Growth and development accounting Flashcards
Explain conditional or unconditional convergence.
Conditional Convergence: Assumes convergence happens only if countries share similar characteristics and policies. In other words it refers to the idea that poorer economies will tend to grow faster than richer ones and thus catch up over time, but this convergence is conditional on the countries having similar structural characteristics, policies, and institutional factors. This concept implies that countries with similar rates of savings, population growth, human capital, and technology levels will converge in terms of per capita income, but only if these conditions are met. They will not converge to the same level as the unconditional, but they will converge to the same level as countries which are as the same structure.
Unconditional Convergence: Assumes convergence happens regardless of differences in structural factors and policies. Also known as absolute convergence, posits that all poorer economies will grow faster than richer ones and eventually converge to the same level of per capita income regardless of their structural characteristics, policies, or institutional factors. This idea assumes that there are no significant differences in factors that affect growth among countries.
Please define and explain the development and growth accounting, respectively.
Growth Accounting: The relative importance of factor accumulation and productivity growth
From the per capita production function
…. (math see review groth)
Can give us insights into what “drove” growth in a country: factor accumulation or productivity
growth?
Development Accounting: A decomposition of relative production levels.
Consider output per worker in a rich and a poor country:
…
The ratio of output per worker can be decomposed into two ratios: Factors of production and
productivity
…
We observe the ratio of output and the ratio of factor inputs. Hence, we can solve for the ratio
of productivities
…
What factors contributes substantially to growth? Which does not, which is a bit surprising?
Capital accumulation tends to contribute substantially to growth for low income countries
Increases in the size and quality of the labour force also contributes to growth, not as much as capital accumulation.
Productivity growth tends to account for a larger share of growth in high income countries.
Education may not affect growth that much, in the data from the lecture. But it is always positive to contributing to growth, which is good, but is not contributing that much. So should we use so much money on education, when we want to increase growth?. The proffesor believe that we have very bad education data and really good capital data. That could affect the way we measure education per worker.
Please define and explain growth accounting
Growth accounting is defined and explained in Weil section 7.2.
Starting from a Cobb-Douglas
macro production function in per worker terms
y = Ak^alpha * h^(1-alpha)
we take the log-transform
derivative with respect to time to get
^y = ^A+ alpha^k * (1-alpha)^h
where hats indicate growth rates.
This shows that the growth rate of output is the sum of the growth rate of productivity (ˆA) and the growth rate of factors of production (alpha^k * (1-alpha)^h). We use this to get an estimate of the growth rate of productivity (the Solow residual):
growth rate of productivity = growth rate of output – growth rate of factors of production ^A = ^y - (alpha^k * (1-alpha)^h). “The technique for deriving the growth rate of productivity is called
growth accounting.” (Weil p. 213).
In the period 2000-2019 on a sample of 124 countries it looks like we have a slightly positive convergence parameter (beta). What does it mean, and who is behind this?
Article Patel (2021)
This means that countries are on average expected to have closed the half the gap in 170 years. This is very slow, but arguing for unconditional convergence.
But
Carl Johan Dalsgaard critizises this view, that they in the article only use the last 20 years and base there arguement on that. If they used the data since 1960, they would not get a beta which is different from zero. They would not be able to conclude that we have unconditional convergence. Therefor Carl Johan does not buy it, because why not using all the years. The normal critic, you can get data to look like everything by changing the different variables or periods. He also argue, that he does not believe that the soon coming years will have the same growth, due to war and increaising problems with getting goods.
Please give a brief summary of the main theories explaining how income inequality affects
economic growth.
The links between inequality and economic growth are described in PRLB chapter 6, Weil
chapter 13 and Berg et al. (2018). There are 5 explicit links from inequality to economic growth
of which only 4 are covered in detail in PRLB and Weil:
a. Following Weil (p. 400), more inequality leads to a higher level of physical capital accumulation. The reason is that more inequality leads to higher total savings because
individuals’ savings rates tend to rise with income. Hence, this link relates high inequality to high growth.
b. A more unequal distribution of income leads to lower human capital accumulation. An important reason is that human capital is embodied (installed in a specific person).
