Dynamic Model #1 Flashcards
Week 7
RBC model can be used to explain SRBC. How do each models help with answering questions?
- Classical and NC models can explain BC fluctuations on Supply-Side, but can’t explain extremity or extensive margins
- Keynesian and NK models can explain BC fluctuations on Demand-Side, explains rigidity and imperfect competition
- DMP model can explain the extensive margin, turning from the LM to Credit Market and the model from static to dynamic
What are some of the stylised facts for stock investment, consumption and output? What phenonena occurs in the credit market?
- VOLATILITY: I>Y>C
- CO-MOVEMENT: ρ(C,Y) = 0.77, ρ(I,Y) = 0.8 [procyclical]
- PERSISTENCE: Hump shape
- CREDIT MARKET: Consumption Smoothing; V(Y) > V(Consumption of non-durables)
- CREDIT MARKET: Excess Variability; V(Y) < V(Consumption durables) ~ V(I)
- Reasons: Durables behave like investment, credit rationing, co-ordination failure
What is the Question, Method and Techniques that can be used for Dynamic Models?
- QUESTION: Consumers, firms and Governments are not only making decision sfor today, but also for later period. How are these decisions weighed up?
- INTERTEMPORAL decision: c Vs. c’ [s Vs. s’]
- METHOD: Addressing the Business Cycle of the Credit Market and its relation to the output market (DYNAMIC)
- TECHNIQUE: Optimisation, Equation solving
What are the assumptions about Credit Market in the dynamic model?
- Assuming that there are 2 period current/future,
- No intratemporal decision [Nd=Ns=1]
- No production and no firms-> consumers are DS and SS of credit market
What is a popular way of representing the dynamic model?
- U(C, C’) = ln c + βln c’
- β is a subjective discount factor- so measures patience
What are the constraints in the dynamic? What are some properties of the combined constraint?
- CURRENT: c+s = y-t [s can be +/-]
- FUTURE: c’ = y’ - t’ + (1+r)s
- Combining the two (s), we get:
c + c’ /(1+r) = y + y’ /(1+r) - t - t’ /(1+r) = Wealth - Endowment Point: (y-t, y’-t’)
- Slope: -(1+r), steepens as it pivots around r
- At E, there is no borrowing/lending- lending is above the point and below the point
How do you find the first order condition for c and c’? What is the intertemporal condition
- Substitute c’ /(1+r) = y + y’ /(1+r) - t - t’ /(1+r) into c
Partial differentiation using the chain rule (multi-variable) = [δU (C,C’) / δC’] * [δC’ / δC] + [δU (C,C’) /δC] - This gives MUc’ * -1/(1+r) + MUc = 0
- Therefore, -1/(1+r) = MUc’ / MUc OR 1+r = MRS (c,c’) [MB=MC]
Which variables are endogenous/exogenous within the dynamic model?
- ENDOGENOUS: c’, c, s
- EXOGENOUS: y, y’, t, t’, r
What happens when there is an increase in y (X-AXIS)?
- An increase in current income creates a parallel shift from E1 to E2
- This also increases c, c’ and s; showing procyclicality
- Consumption Smoothing:
δC < δY
What happens when there is an increase in y’ (Y-AXIS)?
- An increase in future income creates an outwards shift from E1 to E2
- This also increases c and c’, but reduces s
- Consumption Smoothing:
δC’ < δY
What happens differently to budget lines when there is a temporary/permenant increase in income?
- Increase in income temporarily shifts the budget line horizontally
- Increase in income permanently shifts the budget line horizontally and vertically
What is permenant income? Show the formula for permenant income
- PI = the sum of present values of dispensable
endowment of the two periods. - PI (p1) = y + ε - t + [y-ε-t’] / (1+r)
What is Milton Friedman’s permenant income hypothesis?
- C depends on wealth and y
- c + c’ /(1+r) = y + y’ /(1+r) - t - t’ /(1+r) = Wealth = c = c_ + b * we
- PIH leads to consumption smoothing feature and smaller consumption volatility
- In contrast, Keynesianism assumes fixed propensity of current income- higher volatility, so: c = c_ + b*y
What happens when there is an increase in r (graphically) ?
- Pivot of the budget line around E
- SE and IE
- Borrowers lose and lenders win
