Terms of Trade and the Structural Sustainability of the Mining Sector in a Resource-Dependent Economy

Abstract

This study investigates whether external terms of trade (TOT) and mining-sector GDP in Peru share a stable long-run relationship. Although mining has played a central role in the country’s growth trajectory, its performance remains highly exposed to international price cycles, raising questions about its structural sustainability under persistent external shocks. Using quarterly data for 2001–2024, the analysis applies Johansen cointegration techniques and estimates a bivariate Vector Error Correction Model (VECM) to evaluate long-run co-movement and short-run adjustment dynamics. The results identify a single cointegrating relationship in which mining GDP acts as the primary adjustment variable, gradually correcting deviations from long-run equilibrium, while short-run TOT shocks do not exert direct contemporaneous effects on mining growth. The estimated speed of adjustment is low, suggesting a prolonged convergence process consistent with the capital-intensive and rigid structure of the mining sector. Robustness exercises—including estimation with heteroskedasticity and autocorrelation consistent (HAC) standard errors and an extended specification incorporating gross fixed capital formation—confirm the stability of the long-run relationship. These findings indicate that the structural sustainability of mining output depends on the interaction between external price dynamics and the sector’s capacity to adjust to persistent international shocks. The study concludes that, in the Peruvian case, structural sustainability in the mining sector is not determined solely by global price trends, but is also conditioned by domestic productive and institutional factors that govern the speed of adjustment in the presence of sustained external volatility.

1. Introduction

The recent evolution of Peru’s mining sector reflects a combination of sustained productive expansion, substantial investment inflows, and continued exposure to international price cycles. While mining has remained a central pillar of economic growth over recent decades, its trajectory points to a persistent structural reliance on external conditions that lie outside the control of the domestic economy [1,2,3]. Within this context, fluctuations in the external terms of trade (hereafter, terms of trade or TOT) occupy a particularly prominent role. Beyond capturing movements in the relative prices of exports and imports, TOT shapes, in a systematic manner, the incentive structure, revenue streams, and constraints under which the extractive sector operates [4,5]. For small open economies such as Peru, these external price movements constitute a key transmission mechanism for international shocks, directly influencing whether trade-intensive sectors—mining foremost among them—can sustain growth trajectories compatible with structural sustainability [6,7].

The relevance of this dependence becomes more pronounced when mining’s position within Peru’s productive and export structure is taken into account. According to official data from the Ministry of Energy and Mines (MINEM, Lima, Peru), the sector generates 66.5% of total export value [8], contributes close to 17% of GDP [9], and plays a decisive role as a source of fiscal revenue, private investment, and foreign direct investment [8,10]. At the same time, this macroeconomic prominence coexists with a marked sensitivity to volatility in global commodity markets, raising persistent concerns regarding the sector’s ability to maintain a stable growth path under repeated external disturbances [2,11,12].

Over the last two decades, real mining GDP (2007 = 100) expanded from 29.4 billion soles in 2000 to 72.4 billion soles in 2024 [9]. This expansion, however, unfolded alongside pronounced cyclical fluctuations closely aligned with international price movements for copper, gold, and other metallic minerals. Such volatility is visible not only in the sector’s output performance, but also in the behaviour of investment flows, fiscal revenues, and production-expansion decisions [12,13]. The lack of a smooth or stable growth trajectory suggests that mining performance cannot be explained solely by internal dynamics, but instead requires explicit consideration of external shocks and the mechanisms through which these shocks are absorbed—or, in some cases, amplified—within the sector.

Periods of improving TOT are typically associated with higher mining revenues and a more accommodating macroeconomic environment, although they may also coincide with exchange-rate appreciation, increased public spending, and resource reallocations that give rise to structural tensions [14,15,16]. Conversely, sustained deteriorations in TOT tend to restrict investment, tighten financing conditions, and heighten volatility in mining GDP [17]. In both scenarios, the central issue extends beyond the immediate direction of the impact. What ultimately matters is the sector’s capacity to correct the imbalances generated by these disturbances and to reconverge towards a path consistent with its long-run equilibrium [7].

Existing research on resource-based economies and Dutch disease has extensively documented the dependence of mining activity on external cycles [18,19,20]. Nevertheless, much of this literature has concentrated either on the aggregate effects of TOT on overall economic growth or on the spillovers from mining expansion to other sectors. As a result, mining GDP itself is often treated as a conduit for transmitting external shocks to the broader economy, rather than as an endogenous variable characterised by its own dynamic adjustment processes and structural sustainability constraints.

This omission is particularly relevant in the Peruvian case, where the high concentration of exports in metallic minerals has intensified the sensitivity of economic growth to international price cycles. Assessing whether the mining sector maintains a stable long-run relationship with TOT, and whether it systematically corrects deviations generated by international shocks, allows one to move beyond a purely cyclical reading of growth. While most existing studies examine the relationship between TOT and aggregate GDP, there remains a marked scarcity of sectoral evidence that explicitly analyses the dynamic adjustment mechanisms of mining output in response to persistent external disturbances [7,20].

Against this background, the present study contributes to the literature by shifting the focus from aggregate outcomes to the mining sector itself, treating mining GDP as an endogenous variable with its own long-run adjustment dynamics. In addition, the analysis exploits an extended quarterly dataset spanning more than two decades (2001–2024), allowing the empirical assessment to cover multiple commodity cycles and major global shocks within a unified long-run framework.

Starting from the notion that if TOT influences aggregate economic performance, it is reasonable to expect them to shape the evolution of key productive sectors as well, this study seeks to address an existing analytical gap. Accordingly, it examines whether a stable long-run equilibrium can be identified between Peru’s mining-sector GDP and the TOT, and whether the sector systematically adjusts its trajectory when deviations emerge from movements in the TOT themselves.

Within an open-economy setting, TOT affects mining activity through several macroeconomic channels, including fiscal, monetary and aggregate-demand mechanisms. A favourable external environment typically strengthens public finances, improves investment conditions and contributes to macroeconomic stability, thereby supporting sectoral expansion; by contrast, a prolonged deterioration in TOT tends to undermine these mechanisms and constrain sectoral performance [21,22,23]. Although these channels are not modelled explicitly in the present study, it is assumed that, when a stable long-run relationship exists between TOT and mining-sector performance, transmission effects are implicitly incorporated into the series.

In brief, the objective of the research is to assess whether external TOT sustains a long-run relationship with Peru’s mining-sector GDP and to analyse the implications of this relationship for structural sustainability. To achieve this objective, the analysis applies Johansen cointegration methods together with a Vector Error Correction Model (VECM), allowing the identification of shared long-run dynamics and the measurement of how rapidly the system adjusts following external shocks [24,25]. Establishing the existence of such a link implies that the trajectory of the mining sector is not driven solely by internal forces, but remains anchored to a long-run relationship with external TOT, thereby shaping its capacity to sustain growth under conditions of heightened international volatility.

Finally, the findings are aligned with SDGs 8, 9 and 12 in that they provide an empirical basis for understanding how macroeconomic equilibria are translated into sectoral dynamics over time. From a policy perspective, the analysis offers useful guidance for economic authorities, development agencies and cooperation institutions by highlighting that the key challenge lies not in avoiding external exposure, but in managing the adjustment process it entails. In this sense, the results suggest that the sustainability of the mining sector depends on the institutional and productive conditions that shape its capacity to absorb external shocks and to reconverge towards equilibrium, as a matter of structural sustainability.

1.1. Empirical Background

Consistent with the foregoing analysis, studies that examine the relationship between external TOT and mining GDP in a direct manner, adopting an explicitly sectoral and dynamic perspective, remain scarce. A large share of the literature has focused on aggregate economic dynamics or on the behaviour of broad baskets of primary commodities, offering valuable insights into how external shocks are transmitted through key macroeconomic variables such as the exchange rate, fiscal accounts or investment [26,27,28,29]. However, these contributions rarely treat mining GDP as an endogenous variable subject to its own processes of adjustment and long-run convergence, which limits their ability to explain the internal dynamics of the extractive sector. In this respect, although the existing studies do not replicate the same focus adopted here, they do provide a useful conceptual and empirical framework for identifying transmission channels and correction mechanisms that also shape the trajectory of the mining sector.

More recent investigations have advanced the analysis of the nexus between TOT and economic activity by shifting the emphasis from levels to volatility and to the composition of relative prices, a distinction that is crucial for assessing intertemporal adjustment processes. At the aggregate level, evidence for Southeast Asian countries confirms that TOT are linked with growth, although both the direction and magnitude of the effect depend critically on productive structure and the degree of external exposure, reinforcing the need to move away from universal interpretations [30]. In resource-specialised economies, it has been shown that volatility in commodity TOT weakens sectoral performance by interacting with financial constraints, thereby amplifying losses during adverse phases of the external cycle [31]. In India, for example, certain trade-policy decisions—such as export restrictions—introduce additional sources of regulatory uncertainty that affect market stability and production planning [16].

