sou · GTB357d11 · 2006-01-01 00:00:00 — 13 The hourly compensation paid by employers have been obtained as the total compensation divided by the total number of hours worked, as described in the National Accounts. The data on average marginal tax rates have been obtained from du , Ratio. (1 t2) price of leisure is determined by pf (1+t3) (1+t1)(1+t3) (1+t1)(1+t3) is the total tax wedge., where wage is the compensation paid by the employer, t1 is the payroll tax rate, t2 is the income tax rate and t3 is the indirect tax rate. All prices in this study are measured including indirect taxes and wages excluding payroll taxes. The price on leisure is therefore simply the wage rate net of the average marginal tax rate. The simplest formulation would be to use the budget restriction i=1 piqi = pnT + A; for T = h + q See Dowd (1992) or Madden (1995) for similar treatments. 16 An alternative would be to measure non-labor income as is done by Dowd (1992). He measures A as the di¤erence between private disposable income and labor income and sets T = 24. 24 b= the total number of hours available ml= the number of hours worked 1mu= the number of hours worked in home production and labor search by those unemployed 2m(b (l+u))= the number of hours worked in home production and labor search by those outside the labor force nb= the number of subsistence hours worked in home production, sleeping, etc. by the adult population The formula can be simplied to (24 n) b m [l 1u 2(b (l + u))] Data are available on all variables less i and n, for which some assumptions are necessary. The basic assumption is ( 1 = 0:5; 2 = 0:2; n = 12). For a fully employed person this means that the daily leisure time is (24-12-8=4) hours, for an unemployed person it is (24-12-4=8) hours and for a pensionist (24-12-1.6=10.4) hours. As alternatives in a sensitivity analysis we also use1 = 0:4&0:6; 2 = 0:1&0; 3; n = 11&13, a total of 27 combinations. On the whole, elasticities were not very sensitive to this choice. The nal choice was done on a judgemental basis in which the requirement of theoretically correct signs on the parameters was the most important. The empirical results are presented extensively in the data appendix. Here some summary results from the estimations are presented. In general the goodness of t of the estimated equations are satisfactory, which can be seen in Table 2. Summary statistics for estimated demand systems. Stage 1: 1 Group 1: 1_1 Group 2: 2_1 Group 3: 3_1 Group 4: 4_1 Group 5: 5_1 Group 6: 6_1 The rst column shows the goodness of t of the individual equations in In stage 1 R for all equations except Transports are around 0.95. For Transports it is 0.70. The second column shows the mean of the dependent variable revaling that the mean of the budget share of goods consumption for 1980-1998 is 57 percent while for leisure it is 43 percent. The percentage stan- dard error (of the regression) is around 0.35 for all goods except Transports for which it is 0.6 percent. For leisure the standard error is 0.65 percent. The fourth column of Table 2 shows tests for autocorrelation in the individual equations. This test is done by running an unrestricted VAR with 2 lags on the estimated residuals of the systems. The number of observations times R2 is then treated as chi-square distributed with degrees of freedom equal to the number of variables on the right-hand side of each equation, i.e. a LM test17 . The autocorrelation tests show no sign of autocorrelation in the six equations in Stage 1. Turning to Stage 2 it can be noted that the t is generally somewhat lower. 1 Food is the biggest category, accounting for 65 percent within the group and totally (0.65 0.15) 100 = 9.8 percent with a 0.8 percent standard The R = 0:9 for Food but there is some autocorrelation in this equation. 17 See (1984). However, the other equations in Group 1 show no sign of autocorrelation so that autocorrelation in the group as a whole can be statistically rejected. The t of the Housing - Group 2 - equation is 0.95 and the standard error is 0.4 percent. The budget share is 16 percent, 28 percent of total consumption (less leisure). 3 autocorrelation is rejected in all equations. However, the t is rather poor in this group. 