The Demand for New Cars and the Index of Consumer Sentiment

The index ofconsumer sentiment (ICS) has been widely employed as a proxy for future buying confidence to predict future aggregate buying behavior. This study empirically compares two forecast models: the expectation model thatincludes the ICS as an explanatory variable and the traditional model that does not include the ICS. The models are employed to estimate the aggregate demand for new cars in the U.S. from 1976 to 1984. The results indicate that the ICS has a positive relation with new car sales. On the basis of the likelihood dominance criterion, however, the traditional model is preferred to the expectation model. Furthermore, the forecast ability of the expectation model is slightly inferior to the traditional model


Introduction
The index of consumer sentiment (ICS) has been widely employed as a proxy for future buying confidence to predict future aggregate buying behavior. The ICS is especially important determinant for predicting the demand for consumer durable, such as cars, because consumer durable are characterized by extensive decision-making effort (Howard and Sheth, 1969) and therefore typically involve long-term decision planning. For these products, the ICS can be used in order to anticipate major shifts in consumer intentions and buying plans, and thus the demand for these products.
The ICS has mixed performance in estimating aggregate buying behavior. A study by Burch and Gordon (1984) indicated that the ICS might yield little additional explanatory power to the prediction of future buying behavior, because many of economic variables in their study appeared to account for the majority of variance in buying patterns. Another study (Throop, 1991) however, found the opposite result. As an extension of previous car demand studies, the purpose of this study is to compare a model that includes the ICS as an explanatory variable (i.e., the expectation model) and a traditional model that does not include the ICS by empirically estimating the aggregate demand for new cars in the U.S. from 1976 to 1984. The models are estimated with ordinary least squares (OLS) and feasible general least squares (FGLS) that correct for autocorrelated disturbances. They will be evaluated based on the likelihood dominance criterion (LDC) as suggested by Pollak and Wales (1991) and their forecast ability.
The results show that ICS has a positive relation with new car sales. On the basis of the LDC, however, the traditional model is preferred to the expectation model. Furthermore, the forecast ability of the expectation model is slightly inferior to the traditional model. Lastly, the study finds that there has been a structural change for the car demand in 1979.
The paper is organized as follows. Section II provides a literature overview of the study of the demand for durable consumer goods in general, and the demand for cars in particular. It also describes the ICS and its relation to demand for durable goods. Section III provides the model specification, together with data source and collection. In section IV, the regression results, together with diagnostic tests and forecast results are presented. Section V contains conclusion.

