domain: shs qfin

text:
Gilles Dufrénot
email: gilles.dufrenot@univ-amu.fr

William Ginn
email: william.ginn.oba@said.oxford.edu

Marc Pourroy
email: marc.pourroy@univ-poitiers.fr

ENSO Climate Patterns on Global Economic Conditions

Keywords: JEL Classification: C32, F44, O13, Q54 Weather, Oil and Food Prices, Global Macroeconometric Modeling, and Economic Policy Uncertainty

We investigate the role of ENSO climate patterns on global economic conditions. The estimated model is based on a rich and novel monthly dataset for 20 economies, capturing 80.2% of global output (based on 2021 IMF data) over the period 1999:01 to 2022:03. The empirical evidence from an estimated global vector autoregression with local projections (GFAVLP) model links an El Ni ño (EN) shock with higher output and inflation, corresponding with lower global economic policy uncertainty (GEPU). While a shock to the world oil and food price is inflationary, a food price shock leads to elevated GEPU, more so during a LN shock. A main finding is that an increase of the food price can be a source of global vulnerability. The findings indicate that the weather shock impact on global economic conditions is dependent on the climate state. Our result undermines existing studies connecting climate change and economic damage via statistical approach.

Highlights:

• We investigate the transmission of climate shocks on global economic conditions.

• We distinguish between an EN and a LN climate states.

• An EN and a LN shock corresponds with higher consumer price and food inflation, albeit a food price shock elevates GEPU during a LN state.

• Our results undermine studies connecting climate change and economic damage via statistical approach.

Introduction

Two grievances are frequently directed towards the economics profession. On the one hand, economists give little importance to climate issues (e.g., Oswald and Stern, 2019a[START_REF] Oswald | Why does the economics of climate change matter so much, and why has the engagement of economists been so weak[END_REF][START_REF] Noah | Why has climate economics failed us? noahpinion[END_REF], on the other hand, they underestimate the importance of climate effects on the economy (e.g., [START_REF] Nordhaus | Expert opinion on climatic change[END_REF][START_REF] Dietz | Endogenous growth, convexity of damage and climate risk: how Nordhaus' framework supports deep cuts in carbon emissions[END_REF][START_REF] Defries | The missing economic risks in assessments of climate change impacts[END_REF][START_REF] Pezzey | Why the social cost of carbon will always be disputed[END_REF][START_REF] Stern | The social cost of carbon, risk, distribution, market failures: An alternative approach[END_REF]).

An existing strand of literature has sought to establish the impact of climate on economic activity [START_REF] Tol | The economic effects of climate change[END_REF] and has reached the conclusion that climate change impact on activity would be rather limited [START_REF] Tol | The economic impacts of climate change[END_REF]).

Yet, interest in this issue has been renewed by IPCC's publications, which have highlighted several possible temperature increase scenarios (see [START_REF] Stocker | Climate change 2013: The physical science basis[END_REF] for a presentation of different greenhouse gas Representative Concentration Pathway, translated into global temperature trajectories) Economists have sought to use observed climate-growth relation to project future temperature impact on GDP in terms of growth (e.g., [START_REF] Burke | Global non-linear effect of temperature on economic production[END_REF] or levels (e.g. [START_REF] Newell | The gdp-temperature relationship: implications for climate change damages[END_REF].

However, these approaches are not without debate. The existing literature points to two main limitations:

First, the studies focus on average annual temperatures or precipitation, whereas it is extreme events that cause the most damage to activity. This is particularly an issue because climate change can be seen as a change in events distribution, i.e. moving to a fat tailed distribution [START_REF] Field | Managing the risks of extreme events and disasters to advance climate change adaptation: special report of the intergovernmental panel on climate change[END_REF].

Second, when future temperature is projected to be outside the historical conditions observed for a country, the authors use variation observed today across countries to infer climate variation over time, (a critique expressed by [START_REF] Tol | The economic impacts of climate change[END_REF] and [START_REF] Woillez | Economic impacts of a glacial period: a thought experiment to assess the disconnect between econometrics and climate sciences[END_REF]) However, such a projection does not take into account the cost of adapting infrastructures or the depreciation of present investments [START_REF] Bolton | Green swans": central banks in the age of climate-related risks[END_REF]. In other words: projecting the temperature of one country today onto another country tomorrow does not really make sense. This paper addresses a third limitation: we show that the impact of weather shocks on global activity is a function of climate. Therefore, the impact of weather shocks on activity within today's climate cannot be used to infer weather shocks impact on activity with tomorrow's climate. The reason is that the transmission channel of weather shocks on activity are dependant on climate.

We propose a new analytical framework to study the effect of climate on economic activity. We rely on the the Equatorial Southern Oscillation Index (ESOI) as a measure of the ENSO climate phenomenon (see [START_REF] Dufrénot | The effect of ENSO shocks on commodity prices: A multi-time scale approach[END_REF]). This allows us to distinguish between an EN and a LN climate state. Therefore our study does not suffer from a projection bias, neither across time, nor space. On the contrary, we observe that the effect of extreme climate events on activity depends on climate. This paper explores the global dimensions of changing weather patterns and the international oil and food commodity prices as they affect economic conditions. This research overlaps with three strands of literature. The first strand relates to a voluminous body of literature analyzing the effects that changing oil prices have on the macroeconomy (e.g., [START_REF] Hamilton | Oil and the macroeconomy since World War II[END_REF][START_REF] Hamilton | Oil and the macroeconomy[END_REF][START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF][START_REF] Bodenstein | Oil shocks and external adjustment[END_REF][START_REF] Kilian | Oil price shocks: Causes and consequences[END_REF][START_REF] Kang | Oil price shocks, policy uncertainty, and stock returns of oil and gas corporations[END_REF][START_REF] Arouri | Economic policy uncertainty, oil price shocks and GCC stock markets[END_REF], You et al., 2017, among others). Commodity prices (in real terms) tend to be endogenous and pro-cyclical to the global business cycle (e.g., [START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF][START_REF] Kilian | Modeling fluctuations in the global demand for commodities[END_REF]. [START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF] distinguishes between demand and supply shocks in the oil price, and finds that increases in the oil price since 2003 are primarily driven by demand. The similar increases in the food price has raised concerns about inflationary pressures. This is finding is also confirmed by [START_REF] Joëts | Does the volatility of commodity prices reflect macroeconomic uncertainty?[END_REF] for corn, soybeans and wheat. This identification is consistent with Alquist and Kilian, 2010, who finds that the oil price is determined endogenously and simultaneously.

The second strand relates to economic uncertainty. In recent years, numerous researchers have analyzed the effects that commodity prices have on uncertainty. The majority have focued on understanding the influence of oil prices (e.g., [START_REF] Kang | Structural oil price shocks and policy uncertainty[END_REF][START_REF] Antonakakis | Dynamic spillovers of oil price shocks and economic policy uncertainty[END_REF][START_REF] Hailemariam | Oil prices and economic policy uncertainty: Evidence from a nonparametric panel data model[END_REF] and economic policy uncertainty (EPU), a measure developed by [START_REF] Baker | Measuring economic policy uncertainty[END_REF] as an indicator of economic uncertainty. [START_REF] Ginn | Uncertainty and food prices[END_REF] investigate the transmission of the international oil and food price on EPU for the case of India. These authors find that international prices can create a spillover effect on the domestic economy. Uncertainty can also have consequential effects on the macroeconomy relating to firm-investmentment (e.g., Kang et al., 2014, Handley and[START_REF] Handley | Trade and investment under policy uncertainty: theory and firm evidence[END_REF], stock prices (e.g., Kang and Ratti, 2013a[START_REF] Antonakakis | Dynamic co-movements of stock market returns, implied volatility and policy uncertainty[END_REF][START_REF] You | Oil price shocks, economic policy uncertainty and industry stock returns in China: Asymmetric effects with quantile regression[END_REF] and unemployment (e.g., [START_REF] Caggiano | Uncertainty shocks and unemployment dynamics in US recessions[END_REF][START_REF] Caggiano | Economic policy uncertainty and unemployment in the United States: A nonlinear approach[END_REF]. [START_REF] Ginn | Climate disasters and the macroeconomy: Does state-dependence matter? Evidence for the US[END_REF] finds that a natural disaster may create a disturbance which can spill over into aggregate uncertainty such that EPU increases (decreases) during an expansionary (non-expansionary) state.