4 there is autocorrelation in 4_2 - Transports. The t is rather poor in this category - 0.68. Finally, in Group 5 there is autocorrelation in three of the ve groups: 5_1, 5_4 and 5_5, while there is no sign of autocorrelation in the aggregate as revealed in the equation for Group 5 in the Stage 1 estimation. Estimated elasticities are presented in the data appendix. Here, some summary results are presented. In Table 3, the total elasticities dened in (11) are shown. The within-group elasticities - also dened in (11) - are presented in the data appendix. Total long run compensated own-price and total expenditure elasticities. Estimated at mean values for the period 1994-1998. Food including light beer Housing, fuel, and furniture Recreation including cultural activities All compensated own-price elasticities are negative and all total expenditure elasticities are positive. Food, Housing and Leisure are necessities and all other goods luxuries. Price elasticities are relatively low for necessities and relatively high for luxuries which is in line with the intuition. The demand is price inelastic for all goods belonging to the rst three groups of Stage 1 and for Miscellaneous goods, Insurance and Leisure. It is elastic for and recreation and for Books and magazines. The VAT on books were recently reduced from 25 to 6 percent which eventually would lower prices by some 15 percent and conse- quently increase demand by almost 25 percent in the long run (the compensated own-price elasticity is -1.55). However, notice in Table 4 below that the short run elasticity is only -0.15. Total short run compensated own-price and total expenditure elasticities. Estimated at mean values for the period 1994-1998. Food including light beer Housing, fuel, and furniture Recreation including cultural activities Table 4 shows the corresponding short run elasticities. These are the direct e¤ects of changes in prices and total expenditure, i.e. that occur within a quarter. In most cases the absolute value of the elasticity is smaller in the short than in the long run. This supports the interpretation of adjustment costs or habit formation in the demand for these goods. This applies to all total expenditure elasticities except Leisure for which the short run elasticity is 1.23 - a luxury - while being only 0.49 in the long run - a necessity. The short run compensated own-price elasticities are abolutely higher than the corresponding long run elasticities for 8 of the 19 goods, i.e. for all goods in Group 3. Why would the short run elasticity overshoot and exceed the long run elas- ticity? This would likely occur for goods where demand is very exible and the degree of habit formation low. These e¤ects are particularly strong for Clothing and shoes, Household utensils, and Hotels. For these categories the response to a change in the relative price has a large immediate e¤ect but declines in the long run. For the categories Housing, Transports and Miscellaneous the initial response is instead relatively small but increases to reach a peak at the long run value. Short and long run own-price elasticities at temporary and permanent price changes. We can distinguish not only between long and short run elasticities but also between the response to temporary and permanent changes in prices and total expenditure (full income). In Figure 1 the dynamic response to relative price changes are shown. The charts show the own-price elasticities as a response to temporary and permanent changes in relative prices18 . The elasticities in the gure converge to the long run uncompensated own-price elasticities estimated 18 The shocks are one-percentage shocks in the relative prices in the rst quarter in 1994 and the responses are measured as the percentage change in demand and shown for the remainder of the sample period (elasticities).As can be seen in the charts, the long run e¤ects are reached within approximately 2 years. in Stage 1 and given in Table B1 in the data appendix. A temporary price change has a temporary demand e¤ect which lasts for about 2 years. The overshooting property can be seen particularly for Household and personal care and Leisure. The response which could be expected due to the presence of adjustment costs can be noticed in particular for Housing, fuel and furniture, Transports and vacation goods and services. The elasticities also vary over time due to variations in budget shares, prices and full income, as apparent from the denitions of elasticities in (22) - (29). These variations are illustrated in Figures 2 and 3 which show long run com- pensated own-price elasticities and total expenditure elasticities, respectively. As can be seen in Figure 2 the long run compensated own-price elasticities are all negative and fairly stable during the sample period. For some categories there seems to be a shift in the beginning of the 90ie. In absolute terms, the elasticity decreases for Food and Household and personal care and increases for Transports, Miscellaneous and Leisure. and personal care the elasticity decreases from approximately -0.4 to -0.25 while for Mis- cellaneous goods and services the elasticity decreases from about -1.6 to -2.1. The labor supply elasticity is low but become more