Econometric analysis of the Belgian car market

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1 Econometric analysis of the Belgian car market By: Prof. dr. D. Czarnitzki/ Ms. Céline Arts Tim Verheyden Introduction In contrast to typical examples from microeconomics textbooks on homogeneous goods markets, the car market is characterized by product differentiation given the many different brands and types of cars that are available to consumers. The core strategy of car manufacturers is to differentiate their products to the extent that they are unique to the consumer, but still have some commonalities with other cars to optimize manufacturing costs. Because of this interesting nature of the car market, it has been the subject of study in many earlier research. The central aim of this paper is to help better understand the Belgian car market, using different econometric techniques. Starting from economic theory, we aim to model the Belgian car market to derive some interesting insights. We start from a naive estimation approach, which is then improved by applying more advanced tools and techniques to get econometrically correct results, which are in line with economic intuition. From our models we can derive utility for consumers on the Belgian car market and realistic substitution patterns between different car models. These insights both confirm most of the economic intuition underlying the Belgian car market, and provide an opportunity for manufacturers to better understand the market and its competitors to optimize differentiation strategies. In addition, our study confirms the importance of sound implementation of econometric tools to supplement more exact analytical computation and to support research in economics. The remainder of this paper is organized as follows. We present and describe the data used throughout this paper is sections 2 and 3. In section 4 we model consumer utility for consumers on the Belgian car market. Section 5 concludes. Data selection A comprehensive dataset on the European car market between 1970 and 1999, including information on sales and car characteristics, is provided by Goldberg and Verboven (2001). From this dataset, we specifically select the data on the Belgian car market to address our central research goal. The final panel dataset includes 2673 observations on car sales in the Belgian market between 1970 and We reduce the dataset to 9 variables of direct interest: year, model, brand, segment, sales, product characteristics (horsepower and fuel consumption), price and population. Note that the original dataset contains many more variables on the characteristics of the cars (e.g. length, width and height). However, we aim for parsimonious models, which are intuitively easy to understand and only include car characteristics that really matter. In addition, we want to avoid data snooping bias when combining subsets of the long list of characteristics, which are economically hard to motivate, to obtain statistically significant results. From the larger set of car characteristics, we therefore only consider an essential trade-off faced by every car buyer: power versus efficiency. We translate this trade-off using two variables: horsepower versus fuel consumption. A more in-depth description of these variables can be found in Table 1. Additionally, we create 4 instrumental variables from the existing data to be able to deal with endogeneity issues in estimating our economic models (Table 2). The unit of observation is the quantity of a car type sold in a given year. Descriptive analysis Before starting our actual econometric analysis, we can explore the data by collecting some descriptive statistics. First, we might consider the three most popular car types in both 1970 and In 1970, the most popular car model was the Simca 1000, followed by the Volkswagen Beetle and the Opel Rekord. By 1999, consumer preferences have evolved with the Opel Astra being the most popular type of car, followed by the Volkswagen Golf and the Renault Mégane. Recommended for readers of XXx-level bsc-level econometrics specialty NL 21

2 Table 1: List of variables Table 2: List of instrumental variables Recommended bsc-level for readers of XXx-level econometrics specialty NL Obviously a lot has changed in the car market over these 30 years under study. Next, we can also look into the different car segments: subcompact, compact, intermediate, standard and luxury. We see that most sales over the 30-year period are made in the compact segment. The luxury segment has the lowest volume of car sales. With respect to horsepower, we notice the logical monotonously increasing relationship from the subcompact to the luxury segment. The same relationship goes for the average price of the cars per segment. Finally, we can look into the evolution of yearly car sales, which are plotted in Figure 1. Overall, we see that car sales increased over the last 30 years. Nevertheless, a significant drop in car sales is observed during economic crises in the 1980s and 1990s. Consumer utility The central aim of our paper is to obtain a better understanding of the characteristics of the Belgian car market. The descriptive analysis already gave us some first insights. More sophisticated insights can be obtained by modeling the Belgian car market from economic theory. Therefore, we start by modelling the individual consumer utility derived from purchasing a car as a function of its product characteristics. The basic utility function looks as follows. (1) The utility derived by customer k from product j at time t is