Structural identification in the ENSO–Oil Price, direct oil-market pricing, and indirect transmission channels

In joint work with Marco Gallegati, William Ginn, Solomos Solomou, and Kun Tian—Climate Shocks in Global Oil Markets: Time-Varying ENSO Transmission to WTI Spot and Futures Prices—we study how phase-specific El Niño–Southern Oscillation (ENSO) shocks affect real WTI spot and futures prices.

A recurring problem in empirical macroeconomics is that the word correlation is sometimes used too broadly. A regression coefficient is not automatically causal. But the opposite mistake is also possible: structurally identified impulse responses may be described as correlations merely because the paper does not separately quantify every economic mechanism through which the shock reaches the outcome.

Those are different questions. The first concerns identification: is the variation in the shock exogenous, and is the contemporaneous ordering defensible? The second concerns transmission: through which demand, supply, financial, or expectations channels does the identified shock affect oil prices?

Main takeaway. ENSO is a physically external climate disturbance. At monthly frequency, it can be ordered first under a credible short-run restriction because oil-price, oil-supply, global-demand, and exchange-rate innovations cannot contemporaneously generate tropical-Pacific sea-surface-temperature anomalies. The model also conditions on twelve months of ENSO, oil-price, global-demand, global-supply, and exchange-rate history. The resulting local-projection paths are therefore structural dynamic causal responses—not bivariate correlations. The additional responses of global economic activity, global oil production, and the nominal effective exchange rate provide evidence on the indirect channels through which the shock is transmitted.

1. What would an “interesting correlation” look like?

A simple correlational exercise might estimate

\[ op_t=\alpha+\beta ENSO_t+e_t, \]

where \(op_t\) is an oil price and \(ENSO_t\) is a contemporaneous climate indicator.

Such an equation would leave the major identification and dynamics questions unresolved. It would not condition on oil-price persistence, global demand, global oil production, dollar movements, the persistence of the ENSO episode, or the history of the opposite ENSO phase. It would not specify why the climate variable can be treated as an exogenous shock, and it would not trace the adjustment of oil prices month by month.

That is not our empirical design.

We estimate horizon-specific responses of real WTI spot and futures prices to phase-specific absolute Niño 3.4 sea-surface-temperature anomalies. El Niño and La Niña are treated separately, and the dynamic effects are traced over horizons extending to two years. The shock variables are

\[ s_t^{EN}=|SST_t|\mathbf{1}\{EN_t=1\}, \qquad s_t^{LN}=|SST_t|\mathbf{1}\{LN_t=1\}, \]

where \(SST_t\) is the Niño 3.4 anomaly measured in degrees Celsius.

The empirical question is therefore:

\[ \text{How does the path of oil prices change after an identified ENSO shock?} \]

That is an impulse-response question, not a contemporaneous correlation exercise.

2. The shock is identified before its propagation is estimated

The central distinction is between identifying the shock and estimating its propagation.

Consider the monthly system

\[ X_t= \begin{bmatrix} ENSO_t\\ GEA_t\\ GOP_t\\ NEER_t\\ OP_t \end{bmatrix}, \]

where \(GEA_t\) denotes global economic activity, \(GOP_t\) denotes global oil production, \(NEER_t\) is the U.S. nominal effective exchange rate, and \(OP_t\) is the real WTI spot or futures price.

Under a recursive short-run identification, ENSO is ordered first. Let the reduced contemporaneous innovations satisfy

\[ u_t=P\varepsilon_t, \]

where \(P\) is lower triangular and \(\varepsilon_t\) contains mutually orthogonal structural shocks. The first equation is

\[ u_t^{ENSO}=p_{11}\varepsilon_t^{ENSO}, \]

so that

\[ \varepsilon_t^{ENSO}=\frac{u_t^{ENSO}}{p_{11}}. \]

There are no contemporaneous global-demand, oil-supply, exchange-rate, or oil-price shocks mixed into the first innovation. Once the recursive restriction is imposed, the first innovation is the structural ENSO shock, up to normalization.

The short-run restriction identifies the shock. A local projection then estimates its effects at each horizon. Structural identification is not unique to a VAR estimator: the same recursive shock can be used with local projections because identification concerns the contemporaneous impact matrix, whereas the LP concerns dynamic propagation.

A companion EconMacro post develops this point in more detail: Can Local Projections Have Short-Run Restrictions?

