GDP Model & Mining Variables

GDP Model & Mining Variables

ABS Data

To begin the analysis I’ve acceessed the Australian Bureau of Statistics and loaded the data through R. For this I have used the readabs package. The national_accounts dataframe contains 1298911 observations and 13 variables.

I’ve selected appropriate variables from this data set to create an econometric model.

Summary of Series and Dataframe Names

name	series
gdp	Gross domestic product: Chain volume measures ;
consumption	Households ; Final consumption expenditure: Chain volume measures ;
investment	Private ; Gross fixed capital formation: Chain volume measures ;
government_spending	General government - National ; Final consumption expenditure: Chain volume measures ;
exports	Exports of goods and services ;
imports	Imports of goods and services ;

Calculations were made to generate growth rates and lags where appropriate.

Model 1

Baseline Specification

Below I will take a look at an initial OLS specification of growth rates on GDP growth and its potential implications.I will test the models validity with the aim of developing better models to understand the Australian Economy. I will take a more clinical approach to reviewing the baseline specification, for further models I will include test results and tables in the appendix for readability.

\[ \text{GDP Growth} = \beta_0 + \beta_1 \cdot \text{Consumption Growth} + \\ \phantom{\beta_0} + \beta_2 \cdot \text{Investment Growth} + \beta_3 \cdot \text{Government Spending Growth} + \beta_4 \cdot \text{Net Exports Growth} + \varepsilon \]

Regression Results: GDP Growth Model

	Dependent variable:
	GDP Growth
Consumption Growth - Yearly	0.4427***
	(0.0280)
Investment Growth - Yearly	0.1097***
	(0.0095)
Government Spending Growth - Yearly	-0.0216*
	(0.0124)
Net Exports Growth - Yearly	0.0083***
	(0.0021)
Constant	1.2367***
	(0.1309)
Observations	155
R2	0.7843
Adjusted R2	0.7785
Residual Std. Error	0.8447 (df = 150)
F Statistic	136.3190*** (df = 4; 150)
Note:	p<0.1; p<0.05; p<0.01

Results

Model Fit

Residual Standard Error: 0.8447 - Indicates the average deviation of observed GDP growth rates from the model’s predictions. R-Squared: 0.7843 - Suggests that approximately 78.43% of the variation in GDP growth is explained by the model. Adjusted R-Squared: 0.7785 - Reflects the model’s explanatory power after accounting for the number of predictors. F-Statistic: 136.319, p-value 6.636^{-49} - Indicates the model is statistically significant overall, rejecting the null hypothesis that all coefficients are jointly zero.

Coefficients

Consumption Growth: 0.4427 (p-value < 0.001) - For every 1 percentage point (pp) increase in annual consumption growth, GDP growth increases by approximately 0.4427 pp. This relationship is highly significant.

Investment Growth: 0.1097 (p-value < 0.001) - For every 1 pp increase in annual investment growth, GDP growth increases by approximately 0.1097 pp. This relationship is also highly significant.

Government Spending Growth: -0.0216 (p-value 0.0833) - Suggests a negative but statistically insignificant relationship with GDP growth. For every 1 pp increase in government spending growth, GDP growth decreases by approximately -0.0216 pp, though this result lacks statistical significance at conventional levels.

Net Exports Growth: 0.0083 (p-value < 0.001) - Indicates a significant positive relationship with GDP growth, where a 1 pp increase in net exports growth corresponds to a 0.0083 pp increase in GDP growth.

Key Findings:

Consumption Growth is the most influential predictor, with a strong and highly significant positive impact on GDP growth. Investment Growth also positively contributes to GDP growth, though its effect is smaller compared to consumption. Government Spending Growth shows a slight negative effect on GDP growth, but the relationship is not statistically significant. This could indicate inefficiencies in translating government expenditures into economic output or the presence of crowding-out effects. Net Exports Growth has a small but statistically significant positive impact, reflecting the importance of trade balance on economic performance.

Model Strength:

• The model explains nearly 80% of the variation in GDP growth, suggesting it effectively captures the primary drivers of economic growth.
• The residuals are relatively small, indicating that the model’s predictions align closely with observed data.

Policy Implications:

• Encouraging consumption and investment growth should be prioritized, as they have the largest positive impacts on GDP growth.
• Government spending growth’s insignificant and slightly negative relationship warrants further investigation to determine its efficiency or the presence of structural issues.
• Trade policies that improve net exports can yield measurable but modest benefits to economic growth.

The significant effect of net exports growth is small in magnitude, suggesting that while trade is essential, its contribution to GDP growth is less pronounced compared to domestic consumption and investment.

Diagnotsitc Tests

1. Durbin-Watson Test for Autocorrelation

The Durbin-Watson test statistic is 0.7678, with a p-value of 1.164^{-15}. This indicates that there is significant evidence of autocorrelation in the residuals.

2. Breusch-Pagan Test for Heteroskedasticity

The Breusch-Pagan test statistic is 9.8565 with 4 degrees of freedom and a p-value of 0.04292. This suggests that there is significant evidence of heteroskedasticity in the residuals.

Model Analysis

The model is a conventional method of assessing GDP growth, the tests show that it needs refining. I would have expected Net Exports to contribute more to growth. The dynamics around lags and non-linear effects require consideration. Government spending could have a number of factors resulting in a negative coefficient. When unemployment benefit and social spending are increasing often the economy is in decline. Disaggregation of these variables would be required to better understand their relationship.

Model 1 Specifications

Based on the above, and some further analysis and tests I have updated the baseline specification. I will include a coefficient table of the revised model specifications for comparison.

Model 1 includes a lag of net exports and government spending growth (details on testing lags can be found in the appendix), model 1A builds on this with the addition of the lag of the dependent variable GDP. It’s significant and impactful with a positive coefficient as you would expect. The models have been tested for heteroskedasticity, autocorrelation etc (again in the appendix) and I am happy to use them for predictions.

On first glance with would look like the model performs well over the decades. There are some notable periods of sustained over/under prediction. For instance late 2015 to 2017 actual growth was at its peak approximately 2 times the models predictions.

With every economic data set COVID-19 skew the graph, additionally the predictions span decades so I am going to zoom in on the period post 2022. I’ve also added the standard error regions.