written as u kjt. This utility is a function of the following characteristics: horsepower (hp), fuel consumption (li), and price (p). The parameter on horsepower is expected to be positive; the parameter on fuel consumption ought to be negative; the parameter on price should be negative. jt represents the unobserved part of characteristics of product j at time t. Mean utility from product j, which is the same for all consumers k, is represented by jt. kjt is the consumer specific valuation of product j at time t by consumer k. A consumer will prefer to buy product j at time t if for all Equivalently, the probability that consumer k will buy product j is as follows. Figure 1: Evolution of yearly car sales (2) If we assume that the s are independently and identically distributed (i.i.d.) and follow an extreme value distribution, the probability of consumer k buying 22

3 car j at time t can be expressed as follows (3) The obtained theoretical expression for the probability of consumer k buying car j at time t might make us think about logit models as a possible econometric approach. However, in contrast to the case of logit and binary choice models, this probability does not need to be a latent variable that can only be proxied by a binary choice. In fact, these choice probabilities can be interpreted as overall market shares (including the market of people not buying a car), which can be computed from our data. Consequently, the log market share can be written as a linear function of the characteristics. We find the following model, which can be estimated to infer consumer preferences for the different characteristics. (4) Note that s jt is the market share of product j at time t; s 0t is the market share of the outside good at time t (share of people not buying any car at time t). jt represents the mean utility of product j at time t. By building from economic theory and imposing some assumptions, we can avoid having to use binary choice models (probit or logit) and are able to compute an otherwise latent variable. To implement our model without need for probit or logit estimation, we first need to calculate market shares, starting from an estimation of market size, which we approximate by the population divided by four (i.e. approximate number of households). Then, we compute market shares (s jt ) as the sales divided by market size. Next, we calculate outside marketshares per year (s 0t ), which is the share of consumers that do not buy a car. We also include year dummies in our econometric model to pick up effects of changes in consumer utility over time that are common to all car types. Additionally, we also include segment dummies for the same reason. OLS estimation Making the naive assumption that all relevant OLS assumptions are met, we start by estimating our model by OLS. From our estimation, we find that all these s variables are statistically significant. The estimated coefficient on fuel consumption is negative, which seems in line with economic intuition. The estimated coefficient on horsepower is negative; the estimated coefficient on price is positive. These two results are rather puzzling, as it would suggest that, controlling for year and segment effects, and the fuel consumption of a car, consumers appreciate cars that are less powerful and/or more expensive. Given these counterintuitive results, we suspect that the OLS estimation is strongly biased because of the endogeneity of the price variable, which is likely to be correlated with the unobserved product characteristics (which are included in the error term). High valuations of unobserved characteristics will cause demand for the car to be high as well. In return, car producers will charge higher prices, which causes an upward bias in the coefficient estimate for the price regressor. The estimated coefficient on price (i.e. 1.13) is thus obviously too high in the current model. In addition, an OLS estimation strategy is quite naive given that we are working with panel data. A panel data estimation approach might be preferred. Before moving on to more sophisticated estimation strategies, we also reflect on the specification of our model. The (log-)linear form of our model simply follows from our derivation starting from the economic definition of consumer utility, and is thus well motivated. We also test for the assumption of homoscedasticity using both the White test and the Breusch-Pagan test. From both tests, we reject the null hypothesis of homoscedasticity. Therefore, we reestimate the model by OLS, asking for robust standard errors. Obviously, the coefficient estimates do not change. The robust standard errors are now slightly higher, but this does not change anything about our previous interpretation of the results. For the remaining estimations, we always use robust standard errors in drawing statistical inference. Panel data estimation Given that we are working with a panel dataset, it seems straightforward to use panel data estimation techniques. Specifically, we turn to static linear panel data models. To do so, however, we need to make an additional assumption. In our current theoretical model, we include jt as the unobserved product characteristics of product j at time t. Hence, we assume that there is a product-specific effect and thus some unobserved heterogeneity that can change through time. In static linear panel data models, we cannot make this assumption as the unobserved heterogeneity is assumed to be time-constant. The panel data model that we will estimate is the following: (5) To estimate the above model, we first start by defining our data as a panel dataset. Therefore, we have to make some transformations in the data and indicate both the cross-sectional (i.e. type) and time-series (i.e. year) identifiers. Next, we try to estimate a fixedeffects model using the within estimator, controlling for year and segment effects. From this estimation, we can reject the null hypothesis of no unobserved heterogeneity. Hence, pooled OLS estimations will fail. We also notice a non-negligible amount of correlation between the unobserved heterogeneity and our regressors. This finding already indicates that a random effects estimation will probably fail. The estimated Recommended bsc-level for readers of XXx-level econometrics specialty NL 23

