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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.
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.
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.
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
IRF
I Choleski assumption: no impact of output no savings
(M1,2 = 0):
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
IRF
I 2nd assumption: large positive impact of output on savings
(Ms,y = 0.0067)
I Conclusion: results are very sensitive to this assumption!
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
IRF
I 2nd assumption: large positive impact of output on savings
(Ms,y = 0.0067)
I Conclusion: results are very sensitive to this assumption!
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Model
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Model
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Model
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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).
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Counterfactual saving ratesResults
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Counterfactual saving ratesResults
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to 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 ....
Alessandro Mennuni (Southampton) A Neoclassical Approach to 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 ....
Alessandro Mennuni (Southampton) A Neoclassical Approach to 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 ....
Alessandro Mennuni (Southampton) A Neoclassical Approach to 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 ....
Alessandro Mennuni (Southampton) A Neoclassical Approach to 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 ....
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
A concave framework
I The reason for this is that the production possibility
frontier is concave
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Pinning down ρ
I ρ such that
I corr(εa, εv) = 0
I Minimize sum of squares (s− s)
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Pinning down ρ
I ρ such that
I corr(εa, εv) = 0
I Minimize sum of squares (s− s)
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Saving rate �t
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Testing the paradox of thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
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
Testing the paradox of thrift: endogeneity
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!
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Testing the paradox of thrift: endogeneity
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!
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Testing the paradox of thrift: Method 2
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Testing the paradox of thrift: Method 2
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Testing the paradox of thrift: Method 2
I ˆst = ˆst−1 + (st − st−1) σ(s)σ(s) .
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
Testing the paradox of thrift: Method 2
I ˆst = ˆst−1 + (st − st−1) σ(s)σ(s) .
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
07-09 recession
I Saving rate not due to technology shocks moves in opposite
direction than output!
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
07.IV-12.II
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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!
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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!
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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:
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
A Real Business Cycle Model
I Household
max{ct,kt+1,nt}
E0
[ ∞∑t=0
βt
(log(ct)− χ
n1+1/νt
1 + 1/ν
)]
s.t. ct + ptkt+1 = wtnt + ptkt(1 + rt − δ).
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
A Real Business Cycle Model
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
A Real Business Cycle Model
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 .
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
A Real Business Cycle Model
I Firms
maxkt,nt,st∈[0,1]
yt − wtnt − ptktrt
s.t.
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
A Real Business Cycle Model
I Firms
maxkt,nt,st∈[0,1]
yt − wtnt − ptktrt
s.t.
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
A Real Business Cycle Model
I Firms
maxkt,nt,st∈[0,1]
yt − wtnt − ptktrt
s.t.
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
A concave framework
I a generic �rm's revenues are
yt = ct + ptIt,
where
I
ct = Atkat n
1−at (1− st)1−ρ
I
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.
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
A concave framework
I the price equation, which comes from the optimal choice of
st:
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift
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
Alessandro Mennuni (Southampton) A Neoclassical Approach to the Paradox of Thrift