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According to
Daude and Fernández-Arias (2010), the gigantic diversity in income per capita
across countries can be largely attributed to variations in their aggregate
productivity levels (namely TFP). In 2010, the authors found a correlation
coefficient of 0.95 between TFP and income per capita: statistically, “90 percent of the cross-country income
variation in the world today would disappear if TFP were the same across
countries in the world”. TFP hence seems to play a central role in
explaining income per capita diversity across and within regions and in shaping
the roots of economic development (Daude and
Fernández-Arias, 2010). TFP, in fact, has been accounted as a
fundamental of several GDP models; Kohli, Szyf, and
Arnold (2012) provide a comprehensive overview of the main theories.

Charles W. Cobb and Paul H. Douglas introduced Total Factor Productivity
in a long-run equation to estimate potential GDP (Cobb and Douglas, 1928):L and K respectively
represent the labour force and the capital stock embedded in a certain economy,
while their contribution to the production of income is expressed by ? and 1-?,
respectively. Hence, TFP indicates
the amount of GDP produced for a given amount of labour and capital, estimating
the outputs to inputs ratio. This function exhibits constant returns to scale
(by doubling both K and L, Y doubles as well) and diminishing returns for each
input (as capital does not increase, additional labour units produce minor
outputs). These assumptions are also the pillars of the production function
proposed by Robert Solow (1956), whose basic model can be expressed as follows:Output
(Yt) is produced via an aggregate
production function and can grow as the underlying factors A, K and/or L increase
over time. One of the pillars guiding growth theories is that levels of output
per capita vary widely across countries1,
and in the Solow model this variation is largely explained by labour-augmenting
technological progress; technology augments the share of labour in output for a
given capital stock (Badel and Hugget, 2016).
Other studies privilege instead the role of capital-embedded technology, which
is a catalyst for further growth, enabling continued per capita growth andcapital
(Calhoun, 2002). When disembodied, technological
progress can be described as Total Factor Productivity, which in the Solow
model is estimated as a residual for a known increase in the output share of
capital and labour (mnmeconomics, 2011). Jones (2002), and Hepburn and Ward
(2011) introduced the concept of H,
human capital (i.e. education, namely the skill level of L), in their growth models:

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Jones uses H1
as a proxy for the technological level embedded in labour, while TFP assumes
the concept of country’s social infrastructure. Hence, it determines how skills
and technology are combined, capturing a series of collateral forces such as
competition, culture, laws and stability of institutions (Kohli, Szyf, and Arnold, 2012). Niels Mygind (2016) also emphasizes the importance of the
qualitative side of labour (Q) and
the moderating effect of institutions on TFP. His growth model innovatively
considers the impact of raw materials, energy and land (R) as elements of growth, hence capturing the competitive advantage
of natural resources-provided countries:

represents the efficiency by which labour, capital and the other inputs are
combined and used, and it often captures influxes from technological progress (T + Q).
According to Mygind, the allocation of the production factors is strongly
influenced by the behaviour of the economic agents and their incentives are
determined by the rules of game given by the institutions.

In conclusion, TFP is very often just calculated as a residual, meaning
that sometimes it includes technological progress, upgrading of knowledge in
human capital, institutional quality etc.
Efficiency in factor accumulation and its contribution to the output growth can
be evident over a number of years, and is related to a series of factors such
as trade policies, microeconomic adjustment and capacity of the institutions to
allocate resources efficiently. In the short run, TFP can vary mainly because
of demand volatility, which for instance has been very important in the LAC
region since countries have seldom been at full capacity. TFP can also abruptly
changes due to price volatility of raw materials, which explains to large
extent the volatility of GDP in countries such as Chile and Brazil (Mygind,
2016). On this regard, the following paragraph mentions some of the
determinants of scarce TFP.

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