RBC MODEL

Question 1

In RBC, what are the exogenous shocks?

Answer 1

Exogenous shocks to technology (solow residual)

Question 2

What are we hoping to discover with RBC analysis?

Answer 2

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

Question 3

What are these technology shocks?

Answer 3

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.

Question 4

Household assumptions

Answer 4

one infinitely lived representative household

Max utility

Question 5

3 choice variables for households

Answer 5

Consumption
Labour supply
savings

Question 6

Is household problem dynamic / static?

Answer 6

Dynamic - savings today affect consumption tomorrow.

Question 7

Assumptions about firms

Answer 7

one representative firm selling 1 good

max profits

Question 8

Assumption about firm’s technology

Answer 8

Production technology with productivity evolving exogenously and stochastically.

Question 9

How do we make the firm problem static?

Answer 9

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

Question 10

Assumption about markets

Answer 10

all markets perfectly competitive

Question 11

Production function

Answer 11

Yt = At F(Kt, ht)

Question 12

Returns to scale for pf =

Answer 12

CRS

Question 13

What’s the price of output?

Answer 13

We normalise it to 1.

Question 14

Firm’s problem

Answer 14

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

Question 15

2 FOCs for firms

Answer 15

At F’h(Kt, ht) = wt

At F’k(Kt, ht) = rt

Question 16

Household utility depends on…

Answer 16

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

Question 17

Time constraint for households

Answer 17

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

Question 18

Dynamic BC for households

Answer 18

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

Investment = sources of income - consumption

Question 19

What do household’s maximise? subject to what?

Answer 19

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

Question 20

Rational expectations =

Answer 20

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

Question 21

What assumption does RBC make about household expectations?

Answer 21

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

Question 22

Lagrangian for households

Answer 22

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

Question 23

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

Answer 23

1. endogenous variables related in a non-linear way

2. Dynamic system - variables related over time.

Question 24

2 household optimality conditions

Answer 24

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

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

Question 25

explain the optimal labour-leisure FOC

Answer 25

``` 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. ```

Question 26

What's the relationship between wt and ht?

Answer 26

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

Question 27

explain Euler's equation FOC

Answer 27

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.

Question 28

BC of households also gives... IF we assume

Answer 28

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.

Question 29

2 Market clearing conditions

Answer 29

``` htd = ht s Ktd = Kts ```

Question 30

Combine our 5 household / firm FOCs to get 3 =

Answer 30

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

Question 31

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

Answer 31

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

Question 32

How does a computer solve the model? 4 steps.

Answer 32

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

Question 33

2 advantages of quantitative analysis of RBC

Answer 33

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

Question 34

calibration =

Answer 34

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

Question 35

Ideal calibration targets are...

Answer 35

1. Informative on parameters | 2. Not about model's prediction of interest

Question 36

4 common practices for calibration

Answer 36

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

Question 37

Functional form for production fucntion

Answer 37

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

Question 38

Function form for utility function

Answer 38

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

Question 39

6 parameters of our model

Answer 39

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

Question 40

Theta in the utility function measures

Answer 40

relative taste for leisure

Question 41

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

Answer 41

delta - estimate efficiency loss of K = 0.1 /year | alpha = 1/3 = capital share of income

Question 42

What 2 parameters do we use LR features to calibrate?

Answer 42

``` 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. ```

Question 43

How do we calibrate At?

Answer 43

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

Question 44

2 ways we can evaluate RBC model performance

Answer 44

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

Question 45

Output model vs data

Answer 45

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

Question 46

Consumption model vs data

Answer 46

Direction of changes mostly good | But model underpredicts volatility

Question 47

Investment model vs data

Answer 47

Volatility well predicted | But model moves too early

Question 48

Labour input model vs data

Answer 48

Bad fit in terms of timing, and underpredicts volatility.

Question 49

So in terms of volatility how well does RBC do?

Answer 49

Good for high volatility of It | Underpredicts Ct and ht = not enough amplification of shock.

Question 50

So in terms of persistence how well does RBC do?

Answer 50

weaker autocorrelation in model = not enough propagation of shock

Question 51

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

Answer 51

Correctly predicts directions for all but rt | But overstates magnitude of co-movement

Question 52

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

Answer 52

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.

Question 53

3 criticisms of RBC

Answer 53

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.

Question 54

Why is no stabilisation policy needed according to RBC?

Answer 54

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.

Question 55

What is the Classical Dichotomy?

Answer 55

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.

Question 56

Money =

Answer 56

an asset accepted in payment for goods and services.

Question 57

Money demand according to QTM.

Answer 57

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.

Question 58

Money supply =

Answer 58

Set exogenously by CB: Mts = Mt bar

Question 59

Equilibrium QTM

Answer 59

Mt bar V = Pt Yt | LHS all exogenous, Yt determined by RBS = can find Pt endogenously.

Question 60

What does QTM imply?

Answer 60

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.

Question 61

Does money neutrality hold empirically?

Answer 61

Yes 1-1 relation in LR. | But our model is SR, and it does NOT hold in SR - money has real effects.

Question 62

How do we determine the SR effect of money policy?

Answer 62

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