Economics 320
Spring 2000
Final Project
Mei Fong Chan
Wei Chen
Weixin Shi
A Study of the Automobile Market Saturation
as a Cause of the Great Depression
Introduction
"To understand the Great Depression is the Holy Grail of macro economics" (Bernake, 1995). Unfortunately, economists have not yet come with a widely accepted explanation of the cause of the Great Depression. One line of studies suggests that the cause was the overinvestment in the 1920s, which in turn lead to market saturation. Because of the saturation of market, consumption and investment opportunities were exhausted. This initiated the impulse of the Great Depression.
Little empirical work has been done on the overinvestment hypothesis, with the exception of Mercer and Morgan (1972). Mercer and Morgan focus on the automobile industry, one of the most important industries before the Great Depression. They apply the stock adjustment model, (NP_{t} = g (S*_{t} S _{t1} )_{ + d }S _{t1}, which will be discussed in the literature review), to derive the desired demand of automobiles and use the result to estimate the saturation of the market. Their results suggest that the market was saturated under the dynamic definition of automobile, i.e. the rate of change of total automobile stock is smaller than that of the desired stock of automobile. Thus, the market is moving toward saturation.
The accuracy of Mercer and Morgan’s model depends on the specification of the demand function for automobiles. Their model assumes that the desired demand of automobiles depends on the relative price of cars, the income, the existing stock of cars and a time trend. They did not provide any empirical test to support this hypothesis. Our study attempts to modify their model by experimenting with different functional forms and adding independent variables that might be relevant to the demand for automobiles. Our results show that dynamic saturation did occur before the Great Depression start in 1929.
Literature Review
Mercer and Morgan (1972) apply a series of empirical tests to support the hypothesis that the automobile market was tending to saturation by the late 1920s. Their results suggest that the automobile market was saturated under the dynamic saturation, i.e. the movement of market toward a state saturation. The following section summarizes their theoretical framework.
Mercer and Morgan based their study under the definition of dynamic saturation. It is defined as the point where the rate of increase in the existing stock of automobile is greater than the rate of increase in the desired demand. The dynamic definition of saturation is summarized in the following equation:
(1) _{ }
where S^{*}_{t }is the desired demand of automobile and S^{*}_{t1 }is the existing level of automobile at the end of the previous year. If the market is moving toward saturation, equation (1) should have a negative value, and vice versa.
In order to calculate equation (1), desired demand of automobiles must be evaluated. Since desired demand of automobile is an unobservable variable, we used the widely employed stock adjustment model by Gregory Chow (1957) to derive the desired demand. The unobservable desired demand of automobile is represented by:
(2) S^{*}_{t }= a + b RP_{t }+ c Y_{ t }+ dT + eTSQ + f POP
where RP_{t }denotes relative price of automobile, Y_{ t }represents income, T denotes time and TSQ denotes time squared which allow for nonlinear time trend. POP is the population.
Using the widely employed stock adjustment model used by Chow (1957), which suggests that the annual new purchase of automobile in the economy is equal to the excess desired demand over actual stock , adjusted by depreciation as represented in the following equation:
(3) NP_{t} = g (S*_{t} S _{t1} )_{ + d }S _{t1}
Rearrange (3) yields:
(4) NP_{t} = g S*_{t} (g + d ) S _{t1}
where NP_{t} is the total final new purchase, g is the constant adjustment speed, S*_{t} is the desired demand , S _{t1} is the actual existing stock at the end of the previous year, and d is the depreciation rate.
Combining (2) with (4) yields:
(5) NP_{t} = g ( a + b RP_{t }+ c Y_{ t }+ dT + eTSQ + fPOP)(g + d ) S _{t1}
(6) NP_{t} = g a + g b RP_{t }+ g c Y_{ t }+ g dT + g eTSQ +g f POP(g + d ) S _{t1}
Equation (6) shows that once the depreciation rate d is known, the value of g can be easily derived and it’s possible to estimate the desired stock of automobiles. Mercer and Morgan adopt the depreciation rate d calculated by Chow. The econometric estimation of equation (6) thus provides the parameter required to estimate the desired demand of automobile in equation (2).
The Model
Mercer and Morgan's result is replicated and reported in Table 2. The estimated values of desired demand is then use to compute equation (2). Their results suggest that the automobile market is saturated in 1928 and 1929 under the dynamic saturation definition.
The regression model based on equation (6) yields serious multicollinearity problem because population and aggregate real disposable income is highly correlated. As a result, the regression model gives an unexpected sign of the coefficient on population. To solve this problem, per capita data is used:
(7) pNP_{t} = g a + g b RP_{t }+ g c pY_{ t }+ g dT + g eTSQ (g + d ) logS _{t1}
where pNP_{t} is new purchase per capita, pY_{ t }is real disposable per capita, and pS _{t1 }is existing stock of automobile at the end of previous period per capita, T and TSQ are the time variables.
Furthermore, a constant elasticity model is used instead of Mercer and Morgan’s functional form. Changing both the dependent variables and independent variables to logarithmic form allows us to measure the elasticity of dependent variables with respect to the independent variables. The logarithmic form of equation (7) becomes:
(8) log pNP_{t} = g a + g b log RP_{t }+ g c logpY_{ t }+ g dT + g eTSQ (g + d ) logS _{t1}
Because of the change of the functional form, the logarithmic form of desired demand is computed, and has to convert back to its normal form in order to evaluate the degree of saturation according to equation (1) :
Mercer and Morgan’s model is further modified by introducing different relevant variables such as the fuel price, interest rates and mileage of roads in the country. The rationale is that fuel price and interest rates are negatively correlated with new purchase, and the mileage of road is positively correlated with new purchase.
Methodology and Data
The regression model based on equation (6) suggested by Mercer and Morgan using aggregate new purchase as the dependent variable is replicated. The means is presented in table 1. Different modifications that based on the rationale in the previous section are reported in Table 2.1 and Table 2.2. Data used in the following equations are from Chow (1960) and Historical Statistics. Serial correlation is corrected.
Table 1: Means and standard deviation for the independent variables:
Variable N Mean Std Dev Minimum Maximum