3. Why ordering ENSO first is credible at monthly frequency

No recursive ordering is assumption-free. The relevant question is whether the restriction is defensible in economic and physical terms.

For the ENSO–oil-price relationship, the contemporaneous exclusion is unusually clear:

\[ \text{monthly oil-market innovation} \not\rightarrow \text{contemporaneous Niño 3.4 SST anomaly}. \]

Movements in WTI spot prices cannot change the temperature of the tropical Pacific within the same month. Nor can oil-futures-price innovations, exchange-rate shocks, monthly global-demand surprises, or oil-production innovations generate an El Niño or La Niña episode on impact.

The reverse direction is plausible. ENSO can alter weather-sensitive demand, production conditions, refinery operations, transport networks, inventories, agricultural conditions, expectations, and risk pricing. Those effects may begin within the month and continue over subsequent months.

The physical origin of ENSO therefore supports the short-run restriction independently of the observed oil-price response. This is also consistent with the climate–macroeconomics literature, which treats ENSO as externally generated climate variation when estimating its effects on output, inflation, energy prices, and other commodity prices.

4. The model conditions on the standard determinants of global oil prices

The contemporaneous ordering is reinforced by a rich monthly information set. The projections condition on twelve lags of:

  • the phase-specific ENSO shock;
  • the opposite ENSO phase;
  • the WTI spot or futures price;
  • global economic activity;
  • global crude-oil production;
  • the U.S. nominal effective exchange rate.

Schematically, the El Niño projection is

\[ \begin{aligned} op_{t+h}^{WTI,x} =&\;\alpha_h +\theta_h^{EN}s_t^{EN} +\sum_{j=1}^{12}\rho_{j,h}^{EN}s_{t-j}^{EN}\\ &+\sum_{j=1}^{12}\delta_{j,h}^{LN}s_{t-j}^{LN} +\sum_{j=1}^{12}\Gamma_{j,h}’Z_{t-j} +e_{t+h}, \end{aligned} \]

where

\[ Z_t= \left\{ op_t^{WTI,x}, GEA_t, GOP_t, NEER_t \right\}. \]

The La Niña specification is symmetric.

The twelve ENSO lags are especially important because ENSO episodes are persistent. They prevent the coefficient on the current anomaly from merely reproducing the effects of a climate episode that began several months earlier. The model also conditions on the main determinants emphasized in the global oil-market literature: past oil prices, global demand, global supply, and dollar valuation.

In Stata, one implementation is:

lpirf LO LGECON LPROD LNEER SSTLN, ///
    step(25) lags(1/12) ///
    exog(L(0/12).SSTEN) ///
    vce(hac nw 12)

The symmetric La Niña model replaces SSTEN with SSTLN and includes the history of El Niño.

This is a dynamic system with a structurally identified climate shock and a substantial conditioning set. It is not a bivariate association between two contemporaneous series.

5. Local projections estimate the structural causal path

Once the ENSO shock has been identified, the local projection estimates, for every horizon \(h\),

\[ op_{t+h}^{WTI,x} = \alpha_h + \theta_h^p\varepsilon_t^{ENSO,p} + \Gamma_h’\mathcal I_{t-1} + v_{t+h,h}, \qquad p\in\{EN,LN\}. \]

The sequence

\[ \theta_0^p,\theta_1^p,\ldots,\theta_{24}^p \]

is the structural dynamic response of the oil price to the ENSO shock. Local projections estimate this response directly at each horizon rather than iterating a fitted transition matrix.

The time-varying extension allows the response to depend on calendar time:

\[ op_{t+h}^{WTI,x} = \alpha_{h,t} + \theta_{h,t}^p\varepsilon_t^{ENSO,p} + \Gamma_{h,t}’\mathcal I_{t-1} + v_{t+h}. \]

Here \(h\) is the number of months after the shock, while \(t\) is the historical date at which the shock occurs. The shock remains structurally identified; what changes over time is the oil-market environment through which it propagates.

6. Direct oil-market pricing versus indirect transmission

The distinction between the direct oil-market pricing channel and the indirect economic channels is central to interpreting the results.

6.1 The direct oil-market pricing channel

An ENSO shock changes the information set of oil traders, producers, refiners, storage operators, and hedgers. It changes beliefs about future weather-sensitive demand, production disruptions, transportation conditions, inventories, and market tightness. These beliefs can be incorporated into oil prices before the underlying physical and macroeconomic effects are fully realized.

