The price elasticity for alcohol in Sweden 1984 2003

THOR NORSTRÖM Research report The price elasticity for alcohol in Sweden 1984 2003 Introduction The price of alcohol is considered to be one of the most important instruments for regulating overall consumption. This is because the demand for alcohol is sensitive to price changes, and the government has good control over prices through excise taxes. However, the possibilities for a single country like Sweden to pursue a sovereign price policy has decreased as a result of increasing economic integration. Particularly the combination of practically abolished import quotas and low alcohol prices in Denmark and Germany has created a troublesome situation. This has spurred a marked increase in the private import of alcohol which undermines the legitimacy of Swedish alcohol policy. If the Swedish government chooses to adjust excise taxes to the lower levels of other countries it is important to have a solid basis of knowledge for determining the effects on consumption and harm. The aim of this study is to analyse some issues that concern the relationship between the price and demand for alcohol. The next section presents these issues. A Swedish version of this article was published as: Norström, T. (2005) Priselasticiteten för alkohol 1984 2003. In: Gränslös utmaning alkoholpolitik i ny tid. SOU 2005:25, 409 429. ABSTRACT T. Norström: The price elasticity for alcohol in Sweden 1984 2003 AIMS The article addresses the following research questions: (i) How strong is the price elasticity for beer, wine and spirits? (ii) How rapid is the effect of a price change? (iii) Is the price elasticity stable across time and space? (iv) Does an increase in price give a corresponding effect as a decrease? METHODS & DATA The sales data cover Systembolaget s retail sales of beer, wine and spirits for the period from January 1984 to March 2004. The price indexes are based on weighted baskets deflated by a consumer price index. Most of the analyses were performed on quarterly data. The data were analysed using the Box-Jenkins technique for time series analysis. RESULTS The price elasticities as estimated from quarterly data were statistically significant for all beverages; -0.8 for beer, -0.6 for wine and and -1 for spirits. Similar estimates were obtained from monthly data, suggesting a fast consumer response to price changes. The elasticity for beer was weaker during the period 1995 2004 (-0.6) than during the period 1984 1994 (-1.4), but it was no different in southern Sweden than in the remainder of the country. An increase in the price of spirits seems to affect sales as much as a price decrease, that is, the price effect seems 87

to be symmetric. Finally, the results indicated that since 1995 sales of beer and wine increased more, and spirits sales less, than predicted from the development in prices. CONCLUSIONS The study confirms previous findings that the demand of alcoholic beverages is responsive to changes in price; however, price is not the sole factor that drives the trends in sales. The reduced elasticity for beer may be due to the marked drop in beer prices. What are the price elasticities for beer, wine and spirits? Existing reviews concerning price elasticities for alcohol show a large range in the estimates (Ornstein 1980; Ornstein & Levy 1983; Österberg 1995; Österberg 2001). For instance, the estimated elasticities for beer vary between 0 and -3 (Österberg 1995). Also after the elimination of extreme values, large differences remain. These may reflect actual variations across time and space in sensitivity to price, but in addition differences in data quality and model specification have probably much impact on the outcome. When estimating price elasticities one is in many countries confronted with two fundamental methodological problems that hardly apply to Sweden; one concerns the issue of exogenity, the other relates to data quality. Even though one should expect a relationship between price and the demand for alcohol the direction of the link is not evident when a negative correlation is observed. A price increase should decrease demand, but decreasing demand may also induce sellers on the market to reduce their prices. In a free market price cannot be expected to be exogenous (i.e. independent of demand) which complicates estimations of price elasticities. An advantage of the Swedish alcohol market in this context is that prices are not adjusted according to demand but indeed are exogenous. Another advantage is that the data on sales as well as prices are detailed and of high quality. In the US, for instance, price data are based on direct observation in certain stores of the prices for selected brands. Since these brands are not always representative, and only account for a fraction of total sales, these price series have considerable measurement errors that create problems in statistical analyses of the relationship between prices and sales (Young & Bielinska-Kwapisz 2003). Swedish data thus provide a sound methodological basis for estimating the price elasticity for alcohol. How quickly is the impact of a price change realized? It is common to distinguish between short-term and long term elasticity, where the latter is usually the stronger of the two. A motorist who faces an increased petrol price when getting into the station hardly refrains from filling up because of that. On the other hand, it is likely that s/he will reduce driving for pleasure, and, when it is time to replace the car 88

