On the Allocation of Time A Quantitative Analysis of the US and France
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1 A Quantitative Analysis of the US and France Georg Duernecker (University of Mannheim and IIES) Berthold Herrendorf (Arizona State University) August 22, 2014 Duernecker and Herrendorf
2 Motivation What accounts for the cross country differences in time allocation? Prescott (2004) put this question in the focus of quantitative macro Differences in taxes lead to large cross country differences in market hours worked Duernecker and Herrendorf 1
3 Executive summary of our contribution We document new facts about the allocation of NON market hours Hours worked at home have remained roughly constant during This has been the case not only in the US but also in the big European countries We show that the growth model with a household sector can account for this The main forces are differences in taxes and labor productivities The novelty of our work is to MEASURE labor productivity of home production, instead of calibrating it like the literature does Duernecker and Herrendorf 2
4 New facts about the allocation of non market time Multinational Time Use Surveys (MTUS) Home production time vs. leisure Ramey Francis definitions We include travel from/to work in market hours They didn t because they lacked data for the first half of last century Hours expressed as averages over working age population years old shares of disposable time after sleep, personal care, education Definitions of broad categories Number of surveys and participants Duernecker and Herrendorf 3
5 Non market time in Europe and the US during Weekly Hours of Home Work 0.6 Weekly Hours of Leisure USA France Germany UK USA France Germany UK Weekly hours of home work in the OECD Duernecker and Herrendorf 4
6 Market time in Europe and the US during Weekly Hours of Market Work USA France Germany UK Duernecker and Herrendorf 5
7 Accounting for the allocation of non market time We focus on the US and France US had the smallest and France the largest change in leisure France has required data starting in 1970 (Germany and the UK don t) By ending in 2005, we avoid the Great Recession Ramey Francis vs. Aguiar Hurst definitions Duernecker and Herrendorf 6
8 What we do Build a growth model with a household sector Measure the productivity of home production for both the US and France Calibrate the model to match the US time allocation Feed into the model the French taxes and productivities in the market and at home What we find The model easily matches the US time allocation The model generates the French time allocation with constant home hours It is key to use measured instead of calibrated home productivities Duernecker and Herrendorf 7
9 Model Growth model with market and household sector Stand in household Abstracts from heterogeneity in the population Natural first step to account for average hours per working age population Next step is to disaggregate average allocation of time into subcategories Duernecker and Herrendorf 8
10 Environment Endowments One unit of time Initial stocks of market and home capital Duernecker and Herrendorf 9
11 Preferences Households derive utility from Consumption: C Market produced: C m Home produced: C h Leisure: L Utility function U(C, L) = α u log(c C) + (1 α u ) log(l) C = [α c C σ c m + (1 α c )C σ c h ] 1 σc Subsistence term C > 0 implies income elasticity of leisure larger one Duernecker and Herrendorf 10
12 Technology C m + X m B m + X h B h = (K m ) α m (A m H m ) 1 α m C h = [α h (K h ) σ h + (1 α h )(A h H h ) σ h ] 1 σ h Feasibility K j = (1 δ j)k j + X j where j {m, h} 1 = H m + H h + L Duernecker and Herrendorf 11
13 Equilibrium Budget constraint C m + p h X h + (1 + τ x )p m X m = (1 τ w )wh m + (1 τ r )rk m + T Taxes are effective, i.e., relative to consumption taxes: 1 + τ x 1 + τ x 1 + τ c, 1 τ w 1 τ w 1 + τ c, 1 τ r 1 τ r 1 + τ c We define home capital to be consumer durables, which are not taxed Duernecker and Herrendorf 12
14 Definition of equilibrium A competitive equilibrium consists of sequences of effective tax rates {τ xt, τ wt, τ rt }, prices {p ht, p mt, w t, r t }, allocations {H mt, H ht, L t }, {K m,t+1, K h,t+1 }, {X mt, X ht, C mt, C ht } such that taking prices, wages, interest rates, effective tax rates and the initial capital stocks as given, {H mt, H ht, L t, K mt+1, K ht+1, X mt, X ht, C mt, C ht } solve the problem of the household (Details) taking prices and wages as given, (H mt, K mt ) maximize firms profits markets clear. Duernecker and Herrendorf 13
