Nicolas Petrosky-Nadeau

Etienne Wasmer
email: etienne.wasmer@sciences-po.fr.

Shutian Zeng

Shopping Time

Keywords: JEL Classification: D12, E32, J22 Goods market search, time allocation, American Time Use Survey, business cycles

There is a renewed interest in macroeconomic theories of search frictions in the goods market that help solve quantitative puzzles on amplification and persistence of GDP, sales, inventory and advertisement. This requires a deeper understanding of the cyclical properties of the intensive margins of search in this market. Using the American Time Use Survey we construct an indicator of shopping time. It includes both searching and purchasing goods and is based on 25 time use categories (out of more than 400 categories). We find that average time spent shopping declined in the aggregate over the period 2008-2010 compared to 2005-2007. The decline was largest for the unemployed who went from spending more time shopping for goods than the employed to roughly the same, or even less, time. Cross-state and individual regressions indicate procyclical consumer shopping time in the goods market. This evidence poses a challenge for models in which price comparisons are a driver of business cycles.

Introduction

Most if not all markets are subject to various frictions, including informational and search ones.

Adopting this viewpoint has proved sucessful in the analysis of labor and credit markets. More recently, a body of research has modeled search frictional goods markets. This research has allowed for a better understanding of rationing in the goods markets, of GDP, sales, inventory and advertisement, as well as its role in the propagation of business cycles. However, there is no consensus on the cyclicality of an important variable in this search frictional goods market, namely the cyclicality of aggregate effort exerted by consumers, despite the fact that is is akey determinant of sales and therefore profits and inverstment.

In models by [START_REF] Bai | Demand shocks that look like productivity shocks[END_REF] who study the role of demand fluctuations, of [START_REF] Gourio | Customer capital[END_REF] and den [START_REF] Den Haan | Inventories and the role of goods-market frictions for business cycles[END_REF] who study the joint behavior of inventory and GDP and [START_REF] Petrosky-Nadeau | Macroeconomic Dynamics in a Model of Goods, Labor and Credit Market Frictions[END_REF] who focus on amplification and persistence of technology shocks, endogenous consumer shopping effort is procyclical. Notably, it increases with income. In [START_REF] Kaplan | Shopping Externalities and Self-Fulfilling Unemployment Fluctuations[END_REF], consumer effort is exogenous and fixed over time but, by fixing the effort of the unemployed above that of the employed, as the former are assumed to search harder to find better prices, aggregate time shopping appears to be countercyclical.

In this paper we first clarify the various interactions between income, shopping time, and working time, and review the theoretical ingredients needed to support the alternative patterns of covariations with the cycle. We then use the detailed daily time use diaries of the American Time Use Survey (ATUS) conducted by the Bureau of Labor Statistics (BLS) to measure the cyclicality of consumer search in the goods market. In a very related line of research, [START_REF] Hall | The cyclical response of advertising refutes counter-cyclical profit margins in favor of product-market frictions[END_REF] was the first to show the strong procylicality of advertising and its macreoconomic implications, advertising spending being the dual of consumer efforts in the present paper.

From a theoretical perspective, under standard assumptions on utility and cost functions of shopping effort, shopping time, thought of as a combination of effort before purchasing (e.g. comparing prices, hereafter pre-match search effort) and effort while purchasing (hereafter, purchasing effort), is procyclical. Purchasing effort increases with income because higher income reduces the opportunity cost of buying search goods. A less trivial result is that pre-match search effort increases with the surplus from consumption. The consumption surplus itself depends on income. Consumers therefore spend more time and effort to consume following a rise in income.

Prices, when they are bargained, respond positively to income and attenuate the procyclicality 1 result. When quantities can adjust, they respond positively to income and thus further raise the consumption surplus. This strengthens the procyclicality under price bargaining. However, the cyclicality of shopping time disappears under competitive pricing. There are also forces in the opposite direction. In the face of price dispersion and a reservation search strategy for consumers, an increase in income is associated with a higher reservation price less search effort for goods. Similarly, when working time can be chosen freely, shopping effort and working time covary negatively. Hence, a rise in the hourly wage -due for instance to a productivity innovation generating the business cycle -raises hours if the substitution effect dominates the income effect. This leads to less shopping time. Finally, pre-match search effort may occur simultaneously with the effort undertaken while shopping for other goods. This would be a case, say, when in a grocery store an individual spends time searching for new yogurts after having filled the basket with salt, butter, and sour cream.

Whether procyclicality or countercyclicality dominates is, ultimately, an empirical question for which we use the American Time Use Survey (ATUS) from 2003 to 2013. The ATUS includes over 400 distinct time use categories. Our main task is to identify various components of shopping time.

We settle on 25 time use categories that broadly encompass time spent shopping for consumer goods and services, and, separately, on groceries, gas and food (GFC).

We obtain three main results. First, we find that aggregate search by consumers in the goods market declined with the onset of the Great Recession. This is true for each of the employed, unemployed, and nonparticipants. However, we find that the time allocation to finding and acquiring goods and services declined most for the unemployed. Prior to December 2007 the unemployed, and non-participants, spent more time searching in the goods market than the employed. During the Great Recession, the unemployed drastically reduced their time searching for goods and services, spending the same amount of, or even less, time on this activity than the employed by 2012.

Second, there is a positive relation between cross-state variations in GDP per capita and our different measures of search effort in the goods markets. States with the largest declines in GDP per capita tended to have the largest declines in time spent shopping for goods and services. In Michigan, for instance, there was 21% decline in time spent in this shopping category and a 10% decline in GDP per capita. Oklahoma, with a very different experience over the period in question, experienced a 2% increase in GDP per capita and a 20% increase in shopping time.

Third, we find that search effort in the goods market is increasing in individual income and household income. This result is robust to controlling for state of residence and various demographic characteristics such as age, gender, education, and marital status. The one exception is time spent shopping for groceries, gas, and food, which is unrelated to either income variable. Overall, we don't find much evidence in favor of a negative correlation between income and shopping time.

Overall, this body of evidence poses a challenge for theories in which price comparisons are a driver of business cycles, as in recently published work by [START_REF] Kaplan | Shopping Externalities and Self-Fulfilling Unemployment Fluctuations[END_REF].

Fluctuations and the existence of multiple equilibria in the latter arise precisely from the fact that in recessions the unemployed search more for lower priced goods, depressing the economy further. Our investigation of the ATUS data does not support this mechanism.

In contrast, our result confirms a negative correlation between working hours and shopping time found in [START_REF] Aguiar | Time Use During the Great Recession[END_REF]. This is quite natural, since the time budget constraint is less tight in a recession. Households have more time to allocate to various non-work activities. However, this does not imply that forces pushing towards a countercyclicality of shopping time dominate over the business cycles, for the reasons indicated above. Our conclusion is that models where the consumption surplus and search effort in the goods market are procyclical have more empirical support, and are relevant for studying business cycles.