s/he might switch to one that requires less petrol. In this example there is a long-term adjustment to the increased price, so that it takes some time before the price change has reached its full effect. How quickly do drinkers respond to a price change? According to several studies the long-term elasticity exceeds the short-term elasticity in the context of alcohol (Edwards et al. 1994). However, on the basis of these findings it is difficult to infer how the time horizon looks, that is how long time it takes before the impact of a price change is realized. Is the price elasticity stable across time and space? The price elasticity for a product is usually higher if there exists an alternative. Against this background we should expect that the elasticity would become stronger when the travellers allowances increased in January 1995, which made cheaper alcohol more available. One should also expect geographical differences in the elasticity. The increased travellers allowances spurred a marked increase in the private import of beer, particularly in southern Sweden. A study by Norström (2000) shows a clear geographical gradient in this effect: it decreases proportionally to the square of the distance to Helsingborg (where it is strongest). Can a corresponding pattern be found in the sensitivity to price changes? Does a price increase yield a corresponding effect as a decrease in price? Due to the addictive character of alcohol it is conceivable that the price effect is asymmetrical in the sense that a reduction in price yields a stronger impact than a corresponding price increase. Data and methods Sales data refer to Systembolaget s (The State Alcohol Monopoly s) retail sales of beer, wine and spirits expressed in litres of 100% alcohol. Price indexes are based on weighted baskets that are deflated by the cost of living index. Changes in price depend partly on actual price changes, partly on changes in drinkers preferences towards cheaper or more expensive alcohol. The latter source of change implies that the price is not entirely exogenous; however, this drawback has to be weighed against the drawbacks that a fixed basket implies. Original data are on a monthly basis with a regional division (counties) and cover the period January 1984 March 2004. For most of the analyses the data have been aggregated into quarterly data for the whole country. One of the complications that are often encountered in statistical analyses of time series data is that the series are trending, which is also the case here (see figures 1 3). This may give rise to spurious relationships since two series may evolve in the same (or opposite) direction without being causally related to each other. Another complication is the structure of the error term; the error term includes among other things causal factors that are not included in the analysis. One of the prerequisites in ordinary regression analysis is that the error term does not have any structure. In time series analysis this assumption is not realistic since explanatory variables that are left out can be expected to be autocorrelated, that is to have a structure. In the present case there is the additional complication of seasonal variation that is found in monthly and quarterly data. 89

The complications that have been described here are taken into consideration in the technique for time series analysis that has been developed by Box and Jenkins (1976), often referred to as ARI- MA-modelling. By means of differencing the series are made stationary. This means that rather than analysing the relationship between the raw series Y t and X t we analyse the relationship between the changes, that is between Y t and X t, where Y t =Y t -Y t-1. The differencing reduces the risk for spurious relationships, even if it is not eliminated. Another feature of ARI- MA-modelling is that the error term structure is estimated and incorporated into the model. This increases the reliability of the model estimates. A log-log model of the following specification was used: lns t = elnp t + N t S is sales, P real price, and e denotes the elasticity coefficient that is to be estimated. N (noise) is the noise term that includes other causal factors. The noise structure is estimated in terms of autoregressive and moving average-parameters. These are of two kinds; regular: AR(n) and MA(n), respectively (where n denotes the order of the parameter), and seasonal: SAR(n), and SMA(n), respectively. An important criterion of model fit is that the residuals are white noise. This is determined by means of the Box-Ljung test. To illuminate the issue of the temporal stability of the price elasticity separate analyses are performed for the periods 1985:1-1994:4 and 1995:1-2004:1. County specific analyses elucidate the issue of regional differences in the price elasticity. By comparing elasticity estimates based on monthly data with those based on quarterly data we get an indication of how fast a price change is realized. The topic of a possible asymmetry in the price effect is handled through the inclusion of a dummy variable with feasible coding. Results The sales of beer, wine and spirits depict fairly dissimilar trends during the study period (figures 1 3). Sales of beer and wine were fairly stable until 1998, when a strongly increasing trend started. There is a decreasing trend for spirits sales during the entire period. The prices have been fairly stable for all beverages, with no marked trends. The largest price change is noted for beer which decreased by about 15% in January 1997 due to a tax cut. The correlations between the trends in prices and sales are generally negative (table 1), which though should be interpreted with great caution. However, the negative correlations remain after seasonal differencing (table 1, figures 4 6). 90

