Small Business Property Tax Reductions and Firm Productivity

We base our analysis on the UK ONS Annual Respondents Database X, first released in July 2016 combined with Business Structure Database and Prices Survey Microdata. Descriptive statistics of raw data are available in Appendix 2.

The Annual Respondents Database X combines two existing surveys, the Annual Business Inquiry (1998–2008) and the subsequent Annual Business Survey (2009–2014), which firms’ representatives are legally required to complete, producing high response rates. It is a complex stratified sample across size, sector and region. The sample framework is constructed using administrative data on employment and turnover from PAYE⁵ and VAT-registered firms. Importantly for our purposes, it captures information at both the enterprise and local unit levels. We limit the sample to firms that have only one local unit because businesses, with some exceptions, have to use only one property to receive SBRR. We also need to calculate firm’s rateable value and SBRR from the survey reported BR (see Appendix 1).

We combine this data source with the Business Structure Database to acquire the observations from smaller firms that were not included in the Annual Respondents Database X.⁶ The Business Structure Database contains an annual release of a small number of critical variables on all UK registered firms and is complementary to the above business surveys.

The Annual Respondents Database X and Business Structure Database do not directly provide controls for the input price changes that we require for the estimation of productivity. To control for omitted price bias (as defined by Van Beveren, 2012), we do not use the typical approach of employing the inherently biased general gross domestic product, but use the Prices Survey Microdata data, which contains more accurate regional and sector level prices. We devalue to 2016 prices.

To illustrate whether the non-domestic property tax reliefs have any impact on productivity, we could simply estimate:where \({\omega }_{it}\) is the productivity of establishment \(i\) at time \(t\) and error term, \({e}_{it}\), that captures the demand shock \({\rho }_{ij}\) in reduced form. The main parameter of interest is \(\beta\) capturing the effect of any relief, \({\alpha }_{it}\).

Standard estimators such as Ordinary Least Squares would not yield a consistent estimate of \(\beta\) because establishment-level characteristics are unlikely to be independent of each other or local characteristics. Following Gemmell et al. (2019), the first step in addressing the feasible complex relationships is to exploit our large representative dataset to recreate the conditions of a quasi-natural experiment⁷ in which firms that receive SBRR are matched to similar single-unit firms which do not. Our large dataset enables us to use a wide range of observable establishment level characteristics, namely materials, age, investment, rent, output per employee, employment, sector, legal status, turnover and gross value added, to produce matches. The dependent variable is a dummy taking a value if one for those firms that received the relief at least twice between 2003 and 2015 and zero otherwise.

However, instead of the more popular Propensity Score Matching, we match using Coarsened Exact Matching. It uses a more efficient fully blocked randomised experiment rather than attempting to approximate a completely randomised experiment as applied in the Propensity Score Matching, which was found to increase imbalance, model dependence and bias (King & Nielsen, 2019). The SBRR recipient firms are matched 1 year prior to the introduction of SBRR or, in the case of young firms, on their first observable year to corresponding non-recipient firms.

Separate matching is performed for each year starting with 2002, with the non-recipients being excluded from further matching if they matched previously. Thus, most of the matching was performed on 2004 data, 1 year prior to the SBRR introduction in England. This produced a final dataset for the years 2000 to 2015 of 15,047 observations for 1092 firms, 546 SBRR recipients matched to 546 firms which had never received the relief, yet had similar characteristics. To describe the reduction in imbalance after matching, as per Iacus et al. (2009) recommendations, we estimate the \({\mathcal{L}}_{1}\) statistic that includes imbalance with respect to joint distribution and all interactions between recipients and non-recipients. The matching produced a substantial reduction in imbalance with \({\mathcal{L}}_{1}\) decreasing from 0.776 to 0.592 for 2004.⁸

We then expand our specification with variables that provide a more realistic setting for the analysis of heterogeneous establishments. For simplicity, we classify our independent variables as time-varying establishment-specific variables, \({Z}_{it}\), whilst establishment-fixed effects are captured by the intercepts, \({f}_{i}\). That is⁹:

This specification still does not fully identify the complex groupings of firms. Building on the configurational approaches literature (Meyer et al., 1993), we imply that a number of variables are unlikely to be additively separable and permit us a priori to establish a clear mechanism through which the policy affects productivity. Controlling for all feasible interactions would produce a complex number of coefficients, possibly even a unique set of coefficients for each firm, \({\beta }_{it}^{a}\) and \({\beta }_{it}^{b}\). Such estimates would be difficult to interpret given that we cannot establish a defendable identification strategy. The estimates are also likely to be biased, especially for large datasets (Gandomi & Haider, 2015).