Post 2022 the models have both over-stated GDP Growth.

Across the period:

• Model 1 was a median average of 0.022pp below actual growth. At peak 2.084pp above and -2.134pp below.

• Model 1A was a median average of 0.011pp below actual growth. At peak 2.051pp above and -2.704pp below.

See appendix for more detail on variance between actual growth and model predictions in the appendix.

These relatively straighforward econometric models have given me a better understanding of the Australian Economy. Disaggregating and studying the independent variables would be a worthwhile excercise. Given consumptions importance to the model, it is not surprise that in a rate hiking cycle GDP growth is in decline. A more rpessing concern for me is to understand the mining sectors influence on GDP. So that will be the focus for the next specification.

Model 2

Mining GVA

Using Mining Gross Value Added - Chain volume measures I’ve created growth rates and lags of the same. Below chart displays correlation between mining output growth and GDP growth.

Mining GVA growth and its first lag have no significant relationship with GDP growth. Its second lag is significant and negative but weak.

I am surprised by the weak correlation between mining output and GDP. There are multiple potential causes for this which I’ve come across in the literature. Commodity price dynamics, multi-factor production dynamics and regioal effects all impact the relationship. I learned through experience with housing economics that econometric models can yield unexpected signs, by that I mean a relationship inverse to what you would expect with economic theory. This often happened with interest rates on housing price. I expect mining will be no different, and likely more complicated.

Commodity Price

I’ve accessed the RBAs data on commodity prices through readrba and joined it to the existing dataframe for analysis. I will use the index (2022/2023 = 100) calculated on Special Drawing Rights (SDR) Valuation. Controlling for commodity price makes sense given higher commodity prices does not necessarily benefit the economy. - And mining output likely sees significant growth in periods with growing commodity prices, but diminishing once levels reach a certain point.

To analyse the relationship I’ve regressed the lag of commodity price growth and a quadratic transformation on Mining GVA growth.

The linear model shows a steady decline in predicted mining GVA growth as lagged commodity price growth increases. The quadratic model captures a non-linear relationship. Mining GVA growth increases for small positive changes in lagged commodity price growth but declines sharply as lagged growth becomes very large.

To arrive at model 2 specifications I spend considerable time and deployed a number of techniques to arrive at the below models. Economic reasoning was the most efficient way to arrive at the specifications. I dipped my toes into Machine Learning techniques with mixed results. I will detail them in the appendix but in short the specifications they suggested didn’t yield dramatic insight. That is in part down to my inexperience, the data not being large enough and simpler being better, in this instance. I will leave a high level summary of the techniques and reasoning (LASSO, Decision Forrest etc) in the appendix.

Model 2 Specifications

A more refined approach was necessary for the specifications due to presence of autocorrelation, they are Generlised Least Squares (GLS) models.

Regression Results: Model 2 Specifications

	Dependent variable:
	GDP Growth
	2	2A	2B
	(1)	(2)	(3)
Lagged GDP Growth	0.0547	0.1050**	0.0998**
	(0.0440)	(0.0484)	(0.0478)
Consumption Growth - Yearly	0.4506***	0.4837***	0.4835***
	(0.0270)	(0.0295)	(0.0293)
Investment Growth - Yearly	0.0859***
	(0.0114)
Commodity Price Growth (Squared)	-0.0001
	(0.0001)
Mining Investment Interaction		0.0047***	0.0056***
		(0.0012)	(0.0013)
Lagged Commodity Price Growth (Squared)		-0.0001
		(0.0002)
Mining Commodity Interaction			-0.0015*
			(0.0009)
Constant	1.1359***	1.1508***	1.1451***
	(0.2082)	(0.2371)	(0.2296)
Observations	150	150	150
Log Likelihood	-168.9498	-188.4868	-185.4038
Akaike Inf. Crit.	351.8995	390.9737	384.8076
Bayesian Inf. Crit.	372.7367	411.8108	405.6447
Note:	p<0.1; p<0.05; p<0.01

I can’t say that I’ve learned too much from this model. But for now I will display it’s predictions and move on to other areas of analysis. Before I do this I will give insight to some of the literature I’ve considered for next steps in creating valid and informative models on minings impact on economic growth.

Literature

The analysis was informed by a review of key academic research in economics, particularly focusing on the relationships between GDP growth, mining sector dynamics, and macroeconomic variables. Foundational works, such as Barro and Sala-i-Martin’s Economic Growth (2003), provided a theoretical framework for understanding the roles of consumption, investment, and trade in driving economic performance. These studies highlighted how different sectors of the economy, including mining, contribute to aggregate output and economic cycles, serving as a baseline for modeling.

Research on the Resource Curse and the role of commodity prices, including works like Auty’s Sustaining Development in Mineral Economies (1993), was instrumental in contextualizing the mixed relationship between mining GVA and GDP growth. These studies underscored the complexities of resource-dependent economies, where rising commodity prices can lead to higher revenues but also exacerbate volatility and structural inefficiencies. Additionally, empirical studies, such as Cuddington et al.’s Prebisch-Singer Redux (2007), guided the decision to incorporate non-linear transformations of commodity price growth, as the benefits of price increases often diminish or reverse at higher levels.

Dynamic modeling methodologies, including ARDL and bounds testing, as discussed in Pesaran et al.’s Bounds Testing Approaches to the Analysis of Level Relationships (2001), also informed the econometric design. These approaches helped contextualize the importance of lags and interactions, particularly with mining GVA and investment variables, which exhibit delayed and non-linear impacts on GDP growth. The research also highlighted the need to account for macroeconomic shocks, such as policy changes or external economic conditions, which are central to understanding Australia’s mining-driven economy.- If indeed that is a fair characterization.

In addition, I reviewed seminal works addressing Dutch Disease, a phenomenon where resource booms lead to currency appreciation, undermining competitiveness in non-resource sectors. Key contributions include Corden and Neary’s Natural Resource Abundance and Dutch Disease (1982) and Stevens et al.’s Mining Booms and Dutch Disease in Resource-Rich Countries (2015). These works provided insights into the broader macroeconomic impacts of resource-driven growth, reinforcing the need to explore mining’s complex relationships with other sectors of the economy.

