COINCIDENT GROWTH COLLAPSES: BRAZIL AND MEXICO SINCE THE EARLY 1980s

Brazil’s and Mexico’s economies collapsed almost simultaneously in the early 1980s. Their respective outputs per worker remained in a state of near stagnation since then. We develop a comparative analysis to try to understand what went wrong. Macroeconomic magnitudes (capital accumulation and technical progress) exhibit more similarities than differences. These appear more starkly when productivity changes are analyzed at disaggregated levels: by regions, sectors of activity, tradability, firm size, and labor-market informality. Our empirical findings are consistent with a view that Brazil’s economic failure is linked to excessive protectionism; Mexico’s to heightened domestic polarization.


Introduction
It's a tribute to Albert Fishlow's economic acumen that as early as 1978 he argued in favor of Latin America's foreign debt restructuring when most economists and regional policy makers still believed that minor domestic and external policy adjustments were all that was required for economic growth to resume in the region. 1 It took more than a (lost) decade for debt restructuring to be put in place, but even then-and this is something that not even Fishlow could have predicted-growth resumption continued to elude Brazil and Mexico despite substantial domestic reforms.
The drama of Brazil's and Mexico's near stagnation-not secular, but already lasting for 35 long years-is particularly troubling because, after a period of economic populism extending into the 1980s, since the 1990s these countries have strived to put the house in order and follow the precepts of sound economic policy making. Brazil defeated hyperinflation, introduced a fiscal responsibility law, and implemented major income redistribution policies. Mexico opened up its economy, floated the peso, reprivatized its banking system, and executed relevant social programs. All this to no avail, as Figure 1 tells us. Since the early 1980s Brazil and Mexico stopped catching up with the industrial countries, even though in purchasing power terms (PPP) their per capita incomes stand respectively at only 27% and 33% of that of the United States.
Academic articles began asking "Why isn't Mexico rich?" (Hanson 2010) 2 echoing the infamous dictum that "Brazil is the land of the future-and always will be". A comparative analysis seems in order to better understand what went wrong, particularly because there aren't only similarities (as bureaucratic entanglements and entrained cronyism that hamper investment), but also important differences in the economic experience of these countries. Many analysts say that Brazil does not grow because it's a closed economy with very high taxes and interest rates that crowd out the 1 Cf. Fishlow (1978), p. 67-68. 2 See also the negative evaluations of Mexico's economic performance by Kehoe and Ruhl (2010) and Kehoe and Meza (2011).  1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 BRA / US MEX / US private sector. The diagnostic on Mexico tends to the opposite view: the country does not grow because its opening up to foreign trade polarized the economy, delinking the rich North from the poor South, and its government doesn't invest in infrastructure because it can't collect taxes.
These are big issues that we'll consider but are under no illusion to be able to resolve. The contribution that we have to offer are accounting frameworks to analyze the historical evolution of relevant macro and "mesoeconomic" variables, in many cases making use of datasets that only recently have become available. In the process, we develop economic interpretations that are consistent with the empirical findings, while commenting on the controversies that the historical experience of these two countries have evoked in the literature.
The paper is organized as follows. The next section provides a periodization for the growth experiences of Brazil and Mexico since 1950, with emphasis on the years after their respective growth collapses in the early 1980s. Section 3 compares these GDP growth collapses to concurrent sharp falls in capital accumulation, and decompose the latter into variations in savings, capital-output ratios, and relative prices of investment. Adopting the proposed periodization, Section 4 estimates a neoclassical accounting framework for the growth of GDP per worker, analyzing the contributions of capital deepening and total factor productivity for the evolution of labor productivity since 1950. In the process, we do an econometric exercise to estimate the role of the terms of trade and the output gap to the cyclical movements of measured total factor productivity since the early 1980s.
Section 5 introduces "mesoeconomic" variables into the picture to complement the macro analysis of labor productivity in the previous section. In successive subsections, we consider the following dimensions of labor productivity growth: regional, sectorial, traded/non-traded, by firm size, and formal/informal. Conclusions are summarized in Section 6.

Growth collapses: a periodization
Since the 1930s Brazil and Mexico experienced economic growth golden ages that extended through the early 1980s. With the debt crisis, growth submerged in the two countries and remained to date at levels only one-third as high as before. Figure 2 displays the 10-year average GDP growth rates in Brazil and Mexico from 1950 to 2014. The figure makes the parallelism of the two countries' experience evident, either in terms of their pre-1980 fast-growth years, their growth collapses in the 1980s, and their meager growth outcomes since then.
These countries seem to have hit a wall in the early 1980s when they stopped catching up with the industrial countries. Brazil's performance was a little better than Mexico's in the 1970s and during the recent commodity boom. Nonetheless, Brazil's per capita income in PPP terms is still 15% lower than Mexico's.   Figure 3 identify five near-identical sub-periods in the GDP growth trajectories of the two countries since 1950. The first period is the golden age starting for our statistical purposes in 1950 and going to 1980 in Brazil and to 1981 in Mexico. Average GDP growth rates in this period were 7.4% in Brazil and 6.8% in Mexico. There follows the so-called lost decade after the debt crisis of the early 1980s, identified in the table as the period from 1981 to 1992 in Brazil, and from 1982 to 1993 in Mexico. In this phase, yearly GDP growth rates collapsed to 1.4% in Brazil and to 1.7% in Mexico. Next is the period of liberal reforms with subpar growth, characterized by inflation stabilization in Brazil (starting with the implementation of the 1993-94 Real Plan) and trade opening in Mexico (with the enactment of NAFTA in 1994). We denominate growth subpar even though rates doubled from the previous period, because they were lower than anticipated at the inauguration of these major economic reforms. From 1993 to 2003 GDP growth averaged 2.8% in Brazil, while in Mexico it stood at 3.0% from 1994 to 2001. A disconnection in the growth experiences of Brazil and Mexico occurs in the first decade of this century, in a phase that we labeled "China Syndrome". As indicated by this title, the rise of China seems to us to be the major influence for the growth rate disparities in the two countries. China's growth had a very positive influence on Brazil 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 MEXICO BRAZIL (through a major boom in the prices of its exported commodities associated with large capital inflows) and a very negative impact in Mexico (through a tough competition in manufactured exports to a slowly growing US market There is finally the more recent 2011-2014 period, when Brazil suffered from a reversal of the commodity boom and also from domestic economic mismanagement, whereas Mexico, while copying with the slow recovery of the US from the Great Recession, fared better than previously. In this Day After the Great Recession period, GDP growth averaged 2.1% in Brazil and 2.9% in Mexico. Figure 3 makes the contrast between these countries' growth experiences before and after the early 1980s clear. During the Golden Age, Brazil and Mexico grew in the neighborhood of 7% per year; after the early 1980s, average GDP growth rates have been only one-third of that. It is true that population growth slowed down substantially between 1950-80 and 1981-2014, from 2.8% to 1.5% in Brazil and from 3.4% to 2.2% in Mexico. But that did not help to change the dismal picture: in per capita terms post-1980 incomes growth were only a fraction of their pre-1980 rates: Mexico per capita income grew 3.4% a.a. from 1950 to 1981 and 0.7% from 1981 to 2013, while in Brazil GDP per capita growth dropped from 4.5% to 1% a.a.  Table 1 In the next section we investigate the relationship between the GDP growth collapses and capital accumulation, before introducing total factor productivity into the picture in the subsequent section.

