a neoclassical approach to the paradox of thriftalexmen/slides_paradox_of_thrift.pdf ·...

A Neoclassical Approach to the Paradox of

Thrift

Alessandro Mennuni

University of Southampton

October 2, 2013

Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift

Introduction

I What is the e�ect of an increase in the saving rate?

I The paradox of thrift: an increase in the saving rate will

depress economic activity, to the extent to even reduce

savings.

I Conjecture popularized by Keynes but present in earlier

debates since the 18th century (Bernard Mandeville 1714;

John M. Robertson in his 1892 book The Fallacy of Saving).

I Throughout time, it received support within and beyond

academic circles, capturing media attention and a�ecting

the policy debate, despite the fact that there is virtually no

empirical evidence in, or against its favour.

Introduction

savings.

Introduction

savings.

Introduction

savings.

Motivation

I Why this conjecture hasn't been tested before?

I Savings are endogenous and strongly positively correlated

to economic activity.

I Unlike the spending multiplier, which engendered a

multitude of empirical studies, the paradox of thrift

remained uninvestigated because it is hard to identify

exogenous changes in savings.

I I o�er a methodology to identify saving rate changes not

due to the endogenous reaction to the business cycle.

Motivation

Literature

I Structural estimation of an IS-LM model: Deepankar Basu

(2009). Derives some conditions for the paradox. Then

checks whether estimated parameters satisfy conditions.

I Gov spending shocks: large literature. e.g. Blanchard and

Perotti (2002), Mountford and Uhlig (2004). g vs s

I Balance sheet shocks: Mian and Su� (2010) and (2012).

BS vs s

A �rst look through a VAR

I On U.S. data I estimate

xt = Axt−1 + ηt.

where xt = [st, dyt]′.

I We are interested in the IRF of output growth to a saving

rate shock.

Endogeneity

I η is a mixture of the structural shocks ε identi�ed via a

matrix M :

η = Mε.

I IRF's are very sensitive to M . How to pin it down?

I Normalizing the shocks ε to have unitary variance, the

matrix M has to be such that

M ′M = Σ, (1)

where Σ is the covariance matrix of η.

I Because Σ is symmetric, equation (1) pins down three out

of the four parameters in M . A further assumption has to

be made.

I e.g. the Choleski decomposition puts M1,2 = 0. i.e. outputshocks have no contemporaneous impact on the saving rate.

Endogeneity

matrix M :

η = Mε.

M ′M = Σ, (1)

be made.

Endogeneity

matrix M :

η = Mε.

M ′M = Σ, (1)

be made.

Endogeneity

matrix M :

η = Mε.

M ′M = Σ, (1)

be made.

I Choleski assumption: no impact of output no savings

(M1,2 = 0):

Endogeneity

I Figure below shows M2,1: the contemporaneous response of

income to a unitary saving shock, for all possible

alternative assumptions for M1,2 ≡Ms,y.

I 2nd assumption: large positive impact of output on savings

(Ms,y = 0.0067)

I Conclusion: results are very sensitive to this assumption!

I 2nd assumption: large positive impact of output on savings

(Ms,y = 0.0067)

I Conclusion: results are very sensitive to this assumption!

Question

I What is the e�ect of output on savings?

I Economic theory suggests is positive, but how positive?

I I am not able to answer this question without making a

strong assumption

I Alternative strategy:

1. Clean the sample from periods where saving changes weredriven by technology shocks.

2. Then the e�ect of output on savings is still unknown, butresults are robust to this information.

I In other words, I identify periods where we are closer to a

natural experiment in the sense that saving changes were

not due to technology shocks. They could still be due to

other output shocks, but results are robust to that stand.

Question

strong assumption

Question

strong assumption

Question

strong assumption

Question

strong assumption

Question

strong assumption

Question

strong assumption

Methodology

1. A neoclassical business cycle model is used to develop apositive theory of savings through which it is possible toisolate periods when changes in the saving rate are not dueto technological shocks.

I These periods are identi�ed as those when the saving ratemoves in opposite direction to the one predicted by themodel.

2. An S-VAR estimated through these observations isqulitativelly non sensitive to a wide range of assumptions ofthe e�ect of output on savings.

I A conservative (Choleski) identi�cation suggests that a 1%increase in the saving rate leads to half a percentage pointdecrease in output growth.