15 Equilibrium Conditions Allocation of time Equalize marginal utilities of leisure and market work: 1 α u L = α u C 1 σ c C C α cc σ c 1 m (1 τ w )w Equalize marginal utilities of home work and market work: (1 α c )C σ c σ h h (1 α h )A σ h h H σ h 1 h = α c C σ c 1 m (1 τ w )w Duernecker and Herrendorf 14
16 Euler equations For market capital: C 1 σ c (1 + τ x )p m C C C σ c 1 m = β C 1 σ c [ C C C σ c 1 m (1 τ r )r + (1 + τ x )p m(1 δ m ) ] For home capital: C 1 σ c p h C C α cc σ c 1 m = β C 1 σ c C C [ (1 αc )C σ c σ h h α h K σ h 1 h + p h α cc σ c 1 m (1 δ h ) ] Duernecker and Herrendorf 15
17 Connecting the Model to the US Economy Normalizations A m (1970) = A h (1970) = B m (1970) = B h (1970) = 1 Two values for each the two capital stocks Model does not have a balanced growth path Impose p m K m /Y m and p h K h /Y h for 1970, 2005 (OECD) Duernecker and Herrendorf 16
18 Observed parameters β = 0.96: standard value δ m, δ h : depreciation rates of market capital and consumer durables (BEA) α m = 0.37: capital share (BEA) B m = p 1 m, B h = p 1 h and 1970,..., 2005: relative prices of investments (OECD) τ x, τ w, τ r for 1970,..., 2005: average effective tax rates (McDaniel) Duernecker and Herrendorf 17
19 Joint calibration Unobserved parameters α u, α c, α h σ c, σ h C A m, A h for 1971,..., 2005 Targets p h X h /Y m for 1970, 2005 (BEA) H m, H h for 1970, 2005 (MTUS) % (Y m /H m ) for 1971,..., 2005 (OECD) % (Y h /H h ) for 1971,..., 2005 (Own imputation) Duernecker and Herrendorf 18
20 Imputation of value added of home production BEA Methodology underlying satellite accounts for home production Bridgman (2013) has details Bridgman, Duernecker, Herrendorf (2014) apply methodology to OECD countries Income approach to measuring value added Measure inputs Y h = r h K h + w h H h K h : consumer durables (from BEA) H h : hours worked at home (from MTUS) Impute rental prices r h : 10 year T bill rate plus depreciation rate w h : wage of workers in the private households subsector Duernecker and Herrendorf 19
21 Background info about household workers NAICS definition of the private household subsector Industries in the Private Households subsector include private households that engage in employing workers on or about the premises in activities primarily concerned with the operation of the household. These private households may employ individuals, such as cooks, maids, and butlers, and outside workers, such as gardeners, caretakers, and other maintenance workers. Number of household workers US France Hours (millions) 2,273 1, % of aggregate hours Employment (thousands) 2,281 1, % of aggregate employment Source: EU KLEMS Duernecker and Herrendorf 20
22 Targets Data Model Share of hours worked in the market H m Share of hours worked at home H h Share of durables expenditure in GDP p h X h /Y m Capital output ratio in the market p m K m /Y m Capital output ratio at home p h K h /Y h Duernecker and Herrendorf 21
23 Growth rates of productivity and technological change (in %) Key features Data Model Labor productivity of market production Y m /H m home production Y h /H h Technological change in market production A m 1.03 home production A h market investment B m 1.01 home investment B h 3.07 Labor augmenting technological regress at home - Average American forgot how to cook, iron, clean,... - Unlearning by not doing Growth of labor productivity of home production - Massive investments in home durables Duernecker and Herrendorf 22
24 Calibrated parameter values Weight on consumption α u 0.54 Weight on market produced consumption α c 0.79 Weight on home capital α h 0.08 Non homotheticity term C 0.10 Elasticity between home capital and home labor 1/(1 σ h ) 0.88 Elasticity between market and home produced consumption 1/(1 σ c ) 0.76 Duernecker and Herrendorf 23
25 Key features of calibrated parameters C = 0.10: Positive subsistence level of market goods C/C(1970) = 0.17 C/C(2005) = /(1 σ h ) = 0.88: Home capital and home hours are complements Ramey (JEHist, 2009): Elasticity of 0.8 between appliances and home hours Duernecker and Herrendorf 24
26 1/(1 σ c ) = 0.76: Market and home produced consumption are complements Typical elasticity of substitution in the literature around 2 Rogerson, Rupert, Wright (1995) McGrattan, Rogerson, Wright (1997) Rogerson (2008) Micro evidence in the literature is about close market substitutes to home consumption (e.g., food vs. restaurants) individuals who work full time Our calibration is for all market consumption (e.g., home surgery vs. market surgery) all working age individuals Duernecker and Herrendorf 25