Auto stock per capita 34 7.534 2.119 3.513 12.057
New Purchase per Capita 28 2.454 0.771 0.878 4.170
Auto Price 33 148.6 87.295 81.7 449.30
Disposable Income per capita 33 594.35 125.804 394.3 798.00
Population 34 130.15 14.511 106.6 159.7
FUEL 32 92.259 24.035 66.3 163.7
INTEREST 34 3.079 0.833 2.05 5.32
ROAD 31 336050.71 187913.24 169007. 704150.0

Table 2.1 AUTOMOBILE DEMAND REGRESSION RESULTS
Model 
Dependent Variable 
Independent Variables 

Interception 
Relative Price 
Real Disposable Income 
T 
T squared 
Population 
Lag Stock of Auto 
Lag Stock of Auto Per Capita 
Fuel 
Interest 
Road 

1.1 
New Purchase 
583.26 (0.969) 
3.352 (0.464) 
0.0188 (4.129) 
5.758 (0.649) 
0.328 (0.996) 
7.447 (1.233) 
0.308 (1.233) 

1.2 
New Purchase Per Capita 
0.456 (0.587) 
0.018 (6.007) 
0.0128 (8.810) 
0.0283 (0.952) 
0.000209 (0.208) 
0.01286 (4.038) 

1.3 
New Purchase Per Capita 
0.471 (1.043) 
0.0184 (6.259) 
0.0129 (10.085) 
0.22229 (1.658) 
0.0219 (4.124) 

1.4 
New Purchase Per Capita 
1.697 (1.592) 
0.01924 (50160) 
0.0127 (6.415) 
0.2427 (3.8555) 
0.0016 (0.146) 
0.40105 (1.579) 
1.579 0.3.644E7 
Table 2.2 AUTOMOBILE DEMAND REGRESSION RESULTS in LogLog Forms
Model 
Dependent Variable 
Independent Variables 

Interception 
Log Relative Price 
Log Real Disposable Income 
Log Lag Stock of Auto Per Capita 
Log Fuel 
Log Interest 
Log Road 

