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EC201 - MACRO TERM 2 > RBC MODEL > Flashcards

RBC MODEL Flashcards

1
Q

In RBC, what are the exogenous shocks?

A

Exogenous shocks to technology (solow residual)

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2
Q

What are we hoping to discover with RBC analysis?

A

Whether, given the observed fluctuations in technology, the RBC model can reproduce key business cycle facts for our key variables.

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3
Q

What are these technology shocks?

A

Hard to interpret -VE shocks. But take broader interpretation e.g. regulation, taxes, weather - anything that affects output for given level of inputs = supply-side shocks.

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4
Q

Household assumptions

A

one infinitely lived representative household

Max utility

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5
Q

3 choice variables for households

A

Consumption
Labour supply
savings

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6
Q

Is household problem dynamic / static?

A

Dynamic - savings today affect consumption tomorrow.

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7
Q

Assumptions about firms

A

one representative firm selling 1 good

max profits

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8
Q

Assumption about firm’s technology

A

Production technology with productivity evolving exogenously and stochastically.

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9
Q

How do we make the firm problem static?

A

assume firms do NOT own capital - they rent it from households.

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10
Q

Assumption about markets

A

all markets perfectly competitive

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11
Q

Production function

A

Yt = At F(Kt, ht)

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12
Q

Returns to scale for pf =

A

CRS

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13
Q

What’s the price of output?

A

We normalise it to 1.

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14
Q

Firm’s problem

A

Max profit = AtF(Kt, ht) - wtht - rtKt

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15
Q

2 FOCs for firms

A

At F’h(Kt, ht) = wt

At F’k(Kt, ht) = rt

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16
Q

Household utility depends on…

A

U(Ct) + V(lt) - consumption and leisure

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17
Q

Time constraint for households

A

lt = 1 - ht
Leisure = time spent not working
Normalise time endowment to 1

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18
Q

Dynamic BC for households

A

Kt+1 - (1-delta)Kt = wtht + rtKt - Ct

Investment = sources of income - consumption

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19
Q

What do household’s maximise? subject to what?

A

Expected discounted sum of all future instantaneous utilities.
S.t. series of BC - one for each time period.

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20
Q

Rational expectations =

A

1970s - households predict the future in a rational way. Understand how economy works and use all available info = correct on average.

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21
Q

What assumption does RBC make about household expectations?

A

Stronger than RE - we assume perfect foresight = we can get rid of the expectations operator.

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22
Q

Lagrangian for households

A

sum t=0 to infinity B^t [U(Ct) + V(1-ht)] - lamba t [Kt-1 - (1-delta)Kt - wtht - rtKt + Ct]

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23
Q

Why can we not find a solution to household max for most utility forms?

A
  1. endogenous variables related in a non-linear way

2. Dynamic system - variables related over time.

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24
Q

2 household optimality conditions

A
  1. V’(1-ht) = U’(Ct) wt - optimal labour-leisure

2. U’(Ct) = B(1 + rt+1 - delta) U’(Ct+1) - Euler’s equation

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25
Q

explain the optimal labour-leisure FOC

A 
V'(1-ht) = marginal utility cost of working an extra hour in terms of leisure.
U'(Ct)wt = MU gain of working an extra hour in terms of consumption.
26
Q

What’s the relationship between wt and ht?

A

Ambiguous - depends on utility form and how calibrate model. SE means higher Wt = higher ht, but IE means higher Wt lower ht.

27
Q

explain Euler’s equation FOC

A

Shows optimal consumption-savings decision over time.
U’(Ct) = MU cost of giving up 1 unit of C today
B(1 + rt+1 - delta) U’(Ct+1) = MU gain as can invest in 1 extra unit of K, get return, then consume but discounted by B as in future.

28
Q

BC of households also gives… IF we assume

A

The supply of capital
Kt+1 = (1-d)Kt + rtKt + wtht - Ct
assume only way for households to save is to buy capital & rent to firms.

29
Q

2 Market clearing conditions

A 
htd = ht s
Ktd = Kts
30
Q

Combine our 5 household / firm FOCs to get 3 =

A

Get rid of prices wt and rt.

  1. V’(1-ht) = U’(Ct) At Fh(Kt, ht)
  2. U’(Ct) = B(1 + At+1 Fk(Kt+1, ht+1) - d) U’(Ct+1)
  3. Kt+1 = (1-d)Kt + AtF(Kt, ht) - Ct
31
Q

Why can we replace rtKt + wtht with the production fucntion?

A

Because markets are perfectly competitive = zero profit so all income = paid as remuneration to labour and capital.

32
Q

How does a computer solve the model? 4 steps.

A

We want a time series for all endogenous variables in terms of exogenous.

