Impacts of Brexit on corporate productivity in the UK: a regionalism perspective

Corporate TFP is very likely to have volatility due to policy shocks no matter whether such policy shocks are positive or negative. It is important to theoretically examine how policy shocks, such as Brexit-related extreme changes to economic policies, will impact corporate TFP. Existing literature has focussed on several potential mechanisms through which corporate TFP will face fluctuations due to policy shocks.

First, with regard to trade policies, openness of trade can theoretically allow firms to exploit economies of scale and access cheaper and more diverse inputs, boosting productivity (Krugman 1980), and facilitate technology diffusion and R&D spillovers, driving TFP growth (Romer 1990), according to new trade theory and endogenous growth theory. Empirically, Abizadeh and Pandey (2009) investigate impacts of trade openness on growth of corporate TFP and find that an open trade environment will have overall positive impacts on corporate TFP and the services sector benefits most from trade openness while the agricultural and industrial sectors seem not have received significant effects from such environment. This study presents a valuable reference since trade has played a significant role in the UK economy and output provided by the services sector accounts for over 80% among all sectors in the UK.¹ Dovis and Milgram-Baleix (2009) examine the sensitivity of corporate TFP to trade openness and tariffs in Spain and illustrate that corporate TFP is negatively impacted by European tariffs and other trade barriers since more fierce competition due to increasing foreign products in the domestic market and firm imports will encourage innovation and product upgrades, thus lead to improvements in corporate TFP. Yu (2015) also finds that both import and export tariffs discourage improvements in firm-level productivity in China. In the UK, there is also evidence that shows positive correlations between trade and corporate productivity (Harris & Moffat 2015). Brexit has led to the end of free trade between the UK and EU, causing significant uncertainty of trade, and could harm corporate productivity through the channel of trade (Fingleton et al. 2023; Broadbent et al. 2023). Wales is a region with numerous firms that have frequent trade with the EU market, which results in the first hypothesis:

Second, investment, especially FDI, can have critical impacts on corporate TFP as well. Theoretically, the endogenous growth theory also justifies that FDI brings technology transfers, managerial know-how, and R&D spillovers, boosting corporate productivity. Empirically, Li and Tanna (2019) find that inward FDI and corporate TFP are significantly correlated if the roles of human capital and institutions as contingencies are considered. They also claim that the rapidly growing inward FDI boosted by opening-up policies in developing countries can significantly contribute to corporate productivity growth. Baltabaev (2014) adds that shorter distances to FDI countries of origin with frontier technology will make such impact more remarkable in the FDI inward regions. Turning to the case of the UK, Harris and Moffat (2013) find that FDI contributed to the aggregate TFP in the UK for 1997–2008 and the investment-friendly policy in the UK has led to such growth of TFP. Haskel et al. (2007) focus on impacts of FDI on corporate productivity in the manufacturing sector and suggest a robust and significantly positive correlation between a domestic plant’s TFP and the foreign-affiliate share of activity amid an investment-encouraging scheme. Brexit is also expected to bring more barriers to FDI in the UK (McGrattan & Weddle, 2020), thus hinder the growth of corporate TFP, which leads to the second hypothesis:

Third, inward immigration can act as a significant channel through which policy shocks can impact corporate TFP. Immigrants bring skills, education, and training that enhance labour productivity while high-skilled immigrants disproportionately contribute to innovation and TFP growth (Lucas 1988). Empirically, Fassio and Kalantaryan (2020) find that, generally, migrants contribute to the productivity of the sectors in which they are employed with significant heterogeneity across sectors in Europe. Tombe and Zhu (2019) analyse impacts of a representative policy shock, ease of Hukou system in China, on corporate productivity and find that reduction in migration costs causes increase in productivity. Brexit, on the contrary, has imposed additional restrictions on immigration from the EU² while EU labour migrants have occupied 72% of all labour migrants in Wales, according to LFS data. Thus, the third hypothesis is:

Brexit as a policy shock has been considered to have caused negative impacts on corporate TFP in the UK. For instance, Reenen and Yang (2023) refer to historical firm-level data of productivity and find that Brexit has led to inferior corporate TFP for firms in the UK compared to firms in France, Germany, and the US. Bloom et al. (2019) find that firm-level productivity was depressed by Brexit due to growing concerns over economic uncertainty related to Brexit, and firms that are more exposed to international trade, owned by EU countries, and belong to sectors that rely heavily on the UK–EU trade are more likely to suffer from corporate TFP decline due to Brexit.

Nevertheless, it is important to note that, to the best of the author’s knowledge, relevant studies on the impacts of Brexit on corporate TFP in the UK and its regions with firm-level data are extremely inadequate. It does not mean that discussions on how Brexit affected the aggregate TFP in the UK are scarce, given that multiple studies have revealed that Brexit and its relevant uncertainty of UK–EU trade, FDI to the UK, and broader socioeconomic risks in the UK will bring negative impacts on the UK economy measured by aggregate TFP (McGrattan & Waddle 2020; Broadbent et al. 2023; Fingleton et al. 2023). These discussions have provoked insights into potential mechanisms through which Brexit can affect corporate TFP, i.e. trade, FDI, and immigration.