The third strand relates to only a handful of papers to address the transmission that weather shocks has on economic conditions [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF][START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF][START_REF] De Winne | Agricultural price shocks and business cycles-a global warning for advanced economies[END_REF]and Peersman, 2018). [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF] finds that weather shocks has important and statistically important effects on global commodity prices. [START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF] estimates a global vector autoregression to investigate weather shocks for twentyone country/regions. [START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF] find heterogeneous responses of a weather shocks with regard to output growth. [START_REF] Peersman | International food commodity prices and missing (dis) inflation in the euro area[END_REF] find that food price shocks can explain 30% inflation volatility in euro area. De Winne and [START_REF] Peersman | International food commodity prices and missing (dis) inflation in the euro area[END_REF] show that increases in global agricultural commodity prices that are caused by unfavorable harvest shocks in other regions of the world can curtail domestic economic activity.

This paper provides three main contributions to the literature. First, using a rich dataset for nine economies representing circa two-thirds of global output1 , we analyze to what extent a global El Ni ño weather and commodity price shock transmit a disturbance on the global factor economy. This paper is based on monthly data over the period 1999:01 to 2022:03, which has the potential benefit of capturing the short-term temporal effect that weather has on the economy (e.g., [START_REF] Barnston | Why are there so many ENSO indexes, instead of just one[END_REF]), as opposed to using quarterly data as in previous studies [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF], [START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF]. By adding oil and food prices with changing weather conditions to the model, we can explore the global linkages that weather has on these two commodities.

The main contribution of our study is that we incorporate a weather shock transmission channel to the economy. A weather shock that occurs during EN periods brings immediate increase in food price inflation, which later translates into consumer price inflation and, following monetary policy reactions, leads to higher interest rate in the medium run (1 year). The same weather shock occurring during LN periods would lead to a lagged increase in food prices. Consequently, we do not observe second-round effect on consumer prices and the interest rate remains flat. Therefore we can conclude that extreme weather events are transmitted to the economy through different transmission channels depending on the climate state. This result is particularly important because it invalidates the statistical evaluation method mentioned above, used by researchers to predict the effect of climate change on the economy [START_REF] Tol | The economic effects of climate change[END_REF][START_REF] Tol | The economic impacts of climate change[END_REF]. Indeed, the transmission of an extreme weather event on the economy depends on climate, so we cannot use an estimated relationship between weather and economy for a given climate to project it on a future climate: this relationship will no longer exist, the channels of transmission will be heterogenous. Our results corroborate [START_REF] Woillez | Economic impacts of a glacial period: a thought experiment to assess the disconnect between econometrics and climate sciences[END_REF] who perform an ad absurdum demonstration of the limitation of studies connecting climate change and economic damage though a statistical approach.

Our paper contributes to an important literature on ENSO economic impacts (see [START_REF] Smith | The El Ni ño Southern Oscillation and economic growth in the developing world[END_REF][START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF][START_REF] Atems | Exploring asymmetries in the effects of el ni ño-southern oscillation on us food and agricultural stock prices[END_REF] First, we start from a rich data-set to construct a set of global indicators using a large dataset of a time-varying weighted indexation (based on GDP). While previous studies generally focus on one commodity (e.g. [START_REF] Tack | Climate and agricultural risk: measuring the effect of ENSO on US crop insurance[END_REF] on cotton) or a given country (e.g. [START_REF] Ubilava | El Ni ño, La Ni ña, and world coffee price dynamics[END_REF] on Colombia), [START_REF] Mueller | Long-term consequences of short-term precipitation shocks: evidence from brazilian migrant households[END_REF] on Brazil or [START_REF] Mainardi | Cropland use, yields, and droughts: spatial data modeling for burkina faso and niger[END_REF] on Burkina Faso and Niger, we add to the literature by showing that the effects of ENSO operate at the global level.

Second, rather than estimating the partial influence of a partial weather shock in isolation [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF] and [START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF] estimate the transmission of only an EN weather shock), we employ a GFAVLP which allows us to cast the entire data via changing ENSO states. Second, this paper employs a global factor augmented vector error correction model (GVARLP) framework to assess the transmission of shocks on economic uncertainty. As the impact of El Ni ño cannot be reduced to one country, but rather relates to global climate patterns, this paper exploits a global factor model framework which paves the way to understand how climate affects the global economic conditions.

The global structure allows an identification such that oil and food prices are treated endogenously. This framework is an extension of GVAR [START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF], where the model structure partially facilitates an endogenous treatment of oil and non-fuel commodities (based on the US economy). By adding oil and food prices with changing ENSO weather conditions, we explore the global linkages that weather has on these two commodities. The benefit of these contributions allows the estimated economic system to not necessarily remain static within one state of ENSO (EN or LN) conditional that the system has entered into that state. Overall, our model facilitates a way to capture the full data generating process of how the changing ENSO states affect global economic conditions. Incorporating the effects of weather while integrating an endogenous treatment of commodity prices on a global scale is of critical importance to further inform our understanding of the consequential effects of changing climate ex post, an area of paramount importance, considering current assessments of future climate scenarios are shrouded in uncertainty.

The rest of the paper is structured as follows: in Section 2 describes the data. Section 3 discusses the global dimensions of the business cycle considered in the paper. The modelling methodology and empirical results are summarized in Section 4. Section 5 summarizes the paper, with an emphasis of the food price as a source of global vulnerability. Section 6 concludes the paper.

Data

The model is based on 20 economies and includes seven endogenous variables: weather (ENSO The endogenous variables considered include a weather index; industrial production index3 ; the consumer price index (CPI); the world oil price and food commodity price; the short-term interest rate4 ; and EPU. The data is summarized in Table 1. The exogenous variables includes a global financial crisis (GFC) dummy variable [START_REF] Hailemariam | Oil prices and economic policy uncertainty: Evidence from a nonparametric panel data model[END_REF] 5 , CBOE Volatility Index (VIX) and U.S. Infectious Diseases [START_REF] Baker | Policy news and stock market volatility[END_REF] All endogenous variables are converted to logarithm with the exception of the real interest rate and weather index. For consistency, output for China and India7 ; the CPI; and EPU are seasonally adjusted via ARIMA X-12 algorithm from the U.S. Census Bureau. The oil and food price data, denominated in U.S. dollars, is deflated by dividing by the U.S. CPI. Economic uncertainty is based on the global EPU data by [START_REF] Davis | An index of global economic policy uncertainty[END_REF].

The Equatorial Southern Oscillation Index (ESOI) is used as a global measure of weather, which is collected from the National Oceanic and Atmospheric Administration (NOAA).

Global Dimensions of the Business Cycle

Four global variables are considered: ENSO climate index, output, CPI, interest rate, oil price, food price and GEPU. Each are discussed in turn.

Global ENSO Weather Patterns

When a major El Ni ño (La Ni ña) occurs, there is an anomalous loss (increase) of heat from the ocean to atmosphere so that global mean temperatures rise (fall) [START_REF] Mcphaden | Introduction to El Ni ño southern oscillation in a changing climate[END_REF]. The anomalous atmospheric patterns are known as the Southern Oscillation. El Ni ño, La Ni ña Southern Oscillation (ENSO) is one of the most important climate indicators, which has a major influence of global weather conditions (e.g., [START_REF] Ropelewski | Global and regional scale precipitation patterns associated with the El Ni ño/Southern Oscillation[END_REF], [START_REF] Rosenzweig | Climate change and extreme weather events[END_REF][START_REF] Mcphaden | ENSO as an integrating concept in earth science[END_REF] and [START_REF] Dai | Increasing drought under global warming in observations and models[END_REF], Br önnimann et al. ( 2007)). 8ENSO relates to cyclical, environmental conditions that occur across the equatorial Pacific Ocean. Changes to ENSO are due to natural interactions between sea surface temperature, rainfall, air pressure, atmospheric and oceanic circulation. The effects of ENSO, commonly called "teleconnections", emphasize that changing conditions can have a profound effect on global climate, which can in turn directly affect people's livelihoods (e.g., [START_REF] Barlow | ENSO, pacific decadal variability, and US summertime precipitation, drought, and stream flow[END_REF], [START_REF] Diaz | ENSO variability, teleconnections and climate change[END_REF][START_REF] Alexander | The atmospheric bridge: The influence of ENSO teleconnections on air-sea interaction over the global oceans[END_REF]).

