Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? EJ 65: Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? EJ 65: crucial inputs are husband’s and wife’s time spent in domestic production Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? EJ 65: crucial inputs are husband’s and wife’s time spent in domestic production High wage means that time input is costly ... Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? EJ 65: crucial inputs are husband’s and wife’s time spent in domestic production High wage means that time input is costly ... → therefore efficient to match with a partner whose time is cheap Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? EJ 65: crucial inputs are husband’s and wife’s time spent in domestic production High wage means that time input is costly ... → therefore efficient to match with a partner whose time is cheap Note that this is not the specialization logic (substituability between time inputs in the production function, see Pollak 2013) Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? EJ 65: crucial inputs are husband’s and wife’s time spent in domestic production High wage means that time input is costly ... → therefore efficient to match with a partner whose time is cheap Note that this is not the specialization logic (substituability between time inputs in the production function, see Pollak 2013) Problem: counterfactual Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? EJ 65: crucial inputs are husband’s and wife’s time spent in domestic production High wage means that time input is costly ... → therefore efficient to match with a partner whose time is cheap Note that this is not the specialization logic (substituability between time inputs in the production function, see Pollak 2013) Problem: counterfactual PAM even 50 years ago Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
Is matching assortative on Human Capital? Becker’s claim: Negative Assortative Matching (NAM) ‘ ... the correlation between mates for wage rates or for traits of men and women that are close substitutes in household production will tend to be negative. ’ Argument: Positive or Negative Assortative Matching (PAM or NAM): are traits complement or substitute? EJ 65: crucial inputs are husband’s and wife’s time spent in domestic production High wage means that time input is costly ... → therefore efficient to match with a partner whose time is cheap Note that this is not the specialization logic (substituability between time inputs in the production function, see Pollak 2013) Problem: counterfactual PAM even 50 years ago In particular, educated women do not marry uneducated husbands Chiappori (Columbia University) Becker 65 Manchester, March 2015 5 / 9
A simple example CD preferences: U i = C i Q with Q = ( t 1 ) α 1 ( t 2 ) α 2 Chiappori (Columbia University) Becker 65 Manchester, March 2015 6 / 9
A simple example CD preferences: U i = C i Q with Q = ( t 1 ) α 1 ( t 2 ) α 2 Budget constraint: p ( C 1 + C 2 ) = w 1 ( 1 − t 1 ) + w 2 ( 1 − t 2 ) with w i = H i W Chiappori (Columbia University) Becker 65 Manchester, March 2015 6 / 9
A simple example CD preferences: U i = C i Q with Q = ( t 1 ) α 1 ( t 2 ) α 2 Budget constraint: p ( C 1 + C 2 ) = w 1 ( 1 − t 1 ) + w 2 ( 1 − t 2 ) with w i = H i W Transferable utility Chiappori (Columbia University) Becker 65 Manchester, March 2015 6 / 9
A simple example CD preferences: U i = C i Q with Q = ( t 1 ) α 1 ( t 2 ) α 2 Budget constraint: p ( C 1 + C 2 ) = w 1 ( 1 − t 1 ) + w 2 ( 1 − t 2 ) with w i = H i W Transferable utility → surplus: W t 1 , t 2 ( H 1 ( 1 − t 1 ) + H 2 ( 1 − t 2 )) ( t 1 ) α 1 ( t 2 ) α 2 S ( H 1 , H 2 ) = p max α α 1 1 α α 2 ( H 1 + H 2 ) 1 + α 1 + α 2 W 2 = ( H 1 ) α 1 ( H 2 ) α 2 ( α 1 + α 2 + 1 ) 1 + α 1 + α 2 p Chiappori (Columbia University) Becker 65 Manchester, March 2015 6 / 9
A simple example CD preferences: U i = C i Q with Q = ( t 1 ) α 1 ( t 2 ) α 2 Budget constraint: p ( C 1 + C 2 ) = w 1 ( 1 − t 1 ) + w 2 ( 1 − t 2 ) with w i = H i W Transferable utility → surplus: W t 1 , t 2 ( H 1 ( 1 − t 1 ) + H 2 ( 1 − t 2 )) ( t 1 ) α 1 ( t 2 ) α 2 S ( H 1 , H 2 ) = p max α α 1 1 α α 2 ( H 1 + H 2 ) 1 + α 1 + α 2 W 2 = ( H 1 ) α 1 ( H 2 ) α 2 ( α 1 + α 2 + 1 ) 1 + α 1 + α 2 p In particular, second cross derivative: ( H 1 + H 2 ) α 1 + α 2 − 1 � � ( α 1 H 2 − α 2 H 1 ) 2 + α 1 H 2 2 + α 2 H 2 1 − < 0 ⇒ NAM! H α 1 + 1 H α 2 + 1 1 2 Chiappori (Columbia University) Becker 65 Manchester, March 2015 6 / 9