For a futures contract with maturity \(k\), a useful schematic representation is

\[ F_t^{(k)} = E_t(S_{t+k}) + RP_t^{(k)}, \]

where \(F_t^{(k)}\) is the futures price, \(E_t(S_{t+k})\) is the expected future spot price, and \(RP_t^{(k)}\) is the futures risk premium. An ENSO shock can affect the current futures price through either component:

\[ \frac{\partial F_t^{(k)}}{\partial\varepsilon_t^{ENSO}} = \frac{\partial E_t(S_{t+k})}{\partial\varepsilon_t^{ENSO}} + \frac{\partial RP_t^{(k)}}{\partial\varepsilon_t^{ENSO}}. \]

If El Niño is expected to reduce future heating-related demand or relax future market tightness, the expected future spot price may decline. If La Niña signals stronger weather-sensitive demand or greater disruption risk, expected future scarcity and the compensation required for bearing oil-market risk may increase.

The spot price can also adjust through decisions made inside the oil market. Expected future scarcity changes current inventory demand, storage incentives, refinery scheduling, hedging positions, and cash–futures arbitrage:

\[ \varepsilon_t^{ENSO} \rightarrow \text{expectations, inventories, storage, and hedging} \rightarrow S_t. \]

This is called a direct oil-market pricing channel because the shock is incorporated into current spot and futures valuations without requiring a prior observed change in global economic activity, global oil production, or the exchange rate.

“Direct” does not mean “only at horizon zero.” Market participants may update the implications of an evolving ENSO episode over several months. Seasonal demand, production risks, and transport disruptions may become clearer gradually. A delayed medium-horizon price response is therefore fully consistent with direct market repricing.

6.2 The indirect economic channels

ENSO may also affect oil prices through intermediate economic variables:

\[ \varepsilon_t^{ENSO} \rightarrow GEA_{t+j} \rightarrow OP_{t+h}, \] \[ \varepsilon_t^{ENSO} \rightarrow GOP_{t+j} \rightarrow OP_{t+h}, \] \[ \varepsilon_t^{ENSO} \rightarrow NEER_{t+j} \rightarrow OP_{t+h}. \]

The global-economic-activity response informs the demand channel. The global-oil-production response informs the physical supply channel. The NEER response informs the dollar-pricing channel.

Other potential intermediates not yet shown in these figures include physical inventories, refinery utilization, shipping costs, heating-degree days, and the slope of the oil futures curve.

6.3 What the oil-price impulse response contains

The estimated oil-price response is

\[ \theta_h^p = \frac{\partial op_{t+h}^{WTI,x}} {\partial\varepsilon_t^{ENSO,p}}. \]

It is the structural causal response of the oil price to the ENSO shock. It incorporates all paths that operate after the shock, including direct oil-market repricing and indirect transmission through real and financial variables.

Conceptually, one may write

\[ \text{overall oil-price response} = \text{direct oil-market pricing} + \text{indirect economic transmission}. \]

This expression is an economic interpretation, not a numerical mediation decomposition. The additional impulse responses show whether the proposed intermediate variables move in directions consistent with the price response. They do not mechanically assign a percentage of the oil-price effect to each channel. A formal mediation decomposition would require additional assumptions and a different empirical exercise.

7. What the new channel results show

The figures below report structural responses to one-degree phase-specific ENSO shocks. The solid line is the estimated response and the shaded region is the 95 percent confidence interval. Because the oil prices, global activity, production, and NEER are expressed in logs, a coefficient of \(0.02\) is approximately a 2 percent response to a one-degree shock. For a sample-mean phase-specific shock, the response is correspondingly smaller: multiplying by approximately \(0.33\) for El Niño or \(0.39\) for La Niña provides a representative scaling.

7.1 El Niño: lower oil prices, weaker activity, and an early supply expansion

Responses of WTI spot price, global economic activity, global oil production, and the NEER to an El Niño shock
Figure 1. Responses of the WTI spot price and potential transmission variables to an El Niño shock.
Responses of WTI futures price, global economic activity, global oil production, and the NEER to an El Niño shock
Figure 2. Responses of the WTI futures price and potential transmission variables to an El Niño shock.

Oil spot and futures prices

The direct price response is clearly negative at medium horizons. Both spot and futures prices decline progressively, reaching a trough of roughly \(-0.20\) log points around months 10–13 before recovering toward zero. Over a substantial part of this medium-horizon interval, the 95 percent confidence band lies below zero.