elastic during the sample period and increases from about 0.05 to 0.1. This could be due to the tax re- form in the beginning of the 90ies which shifted taxes from labor to goods. We tried to include a dummy for the period before 1990 but it was not statistically signicant. In Figure 3 the long run total expenditure elasticities are shown. They are all positive and lowest for the Food, Housing and Leisure categories. The elasticity drops from about 0.75 to 0.6 for Food, increases from .1 to .2 for Housing and from .4 to .5 for Leisure. Though the elasticities vary they are fairly stable during the sample period. The responses shown in Figure 1 indicate that the initial labor supply response is quite large but declines in the long run. The short run uncompensated response is about -.6 while in the long run the elasticity is about -.4. The compensated response is quite lower - around -.09. The relatively high short run gures may be interpreted as a response in hours to temporary changes in demand with a corresponding change in compensation. In many occupations this increase in compensation may be more or less automatic (and negotiated) and hence both wages and labor supply become exible with respect to excess demand in the short run. These results are in line with what previously have been found by (1983) and and Hansson-Brusewitz (1990) for Swedish household data on mensand womenslabor supply19 . It is interesting to compare the results for demand systems with and without Leisure, since the measurement of Leisure in itself seems uncertain. We do that by estimating the Stage 1 demand system with and without Leisure. The results are presented in Table 5. 19 Surveys of labor supply are Pencavel (1986) and Killingsworth and Heckman (1986). Comparison of uncompensated price and total expenditure elasticities with and without Leisure in Stage 1. At mean values 1994-1998. First, the classication of necessities and luxuries are the same20 , though the total expenditure elasticities are higher particularly for the groups 3, 4, and 5. This depends on Leisure being classied as a necessity with a large budget share. Own-price elasticitities are all negative in the system with Leisure but 2 - Housing, fuel and furniture - has a positive, but insignicant, elasticity in the system without Leisure. Own-price elasticities for groups 4 and 5 are more elastic in the system with Leisure. Notice also that the high positive cross- price elasticity between 5 and 1 - 1.09 - is -0.01 in the system without Leisure. Another high cross-price elasticity in the system with Leisure is between 3 and 2 - -0.87 - which is lower, -0.27, in the system without Leisure. 5.4Comparison with previous results The results are compared to previous empirical results in Table 6. The table is incomplete and only presents a small sample from the literature. Generally, it seems as if the elasticities estimated here are fairly reasonable. 20 Note however that strictly the classication should be done with respect to the compen- sated elasticities. Comparison of uncompensated price and total expenditure elasticities estimated in di¤erent models in Stage 1. a) and (1983) b)Blanciforti and (1983) c)(1993) d)Pollak and (1992) e)(1996) The own-price elasticities for Food and Housing are similar to those found in other studies. This is true also for Household and personal care though this category is probably not directly comparable with other studies. The Transports and Miscellaneous categories turn out to be relatively elastic here with the elasticities -1.84 and -2.12 respectively, which can be compared to the next highest which are -1.09 and -1.62 in (1993). Again, these categories may not be directly comparable. The total expenditure elasticity for Food is in line with other studies while those for Household and personal care, Transports and Miscellaneous seem to be relatively high here. Again, this is not quite comparable to the results in other studies since most of them use total expenditure less the consumption value of Leisure, while here full income is used. This paper has analysed the demand for consumer goods and services as well as the demand for leisure in a simultaneous equations model for Swedish aggre- gate time series data. The usual weak separability assumption between leisure and consumption goods has not been adopted here. A dynamic version of the in error correction form has been estimated and price and total expenditure elasticities for consumption goods and leisure have been estimated simultaneously. All goods and leisure have been divided into 19 categories in a two-stage budgeting process in which the rst stage comprises 6 categories of which Leisure is one. The price of leisure time is estimated as