A related line of inquiry moves beyond aggregate measures and decomposes TOT into narrower baskets—such as energy, manufactured goods, and primary commodities—in order to identify differentiated effects. This approach is particularly informative for sectors with a high dependence on imported inputs. Empirical evidence from Australia, Chile, Norway, Indonesia, and South Africa indicates that commodity price movements contain predictive information about future economic growth, although the strength and direction of this signal depend heavily on each country’s export composition and import requirements [32,33].

Findings for the United States further illustrate this heterogeneity: while technology-related components of TOT are associated with positive growth effects, categories linked to fuels and food exhibit negative relationships [34]. These results highlight that the economic impact of TOT cannot be inferred from their aggregate movement alone, but is shaped by their internal composition. This distinction is particularly relevant for small open economies with a strong concentration in metallic exports, where mining GDP evolves under a fragile equilibrium between external revenue gains and the rising costs of imported inputs and global financial conditions.

Recent evidence for small open economies with high mining dependence—such as Mongolia—and for emerging economies—including Brazil, Chile, Mexico and South Africa—converges on the view that external shocks are transmitted to sectoral performance through combinations of TOT movements, exchange-rate dynamics and input–output linkages. As a result, the final impact is not exhausted by the price of the exported mineral itself, but is amplified by each economy’s productive and trade architecture [35,36,37]. Recent episodes, such as the Russia–Ukraine conflict and the COVID-19 pandemic, have reinforced this pattern by generating disruptions in energy, machinery and imported capital goods, raising operating costs, delaying projects and constraining investment [38,39,40].

This pattern becomes more pronounced when external shocks coincide with logistical frictions and exchange-rate pressures, increasing volatility and planning uncertainty, particularly in energy and metals markets [41,42]. In response, studies for China and Peru document adjustments at the micro and meso levels, such as supply-chain reconfiguration and supplier diversification [43,44,45]. However, these contributions tend to focus on organisational and productive dynamics rather than on the analysis of mining GDP as an endogenous variable within a long-run macroeconomic adjustment framework. Taken together, these findings suggest that mining-sector vulnerability to external disturbances reflects an intertemporal balance between export revenues and imported costs, whose stability depends critically on macroeconomic absorption capacity and the exchange-rate channel [42,46,47].

Beyond the level of the shock itself, studies for Latin American countries—e.g., in Chile, Brazil and Mexico—show that the response of the mining sector is nonlinear and heterogeneous, with differentiated effects on employment, wages and costs depending on productive structure and labour-market frictions [37,48]. From a methodological standpoint, the literature has frequently relied on input–output approaches, SVAR/BVAR models and DSGE frameworks for small open economies in order to capture complex transmission mechanisms [35,37,49,50]. Nevertheless, these approaches tend to prioritise aggregate or multivariate dynamics, relegating the explicit analysis of mining output adjustment as an endogenous variable.

In this line, empirical results converge on three recurrent consequences: (i) higher costs of critical inputs and cost escalation [38,51]; (ii) postponement or rescaling of investment [38,52]; and (iii) greater volatility of mining output, particularly when TOT and the exchange rate operate simultaneously as transmission vectors [42,53]. Yet a systematic treatment of the link between external prices and mining performance from a long-run dynamic adjustment perspective remains largely absent, even where partial approaches exist in mining and financial markets [54].

Overall, although the literature has extensively documented the effects of TOT on mining-intensive economies, a specific gap persists in the analysis of mining GDP as an endogenous variable subject to its own long-run adjustment process in response to persistent external shocks, particularly within parsimonious empirical frameworks. In the Peruvian case, available studies focus on mineral price shocks and their effects on aggregate output or on associated macroeconomic imbalances—such as Dutch disease or exchange-rate appreciation—without explicitly assessing whether the mining sector converges towards a stable equilibrium relationship with external TOT [10,55,56].

In this context, it is relevant to note that, within natural resource economics, the empirical application of VECM and ECM frameworks has become a widely accepted empirical practice for analysing dynamic and long-run relationships between key variables associated with commodity-intensive sectors. These approaches have been repeatedly employed to study interactions between international commodity prices, aggregate output, sectoral production, fiscal revenues and external shocks, allowing short-run adjustment mechanisms and long-run equilibria to be captured simultaneously. The flexibility of the ECM–VECM framework is particularly well suited to contexts characterised by high external volatility and episodes of global disruption—such as those associated with the COVID-19 pandemic or abrupt shifts in commodity markets—inasmuch as it allows structural anchoring between variables to be isolated without imposing full causal identification or requiring the explicit modelling of all transmission channels [57,58,59].

At the international level, while sectoral and comparative approaches do exist, they display substantial methodological heterogeneity and rarely incorporate parsimonious bivariate cointegration schemes aimed at isolating long-run sectoral adjustment, an aspect still underexplored in empirical studies [60,61,62]. In this sense, the adoption of a Johansen cointegration approach and a bivariate VECM in the present study fits within this established methodological tradition, while being specifically oriented towards examining the long-run link and adjustment process between external TOT and mining-sector GDP through an explicit lens of sectoral structural sustainability. This empirical strategy is particularly pertinent in Latin American economies with high mining dependence, where identifying common trends and speeds of correction in response to external shocks constitutes a key input for assessing the sector’s structural sustainability.

1.2. Theoretical Background

In open and highly exposed economies, the external terms of trade (TOT)—understood as the relative price between exports and imports—play a practical role as a signal that shapes disposable income, production costs and, ultimately, the way resources are distributed across sectors [63]. When TOT improve, foreign purchasing power usually expands and external constraints tend to ease. When they deteriorate for a prolonged period, the opposite occurs: margins tighten and essential imported inputs become more expensive [64]. Recent research has moved beyond analysing the level of TOT alone and has increasingly focused on their volatility, stressing that unstable price environments tend to weaken investment decisions and economic activity by increasing macroeconomic and financial uncertainty [65]. From this perspective, TOT can be interpreted as a summary indicator that reflects, at the same time, income gains from exports and cost pressures originating abroad.

In this study, the economic relevance of TOT is approached in a straightforward manner, emphasising their dual role. On the one hand, they affect external income and liquidity; on the other, they transmit changes in the cost of imported inputs to the domestic economy. Because TOT reflect broad movements in international relative prices, they provide useful information about export revenue prospects, dependence on imported inputs and pressures on factor allocation. In practical terms, favourable TOT episodes usually improve access to foreign currency, while adverse movements restrict it and raise operating costs in activities that rely heavily on imported energy, fuels, machinery and capital goods—mining being a clear example [64]. This interpretation guides the empirical strategy adopted in the paper and motivates the use of TOT as a long-run external reference point for primary-exporting sectors in small open economies, without attempting to model each transmission channel separately.

At the macroeconomic level, the link between TOT and GDP is commonly discussed through a set of well-known mechanisms. A first channel operates through income, as higher export prices increase revenues and fiscal resources, supporting both public and private spending. A second channel works through costs: higher prices of key imports—such as energy, machinery and intermediate inputs—reduce margins, lower effective productivity and constrain supply. A third mechanism is related to the real exchange rate and sectoral reallocation, since sustained TOT booms often lead to currency appreciation and a shift of resources towards non-tradable activities, a process frequently associated with Dutch disease dynamics. Finally, financial conditions also matter, as favourable external environments tend to reduce risk premia, ease access to external financing and relax credit constraints [2,21,30,66,67]. Taken together, these channels help explain why similar TOT shocks can generate very different outcomes across economies, depending on their productive structure and financial depth, an issue that is particularly relevant for resource-dependent countries.

From a sectoral point of view, mining is influenced by TOT even when external shocks do not originate within the sector itself. The transmission takes place through several routes: export revenues and their effects on domestic demand and the real exchange rate, the cost of critical imported inputs—especially energy, fuels and heavy machinery—and financing conditions linked to the external cycle and public investment [21,29,68]. For this reason, the analytical framework commonly used to study the aggregate relationship between TOT and GDP can also be applied, without inconsistency, to the behaviour of mining GDP [30,69,70,71].

Within this context, cointegration techniques and error-correction models are particularly appropriate, as they allow long-run co-movement to be distinguished from short-run dynamics without requiring a fully specified structural causal model [72,73]. When variables are cointegrated, the associated Vector Error Correction Model includes an adjustment term that captures the speed at which deviations from the long-run equilibrium are corrected. Statistically significant coefficients indicate systematic reversion towards the equilibrium path [74]. This approach has been widely applied to primary and extractive sectors across different economies, documenting stable forms of external anchoring alongside heterogeneous adjustment speeds [7,75,76]. From an empirical standpoint, it prioritises the identification of long-run linkages and adjustment processes, deliberately abstracting from intermediate transmission channels in order to avoid conditioning on potentially endogenous mechanisms.

When the analytical framework is applied specifically to the mining sector, it leads to three concrete implications that are relevant from an empirical standpoint. First, finding cointegration linking external TOT with mining output should be read as evidence that both variables share a common long-term trajectory. This shared path reflects the joint influence of export revenues, imported input costs and relative-price adjustments operating simultaneously, rather than the action of a single identifiable channel [21,77]. Importantly, this interpretation does not require isolating or modelling each transmission mechanism separately, but instead relies on their combined effect as revealed by the long-run equilibrium.

