THE IMPACT OF VIDEO RECORDERS ON CINEMA ATTENDANCE

Samuel Cameron

Cinema attendances in the United Kingdom and the United States have been subject to severe declines in the post-war period. Fairly

strong evidence (Belson, 1958) exists that the arrival and development of television contributed powerfully to the initial decline. As televisions now populate almost every home we would expect this in- fluence to have worked itself out. The 1980's have seen the arrival of videos as a new threat to cinema takings. Analysts of the industry have been suggesting (Docherty et. al., 1986), (Variety, 1985) that the threat is more apparent than real with demographic factors and/or poor films being the cause of more recent audience declines. These claims derive from casual inspection of ticket receipts (Variety, 1985) or one-off sur- veys of consumer attitudes (Docherty et. al., 1986). To date there has been no concrete evidence offered for or against the impact of video. Such evidence is hard to gather because of data limitations. This is par- ticularly the case for the U.S. where there is the added complication of diffusion of pay TV. The U.K. is free from this complication as pay TV is still extremely rare and monthly price and attendance figures are available until their publication ceased in May 1985. In this note we use a demand equation to discuss what ticket sales would have been in the period (January 1983 onwards) when video access began to gather impetus. Comparison of the equation results with actual ticket sales suggests a marked reduction which may tentatively be attributed to the VCR.

U.K. cinema attendance has fallen relentlessly from 1,635 million in 1946 to 53.26 million in 1984. Only in 1978 did demand rise - by about 20% over 1977 which was seen in the popular media as a revival al-

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though it only brought demand back to 1974 levels. Recently a 'British Film Year' was launched in the hope that publicity would lure back the missing millions. From an economic perspective this would only work if it makes good some information failure or alters consumer taste. Economists will naturally consider price and income factors as the key factors. As there is a coincidence of falling demand with a strong growth of real income it might be inferred that cinema going was an in- ferior good. Cross-section evidence from regressions on 1950's data in Spraos (1962) suggested that the income elasticity of cinema going was zero whilst tables derived from Family Expenditure Survey data for more recent times, in Cameron (1986), indicates a strong positive income elasticity. (1) Investigation of the role of prices requires some consideration of supply behavior. Given that cinemas act as local mo- nopolists there is no supply curve as they should simply select the op- timal point on the demand curve. If we characterize cinemas as treat- ing venue size as exogenous and having no marginal costs of admission then they should select the point where marginal revenue is zero and consequently the elasticity of demand is unity.(2) In these conditions the demand curve is not identified and cannot therefore be estimated. Alternatively we might conjecture that the demand curve could be identified as a result of shifting marginal costs or an ad hoc pricing rule whereby cinemas simply move the price about in an arbitrary fashion as they do not know where the profit-maximizing equilibrium is. It ap- pears (Cameron, 1986) that the demand curve can be identified al- though unbiased estimation is difficult to achieve. Provided that ex- hibitors do pursue profits we should find that demand is highly elastic which seems to be the case. It seems implausible that the fall in demand could be explained by prices being "too high" as this would require that marginal costs are continually shifting up or producers are consistent- ly making larger and larger errors.

In the past the long-run decline in demand would probably be at- tributed to "tastes". However following the development of the goods characteristic theory of consumer behavior the role of tastes is partial- ly supplanted by the notion of changes in consumption technology.(3) For the cinema the pertinent changes in technology were the diffusion of car ownership and the diffusion of television ownership coupled with innovations such as expansion in the number of stations and the intro- duction of color. The effect of car ownership is somewhat ambiguous as although it would make visiting the cinema easier there is a simul- taneous expansion of rival opportunities for the use of time. In terms of direct consumption television viewing is effectively inferior to

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cinema viewing due to having worse visual conditions and a lack of at- mosphere. However is a goods characteristics perspective these are simply inferior characteristics. Television viewing involves zero transport costs and obviates hiring costs for baby-sitters etc. Clearly these features can outweigh the inferior characteristics and result in powerful substitution of television for cinema consumption. The im- portant factor is not the price of television but the extent of ownership as prices can easily stay fixed while there is a powerful substitution ef- fect from wider ownership.