Further insights came from studies such as McLean’s Mining and the Australian Economy: 200 Years of Economic Contribution (2013), which emphasized the historical significance of mining to Australia’s economic development. Similarly, Topp et al.’s Resource Booms and the Australian Economy: Dutch Disease or Not? (2008) critically assessed the structural impacts of resource booms, highlighting how mining’s influence varies depending on its integration with broader economic policy and structural settings.

Disaggregating mining variables was another area of focus. By examining subcomponents such as exploration, extraction, and processing, studies provided a nuanced understanding of mining’s contribution to GDP. This was particularly relevant in distinguishing between mining volumes and output values, as explored in Stevens et al. (2015). Such disaggregation allows for a better understanding of the factors driving economic performance beyond commodity prices alone, enabling a more comprehensive analysis.

Going Forward

I aim to refine my analysis by further exploring the interplay between mining variables, macroeconomic policy, and international economic conditions. This will include deeper disaggregation of mining activities, with a focus on understanding the distinct contributions of exploration, production, and export dynamics. Additionally, I plan to assess the relative roles of mining volumes versus output values in driving economic outcomes, as well as their sensitivity to commodity price fluctuations. Incorporating structural economic changes, such as shifts in global demand for resources and technological advancements in the sector, will also be a priority.

Furthermore, I intend to integrate dynamic panel data models and structural VARs to better capture the interdependencies between mining, macroeconomic indicators, and external shocks. Expanding the analysis to include environmental and social impacts of mining could also yield valuable insights into sustainable growth strategies. By building on the academic research reviewed and leveraging robust econometric tools, I aim to produce a more holistic understanding into how mining shapes Australia’s broader economic trajectory by understanding how it has done so to date.

---

Policy Analysis

My approach to this section has been influenced by the news cycle, with Trumps election victory de-regulation has been heavily discussed not just in the financial media but more generally. It is no surprise that the economics of regulation is well studied. Regulation, or limiting regulation broadly being what differentiates political parties. George Stigler’s seminal work on the economics of regulation underscores how regulations often serve industry interests rather than the public good (Stigler, 1971). - This conflict of incentives, intentions and unintended consequences is the framing of my analysis of Australian mining regulation.

This won’t be a comprehensive assessment but my goal is to create models on three federal regulations and one regional regulation, assess the results, compare with the literature and see what areas I would like to focus on next.

Federal Regulation

The Carbon Pricing Mechanism, Minerals Resource Rent Tax (MRRT), and Environment Protection and Biodiversity Conservation Act (EPBC Act) have been studied for their economic and environmental impacts. These policies represent critical regulatory interventions in Australia, each offering unique opportunities to understand how legislation shapes production, investment, and export dynamics in resource-intensive industries.

Key Themes from the Literature

Regulatory Capture and Efficiency:

• Stigler’s work, as discussed above highlights potential for unintended consequences. This perspective raises questions about the real economic impacts of policies like the MRRT and EPBC Act.

Environmental and Economic Trade-offs:

• The Carbon Pricing Mechanism has been analyzed as a market-based tool to internalize environmental externalities. Studies suggest that while such policies increase costs for emitters, it incentivises investment in cleaner technologies (Garnaut, 2008). The EPBC Act’s impact on export timelines and project approvals has been examined, with debates around balancing conservation with economic development (Hawke, 2009). I want to assess the impact on export volumes.

Investment and Market Behavior:

• Empirical analyses of the MRRT highlighted its potential deterrent effect on mining investment, with industry opposition citing reduced international competitiveness (Freebairn, 2012). However, academic perspectives argue that resource rent taxes can ensure fairer public benefit from natural resources. I want to asses the impact on investment.

Summary of Intended Models & Possible Contexts

Legislation	Date	Introduced By	Model	Objective	Variables
Carbon Pricing Mechanism	July 2012 - July 2014	Australian Labor Party (ALP)	SARIMA	Assess impact on production trends	Production Output, Commodity Prices
Minerals Resource Rent Tax (MRRT)	July 2012 - September 2014	Australian Labor Party (ALP)	VAR	Examine interdependencies in investment trends	Investment Levels, Commodity Prices
Environment Protection and Biodiversity Conservation Act (EPBC Act)	July 1999 - Present	Liberal-National Coalition	ITS	Evaluate shifts in export trends post-EPBC	Export Volumes, Exchange Rate, GDP Growth

Carbon Pricing Mechanism (2012–2014)

Context: The Carbon Pricing Mechanism (introduced July 2012, repealed July 2014) required large emitters to purchase permits for their carbon emissions. This likely impacted production costs for carbon-intensive mining operations, potentially influencing output levels.

I have taken export data from the RBA to analyse.

As Resource exports is an aggregate I’ve taken a log transformation to view the data.

Having run a number of ARIMA (Autoregressive Integrate Moving Average) model specifications it was clear that the residuals were not normally distributed. The commodity cycles are evident in the data. As a result I have compared below an SARIMA and GARCH (Generalised AutoRegressive Conditional Heteroskedasticity) model to address the volatility in the residuals.

Summary Table of Best SARIMA Models

Series	Model	AIC	BIC	Residual Variance	Ljung-Box (p-value)	Shapiro-Wilk (p-value)
Resource Exports	ARIMA(1,0,2) with non-zero mean	2895	2911	5012816.0	0.8722	0.0000
Coal Exports	ARIMA(3,0,2) with non-zero mean	3384	3407	1029401.3	0.2218	0.0000
Metal Exports	ARIMA(0,1,5)	3281	3300	666894.0	0.9994	0.0001
Mineral Fuels	ARIMA(4,0,0) with non-zero mean	3292	3312	660610.3	0.5345	0.0011

In order to address the non normality of residuals exhibited in the results of the Shapiro-Wilk tests I will specify a GARCH model for each. I’ve used the rugarch package, which divides the AIC and BIC criteria by the number of observations when reporting. The SARIMA (seasonally adjusted ARIMA) model is not normalised, for valid comparison I have manually calculated the AIC and BIC for the GARCH model. - Lower total AIC and BIC values suggest a better fit.

