Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Manuscript: Beyond Reserves: A Reproducible Stress-Testing Framework for Strategic Mineral Security in Türkiye

Summary

This paper develops a simulation-based framework for assessing strategic-mineral supply fragility in Türkiye. The framework combines a latent supply-stress index, synthetic monthly return paths, Quandt–Andrews structural-break tests, two-state Markov regime-switching models, Monte Carlo simulations, and a criticality-elasticity measure. The analysis considers three mineral systems—boron, chromium and a rare-earth-linked system—which are intended to represent progressively different exposure architectures.

The paper is ambitious and addresses an important question. I particularly appreciate the authors' emphasis on reproducibility and their attempt to bring tools commonly employed in financial-risk analysis into the critical-minerals literature. The simulation exercise is carefully documented, and the proposed release of the code, calibration files and estimation logs is a strength.

However, I have several substantial concerns regarding the interpretation of the results and, in particular, the distinction between simulation validation and empirical evidence. The most important issue is that the paper calibrates the three mineral systems so that they embody different degrees and compositions of vulnerability and subsequently interprets the recovery of this ordering by the econometric diagnostics as evidence about mineral fragility. In my view, this creates a degree of circularity between assumptions and conclusions.

The paper could make a useful methodological contribution, but the claims need to be substantially reframed and the economic foundations and external validation of the calibration strengthened.

Major comments

1. The distinction between simulation validation and empirical validation needs to be considerably clearer

My main concern is the interpretation of the simulated results. The paper assigns different exposure structures and parameter weights to boron, chromium and the rare-earth-linked system. These calibration choices imply that the systems enter the simulation with different underlying vulnerabilities. The econometric procedures subsequently recover the same ordering.

The authors describe this result as demonstrating that the framework “recovers, without being told to, exactly the exposure ordering” suggested by the strategic-minerals literature. I am not convinced by this interpretation. The econometric estimators may not be explicitly given the ordinal ranking, but the data-generating process generating the observations is.

Consequently, the agreement between the resulting ranking and the assumed exposure architecture primarily establishes internal consistency of the simulation framework, rather than independent evidence that rare-earth-linked systems are empirically more fragile than chromium or boron.

This distinction should be made throughout the Abstract, Sections 4–6 and particularly in statements referring to an “empirical contribution” or “empirical confirmation.” I suggest distinguishing explicitly among:

(i) computational/reproducibility validation;
(ii) internal statistical validation of the estimators against known simulated states; and
(iii) external empirical validation using observed mineral-market data.

The paper performs (i) and (ii), but not (iii). Indeed, the authors themselves acknowledge that estimating the architecture using actual monthly or weekly mineral prices would transform the methodology into a tested empirical claim. This limitation should be central to the interpretation rather than largely deferred to future research.

2. Calibration of the latent stress index requires external economic justification

Closely related to the first point, the weights assigned to processing concentration, substitutability, logistics and other components of the latent stress index appear to drive an important part of the results.

The paper needs to explain more convincingly why these particular weights are economically appropriate. At present, the calibration seems partly motivated by the qualitative characteristics of each mineral and then validated by demonstrating that the resulting simulations reproduce those characteristics.

One way to strengthen the paper would be to discipline these parameters using external data—for example, observed processing concentration, trade concentration, import dependence, substitutability measures, project-development characteristics or historical disruption episodes.

The broader criticality literature has long emphasised that mineral criticality is multidimensional rather than reducible to geological availability. Graedel et al. (2015), for example, conceptualise criticality through supply risk, vulnerability to supply restriction and environmental implications. More recent research also emphasises project-development risks and the interaction between technical and non-technical barriers. Vespignani and Smyth (2024), for example, develop an economic theory in which technical and non-technical barriers generate a back-ended risk premium that affects investment and mineral supply.

Engaging with this literature would provide a stronger economic foundation for the latent stress index.