Capital accumulation and the growth collapses
Both in Brazil and Mexico deep and lasting contractions in capital accumulation were closely associated to the GDP growth collapses that started in the early 1980s. 3 We first display this association and then use a decomposition derived from the savingsinvestment identity to study the components of the capital stock changes.
Figures 4 and 5 show the relationships between the GDP growth rates (dotted lines) and the capital stock growth rates (solid lines) respectively in Brazil and Mexico, from 1950 to 2014. During the Golden Age, the average yearly capital stock growth rate was 8.9% in Brazil and 8.0% in Mexico. In consonance with this rapid growth in the capital stock, average GDP growth rates of this period were 7.4% and 6.8%, respectively in Brazil and Mexico.
In Brazil, the capital stock growth rate started a descent after reaching a peak in 1975. The drop became sharper after 1981, and a through was reached only in 1992. In Mexico, the change of regime was much faster, as it took only one year-1983-for the capital stock growth rate to sink from a peak to a near through, from which it recovered only mildly in subsequent years. In the Near Stagnation era, the average capital stock growth rate stood at only 2.9% in Brazil and 2.8% in Mexico. Correspondingly, average GDP growth rates descended to 2.6% in Brazil and 2.2% in Mexico. On a yearly basis, output growth was rather more volatile than capital growth as can be seen in Figures 4 and 5. As a result the correlations between the capital and output growth series were not particularly high: 0.58 in Brazil and 0.68 in Mexico. The correlation between the capital stock growth rates was a much higher 0.83, which highlights the kinship of these countries' post-WW-II macroeconomic histories. On the other hand, the correlation between the GDP growth rates was a much smaller 0.37.  1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 K' Y' Next we use an expression derived in Bacha and Bonelli (forthcoming) to decompose the capital stock growth rate, and identify for each of the periods in Table 1 the roles of savings, the relative price of investment, and the capital-to-output ratio in the evolution of the capital stocks.
The decomposition for the growth rate of the capital stock can be easily derived from the investment and savings identity in current prices, and is expressed as: 4 where: K' is the growth rate of the capital stock, s is the sum of the domestic with the foreign savings rate (which we denominate simply as the savings rate), p is the relative price of investment (ratio of the implicit price deflator of gross capital formation to the implicit price deflator of GDP), v is the aggregate output to capital stock ratio, and δ is the depreciation rate.
In the following, we'll treat the variables in the right-hand side of equation (1) as parameters, the changes in the values of which lead to changes in the growth rate of the capital stock. We're conscious that this is only a first approximation that ignores the autonomous determinants of investment, such a profit rates, firms' expectations about future demand, credit availability, macroeconomic volatility etc. With this caveat, we hope to show that the exercises to follow will help to illuminate important aspects of the growth experiences of Brazil and Mexico.
Equation (1) shows that the impact of the savings rate on the growth rate of the capital stock depends on the relative price of investment and on the output-to-capital 4 We start from the National Accounts identity: PI I = S, where PI is the implicit price deflator of gross capital formation, I is gross real investment, and S is total savings in current prices. To simplify, inventory changes are netted out of savings. First divide both sides by PIK (where K is the capital stock), then divide and multiply the right-hand side by PYY (where PY is the implicit price deflator of GDP and Y is real GDP), then subtract the capital stock depreciation rate (δ) from both sides, and rearrange to obtain equation (1), where K' = I/K -δ, s=S/PYY, and p = PI/PY. See Bacha and Bonelli (forthcoming) for the derivation of a slightly more elaborate version of this equation that allows for a varying degree of capital stock utilization.  1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 K' Y' ratio. The higher is the relative price of investment (the lower is 1/p) and the lower is the output-to-capital ratio, the lower will be the growth rate of the capital stock for a given savings rate. The depreciation rate also needs to be taken into account -except that, as it varies little in the series we use, it does not contribute to explain the changes in capital accumulation through time. 5  Tables 2 and 3 show the figures for equation (1) respectively for Brazil and Mexico in the periods identified in Table 1.  The most outstanding result in Tables 2 and 3 is that the sharp fall of the capital stock growth rates between the Golden Age and the Near Stagnation period is not accounted for by the evolution of the savings rates. In the thirty-some years before the early 1980s, the average savings rate was 19.4% in Brazil and 16.4% in Mexico. From the early 1980s to 2014, the average savings rate was in fact a bit higher at 19.5% in Brazil and 18.5% in Mexico. This did not prevent the average growth rate of the capital stock to sink 5 Mexico's depreciation rates, as calculated from Hofman's capital data series, turned out to be substantially higher than Brazil's, estimated by us as a residual (but which are in line with the values computed by Lucilene Morandi, from the Fluminense Federal University (UFF), in a forthcoming paper). We were unable to detect the sources of these differences. 6 A direct calculation of p yields results only slightly different from those in Table 3 between these two long periods from 8.9% to 2.9% in Brazil and from 8.0% to 3.4% in Mexico.
The main culprit (by far the main one in the case of Mexico) for the sharp fall in the capital stock growth rate was a deep reduction in the output-to-capital ratio. This seems to have been partly a technological phenomenon, as these economies became more complex and urbanized than in the past. A sector-composition effect may also have had a role, as exemplified by the increasing share of services at the expense of goods-producing sectors. Investment misallocation is a further reason for the decline in the output-tocapital ratio, as we'll discuss below. But, particularly in the case of Mexico, the drop in the capital stock growth rate was too sudden to be explained simply by such structural factors.
Apparently, cost-increasing and demand-depressing factors associated to the early 1980s debt crisis forced a sharp reduction in aggregate output, thus turning idle part of the preexistent capital stock. 7 Initially, the drop in foreign savings also exerted a depressing effect on capital accumulation, as a compensatory increase in domestic savings did not immediately occur. Subsequently, domestic savings recovered, but this happened in a context (particularly in the case of Brazil) in which an inefficient import substitution of capital goods contributed not only to depress the output-to-capital ratio but, more importantly to increase substantially the relative price of investment. 8 More capital intensive production and higher relative investment prices became permanent features of Mexico's and Brazil's economies since the early 1980s. Together they justify the drop in the capital stock growth rate to such lower levels in spite of higher savings rates. Brazil, being a more closed economy, suffered from a sharper rise in the relative price of investment. Mexico's opening up seems to have been able to hold back the rise in the price of investment but did not prevent the output-to-capital ratio from falling even more deeply than in Brazil. Levy (2008, p. 213) argues that the social programs created after the 1980s tilted the investment ratio in Mexico towards the informal sector and this raised the incremental capital-to-output ratio. Ros (2013, Ch. 2) agrees that informality expanded somewhat since the 1980s but argues that this was a consequence not a cause of the low growth rate of the capital stock. We'll have more to say about the role of informality in subsection 5.5 below.
We now turn to the consequences of the evolution of the capital stock together with that of total factor productivity (TFP) for the growth rate of output per worker. The focus on output per worker is justified because changes in labor force growth were a minor factor in the GDP collapses in the two countries. In the Golden Age, labor grew at nearly similar rates in Brazil and Mexico, respectively, at 3.1% and 3.2% per year. In the Near Stagnation age, yearly labor force growth was less, but still a respectable 2.2% in Brazil and an even higher 2.5% in Mexico. These relatively small changes in labor force growth rates permit us to draw attention to the growth of aggregate output per labor, as explained by capital deepening and TFP.