A possible solution to the puzzle Keep Becker’s insights: Chiappori (Columbia University) Becker 65 Manchester, March 2015 7 / 9
A possible solution to the puzzle Keep Becker’s insights: Domestic production, domestic times as inputs Chiappori (Columbia University) Becker 65 Manchester, March 2015 7 / 9
A possible solution to the puzzle Keep Becker’s insights: Domestic production, domestic times as inputs PAM if complementarities in traits Chiappori (Columbia University) Becker 65 Manchester, March 2015 7 / 9
A possible solution to the puzzle Keep Becker’s insights: Domestic production, domestic times as inputs PAM if complementarities in traits Individuals characterized by their HC Chiappori (Columbia University) Becker 65 Manchester, March 2015 7 / 9
A possible solution to the puzzle Keep Becker’s insights: Domestic production, domestic times as inputs PAM if complementarities in traits Individuals characterized by their HC Additional ingredient: HC as an input in domestic production process → obvious justification: children Chiappori (Columbia University) Becker 65 Manchester, March 2015 7 / 9
A possible solution to the puzzle Keep Becker’s insights: Domestic production, domestic times as inputs PAM if complementarities in traits Individuals characterized by their HC Additional ingredient: HC as an input in domestic production process → obvious justification: children Then two opposite forces: Chiappori (Columbia University) Becker 65 Manchester, March 2015 7 / 9
A possible solution to the puzzle Keep Becker’s insights: Domestic production, domestic times as inputs PAM if complementarities in traits Individuals characterized by their HC Additional ingredient: HC as an input in domestic production process → obvious justification: children Then two opposite forces: Educated spouse’s time is more costly ... Chiappori (Columbia University) Becker 65 Manchester, March 2015 7 / 9
A possible solution to the puzzle Keep Becker’s insights: Domestic production, domestic times as inputs PAM if complementarities in traits Individuals characterized by their HC Additional ingredient: HC as an input in domestic production process → obvious justification: children Then two opposite forces: Educated spouse’s time is more costly ... ... but also more productive Chiappori (Columbia University) Becker 65 Manchester, March 2015 7 / 9
A simple example (CCM 2015) CD preferences: U i = C i Q with Q = ( H 1 t 1 ) α 1 ( H 2 t 2 ) α 2 Chiappori (Columbia University) Becker 65 Manchester, March 2015 8 / 9
A simple example (CCM 2015) CD preferences: U i = C i Q with Q = ( H 1 t 1 ) α 1 ( H 2 t 2 ) α 2 Budget constraint: p ( C 1 + C 2 ) = w 1 ( 1 − t 1 ) + w 2 ( 1 − t 2 ) with w i = H i W Chiappori (Columbia University) Becker 65 Manchester, March 2015 8 / 9
A simple example (CCM 2015) CD preferences: U i = C i Q with Q = ( H 1 t 1 ) α 1 ( H 2 t 2 ) α 2 Budget constraint: p ( C 1 + C 2 ) = w 1 ( 1 − t 1 ) + w 2 ( 1 − t 2 ) with w i = H i W Transferable utility → surplus: W t 1 , t 2 ( H 1 ( 1 − t 1 ) + H 2 ( 1 − t 2 )) ( H 1 t 1 ) α 1 ( H 2 t 2 ) α 2 S ( H 1 , H 2 ) = p max α α 1 1 α α 2 W ( α 1 + α 2 + 1 ) 1 + α 1 + α 2 ( H 1 + H 2 ) 1 + α 1 + α 2 2 = p Chiappori (Columbia University) Becker 65 Manchester, March 2015 8 / 9
A simple example (CCM 2015) CD preferences: U i = C i Q with Q = ( H 1 t 1 ) α 1 ( H 2 t 2 ) α 2 Budget constraint: p ( C 1 + C 2 ) = w 1 ( 1 − t 1 ) + w 2 ( 1 − t 2 ) with w i = H i W Transferable utility → surplus: W t 1 , t 2 ( H 1 ( 1 − t 1 ) + H 2 ( 1 − t 2 )) ( H 1 t 1 ) α 1 ( H 2 t 2 ) α 2 S ( H 1 , H 2 ) = p max α α 1 1 α α 2 W ( α 1 + α 2 + 1 ) 1 + α 1 + α 2 ( H 1 + H 2 ) 1 + α 1 + α 2 2 = p In particular ∂ 2 S ( H 1 , H 2 ) = KW ( H 1 + H 2 ) α 1 + α 2 − 1 > 0 ∂ H 1 ∂ H 2 p Chiappori (Columbia University) Becker 65 Manchester, March 2015 8 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Domestic production function crucially important, especially regarding HC formation for children Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Domestic production function crucially important, especially regarding HC formation for children Growth Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Domestic production function crucially important, especially regarding HC formation for children Growth Inequality Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Domestic production function crucially important, especially regarding HC formation for children Growth Inequality ... etc. Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Domestic production function crucially important, especially regarding HC formation for children Growth Inequality ... etc. Empirical implications? Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Domestic production function crucially important, especially regarding HC formation for children Growth Inequality ... etc. Empirical implications? the form of domestic production functions has a potentially crucial impact on matching Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Domestic production function crucially important, especially regarding HC formation for children Growth Inequality ... etc. Empirical implications? the form of domestic production functions has a potentially crucial impact on matching → conversely, observed matching patterns may tell us something about domestic production function Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Conclusions Technical point: complementarity between traits (matching) different from complementarities between inputs (specialization) Complementarities in Becker’s contributions: clearly 73 builds on 65 Domestic production function crucially important, especially regarding HC formation for children Growth Inequality ... etc. Empirical implications? the form of domestic production functions has a potentially crucial impact on matching → conversely, observed matching patterns may tell us something about domestic production function Still much to learn from considering several Beckerian insights jointly Chiappori (Columbia University) Becker 65 Manchester, March 2015 9 / 9
Royal Economic Society
Allocating Household Time: When Does Efficiency Imply Specialization? Robert A. Pollak Washington University in St. Louis and NBER March 31, 2015 1
What Does Economic Theory Teach About Time Allocation? Does the economic theory of time use imply that efficiency requires specialization in multiple-person households (e.g., married couples; cohabiting couples)? This seems to be what Becker claims in the Treatise on the Family (1981; 1991). Why focus on Becker? Because there isn’t much subsequent theoretical work on time allocation. (There is lots of empirical work.) 2
Roadmap Specialization Toward a New New Home Economics: Elements of a Theory of the Household Individuals’ Production Functions and Household Production Function 3
Meaning of Specialization - 1 With two sectors (home and market) 1. Strong (complete) specialization: each spouse allocates time to only one sector 2. Weak (partial) specialization = specialization: one spouse allocates time to one sector, the other spouse allocates time to one sector or to both sectors 3. Nonspecialization: both spouses allocate time to both sectors 4
Meaning of Specialization - 2 The sector specialization claim is not that husbands spend more time in market work than wives, and wives spend more time in household work than husbands. This is wrong for two reasons 1. It introduces a gendering that is not part of the definition of specialization. 2. Sector specialization has a specific technical meaning -- we never observe both spouses working in both sectors. 5
Meaning of Sector Specialization - 3 The theoretical claim is that efficiency requires that at least one spouse allocates zero time to one sector or the other. The time allocations of married men and married women have become more similar over the last 50 years . Both spouses typically spend time in both market work and household work. In rich non- Catholic countries, total time allocated to work by married men and married women is about the same. Burda, Hamermesh, and Weil, “Total Work and Gender: Facts and Possible Explanations” (2012) 6
Some Facts: Household Production “Traditional gender roles do persist in the allocation of time within households. Total hours of housework in married couple households fell more than 20 percent between 1965 and 1995 (Bianchi, Milkie, Sayer, and Robinson, 2000) but, though husbands’ hours of housework increased substantially, wives still performed most of the housework at the end of this period. In the 2005 American Time Use Survey, married women reported an average of 16 hours per week of ‘household activities’ compared to less than 11 hours for men.” Lundberg and Pollak (JEP, 2007) 7