  1. Guess and verify method to find policy functions:Ct = C(Kt, At) ht = h(Kt, At)
  2. Sub into K accumulation to get time series for Kt
  3. Sub Kt into policy functions = time series for Ct and ht
  4. Then find series for Yt, wt, rt
33
Q

2 advantages of quantitative analysis of RBC

A
  1. can estimate magnitudes as well as directions of effect = useful for policy
  2. calculate effects that are ambiguous e.g. wt and ht
34
Q

calibration =

A

assigning values to parameters so that the model is consistent with some empirical facts.

35
Q

Ideal calibration targets are…

A
  1. Informative on parameters

2. Not about model’s prediction of interest

36
Q

4 common practices for calibration

A
  1. direct empirical measures
  2. LR features
  3. calibrate some variables to prediction of interest, then evaluate others
  4. Try some values & explore robustness
37
Q

Functional form for production fucntion

A

F(kt, ht) = Kt^alpha ht^1-alpha

38
Q

Function form for utility function

A

U(Ct) + V(1-ht) = log(Ct) + theta log(1-ht)

39
Q

6 parameters of our model

A

alpha, theta, delta, B, [At]t=0 to infinity

40
Q

Theta in the utility function measures

A

relative taste for leisure

41
Q

2 parameters we use direct measures for and what are they?

A

delta - estimate efficiency loss of K = 0.1 /year

alpha = 1/3 = capital share of income

42
Q

What 2 parameters do we use LR features to calibrate?

A 
B = 1 / 1 + r bar where r bar = 0.016 / quarter is average return to K.
theta = h bar = 0.2 - proportion of day spent working.
43
Q

How do we calibrate At?

A

Postulate a stochastic process

LogAt = plogAt-1 + €t estimate from time series reg. Or At from data on solow residual.

44
Q

2 ways we can evaluate RBC model performance

A
  1. feed time series for At from the data into the model & compare time series of our variables to data
  2. Simulate model using stochastic process for At & compare
45
Q

Output model vs data

A

Good fit for volatility and timing, but not surprising given we’re using At from data and output is a direct function of At.

46
Q

Consumption model vs data

A

Direction of changes mostly good

But model underpredicts volatility

47
Q

Investment model vs data

A

Volatility well predicted

But model moves too early

48
Q

Labour input model vs data

A

Bad fit in terms of timing, and underpredicts volatility.

49
Q

So in terms of volatility how well does RBC do?

A

Good for high volatility of It

Underpredicts Ct and ht = not enough amplification of shock.

50
Q

So in terms of persistence how well does RBC do?

A

weaker autocorrelation in model = not enough propagation of shock

51
Q

So in terms of co-movement how well does RBC do?

A

Correctly predicts directions for all but rt

But overstates magnitude of co-movement

52
Q

Mechanisms through which a positive shock t At affects our key variables.

A

For given factor supplies, MPK and MPL rise –> rt and wt rise. Higher income for household = Ct rises, but some saved = Kt+1 rises too. Shock amplified by higher wt and rt causing higher ht (SE>IE). Shock propagates over time as higher Kt+1 –> higher MPLt+1 etc.

53
Q

3 criticisms of RBC

A
  1. unclear what tech shocks rly are
  2. Failure to explain labour market volatility and in model no invol U which is mainly why we care about BC
  3. extreme policy implications - implies no policy needed.
54
Q

Why is no stabilisation policy needed according to RBC?

A

Fluctuations are efficient responses by households and firms. Agents choose to work less in a recession - no invol U. Perfect comp, perfect info so market = pareto efficient by first welfare theorem.

55
Q

What is the Classical Dichotomy?

A

real and nominal sides of economy completely separate. We describe equilibrium all in real terms - w and r are really w/p and r/p with p=1 so they’re in terms of output.

56
Q

Money =

A

an asset accepted in payment for goods and services.

57
Q

Money demand according to QTM.

A

Mtd V = Pt Yt
V = velocity of money = how many times a unit is used for a transaction each quarter. exogenous and constant.
PtYt = nominal GDP.

58
Q

Money supply =

A

Set exogenously by CB: Mts = Mt bar

59
Q

Equilibrium QTM

A

Mt bar V = Pt Yt

LHS all exogenous, Yt determined by RBS = can find Pt endogenously.

60
Q

What does QTM imply?

A

Exogenous increase in Ms –> 1-1 increase in price level.
gtM = Pi t + gty
Money is neutral - change in MS = no effect on GDP, only causes inflation.

61
Q

Does money neutrality hold empirically?

A

Yes 1-1 relation in LR.

But our model is SR, and it does NOT hold in SR - money has real effects.

62
Q

How do we determine the SR effect of money policy?

A

Vector Auto-regression (VAR) models
Zt = c + A1Zt-1 + … + €t
Zt = vector of real GDP, inflation, indicator of MS.

EC201 - MACRO TERM 2 (10 decks)

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