27 Accounting for the French Time Allocation Impose initial and terminal values on the two capital stocks p j K j /Y j with j {m, h} for 1970, 2005 (OECD) Feed taxes and technological progress into the model τ x, τ w, τ r for 1970,..., 2005 (McDaniel, next slide has graph) B j = 1/p j with j {m, h} for 1970,..., 2005 (OECD) A j with j {m, h} for 1970,..., 2005 so as to hit (Y j /H j ) FR /(Y j /H j ) US (OECD and own imputation, second next slide has graph) Duernecker and Herrendorf 26
28 Taxes in France and the US Effective Tax Rate on Labor, Capital and Investment Labor Tax: USA France Capital Tax: USA France Investment Tax: USA France Duernecker and Herrendorf 27
29 Labor productivities in the US and France Labor Productivity Market and Home Production Market Labor Productivity: USA France Home Labor Productivity: USA France Decomposition of growth of home labor productivity Duernecker and Herrendorf 28
30 Wages of French household workers in comparison Average hourly wages (in current EUR) Total economy Household sector Minimum wage Sources: OECD; EU KLEMS Duernecker and Herrendorf 29
31 US and French hours: model vs. data Market Production Hours USA FRA Data USA Data FRA Home Production Hours USA FRA Data USA Data FRA Leisure Time USA FRA Data USA Data FRA Capital output ratios in the model vs. data Duernecker and Herrendorf 30
32 Intuition Assume there is no capital for simplicity. Then: H m H h = L = [ ] ɛc [ α c Ah (1 τ w ) 1 α c A m 1 α u α u (1 τ w ) + (1 α u ) ] 1 ɛc [ 1 τ w H h C w/p ] where P [ ] α ɛ c c + (1 α c ) ɛ c p 1 ɛ 1 c 1 ɛ c h p h = (1 τ w)w ɛ c A h 1 (1 σ c ) [0, ) Duernecker and Herrendorf 31
33 US Small change in C/C leads to some reallocation from hours worked to leisure Increasing market productivity leads to reallocation away from market hours home and market consumption complements (logic like in Ngai Pissarides) small because CES aggregator close to Cobb Douglas No effects from unchanged labor income taxes Net effects Home hours stay constant because opposing effects offset each other Leisure increases somewhat and market hours decrease somewhat Duernecker and Herrendorf 32
34 France Large change in C/C leads to large reallocation from hours worked to leisure Labor income tax increases lead to further reallocation from hours worked to leisure reallocation of from market to home hours No effects from productivity because market vs. home productivity stays unchanged Net effects Home hours stay constant because opposing effects offset each other Leisure increases a lot and market hours decrease a lot Duernecker and Herrendorf 33
35 What about the marketization of consumption? Marketization hypothesis of Freeman Schettkat Americans replaced home consumption by market consumption Continental Europeans didn t Literature focuses on relative hours Hours don t say much about marketization Both countries have flat home hours US market hours fall somewhat whereas French market hours fall a lot Need relative labor productivities to understand what happened to consumption US: Ratio of market to home productivity rises France: Ratio of market to home productivity rises less than in US Next slide shows implied behavior of market to home consumption Duernecker and Herrendorf 34
36 Ratios of market to home consumption in the data vs. the model Normalize US 1970 ratio to one, express French ratio relative to US Market to home consumption in the data (US 1970 = 1) 2.5 USA France 2 Market to home consumption in the model (US 1970 = 1) 2.5 USA France Duernecker and Herrendorf 35
37 Counterfactuals 1 US with French labor income taxes 2 France with US home technological change 3 Elasticity market vs. home consumption equal two Calibrated home labor productivities (in the spirit of Rogerson (JPE, 2008)) France with US taxes Duernecker and Herrendorf 36
38 Counterfactual 1: US with French labor income taxes Hours of Market Work U.S. Benchmark U.S. with French labor taxes France Hours of Home Work U.S. Benchmark U.S. with French labor taxes France Leisure Time U.S. Benchmark U.S. with French labor taxes France Market work: difference in effective income taxes do most of the job Home work and leisure are off in first half of the sample Duernecker and Herrendorf 37