Still More Facts: Labor Force Particiaption 2008 Labor Force Participation Rates for Married men Married women 25-34 95.3% 69.5% Age 35-44 95.2% 73.8% US data: CPS 8
Widespread Inefficiency? If the economic theory of time use implied that efficiency required specialization in married-couple households, then the prevalence of married-couple households in which both husbands and wives allocate time to both the market sector and household sector would be evidence of widespread inefficiency. An additional claim: Becker makes a further claim that the efficient pattern of specialization is gendered, with wives specializing in the household and husbands in the market. I ignore this further claim about gendering. 9
The Household Production Model and the New Home Economics Becker (Economic Journal, 1965) "A Theory of the Allocation of Time“ Becker wrote: Households are "assumed to combine time and market goods to produce more basic commodities that directly enter their utility functions.“ Becker (1981, 1991) A Treatise on the Family Becker’s household production model remains the lens through which virtually all economists and many other social scientists view time allocation. 10 10 10 10
The Household Production Model There is more than one version of the household production model. Becker (1981, 1991) differs from the earlier versions, Becker (1965) and Michael and Becker (1973) Multiple-person households in the Treatise vs. single-person households in Becker (1965) Human capital: both market and household human capital in the Treatise vs. no human capital in Becker (1965) which is a one period model. 11 11 11
New Issues with Multiple- Person Households Allocation of goods, time and commodities. Alternative models of decision making in multiple- person households: Binding commitments in the marriage market Becker’s altruist model Bargaining within marriage Chiappori’s collective model as reduced form The allocation of goods, time and commodities may or may not correspond to “specialization” 12
The Theoretical Time Use Literature Pollak and Wachter (1975) Gronau (1977) One person households No human capital 13
Specialization Becker dominates time use theory in economics. Becker’s claim: efficiency implies sector specialization, regardless of preferences or bargaining power Becker’s further claim about gendering: husbands in the market; wives at home. 14
Facts and Theory In the light of the facts about labor force participation and about housework cited above, the theoretical claim that efficiency implies sector specialization is (or should be) an embarrassment to economists, unless we accept that many married couple households are inefficient. I return to this later. What does Becker actually say about sector specialization? 15 15 15
Theory: Becker (1981, 1991) - 1 Treatise on the Family : ”Theorem 2.1. If all members of an efficient household have different comparative advantages, no more than one member would allocate time to both the market and household sectors. Everyone with a greater comparative advantage in the market than this member's would specialize completely in the market, and everyone with a greater comparative advantage in the household would specialize completely there." 16 16 16
Theory: Becker (1981, 1991) - 2 Treatise on the Family : "Theorem 2.3. At most one member of an efficient household would invest in both market and household capital and would allocate time to both sectors.” (This is complete statement of Theorem 2.3.) 17 17 17
Perfect Substitutes - 1 Treatise on the Family : Chapter 2 (p. 32), "Since all persons are assumed to be intrinsically identical, they supply basically the same kind of time to the household and market sectors. Therefore, the effective time of different members would be perfect substitutes, even if they accumulate different amounts of household capital..." (italics in original; underline added for emphasis. Perfect substitutes are NOT mentioned in any of the specialization theorems. But perfect substitutes are mentioned in the text and are crucial. 18 18 18
Perfect Substitutes - 2 With perfect substitutes, efficiency implies specialization. No additional assumptions are necessary (well, only one -- the absence of “process preferences”) N one of Becker’s specialization theorems explicitly assume perfect substitutes; if they did, additional assumptions would be unnecessary. The perfect substitutes assumption is a highly restrictive, ad hoc assumption to which economics has no commitment. 19
