WEEK 6 - TFP and Growth Accounting (Solow Residual)

Question 1

What do we assume is the model of the economy when accounting for sources of econ growth?

Answer 1

Y = F(K,L)

• Output (Y) only change if amount of capital (K) or labour (L) changes

Question 2

How can we determine the extent to which Y changes via the change/increase in capital?

Answer 2

If K increases by Δk units

• Invoking definition of MPK tells us that;
• For small changes in K, a change in capital by ΔK units leads to output increase of the (approximate)

So, ΔY = MPK X ΔK

SEE EXAMPLE IN NOTES

Question 3

What is the calculation for the MPK?

Answer 3

MPK = F (K + 1, L) - F (K, L)

Question 4

How can we determine the extent to which Y changes via the change/increase in labour?

Answer 4

If L increases by ΔL units

• Invoking definition of MPL tells us that;
• For small changes in L, a change in capital by ΔL units leads to output increase of the (approximate)

So, ΔY = MPL X ΔL

SEE EXAMPLES IN NOTES

Question 5

What is the calculation for the MPL?

Answer 5

MPL = F (K, L + 1) - F (K, L)

Question 6

How can we determine a change in Y based on the two sources of capital and labour?

Answer 6

Amount of labour, L, changes by ∆L units and the amount of capital, K, changes by ∆K units

Can write that:
∆Y = (MPK x ∆K) + (MPL x ∆L)

Or rewritten as,
∆Y/Y = (MPK x K /Y) ∆K/K + (MPL x L /Y) ∆L/L
(Relation of growth rate of output to growh rate of capital and labour)

Question 7

How do we interpret the (increase in output from increase in K) and (increase in output from increase in L)?

Answer 7

I.E:
(MPK x K)/Y and (MPL x L)/ Y

• MPK x K as the total
  return to capital, and thus (MPK x K )/Y as capital’s share of output
• MPL x L as the total compensation received by labour, and thus (MPL x L)/Y
  as labour’s share of output

Question 8

How can rewrite the Relation of growth rate of output to growth rate of capital and labour?

Answer 8

∆Y/Y = α ΔK/K + (1- α) ΔL/L

Where:

• α is capital’s share
• (1 - α) labour’s share

Common to assume α = 0.3
(Implies 10% increase in capital K, leads to 3% increase in output)

Question 9

How do we rewrite the model of the economy accounting for technological progress?

Answer 9

Y = AF (K,L)

Where:
- A is total factor productivity

Question 10

Acounting for TFP how can we augment the Relation of growth rate of output to growth rate of capital and labour?

Answer 10

ΔY/Y = α ΔK/K + (1-α)ΔL/L + ΔA/A

Output Growth = Capital Contribution + Labour’s contribution + TFP Growth

• Fundamental equation of growth accounting: Permits us to measure all 3 sources of growth
• TFP (Total Factor Productivity) only component that not directly observed

Question 11

How do we rearrange the central growth accounting equation in terms of TFP Growth?

Answer 11

ΔA/A = ΔY/Y - α ΔK/K + (1-α)ΔL/L

ΔA/A term sometime called the Solow Residual (often interpreted as measure of tech progress)

Question 12

For the Hicks- Neutral production function how can we express TFP in per worker terms?

Answer 12

Hick Neutral pf: Y = AKα L1-α

2. Via logs and differentiating:
   A dot/ A = Y dot / Y - αK dot/ K - (1 - α) L dot / L
3. TFP in per worker terms:
   A dot / A = y dot / y - α k dot/k

TFP Growth can be decomposed into output per worker contribution and physical capital per worker contribution weighted by capital share

Question 13

What did Solow intend with the Solow residual?

Answer 13

The residual used to analyse growth in long run

Question 14

What did Edward Prescott suggest with the Solow residual?

Answer 14

Solow residual is useful in

analysing technology change over shorter durations of time

Question 15

What does the Solow residual suggest as its correlated with movements in output?

Answer 15

The fact that the Solow residual is highly correlated with movements
in output suggests that a major cause of recessions is adverse shocks
to technology: this view, combined with the neutrality of money, is at
the heart of real business cycle (RBC) theory.
(Controversial view)