4.0 3.5 3.0 2.5 2.0 1.5 1.0.5 1984-85 -86-87 -88-89 -90-91 -92-93 -94-95 -96-97 -98-99 2000-01 -02-03 -04 Figure 1. Sales of beer (solid line) and real price of beer (broken line). Index 1984:1=1. 2.2 2.0 1.8 1.6 1.4 1.2 1.0.8 1984-85 -86-87 -88-89 -90-91 -92-93 -94-95 -96-97 -98-99 2000-01 -02-03 -04 Figure 2. Sales of wine (solid line) and real price of wine (broken line). Index 1984:1=1. 91

1.4 1.2 1.0.8.6.4.2 1984-85 -86-87 -88-89 -90-91 -92-93 -94-95 -96-97 -98-99 2000-01 -02-03 -04 Figure 3. Sales of spirits (solid line) and real price of spirits (broken line). Index 1984:1=1. 400 000 Beer sales, litres (seasonally differenced) 300 000 200 000 100 000 0-100 000-200 000-300 000 -.3 -.2 -.1 -.0.1 Real price, beer (seasonally differenced).2 Figure 4. Relationship between real price and sales of beer (litres 100%). Seasonally differenced quarterly data 1984:1 2004:1. 92

600 000 Wine sales, litres (seasonally differenced) 400 000 200 000 0-200 000-400 000 -.08 -.06 -.04 -.02 0.00.02.04.06 Real price, wine (seasonally differenced).08 Figure 5. Relationship between real price and sales of wine (litres 100%). Seasonally differenced quarterly data 1984:1 2004:1. 400 000 Spirits sales, litres (seasonally differenced) 200 000 0-200 000-400 000-600 000 -.08 -.06 -.04 -.02 0.00.02.04.06.08 Real price, spirits (seasonally differenced).10 Figure 6. Relationship between real price and sales of spirits (litres 100%). Seasonally differenced quarterly data 1984:1 2004:1. 93

Table 1. Correlation between sales and real price of beer, wine and spirits. Based on quarterly data for the period 1984:1 2004:1 Raw data Seasonally differenced Beer -0.62-0.18 Wine -0.12-0.33 Sprits -0.51-0.38 Estimation of the price elasticitities Table 2 summarizes the results for the price elasticitities (complete model estimates are found in the Appendix). All estimates but one are negative and statistically significant. It can be noted that the elasticity for beer becomes markedly lower after 1994; during the first period it is -1.4, compared to -0.6 during the period after 1994. The elasticity for wine is at approximately the same level during both of the periods. The elasticity for spirits is close to -1 for the early period; the fact that it is insignificant after 1994 is probably due to the small variation in the price of spirits during that period. In comparison it can be mentioned that Assarsson (1991) for the period 1970 1988 estimated the elasticitities for beer, wine and spirits at -1.3, -0.9, and -0.9, respectively. The agreement between Assarsson s estimates and those presented above for the period prior to 1995 is thus fairly good; the largest discrepancy is noted for wine, where Assarsson s estimate was somewhat stronger. It should be mentioned that Assarsson used another techique for time series analysis, and that he also included additional explanatory variables. Models including cross-elasticitities were estimated as well (not shown); e.g., the model for beer included the prices of wine and spirits, in addition to the beer price. In neither of the models for beer, wine and spirits were the cross-elasticitities statistically significant. It is of interest to note that the elasticitities estimated on monthly data hardly differ from those based on quarterly data; the differences are unsystematic and not statistically significant. This would imply that people respond quickly to a change in the alcohol price. The decreasing price elasticitity for beer after 1994 is intriguing. It can hardly be due to limited variation in price, as in the case of spirits. On the contrary, the variation in beer price was largely due to the price cut of 15% in January 1997. This price cut has rather the form of a natural experiment, and inspires a separate analysis. Thus the elasticitity for beer was estimated for a period that was dominated by this price cut, that is, 1995:1 1998:4. Figure 7 indicates a clear and negative relationship between prices and sales (seasonally differenced); this is also verified by the model estima- Table 2. Estimated price elasticities for various time periods Quarterly data Quarterly data Quarterly data Monthly data 1984:1 1994:4 1995:1 2004:1 1984:1 2004:1 1984:1 2004:3 Beer -1.36 *** -0.55 * -0.79 *** -0.90 *** Wine -0.62 ** -0.81 (*) -0.57 ** -0.63 ** Sprits -1.16 *** 0.34-0.96 *** -0.81 *** *** p<0.001; ** p<0.01; * p<0.05; (*) p<0.10 94