Construction of GDP Weighted Global Aggregates

We construct three global economic indicators based on 20 sampled economies using a GDP weighted index.

The global indicators include output (industrial production), CPI and interest rate. The weight of each economy in the index is derived from its economic size (proxied using quarterly nominal GDP data), which is accordingly rebased (i.e., sums to one for each period). We then apply the weights to each of the respective global indicators in the respective quarter, considering the data is monthly. Figure 17 in the Appendix shows that the period-to-period movements are quite stable, yet the relationship over a longer period can evolve.

Global Commodities

The commodities of interest in this study include the international oil and food price. Of the rich literature that considers a commodity price, most papers include the oil price. Our global structure allows an identification such that oil and food prices are treated endogenously. This allows us to analyze the effect that ENSO climate patterns has on important commodity prices.

Figure 2: Global Aggregates Since the early 2000s, the world experienced elevated and persistent prices of many commodities relative to the somewhat more tranquil period after the mid-1980s. Several authors have dubbed this phenomena as a commodity price "super cycle".9 Hamilton ( 2008) motivates an argument of the importance of oil prices; that nine of ten recessions in the US since World War II have been preceded by an increase in oil prices. Yet the same argument can be conveyed for both energy and food prices, at least since the turn of the century on a global scale at the onset of all four recessions (see Figure 3). 10 Kilian and Vigfusson (2017) do not find evidence of a "mechanical relationship" between an increase in the oil price and recessions.

Global EPU

Building on the EPU index by [START_REF] Baker | Measuring economic policy uncertainty[END_REF], [START_REF] Davis | An index of global economic policy uncertainty[END_REF] constructs a measure of GEPU. The GEPU is considered in the empirical analysis. EPU is negatively correlated with the business cycle (e.g., [START_REF] Bloom | The impact of uncertainty shocks[END_REF][START_REF] Baker | Measuring economic policy uncertainty[END_REF]. Using our novel dataset, we estimate a linear OLS regression model as follows:

ln

EPU G t = α + β Y ∆Y G t + β P ∆P G t + β R R G t + β COV ID COV ID t + γτ t + u t (1)
where we consider two models including up to four control variables, which include output growth, aggregate inflation, interest rate and infectious diseases data. The model includes an intercept (α), trend (γ) and an error term (u t ). In Table 2, models (1) and ( 2) are symmetric except the latter includes the infectious diseases dataset. The results suggests that GEPU is associate with lower output growth, lower inflation and higher interest rate, where all coefficients are statistically significant. Further, we find that an increase in infectious diseases is positively associated with EPU and is statistically significant. The linear trend is positive and statistically significant for both models.

Global Variables

The correlation between global variables (output growth, inflation and interest rate) is provided in Table 3.

The correlation for world output growth is quite high with e.g., USA, CAN, EUR and RUS; and somewhat moderate to low for IRL, GBR and CHN. There is moderate to strong correlation between world inflation with the exception of IND, RUS and BRA. The negative correlation for inflation observed between the World (and taking the USA as a secondary benchmark) and IND notably during the GFC and post-COVID. Output and prices are further converted to year-over-year growth rates. See Table 1 for further details.

Methodology and Results

We estimate two models: the first model estimates a GVARLP that includes ENSO, output growth, inflation, interest rate and EPU (henceforth referred to the "baseline" model. The second model extends the baseline model to capture the effects of an international oil and food commodity price (henceforth referred to "extended" model).

The vector autoregression model with local projections (VAR-LP), developed by [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF], is employed to estimate the dynamic responses that a disaster has on macroeconomic conditions. We estimate a linear and non-linear model. For the non-linear model, we estimate the GVARLP where state dependence is based on ENSO for three reasons. First, ENSO can have important economically important effects on commodities and economic activity (e.g., [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF][START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF][START_REF] Dufrénot | The effect of ENSO shocks on commodity prices: A multi-time scale approach[END_REF]. Second, state dependence facilitates an econometric model that can capture the full data generating process of how changing ENSO states affect global economic conditions. 12 Third, an EN and a LN are two opposing climate patterns where there can be a long length of each episode. 13 We analyze the impact of weather shocks on the economy according to the climate state. The main difference between climate and weather is the time length at which we look at events. Therefore, we consider two climate states, EN and LN, while we proxy weather by ESOI shocks. Therefore, we plot IRF that show global economic variables reaction to weather shocks (i.e. ESOI shock) according to climate state (i.e EN or LN).

11 According to the NBER, the recession dates for the U.S. is between 2007:DEC to 2009:JUN. 12 The existing research (e.g., [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF][START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF] analyze the partial effects of an El Nino (a La Nina) shock by "shutting off" the La Nina (El Nino) in their specification. 13 According to NOAA, episodes of EN and LN occur 9 to 12 months, see https://oceanservice.noaa.gov/facts/ninonina.html.

Linear Model

A common representation of a VAR is as follows: 14

y t = α + B(L)y t + t (2)
where y T t is the transpose of a column vector; α is a vector of intercept term; B(L) is an autoregressive lag polynomial; and t is a vector of white noise error terms. Multiplying equation (2) by A 0 yields a VAR represented in structural form:

A 0 y t = ζ + A 0 B(L)y t + u t (3)
for ζ = A 0 α and u t = A 0 t . Matrix A 0 captures the contemporaneous relationship between the variables.

To identify A 0 , a standard Cholseky decomposition is employed imposing a lower triangular matrix. This specification is consistent with [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF], where ENSO is not influenced contemporaneously by the ENSO state.

The impulse responses corresponding to the reduced form and structural form shocks are, respectively, generalized as follows [START_REF] Kilian | How reliable are local projection estimators of impulse responses?[END_REF]:

Φ VAR h = h ∑ l=1 Φ VAR h-l B l , h ∈ {1, 2, ..., H} (4)
and

Θ VAR h = Φ VAR h A -1 0 , h ∈ {1, 2, ..., H} (5)
An alternative approach to estimate the reduced form impulse responses is to fit a linear projection (baseline model) as follows:

y t+h = α h + B h 1 y t + B h 2 y t-1 + ... + B h p y t + t+h (6)
where y T t is the transpose of a column vector; α h is an intercept term; B h i are autoregressive coefficients for future horizon h = 1,...,H; and t+h is a disturbance. As there is serial correlation present in the error terms, the Newey-West correction is used for standard errors. The corresponding structural impulse responses are:

Θ LP h = Φ LP h A -1 0 , h ∈ {1, 2, ..., H} (7)
where A -1 0 is recovered from the estimated model in equation (3) (see [START_REF] Kilian | How reliable are local projection estimators of impulse responses?[END_REF].

Baseline Model

The vector of macroeconomic variables for the baseline model includes the following:

y T t = [ENSO G t , ∆ ln Y G t , ∆ ln P G t , R G t , ln EPU G t ] (8)
where y T t includes incremental disaster data, output growth, inflation, interest rate and EPU. The model also includes a trend term. In this identification setup, weather is weakly exogenous, i.e. weather conditions do not contemporaneously affect global macroeconomic conditions [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF], [START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF], [START_REF] Bastianin | Economic impacts of El Ni ño southern oscillation: evidence from the Colombian coffee market[END_REF]). [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF] estimates a VAR to investigate ENSO and commodity price shocks. [START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF] estimates a global vector autoregression to investigate weather shocks for twenty-one country/regions. [START_REF] Bastianin | Economic impacts of El Ni ño southern oscillation: evidence from the Colombian coffee market[END_REF] estimate a VAR where weather influences Colombian coffee production, exports and price.