Section 2 reviews the various mechanisms at play between income, shopping time, prices, and working time and classifies them into procyclical forces and countercyclical forces. Section 3 describes the ATUS and the time use categories we employ in this study. Section 4 describes aggregate trends in shopping time over the sample period 2003-2012 and according to labor force status. Section 5 then measures the business cycle and income elasticity of time spent searching for goods and services, and discusses some robustness issues. Section 6 discusses the individual regression of shopping time and income. Section 7 concludes.

The cyclical pattern of shopping time

The early search and matching literature considered the market for goods and services as the prototypical setting in which buyers and sellers are engaged in a costly and time consuming process to find and establish trading relationships [START_REF] Diamond | Aggregate demand management in search equilibrium[END_REF]. Firms exert effort and consume resources in order to advertise their products and maintain their customer relationships. Consumers spend time searching, selecting and purchasing to obtain goods and services, adding and removing items from their consumption basket. 1 Departures from market clearing assumptions introduce a range of possible price determination mechanisms that have important implications for equilibrium allocations in the long run and over the business cycle.

A setup for thinking about shopping time

Consumers may spend more or less time shopping. A good framework for thinking about shopping time is to disentangle this time between pre-match effort denoted by e 0 (which may in practice occur while purchasing other goods), and post-match purchasing time e 1 , which transforms time into actual purchasing. For the sake of simplicity, we assume that the relation between the quantity of search good purchased denoted by x is linear in time spent e 1 .

The purpose of this section is to identify the mechanisms that lead to either procyclical or countercyclical shopping time over the business cycle. Although the relevant search margin for the research macroeconomic literature with a search frictional goods market is e 0 , we start by showing that both e 0 and e 1 contain strong procylical forces. Then we focus more on e 0 , which can be thought of as time spent locating products in the goods market. This effort is driven mostly by two different incentives. First, it may be used to match faster with a good, and to thereby enjoy the associated consumption surplus more quickly. Alternatively, it may be used to locate the best price in the presence of price dispersion across sellers. The two motives may be at play simultaneously.

Further, an individual consumer's probability of finding a product in the goods market will depend, in general, on individual effort relative to the effort by other consumers, as well as the amount of consumers and sellers out there in the market.

At the individual level, the probability of finding a particular good is given by (e 0 /ē 0 )λ, where λ is an aggregate contact rate with a product in the goods market, and ē0 is aggregate search effort by other consumers. The contact rate λ depends on the aggregate amount of consumers and sellers in the market. If the aggregate amounts of consumers and sellers in the goods market are denoted by, respectively, C and S, the matching literature typically postulates an increasing aggregate matching function M (ē 0 C, S) that governs the number of matches per unit of time. As such, the aggregate rate of matching for consumers is given by λ = M (ē 0 C, S)/C. 2

Assume that the consumer's preferences are summarized by an increasing and concave utility function v(x, y, l) associating two goods, the search good denoted by x, and all other goods acquired household's consumption basket, see [START_REF] Broda | Product creation and destruction: Evidence and price implications[END_REF] for empirical evidence and Petrosky-Nadeau and Wasmer (2015), [START_REF] Bai | Demand shocks that look like productivity shocks[END_REF][START_REF] Michaillat | An Economical Business-Cycle Model[END_REF][START_REF] Michaillat | An Economical Business-Cycle Model[END_REF] for a modeling approach. den Haan (2013) consider the role of product market imperfections for the business cycle of inventories.

2 Appendix A.1 explores a more general specification of individual consumption match probability where individual and aggregate efforts are complementary, allowing for different consumption effort externalities.

on frictionless markets, y, and leisure l. Leisure is the total time budget, normalized to 1, less hours worked h, and shopping time e 0 and e 1 .

Once in a match with a seller, a consumer spends px out of disposable income ω to consume the search good. The remaining income is spent on the consumption of other goods (called composite to simplify). We use the following compact notation: v(1) = v(x, ω -px, 1 -h -e 1 ) denotes the utility from consuming the search good, and v(0) = v(0, ω, 1 -h -e 0 ) denotes the utility from consuming only the composite good. ∆v ≡ v(1) -v(0) denotes their difference.3 Hence, the value of the consumer's surplus in a marginal goods market match is given as:

Ω c = v(1) -v(0) = ∆v (2)
The properties of ∆v and its derivatives with respect to y and x will be very important for what follows. In particular, we will assume marginal decreasing utility in the three goods (v yy < 0 ; v xx < 0; v ll < 0). Under separability between the two types of goods, the concavity in utility leads in particular to

∆v y ≡ v y (1) -v y (0) > 0 (3)
A marginal unit of consumption of composite good y has a greater value when the agent diverts part of its income to also consume the search good. The same is true under nonseparability when the degree of substituability between the two goods is not strong enough. Appendix A.2 derives this more general case.

Consumers incur a cost to search effort in the goods market described by the returns to leisure v l . We neglect time discounting for simplicity. Given this environment, the generic optimality condition for consumer search effort e 0 states that the marginal utility of leisure is equal to the marginal benefit of effort, that is the expected surplus from finding a good in the product market:

v l (0) = λ ē0 Ω c (4)
This condition states that increasing purchasing time of the search good raises the opportunity cost of time (less leisure), reduces the consumption of the non-search good, and equals the marginal utility from consumption of the search good. The other first order condition on purchasing time e 1 is:

v l (1) = ∂x ∂e 1 [v x (1) -pv y (1)]
The following can already be learned about forces that induce a procyclicality of shopping time.

First, pre-match effort e 0 has the the same cyclicality as the surplus Ω c since the marginal utility of leisure is increasing in e 0 when v ll < 0 Hence, an increase in Ω c will increase search effort e 0 and precisely, Ω c is itself procyclical in the simplest case where prices, hours and x are a-cyclical.

This arises from the fact that, in a boom, higher income ω leads to a lower marginal utility of consumption of the numeraire at a given price of x. Hence, the opportunity cost of consuming the search good (the foregone value of the composite good) is lower, the higher income ω. Therefore, the consumer surplus is procyclical. A similar reasoning shows that shopping time e 1 is also procyclical under separability in utility. Conversely, if hours are procyclical, then the marginal value of leisure is higher, and hence both e 0 and e 1 may be countercyclical. Moreover, if prices are procyclical, then return on consuming goods x is lower (it has a greater opportunity cost in terms of numeraire y) and thus there is an additional force towards countercyclicality. We show this formally in the Appendix.

Whether procyclicality or countercyclicality dominates depends on the utility function and price determination mechanism, but it ends up ultimately in being an empirical question, explored in next Section.

Surplus sharing with a fixed supply of the search good x

Assuming that the supply of the search good is fixed at some level (due to either indivisibility in production, consumption or storage of good x), consider the simplest price setting mechanism.

