to analyse Norwegian business articles published in a daily newspaper.

In a first step, the author uses an unsupervised learning algorithm that will both classify by topic the articles and quantify the degree of uncertainty. Each of the 80 topics may vary in time according to the degree of uncertainty that is related to it. For instance, the measure linked to the topic on Oil price varies whether events related to this topic generate more or less uncertainty.

Then he runs SVAR with narrative sign restrictions à la [START_REF] Antolín-Díaz | Narrative Sign Restrictions for SVARs[END_REF]. Some topics exhibit the usual pattern of uncertainty as more uncertainty results in a decrease in variables used to evaluate the health of an economy. However, it appears that the opposite is true for the topic on Mergers & acquisitions which for uncertainty has a positive effect on the economy. [START_REF] Ferrara | Commodity price uncertainty comovement: Does it matter for global economic growth? CAMA Working Papers 2022-08[END_REF] is the more recent paper to obtain a positive effect. The paper aims at analyzing the effect of commodity prices shock on real economic activity. They use three commodities categories, agricultural, metals and energy that each contain four different commodity prices. They first show that there is a common commodity factor that they interpret as the general uncertainty component as in many studies of the literature. Then, they isolate each pure factor related to each of the three categories of commodities. It appears that the general factor as well as those related to agricultural and metal have a negative effect. However, it turns out that the third pure factor, related to energy, has a short run positive effect. They refer to [START_REF] Punzi | The impact of energy price uncertainty on macroeconomic variables[END_REF] that argue that the risk that oil price goes too high in a near future may induce firms and households to anticipate their energy consumption hence inducing a short run positive effect of uncertainty. Then, they build on this result to construct a more systematic way to identify good and bad uncertainty: bad uncertainty would be in action when commodity prices are increasing whereas good uncertainty would be an action when commodity prices are decreasing. This last estimation yields negative or non significant effects of uncertainty.

To sum up this brief literature review, some studies posit that uncertainty may be good or bad and the others find a positive effect without especially looking for it. Among these studies three of them highlight a very specific component of uncertainty related to business activities or energy prices that indeed has a positive effect. Among the two remaining works, one is in the category of assuming that uncertainty is either good or bad and finds a small positive effect while the other's result that identifies a positive effect of uncertainty is fragile. Our paper is the first to explicitly look for a positive effect of uncertainty without trying to isolate ex ante the positive component of uncertainty.

Positive effect in the theory

Among the papers referred to above, the last two do not develop a theoretical explanation of the positive effect of uncertainty. They instead refer to two old papers by [START_REF] Oi | The Desirability of Price Instability Under Perfect Competition[END_REF] and [START_REF] Hartman | The effects of price and cost uncertainty on investment[END_REF] to which [START_REF] Larsen | Components of Uncertainty[END_REF]) adds Tisdell (1978). [START_REF] Oi | The Desirability of Price Instability Under Perfect Competition[END_REF] shows that competitive firms that maximize short term profits always prefer price instability, hence uncertainty, over price stability. Tisdell (1978) extends the results of [START_REF] Oi | The Desirability of Price Instability Under Perfect Competition[END_REF] to factors' price instability which is also preferred by competitive firms under the same conditions and shows that both output price instability and factors price instability are simultaneously preferred by competitive firms. [START_REF] Hartman | The effects of price and cost uncertainty on investment[END_REF] shows that optimal investment of firms increases or remains unchanged with increased uncertainty in future output prices and/or wage rates and that it is invariant to uncertainty in future investment costs. Using a mean preserving uncertainty, he shows that this result holds quite generally except that it requires the production function to be homogeneous of degree 1. Without going too far in analyzing these results, they mostly lay on the fact firms are risk-neutral. The explanation of [START_REF] Oi | The Desirability of Price Instability Under Perfect Competition[END_REF] and [START_REF] Hartman | The effects of price and cost uncertainty on investment[END_REF] is based on the assumptions of perfect competition. [START_REF] Caballero | On the Sign of the Investment-Uncertainty Relationship[END_REF] shows that if the assumptions of perfect competition are relaxed, firms' investments may fall when uncertainty increases but this relationship could also remain positive if firms have increasing returns to scale under imperfect competition.

As already written above, in [START_REF] Segal | Good and bad uncertainty: Macroeconomic and financial market implications[END_REF] the authors develop a theoretical model in which uncertainty shocks may either be positive or negative. As in [START_REF] Hartman | The effects of price and cost uncertainty on investment[END_REF], the two shocks are mean zero. Both consumption shocks have time varying volatilities that depend on two state variables that represent good and bad macroeconomic uncertainties. They allow a feedback effect of the macro volatilities in that they also affect expected consumption. This means that good and bad macro uncertainties have direct effects on future economic growth as well as on the shocks. As the authors put it, they do not provide a "primitive micro-foundation for this channel, [but they] show direct empirical evidence to support our volatility feedback specification". One important aspect is that agents may dislike uncertainty be it good or bad which implies that the overall effects of uncertainty will be skewed towards bad uncertainty.

That is, good uncertainty has a negative component because it implies volatility. As a consequence, the equity risk premium the authors obtain exhibit a second order moment that is positive, i.e the risk premium increases, whereas the third order moment may be either positive or negative, i.e the risk premium increases or decreases. These two first theoretical channels are rather related to industrial prospects that may have positive effect on future growth. Here we want to suggest another mechanism that would explain a positive effect of uncertainty. This mechanism is related to recent works by Gabaix [START_REF] Papers | A Sparsity-Based Model of Bounded Rationality[END_REF][START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF]. In the first of these two articles Gabaix proposes the sparse max operator in which agents do not observe all the information available at time t. In order to decide which action to undertake they will first have to allocate for each available information x i an amount m i of attention for i = 1, . . . , N . Consequently, the agent does not take into account most of the information available because it is costly to analyze it. The agent observes x s i := m i x i instead of x i and there may have a lot of null m i depending on some parameters.

In the second article, Gabaix develops a behavioral new Keynesian model that is built on a simplified version of [START_REF] Papers | A Sparsity-Based Model of Bounded Rationality[END_REF] as he mostly uses a macroeconomic attention parameter m which somehow represent the mean of the above m i . Similarly, this means that agent are partly myopic since they only observe mx i . As a consequence,

E BR t [z(X t+k )] = mk E t [z(X t+k )]
where the left hand side (LHS) is the expected value of the behavioral agent at time t of the vector of variable X t in k periods and the last term of the right hand side (RHS) is the expectation of a rational agent that corresponds to m = 1 coefficiented by mk which indicates that myopia is increasing with distance to the future.

One of the (many) insights of [START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF] is that with behavioral agents, Ricardian equivalence does not hold anymore. Proposition 7 of this paper is about fiscal policy and concerns a situation with a public deficit d t := T t + r R B t financed with debt in order to allow a lump-sum transfer T to the agents. The value of the government debt evolves as B t+1 = B t + Rd t . This proposition establishes that the new IS curve becomes

x t = M E t [x t+1 ] + b d d t -σ(i t -E t [π t+1 ] -r n0 t ) (1)
We want to focus here on the second term of the RHS: b d d t . It measures the sensitivity to deficits of the agent. It is null if m = 1 (agents are rational) but it is positive otherwise and decreasing in m. As exposed in the appendix of [START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF], this part of the paper requires an additional state vector Z τ that complements the original vector X τ . The agent has then to observe now some additional information that concern precisely deficits. The perceived future taxes are then given by

E BR t [T (Z τ )] = - r R B t + mτ-t E t d τ -r τ -1 u=t d u (2)
The first term of the RHS reflects a Ricardian behavior: If debt was to remain at its level in t, namely B t , then the behavioral agent correctly anticipates that the debt will have to be repaid.

The second term reflects the myopia of the behavioral agent that fails to precisely taking into account of future deficits and their fiscal consequences on its revenues, i.e futures taxes implied by the future deficits. Now come back to [START_REF] Papers | A Sparsity-Based Model of Bounded Rationality[END_REF] that explains how an agent chooses the degree of attention it will bring to each available information. Proposition 1 of this paper establishes the behavior of a behavioral agent that uses the sparse max procedure to choose which x i he will consider and with which degree of attention. The consequences of proposition 1 are that (i) many x i are eliminated, (ii) more attention is paid to more variable x i , (iii) more attention is paid to x i that matter more for the action the agent considers to undertake, (iv) more attention is paid to x i that may generate great losses and (v) more attention is paid generally if the cost of attention is low.

Where do we see uncertainty in this model? One could argue that this is the variance of x i . If this is so, then proposition 1 establishes that more attention is paid to an information that varies more. However, what if the number of x i increases temporarily? What if the number of more variable x s i increases temporarily? We believe that these two possibilities better reflect the idea of a general uncertainty. In order to answer intuitively to these questions, let see how the attention vector is chosen by a behavioral agent (Definition 1 in Gabaix ( 2014)):

argmin m∈[0,1] n 1 2 i,j=1..n (1 -m i )Λ ij (1 -m j ) + κ i=1..n m α i (3)
where Λ ij = -σ ij a x i u aa a x j . σ ij is the covariance of x i and x j , a x i is the marginal effect of x i on the optimal action of the agent and u aa is the second derivative of the utility function with respect to a, the action. κ and α parameterize the psychological cost of paying attention to any variable, the first part is the quadratic loss associated to the fact of not taking the right action because the agent observes m i x i instead of x i .

Assume as Gabaix mostly does that the agent considers the variables as uncorrelated. Consider first the possibility of an increase of the number of variables. If one assumes that the initial total psychological cost paid by the agent before the increase in the number of variables is the maximum the agent can bear2 , then adding any new variable implies that the mean attention vector is reduced, even when α = 1, the value recommended by Gabaix. Indeed, the agent has to allocate the same total cost on n + 1 variables instead on n.

