2. Methodology
2.1. Data and Sources
The present study relies on monthly data spanning from 1993 to 2024. This period captures the ripple effects of three key global disruptions: the 2008 financial crisis, the COVID-19 outbreak and recent oil price fluctuations. By employing this timeline, we were able to trace how India’s macroeconomic variables responded across different phases of volatility. All selected series are captured on a monthly basis and compiled from official sources (Reserve Bank of India, MOSPI, U.S. Energy Information Administration (EIA)). Base year (2011–12 = 100) was considered for Industrial Production (IIP) and Wholesale Price Index (WPI). Oil prices were evaluated using Brent crude prices (USD per barrel), and the exchange rate was assessed as INR per USD. Prior to estimation, all variables were transformed into natural logarithms. Unit root test for stationarity was conducted on first differences of logged series.
Seasonal adjustment was calculated where required using standard filtering procedures. Short data gaps (up to two consecutive months) were interpolated linearly, while longer gaps were excluded from the sample. The sample time period for analysis after preprocessing and alignment to a consistent monthly frequency was January 1993 to December 2024.
2.2. Data and Variable Construction
The analysis employed monthly data for selected key macroeconomic determinants: the Index of Industrial Production (IIP), Wholesale Price Index (WPI), nominal exchange rate (INR/USD) and Brent crude oil prices (US$/barrel). Our study updated historical series to the latest base year. Prior to transformation and estimation, we seasonally adjusted IIP and WPI series using the X-13 ARIMA-SEATS. Further, all series were converted into natural logarithms.
Index of Industrial Production (IIP): Δlog(IIP), a proxy for industrial performance and overall economic activity.
Wholesale Price Index (WPI): Δlog(WPI), represents inflationary trends and cost pressures in the economy.
Exchange Rate (USD/INR): Δlog(INR/USD), captures external sector sensitivity and currency volatility.
International Crude Oil Prices (Brent): Δlog(Brent), serves as the external shock variable, given India’s dependence on oil imports.
Additionally, we measured the Index of Industrial Production (IIP) with the official base year as reported by MOSPI. The Wholesale Price Index (WPI) was expressed using the latest available base revisions. The exchange rate was measured as the nominal INR per US dollar, and lastly, crude oil prices were represented by Brent benchmark prices expressed in US dollars per barrel. For robustness, oil prices were expressed in rupee terms as a log (Brent × INR/USD) to account for the effects of oil prices and exchange rates on the domestic economy.
2.3. Data Cleaning and Crisis Controls
This step deals with handling missing values conservatively due to employment of extensive data. For gaps that are short (two months or less), we interpolated linearly. Longer gaps were dropped to maintain time-series properties. As a robustness check, extreme observations were winsorised at the 1 percent tails, and key models were re-estimated, excluding extreme crisis months. The results remained unchanged, highlighting that the findings were not driven by outliers or data artefacts.
For the global financial crises and COVID-19 crisis, dummies were included as exogenous regressors in the sensitivity checks, although the main analysis relied on the structural identification of oil shocks and formal break tests.
2.4. Pre-Testing and Structural Breaks
We employed ADF and KPSS unit root tests to determine the integration order of data properties. A structural break analysis was conducted using the Zivot–Andrews tests for single breaks and Bai–Perron tests for multiple breaks, with break dates evaluated against the timelines of the global financial crises and COVID-19. Gregory–Hansen tests were utilised as a robustness check for co-integration in the presence of structural breaks.
2.5. Sources of Data Collection
Data on macroeconomic variables such as IIP, WPI and exchange rates were sourced from the RBI and MOSPI, while crude oil price data were obtained from the EIA.
2.6. Econometric Techniques
This section highlights the empirical framework employed to examine distributional and volatility responses to global crises. The empirical framework is structured around the VECM framework to capture long-run equilibrium and short-run adjustment among oil prices, exchange rates, inflation and industrial output. Impulse response functions and variance decompositions are derived from this model to trace transmission mechanisms and assess the importance of shocks. Further, we applied quantile regression to analyse distributional heterogeneity that cannot be captured through mean-based models, specifically during crisis periods when tail risks become economically relevant. Further, ARCH and GARCH models were used separately to examine volatility persistence and clustering rather than as substitutes for the mean dynamics. This structured approach assigned each technique a distinct analytical role, thereby avoiding redundancy while maintaining internal consistency across the empirical results. Lastly, to preserve clarity, diagnostic tests, structural break analysis and robustness checks were reported selectively, with supporting outputs presented in a condensed form.
