Testing the Infrequent Purchases Model Using Direct Measurement of Hidden Consumption from Food Stocks

Transcription

1 Testng the Infrequent Purchases Model Usng Drect Measurement of Hdden Consumpton from Food Stocks John Gbson and Bonggeun Km Abstract Reports of zero expendture on ndvdual commodtes durng the reference perod of a household survey are a frequent but awkward feature of appled demand analyss. These zeros may come from two dstnct phenomena: () genune non-consumpton, whether for economc or non-economc reasons, and () purchases that happen too nfrequently to be captured wthn the survey reference perod, wth hdden consumpton out of stocks. Dstngushng between these types of zeros s dffcult n the dsaggregated survey data ncreasngly used by demand analysts. Hence econometrc models for nfrequent purchases rely on untested hypotheses. In ths paper we test such models, usng data from an unusual household survey where food stocks are measured at the start and end of the survey reference perod. Parameter estmates usng these drect measures of hdden consumpton out of stocks are compared wth estmates from nfrequent purchase models that attempt to recover ths hdden consumpton. The results suggest consderable bas when usng the nfrequent purchase models. Keywords: Engel curves, food consumpton, nfrequent purchase, storage JEL Codes: C81, D12 Department of Economcs, Prvate Bag 3105, Unversty of Wakato, Hamlton 3240 New Zealand (e-mal: jkgbson@wakato.ac.nz) Department of Economcs, Seoul Natonal Unversty, Gwanangno 599, Gwanak-gu, Seoul, Korea (e-mal: bgkm07@snu.ac.kr)

2 I. Introducton Understandng how consumer demand shfts n response to ncome changes s fundamental to many areas of economcs. The surveys used to estmate Engel curves and ncome elastctes typcally observe households for only a short perod; ca days for foods. Because t s possble to eat from food stocks, a household may be observed to spend nothng on a food that t nonetheless eats, causng bas n estmated demand parameters (Keen, 1986). Ths ssue also arses n developng countres, where consumpton s not only from the market but also from own-producton. Eatng s more frequent than harvestng, and n the extreme of seasonal crops that are then stored, the harvest occurs only once whle consumpton out of that harvest lasts for many months. But surveys that ndrectly derve consumpton from questons on purchases, own-producton, and nter-household transfers typcally mss the hdden consumpton from food stocks. 1 Econometrcans have developed nfrequent purchase models that attempt to recover ths hdden consumpton, startng wth the p-tobt model of Deaton and Irsh (1984). These models adopt a two-equaton structure, wth a latent purchase equaton for whether spendng occurs n the survey reference perod followed by a Tobt of the spendng level (ncludng zeros). Consumpton s estmated as the product of the odds of purchase and the observed spendng, and wth a long enough reference perod s observatonally equvalent to spendng. Thus, for households wth postve purchases of a food durng the survey, the reported value s 1/p tmes consumpton durng the survey perod, where p s the rato of the length of the survey perod to the length of the purchase perod. For example, f a household buys a sack of rce every four weeks and the survey reference perod s one week, then p=0.25 and for 1 Some surveys drectly ask about food consumpton, along the lnes of what dd you eat yesterday? but these tend to be used more by nutrtonalsts than economsts, n part because they have lmted nformaton on total household resources, whch are needed to model demand behavour (Deaton, 1997). We do not consder these types of drect consumpton surveys n our analyss below and nstead focus on surveys that are structured accordng to the varous means of acquston of commodtes (purchases, own-producton, transfers), whch ncludes all household budget surveys n developng countres and many lvng standards surveys. 1

3 households buyng rce durng the survey (wth ths probablty beng p, f no household has a corner soluton), the reported expendture s four tmes the rate of weekly consumpton. Clearly ths problem s wder than just one of zero reported purchases. A household may supplement foods purchased durng the survey perod wth takngs from stocks, so that reported spendng s not zero but stll understates actual consumpton n the reference perod. Conversely, spendng may overstate consumpton f stocks are beng bult up durng the survey perod. Allowng other forms of commodty acquston, such as from own-producton and nter-household transfers also does not alter the problem. As long as food has some durablty and there are transactons costs (e.g. the food gardens n the settng provdng the data used below are often an hour travel from dwellngs), consumpton wll occur more frequently than own-producton and there s potentally hdden consumpton out of stocks. The p-tobt and nfrequent purchase models (IPMs) descrbed by Blundell and Meghr (1987) are ncreasngly used because many demand studes now utlse dsaggregated household survey data, so zeros n dependent varables are more common. 2 For example, Nordstrom and Thunstrom (2009) use IPMs to study demand for 32 separate gran products n household budgets, wth the occurrence of zero expendture on ndvdual products as hgh as 92 percent. But despte the growng relevance of these models, there s yet to be a crtcal test of ther dentfyng assumptons, n part because of lack of sutable data. In ths paper, we use unusual data from a survey where food stocks are observed at the start and end of the reference perod, so that hdden consumpton out of stocks can be measured. Despte the attenton of econometrcans to nfrequent purchase and storablty, many surveys assume that food s non-storable and do not measure food stocks. 3 Wth the extra nformaton on the estmated consumpton from stock changes we can dstngush 2 Of the 71 ctatons n the ISI Web of Scence to Deaton and Irsh (1984), 14 are for artcles publshed snce 2005, whle 19 of the 74 ctatons to Blundell and Meghr (1987) are for artcles snce Even n papers that are motvated by the nfrequent purchase problem, the examples that are gven of durablty beyond the short reference perod of the survey exclude food at home (e.g., Kay et al, 1984, p.170), presumably because of the mplct assumpton that food has no storablty. 2