Periodization for the growth of output per worker
This section presents a standard growth decomposition exercise, using an aggregate Cobb-Douglas production function with capital and labor as production factors. Our interest is in the evolution of GDP per worker. The log-linearization of a function of this type results in: where y' is the growth rate of GDP per worker, α is the capital share in GDP, k' is the growth rate of capital per worker, and TFP' is the growth rate of total factor productivity.
Tables 4 and 5 below respectively for Brazil and Mexico show the behavior of the variables in this formula for the periods identified in Table 1. For completeness, the tables also show the values of labor force growth (L') in these periods. In both countries, we set α = 0.45. For Brazil, this value is in line with our previous work (Bonelli and Bacha, 2012) and for Mexico with a forthcoming productivity study of the KLEM-Latin American project. 9 Tables 4 and 5 summarize the extraordinary loss of dynamism of the two economies from the Golden Age to the Near Stagnation era. Between these two long periods, average growth of output per worker fell from 4.2% to 0.4% in Brazil and from 3.4% to -0.2% in Mexico. 10   9 Cf. Hofman et al (forthcoming). 10 Neither labor nor capital were corrected for utilization in these exercises.
Contractions in the growth rates of capital per worker and of TFP divide the responsibility for this collapse, with the former being relatively more important in Brazil and the latter more prominent in Mexico. This proposition is valid for the Near Stagnation era as a whole. In it, output per worker growth was less than zero in Mexico, in spite of a higher contribution of capital to growth than in Brazil, because the Solow residual became very negative in Mexico during this era.
Roles of capital and TFP are nonetheless reversed in the two countries in the more recent Day After the Great Recession phase . In this period, growth of output per worker was equally mediocre in the two countries, but in Brazil capital accumulation recovered while TFP growth sank. In Mexico, on the contrary, capital accumulation dropped while TFP growth improved. A possible reason is that Mexico may be dealing with more success than in the past with the structural sources of its traditional low productivity, but is suffering from a low propensity to invest associated with the economic slowdown of its main trading partner, the US. Meanwhile, in Brazil the end of the commodity boom and government meddling with resource allocation led TFP growth to become negative, even as capital accumulation recovered from the low levels prevailing since the 1980s.
This interpretation needs to be squared off with the high growth rate of TFP in Brazil in the China Syndrome period (2004)(2005)(2006)(2007)(2008)(2009)(2010). Lisboa and Pessoa (2013) argue that this was a deferred consequence of the economic reforms of the 1990s and early 2000s. However, the major commodity boom from which Brazil benefitted may also have boosted TFP growth in this period. The positive association between the terms of trade (ToT) and measured TFP is well documented in the literature, as is the procyclicality of this variable. 11 Both in Mexico and in Brazil, the positive correlations between TFP and the ToT in the 1980-2014 period are very impressive indeed, as seen in Figures 6 and 7, where TFP is measured in the left-hand axis and the ToT in the right-hand axis. Figure 6 displays the close evolution of TFP and the ToT in Mexico: both experienced a sharp drop from 1980 to 1988, followed by near stagnation in the remaining of the period. Figure 7 shows the more complex evolution of TFP and the ToT in Brazil, where, after an initial joint drop, these variables experience ups and downs until 2003, when they both gain substantial traction, to start falling only after 2011. The correlation coefficients between TFP and the ToT in the 1980-2014 period are 0.89 in Mexico and 0.74 in Brazil. Going beyond simple correlations (and using the variables' rates of change instead of their levels in order to avoid possible unit root problems), the OLS regressions in Table 6 confirm that in both countries part of the changes in TFP during the near stagnation period can be explained by the vagaries of the terms of trade and of the economic cycles. The table shows the results of regressions of the rate of change of TFP on the rate of change of the ToT and on alternative measures of the economic cycle: changes in the degree of utilization of the capital stock or in the output gap (in the case of Brazil), and changes in the unemployment rate or the output gap (in the case of Mexico). 12 12 Sources for the data in Table 6  Taken at face value, what these results imply is that a 10% improvement in the ToT raise measured total factor productivity from 0.65% to 0.8% in Brazil and from 0.9% to 1.8% in Mexico (depending on the measure of the cycle that is used). Similarly, a one percentage point increase in the gap in resource use reduces measured TFP by 0.9% in Brazil and from 0.7% to 1.6% in Mexico (depending on the measure for the cycle that is used).
That measured TFP should be so sensitive to the economic cycle comes to us as no surprise, because we were not able to adjust the capital and labor inputs for the intensity of their utilization. When output contracts and labor-hours and capital utilization are reduced following a negative demand shock, such input reductions are not reflected in our measures of labor and capital. Consequently, the result is a lower measured TFP (because output is lower and our measured inputs remain constant, except for the possible reduction in engaged laborers). Mutatis mutandi, the same is valid for a positive demand shock. In summary, the observed procyclicality of TFP' in Table 6 has a lot to do with deficiencies in our measurement of labor and capital inputs. Thus, we can't infer from this procyclicality that other factors such as economies of scale are at play. In order to explain the positive relation of measured TFP with the ToT, a recent literature 13 argues that a ToT improvement generates a real exchange rate appreciation 13 The accepted wisdom is that ToT shocks represent a major source of business cycles in emerging and poor countries. For some relevant literature and a critical view, see Schmidt-Grohé and Urbe (2015). But Kehoe and Ruhl (2008) argue that the positive association of ToT changes with TFP growth observed in the historical data cannot be derived in a model with perfect competition and constant returns to scale. Following on the footsteps of Hall (1990), several authors have recently bypassed this objection with the use of models with monopolistic competition, multi-good settings, trade costs, and/or search environments, in all of which relative intermediate-good import prices are important determinants of that allows a more intensive use of highly taxed intermediate imported goods. These would be more efficient and more diversified than the domestic intermediate goods that they replace, thus raising output with the same inputs of capital and labor. Mutatis mutandi, a ToT deterioration would depreciate the real exchange rate and induce an inefficient substitution of domestic for imported intermediates. In addition, an increase (decrease) in the ToT would raise (reduce) aggregate demand and impact positively (negatively) on measured total factor productivity under increasing returns to scale. Another channel--probably more relevant in Mexico in view of the importance of oil revenue in the government budget--might be from higher (lower) ToT to more (less) infrastructure investment.