Consequently, human capital cannot be used as collateral, leading to a missing (financial) capital market. Therefore, poor people have to fund educational choices out
of retained earnings, wealth or abstention from currently productive work. Because they are poor the marginal cost of doing so may be prohibitively high, exceeding the marginal return. In the end, poorer people underinvest in human capital, leading to lower total
human capital accumulation in economies with more unequal income distribution. This
link relates high inequality to low growth.
c. A more unequal distribution of income may also lead to crime and risk of violent conflicts (sociopolitical unrest). The risk of destruction of output and loss of ownership
of capital implies lower expected return on investment. This leads to lower capital accumulation even without actual conflict. This link relates high inequality to low
growth.
d. In Weil p. 404-405 it is explained how inequality leads to a desire for redistribution. This comes about because an individual with pretax income above the mean would
prefer a redistributive tax rate of zero while individuals with pretax income below the mean will want a positive tax rate. The specific desired tax rate will be higher for
individuals with lower pretax income. The tax rate in a country is assumed determined by a political process involving voting. Thus, the tax rate in the country will be the rate
that is optimal for the voter with the median level of pretax income (the median voter). A higher tax rate may have negative effects on economic growth for two reasons: (1)
lower capital accumulation if taxes are imposed on the margin, and (2) lower efficiency, as explained in Weil p. 406. The overall outcome of the model with political redistribution is that higher pretax inequality leads to lower economic growth.
e. Berg et al. (2018) mentions a link between inequality and growth through an effect of inequality on fertility (the quality/quantity relation). This link relates high inequality to
low growth. Students are not expected to explain this link as it is not well described in the texts.
What are the possible channels through which growth reduces fertility?
Weil (Section 4.4) discusses four possible channels.
(i) Mortality: Declining mortality reduces the desired family size because it is not family size per se that matters but the probability of
having a surviving son. As mortality falls, it becomes possible for families to produce the same
number of surviving adults with lower fertility. (ii) Income growth gives rise to both income
and a substitution effects. The income effect gives rise to more children, while the substitution
effect (when the wage is high, time demanding children are relatively more expensive) leads to
less children. We may assume that income effect dominates at low levels of income while the
substitution effect dominates at high levels of income. (iii) Resource flows between parents and
children: As a country develops, the economic benefits of children tend to fall while the cost of
raising children rises. (iv) Quality-Quantity trade-offs. High income may increase the return to
skill investments (Human capital). This may induce a substitution from quantity (many
children) to quality (few, but well educated children).
Development accounting
Assuming final goods are produced according to the Cobb-Douglas production function
Y = AK^alpha * (hL)^(1-alpha)
, illustrate how development accounting decomposes relative income
differences into factors of production and productivity and discuss the relative order of
magnitude observed across countries using two different development accounting formulations
(say a “short run” and “steady state” type decomposition).
Development accounting is explained in Weil section 7.2.
The two different methods ask two distinct questions:
A) How much of the relative
difference in output per capita in country 1 relative to country 2 can be attributed to one of the
following factors: physical capital per capita, human capital per capita, or productivity, holding
the other two factors fixed?
Starting from the Cobb-
Douglas production function in per worker terms (y = Ak^alpha*h^(1-alpha), y = Y/L, k = K/L) the
productivity in two countries can be compared by creating the ratio of output in country 1
relative to the output in country 2:
Using this decomposition
… (see growth review for math)
Weil finds that 53 percent of the variation
in (log) output per capita across countries can be accounted for by variation in productivity
leaving 47 percent to the factors of production.
B) Here, the hypothetical question is how much of the relative difference in output per capita is
accounted for by relative differences in human capital, the capital output ratio, and productivity?
One objection to this accounting exercise is that physical capital per capita, according to the
Solow model, is expected to endogenously increase in response to increases in human capital or
technology. Endogeneity occurs when an explanatory variable is correlated with the error term in a regression model. In this context, it means that physical capital per capita is not independent of human capital and technological improvements. This correlation makes it challenging to isolate the individual contributions of physical capital, human capital, and technology to differences in income across countries.