In the context of search frictions, this amounts to a price rule that equalizes the surplus to the consumer and the firm, i.e., such that Ω c = Ω f where Ω f is firm's surplus from sellling the good at unit price p in quantity x and at a production cost κ(x). This results in a simple price rule:

xp = ∆v + κ(x) (5)
A positive, procyclical, shock to income dω, keeping the cost κ constant, leads to:

x dp dω = ∆v y 1 + v y (1) > 0 (6)
The assumption that utility is increasing, concave and separable in x and y, implies that the price varies positively with income.4

The cyclicality of the consumer and firm match surpluses follows easily from their definitions.We have under the inequality (3):

dΩ f dω = x dp dω > 0 dΩ c dω = ∆v y -xv y (1) dp dω = ∆v y 1 + v y (1) > 0
Hence, a positive income shock raises the consumer's surplus and, from the optimal search effort condition (4), individual search effort in the goods market. Moreover, the same shock will raise the number of sellers, thus raising λ. Therefore, consumer search effort is procyclical.

In the Appendix, we explore other dimensions for completeness: price bargaining, the endogeneity of the supply of the search good, the existence of significant price dispersion and the endogeneity of the choice of hours worked.

3 Searching for goods and services in the ATUS We focus on time spent in the process of selecting and acquiring goods and services. Overall we select 25 categories out of more than 400, which include time spent traveling associated with purchasing marketized goods and services. A potential 26th category, travel time related to relaxing and leisure, was excluded even if it may include some market activities. Each category is mutually exclusive and sum to total time spent shopping:5

• 1 -Consumer goods and services is divided into three subcategories. The first is time spent shopping other than for groceries, gas, and food. The second is time spent researching purchases. The third corresponds to waiting associated with purchasing services.

• 2 -Groceries, Gas, and Food (GGF) includes all time spent shopping for groceries, gas, and food. We present results for all three subcategories.

• 3 -Travel time includes all travel associated with the purchasing of goods and services.

We focus on the population ages of 24 and 55. We exclude the population aged 16 to 24 because labor force status, such as unemployment and participation, line up very closely with the CPS based rates published by the BLS for all age groups except this younger group. 6 We remove those aged 55 and over because labor farce participation rates for these individuals decline dramatically, whereas our main results emphasize differences across labor force status. We also exclude respondents with a positive amount of unclassified time. In total with have 66,958 individuals in our sample for the baseline results. 7 We use the sample weights provided by the ATUS to aggregate responses to either year or state-year averages. Notes: ATUS, sample restricted to respondents with no unclassified time. Agg.," Emp.," Unem.," and NLF" correspond to Aggregate," Employed," Unemployed," and Not in Labor Force." For the baseline sample of individuals aged 25 to 54, there were 10,434 respondents per year, on average. Marital status refers to the presence of a spouse and does not include unmarried partners.

Aggregate trends in shopping time

The second panel of Figure 1 Average time spent in researching goods and services is small, averaging 0.07 minute a day.

However, we note that nonparticipants spent the most time, 0.20 minute, and that the employed spent on average more time than the unemployed researching goods and services (see Table 4).

Finally, time spent waiting associated with the acquiring of goods and services averages 0.67 minute a day. The employed and unemployed spent about the same amount of time waiting, while individuals not in the labor force wait twice as long, or 1.3 minutes.

Individuals spend on average 8 minutes a day purchasing groceries, gas, and food, the bulk of which is spent purchasing groceries (6 minutes), and an average of 18 minutes a day in travel associated with purchasing goods and services.

The last columns of Table 4 report the time spent shopping for goods and services for men and women, each according to marital status, as well as for individuals age 55 and older. Women spend 15 more minutes a day shopping for goods and services relative to men. The largest difference is in the shopping for goods and services category. Conditioning on marital status reveals little difference in the pattern of time spent searching for and acquiring goods and services across married and single men. Married women spend 7 more minutes a day in total shopping time than single women. Time spent shopping for groceries show the most important differences across married and single women, along with travel time associated with shopping for goods and services. The last column reports that individuals over age 55 spend, on average, 3 more minutes a days shopping than individuals aged 25 to 54.

Shopping time over the business cycle

The ATUS does not cover an entire business cycle at the moment. This renders the discussion of trends and cycle in time use data delicate. We address this question in the first subsection by comparing average time spent shopping for goods and services by individuals in the three years leading up to and three years following the start of the Great Recession. Next, we estimate the elasticity of time spent on different goods market search categories over the business cycle in the manner of [START_REF] Aguiar | Time Use During the Great Recession[END_REF]. That is, we exploit cross-state variations in time spent and a measure of state business cycles. We then look at the relationship between individual and household income and our measure of shopping time, as well as changes in hours of market work. In each section we emphasize differences across labor market statuses. It does not appear appropriate to remove a time trend from the data when the sample does not cover an entire business cycle. Such a transformation will introduce a bias in the direction of the differences that reflects the fraction of the cycle actually covered by the said sample, and on the state of the cycle at the start of the sample. The next section will use cross-state changes in GDP and time use in order to further investigate the cyclicality of shopping time. to commute greater distances to work at scarce jobs. Moreover, the conditional difference in time spent is almost identical to the unconditional difference.

The cycle and goods market search

We find that the largest decline in time spent shopping for goods and services is by the unemployed. Time spent shopping for consumer goods and services declines by 10 minutes for the unemployed, compared with 1.7 minutes for the employed. Both declines are highly statistically significant. This decline is slightly larger for the unemployed after controlling for other individual characteristics. The corresponding time use categories for nonparticipants also declines, but the difference is not statistically significant.

This finding relates to the composition of individuals across labor market statuses and aggregate search effort in the goods market. Prior to the onset of the Great Recession, the unemployed spent more time searching for goods and services than the employed: 24.5 minutes against 15.3 by the employed. As such, the rapid increase in unemployment in 2008 and 2009 could have led to an increase in aggregate search effort in the goods market. The ATUS data show that this was not the case. Shopping time of the unemployed declined to an average of 14 minutes in the 2008-2010 period, below the average of 13.7 for the employed. Since shopping time declined for every labor force status, aggregate search time declined (Panel A of Table 2). Again, the search effort of the unemployed declined most during the recession. By the end of the sample, the unemployed spent less time than the employed searching in the goods market.

Average time spent shopping for groceries, gas, and food, just as travel time associated with shopping, saw essentially no change across time periods. This is true across labor force statuses, with one exception. There is a 2.3 minute decline in time spent shopping for groceries by individuals not in the labor force.