3. The claim that midstream architecture rather than geological scarcity “governs regime fragility” is too strong

The paper argues that its results demonstrate that midstream architecture, rather than geological scarcity, governs regime fragility. This is potentially an important hypothesis, and I agree that processing concentration has become central to critical-mineral security.

However, the simulation cannot establish this proposition independently when processing concentration receives substantial weight in the calibration used to generate the simulated data.

The appropriate conclusion is therefore narrower: conditional on the assumed calibration, the proposed framework is capable of translating stronger midstream exposure into larger estimated regime fragility.

This is still useful, but it is conceptually different from demonstrating that midstream concentration is empirically the dominant determinant of criticality.

The authors should either moderate this claim or conduct additional sensitivity exercises in which the relative weights on upstream scarcity, processing concentration, substitutability and logistics are systematically varied. A global sensitivity analysis would be particularly useful because it could establish whether the mineral ordering survives plausible alternative calibrations.

The recent literature provides substantial support for examining this issue. Chepeliev et al. (2026), for example, emphasise refining bottlenecks, long project-development periods, coproduction constraints, trade policy and environmental factors as interacting sources of critical-mineral supply vulnerability. The paper should connect its stress-index architecture more explicitly to these economic mechanisms.

4. The paper needs a stronger connection to observed critical-mineral price dynamics

There is now empirical evidence showing that critical-mineral prices respond heterogeneously to geopolitical shocks.

Saadaoui, Smyth and Vespignani (2025), for example, examine six critical minerals using constant and time-varying parameter local projections. They show that responses to geopolitical risk differ across minerals, vary over time, and depend partly on non-technical risk. They also find differences between geopolitical threats and realised geopolitical acts.

This evidence is particularly relevant to the present paper because it suggests that the assumed stress-to-price transmission mechanism could potentially be externally calibrated.

I would therefore encourage the authors to provide at least one empirical benchmarking exercise. This does not necessarily require transforming the entire paper into an empirical study. For example, the authors could show whether simulated volatility persistence, break frequencies or stress elasticities fall within plausible ranges observed for actual mineral-price series.

Without such benchmarking, it is difficult to determine whether the synthetic paths are economically realistic even if they are statistically internally consistent.

5. H3 cannot be tested using the model currently estimated

H3 proposes an economically interesting asymmetry: entry into the turbulent regime is rapid whereas recovery is slower, producing hysteresis.

However, as the authors correctly acknowledge later in the paper, the homogeneous two-state Markov transition matrix does not identify this dynamic. Constant transition probabilities provide expected regime durations, but they do not establish whether shocks arrive quickly and dissipate gradually.

This is more than a qualification to the interpretation of H3. The model, as currently specified, does not test the hypothesis as stated.

I therefore suggest one of three alternatives:

(a) reformulate H3 in terms of relative regime persistence, which the existing model can test;

(b) estimate a time-varying transition probability (TVTP) model in which the probability of regime switching responds to the stress index; or

(c) introduce an explicitly asymmetric transition/duration specification.

Option (b) would be particularly consistent with the conceptual framework because the latent stress index could directly enter the transition probabilities.

6. Statistical independence of the four diagnostics should not be overstated

The paper places considerable emphasis on the fact that four different statistical diagnostics generate the same ordering across minerals and interprets this convergence as especially strong confirmation of H2.

I would be more cautious.

The sup-Wald statistic, Markov persistence estimates, criticality elasticity and KS statistics are mathematically different, but they are all calculated from synthetic observations generated by the same underlying data-generating process and calibration parameters. They are therefore not independent pieces of evidence in the economic sense.

Their agreement demonstrates robustness of the simulated ordering across different statistical transformations of the same underlying process. That is useful. But it should not be interpreted as equivalent to four independent empirical tests of the economic hypothesis.

I suggest replacing expressions such as “methodologically independent diagnostics” with language such as “complementary diagnostics applied to a common simulated data-generating process.”

7. The economic interpretation of the Criticality Elasticity Score needs further development

The Criticality Elasticity Score (CES) is potentially one of the more interesting contributions of the paper, but its economic interpretation remains unclear.

