Lastly, it is straightforward in a Bayesian context to express Θ _i_ as a function of several predictor variables, so-called hierarchical co-variates. We denote the vector of these predictors as **_X_**<sup>_H_</sup> _i_<sup>,whichcan</sup> _′ H ′_ be given parameter weights in a matrix _φ_ , giving Θ _i_ = _f_ ( **_X_** _i_<sup>_φ_</sup> ) (Kubinec, 2019). This allows the measurement model to take advantage of a wide array of additional co-variates that are available in our data for the purposes of alleviating sparsity in the data. Because our survey has only one set of observations per firm, and the number of indicators is necessarily limited, estimating a separate intercept for each firm would result in unstable estimates highly dependent on the prior. By parameterizing Θ _i_ with additional survey data— **_X_**<sup>_H_</sup> _i_<sup>can include, for instance, firm perceptions of state-business relations—</sup> we can obtain stable predicted influence scores for an individual firm _i_ with intercepts that vary by country and as such are robustly identified in the posterior. This underlying set of predictors also has the attractive feature of allowing for out-of-sample prediction from surveys without explicit political connections questions, allowing us to expand the index beyond the 41 economies in the original survey data. In the appendix we include a plot of split- _R_<sup>ˆ</sup> values from a model fit with three independent Markov Chain Monte Carlo (MCMC) chains with the Hamiltonian Monte Carlo sampler Stan (Carpenter et al., 2017). The plot shows excellent convergence of the dozens of parameters in the model. We also include a plot of residuals for the two continuous items, government ownership and employee size. This plot shows that the model’s assumptions appear to be approximated by the distributions we assigned to the items.

The model does make an assumption of conditional independence. We assume that the responses for each firm are independent conditional on the country of the firm and all firm-level co-variates in the model. We believe this assumption to be met by design as the data were collected through a confidential survey around the same time, and firms did not have access to the responses of other companies. We also make a conditional independence assumption about items, though the assumption is weaker than for firms. By including two parameters for each item (that is, _γ_ and _β_ ), we allow the discrimination and difficulty to vary by item.<sup>17</sup> It is still plausible that the items could interact with each other, but this is also why we emphasize the interpretation of the model parameters as marginal distributions. Adding interactions between item parameters would only be advisable if we had a theoretical reason to expect those interactions as it would significantly complicate the model’s interpretation. The aim of this model is to permit theoretically informed measurement, not to maximize predictive performance.

# **3 Data and Measures of Political Interactions**

Our data are from the World Bank/EBRD/EIB Enterprise Surveys (ES) in 41 economies in Europe, Central Asia, the Middle East, and North Africa (N=27,613). Section A.3 in the Data Appendix contains basic information about the samples in each economy. The surveys cover well-defined sectors in each economy, including manufacturing, construction, retail and wholesale trade, accommodation, transport,

> since a correct response to a test question (item) is always expected to relate positively to ability. By not bounding direction, our approach follows the ideal points literature from political science (e.g. Clinton et al. (2004)), which estimates parameters on items that are, e.g. legislation, that may polarize politicians to either end of a political spectrum.

> 17See Appendix A.2 for an illustration.

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