Second, the estimated error-correction term becomes informative about how the sector reacts when external shocks push it away from its long-run path. In this sense, the size and significance of the adjustment coefficient offer a practical measure of the mining sector’s ability to absorb and correct external disturbances. A faster pace of convergence is usually associated with stronger structural buffers, while a slow adjustment process points to greater exposure and fragility in the face of persistent shocks [77].

Third, short-term movements need not follow a uniform pattern. In some episodes, mining activity may respond primarily to changes in the cost of imported inputs, whereas in others it may be more closely aligned with fluctuations in export prices. The relative dominance of these forces varies across time, and it is their interaction that ultimately shapes observed short-run outcomes [78].

Building on the approach proposed in [7], this study adopts an operational view of structural sustainability, treating it as an empirical feature that arises from the observed dynamics of the system rather than as an abstract or normative concept. In practical terms, this notion is captured through three complementary dimensions. The first is the presence of a stable long-run linkage between mining GDP and external TOT, which serves as an external reference point for the sector. The second is the behaviour of the error-correction mechanism in the mining GDP equation, whose sign and statistical relevance indicate whether the sector actively adjusts when disequilibria emerge. The third concerns the speed at which such corrections take place, reflecting how rapidly deviations from the long-run path are reduced. Considered jointly, these elements allow for a concise and internally consistent quantitative characterisation of structural sustainability in the mining sector of a small, resource-dependent economy.

2. Materials and Methods

To fulfil the objective of this research, Johansen’s cointegration test and the estimation of a VECM are employed. The empirical strategy is framed within a quantitative and applied perspective, combined with an ex post facto design, since the analysis is based exclusively on data that have already been realised, without introducing any form of experimental intervention on the variables under study. The dataset consists of 96 quarterly observations per variable, spanning the interval from 2001 to 2024, and expressed as index numbers with a base year of 2007, as compiled and disseminated by the Central Reserve Bank of Peru (BCRP, Lima, Peru). The dataset used for the empirical analysis is available in the Supplementary Materials.

The sample begins in 2001 in order to capture the global trade regime that emerged following China’s entry into the World Trade Organization (WTO, Geneva, Switzerland), an event widely recognised as a turning point that reconfigured patterns of commodity demand and relative prices at the international level. This time window encompasses an entire commodity cycle, ranging from the pre-boom phase to the supercycle itself, followed by periods of correction and adjustment, as well as the most recent episodes of global disruption.

With respect to variable construction, the outcome variable is defined as real GDP of the mining sector, whereas the explanatory variable corresponds to the external terms of trade (TOT), measured as the quotient between the Peruvian export price index and its import price index [71]. Consistent with a small open economy setting, TOT are interpreted as being primarily shaped by conditions prevailing in international markets rather than by domestic production dynamics. In econometric terms, however, no strict exogeneity restriction is imposed within the estimated VECM; the adjustment pattern is allowed to be determined empirically.

Given that the original series are expressed as indices, the variables are transformed into logarithms. This transformation facilitates the interpretation of the estimated coefficients, as changes can be read as percentage variations or elasticities, allowing a clearer assessment of the magnitude of the response of mining GDP to movements in TOT.

From an econometric standpoint, the empirical exercise corresponds to an error-correction model (ECM). As noted by Engle and Granger (1987) and Johansen (1995) [24], a single-equation ECM is equivalent to a bivariate VECM when a single cointegrating vector exists, as discussed in [77]. In this study, however, the system formulation is employed to test for cointegration in logarithms using Johansen’s methodology, both for reasons of econometric implementation and to characterise adjustment dynamics within the joint system, including whether the TOT equation displays a statistically meaningful error-correction response under alternative specifications.

It should be noted that the use of a VECM does not impose econometric exogeneity a priori. Consequently, the presence of statistically significant adjustment terms in more than one equation should not be interpreted as evidence of reverse economic causality, but rather as part of the system’s correction dynamics. In this sense, the parsimony of the system responds to an identification criterion aimed at characterising long-run co-movement consistent with external anchoring, rather than at exhaustively reconstructing all transmission channels.

The integration properties of the series are assessed using the ADF and KPSS tests, considering up to four lags, in line with standard practice for quarterly data. This step confirms that the variables display an order of integration consistent with I(1) processes. In addition, the number of lags in the system is determined through the selection of the VAR order in levels, using the AIC, BIC and HQC information criteria, a procedure consistent with Johansen’s approach, given that the VECM constitutes a reparameterisation of that system.

Finally, in order to control for the presence of an extraordinary and non-recurrent shock, a dummy variable associated with the COVID-19 pandemic period is included. This dummy isolates the transitory impact of an exogenous disturbance of exceptional magnitude on productive activity, preventing this episode from distorting the estimation of short-run dynamic adjustment mechanisms and the identification of the long-run equilibrium relationship between mining GDP and TOT. Its inclusion responds to a strictly econometric criterion and does not require imposing exogeneity restrictions on TOT within the estimated system. Under these specifications, the model can be expressed as follows:

$$∆ ln({GDP}_{min,t}) = {\alpha }_0+\sum _{i=1}^{p-1}{\beta }_i∆ ln({GDP}_{min,t-i})+\sum _{j=1}^{p-1}{\gamma }_j∆ ln\left({TOT}_{t-j}\right)+\delta D_{COVID,t}+\lambda {EC}_{t-1}+{\epsilon }_t$$

where:

• ∆ denotes the first difference operator.
• $ln\left({GDP}_{min,t}\right)$ refers to the natural logarithm of real GDP of the mining sector at time t.
• $ln\left({TOT}_{t-j}\right)$ denotes the natural logarithm of the terms of trade (TOT) lagged j periods.
• p indicates the optimal lag length selected according to standard information criteria.
• β_i and γ_j represent short-run dynamic effects associated with mining GDP and TOT, respectively.
• ${EC}_{t-1}$ corresponds to the error-correction term derived from the estimated cointegrating relationship.
• $\lambda$ measures the speed at which deviations from the long-run equilibrium are corrected.
• $D_{COVID,t}$ is a binary variable equal to 1 during the period affected by the COVID-19 pandemic and 0 otherwise.
• $\delta$ captures the temporary impact of the pandemic on mining GDP growth.
• α₀ denotes the intercept term.
• ε_t represents the stochastic disturbance term.

Within a small open economy perspective, TOT provide an economically meaningful internationally driven reference for the long-run relationship, while the VECM estimation allows the data to reveal whether the adjustment dynamics are concentrated in mining GDP or shared across equations. Under this interpretation the error-correction term is defined as:

$${EC}_{t-1}= c + \theta ln\left({TOT}_{t-1}\right) - ln\left({GDP}_{{min}_{t-1}}\right)$$

This normalisation, widely used within Johansen’s (1995) cointegration framework [77], allows a positive coefficient on the error-correction term (λ > 0) to be interpreted as evidence of convergence towards the long-run equilibrium. Within this methodological framework, the empirical analysis is structured around hypotheses that assess both the long-run relationship between mining GDP and the terms of trade, and the sector’s capacity to adjust in response to transitory deviations from equilibrium (see Table 1).

Table 1. Research Hypotheses.

Hypothesis	Formulation	Expected Outcome
H1. Long-run relationship between mining GDP and TOT	H0: There is no cointegration between mining GDP and TOT (r = 0). H1: There is at least one cointegrating vector (r ≥ 1).	Reject H0 to confirm the existence of a long-run relationship.
H2. Adjustment of mining GDP to equilibrium deviations	H0: The error-correction coefficient in the mining GDP equation is equal to zero (λ = 0). H1: The error-correction coefficient is different from zero (λ ≠ 0).	Reject H0 to confirm that mining GDP adjusts to deviations from the long-run equilibrium.

3. Empirical Results

Before turning to the formal econometric tests, it is useful to clarify the logic that guides the empirical sequence adopted in this section. Given the time-series nature of the data and the focus on long-run external anchoring, the analysis proceeds in a stepwise manner, beginning with the statistical properties of the variables and the temporal structure of the system. Establishing these preliminary conditions is essential to ensure that the subsequent cointegration and adjustment results are interpreted within a coherent and internally consistent framework.

3.1. Testing for Unit Roots and Selecting the Lag Structure

In order to establish a sound empirical basis for the cointegration analysis, Augmented Dickey–Fuller and the Kwiatkowski–Phillips–Schmidt–Shin procedures are implemented for lnGDP_min together with lnTOT, considering both their level representations and their first-difference transformations (see Appendix A—Table A1). As a starting point, the ADF tests conducted in levels—under specifications that include both an intercept and a deterministic trend—fail to provide statistical grounds for rejecting the presence of a unit root in either series. For real mining GDP, the computed ADF value equals −2.724 and is associated with a p-value of 0.227, whereas for TOT the corresponding statistic amounts to −2.965 with an associated probability of 0.142. Taken at face value, these outcomes indicate that the two series exhibit persistent non-stationary behaviour when expressed in levels, a pattern that is consistent with underlying long-run movements.