Of the aforementioned authors, the paper by [START_REF] Bastianin | Economic impacts of El Ni ño southern oscillation: evidence from the Colombian coffee market[END_REF] is the only research that considers a symmetric VAR for the Colombian coffee market with regard to both an El Nino and a La Nina weather shock. That is, most papers consider an El Nino shock in isolation. In the linear model, we similarly estimate a symmetric model, which is then extended to a non-linear asymmetric model in Section 4.2. Following [START_REF] Colombo | Economic policy uncertainty in the US: Does it matter for the Euro area?[END_REF], EPU is order last to "purge" uncertainty from contemporaneous movement from macroeconomic indicators. We also include the CBOE Volatility Index (VIX) as an exogenous variable. 15 14 Note that we abstract from deterministic terms with the exception of the intercept term for expositionary purposes. 15 VIX is used as a proxy for international financial volatility. While [START_REF] Baker | Measuring economic policy uncertainty[END_REF] find positive co-movement between the EPU and VIX, there is "substantial independent variation" [START_REF] Baker | Measuring economic policy uncertainty[END_REF], where the former index measures uncertainty due to economic policy that is not captured by financial market risk. [START_REF] Pastor | Uncertainty about government policy and stock prices[END_REF] and [START_REF] Pástor | Political uncertainty and risk premia[END_REF] show that while uncertainty and volatility are correlated, the degree to which political signals over time are known can correspond with investors to update their beliefs about potential future policy choices. Similarly, [START_REF] Białkowski | High policy uncertainty and low implied market volatility: An academic puzzle[END_REF] confirm a link between market volatility and policy uncertainty becomes weaker in an environment characterized by opinion divergence among investors and exceptional performance of the stock market. Consistent with [START_REF] Manopimoke | Dynamic connectedness in emerging Asian equity markets[END_REF], we include the VIX as a control variable for financial market uncertainty, so that EPU will capture the influence of policy uncertainty.

To investigate the dynamic responses from the endogenous variables, the corresponding linear impulse response functions (IRF) relating to shocks to ENSO (Figure 5), output (Figure 6), CPI (Figure 7), interest rate (Figure 8) and EPU (9) are provided. The plot includes the 90% confidence band.

Shock to ENSO

A shock to weather (ESOI) corresponds with an increase in output. Furthermore, the weather shock is inflationary, which results in delayed interest rate response. An ENSO shock results in a decrease (increase) in EPU during an EN (a LN) state.

Shock to Output

A one-standard deviation shock to output corresponds with higher inflation and interest rate. Global EPU declines slighly in period three, noting the confidence interval is quite wide. The decline in global EPU is consistent with [START_REF] Hailemariam | Oil prices and economic policy uncertainty: Evidence from a nonparametric panel data model[END_REF] and [START_REF] Ginn | Uncertainty and food prices[END_REF], who finds that an increase in output reduces EPU for the G7 economies and India, respectively.

Shock to Inflation

We observe that a one-standard deviation shock to inflation results in lower output with a four month lag, with an increase in the interest rate. An inflationary pressure results in an increase of EPU.

Shock to Interest Rate

The transmission of monetary policy remains equivocal insofar that the 20 economies pursue monetary policy that is not necessarily coordinated, but rather the "collective stance" by major central banks [START_REF] Ratti | Oil prices and global factor macroeconomic variables[END_REF]. A one-standard deviation shock to the interest rate results in higher output on impact which turns negative in period 9; a marginal decline of the inflation rate; and an increase in EPU.

Shock to EPU

The IRFs in 9 are consistent with [START_REF] Colombo | Economic policy uncertainty in the US: Does it matter for the Euro area?[END_REF]; an increase in EPU corresponds with lower output, CPI and interest rate.

Non-Linear Model

Considering weather oscillates via an El Nino and a La Nina periods, the extended model is estimated using a VAR-LP model using a non-linear regime-switching framework to critically examine whether the effects of ENSO weather patterns are state-dependent on economic conditions. This allows us to test whether a ENSO weather patterns can create an asymmetry (add references). To test this hypothesis, we specify the prediction of y t+h to differ according to an El Nino ("EN") and La Nina ("LN") state when an ENSO weather anomaly shock (shock t ) hits. That is, y t is estimated that includes a smooth transition function F(ζ t ) that represents the state of the economy:

F(ζ t ) = exp(-γζ t ) 1 + exp(-γζ t ) (9)
where ζ t is a standardized transition variable and γ controls the degree of smoothness of the transition between states. The model has the following functional form:

y t+h = trend t + F(ζ t-1 )(α h,EN + φ h,EN (L)x t-1 + β h,EN shock t )+ (1 -F(ζ t-1 ))(α h,LN + φ h,LN (L)x t-1 + β h,LN shock t ) + t+h (10)
where y t+h is projected on the space generated by a set of control variables (x t-1 ) defined by the endogenous variables (at lag one). The coefficient β h,EN (β h,LN ) corresponds with the estimated impact of climate shock in an EN (a LN) state. Following [START_REF] Auerbach | Measuring the output responses to fiscal policy[END_REF], the transition function is dated t -1 to avoid contemporaneous feedback from policy actions with regard to the state of the economy (i.e., F(ζ t-1 )).

We set γ is to 5. The transition variable (ζ t ) is taken as the deviation of the ENSO cycle from a smooth trend. 16The IRFs for the non-linear model relating to an ENSO shock are presented in Figure 10. The IRFs indicate the importance of how a ENSO weather affects economic conditions based on the state of the climate.

The transition function for the non-linear model is presented in Figure 11, which plots the evolution of the transition variable F(z t ) along the ENSO climate conditions. By construction, a high (low) value of the transition variable corresponds to an El Nino (a La Nina) period. The empirical evidence from the non-linear model (Figure 10) relating to an ENSO shock is no longer consistent with the linear model (Figure 5), insofar that the linear model lacks proper specification along two dimensions.

Firstly, (e.g., [START_REF] Brunner | El nino and world primary commodity prices: warm water or hot air?[END_REF][START_REF] Cashin | Fair weather or foul? The macroeconomic effects of El Ni[END_REF] analyze the partial effects of an El Nino (a La Nina) shock by "shutting off" the La Nina (El Nino) in their specification. Second, the contribution of an ENSO shock can have lagged effects. We conjecture that the GVARLP methodology fills in both of these gaps, such that an ENSO shock cast in the GVARLP model allows for a more robust framework to estimate the economic system to not necessarily remain static within one state of ENSO (EN or LN) conditional that the system has entered into that state. Overall, our model facilitates a way to capture the full data generating process of how the changing ENSO states affect global economic conditions. Incorporating the effects of climate while integrating an endogenous treatment of commodity prices on a global scale is of critical importance to further inform our understanding of the consequential effects of changing climate ex post, an area of paramount importance, considering current assessments of future climate scenarios are shrouded in uncertainty.

Extended Model

The baseline model is extended to include the international oil and food commodity prices:

y T t = [ENSO G t , ∆ ln Y G t , ∆ ln P G t , ∆ ln P G O,t , ∆ ln P G F,t , R G t , ln EPU G t ] (11)
The international oil and food price is ordered after CPI in equation ( 11). Considering the global structure, commodity prices are modeled endogenously, hence there is no information delay where the inclusion of ENSO shocks facilitate an identification to address, in part, why price fluctuations occurred in the first place. Furthermore, we order oil before the food price (e.g., [START_REF] Khan | Macroeconomic effects of global food and oil price shocks to the Pakistan economy: A structural vector autoregressive (SVAR) analysis[END_REF], [START_REF] Khan | Revisiting the macroeconomic effects of oil and food price shocks to Pakistan economy: A structural vector autoregressive (SVAR) analysis[END_REF], [START_REF] Alom | Macroeconomic effects of world oil and food price shocks in asia and pacific economies: application of SVAR models[END_REF] and [START_REF] Ginn | Uncertainty and food prices[END_REF]). Commodity prices (in real terms) tend to be endogenous and pro-cyclical to the global business cycle (e.g., [START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF], [START_REF] Kilian | Modeling fluctuations in the global demand for commodities[END_REF]). [START_REF] Kilian | Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market[END_REF] distinguishes between demand and supply shocks in the oil price, and finds that increases in the oil price since 2003 are primarily driven by demand. The similar increases in the food price has raised concerns about inflationary pressures. This is finding is also confirmed by [START_REF] Joëts | Does the volatility of commodity prices reflect macroeconomic uncertainty?[END_REF] for corn, soybeans and wheat. This identification is consistent with [START_REF] Alquist | What do we learn from the price of crude oil futures?[END_REF], who finds that the oil price is determined endogenously and simultaneously.

Impulse Response Function (Extended Model)

The corresponding IRFs are provided for a shock to ENSO (Figure 12), international oil price (Figure 13), international food price (Figure 14) and EPU (Figure 15).17

Shock to ENSO

Similar to the baseline model, a shock to ENSO (ESOI) corresponds with an increase in output and is inflationary, which in turn elevates the oil and food price (see Figure 12).