Cross-state variations in shopping time

We define the state-level aggregates of time use of category j as follows:

τ j st = Nst i=1 ω ist Nst i=1 ω ist τ j ist , (7)
where τ j ist represents minutes per day by individual i from state s during period t spent on time use category j. N st is the total number of individuals in our sample from state s during period t and ω ist is the ATUS sampling weight. 9 We then construct state-level differences in shopping between The pattern in panel A of Figure 2 is clear. States with the strongest decline in GDP per capita experienced the most significant decline in total shopping time. Likewise, states that saw an increase in GDP per capita also saw an increase in total shopping. In Michigan for instance, there and will not produce estimates as reliable as for the more populous states. We use the average state population between 2003 and 2012 as weights in the regressions to account for this concern regarding the state-level estimates.

was a 21% decline in time spent and a 10% decline in GDP per capita. Oklahoma, with a very different experience over the period in question, experienced a 2% increase in GDP per capita and an 20% increase in shopping time. The regression line has a positive slope with coefficient 1.09, implying that, on average, a 1% decline in state GDP per capita coincided with a 1.1% decline in total time spent shopping.

Time spent shopping for goods and services, in Panel B, shows a similar pattern of decline with the contraction of state GDP. The regression line has a slope of 1.60, implying a stronger positive relation than in the case of total shopping time.

The state-level changes in time spent shopping for groceries, gas, and food or travel time associated with shopping have a weaker positive relation to changes in state GDP per capita, but neither is significant. Most states, especially the most populous, saw virtually no change in the time spent shopping for groceries, gas, and food (see Panel C).

Individual regressions

This section examines the relationships between two measures of income, household and individual, and search activity in the goods market in the ATUS. In the first case we use reported household income brackets. In the second case we use reported weekly earnings in the CPS files. Both approaches uncover a positive relation between income and search effort in the goods market. The results are strongest for shopping for goods and services and time spent traveling associated with shopping. We find no evidence in the time use data that individuals with lower incomes search far and wide.

Household income

We consider the relation between household income and consumer search in the goods market using six income categories: (1) $0 to $24,999; (2) $25,000 to $49,999; (3) $50,000 to $74,999; (4) $75,000 to $99,999; (5) $100,000 to $149,999, and; (6) $150,000 and over, and running the following regression:10

τ j ist = α j + β j F ist + D t + S i + δX ist + ist , (8)
where F ist is a vector of family income categorical variables, D t is a time dummy, S i is a state dummy, and X ist is a vector of demographic and educational variables. 6.1 reports the estimated coefficients on income categories 2 to 6. Each coefficient represents the increment in shopping time for an increment in the household income categories relative to the first household income category $0-$24,999. For instance, total shopping time for households with an income between $100,000 and $150,000 (category 5) is 5 to 7 minutes greater than average shopping time by an individual in a household with income in the $0 to $24,999 bracket (category 1). After controlling for various individual characteristics (column I), this is robust to including both time and state (columns II and III), as well as labor force status dummy variables (column IV).

The three broad subcategories show that both time spent shopping for consumer goods and services, as well as the associated travel time, are increasing in household income, and the differences are highly statistically significant. For instance, households in the $50,000 to $75,000 income bracket (category 3) spend an extra 1.3 minutes shopping for goods and services and an extra 1.8 minutes waiting. Households in the $100,000 to $150,000 income bracket (category 5) spend an extra 3.9 minutes shopping for goods and services and an extra 2.6 minutes waiting. There appears not to be any statistically significant relationship between time spent shopping for groceries, gas, and food and household income.

Individual income

Reported weekly income for employed respondents averages $37,856 per year. We use this information to estimate the following relation between income and search effort in the data:

τ j ist = α j + β j I ist + D t + S i + δX ist + ist , (9)
where j is the time use category, I ist is annual personal income (in thousands of dollars) for individual i in state s, D t is a time dummy, S i a dummy for the individual's state, and X ist is a vector of demographic and educational variables (age, gender, race, education, marital status, and presence of children). The coefficient of interest, β j is reported in Table 6.2, with standard errors in parentheses, for total shopping time and the three broad subcategories: consumer goods and services; groceries, gas, and food; and travel time.

The first row of Table 6.2 reveals that total shopping time is increasing in individual income but that none of the coefficients are statistically significant. The second row indicates that time spent shopping for consumer goods and services is increasing in individual income, yet none of the specifications yield a statistically significant coefficient. Time shopping for groceries, gas, and food, however, declines with income, and the coefficient is highly significant in each of the specifications.

Last, we find that travel time associated with shopping is increasing with individual income, and the coefficient is highly statistically significant in each specification. This suggests that individuals with lower income do not travel further and search wider for goods and services.

Market work and shopping time

In this section we examine the relation of shopping time to time in market work. We apply the same definition of market work in the ATUS as [START_REF] Aguiar | Time Use During the Great Recession[END_REF] and run the following regression:11

τ j ist = α j + β j τ M ist + D t + S i + δX ist + ist , (10)
where τ M ist is the time spent on market work, D t and S i are the time and state dummies, respectively, and X ist is a vector of demographic and educational variables (age, gender, race, education, marital status, and the presence of children). Table 6.2 reports the resulting estimates β j .

The results indicate that a 1 minute decline in market hours is associated with a 0.04 minute decline in shopping time. The impact of diminished hours of the employed on shopping time is very small.

Conclusion

The recent availability of new data sets measuring the inflows and outflows of goods and services in a household's consumption basket [START_REF] Broda | Product creation and destruction: Evidence and price implications[END_REF] and the presence and investment in customer relationships [START_REF] Gourio | Customer capital[END_REF] has lead to a renewal of theories in which search frictions in the goods market play an important role for macroeconomic outcomes. The cyclical properties of the intensive margins in this market, by consumers and firms, have quickly shown themselves to be important to our deeper understanding of dynamics of consumption, employment, and business cycles in general.

A precursor paper by [START_REF] Hall | The cyclical response of advertising refutes counter-cyclical profit margins in favor of product-market frictions[END_REF] had shown that advertisement by firms is very procyclical. In this paper we find, on the other side of the market, that consumers spend a varying amount of time for purchasing goods and products. This shopping time declined significantly with the onset of the Great Recession across all types of individuals, and it is positively correlated with individual and household income. In addition, consumption effort dropped more in states where economic activity decreased relatively more following the financial crisis. We also find that a decline in working time raises shopping time. Nonetheless, employed individuals spent less time shopping during the recession.

Overall, we don't find much evidence in favor of a negative correlation between income and the goods market become independent of the business cycle.12 Second, a similar result holds under the alternative assumption of an exhaustion of profit margins. This would be the case if the market price is such that p = κ(x). The firm's surplus vanishes to zero. If in addition workers and firms bargain on the quantity, the consumption surplus will also vanish. Hence, search effort will not react to the cycle due to the surplus. Consumers may however respond to further entry of firms. An increase in S raises the contact rate λ, implying once again that search effort will be procyclical.

Third, if one assumes that the quantity x is chosen so as to share the surplus equally, while the price is equal to the marginal cost of production with a markup to account for ex post monopoly power, again a large utility from the search good and small utility from the composite leads to a positive effect of income on the surplus and search effort.

U (e 0 ) = v(0, ω) -σ(e 0 ) + e 0 ē0 λ ˆpR (D M (p) -D U (e 0 )) dG(p) (A.7) rD M (p) = v(x, ω -px) + τ [D U (e 0 ) -D M (p)] (A.8)
where p R is the reservation price above which the consumer keeps searching, τ is an exogenous destruction of the consumption match and r is a constant discount rate.