On the basis of the above considerations we estimated a fairly con- ventional demand function with a color television variable added on.(4) The equation was: now ther

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(1) Qc = a¢ + al(Pc/Po) + a2 COL + a3 (Y/Po) + ~ ,." Di + u

i = 1 i where Qc is the quantity of tickets sold, Pc is the price of a ticket, Po is the retail price index, COL is the number of color television licen- ses, Y is average earnings, D are dummy variables, u is a random and independently distributed disturbance term and all other symbols are parameters to be estimated.(5) This equation was estimated on monthly data for 1975-1982. This is a convenient period to use as the spread of color television ownership was the major important change taking place during these years. Estimation of equation (1) en- countered predictable problems of multicollinearity and serial correla- tion. Correct signs were obtained for a2 and a3 but the "t" ratios for these were generally below i in absolute value. In contrast al had al- ways a very large "t" ratio and a negative value giving elasticities of greater than one. As is well known multicollinearity is a much less serious problem when one is engaged in forecasting as properties of the forecasts are not adversely affected. The presence of first-order serial correlation was handled in a mechanistic way through assuming that u could be represented by:

(2) ut = p ut-1 + vt

where v has the properties previously ascribed to u. Substituting (2) into (1) we can estimate p and the parameters of (1) simultaneous- ly by maximum-likelihood. The ML and OLS estimates are displayed in Table 1. It must be stressed that the contribution of'ff to the ex- planation of Qc is included in the reported coefficient of multiple deter- mination.- As can be seen the ML estimates are fairly similar to the

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OLS ones although they are hypothetically more efficient.(6) The availability of a static and an autoregressive version of the model ac- tually presents a choice of forecasting equations.

For convenience let us replace the parameters with v and the vari- ables with Z. Then we could use the O.L.S. forecast

(3) Oc = ~ Zt+j. t+j

This should be less efficient than the ML forecasts, (7) from com- bining (1) and (2), as these take account of the non-zero error term through pet +j-1 (See Pindyck and Rubinfeld (1981), p. 215-6). The ML parameter estimates are, of course, obtained from a quasi-first dif- ference form which requires conversion in order to obtain Qc values. With a non-zero error term equation (3) becomes

(4) Qc = ~'Zt+j + pet+j-1 t+j

substitution for et +j-1 gives:

A

(5) - - (zt + 6c t+j t+j t+j-I t+j-I

Subtracting the term involving the lagged dependent variable from both sides gives us an equation in quasi first-difference form which may be taken to be that used in GLS estimation for first-order serial cor- relation. Thus we may conclude that (5) is the correct form for forecasting Qc. Repeated subsntutlon for Qct +j-t shows that the error term in (4) can be expressed as

(6) et+j-1 = 9 j'l et.

Thus the impact of estimating rho becomes weaker as time passes, except for the special case where~ = 1 .

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TABLE 1, Es t ima tes of t he D e m a n d F u n c t i o n for C i n e m a A t t e n d a n c e

D e p e n d e n t V a r i a b l e Qc Qc

a ~ 4,3 3,7 (4,2) (2,2)

Y/Po 1,8 3 (1) (1,2)

P c / P o -785 .3 -734 ,2 (5 ,1 ) (7,3)

COL - 0 , 0 0 0 0 0 6 -0 ,00002 (0.2) (0,5)

P / 0,8 (12,3)

MONTHLY DUMMY VARIABLES NOT PRINTED

~2 0.62 0,76 F 12,1 19,2 D,W, 0,4 2,1

E s t i m a t e d by; OLS ML

NOTES:

1, F i g u r e s in p a r e n t h e s e s a r e a b s o l u t e "t ° rat ios . 2. F is t he "F" r a t i o for t h e e q u a t i o n , 3, D.W. is t he D u r b i n - W a t s o n s ta t i s t ic for f i r s t - o r d e r s e r i a l c o r r e l a t i o n ,

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We computed forecasts using (5) as well as (1). The two sets of forecasts were extremely close together.