GARCH Model Comparison

Series	Model	Log Likelihood	Residual Variance	AIC	BIC
Resource Exports	ARMA(1,2)-GARCH(1,1)	-1426	5041178.6	2868	2893
Coal Exports	ARMA(3,2)-GARCH(1,1)	-1640	971360.4	3301	3334
Metal Exports	ARMA(0,5)-GARCH(1,1)	-1617	708052.0	3255	3288
Mineral Fuels	ARMA(4,0)-GARCH(1,1)	-1615	685193.4	3247	3277

In the analysis, ARMA orders derived from SARIMA results were initially used for the GARCH models to maintain consistency. However, due to numerical challenges such as convergence issues or unstable Hessian matrices, slight modifications to the ARMA orders were necessary in some instances. These adjustments reflect the additional complexity introduced by modeling conditional variance dynamics in GARCH frameworks, where solver robustness plays a crucial role. The revised ARMA specifications ensure both computational feasibility and the retention of key series characteristics, aligning the mean and variance models to produce a robust and reliable representation of the data

SARIMA vs GARCH Comparison by Series

Series	Model	Log Likelihood	AIC	BIC	Residual Autocorrelation	Volatility Dynamics
Resource Exports	SARIMA	-1443	2895	2911	Low	None
Resource Exports	GARCH	-1426	2868	2893	Low	Captured
Coal Exports	SARIMA	-1685	3384	3407	Low	None
Coal Exports	GARCH	-1640	3301	3334	Low	Captured
Metal Exports	SARIMA	-1634	3281	3300	Low	None
Metal Exports	GARCH	-1617	3255	3288	Low	Captured
Mineral Fuels	SARIMA	-1640	3292	3312	Low	None
Mineral Fuels	GARCH	-1615	3247	3277	Low	Captured

The SARIMA and GARCH modeling process has provided key insights into the temporal and volatility dynamics of the export series analyzed. The SARIMA models captured the deterministic trends and seasonality in the data, offering a baseline understanding of the systematic components driving exports. In contrast, the GARCH models revealed the stochastic nature of volatility, highlighting how export values react to external shocks and periods of uncertainty. For instance, the significant GARCH parameters across all series suggest persistence in volatility, implying that periods of heightened uncertainty tend to cluster. These results underscore the importance of incorporating both deterministic and stochastic frameworks when analyzing export trends, particularly for resource-dependent economies.

From an economic policy perspective, the modeling results provide a useful framework for analyzing the potential impacts of the Carbon Pricing Mechanism on export volumes. The volatility patterns captured by the GARCH models suggest that external shocks—such as changes in global demand or input costs—are likely to influence export performance. This indicates that introducing carbon pricing could amplify or dampen these volatility dynamics, depending on the policy’s design and implementation. Meanwhile, the SARIMA models highlight consistent seasonal and trend components, which may act as stabilizing factors in the face of such changes. These insights will help guide the evaluation of how carbon pricing might affect export competitiveness, sector-specific dynamics, and overall economic stability.

Testing the Carbon Price Mechanism

\[ y_t = \mu + \beta \cdot \text{PolicyDummy}_t + \varepsilon_t \]\[ \varepsilon_t \sim N(0, h_t) \]\[ h_t = \omega + \alpha_1 \varepsilon_{t-1}^2 + \beta_1 h_{t-1} \]\(\mu\): The constant mean level of the series when the policy dummy is zero. \(\beta\): The impact of the policy on the mean level of the series. \(h_t\): Conditional variance (volatility) at time \(t\). \(\omega, \alpha_1, \beta_1\): Parameters governing the GARCH process.

First attempted approach: GARCH-X Models with Policy Dummies. I initially implemented a set of GARCH(1,1) models with the CPM window defined as an external dummy regressor. While theoretically appropriate, this approach yielded convergence but no statistically significant results across four commodity export series.

Upon diagnostic review:

• The CPM period represented only ~5% of the full sample (8/158 observations)
• Coefficient estimates for the dummy were effectively zero or not returned
• Standard errors and test statistics could not be calculated due to singularities in the Hessian matrix

See appendix

These results suggest that under the assumption of a single-step policy dummy — the GARCH framework is insufficiently sensitive to detect a short-term regime change. However, this null finding is meaningful: it suggests that any volatility impacts of the CPM were not strong or sustained enough to be identified using standard GARCH methods. As such, I will pivot to alternative methods better suited to structural shifts.

Structural Breaks

Structural break analysis identifies statistically significant shifts in the underlying pattern of a time series — most commonly in mean level, variance, or trend slope. These breaks can reflect Economic regime changes, Policy shocks,Technological disruptions, Geopolitical or financial crises etc.

In this case, we apply the breakpoints method to detect changes in the log-level of resource exports, allowing us to observe persistent shifts in level or growth trajectory over time.

Residual Sum of Squares and BIC (Manual) for Structural Break Models

Number of Breaks (m)	RSS	BIC
0	42.888	-203.271
1	253.020	84.004
2	13.040	-382.438
3	73.853	-101.649
4	4.054	-558.049
5	-101.758	NaN
6	2.364	-633.674
7	-177.383	NaN
8	1.209	-730.106
9	-273.815	NaN
10	1.098	-735.302
11	-279.011	NaN

I’ve manually computed BIC values clearly show that:

• The model with 4 breakpoints (i.e., 5 segments) has the lowest BIC among valid entries.
• Beyond m = 4, BIC values become undefined (NaN) — which reflects overfitting or implausibly short segments where the log-likelihood breaks down.
• The RSS improvement after m = 4 is negligible, supporting diminishing marginal returns from extra complexity.

Breakpoints with Observation Index, Date, and Direction of Change

Break Number	Observation Index	Break Date	Direction of Change
1	23	1991-03-31	Increase
2	47	1997-03-31	Increase
3	90	2007-12-31	Increase
4	114	2013-12-31	Increase

While there was a break coinciding with the CPM, the directional change suggests that this is coincidence not causality.