This conclusion is further corroborated by the KPSS evidence, where stationarity is statistically rejected for both variables in their level form. Specifically, the KPSS statistic reaches 0.203 for lnGDP_min and 0.192 for lnTOT, with associated significance levels of 0.017 as well as 0.024, respectively, thereby confirming the lack of stationarity in levels.

Once the analysis shifts to first differences, the statistical profile changes markedly. The ADF tests applied to the differenced series clearly overturn the unit-root null for both mining output and TOT, yielding statistics of −5.134 (p-value = 0.0001) and −4.090 (p-value = 0.0065), respectively. In parallel, the KPSS tests for the differenced variables no longer reject the hypothesis of stationarity, with test statistics of 0.044 for lnGDP_min and 0.068 for lnTOT, each linked to p-values exceeding the 10% threshold. Considered jointly, this set of results indicates that lnGDP_min and lnTOT follow integrated processes of order one, I(1). This statistical property legitimises the application of cointegration methods to explore their long-run linkage, and provides a coherent justification for adopting an error-correction specification as the core empirical framework of the analysis.

The selection of the lag order for the VAR system is carried out by jointly considering the AIC, BIC and HQC information criteria. As shown in Table A2 in Appendix A, the results do not converge on a single specification: while the AIC suggests a lag order of four (p = 4), the BIC and HQC favour a slightly more parsimonious structure with three lags (p = 3). Given the quarterly frequency of the series and the nature of the phenomenon under analysis—characterised by cyclical dynamics, persistent external shocks and gradual adjustment processes—alternative specifications with both lag orders are estimated. A comparison of the results indicates that the four-lag model provides a more adequate representation of short-run dynamics, without compromising system stability or the identification of the error-correction mechanism. In particular, this specification captures intertemporal adjustment processes in mining GDP in response to external disturbances with greater precision, while remaining consistent with econometric practice in cointegration studies using long-horizon quarterly macroeconomic series. On this basis, the main empirical analysis proceeds with the specification including p = 4 lags, which strikes an appropriate balance between parsimony and explanatory power.

3.2. Cointegration Results

Under the specification adopted earlier, Johansen’s cointegration test was implemented using a lag structure of four quarters (p = 4). The test was conducted allowing for a constant in the long-run relationship, a specification suitable for I(1) macroeconomic series that do not exhibit a pronounced deterministic trend. This approach captures a stable mean equilibrium between the variables without introducing spurious drift into the system, thereby preserving both parsimony and interpretability. The test results provide clear evidence in favour of a single long-run equilibrium relationship between mining GDP and the terms of trade. The null hypothesis of no cointegration (r = 0) is strongly rejected, as indicated by both the trace statistic (24.652, p = 0.0101) and the maximum eigenvalue statistic (17.931, p = 0.0212). In contrast, the null hypothesis of at most one cointegrating vector (r ≤ 1) cannot be rejected, with trace and maximum eigenvalue statistics of 6.721 and corresponding p-values above conventional significance levels. Taken together, these results indicate the presence of one cointegrating vector, as reported in Table 2.

Table 2. Cointegration Results Based on the Johansen Procedure.

Null Hypothesis (r)	Eigenvalue	Trace Test Statistic	Trace Test p-Value	Max-Eigen Statistic	Max-Eigen p-Value
r = 0	0.17037	24.652	0.0101	17.931	0.0212
r ≤ 1	0.06762	6.721	0.1461	6.721	0.1459

Estimations obtained from author-run procedures using BCRP data and GRETL 2025c.

Establishing r = 1 provides the necessary basis for modelling the joint dynamics of the system through a vector error-correction framework. Accordingly, the analysis proceeds with the estimation of a bivariate VECM, where the error-correction term captures the long-run equilibrium linkage and serves as the mechanism through which short-run deviations are gradually corrected. This approach allows for a precise evaluation of whether mining GDP adjusts systematically in response to disequilibria, while leaving the adjustment pattern to be determined by the estimated error-correction coefficients within the VECM framework. In this way, the cointegration results complete the first stage of the econometric strategy and motivate the subsequent analysis of adjustment dynamics.

3.3. Error-Correction Estimates from the VECM

Once the existence of a cointegrating relationship between the variables is confirmed, the error-correction mechanism (ECM) derived from the bivariate VECM system is estimated. This estimation links short-run dynamics with the process of convergence towards the long-run equilibrium, identifying the speed at which mining GDP corrects deviations associated with movements in the TOT, and, in parallel, exploring how the two series evolve jointly over time under a deliberately restrained econometric specification that privileges clarity over excessive modelling complexity.

The Δln(GDP_min) equation displays a clear and robust autoregressive structure. The first three lags of mining GDP growth exhibit negative and highly significant coefficients (−0.598, −0.587 and −0.406; p < 0.001), providing evidence of an internal correction mechanism whereby episodes of relatively strong expansion tend to moderate in subsequent quarters (see Table 3). This pattern is consistent with the cyclical nature of the mining sector and with the presence of operational and investment lags that shape short-run adjustment. By contrast, the lags of Δln(TOT) are not statistically significant in this equation (p > 0.61 in all cases), indicating that, once the sector’s own dynamics and the long-run relationship are accounted for, recent movements in TOT do not generate immediate or persistent effects on mining GDP growth.

Table 3. Mining GDP adjustment equation (VECM).

Variable	Coefficient	Std. Error	t-Statistic	p-Value	Sig.
ΔlnGDPmin(−1)	−0.598381	0.0829361	−7.215	1.89 × 10−10	***
ΔlnGDPmin(−2)	−0.587462	0.0731397	−8.032	4.26 × 10−12	***
ΔlnGDPmin(−3)	−0.406566	0.0793745	−5.122	1.80 × 10−06	***
ΔlnTOT(−1)	−0.0575610	0.135042	−0.4262	0.6710
ΔlnTOT(−2)	0.0743269	0.145734	0.5100	0.6113
ΔlnTOT(−3)	0.0102444	0.135476	0.0756	0.9399
DCOVID	−0.402042	0.0536050	−7.500	5.08 × 10−11	***
ECM	0.0233506	0.00450916	5.178	1.43 × 10−06	***
Model summary ΔlnGDPmin	R2 = 0.605, Adjusted R2 = 0.569, DW = 1.54

Significance level: *** p < 0.01. Estimations obtained from author-run procedures using BCRP data and GRETL 2025c.

The error-correction term is positive and highly significant (λ = 0.02335; p < 0.001), confirming that mining GDP adjusts systematically in response to deviations from the long-run equilibrium. In quantitative terms, the coefficient implies that approximately 2.33% of the disequilibrium is corrected each quarter under the baseline lag specification adopted in this study. The half-life, calculated as ln(0.5)/ln(1 − |λ|), is around 29 quarters—just over seven years—suggesting a slow but persistent convergence process within the present specification, consistent with the high capital intensity, production rigidities and long investment horizons that characterise the mining sector. The dummy variable associated with the COVID-19 pandemic exhibits a negative and highly significant coefficient (−0.402; p < 0.001), adequately capturing the transitory and exceptional impact of this shock on mining activity without altering the model’s structural dynamics. Taken together, the evidence from the mining GDP equation confirms a gradual yet stable adjustment towards the long-run equilibrium, driven primarily by the sector’s internal dynamics and the error-correction mechanism, rather than by short-run effects originating from the terms of trade.

By contrast, the ΔlnTOT equation exhibits dynamics that are clearly dominated by its own lags and only weakly linked to the performance of the mining sector (see Table 4). The lags of mining GDP growth are not statistically significant (p > 0.16 in all cases), indicating that recent variations in mining GDP do not generate systematic short-run responses in the TOT. In contrast, the first lag of Δln(TOT) is positive and highly significant (0.405; p < 0.001), reflecting very short-run persistence in external relative price shocks. However, subsequent lags are not significant (p > 0.63), which implies that any short-lived inertia dissipates rapidly and does not give rise to a longer-term propagation mechanism.

Table 4. TOT dynamics equation (VECM).

Variable	Coefficient	Std. Error	t-Statistic	p-Value	Sig.
ΔlnGDPmin(−1)	−0.0660118	0.0640003	−1.031	0.3052
ΔlnGDPmin(−2)	−0.0171361	0.0564406	−0.3036	0.7621
ΔlnGDPmin(−3)	−0.0849469	0.0612519	−1.387	0.1690
ΔlnTOT(−1)	0.405707	0.104210	3.893	0.0002	***
ΔlnTOT(−2)	−0.0514266	0.112460	−0.4573	0.6486
ΔlnTOT(−3)	−0.0504968	0.104544	−0.4830	0.6303
DCOVID	−0.0192121	0.0413660	−0.4644	0.6435
ECM	0.00902911	0.00347964	2.595	0.0111	**
Model summary ΔlnTOT	R2 = 0.235, Adjusted R2 = 0.165, DW = 2.00

Significance level: *** p < 0.01, ** p < 0.05. Estimations obtained from author-run procedures using BCRP data and GRETL 2025c.