Where do the Specialization Results Come from? "Pure economics has a remarkable way of producing rabbits out of a hat -- apparently a priori propositions which apparently refer to reality. It is fascinating to try to discover how the rabbits got in; for those of us who do not believe in magic must be convinced that they got in somehow." J. R. Hicks, Value and Capital , 1939 20 20 20 20
Three Omitted Topics 1. Human Capital 2. Joint Production and Process Preferences: Pollak and Wachter (JPE 1975). 3. Leisure: Gronau (JPE 1977) 21 21 21
Does Efficiency in Production Imply Specialization? Becker’s claim: Efficiency in production requires sector specialization, regardless of preferences or bargaining power. Becker’s assumes two “sectors,” a market sector and a household sector. Human capital appears to play a critical role in Becker’s specialization theorems I show that with perfect substitutes, Becker’s default assumption, the specialization results do not depend on human capital. 22 22 22
Comment: Different Comparative Advantages - 1 The hypothesis: “If all members of a household have different comparative advantages…” This hypothesis is easily misinterpreted as an assumption about household technology. It is not. Except in very special cases, comparative advantage depends on the allocation of time within the household. Different comparative advantages is an hypothesis about (efficient) time allocation within the household. Efficient production with both spouses allocating time to both activities requires equal comparative advantages. Think about the first order conditions. 23 23 23
Comment : Different Comparative Advantages - 2 So the theorem says: “If we don’t have an interior solution (ie., both spouses allocating time to both sectors), then we have a corner solution” (at least one spouse does not allocate time to both sectors). This is not a technical criticism of the theorem. Theorems are supposed to be tautologies. But if you thought that “equal comparative advantages” was an hypothesis about household technology and extremely unlikely -- perhaps a set of measure 0 – then you misunderstood the hypothesis. 24 24 24
Many Commodities Suppose there are many household commodities. Lundberg (2008) points out that if there are m household commodities then, for households in which both husbands and wives participate in the market, perfect substitutes implies that husbands specialize in the production of m* of these home-produced commodities and the wives in the production of the remaining m-m* commodities. This may lead to activity specialization, but not sector specialization unless m* = 0 or m* = m. Economies of scope provide incentives for the same spouse to engage in all household activities. 25
Toward a New New Home Economics Primitives in the New NHE - 1 Four components: 1. Preferences 2. Constraints/ (including technology) 3. Governance structure (e.g., Becker’s altruist model; cooperative Nash bargaining) 4. Information structure (leading to transaction costs) 26 26 26
Toward a New New Home Economics: Primitives in the New NHE - 2 1. Preferences: Individuals' utility functions 2. Constraints/ opportunities Budget constraint; time constraints Technology Individuals’ technologies and household technology Production functions 3. Governance structure (e.g., altruist model; Nash bargaining) determines “distribution factors” 4. Information structure (transaction costs; coordination costs). 27 27 27 27
Preferences Preferences (utility functions) for both spouses. Preferences for market goods and home produced commodities (home cooked meal; clean house). Following Becker, assume there are no “process preferences” With process preferences, people care not only about home cooked meals and a clean house, but also whether they spend time cooking or cleaning. Any specialization/ unilateral production conclusion depends on assuming that process preferences are absent or too weak to upset sector specialization. 28 28 28
Why We Need Individuals’ Technologies as well as Household Technology 1. Single-person (one adult) households are intrinsically interesting 2. Marriage market: Compare well-being when single with well-being in particular potential marriage 3. Divorce: Compare well-being in current marriage with well-being if divorced 4. Allocation within marriage (e.g., bargaining) Divorce as outside option in most models Divorce as threat point in some models 29 29 29 29