2.7. Stationarity and Integration Tests
The analysis begins by testing the time-series properties of the selected variables: Index of Industrial Production (IIP), Wholesale Price Index (WPI), exchange rates and global oil prices. Since meaningful econometric modelling requires stationarity, we employ a battery of tests: augmented Dickey–Fuller (ADF) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS).
If the variables are found to be integrated of order one [I(1)], we proceed to the Johansen co-integration framework. The existence of a co-integrating relationship implies a long-run equilibrium between macroeconomic indicators and oil prices.
2.8. Long-Run and Short-Run Dynamics: VECM and ECM
When co-integration is confirmed, we estimate the Vector Error Correction Model (VECM). Before applying co-integration, test lag length criteria were determined by employing AIC, SIC and HQ criteria. The optimal lag length of 2 was selected for further analysis. We estimated the Johansen co-integration test under a specification including an unrestricted intercept and no deterministic trend in the VAR. To allow for mean adjustment, the constant term was restricted to co-integrating space without incorporating deterministic linear trends in the system.
Next, to capture how quickly the deviations from the long-run equilibrium are corrected after a shock, we employed ECM. A negative and statistically significant ECT indicates ineffective adjustment. Model adequacy is assessed through diagnostics, including serial correlation (LM), normality (Jarque–Bera), heteroskedasticity (ARCH–LM) and stability (inverse AR polynomial roots).
The generic form of the error correction model is:
Δyt is the short-term change in a dependent variable such as IIP;
Δxt is the change in independent variables (e.g., oil prices);
λ is the speed of the adjustment;
(yt−1 − γxt−1) is the long-run co-integrating relationship.
This structure allows us to examine both long-term co-integration across variables and short-term deviations triggered by global shocks such as the 2008 Global Financial Crisis (GFC) and the COVID-19 pandemic. Impulse response functions and forecast error variance decompositions were obtained from the estimated VECM model to assess the shock transmission dynamics and their relative contribution to macroeconomic fluctuations. Further, IRFs and FEVD were computed using a Cholesky decomposition of the variance–covariance matrix. The variables were ordered according to an external-to-internal transmission mechanism, placing oil prices first, followed by the exchange rate, inflation and industrial output. This ordering reflects that, within the monthly horizon, global oil prices are exogenous to the Indian economy. Further, due to import bill and external balance effects, exchange rates are allowed to respond quickly to movements in oil price. Inflation is influenced by both oil and exchange rate movements. On the other hand, industrial production is considered an endogenous variable, responding with a lag to external and price shocks. Within this identification framework, global oil price shocks can immediately influence domestic macroeconomic variables, but those domestic variables do not contemporaneously affect global oil prices during the same period. Robustness checks using alternative orderings were assessed, and it was found that they do not materially alter the qualitative impulse response patterns.
2.9. Distributional Effects: Quantile Regression
To account for heterogeneity across the outcome distributions, we applied quantile regression for industrial growth and inflation. To capture heterogeneous responses, we employed quantile regression (
Koenker & Bassett, 1978). This method estimates the relationships at different points of the conditional distribution rather than focusing only on the mean.
The model is specified as
where Qτ(y
t | x
t) is the conditional quantile τ (e.g., 0.10, 0.50, 0.90) of the dependent variable y
t (IIP, WPI or exchange rate) given covariates x
t (oil prices, global shocks). By estimating these quantiles, we could distinguish between weak economic conditions, normal periods and stress episodes without overfitting extreme observations.
Standard errors were obtained through bootstrapping, and the Koenker–Xiao test confirmed significant slope heterogeneity across quantiles. The results revealed that oil price shocks and global crises exerted disproportionately stronger effects at the lower and upper tails of the distribution. This helped us in capturing severe output contractions and inflation surges that are observed in mean-based models. By focusing on economically meaningful quantiles, this framework differentiates normal adjustment dynamics from crisis-driven responses characterised by supply disruptions, exchange rate pressures and cost-push inflation.
2.10. Structural Stability and Break Analysis
To ensure the estimated relationships remain robust across crisis and non-crisis periods, thus avoiding spurious inferences, we employed CUSUM and CUSUMSQ tests so as to detect gradual drifts or sudden shifts in the estimated coefficients.