Consider now the second possibility of more variable x s i . Under the same hypothesis on the total psychological cost then, if α > 1, increasing attention on variable x j if m j was already positive may necessitate to reduce at least one m i such that ∆m j < -∆m i . Consequently, the mean attention is also reduced. If m j was null before its importance increased, then it is when α < 1 that the same could happen. When α = 1, then nothing happens since ∆m j = -∆m i .

We may add that even without the assumption on the total psychological cost those effects should exist under some conditions. The characterization of those conditions is let for future work.

Finally, if one considers that variables are correlated as in 3. Note first that an increase of a x j implies that more attention should be paid to variable x j . But as it is clear in 3, this increase will also affect the choice of the optimal m i . There is no reason to consider that this relationship could not imply a reduction of m i . This being true whatever the values of κ and α.

To conclude, there are a lot of reasons to believe that uncertainty may result in a decrease of m in 1. As a consequence, increased uncertainty would increase myopia of the agents if they are behavioral and then would reinforce the effect of the stimulus enacted by the government.

It is important to be aware that the three theoretical explanations are complementary.

3 Uncertainty and Macroeconomy: a local projection approach

Uncertainty Data

To investigate the impact of uncertainty shocks on economic activity, many measures of uncertainty have been developed from different methodologies. However, many measures represent just one dimension of uncertainty: financial, economic policy, geopolitical,... As these indexes are provided from different methodologies, they provide different information. To take into account this heterogeneity, some works have developed composite indexes. Rusisian Crisis and LTCM

09/11 attacks

Iraq War

Lehman Brothers

US debt ceiling crisis

Government Shutdown

US China Dispute

Note: The index is standardized over the period 1990-2019.

Beyond the first factor that approximate general uncertainty, the second factor of Himounet (2022). This variable discriminates two types of uncertainty shocks: non-financial and financial. The interpretation of this variable is that when this factor is high, the nature of uncertainty shocks is associated with macroeconomics or non-finance (Gulf War, Iraq War, Government Shutdown,. . . ). Inversely, when this variable is low, the nature of uncertainty shocks is linked to finance (LTCM, Dot-Com bubble, Lehman Brothers). We will use this variable to investigate the nature of uncertainty shocks. As both variables are provided by the same PCA, they are orthogonal by construction.

Linear Framework

To investigate the dynamics between macroeconomy and uncertainty, vector autoregressive (VAR) models developed by [START_REF] Sims | Macroeconomics and Reality[END_REF] have been traditionally used in the empirical literature to construct impulse responses. Based on the conventional reduced form VAR model, the notation for the impulse response function is based on the difference between two forecasts [START_REF] Hamilton | Time Series Analysis[END_REF]:

Gulf War

Iraq War

09/11 attacks

US China Dispute

Government Shutdown

Fiscal Cliff US Elections

Note: The index is standardized over the period 1990-2019.

IR(t, s, d

i ) = E (y t+s |v t = d i ; X t ) -E (y t+s |v t = 0; X t ) s = 0, 1, ... (4)
where E(.|.) denotes the best mean squared error predictor, y t is a n × 1 vector, X t denotes the lags of y t (y t-1 , y t-2 , y t-3 ,...), 0 is a n × 1 vector containing 0, v t denotes a vector of reduced-form disturbances, and D is an n × n matrix, whose columns d i contain the relevant experimental shocks. [START_REF] Jordá | Estimation and Inference of Impulse Responses by Local Projections[END_REF] Applying the local projections of [START_REF] Jordá | Estimation and Inference of Impulse Responses by Local Projections[END_REF], we run the following regressions:

y t+s = α s + B s+1 1 y t-1 + B s+1 2 y t-2 + ... + B s+1 p y t-p + u s t+s (5) s = 0, 1, ..., h
where y t is a vector of endogenous variables including our synthetic measure of uncertainty and a set of monthly macroeconomic variables:3 industrial production, unemployment rate, inflation, oil prices, the S&P500 index and the fed funds rate. Impulse responses are computed according to:

ÎR(t, s, d i ) = Bs 1 d i (6) s = 0, 1, ..., h
where d i corresponds to the i th column of the experimental matrix D and the identified structural shock. We construct this matrix following the suggestion of [START_REF] Jordá | Estimation and Inference of Impulse Responses by Local Projections[END_REF], which essentially follows methodologies applied in the traditional VAR literature and begins by estimating a SVAR with a Cholesky decomposition as identification scheme. If the shock is already identified and/or considered as exogenous, there is no need to apply a VAR model and the Cholesky decomposition:4

x t+h = a h + b h shock t + γz t + t+h (7)

x t represents the variable of interest, z t a vector of control variables and shock t represents the identified or exogenous shock. The impulse response of shock t on x t will correspond to the series of coefficients b h for each horizon h.

We apply a Cholesky decomposition as many works which have used VAR models to identify our shocks (See, among many others, [START_REF] Bloom | The Impact of Uncertainty Shocks[END_REF][START_REF] Colombo | Economic policy uncertainty in the US: Does it matter for the Euro area?[END_REF][START_REF] Jurado | Measuring Uncertainty[END_REF][START_REF] Baker | Measuring Economic Policy Uncertainty[END_REF][START_REF] Leduc | Uncertainty shocks are aggregate demand shocks[END_REF][START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF]. Therefore, to compute the impulse response functions, we have to determine the contemporaneous impact matrix with a VAR model applying Cholesky decomposition to identify structural shocks. d i denotes the i th column of the Cholesky decomposition and therefore represents the structural shock to the i th element in y t .

A crucial point is to estimate the contemporaneous impact matrix applying the Cholesky decomposition. The impact of shocks can differ with the ordering of our variables. We order our variables such that:

y =                   SP500 OIL GU Inflation Unemployment rate
Fed funds rate ∆log(Industrial production)

                 
where GU denotes our measure of general uncertainty. We use ∆ log(Industrial Production)

to have a stationary variable (IP I). We order our measure of uncertainty third under the assumption that uncertainty shocks will have an immediate impact on the macroeconomic variables. SP 500 is the ∆ log(Stock market index), it is usually placed first in the literature. We collected this variable on Yahoo! Finance. The second one is OIL, the monthly price of crude oil (West Texas Intermediate) deflated by the consumer price index and also in log difference to have a stationary variable. It is aimed at capturing possible geopolitical foreign influence on US economics contrary to previous works that who did not take it into account. We order these both variables before uncertainty index under the assumption that these variables are unaffected by the uncertainty shock to take into account expectations and identify an unanticipated uncertainty shock. Inversely, the macroeconomic variables will not have an immediate impact on uncertainty. This is a common choice in the empirical literature (See, among others, [START_REF] Bloom | The Impact of Uncertainty Shocks[END_REF][START_REF] Baker | Measuring Economic Policy Uncertainty[END_REF][START_REF] Caggiano | Uncertainty Shocks and Unemployment Dynamics: An Analysis of Post-WWII U.S. Recessions[END_REF][START_REF] Istrefi | Subjective interest rate uncertainty and the macroeconomy: A cross-country analysis[END_REF]. The idea is that agents do not have information about the current macroeconomic conditions [START_REF] Leduc | Uncertainty shocks are aggregate demand shocks[END_REF] because data are not yet available. Inf lation (I) is ranked fourth since price may react quickly after a shock. We place the fed funds rate (F ed) after the unemployment rate (U ) under the assumption that the Federal Reserve will react instantly to an unemployment shock.

Indeed, one objective of the Federal Reserve is a low level of unemployment. 5 The results re- A.1.1. A result which can be surprising is the value of the R 2 for the unemployment and the Fed funds rate which is close to 0.99 even if we have shown the stationarity of the VAR. 6 These results could be due to the fact that their past values are statistically significant contrary to other variables meaning that these variables are strongly linked to their past values.7

Examining the impulse response functions from the local projections, the impact of uncertainty on macroeconomic variables, we find a statistically negative impact on economic activity as almost all works. 8 We get a negative effect on employment during the months following the uncertainty shock with an increase in unemployment (Figure 4). These results highlight a wait and see behavior where firms delay investment and hiring decisions. We get a slightly negative effect on industrial production in the near term. The Fed decreases its rate in order to boost the economy. Source: Author's own calculations.

Notes: The solid black lines correspond to the IRFs. The shaded area denotes the 95% confidence interval.

We run the same exercise with F actor2 as uncertainty variable to investigate the effect of the nature of uncertainty shocks. We replace the general uncertainty index by the second factor (F actor2) in the model. According to its interpretation, a positive shock to this second factor indicates more non-financial uncertainty. We find that a non-financial uncertainty shock has no significant effects on industrial production and unemployment during the months following the shock (Figure 5). We run a VAR but we introduce the product of both factors (GU * F actor2)

instead of each factor alone. It is worth noticing that no caution is needed when introducing this product since these two factors present the quality of being independent from each other by construction from the PCA. Hence this variable is high when both factors are high, i.e when uncertainty is high and non-financial. Remind here that both theoretical frameworks that, according to us, may explain why uncertainty could be positive rely on non financial uncertainty.

Growth option theory relies on an industrial uncertainty whereas Gabaix's theory relies on a general macroeconomic uncertainty. Source: Author's own calculations.

Notes: The solid black lines correspond to the IRFs. The shaded area denotes the 95% confidence interval.

The striking result we obtain is that when the product is shocked it has a short positive and significant impact on industrial production and a lasting negative and significant effect on unemployment (Figure 6). These results show that the variable F actor2 representing the nature of uncertainty does not have a significant effect but its interaction with the overall level of uncertainty can provide a much richer set of results. Hence, as we hypothesized, uncertainty can have a positive effect on the economy. More specifically, uncertainty has a positive effect when it is non financial interacting it with the overall level of uncertainty. However, we do not know exactly what happens in the product GU * F actor2. For instance, the product of both factors may be as high when uncertainty is high and the nature of uncertainty is indeterminate as when the nature of uncertainty is non-financial and uncertainty is moderate. This result is rather a confirming intuition than a robust proof. In order to check whether this intuition is correct using a proper estimation method, we turn to a non linear framework. Source: Author's own calculations.