The similarity between the spot and futures responses is informative. ENSO information is not confined to one segment of the market: it is reflected in both forward-looking contracts and the physical spot market. This is consistent with expectations, storage, inventory adjustment, and spot–futures arbitrage integrating the two markets. The figures do not by themselves establish that futures prices lead spot prices, but they show that the negative El Niño effect is broad-based.

Global economic activity

The central estimate for global economic activity becomes negative after approximately five or six months, reaches its largest decline around months 11–14, and remains negative through much of the medium-horizon window. This timing overlaps with the period in which spot and futures prices are most negative.

The confidence interval frequently overlaps zero, so this should be described as directionally coherent rather than uniformly precise. Nevertheless, the response is consistent with an indirect demand channel:

\[ \text{El Niño} \rightarrow \text{weaker global activity} \rightarrow \text{lower oil demand and prices}. \]

Global oil production

Global oil production initially rises after the El Niño shock, with the positive response concentrated in approximately the first five months. A short-run supply expansion is consistent with downward pressure on oil prices. Production then becomes more volatile: it falls around months 7–9, returns to mildly positive territory at intermediate horizons, and declines again near the end of the response window.

The early production increase is the most economically useful part of this path for interpreting the price response:

\[ \text{El Niño} \rightarrow \text{initially higher oil supply} \rightarrow \text{lower oil prices}. \]

The later oscillation indicates that production is not the sole channel and should not be used as a complete explanation of the persistent price decline.

Nominal effective exchange rate

The NEER response is small relative to the oil-price response and statistically imprecise. The central estimate is mildly positive at some earlier horizons and becomes negative after roughly month 16, but the 95 percent confidence interval generally includes zero.

This is an important null result. It suggests that the negative El Niño oil-price response is not primarily a dollar-valuation phenomenon. The evidence points more strongly toward direct oil-market repricing and real-side demand and supply channels.

El Niño synthesis

The timing suggests a combination of channels. Oil production rises early, potentially easing physical market tightness. Global activity weakens later, reducing oil demand. At the same time, spot and futures prices respond much more strongly than either intermediate variable, which is consistent with a direct pricing channel in which markets capitalize expected future conditions before they are fully realized.

\[ \begin{aligned} \text{El Niño} \rightarrow \begin{cases} \text{direct repricing of expected oil-market conditions},\\ \text{initial supply expansion},\\ \text{subsequent weakening of global activity} \end{cases} \rightarrow \text{lower spot and futures prices}. \end{aligned} \]

7.2 La Niña: higher oil prices, stronger activity, and an early supply contraction

Responses of WTI spot price, global economic activity, global oil production, and the NEER to a La Niña shock
Figure 3. Responses of the WTI spot price and potential transmission variables to a La Niña shock.
Responses of WTI futures price, global economic activity, global oil production, and the NEER to a La Niña shock
Figure 4. Responses of the WTI futures price and potential transmission variables to a La Niña shock.

Oil spot and futures prices

The La Niña price response is positive, large, and more precisely estimated than most of the intermediate-variable responses. Spot and futures prices increase from the early horizons, peak at approximately \(0.30\) log points around months 8–9, and remain positive through much of the 4–14 month interval.

The confidence bands exclude zero over an economically important medium-horizon range. This is the clearest manifestation of the phase asymmetry: La Niña is an inflationary oil-market shock, whereas El Niño is deflationary.

Again, the spot and futures paths are extremely similar. The result is therefore not driven by a single price concept. Climate information appears to be incorporated throughout the integrated oil market.

Global economic activity

Global economic activity rises after a La Niña shock. The response strengthens over the first several months, reaches approximately \(0.02\) log points around months 7–9, and then gradually returns toward zero. The confidence band is above zero over part of the early-to-medium horizon.

This provides comparatively clear evidence for an indirect demand channel:

\[ \text{La Niña} \rightarrow \text{stronger global activity} \rightarrow \text{higher oil demand and prices}. \]

The timing is particularly informative. The positive activity response develops over the same interval in which the oil-price response becomes largest.

Global oil production

Global oil production initially falls, reaching a decline of roughly \(-0.02\) log points near month 2. This short-run supply contraction is consistent with the initial increase in oil prices. Production then oscillates around zero, becoming positive at some medium horizons before weakening again later.

