Trading Down and the Business Cycle by Nir Jaimovich...
Transcript of Trading Down and the Business Cycle by Nir Jaimovich...
Discussion of “Trading Down and the Business Cycle”by Nir Jaimovich, Sergio Rebelo and Arlene Wong
Adrien Auclert
Stanford
Philadelphia Workshop on Macroeconomics and Economic PolicyApril 6, 2018
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 1 / 14
What this paper is about
0.910.920.930.940.950.960.970.980.991.001.01
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US employment after 2007
All employees: Total Nonfarm
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 2 / 14
What this paper is about
0.910.920.930.940.950.960.970.980.991.001.01
Dec
-07
Mar
-08
Jun-
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Dec
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US employment after 2007
All employees: Total Nonfarm All employees: Retail Trade
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 3 / 14
What this paper is about
0.830.850.870.890.910.930.950.970.991.01
Dec
-07
Mar
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US employment after 2007
All employees: Total Nonfarm All employees: Retail Trade
All employees: Manufacturing
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 4 / 14
Decomposing aggregate employment effects
I Consider retail employment H and sales PY as sums over firms ofdifferent quality q ∈ Q
H =∑q
Hq PY =∑q
PqYq
I If sq ≡ PqYq
PY is market share of q, the employment-sales ratio is
h ≡ H
PY=∑q
(PqYq
PY
)(Hq
PqYq
)≡∑q
sqhq
I Consider change in h between two short periods
dh =∑q
(dsq) hq +∑q
sq (dhq)
I Since∑
q dsq = 0, this is also
dh = CovQ (dsq, hq) +∑q
sq (dhq)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 5 / 14
Decomposing aggregate employment effects
I Consider retail employment H and sales PY as sums over firms ofdifferent quality q ∈ Q
H =∑q
Hq PY =∑q
PqYq
I If sq ≡ PqYq
PY is market share of q, the employment-sales ratio is
h ≡ H
PY=∑q
(PqYq
PY
)(Hq
PqYq
)≡∑q
sqhq
I Consider change in h between two short periods
dh =∑q
(dsq) hq +∑q
sq (dhq)
I Since∑
q dsq = 0, this is also
dh = CovQ (dsq, hq) +∑q
sq (dhq)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 5 / 14
Decomposing aggregate employment effects
I Consider retail employment H and sales PY as sums over firms ofdifferent quality q ∈ Q
H =∑q
Hq PY =∑q
PqYq
I If sq ≡ PqYq
PY is market share of q, the employment-sales ratio is
h ≡ H
PY=∑q
(PqYq
PY
)(Hq
PqYq
)≡∑q
sqhq
I Consider change in h between two short periods
dh =∑q
(dsq) hq +∑q
sq (dhq)
I Since∑
q dsq = 0, this is also
dh = CovQ (dsq, hq) +∑q
sq (dhq)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 5 / 14
Decomposing aggregate employment effects
I Consider retail employment H and sales PY as sums over firms ofdifferent quality q ∈ Q
H =∑q
Hq PY =∑q
PqYq
I If sq ≡ PqYq
PY is market share of q, the employment-sales ratio is
h ≡ H
PY=∑q
(PqYq
PY
)(Hq
PqYq
)≡∑q
sqhq
I Consider change in h between two short periods
dh =∑q
(dsq) hq +∑q
sq (dhq)
I Since∑
q dsq = 0, this is also
dh = CovQ (dsq, hq) +∑q
sq (dhq)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 5 / 14
The trading down effect
I Conclusion: change in aggregate retail employment dH is
dH = CovQ (dsq, hq) · PY︸ ︷︷ ︸Trading down effect
+∑q
sq (dhq) · PY + d (PY )︸ ︷︷ ︸Macro effect
(1)
I JRW perform this calculation over the 2007/2012 period:
Quality q Low Middle Highhq 5.41 8.49 10.36dsq 0.07 -0.06 -0.01
CovQ (dsq, hq) -0.23
I Conclusion: trading down effect is negative...I and accounts for >80% of the job loss in retail (54 in manufacturing)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 6 / 14
The trading down effect
I Conclusion: change in aggregate retail employment dH is
dH = CovQ (dsq, hq) · PY︸ ︷︷ ︸Trading down effect
+∑q
sq (dhq) · PY + d (PY )︸ ︷︷ ︸Macro effect
(1)
I JRW perform this calculation over the 2007/2012 period:
Quality q Low Middle Highhq 5.41 8.49 10.36dsq 0.07 -0.06 -0.01
CovQ (dsq, hq) -0.23
I Conclusion: trading down effect is negative...I and accounts for >80% of the job loss in retail (54 in manufacturing)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 6 / 14
The trading down effect
I Conclusion: change in aggregate retail employment dH is
dH = CovQ (dsq, hq) · PY︸ ︷︷ ︸Trading down effect
+∑q