Notes: The solid black lines correspond to the IRFs. The shaded area denotes the 95% confidence interval.

Non linear framework

In the linear framework, we have found that a shock of the nature of uncertainty doesn't have a significant effect whereas uncertainty does have an effect. However, the nature may have an effect depending on the general level of uncertainty or uncertainty may have a different impact depending on the nature of uncertainty. This is what suggests the previous intuitive test using the product of both factors. A non linear framework allows to study the effect of a shock on a variable conditioned to the level of another variable. This intuition comes from the theoretical model of [START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF] assuming that agents are partly myopic. Therefore, they fail to perfectly anticipate future taxes after a stimulus generating an effective stimulus. A corollary of these results is that myopia is exacerbated when uncertainty is high. Following these theoretical arguments, taking the second factor of the PCA of Himounet ( 2022) distinguishing non-financial uncertainty from financial uncertainty as a threshold variable makes no sense

given its non cardinal nature. Therefore, we are going to use the measure of general uncertainty representing the overall level of uncertainty as the threshold variable. Concretely, we aim at studying the effect of a shock on the nature of uncertainty conditioned to various levels of the general uncertainty. This strategy allows to examine the interaction between both measures in another way.

High, moderate and low uncertainty regimes

A great advantage of the local projection methodology is that it can easily be adapted to a nonlinear framework. Ahmed & Cassou, 2021). 9 We apply local projection methods to investigate the impact of the nature of uncertainty shocks in different regimes estimating the state-dependent impulse response functions. We have decided to use a three regimes set-up as our preferred specification in order to properly distinguish the high uncertainty regime from the low uncertainty regime, thus implying that a moderate uncertainty regime also exists. 10We consider the extension of our baseline model with threshold effects:

y t = I(z t-1 < γ 1 )Π L (L)y t-1 + I(γ 1 ≤ z t-1 < γ 2 )Π M y t-1 + I(z t-1 > γ 2 )Π H y t-1 + µ t
where y t is a vector of endogenous variables including our measure of the nature of uncer- We apply the Likelihood Ratio (LR) test to test the linearity (Table A.2.1). The LR test rejects the null hypothesis of linearity. A nonlinear framework is more appropriate to study the impact of shocks. Moreover, the LR test rejects the null hypothesis of two regimes against three regimes. It means that three regimes are more appropriate to study the effect of the non linear effects of the nature of the shocks instead of two regimes. As in the linear framework, we apply local projection that we adapt to a non linear framework such that:

y t+s = I(z t-1 < γ 1 )Π s+1 L (L)y t-1 + I(γ 1 ≤ z t-1 ≤ γ 2 )Π s+1 M y t-1 + I(z t-1 > γ 2 )Π s+1 H y t-1 + µ s t+s
Impulse responses in a high uncertainty regime are computed according to:

ÎR(t, s, d i ) = Πs 1,H d i (8) s = 0, 1, ..., h
Similarly, impulse responses in a low uncertainty regime are computed according to:

ÎR(t, s, d i ) = Πs 1,L d i (9) s = 0, 1, ..., h
And for the moderate uncertainty regime:

ÎR(t, s, d i ) = Πs 1,M d i (10) s = 0, 1, ..., h
where d i is the i th column of the Cholesky decomposition as in the linear framework.

The estimated threshold values of -0.2953414 and 0.5885597 allow to separate shocks of the last two decades as the following graph highlights.

The results for the three different regimes are provided in Figure 8, Figure 9 and Figure 10.

As for the linear framework, we do not have any significant effect of the nature of uncertainty under the low uncertainty regime and there is a very short negative effect on industrial production. However, it turns out that under both the moderate and the high uncertainty regimes, the nature of uncertainty has a positive significant and lasting effect on unemployment. There is a short (a quarter) positive effect on production industrial production under the moderate regime.

One should note that the effect on unemployment is stronger in the moderate uncertainty regime whereas it lasts longer in the high uncertainty regime. 11

In the theoretical literature, "growth options" theories argue that some forms of uncertainty 11 We get results which are qualitatively equivalent for the moderate and high uncertainty regimes extending the regression 7 to our non-linear specification even if they are less significant (Figure A.2.1). F actor2 is considered as the identified shock and the vector of control variables contains the lags of F actor2 and the lags of other macroeconomic variables of our baseline model. can have a positive effect on economic activity. This theory refers more specifically to macroeconomic uncertainty related to technology. During the last decade, many technological advances have appeared and other advances are developing. We can take the example of the rapid development of artificial intelligence (AI). AI will provide growth opportunities that will benefit firms and the economy in the future. However, we do not know which firms and by how much. That is why, there isn't a consequent gain when we examine the response of industrial production since most of the work firms do on AI is R & D.

Another explanation which is not exclusive of the previous one is as follows. [START_REF] Papers | A Sparsity-Based Model of Bounded Rationality[END_REF][START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF] has shown that when a lot of information is available then individuals have to choose which information to analyze and by how much they will do so. It results that when a lot of information is available, individuals are not able to anticipate that an economic stimulus will certainly induces taxes to rise in a quite near future and hence, accordingly, to save money thus suppressing the positive expected effect of the stimulus. In other words, the quantity of Source: Author's own calculations.

Notes: The solid black lines correspond to the IRFs. The red shaded area denotes the 95% confidence interval.

available information shuts down the ricardian equivalence. Importantly, this effect works on the theoretical set-up of Gabaix uniquely when myopia is strong. So, behind this second factor, we could have a distinction between a "positive" macroeconomic uncertainty that could refer to technological progress and a "negative" uncertainty which is financial.

The fact the effect on unemployment is stronger in the moderate regime may seem counterintuitive. We argue however that, concerning the growth theory explanation, the technical uncertainty it involves is not surging as a peak but is rather a lasting phenomenon that corresponds quite well with a moderate uncertainty regime. As for the Gabaix explanation, we argue that under the high uncertainty regime, the negative financial uncertainty is also often there. The negative effect of financial uncertainty on unemployment may attenuate the positive effect in- Source: Author's own calculations.

Notes: The solid black lines correspond to the IRFs. The red shaded area denotes the 95% confidence interval.

duced by the increased myopia of the agents. In other words, the remedy is working but the illness it has to cure is very damaging.

To add an additional evidence to validate these assumptions, we redo our procedure on a subsample as a robustness check: 1990-2006. By doing so we suppress the financial crisis during which uncertainty unambiguously has had a massive negative effect. We redo the PCA of [START_REF] Himounet | Searching the nature of uncertainty: Macroeconomic and financial risks VS geopolitical and pandemic risks[END_REF] applying the same set of uncertainty indexes on this subsample. We do not Several explanations may hold. By suppressing the 2007-2019 period, we originally aimed at reinforcing the positive effect we have highlighted by removing the negative effect of the financial crisis. It appears that we obtain the opposite result: uncertainty is again negative. In fact we have also removed all the positive effect of the industrial uncertainty, i.e all the hightech innovations of the 2007-2019 decade that according to our "growth option" explanation have had a positive effect. Another relies on the theoretical result of [START_REF] Papers | A Sparsity-Based Model of Bounded Rationality[END_REF][START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF] that we interpret simply as the fact that uncertainty restores its efficiency to economic stimulus. As a matter of fact, there has been a large stimulus in the US during the period 2007-2019 that we have also suppressed by shortening the sample.

This additional exercise does not help us to disentangle between both explanations but confirms that they can be convincing. In addition, note that both explanations are not mutually exclusive and may therefore be both valid. We nevertheless can notice that the effect of the nature of uncertainty on the fed's rate is in line with the Gabaix's explanation since the rate increases as usually happens after a stimulus in order to avoid an overheated economy. In order to better test our assumption linked to high-tech innovations, we should construct a measure of uncertainty related to technology. We let this task for future works.

4 Robustness Check

Non linear framework with two regimes

We try here to do the same exercise than before but with two regimes instead of three. The VAR is then the following:

y t = (1 -I(z t-1 > γ)) Π L (L)y t-1 + I(z t-1 > γ)Π H y t-1 + µ t
As we proceed in the whole paper, we use local projections that we adapt to the non-linear framework:

y t+s = (1 -I(z t-1 > γ)) Π s+1 L (L)y t-1 + I(z t-1 > γ)Π s+1 H y t-1 + µ s t+s
Impulse responses in a high uncertainty regime are computed according to:

ÎR(t, s, d i ) = Πs 1,H d i (11) s = 0, 1, ..., h
Similarly, impulse responses in a low uncertainty regime are computed according to:

ÎR(t, s, d i ) = Πs 1,L d i (12) s = 0, 1, ..., h
The estimated threshold value is equal to 0.5938924 (Table A.2.1) It means that when we are above this threshold, the situation is very more uncertain than the average. Here, we investigate the impact of the nature of shocks when we are in a high uncertainty regime and a low uncertainty regime. We find that a non-financial uncertainty shock doesn't have significant effects when we are in the low uncertainty regime (Figure B.2.2). However, we a negative and significant effect on unemployment when we are in the high uncertainty regime (Figure B.2.1).

The decrease of unemployment is persistent for many months. Consequently, the results are qualitatively the same than with three regimes. Note that by construction under two regimes, these are the moderate and the low regimes that are merged into one regime. It is interesting that when doing so, the results of the low regimes "dominate" those of the moderate regime.