The dummy variable associated with the COVID-19 pandemic is not statistically significant in the TOT equation (p = 0.643), indicating that, once the intrinsic dynamics of TOT and the remaining components of the system are controlled for, no systematic short-run effect of this shock can be identified on their behaviour. The error-correction term appears positive and statistically significant (λ = 0.0090; p = 0.011). This result is reported as part of the system’s statistical dynamics and reflects the way in which the TOT participate in the correction process estimated within the VECM framework. At the same time, its magnitude is modest relative to the adjustment coefficient estimated for mining GDP, pointing to an asymmetric correction pattern in which the domestic variable absorbs the bulk of the disequilibrium. However, its economic interpretation is not developed in this section, as the focus of the results analysis is on the behaviour of the mining sector as the adjusting variable; a structural reading of this coefficient is addressed explicitly in the discussion section.

3.4. Robustness Checks and Limitations

To assess the robustness of the baseline results, a set of post-estimation diagnostics was conducted for the preferred VECM specification with four lags, together with a sensitivity check to the lag structure. The objective is not to exhaustively “clean” short-run dynamics, but to verify that the core inferences—namely, the existence of a long-run relationship and a meaningful adjustment mechanism in mining GDP—are not driven by a particular specification choice.

3.4.1. Residual Diagnostics

A set of residual diagnostic tests is reported in Appendix B to assess the adequacy of the estimated system. The Rao F residual autocorrelation tests (Table A3) indicate statistically significant serial correlation up to the fourth lag (p-values between 0.0027 and 0.0116). While this reflects short-run dependence, such persistence is not unusual in quarterly macroeconomic systems, particularly in extractive sectors exposed to external price cycles. The evidence therefore points to dynamic inertia rather than misspecification of the long-run structure. The ARCH LM tests (Table A4) detect conditional heteroskedasticity at lower orders (lags 1 and 2), whereas higher-order statistics are not significant. This pattern suggests the presence of episodic volatility, consistent with commodity-related fluctuations, but no indication of systematic higher-order variance instability.

The residual correlation matrix (Table A5) shows negligible cross-equation correlation (−0.0316), and the eigenvalues of the residual covariance matrix (0.968 and 1.032; Table A6) are balanced and well behaved. Together, these results confirm that the system remains internally stable, with no dominance of one equation over the other. The Doornik–Hansen test (Table A7) rejects multivariate normality at the 5% level (p = 0.0471). However, Johansen–VECM estimates are obtained by maximum likelihood and rely on asymptotic properties; strict finite-sample normality is not required for consistency.

To ensure that statistical inference does not rely on homoskedasticity or normality assumptions, the mining GDP adjustment equation was re-estimated using HAC robust standard errors (Bartlett kernel, bandwidth = 3). As reported in Table A8, the qualitative structure of the results is preserved. The error-correction term retains its sign and remains statistically significant at the 5% level (p = 0.0212), with only a moderate adjustment in magnitude relative to the baseline estimation. The coefficients on the sector’s own lags remain strongly significant, and the COVID dummy continues to exhibit a sizeable and precisely estimated negative effect.

The robustness of the error-correction coefficient under HAC estimation indicates that the long-run adjustment mechanism is not an artefact of residual heteroskedasticity or serial correlation. The principal inference of the model therefore remains economically and econometrically consistent despite the finite-sample disturbances typically observed in macroeconomic time series.

3.4.2. Lag-Length Sensitivity

Although information criteria point to both three- and four-lag specifications, re-estimating the system with three lags confirms cointegration but yields a markedly weaker error-correction mechanism in the mining GDP equation, with an economically negligible speed of adjustment. The cointegration rank remains at r = 1 under both lag lengths, confirming a stable long-run relationship. The difference across specifications concerns the magnitude of the estimated speed of adjustment, a parameter that is well known to be sensitive to the modelling of short-run dynamics in finite samples. By contrast, the four-lag model identifies a statistically robust and economically plausible adjustment process, under the baseline specification, consistent with the slow convergence expected in a sector characterised by high capital intensity and long investment horizons. A comparative summary of both specifications is provided in Appendix C, Table A9. These results support the choice of four lags as the baseline without altering the long-run inference.

3.4.3. COVID-19 Shock

An intervention dummy for the pandemic period is included to isolate an exceptional and transitory disturbance from the underlying dynamics. The dummy is significant in the mining GDP equation and does not affect the estimated cointegrating relationship, indicating that the long-run anchoring to external TOT is preserved once the extraordinary shock is controlled for (see Table 3). Consistently, the same dummy is not statistically significant in the TOT equation, confirming that the dynamics of external relative prices are dominated by global market forces rather than by domestic or episodic shocks.

3.4.4. Expanded Specification with Domestic Control

In order to further assess the robustness of the identified long-run relationship and to ensure that the estimated external anchoring is not confounded by domestic accumulation dynamics, an expanded specification incorporating a domestic control variable is considered. In a capital-intensive sector such as mining, variations in productive capacity are closely tied to investment cycles, exploration expenditure and expansion projects whose effects unfold gradually over time. For this reason, incorporating Gross Fixed Capital Formation (GFCF) allows the specification to account for the broader investment environment within which the sector operates, without departing from the reduced-form nature of the baseline framework.

From an economic standpoint, GFCF constitutes an appropriate control because it proxies the domestic capital accumulation process that conditions output dynamics in the medium and long run. Mining activity depends on large-scale infrastructure, imported machinery and long-gestation projects; fluctuations in aggregate investment therefore reflect changes in financing conditions, expectations and macroeconomic stability that may indirectly shape sectoral performance. By introducing GFCF, the analysis isolates the extent to which the estimated cointegrating relationship reflects genuine external anchoring to the TOT, rather than being driven by domestic investment trends that could otherwise bias the adjustment parameter.

On this basis, the full econometric sequence is re-estimated under the expanded specification, beginning with the corresponding unit-root tests and lag-order selection, in order to examine whether the cointegration results and the estimated speed of adjustment remain qualitatively unchanged. Following the same procedure adopted for the baseline model, the integration properties of lnGFCF were examined using ADF and KPSS tests under specifications including an intercept and deterministic trend. The ADF statistic in levels equals −1.446 (p = 0.8475), failing to reject the unit-root null, while the KPSS statistic reaches 0.435 (p < 0.01), rejecting stationarity. In first differences, the ADF statistic falls to −5.812 (p < 0.001), and the KPSS statistic declines to 0.058 (p > 0.10), indicating stationarity (see Appendix D, Table A10). These results confirm that lnGFCF follows an I(1) process, consistent with the integration order of the baseline variables and supporting the application of Johansen’s cointegration framework in the expanded specification.

The optimal lag length for the trivariate VAR system is then determined using the AIC, BIC and HQC information criteria (see Appendix D, Table A11). The criteria do not converge on a single specification: whereas the BIC favours a parsimonious structure with one lag, both the AIC and HQC select a four-lag model. Given the quarterly frequency of the data and the gradual adjustment dynamics already documented in the baseline results, the four-lag specification is retained. This choice preserves comparability with the original framework and ensures a sufficiently rich representation of short-run dynamics without compromising stability or interpretative coherence.

Johansen’s cointegration test was subsequently implemented for the augmented trivariate system including lnGDPmin, lnTOT and lnGFCF, under the same deterministic specification adopted in the baseline model. The trace statistic rejects the null hypothesis of no cointegration (r = 0) with a value of 44.688 (p = 0.0029), and also rejects the null of at most one cointegrating vector (r ≤ 1) at the 5% level (trace = 21.510; p = 0.0317). By contrast, the maximum eigenvalue statistic rejects r = 0 (23.178; p = 0.0351) but does not reject r ≤ 1 at conventional levels (14.992; p = 0.0677) (see Appendix D, Table A12).

This slight divergence between the trace and maximum eigenvalue statistics is not uncommon in finite samples, particularly in trivariate systems. Importantly, both tests consistently reject the absence of cointegration, thereby confirming the existence of at least one stable long-run relationship within the expanded specification. While the trace statistic points to the possibility of two cointegrating vectors, the maximum eigenvalue test supports a more parsimonious rank of one. In situations where the trace and maximum eigenvalue statistics diverge, standard empirical practice favours adopting the more conservative cointegration rank unless strong additional economic structure justifies a higher dimensional cointegrating space. Given this discrepancy and in line with a parsimonious and economically interpretable specification, the subsequent analysis proceeds under the conservative assumption of a single cointegrating vector.

From an economic standpoint, this decision is coherent with the original objective of the robustness exercise, which is to assess whether the long-run external anchoring identified in the bivariate model persists once domestic capital accumulation is taken into account. The results indicate that the inclusion of GFCF does not eliminate the long-run linkage previously documented. On the contrary, the presence of at least one cointegrating vector confirms that mining GDP remains embedded in a stable intertemporal relationship when both external terms of trade and domestic investment dynamics are jointly considered.