Additionally, the Bai–Perron multiple break was employed to help identify structural shifts associated with major episodes such as the 2008 global financial crisis and the COVID-19 pandemic.
2.11. Volatility Modelling: ARCH–GARCH Family
Macroeconomic and financial series often display volatility clustering, such as periods of high fluctuations and calm intervals. To capture this, we employed the ARCH (
Engle, 1982) and GARCH (
Bollerslev, 1986) models. The conditional variance equation for ARCH(1) is as follows:
and, for GARCH(1,1), is as follows:
where σ
2t denotes conditional variance at time t, ε
2t−1 is the lagged squared residual, and β
1 captures persistence in volatility. The GARCH(1,1) specification has been adopted as a benchmark that captures volatility clustering and persistence in macroeconomic and financial time series. Preliminary comparisons were conducted using information criteria, which indicated no systematic improvement from asymmetric alternatives, and the analysis, therefore, focused on assessing volatility persistence rather than leverage effects. These choices confirmed comparability across variables while avoiding over-parameterisation.
For univariate series, we estimated GARCH(1,1) models with Student-t innovations to capture fat tails, which allowed us to track co-volatility through time and link spikes in correlation to global shocks.
2.12. Diagnostic and Robustness Checks
All the models were validated using a comprehensive set of diagnostics. Residual serial correlation was checked using LM tests, heteroskedasticity with ARCH–LM and normality with Jarque–Bera. The stability was confirmed using inverse AR roots and recursive estimations. Koenker–Xiao slope tests were employed to validate distributional heterogeneity of quantile regression.
Overall, this multi-layered approach enabled a detailed assessment of the dynamic linkages between oil prices, financial crises and India’s macroeconomic variables. These were captured in both the mean and variance dimensions while incorporating structural breaks and distributional asymmetries.
3. Results and Discussions
The results section is framed around VECM as the core framework, with distributional and volatility analysis being employed as complementary tools for interpreting the underlying transmission mechanisms.
This study applies descriptive statistics in
Table 2, offering insights into the behaviour of macroeconomic variables. The results highlight oil prices exhibiting the highest standard deviation at 28.34, with values ranging from
$11.35 to
$133.88 per barrel. These values capture events such as the 2008 spike and the COVID-19 crash in 2020. Moderate variability is seen in exchange rate data, with a mean of ₹55.46 and a standard deviation of 15.52. These values reflect shocks like the 2013 taper tantrum.
While IIP and WPI appear more stable, the negative skewness of IIP (−0.22) suggests longer industrial slowdowns than compared to booms. WPI patterns reveal the asymmetric effects of the inflation shocks. These patterns, as noted in earlier studies (e.g.,
P. Kumar & Singh, 2022), support the use of both symmetric and asymmetric modelling frameworks.
Before engaging in time-series modelling, it is crucial to assess the stationarity of the variables. The ADF test results in
Table 3 indicate that none of the four macroeconomic indicators is stationary in their level forms, as evidenced by
p-values exceeding 0.05. However, after the first differencing, each series achieves stationarity, with a
p-value of 0.00, confirming that they are integrated of order one, I(1). The KPSS test was applied in
Table 4 with the null hypothesis if stationarity provided supportive evidence. At level, the KPSS test concluded with rejecting the null hypothesis, as KPSS statistics exceeded the 5% critical value. However, after first differencing, series were found to be stationary, as the KPSS statistics were less than the corresponding critical values. Together with the ADF results, it was confirmed that all selected variables are first order stationary, i.e., integrated of order one, I(1). The results confirm the application of the Johansen co-integration framework.
P. Sharma and Shrivastava (
2021) and
Upadhyaya et al. (
2023) observed similar I(1) behaviour for the exchange rate, inflation and industrial output. These findings have both methodological and economic implications, supporting the application of co-integration analysis, vector autoregressive and ECM frameworks in subsequent sections, as endorsed by
S. Rizvi et al. (
2022).