Alternative ordering

Uncertainty has been ordered third in the VAR. However, uncertainty has been ordered last by some authors (See, among others, [START_REF] Colombo | Economic policy uncertainty in the US: Does it matter for the Euro area?[END_REF][START_REF] Jurado | Measuring Uncertainty[END_REF][START_REF] Charles | Uncertainty and the macroeconomy: evidence from an uncertainty composite indicator[END_REF].

Uncertainty has been ordered last to remove the measure of uncertainty of the contemporaneous movements of the macroeconomic variables [START_REF] Colombo | Economic policy uncertainty in the US: Does it matter for the Euro area?[END_REF]. There is no consensus on how to order the measure of uncertainty in the vector of endogenous variables. We redo local projections and a SVAR model with a Cholesky Decomposition to identify shocks in ordering our measure of uncertainty in last. This novel ordering implies that all shocks of the system can have a contemporaneously impact on our measure of uncertainty. This alternative ordering could change the dynamic of the system. However, our results are very similar. 12 We have a short-term negative impact on industrial production with our general uncertainty using local projections. There is an effect which isn't statistically different from zero with the second factor.

Applying this ordering in our nonlinear framework, the results are qualitatively identical.

Hodrick Prescott Filter

Following the seminal paper of [START_REF] Bloom | The Impact of Uncertainty Shocks[END_REF], we detrend the variables that are applied in the VAR model applying the Hodrick-Prescott filter except the uncertainty variable. Following [START_REF] Ravn | On Adjusting the Hodrick-Prescott Filter for the Frequency of Observations[END_REF], we take the smoothing parameter λ = 129600 for monthly data. The 13 These results are more significant at a 10% level.

Conclusion

This paper has investigated the effects of uncertainty applying a local projection approach in a linear and a non linear framework. We apply the second factor of the PCA of Himounet ( 2022) distinguishing financial uncertainty from non-financial uncertainty, hence it is about the nature of uncertainty. In the linear framework, this variable doesn't have a significant effect but its interaction with the overall level of uncertainty provides a significant positive effect.

Applying a nonlinear framework to measure the interaction of this variable with the overall of uncertainty in another way, the estimation of a positive effect of the second factor when general uncertainty is above its mean confirms that uncertainty may indeed have a positive effect. Uncertainty associated with this second dimension can refer to macroeconomic uncertainty related to technological progress. Firms don't doubt that technological progress is a source of value creation. However, there is uncertainty on the final gain only. This uncertainty can lead firms to invest and hire. The estimation of a negative effect on the subsample 1990-2006 seems to be another sign of our assumption of technological progress. Another explanation relies on the theoretical works of [START_REF] Papers | A Sparsity-Based Model of Bounded Rationality[END_REF][START_REF] Gabaix | A Behavioral New Keynesian Model[END_REF]. He shows that when agents are strongly myopic, economic stimuli regain in effectiveness. The simple interpretation that we make of his results is that by increasing myopia, uncertainty suppresses the Ricardian equivalence. Therefore, an increased uncertainty restores the effectiveness of an economic stimulus. Again, the results with the subsample 1990-2006 seem to confirm this hypothesis since the large economic stimulus that followed the 2007-2008 crisis disappears from the sample.

All in all, we have showed that uncertainty may indeed be positive when it is non-financial and strong. We have proposed two explanations on this positive effect which both are credible and not exclusive of each other. In order to test whether one is more valid one should construct a measure of technological uncertainty which represents another quite challenging perspective. Source: Author's own calculations.

Notes: The solid black lines correspond to the IRFs. The shaded area denotes the 95% confidence interval.

B.2 Nonlinear Framework: Two Regimes Source: Author's own calculations.

Notes: Except the uncertainty variable (GU ), all variables are detrending applying the HP filter (λ = 129600) The solid black lines correspond to the IRFs. The shaded area denotes the 95% confidence interval. Source: Author's own calculations.

Notes: Except the uncertainty variable (F actor2), all variables are detrending applying the HP filter (λ = 129600)

The solid black lines correspond to the IRFs. The shaded area denotes the 95% confidence interval. Source: Author's own calculations.

Notes: Except the uncertainty variable (F actor2), all variables are detrending applying the HP filter (λ = 129600)

The solid black lines correspond to the IRFs. The shaded area denotes the 95% confidence interval.

  shocks affect consumption growth as well as consumption expectation. This last effect allows uncertainty to have opposed effects. The authors confirm empirically the existence of a positive component of uncertainty using a VAR. Their methodology implies that positive shocks are by nature positive since they correspond to positive semivariances of industrial production. Then they use the predictable component of this measure to capture ex-ante uncertainty. It results that shocks on good uncertainty have lasting (positive) effects on several key macro variables and that it dampens the negative effects of bad shocks. In a similar way, Forni et al. (2021) decomposed uncertainty between two components relying on the methodology of Adrian et al. (2022):

  Haddow et al. (2013) have constructed a global indicator of uncertainty for the United Kingdom based on a principal component analysis (PCA) with several indicators measuring uncertainty in the United Kingdom. Charles et al. (2018) have developed a global measure for the United States applying a dynamic factor model.We are going to apply the measure estimated in Himounet (2022) from a PCA on the period January 1990 to December 2019. Figure1represents this synthetic or general measure over this sample. It can identify different uncertainty peaks corresponding to well identified events like the Gulf War, the Russian financial crisis and Long-Term Capital Management in 1998, the 9/11 attacks, the collapse of Lehman Brothers or the US debt-ceiling dispute in 2011. These are shocks (financial, macroeconomic, geopolitical, policy,...) that increase the general uncertainty.

Figure

  Figure 1: General Uncertainty Index

( 2022 )

 2022 concerns the nature of uncertainty shocks by distinguishing two groups of uncertainty variables. On the Figure 2, the first group of the variables factor map includes non-financial uncertainty: economic policy uncertainty indexes of Baker et al. (2016), the consumer confidence index, the geopolitical risk index of Caldara & Iacoviello (2022),. . . The second group includes variables that are mainly linked to finance: the VIX index, the corporate bond spreads, the financial uncertainty index of Ludvigson et al. (2021),. . . . So, the second factor is a weighted sum of uncertainty indexes where financial indexes have a negative weight and non-financial indexes have a positive weight. Figure 3 plots the second factor (F actor2) of the PCA of Himounet

Figure 2 :

 2 Figure2: Variables Factor Map (Factor 1 and Factor 2) in[START_REF] Himounet | Searching the nature of uncertainty: Macroeconomic and financial risks VS geopolitical and pandemic risks[END_REF]

Figure

  Figure 3: Factor 2

  ported in Figure A.1.1 demonstrate that no unit root lies outside the unit root circle, indicating the stationarity of the VAR. The estimated coefficients of each equation are display in Table

Figure

  Figure 4: Impulse Response Functions

Figure

  Figure 5: Impulse Response Functions

Figure

  Figure 6: Impulse Response Functions

  tainty and the set of monthly macroeconomic variables that we have used in the linear framework. z t is the switching variable which is the measure of general uncertainty. I denotes an indicator function which takes the value of 1 alternatively if the first factor is above the threshold value γ 2 (high uncertainty regime, H), or between the two threshold values γ 2 and γ 1 (moderate uncertainty regime, M ), or below γ 1 (low uncertainty regime, L). Π H (L) is a lag-polynomial of matrices in the high uncertainty regime. Π M (L) is a lag-polynomial of matrices in the moderate uncertainty regime. Π L (L) is a lag-polynomial of matrices in the low uncertainty regime. The threshold values are estimated applying a TVAR model. The threshold values of the switching variable are determined endogenously by a grid search over possible values of the switching variable. The grid is constructed such that the grid is trimmed at a lower and upper bound to ensure a minimal percentage of observations in each regime. In practice, the level is chosen arbitrary. It doesn't exist a general guideline. However, a level around 20% of observations in each regime has often been used. The estimation of the threshold value corresponds to the model with the smallest determinant of the covariance matrix of the error terms µ t .

Figure

  Figure 7: Two thresholds of general uncertainty

Figure 8 :

 8 Figure 8: Impulse Response Functions in a high uncertainty regime

Figure 9 :

 9 Figure 9: Impulse Response Functions in an intermediate uncertainty regime

  Figure 10: Impulse Response Functions in a low uncertainty regime

  results are qualitatively equivalent with a negative effect of a general uncertainty shock(Figure B.3.1) on economic activity with the decline in industrial production and the rise in unemployment. Applying our non linear framework with the general uncertainty as threshold variable, a positive shock on the second has a negative effect on economic activity in a low uncertainty regime(Figure B.3.4). We keep the positive effect in an intermediate uncertainty regime(Figure B.3.5). In the high uncertainty regime, we have a decrease in unemployment and an increase in industrial production which are not significant a 5% level(Figure B.3.6). 134.4 VAR-8In this subsection, we run local projections with our non-linear specification applying the eightvariable VAR model of[START_REF] Bloom | The Impact of Uncertainty Shocks[END_REF];[START_REF] Jurado | Measuring Uncertainty[END_REF];[START_REF] Charles | Uncertainty and the macroeconomy: evidence from an uncertainty composite indicator[END_REF] ordered as follows: the S&P 500 stock index, the manufacturing production (IP I), the level of employment (EM P ), the average hours worked in manufacturing, the wage in manufacturing, the log aggregate CPI, the Federal Funds rate, and uncertainty. The measure of uncertainty is ordered at the end. We identify the shocks with a Cholesky decomposition as previously. The results are less significant but we keep a slightly positive effect of F actor2 on the industrial production and the employment under the high and the moderate regime of uncertainty(Figure B.4.1).