Growth and structural heterogeneity 14 in five dimensions
In the previous sections, we identified a number of parallelisms between the growth experiences of Brazil and Mexico since 1950. In this section, we are interested in the more recent period, in which both countries not only failed to recover their previous high growth rates but saw their respective productivities per worker linger on a state of near stagnation.
There is a basic similarity in these countries' post-1980 macroeconomic experience, which is that either because of policy failures of structural conditions, Brazil and Mexico were unable to undo the increases in the relative price of investment and in the capital intensity of production observed since the early 1980s. They're also unable to raise their respective savings rates sufficiently high to compensate for such investmentdepressing factors.
Beyond this, there are relevant differences in these countries' recent slow-growth experiences. Mexico opened up its economy to trade with the outside world (mostly to the US) and thus succeeded in developing a first-class industrial sector in the country's richer Northern region. However, a similar domestic integration didn't accompany this external integration. The dynamism of the large exporting firms in the North did not feed back to the non-traded, informal, small and medium-sized firms in the country's poorer Southern regions. Since the latter generate not only most of the country's jobs but also a substantial part of its output, the consequence was a very low aggregate labor productivity growth rate.
Thus, the structural heterogeneity between "modern" and "traditional" sectors seems to have widened in Mexico in the post-reform period. In Brazil, in several dimensions this dualism decreased: the poorer North grew faster than the richer South; the lower-productivity agriculture did better than the higher-productivity industry; 15 measured TFP. Cf. Burstein and Cravino (2015), Feenstra el al. (2013), Gopinath and Neiman (2014), Kim (2011). 14 Structural heterogeneity is a term made popular by Anibal Pinto (1970) in Latin America, to denote the extreme inter-and intra-sector differences in productivity provoked by import substitution industrialization in the continent. 15 Productivity in agriculture (including stock breeding) increased by a substantial 5.2% yearly average rate between 1995 and 2013, while in services the average rate was only 0.4% p.a. and in manufacturing nearly zero. For the economy as a whole the corresponding rate was 1.1%. These figures are from an ongoing bigger manufacturing firms did not outflank medium and small firms; informality decreased in the last decade. Brazil's problem seems to have been that in contrast to Mexico's her high-productivity large-manufacturing firms did not integrate into the world economy and thus saw their productivity grow very slowly, except in a few subsectors. This provided a weak lever to move the rest of the economy up. Therefore, the country lingered on in a low overall productivity path, except when the commodity lottery dictated otherwise.
To give some substance to this story, in the following we explore five disaggregated dimensions of the evolution of labor productivity in the two countries, as a complement to the aggregate analysis in the previous section. The dimensions are: geopolitical units, economic sectors, tradability, firm size, and informality.