Beer sales, litres (seasonally differenced) 300 000 200 000 100 000 0-100 000 -.3 -.2 -.1 0.0 Real price, beer (seasonally differenced).1 Figure 7. Relationship between real price and sales of beer (litres 100%). Seasonally differenced quarterly data 1995:1 1998:4. tion (table 3). The estimated elasticitity (-0.60) is on a par with the one found for the entire period after 1994. Is the price effect asymmetric? Two models were estimated to elucidate the issue of whether a price increase and a price decrease are equivalent in terms of absolute effects. The first model (Model 1) included the price series only as explanatory variable. The second model (Model 2) included in addition to the price series a dummy variable (denoted Change), that (after ordinary differencing) took the value 1 if the price increases, -1 if the price Table 3. Price elasticity for beer estimated on seasonally differenced data for the period 1995:1 1998:4 Coeff SE Price -0.60 *** 0.12 Q(4) + 2.18; p> 0.70 *** p<0.001 + Box-Ljung test for autocorrelated residuals (lag 4) decreases, and 0 if the price remains the same. The models were estimated for spirits only, since this is the beverage where the presence of this sort of asymmetry seems most probable. Table 4 shows that the dummy variable did not have any significant effect, nor did it affect the estimate of the price elasticity (the difference between the estimated price elasticity in Model 1 and Model 2 is not statistically significant). Geographical differences in price elasticity To examine the issue of geographical differences in price elasticity, county specific analyses were performed for beer sales during two periods of time: 1984 1994 and 1995 2004. Beer is the beverage for which the availability of alternatives to Systembolaget ought to be largest, especially during the latter period with its increased travellers allowances. According to Norström s study (2000) it is particu- 95

Table 4. Estimated price elasticity for spirits. Change is a dummy variable (see text). Based on regularly differenced quarterly data 1984:1 1994:4 Model 1 Model 2 Coeff SE Coeff SE Price -0.79 ** 0.26-0.90 * 0.35 Change 0.004 0.01 AR1-0.64 0.11-0.64 0.11 SAR1 0.48 0.15 0.48 0.15 SAR2 0.45 0.16 0.45 0.16 Q(4) + 3.35; p> 0.50 3.29; p> 0.51 ** p<0.01; * p<0.05 + Box-Ljung test for autocorrelated residuals (lag 4) larly in southern Sweden that one can observe an increased private import of beer from Denmark after the increased quotas in January 1995. Thus, it is in this area we should expect an excess sensitivity to the beer price, particularly after 1994. According to the results, this is not the case; the average price elasticity for these counties is about the same as in the remainder of the country during both of the time periods (table 5). Further analyses of the county specific elasticity estimates for southern Sweden show no relationship between the price elasticity and the distance to Helsingborg during the early period (figure 8). During the latter period (figure 9) there is Table 5. Price elasticity for beer in southern Sweden and in the rest of Sweden estimated on data for two different time periods. Average (standard deviation in parentheses) of county specific estimates. 1984:1 1994:4 1995:1 2004:1 Southern Sweden* -1.48 (0.13) -0.59 (0.14) Rest of Sweden -1.38 (0.15) -0.56 (0.17) * Southern Sweden includes the municipality of Helsingborg, the municipality of Malmö, and the following counties: Malmöhus, Halland, Kristianstad, Kronoberg, Göteborg and Bohus, Blekinge, and Jönköping. a hint of a relationship in the expected direction, but the spread around the regression line is considerable. Projections of trends in consumption How would the consumption of beer, wine and spirits have evolved during the last ten years if it had been determined solely Price elasticity -1.3-1.4-1.5-1.6-1.7-1.8 0 100 200 Kilometres Figure 8. Relationship between county specific price elasticity for beer (estimated for the period 1984:1 1994:4) and distance to Helsingborg in kilometres. 300 96