the wage rate net of the average marginal tax rate. The estimate of fullincome is then conditional on the mea- surement of leisure time which is subject to a sensitivity analysis in which the number of hours used for home work and labor search is varied across di¤erent population groups. Even if weak separability is assumed when demand is estimated within the di¤erent consumption categories there are relationships beween the categories that can be explored. This is done here and within-group elasticities as well as total elasticities are estimated. Estimations are carried out with the dynamics specied as an error correction model. Homogeneity as well as symmetry restric- tions are imposed. Restrictions are also imposed on the dynamic specication in order to arrive at a coherent system. A weak test of weak separability is done in the form of tests for simultaneity bias. Tests for autocorrelation is also carried out. Equations - in budget share form - are with some exceptions estimated with good t and the elasticities turn out with the correct signs and with reasonable precision. All long run as well as short run compensated as well as uncompensated own-price elasticities are negative and all total expenditure elasticities are positive. Categories classied as necessities with total expendi- ture elasticities less than one have generally lower price elasticities than luxury goods, as is usually the case also in other studies. Necessities are typically Food and Housing. On the other hand, categories like or Books are classied as luxury goods and have long run compensated price elasticities well above minus unity. The price elasticity for Leisure is the labor supply elasticity (with opposite sign). The long run compensated labor supply elasticity is here 0.1 which is in line with previous estimates for Swedish households on micro data. The short run elasticity is higher than the long run elasticity which might reect strong short run intertemporal substitution. In the context of optimal taxation the cross-price elasticities are interesting, especially those between Leisure and the various consumption goods. Generally, these elasticities use to be estimated with much less precision than the own-price elasticities and this is the case here also. Most of the cross-price elasticities are fairly close to zero with some notable exceptions. Alessie, R. and A. Kapteyn (1991), "Habit Forming and Interdependent Preferences in the ", , 101, 404- 419. , J.M., K.A. and (1994), "Estimating Elasticities with the ", Review of Eco- nomics and Statistics, 76, 351-356. , B., (1991a), "Efterfrågan på alkohol i ", Bilaga 1 till Alko- holskatteutredningen, Allmänna förlaget. (1991b), "Alcohol Pricing Policy and the Demand for Alco- hol in ", Demand Study SW/9, , , . (1996), "in ", in Edgerton et al (1996). (1997), "Efterfrågan på tjänster i . Beräkning av efter- frågeelasticiteter och sysselsättningse¤ekter", Bilaga 2 till Tjänstebeskattning- sutredningens betänkande Skatter, tjänster och sysselsättning, SOU 1997:17. Stiglitz (1980), Lectures on Public Economics, Maid- enhead: . (1983), "The E¤ect of Income Taxation on the Labor Supply of Married Men", , 22, 196-197. and U. Hansson-Brusewitz, (1990), "The E¤ect of Taxes on and Female Labor Supply in ", , 25, 317-357. (1994), "Evaluating the ", , 76, 781-793. Chalfant, J.A. (1987), "A ", Statistics, 5, 233-242. , L.R., D.W. (1975), "Transcendental Logarithmic Utility Functions", , 65, 367-383. Deaton, A. and J. Muellbauer (1980a), "", Deaton, A. and J. Muellbauer (1980b), Economics and Consumer Behavior, . Dowd, K. (1992), "Consumer Demand, Full Incomeand Real Wages", Em- pirical Economics, 17, 333-345. Edgerton, D. (1992), "Estimating Elasticities in Multi-Stage Demand Sys- tems", ? Edgerton, D. (1993), "On the Estimation of Separable Demand Models", Economics, 18, 141-146. Edgerton, D., B. , A. Hummelmose, I. Laurila, K. Rickertsen and P.H. (1996), The Econometrics of . With Applications to Food Demand in the Nordic Countries, Kluwer Academic Publishers. (1984), ", Likelihood Ratio, and Lagrange Multiplier Tests in Econometrics", Ch. 13 in Handbook of Econometrics, Vol. 2, eds. Z. Griliches and M.D. Intriligator, : . , L. and N.A. Klevmarken (1990), "E¤ekter på den privata konsum- tionen av de indirekta skatternas prishöjning", i Agell, J., K-G Mäler and J. , Ekonomiska perspektiv på skattereformen, Ekonomiska rådets års- bok. Gorman, W.M. (1959), "Separable Utility and Aggregation", American Eco- nomic Review, 27, 469-481. (1993), "Testing for Separability Between Commodity Demand and Labour Supply in West ", Empirical Economics, 18, 21-56. Kesavan, T, Z.A. , (1993), "Dynamics and Long-Run Structure in U.S. Meat Demand", tural Economics, 41, 