4 between non-consumpton and purchase nfrequency as reasons for zero observed expendture on partcular foods. Moreover, we can form a measure of consumpton for each food that has versmltude (that s, s closer to the truth) over other measures based just on purchases (and other acqustons), and compare parameter estmates that use the drect measures of hdden consumpton out of stocks wth estmates from IPMs that attempt to recover ths hdden consumpton. A further advantage of our data s that the survey reference perod vared across households, so t s possble to test f the IPMs perform better when the reference perod s longer. Such a test would not normally be possble because n most surveys, whle the reference perod may vary across commodtes (longest for sem-durables and shortest for foods), for a gven commodty all households are observed for the same tme. Ths testng of IPMs s needed snce these models rely on dentfyng assumptons to dstngush them from other models of zero expendtures that are derved from qute dfferent household behavor. Specfcally, zero expendtures also may occur because the household s a genune non-consumer of the good, due ether to abstenton (for non-economc reasons such as health or relgous preferences) or to a corner soluton where the household contans potental consumers of the good who cannot afford t at current ncome and prces. In the case of abstenton, the double-hurdle model of Cragg (1971) s typcally used, where a Probt models the partcpaton decson and a Tobt models the expendtures, and economc varables should be excluded from the partcpaton equaton (Jones, 1992). Wth corner solutons, the assumpton s that demand for the good s censored from below at zero and a Tobt model s conventonally used. However, wthout pror nformaton, t s not possble to be certan of the cause of the observed zeros (Meghr and Robn, 1992) and so the choce of emprcal specfcaton s just based on the dentfyng assumptons. The remander of the paper s as follows. In Secton II, we provde a smple measurement error model and relate our model to the estmaton models for non-consumpton 3

5 and nfrequent purchase. In Secton III, we descrbe our data and report the emprcal results. Secton IV concludes wth a summary of the man fndngs. II. Models for Zeros We present a smple model to llustrate how errors n measurng consumpton affect demand analyss. It helps at the outset to dstngush between three consumpton varables: latent * consumpton, y ; actual consumpton durng the survey perod, y ; and observed acqustons (purchases) durng the survey perod, y. Latent consumpton s observable n prncpal, but only f actual consumpton occurs, snce y * s assumed to be normally dstrbuted and hence may be negatve. It s ths latency whch gves rse to the classc Tobt model, wth ts assumpton of censorng at zero (corner solutons), and nothng done n ths paper to drectly measure hdden consumpton from stocks alters that feature of demand data. Observed acqustons durng the survey perod are the sum of actual consumpton, whch ncludes hdden consumpton out of stocks, and an error term: y = y + ε (1) where ε represents the dfference between the two measures. When y = 0 and y > 0 the classc case of zeros due to nfrequent purchases occurs. However, equaton (1) also covers other measurement errors, such as acqurng a small quantty durng the survey perod wth remanng consumpton comng from stocks, or conversely acqurng a much larger quantty than s eaten durng the survey perod and buldng up stocks. When the classc Tobt model s appled to food demand data, t s based on the assumpton that ε = 0, so: y = y = y. (2) * max(0, ) 4

6 and n the regresson model that underles much appled demand analyss, wth latent consumpton as the dependent varable, a set of x consumpton determnants (e.g., ncome) and 2 u ~ N(0, σ ) representng preference heterogenety n demand: y = xβ + u, (3) * the sample lkelhood functon s: ln L=Σ ( lnσ + ln φ(( y xβ)/ σ)) +Σ ln(1 Φ ( xβ / σ)) (4) + 0 where Σ + s the summaton for households wth postve consumpton and Σ 0 s the summaton for households wth zeros, whle Φ() and φ() represent the standard normal cumulatve and densty functons. But when a household survey s not able to observe all consumpton durng the reference perod, because of hdden consumpton from unmeasured food stocks, ε 0, and * cases of y = 0 do not necessarly correspond to max(0, y ) = 0. Thus, these are not genune corner solutons. To deal wth ths, the lterature on IPMs defnes D as a latent varable for whether an acquston (purchase) occurs durng the survey perod ( D > 0 f and only f y > 0 ) and P s the probablty of purchase. Ths yelds: E( y ) = E( y D > 0) P + E( y D 0)(1 P) = E( y D > 0) P (5) and to derve the new censorng rule the lterature assumes that E( y ) = E( y ) or E( y D > 0) P = E( y ) accordng to equaton (5). By usng ths assumpton, the new censorng rule s y * / Φ ( zθ ) f y > 0 y = 0 otherwse (6) 5