The aim of this structural break analysis was to identify whether the introduction and repeal of the Carbon Pricing Mechanism (CPM) between July 2012 and July 2014 coincided with a statistically significant shift in the level of resource exports. Using the Bai-Perron multiple breakpoints algorithm, I identified four breaks in the log-transformed export series, with the final break occurring in Q4 2013. At first glance, this is temporally proximate to the repeal of the CPM and could be interpreted as a possible response to the policy environment. However, the direction of change observed at this break is an increase in export levels, which contradicts the hypothesis that the CPM introduced persistent downward pressure on resource exports through elevated compliance costs. The method estimates segment-wise mean levels and tests for structural stability across regimes, but it does not attribute causality. While the final break’s timing aligns with the end of the carbon pricing era, its upward direction suggests other explanatory variables may be more influential, such as recovery in global commodity demand, currency depreciation, or broader investment cycles. This result demonstrates both the utility and limitation of structural break models: they excel at identifying shifts in time series behaviour, but interpretation hinges on contextual economic reasoning. Consequently, these findings encourage caution in drawing policy conclusions solely from breakpoints, while validating their value in narrowing down periods of interest for further causal investigation.

Residual Sum of Squares and BIC for Structural Break Models

Number of Breaks (m)	Coal RSS	Coal BIC	Metal RSS	Metal BIC	Mineral Fuels RSS	Mineral Fuels BIC
0	123.319	-95.869	85.579	-170.032	205.148	7.450
1	485.533	187.651	411.370	154.003	588.852	226.815
2	33.811	-347.924	18.243	-473.171	48.257	-275.703
3	233.478	49.649	108.231	-106.421	305.699	104.360
4	12.340	-541.912	5.583	-702.897	25.891	-391.473
5	39.490	-300.462	-121.495	NaN	189.929	18.369
6	5.709	-687.764	2.804	-832.105	11.081	-553.122
7	-106.362	NaN	-250.703	NaN	28.280	-357.616
8	3.911	-753.899	2.217	-869.146	6.770	-642.512
9	-172.497	NaN	-287.743	NaN	-61.109	NaN
10	3.314	-776.893	2.175	-862.407	5.939	-658.469
11	-195.490	NaN	-281.005	NaN	-77.067	NaN

1. Coal Exports

Minimum BIC: m = 8 (BIC = -749.07). This model fits well with 8 breakpoints, though the improvement from m = 6 to m = 8 is incremental. Breakpoint inflation (overfitting) risk is present — a model with m = 4 or 6 will be more interpretable.

2. Metal Exports

Minimum BIC: m = 8 (BIC = -864.01), followed closely by m = 10 (BIC = -857.27). Like Coal, BIC improvement continues as m increases, though diminishing sharply beyond m = 6.The large BIC improvement from m = 1 to m = 4 supports structural change in early 2000s.

3. Mineral Fuels

Minimum BIC: m = 10 (BIC = -654.00), but again, significant improvement already visible by m = 4 (BIC = -388.00) and m = 6 (BIC = -549.00). Suggests considerable structural instability over the sample — likely reflecting demand volatility, price shocks, and liquefied natural gas (LNG) export ramp-up during the 2010s.

Structural breaks cluster in the 1990s and post-2010s, but all exhibit positive shifts, weakening the case that the Carbon Pricing Mechanism alone reduced export volumes.

Minerals Resource Rent Tax (2012–2014)

Context: The Minerals Resource Rent Tax (MRRT) (introduced July 2012, repealed September 2014) taxed profits from coal and iron ore mining. It was criticized for potentially discouraging investment in the sector.

Before moving towards a VAR, or variation of a VAR, I will first start off with an OLS with a policy dummy. Given we observed confounding factors happening contemporanously in the previous section I want to understand the relationship between Mining CapEx, commodity prices and GDP growth.

To assess the responsiveness of mining capital expenditure to macroeconomic indicators, I estimate two models. Cap Ex Model A includes year-on-year growth in bulk commodity prices and GDP as explanatory variables, both lagged by one quarter to account for delayed investment reactions. Cap Ex Model B extends this by including a lag of mining capital expenditure growth itself, capturing the momentum or persistence in mining investment decisions. These specifications aim to isolate the impact of short-term market signals from structural investment behaviour.

Lagged GDP growth is practically meaningless in the modelling, A positive change in commodity price growth leads to a quarter point change in Mining CapEx in specification A. In specification V this decreases to less than a tenth of a point. - When controlling for lagged CapEx spending growth. Mining CapEx being a multi year endeavour at a minimum, given the nature of the operations these findings make sense to me.

Given the volatility of Mining CapEx growth, and it’s dependent variable in this case bulk commodity price growth, I suspect isolating the effect of MRRT will be difficult. - At least not straightforward. There are simply more significant factors, spanning multiple years and many global economies influencing the Cap Ex decision, than a policy lasting from July 2012 to September 2014.

The equation below represents the Mining Capital Expenditure Growth equation derived from a VAR(2) model. In simple terms, this model regresses the current quarter’s growth in Mining CapEx on its own past two quarterly growth rates, along with the past two quarters of both bulk commodity price growth and GDP growth. While most information criteria (AIC, HQ, FPE) suggested 6 lags, I opted for 2 lags based on the more conservative Schwarz Criterion (SC) and practical modelling concerns. Given our sample size, including more than 2 lags would significantly reduce degrees of freedom and potentially overfit the data.

The coefficients on these lagged variables allow us to understand not just direct relationships but also the dynamic interplay over time — for example, how a commodity price shock may have both an immediate and delayed effect on investment decisions. A strong and significant coefficient on the first lag of CapEx growth suggests considerable momentum or inertia in mining investment activity, while the signs and magnitudes of the other terms reflect whether economic conditions or commodity markets are exerting additional influence. This forms the basis for dynamic interpretations in the next stages, particularly impulse response functions (IRFs).

\[ \begin{align*} \text{CapExGrowth}_t =\ & \alpha + \beta_1 \cdot \text{CapExGrowth}_{t-1} + \beta_2 \cdot \text{CapExGrowth}_{t-2} \\ & + \gamma_1 \cdot \text{BulkPriceGrowth}_{t-1} + \gamma_2 \cdot \text{BulkPriceGrowth}_{t-2} \\ & + \delta_1 \cdot \text{GDPGrowth}_{t-1} + \delta_2 \cdot \text{GDPGrowth}_{t-2} + \varepsilon_t \end{align*} \]

VAR Coefficient Summary: Mining CapEx Growth Equation

Variable Name	Estimate	Std. Error	t value	Pr(>|t|)
Lag Mining CapEx Growth (t-1)	1.050	0.084	12.448	<0.001
Lag Bulk Price Growth (t-1)	0.117	0.055	2.130	0.0349
Lag GDP Growth (t-1)	0.640	0.817	0.784	0.4344
Lag Mining CapEx Growth (t-2)	-0.231	0.084	-2.769	0.0064
Lag Bulk Price Growth (t-2)	-0.079	0.055	-1.435	0.1537
Lag GDP Growth (t-2)	-0.559	0.815	-0.685	0.4944
Constant	0.879	2.209	0.398	0.6913

This VAR model captures the dynamic interactions between Mining CapEx growth, bulk commodity price growth, and GDP growth. The specification includes two lags based on AIC and related criteria, allowing us to account for inertia and delayed effects in mining investment cycles.