More standard estimators, such as mixed-effects or difference-in-difference estimators, could provide some insight into uniform relationships. However, these relationships are unlikely to be uniform but interaction-dependent because of inherent mistargeting and the subsequent uneven capitalisation amplified by different decision choices. Our reasoning is supported by the results from the difference-in-difference estimator in Table 1 that finds consistently negative but only somewhat significant results, which we further discuss in Section 4.5.

We, thus, require an estimation strategy capable of identifying complex groupings of firms. Empirical studies based on configurational approaches in SBEJ primarily used either standard statistics (Su et al., 2011), limited by assumptions of linearity, or more advanced fuzzy-set Qualitative Comparative Analysis (Hatak et al. 2021, Sperber & Linder, 2019, Wang et al., 2023). This method was found to be prone to subjective bias, require extensive data calibration and heavily rely on prior knowledge (Liu et al., 2017).

Instead, we draw on decision trees that have already been successfully applied in the real estate context with Feldman and Gross (2005) as well as in growth determinants with Tan (2010) and more recently in conjunction with configurational approaches (Graham & Bonner, 2022), who also discussed the advantages of these approaches. They stressed their ability to handle large datasets with various data types, missing values and outliers as well as their ability to capture interrelationships between variables in different parts of the measurement space, which is essential given the varying capitalisation and investment decisions. These approaches are, however, susceptible to overfitting (Cook & Goldman, 1984) and instability (Briand et al., 2009). These issues are addressed in Section 4.6.

We adopt a more recent extension than in Tan’s (2010) and exploit the RE-EM decision tree approach of Sela and Simonoff (2012) and subsequently, Fu and Simonoff (2015). This technique combines estimates from fixed and random effect trees to discover the complex groupings of firms. The random-effects element accounts for the constant differential firm-level factors, whilst the decision tree allows the data to discover the complex groupings of firms and their different levels of productivity without imposing a complex parametric structure.

The RE-EM approach assumes that neither the random effects nor the fixed effects are known and alternates between estimating the regression tree, assuming that the estimates of the random effects are correct, and estimating the random effects, assuming that the estimates from the regression tree are correct. A brief introduction to decision trees is offered in Appendix 4, and a more detailed explanation of the mechanisms of RE-EM is available in Sela and Simonoff (2012).

The RE-EM model is:

The dependent variable, \({\omega }_{it}\), is our bootstrapped estimate of productivity, as discussed below for each firm i in period t. \(Z\) is a matrix of independent variables which may vary over time and firms and \({b}_{i}\) is the vector of random effects. f(.) contains the same variables as Z, although they can differ, which we use to estimate the fixed effects via the decision tree.

Within f(.), we define \({\alpha }_{it}\) as \(g\left(\sum_{j=0}^{4}\left({SBRR}_{t-j}\right), {\rho }_{it}\right)\), i.e. SBRR and four lags to capture medium-term effects and account for the periodicity of the reliefs. We complement these variables with the dummy variable \(\rho\) to capture the initial¹⁰ effects of receiving any relief or uplift in relief, irrespective of level.

We include the broad sectors (s) of wholesale, catering, construction, production, property, retail and other services and foreign ownership. The Office of National Statistics (2017) calculates that UK firms receiving foreign investment have 74% higher productivity than those which do not. As such, we include the dummy variable \(FO\) that takes a value of 1 for firms with a foreign majority owner to account for any systematic effects. In this era of concerns about complex ownership structures and use of complex taxation schemes, we also use the variable \(IO\) to denote a foreign country registration of the firm’s immediate parent firm, as also employed by the ONS. This can be different from \(FO,\) which denotes the ultimate country of the owner.

We also control for firm age (a), whether it is high growth (HGF) and Research and Development (R&D) active. Since the pioneering work of Griliches (1979), productivity models¹¹ have considered technological spillovers to be a side product of R&D activities, as such we control for whether a firm intends to undertake R&D within the next 2 years.

HGF is a dummy taking the value of 1 in the years in which a firm meets the Eurostat-OECD (2007) definition, namely average annualised growth in employment greater than 20% per annum, over a 3-year period with initial employment not lower than 10.

