*266OPINION.
The petitioner claims relief from excess profits tax under the provisions of Code sections 722 (a) and (b) (3) (A). Subsection (a) states the general rule as to relief if the tax is excessive and discriminatory and if the taxpayer establishes a fair and just amount representing normal earnings.
*267Subsection (b) (3) (A) provides that the tax shall be considered excessive and discriminatory if—
(3) the business of the taxpayer was depressed in the base period by reason of conditions generally prevailing in an industry of which the taxpayer was a member, subjecting such taxpayer to
(A) a profits cycle differing materially in length and amplitude from the general business cycle * * *
On the basis of the facts found we conclude that the tax here involved was excessive and discriminatory and that petitioner is entitled to relief under the provisions of the above quoted section of the Code. This section is commonly referred to as the variant profits cycle provision. In order to qualify under this provision, a taxpayer must establish a number of factors. It must establish (a) that its business was depressed in the base period; (b) that it was a member of an industry; (c) that the depression in its business was due to conditions generally prevailing in its industry; and (d) that the foregoing factors subjected the taxpayer to a profits cycle differing materially in length and amplitude from the general business cycle;
The petitioner has undertaken to establish that it meets all of the above qualifying factors. At the outset, it should be noted that by the very nature of the provisions of subsection (b) (3) (A), consideration of any case claiming relief thereunder can not be confined to the base period as is true under other subsections. The provision as to depression in the base period requires comparison with prior years; the provision as to comparison of cycles requires consideration of factors over a longer period of time than the base period. Commissioner’s Bulletin on Section 722, Part IY (B).
Base Period Degression.
It is obvious from the figures in evidence that the business of the petitioner was depressed in the base period in relation to its business in prior periods. The average excess profits net income of Waldorf Division for each of several periods in the history of its operations was as follows:
1922-1935_$868,727.99
1922-1939 _ 742,405. 44
1936-1939 (base period)_5 300,276. 50
The net profits of Waldorf Division and its four affiliated corporations on a consolidated basis for the same period were as follows:
1922-1935_$986, 810. 00
1922-1939_ 862, 044. 50
1936-1939 (base period)_ 425,364.93
*268 Industry.
The parties differ sharply as to whether or not the chain restaurant business, in which Waldorf Division was engaged, constituted an industry within the meaning of subsection (b)(3). Regulations 112, section 35.722-2 (b) (8), on this subject, read in part:
In general an industry may be said to include a group of enterprises engaged in producing or marketing the same or similar products or services under analogous conditions which are essentially different from those encountered by other enterprises. * * *
Commissioner’s Bulletin on Section 722, Part I (F), provides in part:
In most general terms an “industry” comprises a group of business concerns sufficiently homogeneous in nature of production or operation, type of product or service furnished, and type of customers, so as to be subject to roughly the same external economic circumstances affecting their prices, volume and profits. * * *
Without approving or disapproving the above definitions, we think that a holding that the low-priced restaurant chain business constitutes an industry does not do violence to them. The chain restaurants, similar to those of Waldorf Division, operate entirely differently from other types of eating places. Among the distinguishing features was centralized purchasing, with a constant survey of commodity markets to enable them to buy at the lowest possible prices. The purchase of food in large quantities for cash enables them to buy at prices generally lower than other types of restaurants. Menus are prepared by the headquarters’ office, and are limited as to the number of food items offered. Perhaps the most striking difference is that food is prepared in centra] commissaries and sent to the individual restaurants ready to be served from the steam table or counter. No cooking is done in the restaurants except for short orders. Thus, the kitchen equipment in a chain restaurant is meager compared with that of other types of restaurants. The restaurants similar to those of Waldorf Division featured low individual food checks based on their policy of furnishing food at the lowest possible price consistent with making a profit. There is testimony that among business people acquainted with the restaurant business, the operation of the low-priced chains was regarded as an industry separate and distinct from that of other types of eating establishments.
Upon consideration of all the evidence, we are satisfied that the operation of chain restaurants of a type similar to those of Waldorf Division constituted an industry within the meaning of Code section 722 (b) (3) and that the Waldorf Division of the petitioner was a member of that industry.
*269 Conditions in the Industry.
One of the elements of section 722 (b) (3) is that the taxpayer’s business was depressed in the base period by reason of conditions generally prevailing in its industry.