Methodology

1. A neoclassical business cycle model is used to develop apositive theory of savings through which it is possible toisolate periods when changes in the saving rate are not dueto technological shocks.

I These periods are identi�ed as those when the saving ratemoves in opposite direction to the one predicted by themodel.

2. An S-VAR estimated through these observations isqulitativelly non sensitive to a wide range of assumptions ofthe e�ect of output on savings.

I A conservative (Choleski) identi�cation suggests that a 1%increase in the saving rate leads to half a percentage pointdecrease in output growth.

Simulation to isolate savings changes not due to

technology shocks

I An RBC model is simulated with the shocks and initial

conditions identi�ed from the data.

I Then, it is possible to identify periods when the modelprediction of the saving rate moves in opposite direction tothe data.

I This procedure is not common in the literature, where theidenti�ed shocks are only used to estimate their stochasticprocesses.

I This alternative exercise uncovers a puzzle: RBC models

are very poor predictors of the saving rate time series.

I This may prevent the ability of the model to �lter periods

when changes in the saving rate are truly not consequential

to technology shocks.

technology shocks

Concave frontier

I The two shocks (TFP and Investment speci�c technology

shocks) identi�ed through a linear frontier are strongly

negatively correlated.

I This fact is related to the poor �t of the saving rate, and

points to a concave frontier.

I Elaborate a simple extension of the real business cycle

model where the frontier between consumption and

investment goods can be concave.

I With a concave frontier, the model improves dramatically

on the prediction of the saving rate.

Concave frontier

Outline

I Introduce a simple RBC model and relate the inability to

match the saving rate to the lack of curvature.

I Introduce curvature in the transformation frontier and

illustrates the �ndings.

I Tests the Paradox of Thrift hypothesis.

Outline

Correlation between shocks

I Identi�ed shocks:

At =yt

kαt n1−αt

, α = 0.36

Vt = 1/pt.

I I estimate the regression

d ln(At) = 0.00230.0007

− 0.2920.086

d ln(Vt) + εt.

I The correlation is strongly negative:

corr[d ln(A), d ln(V )] = −0.22.

Correlation between shocks

I Identi�ed shocks:

At =yt

kαt n1−αt

, α = 0.36

Vt = 1/pt.

I I estimate the regression

d ln(At) = 0.00230.0007

− 0.2920.086

d ln(Vt) + εt.

I The correlation is strongly negative:

corr[d ln(A), d ln(V )] = −0.22.

Counterfactual saving ratesCalibration

Table: Summary of Parametrization

Parameter Moment to Match Value

β interest rate 0.99δ direct measurement by Cummins-Violante-2002 0.014α labor share 0.36ν micro and macro evidence on Frisch elasticity 0.75, 1.5, 3χ average market hours 11.97, 5.64, 3.87γ0,a OLS 1.003γ0,v OLS 1.004γ1,a OLS 1γ1,v OLS 1ρa ADF and PP tests 1ρv ADF and PP tests 1σεa OLS 0.0069σεv OLS 0.0051

Counterfactual saving rates

I the model is simulated with the time series of innovations

εa,t, εv,t identi�ed from the data and initial conditions for

A0,V0 and k0, all coming from the data.

I To avoid dependence on initial conditions, the model is

compared to the data from 1960 III (the 50th period of

simulation).

Counterfactual saving ratesResults

I The saving rate is very poor:I Let s be the time series of s predicted by the model, and s

the time series realized.

I R2 = 1− var(s− s)/var(s) = −0.036 when ν = 3,

I R2 = −0.013 when ν = 1.5,

I R2 = 0.004 when ν = 0.75.

I The saving rate predicted by the model is counterfactual.

Even the simple mean performs better, leaving a smaller

residual variance.

I This shortcoming is not captured by simply looking at

second moments. Indeed, similarly to other RBC models,

the only major shortcoming notable is that the model

under-predicts the volatility of hours.

I Next we will interpret the negative correlation between the

shocks and the bad �t in the saving rate as being suggestive

of a concave transformation frontier.

I We will extend the model...

I ...and �nally test the Paradox of Thrift.

I This shortcoming is not captured by simply looking at

second moments. Indeed, similarly to other RBC models,

the only major shortcoming notable is that the model

under-predicts the volatility of hours.