Therefore, an alternative formulation of the accounting is sometimes used, for example in Jerzmanowski (2007, p. 2089) and Shastry and Weil (2003, p. 390). Specifically, the
production function (in per capita terms) is rewritten to have the capital-output ratio on the rhs
(the capital-output ratio is constant in a Solow-type steady state):
… (math)
The development accounting is as above with productivity, the capital-output ratio and human
capital
… (math) Ratios
This question is compatible with the steady state of the Solow growth model in which the level
of human capital or productivity has no direct effect on the steady state capital-output ratio. The
bigger exponents on productivity (i.e., 1/(1−α) instead of 1) and on human capital (1 rather than 1 − α) reflect the impact of these variables on output both directly and indirectly through capital per capita. Results in Shastry and Weil (2003) shows that productivity accounts for just below
60 percent using the “steady state” type decomposition.
What is the relative importance of input factors and productivity according to the literature, which uses alpha as 1/3
About 20% of the variation in GDP per worker (y) can be attributed to variation in capital-output ratios (or to capital per worker)
About 10-30% of the variation in GDP per worker (y) can be attributed to variation in human capital (education)
As a results of the above, about 50& of the variation in GDP per worker must be attributed to variation in productivity (TFP). It is not well understood what drives TFP.
Please illustrate and discuss the anticipated impact of human capital on GDP per capita both in
the short run, using growth accounting, and in the long run, based on a Solow-model with
exogenous human capital formation.
Starting with the development accounting, we compare GDP per worker in two countries, assuming they
produce output using the same technology:
… (math in review groth)
This decomposition illustrates the influence of human capital on relative differences in GPD per worker.
Using the decomposition, we can compare, say, India and USA. In 2009, the level of human capital in India
was 2/3 of the level of human capital in USA (Weil, Table 7.2). If this were the only difference between
India and USA, we would expect GPD per worker in India to be ¾ (0.758) of GDP per worker in USA,
assuming that alpha = 1/3.
In the standard Solow model with exogenous human capital, the steady state the ratio of GDP per worker is
… ( math )
where the star on yi indicates steady state levels, si is the savings rates in each country, ni, the population
growth rate and delta_i the capital depreciation rate (i=1,2). The expression shows that in the long run the ratio of GDP per worker will be directly proportional to the ratio of human capital, which is a larger effect than given in the development accounting. The reason for the difference is that capital intensity is endogenous in the Solow model.
The Solow growth model augmented with human capital and population growth can be described
using the equations (i) - (iv). Please explain the economic intuition behind the equations. Please be
as precise as you can.
𝑓(𝑘𝑡) = 𝐴𝑘𝑡
𝛼ℎ𝑡
1−𝛼 (𝑖)
Δk𝑡 = 𝑖𝑡− 𝑑𝑡 (𝑖𝑖)
i𝑡 = 𝛾 ∗ 𝑓(𝑘𝑡) (𝑖𝑖𝑖)
d𝑡 = (𝑛 + 𝛿)𝑘𝑡 (𝑖𝑣)
This question is related to Weil ch. 3 and 6 and PRLB ch. 4.
(i) Is a function for production/income per worker/capita in time period t, where the standard
Solow model has been expanded with human capital, h. A is a total factor productivity
parameter. k refers to the capital stock per worker. 𝛼 is a parameter that controls the share of
production that accrues to capital.
(ii) Is an accounting equation for the change in the capital stock per worker between period t-1
and t. The change in capital stock per capita equals investments per capita, i, minus
depreciation per capita, d.
(iii) Controls investment. Investments are assumed to be a constant share (𝛾) of total production
per capita.
(iv) Controls depreciation per worker. Depreciation consists of true capital depreciation, which is
assumed to be a constant share (𝛿) of the capital stock as well as a capital dilution effect from
population growth, which equals the population growth rate (n) times the capital stock per
worker. This effect arises from the fact that when there is population growth, the existing
capital must be shared between more people, which reduces the amount of capital per capita.
Please discuss whether the Solow Growth model is an adequate framework for understanding
growth and development.
This question is related to Weil ch. 6 as well as PRLB ch. 2 and 4.