The value of searching in the goods market, D U , is maximized by varying the level of effort. The reservation price p R satisfies an indifference condition rD M (p R ) = rD U . In a symmetric equilibrium where e 0 = ē0 , optimal search effort and reservation price are given by the conditions:

η c σ(e * 0 ) = λ ˆpR (D M (p) -D U (e * 0 ))dG(p) (A.9) σ(e * 0 ) + v(x, ω -p R x)-v(0, ω) = λ ˆpR (D M (p) -D U (e * 0 ))dG(p) (A.10)
which combined yield a relation between search effort, income, and the reservation price:

(η c -1)σ(e * 0 ) = v(x, ω -p R x) -v(0, ω) (A.11)
For a given level of the reservation price, the right-hand side is procyclical under concavity of the utility function with respect to income. This is the procyclical channel of income on search effort outlined in earlier sections. The key countervailing force is the movement in the reservation price. If p R varies procyclically, then the second term has a countercyclical component. That is, an increase in the reservation price leads to a decline in the expected payoff to search in the goods market, and reduces the incentive to exert effort in searching. Variations in the reservation price must therefore be studied jointly with variations in effort. Differentiating equation (A.11) (and assuming iso-elastic cost function), we have:

(η c -1)σ (e * 0 )de * 0 = [v y (x, ω -p R x) -v y (0, ω)] dω -xv y (x, ω -p R x)dp R (A.12)
It can be shown that dp r /dω > 0. A reservation price increasing in income limits the positive response of consumer search effort to an income shock.

The link between the distribution of prices and search effort in the goods market is ambiguous. The mechanisms are similar to the relation between wage dispersion and job search. In the labor market, more dispersed wages lead workers, ceteris paribus, to be more picky about wage offers. This raises their reservation wage and reduces the so-called hazard rate (the exit rate from unemployment to employment). To compensate, workers may reduce their search effort if the lower hazard rate discourages them, or raise it if the surplus value of getting better jobs dominates. Transposed to search for products, price dispersion may reduce the reservation price p R with an ambiguous effect on shopping effort.

A.6 Correlation between income, shopping time, and working time

So far, we have assumed that working time was indivisible and the supply of shopping time was elastic, only limited by the cost of supplying effort. We now relax this assumption and generate a setup that allows us to discuss the findings of [START_REF] Aguiar | Time Use During the Great Recession[END_REF] and how they differ from ours.

Let h and e 0 be the two relevant time inputs, working time and shopping effort, respectively. We remain close to the previous analysis, ignoring other nonworking time, and consider an environment similar to Section 2.2 to determine a consumer's optimal choices. We assume that e 0 and h enter additively in the cost of effort function, and that the choice of hours is made before the consumer is actually matched with a good. The consumer knows the matching probability in the goods market m(e 0 ) = e 0 λ/ ē0 and the separation probability in the goods market (denoted by s) so that (s)he expects to be matched α(e 0 ) = m/(m + s) of the time. 14 The first-order conditions for e 0 and h, respectively, are given by: σ (e 0 + h) = λ ē0 Ω c (h) (A.13)

σ (e 0 + h) = α(e 0 ) dv dh (x, hω -px) + (1 -α(e 0 )) dv dh (0, hω) (A.14) where Ω c (h) = v(x, hω -px) -v(0, hω). Inspection of equation (A.13) shows that an increase in h increases the cost of an extra unit of shopping time. However, it also affects the right-hand side. In particular, it raises Ω c by ω [v y (x, hω -px) -v y (0, hω)] which, under the same separability and concavity assumptions as in the benchmark case of Section 2.2, is positive. Hence, we expect an increase in hours worked to decrease shopping time and, reciprocally, a drop in hours worked to raise shopping effort. The response of search effort in the goods market to an income shock, however, is ambiguous and explored empirically in the rest of the paper.

power, a large utility from the search good and small utility from the composite lead to a positive effect of income on the surplus and search effort. Set the price to p = κ x (1 + ), such that the consumer's surplus is ∆v = xp-κ(x) = xκ x (1+ )-κ(x). Then, differentiation of this last equation leads to: dp dx = κ xx (1 + ) = (p/x) (η κ -1) > 0 where η κ is the elasticity of κ with respect to x. Therefore, using equation (A.6), and replacing dp/dw with (dp/dx) × (dx/dω), and using the second part of the equality above, one has: Again, large utility from the search good and small utility from the composite lead to a positive effect of income on the surplus.

B Data

B.1 Shopping Time in the American Time Use Survey

The ATUS classifies diary activities into 18 major categories, and each category has additional second-and third-tier categories. According to the 2003-2012 multiyear lexicon, each activity has a code in the form of "x-y-z," where "x" denotes the first-tier, "y" , the second tier, and "z," the third tier classification. For example, major categories include personal care activities 01, household activities 02, work and work-related activities 05, education 06, etc. The second-and third-tier categories further break down the major categories. For example, under the major category of work and work-related activities, second-tier categories include working 05-01, working-related activities 05-02, other income-generating activities 05-03, job searching and interviewing 05-04, etc. And under the second-tier category of working, the third-tier categories are main job work 05-01-01, other job(s) work 05-01-02, security procedures related to work 05-01-03, etc.

We group the time spent shopping for market goods and services as follows:

Total time shopping for market goods and services:

1. Consumer Goods and Services shopping other than Groceries Gas and Food: 2. Purchasing Groceries, Gas, and Food (GG&F):

(a) Groceries: 07-01-01.

  We use data from the 2003-2013 waves of the ATUS, conducted by the BLS drawing on individuals from the exiting sample of the Current Population Survey (CPS). The types of activities recorded in the ATUS are described in detail in Hammermesh et al. (2005), and have been used to document changes in overall time use during the Great Recession (Aguiar et al. 2013), with a particular emphasis on how individuals reallocate decreased hours of market work to other activities.

Figure 1

 1 Figure 1 plots the annual data for our main components of shopping time, in the aggregateaveraging across all individuals in the sample (solid black line) -and by labor force status. Time spent by the employed is plotted by the red dashed line, time spent by the unemployed by the triangle green line, and time spent by nonparticipants by the blue circled line. Table4 provides

  Aggregate time spent shopping for goods and services, plotted in Panel A of Figure1, averaged 42 minutes per day over the sample period. Two main observation arise from this first look at the data. First, individuals not in the labor force spend the most time shopping for goods and services, an average of 50 minutes a day. Second, individuals not in the labor force and unemployed display a similar pattern of total time spent shopping for goods and services, with a pronounced decline in time spent starting in 2007.