sq (dhq) · PY + d (PY )︸ ︷︷ ︸Macro effect
(1)
I JRW perform this calculation over the 2007/2012 period:
Quality q Low Middle Highhq 5.41 8.49 10.36dsq 0.07 -0.06 -0.01
CovQ (dsq, hq) -0.23Retail jobs lost due to trading down -622,500
Share of initial retail employment -3.2%
I Conclusion: trading down effect is negative...I and accounts for >80% of the job loss in retail (54 in manufacturing)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 6 / 14
The trading down effect
I Conclusion: change in aggregate retail employment dH is
dH = CovQ (dsq, hq) · PY︸ ︷︷ ︸Trading down effect
+∑q
sq (dhq) · PY + d (PY )︸ ︷︷ ︸Macro effect
(1)
I JRW perform this calculation over the 2007/2012 period:
Quality q Low Middle Highhq 5.41 8.49 10.36dsq 0.07 -0.06 -0.01
CovQ (dsq, hq) -0.23Retail jobs lost due to trading down -622,500
Share of initial retail employment -3.2%
I Conclusion: trading down effect is negative...I and accounts for >80% of the job loss in retail (54 in manufacturing)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 6 / 14
Discussion
I Equation (1) is an accounting decomposition
I Has some very significant advantages:I Requires no assumptions!!I Straightforward to implement with the right dataI Generates new and nice stylized facts
I But also has drawbacks:I Challenging to implement in practiceI Accounting 6= causal decompositionI Model section helps with some aspects of this, but could do more
I Next: discuss empirics and model in turn
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 7 / 14
Discussion of empirical results
I Empirical implementation very creative:I Yelp data to measure quality tier as within-sector price tierI Related to a literature on quality measurement in trade
I Several challenges in practice. For instance:1. Requires making heroic extrapolation assumptions for hq
I Why not use Census employment data instead of Compustat?
2. Quantitative results appear quite sensitive to choicesI Counting 2007-2009 as recession period, share of trading down only
20% vs 88% in baseline 2007-2012. Why?I Equation (1) does not deal well with trendsI That said, I am convinced that the qualitative pattern is there
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 8 / 14
From accounting to causal decomposition
I Wanted: ’share of employment loss that was caused by the tradingdown due to the recession’
I Empirical issue: we lack identificationI Theoretical issue: we lack a framework
I Simple model that captures the story the authors have in mind:I Exogenous prices Pq, rental rate R, wage rate W and income YI Consumers have nonhomothetic utility U ({Cq}), income PY ,
demandPqCq = sq ({Pq} ,Y ) · PY
I Firms have homothetic factor demand: Hq = hq ({R,W })PqCq
I Causal effect of change in income PY on employment H is
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 9 / 14
From accounting to causal decomposition
I Wanted: ’share of employment loss that was caused by the tradingdown due to the recession’
I Empirical issue: we lack identificationI Theoretical issue: we lack a framework
I Simple model that captures the story the authors have in mind:I Exogenous prices Pq, rental rate R, wage rate W and income YI Consumers have nonhomothetic utility U ({Cq}), income PY ,
demandPqCq = sq ({Pq} ,Y ) · PY
I Firms have homothetic factor demand: Hq = hq ({R,W })PqCq
I Causal effect of change in income PY on employment H is
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 9 / 14
From accounting to causal decomposition
I Wanted: ’share of employment loss that was caused by the tradingdown due to the recession’
I Empirical issue: we lack identificationI Theoretical issue: we lack a framework
I Simple model that captures the story the authors have in mind:I Exogenous prices Pq, rental rate R, wage rate W and income YI Consumers have nonhomothetic utility U ({Cq}), income PY ,
demandPqCq = sq ({Pq} ,Y ) · PY
I Firms have homothetic factor demand: Hq = hq ({R,W })PqCq
I Causal effect of change in income PY on employment H is
dH =∑q
dHq =∑q
Hq
PqCqd (PqCq)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 9 / 14
From accounting to causal decomposition
I Wanted: ’share of employment loss that was caused by the tradingdown due to the recession’
I Empirical issue: we lack identificationI Theoretical issue: we lack a framework