Regional dimension
In this subsection we investigate the evolution of the dispersion of real per capita incomes among the States in Brazil and Mexico. The analysis considers the 27 Brazilian states and the 32 Mexican federative entities. The periods for which we were able to obtain apparently reliable and uniform data were 1990-2012 for Brazil and 1990-2013 for Mexico. We use the ratio of the standard deviation to the unweighted average real per capita State income (sigma, for short) to answer the question of whether the distribution of per capita income among States narrowed or widened over time. The results are shown in Figure 8 below. It's well-known that in the personal dimension Brazil has a more unequal income distribution than Mexico. Figure 8 shows that this is true in the States dimension as well: Brazil's sigma is always higher than Mexico's. However, in the period under consideration the dispersion of the States' per capita incomes diminishes in Brazil, with its sigma falling research by F. Veloso, S. Marques and B. Coelho, from IBRE/FGV, to whom we express our gratitude for letting us use their unpublished results. In Mexico, a reverse widening pattern is observed since 1996. Initially, Mexico's sigma falls, from 0.50 in 1990 to 0.47 in 1995, but then it increases almost continuously, to end at a value of 0.54 in 2013. 16 Thus, in the regional dimension we observe a tendency for income inequality to increase in Mexico and to decrease in Brazil since the 1990s. The speculation is that manufacturing activity blossomed in Northern Mexico, well integrated to the U.S. but with few linkages to the rest of the country. Meanwhile, oil production stagnated in the country's Southern region. In Brazil, on the contrary, manufacturing activity, which is inward looking and highly concentrated in the country's richer state, São Paulo, lost dynamism. Meanwhile, agriculture and mining, which are outward looking and better disseminated regionally, gained traction with the commodity supercycle. Additionally, minimum wage policies and income transfers through the Bolsa Família program, which benefited Brazil's poorest Northern states, were more effective at income redistribution than in Mexico 17 .

Economic sector dimension
In this subsection, we investigate aspects of the evolution of labor productivity in onedigit economic sectors. The data is from the 10-Sector Database of the Groningen Growth and Development Center (GGDC). 18 This database covers the ten main sectors of the economy as defined in the International Standard Industrial Classification, Revision 3.1. These sectors cover the total economy and are as follows: 1. Agriculture, hunting, forestry and fishing; 2. Mining and quarrying; 3. Manufacturing; 4. Electricity, gas and water supply; 5. Construction; 6. Wholesale and retail trade, hotels and restaurants; 7. Transport, storage, and communication; 8. Finance, insurance, real estate and business services; 9. Government services; 10. Community, social and personal services. Productivity is defined as gross value added per employee, in constant 2005 national prices. The period covered is from 1950-2011.
Our first analysis is on the evolution of the dispersion of labor productivity levels in these sectors in the two countries. In Figure 9, we graph the evolution from 1950 to 2011 of the ratio between the standard deviation and the (unweighted) average productivity level -sigma, for short -in the ten sectors in Brazil and Mexico. It is apparent from this figure that the dispersion of sectorial productivities not only increased through time but became much more pronounced in the Near Stagnation Era. 16 Mexico's sigma of State per capita incomes seems to have fallen in the previous 1970-1989 period, from 0.76 to 0.55, but we are unsure of the comparability of this data with that presented above for the subsequent 1990-2013 period. Brazil's State real per capita incomes data previously to 1990 seem totally unreliable. We thank Bernardo Coelho, from IBRE, for the Brazilian data. 17 According to Ros-Bosch (2013, Graph 3.1), the inflation-corrected minimum wage has remained constant in Mexico since 1996. In Brazil, meanwhile, the inflation-corrected minimum wage doubled in value from 1996 to 2012 (see Bacha and Hoffmann, 2014, Graph 3). See Lustig (2010) for a perceptive analysis of the impact of twenty-five years of reforms on Mexico's poverty and inequality. 18 Cf. Timmer, deVries, and deVries (2014). It is noteworthy that the dispersion of sectorial productivities remained relatively constant in Brazil during most of the import substitution period. This came as a surprise, as we expected to find more heterogeneity in that phase. After 1980, however, there is a very noticeable trend of increasing dispersion in productivity levels among sectors.
In Mexico, according to Figure 9 sigma trend downward in the 1950s and 1960s. This is followed by a pronounced increase that lasted for three decades. After 2003 the movements of Mexico's sigma are not uniform: there is a sharp decrease up to 2008, followed by an increase thereafter. If we exclude mining (that is, oil extraction) from the analysis, the picture that emerges is totally different, however. In this case, there is a slight downward trend in Mexico's sigma throughout the period. That is, both the extraordinary increase in the dispersion of productivity levels after the late 1970s and the declines and increases of this dispersion after 2003 are mostly due to the ups and downs of the oil sector.
The ratio between the sigmas (MEX/BRA) is consistently higher than one, implying higher dispersion in sectorial productivities in Mexico. But the discrepancy between the countries' sigmas tends to decrease through time: the average ratio between them falls from 1.5 in 1950-59 to 1.3 in 2002-2011. Again, most of these movements can be explained by the ups and downs of Mexico's oil sector.
The conclusion is that the structural heterogeneity of labor productivity at the sectorial level became more pronounced in both countries accompanying the slump in GDP growth rates after 1980. From a sectorial perspective, because of the oil sector Mexico is structurally more heterogeneous than Brazil, but the difference between the sigmas of the two countries has decreased recently. Using the same database we aggregated the ten sectors into two: mainly traded (agriculture, mining, and manufacturing) and mainly non-traded (the remaining seven). Except for the inclusion of construction in the latter, this division is roughly similar to  9 2,1 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 Sigma BRA Sigma MEX Ratio MEX / BRA (rhs) one between goods-producing vs. service-producing sectors. We then computed the evolution of the ratio of the labor productivity of the traded to that of the non-traded sector in 1950-2011 in the two countries.
The results are shown separately in Figures 10 and 11 and are also somewhat surprising. First, the relative productivity in the traded (or goods-producing) sector starts from a very low basis. In 1970, the productivity in the traded sector in both countries is only around 15% of the productivity in the non-traded (or service-producing) sectors. Second, starting from this low basis the relative productivity of the traded sector increases exponentially at roughly 3% a.a. in both countries throughout the period under consideration. Thus, toward the end of the series the productivities of the two sectors are roughly at the same level in Mexico and Brazil. In Mexico, the relative productivity of the traded sector seems to be tapering off at the one-to-one ratio while in Brazil it continues to increase but not yet reaching the same level as that of the non-traded sector.