4 Recommended bsc-level for readers of XXx-level econometrics specialty NL coefficients seem quite close to our general intuition. The estimated coefficient on the price variable is negative and significant, as is the estimated coefficient on fuel consumption. For horsepower, we find a nonsignificant positive estimated effect. We can also run a fixed-effects model with the first-difference estimator, from which we find very similar results. Before further discussing the results from these estimations, we need to check for one important underlying assumption: strict exogeneity of the regressors. For the within estimator, we revisit our previous estimation, but now including also leading versions of our regressors. Testing for the joint significance of the estimated coefficients on these leading variables, we conclude that we have to reject our assumption of strict exogeneity. Including level versions of the regressors in the first-difference estimation, we come to the same conclusion. The fact that we cannot validate our assumption of strict exogeneity, and that we observe significant unobserved heterogeneity puts us in front of an estimation problem. One estimation strategy that can help us out of this problem is the use of instrumental variables. Anderson and Hsiao (1981) show that with panel data it might be very easy to find instruments, as different variations and combinations of existing regressors are potentially valid instruments. However, we choose not to follow a similar approach, as this seems to lead to models that lack any form of underlying economic intuition. Instead, we implement an instrumental variable estimation strategy that draws from economically motivated instruments. From these initial IV models, we further sophisticate our analysis to find realistic results. Instrumental variable estimation From the OLS estimation results and economic reality, we already suspect an endogeneity problem of the price variable. Since the two-stage least squares estimator is less efficient than OLS, however, we first want to formally check for endogeneity. We apply both the Hausman test and the regression-based test, using instrumental variables that are suggested by Brenkers and Verboven (2006) and presented in Table 2. We generate four instruments. A first group of two instruments includes the average car characteristics (hp and li) of competing car models belonging to the same car segment. The second set of two instruments is exactly the same, but now for all competing car models across the different car segments. The economic motivation for these instruments comes from Berry, Levinsohn and Pakes (1995), who state that the price of a product does not only depend on the characteristics of that product, but also on the characteristics of competing products (both from the same manufacturer and competing manufacturers). This simply follows from oligopolistic interdependence. The instruments, which are characteristics of competing car models, are therefore assumed to be correlated with the price of a car, but not with the error term (i.e. unobserved car characteristics). From the Hausman test, we reject the null hypothesis of differences in coefficients between an OLS and a 2SLS estimation not being different with a confidence of 99%. However, we find the opposite result using the regression-based test, which does not lead to a rejection of the null hypothesis of the price variable being exogenous. Given the results from the OLS estimation we still suspect an endogeneity problem and thus carry on with the IV estimation using all four instruments. Before applying the IV estimation technique, we need to make sure that our selected instruments are not weak instruments, as this could lead to a large bias on our coefficient estimates. To test for weak instruments, we use the Stock and Yogo (2005) critical values to assess the joint significance of the instruments. Note that, for now, we include all four instruments at once. From the F-test we find a test value of with an associated 5% critical Stock and Yogo value of We thus strongly reject the null hypothesis of weak instruments and can be confident that the 2SLS bias on the coefficient estimates will be lower than 5%. Finally, we perform both a Sargan and Hansen J test to check whether our four instruments are valid. From both tests we strongly reject that our four instruments are jointly valid. The search for valid instruments is often tedious. In our case, we suspected an endogeneity problem, which was only partially confirmed through econometric tests. We confirmed that, together, the four instruments considered from the literature are not weak instruments. However, we cannot confirm the validity of these four instruments and need to conclude that at least one of the instruments is not exogenous. In response to this issue, we restart our