Data and descriptive evidence
The empirical analysis is based on data from between 2800 and 2900 regional submarkets in Slovakia.Footnote 5 Data characterizing market conditions for pharmacies, physicians and dentists are collected on a local level for three time periods (1995, 2001, and 2010).
The number of sellers in each town is calculated using data from the “Register of Economic Subjects” of the Slovak Republic, which should cover all relevant firms. We identify firms as belonging to a particular group based on their main economic activity following the NACE Rev. 1 classification of industries. The Register also provides information on the location of the sellers, which allows us to compute the equilibrium number of firms. Large towns may be divided into several submarkets based on ZIP codes. In total, there are 2843 (2897 and 2926) markets in 1995 (2001 and 2010).
Table 2 provides an overview of the observed market structures, as well as their frequency. As markets with more than seven firms are seldom observed, we pool them to increase the precision of the estimates. This approach is in line with previous applications of the methodology.
Table 2 Summary statistics for the number of firms in markets for professional services in 1995, 2001, 2010 The firm data are merged with market-level information on total population. Demographic variables are available at a highly disaggregated level. As can be seen from Fig. 1, the most common category of towns has a population of fewer than 500 inhabitants. This fine definition of the administrative units allows us to measure variations in local characteristics extremely precisely. The figure also illustrates the close relationship between population and the number of firms, suggesting that the number of inhabitants is a good measure of market size.
To assess the level of market barriers and competitive effects more precisely, it is necessary to build a model which controls for additional municipal specifics, to reflect the fact that consumers differ in their per-capita level of demand. We, therefore, supplement population data with information on the share of young and senior citizens.Footnote 6 These data, as well as the information on the total number of inhabitants, are taken from the “Urban and Municipal Statistics” and as such are provided at the most detailed level. Unfortunately, data on wages and unemployment rates are only available at the district level, as they come from the “Regional Statistics Database” of the Slovak Republic. We provide descriptive statistics for the variables in the Appendix.
Empirical framework
In line with previous work by Bresnahan and Reiss [2] and Schaumans and Verboven [22], we propose that healthcare providers within a given market have identical characteristics. This implies that in a market with N competitors, the level of per-firm per-capita variable profits (v(N)) is the same for all firms. Furthermore, we assume that fixed costs (f) are independent of the number of firms. Per-firm profits are given by \(\pi (N)=v(N)S-f\), where S represents the market size measured by population. In a market with free entry and N firms, revealed preference implies that:
$$\begin{aligned} \pi _{N+1}=v(N+1)S-f<0<v(N)S-f=\pi _N \end{aligned}$$
or equivalently:
$$\begin{aligned} \ln \frac{v(N+1)}{f}+\ln S<0<ln\frac{v(N)}{f}+\ln S. \end{aligned}$$
(1)
To estimate \(\ln \frac{v(N)}{f}\), we collect data on market characteristics (summarised in the matrix X), include firm-fixed effects (\(\theta _{N}\)) and allow for random shocks in expected profitability via an unobservable error term \(\varepsilon\).
$$\begin{aligned} \ln \frac{v(N)}{f}=X\beta -\theta _N+\varepsilon ,\quad \varepsilon \sim N(0, \sigma ^2I). \end{aligned}$$
(2)
The model can then be estimated using an ordered probit specification for the number of firms in any given market (y)Footnote 7:
$$\begin{aligned}&y=N,\quad \text{if } \theta _N \le y^* < \theta _{N+1}\\&y^*=X\beta + \ln S + \varepsilon . \end{aligned}$$
The values of \(\theta _N\) and \(\theta _{N+1}\) measure the changes in the variable profits to fixed costs ratio which can be attributed to market structure. If the two parameters are significantly different from each other, one would conclude that market profitability changes substantially with the entry of the \(N+1\)st competitor.
Note that estimating an ordered probit model on the number of firms in individual markets assumes that these markets are spatially isolated. While the assumption of spatially isolated submarkets might be plausible in Bresnahan and Reiss’ [2] empirical analysis,Footnote 8 the high population density in many Western and Central European countries renders this assumption highly implausible.
A Moran’s I analysis (see Table 3) of our variables of interest also points to the presence of strong spatial autocorrelation both in the number of firms and in the market characteristics.Footnote 9 Particularly for the last two periods, there is correlation in population measures, as certain hubs of economic activity are formed. This shows that similar markets are likely to cluster together and further suggests that unobserved characteristics are also likely to be correlated across space. With this in mind, taking into account not only the level of the latent profitability in a given market, but also in adjacent administrative units, may improve the quality of inference. We therefore follow Lábaj et al. [24] by allowing for spatial autocorrelation across observations. As consumers are likely to demand healthcare services beyond the border of their municipality, we explicitly model interactions across towns and hence implement a model which captures the characteristics of densely populated areas.