Figure 10: Brazil -Ratio of Traded to Non-Traded Sector Productivities 1950-2011
Source: see text.

Figure 11: Mexico -Ratio of Traded to Non-Traded Sector Productivities 1950-2011
Source: see text.
The picture that emerges from this second exercise is only apparently at odds with our first exercise above. There we visualized a dispersion of sectorial productive levels.

Expon. (T-NT MEX)
traded and the (more productive) non-traded sectors. In fact, for the ten sectors as a whole there's little relationship between initial productivity levels and subsequent growth rates of labor productivity. The relevant point is that in both countries labor productivity in the three mainly traded sectors increased faster than in the remaining (non-traded) ones. 19

Tradability dimension
In this subsection, we use a more disaggregated dataset recently produced at the IMF 20 to investigate in more detail the behavior of labor productivity in the traded and non-traded sectors of Brazil and Mexico in the 1989-2009 period. In this case, the data originates from a 35-industry series, with tradability defined by a cut-off rate of a minimum of 10% of exports in gross valued added. Productivity is measured as real value added per worker in constant 2005 Purchasing Power Parity (PPP) U.S. dollars. Hence, productivity levels (not only growth rates) can be compared across countries.
The two lines in Figure 12 display the evolution of the ratios of labor productivity of the traded to the non-trade sectors for Brazil and Mexico. The top line shows the evolution of the productivity ratio (trade to non-trade) in Mexico. In 1989, the two sectors have a similar productivity level, but that of the traded sector grows faster than in the non-trade sector so that by 2009 it is 70% higher than the later (whereas in the Groningen dataset the respective productivities are at a similar level by this date). The second line shows a similar traded/non-traded productivity ratio for Brazil. Initially, the productivity of the trade sector is at 80% of the non-traded sector. But the tendency is for convergence, so that by 2009 the productivity in these two sectors becomes equalized in Brazil.
Hence, for Brazil this dataset confirms the tendency for sectorial productivity convergence (although at a lower speed than in the Groningen project data), whereas in Mexico the trend is one of divergence, with the non-traded sector lagging well behind the traded sector. This result is consistent with the view that in Mexico the traded sector is very dynamic but this dynamism does not spread to the non-traded sector. Meanwhile, in Brazil the trade sector struggles to reach the productivity levels of the non-traded sector. Although agricultural productivity increases rapidly since after 1970 it's productivity still lags behind the other economic sectors, and it is this that explains the relatively lower productivity of the traded sector in Brazil.
Making use of the fact that this dataset is in comparable 2005 PPP U.S. dollars, we also compared the productivities of each sector in Brazil and Mexico. We found that in both sectors Mexico's productivity is higher than Brazil's, with its advantage being more pronounced in the traded sector. We also checked that this is not only because of the importance of agriculture in Brazil's traded sector. A comparison only for the manufactured sector also indicates a higher productivity in Mexico. Moreover, there is hardly a tendency in the 1989-2009 period, as in both sectors the productivity of Brazil relative to that of Mexico remained more or less at the same level throughout the period.

Figure 12: Ratio of traded to non-traded sector productivities -Brazil and Mexico
Source: Mano and Castillo (2015)