To confirm our results were not influenced by data issues or outliers, we again conducted the analysis. This time, effort was made to interpolate short gaps, excluding longer missing data and winsorizing at the 1% tails. The results for unit root, co-integration and other models remained consistent, confirming the robustness of the results. For the Johansen co-integration analysis, we determined the optimal lag length, as showcased in
Table 5, using the following standard information criteria: Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC), and Hannan–Quinn Information Criterion (HQIC). AIC criteria indicated that a lag of 2 was optimal, which we used in the Johansen co-integration tests to capture the relevant dynamics without over-parameterisation.
Before proceeding to the co-integration analysis, we examine whether structural breaks affected the time-series properties of the variables. Given that crises can alter the data-generating process, we apply the Zivot–Andrews and Bai–Perron tests endogenously. These tests help ensure that the long-run relationships are not biased by regime shifts during episodes such as the global financial crisis, the taper tantrum and COVID-19.
The Zivot–Andrews test, with results shown in
Table 6, detected significant structural breaks in the IIP (2009), WPI (2008), exchange rate (2013) and oil prices (2020), consistent with the timing of global crises. Bai–Perron multiple-break tests confirmed additional breakpoints in 2008–09 (global financial crisis), 2013 (taper tantrum episode) and 2020 (the COVID-19 pandemic). These results validate that crisis episodes materially altered the data-generating process, yet the co-integration and VAR estimates remain robust when accounting for regime shifts.
Given that the Zivot–Andrews test permits an endogenous structural break in the unit root testing framework, the integration properties of the variables were re-evaluated under break-adjusted models. The findings supported I(1) behaviour, hence reinforcing that, even after accounting for structural shifts, the order of integration remained unchanged. Next, we explore long-run equilibrium relationships using a co-integration test.
Table 7 presents all variables with
p-values below 0.05, indicating valid co-integrating links. For the null hypothesis of no co-integration (r = 0), both the trace statistic (89.00) and the max-eigen statistic (35.00) exceed their 95% critical values (55.25 and 35.01), leading to the rejection of the null hypothesis and confirming at least one long-run relationship. Oil price and exchange rate exhibit strong connections, suggesting that India’s external sector dynamics are tied to global commodity movements. This finding is consistent with
Alam et al. (
2020), who identified causality between oil prices and exchange rates, and
Sultan et al. (
2020), who established a co-integration between oil price, inflation, and exchange rate. These results support the use of models that accommodate long-run linkages, such as the ECM.
In addition to the trace statistics, the maximum eigenvalues highlight and confirm the presence of at least one stable long-run co-integrating relationship among the variables, which is consistent with the selected lag structure. To ensure that the long-run relationship among the variables is not biased by regime shifts such as the 2008 financial crisis or the COVID-19 pandemic, we apply the Gregory–Hansen test, which allows for a single endogenous structural break in the co-integration relationship (
Guliyev, 2022). The Gregory–Hansen results, as depicted in
Table 8, confirm the existence of long-run co-integration among oil prices, exchange rates, industrial production and inflation, even when structural breaks are allowed. The test is implemented under the level-shift with trend specification, which permits an endogenous structural break in both the intercept and deterministic trend of the co-integrating relationship.
The breakpoints align with known crisis periods (2008 and 2020), validating the robustness of our long-run findings.
To capture the dynamic transmission of global shocks to India’s macroeconomic variables, we estimate impulse response functions from the VECM.
Table 9 below highlights the short-run dynamics from the VECM analysis. Findings observed error term is negative and statistically significant (−0.132,
p = 0.004) for the industrial production equation, indicating approximately 13% of last year dis-equilibrium being rectified each month, showcasing convergence towards equilibrium.
Further, in the short run, changes in oil price are seen to exert a negative and statistically significant impact on industrial output (−0.054,
p = 0.011), consistent with cost-push pressures. Oil prices also demonstrate a positive effect on wholesale inflation (0.047,
p = 0.010), indicating inflationary pass-through, whereas for exchange rate, weaker and statistically less robust effects are observed, demonstrating that most of the changes occur through the long-run error correction mechanism instead of immediate short-run feedback (
Sahu et al., 2014;
P. Kumar & Singh, 2022;
Upadhyaya et al., 2023;
Ahmed & Kaur, 2025). The following tables are interpreted jointly with the impulse response functions to emphasise the dynamic economic significance rather than isolated coefficient magnitudes.
Impulse responses are evaluated using the Cholesky identification scheme and reflect the dynamic effects of a one-standard-deviation shock.