procedure of testing for endogeneity, weak instruments and validity of instruments. Instead of including all four instruments at once, we now choose for the simpler combination of othhp and othli. In other words, we now only take into account the average characteristics of all competing car types in a certain year, and no longer include the average characteristics of competing car types from the same segment in a certain year. Omitting the distinction between all competing cars and competing cars from the same segment might help to better capture the initial motivation (see Berry, Levinsohn & Pakes, 1995) for the instruments. Including only two instruments (average horsepower and fuel consumption of all other car types in a certain year), we are now able to confirm the endogeneity problem from both the Hausman and regression-based test. Both instruments together are also not weak and will result in a bias that is smaller than 5% with a confidence of more than 99%. Note that economically our previous line of reasoning remains valid. The price of a car j is still assumed to 24

5 Figure 2: the crossprice elasticities for a nested model be correlated with the characteristics (i.e. horsepower and fuel consumption) of competing models (i j). These characteristics, however, are not assumed to be correlated with unobserved car characteristics of j. We also confirm this economic intuition through both the Sargan and Hansen J test, which now confirm that our two instruments are valid. Now that we have identified and confirmed the endogeneity problem, and found two valid and nonweak instruments, we can continue with the 2SLS/IV estimation of our model. The estimated coefficient on the price variable is now much lower (-4.08), which confirms the anticipated upward bias obtained with regular OLS estimation. The estimate is still not significant at conventional levels. The sign of the coefficient on horsepower also remains negative, and thus counterintuitive, but is no longer statistically significant at the 5% level. The estimated coefficient on fuel consumption is negative and significant as expected. From the results, we can compute crossprice elasticities between cars, which are defined as follows. (6) With p i the price of car i and s i the market share of car i. As an example and a test for intuitive results, we compute cross-price elasticities between a Mercedes E (car i) and a BMW 5 (car j), and a Mercedes E (car i) and an Opel Astra (car j), for the year For both, we find a cross-price elasticity of Consequently, if the price of a Mercedes E were to increase by 10%, sales of both the BMW 5 and the Opel Astra would increase by 0.053%. This is not really in line with what one would expect, given that a BMW 5 is considered to be a closer substitute to a Mercedes E than an Opel Astra. Therefore, our current model is still not able to correctly capture the underlying characteristics of the Belgian car market. Nested model To overcome the unrealistic substitution patterns, we apply a nested model, which can be defined by the following utility function. (7) Where kgt represents the preference of consumer k for segment g at time t and measures the correlation of consumer preferences over the different products within one segment. This correlation is bounded between 0 and 1. If is equal to 1, the products within one segment are seen as perfect substitutes as the product specific preferences of consumers drop from the equation. If is equal to zero, there is no correlation of consumer preferences across products within the same segment and we arrive to the simple model. Assuming that and follow the extreme kgt kjt value distribution, one can show that the log market shares are again a function of observed and unobserved characteristics. (8) With the market share of product j within its segment g at time t. From this nested model, it should be the case that cars from within the same segment will now be closer substitutes to one another, than cars from other segments, which is more in line with economic intuition. Implementing the nested model requires for the calculation of one additional variable: the market share of product j at time t in segment g. Therefore, we first calculate yearly sales per segment and then calculate market share within a segment as the sales divided by the segment sales. Unfortunately, these segment market shares are again likely to be endogenous as they are correlated with unobserved characteristics jt. The same two characteristics (horsepower and fuel consumption) of competing products are used as instruments. From economic intuition, these product characteristics are believed to be correlated with the segment market share of product j, but not with the unobserved characteristics of product j. From the nested IV estimation, we find a significant estimate of 0.54, which means that cars belonging to the same segment are good substitutes for each other (as expected). The parameter estimate for price has increased a little bit (-2.86), but is still not significant at conventional levels. The sign for horsepower is still slightly negative, but is now turned insignificant. The coefficient estimate on fuel consumption is still significant and in line with ex-ante expectations. The crossprice elasticities for a nested model can be derived as shown in figure 2. Substitution patterns now make more sense. Between the Mercedes E (car i) and the BMW 5 (car j), we find a cross-price elasticity of So, if the price of a Mercedes E were to increase with 10%, sales of BMW 5 would go up by 5.3%. This is ten times as much as previously estimated. The cross-price elasticity between the Mercedes E (car i) and the Opel Astra (car j) is only , so the same price increase of the Mercedes E would only result in 0.037% more sales of the Opel Astra. Recommended bsc-level for readers of XXx-level econometrics specialty NL 25

