The work presented here builds on a large literature on macro-level growth accounting and TFP measurement (Hulten 2010). However, it is important to note that there is also a rich literature on measuring economic efficiency at the sector or firm level, using methods and data that are much more fine-grained than what will be presented here. The focus on the macro scale has advantages, in particular the ability to pick up, however indirectly, the effects of policy and institutional reforms that can have macroeconomic consequences, in addition to technical progress. Using the World Bank _Wealth of Nations_ data also means that we can do broad comparisons of country, regional and income-class performance on TFP growth over time.

The _Wealth of Nations_ data include estimates of fixed capital stocks (based on the Penn World Table), human capital, and stocks and flows of natural resources in both quantity and value terms. To produce the estimates of TFP growth below, the World Bank data are augmented by UN national accounts data on the composition of value added, total remuneration of labor from the Penn World Table, as well as the number of persons employed aged 15 or more from the ILO. We also employ indices of real agricultural output from the FAO.

We begin section 2 by considering the general approach to productivity measurement and the specific issues associated with the incorporation of natural resources into growth accounting, followed by a detailed specification of the methods and data used to measure TFP growth. While it may seem at first glance that adding another factor to the calculation would reduce TFP growth estimates, we will demonstrate that is not always the case. Results of the TFP growth calculations and key findings are highlighted in section 3. The final section sums up the results, identifies how new measures of TFP could be used for policy work in the World Bank, and suggests areas for further work.

# **2. Methods and Data**

TFP growth is not a particularly intuitive concept for many people, but a simple formalization may help. If we compare the growth rate of production in an economy, which is measured by GDP, with a weighted average of the growth rate of the factor inputs to production, we will typically find a gap between the two. This gap is defined to be the growth rate of some unmeasured input to production which we term Total Factor Productivity. Determinants of this gap could include technological change, changes in economic policies and institutions, or changes in the management practices of firms – to name just a few. This section derives the equations used to estimate TFP including natural resources, then discusses the data used and how certain data challenges were addressed.

To formalize the concepts, we denote total factor productivity as A, and its growth rate as g�. Similarly, we denote GDP as Y and its growth rate as g�. We assume that the inputs to production can be categorized as fixed capital K, with growth rate g�, labor L with growth rate g�, and natural resources N, with growth rate g�. If we assume that there are corresponding shares of these factors in value added, denoted s�, s� and s�, then these shares will sum to one. Crucially, there is generally no direct measure of the returns to fixed capital in the SNA, so it is defined as a residual after measuring wages (the contribution of labor to value added) and resource rents (the contribution of natural resources to value added); formally we can say that 3