Examples of Alternative Governance Structures 1. Becker’s altruist model. One spouse as “husband - father-dictator- patriarch” who makes all decisions (Pollak, 1988). 2. Nash bargaining (Manser and Brown; McElroy and Horney; Lundberg and Pollak) 3. Other cooperative and noncooperative bargaining models (e.g., repeated games, two stage games) 4. Chiappori’s “collective model” as a reduced form corresponding to any bargaining model with a unique, Pareto-efficient solution. 30
Information Structure and Transaction Costs Asymmetric information and monitoring. Coordination and household management: Mrs Beeton Becker devotes a section of Chapter 2 to “Shirking, Household Size, and the Division of Labor” in which he discusses “[s]hirking, pilfering, or other malfeasance” Why does the person who cares most about how a particular task is done so often decide to do it herself? Without asymmetric information and monitoring costs, which spouse does a task is independent of which spouse wants it done. 31 31 31
When Do Assumptions about Technology Imply Conclusions about Specialization/ Unilateral Production? It takes very strong assumptions about technology to imply conclusions about “specialization” or “unilateral production” that hold for all possible assumptions about preferences, governance structures and market wage rates. 32 32 32
How Rabbits Got In - 1 Unless marginal products are constant, comparative advantages depend on time allocation. “Different comparative advantages” is assumption about efficient time allocation, not just about technology. For a wide class of assumptions about technology and wage rates, production efficiency requires nonspecialization and implies equal comparative advantages. Different comparative advantages rule out interior solutions (i.e., those in which both spouses allocate time to both sectors). Different comparative advantages implies specialization: a corner solution. 33 33 33
How Rabbits Got In - 2 Perfect substitutes If the spouses time inputs are perfect substitutes, then efficiency in production implies specialization without any additional assumptions (e.g., about additivity, returns to scale, or human capital). 34 34 34
How Rabbits Got In - 3 The theorems assume that there are only two "sectors"-- home and market. But if there are m household commodities then, for households in which both husbands and wives participate in the market, Becker's reasoning implies that husbands specialize in the production of m* of these home-produced commodities and the wives in the production of the remaining m-m* commodities (Lundberg, 2008). This is a kind of specialization, but it is not sector specialization. 35 35 35 35
Royal Economic Society
A simple identi…cation strategy for Gary Becker’s time allocation model Laurens Cherchye Bram De Rock Frederic Vermeulen (Université Libre de Bruxelles) (University of Leuven) (University of Leuven) Royal Economic Society Conference March 31, 2015 CDV (Royal Economic Society Conference) Time allocation March 31, 2015 1 / 16
Introduction 50 years ago, Gary Becker published “A theory of the allocation of time” in the Economic Journal . Laid the foundations of household production theory, together with Gorman (1956) and Lancaster (1966). Households combine market goods and time to produce nonmarket goods, which provide utility. Enormous in‡uence on the literature: Muth (1966), Gronau (1970), Grossman (1972), Michael (1973), Willis (1973), Pollak and Wachter (1975), Rosenzweig and Schultz (1983), Cunha and Heckman (2007), etc. CDV (Royal Economic Society Conference) Time allocation March 31, 2015 2 / 16
Introduction Empirical implementation hampered by the lack of values (‘prices’) for di¤erent time uses. Usual approach: prices of female and male time uses are equal to their respective market wages. This implies a fundamental identi…cation problem. We present a simple solution to this identi…cation problem. Based on variables (‘production shifters’) that are related to the total factor productivities associated with the production of nonmarket goods. CDV (Royal Economic Society Conference) Time allocation March 31, 2015 3 / 16
Overview Becker’s time allocation model. A fundamental identi…cation problem. A simple solution. Conclusion. CDV (Royal Economic Society Conference) Time allocation March 31, 2015 4 / 16
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