Macro 4 Flashcards
Stylized facts of industrialized economies
- The ratio of capital to output has been constant (K/Y = constant in the LR).
- Capital per worker has grown at a sustained rate (K/L > 0).
→ (1+2): output per worker has grown at a sustained rate ((K/L)/(Y/L)).
→ Numerator & denominator grow equally. - Capital and labour have captured stable shares of national income.
- (2+3): wages have grown at a sustained rate.
- (1+3): the real interest rate has been stable.
What are the 5 characteristics of physical capital?
It is productive
Can be produced
Is rival in use
Earns a return
Depriciates
What are the two assumptions of the basic Solow Model?
Constant returns to scale (for any Lambda>0)
Diminishing marginal returns
Cobb-Douglas Function & Properties
Y = K^a L^b. (b = 1-a)
Constant elasticity of output wrt each factor of production
Constant factor income shares
What does one get as w and r for a profit maximising firm with the Solow model and a Cobb-Douglas function?
w = BetaY/L
r = AlphaY/K
What is the formula for capital accumulation?
K(t) = sY(t) - 𝜹K(t)
basic solow, what is the formula for k*?
k* = (s/n+𝜹)**1/1-alpha
basic solow y* ?
k*^a
Increase from s to s’
higher y* and k*
Increase from n to n’
lower y* and k*
Basic solow, Is there growth in steady state?
Not per capita growth, only absolute growth.
(population grows at n)
What does the average level of human capital determine?
How much a worker can produce given the level of physical capital per worker
What is human capital a combination of?
Health and education
What are wages a combination of?
The return to raw labour and human capital
What is used to calculate average human capital? How is it expressed as a formula?
The wage premium of education
h = e**(return of additional year of education * years of education)
What is the economic rationale of the Mincer specification?
More schooling leads to higher wages, aka more schooling is equivalent to more quality adjusted labour)
Exo. Technological Progress in Solow
Y = K^a(AL)^1-a. and A is exogenous and grows costant rate g
Capital accumulation in efficiency terms
.~k = s~y - (n+g+delta)~k
Steady state .~k=0 so ~k* = ?
~k* = (s/n+𝜹+g)**1/1-alpha
Exo Tech Solow, k and y growth ?
Both grow at tech progress = g
In steady state growth rate unaffected by savings or else
Exo Tech Solow, permanent increase in s effect on growth y ?
Leads to a temporary increase in growth y and then gradually returns to g; y itself is not immidiately impacted but it will have a permanent higher level
Exo Tech Solow, drop in g leads to ?
Immidiate drop in growth y pc capita but increase in y efficiency terms
Returns to education
Returns to schooling are not uniform : weakly decreasing marginal return to education
human capital
H = hL
(where h is the mincer thing h = e^( 𝜓*u)
u average years of schooling, psi return to schooling
Long run steady state with e^( 𝜓*u)
Nothing changes in efficiency terms (we divide by AH), but in pc terms we need to multiply everythiing by e^( 𝜓*u)
Remeber e^( 𝜓*u) is a costant
Why Productivity?
Countries also differ in how effective they are at combining factors (physical capital,labor,human capital)
Difference in productivity levels
output = [productivity] * [ factors of production]
Y = [ A^1-a ]* [K^a * (hL)^1-a]
Do we observe variation in productivity levels across countries ?
yes
Developement Accounting Formula
𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 = 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑜𝑢𝑡𝑝𝑢𝑡 / 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛
Issue : mismeasurement in production fact ratio –> leads to mism. in producitivty ratio
main message : diff in output pc not 1-to-1 related to diff in fact ratio
Growth Accounting formula
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑔𝑟𝑜𝑤𝑡ℎ = 𝑜𝑢𝑡𝑝𝑢𝑡 𝑔𝑟𝑜𝑤𝑡ℎ − 𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑔𝑟𝑜𝑤𝑡ℎ
same mismeasurement issues
productivity growth accounts for an important [art of overall growth
Convergence theory ?