Beyond firm-level effects, we explore important national, regional and small (two-digit postcode) location and industry specific effects. We include the regions and nations (r) of Wales, Scotland, North East, North West, Yorkshire and Humberside, East of England, East Midlands, West Midlands, London, South East and South to control for fixed location effects. Given our access to detailed firm-level microdata, we include finer spatial and time-varying indices for Jacob production diversity (PD) and Marshall production specialisation (PS), within small two-digit postcode areas, relative to national SIC (2003) two-digit industry output. Finally, we control for industry concentration at the national level via a Herfindahl–Hirschman Index (HHI).

Various specifications of these indexes may influence the results and their interpretation. In terms of PS and PD, we wanted to ensure that the measures complement each other and can coexist in one equation. Thus, we follow the specification of Modrego et al. (2015), who derive PS as region and sector-specific, whilst PD as region-specific, enabling them to coexist (Van der Panne, 2004). In terms of HHI, we followed the commonly applied design (e.g. in Fairlie et al., 2023), which estimates HHI by squaring each firm’s market share and then summing the resulting numbers.

The PS index captures relative industrial clustering effects. For example, the agglomeration may enable the creation of better labour pools, supplier services or the spillover of incremental process and product innovations. SBRR may interact with these local factors by reducing the assumed financial barriers to adoption or creation of incremental changes. That said, we may also observe increased competition for specific types of premises and a more rapid capitalisation of any tax reliefs.

We calculate the PS index in line with Modrego et al. (2015), Feldman and Audretsch (1999) and Paci and Usai (1999).¹² However, our detailed data enables us to enhance the accuracy of the index by using firm turnover rather than employment to create the index. This produces a less noisy control for productivity than employment and a far more accurate perspective on the concentration and value of activity. The index is:where T is industry i turnover in area j. We calculate the turnover of a given industry (i) in an area (j) as a proportion of all turnover in that area and then place it in relation to national turnover from the same industry as a proportion of national turnover.

We capture any local Jacob (Production) Diversity effects via an index based on the reciprocal of the Gini Coefficient as proposed by Paci and Usai (1999):where \(n\) is the number of industries in region j, \({Q}_{i}\) is the cumulative turnover up to industry \(i,\) then ordered by ascending size. The index, bounded by 0 and 1, increases with variety. Differently to HHI or PS, PD captures whether location, rather than the firm or industry, is at the centre of analysis and drives changes (Florida et al., 2017). Innovation is aided by access to ideas and procedures that firms can copy or modify from a diverse set of industries or knowledge generating institutions within small areas or, given the positive correlation with urban areas, more diverse and stable demand. That said, at our two-digit postcode level, we will observe a substantial degree of variation even within urban areas.

The error term, \({\varepsilon }_{it}\), is assumed to be uncorrelated with the random effects and independent across observations. \({R}_{i}\) is a non-diagonal matrix to account for autocorrelation within firms.

The most apparent first-order effect of SBRR is a reduction in investment in capital. Having said that, for some organisations, this could trigger expenditure in other areas that could be equally effective, including organisational environment, organisational capabilities, types of innovation, external knowledgebase, or even commercialisation that were found to be dominant in researching SME productivity, as recently summarised by Owalla et al. (2022). Considering this in connection with the ideas of heterogeneity in organisations from the configuration approaches literature, discussed in Section 3, we conclude that the concept of comparing total outputs relative to the total inputs used in the production of the output in the SBRR context could provide a fuller picture for our exploratory analysis than focusing on one specific outcome. We also depart from the commonly applied single-factor productivity measures, such as labour productivity, because multi-factor productivity measures better capture the changing trends in the working environment (Owalla et al., 2022) and avoid such limitations as the attribution of all increases of efficiency to one factor (Linna et al., 2010).

Total factor productivity is not directly observed from production functions and consequently needs to be extracted once the weighted sum of inputs has been estimated with controls for simultaneity and selection biases. We resort to control function approaches that are built to overcome these biases (Van Beveren, 2012). We employ Wooldridge’s (2009) approach, which builds on the work of Olley and Pakes (1996) and Levinsohn and Petrin (2003). His single-step GMM framework also overcomes more recent criticism directed towards the control function estimators failing to consistently estimate the labour coefficient in the first stage (Ackerberg et al., 2015). We thus estimate productivity assuming a Cobb Douglas functional form:where \({\omega }_{it}\) is productivity of the ith firm in period t, \({lnGVA}_{it}\) is the firm’s logarithmic gross value added in order to simplify the model and eliminate intermediate inputs, \(K\) is logarithmic capital and \(L\) is logarithmic labour. To reduce selection bias, we averaged estimates from 1000 estimations with missing values replaced by the predictive mean matching with the key variables of unique firm identifier, year, turnover, employment, region, sector and legal status that have almost no missing data from the Annual Respondents Database X or Business Structure Database. For instance, if a firm had all observations but no data for 2005, we would impute the 2005 data 1000 times and produce 1000 datasets, which then were used to estimate 1000 separate models defined in Eq. (6).