Table 3 Spatial autocorrelation in firm numbers and market characteristics Spatial dependence is modelled using a spatial autocorrelated ordered probit model (see [25]), which presumes correlation across latent profitability (\(y^*\)):
$$\begin{aligned} y=N \quad \text{if } \theta _N< y^*< \theta _{N+1} \end{aligned}$$
$$\begin{aligned} y^*=\rho Wy^*+X\beta + \ln S + \varepsilon ,\quad \text{where }\varepsilon \sim N(0,\sigma ^2 I). \end{aligned}$$
(3)
We assume that consumers have a strong preference for healthcare providers which are close by and hence use a W matrix with an exponential specification and elements equal to \(w_{ij}=1/\text{dist}_{ij}^2\), where \(\text{dist}_{ij}\) is the distance between regions i and j. For estimation purposes, the matrix is also row-standardised.Footnote 10
In the presence of spatial autocorrelation in the latent profitability measure, the data are assumed to follow a truncated multivariate normal distribution:
$$\begin{aligned}&y^* \sim TMVN(\mu ,\varOmega )\\&\mu =(I-\rho W)^{-1}(X\beta +\ln S)\\&\varOmega =[(I-\rho W)'(I-\rho W)]^{-1}. \end{aligned}$$
Note that the theoretical interpretation of the spillover effects (measured by the parameter \(\rho\)) is ambiguous, since they measure the effect of a one-unit change in the estimated average neighbourhood profitability. This profitability (denoted by \(Wy^*\)) may rise due to two counteracting reasons: (1) if market characteristics improve (in other words \(\mu\) grows) or (2) if more firms have entered the market (since \(y^*_N<y^*_{N+1}\) by construction). Hence, we would expect a positive value of \(\rho\) if practitioners cluster in certain areas (suggesting that demand effects are more important than competitive effects). If the observed values are negative, this would imply that the aim of the regulator is to offer a supply distribution which is uniform. In this scenario, the central planner will try to make sure that firms are not located too closely to each other to increase efficiency and decrease transportation costs in remote areas. In this case, whenever the neighbourhood profitability \(Wy^*\) grows due to entry, the likelihood of a firm establishing itself in the local market will decrease significantly, resulting in a negative sign of \(\rho\).
The Bayesian MCMC procedure used for the estimation is based on Wilhelm and de Matos [26]. Conditional on the observed number of firms and the characteristics of each market, a draw is taken for the latent profitability from the conditional distribution of \(y^*\) via Gibbs sampling. Once these values are obtained, the model can be estimated using standard Bayesian SAR methods.Footnote 11
Once the parameters in Eq. (3) are identified, we can analyse the ease of entry of the first healthcare provider by calculating the so-called monopoly entry threshold (\(S_1\)), which represents the number of consumers necessary to cover the fixed costs of the first entrant:
$$\begin{aligned} S_1=\exp (\hat{\theta }_1-\bar{X}\hat{\beta }-\hat{\rho } Wy^*). \end{aligned}$$
Changes in the value of \(S_1\) over time would be indicative of changes in the level of entry barriers. A high breakeven population is often a signal for regulatory obstacles to entry, as well as for low expected profitability per capita, even in markets with no additional competitors. By comparing the estimated thresholds across time, it is possible to ascertain to what extent the transition process changed the barriers to entry facing healthcare providers. While the rise in income levels is likely to decrease the threshold for entry by increasing per capita demand, government intervention aimed at raising efficiency may have made it harder for firms in rural areas to remain economically viable. The net effect of these changes is reflected in the estimates of \(S_1\).
Aside from evaluating the ease of entry for providers with a monopoly position, we would also like to access how the competitive pressure exerted by each successive entrant has changed during the transition period. Following Bresnahan and Reiss [2], we focus on the change in per firm breakeven population in order to measure the magnitude of the decrease in profitability attributable to each new firm. If new entrants result in lower markups for incumbent sellers (either through decreasing the price of unregulated services or by increasing costs due to investments in quality), the number of firms will not grow proportionally to population.
We quantify competitive effects by comparing the per-firm break-even population for each market structure:
$$\begin{aligned} s_N=\frac{\exp (\hat{\theta }_N-\bar{X}\hat{\beta }-\hat{\rho } Wy^*)}{N}. \end{aligned}$$
(4)
From these estimates, we construct so-called entry threshold ratios (\(\text{ETR}_N\)):
$$\begin{aligned} \text{ETR}_N=\frac{s_{N^m}}{s_{N}}=\exp (\theta _{N^m}-\theta _N)\frac{N}{N^m} \end{aligned}$$
(5)
where \(N^m\) represents the upper limit of the number of firms in a market.Footnote 12
An increase of entry thresholds with the size of the market (\(s_N < s_{N+1}\)) is an indication of intensified competition. Since we assume that in markets with \(N^m\) firms, competition is at its most intense level (this assumption is valid in markets where entry results predominantly in business stealing, rather than market expansion), an estimate of \(s_N\) for which \(s_{N^m}/s_N=1\) would indicate that N entrants are sufficient for a perfectly competitive outcome.
The intuition behind this conclusion is that consumers have the same level of demand per capita across market structures (a presupposition which is reasonable for healthcare services). Abstracting from competitive effects, we would, therefore, expect the number of providers to grow proportionally to market size. If this is not the case and \(s_{N^m}/s_N>1\), then firms in a competitive market (with \(N^m\) firms) need a larger population to break even than those in a market with only N competitors. This would indicate that healthcare providers in more concentrated markets have higher markups, either due to smaller investments in quality or due to stronger government subsidization. As such, the values of \(\text{ETR}_N\) provide valuable information regarding the effects of government policy and strategic firm behaviour.