While an ENSO weather shock is inflationary, the effect on impact for oil (food) price is more pronounced in an El Nino (La Nina) state.

The increase in output and prices results in an increase in the interest rate during an EN state. Accordingly, an ENSO shock during an EN state results in a decrease in EPU.18

Shock to International Oil Price

A one-standard deviation shock to the international oil price corresponds with a decrease in EPU (see Figure 13), which is not statistically significant. [START_REF] Hailemariam | Oil prices and economic policy uncertainty: Evidence from a nonparametric panel data model[END_REF] find a negative (positive) relationship between oil prices and EPU for a panel of seven OECD (G7) countries. They conjecture the negative relationship prior to the global financial crisis was due to a "positive effect of aggregate demand on oil prices" which created a "conducive environment for the global economy". [START_REF] Ginn | Uncertainty and food prices[END_REF] find that an increase in the oil price results in an increase in EPU for India.

Shock to Food Price

A one-standard deviation shock to the international food price is associated with higher output, inflation (for all price indices) and interest rate (see Figure 14). It turns out that an innovation to the food price can magnify EPU during a LN period. 19 Economically, these results are important if one considers that food prices have been elevated and persistent over the time domain until around 2011, with a subsequent negative decline since (see Figure 2).

Shock to EPU

On impact, a one-standard deviation shock to EPU is associated with lower output; lower CPI and oil inflation; higher food inflation; and lower interest rate (see Figure 15). These results are similar to [START_REF] Colombo | Economic policy uncertainty in the US: Does it matter for the Euro area?[END_REF], who finds an increase in EPU corresponds with lower output, CPI and interest rate.

Discussion on the Importance of Food Prices

The main results indicate that weather shocks have important and asymmetric effects on economic conditions. A closer inspection of the results show that the food price is a central source of vulnerability on a global scale. This conclusion is drawn from three findings. Higher aggregate and food inflation result in an increase in EPU, which are statistically significant, whereas a positive innovation in oil prices decreases EPU, which is not statistically significant. Furthermore, the findings show that an increase in the international food price augments CPI by 0.15% after six months on impact (see Figure 14).

It is therefore natural to ask, why is the international food price a central source of global vulnerability? Drawing on the literature review by [START_REF] Ginn | Uncertainty and food prices[END_REF], this section takes stock of four reasons why the international food price is important.

Food Represents a Sizable Portion of Household Expenditures

The share of food expenditures accounts for 48%, 31% and 20% of consumption on average in low-, middleand high-income countries, respectively [START_REF] Pourroy | Food prices and inflation targeting in emerging economies[END_REF]. 20 This relationship is known as Engel's law (see Figure 16). 21 As food represents a sizable share of income expenditure and is an inelastic good 22 , a sizable price increase in real terms may have an affect, especially for credit-constrained households (e.g., [START_REF] Anand | Optimal price indices for targeting inflation under incomplete markets[END_REF], Ginn and Pourroy ( 2019)).

Reaction and efficiency of monetary policy

Over the past few decades, central banks have focused on price stability as one of, if not the the most important, objectives of monetary policy, a framework described as inflation targeting. 23 Yet, a common thread is how policy makers should react to rising commodity prices, which can inevitably make, inter alia, monetary policy subject to more uncertainty. The initial research in the monetary policy literature (e.g., [START_REF] Aoki | Optimal monetary policy responses to relative-price changes[END_REF], [START_REF] Bodenstein | Optimal monetary policy with distinct core and headline inflation rates[END_REF]) argues that volatile price subsets (e.g., oil and food prices) be stripped away from the objective relating to price stabilization for central banks to the extent that Goodfriend (2007) describes as part of a "consensus model".

The recent literature has reversed course, where the point of departure hinges on the degree of incomplete markets, country-specific characteristics and considering that food prices have been elevated and not necessarily mean-reverting. Recent publications such as [START_REF] Anand | What measure of inflation should a developing country central bank target?[END_REF], [START_REF] Catão | World food prices and monetary policy[END_REF], [START_REF] Pourroy | Food prices and inflation targeting in emerging economies[END_REF], [START_REF] Ginn | Optimal monetary policy in the presence of food price subsidies[END_REF] and Ginn and Pourroy (2020b) find that central banks do not overlook food price inflation, a result in line with central bank management in practice [START_REF] Hammond | State of the art of inflation targeting[END_REF]. Food prices can propagate inflation through its effects on inflation expectations (e.g., Walsh (2011), Ginn andPourroy (2020b)) as a second-round feature on non-food prices.

20 Low-income, middle-income and high-income countries represent those with real per capita income less than 15 percent, between 15 and 45 percent, and greater than 45 percent of the U.S. level, respectively. 21 Engel's law is an empirical regularity, or "stylized fact", named after the statistician Ernst Engel [START_REF] Engel | Die Productions-und Consumtionsverhältnisse des K önigreichs sachsen[END_REF]. 22 The USDA (International Food Patterns) estimates the elasticity of food to be less than one for all countries. 23 See [START_REF] Hammond | State of the art of inflation targeting[END_REF] for a presentation of inflation targeting central banks practices.

Impact on public finance

Rising prices can raise the stakes for fiscal policy-makers confronting ways of alleviating poverty, ensuring food security and maintaining macroeconomic stability. Food inflation may trigger endogenous fiscal policy vis-à-vis a demand driven food price subsidy [START_REF] Ginn | Optimal monetary policy in the presence of food price subsidies[END_REF], which are prevalent, especially in low and middle income countries. Based on a DSGE using Bayesian methods, [START_REF] Ginn | The contribution of food subsidy policy to monetary policy[END_REF] demonstrate that while monetary and fiscal policy may be viewed as achieving a shared policy goal of price stabilization, the interaction of the two policies can be considered a strategic substitute.

Institutional consequences [START_REF] Bellemare | Rising food prices, food price volatility, and social unrest[END_REF] shows that food price spikes are correlated with civil unrest. [START_REF] Arezki | Food prices and political instability[END_REF] find that "during times of international food price increases political institutions in Low Income Countries significantly deteriorated". [START_REF] Gouel | Food price volatility and domestic stabilization policies in developing countries[END_REF] argues that government stabilization policies may be considered as a second-best intervention in the absence of insurance and futures markets.

Conclusion

This paper analyzes the global transmission of weather, the oil price and food price as they relate to economic conditions. This paper employs a GVARLP framework, which is estimated using a rich and extensive monthly data set from 1999:01 to 2022:03 relating to twenty-two economies representing 80.2% of global output (based on IMF data for 2021).

This paper contributes to a narrow literature on the "new climate economy" [START_REF] Dell | What do we learn from the weather? The new climate-economy literature[END_REF] in two ways. First, this paper exploits the global estimation framework vis-à-vis the GVARLP to investigate the global dimensions of climate patterns and commodity shocks.

Second, this research documents the presence of international commodity price heterogeneity on EPU. A shock to the international oil (food) price leads to negative (positive) reaction of EPU. The results have rather nuanced implications for policy with regard to an international disturbance that in turn perturbates global economic uncertainty. Accordingly, we find that the food price is source of vulnerability on a global scale, underscoring the importance of global food price stability.

The results from this research have both immediate and long-term policy implications regarding the adaptation to climate changes. A starting point for short-term policy is to establish sources of vulnerability that could create economic risks. The findings from this paper serve to do just that in a global structure by analyzing the propagation mechanisms through which climate shocks influence economic conditions. These insights are of paramount importance to central bank policies designed to understand sources of price changes to stabilize food and aggregate prices, inter alia. Similarly fiscal policy is subject to endogenous policy responses to smooth household consumption via food subsidy program.

Over the longer term, policy makers should address the adaptation with regard to climate change. Policy needs to address changes to the social and economic systems from multiple fronts. The central bank must craft an appropriate policy response that monitors and addresses sectoral price developments as they relate to the changing business cycle and the effects of climate change. This is of growing importance as climate change is expected to increase the frequency and intensity of weather patterns (e.g., [START_REF] Timmermann | Increased El Ni ño frequency in a climate model forced by future greenhouse warming[END_REF], [START_REF] Chen | Economic implications of potential ENSO frequency and strength shifts[END_REF], [START_REF] An | Interdecadal change of the structure of the ENSO mode and its impact on the ENSO frequency[END_REF]). The impact of climate change may influence the central bank's interest rate, which can in turn influence the stock market and investment decisions. Overlooking the effects of changing weather patterns has on future inflation could potentially move inflation away from central bank's target, thereby weakening central bank's monetary anchoring. Similarly, a weather shock that results in higher food prices may create a source of vulnerability with regards to a combination of debt and taxes needed to finance food subsidies.