To compare the findings to more traditional approaches, we also conduct analysis with a more standard difference in difference estimator that has been widely employed in numerous recent publications in SBEJ (Amamou et al., 2022; Bailey, 2017; Biancalani et al., 2022; Liu et al., 2019; Dosi et al., 2012; Lewis, 2017) that show various specifications and empirical strategies of this approach. There seems to be no consensus on which strategies are preferred, with scholars trading increasingly restrictive assumptions with solutions to various issues, such as heteroscedasticity and autocorrelation.

We primarily follow the empirical strategy adopted in the recent study by Biancalani et al. (2022), who also offer a more detailed explanation of the methodology behind the estimator. Our difference in difference estimator thus departs from the standard specification in that the treatment variable is equal to 1 for firms receiving SBRR and only during years when they actually receive SBRR and 0 otherwise in models (1) to (4). In addition, we incorporate the extent of SBRR in models (5) to (8). We control for firm and time fixed effects in all specifications and cluster standard errors on sectors. We also include similar controls to those in f(.) in Eq. (3) in models (3), (4), (7) and (8). We estimate the treatment effect with the simple fixed effects panel regression in models (1), (3), (5) and (7), which we compare to estimates in models (2), (4), (6) and (8) that use Newey and West’s (1994) automatic bandwidth selection procedure to produce heteroscedastic and autocorrelation consistent estimation of the covariance matrix of the coefficient.

The results suggest that SBRR seems to have an adverse effect on some firms in terms of their productivity, but it does not alleviate a binding constraint for the average company. As reported in Table 1, we find consistently adverse treatment effects but these effects amongst firms seem to vary, as indicated by the relatively high error estimates in models (1) to (4) that resulted in insignificant coefficients. Once we include the extent of SBRR, the negative coefficients are greater, and the error terms are relatively smaller, resulting in a significant relationship but only at a 90% significance level in models (5), (7) and (8), indicating that the likelihood of companies receiving more relief to have lower productivity is greater. For instance, those with 100% SBRR have 0.6% lower productivity, with other variables keeping constant. This, thus, supports the need to explore these nuanced relationships further with such tools as RE-EM trees.

We also perform further model diagnostics to ensure that our model does not suffer from widely known issues. To overcome the issue of overfitting (Cook & Goldman, 1984), we impose a minimum number of observations in each final node. To test stability, we follow the Philipp et al. (2018) framework and implementation. The RE-EM trees achieved the highest stability score for this dataset, a median of 0.82. To assess the accuracy, we use tenfold validation, in which we compare the predictive capacity of our trees to other candidate algorithms. The RE-EM tree achieved a relatively high accuracy when compared to alternative methods. Root mean square error estimates indicate that the RE-EM tree achieved the highest accuracy, but that was not the case with mean absolute error, which accounts for extreme outliers. Based on this estimate, random forests slightly outperformed RE-EM tree. More detailed procedures and results are reported in Appendix 3.

Our paper extends the existing knowledge in SBEJ on how taxation affects small businesses. The consensus is that taxes are detrimental to entrepreneurship (Baliamoune-Lutz & Garello, 2014; Bennett, 2021; Bruce & Mohsin, 2006; Ferede, 2021; Venâncio et al., 2022), including productivity (Romero-Jordán et al., 2020) and tax incentives have positive effects (Liu et al., 2019; Sterlacchini & Venturini, 2019; Venâncio et al., 2022). Our results are contrary to these findings. This difference is likely to result from mistargeting and uneven capitalisation (as discussed in Matikonis, 2020, 2022), from which other than property tax instruments are less likely to suffer.

We find that these relationships are not uniform but highly dependent on the context, extending Hilber’s (2017) synthesis to non-domestic property. For instance, with regard to regional patterns, London has a higher average weighted productivity, but this is related to only a small number of extreme firms, not SBRR. In the rest of the UK, we find for approximately one quarter of observations that higher productivity is associated with greater small area diversity,¹⁴ particularly for younger firms. This finding is counter to Harris and Moffat (2017), who find agglomeration rather than diversity externalities is associated with higher productivity. This is likely to be because our approach accounts for the complex interaction effects of firm, place, industry and policy.¹⁵ Having said that, these findings on small area production diversity do not suggest the central government should focus on building local diversity across the UK, but rather focus should stay on further devolution, enabling the inclusion of finer-grained local dynamics to produce more successful local growth policies.