The authors define the CES as the finite-difference sensitivity of a diagnostic metric to a one-standard-deviation increase in latent stress. This provides a convenient comparative statistic, but several questions arise.

First, because the stress index itself is constructed and calibrated by the authors, the economic meaning of a “one-standard-deviation” shock depends on the calibration. Second, CES values across mineral systems may therefore reflect differences in scaling as well as genuine differences in economic vulnerability. Third, it is unclear how policymakers should interpret, for example, a CES of 2.89 relative to 1.57.

The authors should provide an economic interpretation of the magnitude, not simply the ordering, of this measure. Sensitivity of the CES to alternative normalization of the stress index would also be useful.

More generally, I encourage the authors to connect the CES to existing concepts of supply risk, vulnerability, non-technical risk and project risk rather than presenting it primarily as a statistical construct.

Additional comments

The paper would benefit from somewhat more disciplined terminology throughout. “Empirical,” “validation,” “confirmation” and “evidence” are sometimes used in ways that imply inference about actual mineral markets when the analysis is entirely synthetic. Terms such as “simulation result,” “internal validation,” “model-implied ordering” and “conditional on the assumed calibration” would be more precise.

The distinction between mineral identity and exposure architecture should also be reinforced. The results do not establish that rare earths are intrinsically more fragile than chromium or boron. They demonstrate that the particular rare-earth-linked exposure architecture assumed by the authors generates greater simulated fragility.

Finally, the reproducibility strategy is a genuine strength. The use of deterministic seeds, disclosure of the data-generating process and proposed provision of the simulation code should be retained and perhaps highlighted more strongly as part of the paper's methodological contribution.

Overall assessment

The paper addresses an important problem and proposes an interesting combination of structural-break analysis, regime-switching estimation and Monte Carlo simulation for strategic-mineral risk assessment. The framework is transparent and potentially useful as a stress-testing tool.

The principal issue is not the use of synthetic data itself. Synthetic simulations can be very useful for evaluating statistical methods when the true data-generating mechanism is known. The issue is the interpretation of what those simulations establish.

At present, the manuscript sometimes moves from demonstrating that the statistical framework successfully recovers properties embedded in its data-generating process to making broader claims about the determinants of actual mineral-market fragility. Those are different propositions.

A substantially revised version that clearly positions the paper as a methodological stress-testing framework, strengthens the economic foundations of the calibration, introduces systematic calibration sensitivity analysis and provides some external empirical benchmarking could make a useful contribution to the growing literature on critical-mineral supply risk.

Suggested references

Chepeliev, M., Bekkers, E., Iyer, G., Qiu, Y., Wojtowicz, K., Yarlagadda, B. and Yilmaz, A.N. (2026), ‘Critical minerals and the global supply chain’, Annual Review of Resource Economics, 18, in press.

Graedel, T.E., Harper, E.M., Nassar, N.T., Nuss, P. and Reck, B.K. (2015), ‘Criticality of metals and metalloids’, Proceedings of the National Academy of Sciences, 112(14), 4257–4262.

Saadaoui, J., Smyth, R. and Vespignani, J. (2025), ‘Ensuring the security of the clean energy transition: Examining the impact of geopolitical risk on the price of critical minerals’, Energy Economics, 142, 108195.

Vespignani, J. and Smyth, R. (2024), ‘Artificial intelligence investments reduce risks to critical mineral supply’, Nature Communications, 15, 7304.

Whittle, D. and Yellishetty, M. (2023), ‘Critical minerals: A criticality assessment approach’, in Critical Materials and Sustainability Transition, Chapter 7.

Zhou, J. and Månberger, A. (2024), Critical Minerals and Great Power Competition: An Overview, SIPRI, Stockholm.

Aslan, Y. and Ari, I. (2026), ‘Strategic review of critical minerals policies in Türkiye: Lessons from the US, China and the EU’, Resources Policy, 118, 105951.

