The drivers and impacts of subsidies to steel firms

Annex G. Tackling BMB endogeneity through an instrumental variables (IV) approach

This annex presents robustness checks aimed at correcting for the endogeneity of BMB, which arises due to its countercyclical use by governments during steel industry crises.

As previously noted, governments tend to resort to BMB - and, to some lesser extent, grants - to support steel firms during crises in the steel industry (see Box 1). Since these crises are typically associated with reductions in capacity, regression analysis faces an endogeneity problem: it may appear that BMB (which increases during crises) is causing the reduction in capacity, when in fact, the steel crisis itself is responsible for both the drop in capacity and the increase in BMB. This issue likely explains the negative coefficient found in ‎Annex F.

To address this endogeneity issue, we propose an instrumental variables (IV) approach. We posit that grants can serve as a signaling device or proxy for other types of subsidies, including BMB, particularly in partner economies. The idea is to remove the influence of BMB increases driven by crises, leaving only the “exogenous” part of BMB—the part that influences capacity independently of crises.

Instrumental variables (IV) techniques tackle this problem by finding instruments (variables correlated with BMB but not directly related to steel capacity or crises) to isolate the "exogenous" component of BMB, i.e., the part independent of the steel crisis or other factors affecting capacity. The IV approach operates in two stages: in the first stage, the “exogenous” part of BMB is estimated using instruments, and in the second stage, this predicted value is used in the regression to explain capacity.

In this case, we use the second lag of grants together with government ownership share as instruments.

First, it is easy to verify that both the second lag of grants and government ownership share are strongly correlated with (current) BMB, as simple OLS regressions and p-values confirm this relationship.

Second, we need to argue that neither the second lag of grants nor the government ownership share affects capacity directly, except through their impact on (current) grants, BMB, and other explanatory variables included in the model. In other words, we must establish that these instruments are exogenous for the IV approach.119

Grants likely have a direct effect on capacity, which is a highly persistent variable (once capacity is installed, it remains in place). To account for this, we include the lagged value of capacity as an explanatory variable. This helps capture the previous effects of grants on capacity and most likely renders the second lag of grants exogenous. 220

Is Government Ownership Share exogenous? It could be argued that a higher government ownership share may affect capacity directly, beyond its impact on grants, BMB, and previously installed capacity. For instance, government ownership could provide other benefits, such as better political connections or access to additional financing instruments (as depicted in Figure 2), which can be considered a form of “subsidy.” This could undermine the use of government ownership share as a valid instrument.

First-stage regressions: estimating the exogenous portions of BMB (and grants).

This section summarises key test results for the first-stage regressions of BMB and grants. Results are similar to those found when only BMB was treated as endogenous, though the coefficient for grants is slightly lower, potentially reflecting downward bias.

F test of excluded instruments: this test checks whether the excluded instruments jointly explain the variation in the endogenous variable. A higher F-statistic indicates stronger instruments. For BMB, the F-statistic is 5.30 (p-value = 0.0089), indicating that the instruments have explanatory power.

Sanderson-Windmeijer multivariate F test: this test provides another check for the strength of instruments by accounting for heteroskedasticity and clustering. For BMB, the F-statistic is 8.22 (p-value = 0.0065), while for grants, it is 10.71 (p-value = 0.0021), suggesting that the instruments are valid and strong for both variables.

Underidentification test: the Kleibergen-Paap LM statistic (Chi-sq) tests for underidentification, i.e., whether there are sufficient instruments to identify the endogenous variables. A p-value below 0.05 (Chi-sq = 6.07, p-value = 0.0137) indicates that the model is not underidentified.

Weak identification test: The Kleibergen-Paap Wald F statistic tests the strength of the instruments. The value (4.24) is compared to critical values from the Stock-Yogo table to assess concerns about weak instruments. A statistic exceeding the critical values suggests that the instruments are not weak. Here, the F-statistic of 4.24 lies between the 15% and 25% maximal IV size thresholds, indicating possible weak identification, though not severe.

Stock-Yogo critical values provide guidance on weak instruments based on the maximal bias in IV estimates relative to OLS. A Kleibergen-Paap F-statistic above 7.03 would suggest that weak instruments cause less than 10% bias. However, the F-statistic of 4.24 suggests moderate weakness in the instruments.

Weak-Instrument Robust Inference

This section provides tests that are robust to weak instruments:

Anderson-Rubin Wald test and Stock-Wright LM S statistic: These tests assess the joint significance of the endogenous variables in the main equation, assuming the instruments are valid. Significant p-values (Anderson-Rubin: p-value = 0.0366; Stock-Wright: p-value = 0.0035) indicate that the endogenous variables are significant in explaining the dependent variable, and that the instruments are valid.