Our findings are also supplementary to the existing knowledge in SBEJ, which could add to the variety of the previous findings. For instance, previous studies found that taxation affects firm exits positively and entries negatively that was shown to be the case also for property taxes (Bennett, 2021). Similar findings were found by those that analysed other tax instruments, with results pointing to tax incentives increasing the number of entrants (Liu et al., 2019 and Venâncio et al., 2022). We, thus, suggest that tax incentives are likely to positively contribute to firm entries and reduce exits, but some of those new entrants or sustained firms will potentially become less productive, but this will depend on firm characteristics and location, market and industry dynamics.

We show how configuration approaches, centring on non-linearity and equifinality, could be modelled with decision trees. In this way, we deviate from the not-so-useful concept of ‘average entrepreneur’, as argued by Newbert et al., (2022:4), and model more realistic realities using complex configurations necessary to understand the phenomena (Woodside, 2014). The RE-EM trees, an extension of the decision trees, consider the relationship between independent and dependent variables to be not necessarily linear, enabling the capture of more complex relationships, whilst regression-based approaches fail to do that by centring on net effects instead of differences between groups (Douglas et al., 2020). Decision trees also do not suffer from other common regression-based assumptions, such as lack of multicollinearity, the distribution of errors and independence of observations (Douglas et al., 2020).

Furthermore, the paper showed how machine learning could be jointly applied with more standard econometric techniques to produce a finer-grained analysis when more standard estimators do not offer valuable insight. The more standard difference in difference estimator, reported in Section 4.5, suggested that SBRR has an adverse effect on some firms in terms of their productivity, but it did not alleviate a binding constraint for the average company. The RE-EM trees enabled us to extend these conclusions by departing from the average effect to uncovering the exact groupings of firms whose productivity was impacted by SBRR and showing how these interrelate with firm characteristics and location, market and industry dynamics.

The study provided evidence that the current centralised policy of commercial property tax reductions does not work as an enable of growth. We need more feasible delivery mechanisms that support small businesses. This has implications, first and foremost, for small business owners and their representatives, such as the National Federation of Self Employed & Small Businesses, that campaign to sustain these ineffective commercial property reductions, and whose opinion is given and sought during government consultations, including the relatively recent Fundamental Review of Business Rates (HM Treasury, 2021).

Instead, we need to campaign for a more nuanced and targeted policy incorporating firm characteristics and local drivers and constraints. It could be more fruitful than the current generic policy based on building and land value, as our findings indicate. Having said that, the change in the commercial property fiscal regime is multi-layered and can only be achieved through a truly fundamental review, unlike the two business rates reviews concluded in 2016 and 2021 that resulted in superficial improvements with minimal effort to tackle the more pressing issues concerning the increasingly expansive relief package (Matikonis, 2022).

Broader recommendations from these findings are not to generalise or simplify the effectiveness of tax incentives. Although previous findings on tax incentives signal positive effects (Liu et al., 2019; Sterlacchini & Venturini, 2019; Venâncio et al., 2022), we show that commercial property tax reductions, which suffer from mistargeting and capitalisation, do not result in growth. This is especially relevant for the UK, which recently experienced the damaging effects of introducing poorly justified and unfunded tax incentives during the brief premiership of Liz Truss.

Although the usage of the secondary data source provided a large sample size and enabled us to look at the longer-term effects, another purpose-made, possibly qualitative study of SBRR could include more specific controls and/or specifically focus on uncovering mechanisms explaining why this reduction in productivity is associated with SBRR. Alternative specifications of outcome variable would also be helpful to clarify which aspects of productivity are affected by SBRR. Furthermore, once more recent data is available, further research could also help us understand how retail, hospitality and leisure relief, used as a key tool to support businesses during COVID-19, interrelate with SBRR and affect growth.

In terms of methodology, we extend Graham and Bonner’s (2022) call to small business scholars to explore the potential of machine learning. The studies with different approaches, in different contexts and with different datasets could aid in generalisability. There are also many avenues to use more advanced techniques. For instance, future research could apply causal trees, as described by Athey and Imbens (2016), to better capture treatment effects once the method is fully developed. Further extensions for multidimensional data, such as the Least Absolute Shrinkage and Selection Operator (Belloni et al., 2014), could also be a good option.