Author Response

Dear Reviewer,

Thank you for your careful and constructive evaluation of our manuscript.

Your comments helped us substantially improve the methodological framing, calibration rationale, interpretation of the simulation results, and distinction between internal validation and external empirical evidence.

Please find attached our detailed point-by-point response matrix, together with the corresponding revisions made to the manuscript.

Sincerely,

Hasan Tolga UNAL

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Great job with this original, methodologically attempt to advance strategic mineral risk governance. Y'all address a critical blind spot in conventional raw materials security literature: overreliance on static, geological, and reserve-centric accounting (e.g., reserve-to-production ratios, static HHI scores, etc.) that fail to quantify dynamic volatility propagation, threshold-triggered structural breaks, and regime persistence under geopolitical stress/tension.

By transplanting proven econometric architectures from sovereign debt and energy risk modeling (especially the Quandt–Andrews sup-Wald structural-break test and Hamilton two-state Markov regime-switching autoregression across 90,000 synthetic Monte Carlo iterations), you demonstrate how supply-chain fragility is dictated by midstream processing bottlenecks and substitution inelasticity -- rather than it just being upstream in-ground abundance. Given your first-hand insight/knowledge, Turkey is an ideal analytical cross-section, encompassing an incumbent dominant exporter (Boron), an established mid-tier industrial input (Chromium), and an emerging, midstream-dependent pre-commercial asset (Kızılcaören Rare Earth Elements [REEs]).

Your manuscript is pretty good, mathematically/statistically coherent, and fairly nice work with the reproducible computational science. Nevertheless, before accepting it, several issues must be resolved that will require some work as a major revision. (but definitely excited to review your next iteration!)

1. Circularity & sensitivity of Synthetic Calibration Parameters

In Section 3.2 and Table 2, you calibrate the latent driver weights (ω1​,ω2​,ω3​,ω4​), regime-specific autoregressive persistence (ϕ1​,ϕ2​), conditional volatilities (σ1​,σ2​), and mean shifts (μ1​,μ2​). For example, the REE linked system is assigned a high midstream processing concentration weight (ω2​=0.35) and substitution rigidity (ω3​=0.30), whereas boron is assigned a balanced profile (ω2​=0.20,ω3​=0.20).

--Because your data-generating process is synthetically hard-coded with these exact penalty weights, finding that the REE system exhibits the highest break severity (CES=2.89 vs. 1.57 for boron) and highest turbulent regime persistence comes close to confirming assumptions by construction. Econometrics prove the Hamilton filter and sup-Wald test can recover planted latent parameters, but they do not prove that real-world REE systems exhibit this specific factor sensitivity.

Thus you should conduct a global sensitivity analysis (e.g., Sobol variance decomposition and/or perturbed parameter grid of +/- 20% on ωk​) to demonstrate whether the ordinal ranking (Boron < Chromium < REE) is robust enough  for calibration variations or is highly contingent on chosen point estimates. Furthermore, please clarify in the abstract and section 3 that the empirical result is 'proof of algorithmic recoverability and structural consistency' - it's not an empirical estimation of physical market shocks.

2. Theoretical inconsistency with H3

So for H3, y'all claim that the transition into a turbulent regime is asymmetric relative to the return to stability, such that recovery velocity is systematically slower than shock-entry velocity (i.e. a hysteresis property). Yet, in Section 5.4 you admit that your two-state Markov model uses a time-homogeneous transition matrix (P), which cannot measure instantaneous entry vs. exit velocities.

--A stationary Markov chain with fixed transition probabilities p11​ and p22​ generates geometrically distributed sojourn times (1/(1−pjj​)). While state 2 duration can exceed state 1 duration under compound stress, duration asymmetry is mathematically distinct from state-dependent directional velocity (hysteresis).

This all means you should probably adjust the formulation of H3 in the introduction to mention that it tests duration asymmetry across stress scenarios rather than instantaneous transition velocity / path-dependent hysteresis.

