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Gravity
Key Concepts:
Terms in this set (56)
Cobb Douglas function
Y=z(K^a)(N^1-a)
Total Factor Productivity (TFP)
Measures changes in unobserved inputs
--in a boom, more effort (measure high TFP)
--in a recession, less effort (measure low TFP)
Value added/product approach
Value added-intermediate goods
Major actors, take away things that double count
*look out for goods such as national defense that have
Expenditure approach
C+I+G+(Net exports-imports)
Income Approach
Wage Income + After Tax Profits + Interest Income + Taxes
Price Index
Weighted average of a set of observed prices
that gives a measure of the price level.
• allow us to measure the inflation rate - the
rate of change in the price level.
• A measure of the inflation rate allows us to determine how
much of an increase in GDP is nominal and how much is
real.
RGDP in year 1 dollars, chain method
Year 1 = GDP1
Year 2= gc*GDP1
RGDP in year 2 dollars, chain method
Year 2 = GDP2
Year 1= GDP2 /gc
Implicit GDP Price deflator
(Nominal GDP/Real GDP) * 100
Consumer Price Index (CPI)
includes only goods and services bought by consumers
- a fixed-weight price index
= (Cost of base year quantities at current prices / Cost of
base year quantities at base year prices) * 100
- Our example: if take year 1 as base year, then CPI in
year 1 = 100 and in year 2 = 222.5/130=171.2
Problems in Measuring GDP
1. Economic activity in the underground economy cannot be
measured directly
- this activity might be measured indirectly by
accounting for the use of currency.
- Estimates (F. Schneider, "Shadow Economies and Corruption All
Over the World: New Estimates for 145 Countries.", 2007)
- Developed (13% of GDP) vs developing (36%)
2. Government production is difficult to measure, as the
output (for example defense services) is typically not sold
in the market.
- In NIPA gov't expenditures are valued at cost
GDP and welfare Facts
1. GDP and consumption equivalent welfare are strongly
correlated, but disparities exist
2. Average Western Europe living standards appear much
closer to US (85% for welfare versus 67% for income)
3. Most developing countries (incl. sub-Saharan Africa,
Latin America, southern Asia, China): much poorer than
incomes suggest (shorter lives and extreme inequality)
4. Growth rates are typically revised upward: welfare growth
averaging 3.1% 1980s-2000s vs income growth of 2.1%
- A boost from rising life expectancy of more than a 1%
throughout the world (exception sub-Saharan Africa)
- With this, living standards double in 24 vs 36 years;
After tax profit
Total Revenue-Wages-Interest-Cost of Intermediate goods-Taxes
Three historical economic facts
1) Sustained growth in U.S. Per Capita Real Income, since 1900
--Except for the Great Depression and World War II, growth
in U.S. per capita real income has not strayed far from 2%
per year since 1900.
2) Real Per Capita Income and the Investment Rate
--Across countries, real per capita income and the investment rate are positively correlated.
3) Real Per Capita Income and the Rate of Population Growth
--Across countries, real per capita income and the population growth rate are negatively correlated.
4) Real Per Capita Income and Per Capita Income Growth
1. There is no tendency for rich countries to grow faster than
poor countries, and vice-versa.
- Level of output per capita in 1960 not correlated to
growth in output per capita in years 1960-2007
2. Rich countries are more alike in terms of rates of growth
than are poor countries.
Solow model
• This is a key model which is the basis for the modern
theory of economic growth.
• A key prediction is that technological progress is
necessary for sustained increases in standards of living.
Population growth
N'=(1+n)N
consumption-savings behavior
C = (1 − s)Y
*consumers save a constant fraction of income
Evolution of the Capital Stock
K'=(1-d)K+I
Income-Expenditure Identity
Y=C+I
equilibrium future capital
K'= sY + (1-d)K
K'= szF(K,N) + (1-d)K
Per worker form capital allocation
k'(1+n) = szf(k) + (1-d)k
Rearranged by dividing all by (1+n)
Increase in savings rate s
1) In the steady state, this increases capital per worker and
real output per capita.
2) In the steady state, there is no effect on the growth rates
of aggregate variables.
Increase in the Population Growth Rate n
• Capital per worker and output per worker decrease.
• There is no effect on the growth rates of aggregate
variables.
Increases in Total Factor Productivity z
Sustained increases in z cause sustained increases in per
capita income (usually from tech)
Will economic growth grow continuously?