Table A ‎G.1. Second-stage regression results

	coefficient	p-value
BMB (exogenous part estimated through IV)	0.9247067 (**)	0.029
grants (exogenous part estimated through IV)	11.3315 (*)	0.098
Lagged capacity	0.9770711 (***)	0.000
Lagged EBITDA	0.3076904 (***)	0.000
GDP_steel	-1.78e-06 (**)	0.021
constant	1843.835 (*)	0.007

Source: regression through instrumental variable using Stata software.

BMB: The coefficient for BMB (0.9247) is significant at the 5% level (p-value = 0.029), indicating a positive and significant effect on capacity.

Grants: With a p-value of 0.098, the effect of grants is significant at the 10% confidence level.

Hansen J statistic: Since the model is exactly identified (the number of instruments equals the number of endogenous regressors), the Hansen J statistic is not relevant here as no overidentification test is possible.

Endogeneity test (Chi-sq): This is a Hausman test, presented in the form of a Chi-squared test, which is designed to check for the endogeneity of variables in your model. It checks whether BMB and grants are endogenous.321 With a p-value of 0.1562, we fail to reject the null hypothesis, suggesting that the variables may not be strongly endogenous when taken together. Re-running this test on each variable gives:

• For BMB alone, a p-value of 0.1045, very close to the 10% threshold. BMB is thus borderline endogenous at the 10% threshold.

• For grants alone, a p-value = 0.9119, indicating that, despite its raise during the 2009 steel crises, grants could be considered exogenous.

In conclusion, because BMB is likely endogenous i) based on theory (as it increases during steel crises when capacity tend to decrease); ii) based on empirical results (the negative coefficient in the regression would not make sense), and iii) based on the borderline it’s still reasonable to use IV variables to “instrument it”, as done above. For grants, it is probably not necessary, although the higher coefficient of grants’ impact on capacity found in this annex (compared to the non-IV approach in the core of the paper) shows that there could be some downward bias in its coefficient estimations due to not doing so.

Conclusion

• The instruments (second lag of grants and government ownership share) appear strong based on the F-tests and Sanderson-Windmeijer tests, although the Kleibergen-Paap F-statistic raises moderate concerns about weak identification.

• The Anderson-Rubin and Stock-Wright tests confirm the joint significance of the endogenous variables.

• The second stage regression results show a significant and positive impact from both grant and BMB on capacity: a USD 1 million in cash grants would increase capacity by 11 335 metric tonnes (as compared to between 7 500 to 9 500 metric tonnes when not correcting for endogeneity of steel crises), while a USD 1 million in subsidies through BMB would increase capacity by 924 metric tonnes. Although the impact of grants is thus larger than for BMB when compared to amounts of subsidisation, it is important to notice that in the regression above the effect of BMB is statistically more significant (with a p-value of 0.029) than the one from BMB (p-value of 0.098, close to 10%), and that it concerns only the impact of BMB outside of the steel crises (as discussed in the point below).

• The assessed relationship should be interpreted as the contribution of the structural component of BMB to capacity increases, and does not take into account the fact that, in time of steel crises, BMB probably allowed government to maintain capacity levels at much higher levels than what they would have fallen to. Indeed, the IV approach above in effect removes the countercyclical influence of crises on both BMB and capacity. In other words, the coefficient measures how BMB affects capacity outside of its role as a crisis response. The IV approach intentionally strips away the crisis-driven BMB increases, meaning the coefficient does not capture BMB’s capacity-stabilising role during steel crises. Instead, it focuses on the more structural, long-term contribution of BMB to capacity: a USD 1 million in subsidies through BMB increase capacity by 924 metric tonnes.

Additional instruments were explored which support the main findings

In particular, using patent data from 2004 onwards, firm-level exposure to five broad markets — “Europe,” “North America,” “China,” “OECD Asia-Pacific,” and “Others” — was estimated. Based on these exposure shares, an instrument was constructed by weighting the total amount of grant subsidies provided in each market by the corresponding firm’s exposure to that market. This approach is conceptually comparable to Bartik-style or shift-share instruments widely used in applied economics, where firm-level variation is generated by interacting predetermined exposure shares with aggregate shocks

This constructed variable is clearly correlated with the BMB subsidies received by the firm, and it is reasonable to assume that its influence on firm capacity operates primarily through the channel of firm-level support (i.e. grants and BMB subsidies), rather than through overall subsidy levels in the markets concerned. As such, this instrument can be considered valid and useful for isolating the exogenous component of BMB from its potentially endogenous part. The results are reported below, with grants slightly less significant (a p-value of 11%, above the usual 10% threshold, compared to 9% previously), and both coefficients for BMB and grants impact on capacity consistent with previous estimations.

Table A ‎G.2. Second-stage regression results, with both grants and BMB as regressors

	coefficient	p-value
BMB (exogenous part estimated through IV)	1.005 (**)	0.017
grants	9.916	0.117
Lagged capacity	0.979 (***)	0.000
Lagged EBITDA	0.284 (***)	0.000
GDP_steel	-1.96e-06 (**)	0.016
constant	2031.951 (***)	0.004

Source: regression through instrumental variable using Stata software.