Figure

  Figure B.1.1: Variables Factor Map (Factor 1 and Factor 2)

FigureFigure

  Figure B.1.2: Estimated Threshold values

Figure

  Figure B.1.4: Impulse Response Functions in an intermediate uncertainty regime

Figure

  Figure B.1.5: Impulse Response Functions in a low uncertainty regime

Figure

  Figure B.2.1: Impulse Response Functions in a high uncertainty regime

Figure

  Figure B.2.2: Impulse Response Functions in a low uncertainty regime

Figure

  Figure B.3.3: Two thresholds of general uncertainty

Figure

  Figure B.3.5: Impulse Response Functions in an intermediate uncertainty regime

Figure

  Figure B.3.6: Impulse Response Functions in a high uncertainty regime

  has pointed out that this methodology is not optimal if the VAR does not coincide with the underlying data generating process and has developed a popular alternative approach to impulse responses from VAR: local projection methods. This methodology consists in running a series of predictive regressions of our variable of interest. The impulse responses are computed using regression coefficients. According to the author this method has many advantages. Local projections can be estimated by one equation, they are more robust to misspecification of the data generating process and can easily be adapted to a nonlinear framework.[START_REF] Jordá | Estimation and Inference of Impulse Responses by Local Projections[END_REF] has demonstrated that impulse responses from a VAR and local projection are equivalent if the VAR coincides with the true data generating process.[START_REF] Olea | Local Projection Inference Is Simpler and More Robust Than You Think[END_REF] and[START_REF] Plagborg-Møller | Local Projections and VARs Estimate the Same Impulse Responses[END_REF] have showed that local projections are more robust than the SVAR methodology. Both methodologies lead to the same median impulse responses in the short and medium term.

  Many works have applied local projections to study non linear effects, threshold effects (See, among many others,[START_REF] Owyang | Are Government Spending Multipliers Greater during Periods of Slack? Evidence from Twentieth-Century Historical Data[END_REF][START_REF] Ramey | Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data[END_REF]