The Study of Demand for Durable Goods and Cars
The most commonly applied models that explain consumer purchases of durable goods are based on a simple dynamic stock adjustment model that was first developed by Stone and Rowe (1957). The model can be defined as: D t = a(S t * -S t-1 ) + pS t-1 (1) Where: D t = aggregate demand for the durable in period t.
S t * = desired stock at the end of period t.
S t-1 = Stock of the durable in households' hand at the end of period t-1. a = adjustment stock coefficient. P = depreciation rate.
The first term of the equation indicates the additional amount of stock of the durable that is desired in period t and the second term takes account of any replacement demand that occurs in each time period.
The desired stock is defined as a function of some traditional variables, such as income, price, credit conditions, etc. A number of studies have tried to incorporate a variety of variables in the desired stock equation. Among the most relevant variables are measures for the availability and the cost of consumer credit (Hamburger, 1967;Briscoe, 1977) and the operating costs of the durable (Tishler, 1982). Both variables can be regarded as the costs of complementary products for durable and therefore, are expected to have inverse relation with the demand for durable goods. Others try to improve the short-term adjustment mechanism by defining a variable that is expected to shape short-term demand shifts, such as the rate of unemployment (Westin, 1975).
In many studies, replacement demand is simply defined as a percentage of existing stock. Rhys (1972) noted that the approach does lead to acceptable approximations of replacement demand in stable conditions. This approach requires a very restrictive assumption that depreciation rate is a fixed percentage of total stock of cars. De Pelsmacker (1990) commented that as a result of the durability of a car, its replacement can be postponed or speeded up; therefore, replacement demand is not a fixed percentage of existing stock. It could be very flexible and dependent on some factors reflecting the economic situation.
Katona's study (1974) was the first one to incorporate the behavioral-oriented expectation elements in the empirical analysis of both an aggregate and disaggregate consumption spending. Consumer purchases are made by individuals who are not only able but also willing to purchase. Willingness to purchase is the result of consumer attitudes and expectations concerning the present and future state of the economy. If a consumer is more optimistic about the future state of the economy, then he is more likely to purchase durable goods, which require substantial expenditures and involve long-term decision planning. The opposite holds if the consumer is more pessimistic. Given consumers' expectation of the future economy, consumer expectation measures yield not only information about future purchase but also information about the future course of economic activity.
One of the consumer expectation indexes that has been widely shown to predict future purchases is the ICS. The ICS is seasonally adjusted and is published each month by the Survey Research Center at the University of Michigan. The ICS contains information of consumers' perception of present and future states of economy. It solicits the consumers' opinion as to whether they are better off now than they were a year ago. It is a measure of medium to long-run expectation because its survey questions request judgments concerning future economic conditions in the next year and five years. The ICS also provides an indicator of current purchase intention of consumers. Its survey question asks if it is currently is a good time to buy. Therefore, the ICS emphasizes on purchase intentions in the current period.
The ICS have mixed performance in the prediction of future aggregate buying behavior. Some studies (Hymans (1970), Burch and Gordon 1984)) found that the ICS had little predictive value in explaining consumer durable purchases while other studies (Juster andWatchel (1972), Throop (1991), and Huth et. al. (1994)) have shown that the ICS is useful as a predictor of future buyer behavior. Briscoe noted (1977) that the ICS is frequently found to be highly collinear with some traditional economic variables. Further, Smith (1975) showed that consumers' attitudes and intentions are not necessarily independent of the transitory economic variables, especially the level of unemployment. This is consistent with Huth et. al. (1994) findings that the ICS have strong relationships with unemployment rate and interest cost, the two traditional measures that have been widely used in the study of demand for cars. Lastly, Juster and Wachtel (1974) found that the ICS could not account for the impact of relative prices.
The strong relationship between the ICS and some economic variables should be expected. As mentioned earlier, the ICS is a measure of consumers' perception of current and future economic activities. Consumers incorporate all relevant economic variables, which include interest cost and unemployment rate, when making their expectations; therefore the index should be correlated with the economic variables.

Research Method
Other than measuring purchase intention, the ICS also measures expectation of current and future economic conditions. It does not directly account for the impact of price and income on the demand for durable goods, although price and income are somewhat influenced by economic conditions. If the ICS could replace traditional economic variables such as interest rate and unemployment rate to estimate demand for new cars, the stock adjustment model in equation 1 becomes the following (model 1): D t = f(P t , PCY t , ICS t , S t-1 ) Where P t is the price of cars, PCY t is the per capita income, and ICS t is the index of consumer sentiment 1 .
Price (per capita income) is expected to have a negative (positive) relation with the number of cars sold. The ICS is expected to have a positive relation with car sales because as consumers become more optimistic about future economic condition (i.e., the ICS goes up), they will purchase more cars. The ICS is measured without time lag because, as mentioned earlier, the ICS concerns with the impact of consumers' expectation on current purchase. For simplicity reason, I include the lag of stock of cars as a proxy for car replacement. As the number of cars to be replaced increases, the demand for new cars also increases. Thus, there is a positive relationship between the stock variable and demand for cars.
Model 2 is based on the traditional economic model and is defined as follows: where r t-1 is interest rate and U t-1 is unemployment rate both with one lag structure. This allows for the lag in the relationship between the absorption of information about the cost of credit and the economic condition and its translation into the act of purchasing or not purchasing. Since more than 70% of new car purchase involve long-term financing, higher interest rate results in higher cost to purchase cars and therefore should result in lower demand for new cars. Unemployment rate is a proxy for transitory variable and is expected to have negative relationship with demand for cars. Since I use quarterly data, seasonality may affect new car sales. To control for seasonality, I include three dummy variables for quarter 1, 2 and 3 in both models.
Previous studies have used both linear and exponential models to estimate the demand for cars. Since a priori there is no justification to prefer one over the other, I estimate the models using OLS estimation for both linear and exponential models. To linearize the exponential model, I take a natural log for both the dependent and regressor variables (except for the dummy variables). Then, based on the LDC, I will select the model that generates the highest log likelihood value. The LDC is also used to compare model 1 and model 2.
The LDC is applicable in cases where there is a need to choose between nonnested models. The principle of the LDC is to select a model that maximizes log likelihood value. If the nonnested models contain the same number of parameters, the criterion is to select the one with the higher log likelihood. If the nonnested models contain different number of parameters, the log likelihood's of the models are not directly comparable and they have to be compared to some critical levels that are proposed by Pollak and Wales (1991).