Price elasticity -.3 -.4 -.5 -.6 -.7 -.8 0 100 200 Kilometres Figure 9. Relationship between county specific price elasticity for beer (estimated for the period 1995:1 2004:1) and distance to Helsingborg in kilometers. 300 Million litres 11 10 8 7 6 5 9 4 1995 2000 2003 Figure 10. Actual sales of beer in litres 100% ( ), and sales predicted on the basis of real price and price elasticity estimated on data for the period 1984:1 1994:4 ( ). by the trends in prices. To address this question a series of projections were performed. For instance, for beer the predicted sales for the period after 1994 was calculated on the basis of the price elasticity for beer (as estimated for the early period, that is 1984:1 1994:4) and the trend in beer price. (By multiplying the predicted sales series with a feasible constant, acutal and predicted sales have the same value 1995.) The projections were made separately for wine, beer and spririts; these were further summed into total alcohol sales. The results were aggregated into yearly data. The outcome (figures 10 13) show that wineand beer sales increased markedly more than predicted from price; for spirits the reverse is true. The outcome for total sales is mostly influenced by the results for beer and wine, that is, the increase is stronger than predicted. Million litres 18 17 16 15 14 13 12 11 10 1995 2000 2003 Figure 11. Actual sales of wine in litres 100% ( ), and sales predicted on the basis of real price and price elasticity estimated on data for the period 1984:1 1994:4 ( ). 97

Million litres 11 Million litres 36 34 10 32 9 30 28 8 26 7 1995 2000 2003 24 1995 2000 2003 Figure 12. Actual sales of spirits in litres 100% ( ), and sales predicted on the basis of real price and price elasticity estimated on data for the period 1984:1 1994:4 ( ). Concluding discussion In this study the price elasticities for beer, wine and spirits in Sweden were estimated on the basis of quarterly data for the period from 1984 to the first quarter of 2004. For the period before 1995 the results are close to what has been found in previous research. The elasticity for beer was found to be markedly weaker during the period after 1994 compared to the preceding period (-0.6 and -1.4, respectively). The estimate implying a weaker elasticity accords better with estimates for other countries. One interpretation of the reduced elasticity is that the marked price cut in January 1997 lowered the beer price to a level where variations in price have a weaker effect. It is further possible that beer to an increasing degree became regarded as an everyday commodity, the demand for which thus became less price sensitive. Another circumstance in this context is the following: simultaneously with the tax Figur 13. Actual total sales of alcohol in litres 100% ( ) and sales predicted on the basis of real price and price elasticity esitmated on data for the period 1984:1 1994:4 ( ). cut for strong beer, there was an increase in the tax on weaker beer (2.8 3.5 % by volume) which increased the price by about 0.5 SEK per can (Trolldal 1998). This might have strengthened the effect of the tax cut on strong beer. The sensitivity to the beer price has thus changed over time. It is also easy to believe that there would exist a geographic variation, so that the demand would be more sensitive to price in southern Sweden where it is closer to cheaper alternatives in Denmark and Germany. However, the results did not support this hypothesis. According to the results, the response to a change in the price of alcohol is fast; it made no difference if the time window was a month or a quarter. Further, there did not seem to exist any asymmetry in the price effect; the impact of price increases was as strong as the effect of decreases in price. Finally, projections that were made 98