Table A

 A

	(0.08) 1.86 (2.90) (2.94) B Robustness Checks (0.16) IPI t-2 1.20 (5.81) (5.89)	(0.89) -8.40 (31.47) (31.91)	(0.01) 0.10 (0.24) (0.25)	(0.00) -0.03 (0.10) (0.10)	(0.00) -0.03 (0.09) (0.09)	(0.01) 0.00 (0.39) (0.39)
	Intermediate Uncertainty Regime
	.1.1: Linear Model Results: GU as Uncertainty variable Table A.1.2: Linear Model Results: Factor2 as Uncertainty variable Table A.1.3: Linear Model Results: Product as Uncertainty variable OIL t-2 0.09 0.07 -0.28 -0.00 -0.00 0.00 -0.01 (0.99) (1.98) (10.75) (0.08) (0.03) (0.03) (0.13) IPI t-1 0.77 0.51 -3.52 0.01 -0.04 0.04 -0.12 IPI t-3 0.21 0.93 -1.42 0.02 -0.02 0.02 0.11
	SP500 SP500 SP500 (0.05) -0.13 0.19 (0.65) (0.62) B.1 Subsample 1990-2006 OIL OIL OIL (0.11) SP500 t-1 0.05 SP500 t-3 -0.15 (1.29) (1.23)	GU Factor2 Product (0.58) -3.28 * -0.30 (7.02) (6.67)	Infl Infl Infl (0.00) 0.01 0.00 (0.05) (0.05)	U U U (0.00) 0.00 -0.01 (0.02) (0.02)	FED FED FED (0.00) 0.00 0.00 (0.02) (0.02)	IPI IPI IPI	(0.01) 0.00 0.04 * (0.09) (0.08)
	(Intercept) 0.00 (Intercept) -0.00 -0.00 0.01 (Intercept) -0.00 0.00 (0.13) (0.27)	-0.19 -0.22 -0.17 (1.45)	0.00 0.00 0.00 (0.01)	-0.00 -0.00 -0.00 (0.00)	0.00 0.00 0.00 (0.00) -0.00 -0.00 -0.00 (0.02)
	(0.01) SP500 t-1 -0.03 (0.06) OIL t-1 0.01 (0.03) GU t-1 -0.00 -0.02 * (0.02) -0.02 (0.12) 0.24 * * * (0.06) (0.01) (0.01) Infl t-1 -0.35 -0.31 (0.69) (1.33) U t-1 -0.78 6.91 * (1.63) (3.14) FED t-1 1.59 4.34 (1.78) (3.44) IPI t-1 1.16 * * 1.49 (0.40) (0.78) SP500 t-2 0.01 -0.06 (0.06) (0.12) OIL t-2 0.04 0.01 (0.03) (0.06) GU t-2 0.02 * 0.01 (0.01) (0.02) SP500 t-1 -0.00 0.16 (0.06) (0.11) OIL t-1 0.01 0.26 * * * (0.03) (0.06) Factor2 t-1 0.01 -0.01 (0.01) (0.01) Infl t-1 -0.67 -0.75 (0.70) (1.35) U t-1 0.48 6.98 * (1.65) (3.19) (17.45) (0.14) (0.14) (0.00) -3.69 * * * 0.00 (0.72) (0.01) -0.27 0.01 * * * (0.35) (0.00) 0.73 * * * -0.00 (0.06) (0.00) 7.02 0.34 * * * (8.24) (0.06) 17.44 0.16 (19.40) (0.14) -30.89 0.10 (21.29) (0.15) -13.74 * * 0.01 (4.81) (0.03) -1.05 -0.00 (0.74) (0.01) -0.31 -0.00 (0.36) (0.00) -0.13 0.00 (0.12) (0.00) -1.01 0.01 (0.58) (0.00) 0.76 * 0.01 * * * (0.32) (0.00) 0.72 * * * 0.00 (0.05) (0.00) -0.70 0.33 * * * (7.37) (0.06) -11.75 0.13 FED t-1 0.73 4.77 -19.70 0.13 (1.76) (3.41) (18.64) (0.15) IPI t-1 0.98 * 1.47 4.88 0.01 (0.40) (0.78) (4.26) (0.03) SP500 t-2 -0.02 0.06 0.09 0.00 (0.06) (0.11) (0.59) (0.00) OIL t-2 0.03 0.01 -0.19 -0.00 (0.03) (0.06) (0.33) (0.00) Factor2 t-2 0.00 0.01 0.13 * 0.00 (0.01) (0.02) (0.26) (0.00) SP500 t-1 -0.01 0.12 1.56 0.01 Factor2 t-2 0.02 * 0.02 0.02 0.00 (0.12) (0.24) (1.31) (0.01) SP500 t-2 -0.06 -0.06 -1.17 0.01 R 2 0.28 0.28 0.86 0.42 (0.06) (0.11) (1.28) (0.00) -0.04 0.18 -0.26 0.00 OIL t-1 OIL t-1 0.00 0.26 * * * 1.56 * 0.01 * * * (0.01) (0.02) (0.11) (0.00) -0.14 * 0.01 -0.07 0.00 (0.12) (0.24) (1.30) (0.01) Adj. R 2 0.12 0.13 0.82 0.29 OIL t-3 (0.03) (0.06) (0.68) (0.00) (0.06) (0.13) (0.70) (0.01) Product t-1 0.00 0.01 0.78 * * * 0.00 * Infl t-2 -1.56 0.82 -10.27 0.05 (0.06) (0.13) (0.69) (0.01) OIL t-2 0.02 0.12 0.39 0.00 Num. obs. 357 357 357 357 (0.00) (0.00) (0.06) (0.00) Factor2 t-1 0.02 -0.02 0.88 * * * -0.00 Infl t-1 -0.75 -0.90 1.85 0.32 * * * (0.70) (1.36) (16.13) (0.06) U t-1 0.37 6.88 * 8.94 0.15 (1.67) (3.23) (38.39) (0.14) FED t-1 0.37 3.93 -25.60 0.10 (1.78) (3.44) (40.89) (0.15) IPI t-1 1.00 * 1.42 50.32 * * * 0.00 (0.41) (0.79) (9.39) (0.03) SP500 t-2 -0.04 0.04 1.24 -0.00 (0.06) (0.11) (1.29) (0.00) OIL t-2 0.03 0.01 -0.58 -0.00 (0.03) (0.06) (0.70) (0.00) Product t-2 0.00 0.00 -0.04 -0.00 (0.76) (1.53) (8.27) (0.06) FED t-3 1.35 -10.83 -73.42 -0.35 (2.84) (5.69) (30.82) (0.24) High Uncertainty Regime FED t-1 -3.76 -14.34 -78.85 -0.41 (0.01) (0.03) (0.14) (0.00) IPI t-2 1.22 1.17 1.52 0.13 * (2.93) (5.87) (31.79) (0.25) U t-2 -1.55 -6.88 1.31 -0.03 (3.59) (7.18) (38.91) (0.30) (Intercept) 0.02 -0.00 -0.30 * 0.00 (5.37) (10.74) (58.21) (0.45) U t-3 1.35 8.40 26.39 -0.16 (1.13) (2.25) (12.22) (0.09) U t-1 -8.36 * 10.85 -10.80 0.77 * SP500 OIL Factor2 Infl FED t-2 -2.07 -14.48 -57.74 -1.26 * * (1.41) (2.81) (15.26) (0.12) Infl t-2 0.14 -1.43 0.81 -0.36 * * * (1.29) (2.58) (13.97) (0.11) (4.41) (8.81) (47.77) (0.37) Infl t-3 1.77 0.83 10.35 0.12 (0.01) (0.02) (0.12) (0.00) Table A.2.2: Non linear model Results (0.00) -0.00 (0.00) -0.00 (0.00) 0.00 (0.00) -0.01 (0.02) 0.85 * * * (0.05) -0.07 (0.06) -0.04 * * 0.05 * * * -0.03 (0.00) (0.00) 0.00 0.01 (0.00) (0.01) 0.00 0.01 (0.00) (0.00) -0.00 * * 0.00 (0.00) (0.00) -0.04 0.00 (0.02) (0.09) 0.01 -0.43 * (0.05) (0.22) 1.39 * * * 0.25 (0.05) (0.24) (0.01) (0.01) (0.05) -0.00 0.00 0.03 * * (0.00) (0.00) (0.01) -0.00 -0.00 0.00 (0.00) (0.00) (0.00) -0.00 0.00 -0.00 (0.00) (0.00) (0.00) -0.00 0.00 * 0.01 (0.00) (0.00) (0.01) -0.00 0.00 0.01 (0.00) (0.00) (0.00) 0.00 -0.00 -0.00 (0.00) (0.00) (0.00) -0.01 -0.04 0.01 (0.02) (0.02) (0.09) 0.84 * * * -0.02 -0.45 * (0.05) (0.05) (0.22) -0.12 * 1.43 * * * 0.30 (0.06) (0.05) (0.23) -0.04 * * 0.06 * * * -0.02 (0.01) (0.01) (0.05) -0.00 0.00 * 0.02 * * (0.00) (0.00) (0.01) -0.00 -0.00 0.00 (0.00) (0.00) (0.00) -0.00 -0.00 0.00 (0.00) (0.00) (0.00) -0.00 0.00 0.00 0.00 (0.00) (0.00) (0.02) 0.01 -0.00 -0.00 0.98 0.99 0.44 0.00 * 0.01 (0.00) (0.00) 0.00 0.00 0.00 (0.01) 0.00 0.00 (0.00) (0.00) (0.00) 0.00 0.00 -0.00 (0.00) (0.00) (0.02) 0.98 0.99 0.32 0.01 (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) 0.00 0.00 -0.06 0.08 -0.34 (0.00) (0.00) (0.01) -0.00 0.00 0.01 357 357 357 -0.00 * (0.00) (0.00) -0.00 0.00 -0.00 (0.00) 0.00 -0.04 (0.02) (0.02) 0.80 * * * -0.07 (0.05) (0.05) -0.15 * * 1.40 * * * (0.06) (0.05) (0.23) -0.03 * 0.06 * * * (0.01) (0.01) (0.05) -0.00 0.00 * * (0.00) (0.00) (0.01) -0.00 -0.00 (0.00) (0.00) (0.00) -0.00 -0.00 0.00 * * (0.03) (0.02) (0.10) 0.07 -0.20 -0.18 (0.09) (0.09) (0.38) -0.05 0.82 1.26 * * * 0.00 (0.00) (0.00) -0.05 * 0.04 0.06 (0.10) (0.09) (0.39) 0.18 0.04 0.48 (0.00) (0.12) (0.11) (0.48) 0.02 * * -0.00 0.00 (0.18) (0.16) (0.72) -0.03 0.01 -1.01 * (0.04) (0.03) (0.15) -0.00 0.88 * * * -0.25 * -0.12 0.01 U FED -0.00 -0.64 * * * 0.92 (0.05) (0.04) (0.19) 0.06 -0.01 -0.04 IPI (0.04) (0.04) (0.17) 0.33 (0.14) (0.13) (0.59) 0.04 0.02 0.23 (0.00) (0.00) (0.00) (0.22) Infl t-1 2.26 -0.71 -3.30 0.42 * * * -0.06 -0.03 -0.11 -0.43 U t-2 -3.83 -10.44 -65.13 0.01 0.24 -0.06 0.21 (0.01) (0.02) (0.10) (0.00) (0.00) (0.00) (0.00) Factor2 t-2 -0.01 0.05 * 0.14 0.00 -0.00 -0.00 * -0.00 (0.09) (0.01) (0.02) (0.13) (0.00) (0.00) (0.00) (0.00) -0.01 (1.44) (2.89) (15.65) (0.12) (0.05) (0.04) (0.19) Factor2 t-3 -0.01 0.03 -0.21 * 0.00 0.00 -0.00 0.00 (0.05) (0.10) (0.54) (0.00) (0.00) (0.00) (0.01) * * * p < 0.001; * * p < 0.01; * p < 0.05
	Infl t-2 Infl t-2 Infl t-2 SP500 t-1 SP500 t-3 FED t-2	(0.01) -0.77 (0.01) -0.74 (0.00) -0.75 0.09 (4.05) -0.00 (3.58) 3.21	(0.01) 0.60 (0.01) 0.53 (0.01) 0.58 0.38 * (8.11) 0.13 (7.15) -7.04	(0.07) 1.07 (0.07) -0.96 -0.17 * * -0.00 (0.00) (0.00) -0.17 * * -0.00 (0.00) (0.00) (0.07) (0.00) (0.00) 6.63 -0.17 * * 0.01 0.30 (43.94) (0.34) (0.13) 0.01 * -0.00 0.73 -0.00 -0.01 * * (38.78) (0.30) (0.12) 36.86 -0.23 0.28	(0.00) 0.04 (0.00) 0.04 (0.00) 0.04 * (0.12) (0.00) (0.00) -0.05 -0.05 (0.00) -0.05 (0.54) 0.00 0.00 -0.00 0.06 * * * (0.11) (0.48) 0.05 -0.70