39 Counterfactual 2: France with US home technological change Market Production Hours USA FRA Data USA Data FRA Home Production Hours USA FRA Data USA Data FRA Leisure Time USA FRA Data USA Data FRA French now work more at home because US home labor productivity grows less Duernecker and Herrendorf 38
40 Counterfactual 3: Set 1 1 σ c = 2 and calibrate home labor productivities Market Production Hours USA FRA Data USA Data FRA Home Production Hours USA FRA Data USA Data FRA Leisure Time USA FRA Data USA Data FRA While home hours look fine, there is too little change in market hours and leisure Duernecker and Herrendorf 39
41 More importantly, there now is home ization of consumption Market to home consumption in the data (US 1970 = 1) 2.5 USA France 2 Market to home consumption in the model (US 1970 = 1) 2.5 USA France Calibrated labor productivities Duernecker and Herrendorf 40
42 Conclusion Our contributions We documented new facts about the allocation of time in the US and France We showed that the growth model with home production can account for them We found it s key to use measured instead of calibrated home labor productivities Next steps Extend the analysis to other European countries Understand why home technological change is strong in France and weak in US Duernecker and Herrendorf 41
43 Defensive Slides Duernecker and Herrendorf 42
44 Definitions of market work, home work, and leisure Market Work Home Work Leisure Personal Care and Education Paid work Active sports participation Study, homework Paid work at home Passive sports participation Read books Paid work, second job Walking Read papers, magazines Travel to/from work Religious activities Relax Cook, wash up Civic activities Conversation Housework Cinema or theatre Entertain friends at home Odd jobs Dances or parties Knit, sew Gardening Social clubs Other leisure Shopping Pubs Sleep Childcare Restaurants Dress/personal care Domestic travel Visit friends at their homes Consume personal services Meals and snacks Listen to radio School, classes Free time travel Watch television or video Excursions Listen to records, tapes, CDs Back Duernecker and Herrendorf 43
45 Number of surveys and participants USA Total 1,965 5,807 2,539 6, ,720 16,760 11,187 10,564 Females 1,082 3,264 1,340 3, ,320 6,204 5,902 Males 883 2,543 1,199 2, ,440 4,983 4,662 France Total 2,898 4,633 12,393 Males 1,460 2,202 5,987 Females 1,438 2,431 6,406 Germany Total 2,137 21,801 27,583 Males ,531 12,827 Females 1,192 11,270 14,756 UK Total 8,360 14,301 7,432 10,841 1,422 14,169 3,614 Males 4,163 6,753 2,934 5, ,520 1,646 Females 4,197 7,548 4,498 5, ,649 1,968 Back Duernecker and Herrendorf 44
46 Weekly hours of home work in the OECD Back Duernecker and Herrendorf 45
47 Alternative definitions of market work, home work, and leisure Back Panel (i) Panel (ii) Baseline 1965 Demographics USA Market Home Leisure France Market Home Leisure Panel (iii) Panel (iv) Childcare in leisure Education in leisure USA Market Home Leisure France Market Home Leisure Sources: MTUS Duernecker and Herrendorf 46
48 Household s problem L = β {α t u log(c(t) C) + (1 α u ) log(l(t)) t=0 +η c (t) [( ) α c C m (t) σ c + (1 α c )C h (t) σ 1 c σ c C(t) ] +η h (t) [( ) α h K h (t) σ h + (1 α h )(A h (t)h h (t)) σ 1 h σh C h (t) ] +λ(t) [ [1 τ w (t)]w(t)h m (t) + [1 τ r (t)]r(t)k m (t) + T(t) C m (t) p h (t)x h (t) [1 + τ x (t)]p m (t)x m (t) ] +φ m (t) [ (1 δ m )K m (t) + X m (t) K m (t+1) ] +φ h (t) [ (1 δ h )K h (t) + X h (t) K h (t+1) ] +µ(t) [ 1 L(t) H m (t) H h (t) ]} Back Duernecker and Herrendorf 47
49 Calibrated Technological Progress Technological Progress (normalized, 1970 = 1) Market Production Home Production Market Capital Home Capital Duernecker and Herrendorf 48
50 US and French capital output ratios: model vs. data Back Duernecker and Herrendorf 49
51 Decomposition of annual growth rates of home labor productivity Back US France Total Contribution of capital services Contribution of labor services Duernecker and Herrendorf 50
52 Calibrated labor productivities Counterfactual Labor Productivity Market USA Market France Home USA Home France Back Duernecker and Herrendorf 51
53 Counterfactual 4: France with US effective taxes Hours of Market Work U.S. Benchmark France with U.S. labor taxes France Hours of Home Work U.S. Benchmark France with U.S. labor taxes France Leisure Time U.S. Benchmark France with U.S. labor taxes France Back Duernecker and Herrendorf 52
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