In the two decades following Douglas’s presidential address to the AEA, the Cobb–Douglas regression came to be a familiar and widely used tool in empirical economics. Part II of this book explores this diffusion process, mainly by means of two case studies: the first describing how the regression was adopted by researchers in agricultural economics and the second looking at the uses to which the regression was put by economists seeking to measure and explain economic growth. First, however, I provide some necessary background for the case studies by reviewing three general developments that affected economists’ perception and use of the regression in the 1950s and 1960s.

The introduction provides an overview of the book. Although Paul Douglas is the most important person in the story of the Cobb–Douglas regression, the book is not a biography of Douglas, but of his best known and most successful creation. The book covers the period from the mid-1920s, when Douglas was doing the statistical work that led to the first use of the Cobb–Douglas regression, to the late 1960s, when Douglas’s idea had come to be widely accepted by economists, and the CES production function was emerging as the first popular alternative to the Cobb–Douglas function for estimation of production functions. My perspective is mainly that of a historian of the use of statistical analysis in economics, with particular attention given to the challenges faced by empirical researchers, and the roles played by statistical and economic theory in their development of strategies to overcome them. At various point in the book, I reflect on factors that might have helped the production function regression go from an innovative and controversial statistical procedure to a widely accepted general purpose tool in empirical economics.

A majority of Canadians hold some form of private health care insurance, most commonly obtained as an employment benefit. Private insurance accounts for around 13% of spending on health and its financing role is essentially limited to complementary coverage for services not covered by public insurance programmes. Private supplementary insurance for services covered by the public insurance system effectively does not exist in Canada (the exception is a negligible role in the Province of Québec). This limited role for private insurance in health care reflects the core policy vision for health care financing in Canada, which emphasizes equal access to medically necessary health care, especially physician and hospital services. Compared with many other countries, Canada’s private health insurance market is relatively uncomplicated, viewed in terms of either the products offered or the regulations imposed. Although Canadians regularly debate the relative split between public and private finance overall, and a small set of advocates have persistently pressed for a greater role for private insurance, private insurance has not figured prominently in Canada’s health care policy debates, which since the late 1960s have focused on the publicly funded health care system.

Private health insurance has been a constituent part of the Dutch health system since the early 20th century. Before the major reform in 2006, almost a quarter of the population held so-called pure private health insurance cover as a substitute for sickness fund cover. The 2006 Health Insurance Act created a single, mandatory health insurance scheme covering the whole population under private law. One of its most important consequences was the abolition of the traditional division between statutory health insurance operated by sickness funds and all other insurance schemes including substitutive private health insurance with experience-based underwriting. However, the newly created scheme is not a pure private arrangement (the term ‘pure’ will be explained later in this chapter) but one extensively regulated by the state to protect public interests including, among others, solidarity in health care financing and access to health care.

The role of private health insurance in the Irish health system can be assessed from different angles and from all angles it appears complex. Despite unversal entitlement to public hospital services, private cover – predominantly for hospital services – is purchased by nearly half of the population. This high level of demand has remained buoyant over time in the face of premium increases, adverse economic conditions, reductions in public subsidies and controversy within the market. Also, while private health insurance accounts for less than 15% of total spending on health, it commands a high profile in media and policy discussions and has substantial leverage over how public and private resources are allocated within the health system, particularly in the acute care sector.

The medical savings account model of health insurance in the United States combines a high-deductible health insurance plan‹ A high-deductible health plan is an insurance plan under which the beneficiary is responsible for a substantial amount of expense (the deductible) before the insurer begins paying benefits. US federal law as of 2015 requires a deductible of at least US$1300 for single coverage and US$2600 for family coverage for health saving account-qualified high-deductible health plans ().› with a dedicated savings account used to pay expenses incurred below the deductible. Savings in the plan can roll over from one year to the next and, after some predefined period during which they are dedicated to health spending, can be used for non-health-related expenses.‹ Use of savings for non-health expenses before this predefined period (age 65 under current law), incurs a tax and 20% penalty.› In principle, this model combines the incentives for frugal use of health services that exist in high-deductible health insurance with assurance that the funds required in the event of true medical need will be available.