Figure 1 :

 1 Figure 1: Shopping time: ages 25 to 54 by labor force status

  plots time spent shopping for goods and services other than groceries, gas, and food, and excluding the time spent traveling associated with shopping activities. This is the core measure of search effort by consumers in the goods market. The average time spent in a day over the period 2003-2012 is 16 minutes, with nonparticipants spending the most time, 20 minutes a day. Interestingly, the unemployed start out resembling nonparticipants early in the sample time period, even spending more time shopping for goods and services by a significant margin in 2006. In the second half of the sample, after the onset of the Great Recession, the unemployedt are very similar to the employed in time spent shopping for goods and services. By 2012, the unemployed spend less time shopping for goods and services than the employed.

A

  first step in examining the cyclicality of search time in the goods market, presented in Table2, is to compare the average time spent on our different subcategories over two time periods. This also has the advantage, as argued by[START_REF] Aguiar | Time Use During the Great Recession[END_REF], of smoothing some year-to-year noise in the ATUS. 8 The periods we compared are the expansion years of 2005-2007 prior to the onset of the Great Recession in December 2007, to the following three years, 2008-2010. The sample in Table 2 Panel A are all individuals in the age category 25 to 54, our baseline. Panel B reports the results for employed individuals, while Panels A and B of Table 3, respectively, report the results for unemployed individuals and persons not in the labor force. The first two columns of Table 2 present the average time spent in each category for the two periods. The third column presents the unconditional difference in time spent over the two periods. The last column presents the difference in time spent conditioning on age, education, race, gender, marital status, and the presence of children. Overall time spent shopping saw a statistically significant decline of 2.5 minutes per day in 2008-2010 compared with 2005-2007. A closer examination reveals that the decline is concentrated in the consumer goods and services category. None of the increases in time spent shopping is statistically significant, with the exception of time spent purchasing gas. Presumably individuals are willing8

Figure 2 :

 2 Figure 2: Cross-State variations in shopping time: 2008-2010 vs. 2005-2007

  13

A. 5

 5 Price posting with homogeneous consumers and a given distribution of prices Assume that the search good has different prices in different locations. Consumer search effort is now also motivated by finding better prices. Let G(p) be the c.d.f. of prices. The program of a searching, unmatched consumer with income ω and search effort cost σ(e c ) can be represented by the Bellman equation D U (e c ), while D M (p) describes the asset value of being matched at price p: rD

  x (1) -pv y (1)] dx dω Change in quantity = ∆v y + [v x (1) -v y (1)pη κ ] dx dω

  (a) Shopping for consumer goods: 07-01-04, 07-01-05,07-01-99, 07-99. (b) Researching goods and services: 07-02. (c) Waiting associated with shopping for goods and services: Professional and Personal Care Services: 08-01-02, 08-02-03, 08-03-02, 08-04-03, 08-05-02, 08-06-02, 08-07-02; Household Services not done by self: 09-01-04, 09-02-02, 09-03-02, 09-04-02, 09-05-02; Arts and entertainment: 12-05-04.

Figure

  Figure A.1: Participation and unemployment rates in the ATUS and CPS

Table 1 :

 1 Shopping time by labor force status and by age -minutes per day

	Age:		55+	44.9	17.4		15.7	0.07	1.55	8.48		7.32	0.38	0.78	19.0
		Women	All Married Single	49.8 52.5 45.2	19.8 20.8 18.1		18.9 20.0 17.0	0.09 0.07 0.13	0.82 0.72 1.00	10.0 10.8 8.67		8.31 9.10 6.89	0.39 0.37 0.42	1.33 1.31 1.36	20.0 20.9 18.4
	Ages: 25 to 54	Men	All Married Single	34.2 34.6 33.6	12.3 12.6 11.9		11.8 12.1 11.4	0.06 0.07 0.04	0.51 0.51 0.51	5.82 5.82 5.82		4.22 4.24 4.18	0.42 0.44 0.39	1.18 1.13 1.24	16.0 16.1 15.9
		Labor force status	Emp. Unem. NLF	40.2 47.3 50.1	15.3 18.3 20.0		14.7 17.6 18.4	0.05 0.03 0.20	0.55 0.68 1.32	7.31 10.7 10.3		5.56 9.36 9.06	0.43 0.35 0.30	1.32 0.94 0.95	17.6 18.4 19.8
			Agg.	42.0	16.1		15.3	0.07	0.67	7.91		6.25	0.41	1.25	18.0
			Categories	[-0.1in] Total Shopping Time	[0.05in] Consumer Goods and	Servies	-Consumer Goods	-Researching G&S	-Waiting for services	[0.05in] Groceries, Gas, and	Food	-Groceries	-Gas	-Food	[0.05in] Travel time	[-0.15in]

Table 2 :

 2 Shopping time by period -minutes per day

	Panel A: Full sample
	[0.05in]

Table 3 :

 3 Shopping time by period -minutes per day

	Panel A: Unemployed individuals
	[0.05in]

Notes: ATUS using individual demographic and time use information. Sample restricted to respondents of age 25 to 54 who are unemployed (Panel A) or not in the labor force (Panel B), and have no of unclassified time use. Columns 1 and 2 report average minutes per day spent on various shopping activities during 2005-2007 and 2008-2010. Column 3 reports the unconditional difference and Column 4 reports the conditional difference in a regression controlling for age, education, race, gender, marriage status, and the presence of children. The asterisks *, **, and *** denote statistical significance at 10

Table 4 :

 4 Individual level regression of shopping time on household income

	Category	HH.	I	II	III	IV
		Income
	[-0.15in] Total Shopping Time 2	1.53	1.52	1.41	3.00 ***
		3	1.34	1.42	1.37	3.30 ***
		4	4.01 ***	3.97 ***	3.62 ***	5.73 ***
		5	4.36 ***	4.99 ***	4.45 ***	6.59 ***
		6	4.86 ***	5.69 ***	4.90 ***	6.90 ***
	[0.15in] Consumer Goods and	2	0.86	0.84	0.82	1.52 ***
	Servies
		3	0.41	0.43	0.47	1.32 **
		4	1.85 ***	1.79 ***	1.76 **	2.69 ***
		5	2.75 ***	3.06 ***	2.93 ***	3.86 ***
		6	1.44	1.86 **	1.65 *	2.52 ***
	[0.15in] Groceries, Gas and	2	-0.02	0.00	-0.04	0.45 *
	Food
		3	-0.43	-0.41	-0.45	0.14
		4	-0.34	-0.31	-0.45	0.20
		5	-0.35	-0.30	-0.51	0.15
		6	-0.32	-0.26	-0.54	0.09
	[0.15in] Travel time	2	0.69	0.68	0.63	1.03 **
		3	1.36 ***	1.40 ***	1.35 ***	1.84 ***
		4	2.51 ***	2.49 ***	2.31 ***	2.84 ***
		5	1.96 ***	2.23 ***	2.03 ***	2.58 ***
		6	3.73 ***	4.09 ***	3.79 ***	4.29 ***

Table 5 :

 5 Individual level regression of shopping time on personal incomeThe regression sample is restricted to respondents who are between the ages 25 and 54, have no unclassified time use and have positive personal income (employed). The table reports the estimate of and its standard errors in parentheses. Personal income is in thousands of dollars. Estimates of are multiplied by 100.