	U t-2 U t-2 U t-2 IPI t-1 IPI t-3	(0.72) -1.02 -11.07 * * (1.38) (0.72) (1.40) -0.89 -10.68 * -9.96 (8.56) 5.93 (7.66) (0.73) (1.40) (16.64) -1.12 -10.75 * * -66.19 (0.08) (0.15) (0.83) -0.29 -0.90 7.67 (0.09) (0.18) (0.96) 1.08 0.68 -13.16 (4.68) (9.37) (50.76)	(0.06) -0.15 (0.06) -0.14 (0.06) -0.16 (0.01) -0.11 (0.01) 0.06 (0.39)	(0.02) 0.15 * (0.02) 0.16 * (0.02) 0.16 * (0.00) 0.01 (0.00) -0.05 (0.15)	(0.02) 0.03 (0.02) 0.04 (0.02) 0.04 (0.00) (0.10) (0.10) 0.56 * 0.53 (0.09) 0.53 0.03 -0.09 (0.01) (0.00) (0.01) -0.01 0.29 * (0.14) (0.63)
	FED t-2 FED t-2 FED t-2 OIL t-1 OIL t-3 IPI t-2	(2.11) 0.01 (2.13) -0.36 -5.75 (4.06) -2.46 (4.12) (22.58) (0.18) (25.12) (0.18) 39.93 -0.31 24.59 -0.37 (2.13) (4.12) (48.86) (0.17) 0.20 -4.12 2.12 -0.31 0.03 0.18 0.73 0.01 * (0.99) (1.97) (10.69) (0.08) 0.06 -0.29 * * 0.15 -0.00 (0.94) (1.89) (10.22) (0.08) 0.55 -0.54 0.53 -0.01	(0.07) 0.10 (0.07) 0.12 (0.07) 0.16 -0.00 (0.03) 0.00 (0.03) -0.01	(0.06) -0.24 * -0.22 (0.28) (0.07) (0.28) -0.28 * * -0.17 (0.06) (0.28) -0.24 * -0.25 0.00 (0.03) (0.13) 0.02 * * -0.00 * * 0.00 (0.03) (0.13) 0.00 0.00
	(3.07) 1.03 * (3.07) 0.68 (3.10) 0.55 (0.05) 0.28 * (0.05) Low Uncertainty Regime IPI t-2 IPI t-2 IPI t-2 SP500 t-2 (0.64)	(5.92) 0.16 (5.94) (32.53) (0.25) (36.62) (0.26) -7.53 0.09 * * 0.04 0.23 0.09 * * (5.98) (71.01) (0.25) -0.33 9.40 0.07 * (0.11) (0.58) (0.00) 0.09 0.13 -0.00 (0.10) (0.56) (0.00) (1.28) (6.92) (0.05)	(0.10) -0.03 * (0.10) -0.03 * (0.10) -0.03 * (0.00) -0.00 (0.00) (0.02)	(0.09) 0.00 (0.09) 0.01 (0.09) 0.01 (0.00) (0.41) (0.41) 0.07 0.08 (0.40) 0.11 0.01 0.03 (0.01) (0.00) (0.01) (0.02) (0.09)
	(0.42) 0.07 (0.42) 0.00 (0.43) -0.01 -0.00 SP500 t-3 SP500 t-3 SP500 t-3 Factor2 t-1 (0.13) Factor2 t-3 -0.01 SP500 t-1 -0.28 * SP500 t-3 0.00	(0.80) 0.19 (0.81) 0.18 (0.83) 0.16 -0.02 (0.26) -0.01 -0.12 0.42	(4.96) -1.23 (4.41) 0.28 (9.85) -0.06 (1.42) 0.65 * * * 0.08 -1.05 0.63	(0.03) 0.01 (0.03) 0.01 (0.04) 0.01 (0.01) 0.00 -0.00 * 0.00 0.01	(0.01) -0.00 (0.01) -0.00 * (0.01) -0.00 (0.00) 0.00 -0.00 * * -0.00 0.01	(0.01) -0.00 0.04 * * * (0.06) (0.01) (0.05) 0.00 0.04 * * * (0.01) (0.06) 0.00 0.04 * * * (0.00) (0.02) -0.00 -0.00 -0.00 -0.00 0.00 0.02 -0.00 0.01
	OIL t-3 OIL t-3 OIL t-3 OIL t-2	(0.06) 0.01 (0.06) 0.01 (0.06) 0.01 (0.01) -0.02 (0.01) (0.11) (0.11)	(0.11) -0.10 (0.11) -0.12 * (0.11) -0.12 * (0.01) -0.23 (0.02) (0.22) (0.22)	(0.68) 0.99 * * (0.59) 0.38 (1.28) 0.78 (0.08) -0.54 (0.10) (1.22) (1.22)	(0.00) 0.00 (0.00) 0.00 (0.00) 0.00 (0.00) -0.00 (0.00) (0.01) (0.01)	(0.00) 0.00 * (0.00) 0.00 (0.00) 0.00 (0.00) 0.00 (0.00) (0.00) (0.00)	(0.00) -0.00 (0.00) -0.00 (0.00) -0.00 (0.00) (0.01) (0.01) -0.00 -0.00 (0.01) -0.00 -0.00 0.00 (0.00) (0.00) (0.00) (0.00) (0.02) (0.00) (0.02)
	(0.03) 0.00 (0.00) 0.11 (0.65) 1.70 (1.64) -1.44 (1.77) -0.22 (0.41) 0.11 0.05 357 * * * p < 0.001; * * p < 0.01; * p < 0.05 (0.06) GU t-3 0.02 * (0.01) Infl t-3 0.02 (1.26) U t-3 3.90 (3.17) FED t-3 -1.77 (3.42) IPI t-3 1.24 (0.79) R 2 0.18 Adj. R 2 0.12 Num. obs. 357 (0.03) (0.06) Factor2 t-3 -0.01 -0.01 (0.01) (0.01) Infl t-3 -0.05 -0.11 (0.66) (1.28) U t-3 0.46 3.72 (1.67) (3.24) (17.72) (0.14) (0.35) (0.00) 0.11 0.00 (0.06) (0.00) 3.68 -0.06 (7.78) (0.05) -18.43 -0.02 (19.58) (0.14) -10.13 0.20 (21.15) (0.15) -0.55 0.07 * (4.86) (0.03) 0.78 0.29 0.77 0.25 357 357 (0.32) (0.00) 0.01 -0.00 (0.05) (0.00) -5.02 -0.06 (7.00) (0.05) 25.96 -0.01 FED t-3 -0.27 0.87 -6.11 0.22 (1.75) (3.39) (18.57) (0.14) IPI t-3 -0.58 1.01 -0.37 0.07 * (0.41) (0.79) (4.33) (0.03) R 2 0.08 0.15 0.83 0.29 Adj. R 2 0.02 0.10 0.81 0.24 Num. obs. 357 357 357 357 * * * p < 0.001; * * p < 0.01; * p < 0.05 (0.03) (0.06) (0.69) (0.00) Product t-3 -0.00 -0.01 -0.02 -0.00 -0.00 * * -0.00 * * -0.00 (0.00) (0.00) (0.00) 0.00 0.00 -0.00 (0.00) (0.00) (0.00) -0.03 -0.03 0.11 (0.02) (0.02) (0.09) -0.00 -0.04 -0.08 (0.06) (0.05) (0.22) -0.01 -0.17 * * -0.01 (0.06) (0.05) (0.24) -0.04 * * 0.01 0.17 * * (0.01) (0.01) (0.05) 0.98 0.99 0.32 0.98 0.99 0.28 357 357 357 (0.00) (0.00) (0.00) -0.00 * 0.00 0.00 (0.00) (0.00) (0.00) -0.02 -0.03 0.11 (0.02) (0.02) (0.09) 0.01 -0.02 -0.06 (0.06) (0.05) (0.22) 0.01 -0.16 * * -0.11 (0.06) (0.05) (0.23) -0.04 * * 0.01 0.18 * * * (0.01) (0.01) (0.05) 0.98 0.99 0.31 0.98 0.99 0.27 357 357 357 (0.00) (0.00) (0.00) (0.00) (0.00) (0.06) (0.00) (0.00) (0.00) Infl t-1 -3.06 * 2.71 20.18 0.12 0.03 (0.06) (0.12) (0.64) (0.00) (0.00) (0.00) (0.01) -0.09 * 0.09 Infl t-3 -0.45 -0.64 -16.21 -0.26 * * 0.03 -0.09 * * -0.09 OIL t-1 0.01 0.30 * * 1.18 * 0.01 * * 0.00 -0.00 -0.00 0.01 -0.02 0.61 0.01 0.00 0.00 0.00 OIL t-3 (0.00) Infl t-3 -0.08 -0.11 -21.02 -0.07 -0.00 -0.01 0.11 (0.67) (1.30) (15.38) (0.05) (0.02) (0.02) (1.38) (2.76) (14.98) (0.12) (0.05) (0.04) -0.01 -0.02 0.19 -0.00 -0.00 -0.00 0.00 Factor2 t-2 (0.19) (1.07) (2.14) (11.58) (0.09) (0.04) (0.03) (0.14) (0.05) (0.10) (0.52) (0.00) (0.00) (0.00) (0.01) (0.05) (0.10) (0.53) (0.00) (0.00) (0.00) (0.01) (0.09) U t-3 0.88 3.79 58.52 -0.00 0.05 0.03 -0.07 (1.69) (3.27) (38.83) (0.14) (0.05) (0.05) U t-1 4.41 10.96 -18.87 -0.25 0.84 * * * 0.10 (0.01) (0.02) (0.13) (0.00) (0.00) (0.00) (0.00) -1.19 * * U t-3 -0.79 -0.36 89.19 * 0.23 -0.07 -0.05 1.00 * Factor2 t-1 0.01 0.00 0.76 * * * 0.00 0.00 * -0.00 -0.00 Factor2 t-3 -0.00 -0.04 * 0.07 0.00 -0.00 0.00 * 0.00 * (0.22) FED t-3 -0.53 0.17 22.95 0.19 0.01 -0.17 * * -0.06 (1.76) (3.40) (40.37) (0.14) (0.06) (0.05) (3.19) (6.39) (34.63) (0.27) (0.10) (0.10) -3.78 * * 2.53 2.00 -0.19 0.02 0.03 0.07 Infl t-2 (0.43) (3.38) (6.76) (36.64) (0.28) (0.11) (0.10) (0.45) (0.01) (0.02) (0.12) (0.00) (0.00) (0.00) (0.00) (0.01) (0.02) (0.11) (0.00) (0.00) (0.00) (0.00) (0.23) IPI t-3 -0.69 0.73 -10.34 0.06 -0.03 * 0.01 0.17 * * (0.42) (0.81) (9.60) (0.03) (0.01) (0.01) FED t-1 3.31 10.19 29.66 0.73 * * 0.01 (1.40) (2.79) (15.12) (0.12) (0.05) (0.04) (0.19) 1.55 * * * -0.49 FED t-3 -0.89 4.03 30.73 0.55 * -0.00 0.07 -0.44 Infl t-1 -0.80 -1.63 -20.36 0.29 * * -0.02 0.02 0.11 Infl t-3 -1.14 0.60 -9.48 -0.09 -0.02 0.03 0.25 (0.05) R 2 0.08 0.15 0.71 0.30 0.98 0.99 0.33 Adj. R 2 0.03 0.10 0.70 0.26 0.98 0.99 (3.07) (6.14) (33.30) (0.26) (0.10) (0.09) 6.66 -19.37 * -8.66 -0.60 0.16 0.23 1.15 U t-2 (0.41) (3.18) (6.36) (34.47) (0.27) (0.10) (0.10) (0.43) (1.12) (2.23) (12.11) (0.09) (0.04) (0.03) (0.15) (1.13) (2.26) (12.24) (0.09) (0.04) (0.03) (0.15) 0.29 Num. obs. 357 357 357 357 357 357 357 IPI t-1 2.14 * * 3.57 * * 7.42 0.02 -0.03 (4.47) (8.93) (48.40) (0.37) (0.15) (0.13) (0.60) 0.07 * * * -0.04 IPI t-3 -1.48 * 0.79 -0.87 0.04 -0.08 * * 0.00 0.12 U t-1 0.34 4.07 -4.83 0.06 0.56 * * * -0.05 -0.14 U t-3 0.82 2.60 9.73 -0.04 0.25 * * 0.01 -0.31 * * * p < 0.001; * * p < 0.01; * p < 0.05 (0.65) (1.29) (7.01) (0.05) (0.02) (0.02) 2.00 25.66 153.67 * 0.75 -0.01 -0.07 -0.59 FED t-2 (0.09) (0.73) (1.46) (7.93) (0.06) (0.02) (0.02) (0.10) (2.56) (5.12) (27.77) (0.22) (0.08) (0.08) (0.34) (2.63) (5.25) (28.48) (0.22) (0.09) (0.08) (0.35)
	SP500 t-2 FED t-1 FED t-3	-0.04 (6.62) -1.07 -1.93	0.08 (13.23) 6.54 0.75	1.21 (71.73) -32.01 -5.50	-0.00 (0.56) 0.14 0.09	-0.00 (0.22) -0.22 * -0.04	(0.20) 0.01 * * 1.25 * * * -0.30 * * *	(0.89) 0.02 0.26 0.50