The private health insurance market in Israel offers two voluntary products: the first, offered by the non-profit health plans (HPs), is referred to as supplemental insurance (SI); the second, provided by for-profit insurers, is known as commercial insurance (CI). Both types of cover play a complementary role, covering benefits excluded from the National Health Insurance (NHI) scheme such as dental health care for adults. They also play a supplementary role, providing faster access to care, greater choice of provider and improved amenities (in the private sector), and extended cover of services included in the NHI, such as more physiotherapy or psychotherapy sessions compared with what the NHI offers. The Israeli private health insurance market’s main distinctive feature is the very high levels of population coverage and dual coverage (almost all people who own CI also own SI).

In Germany and Chile, the market for private health insurance exists alongside and “within” a statutory health insurance system that covers a large majority of the population. Private cover comes in two forms: substitutive, chosen to replace statutory cover, which means that the privately insured do not contribute to this aspect of the social security system (unless statutory health insurance is partly funded through the government budget); and complementary or supplementary, allowing people to “top up” publicly financed benefits. In both countries, the vast majority of the population is covered by statutory health insurance. However, some parts of the population, mostly those who are able to afford it, have the option of choosing between private and statutory coverage. In Germany, the group of people given this choice is limited by regulation, with those allowed to “opt out” of the statutory system having to demonstrate that they have earnings above a threshold. Once they have chosen the private option, the possibility of returning to statutory cover is limited. In Chile, choice of substitutive private cover is also dependent on earnings as a private plan is significantly more expensive than contributions to the statutory system, but there is no fixed threshold for those who wish to opt out.

Private health insurance makes a small contribution to spending on health in most countries around the world, but its effect on health system performance can be surprisingly large owing to market failures and weaknesses in public policy. Because private health insurance can have a disproportionate impact, leading to risk segmentation, inequality and inefficiency, it should be considered and monitored with care.

Publicly financed health coverage in France is universal. Nevertheless, in 2015, private health insurance accounted for 13.3% of total spending on health (French Ministry of Health, 2016), one of the highest shares internationally. According to the most recent survey data available, 95% of the population is covered by a complementary health insurance contract that primarily reimburses statutory user charges. Nine out of ten people insured have a private contract while the rest benefit from publicly funded complementary coverage known as Couverture maladie universelle complémentaire (CMUC) due to their low income (Barlet, Beffy & Renaud, 2016; based on the 2012 Health, health care and insurance survey).

South Africa has a dual health system in which the majority of the population is covered by the public health care sector and 16% of the population with higher incomes is covered by voluntary private health insurance delivered through medical schemes. Medical savings accounts (MSAs) were first introduced by medical schemes in 1994 and their usage grew rapidly in the first decade but declined in the second decade. By 2005, MSAs covered 88% of open scheme beneficiaries and 49% of restricted‹ Open schemes must admit all applicants under the principle of open enrolment. Restricted schemes are typically employer or union based, or may be set up for a professional body or other defined group with restricted membership.› scheme beneficiaries but by December 2014 MSA coverage had declined to 67% of open scheme beneficiaries and 18% of restricted scheme beneficiaries. This chapter focuses on MSAs, but more information on medical schemes and private health insurance can be found in Chapter 12 in this volume.

The case studies presented in this chapter provide evidence of varied experience with private health insurance in three middle-income country settings – Brazil, Egypt and India – where there are large and persisting socioeconomic differentials and where private spending accounts for more than half of health care financing. Brazil is a very large private health insurance market with a recently introduced system of regulation whereas Egypt and India are very small markets with minimal regulation. In all three countries private health insurance plays a supplementary role and overwhelmingly covers richer people employed in the formal sector. All three countries are struggling with regulation of the market to enhance transparency, protect consumers and minimize negative effects on the publicly financed part of the health system.