Table 10,
Table 11,
Table 12 and
Table 13 highlight how IRFs trace the response of Industrial Production (IIP), Exchange Rate (ER) and inflation (WPI) to a one-standard-deviation innovation in Oil Prices (OP). Shocks in oil prices are quick enough to reduce industrial output (peak ≈ −0.35% at three months) and raise wholesale prices (peak ≈ +0.25% at three months). Oil shocks also depreciate the INR (peak ≈ +0.8% at three months). A pure exchange rate-depreciation shock further dampens IIP modestly, consistent with the cost-push and imported-input channels. The results are supported by studies conducted by
V. Sharma et al. (
2024).
As witnessed, some short-run coefficients in the VECM appeared numerically small, but their economic relevance lied in their cumulative and dynamic effects. Monthly macroeconomic adjustments typically evolved gradually, with small coefficients accumulating over time through the error correction mechanism and impulse responses. The impulse response functions further provided a clearer economic interpretation by tracing these cumulative effects. For instance, a (−0.14%) response of industrial production to an exchange rate shock meant a persistent decline in output for subsequent months. This reflected higher cost of inputs, which are imported, and reduced investment confidence. These dynamic responses are economically meaningful when evaluated over the full adjustment horizon rather than at a single point estimate.
We have applied forecast error variance decomposition to assess the relative importance of different shocks beyond the impulse responses to get more insightful results. Over a time frame of 1–2 years, oil price shocks have resulted in a major share of the forecast error variance in industrial production (approx. 28%); for inflation (wholesale), it stood around 35%, while exchange rate shocks held a relatively smaller share, explaining the variance around 15% in IIP and 12% in WPI in a time frame of a 24-month horizon. Oil price shocks attributed nearly 32% of exchange rate variance, demonstrating pressures caused by higher import costs and current account dynamics while explaining about 29% of the variability in inflation (
Deheri & Sahu, 2024). While the direction of these responses is broadly consistent with earlier evidence, the magnitude and persistence of the effects vary substantially across crisis regimes, with markedly stronger transmission observed during periods of global stress.
Table 14,
Table 15 and
Table 16 summarise the econometric results and are interpreted jointly with the accompanying discussion to emphasise economic relevance rather than isolated coefficient magnitudes.
In
Figure 4 below, we illustrate a detailed perspective by employing quantile regression. The Koenker–Xiao quantile-process test concludes significant slope heterogeneity across quantiles, validating this approach. Oil prices reveal a statistically significant impact (coefficient = 6.83,
p < 0.05), with stronger effects observed at higher quantiles of inflation and IIP volatility, indicating their dominant role in driving macroeconomic instability during extreme shocks. The conclusions align with those stated by
S. K. A. Rizvi and Itani (
2021) and
Su et al. (
2016). Further, the IIP and WPI reflect weak coefficients, suggesting indirect effects through oil-linked channels, whereas exchange rate had a moderate effect as a transmission channel for external shocks. These results suggest the use of precautionary policy tools at times of external volatility.
The results in
Table 17 report oil shocks to be negative, with stronger effects in the upper quantiles. Exchange rate impacts are also found to be negative, strongest at the median, while WPI is confirmed to be positive across all quantiles, with a peak at the median. The quantile regression results state that shocks in oil price exert disproportionately stronger effects at the upper quantiles of inflation and output volatility. These results state that, during extreme stress episodes such as the global financial crisis and the COVID-19 pandemic, oil price shocks intensify due to supply-side rigidities, exchange rate depreciation and delayed policy transmission.
In contrast, muted effects were observed at lower quantiles, reflecting greater macroeconomic stability during normal periods. These findings concludes that mean-based models mask economically meaningful tail risks, hence understanding vulnerabilities in periods of crisis, as shocks in oil price intensify disproportionately during phases of heightened stress. Conventional mean-based models often fail to capture these dynamics.
Robustness was ensured by incorporating policy dummies for the global financial crisis (2008–09) and the COVID-19 pandemic (2020–21). Their inclusion did not alter the baseline estimates, hence confirming that quantile effects were not influenced by the crisis periods. Bootstrapped standard errors were used to validate their significance.
