Job quality in Denmark

How does job quality impact employee welfare? My research on CEO job quality outlines some of my main views on how employee job quality and welfare can be usefully measured. The measurement of welfare with respect to job quality is important for studying both the effective impact of training programs and the effective impact of strategies to recruit new employees.

Methodology example: CEO job quality

Many studies find that job quality significantly impacts the quality of life (OECD 2018). Studies delving into CEO welfare commonly consider both the stress levels they might undergo at certain firms and the extent of recognition and distinction that numerous CEOs attain as constituents of the economic elite . Further studies have looked at other aspects of CEO job quality that impact CEO welfare. For example, in the United States, it has been found that CEOs have a preference for working at firms headquartered in their home state.

There is also much evidence that CEO quality is relevant to the performance of a firm. Studies delving into CEO quality typically find that CEO skills are general . However, other research also observes that CEOs are usually hired in the sector or firm in which they have previous experience . The observations of general skills and limited mobility are puzzling given the obvious importance of matching higher skilled CEOs to larger firms, so that these superstar CEO general skills can be used to their best advantage.

Our study of the CEO-firm matching market is based on a simple equilibrium analysis where each firm endeavors to hire the best CEO, and each CEO is attracted to the firm offering the best combination of job qualities and pecuniary compensation. Therefore, our model is a major extension of models of the CEO market that account for the matching of CEOs based on how CEO and firm quality impact the performance of firms (\cite{pan2017determinants}), because our model also accounts for how this matching depends on how CEO and firm quality impact the welfare of CEOs. Furthermore, we allow, as in many studies of the marriage market, firms to have diverse multidimensional preferences over CEO types, and CEOs to have diverse multidimensional preferences over firm types.

Executive pay and high rates of income taxation are key features of the CEO market. Our model allows CEO pay to be taxed, which means that we do not assume transferable utility (TU) as is commonly assumed in marriage market models, for example. One implication of imperfect transferable utility is that the assignment of CEOs will generally be inefficient. The key reason in our application is that the job qualities that CEOs value are not taxed while their sources of pecuniary income are taxed . The inefficiencies associated with these tax distortions are relevant to how we solve and estimate our model of a 'stable' CEO-firm matching. For example, in solving for a stable CEO matching in our structural econometric model, we cannot simply use algorithms that exploit the well-known theoretical property of TU matching, where an equilibrium matching maximizes the total joint surplus of all participants . Instead, we solve for the stable matching of CEOs and firms in our model using an Iterative Proportional Fitting Procedure (IPFP) algorithm.

Our model also allows CEO types to be both multidimensional and continuous (i.e., not finite). Multidimensional matching is obviously important for the study of job quality because job qualities are typically multidimensional. For example, OECD (2018) guidelines on the measurement of job quality suggest that job qualities can be divided into six main categories and that different job characteristics contribute to these main categories. The continuity of CEO and firm types is important because there is generally no obvious way to discretize important CEO and job qualities. These realistic assumptions also come at a cost with respect to our selection of a structural micro-econometric model. For example, there are no obvious ways to incorporate alternative suggestions for the specification of unobserved heterogeneity - beyond our standard assumption of logit errors - that have only been proven to be tractable in matching models with TU and a finite number of types.

In our model, we assume a simple rental market of CEO services each year where all pecuniary compensation for the CEO services in that year is accurately measured. This compensation need not be paid in the given year but can be spread over the CEO’s lifetime in the form of stock options and the like. We collect this data from the Danish tax authority, which seeks to measure all sources of pay for CEO services in the current year, including the anticipated value of stock options and so on. Our assumption of accurate CEO compensation data is supported by the finding that data on taxable income at large Scandinavian firms is generally accurate due to their reliance on third-party accounting firms.

Our model is somewhat limited by our assumption that CEOs have linear preferences with respect to earned income. However, we do allow that CEOs have general firm preferences, which can differ across CEO attributes such as wealth and experience, and for different firm attributes such as the firm’s size, sector, and financial position, which may impact CEO stress, for example. Therefore, our model allows that a wealthy CEO might be more likely to avoid a high-stress, high-paying firm, which we can interpret as supporting a lower marginal value of pecuniary income for wealthy CEOs. While our empirical results support such findings, a central limitation of our assumption of linear utility in our structural econometric model is that we cannot explicitly model heterogeneous equilibrium incentive contracts, which might depend on differences in the marginal value of income and risk aversio).