I Next we will interpret the negative correlation between the

shocks and the bad �t in the saving rate as being suggestive

of a concave transformation frontier.

I We will extend the model...

I ...and �nally test the Paradox of Thrift.

Case for a concave frontierWhy corr(At, Vt) < 0 is a sign of concave frontier

I Consider a positive shock At and no change in Vt.

I In this model, a positive shock At increases st.

I With concave frontier this leads to an increase in pt.

I With the misspeci�ed policy functions, the increase in the

price would be attributed to a decrease in Vt.

I At ↑, Vt ↓

I ....

I At ↑, Vt ↓

I ....

I At ↑, Vt ↓

I ....

I At ↑, Vt ↓

I ....

I At ↑, Vt ↓

I ....

Case for a concave frontierImplications for st of corr(At, Vt) < 0

I Vt ↓ induces st ↓

I But instead st increased after positive shock At.

concave framework

Case for a concave frontierImplications for st of corr(At, Vt) < 0

I Vt ↓ induces st ↓

I But instead st increased after positive shock At.

concave framework

A concave framework

I The reason for this is that the production possibility

frontier is concave

Pinning down ρ

I ρ such that

I corr(εa, εv) = 0

I Minimize sum of squares (s− s)

Pinning down ρ

I ρ such that

I corr(εa, εv) = 0

I Minimize sum of squares (s− s)

Pinning down ρ

Table: Curvature Parameter ρ

Method Estimate St.Dev J test (p-value)

1st strategy 0.279 - -

ν = 0.75

2nd strategy 0.233 - -GMM 0.266 0.065 0.424

ν = 1.5

2nd strategy 0.243 - -GMM 0.265 0.047 0.428

ν = 3

2nd strategy 0.252 - -GMM 0.267 0.049 0.432

Saving rate �t

Testing the paradox of thrift

I It is now necessary to identify savings' changes that have

not been consequential to technological shocks and asses

their e�ects on output.

1. Take the periods in which the true data series moves inopposite direction to the one predicted by the model(simulated with the identi�ed technology shocks).

2. In the whole sample, take the residual between the truesaving rate time series, and the one predicted by the model:s− s.

Testing the paradox of thrift: Method 1

Table: Selected Sample

60.IV 64.I 64.III 66.I 70.III 70.IV 77.I79.IV 84.IV 85.IV 86.II 90.II 91.III 92.II92.IV 98.III 01.III 02.I 03.I 09.IV

I On this sample I estimate a VAR

xt = Axt−1 + ηt.

where xt = [st, dyt]′.

I We are interested in the IRF of output growth to a saving

rate shock.

Testing the paradox of thrift: endogeneity

I Although the sample is "clean" from the e�ect of

technology shocks on savings, there may be other output

shocks a�ecting savings.

I 1st assumption: no feedback e�ect from output on savings:

I A 1% increase in the saving rate leads to a 0.5% decrease in

output growth.Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift

I Although the sample is "clean" from the e�ect of

technology shocks on savings, there may be other output

shocks a�ecting savings.

I 1st assumption: no feedback e�ect from output on savings:

I A 1% increase in the saving rate leads to a 0.5% decrease in

output growth.Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift

I Issue: output shocks are likely to have positive e�ects on

savings.

I Impact for all other possible feedback e�ect from output on

savings:

I For positive impact of output on the saving rate, the

negative impact of savings on output is even stronger!

I Issue: output shocks are likely to have positive e�ects on

savings.

I Impact for all other possible feedback e�ect from output on

savings:

I For positive impact of output on the saving rate, the

negative impact of savings on output is even stronger!

I In the whole sample, take the residual between the true

saving rate time series, and the one predicted by the model:

s− s.

I very little variation in s ⇒ s− s ' s− s

I In the whole sample, take the residual between the true

saving rate time series, and the one predicted by the model:

s− s.

I very little variation in s ⇒ s− s ' s− s

I ˆst = ˆst−1 + (st − st−1) σ(s)σ(s) .

07-09 recession

I Saving rate not due to technology shocks moves in opposite

direction than output!

07.IV-12.II

Omitted Monetary Policy?

I Monetary tightening might increase savings and reduceoutput.

I Then what I was calling saving shock might have beenendogenous reaction to monetary policy.

I I include the FED Funds rate and in�ation in the VAR:

I The negative impact of the saving rate on output is even

stronger!