The most defensible interpretation is therefore a short-run supply channel:

\[ \text{La Niña} \rightarrow \text{initially lower oil supply} \rightarrow \text{higher oil prices}. \]

As in the El Niño case, the subsequent oscillation indicates that production alone does not explain the full persistence and size of the price response.

Nominal effective exchange rate

The NEER initially declines modestly and later becomes positive, but the confidence bands are wide and generally include zero. There is therefore little evidence that the dollar exchange-rate channel is the principal source of the La Niña oil-price increase.

The weakness of the NEER response is valuable because it rules out a simple alternative explanation: the oil-price result is not merely the mechanical reflection of a large dollar movement induced by ENSO.

La Niña synthesis

The channel evidence is especially coherent for La Niña. Oil production contracts early, which tightens supply. Global economic activity increases over the medium horizon, which strengthens demand. Spot and futures prices rise strongly over the same period, while the NEER remains comparatively unresponsive.

\[ \begin{aligned} \text{La Niña} \rightarrow \begin{cases} \text{direct repricing of expected market tightness},\\ \text{initial supply contraction},\\ \text{subsequent strengthening of global activity} \end{cases} \rightarrow \text{higher spot and futures prices}. \end{aligned} \]

8. The phase asymmetry extends to the transmission channels

The most striking feature of the results is that the asymmetry is not confined to the oil-price panels. The intermediate variables also tend to move in directions that reinforce the opposite price effects of El Niño and La Niña.

Shock Spot and futures prices Global economic activity Global oil production NEER
El Niño Large medium-horizon decline Negative central estimate at medium horizons; imprecise Initial increase; later oscillation Small and imprecise
La Niña Large and persistent medium-horizon increase Positive early-to-medium response Initial decline; later oscillation Small and imprecise

The most coherent interpretation is therefore:

  • El Niño: direct downward repricing, an early easing of supply, and later weakness in global activity.
  • La Niña: direct upward repricing, an early tightening of supply, and stronger global activity at medium horizons.
  • Exchange rate: no robust evidence that NEER movements drive either phase-specific oil-price response.

This is stronger evidence than a narrative list of possible mechanisms. The intermediate variables respond to the same structurally identified shock, and their timing and signs are broadly consistent with the oil-price paths.

9. Timing helps distinguish the channels

The responses suggest a useful sequencing.

Global oil production reacts relatively early. This is consistent with immediate physical or operational adjustments in production, refining, transportation, or precautionary supply behavior. Global economic activity develops more gradually, which is consistent with a slower demand channel. Oil prices respond over both intervals because they capitalize expected future developments as well as realized market conditions.

For El Niño, the early supply expansion precedes the deepest oil-price decline, while the later weakening in global activity overlaps with the price trough. For La Niña, the initial production contraction is followed by a sustained rise in global activity, and the price response builds over the same medium-horizon window.

This sequencing supports a layered interpretation:

\[ \text{ENSO shock} \rightarrow \underbrace{\text{immediate market repricing and early supply adjustment}}_{\text{short horizons}} \rightarrow \underbrace{\text{broader activity and demand effects}}_{\text{medium horizons}} \rightarrow \text{persistent oil-price response}. \]

The timing does not by itself constitute a formal mediation decomposition. It does, however, provide economically structured evidence that the oil-price paths are supported by both early supply-side movements and later demand-side movements.

10. Statistical precision and responsible interpretation

The oil-price responses are more precisely estimated than many of the channel responses. This is not surprising. The price is the central outcome, while each intermediate variable captures only one part of a broader transmission process.

The evidence should therefore be described with different degrees of strength:

  • The negative El Niño and positive La Niña oil-price responses are the strongest results.
  • The La Niña global-activity response provides relatively clear demand-channel evidence.
  • The early production responses provide plausible and economically coherent supply-channel evidence.
  • The El Niño activity response is directionally consistent but less precisely estimated.
  • The NEER responses are weak, implying little support for a dominant exchange-rate channel.

This hierarchy strengthens rather than weakens the argument. It separates what the data establish most clearly from what they support more tentatively.

11. Why the direct pricing response can be larger than the intermediate responses

The spot and futures responses are economically large relative to the movements in global activity, oil production, and the NEER. This is not puzzling.

Oil prices are forward-looking asset prices. They capitalize expectations about the entire future path of demand, supply, inventories, disruptions, and risk. A modest change in an intermediate flow variable can therefore generate a larger valuation response if it changes expectations about future scarcity over several months.

