The exam questions seen below, even making an allowance for coming from an undergraduate course (nonetheless 13 of the 87 students were graduate students), indicate that the statistical training of economists at Harvard was a fairly low-grade affair even by the late 1930s, only a mechanical manipulation of different measures of central tendency and dispersion with a dash of trend-fitting and seasonal adjustment for good taste.
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Course Listing
Economics 21a 1hf. Introduction to Economic Statistics
Half-course (first half-year). Mon., Wed., Fri., at 10. Associate Professor Frickey.
Source: Announcement of the Courses of Instruction Offered by the Faculty of Arts and Sciences During 1938-39. (Second edition). Official Register of Harvard University, Vol. XXXV, No. 42 (September 23, 1938), p. 147.
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Course Enrollment
Economics 21a 1hf. Associate Professor Frickey.—Introduction to Economic Statistics
Total 87: 13 Graduates, 23 Seniors, 17 Juniors, 25 Sophomores, 6 Freshmen, 3 Others.
Source: Report of the President of Harvard College and Reports of the Departments, 1938-39, p. 98.
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1938-39
HARVARD UNIVERSITY
ECONOMICS 21a1
Part I
(One hour and thirty minutes.)
Answer any THREE questions.
- You are faced with the problem of computing an index of physical production of agricultural products for the years 1910 through 1935.
- What significant differences would you expect to find between the results of indexes computed as the weighted geometric mean of relatives and as the weighted arithmetic mean of relatives? Which average would you choose, and why?
- What difference would you expect to find among indexes computed respectively on the bases 1910, 1926, and 1935? Would you choose one of these three base periods, or some other base period?
- What sort of system of weights would you employ? Why?
- During a given interval in 1936, the wages paid to individual laborers in two New England cloth mills were recorded. A frequency table of wages paid was drawn up for each mill, and from the frequency tables, the following characteristics were computed.
| Mean Wage | Median Wage | Standard Deviation of Individual Wages | |
| Company A | $25 | $25 | 8.367 |
| Company B | $25 | $16 | 23.875 |
- Inferring from the above data, describe the general nature of the frequency distribution of wages for each firm, and compare the wage conditions in the two firms.
- What “typical average” would you choose for the distribution of Company A? For that of Company B?
- The monthly ordinates of trend found by fitting a linear or curvilinear trend line to a time series of price data would be held by some to represent “long-run normal prices”—that is, the values which the price data would have assumed in the absence of short run cyclical disturbances. Others would maintain that these same trend ordinates are merely the outcome of the particular trend—fitting procedures applied by the statisticians, and therefore reflect only his arbitrary definition of what constitutes “trend” and what constitutes “cycle” in the price series. Evaluate the relative merits of these two points of view toward statistical trend lines, and state your own viewpoint.
- In an investigation conducted to ascertain the correlation existing between the value of the assets of firms and the amount of their annual net earnings, the following results were among those obtained. For the specialty store field, the line of regression of annual earnings on asset values gave a “standard error of estimate” of $1000. For the service station field, a similar line of regression of annual earnings on asset values showed a “standard error of estimate” of $500.
Can we conclude from this that the correlation between earnings and assets is twice as great for service stations as for specialty stores? Why or why not? What additional data would you require in order to ascertain the actual correlation in each case and thereby clinch your argument?
PART II
(One hour and thirty minutes.)
Answer question 1, and either 2 or 3.
- (Approximately one hour.) The following is a segment of a time series for which certain statistical values have already been computed.
| 1st quarter | 2nd quarter | 3rd quarter | 4th quarter | |
| 1924 | 21 | 27 | 34 | 40 |
| 1925 | 32 | 36 | 28 | 30 |
| 1926 | 35 | 37 | 31 | 35 |
| 1927 | 36 | 41 | 35 | 39 |
The central ordinate of trend (a), and the annual increment of trend (b), based on annual averages of quarterly data for a longer period, have been found to be as follows: a = 35; b = 4. The center of the trend period for which these quantities were computed falls at the middle of the year 1924.
The median link relatives, showing typical quarter to quarter change for a longer period, have been found to be:
1st q ÷ 4th q = 110
2nd q ÷ 1st q = 105
3rd q ÷ 2nd q = 85
4th q ÷ 3rd q = 112
Given the preceding data, compute for the period 1924 through 1927 the following:
- The quarterly ordinates of trend
- The relatives of actual items to the trend.
- The seasonally adjusted relatives to trend, to the base 100. (This last step will require also the computation of a seasonal index by the Persons method.)
- For the following frequency series, compute the quartile deviation, the coefficient of variation, and determine a good empirical mode. (Show your computations, but do not compute any square roots.)
| Wages (dollars per week) | No. of Men |
| 0—5 | 22 |
| 5—10 | 29 |
| 10—15 | 18 |
| 15—20 | 12 |
| 20—25 | 9 |
| 25—30 | 5 |
| 30—35 | 3 |
| 35—40 | 2 |
- (a) From the data below compute a price index for 1933 on 1932 as a base, using the Fisher formula.
| Commodity | Unit | Price per unit | Physical quantity | ||
| 1932 | 1933 | 1932 | 1933 | ||
| A | bu. | $0.50 | $0.60 | 60 | 50 |
| B | lb. | $3.00 | $3.30 | 22 | 20 |
| C | bu. | $0.30 | $0.24 | 240 | 200 |
(b) If the Fisher formula price index for 1934 on 1933 as a base is 110, and for 1935 on 1934 as a base is 90, construct from the index which you have computed and from the results just given an index for the four years 1932-1935 by which each year is related to a common base.
Mid-Year. 1939.
Source: Duke University, David M. Rubenstein Library. Lloyd Appleton Metzler Papers, Box 9, Folder “Dust Proof File”.
Image Source: Harvard Album 1947.