Figure 1 :

 1 Figure 1: Equatorial SOI

Figure 3 :

 3 Figure 3: International Oil and Food Price

Figure 4

 4 Figure4plots the global data which shows the global dataset captures two major turning points. The top-pane shows a sizable decline in output which occurred during the GFC 11 and onset of the spread of the COVID-19 virus. There was a noticeable decrease in aggregate inflation and interest rate during these two time periods.

Figure 4 :

 4 Figure 4: Global Macro Indicators

Figure 5 :

 5 Figure 5: IRF for ENSO Shock (Baseline Model) ENSO based on EN Specification

Figure 6 :

 6 Figure 6: IRF for Output Shock (Baseline Model) ENSO based on EN Specification

Figure 7 :

 7 Figure 7: IRF for Inflation Shock (Baseline Model) ENSO based on EN Specification

Figure 10 :

 10 Figure 10: IRF for ENSO Shock (Baseline Model) ENSO based on EN Specification

Figure 11 :

 11 Figure 11: Transition Function for ENSO (Extended Model)

Figure 12 :

 12 Figure 12: IRF for ENSO Shock (Extended Model) ENSO based on EN Specification

Figure 13 :

 13 Figure 13: IRF for Oil Shock (Extended Model) ENSO based on EN Specification

Figure 14 :

 14 Figure 14: IRF for Food Shock (Extended Model) ENSO based on EN Specification

Figure 15 :

 15 Figure 15: IRF for EPU Shock (Extended Model) ENSO based on EN Specification

Figure 16 :

 16 Figure 16: Country Food Expenditure and Income

Figure 19 :

 19 Figure 19: IRF for Inflation Shock (Baseline Model) ENSO based on EN Specification

Figure 20 :

 20 Figure 20: IRF for Rate Shock (Baseline Model) ENSO based on EN Specification

  The sample period is monthly which covers 1999:01 to 2022:03. 2

	G t ), output A,t ), interest rate E,t ), food inflation (∆ ln P G t ), oil inflation (∆ ln P G t ), aggregate inflation (∆ ln P G growth (∆ ln Y G
	(R G t ) and GEPU (ln EPU G t ).

Table 1 :

 1 6 . Variable Selection

	Item	Symbol	Source	Description
	ENSO	ENSO G t	NOAA	Equatorial Southern Oscillation Index
	Output	Y t	OECD/FRED	Industrial Production
	Aggregate CPI Oil Price Food Price	P G t P G E,t P G A,t	OECD FRED FRED	CPI: All items Brent Oil Price World Food Price
	Interest Rate	R t	OECD/FRED	Short-term interest rate
	Policy Uncertainty	EPU t	FRED (see [a])	Global EPU
	VIX	V IX t	FRED	CBOE Volatility Index
	Global Financial Crisis	GFC t	NBER (see [b]) GFC dummy variable
	Infectious Disease	COV ID

t FRED U.S. Infectious Diseases tracker [a]: https://www.policyuncertainty.com. [b]: GFC dummy variable set to 1 between 2007:DEC to 2009:JUN, consistent with the NBER recession dates for the U.S.

Table 2 :

 2 Empirical Findings (OLS Regression)

		Dependent variable:
		Global EPU
		(1)	(2)
	α	4.258 * * *	4.272 * * *
		(0.096)	(0.096)
	β P	0.066 * * *	0.058 * * *
		(0.022)	(0.022)
	β Y	-0.023 * * *	-0.020 * * *
		(0.004)	(0.003)
	β R	-0.001 * *	-0.0004 *
		(0.0002)	(0.0003)
	β COV ID		0.011 * * *
			(0.002)
	γ	0.004 * * *	0.004 * * *
		(0.0003)	(0.0004)
	Observations	267	267
	Adjusted R 2	0.641	0.658
	Residual Std. Error	0.284	0.277
	F Statistic	119.509 * * *	103.560 * * *
	Note: *, ** and *** denote significance at 10%, 5% and 1%,
	respectively. OLS robust standard errors are presented in
	parentheses.

Table 3 :

 3 Variable Correlation

	Location	∆ ln Y G t	∆ ln P G t	R G t
	WORLD	1.00	1.00	1.00
	BRA	0.74	0.14	0.57
	CAN	0.80	0.78	0.96
	CHE	0.76	0.73	0.92
	CHL	0.59	0.61	0.76
	CHN	0.41	0.53	0.50
	COL	0.73	0.25	0.84
	CZE	0.86	0.70	0.81
	EUR	0.95	0.88	0.93
	GBR	0.53	0.72	0.93
	HUN	0.90	0.45	0.68
	IND	0.66	(0.01)	0.08
	IRL	0.18	0.67	0.93
	ISR	0.56	0.39	0.80
	JPN	0.90	0.26	0.58
	KOR	0.64	0.59	0.91
	POL	0.83	0.49	0.76
	RUS	0.77	0.15	0.19
	SWE	0.84	0.73	0.84
	TUR	0.81	0.19	0.52
	USA	0.92	0.90	0.91

The

economies include: Brazil ("BRA"), Switzerland ("CHE"), Chile ("CHL"), Canada ("CAN"), China ("CHN"), Columbia ("COL"), Czech Republic ("CZE"), Euro zone (19 countries; "EUR"), United Kingdom ("GBR"), Hungary ("HUN"), Ireland ("IRL"), India ("IND"), Israel ("ISR"), Japan ("JPN"), South Korea ("KOR"), Poland ("POL"), Russia ("RUS"), Sweden ("SWE"), Turkey ("TUR") and the United States ("USA"). Based on IMF data in purchasing power parity terms, the nine economies considered in this paper represent 80.2% of global output, see https://www.imf.org/external/datamapper/NGDPD@WEO/EURO/USA/CAN/CHN/CHL/IND/KOR/BRA/WEOWORLD/COL/ GBR/CZE/HUN/IRL/ISR/JPN/POL/RUS/TUR/SWE/CHE. The Euro zone values are based on the 19 member countries (i.e., Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Portugal, Slovakia, Slovenia, and Spain).

The choice of economies and sample period combination is, in part, based on data availability. The sample period is quite extensive, while the 20 economies considered represent the majority (80.2%) of global output based on nominal GDP indexed in U.S. Dollars using IMF data. The sample period also overlaps with the commodity price booms that occurred in 2004[START_REF] Radetzki | The anatomy of three commodity booms[END_REF].

For India, manufacturing production index (FRED mnemonic INDPRMNTO01IXOBM) is used as opposed to total production index (FRED mnemonic INDPROINDMISMEI), considering data availability (the correlation between the is 0.9918 for Jan 2000 to Dec 2018). For China, we use total production excluding construction (FRED mnemonic CHNPRINTO01IXPYM). As the production index for China includes missing values, the Kalman smoother using an ARIMA state space representation is used to impute missing values.

For India, the interest rate is based on the 90 day Treasury Bill interest rate (e.g.,[START_REF] Patnaik | Monetary policy transmission in an emerging market setting[END_REF],[START_REF] Gabriel | An Estimated DSGE Model of the Indian Economy, The Oxford Handbook of the Indian Economy[END_REF],[START_REF] Saxegaard | An estimated model with macrofinancial linkages for India[END_REF],[START_REF] Anand | Food inflation in India: the role for monetary policy[END_REF] and[START_REF] Ginn | The contribution of food subsidy policy to monetary policy[END_REF]).

The GFC dummy variable is set to 1 between 2007:12 to 2009:06, consistent with the NBER recession dates for the U.S.

COVID-19 emerged as a pandemic in December 2019 and quickly spread across the world, with far-reaching consequences including higher deaths, stagnation of economic growth and elevated uncertainty, which resulted in lock-downs and other precautions to reduce the spread of the virus.

Industrial production for other countries in the sample are already seasonally adjusted.

The NOAA considers ENSO as "one of the most important climatic phenomena on Earth", see https://www.weather.gov/mhx/ ensowhat.