Table B

 B

		.3.2: Regression Results HP: Factor2 as Uncertainty variable Figure B.3.2: Impulse Response Functions (Factor 2)
	0.02	SP500 0.00 Factor2 on SP500 (Intercept)	OIL 0.00 0.04	Factor2 0.00 Factor2 on OIL Infl 0.00	U 0.00	FED -0.00	IPI -0.00
			(0.00)	(0.00)	(0.02)	(0.02)	(0.01)	(0.01)	(0.00)
	0.01	SP500 t-1 0.91 * * * (0.06)	0.14 (0.13) 0.02	-1.50 * (0.67)	0.79 (0.51)	-0.40 * (0.20)	0.41 * (0.19)	0.01 (0.01)
	0	OIL t-1 Factor2 t-1	0.02 (0.04) 0.00	1.15 * * * (0.06) -0.01 0	0.69 * * (0.24) 0.72 * * *	0.91 * * (0.29) 0.03	-0.02 (0.09) 0.01	0.03 (0.09) -0.01	0.01 (0.00) -0.00
	-0.01		(0.00)	(0.01)	(0.06)	(0.04)	(0.02)	(0.02)	(0.00)
	-0.02	Infl t-1 U t-1	-0.01 (0.00) 0.01	0.00 (0.01) 0.07 * -0.02	-0.02 (0.03) -0.07	1.17 * * * (0.06) 0.10	-0.02 (0.02) 0.74 * * *	-0.01 (0.02) -0.08	0.00 (0.00) -0.01 *
	-0.03	(0.01) 0.00 (0.02) 0 4 8 12 16 20 24 28 32 36 FED t-1	(0.03) 0.05 (0.04) 0 4 8 12 16 20 24 28 32 36 (0.12) (0.12) (0.05) -0.15 0.15 -0.17 * * * 1.49 * * * (0.05) (0.13) (0.13) (0.04) (0.04) -0.04	(0.00) (0.00) 0.01 * *
		IPI t-1	1.17	1.83 * *	5.33 *	-0.47	-4.58 * * *	6.42 * *	0.92 * * *
			(0.63)	(0.60)	(2.68)	(3.00)	(1.22)	(2.12)	(0.05)
		SP500 t-2	-0.03	-0.10	1.12	-0.54	0.17	-0.40	0.01
			(0.07)	(0.13)	(0.72)	(0.56)	(0.19)	(0.24)	(0.01)
		OIL t-2	-0.02 -0.31 * * * -0.71 * -0.68 *	0.11	-0.09	-0.01
			(0.04)	(0.07)	(0.28)	(0.27)	(0.10)	(0.10)	(0.00)
		Factor2 t-2	0.00	0.01	0.18 * *	0.02	-0.03	0.00	0.00
			(0.00)	(0.01)	(0.06)	(0.03)	(0.02)	(0.02)	(0.00)
		Infl t-2	0.00	-0.00	-0.01 -0.35 * * *	0.01	0.02	-0.00
			(0.00)	(0.02)	(0.03)	(0.07)	(0.02)	(0.02)	(0.00)
		U t-2	0.00	-0.06 *	0.17	-0.11	0.14 * *	0.06	0.01 * *
			(0.01)	(0.03)	(0.11)	(0.12)	(0.05)	(0.05)	(0.00)
		FED t-2	0.01	-0.04	0.20	-0.14	0.15 * * * -0.52 * * * -0.01 *
			(0.02)	(0.04)	(0.12)	(0.11)	(0.04)	(0.04)	(0.00)
		IPI t-2	-0.84	-1.38 *	-5.25	1.92	2.44 *	-6.39 * * * -0.01
			(0.52)	(0.60)	(2.84)	(2.95)	(1.18)	(1.91)	(0.05)
		R 2	0.88	0.87	0.83	0.89	0.97	0.99	0.96
		Adj. R 2	0.88	0.86	0.82	0.88	0.96	0.98	0.96
		Num. obs.	358	358	358	358	358	358	358
		* * * p < 0.001; * * p < 0.01; * p < 0.05
					59

[START_REF] Forni | Downside and Upside Uncertainty Shocks[END_REF] defined downside uncertainty as the difference between the forecast of the median and the 10th percentile of the future growth. Upside uncertainty is defined as the difference between the forecast of the 90th percentile and the median of the future growth.

It is admittedly a strong assumption but it reflects the more general idea that an agent may be constrained by a maximal psychological cost he can bear.

The data used for the analysis are downloaded from FRED database on the Federal Reserve Bank of St. Louis' website.

Other identification scheme can be applied with local projections: long-run restrictions, identification with external instruments[START_REF] Jordá | Estimation and Inference of Impulse Responses by Local Projections[END_REF][START_REF] Stock | Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments[END_REF][START_REF] Plagborg-Møller | Local Projections and VARs Estimate the Same Impulse Responses[END_REF].

To determine the number of lags, we apply the Akaike information criteria (AIC).

Moreover, both variables do not have a unit root applying the Elliott-Rothenberg-Stock (ERS) test.

We get the same results if we apply the Hodrick-Prescott filter in robustness checks. The VAR of the seminal paper of[START_REF] Bloom | The Impact of Uncertainty Shocks[END_REF] also presents high values of the R 2 .

The effect is significant at the 5% level. Applying local projections, the residuals u t t+s are a moving average of the forecast errors. To correct heteroskedasticity, we compute error bands applying the[START_REF] Newey | A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix[END_REF] method.

This section is linked to a branch of empirical studies investigating non-linear effects of uncertainty (See, among many others,[START_REF] Caggiano | Uncertainty Shocks and Unemployment Dynamics: An Analysis of Post-WWII U.S. Recessions[END_REF][START_REF] Ismailov | Uncertainty and deviations from uncovered interest rate parity[END_REF][START_REF] Alessandri | Financial regimes and uncertainty shocks[END_REF][START_REF] Colombo | The asymmetric effects of uncertainty shocks[END_REF][START_REF] Candelon | Global financial interconnectedness: a non-linear assessment of the uncertainty channel[END_REF].

We extent the R code of the package lpirfs of[START_REF] Adämmer | lpirfs: An R Package to Estimate Impulse Response Functions by Local Projections[END_REF] to add the third regime.

The results and figures are available upon request.

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Source: Author's own calculations. Note: The VAR is specified with 3 lags.

A.2 Nonlinear Model

Linearity VS Two regimes Linearity VS Three regimes Source: Author's own calculations.

Notes: Graphs on the left panel represents impulse response functions in the high uncertainty regime. Graphs on the middle panel represents impulse response functions in the moderate uncertainty regime. Graphs on the right panel represents impulse response functions in the low uncertainty regime. The solid black lines correspond to the IRFs. The red shaded area denotes the 95% confidence interval.


Essyllt Louarn

Michel Heninger

Joël Lemaire

Helene Mestdagh

Sebastien Thomas

Elsa Bauchard

Julien Leprovost

Suivi temps réel de composés dans l'air ou dans l'eau par spectrométrie de masse haute résolution : applications dans le domaine de l'énergie

come

Suivi temps réel de composés dans l'air ou dans l'eau par spectrométrie de masse haute résolution : applications dans le domaine de l'énergie.

Essyllt Louarn, Michel Heninger, Joël Lemaire, Helene Mestdagh, Sebastien Thomas, Elsa Bauchard, Julien Leprovost LCP, UMR8000, CNRS-Université Paris Sud, Université Paris Saclay, Orsay, France AlyXan, Juvisy sur Orge, France

Ionisation chimique

  sont choisis afin d'ioniser sélectivement les analytes et pas les molécules de la matrice (air, eau).La réaction ion-molécule la plus utilisée pour la détection de traces dans l'air ou dans l'eau est la réaction de transfert de proton à partir d'ions H 3 O + (eau protonée)H 3 O + + M  H 2 O + MH +La réaction de transfert de proton est rapide et efficace pour les molécules ayant une affinité protonique plus grande que l'eau (comme les composés aromatiques, les alcools, les aldéhydes, les explosifs nitrés, les narcotiques …) et la réaction n'a pas lieu avec les composés ayant une affinité protonique plus faible que l'eau (ce qui est le cas pour les principaux constituants de l'air N2, O2, Ar ainsi que pour les alcanes, les CFCs,…) . D'autres précurseurs peuvent être utilisés pour étendre les classes de molécules détectables: Dans nos spectromètres FTICR (Fourier Transform Ion Cyclotron Resonance) transportables le champ magnétique est créé par une structure aimantée structurée (cylindre de Halbach) constituée d'aimants permanents qui produit un champ homogène (champ nominal de 1 à 1.5 Tesla). Les ions précurseurs sont formés et sélectionnés dans la cellule ICR. Ils réagissent ensuite avec une impulsion du gaz à analyser. Puis, après excitation des ions le spectre de masse est obtenu par transformée de Fourier du courant image induit par les ions. perméable sert d'interface entre l'eau et le spectromètre de masse Nous avons mis au point des mini membranes qui permettent de sonder les concentrations localement. Par exemple pour suivre les produits formés dans une cellule électrochimique Détection de de gaz legers dans l'eau La détection en masse repose sur l'utilisation d'un quadrupole. L'échantillonnage est réalisée avec une membrane semi perméable à travers laquelle les gaz dissous dans l'eau peuvent passer. L'eau reste bien sur très majoritaire dans le perméat et une concentration en ligne doit être effectuée avant l'analyse en masse. Cette concentration reposera sur la mise en oeuvre d'une technique cryogénique

Remerciements

.

Nous remercions les ateliers de mécanique et d'électronique du LCP pour leur aide, l'ANR pour le financement du projet PLASPAMS dans le cadre duquel nous développons un instrument « tube à dérive + piège linéaire», ainsi que la DGA pour le financement du développement visant à la détection de gaz legers dans l'eau.

Application au suivi d'émission moteur avec des biofuels (collaboration IFPEN) Depollution par Plasmas froids (collaboration LPGP)

On observe la dégradation ici partielle du toluène par un plasma froid.. Les produits de dégradation vont être suivis avec une grande résolution, temporelle (1sec) et en masse (précision <5mDa)

Exemple de la masse 59 où l'on distingue les évolutions temporelles du glyoxal et de l'acétone. Pour que l'instrument soit assez compact l'analyseur sera un piège linéaire. Celui-ci peut fonctionner à des pressions de l'ordre de 10 -3 mbar ce qui réduit les contraintes sur le pompage.

Le gaz buffer sera de l'air ou des m élanges air/gaz rare. Les ions protonés caractéristiques des analytes pourront être sélectionnés en masse, isolés et fragmentés (séquence MS/MS) pour identifier plus précisément les composés présents.

Suivi