The evidence leaves no doubt that the business of the petitioner was depressed in the base period in relation to prior years. The average excess profits net income of Waldorf Division in the base period was only $300,276 as contrasted to $868,727 in the period 1923 to 1935, and $742,405 over the entire period 1923 to 1939. The earnings of the petitioner and its subsidiaries on a consolidated basis averaged only $455,403 in the base period, whereas they had averaged $1,012,275 in the period 1923 to Í935 and $881,246 in the period 1923 to 1939.
The evidence likewise leaves no doubt that the business of other restaurant chains was similarly depressed. It is shown that the average earnings of five representative chains, other than the petitioner, were $2,869,075 in the base period, contrasted with $6,278,413 for the period 1923 to 1935, and $5,476,216 over the longer period 1923 to 1939.
On an index basis, using 100 for the period 1923 to 1939, the earnings of Waldorf Division were 117.5 for 1923 to 1935 and only 43.2 in the base period. The index of earnings of the five representative chains was 114.6 in 1923 to 1935 and only 52.4 in the base period.
The evidence is not limited to figures as to the petitioner and the five representative chains. There is testimony that establishes that the depressed condition of business in the base period existed generally among low-priced restaurant chains, and a number of similar chains were either forced to reorganize or were liquidated. A witness for the petitioner, who has been familiar with the restaurant business for over 30 years and whose corporation has been dealing with restaurants over a longer period, testified that in and immediately prior to the base period the number of failures in the chain restaurant industry was larger than in any period in the previous 50 years.
The evidence adequately shows the reasons for similarity of conditions in the petitioner’s business and of those generally prevailing in its industry. All members of the industry were affected by the same factors. The chains had to pay increased prices for food, but were unable simultaneously to increase the prices that they charged because of consumer resistance. Other costs, particularly that of labor, increased substantially and such increases could not immediately be passed on to customers of the chains.
We conclude that the business of Waldorf Division was depressed in the base period because of conditions that generally prevailed in its industry.
*270 Cycle Question.
The most difficult phase of this case is whether the petitioner meets the variant profits cycle test. In the language of the Code, the taxpayer must have been subjected to “ * * * a profits cycle differing materially in length and amplitude from the general business cycle.”
The case has been tried on the theory that a business cycle is a period of business activity which includes four phases, namely, a period of prosperity, one of recession, one of depression, and one of revival. A complete cycle is measured from a period of prosperity to another period of prosperity, or from a period of depression to another period of depression. The Bulletin on Section 722, Part IY (B), provides that “the general business cycle must be defined as the profits cycle of all corporations.”
Accepting the above definitions for the purposes of this case, the stipulated figures indicate that for all corporations the period 1923 to 1939 represents a profits cycle. The years 1923 to 1929 were a period of prosperity when the index of income went from 135.1 to 192.7. The year 1930 can be said to be one of recession when the index dropped to 90.4. The years 1931 and 1932 were depression years when the indexes were 17.0 and minus 22.6, respectively. The period 1933 to 1939 was one of revival when the index rose from 13.6 to 103.0, with a temporary recession in 1938. The evidence in this case is to the effect that for cycle study purposes short-term movements, such as the recession in 1938, are ignored. In contrast, Waldorf Division’s period of prosperity ran from 1923 through 1930 during which its index figures ranged from a low of 125.8 to a high of 159.6. It might with reason be said that the period of prosperity included the year 1931, as in that year the index was only 7.2 points lower than in the preceding year. The year 1932 was one of recession when the index figure dropped to 98.6. Its depression years were 1933 and 1934 when the indexes dropped to 43.6 and 29.0, respectively. Its recovery period did not start until 1935 when the index rose to 48.6. The recovery period lasted only through 1936 when the index again rose and was 72.8. Then another recession set in and lasted through the 3 succeeding years. It is thus seen that except for the early years of the period 1923 to 1939, Waldorf’s periods of prosperity, recession, and depression did not coincide with those of all corporations.
If we consider the “peak to peak” years as measuring a profits cycle, there is again a lack of coincidence. The first peak for all corporations was in 1929 when the index was 192.7, while Waldorf’s did not occur until 1930 when its index was 159.6. The low point for all corporations was in 1932, whereas Waldorf’s did not occur until 2 *271years later in 1934. On the rising side, all corporations again reached a recognized peak in 1939. In contrast, Waldorf did not reach a peak in any year that marked the rise for all corporations. It had reached a temporary high point in 1936 when its index was 72.8, but in the 2 succeeding years its earnings dropped drastically to a low of 18.4 in 1938, and by 1939 the index had risen only to 37.8. Even if we consider 1936 as Waldorf’s second peak, the result is that its first peak occurred 1 year later than that of all corporations, and its second peak was 3 years earlier. This difference in time in this short span of years marks a material difference in length of the cycles.