5.4
Firm-size dimension In this subsection, we investigate the behavior of labor productivity of small-andmedium-sized vs. large firms. For this, we use the results of a recent report on Mexico by the McKinsey Institute (2014) and special tabulations for the industrial sector from IBGE for Brazil 21 . The data for Mexico is for 1998 and 2008 and is for manufacturing, services, and wholesale and retail commerce. 22 The data for Brazil cover a more extended period, 1996-2013, but is only for manufacturing. Table 7 shows the yearly productivity growth by firm size groups in Mexico from 1998 to 2008, summarized from the McKinsey study. 23 The data exhibits a very clearly pattern: both productivity levels and productivity growth rates increase very substantially with establishment size. According to this data, the smallest firms in the sample, those with up to 10 employees saw their productivity decrease by 6.5% per year (this implies that their productivity at the end of the period was only one-half of its initial levelwhich if true is very impressive indeed). The productivity of the immediately following size group (firms with 11 to 30 employees) also fell in the period. Productivity growth then becomes increasingly more positive as size grows, reaching a respectable 5.9% a.a. for firms with more than 500 employees.
The picture may be exaggerated, but the message is clear: in Mexico the biggest firms display a much higher productivity growth than smaller firms-the productivities of the smallest of which, little as they are, fell substantially in the period. According to McKinsey, the sample of firms under consideration comprises 41% of the economy's valued added. If they're a representative sample of the whole economy the implication is that Mexico's low productivity growth problem resides squarely with its small and medium size firms (those with up to 500 employees), that respond for 42.5% of total value added and 80% of total employment. At the lower end, a sizable proportion of these firms is informal, and this leads to a point raised by Busso, Fazio and Levy (2012), to the effect that for productivity comparisons firm type (formal or informal) is more important than firm size. With an upper size group of firms with 50 or more employees, they find from the 2008 Census that, for the same size, formal firms are more productive than informal ones; and that formal firms with 0-5 employees are more productive than formal firms with 50 or more employees. In Brazil, productivity by firm size for a longer period is available only for the manufacturing sector. 24 Table 8 contains a preliminary computation for the 1996-2013 period. Figures for the smallest firms (0 to 29 employees) are available only for the 2007-13 period. For the whole 1996-2013 period we have comparable data only for firms with more than 30 employees, shown in the last column. The results both for 1996-2013 (30+ employees) and for 2007-13 (all firms) indicate that, contrary to the results for Mexico, the growth rate of productivity decreases with firm size. This is not exactly true in the 1996-2007 period (for firms with 30+ employees only). But even in this case the differences in productivity growth are much smaller than in Mexico, where we saw that the big firms' productivity growth was three times as high as for all firms.  1996-2007 2007-2013 1996-2013 Less than 10 employees 9.5 --3.8 --10 to 29 13.5 --1.5 -- Our results for Brazil are supported by a microdata analysis of firms in the manufacturing sector with 30 or more employees by Gomes and Ribeiro (2014). With firms aggregated in twenty sectors at the two-digit SIC level, they find (to their own surprise, as the literature they quote made them expect the opposite result) that in the 1997-2010 period the covariance between firm size and labor productivity growth was negative in eighteen out of those twenty manufacturing sectors.

Informality dimension
In this subsection, we investigate aspects of the evolution of labor market informality in Brazil and Mexico. Informality is defined as the ratio of informal workers to total employment. In both countries, the definition of informal workers follow ILO norms. 25 We perform two exercises. The first is a regression shown in Table 9 below, in which the dependent variable is the rate of informality in each of the 59 States of Brazil and Mexico in 2012 and the independent variable is the per capita income level of these States. Two dummy variables are included. One is for Mexico, to test if this country has a different informality rate than Brazil. The other is for the southern Mexican state of Campeche, which proved to be an extreme outlier because despite its poverty the proceeds of oil extraction artificially raise its per capita income. The regression shows a clear inverse relationship between informality and income. For each 10% increase in per capita income, the informality rate declines by 2.28pp. More importantly from our point of view, the regression shows that despite being 15% richer Mexico has an informality rate that is 0.5pp higher than Brazil's. 25 See ILO(2014) for comparative data on informality in the G20 countries, including Mexico and Brazil. For Brazil, informal workers are: non-registered employees, non-registered domestic servants, selfemployed workers, workers in the production for own-consumption, workers in the construction for ownuse, unpaid workers. This classification is not official, but its that generally adopted by researchers and by the ILO. In Mexico, there is now an (ILO compliant) official definition of informal workers which is: "...besides the component that works in non-registered economic units or informal sector, other analogous modalities such as those employed in paid domestic work without social security, self-employed workers in subsistence agriculture, and unpaid workers, as well as paid workers without social security whose services are used by registered economic units." Freely translated from INEGI (2014), p. 36. The second exercise is summarized in Figure 13 that describes the evolution of the informality rate in the two countries. This data confirms that Mexico has a higher informality rate than Brazil. Moreover, the impression arising from both the earlier restrictive definition and the more recent ILO compliant definition is that informality in Mexico remained roughly constant throughout the period. This is in contrast to Brazil, where the informality rate declined substantially: from 60% of total employment in 1999 to 47% in 2013. This is only in part due to the higher GDP growth rate of Brazil in the period. Other factors, such as enhanced labor law enforcement and rising business credit seem also to have been important determinants of reduced informality.  1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Brazil -PNAD MEX: tasa de ocupación em el sector informal Rate of informality -INEGI