	Category	I	II	III
	[-0.15in] Total Shopping Time	0.75	1.34	0.64
	[-.05in]	( 0.55 )	( 0.28 )	( 0.61 )
	[.03in] Consumer Goods and	0.40	0.69	0.41
	Servies
	[-.05in]	( 0.60 )	( 0.37 )	( 0.60 )
	[.03in] Groceries, Gas, and Food	-1.00	-0.99	-1.23
	[-.05in]	( 0.00 )	( 0.00 )	( 0.00 )
	[.03in] Travel time	1.35	1.65	1.46
	[-.05in]	( 0.03 )	( 0.01 )	( 0.02 )
	[.05in] Demo. controls	Yes	Yes	Yes
	Time dummy	No	Yes	Yes
	State dummy	No	No	Yes

Table 6 :

 6 Individual level regression of shopping time on market work timeThe table reports the estimate of and its p-value in parentheses. Market work is in terms of minutes per day. Estimates of are multiplied by 100 for readability. An estimate of 1 means that the time use is expected to be 0.01 minutes per day if market work is 1 minute higher.

	Category	I	II	III
	[-0.15in] Total Shopping Time	-8.17	-8.17	-8.18
	[-.05in]	( 0.00 )	( 0.00 )	( 0.00 )
	[.03in] Consumer Goods and	-3.85	-3.85	-3.86
	Servies
	[-.05in]	( 0.00 )	( 0.00 )	( 0.00 )
	[.03in] Groceries, Gas, and Food	-1.24	-1.24	-1.24
	[-.05in]	( 0.00 )	( 0.00 )	( 0.00 )
	[.03in] Travel time	-3.08	-3.08	-3.08
	[-.05in]	( 0.00 )	( 0.00 )	( 0.00 )
	[.03in]	Yes	Yes	Yes
	Demo. Control
	Time Dummy	No	Yes	Yes
	State Dummy	No	No	Yes

On the procyclicality of advertising and customer relationship building expenditures, along with their implications for product market frictions, see[START_REF] Hall | The cyclical response of advertising refutes counter-cyclical profit margins in favor of product-market frictions[END_REF] and[START_REF] Gourio | Customer capital[END_REF]. For a flow approach to a typical

We also denote by a subscript x or y the first-order derivative of any function of x and y. For instance, the full differentiation of the consumption surplus with respect to a change in income ω and price p is given by: d∆v = (vy(x, ω -px) -vy(0, ω)) dω -xvy(x, ω -px)dp = (vy(1) -vy(0)) dω -xvy(1)dp = ∆vydω -xvy(1)dp(1)

See Appendix A.2 for a more general case where the inequality holds under imperfect substitutability between y and x.

Appendix B.1 provides the ATUS time use codes that compose each category.

We have attempted to identify the reasons for this discrepancy with the BLS in private communications but have so far been unsuccessful.

Appendix B provides more details for these deletions. The results for the whole age sample change very little. The results are available upon request.

Unlike the CPS, which is designed to produce reliable estimates at both the state and national level, the ATUS only has a national reliability requirement. Less populous states constitute a smaller proportion of the ATUS sample

The ATUS provides two family income variables -hufaminc for 2002-2009 and hefaminc for 2010-2012 -with the distinction that the second variable has been edited to leave no empty responses.

There are six income categories: (1) $0 to $24, 999; (2) $25, 000 to $49, 999; (3) "$50, 000 to $74, 999; (4) $75, 000 to $99, 999; (5) $100, 000 to $149, 999, and; (6) $150, 000 and over. The table reports the estimated coefficients on income categories 2 to 6. The demographic controls are for age, education, gender, marital status, race, and the presence of children. LFS" stands for the inclusion of a labor force status indicator. We restrict our sample to respondents aged 25-54 and with zero unclassified time for 66,958 observations in total. The asterisks *, **, and *** denote statistical significance at 10%, 5%, and 1% levels, respectively.

The ATUS time use categories used to measure market hours of work are: 05-01, 05-02, 05-99, 18-05.

This is shown in Appendix A.7.1. However, this result does not hold in the general case derived in Appendix A.7.2.

See Appendix A.7.3 for details.

The special case where agents choose hours worked while they search for goods corresponds to the case α(e0) = 0. The special case where agents choose hours worked while they consume corresponds instead to α(e0) = 1.

§ Petrosky-Nadeau thanks Stanford's Hoover Institution where part of this research was conducted for its support. Etienne Wasmer acknowledges support from ANR-11-LABX-0091 (LIEPP), ANR-11-IDEX-0005-02 and ANR 2010 BLANC 1819 01 (EvalPolPub). These views are those of the authors and do not necessarily reflect the views of the Federal Reserve System. The authors thank Bob Hall and Elisa Guglielminetti for comments and discussions. We also thank Thomas Brzustowski for excellent research assistance.

a matter of fact, whereas total time spent purchasing goods and services is about 20 minutes per day, the component of shopping time devoted to comparing prices and products seems to be extremely low in the data. It is about 4 seconds a day on average, given the large number of respondents declaring zero. Moreover, nonparticipants and the employed spent more time than the unemployed in this activity. This may indicate that most of the effort made by consumers in the goods market is unrelated to uncovering better prices.

The data used in this paper are the best available from a macro perspective. More precise information about consumer shopping efforts should be obtained from microeconomic data such as consumer surveys. This is left for future works.

Appendix

A Theory

A.1 Individual consumption probability: a more general specification of prematch search effort

At the individual level, one could assume that the probability of finding a particular good is given by λe 0 / ē1-a 0 , in which a ≥ 0. When a = 0, the most frequent assumption explored in the text, only the ratio of individual to aggregate effort matters for the individual finding rate. In contrast, assuming a positive value for a allows for a potential positive externality from consumer search effort. In essence, if my neighbors search for a good, they may transmit some information to me thereby increasing the probability of locating a particular good.

A key insight here is that allowing for a positive a does not change the results on cyclicality. Indeed, the aggregate level of effort does not change the cyclicality of individual search effort. Assume a utility function where the value of leisure is perfect substitute (linear additive from consumption) ; the model becomes equivalent to having a cost function of effort denoted by σ(e 0 ). Denote by η c its elasticity greater than 1 (convexity). In a symmetric equilibrium, we have d(lnē 0 )/dlnΩ c = (η c -a) -1 . Thus, d(lnē 0 )/dlnΩ c > 0 under the sufficient condition that a < 1 even for positive consumption externality a > 0.