As publication of the data ceased in May 1985 we had 29 observa- tions to forecast. The period 1975-82 was virtually free from the im- pact of video access. The spread of video should generate systematic forecast errors. By 1982 color television access had reached a very high level perhaps approaching saturation. If this was so we might expect under-prediction as too much weight is given, in a linear model, to the television factor. Non-linear models gave similar results to linear ones and in any case it is clear that over-prediction ensues from the linear specification. It is always possible that seasonal effects and/or price and income parameters could shift during the forecast period although there seems no compelling reason why these should account for the results obtained.

While the forecasts are not displayed, when we ran them, the predicted values exceed dramatically the actual values with this dis- crepancy widening as time passes. This is exactly what we would have expected if video diffusion leads to falling attendances. It is not pos- sible to pin down precisely the relationship in terms of ticket sales lost per percentage point rise in video penetration as video use figures are only obtainable on an annual basis. It is not automatic that these results hold for the U.S. cinema industry but they are, at the least, suggestive.

Temple University

Footnotes

1. Data from Australian household surveys, for the 1970's, also indi- cates a strong positive income elasticity (Throsby and Withers, 1979), p. 104.

2. Assuming profit maximizing behavior.

3. Pioneered by Muth (1966) and Lancaster (1972). Becker's (1965) allocation of time theory is a closely related development which could equally well be used to illustrate the determinants of cinema going.

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4. Discussion here is brief. Variations on this equation are discussed and reported in Cameron (1986). Non-linear formulations are not reported as they do not significantly alter the conclusions reached.

5. The intercept is December and the eleven dummy variables repre- sent the other months. The pattern of seasonal variation for the cinema in the U.K. is displayed and discussed in Cameron (1986).

6. In this paper serial correlation is regarded as a "convenient simplification rather than a nuisance" as argued by Hendry and Mizon (1978) in view of the uncertainty surrounding the precise dynamic representation of consumer behavior. The greater ef- ficiency of the ML estimates relies on~ having a strong relation- ship with the true value of rho which, in this case, would be jus- tified by the large sample. Given that," is estimated from O.L.S. residuals there is still a downward bias as these are constrained to sum to zero.

7. Given that serial correlation does not make O.L.S. estimates biased the forecast that would be obtained by using the ML estimate of p in (3) should be identical to the O.L.S. forecast. Given the ex- igencies of actual data this will not be exactly the case. A forecast using the ML estimates is not efficient if the error term is set to zero given that we have specified an autoregressive model.

References

Becker, G.S. "A Theory of the Allocation of Time," Economic Jour- nal 75 (2) (1965) pp. 493-517.

Belson, W.A. "The Effects of Television on Cinema Going," Audio- Visual Communication Review 6(2) (1958), pp. 131-139

Cameron, S. "The Supply and Demand for Cinema Tickets: Some U.K. Evidence," Journal of Cultural Economics 10(1) (June, 1986) pp. 38-62.

Docherty, D., Morrison, D.E. & Tracey, M. "The British Film Industry and the Declining Audience: Demythologizing the Technologi- cal Threat," Journal of Communication 36(4) (1986).

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Hendry, D. & Mizon, G. "Serial Correlation as a Convenient Simplification not a Nuisance: A Comment on a Study of the Demand for Money by the Bank of England," Economic Journal 88 (331) (1978) pp. 549-563.

Lancaster, K. "Operationally Relevant Characteristics in the Theory of Consumer Behavior," in Peston, M. & Corry, B. (eds.) Essays in Honor of Lord Robbins. London: MacMillan, 1972.

Muth, R. "Household Production and Consumer Demand Functions." Econometrica. 34, (1966)

Pindyck, R.S. & Rubinfeld, D.L. Econometric Models and Economic Forecasts. New York: McGraw-Hill, 1982. 2nd edition.

Spraos, J. The Decline of the Cinema. London: George Allen & Unwin, 1962.

Throsby, C.D. & Withers, G.A. The Economics of the PerfonningArts. London and New York: St. Martin's Press, 1979.

Varieo,, "Ancillaries no alibi for B.O. Blahs". 323 (12) (July 23rd, 1985) p. 3 and p. 26.

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