Conclusions
It has become a cliché for economists to paraphrase Tolstoy's Anna Karenina's first paragraph that all happy families are alike; each unhappy family is unhappy in its own way. But the quotation agrees quite well with Brazil's and Mexico's experiences since the early 1980s. Not quite from a macro perspective, as both countries saw their GDP growth rates and capital accumulation sink nearly synchronically. They experienced a similar lost decade in the 1980s, and introduced liberalizing economic reforms in the 1990s. The rise of China made their economic fortunes differ for a while in the first decade of the century. But after the Great Recession they both are finding it difficult to resume decent growth rates. Despite these macro similarities, when we go deeper into the evolution of their respective economic structures, we find that Brazil and Mexico have become unhappy each on its own way.
In the first part of the paper, we identified in both countries contractions in capital accumulation that were both deep and lasting and were closely associated to the GDP growth collapses that started in the early 1980s. The slumps in capital accumulation were not, however, associated with declines in savings rates, as these either remained constant or increased after 1980. The culprits for the disaster were substantial increases in the capital-output ratio in Mexico and in the relative price of investment in Brazil. They coincided with the debt crisis of the early 1980s and the subsequent policy responses to it: inefficient capital goods import substitution in Brazil, informality-inducing social policies in Mexico.
We next drew attention to the evolution of aggregate output per worker as explained by capital deepening and total factor productivity (TFP). Our data shows the extraordinary loss of dynamism of the two economies after the early 1980s. Between 1950Between -1980Between /81 and 1981Between /82-2014, the yearly growth of output per worker fell from 4.2% to 0.4% in Brazil and from 3.4% to -0.2% in Mexico. Contractions in the growth rates of capital per worker and of TFP divide the responsibility for this collapse, with the former being relatively more important in Brazil and the latter more prominent in Mexico.
The story is different in the more recent 2011-2014 period. Growth of output per worker was equally mediocre in the two countries, but in Brazil capital accumulation recovered while TFP growth sank. In Mexico, on the contrary, capital accumulation dropped while TFP growth improved. The speculation is that, more recently, Mexico may be dealing with more success than in the past with the structural sources of its traditional low productivity, but is suffering from a low propensity to invest. Meanwhile, in Brazil the end of the commodity boom and government mismanagement seems to have led TFP growth to become negative, even as capital accumulation recovered from the very low levels prevailing since the 1980s.
An econometric exercise suggested that the yearly changes in TFP in the 1981-2014 period can at least partially be explained by the changes in the output gap and in the terms of trade.
The conclusion of the first part of the paper was that there are basic macroeconomic similarities in these countries' post-1980 experiences: because of either policy failures or structural conditions, Brazil and Mexico were unable to undo the increases in the relative price of investment and in the capital intensity of production experienced since the early 1980s. They were also unable to raise their savings rates sufficiently high to compensate for such investment-depressing factors. The result is that investment contracted and growth lost strength after the 1980s.
The second part of the paper explored five disaggregated dimensions of the evolution of labor productivity in the two countries. The dimensions are: geopolitical units, economic sectors, tradability, firm size, and informality. In the regional dimension, we observed a tendency for income inequality to increase in Mexico and to decrease in Brazil since the 1990s. The speculation is that manufacturing activity blossomed in Northern Mexico, well integrated to the U.S. but with few linkages to the rest of the country. In Brazil, on the contrary, manufacturing activity, which is highly concentrated in the country's richer state, lost dynamism. Meanwhile, agriculture and mining, which are better disseminated regionally, gained traction with the commodity supercycle. Additionally, cash transfers and minimum wage policies were more effective at income redistribution than in Mexico.
We considered next the evolution of labor productivity in ten economic sectors that cover the whole economy. The conclusion is that the heterogeneity of labor productivity at the sectorial level became more pronounced in both countries accompanying the slump in GDP growth rates after 1980. From a sectorial perspective-basically because of the oil sector--Mexico is structurally more heterogeneous than Brazil, but the difference between the two countries seems to have decreased recently.
Subsequently, we used a more disaggregated dataset to investigate in more detail the behavior of labor productivity in the traded and non-traded sectors of Brazil and Mexico in the 1989-2009 period. This dataset confirmed the tendency for sectorial productivity convergence in Brazil, whereas in Mexico the trend was one of divergence, with the non-traded sector lagging well behind the traded sector. This result is consistent with the view that in Mexico the traded sector is very dynamic but this dynamism does not spread to the non-traded sector. Meanwhile, in Brazil the traded sector struggles to reach the productivity levels of the non-traded sector.
The next exercise was a comparison of the evolution of labor productivity according to firm size. The picture that emerged for Mexico was clear: the biggest firms display a much higher productivity growth than smaller firms-the productivities of the smallest of which, trifling as they are, fell in the 1998-2008 period. The implication is that Mexico's low productivity growth problem resides squarely with its small and medium sized firms, a large proportion of the employment of which is informal. For Brazil, the picture was very different: the productivity growth rates of small and medium-sized firms in the manufacturing sector were similar to that of the country's largest firms-and they all were very low.
Finally, we confirmed that Mexico has a higher rate of informality than Brazil in spite of its higher per capita income. Moreover, the impression arising from our data is that informality in Mexico remained roughly constant since the mid-1990s. This is in contrast to Brazil, where the informality rate declined from 60% of total employment in 1999 to 47% in 2013.
We concluded that there are relevant "mesoeconomic" differences in these countries' recent slow-growth experiences. Mexico opened up its economy to trade with the outside world and thus succeeded in developing a first-class industrial sector in the country's richer Northern region. A similar domestic integration didn't accompany this external integration. The dynamism of the large exporting firms in the North did not feed back to the non-traded, informal, small and medium-sized firms in the country's poorer Southern regions. Since the latter generate not only most of the country's jobs but also a substantial part of its output, the consequence was a very low aggregate labor productivity growth rate.
Thus, the disparity between "modern" and "traditional" sectors seems to have widened in Mexico. In Brazil, in several dimensions this dualism decreased: the poorer North grew faster than the richer South; the lower-productivity agriculture did better than the higher-productivity industry; bigger manufacturing firms did not outflank medium and small firms; informality decreased in the last decade. Brazil's problem seems to have been that in contrast to Mexico's her high-productivity large-manufacturing firms did not integrate into the world economy and thus saw their productivity grow very slowly. This provided a weak lever to move the rest of the economy up. Therefore, the country lingered on in a low overall productivity path, except when the commodity lottery dictated otherwise.
Our survey remained incomplete because we didn't discuss many issues that are present in the debate on the reasons for the near stagnation of Brazil and Mexico: lack of government investment in infrastructure; insufficient investment in human capital; distorting tax burdens; failed competition policies; labor market rigidities; poor governance and rule of law; overvalued real exchange rates; inadequate composition of foreign trade; deindustrialization; lack of bank credit to the private sector; and high real interest rates.
Pending a further analysis of these issues, the bottom line of our investigation is that overcoming the so-called middle-income trap seems to require both domestic and foreign economic integration. Brazil's and Mexico's growth collapses show that achieving them at the same time is not an easy task for big middle-income countries.