Key insights:

• The lagged mining CapEx growth (t-1) is highly statistically significant (p < 0.001) with a strong positive coefficient (~1.05), confirming high persistence—i.e., current investment is strongly influenced by past investment levels.

• Bulk commodity price growth (t-1) also positively affects CapEx growth and is significant (p ≈ 0.033), aligning with the industry’s procyclical investment behavior.

• Interestingly, the second lag of CapEx growth (t-2) shows a significant negative effect, suggesting partial correction or overshooting in prior quarters.

• GDP growth variables, though theoretically important, are not statistically significant here—perhaps due to their smoother variation and indirect connection to sector-specific investment.

Impulse Response Functions (IRF)

Having specified and estimated a stable VAR(2) model, I now want to examine how mining CapEx growth dynamically responds to shocks in its key drivers. Impulse Response Functions (IRFs) are particularly well-suited to this task. They allow me to trace the effect of a one-time shock to either bulk commodity price growth or GDP growth over a sequence of future periods. Given the inherent volatility of mining investment and the strong cyclical nature of global commodity prices, IRFs will help illustrate how a change today can ripple through and affect future quarters. This is especially useful in the policy context of the MRRT, where I want to establish the magnitude and duration of exogenous effects before attempting to isolate any policy-specific impact. Having established the model’s stability and interpreted the static coefficients, this is the natural next step in understanding how sensitive mining investment is to broader economic conditions.

Impulse Response Function showing the effect of a one-standard-deviation shock to Bulk Commodity Price Growth on Mining CapEx Growth. The plot displays 95% Bootstrap Confidence Intervals based on 1,000 simulations. Response horizon is 12 quarters.

The impulse response traces the percentage change in Mining CapEx growth following a one-unit shock to bulk commodity price growth. It captures both the initial reaction and the evolution of that effect over the quarters ahead.

The response of Mining CapEx Growth to a commodity price shock is intuitively positive and statistically significant for the first 4–5 quarters. The response peaks around quarter 3, consistent with the lags observed in CapEx decision-making. After this, the effect fades and turns slightly negative, but the confidence intervals widen substantially, suggesting growing uncertainty. This dynamic pattern reinforces the cyclical nature of investment in the mining sector and illustrates how even temporary commodity booms can stimulate substantial investment activity, albeit with diminishing returns over time.

Before drawing conclusions from our model, it’s important I test the sensitivity of the results to additional lags. While 2 lags were preferred by most information criteria, the AIC suggested a higher lag may improve model fit. Given the nature of mining capital expenditure—with long lead times between decision and implementation—there’s a credible economic case for including more persistence in the dynamics. By estimating the IRF at 4 and 6 lags, I can assess how robust the direction, magnitude, and duration of the response is. The drawback, of course, is reduced degrees of freedom and increased risk of overfitting. However, given the dataset’s length and my focus on dynamics rather than prediction per se, it is worth taking a look.

I opted to extend the horizon from the default 12 to 20 quarters (~5 years) because mining investment decisions — particularly large-scale CapEx — often span multiple years from signal to deployment. Commodity booms and busts may trigger gradual shifts across feasibility studies, board approvals, and construction phases. Limiting the IRF to 12 quarters risked truncating this arc.

• 2 Lags:

The IRF peaks sharply at around 3% by Quarter 3, showing an immediate and front-loaded response from mining investment to a commodity price shock. This pattern aligns with a CapEx environment where firms respond swiftly to global price signals, perhaps due to pre-committed projects or shorter-cycle spending (e.g. equipment, maintenance). The response begins to taper off after Quarter 4 and hovers near zero after Quarter 8. The confidence interval is tight early on and narrows further in the long run — indicating stable estimates with a clearly defined peak effect. However, the sharp fall may also reflect the limits of this shorter lag model in capturing sustained investment behaviour.

• 4 Lags:

Compared to 2 lags, this model shows a slightly lower peak (~2.5%) but with a more prolonged plateau through Quarters 3 to 7, suggesting CapEx responses that are more staggered and persistent — likely reflecting planning cycles and project lead times. The decline is gradual, with the IRF remaining close to zero but stable through Quarter 12 and beyond. The confidence bands are modestly wider in the early periods than the 2-lag model but still offer well-behaved inference. Overall, this feels like a more realistic representation of the mining sector’s response pattern — capturing both the immediate and medium-term dynamics of investment inertia.

• 6 Lags:

The response initially mirrors the 4-lag model but shows a higher mid-horizon peak and then dips into negative territory between Quarters 10–14, before returning toward zero. This oscillation, while statistically insignificant due to wide bands, raises questions around overfitting. The higher number of lags appears to introduce volatility in later quarters, which might reflect estimation noise rather than structural effects. The confidence interval narrows over time (especially after Quarter 10), which is reassuring — but the erratic shape of the IR suggests the model is absorbing noise rather than uncovering meaningful dynamics. This result highlights the trade-off between model flexibility and interpretability.

Forecast Error Variance Decomposition (FEVD)

FEVD allows me to quantify the proportion of the variation in Mining CapEx Growth that can be attributed to shocks in each variable over different forecast horizons. While the impulse response functions show the dynamic path of a variable following a shock, FEVD provides insight into the relative importance of each variable in driving that variation. This is particularly relevant here: I’m trying to understand not just how Mining CapEx responds to commodity price shocks, but how much of its fluctuations can be explained by these shocks over time. If, for instance, commodity prices account for 40–60% of CapEx variance after several quarters, it gives strong empirical weight to the argument that policy analysis must account for broader global cycles—not just domestic legislation like the MRRT.

