to allow for the inclusion of a set of municipality-level characteristics _Xit−τ_ that are presumed to exert an influence on mean per capita income growth.

This _Xit−τ_ set includes components of public spending and revenue across municipalities at the initial year of each period under study, which is relevant in light of the reforms in the federal transfer system undertaken in the 1990s. In particular, the 1998 reform that introduced Ramo 33, which aimed at redistributing additional fiscal revenues to subnational governments for social development, has allowed municipalities to benefit from larger volumes of federal transfers. For example, average per capita unconditional (participaciones federales) and conditional (Ramo 33) federal transfers, respectively, increased twofold and threefold in real terms in 2000–14 (see annex, panel b).

Making equation (4) conditional on, for instance, total per capita public expenditure in the initial year reveals that the speed of convergence over 1992–2014 jumped from the 0.7 percent found in the absolute setting to 1.2 percent and that the pace of conditional income convergence was, again, particularly rapid in the first five years of the 2000s. Although there was no evidence of absolute income convergence in the 1990s, conditional convergence did record a rate of 1.6 percent in these years, and it was significant at the 1 percent level (table 2, panel a).<sup>9</sup> Table 2, panels b and c show, respectively, the estimates in urban and rural municipalities, with two particular results. First, income convergence occurred, again, at a more rapid pace in rural municipalities than in urban ones in all periods under study. Second, and consistent with the whole sample, there are signs of conditional convergence in urban municipalities in the 1990s, at an annual rate of 2 percent.

The conditional model shifts the convergence rates upward in most cases relative to the absolute model. The only exception is 2005–10 when the magnitude of income convergence remained virtually unchanged. A plausible explanation is that the coefficient of initial per capita public spending was negative during those years when the economy was hit by various adverse shocks. The expectation, confirmed in the remaining cases, is that the point estimate of the variable is positive and significant,

> 9The focus is on total public spending only because no sizable differences in the rates of convergence appear if particular components of public spending or revenues are used instead, and this reduces the sample significantly because no disaggregated public finance data are available for all municipalities (see tables 2–11 and 17–26 in the ancillary file). Moreover, to exploit the panel dataset of municipalities and control for time-invariant factors, conditional convergence is estimated using fixed effects models, which consistently confirm convergence, as in the standard ordinary least squares model. Random effects specifications also produce coefficients with the same signs. As extra robustness checks, 5-year and 10-year averages are used for the public spending variables and generalized method of moments (GMM) techniques. The results are again consistent; that is, poor municipalities converge at a faster rate when compared to rich municipalities.

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