3. Execution Discrepancy: N = 3,000 vs. N = 10,000 Monte Carlo Grid

For Sec 3.2 & Sec 3.7, specify an experimental grid of N=10,000 replications across 3×3×10,000=90,000 price paths. However, in Sec 4 you state that the presented results were executed at N=3,000 (27,000 paths) due to computational tractability within the drafting environment, deferring N=10,000 to production release.

--While metric convergence at around an N of 2,000ish is plausible, presenting provisional sample sizes undercuts the reproducibility standard advocated in your paper. Resolving this means y'all should report the full N=10,000 simulation run in the revised manuscript. Make sure all confidence bands and Kolmogorov–Smirnov test statistics in Table(s) 4-7 reflect the finalized N=10,000 iterations.

4. Discrepancy between Methodological Description & Test Implementation (Chow vs. sup-Wald)

So when you specify the Quandt–Andrews sup-Wald test for an unknown structural break, there is a disjuncture because Section 5.10 discloses that the actual algorithm applied in Section 4.1 was a "Chow-type mean-shift statistic rather than the fully specified sup-Wald test against a joint intercept-and-variance break." This creates an internal contradiction b/w the formal mathematical methodology (Equation 6) and the actual Python code execution. Given volatility shifts (σ1​→σ2​) are a primary feature of geopolitical mineral disruptions, omitting variance-break testing in the actual execution weakens structural-break narrative.

--Update your Python script to execute the Quandt–Andrews sup-Wald test accounting for joint mean and variance shifts OR align Section 3.4 to reflect what was computed, discussing the variance omission as a known limitation.

5. Bridging Framework to Tangible Industrial/Geopolitical Policy

Your recommendations in Section 5.9 provide a theoretical distinction between export maximization (boron), midstream refining integration (chromium), and contingency stockpiling/separation technology (like Kızılcaören REEs). However, your translation is still too abstract.

--When it comes to real-world great power competition [GPC] (e.g., export restrictions, weaponized mineral interdependence, Chinese midstream processing dominance, etc.), national stockpiling authorities need actionable decision rules. Thus, you should consider how a national security council (or raw materials agency) would establish explicit warning thresholds based on the elasticity score?

6. Integrate Defense-Critical Mineral and Geopolitical Trade-Bloc Literature

So in the introduction you argue that existing mineral security literature lacks dynamic, scenario-based shock propagation architectures and fails to formalize how midstream processing concentration impacts system fragility. While this critique is valid regarding traditional geological surveys, the manuscript currently overlooks recent scholarship on Defense Critical Minerals (DCMs), geopolitical trade bloc fragmentation, and national security doctrine.

--Give your background (HAVELSAN Inc), situating the mathematical stress-testing model within real-world defense acquisition and geopolitical alliance dynamics would really enhance policy impact and disciplinary relevance:
              [1] DCMs & Scenario-Based Vulnerability: Connect mineral dependencies to defense readiness, weaponized supply lines, and scenario planning in national security doctrine (e.g., Amoah, Bazilian, & Matisek, Comparative Strategy, 2026 [https://www.tandfonline.com/doi/pdf/10.1080/01495933.2025.2609236]; Vivoda, Matthews, & Andresen, Comparative Strategy, 2025 [https://www.tandfonline.com/doi/pdf/10.1080/01495933.2025.2456427]). Incorporating these frameworks will sharpen the justification for why defense contractors and sovereign states require continuous, AI- and simulation-driven supply chain monitoring.

              [2] Geopolitical Trade Blocs & Supply Fragmentation: Critical minerals governance in the context of competing economic blocs (e.g., Western Minerals Security Partnership / RBITS v. BRICS+ expansions; see Vivoda, Matthews, & McGregor, Resources Policy, 2024 [https://www.sciencedirect.com/science/article/pii/S0301420723012989]). This provides you a good empirical aspect/grounding for "escalation" and "criticality" scenario definitions.

