where δ<sup>∗</sup> _j_ k<sup>and δ∗</sup> _j_ l<sup>denote the equilibrium share of capital and labor allocated to sector</sup><sup>_j_respectively.</sup> The above equation is flexible enough so that the marginal effects of changes in capital and labor stock (through changes in participation and employment rates) on aggregate productivity can be isolated in addition to marginal gains from allocation of resources across sectors. Nonetheless, it is clear from equations 8 and 9, that the relative allocation of resources across sectors is independent of changes in stock of aggregate resources.5 Hence, given the focus of this paper on sectoral gaps in productivity, I abstract from marginal gains due to growth in stock of resources and consider only the marginal effects of reallocation of resources across sectors.6 Finally to take this equation to data, I normalize the final good as the numeraire. I discuss the data that I use to carry out the quantitative exercise in the next section.

# **3 Data**

The bulk of the data used in the analysis are taken from the World Development Indicator (WDI) online database. Specifically, I use the following series from the database: value added at sector level (provided in constant 2005 US dollars) and employment at sector level (provided as percentage of total employment). Apart from these six series, I use data from Global Trade Analysis Project (GTAP) to estimate the sector labor share of income at sector level.

The WDI data on sectoral share of employment are originally sourced from the International Labor Organization’s (ILO) Key Indicators of the Labour Market Database. This annual series on sectoral share is often constructed using different sources for the same country over time. The annual series starts from 1980 for some countries and there is a wide variation with respect to the annual observations available across countries. However, there are two major concerns with regards to using the data as provided for the analysis of this paper.

1. For many country-years, the source used is not representative of the country. For instance, the sectoral share of employment in Argentina for many years is constructed from sources that surveyed only the Greater Buenos Aires area. Even in recent years, the data is based on surveys carried out in main cities or metropolitan areas. As such, it is highly likely that the

> 5It is important to note that this independence is a direct result of the model specification that abstracts from differences in resource accumulation across sectors. The independence would cease to exist if one allows for different accumulation process across sectors in presence of barriers on marginal flow of resources from period to period. For example, if the rate of population growth is different across sectors and there are frictions to movement of additional labor that flows to a particular sector, then the resource allocation would not be independent of population growth. On the other hand, the model abstracts from dynamic adjustments and focuses on allocation of aggregate resources which helps in isolating the marginal gains from a better allocation.

> 6The second and the third terms of equation 13.

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