7 where Φ ( zθ ) = P s the probablty of purchase from a model where D = zθ + w and the z are determnants of purchase probablty and w ~ N (0,1). Under ndependence, 4 the probablty that postve consumpton occurs wth no purchase occurrng over the short survey perod s (1 Φ( zθ )) Φ ( xβ / σ) and the correspondng sample log-lkelhood functon s 0 ln L=Σ ( lnσ + 2ln Φ ( xβ / σ) + ln φ(( Φ( zθ) y xβ) / σ))) + +Σ ln(1 Φ( zθ) Φ ( xβ / σ)), (7) When Φ ( z θ ) = 1 or a good s non-storable, equaton (7) becomes the Tobt model of equaton (4). The dscrepancy between acqustons, y and consumpton, y that s caused by storablty s corrected by the nfrequent purchase model by the assumpton, E( y ) = E( y ). However, f some non-consumpton zeros are ncorrectly treated as nfrequent purchase zeros, then the estmate of Φ ( zθ ) = P s upwardly based and the nfrequent purchase model overestmates consumpton. The falure of ths assumpton may also cause based estmates of ncome elastctes of demand and t s that emprcal mplcaton that we focus on here. III. Emprcal Analyss A. Survey Context Data used n ths paper come from the 1996 Papua New Gunea Household Survey (PNGHS), based on a random sample of 1200 households for whom 1144 have complete nformaton on all varables used here. Some results are reported separately for rural (n=830) and urban (n=314) sub-samples snce the transactons costs of food acquston and resultng ncentves to store food may vary by sector. The PNGHS s a mult-topc survey smlar to the Lvng 4 Many subsequent papers usually focus on dstrbutonal assumptons of the estmaton technques developed by Deaton and Irsh (1984) and Blundell and Meghr (1987) n ther applcatons to tobacco (Kmh, 1999), clothng demand (Majma, 2008), savngs and remttances (Snnng, 2007). 6

8 Standards Measurement Surveys of the World Bank. 5 Consequently, the food consumpton module s less detaled than n household budget surveys, wth only 36 separate food groups dstngushed, rather than the 100 or more typcally used for a budget survey. But even wth these less detaled groups, almost 55 percent of households reported zero expendtures (ncludng zero non-market acqustons) on the typcal food group durng the survey perod and the food wth the fewest reported zeros stll had 13 percent report zeros. A key feature of the survey for our purposes s that t used bounded recall, where ths desgn was orgnally chosen to restrct the scope for telescopng errors. 6 Specfcally, the start of the recall perod was sgnaled by the frst ntervew and n the second ntervew households were asked about purchases, own-producton and net transfers receved n the tme elapsed snce the frst ntervew. Ths desgn gves two potental advantages for testng IPMs; varaton n the perod over whch consumpton s observed, and the possblty of measurng startng and endng food stocks so that what s typcally hdden consumpton out of food stocks can be drectly observed. In terms of the varaton n recall length, the second vst was desgned to be approxmately two weeks after the frst ntervew. However the very dffcult topography and poor transport nfrastructure n PNG meant these return vsts were sometmes sooner and other tmes later, dependng on the logstcs of movng survey teams around. Whle the medan bounded recall perod was 14 days, the standard devaton s 3.65 days. Almost eght percent of households had a recall perod of only one week and one percent had a three-week recall. Hence there s some varablty n the length of the observaton perod, whch we can use to test the hypothess that the performance of IPMs mproves when the observaton perod lengthens. Ths would not be possble n other surveys, whch ether use a dary for a fxed 5 Detals on the survey and data downloads are avalable at: 6 Wth telescopng, a respondent compresses purchase occasons and other forms of acquston that occurred over a longer perod of tme nto the reference perod and thus the reported value of acqustons exceeds the true value over that perod. 7