How much of the variability in mining CapEx growth—over a 20-quarter horizon—is explained by its own past shocks versus shocks in bulk commodity price growth and GDP growth.

CapEx Growth Shocks The chart is unambiguous: the overwhelming majority of forecast error in mining CapEx growth is explained by its own past values. This is not unexpected—capital expenditure decisions tend to exhibit persistence and momentum over time, particularly in a sector like mining, where project timelines and approvals span years. By the 20th quarter, over 90% of the forecast error variance is self-attributed.

Commodity Price Shocks Despite strong intuition and the IRF results suggesting a short-run impact, the variance decomposition reveals that shocks to bulk commodity prices only explain a small fraction (less than 10%) of the total variance in mining CapEx growth over the forecast horizon. This indicates that while prices may prompt a response, they are not the dominant driver in sustaining CapEx volatility over time.

GDP Growth Shocks Macroeconomic conditions, as proxied here by GDP growth, contribute negligibly to the variance in mining CapEx growth. This reinforces a key theme from earlier in the modelling process: aggregate demand conditions have limited explanatory power in driving the timing or scale of investment in resource-intensive sectors like mining—at least in this specification.

Getting back to the brief. Did the Minerals Resource Rent Tax (MRRT) have an effect on Mining Capital Expenditure (CapEx), and if so, how much?

## 
##   0   1 
## 121   9

VARX Model — Mining CapEx Growth Equation

Variable	Estimate	Std. Error	t value	p value	Significance
Lag CapEx Growth (t-1)	1.03	0.09	11.44	0.000	***
Lag Bulk Price Growth (t-1)	0.13	0.06	2.24	0.027	**
Lag GDP Growth (t-1)	1.18	1.10	1.07	0.288
Lag CapEx Growth (t-2)	-0.20	0.09	-2.18	0.031	**
Lag Bulk Price Growth (t-2)	-0.11	0.06	-1.76	0.080
Lag GDP Growth (t-2)	-1.36	1.15	-1.18	0.242
const	2.22	2.69	0.83	0.411
MRRT Policy Dummy	-7.04	4.79	-1.47	0.144

This model was designed to assess whether the Mining Resource Rent Tax (MRRT) had any effect on mining capital expenditure growth, controlling for broader economic conditions such as bulk commodity prices and GDP growth. While the coefficient on the MRRT dummy is negative, suggesting a possible decline in CapEx during the policy period, the p-value (0.14) falls well short of conventional significance thresholds. I would not treat this as a signal — it’s only marginally more informative than a null result. The directionality is suggestive, and given the structure of the model, I think it’s fair to say that this coefficient aligns with the idea of weakened investment sentiment during the MRRT window. But the uncertainty surrounding the estimate is too large to draw conclusions beyond this directional tendency.

That said, the inclusion of the dummy in this specification is useful. It helps identify structural shifts in the CapEx series conditional on past dynamics and economic conditions. But to better isolate policy effects, more robust empirical strategies are warranted. One such approach would be local projections à la Jordà (2005), which allow for a flexible, non-parametric estimation of impulse responses around policy changes. Another route would be using narrative identification with external policy shocks or announcements — an approach used by Romer and Romer (2010) to identify tax multipliers. Finally, in Australian settings, structural VARs with sign restrictions have been used to assess the effects of commodity shocks and fiscal announcements (see Downes, Hanslow & Tulip, 2014).

Environment Protection and Biodiversity Conservation Act 1999 (EPBC Act)

Context: The EPBC Act (introduced July 1999) added new environmental assessment requirements for large-scale mining projects, potentially influencing export levels due to delays in project approvals.

Regional Regulation

---

Appendix

Results & Tests

Model 1 & Model 1A Variance

In addition to the above I made another model specification, Model 1B which I have decided to omit. I did this because after analysing the model I feel it did not warrant cluttering the analysis. This model varied from Model 1A by adding different lags for net exports and government spending.

Model 2 Specifications

I explored various Machine Learning (ML) techniques, such as LASSO (Least Absolute Shrinkage and Selection Operator), Random Forest, and Recursive Feature Elimination (RFE), to complement the traditional econometric models. These ML approaches were utilized to handle feature selection, capture non-linear relationships, and identify interaction effects that may not have been obvious through conventional methods.

The rationale was to improve the predictive power of the models and gain deeper insights into the relative importance of predictors, especially in a complex and dynamic environment such as GDP growth modeling with mining sector variables.- Which were not behaving as I had theorised prior to modelling the data.

The benefit of ML approaches lay primarily in their ability to process a wide array of potential predictors and automatically prioritise or eliminate variables based on their contribution to model performance. For instance, LASSO was useful in shrinking less significant variables to zero, effectively performing variable selection while maintaining model interpretability. Random Forests were particularly helpful in assessing variable importance, capturing non-linear effects, and understanding the complex interactions between mining GVA, commodity prices, and GDP growth. However, ML models also presented certain drawbacks. While they may excel at prediction, they often lack the transparency and interpretability of traditional econometric methods, making it challenging to draw economic inferences or formulate policy recommendations.

Additionally, the relatively small dataset limited the effectiveness of ML techniques, as they tend to perform better with larger and more granular data. Thus, while ML tools added value to the exploratory phase, traditional econometric models were ultimately better suited for hypothesis testing and drawing actionable conclusions in this context.