Little need be said as to the difference in amplitude of the cycles. The index figures make it clear that there was a marked difference in that respect. The contrast is sharp in any period or year that may be selected. For example, Waldorf’s index for 1923 to 1935 was 117.5 while that of the general business cycle as measured by the income of all corporations was 101.9. The comparison for the base period is 43.2 for Waldorf and 94.9 for all corporations. Waldorf did not have a minus index figure in any year from 1923 to 1939, whereas the index for all corporations dipped to a minus of 22.6 in 1932. If we take Waldorf’s cycle as being the period 1930 to 1936, the indexes are 159.6 and 72.8, respectively. If we consider the cycle of all corporations to be the years 1929 to 1936, the indexes are 192.7 and 105, respectively. Thus, the amplitude was markedly different, no matter what period be regarded as a cycle.
The similarity of the earnings pattern of Waldorf Division and that of representive industry members, as well as the dissimilarity between the earnings pattern of Waldorf and its industry on the one hand, and business in general on the other, can be demonstrated by means of a Pearsonian correlation. A Pearsonian correlation is a method of determining the tendency of things to vary together. This method is a recognized statistical device. If two quantities correlate perfectly, the coefficient of correlation is expressed as plus 1. If there is no correlation, the coefficient is zero. The closer to plus 1 (or 1.00) the coefficient of correlation is, the closer the degree of correlation. The Pearsonian coefficient of correlation does not involve averages but involves comparison of pairs of index numbers in each year.
The coefficient of correlation of Waldorf Division earnings for the period 1923 to 1939 compared with the aggregate earnings of Thompson’s, Childs, Bickford’s, and the two Horn & Hardart chains (hereinafter sometimes referred to as the “five chains”) for the same years is plus .935, which is an unusually good correlation. If the earnings of Waldorf System, Inc., are added to the earnings of the 5 chains and the combined earnings of these 6 chains compared with Waldorf Division over the years 1923 to 1939, a coefficient of correlation of plus .957 results. This is an even better correlation.
*272Comparing the aggregate earnings of the 5 chains for the period 1923 to 1939 with earnings of all United States corporations for the same period results in a correlation coefficient of plus .377 which is an extremely poor correlation. If the earnings of Waldorf System, Inc., are added to the aggregate earnings of the 5 chains and this total compared with the earnings of all United States corporations for the same period, 1923 to 1939, the coefficient of correlation is only plus .579, which is not good. If earnings of Waldorf Division are added to the earnings of the 5 chains and this total is compared to earnings of all corporations for the period 1923 to 1939 the coefficient of correlation becomes only plus .552.
The earnings of the 5 chains and the earnings of Waldorf Division vary together during the period 1923 to 1939, and these two vary separately and distinctly from the earnings of all corporations.
The chain restaurant industry lags 2 years behind all corporations so far as net earnings are concerned. This means that comparable points on the respective cycles occur 2 years later in the chain restaurant industry than for all corporations. In speaking of a 2-year lag in the chain restaurant industry, this does not mean exactly 24 months in one cycle and 24 months in the next cycle. The lag might vary a little. The description of a 2-year lag is in terms of what is reasonable and what appears to be true and the lag might be longer than 2 years.
If earnings of the 5 chains are lagged 2 years (their earnings are all pushed back by 2 years) and compared with all corporation’s earnings for 1923 to 1939, then the coincidence is very marked. The coefficient of correlation in such a case is very good, being plus .818 for the years 1923 to 1939. This is so even though there are up and down movements throughout this period. Both lines on the graph tend to go upward and the lines coincide very closely. The amount of difference between the lines is very small. The amount by which either series goes up or down is very little, and generally the lines parallel each other very closely. In a similar fashion, if earnings of Waldorf System, Inc., are added to those of the 5 chains and their combined earnings, with a 2-year lag, are compared with the earnings of all corporations for 1923 to 1939, the coincidence is marked. The coefficient of correlation in such a case is plus .832 for the years 1923 to 1939, which is an excellent correlation. If earnings of Waldorf Division only are added to those of the 5 chains and these earnings are lagged by 2 years and compared with earnings of all corporations, the coefficient of correlation is plus .825 for the years 1923 to 1939. The earnings of the Waldorf System taken alone and lagged 2 years produce a coefficient of correlation of .803 in comparison with the earnings of all United States corporations.