9 perod (typcally two weeks) or else use a sngle vst (unbounded) recall where the respondent s asked about acqustons n the last week, fortnght or month, wth the perod dependng on the type of commodty, but wth no varaton across households n the recall perod for the same commodty. In terms of observng what typcally s hdden consumpton from stocks, durng the frst ntervew the enumerators weghed the begnnng food stocks for 18 foods. The endng stocks of these same foods were reweghed at the second ntervew so that stock change could be measured. Several of these foods are not produced by households (e.g., rce and flour are mported, and sugar, canned fsh and canned meat are commercally produced). Stockng of these foods reflects nfrequent purchase behavor, possbly to explot pecunary economes from buyng larger volumes (e.g. a 25-kg rce sack). In ths respect, these foods are no dfferent to the stuaton n prevous uses of IPMs n developed countres. In terms of the own-produced foods, are all harvested non-seasonally snce PNG s n the humd tropcs and lacks both a regular monsoon and a dry season. In ths regard, the settng s smlar to equatoral Afrca (e.g. Rwanda, Burund and Uganda). Despte the lack of seasonalty, harvestng s not as frequent as consumpton due to transactons costs, snce food gardens can be more than an hour walk from the dwellng, especally n the mountanous hghlands areas. Also, relgous and socal commtments mean that people do not go to ther food gardens every day. The locally produced crops are manly plantans and root crops, whch are storable for about a month. These locally grown foods are also wdely purchased, but nfrequently due to the transactons costs of gong to market, snce the rural populaton s poorly served by roads and many markets only open for lmted tmes each week. 7 7 Gbson and Rozelle (2003) note that the average household n PNG s 2.5 hours from the nearest road, and 3 hours from the nearest government staton (the equvalent of a market town). Hence there are large transactons costs n gong to market. 8

10 These purchase and producton characterstcs mean that household food stocks may be large, but not so mpossbly large as to prevent accurate measurement. For example, the foods wth the largest stocks recorded were cassava and yams, wth average holdngs of about nne klograms (kg) amongst stockholders, and a maxmum of 90 kg. For a famly of fve, ths maxmum stock could feed them for 20 days f the stocked food provded half of daly calores. Hence ths s far shorter storage than may occur n hghly seasonal envronments but stll exceeds the reference perod used by almost all surveys and so allows a role for hdden consumpton from stocks. Amongst the store-bought foods, rce was most heavly stocked, wth average holdngs of 7 kg amongst stockholders and a maxmum of 50 kg. Stocks of other store-bought foods averaged about 2 kg (flour and sugar) or less than one kg (canned foods), wth maxma of 25 kg (flour and sugar) or up to 10 kg (canned foods). Ths unusual envronment, where t s feasble to measure food stocks at the start and end of the survey, s of lttle nherent nterest snce few other countres have the same characterstcs. But t provdes a good opportunty to test the nfrequent purchases model snce we are unaware of any survey elsewhere n the world where hdden consumpton from food stocks has been drectly measured n ths manner. B. Descrptve Results Table 1 reports descrptve statstcs on the mportance of hdden consumpton from stocks. Although stock measurements were made for 18 foods, we focus here only on 10 of them, gnorng the fresh meats, sago and sweet potato. The fresh meats are the one group of foods where corner solutons may represent non-economc motvatons (e.g., PNG has many Adventst households wth relgous prohbtons on eatng pork). To allow the cleanest comparsons between the Tobt on y and the IPM on y we exclude the meats, whch may have non-economc reasons for zeros. Sago s gnored because t s only grown and consumed n a small area of PNG whle sweet potato s gnored because ts IPM estmates would not 9

11 converge. Nevertheless, the 10 foods consdered comprse just under one-quarter of the total household budget, rangng from banana at 5.6 percent to flour at 0.7 percent (Table 1). The budget shares are smlar, whether based on consumpton, y or observed acqustons, y. Ths s to be expected n a non-seasonal envronment, snce households may be addng to, as well as runnng down, food stocks. 8 How mportant s hdden consumpton from food stocks? The thrd column of Table 1 reports the proporton of households who recorded zero acqustons of each food durng the survey perod but for whom consumpton actually occurred out of stocks. One-sxth of households reported no acquston of bananas (plantans), but actually consumed them from stocks. Whle the proportons are lower for the other foods, averagng just over sx percent, there s stll a non-trval fracton relyng entrely on storage to provde ther consumpton of each food durng the survey perod. (Table 1 about here) Even though the proportons n column 3 relate to the zero expendtures (acqustons) that motvated the development of IPMs, ths s not the full extent of hdden consumpton. In column 4, the proporton of households acqurng less food durng the survey than ther consumpton out of stock s reported. Ths stuaton can be thought of as partally-hdden consumpton and s surprsngly frequent. Around one-quarter of households consumed more coconut, sugar, yams and rce from stocks than ther recorded acqustons, whle for the other foods the proportons are at least one-tenth. That both store-bought and own-produced tems are n the group where a hgh proporton of households have partally hdden consumpton ndcates that the nfrequent purchase ttle s a msnomer and that the problem of hdden consumpton from food storage s more wdespread than prevously thought. 8 In a country where an annual harvest s stored and then consumed over many months, t would be expected that y > y for any survey that occurs outsde the harvest perod. 10