I Simple model that captures the story the authors have in mind:I Exogenous prices Pq, rental rate R, wage rate W and income YI Consumers have nonhomothetic utility U ({Cq}), income PY ,
demandPqCq = sq ({Pq} ,Y ) · PY
I Firms have homothetic factor demand: Hq = hq ({R,W })PqCq
I Causal effect of change in income PY on employment H is
dH =∑q
hqdsqPY +∑q
hqsqd (PY )
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 9 / 14
From accounting to causal decomposition
I Wanted: ’share of employment loss that was caused by the tradingdown due to the recession’
I Empirical issue: we lack identificationI Theoretical issue: we lack a framework
I Simple model that captures the story the authors have in mind:I Exogenous prices Pq, rental rate R, wage rate W and income YI Consumers have nonhomothetic utility U ({Cq}), income PY ,
demandPqCq = sq ({Pq} ,Y ) · PY
I Firms have homothetic factor demand: Hq = hq ({R,W })PqCq
I Causal effect of change in income PY on employment H is
dH = CovQ (dsq, hq) · PY︸ ︷︷ ︸Trading down effect
+∑q
hqsqd (PY )︸ ︷︷ ︸Macro effect
(2)
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 9 / 14
Comments on the model
I Equation (2) is the same as (1), but is model-basedI On labor demand side, need average = marginal to avoid extra termI Key remaining question is where prices and incomes come fromI This is what GE models help us do!
I The model has these ingredients but loses track of (1)–(2)I Quality/quantity model has a unique quality in equilibriumI Used to get RBC amplification and comovementI Heterogeneous agent similarly a bit underexploitedI My advice: use Stone-Geary model instead, see if model and data
decompositions can be reconciledI Would round up the paper very nicely
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 10 / 14
Comments on the model
I Equation (2) is the same as (1), but is model-basedI On labor demand side, need average = marginal to avoid extra termI Key remaining question is where prices and incomes come fromI This is what GE models help us do!
I The model has these ingredients but loses track of (1)–(2)I Quality/quantity model has a unique quality in equilibriumI Used to get RBC amplification and comovementI Heterogeneous agent similarly a bit underexploitedI My advice: use Stone-Geary model instead, see if model and data
decompositions can be reconciledI Would round up the paper very nicely
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 10 / 14
The model of production
I Production function has the form
Y = A
[α
(L
q
) ε−1ε
+ (1− α)Kε−1ε
] εε−1
I Assumptions:
1. If q doubles, would need to double L to produce same Y
2. When ε < 1, increase in q raises MPL relative to MPK
FLFK
=α
1− α(q)
1−εε
(L
K
)− 1ε
=W
R
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 11 / 14
The model of production
I Production function has the form
Y = A
[α
(L
q
) ε−1ε
+ (1− α)Kε−1ε
] εε−1
I Factor demand properties, if α ≡ initial labor share and ε < 1:
1. Higher quality goods are more expensive, dPP = αdq
q
2. Firms employ more capital to produce each unit, with dKK
⌋Y
= εαdqq
3. Firms also employ more labor dLL
⌋Y
= [εα + 1− ε] dqq
4. Relative labor intensity increases dL/KL/K
⌋Y
= (1− ε) dqq
I Nice homothetic form capturing differential labor intensity by q
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 12 / 14
The model of quality/quantity choice
I Consumers choose
maxU (C , q) ≡ q1−θ
1− θlogC
s.t. P (q)C = y
I FOC is
(1− θ) logC =qP ′ (q)
P (q)
I Recall from production side that qP′(q)P(q) = labor share
I RBC model relies on procyclical labor share as key driving mechanismI Would be nice to also confront this prediction to the aggregate data
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 13 / 14
Conclusion
I Very nice and thought-provoking paper:I New stylized fact: consumers traded down in the retail sector during
the great recessionI New decomposition of aggregate employment change, with creative
implementation
I The empirical and theoretical sections could be unified by computingthe sufficient statistic
CovQ (dsq, hq)
in the model with multiple goods and comparing it to the data
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 14 / 14
Additional slides
Thank you!
Adrien Auclert (Stanford) Discussion of Jaimovich-Rebelo-Wong April 6, 2018 15 / 14