Linear vs. Exponential Models
For model 1, the log likelihood's for the linear and the exponential models are -28.73 and -27.52 while for model 2, they are -26.33 and -25.13 respectively. Since the linear and the exponential models contain the same number of parameters, the criterion is to select the one with higher log likelihood. The exponential model has higher log likelihood than the linear model for both model 1 and model 2. Based on this, the exponential model is selected to estimate the demand for cars.

The Expectation Model vs. The Traditional Model
The results of the OLS regressions for model 1 and 2 are shown in Table 1. In both models, the dummy coefficients for quarter 2 are significantly greater than zero (p<0.001). The dummy coefficient for quarter 1 is significant at 5% of less only in model 2. This indicates that new car sales in quarter 1 and 2 are significantly higher than quarter 4. Thus, seasonal factor plays an important factor in estimating new car sales. For model 1, except for the stock variable, all coefficients are significant and are in the expected direction. The insignificance of the stock variable may be due to its noisy measure of replacement demand for cars. The use of stock variable requires a stable condition, but during the period of the study, the demand for cars was marked by a structural change and surrounded by unstable economic conditions. This issue is addressed in later sub-section. Model 1 and model 2a are reestimated with the correction of autocorrelation of order 5. The residuals are assumed to follow an autoregressive process of order 5 (AR (5)). The correction and the estimation procedures are based on feasible general least squares (FGLS) 3 . The regression results for model 1 and model 2a are presented in Table 3. Where z is a vector of regressor variables.
All tests for model 1 and model 2a fail to reject the hypothesis that the residual variance is homoscedastic. It appears that heteroscedasticity is not a problem in this series. Both models, except for the dummy coefficient in the third quarter, the standard errors and the t-ratios of the coefficients substantially improve. The adjusted R-square of both models also increase. A FGLS estimation is more efficient than an OLS estimation if the matrix of the difference between the covariance matrix of OLS and FGLS estimations is positive definite.
The matrix is a positive definite if all its eigenvalues are greater than zero. For model 1 and 2a, not all eigenvalues of the matrix is greater than zero, implying that no conclusion can be made regarding the efficiency of the FGLS model relative to the OLS model. Thus, even though most t-ratios of both models improve, the FGLS estimation is not more efficient than the OLS estimation 4 .