12 To provde an estmate of the overall mportance of hdden consumpton for each food, column 5 reports the weghted average of the proportons n columns 3 and 4. Accordng to ths average, hdden consumpton from storage s most mportant for banana, coconut, rce and sugar. These foods offer the most favorable condtons for the IPMs because when the degree of storablty of a food ncreases more of the zeros are due to nfrequent purchase. Hence, fewer non-consumpton zeros (corner solutons) wll ncorrectly be assumed to be nfrequent purchase zeros. Thus, a negatve relatonshp between the degree of bas n the IPMs and the storablty of foods s expected. C. Econometrc Results Recall from Secton 2 that the am of the IPMs s to gve parameter estmates that rely not just on observed acquston of the food but also on the hdden consumpton recovered by the latent purchase equaton. To see how well ths procedure works n practce, we estmate two sets of demand models, whch are both n budget share form. The frst apples the classc Tobt model to y, our data on actual consumpton durng the survey perod that uses the drect measurements of what typcally would be hdden consumpton out of stocks. We use a Tobt model snce observng ths hdden consumpton does nothng to obvate the censorng at zero due to corner solutons. The second model s an nfrequent purchases model, appled to the survey data on y (acqustons, as measured from purchases, own-producton and net transfers) whch gnores the hdden consumpton from stock changes. Snce equatons (4) and (7) have the same parameters from the underlyng lnear model of latent demand, we should get the same ncome elastctes of demand, from the two sets of estmates. The budget shares for the demand model are based on shares of total expendture, 9 whch n addton to the 36 foods, ncludes 20 types of frequently purchased non-foods, an 9 Therefore we do not assume any mult-stage budgetng, and the estmated expendture elastctes can be drectly nterpreted as ncome elastctes, rather than needng to be frst combned wth parameters from a multstage budget allocaton equaton. 11

13 annual recall of 31 nfrequent expenses and the value of the flow of servces from durables and owner-occuped dwellngs. The measure of household ncome used s the logarthm of real total expendture per capta, whch s deflated for prce dfferences over both tme (the survey was staged over 12 months) and space (deflators for fve regons). Ths s the best estmate of permanent ncome avalable from the survey and captures the total economc resources avalable to households. We also use household sze and the share of household members n varous age and gender groups, the characterstcs of the household head (under the assumpton that ths person has some nfluence over famly dets) and the regon n whch the household s located as control varables n the Engel curve estmaton. How well do the IPMs replcate the results of usng Tobt on the data where the hdden consumpton out of stocks s drectly measured? The results n Table 2 suggest that the IPMs provde substantally based estmates of the elastctes, compared wth what s calculated from drect measurement of consumpton from stocks. For example, although flour, sugar, and canned meat are all luxures accordng to the Tobt estmates, the ncome elastctes estmated by the IPMs are only 0.45, 0.72 and The pattern of lower ncome elastctes comng from the IPMs holds for eght of the ten foods studed, and for fve of the eght there s no overlap of the 95 percent confdence ntervals for the ncome elastctes for the same food from the two estmaton procedures. Amongst these fve wth statstcally sgnfcant dfferences n the ncome elastctes, the degree of bas n the IPM estmates ranges from 30.2 percent for rce to 81.4 percent for flour. (Table 2 about here) The ncome elastctes from budget share models are calculated as: ( w) [ β + 1], where β s the coeffcent on ncome n the budget share regresson and w s the budget share. The 10 Readers n rch countres may be surprsed that ncome elastctes of food demand could be so hgh. But n a poor country (headcount poverty from PNGHS was 38 percent) wth sgnfcant undernutrton (42 percent of the PNG populaton dd not meet food energy requrements), food overall has a hgh ncome elastcty of demand, and these partcular foods have been ntroduced to the det and are effectvely luxures. 12