For example,[START_REF] Radetzki | The anatomy of three commodity booms[END_REF] identifies the commodity price booms also occurred in the early 1950s, 1973/1974 and 2004 as the start of the third commodity price boom since the second world war.

To illustrate this point, Figure3shows the international oil and food price movements against recession dates for 35 OECD member and non-member countries, where latter is used as a proxy for a global recessionary period.

The trend is based on the Hodrick-Prescott filter with smoothing parameter λ = 129,600 (see e.g.[START_REF] Ravn | On adjusting the Hodrick-Prescott filter for the frequency of observations[END_REF]), a standard value for data at monthly frequency.

For brevity, the IRFs for the extended model relating to output (Figure22), CPI (Figure23) and interest rate (Figure24) are provided in the Appendix.

These results are consistent with the OLS regression results in Table2, which shows GEPU increases with higher inflation and lower output and interest rate.

[START_REF] Bastianin | Economic impacts of El Ni ño southern oscillation: evidence from the Colombian coffee market[END_REF] similarly found that a LN is more harmful than an EN for Colombian coffee, considering the former is associated with lower production which in turn corresponds with a higher price.

* The project leading to this publication has received funding from the French government under the "France 2030" investment plan managed by the French National Research Agency (reference: ANR-17-EURE-0020) and from the Excellence Initiative of Aix-Marseille University -A*MIDEX. C.

Appendix

GDP Weighted Global Aggregator

Additional IRFs: Baseline Non-Linear Model

The IRFs relating to shocks to output, inflation and the interest rate are provided below:

Additional IRFs: Extended Non-Linear Model

The IRFs relating to shocks to output, inflation and the interest rate are provided below:


Andy Zhang

Mehdi Boudissa

Maxime Nemo

Jérôme Tonetti

Matthieu Chabanas

Towards a learning-based CT segmentation of acetabular fractures

Keywords: Semantic segmentation, Neural networks, Fracture segmentation, Acetabulum, Orthopaedic surgery

Fractures of the acetabulum, the cavity of the hip that hosts the femoral head, are complex to understand, plan, and surgically reduce. Segmenting bone fragments in CT scans is fundamental for assisting surgeons in their therapeutically process, and can benefit from recent learning-based advances. In this paper, we extended a learning-based network for the semantic segmentation of 6 pelvic bones: left and right hip, left and right femur, sacrum, and lumbar spine. This semantic segmentation is then process by a surgeon to separate fracture fragments, similarly to an existing baseline process. Results on 6 fracture cases show a qualitative improvement of the final fragment segmentation quality. Mostly, the segmentation time is statistically significantly reduced from 94 min to 18 min, in mean, which is a promising step towards using such learning-based method in preoperative clinical routine.

INTRODUCTION

Medical image segmentation is an essential process in many image-guided procedures. This is especially the case for acetabular surgery, where the segmentation of bone fragments is a core step to assist in analysing the fracture, planning the surgery, and for guiding procedures. [START_REF] Cimerman | Preoperative planning in pelvic and acetabular surgery: the value of advanced computerised planning modules[END_REF][START_REF] Fornaro | An interactive surgical planning tool for acetabular fractures: initial results[END_REF][START_REF] Boudissa | Does semi-automatic bone-fragment segmentation improve the reproducibility of the letournel acetabular fracture classification?[END_REF][START_REF] Boudissa | Computer assisted surgery in preoperative planning of acetabular fracture surgery: state of the art[END_REF][START_REF] Boudissa | Planning acetabular fracture reduction using a patient-specific biomechanical model: a prospective and comparative clinical study[END_REF] Numerous methods, usually semi-automatic, have been proposed to segment fractured pelvis with standard segmentation method like region growing, wavelets, or active shape modeling. [START_REF] Vasilache | Unified wavelet and gaussian filtering for segmentation of CT images; application in segmentation of bone in pelvic CT images[END_REF][START_REF] Fornaro | Semi-automatic segmentation of fractured pelvic bones for surgical planning[END_REF][START_REF] Wu | Fracture Detection in Traumatic Pelvic CT Images[END_REF] With the advent of Deep Learning as a state-of-the-art segmentation approach, several authors have addressed bone segmentation in non-fracture contexts. [START_REF] Klein | Automatic bone segmentation in wholebody CT images[END_REF] Still, only a few works are dedicated to segmenting the pelvic area [START_REF] Liu | Deep learning to segment pelvic bones: large-scale CT datasets and baseline models[END_REF] or localizing pelvic fracture lines. [START_REF] Wang | Weakly supervised universal fracture detection in pelvic x-rays[END_REF][START_REF] Ukai | Detecting pelvic fracture on 3D-CT using deep convolutional neural networks with multi-orientated slab images[END_REF] In previous studies [START_REF] Boudissa | Does semi-automatic bone-fragment segmentation improve the reproducibility of the letournel acetabular fracture classification?[END_REF][START_REF] Boudissa | Planning acetabular fracture reduction using a patient-specific biomechanical model: a prospective and comparative clinical study[END_REF] we proposed a semi-automatic segmentation method. Bones were first segmented using region growing, followed by significant manual refinements. After this semantic segmentation, the different bone fragments were manually separated which corresponds to an instance segmentation. The objective of this study was to replace the semantic segmentation phase by a fully-automated learning-based segmentation, then to evaluate its impact on the instance segmentation phase and in terms of total segmentation time.

We extended the cascade 3D U-Net framework proposed by Liu et al. (2021) [START_REF] Liu | Deep learning to segment pelvic bones: large-scale CT datasets and baseline models[END_REF] for the automatic semantic segmentation of 6 bone structures of the pelvis: left & right hip, left & right femur, sacrum, and lumbar spine. The fracture fragments were thus segmented manually as in our baseline procedure. Results on 6 fracture cases show a clear qualitative improvement of the final fragment segmentation quality. Mostly, the segmentation time is statistically significantly reduced from 94 min to 18 min, in mean, which is a promising step towards using such learning-based method in preoperative clinical routine.

Contact: mboudissa@chu-grenoble.fr, matthieu.chabanas@univ-grenoble-alpes.fr

MATERIAL AND METHODS

Datasets

The initial neural network from Liu et al. (2021) 10 was re-trained/tested with 110 CT scans and labels from their open source CLINIC and CLINIC-metal datasets available at https://github.com/ICT-MIRACLE-lab/ CTPelvic1K. Most of the cases from these datasets have a pelvic ring fracture, and about 10% of them have an acetabular fracture. The CLINIC-metal set also contains post-operative CT with metal artifacts generated by the fixation screws and plates.

In addition to these publicly available datasets, we included 6 pre-operative CT scans from the Grenoble University Hospital, France. All cases have a fracture of the acetabulum, sometimes combined with a pelvic ring fracture. Patients signed an informed consent prior to surgery, with the approval of the local ethics committee (RCB 2022-A01472-41).

Baseline segmentation method

In our previous studies, [START_REF] Boudissa | Planning acetabular fracture reduction using a patient-specific biomechanical model: a prospective and comparative clinical study[END_REF][START_REF] Boudissa | Computer-assisted surgery in acetabular fractures: Virtual reduction of acetabular fracture using the first patient-specific biomechanical model simulator[END_REF] we proposed a semi-automatic procedure based on the open-source application ITK-SNAP (www.itksnap.org). [START_REF] Yushkevich | User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability[END_REF] This procedure consists in successive stages:

1. the segmented volume is first cropped around the region of interest: the fracture fragments and the bones connected to these fragments through ligaments. Non-relevant structures are ignored.

2. A semantic segmentation is then performed to identify bone tissue. After a thresholding initialization, seeds are manually set to initiate a region growing algorithm. [START_REF] Yushkevich | User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability[END_REF] This phase has proven to be quite difficult as the method tends to stop on every discontinuity, not only the fracture lines but the discontinuities artifically created by the thresholding operation in areas where the bone is very thin. Thus, a significant number of initial seeds is required. Many leeks also occur along cancellous bone, where the signal is never clearly defined.

3. Manual refinement is always necessary to clean the semantic segmentation, expand under-segmented areas, and trim over-segmented ones.

4. Finally, the different fragments are manually separated. This stage is analogous to an instance segmentation.

As reported over 10 patients, 5 the total segmentation time was 82 ± 18 minutes [range 60-120]. For the 6 cases selected for this study, the mean segmentation time was 94 minutes.