b. Test for structural change
The period covered in this study is from 1976 to 1985. During this period, the American economy has gone through a business cycle, starting from a recovery from 1973-75 recession to another recession that started in early 1980 and ended in early 1983.
Beginning in 1979, the price of oil has more then doubled before it leveled off in 1983.There was also a change in the class structure of car sales.
The share of subcompact, compact, and import cars of the total new car sales has substantially increased since 1976. In 1976 the share of subcompact, compact and import cars was 48.8%, while in 1980 it jumped to 63.1%. It has decreased slightly since then. All of these changes may affect the relationship between the regressor variables and new car sales.
To investigate whether there was a structural change in the demand for cars during 1976-84, I perform the Chow test, which gives a test for structural change.
Since the exact period where the structural change occurred is unknown, a set of sequential chow test statistics is generated. Each set splits the sample of dependent and regressor variables in 2 pieces at every possible point. The structural change occurs in period where the Chow statistic is greater than the critical level. At 5% critical level, for model 1there were three periods those results in significant Chow test. 4 Both LM and BPJ tests do not indicate whether the residuals follow an autoregressive (AR) process or a moving average (MA) process. To determine which corrected error specification results in efficiency gain in model 1 and 2a, I run FGLS on models with AR(5) and MA(5) corrections. The efficiency tests do not indicate that models with AR(5) are better than those with MA(5). Generally, however, the tratios of AR(5) models are higher than those of MA(5). Further, the adjusted R-squares of AR(5) models generally are higher than the adjusted R-squares of MA(5) models. Therefore, I select AR(5) as the structure of the residuals. however, the coefficients must be interpreted with caution because the degree of freedom of the first subperiod is very low. For the second sub-period, the regression results are similar to those for the combined sample. One noted difference is that the t-ratios generally are higher than the t-ratios in the combined sample. In addition, the stock variable becomes significantly negative in model 1. In summary, the regression results show that the coefficients for price, per capita income, and stock variables change substantially before and after the third quarter of 1979; however, due to small sample, the results must be cautiously interpreted.

Forecast
I use the holdout sample to compare the forecast accuracy of model 1 and model 2a. Three measures are used for assessing the predictive accuracy of the models: Root means squared error (RMSE), mean absolute error (MAE), and Theil U statistics. Large values of measures indicate a poor-forecasting performance. For the third quarter, only the forecast interval of the OLS-model 2a includes the actual value. The actual value is slightly above the upper interval of other models. Examination of the data reveals that car sales in that period were highly above their usual pattern. Compared to car sales in the same quarter of previous year, the car sales jumped more than 20%. At the same time, the consumer sentiment index decreased, the new car price index increased, and the per capita income remained stable. The decrease in the prime rate was the only change that was consistent with the jump in car sales. It also explained the more accurate forecast or model 2a in that quarter.

Conclusion
The study examines whether a car demand model that is based on the ICS (i.e., the expectation model) is preferred to a traditional model that includes the prime rate. As expected, the ICS is positively related to new car sales, however, based on the LDC, the traditional model is preferred to the expectation model. The ICS does not provide additional explanatory power beyond what already explained by the prime rate and other regressor variables. In addition, on the basis of RMSE, the forecast ability of the expectation model is inferior to the traditional model. These results are consistent with the finding of Burch and Gordon (1984). Lastly, the study found that there has been a structural change for the car demand in 1979.
Like all other studies, this one has its limitations and weaknesses, several of which deserve mention. First, the study uses aggregate data and therefore ignores the fact that automobiles are differentiated products. The ideal approach would be to use disaggregate data and estimate the demand system for a set of differentiated products. In the case of automobiles, though, these techniques are inapplicable. There are over one hundred models available and few models are available for more than four consecutive years. Levinsohn in Baldwin (1988) offers an interesting approach to overcome this problem. Second, the study employs time-series technique to estimate the car demand. This technique has a restrictive assumption that products and tastes or any other structural change remain constant over the period of estimation. Chow test or any other method can be used to detect these changes; however, if the changes occur gradually the detection would be difficult and unreliable. Lastly, the study employs regression models to predict demand for cars. Huth et al. (1994) commented that the methodology is not well suited to the dynamic movement of consumer buying confidence or sentiment and consumer purchase variables over time. He suggested to use vector autoregression time-series techniques to determine whether one variable leads, lags, or moves contemporaneously with another variable.
P-values are based on two-tail test.