A.2 Non-separable utility

One could write the utility function as:

where X and Y are increasing concave functions of their input, and Z is a complementary function with ∂ 2 Z/(∂y∂x) > 0 and Z(0, y) = Z(x, 0) = 0. This reflects the interaction between x and y. b is a scalar that may be zero in the case of perfect separability, and positive (negative) depending on the degree of complementarity (substitutability) between the two consumption goods. The important property for the main discussion on consumer search effort is the sign of

The first term in brackets is positive due to the concavity of utility in goods y. If the second term is assumed to be positive, e.g., if Z(x, y) = xy, it is sufficient that the value of b is not too negative, e.g. Z(x, y) = xy, it suffices that b is larger than the negative of Y y (ω -px) -Y y (ω) to preserve a positive sign of ∆v y .

A.3 Price setting -Nash bargaining:

The results are similar under a formal Nash-sharing rule with the exception that the marginal utility of the composite good y now affects the bargained price. Assuming equal bargaining weights, the price is set to maximize the Nash-product [∆v] 1/2 [px -κ(x)] 1/2 , and must satisfy a sharing rule similar to equation ( 5) but with the marginal utility of goods y appearing in the denominator of the consumption surplus ∆v:

A positive, procyclical, shock to income ω, dω, keeping the marginal cost κ constant, leads to (see Appendix for the derivation):

x dp dω = ∆v y v y (1) -v yy (1)∆v 2v 2 y (1) -v yy (1)∆v with the same conclusion as we found previously by the fact that v yy < 0. The effect of an income shock on the price and surplus remains positive. It is still the case that consumer search effort is procyclical.

A.4 Endogenous supply of the search good x

On the other side of the market, a seller has a cost of providing the search good κ(x), with κ x , κ xx > 0. The seller's surplus to the match is

Fixing e 1 , we now assume that, at the time of the match, sellers can react to the demand of matched consumers by varying instantaneously their production of x at cost κ(x). Different pricing and bargaining assumptions may be introduced here.

A.4.1 Nash-bargaining on both price p and quantity x

Assume that the seller and the consumer can bargain over two dimensions: p and x. The Nash problem is:

The maximization of the Nash-product with respect to the price leads to a pricing rule identical to equation (A.2). The maximization of the Nash-product with respect to the quantity produced leads to

Combining (A.2) and (A.4) leads to the equality between the marginal production cost and the marginal utility of the good divided by its marginal utility cost:

Again, the key for the elasticity of consumer search effort to an income shock is the response of the surplus Ω c = ∆v. This can be decomposed by differentiating equation (2) into income, quantity, and price effects:

Change in income:>0

Change in price

The direction of search effort with endogenous price and quantity is ambiguous. The income effect raises the surplus but, if the price increases with income, this will reduce the surplus. Moreover, the quantity effect may increase or decrease the surplus depending on the sign of the bracketed term, which is positive if the marginal utility from consumption 1 (being able to consume the search good) exceeds its opportunity cost pv y . One may presume that the production of the search good in a match is increasing in income ω and decreasing in the price p, while the price increases with income. In that case, under small marginal utility of the composite good y (small v y ) and large marginal utility from the search good (large v x ), the positive effect would dominate.

A.4.2 More specific cases

Some additional results can be obtained in specific cases. First, if utility is linear in y , then both x and p become independent of income ω. Therefore the consumer's surplus and search effort in A.7 Supplemental Appendix to Section A.4.1: Optimal consumption choice when x is endogenous A.7.1 Simpler case of y as a numeraire

Start from equations (A.2) and (A.4). Under separability and constant marginal utility for the composite (the case of a numeraire) these equations simplify to: .16) where v(1) = X(x) + (ω -px) and ∆v = X(x) -px. This implies that ∆v is independent of income, and therefore replacing xp -κ(x) in the equation (A.15):

This last equality implies that x is such that the elasticity of the function g(x) ≡ X(x) + κ(x) is 1. It follows that both the price and quantity of x are independent of income, and so is the surplus.

A.7.2 General case under separability of x and y

The full system represented by equations (A.2) and (A.4) must be differentiated to obtain the variations of p and x in response to a change in ω. Before doing so, one can rewrite the utility function v(x, y) = X(x) + Y (y) and manipulate the two equations to obtain:

The second equation can be differentiated to obtain:

The functions are evaluated at consumption point 1. That is, Y and its derivatives are evaluated at ω -px , and X and κ and their derivatives are evaluated at x. This equation defines a linear relation between dp, dx, and dω. The first equation can also be differentiated to provide another linear relation between these variations:

where d∆v can be obtained as

In this general case, both x and p vary with income ω.

A.7.3 Markup pricing and bargaining over quantity

If one assumes that the quantity x is chosen so as to divide the surplus into equal shares, while the price is equal to the marginal cost of production with a markup to account for ex post monopoly (b) Gas: 07-01-02.

(c) Food: 07-01-03.

3. Travel Time associated with shopping for goods and services: 18-07, 18-08, 18-09, 18-12-04.

B.2 Labor force status in the ATUS

The ATUS sample is a subset of the CPS sample. We verify how the estimates of labor force status -employed, unemployed, and nonparticipant -line up with the population estimates provided by the BLS based on the CPS. The five possible labor force statuses in the ATUS are: (1) employed -at work; (2) employed -absent;

(3) unemployed -on layoff; (4) unemployed -looking, and; ( 5) not in the labor force. Let D i be the dummy variable for labor status, which equals one when the correspondent is in a given labor status and zero otherwise. The formula for calculating the percentage of the population in one labor status is given by:

where wt i is the final weight assigned by ATUS. The formula can be applied to a subsample of the same interview year and age group. We compare the implied labor participation rate and unemployment rate from ATUS to those provided by the BLS. The ATUS labor participation rate is defined as the sum of employed and unemployed as percentages of population, and the unemployment rate is defined as the ratio of unemployed to the sum of employed and unemployed. The CPS participation rate is the ratio of the civilian labor force to the civilian non-institutional population, and the unemployment rate is the ratio of the unemployment level to the civilian labor force. Annual participation and unemployment rates from both ATUS and BLS are plotted in Figure B.2. The ATUS participation rate for the age group 16 and over is 5.6% higher than the CPS rate, on average. A closer look and different age groups reveals that the difference is 15.2% for the 16 to 24 age category, 3.3% for ages 25 to 54, and 3.7% for ages 55 and over. The ATUS unemployment rate for ages 16 and over is 1.1% higher than the CPS rate, on average. Again, the difference is largest for the 16 to 24 group, 5.5%, while it negligible for those between 25 and 54, -0.1%, and for those over 25 is 0.4%.

Age 55 and Over

The solid line and dashed line represent the CPS and ATUS, respectively. The left column of figures compare the participation rates from ATUS and CPS, and the right column of figures compares the unemployment rates from ATUS and CPS. For ATUS, the participation rate is calculated as the sum of employed and unemployed as a percentage of the population, the unemployment rate is the ratio of the unemployed to labor market participants. For CPS, we calculate the participation rate as the ratio of the civilian labor force to the civilian noninstitutional population, and unemployment rate as the unemployment level to the civilian labor force.