6. For Table 5, Cohen's collapses due to marginal class degeneration. To avoid misinterpretation, consider reporting raw classification accuracy (po​) or the Matthews correlation coefficient alongside κ.

7. Finally, sec 5 & sec 6 have a lot of rhetorical inflation and repetitive metadiscourse. Please  thoroughly revise both to be less AI/LLM sounding to be more direct and focused on important/tangible parameters and policy trade-offs, rather than philosophical abstractions of the epistemological beauty of synthetic modeling.
Also the intro section has a few overly AI/LLM-sounding phrases that need to be fixed, such as "The Turkish case is therefore deployed not as a geopolitical narrative device, but as a portfolio of exposure archetypes against which a general stress-testing methodology can be calibrated and, in principle, falsified [10]"
Also, this needs to be rewritten in the Intro too because it's too AI/LLM'ish: "What began as a taxonomic exercise, cataloguing which elements are scarce, substitutable, or geographically concentrated, has evolved into a demand for dynamic instruments capable of quantifying how mineral price systems behave once geopolitical stress exceeds the threshold of ordinary market absorption [1]. This evolution mirrors, almost precisely, the intellectual trajectory that reshaped financial risk management after successive currency, banking, and commodity crises: static exposure metrics gave way to regime-conditional, scenario-based architectures"

8. At least 3 sentences should be dedicated to telling us defense and industrial importance of Boron, Chromium, and Turkish-specific REEs

Author Response

Dear Reviewer,

Thank you for your careful and constructive evaluation of our manuscript.

Your comments helped us improve the methodological consistency, calibration framing, policy relevance, statistical interpretation, and defense-critical-minerals context of the study.

Please find attached our detailed point-by-point response matrix, together with the corresponding revisions made to the manuscript.

Sincerely,

Hasan Tolga UNAL

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This well-written manuscript was about the transfer of financial risk modelling to the application of critical minerals, for the use of investment/financial institutions. The abstract makes it clear that the modelling of risk is by simulation and for method development. The introduction clearly articulates the context of commodity choices for case study investigation and proceeds to systematically and logically describe the research approach, which is very necessary for a technical paper of this kind. Since methodological development is the key ambition of the paper, I am a useful reviewer as someone interested in critical minerals, coming to these kinds of equations for the first time. The ease with which I (not an economist) access the modelling information is likely to be representative of many users of the manuscript. I was not always able to process the meaning of the equations where parameters were not completely or clearly described. However, the results are summarised very neatly by the assertion that ‘a transplanted financial-econometric diagnostic architecture recovers, without being told to, exactly the exposure ordering that the strategic-mineral literature has argued for on qualitative grounds alone’ (lines 466 – 468). This is somewhat a function of the input parameters that are premised on qualitative knowledge and therefore premised to show the intended outcomes. Nevertheless, the quantification of otherwise qualitative evidence is a necessary mechanism by which to ‘prove’ that close attention should be paid to criticality of type H2. Since the modelling is for financial purposes, it does not seek to specifically identify and mitigate any risk. However, it would be interesting to see how this work would be used by those more entrenched in mineral criticality. I found the discussion section 5.2 about nonlinearity very compelling and likely to prompt further research about the point that escalation of risk plateaus, and at what point along that plateau the ‘real’ system (using observed rather than simulated variables) reaches a critical point. This is included in the second of the follow-on research strands of empirical validation, suggested at the end of the discussion, which are all very nicely framed. Since this research can clearly lead to further understanding and provide a foundation for future research, I strongly support its publication.

My minor queries focus primarily on the methodology:

Line 80. It is not entirely transparent what are the two diagnostic layers – are these regime-switching and structural-break methods, or nonlinearity and threshold-dependent persistence?

Line 153. Can you explain the term logistics friction, which is neither as intuitive as the other variables nor as present in the critical minerals discourses?

Line 159-161. Can you insert ‘(w)’ after weighting in the text and ‘(Rt)’ after latent stress index, in order to complete the text description of the equation? I am assuming I have these correct.