139-153. Killingsworth, M.R. Heckman, (1986), "Female Labor Supply: A Survey", in Handbook of Labor Economics, Vol. 1, eds. O. Ashenfelter and R. Layard, : . Klevmarken, N.A. (1979), "A Comparative Study of Functions", , 10, 165-191. Klevmarken, N.A. (1981), On the Approach to Demand Analysis, : . Madden, D. (1995), "Labour Supply, Commodity Demand and Marginal Tax Reform, , 105, 485-497. Pencavel, J. (1986), "Labor Supply of Men: A Survey", in Handbook of Labor Economics, Vol. 1, eds. O. Ashenfelter and R. Layard, : . Pollak, R.A. (1981), "Demographic Variables in Demand Analysis", Econometrica, 49, 1533-1551. Pollak, R.A. (1992), Specication and Esti- mation, : . Pudney, S.E. (1981), "An Empirical Method of Approximating the Separable Structure of Consumer Preferences", Review of Economic Studies, 48, 561-577. (1992), Microeconomic Analysis, : . Long run uncompensated price elasticities Long run total expenditure elasticities Long run compensated price elasticities Long run uncompensated price elasticities Long run total expenditure elasticities Long run compensated price elasticities Short run uncompensated price elasticities Short run total expenditure elasticities Short run compensated price elasticities Short run uncompensated price elasticities Short run total expenditure elasticities Short run compensated price elasticities Long run uncompensated price elasticities Long run total expenditure elasticities Long run compensated price elasticities Standard errors of uncompensated price elasticities Standard errors of total expenditure elasticities Standard errors of compensated price elasticities Standard errors of uncompensated price elasticities Standard errors of total expenditure elasticities Standard errors of compensated price elasticities Standard errors of uncompensated price elasticities Standard errors of total expenditure elasticities Standard errors of compensated price elasticities Standard errors of uncompensated price elasticities Standard errors of total expenditure elasticities Standard errors of compensated price elasticities Standard errors of uncompensated price elasticities Standard errors of total expenditure elasticities Standard errors of compensated price elasticities Long run uncompensated price elasticities. Calculated at mean values. -0.061407 -0.012039 -0.025400 -0.011718 -1.996960 0.104168 0.160538 0.379566 -0.324142 -0.688106 -1.622606 Long run total expenditure elasticities. Calculated at mean values. Long run compensated price elasticities. Calculated at mean values. -0.028225 -0.005644 -0.011836 -0.005554 -1.851061 0.132370 0.219953 0.406833 -0.288914 -0.613717 -1.588469 Long run uncompensated price elasticities. Calculated at 1994-1998 mean values. -0.070242 -0.014693 -0.031830 -0.014576 -2.006127 0.111567 0.168793 0.397719 -0.313151 -0.670373 -1.596716 Long run total expenditure elasticities. Calculated at 1994-1998 mean values. Long run compensated price elasticities. Calculated at 1994-1998 mean values. -0.038018 -0.007943 -0.017174 -0.007952 -1.866718 0.140734 0.231823 0.426464 -0.276005 -0.589918 -1.560017 Short run compensated price elasticities. Calculated at mean values. -0.021744 -0.304484 Short run total expenditure elasticities. Calculated at mean values. Short run compensated price elasticities. Calculated at mean values. -0.002656 -0.005023 -0.001657 -0.386887 -0.122249 -0.646178 -1.586865 -0.517446 Short run uncompensated price elasticities. Calculated at 1994-1998 mean values. -0.005192 -0.001097 -0.002391 -0.001069 -0.004744 -0.001002 -0.002184 -0.000976 -0.021614 -0.316230 Short run total expenditure elasticities. Calculated at 1994-1998 mean values. Short run compensated price elasticities. Calculated at 1994-1998 mean values. -0.456257 -0.209973 -0.605388 -1.443442 -0.651449 -0.376686 Long run uncompensated price elasticities. Calculated at 1994-1998 mean values. Long run total expenditure elasticities. Calculated at 1994-1998 mean values. 0.453754 0.527394 1.451610 1.797440 1.503694 Long run compensated price elasticities. Calculated at 1994-1998 mean values. Statistical significance of elasticities Stage 1: Standard errors and p-values evaluated at mean values for the period 1994-1998. Estimated uncompensated price elasticities and the total expenditure elasticity, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero. Estimated compensated price elasticities, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero. (-0.09) Group 1: Standard errors and p-values evaluated at mean values for the period 1994-1998. Estimated uncompensated price elasticities and the total expenditure elasticity, standard errors (within parentheses) and p-values [within brackets] for the null hypothesis that the elasticity equals zero.