Omitted Monetary Policy?

I Monetary tightening might increase savings and reduceoutput.

I Then what I was calling saving shock might have beenendogenous reaction to monetary policy.

I I include the FED Funds rate and in�ation in the VAR:

I The negative impact of the saving rate on output is even

stronger!

Omitted Credit Shocks?

I A credit shock might increase savings and reduce output.I Were these saving shocks credit shocks?

I I include in the VAR the spread between Government and

Baa Corporate Bonds Yield:

Conclusion

I To test the paradox of thrift, a real business cycle model is

used to mitigate the reverse e�ect of output on savings.

I After doing this, the response of output to savings is

qualitatively robust to a wide range of assumptions on the

reverse e�ect that any other output shocks may have on

savings.

I Under a conservative identi�cation assumption, a 1%increase in the saving rate leads to half a percentage point

decrease in output growth.

Conclusion

savings.

Conclusion

savings.

Implications for Future Work

I Why an increase in the saving rate leads to a decrease in

output?

I Why some times it does not happen?

I Other shocks matter too.

I But maybe the composition of savings could shed light onthe issue.

A Real Business Cycle Model

I Household

max{ct,kt+1,nt}

[ ∞∑t=0

(log(ct)− χ

n1+1/νt

1 + 1/ν

s.t. ct + ptkt+1 = wtnt + ptkt(1 + rt − δ).

I Production

yt = Atkαt n

1−αt

I Law of motion for capital

kt+1 − kt(1− δ) = VtAtkαt n

1−αt st,

I Consumption

ct = (1− st)Atkαt n1−αt

I st ∈ [0, 1] is the fraction of physical production allocated to

investment.

I The two shocks evolve according to the following processes:

Vt = γ0,vγt1,vV

ρvt−1e

εv,t , ρv ≤ 1,

At = γ0,aγt1,aA

ρat−1e

εa,t , ρa ≤ 1.

I εv,t and εa,t are independently and identically distributed

random variables with standard deviation σεv and σεa .

I Firms

maxkt,nt,st∈[0,1]

yt − wtnt − ptktrt

yt = (1− st)Atkαt n1−αt + ptVtstAtkαt n

1−αt .

I First order conditions:

αAtkα−1t n1−αt (1− st + ptVtst) = ptrt

(1− α)Atkαt n−αt (1− st + ptVtst) = wt

and for an interior st pt = 1/Vt.I The price equation re�ects the fact that �rms can choose

what to produce with no costs and lies at the core of the

b.c. shortcomings.

CorrelationAlessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift

I Firms

maxkt,nt,st∈[0,1]

1−αt .

b.c. shortcomings.

I Firms

maxkt,nt,st∈[0,1]

1−αt .

b.c. shortcomings.

A concave framework

I a generic �rm's revenues are

yt = ct + ptIt,

ct = Atkat n

1−at (1− st)1−ρ

It = VtAtkat n

1−at s1−ρt .

ρ ∈ [0, 1)

I The �rm problem becomes

maxk,n,s∈[0,1]

Atkat n

1−at

[(1− st)1−ρ + ptVts

1−ρt

]− wn− rpk.

A concave framework

I the price equation, which comes from the optimal choice of

ptVt =(1− st)−ρ

s−ρt.

I pt depends on Vt, but also on st, i.e. the relative demand

for the two goods.

Figure

Is a gov spending shock not a saving rate shock?

I Other things equal, a g shock reduces savings. However

1. A g shock could crowd out private consumption, therebyincreasing rather than decreasing the private saving rate.

2. Gov. savings and private savings may operate in di�erentways, the �rst goes through the government, the secondthrough the �nancial sector.

3. Gov. spending has more direct tax e�ects.

Literature

Is a balance sheet shock not a saving rate shock?

I While �nancial shocks can a�ect the saving rate, the e�ect

of a �nancial shock does not rely on saving rate changes.

I Likewise, the e�ects of a change in the saving rate may not

be con�ned to the ones that follow from �nancial shocks. In

fact, a saving rate increase may well improve �nancial

conditions by increasing the supply of loanable funds, yet it

may have negative aggregate e�ects.

I Furthermore, the saving rate can change independently of

�nancial shocks.

Literature

�nancial shocks.

Literature

�nancial shocks.

Literature

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