on the basis of the results indicated that after 1995 alcohol sales increased more than what was to be expected on the basis of trends in prices. This illustrates the simple fact that the sales of alcohol are affected by many other factors than price, and that these factors have evolved in a direction that has spurred sales. The increased availability is probably crucial in this context: an increased number of outlets, longer sales hours (not least the Saturday opening), and increased self-service. Studies have shown that the introduction of self-service (Skog 2000) as well as Saturday opening (Norström & Skog 2003) increased sales, but it would be of interest to see a study that analyses the total impact of all the factors that affect sales. As appears from figures 10 13, much remains to be explained also after the price effect has been accounted for. Thor Norström Swedish Institute for Social Research Stockholm University S-106 91 Stockholm Sweden E-mail: totto@sofi.su.se REFERENCES Assarsson, B. (1991): Efterfrågan på alkohol i Sverige 1970 1988 (Alcohol demand in Sweden 1970 1988). Appendix 1, SOU 1991: 52, Allmänna Förlaget Box, G.E.P. & Jenkins, G.M. (1976): Time series analysis: Forecasting and control. London: Holden-Day Edwards, G. & Anderson, P. & Babor, T.F. & Ferrence, R. et al. (1994): Alcohol policy and the public good. Oxford: Oxford University Press Norström, T. (2000): The geography of crossborder trading of alcohol. In: Holder, H. (ed.): Sweden and the European Union. Changes in national alcohol policy and their consequences, pp. 121 135. Stockholm: Almqvist & Wiksell Norström, T. & Skog, O.-J. (2003): Saturday opening of alcohol retail shops in Sweden: an impact analysis. Journal of Studies on Alcohol 64: 393 401 Ornstein, S.I. (1980): Control of alcohol consumption through price increases. Journal of Studies on Alcohol 41: 807 818 Ornstein, S.I. & Levy, D. (1983): Price and income elasticities and the demand for alcoholic beverages. In: Galanter, M. (ed.): Recent developments in alcoholism, pp. 303 345. New York: Plenum Skog, O.-J. (2000): An experimental study of a change from over-the-counter to self-service sales of alcoholic beverages in monopoly outlets. Journal of Studies on Alcohol 61: 95 100 Trolldal, B. (1998): Ändrade villkor för svensk alkoholpolitik (Changed conditions for Swedish alcohol policy). In: Kühlhorn, E. & Björ, J. (eds.): Svenska alkoholvanor i förändring (The changing Swedish drinking habits). sid. 10 20. Kristianstad: Sober Young, D.J. & Bielinska-Kwapisz A. (2003): Alcohol consumption, beverage prices and measurement error. Journal of Studies on Alcohol 64: 235 238 Österberg, E. (1995): Do alcohol prices affect consumption and related problems? In: Holder, H. & Griffith, E. (eds.): Alcohol and public policy, pp. 145 163. Oxford: Oxford University Press Österberg, E. (2001): Effects of price and taxation. In: Heather, N. & Peters, T.J. & Stockwell, T. (eds.): International handbook of alcohol dependence and problems: Part VI: Prevention of alcohol problems, pp. 685 698. Chichester: John Wiley & Sons Ltd. 99

Appendix Table A1. Price elasticity for beer, wine and spirits estimated on seasonally and regularly differenced quarterly data for the period 1984:1 2004:1 Beer Wine Sprits Coeff SE Coeff SE Coeff SE Price -0.79 0.18-0.57 0.18-0.96 0.18 AR1-0.54 0.09-0.50 0.10-0.41 0.11 SAR1-0.37 0.11-0.85 0.10-0.95 0.09 SAR2-0.55 0.10-0.68 0.09 Q(4)* 5.15; p>0.27 5.06; p>0.28 3.11; p>0.54 *Box-Ljung test for autocorrelated residuals (lag 4) Table A2. Price elasticity for beer, wine and spirits estimated on seasonally and regularly differenced monthly data for the period 1984:1 2004:3 Beer Wine Sprits Coeff SE Coeff SE Coeff SE Price -0.90 0.20-0.63 0.19-0.81 0.14 AR1-0.92 0.05-0.15 0.05-0.89 0.06 AR2-0.59 0.05 0.26 0.05-0.60 0.06 AR3 0.67 0.05 MA1 0.55 0.07 SAR1-0.54 0.06-0.64 0.06-0.75 0.06 SAR2-0.34 0.07-0.47 0.06-0.53 0.06 Q(12)* 28.21; p> 0.01 25.68; p> 0.01 22.27; p> 0.03 *Box-Ljung test for autocorrelated residuals (lag 12) Table A3. Price elasticity for beer, wine and spirits estimated on seasonally and regularly differenced quarterly data for the period 1984:1 1994:4 Beer Wine Sprits Coeff SE Coeff Se Coeff Se Price -1.36 0.35-0.62 0.22-1.16 0.19 AR1-0.63 0.13-0.58 0.14-0.52 0.14 SAR1-0.27 0.19-0.84 0.16-0.97 0.12 SAR2-0.67 0.16-0.75 0.12 Q(4)* 5.02; p>0.29 2.81; p>0.59 0.55; p>0.96 *Box-Ljung test for autocorrelated residuals (lag 4) 100

Table A4. Price elasticity for beer, wine and spirits estimated on seasonally and regularly differenced quarterly data for the period 1995:1 2004:1 Beer Wine Sprits Coeff SE Coeff SE Coeff SE Price -0.55 0.21-0.81 0.46 0.34 0.99 AR1-0.28 0.18-0.29 0.18-0.39 0.18 SAR1-0.53 0.15-0.56 0.16-0.53 0.18 Q(4)* 1.24; p> 0.87 3.12; p>.53 8.17; p> 0.08 *Box-Ljung test for autocorrelated residuals (lag 4) 101