# **3. Methodology**

## **3.1 Convergence in Labor Productivity and GDP per capita**

In the literature, the most commonly applied test for convergence is to examine whether regions which are further away from the frontier in labor productivity are growing faster, where growth is measured over a long period of time to iron out the effects of cyclical shocks.<sup>8</sup> This test captures the process of catching up. Our main econometric specification implements this test through OLS regressions on department and industry (or, sector) level data.

Measuring labor productivity as value added per worker, we estimate the following regression which measures the association between initial level of labor productivity _yijt‐ι_ in department _j_ and sector _i_ and its (annualized) growth rate (in logs) over 2002‐2012 . A positive β implies that departments with lower levels of initial labor productivity grew faster, converging to leading regions.

For each of the three broad sectors (primary, secondary and tertiary sectors), we first estimate a standard convergence regression in which the relationship between growth and initial values of labor productivity for the sector as a whole is estimated across the 24 departments. Next, we estimate “pooled” convergence regressions for sub‐sectors (or, industries) within each of the three sectors. For instance, the primary sector is split into three industries: agriculture, fishing and mining. This regression should have 64 (24 times 3) observations.<sup>9</sup> The pooled regressions assume that the rate of convergence is common across industries within the same broad sector. Industry fixed effects are included to account for industry‐specific trends and industry‐specific frontier levels of labor productivity.<sup>10</sup> Department fixed effects control for fixed department characteristics that might have a common effect on growth rates across industries. Since department fixed effects absorb department‐level differences in policies and institutions, regressions with those fixed effects may be interpreted as conditional convergence regressions. These regressions identify within‐department, cross‐industry convergence by exploiting the fact that the distance to the frontier productivity level varies across industries within the same department. Thus, the pooled regression specification is

> 8 In the growth and convergence literature, this is known as the concept of beta convergence. Convergence also means that the cross‐sectional dispersion in productivity should be falling over time. This is known as sigma convergence. Even if lagging regions are growing faster, new shocks can increase the cross‐sectional dispersion in productivity. Hence, beta convergence does not necessarily imply sigma convergence.

> 9 In practice, the number of observations can be lower because of missing sub‐sector observations.

> 10 This is to account for the fact that in the standard derivation of the convergence equation, it is not the absolute initial level of productivity that matters for the effect of convergence on growth rates but rather, its distance from the steady‐state (or frontier) value. When the regression is estimated for a single industry group with common frontier values across departments, it does not matter whether one uses the absolute initial level of productivity or its gap from the common frontier. When the regression includes multiple industries in the same department, the industry fixed effects adjust for any differences in the frontier value across industries.

7