1.5 
Log New Purchase Per Capita 
11.69 (3.941) 
1.411 (4.529) 
3.029 (5.748) 
0.761 (3.670) 
0.00837 (0.1500) 
0.0925 (0.606) 
0.1722 (0.434) 
1.6 
Log New Purchase Per Capita 
10.563 (8.897) 
1.339 (7.572) 
3.0539 (11.149) 
0.7554 (4.591) 
Equation 1.1 is the regression model suggested by Mercer and Morgan. According to the replicated result, a one million increase in population can cause 8.89 millions reduction of automobile purchases. It violates the basic economic theory that as population grows up, the total quantity demanded should increase correspondingly. One possible explanation of the unexpected sign of the coefficient on population is the existence of multicollinearity. Since population is highly correlated to another independent variables, the total amount of real disposable income in the economy. To overcome multicollinearity we use per capita data in regression 1.2 through 1.4. The total R Squared values show that all the per capita models perform better than the aggregate model.
Equation 1.2 is the per capita version of equation 1.1. Notice that in equation 1.2, both time and time squared is statistically insignificant. The t ratio for T and TSQ in the estimated equation is —0.953 and 0.208 respectively. It means we cannot reject the null hypothesis even at 20% significance level. Including only T and leaving out TSQ shows that time is not statistically significant in per capita form. (Regression 1.3)
Different independent variables are experienced in regression 1.4. Fuel price is added because it is a compliment of automobiles. Economic theory suggests that fuel price might be negatively correlated to the quantity demand of automobiles. Lagged fuel price is used here based on the hypothesis that consumption decisions are related to the fuel price at the previous year. We use the logarithmic form to estimate the cross price elasticity between fuel price and automobile demand in regression 1.5. However, both regression result shows that fuel price is not a major determinant of demand for automobiles.
Another possible variable that determines the automobile purchases is the interest rate. Regression 1.4 included the real interested rate lagged one year. Although installment payments for car purchases were not common in the twenties, interest rates is a good proxy for the opportunities costs of consumption. The t statistics nonetheless shows that lagged interest rates is not statistically significant in determining the automobile consumption behavior. Again, the logarithmic form illustrates the same result in regression 1.5.
Finally, lagged mileage of roads is added in the regression model. It is generally agreed that one of the causes of the expansion of automobile consumption was the expansion of the complimentary goods. Among all the complementary goods, road construction gave the most significant influence. The regression model in both level and logarithmic form do not provide evidence to support this hypothesis.
The best regression model is equation 1.6. Although its Rsquared is not the highest among the regression models using the logarithmic function, all the independent variables turn out to be significant. In addition, the log model is theoretically a better predict of the automobile demand because it allows us to estimate the percentage change of new car purchase due to a percentage change in the independent variables. Desired demand for automobiles is then computed based on this model and the dynamic definition of saturation based on equation 1 yields the results in table 3. The results in Table 2 indicate that a dynamic saturation was reached in 1926 and 1927, and most importantly, in 1929.
Table 2: Automobile Market Condition : 1922 1939
Year 
Auto Stock per capita 
Desired stock per capita 

1922 
5.426 
7.544 
0.1871 
1923 
6.888 
9.704 
0.0168 
1924 
7.849 
10.488 
0.058 
1925 
8.418 
12.019 
0.073 
1926 
8.928 
11.167 
0.131 
1927 
8.774 
10.468 
0.045 
1928 
9.13 
11.794 
0.086 
1929 
9.698 
12.423 
0.008 
1930 
9.092 
11.553 
0.007 
1931 
8.106 
9.217 
0.093 
1932 
6.915 
6.509 
0.146 
1933 
6.34 
6.466 
0.076 
1934 
6.172 
6.661 
0.056 
1935 
6.53 
8.316 
0.191 
1936 
7.515 
9.623 
0.006 
1937 
8.343 
11.190 
0.052 
1938 
7.786 
9.165 
0.114 
1939 
7.719 
10.676 
0.173 
Analysis and Results
The result from our model yields several unexpected findings. First of all, it is
shown that consumption decision on automobiles in the twenties was not as rational as the conventional economic theory suggested. Opportunity costs and availability of complimentary goods and their prices does not have a significant impact on consumption.
Furthermore, both expected income and real disposable income are used and is shown that the differences are not statistically significant. This suggests that Friedman’s permanent income hypothesis (1957) does not make a significant difference in the automobile consumption decision.
Moreover, it is often suggested that the number of households is more important than the population in determining consumer durable, such as automobiles. This is a significant findings as many economists (Szostak, 1995) uses the fact that the automobile per household ratio is almost 80% as an evident to support the overinvestment theory. We replace population with household, but it did not improve the model significantly.
Finally, our findings do support the overinvestment hypothesis that the automobile market was saturated in 1929. The automobile market was saturated.
Further research can be done on the reliability of Mercer and Morgan’s definition of saturation. Also, a careful study of the credit availability, installment financing arrangement, both age and geographic population distribution, and wealth may able to provide more insight in explaining the consumption behavior of the automobile industry. In addition, since data for the years after 1953 are available, including more data may substantially improve our results. The complexity however, lies in the measurement of the new car equivalent stock using Gregory Chow’s method.
Conclusion
In this paper, we have argued that tests of dynamic saturation hypothesis for the United States automobile market in the twenties should be based on an specified automobile demand model, which requires some serious consideration of the functional form of the demand function. The reported saturation estimate indicates that the automobile market was saturated at 1929. The estimates suggest the need for more detailed evaluation of the overinvestment thesis for the late twenties, not only for the automobile industry, but for other major industry as well. An evaluation of the definition of dynamic saturation should also be studied in more details.
References
Chow, G. 1957. Demand for Automobiles in the United States
________ 1960. The Demand for Durable Goods
Mercer L., Morgan W. 1972. Alternative Interpretation of Market Saturation: Evaluation for the Automobile Market in the Late Twenties. Explorations in Economic History, p.2680.290