The estimation of the trivariate VECM provides a more demanding environment within which to assess the robustness of the long-run relationship previously identified. Once domestic capital formation is incorporated into the system, the adjustment dynamics become more nuanced, yet the core structural pattern remains intact. In the mining GDP equation (see Appendix D, Table A13), the error-correction term remains negative and highly significant (−0.0162; p < 0.001), confirming that the sector continues to adjust towards the long-run equilibrium. In quantitative terms, the implied speed of convergence declines relative to the bivariate specification (0.0233), indicating that approximately 1.6% of the disequilibrium is corrected each quarter under the expanded system, illustrating that the magnitude of the adjustment coefficient depends on the underlying model specification. This moderation in the adjustment coefficient is economically coherent: once domestic capital accumulation is explicitly modelled, part of the convergence mechanism is absorbed by the investment channel. Nevertheless, the essential result is preserved—mining GDP remains an adjusting variable rather than a passive follower of short-run shocks.

By contrast, the TOT equation (Appendix D, Table A14) exhibits a non-significant error-correction term (−0.0023; p = 0.421), in contrast with the weaker but statistically significant coefficient observed in the bivariate setting. Accordingly, in the expanded specification the data are consistent with weak exogeneity of the TOT with respect to the long-run parameters, while the baseline bivariate model is interpreted in terms of asymmetric adjustment rather than strict exogeneity within the estimated system. Once domestic investment is controlled for, the evidence that TOT responds to disequilibrium largely disappears, strengthening the view that external relative prices operate as an anchor rather than as an adjusting variable within the Peruvian context.

A notable development concerns the behaviour of GFCF itself (Appendix D, Table A15). The error-correction coefficient in the ΔlnGFCF equation is negative and strongly significant (−0.0420; p < 0.001), suggesting that domestic investment also participates in restoring long-run equilibrium. This finding does not weaken the external anchoring hypothesis; rather, it indicates that capital formation reacts endogenously to disequilibria involving external prices and sectoral output. In practical terms, the adjustment process is now distributed across productive activity and investment dynamics, reflecting the structural interdependence between output capacity and capital accumulation.

Short-run dynamics further corroborate this reading. In the mining GDP equation, lagged changes in GFCF are negative and statistically significant across the first three lags (p < 0.05), while lagged changes in TOT remain statistically insignificant. Thus, domestic investment exerts a measurable short-run influence on mining growth, whereas external price movements continue to operate primarily through the long-run channel captured by the cointegrating vector. The COVID-19 dummy retains a negative and highly significant coefficient in both the mining and GFCF equations, confirming the transitory yet pronounced impact of that shock without altering the structural properties of the system.

Taken together, the trivariate specification does not overturn the main conclusions of the baseline model. The existence of at least one stable long-run relationship is preserved, mining GDP remains an adjusting variable, and the TOT continue to function as an economically exogenous anchor. What changes is the interpretation of exogeneity “within the estimated system”: once domestic investment dynamics are accounted for, the TOT no longer display a statistically meaningful error-correction response, and the long-run correction is absorbed by domestic variables. This does not alter the structural logic of the model, but rather the distribution of the adjustment burden, which now reflects the joint role of sectoral output and domestic capital formation in restoring equilibrium.

3.4.5. Sub-Sample Stability Analysis

Given that the full sample spans markedly different phases of the international commodity cycle, the stability of the long-run relationship is further assessed through a sub-sample analysis. The period 2001–2012 broadly corresponds to the commodity expansion phase, while 2013–2024 reflects the subsequent post-boom environment characterised by more moderate and volatile external price dynamics. Splitting the sample along this cycle-based partition allows an assessment of whether the estimated cointegrating relationship remains broadly stable over time or is largely influenced by a particular phase of the commodity cycle. To ensure comparability, the same econometric framework adopted in the baseline specification is applied to each sub-period.

For the first sub-period (2001:1–2012:4), unit-root testing confirms that both lnGDP_min and lnTOT retain the integration order identified in the full sample. In levels, the ADF statistics do not reject the unit-root null (−1.92 for mining GDP; −2.70 for TOT), whereas first differences are clearly stationary (p < 0.01). The KPSS results are consistent with this diagnosis, rejecting stationarity in levels for mining GDP and not rejecting it in first differences (see Appendix E, Table A16). The statistical profile therefore supports treating both variables as I(1) within the expansion phase. Lag selection for the VAR system yields a partial divergence: AIC and HQC favour three lags, while BIC selects one (see Appendix E, Table A17). Given the quarterly frequency and the need to avoid over-compressing short-run dynamics in a small sample, the Johansen test is implemented with three lags.

Cointegration results indicate a stable long-run relationship during this phase. The trace statistic rejects the null of no cointegration (22.095; p = 0.0317), while the null of at most one vector cannot be rejected (see Appendix E, Table A18). Accordingly, r = 1 is retained. The VECM estimates preserve the baseline adjustment pattern. In the ΔlnGDP_min equation, the error-correction term is negative and statistically significant (−0.0496; p = 0.0016), implying that roughly 5% of the disequilibrium is corrected each quarter (see Appendix E, Table A19). Short-run effects are driven mainly by the sector’s own second lag, whereas lagged changes in TOT remain statistically insignificant. In contrast, the ΔlnTOT equation displays no significant error-correction term (p = 0.3175), with short-run persistence captured solely by the first lag of TOT growth (see Appendix E, Table A20).

The adjustment mechanism therefore remains concentrated in mining GDP during the commodity expansion period, while external prices exhibit no systematic feedback from domestic output. In sum, the 2001–2012 sub-sample reproduces the core features of the baseline specification: one cointegrating vector and an asymmetric adjustment process anchored in mining GDP.

For the second sub-period (2013:1–2024:4), unit-root testing reveals a more nuanced statistical profile (see Appendix E, Table A21). In levels, the ADF statistic rejects the unit-root null for lnGDP_min (−3.74; p = 0.0195), while lnTOT does not reject it (−3.05; p = 0.1185). In first differences, both variables are clearly stationary (p < 0.01). The KPSS results do not reject stationarity in levels at conventional thresholds, although the statistic for mining GDP lies close to the 5% critical value, indicating borderline persistence rather than clear-cut level stationarity. Taken together, the evidence suggests that lnTOT continues to display an I(1) pattern, whereas lnGDP_min exhibits weaker stochastic persistence relative to the expansion phase, while remaining stationary in first differences.

Lag selection for the VAR system again produces divergence across criteria (see Appendix E, Table A22). The AIC favours four lags, BIC selects one, and HQC points to two. Given the limited sample size and the need to balance parsimony with sufficient short-run dynamics, the Johansen procedure is implemented with two lags. The cointegration tests do not provide evidence of a stable long-run relationship during this period (see Appendix E, Table A23). For the null of no cointegration (r = 0), the trace statistic is 11.40 (p = 0.5371) and the maximum eigenvalue statistic is 10.35 (p = 0.3144), both well above conventional significance thresholds. The null of at most one cointegrating vector is likewise not rejected. The results therefore indicate the absence of cointegration between lnGDP_min and lnTOT in the post-2013 environment, suggesting that the long-run association observed during the expansion phase does not extend to the subsequent period characterised by lower and more volatile external price conditions.

Taken together, the sub-sample evidence indicates that the long-run association identified in the full sample is not the mechanical outcome of pooling structurally distinct periods. Rather, it appears to be closely linked to the external price environment prevailing during the commodity expansion phase. The absence of cointegration in the post-2013 sub-period suggests that the transmission of external TOT shocks to mining GDP is not uniformly persistent across regimes, but instead contingent on broader international conditions. In this sense, the long-run relationship documented in the baseline specification cannot be interpreted as a statistical artefact of averaging across heterogeneous phases, but as a regime-sensitive mechanism that becomes economically meaningful under sustained commodity-price expansion.

3.4.6. Limitations

The analysis adopts a deliberately parsimonious baseline bivariate framework and does not rely on a multivariate specification with a broad set of control variables (e.g., real exchange rate, fiscal stance, investment or financial conditions). This choice is intentional and reflects both an identification strategy and objective data constraints, aimed at isolating the long-run external anchoring and the adjustment dynamics of mining GDP, rather than decomposing intermediate transmission channels that may be jointly endogenous. For robustness purposes, an extended specification including gross fixed capital formation was estimated; however, this exercise is treated strictly as a complementary test and does not alter the central bivariate structure that guides the interpretation of the results. For this reason, the estimated cointegrating relationship is read as reduced-form evidence of long-run anchoring, rather than as a complete structural representation of all underlying driving forces or causal mechanisms. In this study, structural sustainability is explicitly examined from an economic perspective, with emphasis on dynamic consistency and adjustment capacity over time, in line with previous sectoral applications that operationalise sustainability in economic-dynamic terms rather than in its broader social or environmental dimensions [7,20]. Accordingly, the results should be understood as characterising sectoral stability and gradual correction, not as a full structural model of sectoral transmission. Within this scope, the study contributes by applying this reduced-form perspective to the mining sector, where comparable evidence remains limited, as motivated and grounded in the literature review. Future research may extend this approach by introducing selected controls, sector-specific price indices or richer datasets, as data availability improves, to refine the mapping between external shocks and mining activity.