Our structural micro-econometric model offers a simple framework to estimate the value of compensating differentials earned by CEOs in different jobs . Estimating compensating differentials in any labor market is potentially challenging due to the issues of unobserved selection by employers. This is also a key concern in the market for CEOs, as matching will generally be assortative and the largest and most productive firms will typically seek the most talented CEOs. However, if these firms also offer the intangible benefits of greater fame and prestige, assortative matching on skills also implies that such firms will also typically pay higher wages. Therefore, to address this issue of selection, we follow recent work by Lamadon et al (2021) and adopt a two-sided matching model that allows for assortative matching. However, since matching in the CEO market is one-to-one, we can adopt an even more general theoretical model that tractably implements heterogeneous employers and other features of the CEO market that are relevant to how CEOs are compensated and selected by firms.

Perhaps the most important limitation of simply applying the matching model of Lamadon et al (2021) to the market for CEOs is that this model would not seek to simultaneously estimate both the firm's and the worker’s problem. One key concern is that Lamadon et al only allow for unidimensional sorting, with workers differing along a characteristic X, which is scalar. Not only is sorting then unidimensional, but this limitation also implies that the same attribute matters for productivity AND preferences. In our model, we allow multiple attributes to matter, and matching is allowed to be multidimensional, but more importantly, some attributes may matter only for productivity and some may matter only for preferences. For example, we find that some CEO characteristics matter for productivity while others matter for CEO preferences. These possibilities are found to be important in our estimates. For example, we estimate a "legacy" factor that ties CEOs to a sector but does not impact their productivity.

There are other reasons why it is useful to estimate the firm’s problem with respect to hiring CEOs. By estimating the firm’s decision problem, as we do in this paper, we allow firm objectives to differ with respect to firm types and with respect to what the firm is maximizing. Therefore, by estimating the firm’s problem, we gain an understanding of what data on firms is useful for predicting which CEOs are hired and what data on firm performance, such as data on profitability, best describes firms’ actual objectives. Our estimates confirm that there is important heterogeneity in firm objectives with regard to CEOs and that administrative data on year-end firm profits can be used as a measure of firm performance that significantly improves the precision of these estimates. These findings are in line with the key findings in the CEO compensation literature.

In our empirical model, we assume that unobserved heterogeneity impacts both the ‘productivity’ of firms and the ‘welfare’ of CEOs. We follow \cite{ChooandSiow2006} and assume logit unobserved heterogeneity that is also separable. Separability means that we assume that the unobserved heterogeneities on each element of the match surplus are drawn independently of each other, conditional on each observed firm and CEO type. As in many other applications, the logit error assumption is used primarily for tractability. This is useful for modeling the market for CEOs, because we can then relax the assumptions of transferable utility and finite types. The cost of this assumption is that it imposes structure on the unobserved heterogeneity such that we assume that this heterogeneity satisfies the assumption of IIA (Independence of Irrelevant Alternatives), which is associated with McFadden's (1980) famous red bus-blue bus problem. Concerns with this assumption regarding unobserved heterogeneity are raised by G and S in the context of marriage market matching models, where match surplus between male and female types is identified from the probability of their being matched to each type on the other side of the market and their being single. While the CEO market also provides considerable information to the process of matching, both in terms of match productivity and transfers within the match, it remains difficult to fully consider the implications of the logit error assumption, as there are no tractable alternative assumptions for unobserved heterogeneity that allow for the general assumptions on transfers and types that we use in our analysis.

Since our empirical model does not require us to make strong assumptions about what CEOs and firms are maximizing and what factors go into each agent’s decisions, our model can speak to different perspectives about CEO compensation. For example, two main perspectives are the 'rent extraction view' and the 'shareholder value view'. The ‘shareholder value view', which is often employed in models that assume CEOs are hired for their contribution to firm profits, emphasizes that shareholder value is always maximized and that shareholders give weight to the problem that CEOs must be hired subject to market forces, and that CEO contracts must provide appropriate incentives for CEO participation and effort . In the influential rent extraction view, the key assumption is that boards controlling the firm might pursue objectives that are not in the interest of the shareholders. Our methods support a simple model where firms aim to maximize year-end accounting profits. We also find that simple explanations based on compensating differentials go a long way in addressing some of the key points of debate over which view is supported by key observations. For example, we find that CEOs derive a positive amenity value from managing firms with high equity value, which suggests that CEOs are paid more in firms with more stringent oversight (rather than being paid less, as might be predicted by the view that these contracts do not serve shareholder value). Furthermore, we show that an amenity for firms in the CEOs' own industry offers a simple market-based argument for the low mobility of CEOs with general skills.