For example, a short-run decline in global production after La Niña may be quantitatively modest, yet it can signal a tighter inventory path, greater disruption risk, and stronger expected future demand. Futures and spot prices may then adjust by more than the current production response alone would suggest.

Likewise, the similarity of spot and futures responses is consistent with an integrated market in which expectations affect storage and inventory decisions, thereby transmitting future scarcity information into current spot prices.

The large oil-price response is therefore consistent with a combination of:

  • direct capitalization of expected future fundamentals;
  • risk-premium adjustment;
  • inventory and storage responses;
  • early production movements;
  • subsequent global-demand changes.

12. Economic magnitude

At six- to twelve-month horizons, El Niño shocks lower real WTI futures prices, whereas La Niña shocks raise them. Scaling the one-degree estimates by the sample mean phase-specific anomalies—approximately \(0.33^\circ C\) for El Niño and \(0.39^\circ C\) for La Niña—implies:

  • declines of about 4.1–6.8 percent after the sample-mean El Niño shock;
  • increases of about 8.3–11.5 percent after the sample-mean La Niña shock.

These effects are large relative to estimates often reported for broad non-oil commodity aggregates. The channel evidence helps explain why oil may be especially sensitive: oil is simultaneously a physical input, an inventory asset, a globally traded dollar-denominated commodity, and the underlying of deep futures markets.

13. Time variation remains central

The channel figures above summarize average structural responses. The TVP-LP results add another dimension: the same measured ENSO shock can have different effects depending on when it occurs.

Recent episodes appear to generate stronger oil-price responses. A natural interpretation is that direct market repricing has strengthened as climate monitoring, forecasting, market attention, supply-chain integration, inventory management, and futures-market depth have evolved.

The indirect channels may also have changed. The sensitivity of global activity, oil production, transport networks, and inventories to ENSO need not be constant across historical oil-market regimes. This is why the time-varying model is not a secondary robustness exercise: it is central to understanding how structural climate shocks interact with an evolving market environment.

14. Predictability does not eliminate causality

ENSO conditions can be partly forecastable. That does not make them endogenous to oil prices.

A hurricane can be forecast before landfall and still cause economic damage. A predetermined policy change can be announced in advance and still have causal effects. An ENSO episode can be monitored and priced by futures traders without becoming caused by the oil market.

Anticipation affects the timing of the pricing response. It does not reverse the physical causal ordering:

\[ \text{oil-price news} \not\rightarrow \text{monthly Niño 3.4 SST}. \]

The twelve-lag specification also conditions on the development of the ENSO episode, reducing the possibility that the current coefficient merely captures its persistent past.

15. Bottom line

The ENSO–oil-price results cannot accurately be described as a collection of interesting correlations.

The empirical design has five defining features:

  1. ENSO is a physically external climate disturbance.
  2. ENSO is ordered first under a credible monthly short-run restriction.
  3. The first-ordered innovation is the structural ENSO shock, up to normalization.
  4. The model conditions on twelve months of ENSO, oil-price, global-demand, global-supply, and exchange-rate history.
  5. Local projections estimate the structural causal response at each horizon, while TVP-LPs allow that response to evolve across historical market environments.

The paper directly estimates the structural causal response of WTI spot and futures prices to ENSO shocks. The new channel results show that El Niño and La Niña also produce asymmetric responses in global economic activity and global oil production, while the NEER response is weak.

The resulting interpretation is richer than a simple direct-versus-indirect dichotomy. ENSO information is incorporated directly into oil-market valuations, while real-side supply and demand adjustments reinforce the price response over time. Mechanism analysis explains the causal effect; it does not create it.

References

Cashin, P., Mohaddes, K., and Raissi, M. (2017). “Fair Weather or Foul? The Macroeconomic Effects of El Niño.” Journal of International Economics, 106, 37–54.

Inoue, A., Rossi, B., and Wang, Y. (2024). “Local Projections in Unstable Environments.” Journal of Econometrics, Volume 244, Issue 2, September 2024, 105726.

Jordà, Ò. (2005). “Estimation and Inference of Impulse Responses by Local Projections.” American Economic Review, 95(1), 161–182.

Montiel Olea, J. L., and Plagborg-Møller, M. (2021). “Local Projection Inference Is Simpler and More Robust Than You Think.” Econometrica, 89(4), 1789–1823.

Plagborg-Møller, M., and Wolf, C. K. (2021). “Local Projections and VARs Estimate the Same Impulse Responses.” Econometrica, 89(2), 955–980.

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