14 estmates reported n Table 2 are evaluated at the mean budget shares. Hence, the ncome elastctes could dffer ether because average budget shares dffer, or because of dfferent estmates of β. In fact, the average budget shares are very smlar when usng ether acqustons or consumpton (as seen prevously n columns 1 and 2, Table 1). However, the estmates of β are statstcally sgnfcantly dfferent between the IPM results on acqustons and the Tobt results on consumpton so the bas n the ncome elastctes s comng from the parameter estmates of the IPMs. 11 In addton to showng the large bases n the IPM estmates of the ncome elastctes, the results n Table 2 also llustrate the negatve correlaton between the bas and the degree of storablty of the food. When the bas estmates n column 5 are compared wth ether the share of households recordng zero acqustons of each food but for whom consumpton actually occurred out of stocks (column 3, Table 1) or the share wth smaller acqustons than the consumpton from stocks (column 4, Table 1), sgnfcant negatve relatonshps are apparent. The Spearman (rank) correlaton coeffcents are and -0.56, and both are statstcally sgnfcant at the p<0.09 level. Thus, the foods that have the hghest degree of storablty have the least bas n the IPM estmates, because wth hgher storablty more of the zeros are actually due to nfrequent purchase and so there s less scope for non-consumpton zeros (corner solutons) to be ncorrectly treated as nfrequent purchase zeros. The IPM elastcty estmates n Table 2 are from equatons wthout excluson restrctons, so that x = z. From our readng of the lterature, ths s common practce n the appled 11 Another concern wth the elastctes n Table 2, and wth the unreported parameter estmates from the Tobts and IPMs underlyng them, may be that there s a logcal nconsstency n usng a dependent varable that ether does or does not measure hdden consumpton from stocks, whle the emprcal proxy for the man ndependent varable ncome always uses the data on consumpton out of stocks for the 18 foods where stocks were measured. We beleve that the more comprehensve the measure of consumpton, whch here ncludes stock change, the better t wll proxy permanent ncome of the household. However, we also redefned total per capta consumpton to exclude the contrbuton of stock changes and used ths (worse) proxy for permanent ncome n a replca of the regressons that contrbute to Table 2. The result of a sgnfcant downward bas n the estmates of the ncome elastctes from the IPMs was unchanged. For the fve foods wth sgnfcant dfferences between the IPMs and the Tobts, the new estmates of the ncome elastctes were (IPM, Tobt): sugar (.759, 1.477), tnned meat (.537, 1.300), flour (.467, 2.345), tnned fsh (.494,.949), rce (.701,.958). 13

15 demand studes that use IPMs; the same set of covarates used to explan demand are used to predct whether a purchase occurs n the survey perod. Relyng on functonal form assumptons to dentfy parameters may not produce robust results, as the lterature on excluson restrctons n Heckman models has shown. 12 We therefore re-estmated the IPMs wth varous exclusons mposed. To reduce clutter, the results shown n Table 3 are for just two of the foods where the IPM ncome elastctes showed sgnfcant dfferences from the Tobt elastctes; rce and sugar. Imposng a varety of excluson restrctons makes no dfference to our concluson that ncome elastctes from the IPMs substantally understate the ncome elastctes comng from the more correct procedure of the Tobt model appled to data where hdden consumpton out of stocks s drectly measured (Table 3). The excluson restrctons that we used are for varables that relate to the transactons costs of gong to stores or markets, whch could make households shop nfrequently and stock foods, and the scope for food storage n the home. Specfcally, for transactons costs we use the number of hours needed to reach the nearest transportaton network (road, arstrp or boat launchng place), the number of trade stores and markets n the respondent s vllage, and an ndex of market development (the total number of stores, markets and transport busnesses n the vllage). For storage opportuntes we use the floor area of the dwellng and whether t has an ron roof. These varables almost always have the predcted sgn n the frst stage model for whether a purchase s reported (negatve for remoteness and dwellng attrbutes, postve for the others) and are statstcally sgnfcant. But ncludng these varables n the purchase probablty equaton but not n the demand equaton makes almost no dfference to the ncome elastcty estmated by the IPMs. The ncome elastcty estmates for sugar range from , compared wth when no excluson restrctons are used, and for rce from compared wth when 12 See for example XXX (YYYY). Bonggeun can you fnd a reference n labour lterature to a paper crtcsng lack of excluson restrctons. Maybe even to Deaton 1997 f nothng comes to hand. 14

16 just relyng on the functonal form assumptons. Thus the bas n the IPM estmates of the elastctes does not appear to be comng from ncorrect excluson restrctons. Next we turn to explan why the IPM provdes systematcally based estmates. Although the recall perod averaged 14 days, t vared from about 8 to 25. Wth ths varance n the observaton perod, we can devse another test for the assumpton of E( y ) = E( y ). We hypothesze that the IPM should work better for households who had a longer recall perod than those wth shorter, thus we could splt the sample n half and test for better performance of the IPM wth the longer observaton perod (greater than or equal to 14 days). Table 4 confrms our predcton and the dscrepancy between the ncome elastctes of purchase and that of consumptons becomes much smaller wth the longer observaton perod. The pattern s smlar for nne foods as the ncome elastctes of consumpton substantally decrease from those of the full sample whle those of purchase do not change from those of the full sample. One way to nvestgate the causes of bas s to see whether the basc assumpton of nfrequent purchase models s vald by drectly comparng two measures of expendtures: the self-reported purchase expendture, y and the true consumpton, y. Snce storablty of goods s assumed to cause the dscrepancy between self-reported expendtures and true consumptons, the IPM assumes that observed and latent expendtures are the same on average over the long survey or observaton perod as the dentfyng assumpton, E( y ) = E( y). As the IPM argues, the dscrepancy between y and * y could be manly caused by storablty of purchased goods (e.g. storable purchased 20 kg rce sack n urban areas of PNG). The assumpton of E( y ) = E( y ) wll be safe for the case of purchased storable goods, but t may not be vald for the case of seasonally produced goods. For the 15