Rich and poor tend to converge in terms of income per capita
Inconsistent with evidence
Prediction of convergence within the model
The model does not predict a negative relation between GDP and growth rate, instead the opposite a ** positive relation**
Per type of country we see negative relation (the ones with low s)
Absolute convergence hypothesis
There is a negative relationship between growth rate of y and y itself
Conditional convergence
Solow model does not predict absolute convergence, it instead predicts country-specific convergence
Conditional convergence within the model
the growth rate depends on how far a country is from its own steady state (the further below, the higher the growth rate)
Empirical evidence lends support to this hypothesis
What causes technological progress?
Innovation: new ideas!
nature of ideas
Disembodied: easy to transfer/ hard to protect
Nonrivarly –> high cost of creation & low cost of reproduction
Varying level of excludability : ploicy and institutions (patetns, subsidies protection)
Invest in R&D ?
- Advantage of creation
- market size
- duration of advantage
- uncertainty
Romer Model Endogenous Tech Progress
Advanced economies tech progress drvien by R&D, sotto A(t) puntino
𝐴 (𝑡) = 𝜃𝐿(𝑡)^𝜆 * 𝐴(t)^𝜙
𝜃 > 0; 𝜆 ∈ (0,1) ; 𝜙< 1
What is 𝜃 and La in romer model
Productivity parameter, share of workers in R&D
𝜆 in romer model
Duplication of efforts, stepping on toes effect.
The higher the better, researchers are getting in their way less
𝜙 in romer model
Effect of current tech/ideas on productiivty of researchers.
**knolwewdge spillovers:
* Fishing out, harder to come with something out after everything is discovered
* Standing on shoulder, previous tech helps creating new tech
Fishing out dominates 𝜙<0 ; Standing on shoulders dominates 𝜙 (0,1)
labor allocation
- Production of goods (workers): 𝐿y
- Creation of ideas (researchers): 𝐿a
romer model gA
gA = 𝜃𝐿a(𝑡)^𝜆 / 𝐴(t)^1-𝜙
growth in steady state ?
same as in solow gy = gk = gA
gA costant in steady state (BGP)
growth of gA=0
gA* = 𝜆n / 1-𝜙
Innovation policy
Increase in Sr affects long run level of y (y*)
however no effect on growth rate of y
Also ambigous effect:
higer sr –> higer R&D effot –> higer A
higer sr –> less labor in production of goods
Malthusian dynamics
increase in living standards –> increase in population –> facilitating innovation –> sustained growth –> sustained improvements in living standards
before 1800
low income and low growth
after 1800
high income and high growth
slow down in fertility in modern times
Malthusian model
Y = BX^βL^(1-β)
X fixed factor land
B level of tech
income pc y = B*( X/L)^β
population dynamics
gL = 𝜃(y- c_ )
c_ subsistence consumption
Steady state in Malthusian model
Stagnant population gL= 0
Stagnant income pc gy = 0 , y* = c_
Explains stagnant living standards pre-1800
one-off tech increase in Malthusian model
Shifts curve to right (B + ΔB) , higher L*
y* = c_
Continuous tech progress (Exogenous)
recall y=B*( X/L)^β
gy= gB + β(gX - gL) = gB - βgL
gB = βg
gy = β(g - gL)
Steady state with continous tech progress
gL* = g >0 , pop. will grow in steady state
gy* = 0 , y* = g/𝜃 + c_ no sustained growth in income pc
Continuous tech progress (Endogenous)
gB comes from the Romer model
gB = v(sr*𝐿)^𝜆 / B^1-𝜙
Kremer Model
The rate of pop growth is increasing in pop size
gB = L (recall gB = gβ)
gL = g = L / β
Virtous cycle gL >0 –> L increases –> gB increases –> gL >0 –> L increases
Empirical evidence kremer model
In most recent years ever increasing gL and gB not observed
Refined population dynamics
gL peaks at some value of y
Transition to sustained growth
- escape trap : shock shifting y (black death didn’t work implausible somenthing else will)
- eliminate trap : shift g super up , pop growth settles in the long run at n*
Post malthusian regime
gB = 𝜆n* / 1-𝜙
gy = gB - βn*
β use of land in production on, less of it drags on growth, evidence declining of β (land less important for production) -> easier to escape Malthusian trap
Parents utility maxmiziers care about ?