*273A comparison of the combined earnings of Thompson’s and Childs on the one hand, with the combined earnings of Waldorf Division and Clark on the other, both over the period 1923 to 1939, results in a correlation coefficient of plus .78, which is good. In a similar fashion, when combined earnings of Waldorf Division, Clark, Thompson’s, and Childs over 1923 to 1939 are compared with earnings of all corporations over the same period with no time lag the coefficient of correlation is plus .27, very low. If earnings of these same companies are pushed back 2 years and compared with earnings of all corporations over the period 1923 to 1939, the coefficient of correlation becomes plus .85, which is very high. If Waldorf Division and Clark’s combined earnings are compared with all corporate earnings over 1923 to 1939, the correlation is plus .30 which is poor. Making the same comparison with a 2-year lag for the earnings of Waldorf and Clark results in the amazingly high correlation of plus .96.
The earnings pattern and the 2-year lag detailed above, which is characteristic of the petitioner and of the members of its industry, is attributable largely to the low price charged by the chain restaurant industry to its customers and the reaction of customers to increases and decreases in the low price. In a period of general recession the low prices charged to customers tended to maintain the customer level while food and labor costs dropped. At the same time prices to customers were lowered slowly but had a rate of decrease which was slower than costs. As a result the profits of the petitioner and of its industry generally tended to increase. This was true during 1929 through 1932. On the other hand, during a period of general recovery, food, labor, and other costs increased at a more rapid rate than the prices charged to customers because of customer resistance. Sales in the meantime remained constant with a resulting decline in profits. This was true throughout the period 1933 to 1939.
The sum of these considerations is a rational and characteristic relationship between the petitioner’s profit cycle and that of business in general, which considered in the light of the provisions of section 722 (a) and (b) (3) (A) of the Internal Revenue Code entitles the petitioner to relief, for the petitioner has met all of the tests requisite to relief imposed by that section.
Reconstruction.
We have found what would be a fair and just amount representing normal earnings to be used as a constructive average base period net income.
The Commissioner’s Bulletin on Section 722 states that the reconstruction will take the form of finding the average income of the taxpayer for another series of years than the base period which can be *274considered as normal. It further provides that in ascertaining income in other years it is desirable to use data conforming as nearly as possible to the definition of excess profits net income. Bulletin on Section 722, Part IV (C). In suggesting several figures that may be used as constructive average base period net income, the petitioner has followed the pattern of the provisions of the Bulletin. The figures proposed are taken from Exhibit 5-E attached to the stipulation which shows the excess profits net income of Waldorf Division for each year from 1922 through 1939 and the average by three groups of years.
One figure suggested is the average income for the entire period 1922 to 1939 in the amount of $742,405.44. It would appear that this is not a proper figure as representing normal earnings since it includes income for the period 1936 to 1939 in which we have held that the petitioner’s business was depressed.
Another suggested figure is the average income for the period 1922 to 1935 in the amount of $868,727.99. This would also appear to be an improper figure since in the years covered by the greater part of this span Waldorf Division had its highest earnings. This factor more than outweighs the fact that the period also includes the recession and depression years.
The final suggested figure is the amount of $782,092.90 which is the average of income for the years 1926 through 1935. The argument in support of this figure is that the period covered starts 1 year after a pit in 1925 and ends 1 year after a pit in 1934. (The indexes for 1925 and 1926 are 133.3 and 151.7, respectively, and for 1934 and 1935 they are 29.0 and 48.6). This seems like a reasonable view. The period covered includes both good and bad earnings years and'is a reasonable span of time.
We think the evidence establishes all the factors requisite to qualify petitioner for relief under the above cited provisions of the statute.
The respondent stresses the point that on or about January 1,1935, Waldorf System, Inc., (parent) assumed, as he contends, the obligations of Ginter Restaurant Company under certain real estate leases on properties in Boston and thereby sustained losses in the following amounts:
1935_$115,812.10
1936_ 98, 272. 04
1937_ 95,818.94
1938_ 122,431. 58
1939_ 118, 799. 76
Average, 1936-1939_ 108,830. 73
No findings have been made on this point. The respondent’s view is that the above losses are properly chargeable to Ginter rather than to Waldorf and should not be taken into consideration in determining Waldorf’s income. If it be assumed that the respondent’s position is *275correct, the addition of the $108,830.73 to Waldorf’s income for the base period would raise the average for the base period only to $409,107.24, instead of $300,276.51, which would still leave Waldorf’s income depressed in relation to prior periods.
Reviewed by the Special Division.
Decisions will be entered under Rule 50.