17 storablty of purchased goods, the type of measurement error ( ε ) would be random. It s because some households purchased 20 kg rce sack just before the survey started and so usng typcal survey would have lower than true expendture of goods, and others who purchased durng the survey and had not consumed all by the end of survey perod would have reported expendtures hgher than true consumptons. Ths type would lead to that observed and latent expendtures are the same on average over the long survey or observaton perod as the dentfyng assumpton, E( y ) = E( y ). However, the measurement errors n the seasonally produced storable goods are more lkely to be non-random because outsde of the harvest perod, the households are only drawng down ther stocks, not ncreasng the stocks. There s not counterpart to buyng a 20 kg rce sack durng the survey perod. Ths type of measurement errors would lead to E( y ) = E( y ). Ths predcton s confrmed by our data and Column 1 of Table 3 shows that the assumpton of E( y ) = E( y ) s rejected at conventonal level of sgnfcance for four foods under H : ( ) ( ) 1 E y < E y. Especally, the assumpton s rejected for three foods (sugar, flour, and rce) where there s no overlap wth the 95 percent confdence ntervals surroundng the ncome elastcty wth true consumptons. Furthermore, f the type of errors s dependent on where people lve and ts correspondng purchase and self-producton patterns, then the test results for the assumpton of E( y ) = E( y ) may be dfferent between urban and rural areas where there s dfference n the structure of rural and urban dets. For example, on any gven day, almost 90 percent of urban resdents may be found eatng rce whle the rate for rural resdents s only one-quarter. The error types due to locaton specfc consumpton patterns could lead to dfferent test results across areas and Column 2 and 3 of Table 5 support ths predcton. For fve foods, the assumpton s rejected n one area (ether urban or rural) but not n the other area. Table 4 16

18 provdes the alternatve test results for the assumpton of E( y ) = E( y ) wth H : ( ) ( ) 1 E y E y. IV. Concluson Reports of zero expendture on ndvdual commodtes durng the reference perod of a household survey are a frequent but awkward feature of appled demand analyss. Infrequent purchase models have been developed to deal wth ths problem of hdden consumpton out of household stocks but have not been able to be tested because of lack of sutable data. In ths paper we use data from an unusual household survey wth drect observaton of food stock changes durng the perod of the survey. Parameter estmates usng these drect measures of hdden consumpton out of stocks are compared wth estmates from nfrequent purchase models that attempt to recover ths hdden consumpton. For fve out of the ten foods used n the test, the nfrequent purchase model gave a sgnfcantly dfferent estmate of the ncome elastcty of demand for the food than dd the Tobt model appled to the data that drectly measured hdden consumpton from stocks. Specfcally, the ncome elastcty was based downwards for all fve of these foods. The bas s much smaller for the sub-sample of households for whom expendtures were measured over a longer perod. Thus, the IPM works least well when appled to demand data observed over a short observaton perod, whch s the type of stuaton that the model s desgned for. These results suggest that further effort should be made to test the nfrequent purchases models that have been developed n the lterature, and to come up wth robust procedures for uncoverng hdden food consumpton from stocks. 17

19 References Bozot, C., Robn, J-M., and M. Vsser. (2001), The demand for food products: An analyss of nterpurchase tmes and purchased quanttes, The Economc Journal, 111(Aprl): Blsard, N. and Blaylock, J. (1993), Dstngushng between market partcpaton and nfrequency of purchase models of butter demand, Amercan Journal of Agrcultural Economcs, 75(2): Blundell, R. and Meghr, C. (1987), Bvarate alternatves to the Tobt model, Journal of Econometrcs, 34: Deaton, A. and Irsh, M. (1984), Statstcal models for zero expendtures n household budgets, Journal of Publc Economcs, 23: Deaton, A. (1997). The Analyss of Household Surveys: A Mcroeconometrc Approach to Development Polcy. Baltmore: Johns Hopkns Unversty Press. Gbson, J. and Rozelle, S. (2003), Poverty and access to roads n Papua New Gunea, Economc Development and Cultural Change, 52: Jones, A. (1992), A note on computaton of the double-hurdle model wth dependence wth an applcaton to tobacco expendture, Bulletn of Economc Research, 44: Kay, J., Keen, M., and Morrs, C. (1984), Estmatng consumpton from expendture data, Journal of Publc Economcs, 23: Keen, M. (1986), Zero expendtures and the estmaton of Engel curves, Journal of Appled Econometrcs, 1: Kmh, A., (1999), Double-hurdle and purchase-nfrequency demand analyss: A feasble ntegrated approach, European Revew of Agrcultural Economcs, 26(4): Majma, S. (2008), Fashon and frequency of purchase: womenswear consumpton n Brtan, , Journal of Fashon Marketng and Management, 12(4): Meghr, C. and Robn, J. (1992). Frequency of purchase and the estmaton of demand Systems, Journal of Econometrcs, 53:

20 Nordström, J. and Thunström, L. (2009) The mpact of tax reforms desgn to encourage healther gran consumpton, Journal of Health Economcs, 28: Newman, C., Hencon, M., and Matthews, A. (2001). Infrequency of purchase and doublehurdle models of Irsh households' meat expendture European Revew of Agrcultural Economcs, 28(4): Shnnng, M. (2007), Determnants of savngs and remttances: Emprcal evdence from mmgrants to Germany, IZA Dscusson Paper No

21 Table 1. Sample Statstcs and Storablty Parameters, PNG data, N=1144 Varable Budget Shares Proporton of zeros wth hdden y y consumpton Proporton of all households wth hdden consumpton Average Storablty Mean(SE) Mean(SE) Proporton Proporton Proporton Sugar.0089(.0144).0093(.0170) Tnned meat.0165(.0007).0167(.0008) Flour.0066(.0184).0082(.0299) Tnned fsh.0173(.0243).0173(.0243) Banana.0561(.0852).0549(.0835) Coconut.0126(.0262).0132(.0260) Yam.0189(.0579).0189(.0560) Cassava.0112(.0318).0111(.0306) Rce.0380(.0490).0410(.0510) Taro.0397(.0797).0389(.0763) Note: average storablty s a weghted average of the shares wth completely hdden consumpton from stocks (column 3) and the shares wth partally hdden consumpton from stocks (column 4). 20

22 Table 2. Expendture Elastctes, PNG data, N=1144 Varable Acqustons (1) SE Consumpton (2) SE Bas (=1 (1)/(2)) Sugar a Tnned meat a Flour a Tnned fsh a Banana Coconut Yam Cassava Rce a Taro Note: Superscrpt a ndcates that there s no overlap of the 95 percent confdence ntervals for the ncome elastcty estmates n column (1) and column (2). 21

23 Table 3. Senstvty Analyss: Use of Varous Excluson Restrctons Varable Sugar Rce No Excluson Restrcton IVs IPM Income Elastcty Bas Acquston Decson Coeffcent (SE) IPM Income Elastcty Bas Acquston Decson Coeffcent (SE) IV1: Hours to Nearest Transportaton IV2: # of Trade Stores n Vllage (.0003) c (.0005) c (.0091) c (.0210) c IV3: # of Markets n Vllage (.0410) (.0694) c IV4: Index of Market Development (.0073) c (.0216) c IV5: Floor Area of Dwellng (.0019) (.0020) b IV6: Dwellng has Iron Roof (.1108) c (.1181) b Note: Superscrpt a, b and c represent the levels of statstcal sgnfcance of 10%, 5% and 1% respectvely. 22

24 Table 4. Expendture Elastctes wth Dfferent Observaton Perods Varable Bas Bas Bas Total Sample Longer Observaton Shorter Observaton N=1144 Perod, N=633 Perod, N=511 Sugar Tnned meat Flour.814 N/A.914 Tnned fsh Rce

25 Table 5. Tests for the Assumpton of the IPM, PNG data, N=1144 Varable Total Rural N=1144 N=830 D = E( y ) E( y) t-test t-test H : E( y ) = E( y) 0 HEy : ( ) Ey ( ) 1 Urban N=314 t-test Sugar p =.136 p =.201 p =.402 Tnned meat p =.256 p =.421 p =.424 Flour p =.028 b p =.035 b p =.534 Tnned fsh p =.879 p =.855 p =.980 Banana.0011 p =.244 p =.150 p =.132 Coconut p =.021 b p =.010 a p =.883 Yam.0006 p =.924 p =.961 p =.767 Cassava p =.791 p =.517 p =.154 Rce p =.018 b p =.148 p =.010 b Taro.0007 p =.361 p =.338 p =.847 Note: Superscrpt a, b and c represent the levels of statstcal sgnfcance of 10%, 5% and 1% respectvely. 24

26 Income Elastctes: Sugar Consumpton+Tobt Acquston+IPM Acquston+Tobt % Confdence Interval Income Elastctes: Rce Consumpton+Tobt Acquston+IPM Acquston+Tobt % Confdence Interval 25