1) Delong (1998)
--growth used to be slow, since industrialization has gotten much faster
2)Robert Gordon (2016)
--1879 to 1980 was the special century and glory days are behind us
3) Joel Mokyr (2015)(optimistic)
difficult to predict breakthroughs
Convergence in the Solow growth model
If two countries are initially rich and poor, but identical in
all other respects, they will converge in the long run to
the same level and rate of growth of per-capita income.
• This is called 'absolute convergence'
• But we have seen little evidence of that in the world
• However more evidence for it within specific regions
(less heterogeneity)
• Example: states in US and Europe
Conditional convergence
• Countries differ in some aspects (eg. savings rate, TFP)
• They converge to their own steady state
• Can savings rate do it?
• Mankiw, Romer and Weil (1992): savings rate are just
not that different to explain GDP per capita through the
standard Solow model
What Can Explain Persistent Differences Across Countries In the World in Per-Capita Income?
• Perhaps there can be persistent differences in total factor
productivity across countries.
• By and large, in the data rich countries (countries with
high GDP per worker) have high TFP (i.e. are very
productive) and poor countries have low TFP (i.e. are not
very productive).
Sources of differences in TFP
1) Knowledge and education: high correlation between
an index of human capital and GDP per capita
2. Climate: countries located in climates closer to the
Equator tend to be poor relative to countries located
further from the equator
3. Institutions: colonial development with European style
legal institutions are associated with higher growth
4. Barriers to adoption: corruption, vested interests (gov't
subsidies, trade restrictions, union power)
5. Finance: developed financial system intermediates
efficiently funds, facilitates innovation
6. Free trade: open economies grow significantly faster
Profit Maximization
MPN = w
Max N (F(K,N)) -wN
CPI
hold quantity fixed and change prices in calculation (yr one base only use yr 1 Q, yr 2 base oonly use yr 2 Q), higher inflation rate bc if relative prices go by more CPI keeps quantity fixed and doesnt accunt for demand that would droop from loower prices, prooblem for like soocial security
why three approaches shoold be the same
Value added is sold --> seen as expenditure by whomever sold it to--> output producedd income fr someone in the econ
RDGP2 GC
GDP1*gc
RGDP1 GC
GDP2/gc
why rgdp understated
doesnt take into acct tech, quality of goods
properties of prod function
constant returns to scale, decreasing marginal ret to scale, pos marg ret to scale
maximizing profits
max and take derive of:
y-wN
to find the tangency point where MPn is w
TFP model
have to take a stand on inputs and production function as cannot be directly measured
factor input share
(wN)/y
=
(MPn*N)/y
=
1-a for cobb douglas
(ex is 0.7 for US as about 70% of income goes to wages)
zanalyst vs ztrue
calc using prod function, might need to take the log
capacity/ capital utilization
use capital more in booms, measured by Uk (phys cap utilizatioon), can use proxies like electricity
in real econ save in
physical capital
when markets clear
S=I, I=sY
savings rate
investment/output
equating steady state numerically
take capital accu equ of Kt+1-Kt where they are equal and 0 is savings-depreciation
Inada conditions
lim k goes to zero of f'(k) is infinity
lim k goes to infinity of f'(k) is zero
In steady state
K=k* x N as grows at pop growth
As savings rate increases
k
will stay steady then increase gradually overtime before settling at new higher k
optimal consumption, C*
when income is equal to savings (or can call investment)
=zf(k
)-szf(k
)
=zf(k
)-(n+d)k
take derivative of second equation wrt k
to find when the slope is zero, that k will be the golden rule k
golden rule k
when zf'(k*) aka MPk is equal to n+d (aka how much investment needed)
golden rule savings rate
[(n+d)kgr/(zf(kgr))]
If savings less than gr savings
consumptiooon will stay flat, ddip shoortly over time then rise gradually to new higher level
if savings greater than gr savings
consumptiooon will gradually grow to new consumptioon rate that is higher in long term
if populatioon grows
level of capital needed is lwoered
golden rule for capital
MPk= zf'(k*)=n+d
Gov't spending in the solow model
T=G is assumption that make
K'=s(Y-G) + (1-d)K = sY-gN + (1-d)K
in graph would have sg +(n+d)k = szf(k)
growth rate of income per capita:
[(Y'/N')-(Y/N)]/(Y/N)
=(new-old)/old
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