Although seldomly discussed in the UK, impacts of Brexit on corporate TFP should present spatial and corporate heterogeneity due to multiple reasons including differences in initial levels of local economic growth and firms’ own business performance. The heterogeneity issue in the topic of how corporate TFP responds to policy shocks is thoroughly discussed in China. For instance, Liu et al. (2021) reveal that the financialisation project of manufacturing enterprises will have heterogeneous impacts on corporate TFP in China, i.e. firms with initially higher TFP and private ownership will benefit more from the project than other kinds of firms. Zhang and Du (2020) claim that firms in more developed regions and with higher-level green technology will receive more significant effects on corporate TFP from the green development strategy in China. As such, this study will also try to examine the potential heterogeneity of impacts of Brexit on corporate TFP in Wales, which leads to the final hypothesis:

Although there are a great number of existing studies on Brexit and its impact on corporate TFP, there are still significant research gaps. First, the majority of these studies focus on this issue from a national perspective without highlighting spatial heterogeneity across the UK with a scope of regionalism. Second, few studies have discussed potential mechanisms through which Brexit influenced corporate TFP in the UK. Finally, the Welsh economy and Welsh firms with close economic ties with the EU have been too long ignored, while such analysis is critical for many other firms sharing strong connections with the EU. This study aims to fill these gaps with advanced methodologies and up-to-date data.

The dependent variable of this study is corporate TFP. There are three primary approaches used in academic research to calculate total factor productivity (TFP). The initial approach falls under the parameter method, exemplified by Solow’s residual method and stochastic frontier analysis (Fuentes & Morales 2011). However, the stochastic frontier function’s functional form and distribution assumptions are often too stringent for practical application. The second type encompasses nonparametric methods like the data envelope analysis (Danquah et al. 2014; Zhu et al. 2018), which relies entirely on data-driven techniques.

The final approach is the semiparametric method, typified by the Levinsohn–Petrin (LP) methods (Levinsohn & Petrin 2003). This method involves first estimating the coefficients of independent variables to discern the influence of state variables on intermediate inputs versus outputs. Subsequently, this method estimates the coefficients of state variables and independent variables and can effectively address endogeneity and sample selection bias issues arising from the correlation of TFP within residual input factors. Thus, this study adopts the LP method to proceed with empirical analysis.

The essential idea of the LP method is to utilise the intermediate input of a firm as a proxy variable for corporate TFP. It assumes that the firm makes business decisions based on current productivity of this firm. Equation (3) shows the typical relationship between enterprise input and output, where \(y_{{{\text{it}}}}\) represents corporate output; \(W_{{{\text{it}}}}\) represents the free variable measured by payroll reflecting the cost of labour; \(X_{{{\text{it}}}}\) is a state variable often measured by enterprise capital; \(\omega_{{{\text{it}}}}\) denotes the corporate TFP; \(\varepsilon_{{{\text{it}}}}\) is the white noise.

According to Levinsohn and Petrin (2003), corporate TFP can thus be estimated by Eq. (4). LP method assumes that corporate TFP conforms to the first-order Markov process, where \({\Omega }_{i,t - 1}\) means the decision information set and \(\xi_{{{\text{it}}}}\) is productivity shock which is irrelevant to corporate TFP and state variables.

LP method also assumes that the intermediate input \(M_{{{\text{it}}}}\) depends on \(X_{{{\text{it}}}}\) and \(\omega_{{{\text{it}}}}\) while \(M_{{{\text{it}}}}\) will increase monotonously with \(X_{{{\text{it}}}}\) and \(\omega_{{{\text{it}}}}\). Equation (6) can be derived from Eq. (5).

Then, insert Eq. (6) into Eq. (3) to get Eq. (7), where \(\varphi_{{{\text{it}}}} \left( {M_{{{\text{it}}}} ,X_{{{\text{it}}}} } \right)\) is equal to \(\gamma X_{{{\text{it}}}} + h\left( {M_{{{\text{it}}}} ,X_{{{\text{it}}}} } \right)\).

As is shown in Eq. (7), a third-order polynomial containing the \(M_{{{\text{it}}}}\) and \(X_{{{\text{it}}}}\) is replaced by the term \(\varphi_{{{\text{it}}}} \left( {M_{{{\text{it}}}} ,X_{{{\text{it}}}} } \right)\). Thus, Eq. (7) can be estimated by OLS to obtain estimated coefficient \(\hat{\beta }\) of \(W_{{{\text{it}}}}\), so that Eq. (8) can be derived, where \(\eta_{{{\text{it}}}} = \xi_{{{\text{it}}}} + \varepsilon_{{{\text{it}}}}\).