Should BMB and grants be included separately in the regressions, their significance increases as well as their weights (which increase by about 80%). This is understandable given the correlation between grants and BMB. The tables below report the results of those separate regressions for BMB and grants:

Table A ‎G.3. Second-stage regression results, BMB alone

Explained variable: capacity	coefficient	p-value
BMB (exogenous part estimated through IV)	1.691 (**)	0.032
Lagged capacity	0.984 (***)	0.000
Lagged EBITDA	0.321 (***)	0.004
GDP_steel	-1.58e-06 (**)	0.028
constant	1647.577 (***)	0.010

Table A ‎G.4. Second-stage regression results, grants alone

Explained variable: capacity	coefficient	p-value
grants (exogenous part estimated through IV)	18.444 (***)	0.001
Lagged capacity	0.977 (***)	0.000
Lagged EBITDA	0.222 (***)	0.001
GDP_steel	-1.97e-06 (**)	0.002
constant	2113.271 (***)	0.000

Consideration related to dynamic panels

Including the lagged value of capacity as a regressor can introduce the so-called Nickell bias in fixed effects estimators, potentially affecting not only the coefficient on the lagged dependent variable but also the estimated effects of explanatory variables such as grants and BMB. This bias arises because, in short panels, the transformation used to eliminate firm-specific effects (e.g., within transformation) makes the lagged dependent variable mechanically correlated with the error term.

Nevertheless, our panel dataset, with N = 47 firms and T = 18 years, can be considered moderately long. In such settings, the Nickell bias becomes increasingly negligible as T grows, and the use of dynamic panel estimators such as Arellano-Bond is generally not recommended. These estimators are designed for "small T, large N" panels, and when applied to small-N contexts, they can suffer from weak instrument problems, overfitting due to instrument proliferation, and unreliable asymptotic properties.

In contrast, using a standard fixed effects estimator with clustered standard errors remains appropriate and efficient in panels with sufficient time dimension. Thus, we retain the fixed effects specification in our main regressions, including the lagged dependent variable while controlling for firm and time effects.

As an additional robustness check and given that the coefficient on lagged capacity is consistently close to one (around 0.97–0.98), we re-estimate the model using the change in capacity as the dependent variable, while retaining the same set of regressors as in the two previous specifications. This transformation effectively shifts lagged capacity from the left-hand side to the right-hand side of the equation. The resulting estimates are broadly consistent with the baseline results, confirming the robustness of our findings.

Table A ‎G.5. Second-stage regression results, with both grants and BMB as regressors

Explained variable: capacity changes, i.e. “Capacity-L.capacity”	coefficient	p-value
BMB (exogenous part estimated through IV)	1.145 (**)	0.023
grants	8.014	0.171
Lagged EBITDA	0.189 (***)	0.003
GDP_steel	-1.80e-06 (**)	0.024
constant	1510.412 (***)	0.026

Source: regression through instrumental variable using Stata software.

Table A ‎G.6. Second-stage regression results, BMB alone

Explained variable: capacity changes, i.e. “Capacity-L.capacity”	coefficient	p-value
BMB (exogenous part estimated through IV)	2.125 (**)	0.040
Lagged EBITDA	0.240 (***)	0.073
GDP_steel	-1.55e-06 (**)	0.033
constant	1225.285 (**)	0.042

Table A ‎G.7. Second-stage regression results, grants alone

Explained variable: capacity changes, i.e. “Capacity-L.capacity”	coefficient	p-value
grants (exogenous part estimated through IV)	14.947 (***)	0.011
Lagged EBITDA	0.130 (***)	0.005
GDP_steel	-1.82e-06 (**)	0.006
constant	1644.157 (***)	0.003

Notes

← 1. ¹⁹ If y is the explained variable (capacity) and y the explanatory variable (BMB), and y=a.x +b.y + u the regression of y and other explanatory variables x (EBITDA, indebtedness, etc), the condition of exogeneity for the instrument z is that Cov(u, z)=0.

← 2. ²⁰ Including lags of capacity as an exogenous variable helps account for the persistence in capacity over time, including any effect that lagged grants might have had on capacity in earlier periods. This adjustment means that lagged grants may have influenced capacity in previous periods (they almost certainly have), but, because we are explicitly controlling for lagged capacity in the model, any lingering or indirect effect that lagged grants had on previous capacity levels is captured by the lagged capacity variable itself. This thus strengthens the exogeneity of lagged grants.

← 3. ²¹ The difference between this and a Durbin-Wu-Hausman test is minor - both tests serve the same purpose of detecting endogeneity, but they differ slightly in their computation and distribution: the Durbin test uses an F-statistic, whereas the Hausman test uses a Chi-sq statistic.