4. Discussion

The empirical results suggest the existence of long-run external anchoring between external TOT and Peru’s mining GDP, together with a gradual correction mechanism through which the sector adjusts its trajectory in response to persistent external disturbances. The identification of a single cointegrating vector through Johansen’s test, combined with a statistically significant error-correction term (ECM) in the mining GDP equation, provides robust evidence that the sector’s dynamics are not independent of the external cycle, but are structurally conditioned by it [7,21,24], within the context of a highly resource-dependent economy such as Peru.

From an economic perspective, the fact that the ECM coefficient in the mining GDP equation is positive and highly significant (λ = 0.02335; p < 0.01) indicates that the sector systematically corrects deviations from its long-run equilibrium with TOT. In quantitative terms, the speed of adjustment—around 2.3% per quarter—as estimated under the baseline lag specification adopted in this study implies a half-life of approximately 29 quarters, that is, just over seven years. This result suggests that Peruvian mining exhibits a persistent but slow capacity to absorb external shocks, consistent with the high capital intensity, long investment horizons and technological rigidities that characterise extractive activities [35,37,77].

Importantly, this adjustment mechanism remains statistically robust when the mining GDP equation is re-estimated using HAC robust standard errors. The error-correction term preserves its sign and remains significant at the 5% level, with only a moderate adjustment in magnitude, confirming that the long-run transmission channel is not an artefact of residual heteroskedasticity or short-run serial correlation. The qualitative structure of the dynamic system is therefore preserved under alternative inference procedures.

This interpretation is reinforced by the estimated short-run structure of the VECM. The first three lags of mining GDP growth display negative and highly significant coefficients (−0.598, −0.587 and −0.406), pointing to strong internal inertia and endogenous correction mechanisms. By contrast, the lags of TOT are not statistically significant in the mining GDP equation (p > 0.61 in all cases), indicating that external shocks are not transmitted immediately, but primarily through the long-run adjustment captured by the ECM. This pattern is consistent with recent evidence from commodity markets, where external disturbances dominate system dynamics and short-run interactions play a secondary role relative to intertemporal adjustment mechanisms [79]. It also aligns with the notion that the effects of TOT on capital-intensive sectors operate cumulatively rather than through mechanical quarterly impacts, particularly when imported-cost and financing channels dominate over export-price effects in the short run [30,31,42].

From a small open economy perspective, the estimated dynamics of TOT reinforce their economically exogenous character. In the Δln(TOT) equation, the lags of mining GDP growth are not significant (p > 0.16), whereas the first lag of TOT itself is positive and highly significant (0.405; p < 0.01), reflecting short-run persistence driven by global factors. Although the error-correction term appears statistically significant in this equation (λ = 0.0090; p < 0.05), this result should not be interpreted as evidence that mining GDP determines the behaviour of TOT within the system, nor as an indication of economic bi-causality. Rather, it reflects the statistical properties of the VECM representation, in which the error-correction mechanism may appear in more than one equation even when one variable is largely determined outside the domestic economic structure. Within a VECM framework, the presence of a significant ECM in more than one equation reflects the statistical mechanics of the system and does not invalidate the structural interpretation when, from an economic standpoint, one of the variables—here TOT—is determined in international markets and lies beyond the control of the domestic economy [2,21,30,64]. Accordingly, the interpretation relevant for structural sustainability rests primarily on the behaviour of mining GDP as the adjusting variable.

The trivariate specification incorporating GFCF does not alter this hierarchy. While investment deepens the internal transmission mechanism and slightly refines the estimated coefficients, the core cointegrating relationship between TOT and mining GDP remains stable, and the direction of adjustment continues to be concentrated in the domestic sector. In this extended specification, the error-correction term in the TOT equation does not display robust statistical significance, which further supports the interpretation that the long-run adjustment dynamics are primarily absorbed by domestic variables rather than by the external price indicator itself. The inclusion of GFCF therefore strengthens the structural interpretation without displacing the bivariate framework as the principal empirical anchor of the study.

In light of this evidence, the structural sustainability of the mining sector can be understood as an emergent property of the system’s dynamic behaviour, as operationalised in the theoretical framework. On the one hand, the existence of cointegration confirms the presence of stable external anchoring, indicating that the sector does not permanently decouple following international shocks. On the other, the sign and significance of the error-correction term (λ > 0, p < 0.01) point to an effective—albeit gradual—capacity to absorb disturbances and reconverge towards the long-run equilibrium. The low magnitude of the adjustment parameter, however, introduces a form of temporal vulnerability: when external shocks overlap before the effects of previous disturbances have fully dissipated, pressures accumulate on investment, operating costs and production planning. Importantly, this slow speed of adjustment does not imply the absence of long-run stability or sectoral breakdown, but rather reflects the structural characteristics of capital-intensive extractive activities, where convergence is gradual by nature and contingent on institutional and financial buffering mechanisms. This feature is particularly relevant in resource-dependent economies and in a sector characterised by irreversible projects and high sunk costs [7,77].

The significance and negative sign of the COVID-19 shock in the mining GDP equation (−0.402; p < 0.01) further reinforce this interpretation. The coefficient captures the exceptional and transitory impact of a global disturbance that directly affected domestic productive activity, without altering the long-run equilibrium relationship between mining GDP and TOT. The lack of significance of this dummy in the TOT equation indicates that, once the intrinsic dynamics of external relative prices are controlled for, the pandemic did not modify their structural trajectory, thereby preserving the identified external anchoring.

Sub-sample analysis further qualifies this interpretation. The cointegrating relationship is clearly supported during the commodity expansion phase (2001–2012), whereas no robust evidence of long-run cointegration emerges in the post-2013 period. This temporal concentration suggests that external anchoring is strongest during sustained favourable price cycles, while weaker or statistically indistinct under more moderate and volatile external conditions. Rather than contradicting the baseline result, this pattern indicates that the strength of the long-run linkage is itself conditioned by the phase of the commodity cycle.

These findings speak directly to the recent literature on extractive sectors in resource-dependent economies. Studies for Australia, Chile, Norway and South Africa show that international commodity prices condition sectoral performance mainly through intertemporal adjustment processes, especially when imported costs, energy and heavy machinery play a central role in the productive structure [32,33,37,42]. The evidence for Peru aligns with this view, particularly during sustained commodity expansions: TOT matter, but their effects materialise through the long-run equilibrium and the correction mechanism rather than through immediate impacts on quarterly growth.

From a broader development perspective, the results do not allow for a normative classification of Peru as a “successful” or “failed” resource-based economy. Rather, they show that the mining sector remains structurally anchored to external price cycles, making long-term performance conditional on how these external shocks are managed domestically. In this sense, the findings are consistent with the SDGs’ emphasis on resilience and sustainability: favourable TOT episodes create opportunities, but do not guarantee durable outcomes in the absence of complementary domestic strategies. Policies aimed at macroeconomic stabilisation, productive diversification, and domestic value upgrading emerge as natural avenues to mitigate external dependence and strengthen long-run sustainability. While the present study does not evaluate these channels explicitly, it provides an empirical basis for future research examining how resource-dependent economies can move from external anchoring towards more diversified and value-intensive growth paths.

From a methodological standpoint, it is important to stress that the cointegration and VECM approach implicitly incorporates a notion of causality in the Granger sense. The existence of cointegration, together with a significant ECM in the mining GDP equation, is consistent with long-run Granger causality from TOT to mining GDP, even when short-run TOT lags are not significant. Within this framework, additional Granger causality tests would be redundant, as the VECM already identifies the direction of adjustment and the relevant channel of dynamic transmission [72,73,74].

Taken together, the results allow the conclusion that Peruvian mining exhibits conditional resilience: it returns to its equilibrium trajectory following external disturbances, but does so at a slow pace that limits its absorption capacity in the face of persistent or overlapping shocks. From a policy perspective, this suggests that efforts to strengthen the sector’s structural sustainability should prioritise temporal buffering mechanisms—such as countercyclical financing, regulatory stability and critical infrastructure—capable of reducing the intertemporal frictions of adjustment, rather than interventions aimed at altering the long-run link with international prices, which remains beyond the control of the domestic economy [21,42,53].

4.1. Economic Policy Implications

The evidence points to a clear policy implication: economic policy should prioritise the reduction in structural frictions that delay the adjustment of mining activity to external shocks, rather than attempting to influence international prices that lie beyond the reach of the domestic economy [80]. From this perspective, the empirical results indicate that the effective margin for intervention is not located in the long-run anchoring of the sector to TOT, but in the length of time required to converge back to that equilibrium. In practical terms, this concerns the institutional, regulatory, and operational conditions that shape the speed of adjustment identified by the VECM—an issue of particular relevance in resource-dependent economies, where exposure to external shocks is typically concentrated in a small number of key sectors [81]. This interpretation is reinforced by the robustness of the estimated adjustment dynamics across alternative specifications, which consistently identify the domestic sector as the locus of adjustment following external price shocks. Within this setting, improvements in regulatory clarity and administrative efficiency can play a decisive role in reducing project response times. Stable regulatory environments and faster authorisation procedures allow investment and production decisions to adapt more swiftly to external cycles, directly affecting the estimated adjustment parameter during adverse episodes [82].