Lines 169-175 describe the location and overall character of the case studies. I think it is in the wrong place and would recommend it is moved up to the end of section 2.1. It then precedes the modelling detail, which would flow nicely from line 168/169 into section 3.

Line 226. Some of the terms in the equation remain undefined in the text. Are they standard terms that modellers would know but other readers would not? Are we to assume that they are constants/integers?

Line 229. Rt was used first on line 161, without proper definition. I assume it is latent stress index again, but the heading of 3.3 also states regime path and return generation which could be an R. Some clarity is needed for the reader.

Lines 229-235. This is one sentence – could it please be broken into multiple sentences to aid clarity?

Line 237. Does the term st* denote true regime substitution rigidity, rather than just true regime? If not,  the great similarity of parameters St and st* can be confusing.

Line 239. One of the terms in the equation remains undefined, as with line 226.  The rest I found in table 2. It is clear that the weightings are proportional and unit-free, but it is not clear how the bottom three variables are calibrated. And can a footnote to the table be added to explain what is meant by is AR persistence?

Line 263. Is there a typo in the description of the variable? Division line missing under max?

Line 270. Is there a typo in the equation? Division line missing under sup?

Lines 335-336. Is the notation above the p supposed to be the same on the two lines – one of them appears stretched relative to the other? By comparison with Table 5, I think the typo is with p11 on line 335.

Line 397. Is this a footnote to the table that has been merged into the text accidentally?

Author Response

Dear Reviewer,

Thank you for your careful, constructive, and encouraging evaluation of our manuscript.

Your comments helped us improve the clarity and accessibility of the methodological explanations, parameter definitions, equations, notation, and table notes.

Please find attached our detailed point-by-point response matrix, together with the corresponding revisions made to the manuscript.

Sincerely, 

Hasan Tolga UNAL

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Na

Author Response

Dear Reviewer,

Thank you for your minor revision.

In response, the methodological explanations accompanying the figures and tables have been expanded, and all additions are highlighted in red in the revised manuscript.

Sincerely, 

Hasan Tolga UNAL

Reviewer 2 Report

Comments and Suggestions for Authors

Substantial improvement. You've taken my feedback seriously, and the paper is much stronger. The distinction between a synthetic methodological demonstration and an empirical assessment is now much better, and your treatment of the hypotheses is well-qualified. From a strategic studies and mineral-security perspective, this is a useful/compelling proof of concept.

I'm recommending acceptance with minor fixes, but we need to nail down these 2 details. Consider these please:

1. Question about Equation 2: For your autoregressive specification it seems to use a contemporaneous term. I think you might need to show the lagged term (x*_{k,t-1}) ... I suspect you intended this and used it in your code. Just double check this since I'm not a total expert in this aspect.

2. For the values in Table 3, are these the latent calibration targets or the realized means after the logistic transformation? Please clarify/fix

Author Response

Dear Reviewer,

Thank you for your constructive comments. In response;

Comment 1: 

That is correct that the autoregressive specification should contain the lagged state x^{*}_{k,t-1}, rather than the contemporaneous state x^{*}_{k,t}, on the right-hand side. We have corrected Equation (2) accordingly. The revised equation now accurately represents the mean-reverting AR(1) process used in the computational implementation.

Comment 2:

 

Thank you for requesting this clarification. The values reported in Table 3 are scenario-specific calibration targets m_{k,s}, not realized means calculated after the logistic transformation. These targets are mapped onto the unbounded Gaussian scale through c_{k,s}=\log[m_{k,s}/(1-m_{k,s})] and are used to center the autoregressive processes in Equation (2). Because Equation (3) applies a nonlinear logistic transformation and the simulated processes include stochastic innovations, the realized means of the bounded drivers may differ slightly from the reported targets. We have revised the accompanying paragraph, the title of Table 3, and its note to make this distinction explicit.

All additions are highlighted in red in the revised manuscript.

Sincerely,

Hasan Tolga UNAL