Learning-based semantic segmentation

For the semantic segmentation of the pelvic bones, we adapted the open-source deep learning network proposed by Liu et al. (2021). [START_REF] Liu | Deep learning to segment pelvic bones: large-scale CT datasets and baseline models[END_REF] This network is composed a two 3D nnU-Net 15 working in cascade on low resolution and then full resolution CT volumes. The 4-class output is then post-processed based on a Signed Distance Function (SDF) filtering [START_REF] Perera | Motion segmentation of truncated signed distance function based volumetric surfaces[END_REF] to avoid the removal of isolated fractured bone fragments from the segmentation.

The initial multi-class network labels 4 classes referred as the left hip, right hip, sacrum, and lumbar spine. A fundamental structure to plan surgery is the femoral head, which is tighly connected to the acetabulum via the acetabular capsule. In the case of a fracture, this ligament capsule can be partially torn off and the femoral head can be in contact with surrouding bone fragments or even be dislocated from the joint. We therefore added two classes to the network's output and annotation set: left femur and right femur.

The network modification was straightforward as we simply increased the number of classes from 4 to 6 in the decoder of the low resolution 3D nnU-Net and in both the encoder and decoder of the full resolution U-Net. However, due to the change of dimension of the layers, we could not simply refine or transfer the network weights from the original paper and instead had to fully retrain the network.

Similarly to Liu et al. (2021), 10 an iterative procedure was followed to create the femoral annotations. Both femurs were first manually segmented on 20 cases using ITK-SNAP (www.itksnap.org). [START_REF] Yushkevich | User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability[END_REF] The network was then trained with these cases, and used to infer femur annotations in 10 new cases. After manual refinement, the 10 corrected annotations were added to the training set. Note that only the femur annotations were conserved from the last inference, and merged with the original 4-class open source annotations. This process was repeated to obtain a 6-class annotation on 70 cases, when basically no manual refinement were needed for the femurs. These 70 cases came from the publicly available CLINIC and CLINIC-metal datasets. The 40 remaining cases from these datasets were left for testing.

Experiments and evaluation protocol

We studied how the learning-based semantic segmentation could benefit the overall segmentation process. The semantic network replaced the first steps of our baseline method (section 2.2) and we simply performed the fragments identification and separation starting from the network output inference.

After training the 6-class segmentation network on public images, we used the network to automatically infer the classes on 6 cases from the Grenoble University Hospital. Then, an orthopaedic surgeon manually segmented the instances from the network output. The 6 cases had already been segmented for a previous study, by the same surgeon, so we could compare the different results. Three models were compared: baseline manual instance segmentation after a semi-automatic, region-growing segmentation (section 2.2).

1-class semantic manual instance segmentation from the automatic, 1-class semantic segmentation. The 6 output classes of the network were re-labelled with a single "bone" label, to mimic the output of the baseline region-growing method.

6-class semantic manual instance segmentation from the automatic, 6-class semantic segmentation (left and right hip, left and right femur, sacrum, lumbar spine).

Two metrics were considered. We first evaluated the quality of the different models. We could not use a quantitative metric such as the DICE coefficient since the baseline models were not complete (only the regions of interest were segmented with refinement, others regions were roughly curated or totally discarded). We thus only verified that the number of fracture fragments was the same, and then we qualitatively evaluated the quality of the segmented instances. The second metric was the total curation time. The semantic segmentation was automatically performed on a DELL Ampere server, then when added the time needed for the manual instance segmentation.

RESULTS AND DISCUSSION

Semantic segmentation

The modified network was first evaluated. The model was retrained on 70 cases of the 110 cases segmented with 6 classes, and tested on the remaining 40 cases. The Dice coefficients for the initial classes (left and right Hip, sacrum, and lumbar spine) were all between .98 and .99 in mean, which is no different than the results reported in. [START_REF] Liu | Deep learning to segment pelvic bones: large-scale CT datasets and baseline models[END_REF] This was unexpected as only 70 volumes were used to retrain the model instead several hundreds. Similar Dice coefficients were obtained for the left and right Femur, which validated the extension of the model from 4 to 6 classes. While these results are already excellent, we plan to continue the iterative process to segment femurs on all public images to fully benefit from the size of the datasets and increase the robustness of the semantic network.

Qualitative comparison of the segmentations

Unfortunately, the baseline and network-based results could not be quantitatively compared with metrics such as the Dice coefficient or Haussdorf distance. The reason is that baseline segmentations are limited to an area around the fracture, while the whole pelvis is systematically segmented with the network. In addition, areas far the fracture or irrelevant for the simulation planning were not refined during the baseline process. For example, the femur was never separated from the acetabulum on the side opposite the fracture.

The different results were thus qualitatively compared by the surgeon, yielding the following comments: • The segmentation is always clearly improved for all cases.

• First, classes already labelled do not have to be manually separated which is a direct benefit. This is especially relevant for the femurs, the sacrum, and the pubic symphysis. Note that the femur was correctly separated even in cases with a severe dislocation (see Figure 2), even if such configuration was never present in the training dataset.

• The overall 3D aspect is more pleasing since the pelvis is totaly segmented, and "holes" in areas where the cortical bone is thin (e.g. in the middle of the iliaque) are much smaller if not absent (see Figure 1).

• The semantic segmentation was not perfect, though, and several small fragments or extremities were either over-(cases 1 & 3) or under-segmented (cases 4 & 5). These defects still had to be manually refined similarly to the baseline procedure.

• Finally, unseparated fragments with a common label after the 6 class-segmentation (e.g. left hip) were easier to separate than from the baseline region growing output.

Computation times

Table 1 reports the computation times for all segmentation models, on 6 fracture cases from our center. The time analysis yields:

• The automatic 6-class semantic network took 3 to 6 minutes to perform a case, with a strong correlation with the number of slices in the CT scan.

• Separating the fragment instances from the semantic 1-class inferences took 24.5 minutes in mean. Even after adding the network computation time, this is a statistically significant reduction compared to the baseline time.

• this reduction is even more significant when fragments are segmented from the 6-class inferences, with a segmentation time reduced to 13 minutes in mean from more than 90 minutes.

CONCLUSION

Automatizing the semantic segmentation of pelvic bones with a learning-based network has proven to be a significant step for the segmentation of bone fractures. First, the quality of the fracture segmentation is consistently improved. However, the main benefit is the significant reduction of the total segmentation time, bringing the method towards a use in routine clinical planning.

Future works include completing the femur segmentation of the public datasets, and potentially improving the SDF post-processing 10 to better segment small comminuted fragments and thin extremities. In a longer term, we plan to investigate the automatization of fragments separation using graph cut methods or panoptic segmentation networks such as Mask R-CNN. [START_REF] Abdulla | Mask r-cnn for object detection and instance segmentation on keras and tensorflow[END_REF]

Figure 1 .

 1 Figure 1. Segmentation of case 2. Top row, from left to right: CT images, baseline segmentation, automatic 6-class segmentation, and final fracture segmentation after fragment separation. Bottom row: 3D view of the baseline, 4-class segmentation from Liu et al. (2021), and final segmentation.

Figure 2 .

 2 Figure 2. Segmentation of cases 1, 6, 3. From left to right: CT images with final segmentation, 3D view of the baseline and final segmentation. Table 1. Computation times for the different segmentation methods: baseline, instance segmentation from the automatic 1-class semantic segmentation, instance segmentation from the automatic 6-class semantic segmentation.

Table 1 .

 1 Computation

	Case # slices	# labels	baseline (min)	semantic network (min)	from 1-class semantic (min)	from 6-class semantic (min)
	1	458	7	90	6.12	30	18
	2	489	9	70	5.36	22	15
	3	236	9	120	3.35	20	8
	4	259	8	100	5.17	25	12
	5	430	7	90	5.43	35	17
	6	137	9	-	3.19	15	8
	mean computation time (min)	94	4.77	24.5	13

times for the different segmentation methods: baseline, instance segmentation from the automatic 1-class semantic segmentation, instance segmentation from the automatic 6-class semantic segmentation.

ACKNOWLEDGMENTS

This work has been supported by the French National Research Agency through the frameworks "Computer Assisted Medical Interventions" (ANR-11-LABX-0004 CAMI Labex) and by the "Multidisciplinary Institute in Artificial Intelligence" (ANR-19-P3IA-0003 MIAI@Grenoble Alpes).