6 Recommended bsc-level for readers of XXx-level econometrics specialty NL Measurement error From the IV estimation of the nested model we already obtained satisfactory results on the characteristics of the Belgian car market. Despite substitution patterns and the signs of most variables being in line with economic intuition, our results suffer from a lack of statistical power. Therefore, we might suspect that we have still not arrived at the best possible specification of the model. One possibly remaining issue with the current estimation strategy is an errors-in-variable or measurement error problem. In modeling consumer utility, we have included different characteristics of a car. Conceptually, we can synthesize the car decision to a trade-off between cost and performance, with performance including the power-efficiency trade-off. As the cost or price of a car is perfectly observable, we do not suspect any problems. However, the performance of a car is not readily observable and calls for the use of proxies. In our case we have used two proxy variables: horsepower and fuel consumption of the car. Instead of including both proxies together, it might be wiser to instrument proxies with one another to reduce the bias on the estimate of the coefficients. Intuitively, horsepower is the proxy closest to what we consider the pure performance of car. In addition to the instrumenting of price and the log of group market share, we therefore also instrument horsepower with the other proxy for car performance: fuel consumption. Doing the suggested estimation is very cumbersome, as we now have three endogenous variables in our model. To be able to deal with these kind of problems, we use three-stage least squares (3SLS) regression. 3SLS can be seen as an extension of 2SLS, in the same way as generalized least squares (GLS) are an extension of OLS. 2SLS consists of two steps and only focuses on a single equation, ignoring simultaneous correlations of error terms in the underlying model. To solve for this problem, a third step is added to 2SLS to account for these correlations. The 3SLS framework also accommodates for the simultaneous instrumenting of three endogenous variables with two distinct sets of instruments. For the price and log group market share endogenous variables, we use the same instruments as before: average horsepower and fuel consumption of all competing cars in the same year. To deal with the anticipated measurement error, we instrument horsepower with the fuel consumption variable. As before, we also control for year and segment effects. From the 3SLS estimation, we find results that are strongly significant and completely in line with economic intuition. The estimated coefficient on the price variable is and strongly significant. The coefficient on the log group market share is estimated to be 0.792, and is strongly significant. Cars from the same segment are hence very good substitutes for one another. The coefficient on horsepower is now turned positive and is also strongly significant. From this, we conclude that there was indeed an errors-in-variable problem that needed to be dealt with in a better way than before. We can also revisit our calculation of substitution patterns. Given the new results, we find a cross-price elasticity of 4.12 between a Mercedes E and a BMW 5. Thus, if the price of a Mercedes E were to increase by 10%, the sales for a BMW 5 would increase by 41.2%. However, an identical price increase of a Mercedes E would only result in an increase of Opel Astra car sales by 0.089%. This substitution pattern seems perfectly in line with expected intuition. Conclusion From our econometric analysis, we have managed to model the Belgian car market in a realistic way. Controlling for measurement error, anticipated relations between car characteristics and market share are entirely confirmed from the model. Additionally, using nested models we are able to estimate realistic cross-price elasticities, which are intuitively very appealing to car manufacturers. From our model and provided that the necessary data are available, car manufacturers can further examine the car market and their true competitors, which can lead to more effective product differentiation strategies and hence more profitable operations. Our example emphasizes the importance and power of sound econometric estimation as exact analytical computations of cross-price elasticities are typically either infeasible or unreliable. References Anderson, T. and Hsiao, C. (1981). Estimation of dynamic models with error components. Journal of American Statistical Association, 76(375): Berry, S., Levinsohn, J., and Pakes, A. (1995). Automobile prices in market equilibrium. Econometrica, 63(4): Brenkers, R. and Verboven, F. (2006). Liberalizing a distribution system: The European car market. Journal of the European Economic Association, 4(1): Goldberg, P. and Verboven, F. (2001). The evolution of price dispersion in the European car market. Review of Economic Studies, 68(4): Stock, J. and Yogo, M. (2005). Testing for weak instruments in linear IV regression. In Andrews, D., editor, Identification and inference for econometric models, pages Cambridge University Press, New York. 26

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