redistributionrecession.com

a look at

The Residual Method

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2007 2008 2009 2010 2011 2012 2013 2014

Hou

rs p

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apita

, Dec

-200

7 =

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SA

Em

ploy

ees p

er 1

000

pers

ons,

SAFigure 2.1. Employment and Hours per Person, Jan-2007 to Feb-2014

Civilian employment - 30

Nonfarm payroll employees

Hours worked index (right scale)

• Many factors potentially reduced labor hours after 2007.

• Some factors are better understood, or more easily quantified, than others.

• Step 1: Quantify the impact of the better-known factors.

Overview

• Step 2: Subtract that impact from the actual labor hours change to get a “residual” change– Residual is a model of what would have

happened to labor hours but for the influence of the better-known factors.

– Residual is a model of the combined impact of all other factors.

• If the residual change is found to be insignificant, that is a result and not an assumption.

Overview

• Interested in outcome y.

• Some factors x affecting y are better understood, or more easily quantified, than others .

y = f(x,)

• x is well measured and fx is knowndy = fxdx + fd

• e.g., growth accounting explains output growth with growth in labor and capital, plus a “Solow residual”

• e.g., gender wage gap is explained by gender hours and education gaps, plus a “discrimination” residual

Generic Version

• The age of the population affects the amount of labor, because age is associated with willingness to work.

• Step 1: Examine the effect of aging.– How is the age distribution different at

each date t than it was before the recession began?

– How is aging related to hours worked? e.g., examine 2007 cross-section hours-age profile (including zeros for people not working).

Product is (estimate of) the impact of aging on date t hours worked.

Baby Boom vs. Other Factors

• Step 2: Subtract that impact from actual or “unadjusted” hours series to get residual or “age-adjusted” series.– Because the aging impact is negative, the

residual hours series exceeds the actual hours series.

• Reach conclusions about non-age factors without knowing much about them.

Baby Boom vs. Other Factors

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2008 2009 2010 2011 2012 2013

Hou

rs p

er c

apita

, Dec

-200

7 =

100,

SA

Hours Worked per Capitawith and without age adjustments, Jan 2008 - Aug 2013

actual/unadjusted

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2008 2009 2010 2011 2012 2013

Hou

rs p

er c

apita

, Dec

-200

7 =

100,

SA

Hours Worked per Capitawith and without age adjustments, Jan 2008 - Aug 2013

unadjusted

Age-adjusted

• Conclusions:– The omitted/non-age factors have partly,

but not fully, returned to their pre-recession values.

– The omitted factors are most of what happened.

– The residual method does not assume that omitted factors are negligible.

• Step 1: Calculate the impact of each known factor separately. Include interaction term impacts, if known.

• Step 2: Subtract each impact term from the actual hours series.

• The residual shows (an estimate of) the impact of all of the remaining “unknown” factors (a.k.a., omitted factors).

• The size of the residual does not depend on assumptions about the omitted factors, but rather on the size of the impact of the known factors

Multiple Known Factors

• Payments to the poor and unemployed affect the amount of labor, because those payments reduce reward to working by reducing what are person loses by working less.

• Step 1: Examine the effect of safety net expansions.– What did the expansions add to the

average marginal tax rate?– How much does each tax rate point affect

the quantity of labor (prior literature on wage elasticities of labor supply and labor demand).

Product is (estimate of) the impact of safety net expansions on date t hours worked.

Redistribution vs. Other Factors

• Step 2: Subtract that impact from actual hours series to get residual or “MTR-constant” series.– Because the safety net impact is negative,

the residual hours series exceeds the actual hours series.

• Reach conclusions about non-safety-net factors without knowing much about them.

Redistribution vs. Other Factors

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k ho

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Figure 11.1. Labor Market Outcomes if Redistribution had Remained Constant

Actual

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k ho

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Figure 11.1. Labor Market Outcomes if Redistribution had Remained Constant

Hypothetical, with labor supply elasticity of 0.75

Actual

• Conclusions:– The omitted factors noticeably depressed

the labor market, but

– Redistribution/safety net expansions mattered more

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2007 2008 2009 2010 2011

Infla

tion-

adju

sted

$ p

er y

ear

unem

ploy

edFigure 1.1. Government Safety Net Benefit Rules Compared with

Hours Not At Work

Generosity of program rules for the unemployed

7,500

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7,625

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2007 2008 2009 2010 2011

Hou

rs p

er a

dult,

seas

onal

ly a

djus

ted

(SA

) ann

ual r

ate

Infla

tion-

adju

sted

$ p

er y

ear

unem

ploy

edFigure 1.1. Government Safety Net Benefit Rules Compared with

Hours Not At Work

Generosity of program rules for the unemployed

Average hours NOT at work (right scale)