The null hypothesis of equal coefficients across the 0.10, 0.50, and 0.90 quantiles (p < 0.05) was rejected by the Koenker–Xio slope test, suggesting that oil and exchange rate shocks have heterogeneous impacts on macroeconomic outcomes. The stronger coefficients were witnessed at the upper quantiles, reflecting phases of rigidities in supply-side, depreciation of exchange rate and delays in policy transmission. All these amplified the pass-through of oil price shocks to inflation and output. In contrast, the relatively muted responses around the median reflect more effective adjustment under normal macroeconomic conditions. This asymmetry explains why mean-based models understate risks during episodes of crisis.
The ARCH–LM test was applied to examine autoregressive conditional heteroskedasticity in residuals.
Table 18 indicates significant ARCH effects in the oil price and exchange rate equations, suggesting that volatility depends on the previous shock patterns. These results justify the use of GARCH models to capture dynamic variance structures, as reported in prior studies by
Mahalwala (
2022) and
S. K. A. Rizvi and Itani (
2021). For India, with its high energy import dependence, ARCH behaviour indicates lingering shock effects, underscoring the need for price stabilisation buffers during volatile periods. The ARCH–LM results provide a basis for applying GARCH models to capture time-varying volatility in India’s response to global shocks.
The GARCH(1,1) results presented in
Table 19 confirm the
presence of volatility clustering across all variables, in line with the ARCH–LM findings. The sum of α and β is close to unity (0.92–0.94), suggesting
high persistence of volatility, where shocks in variables have prolonged effects. These results align with the findings of
Bhatia and Gupta (
2021) and
Maharana et al. (
2024). The results present that oil prices showcase the strongest ARCH effect, with α = 0.30, indicating immediate and sharp reactions to global shocks, whereas the exchange rate and IIP displayed prolonged volatility persistence, as highlighted by the GARCH term.
These results are consistent with this study’s objectives, as they reinforce the vulnerability of India’s macroeconomic variables to external disruptions.
As evident in the results shown in
Table 19, the ARCH and GARCH coefficients are positive and statistically significant across all series. Volatility persistence remained quite high, with α + β equal to 0.93 for IIP, 0.94 for exchange rate, 0.83 for inflation (WPI) and 0.92 for oil prices, reflecting gradual decay of shocks. The estimated Student-t degrees of freedom ranged between 6.5 and 8.2, supporting fat-tailed residuals. Further, it can be concluded that Ljung–Box and ARCH–LM tests do not detect remaining serial correlation or ARCH effects, hence indicating that the GARCH(1,1) specification captured conditional heteroskedasticity.
Further, we have employed cumulative sum control to examine the temporal stability of the model coefficients through the CUSUM test. The cumulative sum of recursive residuals was plotted against critical bounds at a 95% confidence level (
Bhattacharjee & Das, 2021). The CUSUM plots (
Figure 5,
Figure 6,
Figure 7 and
Figure 8) show that the lines for all macroeconomic indicators remain within the confidence bands throughout the selected time frame, indicating stability of the coefficient. In the early IIP series, around 1992–1993, fluctuations can be observed, likely economic restructuring in the post-liberalisation period. However, these deviations are brief, and the model stabilises thereafter. While previous studies confirmed structural breaks in exchange rates during global crises, our findings demonstrate relative stability. Further, our findings show that the WPI and oil prices remained stable within bounds. The stability of these macro-variables during volatile global conditions underscores the necessity for consistent policy signalling.
The CUSUM statistic for all selected variables remained within the 5% critical bounds, suggesting stability in the parameters for the selected sample period.
Lastly, in our analysis, we employed White’s test (
Table 20), confirming heteroskedasticity, yet the key coefficients remain robust. The exchange rate shows a strong negative effect (–1.27,
p = 0.00), WPI exerts a persistent positive impact (1.56,
p = 0.00), and oil prices display a short-run negative effect (−0.22).
Robust standard errors improve the credibility of the model interpretation.
S. Kumar et al. (
2022) reported similar results.
The Durbin–Watson statistics in
Table 21 were employed to check for autocorrelation. All variables fell within the acceptable (1.5–2.5) range, confirming no autocorrelation in residuals. IIP (1.984), exchange rate (1.988), and WPI (2.060) indicate error terms are white noise. In our case, the stable d-stat values further reinforce the robustness of the modelling framework, particularly when used for forecasting or policy simulation under global uncertainty. Heteroskedasticity-robust standard errors yield qualitatively similar inferences, indicating that the results are not sensitive to variance misspecification.