Construct \(\hat{\omega }_{{{\text{it}}}} = \delta_{0} + \delta_{1} \omega_{i,t - 1} + \delta_{2} \omega_{i,t - 1}^{2} + \delta_{3} \omega_{i,t - 1}^{3} + \theta_{{{\text{it}}}}\) to calculate the nonparametric consistency estimate of expected value \(\hat{E}\left[ {\omega_{{{\text{it}}}} |\omega_{i,t - 1} } \right]\). Since we have known \(\widehat{{\omega_{{{\text{it}}}} }} = \widehat{{\varphi_{{{\text{it}}}} }} - \gamma X_{{{\text{it}}}}\) and \(\hat{\omega }_{i,t - 1} = \hat{E}\left[ {\omega_{{{\text{it}}}} |\omega_{i,t - 1} } \right] + \xi_{{{\text{it}}}}\), these two equations can be inserted into Eq. (8) and we can get Eq. (9).

Thus, the residual \(\eta_{it} = \xi_{it} + \varepsilon_{it}\) can be obtained from Eq. (9), which is corporate TFP:

Additionally, it is important to note that the LP method leads to revenue TFP with potential markup. However, existing studies on impacts of Brexit on corporate TFP in the UK, such as Bloom et al. (2019), have revealed that markup is not the channel through which Brexit imposed impacts on corporate TFP, since trends of markup are found to be identical for firms in the UK and other countries, at least before 2020. Thus, it is safe to apply LP method in this study with markup controlled. Meanwhile, the author adopts Ackerberg–Caves–Frazer (ACF) approach (Ackerberg et al., 2015) to address potential non-monotonicity in input choices post-Brexit. The results remained consistent with our initial estimates, suggesting that Brexit-related bias on intermediate factors is minimal.

For the fixed-effect analysis, the independent variable is \(U_{{{\text{it}}}} \times {\text{Post}}_{t}\) in the form of an interaction term that denotes how and when each firm in Wales was impacted by Brexit-related uncertainty. \(U_{it}\) comes from the Brexit Uncertainty Index (BUI) which combines the BUI data released by Bank of England in 2016–2019 (Bloom et al. 2019) and the BUI data released by Chun et al. (2023) from the University of Birmingham in 2013–2019. The BUI by Chun et al. (2023) consists of multiple novel news-based indicators of Brexit uncertainty at both aggregate and topic-specific level for the UK economy and business environment based on textual analysis and machine learning methods. They also include data analysis on key words of Brexit and business uncertainty in news, business reports, corporate annual reports, and social media in the UK to estimate how business owners responded to Brexit and relevant concerns. More specifically, following Chun et al. (2023) and Bloom et al. (2019), \(U_{it}\) shows firm-specific exposure to Brexit-related uncertainty through the following equation:where \({\text{Brexit}}_{{{\text{it}}}}\) represents logarithmic frequency of the word “Brexit” on all reports released by each sample firm in each year, and this textual analysis uses machine learning and natural language processing (NLP) techniques to count the frequency of Brexit-related terms; \({\text{EUT}}_{{{\text{it}}}}\) means the proportion of EU-related trade in total trade volumes of the specific firm in a year; \({\text{EUI}}_{{{\text{it}}}}\) means the proportion of EU-related investment in the specific firm in a year. After reviewing empirical results from Chun et al. (2023) and Bloom et al. (2019) and calibration, values of \(\alpha_{0}\), \(\beta_{1}\), \(\beta_{2}\), \(\beta_{3}\) are 0.3, 0.5, 0.3, and 0.2, respectively. For the PSM-DID analysis, the independent variable is the Brexit dummy which presents in the form of \({\text{Treat}}_{i} \times {\text{Post}}_{t}\) representing whether the firm \(i\) was directly impacted by Brexit in year \(t\), where \({\text{Treat}}_{i}\) will equal to 1 if this firm is located in Wales and 0 if this firm is in Brittany, and \({\text{Post}}_{t}\) will equal to 1 if \(t\) is larger than 2016.

As is discussed in previous sections, numerous scholars have found that Brexit-related uncertainty might have caused significant effects on FDI inflow to the UK, international migration to the UK, and international trade for the UK with its trade partners, especially EU countries. Meanwhile, whether these channels have moderating effects on corporate TFP for individual firms in Wales depends on whether firms are vulnerable to Brexit. Hence, this study incorporates EU-related FDI inflow, inward migration, and trade into the benchmark model and establishes a set of equations that perform the mechanism tests.

Economic development status and local economic growth might significantly impact corporate productivity in a certain region (Ding et al. 2016). Meanwhile, initial business performance and endowments might affect the development of corporate TFP for firms as well (Duguet, 2006). Therefore, this study uses several control variables that belong to both macrolevel and corporate level: (1) on the macrolevel, they include GDP per capita, unemployment rates, inflation rates, FDI inflow, and total trade volumes in Wales; (2) on the corporate level, they include total revenue, return-on-asset, net profit margin, number of employees, capital-output ratio, current ratio represented by the debt-to-asset ratio, and the length of business operation.

The research area of this study covers all 22 local authorities in Wales since each local authority has at least one sample firm according to the database utilised for this study (See Fig. 1). It is found that firms in South Wales are significantly more than those in other parts of Wales.