This gives us an expression for the firm-level markup in terms of observable 𝛼𝑖𝑡𝑉 and the unobserved (but estimable) 𝜃𝑖𝑡𝑉 . The procedure below is all about consistently estimating this output elasticity. Estimation  We generally follow De Loecker and Eeckhout (2017, 2018) and Díez et al (2018) in our empirical application of the theory above. The production function they take to the data is given by 𝑦𝑖𝑡 = 𝑓(𝑣𝑖𝑡 , 𝑘𝑖𝑡 ; 𝜷𝑗 ) + 𝜔𝑖𝑡 + 𝜖𝑖𝑡  for all 𝑖 ∈ 𝑗 (𝐴4)  40  All speeches are available online at www.bankofengland.co.uk/speeches  40  where 𝑖 indexes a firm and 𝑗 denotes a 2-digit SIC07 industry, lower cases denote logs, 𝑦𝑖𝑡 denotes deflated net sales, 𝑣𝑖𝑡 denotes deflated cost of goods sold (COGS) (which are taken to be a measure of variable inputs), 𝑘𝑖𝑡 denotes deflated net plant, property & equipment (PPE), 𝜔𝑖𝑡 denotes unobserved (to the econometrician) technology, and 𝜖𝑖𝑡 denotes the measurement error of net sales. Note that the production function parameters 𝜷𝑗 are assumed to be industry-specific and time-invariant. We consider two specifications for 𝑓: Cobb-Douglas and translog. Under the former, the output elasticity with respect to COGS is exactly equal to 𝛽𝑗𝑣 . Under the latter, the output elasticity with respect to COGS is equal to 𝛽𝑗𝑣 + 2𝛽𝑗𝑣𝑣 𝑣𝑖𝑡 + 𝛽𝑗𝑣𝑘 𝑘𝑖𝑡 . A key challenge in estimating (A4) is the endogeneity of optimal input choices with respect to technology 𝜔𝑖𝑡 .
In China, for example, the service sector has grown to more than half of GDP in 2015, much of it driven by a surge in e-commerce and the expansion in logistical services required to support it. Moreover, as the cost of digital technology declines, a wider range of services are becoming more tradable including design, marketing, business processes, and education. Thus not only has the service sector 3  become more important within a country, the share of international trade in services has also increased markedly. The third, and perhaps most unsettling transitional force, is the ultra-accommodative monetary policy stance adopted by major advanced economies. What started out as extraordinary responses to a precipitous crisis, unconventional monetary policy measures have not only been maintained, but in many cases have been applied more intensively with ever greater degree of experimentation and radicalism. It is striking that after all this time, the crisis mentality among policy circles has yet to fully abate. The agglomeration of these transitional forces has had profound impacts on economies the world over. Together, the slowdown in world trade and the shift to services have underpinned important changes in inflation and growth dynamics. In terms of inflation, globalization has for many years increased the importance of foreign factors in price dynamics. Persistently low and more synchronized inflation is partly attributable to the effects of rising competitive pressures in world markets as well as common forces such as falling energy prices. As global trade adjusts, the influence of external factors has regained prominence.