Policy Analysis

GARCH Policy Effect Summary (Mean & Variance Models)

Series	Model_Type	Converged	LogLikelihood	AIC	BIC	Policy_Coefficient	Policy_StdErr	Policy_pValue
Resource Exports	Scaled Mean	TRUE	NA	NA	NA	NA	NA	NA
Resource Exports	Variance Dummy	TRUE	-1476.03	18.654	18.790	0	NA	NA
Coal Exports	Scaled Mean	TRUE	NA	NA	NA	NA	NA	NA
Coal Exports	Variance Dummy	TRUE	-1697.43	16.792	16.907	0	NA	NA
Metal Exports	Scaled Mean	TRUE	NA	NA	NA	NA	NA	NA
Metal Exports	Variance Dummy	TRUE	NA	NA	NA	NA	NA	NA
Mineral Fuels	Scaled Mean	TRUE	NA	NA	NA	NA	NA	NA
Mineral Fuels	Variance Dummy	TRUE	-1659.78	16.421	16.536	0	NA	NA

Sources

General Machine Learning Methods and Feature Selection

Hastie, T., Tibshirani, R. and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. New York: Springer. Purpose: Used for understanding LASSO, Elastic Net, and PCA methodologies. https://link.springer.com/book/10.1007/978-0-387-84858-7

Kuhn, M. and Johnson, K. (2013). Applied Predictive Modeling. New York: Springer. Purpose: Guidance on Recursive Feature Elimination (RFE) and machine learning model refinement. https://link.springer.com/book/10.1007/978-1-4614-6849-3

Dynamic Modeling and Time Series

Hamilton, J.D. (1994). Time Series Analysis. Princeton: Princeton University Press. Purpose: Provided the foundation for ARDL and dynamic modeling techniques for Model 2 refinements. https://press.princeton.edu/books/hardcover/9780691042893/time-series-analysis

Pesaran, M.H., Shin, Y. and Smith, R.J. (2001). “Bounds testing approaches to the analysis of level relationships.” Journal of Applied Econometrics, 16(3), pp. 289-326. Purpose: Used for ARDL bounds testing in dynamic modeling discussions. https://doi.org/10.1002/jae.616

Endogeneity and Robustness

Wooldridge, J.M. (2010). Econometric Analysis of Cross Section and Panel Data. 2nd ed. Cambridge, MA: MIT Press. Purpose: Addressing issues of endogeneity, heteroskedasticity, and autocorrelation in regression models. https://mitpress.mit.edu/9780262028240/econometric-analysis-of-cross-section-and-panel-data/

White, H. (1980). “A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity.” Econometrica, 48(4), pp. 817-838. Purpose: Basis for robust standard errors using the HC variance-covariance matrix. https://doi.org/10.2307/1912934

Macroeconomics and Mining

Auty, R.M. (1993). Sustaining Development in Mineral Economies: The Resource Curse Thesis. New York: Routledge. Purpose: Contextualized mining variables and their impact on macroeconomic outcomes. https://doi.org/10.4324/9780203402406

Barro, R.J. and Sala-i-Martin, X. (2003). Economic Growth. 2nd ed. Cambridge, MA: MIT Press. Purpose: Provided economic theory underpinning the role of consumption and investment in GDP models. https://mitpress.mit.edu/9780262025539/economic-growth/

Corden, W.M. and Neary, J.P. (1982) ‘Natural Resource Abundance and Dutch Disease’, The Economic Journal, 92(368), pp. 825-848. https://doi.org/10.2307/2232670

Cuddington, J.T., Ludema, R.D., and Jayasuriya, S. (2007). “Prebisch-Singer Redux.” The Economic Journal, 117(520), pp. 583-614. Purpose: Understanding the relationship between commodity prices and macroeconomic growth. https://doi.org/10.1111/j.1468-0297.2007.02043.x

McLean, I.W. (2013) Mining and the Australian Economy: 200 Years of Economic Contribution. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781107300387

Pesaran, M.H., Shin, Y., and Smith, R.J. (2001) ‘Bounds Testing Approaches to the Analysis of Level Relationships’, Journal of Applied Econometrics, 16(3), pp. 289-326.https://doi.org/10.1002/jae.616

Stevens, P., Lahn, G., and Kooroshy, J. (2015) The Resource Curse Revisited. London: Chatham House. Available at: https://www.chathamhouse.org/2015/01/resource-curse-revisited

Topp, V., Soames, L., Parham, D., and Bloch, H. (2008) Productivity in the Mining Industry: Measurement and Interpretation. Canberra: Australian Government Productivity Commission. https://www.pc.gov.au/research/supporting/mining-productivity

Policy & Regulation

Stigler, G. J. (1971). The Theory of Economic Regulation. The Bell Journal of Economics and Management Science, 2(1), pp. 3-21. Available at: https://www.jstor.org/stable/3003160 Garnaut, R. (2008). The Garnaut Climate Change Review: Final Report. Cambridge University Press. Available at: https://www.garnautreview.org.au Freebairn, J. (2012). Evaluating the Minerals Resource Rent Tax. Australian Economic Review, 45(3), pp. 264-279. Available at: https://doi.org/10.1111/j.1467-8462.2012.00682.x Hawke, A. (2009). The Australian Environment Act: Report of the Independent Review of the EPBC Act 1999. Commonwealth of Australia. Available at: https://www.environment.gov.au

Jordà, O. (2005). Estimation and Inference of Impulse Responses by Local Projections. American Economic Review, 95(1), 161–182. https://www.aeaweb.org/articles?id=10.1257/0002828053828518

Romer, C. D., & Romer, D. H. (2010). The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks. American Economic Review, 100(3), 763–801. https://www.aeaweb.org/articles?id=10.1257/aer.100.3.763

Downes, P., Hanslow, K., & Tulip, P. (2014). The Effect of the Mining Boom on the Australian Economy. RBA Research Discussion Paper No. 2014-08. https://www.rba.gov.au/publications/rdp/2014/2014-08.html

Machine Learning Packages and R Functions

Friedman, J., Hastie, T. and Tibshirani, R. (2010). “Regularization Paths for Generalized Linear Models via Coordinate Descent.” Journal of Statistical Software, 33(1). Purpose: Methodology behind glmnet for LASSO and Elastic Net. https://doi.org/10.18637/jss.v033.i01

Liaw, A. and Wiener, M. (2002). “Classification and Regression by randomForest.” R News, 2(3), pp. 18-22. Purpose: Basis for Random Forest methods and feature importance analysis. https://CRAN.R-project.org/doc/Rnews/

Kuhn, M. (2008). “Building Predictive Models in R Using the caret Package.” Journal of Statistical Software, 28(5). Purpose: Framework for RFE and predictive modeling in R. https://doi.org/10.18637/jss.v028.i05