- Quantity of children: number
- Quality of children: education
Number of offspring (m) depends on ?
Positively on resources spent on having children (M)
Negatively on income pr (y), opp. cost when rich (parents time more valuable)
m = nM/y
n>0 parameter
schooling per child (u)
u = E + u_
E resources spent on education
u_ sum of basic skills
Budget constrain in children
y = c_ + M + E
Utility of parents V
V = ln(m) + ln(u)
than you substitute m and u , and max respect to E
pop growth economic dynamics
It is equal to generational growth, children that come from 2 parents n = (m -2)/2
population dynamics driven by m
m increases with y, higher income frees resources –> more kids , if income y too high m decreases, parents spend in education
Danger of nonrenewable resources
they get depleted upon use and do not regenerate, tech progress fundamental for sustained growth it needs to compensate for growing pop and declining resources
the role of reserves
they get depleted as energy is used,
a fraction of these is continuosly used to, they decline at rate Se
Growth rate y with non ren. resources
higer n –> lower gy (more people less E)
higher Se –> lower gy (resources depletion drags growth)
factor prices and scarcity
as resources get depleted relative price should increase
No evidence showing this trend
Problematic underlying assumptions
- costant decline of reserves
(could be undeveloped resources transformed into developed reserves) - Costant factor income share of resources
CES costant elasticity of substitution production function
F(K,E) = (K^rho + (Be*E)^rho)^1/rho
what is rho (rho <1)
determines the elasticity of substitution (sigma) between capital and energy . sigma = 1/ 1- rho
K and E substitute when ?
sigma > 1 , 0 < rho < 1
K and E complements when ?
sigma <1 , rho <0
evidence on factor shares
declining E/Y
high elasticity of substitution
sigma >1 , 0<rho<1
Energy can be easily substituted by capital
Pronlem, if E goes to 0, economy can still produce K
fast (energy-saving) tech. progress
Low elasticity of substitution, sigma <1 , rho<0, factor shares decline if there is sufficient growth in tech
economic impact on enviroment
emissions of GHG , climate change, damages , lower output, lower consumption
enviroment in utility function V
V = u(Ct) + theta * v(Rt+1)
Positively depend on Consumption and remaninig resoruces
Trade-off
Higher consumption requires more resources use
Social infrastructure and performance
Policies :Taxes, subsidies, regulation
Institutions: Property protection, polictical stability, culture ecc Favor or not R&D and progress
Investment decsions
Value of business Pi > Fixed cost F
Determinants of F
Red tape (excessive regulation)
Corruption
Determinants of Pi
Market size
Diversion of firms resources
Political stability
resource allocation
economic performance thorugh correct allocation , which projects firms to fund, provision of public good.
Misallocation -> rent-seking, idle factors, policy distortions , frictions ecc
Historical events source of exogenous variation in institutions
Acemoglu Johnson robinson paper , on european settleres mortality the change in instutitions and developement of country
Dell(2010), Perù mining Mita
Peorple forced to go mining, now the same areas have low household consumption and stunted growth
Dincecco & Katz(2014)
Fiscal centralization saw higher growth than fragmented regimes
Economic rational
Fiscal centralization : Reduce free-rding, increase extractive capacity.
Limited gov: prevent wasteful spending, better provision of public services
Acemoglu et al. (2019) from non democracy to democracy
Transitioning to democracy increases 20percent GDP per capita
Empirical challenges
- Measurements errors in democracy indices
- Unobserved differences betweeen democracies and nondemocracies (cultural, institutional ecc ) can influence GDP
- GDP dynamics, democractization precedeed by downturn : effect bieased by recovery