The Solow growth model is a useful tool for understanding economic growth. It provide insights into
relationships between income and investment, savings, population growth, human capital as well as
technological change. It also provides a theory of how the economy reaches a new steady state
equilibrium as a result of changes in these variables. The production function of the Solow model allows us
evaluate the relative importance of different production factors as well as to undertake growth accounting
in order to analyze why some countries are rich and other countries less rich. However, there are also
factors that can be important for growths that are left out, such as political stability or export-oriented
policies. Further, a high income per capita is not equivalent with high living standards. One reason is that
much income could be used for savings instead of consumption. While this may allow higher income
tomorrow, it does not improve living standards today.
The Solow model is however not sufficient for understanding economic development. This is because
economic development as a concept is broader than just economic growth. While many development
outcomes are often correlated with economic growth (or income per capita in levels), the correlation is far
from perfect. Other outcomes could, among other things, include poverty, inequality and education and
health outcomes. These factors do not enter, or enter only as explanatory factors (rather than as
important outcomes in their own rights), in the Solow model.
Jones & Klenow (2016)1 use an alternative approach to measure development, using equation 1 as
their starting point. Please discuss the intuition behind their approach, referring to equation 1.
100 𝑈 = 𝐸 [∑ 𝛽𝑎 ∗ 𝑢(𝐶𝑎, 𝑙𝑎)𝑆(𝑎)] (1)
𝑎=1
This question is related to Jones & Klenow (2016).
Jones & Klenow (JK, 2016) use a framework of expected utility in order to make international comparisons of welfare across countries. The basic idea is to specify expected utility (U) as a function of discounted utility (u) over consumption (c) and leisure (l) over the course of a person’s life. Yearly utility is discounted and summed over ages 1 to 100. 𝛽 is the yearly discount factor and S(a) is the probability of being alive at
age (a) – dead people get zero utility. This person is a fictitious person who does not know how her life will
turn out. Thus, JK assumes that she will draw from the cross-sectional distributions of consumption, leisure and mortality of a given country.
JK goes on to calculate a consumption-equivalent measure of the welfare of one country compared to another. JK do this by asking how much one must scale annual consumption in some country i in order to make the person indifferent between living in country i and in the US.
What are the benefits of using the method of Jones & Klenow? What criticisms can be raised
against the Jones & Klenow framework?
This question is related to Jones & Klenow (2016) and PRLB ch. 2.
JK motivates their measure by noting that GDP is a flawed measure of economic welfare, in part due to the
reasons discussed in question 3 and also discussed in PRLB ch. 2. Like GDP, it is possible to compute using
widely available data and it allows for international comparisons. Compared to a GDP measure, the JK
measure has several benefits, including:
- Focusing on consumption instead of income – this allows JK to differentiate between those
countries who spend much of their income on savings, compared to consumption.
- Negative effect of inequality is built in: Because JK assumes decreasing marginal utility within a
framework of expected utility, inequality affects the consumption-equivalent welfare measure
negatively.
- Compared to other attempts at international welfare measurements such as the HDI index, the JK
approach is grounded in economic theory.
JK also discuss downsides to their approach, including:
- Using a single utility function for all countries, even though this may not be realistic
- Life expectancy is used as a measure of health and morbidity is ignored, even though it may well
affect utility
- There are other factors of life than consumption and leisure that may plausibly enter the utility
function. JK mention the quality of the natural environment, public safety, or political freedom,
although there may be others.
The main results table of Jones & Klenow is shown in table 1. Please discuss the main findings of
the table. In your discussion, you may focus only on the first row for each country (i.e. ignore the
“micro” results).
This question is related to Jones & Klenow (2016).
The table shows the main results of JK. The first column shows the consumption-equivalent measure, 𝜆, as compared to the US. The second column shows the income level relative to the US. The third column is the log-ratio between 𝜆 and the relative income levels. The remainder of the columns decompose this ratio
into its component parts.
JK’s discussion includes the following findings:
- There is a substantial correlation between GDP per capita and 𝜆.
- The gap in “welfare”, i.e. 𝜆, relative to the US, are smaller for Western European countries than
for then the gap in their income. This is primarily caused by higher life expectancies in
Western Europe
- The gap in overall well-being between the US and poorer countries is even bigger than the gap in their incomes. There are several reasons for this, including lower life expectancies, lower consumption
shares of income as well as higher consumption inequality in many of the included poorer
countries.
- The conclusion from these two last findings is that global inequality in welfare (between countries)
is higher than global inequality in income.