Along the same lines, the establishment of countercyclical financial instruments—such as stabilisation funds or credit facilities explicitly linked to the external cycle—would help contain the persistence of downturns during periods of TOT deterioration. These mechanisms are especially pertinent in a sector marked by high sunk costs and long investment horizons. In parallel, policies aimed at easing rigidities in the cost structure of imported inputs and addressing logistical constraints can enhance the sector’s capacity to absorb unfavourable shifts in external relative prices without triggering prolonged contractions in activity [83]. Taken together, such measures leave the long-run equilibrium relationship between mining GDP and TOT unchanged, but they do shorten the period over which adjustment takes place, thereby strengthening the sector’s dynamic response under persistent external stress. In this sense, the policy challenge lies less in attempting to modify the external price environment than in strengthening the domestic institutional and operational frameworks that determine how rapidly mining activity can respond to it.

In the Peruvian context, these frictions extend beyond regulatory and financial dimensions to include institutional and social factors over which public policy retains direct leverage. The persistence of illegal mining activities and recurrent social conflicts in mining regions generate operational disruptions, project delays, and higher compliance costs, effectively lengthening the adjustment process following external shocks. Viewed in this way, informality and social conflict are not merely governance concerns; they also function as economic rigidities that slow the adjustment dynamics captured by the VECM, constraining the sector’s ability to reconverge promptly towards its equilibrium path.

This emphasis on internal structures and absorptive capacity is consistent with earlier evidence showing that the economic impact of external conditions or international policy regimes depends less on the size of the shock itself than on the domestic mechanisms through which it is transmitted. Accordingly, reinforcing the structural sustainability of the mining sector calls for a policy strategy centred on easing institutional, social, and operational constraints that prolong adjustment, rather than on attempting to modify an external anchoring that remains exogenous to the domestic economy. Such an approach becomes particularly relevant in periods of heightened volatility in international commodity markets, when slower adjustment processes can amplify the economic costs of adverse price cycles.

4.2. Future Research

Taking into account the limitations recognised in this study, future research could extend the analytical framework and offer a more nuanced understanding of the channels through which TOT shape the structural sustainability of Peru’s mining sector. A natural starting point would be to further relax the bivariate setting as more granular and internally consistent sectoral data become available. Introducing variables linked to imported input costs, financing conditions, private investment in exploration and capacity expansion, or public spending on logistical infrastructure would make it possible to trace more precisely how external shocks propagate into mining activity, building on the robustness exercises that incorporate investment as an additional control while preserving the core bivariate interpretation.

A second promising direction concerns intra-sectoral heterogeneity. Relying on an aggregate indicator such as mining GDP masks important differences across segments with distinct productive structures, operational scales, and investment horizons, including large-scale metallic mining, polymetallic operations, and smaller-scale activities. Accounting for these differences could uncover heterogeneous adjustment speeds and uneven degrees of structural vulnerability to adverse TOT cycles—dimensions that remain largely hidden under an aggregate perspective.

In addition, it would be pertinent to advance towards approaches that move beyond the dynamic stability of the system. Analyses that integrate interdependencies with other sectors, persistent institutional rigidities, social conflict or regulatory constraints would enrich the interpretation of long-run adjustment and complement the parsimonious approach adopted here. Finally, applying this empirical framework to other resource-intensive economies—in Latin America, Africa or Asia—would allow an assessment of the external validity of the results and the development of a comparative research agenda on structural sustainability in extractive sectors, particularly in resource-dependent economies where adjustment dynamics in the face of external shocks represent a recurrent challenge.

5. Conclusions

The econometric results suggest that Peru’s real mining GDP maintains a long-run relationship with external TOT. The identification of a single cointegrating vector through Johansen’s test, with rejection based on both the trace and maximum eigenvalue statistics, confirms the first hypothesis and places the sector within a structural dynamic that cannot be understood independently of the external cycle. In a small open economy dependent on natural resources, this finding is interpreted as evidence of external anchoring: the trajectory of mining GDP does not evolve in isolation, but rather fluctuates around a long-run equilibrium conditioned by movements in international relative prices. In the short run, the results draw a clear distinction between the sector’s internal dynamics and the immediate transmission of external shocks. The Δln(GDP_min) equation exhibits a pronounced autoregressive pattern, with negative and highly significant lags, suggesting that mining activity corrects recent expansions or contractions through internal adjustment mechanisms. By contrast, the coefficients on ΔlnTOT are not statistically significant, indicating that TOT shocks do not materialise as direct quarterly impacts on mining GDP growth, but operate primarily through the long-run linkage captured by the error-correction mechanism.

The statistical significance of the ECM in the Δln(GDP_min) equation lends support to the second hypothesis and indicates that the mining sector responds only gradually to departures from its long-run equilibrium with TOT. This pattern of convergence points to a form of conditional resilience: mining activity does return towards equilibrium, but over an extended adjustment horizon that is consistent with high capital intensity, lengthy investment cycles, and the operational rigidities typical of extractive industries. From the standpoint of structural sustainability, this implies that sectoral stability hinges not merely on the existence of a long-run equilibrium, but also on the effective capacity to bear and manage the economic costs associated with a slow correction process—a feature commonly observed in resource-dependent economies. Importantly, this adjustment mechanism remains statistically robust when the mining GDP equation is re-estimated using heteroskedasticity and autocorrelation consistent (HAC) standard errors, confirming that the identified long-run correction process is not driven by residual variance distortions or short-run serial dependence.

The inclusion of the COVID-19 dummy provides further corroboration. Its coefficient is negative and highly significant in the Δln(GDP_min) equation, capturing the impact of an exceptional global disruption that sharply affected domestic productive activity. At the same time, its lack of statistical significance in the TOT equation suggests that, once the intrinsic dynamics of external relative prices are accounted for, the pandemic did not alter the long-run external anchoring identified through cointegration. This evidence reinforces the interpretation of structural sustainability as a dynamic property that can be placed under strain by extraordinary shocks without implying a rupture of the long-run equilibrium itself.

Taken together, the findings point to a central conclusion: the structural sustainability of Peru’s mining sector, as defined in this study, rests on the joint presence of external anchoring through cointegration and a capacity for reconvergence captured by a significant ECM, albeit with a slow speed of adjustment that introduces a dimension of temporal vulnerability. In practical terms, the sector does not drift permanently away from equilibrium in the face of international shocks, yet the time required to correct imbalances is sufficiently long for persistent or overlapping adverse disturbances to magnify costs, delay investment decisions, and tighten intertemporal constraints. Crucially, this gradual adjustment should not be interpreted as evidence of sectoral failure or long-run instability, but as a structural feature of capital-intensive extractive activities, where convergence is inherently slow and contingent on the availability of institutional and financial buffering mechanisms. Complementary robustness exercises reinforce this interpretation: the extended trivariate specification incorporating gross fixed capital formation preserves the long-run linkage between mining GDP and TOT, while the direction of adjustment continues to be concentrated in the domestic sector, and the terms of trade remain broadly consistent with an externally driven anchor in a small open economy context.

From a longer-term perspective, these results should not be interpreted as a definitive judgement on Peru’s development trajectory, but rather as evidence that mining-sector outcomes remain conditional on how external exposure is managed over time. External price upswings may ease constraints, yet sustaining progress ultimately requires complementary domestic advances in diversification, institutional capacity and value creation. While such dimensions fall outside the scope of the present econometric analysis, the adjustment dynamics identified here highlight their relevance for long-run sustainability. Additional sub-sample analysis suggests that the strength of the cointegrating relationship is particularly evident during the commodity expansion phase of the early 2000s, whereas the post-2013 period does not display equally robust statistical evidence of long-run cointegration. This temporal pattern indicates that external anchoring may intensify during sustained favourable price cycles, while becoming less pronounced under more moderate and volatile international conditions.

Beyond the Peruvian context, these results provide a replicable empirical framework for examining extractive sectors in other resource-dependent economies, where structural sustainability is shaped less by the elimination of external exposure than by the ability to absorb and manage it in an orderly and economically coherent manner. In this sense, the study engages directly with the Sustainable Development Goals—particularly those related to sustained economic growth, efficient resource use and productive resilience—by emphasising that mining-sector sustainability requires institutions, policies and operational frameworks capable of reducing intertemporal adjustment frictions, rather than interventions aimed at altering external prices that lie beyond domestic control. In doing so, the paper contributes to an applied reading of structural sustainability in natural resource–intensive sectors, showing that the core challenge lies not in avoiding dependence on the external cycle, but in containing the economic and social costs associated with slow adjustment processes in contexts of heightened international volatility.